6(y - 7z) This is a product with a whole number greater than 1 (6), since we factored out a 6 from the original expression.
What is a factor?A factor is an expression or number that evenly divides another expression or number without leaving a remainder.
According to question:To factor the expression 6y - 42z, we need to find the greatest common factor (GCF) of the two terms.
The GCF of 6y and 42z is 6, since both terms are divisible by 6. We can factor out the 6 from both terms, leaving:
6(y - 7z)
Notice that the term inside the parentheses (y - 7z) cannot be factored any further, since there is no common factor other than 1. Therefore, the fully factored form of 6y - 42z is:
6(y - 7z)
This is a product with a whole number greater than 1 (6), since we factored out a 6 from the original expression.
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Locate each of the stations on the accompanying map of California. Us a compass to drawa circle centered on each city station with a radius corresponding to the distance determined to the epicenter from that station. The horizontal scale in kilometers is provided on the map
To locate the stations and draw cirradius cles on the map of California, follow these steps:
1. Identify the city stations on the map: Find the city stations indicated on the map, such as San Francisco, Los Angeles, and San Diego.
2. Use a compass: Set your compass to the scale provided on the map.
For example, if the scale says 1 inch = 100 km, adjust your compass accordingly.
3. Determine the distance from the epicenter: Based on the information provided, determine the distance from each city station to the epicenter. If it is not provided, refer to additional resources or data.
4. Draw the circles: Place the compass point on each city station and draw a circle with a corresponding to the distance determined in
step 3. Ensure the radius is in scale with the map.
5. Identify the epicenter: The point where all the circles intersect is the approximate location of the epicenter.
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which of the following is the most likely to call up mental images of specific sights, sounds, tastes, or smells?
This connection makes smells particularly powerful in triggering memories and emotions.
The sense of smell is the most likely to call up mental images of specific sights, sounds, tastes, or smells. This is because the olfactory system, which is responsible for the sense of smell, is closely linked to the brain's limbic system, which is involved in emotions and memory. This connection makes smells particularly powerful in triggering memories and emotions.
The olfactory system, which is responsible for the sense of smell, is unique in its connection to the brain's limbic system, which is involved in processing emotions and memory. When we smell something, the odor molecules enter our nose and are processed by specialized sensory neurons in the olfactory epithelium. These neurons then send signals to the olfactory bulb, which is located in the brain and is the first site of olfactory processing.
From there, the olfactory information is sent to several brain regions, including the amygdala and hippocampus, which are both part of the limbic system. The amygdala is involved in processing emotions and is responsible for generating feelings of pleasure, disgust, or fear in response to smells. The hippocampus, on the other hand, is involved in forming new memories and is responsible for encoding information about the context in which a smell is experienced.
The strong connection between the olfactory system and the limbic system makes smells particularly powerful in triggering memories and emotions. For example, the scent of freshly baked bread may evoke memories of childhood mornings spent in the kitchen with a loved one, while the smell of a certain perfume may remind you of someone special. Additionally, certain smells may elicit strong emotional responses, such as the smell of smoke triggering feelings of panic and fear in someone who has experienced a fire.
Overall, the sense of smell is closely linked to our emotional and memory centers, making it a powerful tool for triggering mental images of specific sights, sounds, tastes, or smells.
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each time a hurricane arrives, a new home has a 0.4 probability of experiencing damage. the occurrences of damage in different hurricanes are mutually independent. calculate the mode of the number of hurricanes it takes for the home to experience damage from two hurricanes.
As per the given probability, the mode of the number of hurricanes it takes for the home to experience damage from two hurricanes is either one or two hurricanes, depending on which sequence is more likely to occur.
The probability of the DD sequence is 0.4 x 0.4 = 0.16. This means that there is a 16% chance that the home will experience damage in both the first and second hurricanes.
The probability of the DN sequence is 0.4 x 0.6 = 0.24. This means that there is a 24% chance that the home will experience damage in the first hurricane but not in the second hurricane.
The probability of the ND sequence is 0.6 x 0.4 = 0.24. This means that there is a 24% chance that the home will not experience damage in the first hurricane but will experience damage in the second hurricane.
To determine the mode of the number of hurricanes it takes for the home to experience damage from two hurricanes, we need to consider which sequence is most likely to occur.
In this case, the DN and ND sequences have the same probability, which means that there are two possible modes: one and two hurricanes.
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what is the solution set for this inequality -8x + 40 > -16
Answer:
x < 7
Step-by-step explanation:
You want the solution set for the inequality -8x +40 > -16.
SolutionDivide both sides by -8, and we have ...
x -5 < 2
x < 7 . . . . . . add 5
The solution set for this inequality is {x | x < 7}.
__
Additional comment
There are many ways to describe a solution set. We have used some different ways. You will want to use a method of describing the set that is appropriate to your answer checker.
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Joesph has a bag filled with 2red, 4green, 10yellow, and 9 purple marbles. Determine P(not green) when choosing one marble from the bag.
92%
84%
48%
16%. PLS HELP
[tex]10 + 9 + 2 + 4 = 25[/tex] possible outcomes
[tex]25 - 4 = 21[/tex] outcomes that are not green
[tex]\dfrac{21}{25}[/tex] chance that you don’t choose green
[tex]\frac{21}{25}=\bold{84\%}[/tex]
ezra is redrawing the blueprint shown of a stage he is planning to build for his band. by what percentage should he multiply the dimensions of the stage so that the dimensions of the image are 12 the size of the original blueprint? what will be the perimeter of the updated blueprint?
The perimeter of the updated blueprint will be 24 times the sum of the original length and width.
If Ezra wants to multiply the dimensions of the stage by a certain percentage to make the image 12 times larger than the original, he needs to find out what percentage that is.
To do this, he can divide the desired size of the new stage by the original size of the stage, and then multiply by 100 to get the percentage increase. So, if the original blueprint dimensions are x by y, and he wants to make the image 12 times larger, the new dimensions will be 12x by 12y.
To find the percentage increase, he can use the following formula:
Percentage increase = [(new size - original size) / original size] x 100
In this case, the new size is 12 times the original size, so the formula becomes:
Percentage increase = [(12x * 12y - x * y) / (x * y)] x 100
Simplifying this expression gives:
Percentage increase = [(144xy - x * y) / (x * y)] x 100 = 14300%
Therefore, Ezra needs to multiply the dimensions of the stage by 14300% to make the image 12 times larger than the original blueprint.
To find the perimeter of the updated blueprint, he can use the formula for the perimeter of a rectangle, which is: Perimeter = 2(length + width)
In this case, the length and width have been multiplied by 12, so the new perimeter becomes:
Perimeter = 2(12x + 12y) = 24(x + y)
Therefore, the perimeter of the updated blueprint will be 24 times the sum of the original length and width.
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plot four different points whose -coordinates are half their -coordinates. do these points lie on a line?
The four points with y-coordinates half their x-coordinates are (0,0), (2,1), (4,2), and (6,3). These points do lie on a line, as they all satisfy the linear equation y = x/2.
To plot four points whose y-coordinates are half their x-coordinates, we can choose any four values of x and then compute the corresponding values of y using the equation y = x/2. For example
If x = 0, then y = 0/2 = 0, so the first point is (0,0).
If x = 2, then y = 2/2 = 1, so the second point is (2,1).
If x = 4, then y = 4/2 = 2, so the third point is (4,2).
If x = 6, then y = 6/2 = 3, so the fourth point is (6,3).
We can plot these points on a coordinate plane
As we can see from the plot, the four points do lie on a straight line. This is because the equation y = x/2 is the equation of a linear function with slope 1/2 and y-intercept 0. Therefore, any two points on this line will have a constant slope between them, and thus the four points will be collinear.
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What numbers fill the boxes in this equation?
By algebra properties, the complete algebraic equation is now described:
a · x · (x + 3) + 7 · x · (2 · x + 1) = 5 · x · (a · x + 5), where a = 7 / 2.
How to complete an algebraic equation by comparing the terms
An algebraic equation is shown herein, this expression must completed by filling the blanks. This can be done by clearing a variable through algebra properties:
a · x · (x + 3) + 7 · x · (2 · x + 1) = 5 · x · (a · x + 5)
a · x² + 3 · a + 14 · x² + 7 · x = 5 · a · x² + 25 · x
(a + 14) · x² + 7 · x + 3 · a = 5 · a · x² + 25 · x
Then, by comparing terms:
a + 14 = 5 · a
14 = 4 · a
a = 14 / 4
a = 7 / 2
The complete expression is introduced below:
(7 / 2) · x · (x + 3) + 7 · x · (2 · x + 1) = 5 · x · [(7 / 2) · x + 5]
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The perimeter of a rectangular garden is 43. 8 feet. Its length is 12. 4 feet what is its width
The width of the rectangular garden is 9.5 feet.
Given that the perimeter of a rectangular garden is 43.8 feet and its length is 12.4 feet.
Let's assume the width of the rectangular garden be "w".
Now we need to find the width of the garden.
Solution: Perimeter of a rectangular garden is given by the formula: P = 2(l + w)
where l = length and w = width.
Substituting the given values in the above formula,
we get43.8 = 2(12.4 + w)
We can solve for "w" by simplifying the above equation.
43.8 = 24.8 + 2w43.8 - 24.8 = 2w19 = 2w
Dividing both sides by 2,we get
w = 9.5 feet.
Therefore, the width of the rectangular garden is 9.5 feet.
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using a single composite transformation matrix for k transformations of n points, what is the required number of multiplications?
The required number of multiplications using a single composite transformation matrix for k transformations of n points is n × k.
In computer graphics, composite transformation matrices are used to transform points and shapes. These matrices are created by combining multiple transformations into a single matrix, allowing for efficient processing of large amounts of data. The number of multiplications required to perform a composite transformation depends on the number of points being transformed and the number of transformations being applied.
If there are n points and k transformations, then the required number of multiplications is n × k.
This is because each point needs to be multiplied by the composite transformation matrix k times.
Therefore, the total number of multiplications is n × k.
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A researcher randomly selects 95 high school swimmers and asks them which swim stroke is their strongest and which bathing suit brand they prefer, brand A or brand B. The two-way table displays the data. Suppose one of the students is randomly selected. Let B = the student prefers brand B and F = the student’s strongest stroke is freestyle.
A 5-column table with 3 rows. Column 1 has entries brand A, brand B, total. Column 2 is labeled breast with entries 15, 18, 33. Column 3 is labeled freestyle with entries 19, 26, 45. Column 4 is labeled butterfly with entries 10, 7, 17. Column 5 is labeled total with entries 44, 51, 95. The columns are titled swim stroke and the rows are titled brand preference.
Which of the following is the correct value and interpretation of P(F|B)?
Answer: 0.51
Step-by-step explanation:
To find the value of P(F|B), we need to use the formula:
P(F|B) = P(F and B) / P(B)
where P(F and B) is the probability that a student prefers brand B and their strongest stroke is freestyle, and P(B) is the probability that a student prefers brand B.
From the given table, we can see that:
P(F and B) = 26/95
P(B) = 51/95
Therefore, we can calculate
:P(F|B) = (26/95) / (51/95) = 26/51 ≈ 0.51
So, the correct value of P(F|B) is approximately 0.51, which can be interpreted as the probability that a student's strongest stroke is freestyle given that they prefer brand B.
The point on the graph represents Ann's location. She is using a metal detector on the beach to see what she can find. Each unit on the graph represents 2 feet. A pile of bottle caps is located at (4, -10). Find the length of the most direct path between Ann and the pile of bottle caps. Round to the nearest whole number.
Answer:
30 feet
Step-by-step explanation:
Coordinates of Ann: (-4,3)
Coordinates of bottle caps: (4,-10)
Distance from Ann to bottle caps can be found out using the distance formula:
[tex]x_2=4, x_1=-4\\y_2=-3,y_1=-10\\Distance=\sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2 } \\=\sqrt{(4-(-4))^2 + ((-10)-3)^2} \\=15.26\\15\text{ is the answer}[/tex]
the stopping distance s of a car varies directly as the square of its speed v. if a car traveling at 40 mph requires 80 ft to stop, find the stopping
If a car traveling at 40 mph requires 80 feet to stop, the stopping distance S of a car varies directly as the square of its speed v and is equal to 180 feet.
Given, the stopping distance S of a car varies directly as the square of its speed v. So the relation can be represented as,
S ∝ v2
Here, the constant of proportionality is k.
S = kv2 ——— (1)
Given, when the speed v = 40 mph, stopping distance s = 80 feet.
Therefore, from equation (1), we have
80 = k × 402
k = 80/1600
k = 0.05
Hence, the relation between the stopping distance S and the speed v of the car can be given as
S = 0.05v2
To find the stopping distance S of the car at speed v = 60 mph, substitute v = 60 in the above equation.
S = 0.05 × 602
S = 0.05 × 3600
S = 180 feet
Therefore, the stopping distance of a car traveling at 60 mph would be 180 feet.
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Your home security system requires a six character code for activation. It contains two letters followed by four digits, 0 - 9. The first character can be any letter and the second cannot be a vowel. The first digit cannot be zero and the last three characters can be any digits. Repetitions are allowed for letters and digits. How many security codes are possible? Show work.
Therefore , the solution of the given problem of probability comes out to be there are 54,540,000 different security number combinations.
What precisely is probability?A procedure's criteria-based systems' main objective is to ascertain the likelihood that an assertion is accurate or that a particular event will take place. Chance can be represented by any number range between 0 and 1, where 0 is commonly used to indicate the possibility of something may be and 1 is usually employed to indicate a degree of confidence. A probability diagram shows the likelihood that a particular occurrence will occur.
Here,
The alphabet consists of 26 characters, and 5 of them are vowels.
(A, E, I, O, U).
Consequently, there are 21 vowels available for the second letter.
Any one of the 26 letters can be used as the first word.
Therefore, there are 21 options for the second character and 26 options for the first letter.
Consequently, there are 9 options for the first number.
There are 10 options for each of the last three numbers since they can be any of the digits from 0 to 9.
Consequently, there are a total of the following protection codes:
=> 26 x 21 x 9 x 10 x 10 x 10 = 54,540,000
Thus, there are 54,540,000 different security number combinations.
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according to the myplate analysis report, empty calories should exceed no more than 362 calories for someone like miya. how many empty calories did miya consume on this 1-day menu? a. 793.34 empty calories b. 693.74 empty calories c. 593.54 empty calories d. 352.74 empty calories
352.74 empty calories did miya consume on this 1-day menu.
Hence option d. 352.74 empty calories is correct.
According to the my plate analysis report, how many empty calories did Miya consume on this 1-day menu.
Empty calories refer to those calories that are devoid of any nutrient and provide only energy.
Miya's 1-day menu needs to be analyzed to determine the empty calories count.
The options provided are:
a. 793.34 empty calories
b. 693.74 empty calories
c. 593.54 empty calories
d. 352.74 empty calories.
Let us understand the concept of empty calories in detail.
Empty calories refer to the calories provided by foods that contain little to no nutrients, like vitamins and minerals. Common sources of empty calories are sugary snacks and alcohol.
Though these foods provide energy, they lack the essential vitamins, minerals, and fiber that the body requires for optimal health.
Therefore, empty calories should be limited in the diet.
To determine the empty calories consumed by Miya, we need to know the nutrient content of her 1-day menu.
Once the nutrient content is known, we can subtract the total calories from empty calories to determine the number of calories that are not empty.
Let us assume that Miya's total calorie intake for the day is 1500 calories. Out of this, the my plate analysis report says that empty calories should not exceed 362 calories.
Therefore, the non-empty calories will be: 1500 - 362 = 1138 calories
From this, we can determine the correct option.
Let us substitute the values given in the options :
a. 793.34 empty calories: 1500 - 793.34 = 706.66
non-empty calories, which is less than 1138.
Therefore, this option is incorrect.
b. 693.74 empty calories: 1500 - 693.74 = 806.26 non-empty calories, which is less than 1138.
Therefore, this option is incorrect.
c. 593.54 empty calories: 1500 - 593.54 = 906.46 non-empty calories, which is less than 1138.
Therefore, this option is incorrect.
d. 352.74 empty calories: 1500 - 352.74 = 1147.26 non-empty calories, which is greater than 1138.
Therefore, this option is the correct answer.
So, the number of empty calories consumed by Miya on this 1-day menu is 352.74 empty calories.
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Find the missing dimension of the trapezoid. 8 in. h 12 in. A = 40 in. h=___in
Answer: h=4
Step-by-step explanation:
Square both sides of this: √2-x = x
Answer:
[tex]2 - x = x^2[/tex]
Step-by-step explanation:
Assuming the form is:
[tex]\sqrt{2 - x} = x \\(\sqrt{2-x})^2 = (x)^2\\2 - x = x^2\\[/tex]
Further solving:
[tex]0 = x^2 +x - 2\\0 = (x+2)(x-1)\\x = -2, 1\\x = 1[/tex]
x is only 1 because of the domain of the original equaiton.
4. Financial Literacy Tickets to a play cost $10 for
members and $24 for nonmembers. Write an expression
to find the total cost of 4 nonmember tickets and
2 member tickets. Then find the total cost. (Example 6)
H
the total cost of 4 nonmember tickets and 2 member tickets would be $116.
Why it is and what is financial literacy?
The expression to find the total cost of 4 nonmember tickets and 2 member tickets would be:
4($24) + 2($10)
This expression represents the cost of 4 nonmember tickets at $24 each, and 2 member tickets at $10 each.
To find the total cost, we simply need to evaluate this expression using basic arithmetic:
4($24) + 2($10) = $96 + $20 = $116
Therefore, the total cost of 4 nonmember tickets and 2 member tickets would be $116.
Financial literacy is the knowledge and skills required to manage one's personal finances effectively. It encompasses a range of topics, including budgeting, saving, investing, managing debt, understanding financial products such as credit cards and loans, and planning for retirement. Financial literacy also involves an understanding of financial concepts such as interest rates, inflation, and risk management.
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matrix flipped 3 coins. what is the probability that all three coins will land on the same side
Answer:
When flipping a coin, there are two possible outcomes: heads or tails. The probability of getting heads on any one flip is 1/2, and the probability of getting tails is also 1/2.
To find the probability that all three coins will land on the same side (either all heads or all tails), we can use the multiplication rule of probability, which states that the probability of two independent events occurring together is the product of their individual probabilities.
So, for each coin flip, there are two possible outcomes, and the probability of getting either outcome is 1/2. To find the probability that all three coins will land on the same side, we need to find the probability of getting either all heads or all tails.
The probability of getting all heads is:
(1/2) x (1/2) x (1/2) = 1/8
Similarly, the probability of getting all tails is also 1/8.
So, the probability of all three coins landing on the same side is:
1/8 + 1/8 = 2/8 = 1/4
Therefore, the probability that Matrix will flip 3 coins and all three coins will land on the same side is 1/8 or 0.125, which can also be written as a fraction or percentage.
answer for this algebra question (2⋅3) 2 −5 2 =
Answer:
First, we evaluate the expression inside the parentheses: 2⋅3 = 6.
Next, we evaluate the exponent: 6² = 36.
Finally, we subtract 5² = 25 from 36: 36 - 25 = 11.
Therefore, the value of the expression (2⋅3)² − 5² is 11.
Enlarge shape A by scale factor 3.5 with centre of enlargement (8, -7).
What are the coordinates of the vertices of the image?
Thus, the vertices of the larger square have the following coordinates: (-6, 7), (1, 7),(1, 0), and (-6 ,0).
Explain about the scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a variable size is known as a scale factor (bigger or smaller).
The procedures below can be used to increase form A by a scale factor of 3.5 with the centre of enlargement at (8,-7).
Transform the square so that its origin is where the centre of enlargement is (0,0).
To do this, we deduct each vertex's coordinates from the centre of enlargement (8,-7):
A = (4 - 8, -3+ 7) = (-4, 4)
B = (6 -8, -3 + 7) = (-2, 4)
C = (6 - 8, -5 + 7) = (-2, 2)
D = (4 - 8, -5 + 7) = (-4, 2)
Multiply the coordinates of the each vertex by the scaling factor (3.5) to enlarge the translated square:
A = (-14, 14)
B = (-7, 14)
C = (-7, 7)
D = (-14, 7)
By adding those coordinates of the centre of the enlargement (8,-7) to each vertex, move the square from its larger state back to its original one:
A = (-14 + 8, 14-7) = (-6, 7)
B = (-7 + 8, 14-7) = (1, 7)
C = (-7 + 8, 7-7) = (1, 0)
D = (-14 + 8, 7-7) = (-6 ,0)
As a result, the vertices of the larger square have the following coordinates: (-6, 7), (1, 7),(1, 0), and (-6 ,0).
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This quarter, a local gym has 759 members. That is 65% more than it had last quarter, due to a change in rates. How many members were there last quarter?
Answer:
759=165% of last quarters members so you could divide by 1.65(move the decimal place twice to the left) so you get 460 people were there last quarter
Step-by-step explanation:
10) A thermometer showed a temperature of 28° C. 9C = 5 (F32) can be used to find the in degrees Fahrenheit, F, given the in degrees Celsius, C. What was the in degrees Fahrenheit? temperature temperature temperature
Step-by-step explanation:
Using the formula F = (9/5)*C + 32, where C is the temperature in Celsius and F is the temperature in Fahrenheit, we can find the temperature in Fahrenheit:
F = (9/5)*C + 32
F = (9/5)*28 + 32
F = 82.4
Therefore, the temperature in degrees Fahrenheit is 82.4°F.
Lin completes a 5K using a combination of walking and running. Here are four graphs that represent four possible situations. Each graph shows the distance, in meters, as a function of time, in minutes.
Graph 1
Graph 2
Graph 3
Graph 4
Match each description with a graph that could represent it.
A:
Lin starts out running, but then slows down to a jog. After 10 minutes, she stops for a water break. She then runs the rest of the way.
B:
Lin starts the race walking, gradually getting faster and faster.
C:
Lin jogs at a steady pace for the entire race.
D:
Lin starts out walking, then moves to a steady run. After 15 minutes, she stops to stretch a cramped leg. Then, she walks the rest of the way.
.Graph 4: A - Lin initially jogs after starting off running. She comes to a stop for a water break after ten minutes. After that, she continues to run.
what is graph ?A graph in mathematics is a picture of a group of things and the connections or interactions between them. The connections or relationships between the objects in a graph are typically represented by lines or edges, whereas the objects themselves are typically represented by points or vertices. Many different real-world phenomena, including social networks, transportation networks, and financial markets, are modelled and represented using graphs. Also, they can be used to examine and research many traits and qualities of things and interactions, like connectedness, separation, and clustering.
given
Graph 1: Lin begins by walking before gradually transitioning to a steady run. She pauses after fifteen minutes to stretch her strained leg. She continues to walk the remaining distance.
Graph 2: B - Lin begins the race by strolling and then progressively picks up speed.
Graph 3: C - Lin maintains a constant speed throughout the entire race.
Graph 4: A - Lin initially jogs after starting off running. She comes to a stop for a water break after ten minutes. After that, she continues to run.
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Amazon uses a box where the volume can be represented by the expression x^3-2x^2-15x. What are the possible dimensions of the box?
Answer:
See below.
Step-by-step explanation:
The volume of the box is given by the expression.
V(x) = x^3 - 2x^2 - 15x
To find the possible dimensions of the box, we need to solve for the values of x that make the volume positive. A box with negative volume is not physically meaningful.
Setting V(x) > 0, we get.
x^3 - 2x^2 - 15x > 0
Factorizing the left-hand side, we get.
x(x^2 - 2x - 15) > 0
Now, we can find the values of x that make each factor positive.
For x > 0, both factors are positive.
For x^2 - 2x - 15 > 0, we can factor it as (x - 5)(x + 3) > 0. This inequality is true when x < -3 or x > 5.
Therefore, the possible dimensions of the box are.
x > 0 and x < -3, or
x > 0 and x > 5.
However, we need to remember that the dimensions of a physical box must be positive. Therefore, the only valid solution is,
x > 0 and x > 5.
So the possible dimensions of the box are.
Length, width, and height > 5 units.
Answer:
Factor the polynomial.
x
(
x
−
5
)
(
x
+
3
Step-by-step explanation:
A boat heading out to sea starts out at Point AA, at a horizontal distance of 787 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 13^{\circ} ∘ . At some later time, the crew measures the angle of elevation from point BB to be 2^{\circ} ∘ . Find the distance from point AA to point BB. Round your answer to the nearest tenth of a foot if necessary.
After answering the prοvided questiοn, we can cοnclude that Rοunding equatiοn tο the nearest tenth οf a fοοt, we get the final answer οf apprοximately 205917.5 feet.
What is equatiοn?An equatiοn is a statement in mathematics that states the equality οf twο expressiοns. An equatiοn has twο sides that are separated by an algebraic equatiοn (=). Fοr example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The gοal οf equatiοn sοlving is tο determine which variable(s) must be changed in οrder fοr the equatiοn tο be true. Simple οr cοmplicated equatiοns, regular οr nοnlinear equatiοns, and equatiοns with οne οr mοre factοrs are all feasible. In the equatiοn "x² + 2x - 3 = 0," fοr example, the variable x is raised tο the secοnd pοwer. Lines are used in a variety οf mathematical disciplines, including algebra, calculus, and geοmetry.
Let's first draw a diagram to visualize the problem:
Lighthouse
|
|
| 13 degrees
A |-------------* 787 feet
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* B
2 degrees
From triangle ABL:
tan(13 degrees) = h/787 feet
where h is the height of the lighthouse above sea level.
[tex]$\begin{array}{l}{\rm{t a n(2^{\circ})=h/(787-x)f e e t}}\\ {{\rm h=787\ f e e t \times t a n(13^{\circ})162.0\ f e e t}}\\ {{\rm x=787 f e e t-h/t a n(2^{\circ})205\ fe e t}}\end{array}$[/tex]
Therefore, the distance between AA and BB is approximately:
[tex]$\begin{array}{l}\rm {\sqrt{(787\ f e e t)^{2}+x^{2})}\\\rm=205917.5\ f e e t\\\rm=39118.2\ m e t e r s \end{array}$[/tex]
Rounding to the nearest tenth of a foot, we get the final answer of approximately 205917.5 feet.
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PLEASE HELP !!!
Questions 3-6
The answer of the given question are, (3) the speed of the plane in still air is 135 km/h and the speed of the wind is 23 km/h. (4) the price of a senior citizen ticket is $8 and the price of a child ticket is $14. (5) the number is 43. (6) the speed of the boat in still water is 12 mph and the speed of the current is 9 mph.
What is Variable?In mathematics, variable is symbol or letter that represents value that can change or vary in given context or problem. Variables are often used in mathematical equations and formulas to express relationships between different quantities or to describe patterns and trends.
3). assume the speed of plane in still air "p" and speed of the wind "w". We can set up two equations based on the given information:
p + w = 158 (since the plane is flying with the wind)
p - w = 112 (since the plane is flying against the wind)
Adding the two equations together eliminates the w variable:
2p = 270
So p = 135 km/h. To find w, we can substitute this value into one of the original equations:
135 + w = 158
w = 23 km/h
Therefore, speed of plane in still air is 135 km/h and speed of the wind is 23 km/h.
4). Let's call the price of a senior citizen ticket "s" and the price of a child ticket "c". We can set up two equations based on the given information:
3s + 1c = 38
3s + 2c = 52
Subtracting first equation from the second eliminates the s variable:
c = 14
Substituting the value into first equation gives:
3s + 1(14) = 38
So 3s = 24 and s = 8
Therefore, the price of a senior citizen ticket is $8 and the price of a child ticket is $14.
5). Let's call the tens digit of the number "t" and the ones digit "u". We know that:
t + u = 7 (since the sum of the digits is 7)
10u + t - (10t + u) = 9 (since reversing the digits increases the number by 9)
Simplifying the second equation gives:
9u - 9t = 9
Dividing by 9 gives:
u - t = 1
Now we can solve for t in terms of u:
t = u - 1
Substituting the into first equation we get:
u - 1 + u = 7
So 2u = 8 and u = 4
Therefore, the number is 43.
6). Let's call the speed of the boat in still water "b" and the speed of the current "c". We know that:
b + c = 210/10 = 21 (since distance = rate × time)
b - c = 210/70 = 3 (since distance = rate × time)
Adding the two equations eliminates the c variable:
2b = 24
So b = 12 mph. Substituting the value into one of original equations gives:
12 + c = 21
So c = 9 mph.
Therefore, the speed of the boat in still water is 12 mph and the speed of the current is 9 mph.
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Which equation is not a solution for the orders pairs y>-1/2x+5 and y<=3x-2
A) 5,3)
B) 4,3)
C) 3,4)
D) 4,4)
Pelase help me it’s an emergency
the equation y = 4x - 3 is also not a solution for the ordered pairs y > -1/2x + 5 and y ≤ 3x - 2.
What is inequality?
Mathematical expressions with inequalities on both sides are known as inequalities. In an inequality, we compare two values as opposed to equations. In between, the equal sign is changed to a less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
To determine which equation is not a solution for the ordered pairs y > -1/2x + 5 and y ≤ 3x - 2, we can substitute different ordered pairs into the equations and see if they satisfy the inequalities.
For example, the ordered pair (0, 0) satisfies the inequality y > -1/2x + 5, since 0 > (-1/2)(0) + 5 = 5, and it satisfies the inequality y ≤ 3x - 2, since 0 ≤ 3(0) - 2 = -2.
Now, let's try the equations:
y = -x + 4
y = 4x - 3
Substituting (0, 0) into y = -x + 4, we get y = -0 + 4 = 4, which does not satisfy the inequality y > -1/2x + 5, since 4 is not greater than (-1/2)(0) + 5 = 5. Therefore, the equation y = -x + 4 is not a solution for the ordered pairs y > -1/2x + 5 and y ≤ 3x - 2.
On the other hand, substituting (0, 0) into y = 4x - 3, we get y = -3, which also does not satisfy the inequalities, since -3 is not greater than 5 or less than or equal to -2.
Therefore, the equation y = 4x - 3 is also not a solution for the ordered pairs y > -1/2x + 5 and y ≤ 3x - 2.
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batman is taking a midnight stroll through gotham and sees the bat signal in the sky . if batman is 320 feet from the foot of the bat signal and the angle of elevation is 42* , find the height of the bat signal?
The height of the bat signal is about 214.12 feet.
Finding the Height of the Bat Signal from Batman's PositionTo find the height of the bat signal from Batman's position, we can use trigonometry.
The angle of elevation is the angle between the line of sight and the horizontal plane.
Using sine, we can set up the following equation:
sin(42) = height / 320
Solving for the height, we get:
height = 320 * sin(42)
Using a calculator, we can calculate the height to be approximately 214.12 feet.
Therefore, the height of the bat signal is about 214.12 feet.
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The ratio of ounces to pounds is 16:1. A veterinarian is treating a dog that weighs 46 pounds. To calculate the correct amount of medicine, the vet must convert the dog's weight
ounces. Which ratio shows the conversion to ounces?
The correct option is c: 46lb x (16 oz / 1lb). Thus, amount of medicine given for the weight of dog in ounce is 736 ounce.
Explain about the unit conversion?The same attribute is expressed using a unit conversion, but in a different measurement unit. For example say, time can be mentioned in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
Measurements are frequently offered in one set of measurements, like feet, but are required in another set, like chains. A conversion factor is a mathematical equation that facilitates an equal exchange of feet for chains.
Given data:
ratio of ounces to pounds = 16:1
16 ounce / 1 pound
Let the weight of dog in ounce be 'x'.
weight of dog in pounds = 46 pounds.
ratio : x ounce / 46 pounds
Equating both ratios:
16 ounce / 1 pound = x ounce / 46 pounds
Cross multiplying:
x = 16*46 ounce
x = 736 ounce
The correct option is c: 46lb x (16 oz / 1lb)
Thus, amount of medicine given for the weight of dog in ounce is 736 ounce.
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Complete question is-
The ratio of ounces to pounds is 16:1. A veterinarian is treating a dog that weighs 46 pounds. To calculate the correct amount of medicine, the vet must convert the dog's weight
ounces. Which ratio shows the conversion to ounces?
The full question is attached.