The linear relationship between the number of bean stalks, n, and the yield, y, is y = -0.5n + 40. This equation can be used to predict the yield of beans for any number of bean stalks planted by the farmer.
To find the linear relationship between the number of bean stalks, n, and the yield, y, we can use the two data points provided by the farmer. We know that when 30 stalks are planted, each plant yields 25 oz of beans, and when 32 stalks are planted, each plant yields 24 oz of beans.
First, we need to find the slope, m, of the line. We can use the formula:
m = (y2 - y1) / (x2 - x1)
where x1 = 30, y1 = 25, x2 = 32, and y2 = 24.
m = (24 - 25) / (32 - 30) = -0.5
Next, we need to find the y-intercept, b, of the line. We can use the point-slope form of the equation:
y - y1 = m(x - x1)
where x1 = 30 and y1 = 25.
y - 25 = -0.5(x - 30)
y - 25 = -0.5x + 15
y = -0.5x + 40
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Can someone do this for
Me
1. The two triangles are congruent, ASA criteria. angle H ≅ angle M, HY ≅ MN and EY ≅ AN using CPCT. 2. The two triangles are congruent, ASA criteria. AT ≅ AP, by CPCT. Angle T ≅ angle P. CT ≅ RP, by CPCT.
What are congruent triangles?Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. In mathematics, the term "congruent" refers to figures and shapes that can be flipped or rearranged to match up with other ones. These forms can be mirrored to produce related shapes.
If two shapes are similar in size and shape, they are congruent. We can also state that if two shapes are congruent, then their mirror images are identical.
1. For the given triangle HEY and triangle MAN we see that,
angle E ≅ angle A
angle Y ≅ angle N
and HE ≅ AM
Thus, the two triangles are congruent using the ASA criteria.
Also angle H ≅ angle M (CPCT)
HY ≅ MN
EY ≅ AN using CPCT.
2. For triangle CAT and PAR we have:
angle A ≅ angle A (vertically opposite angles)
Angle C ≅ angle R
AC ≅ AR
Thus, the two triangles are congruent using the ASA criteria.
Also, AT ≅ AP, by CPCT
Angle T ≅ angle P, by CPCT
CT ≅ RP, by CPCT.
3. For the triangles ACL and triangle ARS:
AC ≅ AR and angle 1 ≅ angle 2 (Given)
Also, angle A = angle A (Vertically opposite angle)
Thus, the two triangles are congruent using ASA criteria.
Now, angle 3 ≅ angle 4 using CPCT.
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need done asap only have 2 min
Answer 6
Step-by-step explanation: A = 1/2 bh, 6 x 2 is 12 and 1/2 of 12 is 6
A quick quiz consists of a true/false question followed by a multiple-choice question with 4 possible answers. If both questions are answered with random guesses, find the probability that both responses are correct.
For given Sample Space, the probability that both responses are correct is 12.5%.
What exactly is a sample space?A sample space is the collection of all potential results of an experiment or random process in probability theory. It is a key idea that allows us to define and assess event probability.
Consider the following experiment: rolling a six-sided die. This experiment's sample space is the set of all potential results of rolling the dice, which are 1, 2, 3, 4, 5, 6. Each member of the sample space indicates a possible experiment outcome.
Now,
The probability of answering the true/false question correctly by random guess is 1/2, since there are two possible choices.
The probability of answering the multiple-choice question correctly by random guess is 1/4, since there are four possible choices.
The probability of both events happening together = product of individual probabilities:
P(correct on both) = P(true/false correct) × P(multiple-choice correct)
= (1/2) × (1/4)
= 1/8
= 0.125
Therefore, the probability that both responses are correct is 0.125 or 12.5%.
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24 = 3(y + 6) someone can help me please?
An equation is a mathematical statement that shows that two expressions are equal. It typically includes variables, constants, and mathematical operators such as addition, subtraction, multiplication, and division. Equations can be used to model a wide range of real-world situations, and they are an essential tool in many fields of study, including physics, engineering, and economics.
How to solve the given equation?To solve for y, we need to isolate y on one side of the equation. We can do this by first distributing the 3 on the right-hand side:
24 = 3y + 18
Next, we can isolate 3y by subtracting 18 from both sides:
24 - 18 = 3y
6 = 3y
Finally, we can solve for y by dividing both sides by 3:
y = 2
Therefore, the solution to the equation 24 = 3(y + 6) is y = 2.
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[UGRENT]
What equation is equivalent to log₃(x+5) = 2?
Answer:
x=4
Step-by-step explanation:
We can solve for x by using the definition of logarithms.
log₃(x+5) = 2 can be rewritten in exponential form as 3² = x + 5.
Simplifying 3² gives 9, so we have:
x + 5 = 9
Subtracting 5 from both sides, we get:
x = 4
Therefore, the equivalent equation is x = 4.
sandra tossed a coin 3 times.wich tree diagram shows al the possible outcomes of the coin landing heads up or tails up
8 possible sequences in total. Thus, A tree with 8 outcomes, option 1 is correct.
What is a tree diagram?A diagram with a structure of branching connecting lines, representing different processes and relationships.
Here is a tree diagram showing all the possible outcomes of Sandra tossing a coin three times:
In the diagram, each branch represents the outcome of one toss of the coin. The letters "H" and "T" represent "heads" and "tails," respectively. Each path from the top of the tree to a bottom node represents a possible sequence of coin tosses, and there are 2³ = 8 possible sequences in total.
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Complete question:
Sandra tossed a coin 3 times. Which tree diagram shows al the possible outcomes of the coin landing heads up or tails up.
A tree with 8 outcomes
A tree with 12 outcomes
A tree with 9 outcomes
A tree with 6 outcomes
what is the value of X6.75+3/8 X equals 13 1/4
Answer:
[tex]x = 1 \frac{49}{57} [/tex]
Step-by-step explanation:
[tex]6.75x + \frac{3}{8} x = 13 \frac{1}{4} [/tex]
Multiply the whole equation by 8, to eliminate the fractions:
[tex]54x + 3x = 106[/tex]
[tex]57x = 106[/tex]
Divide both parts of the equation by 57:
[tex]x = \frac{106}{57} = 1 \frac{49}{57} [/tex]
You are in a soapbox racing competition. In each heat, 10 cars race and the positions of the cars are randomly assigned. What is the probability that you are chosen to be in the first or second position of the heat in which you are racing. Explain
The probability of being in the first or second position in a heat with 10 cars can be calculated by finding the total number of ways that the cars can be arranged in the heat and then dividing by the number of ways that result in being in the first or second position.
There are 10 cars in the heat, so there are 10 possible positions for the first car, and once that car has been assigned a position, there are 9 possible positions remaining for the second car, and so on. Therefore, the total number of ways that the cars can be arranged is:
10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
This is equivalent to 10! (read as "10 factorial"), which is the product of all the positive integers from 1 to 10.
To be in the first or second position, there are 2 possible positions out of the 10 total positions in the heat. So, the number of ways to be in the first or second position is:
2 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
which is equivalent to 2 x 9!, since we only need to consider the arrangements of the remaining 9 cars after we have assigned ourselves to one of the first two positions.
Therefore, the probability of being in the first or second position is:
(2 x 9!) / 10!
Simplifying this expression, we get:
(2 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)
which simplifies further to:
2 / 10
or:
1 / 5
So, the probability of being in the first or second position is 1/5 or 0.2, which means that there is a 20% chance of being in one of those positions in any given heat.
Select the correct answer from each drop-down menu.
AABC is similar to ADEF. The ratio of the perimeter of AABC to the perimeter of ADEF is 1:10. The longest side of ADEF measures 4
The length of the longest side of AABC is
2
4
16
30
units. The ratio of the area of AABC to the area of ADEF is 1:100 v
Reset
Next
Triangle ABC's longest side is found as 4 units. Thus, Triangle DEF has a 100-times larger area than triangle ABC.
Explain about the ratios:A ratio is a tool being used compare the sizes of two or more quantities with relation to one another in mathematics. By making amounts easier to understand, ratios enable us to evaluate and express quantities.
Equivalent fractions equate to equivalent ratios.a is the antecedent whereas b is the consequent in the ratio a: b.In a ratio, the roles of antecedent with consequent cannot be switched.Given that both triangles remain similar, triangle DEF is 10 times larger than triangle ABC according to the ratio 1:10.
Triangle ABC's longest side will just be 1/10 of triangle DEF's longest side, or 4, since its longest side is 40.The square of a ratio of the sides of two comparable triangles is the ratio of respective areas.While the ratio of sides in this instance is 10/1 = 10, the ratio of areas forms : 10² = 100Thus, Triangle DEF has a 100-times larger area than triangle ABC.
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A net of a rectangular prism is shown.
A net of a rectangular prism with dimensions 5 and three-fourths centimeters by 4 centimeters by 11 and three-fourths centimeters.
What is the surface area of the prism?
five hundred fifty and one-fourth cm2
four hundred twelve and three-fourths cm2
two hundred seventy-five and one-eighth cm2
one hundred thirty-seven and nine-sixteenths
Thus, the surface area of the rectangular prism is found as : S = 275 ¹/₈ cm².
Explain about the rectangular prism:A rectangular prism is one of the more usual shapes for prisms. One definition of a rectangular prism is a prism with rectangle-shaped bases. An other faces also were rectangles because the bases are rectangles. These are a rectangular prism's characteristics:
two parallel rectangular basesCongruent as well as parallel rectangles on three facestotal of six rectangular facesGiven dimensions for the rectangular prism :
Length l = 11 ³/₄ cm = 47/4 cm = 11.75 cmwidth w = 5 ³/₄ cm = 23/4 cm = 5.75 cmheight h = 4 cmThen ,
surface area of the prism S = 2(lw + wh + hl)
Put the values:
S = 2(11.75*5.75 + 5.75*4 + 4*11.75)
S = 2*137.5625
S = 275.125
S = 275 ¹/₈ cm²
Thus, the surface area of the rectangular prism is found as : S = 275 ¹/₈ cm².
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Determine the leading coefficient of the polynomial graphed below.
The leading coefficient of the polynomial is 4.
The leading coefficient of a polynomial, we first need to understand what the leading term of the polynomial is.
The leading term is the term with the highest degree in the polynomial.
For example, in the polynomial [tex]3x^4 + 2x^3 - 5x^2 + 4x - 1[tex], the leading term is 3x^4.
To determine the leading coefficient of a polynomial, we simply look at the coefficient of the leading term. For example, in the polynomial [tex]3x^4 + 2x^3 - 5x^2 + 4x - 1[/tex], the leading coefficient is 3.
Now, let's apply this concept to the polynomial graphed below. From the graph, we can see that the polynomial has a degree of 2, meaning that the highest power of x in the polynomial is 2.
Therefore, the leading term of the polynomial is [tex]ax^2[/tex], where a is the leading coefficient.
The vertex is the point on the graph where the polynomial reaches its maximum or minimum value. In this case, the vertex is located at [tex](-2, 4)[/tex]
Since the vertex is the highest point on the graph, we know that the coefficient of x^2 must be positive.
In this case, the value of y at the vertex is 4.
Therefore, the leading coefficient of the polynomial is 4.
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Tami has two jobs and can work at most 20 hours each week. She works as a server and makes $6 per hour. She also tutors and makes $12 per hour. She needs to earn at least $150 a week. Choose the first inequality that represents this scenario
Answer:
B?
Step-by-step explanation:
Matthew gets paid $12 per hour. Which graph has a slope that best represents this rate? 15 POINTS!
Answer: While I cannot give an exact answer without additional context, the answer should have a slope of 12, and should look like the image below.
Answer:
12
Step-by-step explanation:
Edward's grandmother used to make him Pannukakku when he was little. He wants to surprise
her by making it himself. The recipe he found requires a 9-in. by 13-in. rectangular pan.
Edward would like to use a round cast iron pan like his grandmother does.
What is the area of a 9-in. by 13-in. pan?
22 in.²
44 in.²
108 in.² 117 in.²
Answer:
117in
Step-by-step explanation: 9in x 13in=117in
So, Edward needs to use a round cast iron pan with a radius of 177 inches to have the same area as the rectangular pan. correct answer is (d).
How to find area of the circle?To find the area of a circle, you need to know its radius (the distance from the center of the circle to any point on its perimeter). Once you know the radius, you can use the following formula:
[tex]Area = \pi * radius^2[/tex]
where π (pi) is a mathematical constant approximately equal to 3.14159.
So, to find the area of a circle, follow these steps:
Measure the radius of the circle.
Square the radius (multiply it by itself).
Multiply the squared radius by π.
Round your answer to the desired number of decimal places (usually 1 or 2).
The area of a 9-in. by 13-in. rectangular pan is:
Area = length x width = 9 in. x 13 in. = 117 in.²
So, the area of the rectangular pan is 117 in.².
To use a round cast iron pan with the same area, Edward needs to find the radius of the circle with an area of 117 in.²:
Area of a circle = πr²
[tex]= \pi r^2[/tex]
[tex]= 117 in.^2 /[/tex]
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the complete question: Edward's grandmother used to make him Pannukakku when he was little. He wants to surprise.
her by making it himself. The recipe he found requires a 9-in. by 13-in. rectangular pan.
Edward would like to use a round cast iron pan like his grandmother does.
What is the area of a 9-in. by 13-in. pan?
[tex](a) 22in^{2} \\(b)44in^{2} \\(c)108in^{2} \\(d)117in^{2}[/tex]
Please help solve the problem
Answer:
y = 3 cot (1x)?
Step-by-step explanation:
Solve the inequality and enter your solution as an inequality comparing the variable to your solution. 30 + x > 83
Answer:
x > 53
30 + x > 83
Subtract 30 from both sides:
x > 53
Therefore, the solution is:
x > 53
I need help with this please
Step-by-step explanation:On a coordinate plane you move 9 to the right and 2 up
Find the sum of (-3x⁵- 4x + 3) and (2x⁵- x +
3)
Answer:20
Step-by-step explanation:
Answer:
[tex]-x^{5} -5x+6[/tex]
Step-by-step explanation:
The half life of a drug in the body is 5 hours. By what factor b is the amount ofdrug in the body multiplied by for each passing hour
Answer:
The factor by which the amount of drug in the body is multiplied by each passing hour can be found using the formula:
b = 1/2^(t/h)
where:
t = time elapsed (in hours)
h = half-life of the drug
In this case, the half-life of the drug is 5 hours, so we have:
h = 5 hours
For each passing hour, the time elapsed increases by 1 hour, so we can calculate the factor b after 1 hour as:
b = 1/2^1/5
b = 0.63
This means that after 1 hour, the amount of drug in the body is multiplied by 0.63. After 2 hours, it is multiplied by 0.63 again, and so on.
The running back for the Bulldogs football team carried the ball 9 times for a total loss of 15/3/4 yards. Find
the average change in field position on each run. Enter the average change as a simplified mixed number.
The average change in field position on each run was a loss of 7/4 yards.
What is mixed number?A mixed number in mathematics is a number that combines a whole number and a fraction. The entire number and the fraction are often separated by a space or a plus sign when writing mixed numbers. As an illustration, the mixed number 2 1/3 stands for the sum of 2 and 1/3. By dividing the entire number by the fraction's denominator and adding the numerator, mixed numbers can be transformed into improper fractions. For instance, we would multiply 2 by 3 and add 1 to get 7, which is an incorrect fraction of 2 1/3. In order to obtain 7/3, we would then write the fraction using the same denominator as the original fraction.
The total change in position for a total loss of 15/3/4 yards is:
Total change in field position = - (15 + 3/4) yards
Given the, number of runs = 9
Thus:
Average change in field position = Total change in field position / Number of runs
Average change in field position = (- 15 - 3/4) yards / 9
Average change in field position = (- 63/4) yards / 9
Average change in field position = - 7/4 yards
Hence, the average change in field position on each run was a loss of 7/4 yards.
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40 points!!!
1. The diagonal of the base of the box is shorter than the length of the wind chime. 2. The interior diagonal of the box shorter than the length of the wind chime. 3. The wind chime will not fit in the box.
What is diagonal?A diagonal is a line segment that connects two polygonal corners (vertexes), although it is not an edge (side). In other words, it connects any two polygonal vertices that are not neighboring. So, when we directly link any two vertices that are not connected by any sides, we may draw the diagonals in a polygon. A diagonal is a line that runs straight across the vertices of a polygon and joins its opposing corners. In other terms, a line segment connecting any two non-adjacent corners is a polygon's diagonal. Depending on how many sides a polygon has, distinct polygons may have a variable number of diagonals.
Given that the length of the wind chime is 16 inches thus,
1. diagonal of base of the box = √10²+8² = √164 = 12.8
Hence, the diagonal of the base of the box is shorter than the length of the wind chime.
2. interior diagonal of the box = √6²+8²+10² = √200 = 14.14
The interior diagonal of the box shorter than the length of the wind chime
3. The wind chime will not fit in the box
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You pick a card at random. Without putting the first card back, you pick a second card at random. 4 5 6 7 What is the probability of picking a 7 and then picking a 7? Write your answer as a percentage.
The probability of picking a 7 and then picking a 7 is 8.33%.
EquationsSince we are not replacing the first card before drawing the second one, the probability of drawing a 7 on the first card is 1/4. After drawing the first card, there are three remaining cards, and only one of them is a 7. Therefore, the probability of drawing a 7 on the second card given that the first card was a 7 is 1/3.
Using the multiplication rule of probability, the probability of drawing a 7 on the first card and then drawing a 7 on the second card without replacement is
P(7 on the first card) x P(7 on the second card | 7 on the first card) = (1/4) x (1/3) = 1/12
P(7 on the first card and then a 7 on the second card) = 1/12 x 100% = 8.33%
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Of the 50 students Bryson surveyed, 15 are twelve years old, 20 are thirteen years old, and 15 are fourteen years old. If there are approximately 600 students at King Middle School, what is the best estimate of the proportion of students who are twelve, thirteen, and fourteen years old?
Answer:
Step-by-step explanation:
If 15 out of 50 students are twelve years old, we can estimate the proportion of twelve-year-olds in the whole school as follows:
Proportion of twelve-year-olds = 15/50
Simplifying this fraction by dividing both numerator and denominator by 5, we get:
Proportion of twelve-year-olds = 3/10
Similarly, if 20 out of 50 students are thirteen years old, we can estimate the proportion of thirteen-year-olds in the whole school as:
Proportion of thirteen-year-olds = 20/50
Simplifying this fraction by dividing both numerator and denominator by 10, we get:
Proportion of thirteen-year-olds = 2/5
Finally, if 15 out of 50 students are fourteen years old, we can estimate the proportion of fourteen-year-olds in the whole school as:
Proportion of fourteen-year-olds = 15/50
Simplifying this fraction by dividing both numerator and denominator by 5, we get:
Proportion of fourteen-year-olds = 3/10
Therefore, the best estimate of the proportion of students who are twelve, thirteen, and fourteen years old in the school, respectively, is:
3/10 are twelve years old
2/5 are thirteen years old
3/10 are fourteen years old
Smithson Mining operates a silver mine in Nevada. Acquisition, exploration, and development costs totaled $7.6 million. After the silver is extracted in approximately five years, Smithson is obligated to restore the land to its original condition, including constructing a wildlife preserve. The company’s controller has provided the following three cash flow possibilities for the restoration costs: (1) $700,000, 25% probability; (2) $750,000, 40% probability; and (3) $850,000, 35% probability. The company’s credit-adjusted, risk-free rate of interest is 8%.
What is the book value of the asset retirement liability at the end of one year?
Assuming that the actual restoration costs incurred after five years are $796,000, what amount of gain or loss will Smithson recognize on retirement of the liability?
Smithson will recognize the loss. So,the amount of loss will Smithson recognize on retirement of the liability is $309,248.85.
What is profit or loss?Profit or loss is the financial gain or loss resulting from the difference between revenue and expenses in a business or financial context.
Book value of ARL = Present value of estimated cash flows for ARL - Accumulated depreciation and amortization
PV = PMT x (1 - 1 / (1 + r)ⁿ) / r
The formula for weighted average is:
Weighted average = (Cash flow 1 x Probability 1) + (Cash flow 2 x Probability 2) + (Cash flow 3 x Probability 3)
PV = (700,000 x 0.25 x (1 - 1 / (1 + 0.08)⁵) / 0.08) + (750,000 x 0.4 x (1 - 1 / (1 + 0.08)⁵) / 0.08) + (850,000 x 0.35 x (1 - 1 / (1 + 0.08)⁵) / 0.08)
PV = $2,317,283.36
Since this is the end of the first year, the accumulated depreciation and amortization is simply the present value of the estimated cash flows for the first year:
Accumulated depreciation and amortization = (700,000 x 0.25 / (1 + 0.08)) + (750,000 x 0.4 / (1 + 0.08)) + (850,000 x 0.35 / (1 + 0.08))
Accumulated depreciation and amortization = $1,830,532.21
Finally, we can calculate the book value of the ARL at the end of one year:
Book value of ARL = Present value of estimated cash flows for ARL - Accumulated depreciation and amortization
Book value of ARL = $2,317,283.36 - $1,830,532.21
Book value of ARL = $486,751.15
Therefore, the book value of the asset retirement liability at the end of one year is $486,751.15.
Loss = Actual restoration costs - Book value of ARL
Loss = $796,000 - $486,751.15
Loss = $309,248.85
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These are just a few examples of real life situations where you might need to find the volume or surface area of a shape. There are many other situations where this knowledge is useful, including in scientific research, medical imaging, and many other fields.
What is volume?In mathematics, volume is the amount of space occupied by an object or a shape. It is a measure of how much three-dimensional space an object or a shape takes up. Volume is typically measured in cubic units such as cubic meters (m³), cubic centimeters (cm³), cubic feet (ft³), or cubic inches (in³).
Here,
There are many real life situations where you might need to find the volume or surface area of a shape. Here are some examples:
Packaging and Shipping: In order to package and ship products, companies need to know the volume and surface area of the products and their packaging. For example, a shipping company needs to know the volume and surface area of a package in order to determine how much space it will take up in a truck or airplane, and how much packaging material will be required.
Construction: Architects, engineers and builders need to know the volume and surface area of building materials such as concrete, steel, bricks, and insulation in order to estimate the amount of materials required for a project. They also need to know the volume of a space to determine the amount of materials required to fill it, such as the amount of concrete required to fill a foundation or the amount of insulation needed to insulate a room.
Cooking and Baking: When cooking or baking, you may need to measure the volume or surface area of a container or cooking vessel to ensure that the recipe will fit and cook or bake properly. For example, you might need to measure the volume of a baking dish to know how much batter to use, or measure the surface area of a frying pan to know how much oil is needed.
Gardening and Landscaping: In gardening and landscaping, you may need to know the volume of soil required to fill a raised bed or the surface area of a lawn in order to determine the amount of fertilizer or weed killer required.
Industrial Design: In industrial design, designers need to know the volume and surface area of products in order to determine the materials required for production and to ensure that the product will fit in its intended location. For example, a designer may need to know the volume and surface area of a water tank to determine its capacity and the amount of materials required to build it.
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the temperature T, in degrees Fahrenheit, during the day can be modeled by the equation T(x)=-0.07x^2, where x is the number of hours after 6 a.m. At what time is the temperature a maximum? What is the maximun temperature?
Answer: To find the time at which the temperature is maximum, we need to find the vertex of the quadratic function T(x) = -0.07x^2. Recall that the x-coordinate of the vertex of a quadratic function f(x) = ax^2 + bx + c is given by -b/2a. In this case, a = -0.07 and b = 0 (since there is no linear term), so the x-coordinate of the vertex is x = -b/2a = -0/(-0.14) = 0.
Since x is the number of hours after 6 a.m., the time corresponding to x = 0 is 6 a.m. Therefore, the temperature is a maximum at 6 a.m.
To find the maximum temperature, we evaluate T(0) = -0.07(0)^2 = 0. Therefore, the maximum temperature is 0 degrees Fahrenheit. Note that this result makes sense, since the quadratic function T(x) = -0.07x^2 is a downward-facing parabola, which means that the temperature decreases as the number of hours after 6 a.m. increases.
Step-by-step explanation:
Write the statement in words. Let p="The plane is on time." Let q="The sky is clear."
Q->~P
It asserts that if the sky is clear, then it is not possible for the plane to be on time.
Define hypothesisIn general, a hypothesis is a proposed explanation or tentative answer to a research question or problem. It is a statement that can be tested through investigation and analysis of data.
The statement "q -> ~p" can be interpreted as "If the sky is clear, then the plane is not on time."
This is a conditional statement, where q represents the hypothesis or condition ("the sky is clear") and ~p represents the conclusion or result ("the plane is not on time").
It asserts that if the sky is clear, then it is not possible for the plane to be on time.
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Quadrilateral ABCD with vertices A(0, 6), B(-3, -6), C(-9.-6), and D(-12, -3):
a) dilation with scale factor of 1/3 centered at the origin
b) translation along the vector (-5, -1)
Part (a)
Answers:
A' = (0, 2)
B' = (-1, -2)
C' = (-3, -2)
D' = (-4, -1)
Explanation:
Multiply each coordinate by 1/3.
For instance,
[tex]B(-3,-6) \to B( -3*(1/3), -6*(1/3) ) \to B \ '(-1, -2)[/tex]
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Part (b)
Answers:
A' = (-5, 5)
B' = (-8, -7)
C' = (-14, -7)
D' = (-17, -4)
Explanation:
Subtract 5 from the x coordinate. Subtract 1 from the y coordinate. This moves each point 5 units to the left and 1 unit down.
I'll show an example using point C.
[tex](\text{x},\text{y})\to(\text{x}-5,\text{y}-1)\\\\(-9,-6)\to(-9-5,-6-1)\\\\(-9,-6)\to(-14,-7)\\\\[/tex]
Therefore, C(-9,-6) moves to C ' (-14,-7)
Replace ∗ with a monomial so that the trinomial may be represented by a square of a binomial:
0.01b^2+ ∗ +100c^2
The square of the binomial that represents the trinomial is [tex](0.1b+10c)^{2}[/tex], and the missing monomial is 10bc.
What is Trinomial ?
A trinomial is a polynomial that consists of three terms. In algebra, a term is a combination of a constant and one or more variables, multiplied together. A trinomial, therefore, is a polynomial that has three such terms.
To represent the trinomial 0.01[tex]b^{2}[/tex]+ ∗ +100[tex]c^{2}[/tex] as a square of a binomial, we need to find a monomial that can be added to it to form a perfect square trinomial.
To do this, we can take the square root of the first and last terms of the trinomial and multiply them together:
√(0.011[tex]b^{2}[/tex]) = 0.1b
√(100[tex]c^{2}[/tex]) = 10c
Multiplying these square roots together, we get:
0.1b * 10c = b * 1c * 10 = 10bc
So, the missing monomial is 10bc. Adding this monomial to the original trinomial gives us:
0.011[tex]b^{2}[/tex] + 10bc + 100[tex]c^{2}[/tex] = [tex](0.1b+10c)^{2}[/tex],
Therefore, the square of the binomial that represents the trinomial is [tex](0.1b+10c)^{2}[/tex], and the missing monomial is 10bc.
To learn more about Trinomial from given link.
https://brainly.com/question/11202722
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A rectangular prism and a cylinder both have a height of 8 m, and their cross-sectional areas are equal at every level parallel to their respective bases.
A rectangular prism and a cylinder both have a height of 8 meters. The rectangle has base dimensions of 5 meters by x. The cylinder has a radius of 3 meters.
Complete the steps to find the width of the prism.
Find the volume of the prism.
V =
m3
Find the volume of the cylinder.
V =
m3
Set the volumes equal to each other and solve for x. Round to the nearest tenth.
x =
m
First, we need to find the cross-sectional area of each figure:
Cross-sectional area of the rectangular prism: 5x square metersCross-sectional area of the cylinder: π(3^2) = 9π square meters
Since the cross-sectional areas are equal at every level, we can set up the following equation:
5x = 9π
Solving for x, we get:
x = 9π/5
Now, we can find the volume of the rectangular prism:
V = 5x * 8 = 72π cubic meters
And the volume of the cylinder:
V = π(3^2) * 8 = 72π cubic meters
Since the volumes are equal, we can set up the following equation:
72π = 72π
Simplifying, we get:
9πx = 40π
Solving for x, we get:
x = 40/9
Rounding to the nearest tenth, we get:
x ≈ 4.4 meters
Therefore, the width of the rectangular prism is approximately 4.4 meters.