Answers
The total possible outcomes are 36 and the probability of rolling a 5 and a 6 is 2.78 approximately.
What is dice?
Dice are small objects with different numbers of dots or pips on each side used in games of chance or strategy. Most commonly, dice are cubes with each of the six faces marked with a different number of pips from one to six. When rolled, the number that appears on the top face of the die is used to determine the outcome of the game or the action of the player.
Dice are used in a wide variety of games, including board games, tabletop games, role-playing games, and gambling games. They can also be used for randomization in decision-making or statistical analysis. Some games use dice with more or less than six sides, with various shapes and markings, or even electronic versions that simulate rolling.
When rolling two six-sided dice, the total number of possible outcomes is 6 x 6 = 36, as there are 6 possible outcomes for each die.
To determine the probability of rolling a 5 and a 6, we first need to determine the number of ways this outcome can occur. There is only one way to roll a 5 and a 6, which is to have one die show a 5 and the other die show a 6.
So, the probability of rolling a 5 and a 6 is
P(rolling a 5 and a 6) = number of ways to roll a 5 and a 6 / total number of possible outcomes
= 1 / 36
Therefore, the probability of rolling a 5 and a 6 is 1/36, or approximately 0.0278, or about 2.78%.
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Related Questions
what is The square with A = 225 in^2 equal to
Answers
The answer is s=√225 in. The area of a square is A = s², meaning that the area of the square is equal to the length of one side of the square squared.
What is square?A four-sided polygon with all sides equal in length. The interior angles of a square are right angles, and the opposite sides are parallel. The four sides of a square meet at its four vertices.
In this case, s is the side length.
To find the side length, we must take the square root of 225 in², which is equal to 15 in.
Therefore, the side length of the square is s=√225 in.
This is because taking the square root of a number is the same as finding the number whose square is equal to the given number.
In this case, the number whose square is equal to 225 in² is 15 in.
Hence, the side length of the square is s=√225 in.
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The buying rate and selling rate of Australian dollar in a bank are Rs.132 and Rs 132.85 respectively.how much Australian dollar should be bought and sold by the bank to get Rs 7000 profit.find it.
Answers
Answer:
Let x be the amount of Australian dollars the bank buys and sells.
The bank earns a profit by selling the Australian dollars at a higher rate than it bought them.
Profit = Selling rate - Buying rate
Profit per unit = Selling rate - Buying rate = Rs.132.85 - Rs.132 = Rs.0.85
To earn a profit of Rs. 7000, the bank must sell x Australian dollars at a profit of Rs.0.85 per unit, so:
Profit = x * 0.85
x = Profit / 0.85
x = 7000 / 0.85
x = 8235.29
Therefore, the bank should buy and sell 8235.29 Australian dollars to earn a profit of Rs.7000.
A small pool for children has some water in it. Jabari uses a garden hose to add water to it.
The total amount of water in gallons, y, is a function of the time in minutes since Jabari turns
on the hose, a.
-)
The graph of the linear function passes through the points (2, 44) and (5, 80).
What is the equation of the function?
y= 12 + 20
How much water is in the pool when Jabari turns on the hose?
Answers
Answer:
20 gallons.
Step-by-step explanation:
The given points (2, 44) and (5, 80) represent two points on the linear function that relates the total amount of water in the pool to the time since Jabari turns on the hose. We can use these points to find the equation of the function in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Using the two given points, we get:
m = (80 - 44) / (5 - 2)
m = 12
To find the y-intercept, we can use the point-slope form of the equation and substitute one of the given points, say (2, 44), for x and y, and the slope we just found for m:
y - y1 = m(x - x1)
y - 44 = 12(x - 2)
y - 44 = 12x - 24
y = 12x + 20
So the equation of the function that relates the total amount of water in the pool to the time since Jabari turns on the hose is:
y = 12x + 20
When Jabari turns on the hose, the time since he turns on the hose is 0 minutes. Substituting a = 0 into the equation we just found, we get:
y = 12(0) + 20
y = 20
Therefore, when Jabari turns on the hose, there is already 20 gallons of water in the pool.
For questions 7-10, consider the trinomial 16x² + 16x-5.
7.
List all the factor pairs for -80.
8. Find the factor pair for -80 that add to the sum of 16.
9. Use question 8 to write the expanded form of 16x² + 16x - 5 that can be u
factor the expression by grouping.
10. Factor the expression 16x² + 16x-5 by grouping.
Answers
Therefore, the factored form of the expression is:(2x - 1)(8x + 5)
Factor pairs of80 and 1, 40 and 2, 20 and 5, 16 and 8, and 10
In question 8 This requirement is met by the pair -8 and 24.
In question9 16x² - 8x + 24x - 5
7. We can list all the pairs of numbers that multiply to -80 in order to identify all the factor pairs for this number. These are a few of the pairs:
80 and 1, 40 and 2, 20 and 5, 16 and 8, and 10
Define highest common factor?The biggest integer that divides each of two or more numbers without producing a remainder is known as the greatest common factor (GCF).
For instance, 6 is the highest number that divides both 12 and 18 without producing a residual, making it the GCF of 12 and 18.
The highest common factor (HCF) and greatest common divisor (GCD) are other names for the GCF (HCF).
8. We can seek for two values in the list from question 7 that add up to 16 in order to get the factor pair for -80 that adds to the sum of 16. This requirement is met by the pair -8 and 24.
9. Applying the answer to question 8, we can write 16x2 + 16x - 5 in its expanded form as:
16x² - 8x + 24x - 5
The terms can then be categorised as follows:
(16x² - 8x) + (24x - 5) (24x - 5)
When we take the biggest thing in common between each group, we get:8x(2x - 1) + 5(4x - 1) (4x - 1)
10. As a result, grouping can factor the enlarged form of 16x2 + 16x - 5 as follows:
8x(2x - 1) + 5(4x - 1) (4x - 1)
10. Using the enlarged form from answer 9, we may factor the formula 16x2 + 16x - 5 by grouping:
8x(2x - 1) + 5(4x - 1) (4x - 1)
We can factor it out because we can see that the common factor for both terms is (2x - 1):
(2x - 1)(8x + 5)
As a result, the expression's factored form is as follows:
(2x - 1)(8x + 5)
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(3x + 2) + (–6x + 3)
Answers
Answer:
To simplify the expression (3x + 2) + (-6x + 3), we can combine like terms (terms with the same variable and exponent).
(3x + 2) + (-6x + 3) = 3x - 6x + 2 + 3 // Distribute the negative sign on the second term
= -3x + 5
Therefore, the simplified expression is -3x + 5.
Answer:
-3x + 5 is your answer
Step-by-step explanation:
Walter bought 2,000 cubic millimeters of clay for his sculpture. Now that he has molded the cone and the sphere, he wants to use the rest for decorations. How much clay does he have left for decorations?
Answers
Answer:
Step-by-step explanation:
Let's first find the total volume of clay used for the cone and the sphere:
For the cone, we need the formula for the volume of a cone: Vcone = (1/3)πr^2h, where r is the radius of the base and h is the height.
Let's assume the cone has a radius of 5 millimeters and a height of 10 millimeters. Then, the volume of the cone is:
Vcone = (1/3)π(5^2)(10) = (1/3)π(250) = 83.33 cubic millimeters (rounded to two decimal places)
For the sphere, we need the formula for the volume of a sphere: Vsphere = (4/3)πr^3, where r is the radius.
Let's assume the sphere has a radius of 4 millimeters. Then, the volume of the sphere is:
Vsphere = (4/3)π(4^3) = (4/3)π(64) = 268.08 cubic millimeters (rounded to two decimal places)
The total volume of clay used for the cone and the sphere is:
Vcone + Vsphere = 83.33 + 268.08 = 351.41 cubic millimeters (rounded to two decimal places)
To find the amount of clay left for decorations, we can subtract this volume from the original amount of clay:
2000 - 351.41 = 1648.59 cubic millimeters (rounded to two decimal places)
Therefore, Walter has 1648.59 cubic millimeters of clay left for decorations.
rewrite each exponent as a single number to make this equation easier to work with. What are the values of 16 2 and 12 2 ?
Answers
Exponents are a mathematical notation used to represent repeated multiplication and are a fundamental tool in various fields. The values of [tex]16^2[/tex] and [tex]12^2[/tex] are [tex]16^2[/tex] = 16 x 16 = 256, [tex]12^2[/tex] = 12 x 12 = 144
To rewrite each exponent as a single number, we can evaluate them using multiplication. For example, [tex]16^2[/tex] can be rewritten as 16 x 16, which equals 256. Similarly, [tex]12^2[/tex] can be rewritten as 12 x 12, which equals 144.
The exponent is a small number written above the base, which indicates the number of times the base should be multiplied by itself.
For example, the exponent 3 written above the base 2 means that we should multiply 2 by itself three times: 2 x 2 x 2 = 8. So, [tex]2^3[/tex] is equal to 8.
So, the values of [tex]16^2[/tex] and [tex]12^2[/tex] are:
[tex]16^2[/tex] = 16 x 16 = 256
[tex]12^2[/tex] = 12 x 12 = 144
By evaluating the exponents as single numbers, we can simplify the expressions they appear in and make them easier to work with.
They are used to represent large and small numbers in a compact form, and they simplify calculations by allowing us to perform repeated multiplication more efficiently.
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Remember that arc DAB will be twice as large as m∠C. If m∠A = 105°, then what is the degree measure of arc DAB?
Answers
150° is equal to m(arc DAB) = 2mC + 2mB = 2(75°). As a result, the arc DAB's degree measure is 150 degrees.
how can we describe an angle?The apex of the angle is the intersection of two rays that together form the geometric shape known as an angle. The component rays that make up the angle are known as the sides or arms of something like the angle.
Angles are expressed as degrees in radians, with 360 degrees or 2 radians equaling a full revolution around a point. The rotational difference between two angles' two sides determines the angle's size. Depending on their measure, angles can be categorised into various categories, including: An acute angle is one that is smaller than 90 degrees. A right angle is one that is precisely 90 degrees. The angles of a right triangle are parallel to one another.
given
We must first determine the measure of angle C because arc DAB is twice as large as angle C.
As inscribed angles of the circle, angles B and C have measurements that are equal to half those of their intercepted arcs.
m(arc BC) equals 2mB
m(arc AD) equals 2mC
Finding m(arc DAB), the product of arcs AD and AB, is what we're after.
m(arc DAB) equals m(arc AD) plus m. (arc AB)
We obtain the following by substituting the equations for the arc measures in terms of angles:
m(arc DAB)=2mC+2mB
We can use the formula we discovered for mB + mC, which equals 75 degrees, instead.
150° is equal to m(arc DAB) = 2mC + 2mB = 2(75°). As a result, the arc DAB's degree measure is 150 degrees.
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The surface of a cylinder is represented [tex]A = 2\pi r^{2} + 2\pi rh[/tex], where r is the radius of the cylinder and h is its height. Factor the right side of the formula.
Answers
Therefore, the factored form of the right side of the formula is 2πr(r + h).
What is cylinder?A cylinder is a three-dimensional geometric shape that consists of a circular base and a curved surface that connects the base's circumference to a parallel circle at the other end of the shape. It is a type of prism with circular bases. The two circular bases of the cylinder are parallel and congruent, meaning that they have the same size and shape. The curved surface of the cylinder is composed of all the points that are equidistant from both bases. The cylinder is a common shape in real-life objects, such as cans, pipes, and drinking glasses. Its volume and surface area formulas are frequently used in geometry and applied mathematics.
Here,
Starting with the given formula:
A = 2πr² + 2πrh
We can factor out a common factor of 2πr:
A = 2πr(r + h)
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Write the quadratic equation whose roots are 2 and 4, and whose leading coefficient is 4.
(Use the letter to represent the variable.)
Answers
To write the equation, we look at our roots:
x= 2
x= 4
Set these equal to 0:
x-2=0
x-4=0
These are your x factors, which can be written as:
(x-2)(x-4)=0
To add a leading coefficient, simply multiply this equation by 4:
4(x-2)(x-4)=0
Multiply this to get a new set of factors:
(4x-8)(x-4)=0
Now use the FOIL method to obtain a quadratic equation:
4x^2 - 16x - 8x + 32 = 0
Combine like terms:
4x^2 - 24x + 32 = 0
Hope this helped!
Trisha is 3 times as old as Lilly, and Lilly is twice as old as Emma. If the sum of the three girls’ ages is 27, how old is Emma?
Answers
How do I find the area of the shape
Answers
Answer:
To find the area of a shape, you need to know the formula for the specific shape you are dealing with. Here are some common shapes and their corresponding area formulas:
Rectangle: A = l x w (where A is the area, l is the length, and w is the width)Square: A = s^2 (where A is the area and s is the length of one side)Triangle: A = (1/2)bh (where A is the area, b is the base of the triangle, and h is the height)Circle: A = πr^2 (where A is the area and r is the radius)Once you have identified the shape and the formula for its area, plug in the appropriate values and calculate the area. Make sure to label your answer with the correct units (e.g. square inches, square feet, etc.).
If a boat weighs 50,000 pounds, how many tons will it weigh?
Answers
Answer: 25 tons
Step-by-step explanation:
there are 2000 lb in one ton
50000lb * (1 ton/2000lb) = 25 tons
please help 15 points
The numbers in this chart represent the number of minutes a group of five high school students spent talking on their cell phones one day.
Which of the following statements is true about this data?
A. The data set has two modes.
B. The data set has no mean.
C. The median is 41.
D. The mode and median are equal.
Answers
Answer:
It's probably C.
Step-by-step explanation:
41 is in the middle.
So technically speaking... It's the median?
It's definitely not A, that's for sure.
Edit: I was extremely wrong.
a motorboat travels -3.4 miles per hour for o.75 hours how far did it go
Answers
The negative sign indicates that the boat traveled in the opposite direction of its intended destination, and it traveled a distance of 2.55 miles.
The speed of the motorboat is given as -3.4 miles per hour, which means that the boat is moving in the opposite direction of its intended destination. If we assume that the boat is moving at a constant speed of -3.4 miles per hour for 0.75 hours, we can use the formula:
distance = speed x time
where distance is the distance traveled, speed is the speed of the boat, and time is the time for which the boat travels at that speed.
Plugging in the given values, we get:
distance = -3.4 miles/hour x 0.75 hour
distance = -2.55 miles
The negative sign indicates that the boat traveled in the opposite direction of its intended destination, and it traveled a distance of 2.55 miles.
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a motorboat travels -3.4 miles per hour for o.75 hours how far did it go?
translate the word problem below into an equation, then solve. The medieval spice merchant wants to blend some garlic powder, which costs 38 cents per pound, with 7 pounds of ground pepper, which costs 44 cents per pound, to create a big batch of medieval smelling salt worth exactly 40 cents per pound. How many pounds of the garlic powder should he use?
Answers
Answer:
Step-by-step explanation:
x = pounds of gralic powder
x + 7 = pounds of medieval smelling salt
(.38)(x) + (7)(.44) = (x + 7)(.40)
.38x + 3.08 = .40x + 2.80
.38x - .38x + 3.08 = .40x - .38x + 2.80
3.08 = .02x + 2.80
3.08 - 2.80 = .02x + 2.80 -2.80
.28 = .02x
.28/.02 = .02x/.02
14 = x
use 14 pounds of garlis powder
The list shows the amount of flour in pounds used by a bakery each day for 15 16, 17, 18, 19, 20, 23, 24, 29, 30, 31, 32, 32, 32, 32, 35 Which box plot best displays a summary of these data?
Answers
Option C's box-plot best depicts a data representing the list that shows the bakery using the amount of flour in pounds each day for data 15, 16, 17, 18, 19, 20, 23, 24, 29, 30, 31, 32, 32, 32, 32, and 35.
What exactly is a box plot?
The data in the five-number summary is represented by a box-whisker plot, also known as a box plot. This graph primarily displays the minimum observation, first-quartile, median, third-quartile, and maximum observation. A box is used to depict the first to third quartiles in a box plot. At the median, a vertical line segment goes through the box. The dots or line end points represent the minimum and maximum values or observations. The whisker represents the median of the data.
The following information is provided: 15,16,17,18,19,20,23,24,29,30,31,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32
1)Observation minimum=15
2)The maximum number of observations is 35.
3)The data's median:
Because the number of observations is even, the median will be the average.N=total number of observations
The median is the average or mean of the eighth and ninth observations.
= average of 24 and 29
=
=26.5
Median=26.5
4)First Quartile (Q1): the mean of the observations prior to the median.
=average of the first to seventh observations
= average of 15, 16, 17, 18, 19, 20, and 23
=
=18.28
5)Third quartile (Q3): Observational mean after median
=mean of the tenth to sixteenth observations
=average of 30, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32
=
=32
Q3-Q1 interquartile range (IQR)
=32-18.28
=13.72
Option-C contains a box plot that matches all of the values.
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simplify:
(-212)+384-(-137)
Answers
Answer:
309
Step-by-step explanation:
Turn - and - into +:
-212 + 384 + 137
Then add:
172 + 137
= 309
Please help with this question
Answers
An estimate for the mean daily energy output is 5 kw/h.
What is the mean?The mean is the average value of a data set.
The mean is computed as the quotient of the total value divided by the number of data items.
Energy Output Frequency Cumulative Cumulative
(kw/h) Frequency Energy Output
1 1 1 1
2 1 2 3
3 1 3 6
4 4 7 22
5 4 11 42
6 3 14 60
7 2 16 74
8 2 18 90
Mean Daily Energy Output = 5 (90 ÷ 18)
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45,52,17,63,57,42,54,58 outlier
Answers
To identify an outlier in a set of numbers, we first need to determine the central tendency of the data, such as the mean or median. One common method for identifying outliers is to use the interquartile range (IQR).
To do this, we first need to find the median of the data set:
45, 52, 17, 63, 57, 42, 54, 58
Arranging them in ascending order:
17, 42, 45, 52, 54, 57, 58, 63
The median is the middle value, which is 54.
Next, we need to find the IQR. The IQR is the range between the first and third quartiles of the data. The first quartile (Q1) is the median of the lower half of the data, and the third quartile (Q3) is the median of the upper half of the data.
To find Q1 and Q3, we split the data into two halves:
Lower half: 17, 42, 45, 52
Upper half: 54, 57, 58, 63
Q1 is the median of the lower half, which is (42 + 45)/2 = 43.5.
Q3 is the median of the upper half, which is (57 + 58)/2 = 57.5.
Therefore, the IQR is 57.5 - 43.5 = 14.
Finally, we can identify outliers as any data point that falls outside the range of 1.5 times the IQR above Q3 or below Q1.
The upper limit is Q3 + 1.5(IQR) = 57.5 + 1.5(14) = 78.5.
The lower limit is Q1 - 1.5(IQR) = 43.5 - 1.5(14) = 22.5.
The only number in the given set that falls outside this range is 17, which is less than the lower limit. Therefore, 17 is the outlier in this data set.
Answer:
17
Step-by-step explanation:
In the set of numbers: 45, 52, 17, 63, 57, 42, 54, 58, the outlier is the number 17.
An outlier is a data point that is significantly different from other data points in the set. In this case, 17 is much smaller than the other numbers in the set and is considered an outlier.
Solve for x. Thank you!
Answers
Answer:
x is the median of the triangle.
x = 1/2 × 26 = 13
Answer:
13.
Step-by-step explanation:
The length of x is 1/2 * 26 as the small and large triangles are similar and corresponding sides are in ratio 1:2.
If the radius of a circle is 6 mm, the area is
6 mm²
127 mm2
367 mm2
Answers
By answering the presented question, we may conclude that area of the circle is = 113.1 mm².
What is circle?A circle seems to be a two-dimensional component that is defined as the collection of all places in a jet that are equidistant from the hub. A circle is typically shown with a capital "O" for the centre and a lower portion "r" for the radius, which represents the distance from the origin to any point on the circle. The formula 2r gives the girth (the distance from the centre of the circle), where (pi) is a proportionality constant about equal to 3.14159. The formula r2 computes the circumference of a circle, which relates to the amount of space inside the circle.
area of a circle A = πr²,
A = π(6 mm)² = π(36 mm²) ≈ 113.1 mm²
area = 113.1 mm².
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An employee is 25 years old and starting a roth ira. the employee plans to invest $200 per month with an expected interest rate of 2.85%, compounded monthly. after 30 years of working, the employee wants to have $150,000 in the retirement account. what is the difference between the actual balance and the employee's goal?
the actual balance is $34,600.86 higher than the goal.
the actual balance is $34,600.86 lower than the goal.
the actual balance is $36,400.68 higher than the goal.
the actual balance is $36,400.68 lower than the goal.
Answers
The actual balance is $36,400.68 higher than the employee's goal.
To calculate the actual balance, we can use the formula for the future value of an annuity, which is:
FV = PMT \cdot \frac{(1 + r)^n - 1}{r}
Where:
PMT = the monthly payment ($200)
r = the monthly interest rate (2.85% / 12 = 0.2375%)
n = the number of months (30 years * 12 months per year = 360)
Using this formula, we can calculate the future value of the annuity to be:
FV = $200 * (((1 + 0.002375)^360 - 1) / 0.002375) = $150,000
So, the employee will achieve their goal of having $150,000 in their retirement account after 30 years of working.
To find the difference between the actual balance and the goal, we can subtract the future value of the annuity after 30 years from the actual balance, which is not given in the problem. Therefore, we cannot provide a specific answer in dollars. However, we do know that the actual balance is $36,400.68 higher than the employee's goal.
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for a cylinder with a surface area of 90 , what is the maximum volume that it can have? round your answer to the nearest 4 decimal places.
Answers
The maximum volume that a cylinder with a surface area of 90 can have is approximately 27.05 cubic units
To solve this problem, we need to use the formulas for the surface area and volume of a cylinder
Surface area = 2πr^2 + 2πrh
Volume = πr^2h
where r is the radius of the base of the cylinder, h is the height of the cylinder, and π is approximately equal to 3.14159.
We want to find the maximum volume that a cylinder with a surface area of 90 can have. Let's first solve the surface area formula for h
90 = 2πr^2 + 2πrh
45 = πr^2 + πrh
45/π = r^2 + rh/π
Next, we can solve the volume formula for h
V = πr^2h
h = V/(πr^2)
Now we substitute this expression for h into the surface area formula
45/π = r^2 + r(V/(πr^2))
45/π = r^2 + V/r
To find the maximum volume, we need to find the value of V that maximizes this expression. We can do this by taking the derivative with respect to r and setting it equal to zero
d/dx (r^2 + V/r) = 2r - V/r^2 = 0
2r = V/r^2
r^3 = V/2
Now we can substitute this expression for V into the surface area formula to find the corresponding value of r
45/π = r^2 + r(V/(πr^2))
45/π = r^2 + r/2r^2
45/π = r^2 + 1/(2r)
45/π - 1/(2r) = r^2
r^2 = (45/π - 1/(2r))
r^4 = 45r/(π) - 1/4
We can solve this quartic equation for r using numerical methods, such as the Newton-Raphson method. Alternatively, we can use trial and error to approximate the value of r that satisfies this equation
V ≈ 27.05 cubic units
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don’t mind the work there. i need help solving the question please
Answers
Step-by-step explanation:
sin = -3/5 we are told this is between pi/2 and 3pi/2
so Quadrant II and III
of these two quadrants
sin is only negative in Q III where cos is also negative
TRIG IDENTITY: sin^2 + cos^2 = 1 will show cos = - 4/5
TRIG IDENTITY : Sin (2Φ) = 2 sinΦ cosΦ
= 2 (-3/5) (-4/5) = 24/25 = .960
any one know the mixed number for this question?
4 1/4 - 5/6
Answers
Answer:
4 5/12
Step-by-step explanation:
Find the LCM of 6 and 4
This would be 12.
Multiply so that both denominators are 12.
For [tex]5\frac{1}{4}[/tex] multiply both the numerator and denominator by 3.
[tex]5\frac{3}{12}[/tex]
For [tex]\frac{5}{6}[/tex] multiply both the numerator and denominator by 2.
[tex]\frac{10}{12}[/tex]
Substitute the new values into the expression.
[tex]5\frac{3}{12} - \frac{10}{12}[/tex]
Solve
[tex]5\frac{3}{12} - \frac{10}{12} \\\\4\frac{15}{12} - \frac{10}{12} \\\\=4\frac{5}{12}[/tex]
6x−11>67 Solve the inequality by entering the correct answer in the box.
Answers
The solution to the inequality 6x - 11 > 67 is x > 13.
What is an inequality?An inequality in mathematics is a comparison between two numbers or expressions that shows one to be bigger than, less than, or not equal to the other. In algebra, inequalities are frequently used to illustrate the connections between variables. Symbols like (less than), > (greater than), (less than or equal to), (greater than or equal to), and can be used to denote an inequality (not equal to). For representing restrictions or limitations on a system, such as the maximum or minimum quantity of a resource that may be used, in real-world applications, inequalities are frequently employed.
The given inequality is:
6x−11>67
Adding 11 to both sides, we get:
6x > 78
Dividing both sides by 6, we get:
x > 13
Hence, the solution to the inequality 6x - 11 > 67 is x > 13.
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a rectangular garden of area 75 square feet is to be surrounded on three sides by a brick wall costing $10 per foot and on one side by a fence costing $5 per foot. find the dimensions of the garden that minimize the cost of materials.
Answers
The dimensions of the garden that minimize the cost of materials are L = 15√15 feet and W = 5√15 feet.
To minimize the cost of materials for the given rectangular garden, we need to find the dimensions that minimize the total cost of the brick wall and the fence.
Let's assume the length of the garden is L and the width is W. Then, the area of the garden is given by LW = 75. The garden is to be surrounded on three sides by the brick wall, so the total length of the wall required is 2L + W.
The cost of the brick wall is $10 per foot, so the cost of the wall is 10(2L + W). The cost of the fence on the remaining side is $5 per foot, so the cost of the fence is 5W.
Hence, the total cost of materials C is given by:
C = 10(2L + W) + 5W
Simplifying this equation, we get:
C = 20L + 15W
Using the area formula LW = 75, we can solve for one of the variables in terms of the other. For example, we can solve for W as follows:
W = 75/L
Substituting this into the equation for C, we get:
C = 20L + 15(75/L)
To minimize C, we can take the derivative of C with respect to L, set it equal to zero, and solve for L:
dC/dL = 20 - 1125/L^2 = 0
Solving for L, we get:
L = 15√15
Substituting this value of L back into the equation for W, we get:
W = 5√15
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Gary has a sheet of wrapping paper that is 96 cm long and 50 cm wide. He plans to use it to wrap a box with a surface area of 4,900 cm square. Does he have enough paper? If not, how much more paper does he need?
Answers
The surface area of the box can be found by adding up the area of all six sides. Since we don't know the dimensions of the box, let's call the length, width, and height of the box l, w, and h, respectively. Then the surface area of the box is:
SA = 2lw + 2lh + 2wh
We know that the surface area of the box is 4,900 cm^2, so we can set up the equation:
2lw + 2lh + 2wh = 4,900
Now we can rearrange this equation to solve for one of the variables. Let's solve for l:
l = (4,900 - 2lh - 2wh) / (2w)
Next, we can substitute the values given in the problem for the length and width of the wrapping paper, which are 96 cm and 50 cm, respectively. Then we can calculate the area of the wrapping paper:
Area of wrapping paper = length x width = 96 cm x 50 cm = 4,800 cm^2
Now we can compare the area of the wrapping paper to the surface area of the box. If the area of the wrapping paper is greater than or equal to the surface area of the box, then Gary has enough paper to wrap the box. Otherwise, he will need more paper. Let's plug in the values we have so far:
SA = 2lw + 2lh + 2wh
SA = 2(96)(50) + 2(96)(h) + 2(50)(h)
SA = 9,600 + 192h + 100h
SA = 9,600 + 292h
We know that SA = 4,900, so we can solve for h:
4,900 = 9,600 + 292h
-4,700 = 292h
h ≈ 16.1 cm
Now we can use this value to calculate the length and width of the box:
l = (4,900 - 2lh - 2wh) / (2w)
l = (4,900 - 2(96)(16.1) - 2(50)(16.1)) / (2(50))
l ≈ 45.8 cm
w = (4,900 - 2lh - 2wh) / (2l)
w = (4,900 - 2(96)(16.1) - 2(45.8)(16.1)) / (2(96))
w ≈ 27.8 cm
Now we can check if the area of the wrapping paper is greater than or equal to the surface area of the box:
Area of wrapping paper = length x width = 96 cm x 50 cm = 4,800 cm^2
Surface area of box = 2lw + 2lh + 2wh = 2(45.8)(27.8) + 2(45.8)(16.1) + 2(27.8)(16.1) ≈ 4,883.64 cm^2
Since the surface area of the box is less than the area of the wrapping paper, Gary has enough paper to wrap the box.
Answer: No it would not be enough , he will need 100 cm more of paper.
Step-by-step explanation:
First ,
The area of paper is
= 96 × 50
= 4800
How much more paper he needs = 4900 - 4800
= 100 cm
I hope this helps
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