6 in.
15 in.
12 in.
Find the surface area of the prism
I

The system of two equations can be represented as y = 10x + 40 and

y = 12x + 28.

The system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution if a system of equations only has two linear equations with two variables.

Because there are only three possible methods to graph two straight lines in the plane, there are only three matching forms of solution for a given system of equations.

Let, 'x' represent the number of days and 'y' represent the total cost.

Plan A can be represented as y = 10x + 40.

And, PlanB be can be represented as y = 12x + 28.

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If the spherical snowball is melting , then the rate at which the radius changing after 6.5 hours is 0.208 ft/h  .

A spherical snowball has volume = 260 ft³ that is melting at a rate of 11 cubic feet per hour, while remaining spherical.

We have to find the rate at which the radius is changing after 6.5 hours.

So , let "V" = volume of snowball, "r" = radius of snowball, and "t" = time.

Volume Of Sphere is  V = (4/3)πr³ and dV/dt = -11 ft³/h ;

So,  dr/dt when t = 6.5 hours. is dV/dt = (dV/dr)×(dr/dt)  ;

derivative of volume formula with respect to "r", we get:

⇒ dV/dr = 4πr²   ;

Substituting the given values in chain rule equation, we get:

⇒ -11 = (4/3)πr² × dr/dt  ;

⇒ dr/dt = -11/((4/3)πr²)

For  rate of change of the radius when t = 6.5 hours, we find the radius at that time.

The initial volume of the snowball = 260 ft³.

After 6.5 hours of melting at a rate of 11 ft³/h, the remaining volume will be:  V = 260 - (11 × 6.5) = 188.5 ft³   ;

So , V = (4/3)πr³

⇒ 188.5 = (4/3)πr³

⇒ r³ = (188.5 × 3 / (4π))   ;

≈ 3.55ft

Now we substitute r = 3.55 feet

⇒ dr/dt = -11/[(4/3)π(3.55)²]  ;

⇒ dr/dt ≈ -0.208 ft/h  ;

Therefore , the rate at which radius is changing after 6.5 hours is approximately 0.208 feet per hour and negative sign represents that radius is decreasing  .

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Given one point and a slope:

To graph the line plot the given point first.

Then find the second point, consider the slope by adding 1 to the x-coordinate and -5 to the y-coordinate, this gives us:

Next, plot the second point (-2, - 9).

Now connect the two pints and extend either side. This is the line you need.

Answer:

Lisa would need to score 97 on her 5th test.

Step-by-step explanation:

If Lisa has an average score of 82 on 4 tests, then the total sum of her scores would be 82 multiplied by 4, which is equal to 328.

If she wants an average final score of 85 over 5 tests, then the total sum of her scores needs to be 425 (i.e. 85 multiplied by 5).

To determine what she needs to get on her 5th test we need to subtract 328 from 425.

425 - 328 = 97

The cost to print 50 photos is $12.50

What is proportion?

The proportion formula is used to determine whether or not two ratios or fractions are equal.

We can use a proportion to find the cost to print 50 photos based on the cost to print 20 photos. Since Ms. Morris charges $5.00 to print 20 photos, we can set up the proportion:

[tex]\frac{cost \ of \ 20\ photos}{number \ of\ photos } =\frac{cost \ of \ 50 \ photos}{number\ of \ photos}[/tex]

Plugging in the given values, we get:

$5.00 / 20 photos = x / 50 photos

Simplifying, we can cross-multiply to get:

20 photos * x = $5.00 * 50 photos

Multiplying and simplifying further, we get:

20x = $250.00

Dividing both sides by 20, we get:

x = $12.50

Therefore, the cost to print 50 photos is $12.50.

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Answer: If there is a proportional relationship between the number of pitchers of lemonade Karen wants to make, x, and the number of lemons she needs, y, and the equation modeling this relationship is y = 5x, then we can find the number of pitchers Karen can make with 15 lemons by solving for x:

15 = 5x

Dividing both sides by 5:

3 = x

So Karen can make 3 pitchers of lemonade with 15 lemons.

Step-by-step explanation:

Answer:

Os = {W, X, Y, Z}

Step-by-step explanation:

The sample space for the experiment is the set of all possible outcomes, in this case, W, X, Y, and Z. It represents all the outcomes that can occur in a single trial of an experiment. The sample space is usually denoted as a set, and the elements in the set are the individual outcomes. In this case, the sample space is the set {W, X, Y, Z}.

Answer:

the answer is the last one

Step-by-step explanation:

os= {w, x, y, z}

Answer:

A parallelogram is a quadrilateral with 2 pairs of parallel sides

Answer:

-2,-4,-8,-16

common ratio of geometric sequence shown is -2

this sequence is in the decreasing form.

the next number in this sequence is -32

I hope that helps.

The exponential equation is given by the function y = 30.5(0.7)ˣ

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

The standard form of an exponential equation is:

y = abˣ

where b is the rate of change and a is the initial value.

Let y represent the number of games sold x years since 2015.

From the graph, at point (0, 30.5):

30.5 = ab⁰

a = 30.5

Also, at point (1, 21.35):

21.35 = ab¹;     but a = 30.5, hence:

21.35 = 30.5b

b = 0.7

The equation is y = 30.5(0.7)ˣ

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One reason for using a t distribution instead of the standard normal curve to find critical values when calculating a level c confidence interval for a population mean is that (b) z requires that you know the population standard deviation s.

The t distribution is used when the population standard deviation is unknown and is estimated from the sample. The t distribution has fatter tails than the standard normal curve, which makes it more appropriate for smaller sample sizes. When the sample size is large, the t distribution approaches the standard normal curve, and the z distribution can be used instead.

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The standard deviation is used more frequently then the variance because  standard deviation is more stable and less sensitive to outliers.

The Standard Deviation and Variance are defined as two closely related measures of the spread or dispersion of a set of data.

The Variance is defined as average of squared differences from mean, while Standard Deviation is square root of variance.

The reason why the standard deviation is used more frequently than  variance is because the standard deviation is expressed in same units as the original data, whereas  the variance is expressed in squared units.

For Example, if we measure  heights of a group of people in inches, the standard deviation will be expressed in inches, whereas variance will be expressed in square inches.

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well, let's get the info first.

so going forth the Cheetah goes 70mph and going back it modestly does 40mph.

can we say that on average it did 55mph?

well, what's that?  on average means, that in total if we sum all units up and divide them evenly by relevant intervals, that's our average value.

well, let's see both intervals, on is forth and another is back 2 intervals, and the speed values are 70 and 40, so the average will really be (70 + 40) ÷ 2 = 55, that is an average of 55mph, so yes, we can say that.

A)

since an hour is 60 minutes, the Cheetah is really doing 70 miles per 60 minutes, or we can say

[tex]70\cdot \cfrac{miles}{~~\begin{matrix} hour \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{~~\begin{matrix} hour \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{60~minutes}\implies \cfrac{70}{60}\cdot \cfrac{miles}{minutes} \implies 1.1\overline{66}\frac{miles}{minutes}[/tex]

[tex]{\Large \begin{array}{llll} \stackrel{\textit{miles covered}}{m(t)}~~ = ~~1.1\overline{66}t \end{array}}[/tex]

B)

[tex]\stackrel{\textit{miles covered}}{m(t)}~~ = ~~1.1\overline{66}t\implies \stackrel{t=10}{m(10)=1.1\overline{66}(10)}\implies \stackrel{\textit{miles in 10 minutes}}{m(10)=11.\overline{66}}[/tex]

Answer: 25

Step-by-step explanation: 5x5 =25

Answer: 25

20% is one-fifth of a whole. This means we must multiply our known number times five.

5 x 5 is 25.

To make sure that our answer is correct, we can figure out the 20% of 25, which is 5.

This means that  25 is our correct answer.

I hope this helps & good luck <3 !!!

Answer: 11.7 in.

Step-by-step explanation:

I don't really know this stuff myself since I'm in 8th grade, but I can say that AA is 12in. long. I measured the length of A'C, and it was a little shorter than AA. So therefore, I think the answer is 11.7 in. I just wanted to help you out.

The board should be 28 inches long.

What is an expression?

An expression or mathematical expression in mathematics is a finite combination of symbols that is well-formed in accordance with context-dependent principles.

Let's call the length of the first part "x". Then, the length of the second part would be x + 6 inches. The total length of both parts is 50 inches, so we can set up an equation to solve for x:

x + (x + 6) = 50

Expanding and solving for x:

2x + 6 = 50

2x = 44

x = 22

So, the first part should be 22 inches long, and the second part should be 22 + 6 = 28 inches long.

The board should be 28 inches long

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Answer:

The expression is a summation, or the sum of a sequence of terms. Each term is equal to 900 * (1.04)^n+1, where n starts at 1 and goes up to infinity.

To calculate this sum, we would need to find the limit of the sequence as n approaches infinity. However, finding the exact value of this sum is not possible and would require the use of mathematical tools like mathematical analysis.

To estimate the value, we can use a calculator or spreadsheet to calculate the sum for a finite number of terms and then see how the sum changes as we increase the number of terms. For example, if we calculate the sum for n = 1 to 100, we would get an estimate of the value. If we then calculate the sum for n = 1 to 200, we would get a closer estimate.

In this case, we can round the expression to the nearest integer, which would be 53.

Step-by-step explanation:

Answer:

Straight line Depreciation

The perimeter of the rectangle is 36 cm.

A rectangle is a two-dimensional figure with length and width.

The area of a rectangle is Length x width.

We have,

Length = 10 cm

Width = 8 cm

Now,

The perimeter of the rectangle.

= 2 (length + width)

= 2 (10 + 8)

= 2 x 18

= 36 cm

Thus,

The perimeter of the rectangle is 36 cm.

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The complete question.

The length ad width of a  rectangle is 10 cm and 8 cm.

Find the perimeter of the rectangle.

a) 28

b) 12

c) 6.4

d) 36

Answer:ab

Step-by-step explanation:

because..........

Charlie could have used quota sampling instead of non-random sampling.

Given is that Charlie is studying the time it takes members of his company to travel to the office. He stands by the door to the office from 08 : 40 A.M. to 08 : 50 A.M. one morning and asks workers, as they arrive, how long their journey was.

Charlie could have used quota sampling instead of non-random sampling. He could have selected a sample that reflects the characteristics of the whole population.

Therefore, Charlie could have used quota sampling instead of non-random sampling.

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{COMPLETE QUESTION IS -

Charlie is studying the time it takes members of his company to travel to the office.

He stands by the door to the office from 0840 to 0850 one morning and asks workers, as they arrive, how long their journey was.

State and briefly describe an alternative method of non-random sampling Charlie could have used to obtain a sample of 40 workers.}

The work required to stretch the spring an additional 3 inches is 10.125 foot-pounds.

We can use Hooke's law to find the force required to stretch the spring 4 inches from its natural length:

[tex]F = kx[/tex]

where F is the force in pounds, x is the displacement in inches, and k is the spring constant in pounds per inch (which we want to find).

Since 18 foot-pounds of work is required to stretch the spring 4 inches, we know that the work done is equal to the potential energy stored in the spring:

[tex]W = (1/2) k x^2[/tex]

Solving for k, we get:

[tex]k = (2W) / x^2[/tex]

Plugging in the values for W and x, we get:

[tex]k = (2 * 18) / (4^2) = 2.25[/tex]

So the spring constant is 2.25 pounds per inch.

Now we can use Hooke's law again to find the force required to stretch the spring an additional 3 inches:

[tex]F = kx[/tex]

= [tex]2.25 * 3[/tex]

= 6.75 pounds

Finally, we can find the work required to stretch the spring an additional 3 inches:

[tex]W = (1/2) k x^2[/tex]

= [tex](1/2) * 2.25 * 3^2[/tex]

= 10.125 foot-pounds

Therefore, the work required to stretch the spring an additional 3 inches is 10.125 foot-pounds.

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By evaluating both equations in x = 8 we will see that the hawk will be closer to the ground.

We know that the height of the hawk is modeled by:

y=−20x+350

And the height of the eagle is modeled by:

y=−10x+400

Now we need to evaluate both equations in x = 8.

hawk:

y = -20*8 + 350 = 190

For the Eagle:

y = -10*8 + 400 = 320

We can see that the hawk is closer to the ground.

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Answer: no exact answer

Step-by-step explanation:

A measurement that shows the circumference of each of the buttons in centimeters is: D. 37.7 cm.

Mathematically, the area of a circle can be calculated by using this formula:

Area of a circle = πr²

Where:

r represents the radius of a circle.

By substituting the radius into the formula for the area of a circle, we have the following;

Area of a circle = πr²

36π = π × r²

Radius, r = √36

Radius, r = 6 centimeters.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

Circumference of a circle = 2πr

Circumference of a circle = 2 × 3.14 × 6

Circumference of a circle = 37.7 cm.

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Complete Question:

Rolando is making buttons that are shaped like circles. Each button has an area of 36π square centimeters. Which measurement shows the circumference of each of the buttons in centimeters?

Answer

A 113.1 cm

B 18.8 cm

C56.5 cm

D 37.7 cm

The least common denominator of the number 2, 3, 4, 7 is found to be 42.

Here, the least common denominator of the following numbers is asked,

2, 3, 4, 7

Now, first understand the meaning of least common denominator, it is basically meant that what is that least common value that will divide all of the four above mentioned numbers. So, it is actually ased about the least common multiple (LCM).

We can find the value which will be a multiple of all those numbers,

4 is multiple of 2 but 3 and 7 are not.

6 is a multiple of 2 and 3 but 7 is not.

42 is the number that is multiple of 6 as well as 7 and it also the smallest number doing so.

So, the least common denominator of 2, 3, 4, 7 is 42.

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Complete question - What is the least common denominator of 2, 3, 7, 4.

Answer:

16.5 cm²

Step-by-step explanation:

the measure of an exterior angle (32°) is found by dividing the difference between the measures of the intercepted arcs (54° and arc abject BF) by two.

32 = (BF - 54)/2

64 = BF - 54

arc angle BF = 64 + 54 = 118°

the area of that sector is

pi×r² × 118/360 = pi×4² × 118/360 = pi×16 × 118/360 =

= pi×2 × 118/45 =

= 16.47590814... ≈ 16.5 cm²

To solve the given equations multiply equation 1 with - 2 and the solutions are x = 1 and y = 2.

In mathematics, the Elimination method is about deleting one of the words containing any of the variables to make the calculations easier.
To solve the equations, multiply or divide a number by the equation(s) until all of the variable terms' coefficients are the same.

The term is then eliminated or removed from the result by adding or subtracting from both equations.

Here we have

Equation 1: 2x - 5y = -8

Equation 2: 4x + 5y = 14  

We can multiply given equations as follows

To eliminate 'x' terms multiply the multiply equation 1 with -2

-2 × Equation 1 =>  - 4x + 10y = 16  ---- (Equation 3)  

Now add Equation (2) and Equation (3)

=> 4x + 5y - 4x + 10y = 14 + 16

=> 15y = 30

=> y = 2

Now substitute y = 2 in equation (2)

=> 2x - 5(2) = -8

=> 2x - 10 = -8

=> 2x = 2

=> x = 1  

Therefore,

To solve the given equations multiply equation 1 with - 2 and the solutions are x = 1 and y = 2.

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Answer:

Non biased (kind of)

Step-by-step explanation:

It depends on how they randomly chose but if it was truly random it would be non biased as many people will read newspapers for things such as sports or catalogs