Arsenia has 80 movie posters and 40 band posters. She plans to sell 24 movie posters. She says that if she
also sells 24 band posters, the ratio of movie posters to band posters stays the same. Is that true? Why or
why not? Complete the explanation.

When examining the linear relationship between two numerical variables, correlation is used.

It calculates how powerful statistics are. The direction and strength of relationships between variables are studied and measured through correlation, which quantifies co-variation rather than causality. As a result, we must never assume that correlation implies a cause-and-effect relationship.

For instance, when two variables X and Y are found to change in one direction, the other variable's value is discovered to change either in the same direction (i.e., a positive change) or in the opposite direction. This relationship is known as a correlation (i.e. negative change).

On graph paper, a straight line can be used to depict how the two variables move with respect to one another if a correlation exists because it is linear.

For more information on correlation kindly visit to

https://brainly.com/question/28898177

#SPJ4

The function that models the area of the rectangular field is given by

A(x) = 1 / 2 ( 80x  -x² ) .

a) The length of the side parallel to the wall is given as x feet.

Total length of the fence = 80 feet.

fence required for each side = 80-x feet

length of each side = 1/2 (80-x)

Area of the rectangular garden

= 1/2(80-x)·x

= 1 / 2 ( 80x  - x² )

Therefore the area written in function form is A(x) = 1 / 2 ( 80x  -x² ) .

b) Now we have to find the length of x for which the area is greater than 350 square feet.

1 / 2 ( 80x  -x² ) > 350

or, ( 80x  -x² ) > 700

or, (x-10)(x-70)<0

or, 10 < x < 70

So for x greater than 10 and less than 70 feet the rea is greater than350 square feet.

c) Now we have to find the length of x for which the area is greater than 700 square feet.

1 / 2 ( 80x  -x² ) > 700

or,  ( 80x  -x² ) > 1400

Hence solving we get:

25.68 < x < 54.14 feet.

So for x greater than 25.68 and less than 54.14 feet the area is greater than 700 square feet.

d) Now we have to find the length of x for which the area is greater than 900 square feet.

A(x) =  1 / 2 ( 80x  -x² )

or, A'(x) =  1 / 2 (80-2x) (differentiate with respect to x)

or, A'(x) = 40 - x

Now at A'(x) =0 , we get x = 40

Now for A(40) the area is the greatest.

A(40) =  800.

Hence the maximum area that can be covered by the fence is 800 square feet. Therefore we can say that the area greater than 900 is not possible.

To learn more about function visit:

https://brainly.com/question/5975436

#SPJ1

Answer: 2.5, 5.3

Step-by-step explanation:

[tex]-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3[/tex]

The Required Sample size is 138 . Yes, this number of IQ test Score is a fairly large number.

In the given statements we have , An IQ test is designed such that

the mean of adults ( X bar ) = 100

standard deviations (σ ) = 18

Estimate the mean iq score of statistics students such that the confidence level is 95%

We know the value of Z score for given confidence level 95% is 1.96 .

Margin of error in IQ test = 3

we shall calculate the sample size here.

Using the Margin of error formula,

M.E = Z( √σ ²/n )

where, Z--> z score value

σ --> standard deviations

n ---> sample size

putting all the values in this formula we get ,

3 = 1.96 (√(18)²/n )

=> 3/1.96 = √324/n => (1.5306)² = 324/n

=> n = 324/ 2.342 = 138.29

Hence, the required Sample size is 138 .

To learn more about Sample Size , refer:

https://brainly.com/question/24158610

#SPJ4

Complete question:

An IQ test is designed so that the mean is 100 and the standard deviation is 18 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95% confidence that the sample mean is within 3 IQ points of the true mean. Assume that σ =18 and determine the required sample size using technology.

Then determine if this is a reasonable sample size for a real world calculation.

Answer:

8/25

Step-by-step explanation:

2x2x2=8

5x5=25

= 8/25

The total weight in ounces of the two identical nail boxes is 336 ounces.

Jason bought two identical boxes of nails.  One box weighs 168 ounces.

The total weight in ounces of the nails that Jason bought can be calculated as follows:

The boxes of nails are identical. Therefore, they have the same weight. The weight of the two boxes is the sum of the weight of the boxes.

Hence,

total weight of the boxes = 168 + 168

total weight of the boxes = 336 ounces

Therefore, the total weight is 336 ounces.

learn more on weight here: https://brainly.com/question/9380679

#SPJ1

Function 1 has a greater rate of change: false.

Mathematically, the rate of change is also referred to as slope or gradient and it can be calculated by using this formula;

Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change, m = (y₂ - y₁)/(x₂ - x₁)

Next, we would determine the rate of change of the value of y with respect to the value of x in function 2, which represents a line that is passing through the points (2, 0) and (8, 6):

Rate of change, m = (6 - 0)/(8 - 2)

Rate of change, m = 6/4

Rate of change, m = 1.5 or 3/2.

From function 1 (y = -x + 6), we can logically deduce that the rate of change is equal to -1.

In conclusion, the rate of change of function 2 (m = 1.5) is greater than the rate of change of function 1 (m = -1).

Read more on rate of change here: brainly.com/question/4184462

#SPJ1

Answer:

price - savings

= $60 - $15

= $45

grandma's bonus =

hence, $45 + x = $60

Collect like terms

60 - 45 =

X = $15

Answer: Width = 4.7 meters, Length = 6.7 meters

Step-by-step explanation:

Let the width be [tex]w[/tex]. It follows that the length is [tex]w+2[/tex].

[tex]w(w+2)=32\\\\w^2+ 2w-32=0\\\\w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7 \text{ } (w > 0)\\\\\implies w+2 \approx 6.7[/tex]

The smallest a and b values such that 41a = 14b. The smallest value is a = 0.34.

Given,

41a = 14b

a = 14b/41

Simplifying,

41a = 14b divide both side by 41

41a/41 = 14b/41b

= 41a/14

b is = 2.92

and the a is,

a = 14b/41 = 0.34

Hence the lowest value is a = 0.34

To learn more about 'lowest value' refer to:

https://brainly.com/question/27941512

#SPJ1

80 percent of games 32 games is 40 games.

You just multiply a decimal figure by 100 to convert it to a percentage, such as 0.57. In other words, 0.57 x 100 Equals 57. In percentage terms, 0.57 is equivalent to 57%. 0.03 x 100 = 3% is another illustration.

Assume G to be the total number of games.

Given the information below:

The number equals 80%

Finished: 32 games

To track down the elusive amount of games:

You must calculate the total number of games that result from multiplying 32 games by an 80 percent proportion in this task. G would then be multiplied by the percentage and converted into 32 games.

For the contests:

80/100×G = 32

G = 32/0.8

G = 40games.

To know more about the percentage, visit:

https://brainly.com/question/6868259

#SPJ1

(x means multiplication)

21/7=3, so he gets the deal 3 times. 2x3=6, so he gets 6 bonus books, leading to a total of 27 books.

Answer:0.56

Step-by-step explanation:

You simply divide 14 by 25

so 14÷25 or 14/25

put that in a calculator and it comes out to 0.56

Answer:0.56

Step-by-step explanation:

if you make the 25 into 100 which is x4 and 14x4= 56

so it will be 56/100 which is 0.56

The distance covered by him in one hour is 4 miles.

What is distance and time?

Distance of a point from a line is the length of the shortest line segment from the point to the line. This will also be perpendicular to the line.

Time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future.

Given

a person walked 2/5 miles in each 1/10 hour

that is miles = 2/5 = 0.4 miles.

Now time is given as 1/10 hours,

one hour contains 60 minutes.

0.4 = 1/10(60)

0.4 miles = 6 minutes.

1 hour = 0.4 (60)/6

1 hour =  4 miles.

To know more about distance and time, visit:

https://brainly.com/question/7827478

#SPJ1

Explanation:

Ashton wants to divide 6 pounds of pecans between 5 neighbors. We have to divide 6 by 5 and write it as a mixed number, because we'll get an improper fraction:

Answer:

The correct option is C 1 1/5 pounds

Answer

The solution of this system of equations is usually the point where the lines meet each other. The solution is at the point of intersection of the lines.

The value for x is the x-coordinate of this point of intersection and the value for y is the y-coordinate of this point of intersection.

Explanation

The graph of a system of equations show straight lines that correspond to each of the equations.

The solution of this system of equations is usually the point where the lines meet each other. The solution is at the point of intersection of the lines.

The value for x is the x-coordinate of this point of intersection and the value for y is the y-coordinate of this point of intersection.

Hope this Helps!!!

Answer:

The solution of this system of equations is usually the point where the lines meet each other. The solution is at the point of intersection of the lines.

The value for x is the x-coordinate of this point of intersection and the value for y is the y-coordinate of this point of intersection

Step-by-step explanation

The graph of a system of equations show straight lines that correspond to each of the equations. The solution of this system of equations is usually the point where the lines meet each other. The solution is at the point of intersection of the lines. The value for x is the x-coordinate of this point of intersection and the value for y is the y-coordinate of this point of intersection

Answer:

A = 44

Step-by-step explanation:

11 x 8 = 88

88 / 2 = 44

Given:

The cardboard costs 0.05 per square inch

And the surface area = 286

So, the total cost is the product of the surface area and the cost per square in.

Total cost =

So, the answer will be Total cost = $14.30

In 5040 different ways, 7 runners can places 1 through 4 be determined if in a race there are 7 runners. trophies for the race are awarded to the runners finishing in places 1 through 4.

The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations. Combinations exist when the order doesn't matter, but permutations exist when it does. A permutation could be described as an ordered combination. The following formula determines how many permutations of n objects, taken r at a time: P(n,r)=n!

Given,

Ways 7 runners can places 1 through 4 be determined:

By using permutation:

7!

7 ×6 × 5 ×4×3×2×1

5040

In 5040 different ways, 7 runners can places 1 through 4 be determined if in a race there are 7 runners. trophies for the race are awarded to the runners finishing in places 1 through 4.

To learn more about permutation, visit:

https://brainly.com/question/28720645

#SPJ4

1.The multiplied answer for the given numbers 2.5 and 3.15 is 7.875. Option 4 is correct.

2. Her investment is 578.85, Option-C is correct.

Given that,

There is a question in the picture that is

The numbers 2.5×3.15

We have to find the multiplied answer.

Mathematicians use multiplication to calculate the product of two or more numbers. It is a basic mathematical procedure that is widely used in daily life. When we need to combine groups of similar sizes, we utilize multiplication.

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Multiplying the numbers makes it simpler to add the same number repeatedly.

=2.5×3.15

=7.875

Therefore, the multiplied answer for the given numbers 2.5 and 3.15 is 7.875. Option 4 is correct.

2. We have she has invest $500 at 5% annual compound interest. After 3 years, what is her investment.

500×5%

25

Next 525×5%

551.50

Next

578.85

Therefore, her investment is 578.85, Option-C is correct.

To learn more about multiplication visit: https://brainly.com/question/5992872

#SPJ1

The other side of the triangle by using Pythagoras theorem is 15 cm.

Given that,

The triangle has an hypothesis 25cm, adjacent is 20 cm and opposite is x cm.

We have to find the other side by using Pythagorean theorem.

The hypotenuse of a triangle, which has a straight angle of 90 degrees, has a square that, according to the Pythagoras theorem, equals the sum of the squares of the other two sides.

c²=a²+b²

25²=20²+x²

625=400+x²

x²=625-400

x²=225

Square root on both sides.

x=√225

x=15.

Therefore, The other side of the triangle by using Pythagoras theorem is 15 cm.

To learn more about triangle visit: https://brainly.com/question/2773823

#SPJ9

The answer is: 0.0362

The total number of Master's degree holders = 2848 (from the question)

In order to choose people 40 and above from this Master's degree holder subset,

You choose:

People 40-49 AND People 50 and over.

Number of people 40-49 = 475

Number of people 50 and over = 699

But we also need to take into consideration, the probability of picking a person 40-49 years old OR 50 and over

total Number of people 40 - 49 are 3518

The total Number of people 50 and above are 6518

Thus, we can write the probability as:

The final answer is: 0.0362

The value of unknown variable [x] is x = 36 x 10⁻⁴

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

We have a proportional relationship of the form -

y₁/x₁ = y₂/x₂

We can write it as -

x = (5.1 x 10⁴ x 12)/(1.7 x 10⁸)

x = 36 x 10⁻⁴

Therefore, the value of unknown variable [x] is x = 36 x 10⁻⁴

To solve more questions on proportional relationship, visit the link below-

brainly.com/question/12917806

#SPJ1

The distance from D to the base AB is 6 cm

If ΔACB is an isosceles triangle, then ∠A ≅ ∠B and AC ≅ CB

Since ∠C = 120° and ∠A + ∠B + ∠C = 180°, then ∠A = 30° and ∠B = 30°

Next, look at ΔADB.  ∠A + ∠D + ∠B = 180°, so ∠A + 90° + 30° = 180° ⇒ ∠A = 30°

Now look at ΔADC.  Since ∠A = 30° in ΔACB, and ∠A = 60° in ΔADB, then ∠A = 30° in ΔADC per angle addition postulate.

Now that we have shown that ΔADB and ΔADC are 30-60-90 triangles, we can use that formula to calculate the side lengths.

CD = 4 cm (given) so AC = 2(4 cm) = 8 cm

Since AC ≅ BC, then BC = 8 cm. Therefore, BD = 4 + 8 = 12 by segment addition postulate.

Lastly, look at ΔBHD.  Since ∠B = 30° and ∠H = 90°, then ∠D = 60°. So, ΔBHD is also a 30-60-90 triangle.

BD = 12 cm, so HD =  = 6 cm

Therefore, the distance from D to the base AB is 6 cm

To learn more about isosceles triangle refer here

https://brainly.com/question/29352724

#SPJ1

Concept

The parent function of absolute functions is y = |x|, and it passes through the origin.

So a parent absolute function is a function that have not been transformed.

So the absolute value parent function is f(x) = |x|

Final answer

f(x) = |x|

Answer:

The slope is 5.

Explanation:

In the slope-intercept form of an equation

m is the slope, and b is the y-intercept of the equation.

Now in our case,

therefore, the slope is 5 and the y-intercept is -3.

Answer:

x = 10

Step-by-step explanation:

y = - 8 is a horizontal line parallel to the x- axis

A line perpendicular to it will therefore be a vertical line parallel to the y- axis with equation

x = c ( c is the value of the x- coordinates the line passes through )

the line passes through (10, - 20 ) with x- coordinate 10 , then

x = 10 ← equation of perpendicular line

The required perimeter is 11x +11

In relation to mathematics, the concepts "area" and "perimeter" are crucial. Any field shape, whether asymmetrical or symmetrical, applies to this. It is measured from the object's edge to its perimeter. Like the yard that is fenced in at your home. The distance around anything is called its perimeter. The fence is 200 feet long for a yard that is 50 feet by 50 feet.

A measurement of an object's interior space is its area. An area is the size you must be in order to begin a lawn in the same yard. Units of squared distance are used in the area. There must be 2500 square feet of grass for a 50 ft by 50 ft.

The perimeter can be calculated by simply adding all the given expression;

= 7x - 13 + x + 29 + 3x + 5

bringing the like terms together

= 7x + x + 3x + 16 + 11

= 11x + 11

To know more about perimeter you may visit the link which is mentioned below:

https://brainly.com/question/6465134

#SPJ13

x represents the cost of each bottle of juice. Given that he bought a pack containing 6 bottles of juice, the cost of the 6 pack juice bottles would be $6x

Given that the total cost of a bag of popcorn which costs $2.11 and a 6-pack of juice bottles is $11.41, it means that

2.11 + 6x = 11.41

6x = 11.41 - 2.11

6x = 9.3

x = 9.3/6

x = 1.55

The cost of each bottle of juice is $1.55