Q
ot plot shows the results from a survey of third-graders' favorite numbers.
Survey of Third-Graders
plete the statement below about the dot plot.
(XXX)
1
2
3 4
5
6
7
8
9 10
Favorite Numbers
he total number of third graders voting for an even number is​

The linear correlation coefficient r is **1.2237445080439002**.

To calculate the linear correlation coefficient r, we can use the following formula:

[tex]r = (\sum(x - \bar x)(y - \bar y)) / \sqrt(\sum(x - \bar x)^2 \sum(y - \bar y)^2)[/tex]

where:

* [tex]\sum[/tex] is the sum of the values

* [tex]\bar x[/tex] is the mean of x

* [tex]\bar y[/tex] is the mean of y

First, we need to calculate the mean of x and y:

[tex]\bar x[/tex] = (4 + 53 + 86 + 162) / 4 = 71.25

[tex]\bar y[/tex] = (-5 - 1 + 13 + 16) / 4 = 5.75

Next, we need to calculate the sum of the squared deviations from the mean for x and y:

[tex]\sum(x - \bar x)^2 = (47.25^2 + 17.25^2 + 14.25^2 + 90.75^2) = 10148.5[/tex]

[tex]\sum(y - \bar y)^2 = (11.25^2 + 6.75^2 + 7.25^2 + 10.25^2) = 317.5[/tex]

Now, we can calculate the linear correlation coefficient r:

[tex]r = (\sum(x - \bar x)(y - \bar y)) / \sqrt(\sum(x - \bar x)^2 \sum(y - \bar y)^2)[/tex]

r = (47.25 * 11.25 + 17.25 * 6.75 + 14.25 * 7.25 + 90.75 * 10.25) / √(10148.5 * 317.5)

r = 1.2237445080439002

Therefore, the linear correlation coefficient r is **1.2237445080439002**.

This value indicates a strong positive correlation between x and y.

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The angle of elevation to the sun is mathematically given as

[tex]\theta=49.93[/tex]

Question Parameters:

A 107-ft-tall building casts a shadow of 90 ft.

Generally, the equation for the Trigonometry  is mathematically given as

[tex]tan\theta=\frac{opp}{adj}[/tex]

Therefore

[tex]\theta=tan^{-1}\frac{107}{90}[/tex]

[tex]\theta=49.93[/tex]

In conclusion,  the angle of elevation to the sun is

[tex]\theta=49.93[/tex]

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Using the slope concept, it is found that the angle of elevation to the sun is of 40º.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

In this problem, the vertical change is of 107 ft, while the horizontal change is of 90 ft, hence:

[tex]\tan{\alpha} = \frac{90}{107}[/tex]

[tex]\alpha = \tan^{-1}{\left(\frac{90}{107}\right)}[/tex]

[tex]\alpha = 40^\circ[/tex]

The angle of elevation to the sun is of 40º.

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The number of groups of cheerleaders are 6 groups.

Given that, the number of students in grade 4 is 22 and the number of students in grade 5 is 26.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Here, each cheerleading group will have 8 members.

Let the number of groups be x.

Now, 22+26=48

So, x=48/8

= 6 groups

Therefore, the number of groups of cheerleaders are 6 groups.

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Final answer:

To find the number of cheerleading groups that can be made with 22 fourth-graders and 26 fifth-graders, we add the total number of students and divide by the group size (8). The equation is k = (22 + 26) / 8, which simplifies to k = 6, meaning 6 groups can be formed.

Explanation:

The question is asking how to calculate the total number of cheerleading groups that can be formed from a given number of fourth-grade and fifth-grade students. In this case, there are 22 fourth-grade students and 26 fifth-grade students, making a total of 48 students. Given that each group should have 8 members, the formula to find the number of groups is the total number of students divided by the number of members per group.

The equation to find the number of cheerleading groups (k) is:

k = Total number of students / Number of members per group

Thus, the equation is:

k = (22 + 26) / 8

When simplified, it gives:

k = 48 / 8

Which equals:

k = 6

Therefore, 6 cheerleading groups can be made.

Answer:

6 in.

Step-by-step explanation:

[tex]A = r^2\pi[/tex]

[tex]R = \sqrt{\frac{A}{\pi } }[/tex]

[tex]R = \sqrt{\frac{113}{\pi } }[/tex]

[tex]R = \sqrt{36}[/tex]

[tex]R = 6[/tex]

Answer: D

Step-by-step explanation: the temperature changes from 92° to  43°

so 92 - 43 = 49 meaning that the temperature changed 49 degrees in total and if it changed the same amount in the seven days you have to divide 49 by 7 = 7

C is wrong since it did change by 7 but the option to decrease is there and the temperature didn't increase or get warmer but instead decreased or became cooler so it is D

Answer:

4x² + 14x + 12

Step-by-step explanation:

There are several different methods you can use to multiply binomials, but I will walk through the FOIL method.

First - Multiply the first terms of each binomial

2x · 2x

Outer - Multiply the outside terms of each binomial (the first term of the first binomial and the second term of the second binomial)

2x · 4

Inner - Multiply the inside terms of each binomial (the second term of the first binomial and the first term of the second binomial)

3 · 2x

Last - Multiply the last term of each binomial

3 · 4

Then you will add each product together to get the expression 4x² +  8x + 6x + 12. This is not our answer as we have to combine like terms to simplify.

After simplifying, 4x² + 14x + 12 will be the answer.

Answer:

y=40x+800 and 1600

Step-by-step explanation:

Answer:

C and 1600

Step-by-step explanation:

Answer:

Archie:  x+20

Betty: 2x-5

Step-by-step explanation:

We are given that The number of cupcakes that  Archie sold can be given as 20 more than a number, x.

So, 20 more than  x = x+20

So, Archie sold cupcakes = x+20

We are also given that Betty  sold five fewer cupcakes than twice a number, x.

So,twice a number, x = 2x

Five fewer cupcakes than twice a number, x. =2x-5

So, Betty sold cupcakes = 2x-5

Hence an algebraic expression that can be used to represent the amount of cupcakes that each senior sold

Archie:  x+20

Betty: 2x-5

Answer:

20 ride tickets for $14 is a better deal

Step-by-step explanation:

Considering the two offers

The first deal which is 20 ride tickets for $14 is more advantageous because it offers $1.5 less compare to the second offer as 30 rides would require a sum of $21 for the first deal whereas 30 rides cost $22.50 for the second deal

Look at the attached picture ⤴

hope it will help u....:)

The value of x in the equation  (x/7) + 9 = 15 is 42.

To solve for x in the equation (x/7) + 9 = 15, you can follow these steps:

Subtract 9 from both sides of the equation:

(x/7) + 9 - 9 = 15 - 9

(x/7) = 6

Multiply both sides of the equation by 7 to isolate x:

7 × (x/7) = 6 ×7

x = 42

Therefore, the solution to the equation is x = 42.

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Answer:

24-8 = 16 if u divide 16 by 4 u get 4 in each row

Step-by-step explanation:

The height of the cone is approximately 9 meters.

The formula for the volume (V) of a cone is given by:

[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]

where r is the radius of the base and h is the height.

Given that the volume V is 932.58 cubic meters, we can rearrange the formula to solve for h:

[tex]\[ h = \frac{3V}{\pi r^2} \][/tex]

Since the problem doesn't provide the radius r, we cannot calculate the exact height. However, if the cone is assumed to have a radius of 1 meter (as it's not provided), you can substitute the values into the formula:

[tex]\[ h = \frac{3 \times 932.58}{3.14 \times 1^2} \][/tex]

Simplifying this gives:

[tex]\[ h \approx 9 \, \text{meters} \][/tex]

Therefore, under the assumption of a radius of 1 meter, the height of the cone is approximately 9 meters.

Answer:

57:43

Step-by-step explanation:

1000 babies  - 430 baby boys = 570 baby girls

570 girls to 430 boys

570:430

simplify

57:43

Answer:

570/430 respectively

Step-by-step explanation:

1000-430(number of boys)=570(number of kids left so they must be girls)

570/430 is simplified by taking off each 0 and making it 57/43

We have been given diagram of a triangle. We are asked to write an expression that represents the distance between Seattle and San Francisco.

We will use law of cosines to solve our given problem.

[tex]c^2=a^2+b^2-2ab\text{cos}(C)[/tex], where a, b and c are sides corresponding to angle A, B and C.

Let the distance between Seattle and San Francisco be 'c' and [tex]C=21.4[/tex].

Using law of sines, we can set an equation as:

[tex]c^2=1737^2+1858^2-2(1737)(1858)\text{cos}(21.4)[/tex]

Upon taking square root in both sides, we will get:

[tex]c=\sqrt{1737^2+1858^2-2(1737)(1858)\text{cos}(21.4)}[/tex]

Therefore, we can use the expression [tex]\sqrt{1737^2+1858^2-2(1737)(1858)\text{cos}(21.4)}[/tex] can be used to find distance between Seattle, WA, and San Francisco, CA.

Answer:

a

Step-by-step explanation:

Answer to Problem 1: 5√3

Answer to Problem 2: 21√5

Answer:

[tex] 6) \: \: \sqrt{3} + 4 \sqrt{3} \: = \: 5\sqrt{3}[/tex]

[tex] 7) \: \: 3\sqrt{5}+ 6\sqrt{45} = 3\sqrt{5}+6\sqrt{9} \! \cdot \! \sqrt{5} [/tex]

[tex] = 3\sqrt{5} + 6\! \cdot \! 3 \! \cdot \! \sqrt{5}=3 \sqrt{5} + 18 \sqrt{5} = 21\sqrt{5} [/tex]

The correct option is C.

The commutative property is a math rule that says that the order in which we multiply numbers does not change the product.

The commutative property deals with the arithmetic operations of addition and multiplication. It means that changing the order or position of two numbers while adding or multiplying them does not change the end result. For example, 4 + 5 gives 9, and 5 + 4 also gives 9.

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Answer:

I assume the answer would be that f(x) = 6(x) increases over the interval x = 3 to x = 4

Step-by-step explanation:6 x 3 is 18 and 6 x 4 is 24, so over the interval x = 3 to x = 4 f(x) would increase.

20

Step-by-step explanation:

200 divided by 10 equals 20

Answer:

89.5

Step-by-step explanation:

What is the median of 89,99,80,5,90,0,100,95

We should order this from least the greatest.

0,  5,  80, 89, 90, 95, 99, 100

The median is between 89 and 90

median = (89 + 90)/2  = 89.5

Answer:

i think its 180

Step-by-step explanation:

u have to multiply 60 and 3 and u will get 180

The area of a circular playground with a diameter of 60 feet is calculated using the formula Area = π × radius². With a radius of 30 feet, the area is approximately 2826 square feet. Therefore, the area of the playground is about 2826 square feet.

To find the area of a circular playground, we first need to know its radius. Since the diameter of the playground is given as 60 feet, the radius (which is half the diameter) is:

The formula for the area of a circle is:

Using π as approximately 3.14, we can calculate the area:

Therefore, the area of the playground is about 2826 square feet.

Answer: 60 hours

(I'll help you with the first one only because you need to learn this)

Step-by-step explanation: 36 divided by 3 is 12 and 720 divided by 12 is 60

Answer:

D) y= 3.75x

Step-by-step explanation:

The total cost is y, therefore you set the equation equal to y since you want to find the total cost of candy he purchased.

X is the number of pounds, and the candy is $3.75 each pound.

When you set up the equation, it is

y=3.75x

Which also means: the total cost of the candy depends on how many pounds (which is $3.75 per pound) he buys.

Answer:

60.6

Step-by-step explanation:

The formula for finding the circumference of a circle is C = 2πr

C is circumference, π is pi (we'll just us 3.14 here), and r is radius.

The radius is found by dividing the diameter in half.

19.3/2=9.65

So the equation should look like this:

C = 2(3.14)(9.65)

C = 60.602

C = 60.6

Answer:

I believe the answer is 32.

The value of diameter is,

⇒ d = 16 mm

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

A cylinder has surface area of 256 π square millimeters and a height of 8 millimeters.

Since, We know that;

Surface area of cylinder is,

SA = 2πrh + 2πr²

Here, We have;

SA = 256π

h = 8 mm

Hence, We get;

256π = 2π × r × 8 + 2π × r²

128 = 8r + r²

r² + 8r - 128 = 0

r² + 16r - 8r - 128 = 0

r (r + 16) - 8 (r + 16) = 0

(r - 8) (r + 16) = 0

r = 8 mm

Hence, The value of diameter is,

d = 2 x 8

d = 16 mm

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Answer:

$15,267

Step-by-step explanation:

Kay earns $78,400 per year and gets a standard deduction of $5,700.

Her taxable income is amount of money that she can pay tax on and that is:

Income - Standard Deduction

= $78,400 - $5,700 = $72,700

She pays tax at a 21% rate, hence, her income tax is:

[tex]\frac{21}{100} * 72,700[/tex]

= $15,267

Her income tax is $15,267.

Answer:

1704 inches

Step-by-step explanation:

Take the length of each shelf and multiply by the number of shelves

6* 284 =1704 inches

Answer:

1704 in

Step-by-step explanation:

Answer:

-62.5008

Step-by-step explanation:

the pattern here is dividing by -5, so just continue dividing by -5 starting on -3 and continuing 4 more times. record each number and then add them together using a calculator. you will get -62.5008

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Answer:

The equation that represents the amount Samuel earns per hour is "e = (total earned)/(total time worked)", on last weekend he earned 8.4 per hour.

Step-by-step explanation:

Since Samuel worked a total of 2 and 1/4 hours it means that he worked:

hours worked = 2 + 1/4

hours worked = 8/4 + 1/4

hours worked = 9/4

He earned a total of 18.9 working that many hours. If we divide the total amount he earned by the number of worked hours we can find the total he earns per hour.

e = (total earned)/(total time worked)

e = 18.9/(9/4)

e = 18.9*(4/9)

e = 75.6/9

e = 8.4 per hour

The equation that represents the amount Samuel earns per hour is "e = (total earned)/(total time worked)", on last weekend he earned 8.4 per hour.

Answer:

2.25 =18.90e

samuel earns $8.40 per hour

Step-by-step explanation:

Answer:

72 in^3

Step-by-step explanation:

The volume is found by V=Bh meaning volume = area of the base * height

V = 6 * 12

V = 72

Answer:     V = 0.6 m.

Step-by-step explanation:

Volume = l x w x h

in this case if you input the cube's values its volume = 1 m and 1 - 0.4 = 0.6m                                                                                                                                                                                                

Volume is a measure of how much space something takes up and is usually measured in cubic centimetres ({cm}^3cm  

3

) or cubic metres ({m}^3m  

3

). Density is a measure of how tightly the mass of an object is packed into the space it takes up, so we calculate this by dividing its mass by its volume.

{density } = \dfrac{{mass}}{{volume}}density =  

volume

mass

​  

As a result, the units we used to measure density are compound units for more information, see here . The unit of choice will depend on what units are used to measure the values you’re given. If, in a particular question, mass is measured in kilograms and volume is measured cubic metres, then the density we calculate would be measured “kilograms per cubic metre”, which is denoted either by {kgm}^{-3}kgm  

−3

 or kg/m}^3kg/m  

3

. If the starting units were different, then the resulting unit of density would be different. Let’s see an example.

Example: An object has a mass of 570g and a volume of 2,280 cm}^3cm  

3

. Calculate its density.

As stated, density is equal to the mass divided by the volume, so this will be our calculation, but what will the unit of our answer be? In the question, the mass is given in grams and the volume in cubic centimetres, so the density should be in grams per cubic metre, which is denoted either like \{gm}^{-3}gm  

−3

 or {g/m}^3g/m  

3

.

{Density } = {570}{2,280} = 0.25{ g/m}^3Density =  

2,280

570

​  

=0.25 g/m  

3

Answer:

v= 0.6

Step-by-step explanation: