What is the slope of the line that contains these points?
x
12
13
14
15
y
-4
2
8
14

Answer: the value us 2.064

Step-by-step explanation:

To determine the t value, we would need the t distribution table. Since degree of freedom is known as 24, we would determine alpha/2

A 95% confidence level is 95/100 = 0.95

1 - alpha = 0.95

alpha = 1 - 0.95

alpha = 0.05

alpha/2 = 0.05/2 = 0.025

this is the area to the left. The area to the right 1 - 0.025 = 0.975

alpha/2 = 0.975

Looking at the t distribution table, the t value is

2.064

Answer:

188 children and 145 adults were admitted in the park.

Step-by-step explanation:

Given:

The admission fee at an amusement park is $1.50 for children and $4 for adults.

Total $862 collected on a certain day when 333 people enter the park.

Now, to find the children and adults admitted in the park.

Let the number of children admitted be [tex]x.[/tex]

And the the number of adults admitted be [tex]y.[/tex]

So, the total people enter the park:

[tex]x+y=333\\\\x=333-y\ \ \ ...(1)[/tex]

Thus, the total amount collected of the admission fee:

[tex]1.50(x)+4(y)=862\\\\[/tex]

Substituting the value of [tex]x[/tex] from equation (1):

[tex]1.50(333-y)+4(y)=862\\\\499.50-1.50y+4y=862\\\\499.50+2.50y=862\\\\Subtracting\ both\ sides\ by\ 499.50\ we\ get:\\\\2.50y=362.50\\\\Dividing\ both\ sides\ by\ 2.50\ we\ get:\\\\y=145.[/tex]

Thus, the number of adults = 145.

Now, to get the number of children by substituting the value of [tex]y[/tex] in equation (1) we get:

[tex]x=333-y\\\\x=333-145\\\\x=188.[/tex]

Hence, the number of children = 188.

Therefore, 188 children and 145 adults were admitted in the park.

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

An aquarium tank can hold 6600 liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can fill the tank in 55 minutes. The second pipe can fill the tank in 66 minutes by itself. When both pipes are working together, how long does it take them to fill the tank?

Given Information:

Time to fill tank by first pipe = 55 minutes

Time to fill tank by first pipe = 66 minutes

Total capacity  of tank = 6600 liters

Required Information:

Time required to fill tank when both pipes are working together = ?

Answer:

Time required to fill tank when both pipes are working together = 30 mins

Step-by-step explanation:

The rate of filling the tank of the first pipe is,

first pipe = [tex]\frac{6600}{55} = 120[/tex] [tex]L/m[/tex]

The rate of filling the tank of the second pipe is,

second pipe = [tex]\frac{6600}{66}= 100[/tex] [tex]L/m[/tex]

Let x is the time to fill the tank when both pipes are used so the equation becomes,

[tex]120 + 100 = \frac{6600}{x}[/tex]

[tex]120x + 100x = 6600[/tex]

[tex]220x = 6600[/tex]

[tex]x = \frac{6600}{220}[/tex]

[tex]x = 30[/tex] [tex]mins[/tex]

Therefore, it would take 30 minutes to fill the entire tank when both pipes are used to fill the tank.

Answer:

The missing side is 18 inches

Step-by-step explanation:

Since in the smaller rectangle the sides are 2.5in x 6in and one side for the larger rectangle is given, you can make an equation.

[tex]\frac{2.5}{6}=\frac{7.5}{x}[/tex]

Then you can cross multiply.

2.5x=45

Divide by 2.5 on both sides.

x= 18

Answer:

18

Step-by-step explanation:

if it is a ratio like 2.5:6 the the answer will be 18 because if you do 2.5 over 7.5 that comes out to a total of 0.33 and thats rounded so if you do 6 over .33 then the answer will be 18

Answer:

-6.66

Step-by-step explanation:

Answer:

-6.6 (the 6 on the right is repeating)

Step-by-step explanation:

4.56

Step-by-step explanation:

Hope this helps :)

The unit price of the tee shirts that Jay bought is calculated by dividing the total cost ($68.40) by the number of tee shirts (15), coming to a unit price of $4.56 per tee shirt.

The question is asking for the unit price of the tee shirts that Jay bought. To find the unit price, you'll divide the total price by the number of units (tee shirts) purchased. This is a straightforward division of the total cost by quantity.

So, Jay's total cost is $68.40 for 15 tee shirts. To calculate the unit price:

So, $68.40 / 15 = $4.56.

Therefore, the unit price for the tee shirts that Jay bought is $4.56.

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The surface area of the prism is 72 cm².

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface.

We have a prism in the shape of cuboid.

length = 6 cm, Width = 3 cm, Height = 2 cm

So, Surface Area of Cuboid

= 2 (lw + wh + lh)

= 2 ( 18 + 6 + 12)

= 2 (36)

= 72 cm²

Thus, the surface area of prism is 72 cm².

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Answer:

(-2, -4)

Step-by-step explanation:

–2x + 2y = -4

3х + Зу = -18

Divide the first equation by 2

–2x/2 + 2y/2 = -4/2

-x +y = -2

Divide the second equation by 3

3х/3 + Зу/3 = -18/3

x + y = -6

Add these equation together

-x +y = -2

x + y = -6

-------------------

0x + 2y = -8

2y = -8

Divide each side by 2

2y/2 = -8/2

y = -4

Now we need x

x+y = -6

x-4 = -6

Add 4 to each side

x-4+4 = -6+4

x = -2

The price of the cookbook is $40, and the price of the science fiction novel is $15. This was determined by setting up and solving a system of equations based on the sales data provided for two different days.

The student has asked to determine the price of each book based on the sales data for two days. This is a system of equations problem in which we have two equations with two unknowns, representing the prices of two different books. Let's denote C as the price of the cookbook and S as the price of the science fiction novel. From the information given:

4C + 5S = 235 (sales on the first day).

3C + 4S = 180 (sales on the second day).

By solving these two equations simultaneously, we can find the exact prices for both books.

Step 1: Multiply the second equation by 4/3 to align the coefficient of C with the first equation:

([tex]\frac{4}{3}[/tex])(3C + 4S = 180)

4C + ([tex]\frac{16}{3}[/tex])S = 240

Step 2: Subtract the first equation from this new equation:

[([tex]\frac{16}{3}[/tex])S - 5S] = [240 - 235]

[tex]S = \frac{5 }{ \frac{16}{3} - \frac{15}{3}}[/tex]

[tex]S = \frac{5 }{ \frac{1}{3}}[/tex]

S = $15 (price of the science fiction novel)

Step 3: Substitute the value of S in one of the original equations to find C:

3C + 4(15) = 180

3C + 60 = 180

3C = 120

C = $40 (price of the cookbook)

Answer:

(5x−2) and (x+2)

Step-by-step explanation:

Answer:

(5x-2)(x+2)

If you want to check your answer mulitply (5x-2)(x+2) and you get the same

trinomial 5x2 + 8x - 4.

Answer: B and A

Step-by-step explanation:

(X+3)2 = 2×x + 2×3

= 2x + 6

Likewise

2(x+3) = 2×x +. 2×3

= 2x + 6

Hence they are both same

2.(X +3) still equivalent to 2x +6

Answer:

A and B

Step-by-step explanation:

In this question, we are asked to pick the options which have the same value as the expression in the question.

Firstly, let’s expand the main expression in the question.

Mathematically, expanding this, we have 2x + 6

now let’s consider the options one after the other.

Options A and B are correct as they mean the same thing and would refer to the expression in the question.

Option c is wrong. Expanding option c would yield 2x + 4

option d is wrong as the multiplication is only between 2 and x and does not cover 3. This makes the expression as 2x + 3

option E is is also wrong as it is same as D but expressed in another fashion

option F is is wrong also as expanding would give 6 + 3x which is different from 2x + 6

Answer:

The total of a triangle like all the angles added together have to equal 180 degrees

2

the second answer choice

Step-by-step explanation:

115+25+35= 175

end result isn't 180 so no!

115+32+33= 180

end result is 180 so yes!

120+35+35= 190

end result isn't 180 so no!

120+30+20= 170

end result isn't 180 so no!

Answer:

Multiple possible without box count: 1,2,3,4,6,12,24

Step-by-step explanation:

Without knowing how many boxes there are you can get multiple answers

if there are 24 boxes then 1 apple goes into each box

if there are 12 boxes then 2 apples can go into each box

if there are 8 boxes then 3 apples can go into each box

if there are 6 boxes then 4 apples can go into each box

if there are 4 boxes then 6 apples can go into each box

if there are 2 boxes then 12 apples can go into each box

if there is 1 boxes then 24 apples can go into that box

with added information i can edit my answer

Answer:

b) It is the common difference.

Step-by-step explanation:

In arithmetic sequence the difference between one term and other term is constant. The slope of the line related to the arithmetic sequence is Common Difference.

In arithmetic sequence the difference between one term and other term is constant

We need to find how slope of the line related to the arithmetic sequence.

A common difference is a difference between any term and its preceding term in an arithmetic sequence. The slope of the line related to the arithmetic sequence is common difference.

Therefore common difference is related to arithmetic sequence.

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Step-by-step explanation:

x + y = 6 ...................equation 1

x - y = 10 ..................equation 2

Solving equation 1 and 2

x + y = 6

x - y = 10

2x = 16

x = 16 /2

Therefore x = 8

Now

putting x = 8 in equation 1

8 + y = 6

y = 6 -8

y = -2

hope it was helpful :)

Answer:

x=8 and y= -2

Step-by-step explanation:

x+y=6

x-y=10      +              ( add them together)

-----------------

2x=16                          ( substitute/ plug x back in )

x=8

8+y=6

8-y=10

y=-2

Answer:

4. a vertex at (0, 96) is CORRECT

5. the center at (0, 0) is CORRECT

From the given equation,

a = 40

b = 96

(h,k) = (0,0), the center

The vertices are at (0,96) and at (0, -96).

The curves open upward and downward.

c² = a² + b² = 40² + 96² = 10816

c = 104

Therefore the foci are at (0, -104) and (0, 104).

Check the given answers:

1. a focus at (104, 0) is INCORRECT

2. a focus at (0, -96) is INCORRECT

3. a vertex at (-40, 0) is INCORRECT

4. a vertex at (0, 96) is CORRECT

5. the center at (0, 0) is CORRECT

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Answer:

a vertex at (0,96)

the center at (0,0)

Step-by-step explanation:

edge

Answer:

$1.1

Step-by-step explanation:

First take if 110% is equals to $1.21 what about 100%

1.21×100=121÷110= $1.1

The surface area of the cereal box is 2600 square centimeters. Volume of the cereal box is 7500 cubic centimeters.

The surface area of the cereal box in the image is 2600 square centimeters. The volume of the cereal box is 7500 cubic centimeters.

To calculate the surface area, we need to find the area of each of the six faces of the box and add them all up. The two largest faces have dimensions 25 cm by 30 cm, so their area is 25 * 30 = 750 square centimeters each. The two next-largest faces have dimensions 10 cm by 30 cm, so their area is 10 * 30 = 300 square centimeters each. The two smallest faces have dimensions 25 cm by 10 cm, so their area is 25 * 10 = 250 square centimeters each. Therefore, the total surface area of the box is 750 + 750 + 300 + 300 + 250 + 250 = 2600 square centimeters.

To calculate the volume, we simply multiply the length, width, and height of the box together. The length is 25 cm, the width is 10 cm, and the height is 30 cm, so the volume is 25 * 10 * 30 = 7500 cubic centimeters.

Here is a table summarizing the surface area and volume of the cereal box:

|      Property   |                 Value                 |

|--------------------|--------------------------------------|

| Surface area | 2600 square centimeters|

|      Volume     |  7500 cubic centimeters |

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Answer:

The total cost of purchase of Matt and Natalie are $29.41

Step-by-step explanation:

We are given the following in the question:

Cost of clothing without tax = $27.75

Tax percentage = 6%

Amount of tax on clothing =

[tex]=6\%\times 27.75\\\\=\dfrac{6}{100}\times 27.75 \\\\=1.665\approx \$1.66[/tex]

Total cost of purchase =

=Total bill without  tax + Amount of tax

[tex]=27.75+1.66\\=\$29.41[/tex]

Thus, the total cost of purchase of Matt and Natalie are $29.41

Answer:

2 cents per ounce

Step-by-step explanation:

divide 1.07 by 52 to get 2 cents

Answer:

A =176 cm^2

Step-by-step explanation:

The area of a trapezoid is found by

A =1/2 (b1+b2) *h

where b1 and b2 are the lengths of the bases

A =1/2(12+10) *16

A = 1/2(22)*16

A =176 cm^2

Answer:

Sample response: The Smith family has 2 choices to make, color

and style. By the fundamental counting principle, the product of the

number of choices of color and style must equal 8. So, there could be 1

color and 8 style choices, 2 colors and 4 styles, 4 colors and 2 styles,

or 8 colors and 1 style.

Step-by-step explanation:

The smith can have 1 style and 8 colors, 2 styles and 4 colors, 4 styles and 2 colors, and 8 styles and 1 color.

A permutation can be defined as the number of ways a set can be arranged, order matters but in combination, the order does not matter.

We have:

Smith family is shopping for a new car and they are basing their decision on color and style.

The total possible outcomes = 8

By the principle of counting the smith family has four choices.

The above are the factors of 8 because smith has a total number of 8 possible outcomes.

Thus, the smith can have 1 style and 8 colors, 2 styles and 4 colors, 4 styles and 2 colors, and 8 styles and 1 color.

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Answer:

13 cm

Step-by-step explanation:

Volumes should be equal

20 × 70 × 29 = 3.14 × 31² × h

h = 13.4546683723 cm

Answer:

a) No there is no certain number of texts when two plans cost the same

b) On plan A 1 text and on plan B 2 text

Step-by-step explanation:

Let us calculate the per text charge for both the plans

Plan A

Total monthly charge of the plan [tex]= 5[/tex] dollars

Number of cents is a dollar [tex]= 100[/tex]

Total cents in five dollars [tex]= 5* 100 = 500[/tex] cents

Total number of days in a month [tex]= 30[/tex]

Charge per day

[tex]= \frac{500}{30} \\= \frac{50}{3} \\= 16.67[/tex]

Now, if only one text is send in a day, the total charge of the text will be

[tex]16.67 + 3[/tex]

[tex]19.67[/tex] cents per text or [tex]20[/tex] cents per text

Plan B

No charge for the month + $ [tex]10[/tex] cents per text

[tex]=[/tex]  $ [tex]10[/tex] cents per text

a) No there is no certain number of texts when two plans cost the same

b) On plan A 1 text and on plan B 2 text

Answer:

$41.685        

Step-by-step explanation:

Given:-

- The material cost per square foot, C = $1.25

- The two boxes have the dimensions:

         Box 1 : ( 9 x 9 x 10 ) in

         Box 2: ( 11 x 7 x 10 ) in

Find:-

so how much does a company save by choosing to make 50 of Box 2 instead of Box 1?

Solution:-

- We will first determine the surface areas of the two boxes Box 1 ( A1 ) & Box 2 (A2).

               A1 : 2*( 9*9) + 4*( 9*10) = 522 in^2 = 43.5 ft^2

               A2 : 2*(11*7) + 2*(11*10) + 2*(7*10) = 514 in^2 = 42.833 ft^2

- Determine the cost for each box:

               Cost of box 1 = A1*C = 43.5*$1.25 = $54.375

               Cost of box 2 = A2*C = 42.833*$1.25 = $53.5413

- The amount saved by the company by choosing to make 50 Box 2 as compared to 50 Box 1:

               Amount saved = 50*(Cost of box 1 - Cost of box 2)

                                         = 50*( 54.375 - 53.5413 )

                                         = $41.685        

The measure of angle CBD in a regular pentagon with perimeter 60 cm is 108°. This conclusion assumes that CBD refers to an internal angle of the pentagon and is based on the formula for internal angles of a regular polygon.

The subject of the question is related to a regular pentagon which is a polygon with 5 equal sides and equal angles. If the perimeter of the regular pentagon is 60 cm, it means each side measures 60/5 = 12 cm.

The question is asking for the measure of angle CBD. In a regular pentagon, angles are not directly named but it's likely referring to an internal angle of the pentagon. Based on this assumption, we can calculate the measure of an internal angle of a regular polygon using the formula: (n-2) x 180° / n where 'n' is the number of sides. Substituting '5' in place of 'n' because a pentagon has 5 sides, we get (5-2) x 180° / 5, which results in 108°. Therefore, if CBD is an internal angle then it measures 108 degrees.

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Answer: 75

Step-by-step explanation:

Step-by-step explanation:

In order to cover his backyard with sod, he needs to cover the area of the backyard.

His backyard is a rectangle, and area of a rectangle represented by A is given as l*w

Where,

is the length, and

is the width

So, the area of Jim's backyard is square yards.

l*w=12/5/6*10/2/5=2002/15 or 133.466

The area of each sods are solved using the area of the rectangle formula.

l*w=1/1/3*1/1/3=16/9

To find HOW MANY of these sods we would need to cover the whole backyard, we divide the backyard area by each sod area:

=2002/15 divided by 16 /9=3003/40or 75.075

Since, fractional sods can't be bought, Jim has to buy 75 sods approximately .