How is the volume of a prism calculated?
add the area of the base to the height
subtract the area of the base from the height
multiply the area of the base by the height
divide the area of the base by the height

Answer:

[tex]y=0.25x[/tex]

The graph in the attached figure

Step-by-step explanation:

we have

[tex](0,0),(8,2)[/tex]

Remember that

If the equation of the line passes through the origin

then

The equation of the line represent a direct variation

so

it can be expressed in the form [tex]y=kx[/tex]

The constant of proportionality k is equal to the slope m

step 1

Find the slope

[tex]m=(2-0)/(8-0)=0.25[/tex]

The equation of the line is equal to

[tex]y=0.25x[/tex]

The graph in the attached figure

Answer:

Option B

Step-by-step explanation:

Given  

Two Data sets

Class A :{ 2, 5, 7, 6, 4, 3, 8, 7, 4, 5, 7, 6, 3, 5, 4, 2, 4, 6, 3, 5}

Class B : {3, 7, 6, 4, 3, 2, 4, 5, 6, 7, 2, 2, 2, 3, 4, 5, 2, 2, 5, 6}

In order to check the options we will have to find the mean and median of both data sets.

So for Class A:

Mean= x =(Sum of values)/(Number of values)

=96/20

=4.8

For median the data has to be arranged in ascending order, so

2, 2,3,3,3,4,4,4,4,5,5,5,5,6,6,6,7,7,7,8

Median will be the average of middle two values as the number of items are odd.

Median=(5+5)/2

=10/2

=5

Range = 8-2 = 6

For Class B:

Mean= x =(Sum of values)/(Number of values)

=80/20

=4

For median, arranging the values

2,2,2,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7

Median=(4+4)/2

=8/2

=4

Range = 7-2 = 5

We get,

Mean of class A > Mean of Class B

Median of Class A > Median of Class B

Range of Class A > Range of Class B

We observe that only option B is correct for the given data sets..

Answer:

[tex](x +3)^2 + (y-4)^2 = 4[/tex]

Step-by-step explanation:

The general equation of a circle is

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

In this equation, 'r' represents the radius of the circle and (h,k) represents the central point of the circle.

Radius of the circle is half of the diameter = d/2

From figure, ther diameter of the circle is calculated using (y2-y1) or (x2-x1)

In this figure,

y2 = 6

y1 = 2

d = (y2 - y1) = 6-2 =4

This can also be verified using the values of x

x2 = -1

x1 = -5

d = (x2 - x1) = (-1 - -5) = (-1 + 5) = 4

Also,

r = d/2 = 4/2

r = 2

h represents the horizental distance and k represents the vertical distance of the center of the circle from the origan (0,0).

Therefore,

h = 0 - 3 = -3 as the center of circle is 3 units left to the origan

k = 0 + 4 = 4 as the center of circle is 4 units above to the origan

Therefore the equation of circle becomes

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

[tex](x-(-3))^2 + (y-(4))^2 = 2^2[/tex]

[tex](x +3)^2 + (y-4)^2 = 4[/tex]

Answer:

A

Step-by-step explanation:

?? That a tuff one.hope u find the answer soon

Answer:

Is this a question?

Step-by-step explanation:

You're correct, but this isn't a question...

Answer:

72 sq. inch.

Step-by-step explanation:

9 inches in feet is 9/12 = 0.75 feet.

We can set up a ratio to figure out the width of the scale drawing.

[tex]\frac{36}{0.75}=\frac{32}{x}[/tex]

This means "if 36 feet is 0.75 feet in drawing, how much (let that be x) is 32 feet?"

let's cross multiply and solve for x:

[tex]\frac{36}{0.75}=\frac{32}{x}\\36x=32*0.75\\36x=24\\x=\frac{24}{36}=\frac{2}{3}[/tex]

So width is 2/3 feet and length is 0.75 feet.

Converting back to inches (since we need the area in sq. inches):

2/3 feet = 2/3 * 12 = 8 inches, and

0.75 feet = 0.75 * 12 = 9 inches

Hence, area is 8 * 9 = 72 sq. inches.

Answer:

1 and 1/4

Step-by-step explanation:

3/4 + 1/2 = 3/4 + 2/4 = 5/4 = 1 1/4

Answer:

[tex]1\frac{1}{4}[/tex]

Step-by-step explanation:

In order to calculate this you just have to add up both of the values that you are given, and to do that, you first have to convert the the values into the same denominator:

[tex]\frac{1}{2} +\frac{3}{4} =\frac{2}{4}+\frac{3}{4}  =\frac{2+3}{4} =\frac{5}{4} =1\frac{1}{4}[/tex]

So the value of the addition of both would be: [tex]1\frac{1}{4}[/tex]

Answer:

[tex]2^{2} \times a \times b^{2}=4ab^{2}[/tex]

Step-by-step explanation:

Greatest common factor of two or more terms is the largest(greatest) possible term which exactly divides all the given term. For example the greatest common factor of 20 and 30 is 10 as 10 is the largest possible number that can exactly divide 20 and 30 without leaving any remainder. GCF is found as the product of all the common factors

Given terms are:

[tex]8a^{3} b^{2} =2^{3}\times a^{3}\times b^{2}[/tex]

[tex]12ab^{4}=4 \times 3 ab^{4} =2^{2} \times 3 \times a \times b^{4}[/tex]

From the above factors we can see that the common factors are:

[tex]2^{2} , a , b^{2}[/tex]

Therefore, the greatest common factor will be:

[tex]GCF=2^{2} \times a \times b^{2}=4ab^{2}[/tex]

The greatest common factor of 8a³b² and 12ab⁴ is 4ab², found by identifying the smallest powers of the common factors in each term.

To find the greatest common factor (GCF) of the given terms, we need to identify the highest power of each variable that appears in both terms.

The prime factorization of 8 is [tex]\(2^3\)[/tex], and the prime factorization of 12 is [tex]\(2^2 \times 3\)[/tex]. Thus, the greatest common factor of the coefficients is [tex]2^2 = 4.[/tex]

For the variables a and b:

- [tex]\(a^3\)[/tex] appears in the first term.

- a appears in the second term.

- [tex]\(b^2\)[/tex] appears in both terms.

So, the greatest common factor of [tex]\(a^3 b^2\) and \(ab^4\) is \(ab^2\).[/tex]

Therefore, the greatest common factor of [tex]\(8a^3 b^2\) and \(12ab^4\) is \(4ab^2\).[/tex]

Answer:

log 13 = 1.1139

Step-by-step explanation:

log 13 = 1.1139

Answer:

log 13 = 1.1

Step-by-step explanation:

Given  : log 13.

To find : What is the value round your answer to the nearest tenth.

Solution : We have given log 13.

log 13 = 1.113.

Nearest tenth = 1.1

Therefore, log 13 = 1.1

To find the missing value in the equation, we add -4.5 and 4.4 first, then solve for the missing value.

To find the missing value, we need to solve the equation. Start by adding -4.5 and 4.4. (-4.5 + 4.4 = -0.1)

Now we have: -0.1 + ___ = 0

To solve for the missing value, subtract -0.1 from both sides of the equation: ____ = 0 + 0.1 = 0.1

The missing value is 0.1.

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Final answer:

The missing value is 0.1.

Explanation:

This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 4.90, b = -14.3, and c = -20.0.

To solve for the missing value, we can rearrange the equation:

-4.5 + 4.4 + ____ = 0

Simplifying the equation, we get:

-4.5 + 4.4 + ____ = 0

-0.1 + ____ = 0

By adding 0.1 to both sides of the equation, we can isolate the missing value:

____ = 0.1

Therefore, the missing value is 0.1.

The area of the yellow sector is 15/8 π in² in pi form.

Quartiles are 3 points such that they create four groups in the data. For the following set of data, the value of the lower quartile is 78.

When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.

Quartiles are then selected as 3 points such that they create four groups in the data, each group approximately possessing 25% of the data.

Left to right is said in the assumption that data were arranged increasingly from left to right.

The given data set has 9 points, therefore, the first quartile will have the average value of the 2nd and the 3rd number when arranged in increasing order. Therefore, the value of the first quartile will be,

First quartile = (75+81)/2 = 78

Hence, For the following set of data, the value of the lower quartile is 78.

Learn more about Quartiles:

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First, let's look at the formulas for the area of square and area of the rectangle.

[tex]A_{square}=a^2[/tex]

[tex]A_{rectangle}=a\cdot b[/tex]

And what this exercise states is that the areas are the same. So:

[tex]A_{square}=A_{rectangle}\Longrightarrow a^2=a\cdot b[/tex]

Now put in the data.

[tex]a^2=2\cdot8[/tex]

Solve for [tex]a[/tex]:

[tex]a=\sqrt{2\cdot8}=\sqrt{16}=\boxed{4}[/tex]

The side of the square garden plot is 4 meters.

Hope this helps.

r3t40

Answer:

3.5 feet / per minute

Step-by-step explanation:

3 1/2 feet / minute = 3.5 feet / minute

hope this helps :)

Answer:

96

Step-by-step explanation:

for every 3 cars there is 2 trucks

If you have 144 cars then we divide 144 by 3 to get 48

That is not the answer though because that would be a 3/1 ratio

We then multiply 48 by 2 to get 96

To find the number of trucks at the dealership, we interpret the ratio 3:2, meaning that for every 3 cars, there are 2 trucks. We figure out that '1' in the ratio is equivalent to 48 vehicles. So, we multiply the trucks component of the ratio (2) by this value to get 96 trucks.

To solve this problem, you must interpret the ratio of cars to trucks as 3:2. This means for every 3 cars, there are 2 trucks. We need to use this ratio to find out how many trucks there are if there are 144 cars.

The first step is to figure out what proportion 144 cars represents within the ratio. To find this, we can divide the number of cars by the cars component of the ratio (3) which gives us: 144 ÷ 3 = 48.

Now we know that '1' in our ratio represents 48 vehicles. So to find out how many trucks, we multiply the trucks component of the ratio (2) by this value, which gives us: 48 x 2 = 96 trucks.

Therefore, if there are 144 cars at the dealership, there are 96 trucks.

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Answer:

never

Step-by-step explanation:

The given path equation describes a path that starts at h(0) = 5, decreases to h(2) = -7, then increases without bound.

Assuming the projectile stops moving when h(x) = 0, it starts at its maximum height at ...

x = 0

Answer:

Step-by-step explanation:

f,d,e

Answer:

F, C, B

Step-by-step explanation:

Just look at where the two graphs intersect and then correspond that point with the color and letter.

Answer:

8, substitute 12 into the equation and then subtract it from 12

Step-by-step explanation:

D. 83 deggrees I think hopeful

Answer: D

Step-by-step explanation:

That angle is smaller than a “right angle”. A “right angle” is 90 degrees. Therefore, the missing angle measure is less than 90 degrees.

Answer:

2x³ + x² - 14x - 7

Step-by-step explanation:

The product of f(x) and g(x) is

(2x + 1)(x² - 7)

Each term in the second factor is multiplied by each term in the first factor

2x(x² - 7) + 1 (x² - 7) ← distribute both parenthesis

= 2x³ - 14x + x² - 7

= 2x³ + x² - 14x - 7 ← in standard form

Answer: Third Option

[tex]P (M\ or\ N) = 0.8[/tex]

Step-by-step explanation:

In this case, we have two non-disjoint events.

 So the probability of M or N occurring is

[tex]P (M\ or\ N) = P(M) + P(N) - P (M\ and\ N)[/tex]

We know that in this problem

[tex]P(M) = 0.7\\\\P(N) = 0.5[/tex]

[tex]P(M\ and\ N) = 0.4[/tex]

So

[tex]P (M\ or\ N) = 0.7 + 0.5 - 0.4[/tex]

[tex]P (M\ or\ N) = 0.8[/tex]

The answer is the third option

Answer:

[tex]\large\boxed{\cot\theta(\tan\theta+\cot\theta)=1+\cot^2\theta=\dfrac{1}{\sin^2\theta}=\csc^2\theta}[/tex]

Step-by-step explanation:

[tex]\text{Use}\\\\\text{distributive property:}\ a(b+c)=ab+ac\\\cot\alpha\tan\alpha=1.\\\\======================\\\\\cot\theta(\tan\theta+\cot\theta)=(\cot\theta)(\tan\theta)+(\cot\theta)(\cot\theta)\\\\=1+\cot^2\theta\\\\\text{If you want next transformation, then use:}\\\\\cot\alpha=\dfrac{\cos\alpha}{\sin\alpha}\\\\\sin^2\alpha+\cos^2\alpha=1\\\\=======================[/tex]

[tex]=1+\left(\dfrac{\cos\theta}{\sin\theta}\right)^2=1+\dfrac{\cos^2\theta}{\sin^2\theta}=\dfrac{\sin^2\theta}{\sin^2\theta}+\dfrac{\cos^2\theta}{\sin^2\theta}=\dfrac{\sin^2\theta+\cos^2\theta}{\sin^2\theta}\\\\=\dfrac{1}{\sin^2\theta}\\\\\text{If you want next transformation, then use:}\\\\\csc\alpha=\dfrac{1}{\sin\alpha}\\\\=\left(\dfrac{1}{\sin\theta}\right)^2=(\csc\theta)^2=\csc^2\theta[/tex]

Answer:

B

Step-by-step explanation:

7 serving multiplied by 2 is equal to 14

Answer:

the answer is prob B i am i on usatest prep and it is correct

Step-by-step explanation:

Answer: 75 students

Step-by-step explanation:

15% of 500= 75

Answer:

10y + 2

Step-by-step explanation:

The formula for the perimeter of a rectangle or square is [length + length + width + width = perimeter  or  2(length) + 2(width) = perimeter]

Our length here is y + 2. Either formula you use, [(y+2) + (y+2) or 2(y+2)] you should get the answer 2y + 4.

Next our width. The width is 4y-1. Either formula you use, [(4y-1) + (4y-1) or 2(4y-1)] you should get 8y - 2.

Then, simply add (2y+4) and (8y-2) to get 10y + 2. So, the perimeter of the garden is 10y + 2.

I hope this helps!

Answer:

Estimated cost; $9

Exact amount; $9.69

Step-by-step explanation:

We are told that ​Annie bought 3/4 kg of cocoa powder, which cost $12.92 per kg.

a.

We are required to estimate the cost of the 3/4 kg of cocoa powder given that 1 kg costs 12.92

We can round down the cost of a kg to obtain $12 per kg. Therefore, 3/4 of a kg will cost approximately;

(3/4) of 12

= (3/4)*12 = $9

Thus the estimated cost is $9

b.

We are required to determine the the exact amount she had to pay for the 3/4 kg of cocoa powder;

1 kg cost 12.92

3/4 of a kg will cost;

(3/4) of 12.92

= (3/4) * 12.92

Using a calculator we have;

9.69

Therefore, the exact amount paid was $9.69

Answer:

Part a) The estimate cost is about $9

Part b) The exact cost is $9.69

Step-by-step explanation:

we know that

Annie bought 3/4 kg of cocoa powder, which cost $12.92 per kg

Part a

To find the estimate cost round the numbers and multiply

we have

[tex]\$12.92=\$12[/tex] -----> round down

so

[tex]\frac{3}{4}(12)=\$9[/tex]

Part b

To find the exact amount she had to pay, multiply 3/4 by $12.92

so

[tex]\frac{3}{4}(12.92)=\$9.69[/tex] ----> exact value

Answer: 630 apples in the delivery

Step-by-step explanation: There are 15 pieces of fruit. 15 is the only number by 3 to get a even 5. So their are 5 oranges in each bag and 10 apples(because they are doubled) now there are 10 apples in each bag and 63 bags. You multiply 63x10=630

Therefore 630 is your answer

Answer:

A) 0.38

Step-by-step explanation:

By SOH CAH TOA, the sine of an angle is its opposite side divided by the hypotenuse.

The opposite of ∠C is 5, and the hypotenuse is 13.

So, sin(C) = 5/13 ≈ 0.38.

For this case we have to define trigonometric relations of rectangular triangles that the sine of an angle is given by the leg opposite the angle on the hypotenuse of the triangle. That is to say:

[tex]Sin (C) = \frac {5} {13}\\Sin (C) = 0.38[/tex]

Answer:

Option A

Answer:

Small box weighs 13.75 kg & large box weighs 15.75 kg

Step-by-step explanation:

We can write 2 simultaneous equation and solve for weight of each box.

Let weight of large box be l and small box be s.

"3 large boxes and  5 small boxes has a total weight of  116 kilograms":

[tex]3l+5s=116[/tex]

and

"9 large boxes and  7 small boxes has a total weight of  238 kilograms":

[tex]9l+7s=238[/tex]

Now we can solve for l in the 1st equation and put it into 2nd equation and get s:

[tex]3l+5s=116\\3l=116-5s\\l=\frac{116-5s}{3}[/tex]

now,

[tex]9l+7s=238\\9(\frac{116-5s}{3})+7s=238\\3(116-5s)+7s=238\\348-15s+7s=238\\348-238=15s-7s\\110=8s\\s=\frac{110}{8}=13.75[/tex]

now we plug in 13.75 into s into equation of l to find s:

[tex]l=\frac{116-5s}{3}\\l=\frac{116-5(13.75)}{3}\\l=15.75[/tex]

ANSWER

60 buttons.

EXPLANATION

Let the number of buttons in the container be x.

Then the number of buttons that are black are:

[tex] \frac{7}{10} x[/tex]

The number of buttons that are white

[tex] \frac{3}{10} x[/tex]

The difference between the white and the black buttons

[tex] \frac{4x}{10} = 24[/tex]

Solve for x.

[tex]4x = 240[/tex]

[tex]x = \frac{240}{4} [/tex]

[tex]x = 60[/tex]

Hence there are 60 buttons in the container.