Match the shape with the correct formula for finding the area. 1. Rectangular Prism rl + r2 2. Triangular Prism 2B + Ph 3. Pyramid 2rh +2r2 4. Cylinder 2ll + l2 5. Cone 2lw + 2lh + 2wh

The surface area of the pyramid is 156 square inches. It is found by computing the area of the base, then adding it with the product of half of the base perimeter and the slant height.

The problem involves finding the surface area of a pyramid with a square base. The surface area of a pyramid is given by the formula Base area + 1/2 * Perimeter of the base * Slant height.

First, let's compute the area of the base, the base is a square with sides of 6 inches. This gives us 6 * 6 = 36 square inches.

Secondly, the perimeter of a square is simply the length of one side multiplied by 4, which gives us 6*4 = 24 inches. Then multiply this by the slant height, which is 10 inches, then by 1/2, we have 0.5 * 24 * 10 = 120 square inches.

Finally, adding the base area and the latter computation gives: 36 + 120 = 156 square inches. Therefore, the surface area of the wooden pyramid puzzle is 156 square inches.

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The surface area of the wooden pyramid puzzle with a base side length of 6 inches and a slant height of 10 inches is 156 square inches.

To find the surface area of the wooden pyramid puzzle, we need to calculate the area of each face and then sum them up. The base of the pyramid is a square with side lengths of 6 inches, so the area of the base is 6 inches multiplied by 6 inches, which gives us 36 square inches. The four triangular faces have the same area since the pyramid is symmetrical, so we just need to calculate the area of one triangular face.

The height of the pyramid is given as 10 inches, and since it is a right triangle, we can use the formula for the area of a triangle: (base x height) / 2.

The base of the triangle is the length of one side of the square base, which is 6 inches. Therefore, the area of one triangular face is (6 inches x 10 inches) / 2 = 30 square inches.

Since there are four triangular faces, the total area for all the triangular faces is 4 x 30 square inches = 120 square inches. Finally, we can sum up the areas of the base and the triangular faces to find the surface area: 36 square inches + 120 square inches = 156 square inches.

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The answer is:

[tex]Area_{circle}=\pi *radius^{2}[/tex]

or

[tex]Area_{circle}=\pi *(\frac{diameter}{2})^{2}[/tex]

We can calculate the area of any circle using the following formula:

[tex]Area_{circle}=\pi *radius^{2}[/tex]

Where,

π, is a constant used to calculate the area of the circle.

radius, is the distance from the center to any point of the circle.

Also, we have that:

[tex]radius=\frac{diameter}{2}[/tex]

So, we can rewrite the equation by the following way:

[tex]Area_{circle}=\pi *(\frac{diameter}{2})^{2}[/tex]

Have a nice day!

Answer:

Use formula:

[tex]Area of circle = \pi (radius)^2 =\pi (r)^2[/tex]

Step-by-step explanation:

We need to find about how to calculate the area of a circle.

And match with the given choices. Where given choices are:

Area of a circle is equal to the diameterdiameter

squaredradiusradius squared times diameterheightpiwidth.

I'm not sure what exactly you have typed as choices are not written in proper way.

But I can still answer that.

You just need to apply formula of the area of circle which is given by:

[tex]Area of circle = \pi (radius)^2 =\pi (r)^2[/tex]

Answer:

the answer is B.  145 sq. ft.

Step-by-step explanation:

find the area of the first 2 triangles

A = 1/2 bh

A = 1/2 ba

a = 1/2 (11 ft.) (5 ft)

a =  27.5 sq ft.

A = 1/2 cb

a = 1/2 (5 ft) (7 ft)

a = 17.5 sq. ft

find the area of the rectangle

A = lw

a = (11 ft.)(5 ft.)

a = 55 sq. ft

Then add all together

2(27.5 sq.ft) + 2(17.5 sq. ft) + 55 sq.ft. = 145 sq. ft.

Answer:

Step-by-step explanation:

Same side interior angles

Answer:

Step-by-step explanation:

Observe in the image that [tex]\angle 1[/tex] and [tex]\angle 2[/tex] are inside the inclined pair of lines, that position is called interior angles, also notice that they are at the same side of the horizontal line.

Therefore, the correct description of that pair of angles is "same-side interior angles", because they are inside the pair of lines, and at the same side of the horizontal line.

Answer:

x=36

Step-by-step explanation:

The angle right under 3x is 2x, because alternate exterior angles between parallel lines are equal. Those two angles add up to 180, because they are formed by a strait line intersecting with another straight line. This means that 5x = 180 or x=36.

Answer:

6840

Step-by-step explanation:

Here, the order matters (1st, 2nd, and 3rd), so we need to use permutations.

There are 20 people who can get in first place.  After that, there are 19 people who can get in second place.  Finally, there are 18 people who can get in third place.  So:

20 * 19 * 18 = 6840

Number of the  ways can they finish in first, second, and the third-place is 6840

The linear arrangement of the set of the orders or the linear arrangements of the numbers is called the permutation.

Here, the order matters (1st, 2nd, and 3rd), so we need to use permutations.

There are 20 people who can get in first place.  After that, there are 19 people who can get in second place.  Finally, there are 18 people who can get in third place.  So:

20 x  19  x  18 = 684

Therefore Number of the  ways can they finish in first, second, and the third-place is 6840

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Answer:

[tex]x=66[/tex]

Step-by-step explanation:

Since  MN and MP are tangent to circle O, they create 90° angles at the points of intersection.

We also know that this is a quadralateral, so the interior angles add up to 360.

We can make an equation with this information.

[tex]114+90+90+x=360[/tex]

[tex]294+x=360[/tex]

[tex]x=66[/tex]

By property of tangent, the value of x is Option(C) 66° .

The properties of tangent are as follows -

Given that point O is the center if the circle also given MN and MP are tangent to O.

Thus by the property of tangent, ∠OPM and ∠ONM is equal to 90° as both the tangents intersect at the points P and N .

Also from property, we know that -

⇒ ∠ONM + ∠OPM + 114° + x° = 360°

⇒  90° + 90° + 114° + x° = 360°

⇒ 294° + x° = 360°

∴  x = 360° - 294° = 66°

Therefore, by property of tangent, the value of x is Option(C) 66° .

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Answer:

The range of f(x) is {-2 , 16 , 34 , 52} ⇒ answer d

Step-by-step explanation:

* Lets talk about the domain and the range of a function

- The domain is the values of x (input)

- The range is the value of y of the corresponding x (output)

∵ f(x) = 3x + 4

∵ The domain is {-2 , 4 , 10 , 16}

- To find the corresponding range substitute the values of x in f(x)

∵ x = -2

- Substitute x by -2 in f(x)

∴ f(-2) = 3(-2) + 4 = -6 + 4 = -2

∵ x = 4

- Substitute x by 4 in f(x)

∴ f(4) = 3(4) + 4 = 12 + 4 = 16

∵ x = 10

- Substitute x by 10 in f(x)

∴ f(10) = 3(10) + 4 = 30 + 4 = 34

∵ x = 16

- Substitute x by 16 in f(x)

∴ f(16) = 3(16) + 4 = 52

∴ The range of f(x) is {-2 , 16 , 34 , 52}

ANSWER

[tex]P(A and B) = \frac{39}{200} [/tex]

EXPLANATION

If A and B are independent events, then,

P(A and B)=P(A)×P(B)

It was given that:

[tex]P(A) = \frac{3}{10} [/tex]

and

[tex]P(B) = \frac{13}{20} [/tex]

[tex]P(A \: and \: B) = \frac{3}{10} \times \frac{13}{20} [/tex]

[tex]P(A and B) = \frac{39}{200} [/tex]

the probability of events A and B occurring together, P(A and B), is 39/200 or, when simplified, 0.195.

The subject of the question is finding the probability of both independent events A and B occurring together, which is represented by P(A and B). To calculate this, you simply multiply the probability of event A by the probability of event B since they are independent. Given that P(A) = 3/10 and P(B) = 13/20, the calculation would be as follows:

Thus, the probability of events A and B occurring together, P(A and B), is 39/200 or, when simplified, 0.195.

Answer:

69

Step-by-step explanation:

To find the total sum of all the tests, you multiply 93 by 7 or 651. Multiplying 90 and 8, you get 720. So 720-651 is 69.

Answer:

100c + 34

Step-by-step explanation:

100c+4 that’s the answer

there are 80 buttons

7/10

3÷24=8 8×7=56 56+24=80

The total number of buttons in the container is 60. This was calculated by setting up an equation using the given proportion of black buttons and the difference between the number of black and white buttons.

Let the total number of buttons in the container be x. Given that 7/10 of the buttons are black, this means 7/10 of x, or (7/10)x, represent the number of black buttons. The remaining 3/10 of x are white buttons. The difference between the number of black and white buttons is 24, so we can set up the following equation:

(7/10)x - (3/10)x = 24.

Simplifying the equation by subtracting the fractions results in (4/10)x = 24.

We can then simplify this further by dividing both sides by the coefficient of x, which is (4/10), to find x.

x = 24 / (4/10) = 24 * (10/4) = 24 * (2.5) = 60.

So, there are 60 buttons in the container in total.

Answer:

600 cl

Hope this helps :)

Have a great day !

5INGH

Step-by-step explanation:

5 : 1

We know that there is 120 cl of orange squash so

( Water : orange squash )

5 : 1

? : 120

We are multiplying by 120 to get from 1 to 120 so we must multiply by 120 to get from 5 to ?.

So,

5 × 120 = 600

Answer:

600 cl

Step-by-step explanation:

1 unit of orange = 5 units of water

120 units of oranges = 120 x 5 = 600 units of water

600 units of water = 600 cl of water

Answer:

(-6,4)

Step-by-step explanation:

The equations are:

[tex]x^2+4y^2=100\\4y-x^2=-20[/tex]

Solving for x^2 of the 2nd equation and putting that in place of x^2 in the 2nd equation we have:

[tex]4y-x^2=-20\\x^2=4y+20\\-------\\x^2+4y^2=100\\4y+20+4y^2=100[/tex]

Now we can solve for y:

[tex]4y+20+4y^2=100\\4y^2+4y-80=0\\y^2+y-20=0\\(y+5)(y-4)=0\\y=4,-5[/tex]

So plugging in y = 4 into an equation and solving for x, we have:

[tex]x^2=4y+20\\x=+-\sqrt{4y+20} \\x=+-\sqrt{4(4)+20} \\x=+-\sqrt{36} \\x=6,-6[/tex]

So y = 4 corresponds to x = 6 & x = -6

The pairs would be

(6,4) & (-6,4)

we see that (-6,4) falls in the 2nd quadrant, thus this is the solution we are looking for.

The mean of the data is 4.5 and the median of the data is 5.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

To find the mean of the data, we add up all the values and divide by the total number of values:

2 + 7 + 5 + 4 + 3 + 3 + 5 + 5 + 6 + 5 = 45

There are 10 values, so:

mean = 45 / 10 = 4.5

Therefore, the mean of the data is 4.5.

To find the median of the data, we need to first put the values in order from smallest to largest:

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

There are 10 values, which is an even number, so we take the average of the two middle values:

median = (5 + 5) / 2 = 5

Therefore,  the mean of the data is 4.5 and the median of the data is 5.

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The answer is 14

0.4r-7=-.3r+2.8

Add 7 to both sides. -7+7=0 so it cancels on the left. 2.8+7=9.8.

0.4r=-.3r+9.8.

Add .3r to both sides. -.3r+3r=0 so it cancels on the right. 0.4r+.3r=0.7r.

0.7r=9.8

Divide 0.7 to both sides. 9.8 divided by 0.7 = 14

So r=14

Answer:

all work is pictured and shown

ANSWER

[tex]{( - 2)}^{ - 3} =- \frac{1}{ 8} [/tex]

EXPLANATION

We want to simplify;

[tex] {( - 2)}^{ - 3} [/tex]

Recall that,

[tex] {a}^{ - m} = \frac{1}{ {a}^{m} } [/tex]

[tex]{( - 2)}^{ - 3} = \frac{1}{{( - 2)}^{ 3}} [/tex]

We multiply out to get,

[tex]{( - 2)}^{ - 3} = \frac{1}{{- 2} \times - 2 \times - 2} [/tex]

[tex]{( - 2)}^{ - 3} = \frac{1}{ - 8} [/tex]

The correct choice is B.

Folder = 1.25$

Notebook = 4.5 $

Folder =x

Notebook = y

The cost of one folder if the prices did not change between the days, for this case, is $1.25

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

Given that:

To find:

Cost of one folder.

Assume that:

Then, from the given condition, we get:

Amount spent in buying 3 folders and 1 notebook = 3x + 1y dollars = $8.25

And, amount spent in buying 2 folders and 3 notebook = 2x + 3y dollars = $16

Thus, we get two equations as:

[tex]3x + 1y = 8.25\\2x + 3y = 16[/tex]

From the first equation, getting 'y' in terms  of 'x', we get:

[tex]y = 8.25 - 3x[/tex]

Substituting this in second equation, we get:
[tex]2x + 3(8.25 - 3x) = 16\\2x +24.75 -3x = 16\\(2-9)x = 16 - 24.75\\-7x = -8.75\\7x = 8.75\\x = 8.75/7 =1.25 \: \rm dollars[/tex]

As we have Cost of one folder = $x

Thus, the cost of one folder if the prices did not change between the days, for this case, is $1.25

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Answer:

7/8

Step-by-step explanation:

Answer:

7/8

Step-by-step explanation:

Answer:

The answer is B 48 cm squared.

Step-by-step:

First divide into smaller sections. Then you will do Length times height.

9 x 4 = 36

6 x 2 = 12

36 + 12 = 48

I would go for C ten college students are chosen to taste test a new cereal

Answer:

the answer is A

Step-by-step explanation:

a measure of center for a numerical data set summarizes all of its' values with a single number; man and median are measures of center

a measure of variation describes how the numerical data varies with a single number; interquartile range and mean absolute deviation are measures of variation

***so the mean of the data summarizes the number of cars each salesperson sold last week***

Answer:

Step-by-step explanation:

You would take the area of half of a circle plus the area of a rectangle.  You don't have measures there, but the formula would be

[tex]A=\frac{\pi r^{2} }{2}+(l*w)[/tex]

Since the difference between steps 1 and 2 is that 2x was subtracted from both sides, i'm pretty sure the answer is B, the Subtraction property of equality. Hope this helps you!

Answer:

B) Subtraction property of equality

Step-by-step explanation:

4x - 7 = 2x + 9

Subtract 2x from each side using the subtraction property  of equality

4x -2x  - 7 = 2x-2x + 9

2x -7 = 9

Answer:

y =1/27

Step-by-step explanation:

Howdy!

If P = (-3, y) lies on the graph of y=3^x, then, to find the value of 'y' we need to substitute the point P into the equation:

To solve this, remember that [tex]a^{-b} = \frac{1}{a^{b}}[/tex]

Then:

y = 3^x

y = 3^(-3)

y = 1/27

So P= (-3, 1/27)

The correct option is y =1/27

Answer:

The correct answer option is 1/27.

Step-by-step explanation:

We are given the following equation and we are to find the value of y when the point (-3, y) lies on the graph of the given equation:

[tex] y = 3 ^ { x } [/tex]

So we will substitute the given value of x from the point (-3, y) in the equation to get y:

[tex] y = 3 ^ { - 3 } [/tex]

[tex] y = \frac { 1 } { 2 7 } [/tex]

11 inches...............

there are 12 inches in 1 foot, so one inch is twelve times shorter.

Answer:

P = 83%

Step-by-step explanation:

In this problem we have the ages of all new employees hired during the last 10 years of normally distributed.

We know that the mean is [tex]\mu = 31[/tex] years and standard deviation is [tex]\sigma = 10[/tex] years

By definition we know that if we take a sample of size n of a population with normal distribution, then the sample will also have a normal distribution with a mean

[tex]\mu_m = \mu[/tex]

And with standard deviation

[tex]\sigma_m = \frac{\sigma}{\sqrt{n}}[/tex]

Then the average of the sample will be

[tex]\mu_m = 31\ years[/tex]

And the standard deviation of the sample will be

[tex]\sigma_m =\frac{10}{\sqrt{10}} = 3.1622[/tex]

Now we look for the probability that the mean of the sample is greater than or equal to 28.

This is

[tex]P ({\displaystyle{\overline {x}}}\geq 28)[/tex]

To find this probability we find the Z-score

[tex]Z = \frac{X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z = \frac{28 -31}{\frac{10}{\sqrt{10}}} = -0.95[/tex]

So

[tex]P({\displaystyle{\overline {x}}}\geq 28) = P(\frac{{\displaystyle {\overline {x}}}-\mu}{\frac{\sigma}{\sqrt{n}}}\geq\frac{28-31}{\frac{10}{\sqrt{10}}}) = P(Z\geq-0.95)[/tex]

We know that

[tex]P(Z\geq-0.95)=1-P(Z<-0.95)[/tex]

Looking in the normal table we have:

[tex]P(Z\geq-0.95)=1-0.1710\\\\P(Z\geq-0.95) = 0.829[/tex]

Finally P = 83%

Answer:

[tex]Area of circle = \pi (radius)^2 =\pi (r)^2[/tex]

Step-by-step explanation:

We need to find about how to calculate the area of a circle.

And match with the given choices. Where given choices are:

Area of a circle is equal to the diameterdiameter

squaredradiusradius squared times diameterheightpiwidth.

I'm not sure what exactly you have typed lol :)

But I can still answer that.

You just need to apply formula of the area of circle which is given by:

[tex]Area of circle = \pi (radius)^2 =\pi (r)^2[/tex]

Answer:

radius squared times pi

Step-by-step explanation:

edge

Answer:

The measure of angle b (angle dbc) is [tex]54\°[/tex]

The measure of angle c is [tex]59\°[/tex]

The measure of angle d is [tex]67\°[/tex]

Step-by-step explanation:

Let

x-----> measure of angle b (angle dbc)

y----> measure of angle c

z----> measure of angle d

Remember that

The sum of the internal angles of a triangle must be equal to 180 degrees

so

[tex]x+y+z=180\°[/tex] -----> equation A

[tex]x=y-5[/tex] -----> equation B

[tex]z=y+8[/tex] ----> equation C

Substitute equation B and equation C in equation A and solve for y

[tex](y-5)+y+(y+8)=180\°[/tex]

[tex]3y+3=180\°[/tex]

[tex]3y=177\°[/tex]

[tex]y=59\°[/tex]

Find the value of x

[tex]x=59\°-5\°=54\°[/tex]

Find the value of z

[tex]z=59\°+8\°=67\°[/tex]

The measures of each angle of the triangle are

The measure of angle b (angle dbc) is [tex]54\°[/tex]

The measure of angle c is [tex]59\°[/tex]

The measure of angle d is [tex]67\°[/tex]

Answer: 7 and 3

Step-by-step explanation: 7 + 3 = 10 and 7-3 = 4