A rectangular prism is 25 inches wide, 5 inches long and 6 inches high.
What is the exact volume of the prism?
125

The speed of the Elvira is 6.545 miles per hour. Then the speed of the Altheia will be 0.545 miles per hour.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

Let the speed of the Elvira be x. Then the speed of the Altheia will be (x - 6).

Let the distance between the coffee shop and Elvira's house be d.

Then the distance between the coffee shop and Altheia's house will be (3.6 - d).

Then we have

x = d / 0.5 ...1

(x - 6) = (3.6 - d) / 0.6 ...2

In solving the equations 1 and 2, we have

x = 6.545 and d = 3.2725 miles

Then the speed of the Elvira is 6.545 miles per hour. Then the speed of the Altheia will be 0.545 miles per hour.

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Answer:

If the cost of 3 notebooks is 30.30, we can infer the cost of one notebook is 10.10.

Step-by-step explanation:

[tex]10.10 * 15 = x[/tex]

[tex]10.10 * 15 = 151.5[/tex]

Hi student, let me help you out! :)

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We are asked to find the cost of 15 notebooks, given that the cost of 3 notebooks is 30.30.

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

So we divide the cost of three notebooks (30.30) by 3:

[tex]\star~\large\pmb{30.30\div3}[/tex]

[tex]\star~\large\pmb{10.10}[/tex]

That's the cost of 1 notebook. Now, multiply that times 15 (we're asked to find the cost of 15 notebooks).

[tex]\star~\large\pmb{10.10\times15}[/tex]

This gives us:

[tex]\star~\large\pmb{151.5}[/tex]

That's the cost of 15 notebooks if the cost of one notebook is 10.10.

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The shaded area expressed as a fraction, a decimal, and a percent of the whole is 23/100, 0.23 and 23% respectively

From the question, we are to express the shaded area as a fraction, a decimal, and a percent of the whole.

In the diagram, there are 100 total squares and 23 of them are shaded

Expressing the shaded area as a fraction, we get

[tex]\frac{23}{100}[/tex]

Expressing the shaded area as a decimal, we get

[tex]\frac{23}{100}[/tex] = 0.23

Expressing the shaded area as a percent , we get

[tex]\frac{23}{100}\times 100\%[/tex] = 23%

Hence, the shaded area as a fraction, a decimal, and a percent of the whole is 23/100, 0.23 and 23% respectively

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The triangle △ABC and △DEC are similar to each other. Then the correct option is A, B, and D.

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

Right triangle ABC is reflected over AC.

Then dilated by a scale factor of Two-thirds to form triangle DEC.

The triangle △ABC and △DEC are similar to each other.

△ABC ≅ △DEC

The dilation is 2/3. Then we have

DE / AB = 2 / 3

     3AB = 2DE

∠B ≅ ∠E = 90

There is no effect of dilation on angle.

Then the correct option is A, B, and D.

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Answer:

A. △ABC ~ △DEC

B. ∠B ≅ ∠E

D. 3DE = 2AB

Step-by-step explanation:

got it right on edge 23

[tex]\huge\boxed{Formula: r= \frac{d}{2}}[/tex]

Substitute the values according to the formula.

[tex]r=\frac{94}{2}[/tex]

[tex]\large\boxed{r=47 \: cm}[/tex]

Now, let's find the area.

[tex]\huge\boxed{Formula:a= \pi{r}^{2}}[/tex]

So, we'll have to multiply π, 47 and 47.

Substitute the values according to the formula.

[tex]a= \pi{47}^{2}[/tex]

[tex]a= 6939.778172 \: {cm}^{2}[/tex]

[tex]\large\boxed{a= 6939.8 \: {cm}^{2}(1 \: d.p)}[/tex]

Hence, the area of the given circle is 6939.8 square centimeters.

Hi student, let me help you out! :)

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We are asked to find the radius & area of the circle.

To find the [tex]\star\bf{radius}\star[/tex], we divide the diameter by 2:

[tex]\star~\bf{94\div2}[/tex]

[tex]\star~\bf{Radius=47}\star[/tex]

Now that we have the radius, let's compute the area! :)

///\\\///\\\///\\\///\\\///\\\////\\\///\\///\\\///\\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\//\\\//\\

                            Calculating the Area

We can work out the area of a circle by using this formula:

[tex]\star\boxed{\pmb{A_{(circle)}=\pi r^2}}\star[/tex]

Where

[tex]\dag[/tex] A=Area of a circle

[tex]\dag[/tex] [tex]\pi =3.14...[/tex]

[tex]\dag[/tex] r=radius

Have you noticed the [tex]\large\pmb{^2}[/tex] next to r? This tells us that we should multiply the radius times itself.

Now it's time to substitute the values:

[tex]\star~\large\pmb{A=3.14\times47^{2}}\star[/tex]

Let's simplify it. The acronym PEMDAS will help us, and we won't make any mistakes in the Order of Operations! :)

Here's what it stands for:

P=Parentheses

E=Exponents

M=Multiplication

D=Division

A=Addition

S=Subtraction

2 is an exponent.

So what do you think we should do first?

[tex]\square[/tex] Square 47.

[tex]\square[/tex] Multiply 3.14 times 47 and then square.

That's right, we should square 47 first. :)

[tex]\star~\large\pmb{A=\pi \times2209}}\star[/tex]

Now, according to PEMDAS, we should multiply pi times 2209; after multiplying, we obtain:

[tex]\star~\large\pmb{A=6936.8\:cm^2}\star[/tex]

Remember, the area of any shape is measured in units squared.

[tex]\ddot\bigstar[/tex] Remember this...

[tex]\fbox{\bf{The\;area\;of\;any\;shape\;is\;measured\;in\;units\;squared}}[/tex]

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[tex]\bigstar\footnotesize\pmb{M^ar_ib^el\;Peri}[/tex]

Answer:

50

Step-by-step explanation:

Answer:

y= -6

Step-by-step explanation:

-4x and 4x are canceled out. -2y+8y= 6y. -12-24=-36

You are left with 6y=-36 . Divide from both sides and -36/6 is -6. So, y=-6.

Hope this helped.

The shape of the resulting cross-section will be equal to the trapezoid.

A trapezoid is a quadrilateral having four sides whose two sides are parallel to each other and the other two sides are nonparallel to each other.

As it is given in the question the figure is sliced through points J. K. and When the shape is sliced from the given points it will create the trapezoidal shape that will have two parallel sides and the other two sides are Non-parallel

Therefore the shape of the resulting cross-section will be equal to the trapezoid.

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Answer:

Trapezoid

Step-by-step explanation:

I got it right on Edmentum

Hook me up with a 5 star and a thanks :)

Answer:

175 ft^2

Step-by-step explanation:

split the pentagon into 5 triangles with base length 10ft and height 7ft. each triangle then has an area of 10 * 7 * 1/2 = 35 ft^2

then the pentagon has an area 35*5 = 175 ft^2

The u-x and o-x from the given parameters of the population and the sample size will be u =28 and standard deviation is 5.

From the information given about the population and sample mean, the values include:

u=27 o=5 n=14

The standard deviation will be:

= 5/✓14

= 5/3.74

= 1.34

Therefore, u-x and o-x from the given parameters of the population and the sample size will be u =28 and standard deviation is 1.34.

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Answer:

it is 18

Step-by-step explanation:

Answer:

area = 62ft

Step-by-step explanation

so you section the polygon into a big rectangle and 2 small rectangles

the area of the small rectangle will be 2ft x 3ft which will be 6 ft, and as there are 2 of them the area of it will be 12ft

the area of the big rectangle will be 10ft x 5ft, as 8ft - 3ft is 5ft so 5x10=50ft

now add the areas you got, 50+12 which is 62ft

hope this helps:)

Answer:

C.) The variable x represents the independent variable

Step-by-step explanation:

The variable "x" is the independent variable because that is the value that we can manipulate. We cannot manipulate the dependent variable because it is determined by the independent variable. In that case, "y" would be the dependent variable because its value is dependent on what "x" is.

A.) is incorrect because g(x) symbolizes the input of the variable "x" into the g function.

B.) is incorrect because "x" is the input.

D.) is incorrect because "x" is the input.

Answer:

w = 5

Step-by-step explanation:

24w = (14)10

2w + 4 = 10 + 4

2w = 10

w = 5

Two numbers multiply the value on top (-84) and add to the value on the bottom (17) is 21 and -4.

Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. Multiplication essentially means the repeated addition.

The two given numbers are -84 and 17.

We need to write two numbers that multiply to the value on top (-84) and add to the value on the bottom (17).

If we multiply 21 and -4, we get the product as -84.

That is, 21×(-4)=-84

If we add 21 and -4, we get the sum as -17.

That is, 21+(-4)=21-4=17

Therefore, two numbers multiply the value on top (-84) and add to the value on the bottom (17) is 21 and -4.

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The expression that is equivalent to the complex number 10 + 3i is (4+7i)-2i(2+3i)

Complex numbers are square root of negative numbers. They are expressed as a + bi

Using the expression

(4+7i)-2i(2+3i)

Expand

4 + 7i - 4i -2i(3i)

4 + 3i - 2(-3)

4 + 6 + 3i

10 + 3i

Hence the expression that is equivalent to the complex number 10 + 3i is (4+7i)-2i(2+3i)

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Answer:

51 pounds, 48 pounds, 44 pounds and 40 pounds in that chronological order.

The slope and y-intercept of the equation are - 3 / 2 and 7 respectively.

The slope and y-intercept of an equation can be easily found using slope intercept equation.

y = mx + b

where

Therefore,

3x + 2y = 14

2y = -3x + 14

y = -3 / 2 x + 7

Therefore,

slope = - 3 / 2

y-intercept = 7

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A function assigns the values. The function will move down by 3 units.

A function assigns the value of each element of one set to the other specific element of another set.

The graph of the function is given below. Now if 3 is replaced by a 0, then the y-intercept of the function will become zero while keeping the slope the same. Therefore, the function will move down by 3 units.

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If the definitions of type I and type II regions is the same as in the link provided, then as a type I region the integration domain is the set

[tex]R_{\rm I} = \left\{(x,y) \mid 0 \le x \le 3 \text{ and } \sqrt{x+1} \le y \le 2\right\}[/tex]

and as a type II region,

[tex]R_{\rm II} = \left\{(x,y) \mid 0 \le x \le y^2-1 \text{ and } 1 \le y \le 2\right\}[/tex]

where we solve y = √(x + 1) for x to get x as a function of y.

A. The area of the type I region is

[tex]\displaystyle \iint_{R_{\rm I}} dA = \int_0^3 \int_{\sqrt{x+1}}^2 dy \, dx = \int_0^3 (2 - \sqrt{x+1}) \, dx = \boxed{\frac43}[/tex]

B. The area of the type II region is of course also

[tex]\displaystyle \iint_{R_{\rm II}} dA = \int_1^2 \int_0^{y^2-1} dx \, dy = \int_1^2 (y^2-1) \, dy = \boxed{\frac43}[/tex]

I've attached a plot of the type II region to give an idea of how it was determined. The black arrows indicate the domain of x as it varies from the line x = 0 (y-axis) to the curve y = √(x + 1).

Answer:I think it would be 84 + 0.45m + 108.

Which simplified could be 0.45m + 192.

hope this helps!

Step-by-step explanation:

Answer:

131

Step-by-step explanation:

Answer:

D) 9

Step-by-step explanation:

x = ½ × 13 = 6.5

y = ½ × 5 = 2.5

6.5 + 2.5 = 9

So the length of PC is 9

HOPE THIS HELPS AND HAVE A NICE DAY <3

(1) The missing term in the sequence, a₁₂  = 0.8.

(2) The missing term in the sequence, a₈ = 102.5.

(3) The missing term in the sequence, a₈ = 111.

(4) The missing term in the sequence, a₁₂ = -19.

(5) The missing term in the sequence, a₁₂ = 94.

(6)  The missing term in the sequence, a₆ = 40.

(7)  The missing term in the sequence, a₃₆ = -52.

(8)  The missing term in the sequence, a₂₁ = -58.

The missing term in the sequence is determined as follows;

Tₙ = a + (n - 1)d

T₄ = a + 3d

18.4 = a + 3d  ---(1)

T₅ = a + 4d

16.2 = a + 4d  ---(2)

subtract (1) from (2)

-2.2 = d

18.4 = a + 3(-2.2)

a = 25

a₁₂  = a + 11d

a₁₂  = 25 + 11(-2.2)

a₁₂  = 0.8

a₂ = a + d

57.5 = a + d -- (1)

a₅ = a + 4d

80 = a + 4d  --- (2)

solve (1) and (2)

d = 7.5

a = 50

a₈ =  a + 7d

a₈ = 50 + 7(7.5)

a₈ = 102.5

a₁₀ = a + 9d

141 = a + 9d --- (1)

a₁₃ = a + 12d

186 = a + 12d --- (2)

Subtract (1) from (2)

d = 15

a = 6

a₈ = a + 7d

a₈ = 6 + 7(15)

a₈ = 111

a₂₂ = a + 21d

-49 = a + 21d ---- (1)

a₂₅ = a + 24d

-58 = a + 24d --- (2)

subtract (1) from (2)

d = -3

a = 14

a₁₂ = a + 11d

a₁₂ = 14 + 11(-3)

a₁₂ = -19

a₄ = a + 3d

-2 = a + 3d --- (1)

a₈ = a + 7d

46 = a + 7d ---- (2)

Subtract (1) from (2)

d = 12

a = -38

a₁₂ = a + 11d

a₁₂ = -38 + 11(12)

a₁₂ = 94

a₉ = a + 8d

64 = a + 8d --- (1)

a₁₂ = a + 11d

88 = a + 11d --- (2)

Subtract (1) from (2)

d = 8

a = 0

a₆ = a + 5d

a₆ = 0 + 5(8)

a₆ = 40

a₂₀ = a + 19d

-4 = a + 19d ---- (1)

a₂₃ = a + 22d

-13 = a + 22d --- (2)

Subtract (1) from (2)

d = -3

a = 53

a₃₆ = a + 35d

a₃₆ = 53 + 35(-3)

a₃₆ = -52

a₂₈ = a + 27d

5 = a + 27d ---- (1)

a₃₃ = a + 32d

50 = a + 32d --- (2)

Subtract (1) from (2)

d = 9

a = -238

a₂₁ = a + 20d

a₂₁ = -238 + 20(9)

a₂₁ = -58

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Answer:

Step-by-step explanation:

[tex]\text {modulus of z } = =\sqrt{\left( -3\right)^{2} +\left( 1\right)^{2} } =\sqrt{9+1} =\sqrt{10}[/tex]

Answer:

square root of 10

Step-by-step explanation:

[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{\underline{y} varies inversely with \underline{x}}}{y=\cfrac{k}{x}}\qquad \textit{we also know that} \begin{cases} y=49\\ x=17 \end{cases} \\\\\\ 49=\cfrac{k}{17}\implies 833=k~\hfill \boxed{y=\cfrac{833}{x}} \\\\\\ \textit{when y = 7, what is "x"?}\qquad 7=\cfrac{833}{x}\implies x=\cfrac{833}{7}\implies x=119[/tex]

The triangles with the side lengths 10 ft, 24ft, 26 ft, is a right triangle while a triangle with side lengths of 7 yd, 5 yd, 9 yd is NOT based on the Pythagorean theorem.

A triangle is said to be a triangle based on the Pythagorean theorem, if the square of the longest side equals the sum of the squares of the other smaller sides of the triangle.

9² = 7² + 5²

81 = 74 (NOT TRUE), therefore, the triangle with the side lengths 7 yd, 5 yd, 9 yd, is not a right triangle.

26² = 10² + 24²

676 = 676 (TRUE), therefore, the triangle with the side lengths 10 ft, 24ft, 26 ft, is a right triangle.

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Answer:

6, 8, 10

Step-by-step explanation:

Where:

a = 6

b = 8

c = 10

Pythagorean theorem: [tex]a^2 + b^2 = c^2[/tex]

[tex]6^2 + 8^2 = c^2[/tex]

[tex]36 + 64 = c^2[/tex]

[tex]100 = c^2[/tex]

c = [tex]\sqrt{100}[/tex]

c = 10

Answer:

1120π grams

==> 3518.58 grams  using value of π = 3.14159 or

==> 3520 grams using value of π = 22/7

Step-by-step explanation:

Volume of a cylinder = πr²l where r is the radius of the base and h is the length of cylinder

The diameter of the cylinder, d = 8cm and radius = d/2 = 4cm

Length = 1 meter = 100 cm

Here, volume V = π.4².100 =  π x 16 x 100 = 1600π cm³

Since 1 cm³ has a mass of 0.7gm total mass
M = 0.7V = (0.7)1600π =1120π gm

Using the ratio 22/7 for pi we get
M =  1120 x 22/7  = 3520 g

If we use the more accurate value of π as 3.14159 then we get
M = 1120 x 3.14.159 = 3518.58 g which is more accurate