Find the surface area of the rectangular prism.

Answer:

9 hours of work

Step-by-step explanation:

306/17 = 18 per hour

so 162/18 = 9

Answer:

9 hours

Step-by-step explanation:

We can make a proportion and solve

She makes $306 for 17 hours of work,and she makes $162 for x hours of work

306/17=162/x

Cross multiply

306*x=17*162

306x=2754

Now we need to solve for x, by getting x by itself. x is being multiplied by 306; to undo this, divide both sides by 306

306x/306=2754/306

x=9

So, she needs to work 9 hours to make $162

Answer:

As the property of tangent line of circle, the 2 right triangles ABC and ADC are congruent.

=> AB = AD or j = k

j = 25x^2 + 100x + 9

k = 21x^2 + 100x + 18

=> 25x^2 + 100x + 9 = 21x^2 + 100x + 18

=> 4x^2 = 9

=> x^2 = 9/4 = (3/2)^2

=> x = 3/2 ( -3/2 value is not valid)

Hope this helps!

:)

Here is the correct interpretation of the question with the help of the text editor tool.

Use a parameterization to find the flux [tex]\int\limits \int\limits_s \ F. \ n \ d \sigma[/tex] of F = z²i + xj - 2zk in the outward direction

(normal away from the x-axis) across the surface cut from the parabolic cylinder z = 16 -y²  by the planes x = 0 , x = 1, and z = 0 .

The flux is                  .

Answer:

[tex]-\frac{512}{3}[/tex]

Step-by-step explanation:

F(x,y,z) = (z² ,x , - 2z)

To find the flux across a surface : [tex]\int\limits \int\limits_s \ F. \ n \ dS = \int\limits \int\limits_D \ F. (r_u * r_v) \ dA[/tex]

The sphere z is given as =  16 -y²,    above x = 0 , x= 1, and z = 0

When z = 0 ⇒ 16 - y² = 0

⇒ y = ± 4

The parameterization is y=v⇒z= 16 -v²    and x= u

⇒ r = (x,y, z) = ( u,v,16 - v²)

with 0 ≤ u ≤ 1      and     -4 ≤  v ≤  4

However the normal vector can now be determined as :

[tex]r_u = (1,0,0) , \ \ \ r_v = (0,1, - 2v)[/tex]

[tex]n = r_u*r_v = \left[\begin{array}{ccc}i&j&k\\1&0&0\\0&1&-2v\end{array}\right] = (0,2v,1)[/tex]

[tex]\int\limits \int\limits_s \ F. \ n \ dS = \int\limits \int\limits_D \ F. (r(u,v)) .(r_u*r_v)dA[/tex]

[tex]=\int\limits^1_0 \int\limits^4_{-4} [(16-v^2)^2 , u , -2 (16-v^2)](0,2v,1)dvdu[/tex]

[tex]=\int\limits^1_0 \int\limits^4_{-4} [2uv-2(16-v^2))dvdu[/tex]

[tex]=\int\limits^1_0 (uv^2 -32v+ \frac{2v^3}{3})^ ^4}__{-4}} du[/tex]

[tex]=\int\limits^1_0 (u(16-16)-32(8)+\frac{2}{3}(128))du[/tex]

[tex]= \int\limits^1_0 (-\frac{512}{3})du[/tex]

[tex]= - \frac{512}{3}(u)^ ^1}__0[/tex]

= [tex]-\frac{512}{3}[/tex]

The flux of a vector field across a surface is calculated by computing the surface integral of the vector field in the direction normal to the surface. This involves parametrizing the surface and taking antiderivatives based on the defined area. The direction of the flux is crucial as it determines the sign of the flux.

To find the flux of the vector field upper Case Bold F across a surface, we need to compute the surface integral of upper Case Bold F in the given direction. For the given problem, the surface is defined by the parabolic cylinder z = 1 - y^2 and the planes x = 0, x = 1, z = 0. We parametrize this surface using two parameters x and y, with x ranging from 0 to 1, and y ranging from -1 to 1.

We then compute the surface integral by taking the antiderivative of the defined area with the boundaries of surface as the integral's bounds. This process might involve computation of multiple integrals if the surface is composed of multiple parts.

Note that the direction of the flux, which is normal away from the x-axis, is important for the calculation, as it determines the sign of the flux. The flux is positive if the angle between the vector field and the outward normal to the surface is less than 90 degrees, and negative otherwise.

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Answer:

4.45

Step-by-step explanation:

Answer:

4.04

Step-by-step explanation:

6.35/ 1.57= 4.044585987261146‬

round to nearest hundredth is where the 4 is located at so its 4.04

Answer:

a=7.8

<C=84.8°

<B=44.19

Step-by-step explanation:

Answer:

Step-by-step explanation:

What it means to "solve for a triangle" is to basically find ALL the missing parts, which in this case, are the lengths.

You are given the angles of the triangle, which we can use to help find the lengths.

By using sin, cos, and tan we can find the missing lengths

** quick side note, an easy way to remember how to use sin, cos, tan is SOH CAH TOA. In other words "for sine, multiply the opposite and hypotenuse, for cosine, multiply adjacent and hyp., and for tan, multiply opposite and adj.

start w/ solving for an angle (it doesn't matter which one but ill do A)

Bc you aren't given any side lengths, you have it a little easier by having to only use one method of SOH CAH TOA to solve. The method is sine

Using your calculator, type in sin(degree) or sin(51), and  you should get

= 0.777145 OR 0.8

** make sure your calculator is is DEGREES not RADIANS

Now do this for the rest of the angles:

sin(7)= 0.1

sin(10)= 0.2

You have all the lengths (0.8, 0.1, 0.2) add them together to find the perimeter and if you want to find the area use Bh/2. But to find the area you must have a height, which you don't have

To find the height use formula: sqrt/( S(S-A)(S-B)(S-C)

A, B, C are the sides you've found using sine, and S is 1/2( A+B+C) or fast math is 0.55.

Plug in the values and solve :)

Answer:

answer is c

Step-by-step explanation:

correct me if im wrong but it should be

Answer:

i believe its C

Step-by-step explanation:

Answer:

6%

Percentage of teachers = 6%

Step-by-step explanation:

Given;

Number of grade k-2 students = 137

Number of grade 3-5 students = 145

Total = 300

Number of teachers = 300 - (137+145) = 18

Percentage of teachers = (number of teachers÷total)× 100%

%T = (18/300) × 100

%T = 6%

Answer:

7.6 feet

Step-by-step explanation:

The radius of a circle is halfway through. The diameter is the full way through. So what you do is multiply the radius by two. In this case, it's 3.8*2.

Answer:

7.6 ft

Step-by-step explanation:

The diameter of a circle is 2 times the length of the radius.

The formula to find the diameter is

d=2r

d= diameter

r= radius

Since the radius of this circle is 3.8, when multiplied by its self, it is 7.6 feet.

I hope this helped! :)

Answer:

1st one the other 2 are linear

Answer:

the first one

Step-by-step explanation:

the other two are linear.

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image for the step by step explanation of the answer to the question

Answer:

x = 7+√(3), 7-√(3)

Step-by-step explanation:

x^2 - 14x + ___ = -46 + ___

x^2 - 14x + 49 = -46 + 49

(x-7)^2 = 3

√(3) = x-7

x = 7+√(3), 7-√(3)

The value of x is x = 7+√(3), 7-√(3)

Completing the square means writing a quadratic in the form of a squared bracket and adding a constant if necessary.

Given:

x² - 14x ++46 = 0

x² - 14x ++46 + 7²- 7² = 0

x² - 14x + 7² +46 - 49 = 0

(x- 7)² - 3=0

(x- 7)² = 3

x = 7+√(3), 7-√(3)

Learn more about completing the square method here:

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Answer:

a) 1/2

Step-by-step explanation:

All we have to do is simply find the probability of selecting a triangle, find the  probability of selecting a circle and then add them together.

There are a total of 10 shapes in the box.

There are 3 triangles, so, the probability of picking a triangle is:

3/10

There are 2 circles, so, the probability of selecting a circle is:

2/10

Adding them together yields:

3/10 + 2/10 = 5/10 = 1/2

The probability of selecting a triangle or circle is 1/2.

Answer:

The answer is store A

Step-by-step explanation:

Since its simple to see 12 is divisible by 6. It equals 2. So the store sells each bottle for 2 dollars. Store A on the other hand is a little difficult but the same thing just divide 18 by 10 to get your outcome of 1.8

Answer:

3.5 square cm

Step-by-step explanation:

[tex]Area \: of \: both \: squares \\ = {2}^{2} + {3}^{2} \\ = 4 + 9 \\ = 13 \: {cm}^{2} \\ \\ Area \: of \: both \: right \: \triangle s \\ = \frac{1}{2} \times (2 + 3) \times 2 + \frac{1}{2} \times3 \times 3 \\ = 5 \times 1+ 1.5 \times 3 \\ = 5 + 4.5 \\ = 9.5 \: {cm}^{2} \\ \\ Area \: of \:shaded \: region \\ = Area \: of \: both \: squares\\ - Area \: of \: both \: right \: \triangle s \\ = 13 - 9.5 \\ \purple { \boxed{ \bold{Area \: of \:shaded \: region = 3.5 \: {cm}^{2} }}}[/tex]

Answer:subtracting 8 from both sides

Step-by-step explanation:

Answer:

The answer is C, subtracting 8 from both sides

Step-by-step explanation:

The second answer is A, -8

assuming youre on edg

Answer:

The best estimate is 100 per month

Step-by-step explanation:

Take 618 and divide by 6 to get the exact amount

We want an estimate

Round 618 to 600

600/6 = 100

Answer:

A

Step-by-step explanation:

It is $100

Answer: its b. i suck at explaining so sorry lol but its b

Answer: 6

Step-by-step explanation: 2 / 1/3 = 6

Final answer:

To find out how many 1/3 inch cubes can fit into a 2 inch cube, calculate the volume of both cubes and divide the larger volume by the smaller. The result is 216 such cubes can fit into a 2 inch cube.

Explanation:

To determine how many 1/3 inch cubes can fit into a 2 inch cube, we first need to calculate the volume of the larger cube, which is 2 inches x 2 inches x 2 inches = 8 cubic inches. Next, we calculate the volume of the smaller cube which is (1/3 inch) x (1/3 inch) x (1/3 inch) = 1/27 cubic inch. To find how many smaller cubes fit into the larger one, we divide the volume of the larger cube by the volume of the smaller cube: 8 cubic inches / (1/27) cubic inch = 216. Therefore, 216 smaller cubes, each 1/3 inch on a side, can fit into a 2 inch cube.

The value of x in the given question is: x = y/5

How to change the subject of the formula?

We are given that the function for getting y is:

y = 5x

Now, to make x the subject of the formula, we will use division property of equality to divide both sides by 5 to get:

y/5 = 5x/5

x = y/5

Thus, the value of x in the given question is:

x = y/5

Answer: 31%

Step-by-step explanation: We need to find the amount deducted from the check which is $101.15. Keep in mind that this is the amount DEDUCTED, so if we add it to the net pay we will get the full amount which is $330.

Now we can do some math.

101.5 x 100 / 300 = 30.6515152% or 31%

The percentage of gross income going to taxes and FICA will be 38.75%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

To the nearest one percent, the percentage of gross income going to taxes and FICA is: 44% 31% 69% 11%

P = [(0.44 + 0.31 + 0.69 + 0.11) / 4] x 100

P = (1.55 / 4) x 100

P = 0.3875 x 100

P = 38.75%

The percentage of gross income going to taxes and FICA will be 38.75%.

More about the percentage link is given below.

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Answer:

y = -8/7x +4

Step-by-step explanation:

7/4y=-(2x-7)

Distribute the minus sign

7/4y=-2x+7

Multiply each side by 4/7

4/7*7/4y=4/7*-2x+7*4/7

y = -8/7x +4

Answer:

y = -8/7x + 4

Step-by-step explanation:

1) First remove the parentheses

7/4 y = -2x + 7

2) Then multiply by 4 to get rid of the denominator

7y = -8x +28

3) Now divide by 7 on both sides, this way you'll isolate the y variable on the left side

y = -8/7x +4

ask me questions if u have any

Answer:

Data Set 2, seventh graders:

Center: The median value is 54. (Count to the middle: it's the tenth value.) The set is bimodal, with modes at 53 and 55. (The mode is the number that occurs most frequently.)

Shape: The set looks to be fairly symmetrical, though data lies closer to the right than the left.

Spread: The range is 60-50 = 10, so it's less spread out than the sixth graders.

Answer:

-12

(someone check)

Answer: -12

Step-by-step explanation:

|-16|=16, (-2)^2=4, 4^2=16

So, (16÷4) -16 = -12

Answer: $585

Step-by-step explanation:

Find the area of the trapezoid (Area: 117 sq ft)

Multiply the area by 5 because each square feet is $5

And vola your answer!

Answer:

15,236 sq in

Step-by-step explanation:

First, you have to split the net into three rectangles and two triangles

step 1

triangular base area

1/2 bh = 1/2 (44 in)(64 in)

= 1/2 (2,816 sq in)

= 1,408 sq in.

2 x 1,408 sq in = 2,816 sq in.

step 2

end rectangle area

lw = (68 in)(69 in)

= 4,692 sq in

2 x 4,692 sq in = 9,384 sq in

Now find the area of the middle rectangle

lw - (69 in) (44 in) = 3,039 sq in.

then add all the areas together

2,816 + 9,384 + 3,036 = 15,236 sq in

Hope this helps :)

Answer:

x= 12 units.

Step-by-step explanation:

To solve this equation, we can find each half of the base using the Pythagorean theorem. We will use 'x' as denoting each HALF of the base:

45= 3²+x²

Subtracting from both sides will give us:

36= x²

x=6.

However, the base in this problem is '2x' because 'x' is HALF of the base.

2(6)= 12 units.

Final answer:

By dividing the total cost of 5 fruit bars by 5, we get the cost per bar, which is $0.79. Then, dividing $12 by $0.79 per bar, we find that you can buy 15 bars with $12.

Explanation:

To determine how many frozen fruit bars can be purchased with $12 when 5 bars cost $3.95, we first need to calculate the cost per bar. We do this by dividing the total cost of 5 bars ($3.95) by the number of bars (5), giving us:

Cost per bar = $3.95 ÷ 5 = $0.79 per bar.

Next, we divide the total amount of money available ($12) by the cost per bar to find out how many bars can be bought:

Number of bars = $12 ÷ $0.79 per bar

When we do the calculation, we get:

Number of bars = 15.19 bars

Since we can't buy a fraction of a bar, we round down to the nearest whole number:

Number of bars that can be bought = 15 bars

Therefore, with $12, you can buy 15 frozen fruit bars.

The width of the yard is 6 meters, calculated using the Pythagorean theorem with one side as 8 meters and the other side as the unknown width.

We can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the two sides of the triangle represent the length and width of the yard, and the hypotenuse represents the distance between the gopher's holes.

Let's denote the width of the yard as (w). According to the problem:

Length of the yard (L) = 8 meters

Distance between the gopher's holes (h) = 10 meters

Width of the yard ((w)) = ?

We can set up the following equation using the Pythagorean theorem:

[tex]\[ w^2 + 8^2 = 10^2 \][/tex]

[tex]\[ w^2 + 64 = 100 \][/tex]

[tex]\[ w^2 = 100 - 64 \][/tex]

[tex]\[ w^2 = 36 \][/tex]

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

[tex]\[ w = 6 \, \text{meters} \][/tex]

Therefore, the width of the yard is 6 meters.

Answer:

2.3+r=7.1

move all terms to the left:

2.3+r-(7.1)=0

add all the numbers together, and all the variables

r-4.8=0

move all terms containing r to the left, all other terms to the right

r=4.8 is the answer

Answer:

r = 4.8

Step-by-step explanation:

2.3 + r = 7.1

r + 2.3 = 7.1

r = 7.1 - 2.3

r = 4.8

Answer:

-64

Step-by-step explanation:

Answer:

[tex]-64=64cos(\pi )+64i/ sin(\pi )[/tex]

Step-by-step explanation:

For a complex number a + bi, polar form is given by [tex]r(cos(0)+ i sin(0))[/tex], where [tex]r = \sqrt{a^2+b^2}[/tex] and [tex]a = atan(\frac{b}{a} )[/tex]

In this case, we have [tex]a = -64[/tex] and [tex]b=0[/tex]

Therefore, [tex]r = \sqrt{(-64)^2+(0)^2} =64[/tex]

Also, [tex]0 = atan(\frac{0}{-64} )+\pi =\pi[/tex]

Which means that, [tex]-64=64cos(\pi )+64i/ sin(\pi )[/tex]!!!

I'm happy i finally got it!