Multi-Select Technology-Enhanced

Answer:

38.6 miles

Step-by-step explanation:

The scenario has been modeled as a triangle, where A, B and C are the angles and a, b and c are the sides opposite the angles.

Side c

AB = 34 miles

Angle B

90° - 53° = 37°

Angle A

90° + 21° = 111°

Interior angles of a triangle sum to 180°

⇒ A + B + C = 180°

⇒ 111° + 37° + C = 180°

⇒ 148° + C = 180°

⇒ C = 180° - 148°

⇒ C = 32°

To find the measure of side b (AC), use the Sine Rule.

Sine Rule

\(\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

Substitute the values into the formula:

\(\implies \sf \dfrac{AC}{\sin 37^{\circ}}=\dfrac{34}{\sin 32^{\circ}}\)

\(\implies \sf AC=\dfrac{34\sin 37^{\circ}}{\sin 32^{\circ}}\)

\(\implies \sf AC=38.61288345...\)

\(\implies \sf AC=38.6\:miles\:(nearest\:tenth)\)

Therefore, weather station A is 38.6 miles from the storm.

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Answer:

\(y=-\frac{3}{2}\)

Step-by-step explanation:

\(\text{y = kx where k is a constant.}\)

\(6 = -4k\\k = \frac{6}{-4} =-\frac{3}{2}\)

The percentage of pies baked that were not apple was 33.33 %

What is Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

Given data ,

The number of apple pies baked at the bakery = 13

The number of pecan pies baked at the bakery = 4

The number of pumpkin pies baked at the bakery = 3

So ,

Total number of pies baked at the bakery =
Number of apple pies baked at the bakery + Number of pecan pies baked at the bakery + Number of pumpkin pies baked at the bakery

Total number of pies baked at the bakery = 13 + 4 + 3

                                                                      = 21

Now ,

The number of pies that were not apple = Number of pumpkin pies baked at the bakery + Number of pecan pies baked at the bakery

The number of pies that were not apple = 4 + 3

                                                                   = 7

And ,

The percentage of pies that were not apple =

( The number of pies that were not apple / Total number of pies baked at the bakery ) x 100 %

The percentage of pies that were not apple = ( 7 / 21 ) x 100 %

                                                                         = ( 1 / 3 ) x 100 %

                                                                         = 33.33 %

Hence , the percentage of pies that were not apple is 33.33 %

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Answer:

5 cups

Step-by-step explanation:

HOPE THIS HELPS!!

Answer:

Amount of water are equivalent = 15,000

Step-by-step explanation:

Given:

5 ppb (parts per billion)

Drop of water = 75,000

Find:

How many gallons of water are equivalent

Computation:

Amount of water are equivalent = Drop of water / Parts per billion

Amount of water are equivalent = 75,000 / 5

Amount of water are equivalent = 15,000

Answer:

9 1/8 ribbon would be remaining

Answer:

what you are looking? if you need a answer I think it is 24t^7 but tell me what are you looking

Answer:

24

Step-by-step explanation:

Answer:

-21

Step-by-step explanation:

-25+ 2²

evaluate -5²

evaluate -2²

subtract

Answer:

it is too blury to read

Step-by-step explanation:

let's reword that

some value "x" increased by 20% and it ended up at 6, the hell is "x" anyway?

well, the value was really "x", oddly enough is the 100%, and if we increase it by 20%, that makes it 100% + 20% = 120%, and we know that is 6, hmmmm

\(\begin{array}{ccll} Amount&\%\\ \cline{1-2} x & 100\\ 6& 120 \end{array} \implies \cfrac{x}{6}~~=~~\cfrac{100}{120} \implies \cfrac{ x }{ 6 } ~~=~~ \cfrac{ 5 }{ 6 }\implies x=5\)

Answer:

\(64\)cm³

Step-by-step explanation:

\(8 \times 2 \times 4 \\ = 64\)

Answer:

64

Step-by-step explanation:

Hello There!

The formula for volume of a rectangular prism is

\(V=lwh\)

where w = width

l = length

h = height

They give us the following dimensions

height = 4

width = 2

length = 8

all we have to do is plug in the values

\(V=2(4)8\\2*4=8\\8*8=64\\V=64\)

Thus the answer is 64

Using the normal distribution, the areas to the left are given as follows:

a) 0.7910.

b) 0.6664.

c) 0.3707.

d) 0.8508.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

Hence:

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y=-2x+5 is the slope-intercept equation for a line that goes through the point (4,-3) and 5 is the value of b.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We have to find the slope-intercept equation for a line that goes through the point (4,-3)--with a slope of -2

m=-2

Now let us find the y intercept

-3=-2(4)+b

-3=-8+b

-3+8=b

5=b

Hence, y=-2x+5 is the slope-intercept equation for a line that goes through the point (4,-3) and 5 is the value of b.

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Answer: The height of the telephone pole = $15.046

Step-by-step explanation:

Given: Angle of elevation= 62 degrees.

Distance of Ben from the base of the pole = 8 feet

According to trigonometry, we have

\(\tan x=\dfrac{\text{side opposite to x}}{\text{side adjacent to x}}\)

i.e.

\(\tan 62^{\circ}=\dfrac{\text{ height of the telephone pole}}{8}\\\\(1.880726)=\dfrac{\text{ height of the telephone pole}}{8}\\\\\text{ Height of the telephone pole} = 8\times 1.880726\approx15.046\)

Hence, The height of the telephone pole = $15.046

Answer:

x - 4 yards.

Step-by-step explanation:

Given:

Area of rectangle = 3x^2 - 12x square yards

Width = 3x yards

To find:

Length of rectangle

Solution:

The area of a rectangle is equal to the product of its length and width.

Area of rectangle = Length * Width

Substituting the given values, we get:

3x^2 - 12x = Length * 3x

Length =( 3x^2 - 12x )3x

Length = x-4

Therefore, the length of the rectangle is x - 4 yards.

Answer: The length of the rectangle is x - 4 yards.

Step-by-step explanation:

We can create an equation to solve this word problem, where the variable L = length.

3x  ×  L  = \(3x^2 - 12x\)

We need to solve for the variable L, to find the length of the rectangle.

First lets factor the right side of the equation to make it easier to divide with.

3x  ×  L  = \(3x^2 - 12x\)

We can factor out 3x from the right side of the equation.

3x  ×  L  = 3x(x - 4)

Now we need to get the variable L by itself (isolating the variable). In order to do that, we can divide both sides by 3x.

3x ×  L  = 3x(x - 4)

/3x           /3x

L = x - 4

The length of the rectangle is x - 4 yards.

Answer:

20%

Step-by-step explanation:

12/60 (divided) makes 0.2, converted to a percent is 20%

The area of the rectangle with given length and width is 137.6 cm²   .

In the question ,

it is given that ,

the length of the rectangle = 64/5 cm    and

the width of the rectangle = 43/4 cm

we know that the formula for the Area of rectangle is

Area = length × width

Substituting the value of length as 64/5 and width as 43/4 .

we get ,

Area = 64/5 × 43/4

= (64 × 43)/(5 × 4)

Simplifying further ,

we get ,

= 2752/20

= 137.6 cm²

Therefore  , The area of the rectangle with given length and width is 137.6 cm²   .

The given question is incomplete , the complete question is

What is the area of the the rectangle with length 64/5 cm and width 43/4 cm ?

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The coordinates of point B are (-3, 17).

The given equation is M = I₁ + I₂ = 31 + 32.

Now let's substitute in our given values:

(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)

We will now set up two equations to solve for our two unknowns, x₂ and y₂:

Equation 1: (-5 + x₂) / 2 = -4

Multiply both sides by 2:

-5 + x₂ = -8

Add 5 to both sides:

x₂ = -3

This gives us the x-coordinate of point B.

Equation 2: (-5 + 2 + y₂) / 2 = 7

Simplify:

(-3 + y₂) / 2 = 7

Multiply both sides by 2:

-3 + y₂ = 14

Add 3 to both sides:

y₂ = 17

This gives us the y-coordinate of point B.

Therefore, the coordinates of point B are (-3, 17).

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To find the exact value of (7π/6) using the unit circle, locate the angle (π/6) on the unit circle in the second quadrant, determine the coordinates, and adjust the y-coordinate to be negative. The final answer is (√3/2, -1/2). This answer is obtained by understanding the reference angle and using the coordinates of the point where the angle intersects the unit circle.

To find the exact value of (7π/6) using the unit circle, follow these steps:

1. Start by understanding the reference angle. The reference angle for (7π/6) is (π/6).

2. Locate the angle (π/6) on the unit circle. This angle lies in the second quadrant.

3. Determine the coordinates of the point where the angle intersects the unit circle. For (π/6), the x-coordinate is √3/2 and the y-coordinate is 1/2.

4. Since (7π/6) lies in the second quadrant, the x-coordinate will remain the same, but the y-coordinate will be negative. Therefore, the coordinates for (7π/6) are (√3/2, -1/2).

5. The exact value of (7π/6) is (√3/2, -1/2).

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Solution :

Along the edge \($C_1$\)

The parametric equation for \($C_1$\) is given :

\($x_1(t) = 9t , y_2(t) = 0 \ \ for \ \ 0 \leq t \leq 1$\)

Along edge \($C_2$\)

The curve here is a quarter circle with the radius 9. Therefore, the parametric equation with the domain \($0 \leq t \leq 1 $\) is then given by :

\($x_2(t) = 9 \cos \left(\frac{\pi }{2}t\right)$\)

\($y_2(t) = 9 \sin \left(\frac{\pi }{2}t\right)$\)

Along edge \($C_3$\)

The parametric equation for \($C_3$\) is :

\($x_1(t) = 0, \ \ \ y_2(t) = 9t \ \ \ for \ 0 \leq t \leq 1$\)

Now,

x = 9t, ⇒ dx = 9 dt

y = 0, ⇒ dy = 0

\($\int_{C_{1}}y^2 x dx + x^2 y dy = \int_0^1 (0)(0)+(0)(0) = 0$\)

And

\($x(t) = 9 \cos \left(\frac{\pi}{2}t\right) \Rightarrow dx = -\frac{7 \pi}{2} \sin \left(\frac{\pi}{2}t\right)$\)

\($y(t) = 9 \sin \left(\frac{\pi}{2}t\right) \Rightarrow dy = -\frac{7 \pi}{2} \cos \left(\frac{\pi}{2}t\right)$\)

Then :

\($\int_{C_1} y^2 x dx + x^2 y dy$\)

\($=\int_0^1 \left[\left( 9 \sin \frac{\pi}{2}t\right)^2\left(9 \cos \frac{\pi}{2}t\right)\left(-\frac{7 \pi}{2} \sin \frac{\pi}{2}t dt\right) + \left( 9 \cos \frac{\pi}{2}t\right)^2\left(9 \sin \frac{\pi}{2}t\right)\left(\frac{7 \pi}{2} \cos \frac{\pi}{2}t dt\right) \right]$\)

\($=\left[-9^4\ \frac{\cos^4\left(\frac{\pi}{2}t\right)}{\frac{\pi}{2}} -9^4\ \frac{\sin^4\left(\frac{\pi}{2}t\right)}{\frac{\pi}{2}} \right]_0^1$\)

= 0

And

x = 0,  ⇒ dx = 0

y = 9 t,  ⇒ dy = 9 dt

\($\int_{C_3} y^2 x dx + x^2 y dy = \int_0^1 (0)(0)+(0)(0) = 0$\)

Therefore,

\($ \oint y^2xdx +x^2ydy = \int_{C_1} y^2 x dx + x^2 x dx+ \int_{C_2} y^2 x dx + x^2 x dx+ \int_{C_3} y^2 x dx + x^2 x dx $\)

                        = 0 + 0 + 0

Applying the Green's theorem

\($x^2 +y^2 = 81 \Rightarrow x \pm \sqrt{81-y^2}$\)

\($\int_C P dx + Q dy = \int \int_R\left(\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}\right) dx dy $\)

Here,

\($P(x,y) = y^2x \Rightarrow \frac{\partial P}{\partial y} = 2xy$\)

\($Q(x,y) = x^2y \Rightarrow \frac{\partial Q}{\partial x} = 2xy$\)

\($\left(\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y} \right) = 2xy - 2xy = 0$\)

Therefore,

\($\oint_Cy^2xdx+x^2ydy = \int_0^9 \int_0^{\sqrt{81-y^2}}0 \ dx dy$\)

                            \($= \int_0^9 0\ dy = 0$\)

The vector field F is = \($y^2 x \hat i+x^2 y \hat j$\)  is conservative.

Answer:B

Step-by-step explanation:

I just know k?

Answer:

B

Step-by-step explanation:

The dots form a line that passes through the orgin

Yes it is yep correct 1000% 10000000000000%

Answer:

for which m is the slope, b is the y-intercept, x is any x value and y is any y value. By looking at the equation of the trend line, you can determine the y-intercept. For example, if the equation of the trend line is y=2x+5, the y-intercept is 5. You would receive this same answer if you let x = 0.

Step-by-step explanation:

Like terms are terms that have same variable. For example:

The thing that you need to becareful is about the degree. Even though x² and x both are also x-term, but they are not considered like terms. So basically like terms are terms that have same variable and same degree.

Given the expression below:

\( \large{2x + 2y + {x}^{2} - x + {x}^{2} }\)

From the expression:

Arrange in better form for our calculation.

\( \large{(2x - x) + 2y + ( {x}^{2} + {x}^{2} )} \\ \large{x + 2y + 2 {x}^{2} }\)

You might also want to arrange the expression degree (optional but recommended).

\( \large{2 {x}^{2} + x + 2y}\)

Answer

Answer:

2x² + x + 2y

Step-by-step explanation:

2x + 2y + x² - x + x²

combine like terms

2 x - x + 2 y + x² + x²

x + 2 y + 2x²

rewrite the equation. ..( optional )

2x² + x + 2y

The height of rectangular prism B is 5 yards.

Let's first find the volume of rectangular prism B:

The volume of the solid figure = Volume of prism A + Volume of prism B

180 = 75 + length × width × height of prism B

105 = length × width × height of prism B

We know that the length of prism B is 7 yards and the width is 3 yards,

Substitute those values:

105 = 7 × 3 × height of prism B

105 = 21 × height of prism B

height of prism B = 105/21

height of prism B = 5

Therefore, the height of rectangular prism B is 5 yards.

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Thus, Ron's share is $24,000, Nick's share is $18,000, Mary's share is $18,000, and Margaret's share is $72,000.

Let's denote the original scholarship amount as "P."

According to the given information, Margaret receives $72,000, which means the remaining scholarship amount for the other three individuals is P - $72,000.

Ron receives 1/3 of the scholarship, which can be represented as (1/3)(P - $72,000). Nick receives 1/4 of the scholarship, which can be represented as (1/4)(P - $72,000). Mary receives the same as Nick, so Mary's share is also (1/4)(P - $72,000).

Now, we can sum up all the shares to equal the original scholarship amount:

Ron's share + Nick's share + Mary's share + Margaret's share = P

(1/3)(P - $72,000) + (1/4)(P - $72,000) + (1/4)(P - $72,000) + $72,000 = P

To simplify the equation, we can combine like terms:

(P/3 - $24,000) + (P/4 - $18,000) + (P/4 - $18,000) + $72,000 = P

Combining the fractions and constants:

(4P + 3P - 3P + 12P)/12 - $24,000 - $18,000 - $18,000 + $72,000 = P

16P/12 - $48,000 = P

Multiplying both sides of the equation by 12 to eliminate the denominator:

16P - $576,000 = 12P

Subtracting 12P from both sides of the equation:

4P = $576,000

Dividing both sides of the equation by 4:

P = $144,000

Therefore, the original scholarship amount is $144,000.

Ron's share: (1/3)($144,000 - $72,000) = $24,000

Nick's share: (1/4)($144,000 - $72,000) = $18,000

Mary's share: (1/4)($144,000 - $72,000) = $18,000

Margaret's share: $72,000

Thus, Ron's share is $24,000, Nick's share is $18,000, Mary's share is $18,000, and Margaret's share is $72,000.

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