Question 6 of 10
What is the approximate value of x in the diagram below? (Hint: You will need
to use one of the trigonometric ratios given in the table.)
23
54°
90°
OA. 18.61
OB. 39.12
C. 31.64
36°
sin 36
cos 36
tan 36
0.588
≈ 0.809
0.727

The pints of vegetable stock the chef needs is [tex]3\frac{1}{2}[/tex].

The first step is to determine the unit of conversion of cups to pints.

1 cup = 0.5 pints

To convert cup to pints, multiply 7 by 0.7

7 x 0.5 = 7/2 = [tex]3\frac{1}{2}[/tex]

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See the graph in the attached image.

The heights of the gondola are the same at 8.019 seconds and 26.446 seconds

Ferris wheel 1

The given parameters are:

The above means that:

The sine function is represented as:

y = Asin(2π/T)t + c

Where

c = Amplitude - Minimum

c = 7 - 1.5

c = 5.5

So, we have:

y = 7sin(2πt/16) + 5.5

y = 7sin(πt/8) + 5.5

Shift to the left by π/2

y = 7sin(πt/8 - π/2) + 5.5

Ferris wheel 2

The given parameters are:

The above means that:

The sine function is represented as:

y = Asin(2π/T)t + c

Where

c = Amplitude - Minimum

c = 8 - 2

c = 6

So, we have:

y = 8sin(2πt/20) + 6

y = 8sin(πt/10) + 6

Shift to the left by π/2

y = 8sin(πt/10 - π/2) + 6

Hence, the equations of the wheels are y = 7sin(πt/8 - π/2) + 5 and y = 8sin(πt/10 - π/2) + 6

See attachment for their graphs

From the attached graph, we have:

f(x) = g(x) = 12.5 at x = 8.019

f(x) = g(x) = 9.511 at x = 26.446

Hence, the heights of the gondola are the same at 8.019 seconds and 26.446 seconds

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The dimensions of the crate that will minimize the total cost of material are 10, 10, and 29.

The volume will be:

= Length × Width × Height

= lwh

For the square base, w = l

2880 = w²h

The cost function will be:

C = 12wl + 4wh + 4lh

Put l = w.

C = 12w² + 8wh

C = 12w² + 8w(2880/w²)

C = 12w² + 23040/w

Differentiate with respect to w

C'(w) = 0

24w = 23040/w²

24w³ = 23040

w³ = 960

w = 10 approximately

The length is 16 as well as they are the same. The height will be:

= 2880/w²

= 2880/10²

= 28.8 = 29

Therefore, the dimensions are 10, 10, and 29.

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The approximate value of cos theta in the quadrant indicated is 0.4232

Given the expression below;

sin theta = -0.906

Determine the value of theta

sin theta = -0.906

theta = arcsin(-0.906)
theta = -64.95 degrees

In the 4th quadrant;

theta = 360 - 64.95

theta = 295.04 degrees

Determine the value of cosine theta

Cos theta = cos 295.04
cos theta = 0.4232

Hence the approximate value of cos theta in the quadrant indicated is 0.4232

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Option A graph represents  S(x).

Function is a statement that relates tow variables.

It is given that

the side length of the larger frame S(x)

S(x) =  [tex]\rm 3 \sqrt{x -1}[/tex]

X is the area of the smaller frame in square inches

A square root function is given by

s(x) = [tex]\rm \sqrt{x}[/tex]

when the graph is shifted towards right and stretched by  3 , due to which the graph is taller as compared to the parent graph and

Therefore Option A graph represents  S(x).

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1) You can find the number of possible methods through a tree diagram or the fundamental counting principles.

2) The total number of combinations is 360

To find the total number of combinations,

A Tree Diagram is a the various possibilities in a pictorial way. The diagram begins with a single point, which represents the initial decision, then branches out to indicate all possible outcomes for each successive option.

The Fundamental Counting Principle tells us that if there are 'n' ways doing a thing and 'm' ways to do another, there are n x m ways to do both. Which means that the total number of outcomes equals the product of the number of ways each job can completd.

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Answer:

water pollution or any one of them.

Step-by-step explanation:

Technically, these are all issues in the Netherlands.

However, based on a statista opinion chart of Netherland concerns, the biggest concern at the moment is pollution.

So, picking any of these might work because they are all issues - but I found that the environmental one is most likely to be correct.

Answer:

Water pollution

Explanation:

"Crime (48 percent) and environmental pollution (45 percent) are most often seen as (very) serious problems." - cbs

Using proportions, it is found that the number of hours for which she practiced her role on Tuesday is:

[tex]\frac{5}{9}[/tex]

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

On Wednesday, she practiced 5/6 of an hour, and on Tuesday she practiced 2/3 of Wednesday's amount, hence the number of hours she practiced on Tuesday was of:

[tex]n = \frac{5}{6} \times \frac{2}{3} = \frac{10}{18} = \frac{5}{9}[/tex].

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The values of k (i.e. +3 and -2) in functions b and c change the rational graph by (b) shifts right/left

The functions are given as:

[tex]y = \sqrt x[/tex]

[tex]y = \sqrt {x + 3[/tex]

[tex]y = \sqrt {x - 2[/tex]

See attachment for the graphs of the three functions.

From the attached graph, we can see that [tex]y = \sqrt {x + 3[/tex] and [tex]y = \sqrt {x - 2[/tex] are at the left and right of the function [tex]y = \sqrt x[/tex]

Hence, the values of k in functions b and c change the rational graph by shifting it right/left

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The expression 1.54x10^28 not in scientific notation form is 15400000000000000000000000000

The expression is given as:

1.54x10^28

Evaluate the product

1.54x10^28 = 15400000000000000000000000000

Hence, the expression 1.54x10^28 not in scientific notation form is 15400000000000000000000000000

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Since for each trial there are more than two outcomes, the random variable x is not a binomial variable.

Three things are required:

In this problem, for each trial, there are six possible outcomes for the sum, hence the random variable x is not a binomial variable.

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Answer:

3:4

Step-by-step explanation:

If you divide both sides by 7, you shall get 3:4

Answer:

36 Adult Tickets. 352 Student Tickets

Step-by-step explanation:

Firstly, we have to create 2 expressions to solve a problem like this. If we use the variable s to mean student and a to mean adult, we can create the expressions:

3s + 6a = 1272 to represent how much they made with all ticket sales

s = 10a - 8 to represent how many student tickets there are.

Now, we plug our definition of s into the first expression to get:

3(10a - 8) + 6a = 1272

30a - 24 + 6a = 1272

36a - 24 = 1272

36a = 1296

a = 36

We have determined the number of adult tickets so we can move on to the number of students:

s = 10(36) - 8

s = 360 - 8

s = 352

Question Solved

Hello,

2,75 % = 2,75/100 = (2,75 × 100)/(100 × 100) = 275/10000 = 11/400

Answer:

4,9,14,19,24,29,34,39

The required slope of A is 1 or Ф = 45° and for B is infinte or Ф = 90°

use the m=y2-y1/x2-x1 to find the slope of the line that goes through each pair of points A.(5,7) and (-4,-2) B.(1,3) and (1,-10)

slope is define as the angle at which line is inclined and for draw tangent over a curve.

m=y2-y1/x2-x1

For, A (5, 7),(-4, -2)
m=-2-7/-4-5
m=1
or TanФ=1
Ф = 45°

For, B(1, 3), (1,-10)
m=-10-3/1-1
m= ∞ or Ф = 90°

Thus the required slope of A is 1 or Ф = 45° and for B is infinte or Ф = 90°

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Answer:

[tex]\frac{\sqrt{15} }{2}[/tex]

Step-by-step explanation:

[tex]\sqrt{f(\frac{3}{2} )[/tex] , substitute [tex]\frac{3}{2}[/tex] to x

[tex]f(\frac{3}{2} )=4(\frac{3}{2} )-(\frac{3}{2} )^2[/tex] = [tex]\frac{15}{4}[/tex] or 3.75

[tex]\sqrt{f(\frac{3}{2} )[/tex]=[tex]\sqrt{3.75}[/tex] = [tex]\frac{\sqrt{15} }{2}[/tex]

As a result of climatic peculiarities the seasonal changes of oak tree in Florida and oak in Maine are distinguished such that the differences are remarkably satisfactory.

We know that many oaks are native to Florida and some of the Florida oaks include;

Northern red oaks can also be found in northern Florida. Some other oak trees in Florida include;

From the information above, we can conclude that as a result of climatic peculiarities the seasonal changes of oak in Florida and oak in Maine are distinguished such that the differences are remarkably satisfactory.

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Answer:

y = x/3

Step-by-step explanation:

y = 3x

x = 3y

3y = x

y = x/3

⊱_____________________________________________________⊱

Answer:

Step-by-step explanation:

[tex]\large\displaystyle\begin{gathered} \rm{To \ find \ the \ inverse, \ switch \ the \ places \ of \ x \ and \ y} \\ \sf{ y=3x} \\ \sf{x=3y} \\ \rm{Now \ solve \ for y} \\ \sf{x/3=y} \\ \sf{\dfrac{x}{3}=y \end{gathered}[/tex]

done !!

⊰______________________________________________________⊱

The option that is better is that compounded twice annually with 61.5 interest than the simple interest for 60.

Simple interest is the amount obtained from a money invested or loaned over a specific period of time with a specific interest rate.

Analysis.

Let the principal to be used be 600

Compound interest compounded annually twice, which means the tenor of interest is two years.

first year interest

I = PRT/100

P= 600, R = 5%, T = 1

I = 600 x 5 x 1/ 100 = 30

Principal for second year = principal first year + interest

                                          = 600 + 30 = 630

interest for second year = 630 x 5 x 1/ 100 = 31.5

Compound interest  = 30+31.5 = 61.5

For simple interest, duration is 2 years,

I = PRT/100

I = 600 x 5 x 2/100 = 60

In conclusion, The account that earns 5% compounded twice annually is the better one since it accrues more interest.

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Answer: 15cm and 5cm

Step-by-step explanation:

A rectangle's area is the product of the length and width

Given length x and width y, 2x+2y = 40 and x*y = 75.

Verifying my answer:

2(15)+2(5) = 40

30+10 = 40

40 = 40

15*5 = 75

75= 75

This is a week late so I hope this helped.

The length and the width of the rectangle​ are 15cm and 5cm respectively

The given parameters are:

Area (A) = 75

Perimeter (P) = 40

The area of a rectangle is LW, while the perimeter is 2(L + W)

So, we have:

LW = 75

2(L + W) = 40

Divide by 2

L + W = 20

Make L the subject

L = 20 - W

Substitute L = 20 - W in LW = 75

(20 - W)W = 75

Expand

20W - W^2 = 75

Rewrite as:

W^2 - 20W + 75 = 0

Expand

W^2 - 15W - 5W + 75 = 0

Factorize

(W - 15)(W -5) = 0

Split

W - 15 = 0 or W - 5 = 0

Solve for W

W = 15 or W = 5

Recall that:

L= 20 - W

So, we have

L = 20 - 15 or L = 20 - 5

This gives

L = 5 or L = 15

Hence, the length and the width of the rectangle​ are 15cm and 5cm respectively

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The volume of the storage bin given the radius and heights is 1050.79ft³.

The volume of the storage bin is the sum of the volume of the cylinder and the cone. A cylinder is a three-dimensional object that is made up of a prism with a circular base.

Volume of a cylinder = πr²h

Where:

3.14 x 5.7² x 7.5 = 765.14 ft³

A cone is a three dimensional object that tapers from its circular base to its apex.

Volume of a cylinder = 1/3πr²h

Where:

1/3 x 3.14 x 5.7² x 8.4 = 285.65 ft³

Volume of the container =  285.65 ft³ + 765.14 ft³ = 1050.79ft³

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Answer:

The third option. he didnt make a mistake

Step-by-step explanation:

Answer:

Gabi did not make a mistake.

Step-by-step explanation:

To find j, Gabi needs to multiply both sides of the equation by 10. 80*10 = 800, so therefore j = 800. Both steps are correct.

A function assigns the values. For every increase of 1 ounce in frozen yogurt the cost will increase by $49.

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

Given the frozen yogurt store charges C dollars for w ounces of frozen yogurt, C can be modelled by C = 49w+80/100. Therefore, for every increase of 1 ounce in frozen yogurt the cost will increase by $49.

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Answer:

C

Step-by-step explanation:

The area of a rectangle is lw or length * width.

We can add the parts to make up the whole of each side.

Thus, for the entire width, we have 4x+3 and for the entire length we have 8 + 5x.

To solve for area in terms of x, we just multiply our width and length, which gives us:  

[tex](4x+3)(8+5x)\\32x+20x^2+24+15x\\20x^2+47x+24[/tex]

Answer:

the scale factor is either 4 or 1/4 depending if you are going from the model to the actual or the actual to the model.

Step-by-step explanation:

s= scale factor

2s = 8  Divide both sides by 2

x = 4

If I do the other way:

8s = 2 Divide both sides by 8

s = 1/4

The distance traveled by the driver during her reaction time based on her speed was 44 feet.

find the speed in feet per second to be:

= (40 x 5,280 feet per hour) / Number of seconds in an hour

= 211,200 / 3,600

= 58.67 feet per second

With a reaction speed of 3/4 seconds, the distance traveled is:

= 58.67 x 3/4

= 44 feet

Full question is:

The driver of a car traveling at a speed of 40 miles per hour had to stop the car quickly. Using the driver's speed in feet per second, how far did her car travel during her reaction time of 3/4 of a second?Round your answer to two decimal places

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Answer:

≈ 9613.64 mph

Step-by-step explanation:

First we convert ft/s to ft/hr.

14100 ft/s*3600 = 50,760,000 ft/hr

Now we convert the feet to miles.

50,760,000 ft/hr ÷ 5280 ≈ 9613.64 mph

So in conclusion, 14100 ft/s is approximately 9613.64 mph.

The triangle with points at (2, 4), (4, 2), (9, 6) was reflected across the line y = 3 to get the points (2, 2), (4, 4), (9, 0)

Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.

The triangle with points at (2, 4), (4, 2), (9, 6) was reflected across the line y = 3 to get the points (2, 2), (4, 4), (9, 0)

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