A simple random sample of size nequals=200200 drivers were asked if they drive a car manufactured in a certain country. of the 200200 drivers​ surveyed, 105105 responded that they did. determine if more than half of all drivers drive a car made in this country at the alpha equals 0.05α=0.05 level of significance. complete parts ​(a) through ​(d).

Answer:

  1/2sin(6x) + 1/2sin(2x)

Step-by-step explanation:

You can look up the formulas for the product identities for sine and cosine, or you can guess and check using a graphing calculator. I did the calculator solution first (see the first attachment), then looked up the identities so I can tell you what they are (see the second attachment).

__

These identities are based on the sum and difference angle identities:

  sin(α+β) +sin(α-β) = (sin(α)cos(β) +sin(β)cos(α)) + (sin(α)cos(β) -sin(β)cos(α))

  = 2sin(α)cos(β)

Dividing by 2 gives the identity of interest in this problem:

  sin(4x)cos(2x) = (1/2)(sin(4x +2x) +sin(4x -2x))

  sin(4x)cos(2x) = (1/2)(sin(6x) +sin(2x))

Answer:   1/2sin(6x) + 1/2sin(2x)

Step-by-step explanation:

took the test and got a 100

Answer:

about 75 percent of its force

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.  The calculation for the minimum payment is ...

  0.035 × $7600.97 = $266.03

__

2. The answer choices assume that Jorge makes a payment of $266.03 each month. After the first month, the minimum payment due is less than that amount. If Jorge only pays the minimum payment each month the balance will decrease by about 1.5% each month, and it will take about 31 years before the minimum payment is below $1.

The TVM Solver says it will be about 43 months for the card to be paid off if Jorge pays $266.03 each month.

Answer:

Step-by-step explanation:

These are independent non-ordered events. The faculty members chosen don't affect the students and vice versa. There is no issue with replacement, and the only limitation is the number of people allowed to serve.

12C4*15C5

495*3003=1,486,485 ways

The dimensions that minimize the total cost of material for the shipping crate are:

- Length: 24 feet

- Width: 24 feet

- Height: 8 feet

To solve this problem, we can start by writing down the volume formula for a rectangular box with a square base:

Volume = Length × Width × Height

Given that the volume is 3072 ft³, we have:

3072 = L × W × H

We also know that the material for the top and sides costs $4 per square foot and the material for the bottom costs $2 per square foot. Let's denote the areas of the top, bottom, and sides as A_top, A_bottom, and A_sides, respectively.

A_top = L × W

A_bottom = L × W

A_sides = 2 × (L × H + W × H)

The total cost, C, can be expressed as:

C = 4 × (A_top + A_bottom) + 2 × A_sides

C = 4 × (L × W + L × W) + 2 × 2 × (L × H + W × H)

C = 8LW + 4LH + 4WH

We can substitute the volume equation into the cost equation to eliminate one variable. Let's express L in terms of W and H from the volume equation:

L = 3072 ÷ (W × H)

Now substitute L into the cost equation:

C = 8(3072 ÷ (WH))W + 4(3072 ÷ (WH))H + 4WH

C = 24576 ÷ H + 12288 ÷ W + 4WH

To minimize C, we take the derivative with respect to W and H, set them equal to zero, and solve for W and H:

∂C/∂W = -12288/W² + 4H = 0

∂C/∂H = -24576/H² + 4W = 0

Solving these equations gives us W = 24 and H = 8, which leads to L = 3072 ÷ (24 × 8) = 16.

So, the dimensions that minimize the total cost of material are Length: 24 feet, Width: 24 feet, and Height: 8 feet.

Complete Question:
A shipping company must design a closed rectangular shipping crate with a square base. The volume is 3072ft3. The material for the top and sides costs $4 per square foot and the material for the bottom costs $2 per square foot. Find the dimensions of the crate that will minimize the total cost of material.

Answer:

More than doubled

Step-by-step explanation:

The troop "strength" is basically just troop number. It went from about 200,000 to about 500,000.

US troop strength is more than doubled. The correct option is A.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

From the given data we can see that the troop "strength" is basically just troop number. It went from about 200,000 to about 500,000.

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Answer:

76800 cases

Step-by-step explanation:

The number of cases of new infectious diseases reported last year= 150 cases

Number of cases are going to be double every year

Number of the cases in next or first year=150+150=300

Number of the cases in next or second year=300+300=600

Number of the cases in next or third year=600+600=1200

Number of the cases in next or fourth year=1200+1200=2400

Number of the cases in next or fifth year=2400+2400=4800

Number of the cases in next or sixth year=4800+4800=9600

Number of the cases in next or seventh year=9600+9600=19200

Number of the cases in next or eight year=19200+19200=38400

Number of the cases in next or ninth year=38400+38400=76800

Hence , the total number of cases are 76800 cases

Answer:

38,400

Step-by-step explanation:

The answer above me is wrong

Got it right on the test

Answer:

[tex]tan(\theta)=-\frac{7}{6}[/tex]

[tex]sec(\theta)=\frac{\sqrt{85} }{6}[/tex]

[tex]cos(\theta)=\frac{6\sqrt{85} }{85}[/tex]

[tex]sin(\theta)=-\frac{7\sqrt{85}}{85}[/tex]

[tex]cosec(\theta)=-\frac{\sqrt{85}}{7}[/tex]

Step-by-step explanation:

[tex]cot (\theta) = -\frac{6}{7}[/tex]

a) Since,

[tex]tan(\theta) = \frac{1}{cot(\theta)}[/tex]

[tex]tan(\theta) = \frac{1}{-\frac{6}{7} }=-\frac{7}{6}[/tex]

b) Also, according to the Pythagorean identity:

[tex]sec^{2}(\theta)=1+tan^{2}(\theta)[/tex]

Using the value of tan([tex]\theta[/tex]), we get:

[tex]sec^{2}(\theta)=1+(-\frac{7}{6} )^{2}\\\\ sec^{2}(\theta)=\frac{85}{36}\\\\ sec(\theta)=\pm \sqrt{\frac{85}{36} } \\\\ sec(\theta)=\pm \frac{\sqrt{85} }{6}[/tex]

Since, secant is positive in 4th quadrant, we will only consider the positive value. i.e.

[tex]sec(\theta)=\frac{\sqrt{85} }{6}[/tex]

c) Since,

[tex]cos(\theta)=\frac{1}{sec(\theta)}[/tex]

Using the value of secant, we get:

[tex]cos(\theta)=\frac{1}{\frac{\sqrt{85} }{6} } =\frac{6\sqrt{85} }{85}[/tex]

d) According to Pythagorean identity:

[tex]sin^{2}(\theta)=1-cos^{2}(\theta)\\sin(\theta)=\pm \sqrt{1-cos^{2}(\theta)}[/tex]

Since, sine is negative in fourth quadrant, we will consider the negative value. Using the value of cosine, we get:

[tex]sin(\theta)=-\sqrt{1-(\frac{6\sqrt{85} }{85})^{2}}=-\frac{7\sqrt{85}}{85}[/tex]

e) Since,

[tex]cosec(\theta)=\frac{1}{sin(\theta)}[/tex]

Using the value of sine, we get:

[tex]cosec(\theta)=\frac{1}{-\frac{7\sqrt{85} }{85}}=-\frac{\sqrt{85}}{7}[/tex]

Answer:

  sin θ = 4/5

Step-by-step explanation:

The Pythagorean theorem tells you the distance (h) from the origin to the terminal point:

  h² = (-3)² +(4)² = 25

  h = 5 . . . . . . . . take the square root

The mnemonic SOH CAH TOA reminds you ...

  Sin = Opposite/Hypotenuse

For angles other than 1st-quadrant angles, it can sometimes be difficult to identify the relevant sides of the relevant triangle. If the angle were a 1st-quadrant angle, it would be clear that the side opposite the angle is the y-coordinate of the point on the terminal side. That remains the case for all angles. The hypotenuse is always the positive distance from the origin to the terminal point.

So, you have

  sin θ = opposite/hypotenuse = 4/5

Answer:

The value of a is 10 and the value of b is 6

Step-by-step explanation:

* Lets revise how to solve the problem

- Remember in the number with exponent

-  a^n × a^m = a^(n + m)

- a^n ÷ a^m = a^(n - m)

Lets solve the problem

∵ [tex]\frac{7^{2}.7x^{8}}{7x^{4}}[/tex]

- Lets use the rule above

∵ [tex]7^{2}.7^{8}=7^{2+8}=7^{10}[/tex]

∴ [tex]\frac{7^{2}.7^{8}}{x^{4}}=\frac{7^{10}}{7^{4}}[/tex]

∵ [tex]\frac{7^{10}}{7^{4}}=\frac{7^{a}}{7^{4}}[/tex]

∴ a = 10

∵ [tex]\frac{7^{10}}{7^{4}}=7^{10-4}=7^{6}[/tex]

∵ [tex]7^{6}=7^{b}[/tex]

∴ b = 6

* The value of a is 10 and the value of b is 6

Answer: 10 and 6 for the next one its 2, 3, and 8

Step-by-step explanation: i hope this helps :)

Answer:

In vertex form it's [tex]y=(x+7)^2-9[/tex]

In standard form it's [tex]y=x^2+14x+40[/tex]

Step-by-step explanation:

We can use the vertex form to solve for a in

[tex]y=a(x-h)^2+k[/tex]

"a" is the number out front that dictates the steepness, or lack thereof, in a parabola.  That means that we need h and k (which we have in the vertex) and we need x and y (which we have in the form of one of the zeros).  Filling in using a vertex of (-7, -9) and a coordinate point (-7, 0):

[tex]0=a(-4-(-7))^2-9[/tex] simplifies a bit to

[tex]0=a(-4+7)^2-9[/tex] simplifies a bit more to

[tex]0=a(3)^2-9[/tex] and

[tex]0=a(9)-9[/tex] so

[tex]0=9a-9[/tex],

[tex]9=9a[/tex] and finally,

a = 1

Phew!  So there is the a value.  Now we can simply fill in the formula completely, using the vertex as our guide:

[tex]y=(x+7)^2-9[/tex]

In standard ofrm that is

[tex]y=x^2+14x+40[/tex]

We can check ourselves for accuracy by factoring that standard polynomial using whatever method of factoring you like for quadratics and get that the roots are in fact x = -10, -4

The only reason we needed the zeros is to use one of them as the x and y to solve for a.  

Answer:

A).  (7, 0) The time it takes to empty the water in the  pool.

Step-by-step explanation:

If we extend the values we see that they are

x f(x)

5 10

5 5

7 0

So at time 7 minutes the pool is empty.

Answer:

(7, 0); the time it takes to empty the water in the pool

Step-by-step explanation:

The following table shows the amount of water leaking from an inflatable pool as a function of time:

x (time in minutes)    f(x)

0                            35

1                            30

2                            25

3                            20

4                             15

f(x) represents the amount of water in the pool. x intercept is the point where f(x) is 0 .At x intercept the amount of water in the pool is 0.

WE need to find out the point where f(x) becomes 0

F(x) is decreasing by 5. LEts extend the table till we get f(x) becomes 0

Decrease f(x) by 5

x (time in minutes)    f(x)

3                            20

4                             15

5                                  15-5=10

6                                  10-5=5

7                                   5-5=0

When x=7, f(x)=0. (7,0) is the x intercept.

(7, 0); the time it takes to empty the water in the pool

hihi! so the ratio 2:1:3 can be rewritten as 2/6 (red) 1/6 (blue) and 3/6 (yellow).

this is because you have 2 floz of red, 1 floz of blue, and 3 floz of yellow, which adds up to 6 floz of paint total in your ratio.

since you have 18 fl. oz. of paint, you multiply the ratio 3/6 by 18 to get 9 fl. oz. of yellow paint.

hope this helps!

There would be of 9 ounces yellow paint needed.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

The total quantity of fluid of paint= 18 ounces,

And the ratio of red, blue and yellow paint = 2:1:3

Let the multiplying factor in ratio is x,

So, total paint will be 6x,

According to given condition,

6x = 18 ounces,

x = 3 ounces

Since yellow paint is 3x,

So 3x = 9 ounces

9 ounces yellow paint is required,

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Answer:

The interest paid is $1575.

Step-by-step explanation:

Given is:

Monthly loan payment = $1857

Loan amount = $300000

Rate = 6.3% annual

So, monthly rate will be = [tex]6.3/12/100=0.00525[/tex]

Hence, we will calculate the interest for month.

[tex]0.00525\times300000=1575[/tex] dollars

So, interest paid = $1575.

Principle paid = [tex]1857-1575=282[/tex] dollars

Answer:

  p² > 4/3(1 -p)

Step-by-step explanation:

Assuming candy selections are independent from one to the next, the probability of getting Coffee Toffee twice in a row will be p². The probability of getting some other selection than Coffee Toffee will be 1-p.

Lisa wants ...

  p² > (4/3)(1 -p)

_____

This has solution p > 2/3.

Answer:

Step-by-step explanation:

Explanation:

Step 1: find the mean of the data

Step 2: subtract the mean from every data value

Step 3: find the absolute values of the differences from Step 2

Step 4: find the mean of the absolute values from Step 3. This is the MAD.

_____

The mean and absolute value have their usual definitions.

The mean is the sum of a set of numbers, divided by the number of numbers in the set.

The absolute value is the numerical value of a number with its sign changed to positive, if it isn't already. For example, |-1| = 1 and |1| = 1. The vertical bars signify the absolute value of their contents.

Step-by-step explanation:

The only exception to that is that when you have a negative outside of the absolute value symbol, you will get a negative answer.

Ex: -|3| = -3

I am joyous to assist you anytime.

Answer:

Choice A) [tex]F(x) = 3\sqrt{x + 1}[/tex].

Step-by-step explanation:

What are the changes that would bring [tex]G(x)[/tex] to [tex]F(x)[/tex]?

[tex]G(x) = \sqrt{x}[/tex]. The choices of [tex]F(x)[/tex] listed here are related to [tex]G(x)[/tex]:

The expression in the braces (for example [tex]x[/tex] as in [tex]G(x)[/tex]) is the independent variable.

To shift a function on a cartesian plane to the left by [tex]a[/tex] units, add [tex]a[/tex] to its independent variable. Think about how [tex](x-a)[/tex], which is to the left of [tex]x[/tex], will yield the same function value.

Conversely, to shift a function on a cartesian plane to the right by [tex]a[/tex] units, subtract [tex]a[/tex] from its independent variable.

For example, [tex]G(x+1)[/tex] is [tex]1[/tex] unit to the left of [tex]G(x)[/tex]. Conversely, [tex]G(x-1)[/tex] is [tex]1[/tex] unit to the right of [tex]G(x)[/tex]. The new function is to the left of [tex]G(x)[/tex]. Meaning that [tex]F(x)[/tex] should should add [tex]1[/tex] to (rather than subtract [tex]1[/tex] from) the independent variable of [tex]G(x)[/tex]. That rules out choice B) and D).

The graph of [tex]G(x)[/tex] is stretched vertically. However, similarly to the graph of this graph [tex]G(x)[/tex], the graph of [tex]F(x)[/tex] increases as [tex]x[/tex] increases. In other words, the graph of [tex]G(x)[/tex] isn't flipped about the [tex]x[/tex]-axis. [tex]G(x)[/tex] should have been multiplied by a number that is greater than one. That rules out choice C) and D).

Overall, only choice A) meets the requirements.

Since the plot in the question also came with a couple of gridlines, see if the points [tex](x, y)[/tex]'s that are on the graph of [tex]F(x)[/tex] fit into the expression [tex]y = F(x) = 3\sqrt{x - 1}[/tex].

Answer:

f(x) =3 sqrt(x+1)

Step-by-step explanation:

We notice two things about the graph, it has a shift to the left and is steeper

First the shift to the left

f(x) = g(x + C)  

C > 0 moves it left

C < 0 moves it right

g(x) is 0 at x=0   f(x) is 0 at  x=-1

We are moving it 1 unit to the left

This means our "c" is 1

f(x) = sqrt( x+1)

Now we need to deal with the graph getting steeper

f(x) = Cg(x)  

C > 1 stretches it in the y-direction

0 < C < 1 compresses it

Since it is getting taller, "c" must be greater than 1

Remember the - sign means it is a reflection across the x axis, which we do not have

f(x) =3 sqrt(x+1)

Answer:

<1 = 100

<2 = 80

Step-by-step explanation:

Angle 1 and angle 2 are supplementary

Supplementary angles add to 180 degrees

<1 + <2 = 180

The angles are in a ratio of 5 to 4

Multiply by x to get the measure of each angle

<1 = 5x  <2 = 4x

5x+4x = 180

Combine like terms

9x = 180

Divide by 9

9x/9 =180/9

x =20

<1 = 5x = 5*20 = 100

<2 = 4x = 4*20 = 80

Answer:

he's right

Step-by-step explanation:

or she i dont discriminate

Answer: 68.86 inches

Step-by-step explanation:

Given : In a survey of women in a certain country having

Mean : [tex]\mu=64.3\text{ inches}[/tex]

Standard deviation : [tex]\sigma=2.77\text{ inches}[/tex]

The z-value corresponds to 0.095 is 1.645.  [Using standard normal distribution table]

The height that represents the 95th percentile is given by :-

[tex]H=z\times\sigma+\mu\\\\=1.6449\times2.77+64.3=68.856373\approx68.86\text{ inches}[/tex]

Hence, the height represents the 95th ​percentile = 68.86 inches.

Answer:

95th ​percentile = 68.86 inches.

Step-by-step explanation:

Just took quiz :)

Answer:

  7 +1.25m = 43.25

Step-by-step explanation:

Let m represent the number of minutes on the trampoline. Then the charge (in dollars) for minutes you're on it is 1.25m. The entrance fee is added to that to give the total charges:

  7 + 1.25m = 43.25

Answer: 1.12

Step-by-step explanation:

The confidence interval for the mean [tex]\mu[/tex] and margin of error E is given by :-

[tex](\mu-E,\ \mu+E)[/tex]                                             --------------(1)

The given confidence interval : (0.21, 2.45)              -------------(2)

From (1) and (2), we  have

[tex]\mu-E=0.21-------(3)\\\\\mu+E=2.45--------(4)[/tex]

Subtract equation (3) from (4), we get

[tex]2E=2.45-0.21\\\\\Rightarrow\ 2E=2.24\\\\\Rightarrow\ E=\dfrac{2.24}{2}=1.12[/tex]

Hence, the margin of error is 1.12 .

The margin of error can be calculated as half the width of the confidence interval.

The margin of error can be calculated by finding half the width of the confidence interval. In this case, the confidence interval is (0.21, 2.45), so the width is 2.45 - 0.21 = 2.24. Therefore, the margin of error is half of this width, which is 2.24/2 =

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Answer:

That is known as a Vertex

A figure formed by two rays that share a common endpoint is known as an angle. The common endpoint is known as the vertex, while the rays are considered the sides of the angle.

In mathematics, a figure formed by two rays that share a common endpoint is known as an angle. The common endpoint is referred to as the vertex and the rays are referred to as the sides of the angle.

Rays in the context of angles means a straight line that starts from a point (vertex) and extends indefinitely in a particular direction. For example, in a page of a book when it is half open, the two visible pages represent the rays, and where the pages meet (the spine) represents the vertex.

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Answer:

x=15

Step-by-step explanation:

165+x=180

x=180-165

x=15

Answer:

15° = x

Step-by-step explanation:

By the Supplementary Angles Theorem, you add m<x by 165, and set that equal to 180°, or π. Of course you have to do the inverse of addition in order to get this, so deduct 165 from 180 to end up with 15.

Answer:

1. 2.12 seconds

2. 10 feet

Step-by-step explanation:

1. "Pekka tosses a ball out of a window that is 40 feet in the air.  Its initial velocity is 15 feet per second.  The path of the ball is represented by:

h = -16t² + 15t + 40

How long does it take for the ball to hit the ground (in seconds) rounded to the nearest hundredth?"

When the ball hits the ground, its height is 0:

0 = -16t² + 15t + 40

0 = 16t² − 15t − 40

Solve with quadratic formula:

t = [ -b ± √(b² − 4ac) ] / 2a

t = [ 15 ± √(225 + 2560) ] / 32

t ≈ 2.12 or -1.18

t must be positive, so t = 2.12 seconds.

2. "Tricia bounces a ball in front of her feet.  The path of the ball from the time it hits the ground until it lands on the floor is represented by:

f(x) = -2(x − 3)² + 10

Assuming that Tricia's feet are located at the origin (0, 0), what is the maximum height of the ball (in feet)?"

The function is a parabola.  The vertex of this parabola is at (3, 10).  So the maximum height is 10 feet.

Answer:

8.

Step-by-step explanation:

It's none of those. It is 8, because 8 is a factor of 40 ( and of 8 of course).

Answer:

none of the above.

Step-by-step explanation:

when we talk about greatest common factor of  8 x  and 40 y

8 x = 2× 2× 2 × x........................................(1)

40 y = 2 × 2 × 2 × 5 × y..............................(2)

when we see both equation (1) and (2 )

then we can clearly see

that the greatest common are 2 × 2 × 2

so, the greatest common will be 2 × 2 × 2 = 8

hence , the correct answer will be none of the above.

Answer:

  The supposition is incorrect.

Step-by-step explanation:

The growth rate of a child is not constant, so height versus time does not look like a straight line. Nothing is wrong with the prediction made using the false assumption. You can conclude anything you like when you start with a false premise.

Answer:

A) 420 seconds = 7 minutes

B) 8 times

Step-by-step explanation:

A) After how many second would all three things happen together again?

Solution:

His clock ticked every 5 seconds , a tap was dripping every 7 seconds and     his pet dog snored every 12 seconds. It all happens simultaneously = 5*7*12=420 seconds

B) How many times would all three things happen together again between    midnight and one o'clock

Since all these events happen together after every 420 sec = 7 mins and there are 60 mins between midnight and 1 o'çlock , thus 60/7 = 8 times ....

Answer:

Step-by-step explanation:

When the points designating each triangle are considered in order, they are seen to be in clockwise order. Segment FG is oriented to the west, while corresponding segment VW is oriented to the east. This means the figure could have been rotated 180° or reflected across a point. Either way, some translation may be necessary to align the figures as shown.

Possible transformations include ...

___

If one of the triangles is reflected across the midpoint of GW, it will coincide with the other triangle. Hence only one reflection across a chosen point is required. Of course, reflection across a point is identical to rotation 180° about that point. For any other point of reflection or rotation, translation will be involved.

Answer:

rotation, then translation

Step-by-step explanation:

rotation, then translation

Answer:

Test statistic = z = 1.01264

Step-by-step explanation:

p = 0.25

q = 1 - p = 0.75

n = 520

x = 140

[tex]psample = \frac{x}{n} = \frac{140}{520} = 0.26923[/tex]

[tex]z = \frac{psample - p}{\sqrt{\frac{p*q}{n} } } =\frac{0.26923 - 0.25}{\sqrt{\frac{0.25 * 0.75 }{520} } } = \frac{0.01923}{\sqrt{\frac{0.1875}{520} } } = \frac{0.01923}{\ 0.01899} = 1.01264[/tex]

Answer:

18 cubic units

Step-by-step explanation:

There are 18 cubic units in a box that is 3 units high.

3 x 3 = 6

6 x 2 = 18