Based on a poll of 200 citizens, a community action group claims that 40% of the population is in favor of a curfew for children under 18 on weekday nights. A local parent group claims that the poll is not valid and that only 22% of the citizens favor a curfew. To determine whether this sample supports the population proportion of 0.40, a simulation of 100 trials is run, each with a sample size of 50 and a point estimate of 0.22. The minimum sample proportion from the simulation is 0.15, and the maximum sample proportion from the simulation is 0.27. The margin of error of the population proportion is found using an estimate of the standard deviation. What is the interval estimate of the true population proportion?

Answer:

The relationship is linear; y – 5 = 5/4*(x – 1)

Step-by-step explanation:

We have been given the following data set;

x: 1, 5, 9, 13

y: 5, 10, 15, 20

The values of x increase by 4 while those of y increase by 5. This would imply that the average rate of change between any pair of points is a constant and thus the relationship exhibited by the data is linear.

The average rate of change is equivalent to the slope;

(change in y) / (change in x)

Using the first two pair of points we have;

(10-5) / ( 5-1) = 5/4

The point-slope form of equation of the line is thus;

y - 5 = 5/4 (x - 1)

Answer:

B. 60

Step-by-step explanation:

The opposite sides of a parallelogram are parallel and congruent.

This implies that:

|UV|=|XW|

From the diagram; |UV|=15

and [tex]|XW|=\frac{1}{4}y[/tex]

We equate the two side lengths to get:

[tex]15=\frac{1}{4}y[/tex]

We multiply both sides by 4 to obtain:

[tex]4\times 15=4\times \frac{1}{4}y[/tex]

This implies that:

y=60

Answer:

B!

Step-by-step explanation:

Answer:

Part 1) [tex]sin(\theta)=\frac{\sqrt{10}}{10}[/tex]

Part 2) [tex]cos(\theta)=-3\frac{\sqrt{10}}{10}[/tex]

Part 3) [tex]tan(\theta)=-1/3[/tex]

Step-by-step explanation:

we know that

The angle is in the second quadrant  so the sine is positive, the cosine is negative and the tangent is negative

step 1

Find the radius r applying the Pythagoras theorem

[tex]r^{2}=x^{2} +y^{2}[/tex]

substitute the given values

[tex]r^{2}=(-3)^{2} +(1)^{2}[/tex]

[tex]r^{2}=10[/tex]

[tex]r=\sqrt{10}\ units[/tex]

step 2

Find the value of [tex]sin(\theta)[/tex]

[tex]sin(\theta)=y/r[/tex]

substitute values

[tex]sin(\theta)=1/\sqrt{10}[/tex]

Simplify

[tex]sin(\theta)=\frac{\sqrt{10}}{10}[/tex]

step 3

Find the value of [tex]cos(\theta)[/tex]

[tex]cos(\theta)=x/r[/tex]

substitute values

[tex]cos(\theta)=-3/\sqrt{10}[/tex]

Simplify

[tex]cos(\theta)=-3\frac{\sqrt{10}}{10}[/tex]

step 4

Find the value of [tex]tan(\theta)[/tex]

[tex]tan(\theta)=y/x[/tex]

substitute values

[tex]tan(\theta)=-1/3[/tex]

Answer:

In the figures attached, the complete question is shown.

What is the difference between a minor arc and a major arc?

the measure of a minor arc is less than 180°

the measure of a major arc is greater than 180°

How many letters do we use to name a MINOR arc? 2

How many letters do we use to name a MAJOR arc? 3

How many degrees are in a semi-circle? 180°

How many letters to name a SEMI CIRCLE? 3

1. Name of arc: AB Type of arc: minor

2. Name of arc: ADB Type of arc: major

3. Name of arc: PSQ  Type of arc: semi-circle

4. AE: minor

5. AEB: semi-circle

6. FDE: semi-circle

7. DFB: major

8. FA: minor

9. BE: minor

10. BDA: semi-circle

11. FBD: major

12. PQ and ST

13. QPT and  PUS

14. PUT and QPU

15. There are 360° degrees in a circle.

16. There are 180° degrees in a semi-circle.

17. The measure of the arc is equal to the measure of the central angle.

18. mPQ: 50°, mPXQ: 310°

19. mPQ: 90° , mPRQ: 270°

20. mPQ: 150° , mPXQ: 210°

21. mQS: 45°, mQRS: 315°

22. mGH: 30°, mGFH: 330°

23. mAB: 75°, mADB: 285°

Answer:

y = 4

That's a straight line.

The slope is 0.

There is no x-intercept.

The y-intercept is 4.

I'm only a few Brainliests away from ranking up, so one would be much appreciated. Thank you, and good luck!

Answer:

the slope is 0

the x intercept is 0

the y intercept is 4

Answer:

Option C. 44 degree

Step-by-step explanation:

Let

A-----> the angle of the elevation of the sun

we know that

The tangent of angle A is equal to divide the opposite side angle A by the adjacent side angle A

In this problem

The opposite side is 30 meters

The adjacent side is 31 meters

[tex]tan(A)=\frac{30}{31}[/tex]

[tex]A=arctan(\frac{30}{31})=44\°[/tex]

Answer:

Final answer is approx 6.644 years.

Step-by-step explanation:

Given that a company sold 5.75 million motorcycles and 3.5 million cars in the year 2010. The growth in the sale of motorcycles is 16% every year and that of cars is 25% every year.

So we can use growth formula:

[tex]A=P\left(1+r\right)^t[/tex]

Then we get equation for motorcycles and cars as:

[tex]A=5.75\left(1+0.16\right)^t[/tex]

[tex]A=3.5\left(1+0.25\right)^t[/tex]

Now we need to find about when the sale of cars will be more than the sale of motorcycles. So we get:

[tex]3.5\left(1+0.25\right)^t>5.75\left(1+0.16\right)^t[/tex]

[tex]3.5\left(1.25\right)^t>5.75\left(1.16\right)^t[/tex]

[tex]3.5\left(1.25\right)^t>5.75\left(1.16\right)^t[/tex]

[tex]\frac{\left(1.25\right)^t}{\left(1.16\right)^t}>\frac{5.75}{3.5}[/tex]

[tex]\left(\frac{1.25}{1.16}\right)^t>1.64285714286[/tex]

[tex]t\cdot\ln\left(\frac{1.25}{1.16}\right)>\ln\left(1.64285714286\right)[/tex]

[tex]t>\frac{\ln\left(1.64285714286\right)}{\ln\left(\frac{1.25}{1.16}\right)}[/tex]

[tex]t>6.6436473051[/tex]

Hence final answer is approx 6.644 years.

Final answer:

To determine when car sales will surpass motorcycle sales given their growth rates, we use exponential growth formulas for both, set them equal to find the crossover point, and solve for the time required.

Explanation:

To find when the sale of cars will be more than the sale of motorcycles given their respective annual growth rates, we'll use the concept of exponential growth.

The initial sale of motorcycles is 5.75 million with an annual growth rate of 16%, and the initial sale of cars is 3.5 million with an annual growth rate of 25%. We will set up an equation where the sales of cars equals the sales of motorcycles and solve for the number of years it takes for this to occur.

The formula for exponential growth is:

Final Amount = Initial Amount × (1 + Growth Rate) ^ Years

For motorcycles, the formula becomes:

M = 5.75 × (1 + 0.16)^t

For cars, the formula becomes:

C = 3.5 × (1 + 0.25)^t

We want to find when C > M, so we set the formulas equal to each other and solve for t:

5.75 × (1 + 0.16)^t = 3.5 × (1 + 0.25)^t

After finding a common base and applying logarithms, we can solve for t, the number of years until the sale of cars surpasses that of motorcycles.

Answer:

x = 74°

Step-by-step explanation:

The angle whose vertex lies on the circle, that is angle x is one- half the measure of it's intercepted arc, that is

x = 0.5 × 148° = 74°

Answer:

  x = √5

Step-by-step explanation:

The Pythagorean theorem tells you the square of the diagonal is the sum of the squares of the two sides:

  (√7)² = (√2)² + x²

  7 = 2 + x² . . . . . . simplify

  5 = x² . . . . . . . . . subtract 2

  √5 = x . . . . . . . . . take the square root

Answer:

x = 8.3

Step-by-step explanation:

Given a tangent and 2 secants drawn to the circle from an external point then

The square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant.

Using the secant with measure 4 + x, then

4(4 +x) = 7²

16 + 4x = 49 ( subtract 16 from both sides )

4x = 33 ( divide both sides by 4 )

x = 33 ÷ 4 = 8.25 ≈ 8.3 ( nearest tenth )

Answer:

B. 4n+2

Step-by-step explanation:

You are given the pattern 6, 10, 14, 18, 22

Rewrite it as

[tex]a_1=6\\ \\a_2=10\\ \\a_3=14\\ \\a_4=18\\ \\a_5=22[/tex]

Note that

[tex]a_2-a_1=a_3-a_2=a_4-a_3=a_5-a_4=4[/tex]

This means that given pattern is a part of arithmetic sequence with

[tex]a_1=6\\ \\d=4[/tex]

So, the nth term of this arithmetic sequence is

[tex]a_n=a_1+(n-1)d\\ \\a_n=6+4(n-1)\\ \\a_n=6+4n-4\\ \\a_n=4n+2[/tex]

Answer:

[tex]A=\$164,944.20[/tex]

Step-by-step explanation:

we know that

[tex]A=V(1+r)^{Y}[/tex]

In this problem we have

[tex]r=5\%=0.05[/tex]

[tex]V=\$135,700[/tex]

[tex]Y=4\ years[/tex]

substitute in the formula and solve for A

[tex]A=\$135,700(1+0.05)^{4}=\$164,944.20[/tex]

Answer:

Here's what I get.

Step-by-step explanation:

Question 10

The general equation for a sine function is

y = a sin[b(x - h)] + k

Here's what the parameters control:

a = amplitude

k = vertical shift

b = the period (period = 2π/b; If period = 2π/3, b = 3)

h = horizontal shift

Reflect across y-axis (x ⟶ -x)

Your sine function will be:

[tex]\begin{array}{rllll}y = & a \text{ sin}[ & b(x- & h)] + & k)\\& \downarrow & \downarrow & \downarrow & \downarrow\\& 4 & 3 & \frac{\pi}{4} & 3\\\end{array}[/tex]

Here are the effects of each parameter.

(a) Amp = 4

Increases the amplitude by a factor of 4 (Fig. 1)

(b) Up 3

k = 3. The graph shifts up three units (Fig. 2).

(c) Period = 2π/3

Set k = 3. The period changes from 2π to 2π/3 (Fig. 3).

Notice that you now hav3 three waves between 0 and 2π, where originally you had one.

(d) Right π/4.

Set h = 4. The graph shifts right by π/4.

notice how the trough at ½π shifts to ¾π.

(e) Reflect about y-axis

Set x equal to -x. Notice how the trough at (¾π, -1) is transformed to the trough at (-¾π, -1) (Fig. 5).

Question 12

y = a cos[b(x - h)] + k

a = 2

Per = 10π/3 ⟶ b = 3/5

h = 0

k = 0

Reflect over x-axis: y ⟶ -y

(a) a = 2

The amplitude is doubled.

(b) Per = 10π/3 ⟶ b = 3/5

The period (peak-to-peak distance) lengthens to 10π/3.

(c) Reflect about x-axis (y ⟶ -y)

All peaks are transformed into troughs and vice-versa.

Answer:

Part 4) [tex]sin(\theta)=\frac{12}{13}[/tex]

Part 10) The angle of elevation is [tex]40.36\°[/tex]

Part 11) The angle of depression is [tex]78.61\°[/tex]

Part 12) [tex]arcsin(0.5)=30\°[/tex]  or [tex]arcsin(0.5)=150\°[/tex]

Part 13) [tex]-45\°[/tex]  or [tex]225\°[/tex]

Step-by-step explanation:

Part 4) we have that

[tex]cos(\theta)=-\frac{5}{13}[/tex]

The angle theta lies in Quadrant II

so

The sine of angle theta is positive

Remember that

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

substitute the given value

[tex]sin^{2}(\theta)+(-\frac{5}{13})^{2}=1[/tex]

[tex]sin^{2}(\theta)+(\frac{25}{169})=1[/tex]

[tex]sin^{2}(\theta)=1-(\frac{25}{169})[/tex]  

[tex]sin^{2}(\theta)=(\frac{144}{169})[/tex]

[tex]sin(\theta)=\frac{12}{13}[/tex]

Part 10)

Let

[tex]\theta[/tex] ----> angle of elevation

we know that

[tex]tan(\theta)=\frac{85}{100}[/tex] ----> opposite side angle theta divided by adjacent side angle theta

[tex]\theta=arctan(\frac{85}{100})=40.36\°[/tex]

Part 11)

Let

[tex]\theta[/tex] ----> angle of depression

we know that

[tex]sin(\theta)=\frac{5,389-2,405}{3,044}[/tex] ----> opposite side angle theta divided by hypotenuse

[tex]sin(\theta)=\frac{2,984}{3,044}[/tex]

[tex]\theta=arcsin(\frac{2,984}{3,044})=78.61\°[/tex]

Part 12) What is the exact value of arcsin(0.5)?

Remember that

[tex]sin(30\°)=0.5[/tex]

therefore

[tex]arcsin(0.5)[/tex] -----> has two solutions

[tex]arcsin(0.5)=30\°[/tex] ----> I Quadrant

or

[tex]arcsin(0.5)=180\°-30\°=150\°[/tex] ----> II Quadrant

Part 13) What is the exact value of [tex]arcsin(-\frac{\sqrt{2}}{2})[/tex]

The sine is negative

so

The angle lies in Quadrant III or Quadrant IV

Remember that

[tex]sin(45\°)=\frac{\sqrt{2}}{2}[/tex]

therefore

[tex]arcsin(-\frac{\sqrt{2}}{2})[/tex] ----> has two solutions

[tex]arcsin(-\frac{\sqrt{2}}{2})=-45\°[/tex] ----> IV Quadrant

or

[tex]arcsin(-\frac{\sqrt{2}}{2})=180\°+45\°=225\°[/tex] ----> III Quadrant

Answer:

[tex]\boxed{5x^{11}, x < 0}[/tex]

Step-by-step explanation:

[tex]5\sqrt{x^{22}}[/tex]

Remember that we evaluate the term under the radical first.

Even though x < 0, x²² > 0

So,

[tex] 5\sqrt{x^{22}} = 5x^{11}[/tex]

The simplified expression is

[tex]\boxed{5x^{11}, x < 0}[/tex]

Answer:

20, 26, 35, 18

Step-by-step explanation:

So starting at row 129, we look at the sequence two-digits at a time without overlapping.  If that number is between 01 and 43, then they get selected.

The first two digits are 20.  That fits between 01 and 43, so that member gets selected.

Next, we have 26.  That also fits.

After that we have 64.  Nope, too high.

98 and 44 are also too high.

35 fits though.  So does 18.

So the members that get selected are 20, 26, 35, 18.

[tex]C=2\pi r =2\pi10=20\pi\approx\boxed{62.8}[/tex]

The answer is D.

The circumference of a circle with a radius of 10 inches is approximately 62.8 inches, calculated using the formula C = 2πr, resulting in the answer choice D. 62.8.

To calculate the circumference of a circle when the radius is given, we use the formula C = 2πr. Given that the radius (r) of the circle is 10 inches, we can calculate the diameter (d) as 2×10 inches, which equals 20 inches. Now, we multiply the diameter by π (approximately 3.1416) to find the circumference:

C = πd = 3.1416 × 20 inches = 62.832 inches.

Based on standard rounding rules, this is approximately 62.8 inches. Thus, the correct answer is D. 62.8 square inches.

The answere is 213 boxes

If you add 3 dozens to 14 dozens of boxes of envilopes , then you get 17 dozens of boxes of envilopes.Then of you sum up the 1/2 (2/4 ) with the 1/4.You get 3/4. Finally, you add 17 dozens to 3/4 of a dozen you get 17 3/4 dozens( wich is 213 boxes )

Answer:

b.  .897x - 3.790 (that's in slope-intercept form; same thing as putting the y-intercept first)

Step-by-step explanation:

On your calculator, hit the "stat" button.  Hit #4 to "ClrList", then hit 2nd and the number 1 to clear the list in L1.  Then do the same to clear the list in L2.  Hit #4, then hit 2nd and the number 2 to clear the list in L2.

Hit "stat" then 1 (edit) and you'll be at your table to enter the values.  Use the left arrow key if needed to make sure you're entering your first values under column L1, which is our x values.  Enter one at a time, hitting "enter" after each, even the last one.  Then arrow over to the right and enter the y values one at a time under L2.  Hit enter after each, even the last one.  When you're done, hit "stat" again and arrow over to "calc".  If you have a TI 83, choose "4:LinReg" and hit "enter".  If you have a TI 84+, you will have to arrow down to choose "calculate".  When the word "calculate" is highlighted, hit enter and you'll have your equation!

  Equation of the regression line for the data given will be represented by the equation given in option B.  

    By using the utility for the regression line of the given data, equation of the regression line will be,

y = 0.89745x - 3.79005

y = 0.897x - 3.79

Or y = -3.79 + 0.897x

   Therefore, equation of the regression line given in option B will be the answer.

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Answer:

Step-by-step explanation:

number3

Answer:

There are 13 boys in Mr. Marshals class

Step-by-step explanation:

Hello there! Mr. Marshal has 9 boys.

To find the number of boys Mr. Marshal has, start by finding the ratio. If there are 6 boys and 14 girls, the boys to girls ratio is 6:14. Simplified, the ratio is 3:7. So, if there are 21 girls, you want to find how many boys there are. To find this, find what you need to multiply 7 by to get 21 by and multiply 3 by that number.

21/7 = 3.

So, now we multiply 3 by 3 to get the number of boys.

3 x 3 = 9.

This means there are 9 boys, with a ratio of 9:21. If we simplify this, we get 3:7, making this answer correct.

I hope this helps and have a great day!

Answer: The volume is about 226 feet squared

Step-by-step explanation:

Answer:

The measure of angle y is [tex]m\angle y=54\°[/tex]

Step-by-step explanation:

we know that

The inscribed angle is half that of the arc it comprises.

[tex]m\angle y=\frac{1}{2}(108\°)=54\°[/tex]

The answer is does matter.

What we have here is called INTERSECTING CHORDS IN A CIRCLE.

The equation is:

10 times x = 7 times 7

10x = 49

x = 49/10

x = 4.9

answer 4.9cm

10times x=7times7(multiple it)

10x=49

x=49/10

x=4.9

Answer:

28

Step-by-step explanation:

If we set up our equation using the unknown number of hot dogs and corn dogs with their individual prices attached to them, we can set the sum of them equal to $201.  We know that a hot dog costs $3, so we can represent hot dogs monetarily by attaching the cost of a single hot dog to the h.  For example, if a hot dog costs $3, and we represent the expression as 3h, with h being the number of hot dogs sold, if we sell 4 hot dogs at $3 apiece, we make $12.  If we sell 6 hot dogs we will make $18.  The same goes for the corn dogs.  We don't know how many corn dogs or hot dogs we sold, but we do know that the sales of both made $201.  So our expression for that is

3h + 1.50c = 201

That's great, but we have too many unknowns, and that's a problem.  So let's look back up to where we are told that the number of hot dogs is 3 less than 2 times the number of corn dogs.  "3 less than" is -3 algebraically.  "Twice the number" is 2times  and the words "is" and "was" represent the = sign.  So putting those words into an algebraic equation looks like this:

h = 2c - 3

That says "the number of hot dogs was twice the number of corn dogs less 3".  Now that we have an expression for hot dogs we can sub it into our money equation in place of h:

3h + 1.5c = 201 becomes 3(2c - 3) + 1.5c = 201

Now we have an equation with only c's in it.  

Distribute through the parenthesis to get

6c - 9 + 1.5c = 201

Simplify to 7.5c = 210

Now divide by 7.5 to get that c = 28.

Now that we know that, we go back with that number and sub it in for c in

h = 2c - 3 -->  h = 2(28) - 3 gives us that the number of hot dogs sold was 53

The total number of corn dogs sold is 28 corn dogs and number of hotdogs is 53

let

h = number of hotdogs

c = number of corndogs.

cost of hotdog = $3

corn dog = $1.50

The equation:

3h + 1.50c = 201 (1)

h = 2c - 3 (2)

substitute (2) into (1)

3(2c - 3) + 1.50c = 201

6c - 9 + 1.50c = 201

7.50c - 9 = 201

7.50c = 201 + 9

7.50c = 210

c = 210/7.50

c = 28

Therefore,

h = 2c - 3

= 2(28) - 3

= 56 - 3

= 53

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Answer:

  1,417.64 km³

Step-by-step explanation:

The formula for the volume of a cylinder in terms of its diameter is ...

  V = (π/4)d²·h

Fill in the given numbers and do the arithmetic.

  V = π/4×(19 km)²×(5 km) ≈ 1,417.64 km³

The volume of a cylinder is found using the formula V = πR²h. To find the radius, we divide the diameter by 2, giving us 9.5 km. The volume is therefore approximately 1413.716 km³.

To find the volume of a cylinder, we use the formula: V = πR²h. In this case, we are given the diameter and height of the cylinder. The diameter is double the radius, so to find the radius, we divide the diameter (19km) by 2, which gives us 9.5km. Substitute the radius and height into the formula, we get: V = π * (9.5 km)² * 5 km.

Now, we can calculate it. π is approximately 3.14159, (9.5 km)² equals 90.25 km², and multiply it all together with the height (5 km), we get approximately 1413.716 km³.

This is the volume of the cylinder.

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Answer:

The balance of Dianne's register should be $359.41

Step-by-step explanation:

We can begin at the ending balance on the bank statement at $578.30

Then a check is written for $219.25, so a debit

Next a deposit is made for $140.36, so a credit

Then a withdrawal is made for $140.00, so a debit

This means we can make the equation

[tex]578.30-219.25+140.36-140.00=359.41[/tex]

Answer:

-11, 11

Step-by-step explanation:

You have to find when the function crosses the x-axis. You could find this using algebra by solving for x in the equation but I prefer to simply graph it using something like desmos and see when it crosses the x-axis. Doing that I can see the answers would be -11 and 11

Answer:

x = -11,11

Step-by-step explanation:

G(x)=4x^2-484

To find the zero's, set the function equal to zero

0 = 4x^2 - 484

Add 484 to each side

484 = 4x^2 -484+484

484 = 4x^2

Divide each side by 4

484/4 = 4x^2/4

121 = x^2

Take the square root of each side

sqrt(121) = sqrt(x^2)

±11 =x

x = -11,11

Answer:

3x^2+2x-1

Step-by-step explanation:

Start by plugging in the 2 equations into their assigned places then simplify.

Answer:14

Step-by-step explanation:( 3X2+1)-(1-X)

=3X2+1 -1+X

=3X2+X

ANY WHERE WE SEE X WE PLACE 2

=3(2)(2)+2

3*4+2

=12+2

14