The radius of circle is 11 miles. What is the area of a sector bounded by a
300° arc?

Complete Question

According to a study done by the Gallup organization, the proportion of Americans who are satisfied with the way things are going in their lives is 0.82. Suppose a random sample of 100 Americans is asked "Are you satisfied with the way things are going in your life?"

What is the probability the sample proportion who are satisfied with the way things are going in their life is greater than 0.85

Answer:

The probability is  [tex]P(X > 0.85 ) = 0.21745[/tex]

Step-by-step explanation:

From the question we are told that

   The population proportion is [tex]p = 0.82[/tex]

   The value considered is  x  =  0.85

     The  sample size is  n = 100

The standard deviation for this population proportion is evaluated as

        [tex]\sigma = \sqrt{\frac{p(1-p)}{n} }[/tex]

substituting values

       [tex]\sigma = \sqrt{\frac{0.82(1-0.82)}{100} }[/tex]

      [tex]\sigma = 0.03842[/tex]

Generally the probability that probability the sample proportion who are satisfied with the way things are going in their life is greater than x is mathematically represented as

       [tex]P(X > x ) = P( \frac{X - p }{ \sigma } > \frac{x - p }{ \sigma } )[/tex]

Where  [tex]\frac{X - p }{ \sigma }[/tex] is  equal to Z (the  standardized value of X ) so  

         [tex]P(X > x ) = P( Z> \frac{x - p }{ \sigma } )[/tex]

substituting values

        [tex]P(X > 0.85 ) = P( Z> \frac{ 0.85 - 0.82 }{ 0.03842 } )[/tex]

        [tex]P(X > 0.85 ) = P( Z> 0.78084)[/tex]

from the standardized normal distribution table [tex]P( Z> 0.78084)[/tex] is  0.21745

So  

      [tex]P(X > 0.85 ) = 0.21745[/tex]

Answer:

Option E

Step-by-step explanation:

y = x /3

let x = 1, 2, 3

y = 0.333, 0.667, 1

y = x/2 + 40

let x = 1, 2, 3

y = 40.5, 41, 41.5

y = x

let x = 1, 2, 3

y = 1, 2, 3

y = 2x + 50

let x = 1, 2, 3

y = 52, 54, 56

y = 3x - 20

let x = 1, 2, 3

y = -17, -14, -11

The standard deviation is the spread of data, the data that is most spread is option E.

Answer:

x + 2y = 6

2y = -x + 6

y = -1/2x + 3

So, you will have a downward sloping, less steep line with an intercept at (0, 3).

You can use the Math is Fun Function Grapher and Calculator to graph the line.

Hope this helps!

Answer:

The  sample needed is  [tex]n =150[/tex]

Step-by-step explanation:

From the question we are told that

   The margin of error is  [tex]E = 0.08[/tex]

   The confidence level is  [tex]C = 95 \% = 0.95[/tex]

Given that the confidence level is  95% the level of significance is mathematically represented as

          [tex]\alpha = 1 - 0.95[/tex]

           [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the z-table , the value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

The reason we are obtaining critical value of    [tex]\frac{\alpha }{2}[/tex] instead of    [tex]\alpha[/tex] is because  

[tex]\alpha[/tex] represents the area under the normal curve where the confidence level interval (   [tex]1-\alpha[/tex] ) did not cover which include both the left and right tail while  

[tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the margin of error

The sample size is mathematically represented as    

            [tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \r p[1-\r p][/tex]

Here [tex]\r p[/tex] is sample proportion of people that supported her and we will assume this to be 50% =  0.5

So

            [tex]n = [\frac{1.96}{ 0.08} ]^2 * [0.5 (1- 0.5)][/tex]

           [tex]n =150[/tex]

Answer:

0.5 seconds and 1.5 seconds.

Step-by-step explanation:

h(t) = -16t^2 + 32t + 2

14 = -16t^2 + 32t + 2

16t^2 - 32t - 2 + 14 = 0

16t^2 - 32t + 12 = 0

8t^2 - 16t + 6 = 0

4t^2 - 8t + 3 = 0

(2x - 3)(2x - 1) = 0

2x - 3 = 0

2x = 3

x = 3/2

x = 1.5

2x - 1 = 0

2x = 1

x = 1/2

x = 0.5

So, the ball was at 14 feet at 0.5 seconds and 1.5 seconds.

Hope this helps!

Answer:

D. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.

Step-by-step explanation:

Correct answer is in bold. Incorrect answer have the mistakes put between stars ***   ***.

50 POINTS!!!! I ALSO GIVE BRAINLIEST, BUT YOU HAVE TO ANSWER QUICK Choose the correct graph of the given system of equations. A pair of linear equations is shown: y = −x + 1 y = 2x + 4 Which of the following statements best explains the steps to solve the pair of equations graphically?

A. On a graph, plot the line y = −x + 1, which has y-intercept = ***−1*** and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution.

B. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = ***1***, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution.

C. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = ***−2*** and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.

D. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.

Answer:

y = -4

Step-by-step explanation:

4x + 5y = -12 ....eq1

-2x + 3y = -16 ...eq2

From eq1, solve for x:

4x + 5y = -12

4x = -12 - 5y

x = -12 - 5y/4

From eq2, substitute value of x:

-2(-12-5y/4) + 3y = -16

3y - 2 (-5y-12/4) = -16

3y - 2(-5y-12)/4 = -16

12y - 2(-5y - 12) = -16

4*3y - 4*2(-5y-12)/4 = 4*(-16)

12y - 2(-5y-12) = -64

12y + 10y + 24 = -64 (divide both sides by common factor 2)

6y + 5y + 12 = -32

11y = -32 - 12

11y = -44

Divide both sides by 11

11y/11 = -44/11

y = -4

Answer:

Below

Step-by-step explanation:

The average speed is given by the following formula:

● V = d/t

● d is the distance covered

● t is the time spent to cover the distance d

■■■■■■■■■■■■■■■■■■■■■■■

Ava takes 8 minutes to go from mile marker 0 to mile marker6.

● the distance Ava traveled is 6 miles

● the time Ava spent to reach mile marker 6 is 8 minutes

So the average speed of Ava is:

● V = 6/ 8 = 3/4 = 0.75 mile per min

●●●●●●●●●●●●●●●●●●●●●●●●

Let's The equation of the line that links the number of milemarkers (n) and the time (t).

Ava went from mile marker 0 to mile marker 6.

At t=0 Ava just started travelling from mile marker 0 to 1.

Afrer 8 minutes,she was at mile marker 6.

So 8 min => 6 mile markers (igonring mile marker 0 since the distance there was 0 mile)

6/8= 0.75

Then n/t = 0.75

● n = 0.75 * t

Let's check

● n= 0.75*4 = 3

That's true since after 4 minutes Ava was at mile marker 3.

Complete question:

The line graph relating to the question was not attached. However, the line graph has can be found in the attachment below.

Answer:

17,209

Step-by-step explanation:

The line graph provides information about alcohol-related highway fatalities between year 2001 to 2010.

Determine the average number of alcohol-related fatalities from 2001 to 2006. Round to the nearest whole number.

The average number of alcohol related fatalities between 2001 - 2006 can be calculated thus :

From the graph:

Year - - - - - - - - - - Number of fatalities

2001 - - - - - - - - - - 17401

2002 - - - - - - - - -  17525

2003 - - - - - - - - -  17013

2004 - - - - - - - - - 16694

2005 - - - - - - - - - 16885

2006 - - - - - - - - - 17738

To get the average :

Sum of fatalities / number of years

(17401 + 17525 + 17013 + 16694 + 16885 + 17738) / 6

= 103256 / 6

= 17209.333

Average number of alcohol related fatalities is 17,209 (to the nearest whole number)

Correct question:

A motorcycle stunt rider jumped across the Snake River. The path of his motorcycle was given

approximately by the function H(t) = - 0.0004.x2 + 2.582 + 700, where H is measured in

feet above the river and is the horizontal distance from his launch ramp.

How high above the river was the launch ramp?

What was the rider's maximum height above the river, and how far was the ramp when he reached maximum height?

Answer:

A) 700 feet ; 4866.7025 feet above the river

3227.5 Feets from the ramp

Step-by-step explanation:

Given the Height function:

H(t) = 0.0004x^2 + 2.582x + 700

H = height in feet above the river

x = horizontal distance from launch ramp.

How high above the river was the launch ramp?

H(t) = - 0.0004x^2 + 2.582x + 700

To find height of launch ramp above the river, we set the horizontal distance to 0, because at this point, the motorcycle stunt rider is on the launch ramp and thus the value of H when x = 0 should give the height of the launch ramp above the river.

At x = 0

Height (H) =

- 0.0004(0)^2 + 2.582(0)+ 700

0 + 0 + 700 = 700 Feets

B) Maximum height abive the river and how far the rider is from the ramp when maximum height is reached :

Taking the derivative of H with respect to x

dH'/dx = 2*-(0.0004)x^(2-1) + 2.582x^(1-1) + 0

dH'/dx = 2*-(0.0004)x^(1) + 2.582x^(0) + 0

dH'/dx = - 0.0008x + 2.582

Set dH'/dx = 0 and find x:

0 = - 0.0008x + 2.582

-2.582 = - 0.0008x

x = 2.582 / 0.0008

x = 3227.5 feets

To get vertical position at x = 0

Height (H) =

- 0.0004(3227.5)^2 + 2.582(3227.5)+ 700

- 4166.7025 + 8333.405 + 700

= 4866.7025 feet

4866.7025 feet above the river

3227.5 Feets from the ramp

Using quadratic function concepts, it is found that:

The height after x seconds is given by the following equation:

[tex]H(x) = -0.0004x^2 + 2.582x + 700[/tex]

Which is a quadratic equation with coefficients [tex]a = -0.0004, b = 2.582, c = 700[/tex]

The height of the ramp is the initial height, which is:

[tex]H(0) = -0.0004(0)^2 + 2.582(0) + 700 = 700[/tex]

Thus, the launch ramp was 700 feet above the river.

The maximum height is the h-value of the vertex, given by:

[tex]h_{MAX} = -\frac{\Delta}{4a} = -\frac{b^2 - 4ac}{4a}[/tex]

Then, substituting the coefficients:

[tex]h_{MAX} = -\frac{(2.582)^2 - 4(-0.0004)(700)}{4(-0.0004)} = 4866.7[/tex]

The maximum height is of 4866.7 feet.

The horizontal distance is the x-value of the vertex, given by:

[tex]x_V = -\frac{b}{2a} = -\frac{2.582}{2(-0.0004)} = 3227.5[/tex]

The ramp was 3227.5 feet along when he reached maximum height.

A similar problem is given at https://brainly.com/question/24705734

Answer:

You didn't put an attachment to show what solid you wanted rounded

Step-by-step explanation:

Answer:  12 Tbsp

Step-by-step explanation:

Note: 1 Tbsp = 3 tsp

2 tsp x 21 = 42 tsp

42 tsp ÷ 3 = 12 Tbsp

Answer:

x should equal 1

Step-by-step explanation:

(1*129)-3=126

129-3=126

126=126

Answer:

x=1

Step-by-step explanation:

We can start by adding 3 to both sides to get rid of the -3

That leaves us with 129x=129

It ends up working out really evenly because by dividing both sides by 129, we are left with x=1

Answer: 7.5 ounces of  7% acid solution is mixed with 12.5 ounces of 23% acid solution to obtain 20 oz of a 17% acid solution.

Step-by-step explanation:

Let x = Ounces of 7% acid solution

y=  Ounces of 23% acid solution

According to the question , we have two linear equations:

x+y=20    

i.e. y=20-x  ...(i)

0.07 x+ 0.23y =0.17 (20)

i.e.  0.07x+0.23y= 3.4 ...(ii)

Substitute value of y from (i) in (ii) , we get

0.07x+0.23(20-x)= 3.4

⇒ 0.07x+4.6-0.23x=3.4   [distributive property]

⇒ 0.07x-0.23x=3.4-4.6 [subtract 4.6 from both sides]

⇒ -0.16x=-1.2

⇒  x = 7.5    [divide both sides by-0.16]

put value of x in (i) , we get y= 20-7.5 =12.5

Hence, 7.5 ounces of  7% acid solution is mixed with 12.5 ounces of 23% acid solution to obtain 20 oz of a 17% acid solution.

Answer:

A 23 of people who prefer plan 1 are from the 35-45 age group and 42% of people from the 46-55 age group prefer plan 2.

Step-by-step explanation:

add everyone who prefers plan 1 = 60

age 36-45 / total of plan 1 = 14/60 = .23 or 23%

add everyone in age group 46-55 = 50

in age group 46-55 and prefers plan 2 = 21 / 50 = 0.42 or 42%

Answer:

[tex]\boxed{\mathrm{Option \ B}}[/tex]

Step-by-step explanation:

Total people in 36 - 45 age group = 50

Who prefer plan I = 14

%age of people preferring plan 1 among 36-45 age group:

=> [tex]\frac{14}{50} * 100[/tex]

=> 0.28 * 100%

=> 28%

Now,

Total People in 46-55 age group = 50

Those who prefer plan II = 21

%age of people preferring plan II among 46-55 age group:

=> [tex]\frac{21}{50} * 100[/tex]

=> 0.42 * 100%

=> 42%

Answer:

16 Years

Step-by-step explanation:

Answer:

The integers are the numbers such that:

- The distance between consecutive integers is always of 1 unit and the integer numbers only have zeros after the decimal point, such that the set is: Z = {..., 0, 1, 2, 3, 4, ......}

74) No digits after the decimal point, so this is an integer.

3.49) we have digits after the decimal point, so this is not an integer.

4/7) 4 is smaller than 7, so 4/7 is smaller than one and larger than zero,

one and zero are consecutive integer numbers, so 4/7 can not be an integer number.

You also can solve the division and find that the quotient has digits after the decimal point.

148.29) This number has digits after the decimal point, so this is not an integer number.

8/1) here we have 8 divided by one, we know that:

8/1 = 8

8 has no digits after the decimal point, so this is an integer.

Answer:

x = -6

Step-by-step explanation:

3(x+4)-1=-7

Add 1 to each side

3(x+4)-1+1=-7+1

3(x+4)=-6  

Divide by 3

3/3(x+4)=-6/3

x+4 = -2

Subtract 4 from each side

x+4-4 = -2-4

x = -6

Answer:

Step-by-step explanation:

[tex]3(x + 4) - 1 = - 7[/tex]

Distribute 3 through the parentheses

[tex]3x + 12 - 1 = - 7[/tex]

Calculate the difference

[tex]3x + 11 = - 7[/tex]

Move constant to R.H.S and change it's sign

[tex]3x = - 7 - 11[/tex]

Calculate

[tex]3x = - 18[/tex]

Divide both sides of the equation by 3

[tex] \frac{3x}{3} = \frac{ - 18}{3} [/tex]

Calculate

[tex]x = - 6[/tex]

hope this helps

Best regards!!

Answer:

Step-by-step explanation:

Let larger number be x

Let smaller number be y

[tex]x = 5 + y[/tex]---> equation (i)

[tex]y = \frac{1}{2} x[/tex]

[tex]x = 2y[/tex]-----> equation (ii)

Equate equation (i) and (ii),

[tex]5 + y = 2y[/tex]

Move variable to L.H.S and change its sign:

Similarly, Move constant to R.H.S and change its sign

[tex]y - 2y = - 5[/tex]

[tex] - y = - 5[/tex]

The difference sign (-) will be cancelled on both sides

[tex]y = 5[/tex]

Putting the value of y in equation (ii) in order to find the value of X ( larger number)

[tex]x = 2y[/tex]

Plug the value of y

[tex] = 2 \times 5[/tex]

Calculate the product

[tex] = 10[/tex]

Hence,

Smaller number = 5

Larger number = 10

Hope this helps..

Best regards!!

Answer:

10 and 5

Step-by-step explanation:

Let the first number be x.

Let the second number be y.

x = 5 + y

y = 1/2x

Plug y as 1/2x in the first equation.

x = 5 + (1/2x)

Solve for x.

Subtract 1/2x on both sides.

x - 1/2x = 5 + 1/2x - 1/2x

1/2x = 5

Multiply both sides by 2.

2(1/2x) = 2(5)

x = 10

Plug x as 10 in the second equation.

y = 1/2(10)

Solve for y.

y = 5

x = 10

y = 5

The two numbers are 10 and 5.

10 is the larger number.

5 is the smaller number.

Answer: 4 miles

Step-by-step explanation:

If Ashley ran 1 mile 4 times, she ran 1+1+1+1, or 1*4, or 4 miles.

Hope it helps <3

Amplitude:4

Equation of Midline: 2

Period of function:3

Function shifted left:0.5

Function shifted up: 2

From the graphed cosine function we are given, we have;

1) Amplitude = 4

2) Equation of midline; m = 2

3) Period of the function = 3π

4) The function shifted 0.5 units left.

5) The function shifted 2 units up.

Read more; https://brainly.com/question/16280305

Answer:

The factors are (4x-1) and (2x+3)

Step-by-step explanation:

The factors of 8x^2 + 10x -3 can be found by grouping terms

8x^2 - 2x  + 12x - 3

2x (4x -1)  + 3(4x-1)

(4x-1)(2x+3)

Answer:

RA

Step-by-step explanation:

Answer:

[tex]\displaystyle b = 5[/tex]

General Formulas and Concepts:

Calculus

Integration

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Area of a Region Formula:                                                                                     [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \int\limits^b_1 {5x + 7} \, dx = 88[/tex]

Step 2: Solve

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Answer:5

Step-by-step explanation:

got it right

Answer:

its D. -3c

Step-by-step explanation:

just took the test

The expression that is equivalent to the expression [(6c² + 3c)/(-4c + 2)] ÷ [(2c + 1)/(4c - 2)] is; -3c

[(6c² + 3c)/(-4c + 2)] ÷ [(2c + 1)/(4c - 2)]

[3c(2c + 1)/(-2(2c - 1))] ÷ [(2c + 1)/(2(2c - 1)]

3/2 ÷ 1/5 is the same as; 3/2 × 5/1

Applying this same method to our question gives;

[3c(2c + 1)/(-2(2c - 1))] × [(2(2c - 1)/(2c + 1)]

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Answer:

I got x=3,-3

Step-by-step explanation:

Squares are the results of multiplying a value by itself. The value of x in the given equation 2x² - 5 = 13 is -3 and 3.

Squares are the results of multiplying a value by itself. Whereas the square root of a number is a value that when multiplied by itself yields the original value. As a result, both are vice versa approaches. For example, the square of 2 is 4 and the square root of 4 is 2.

The value of x for the given equation 2x²-5=13, can be solved as shown below.

2x² - 5 = 13

Add 5 on both the sides of the equation,

2x² - 5 + 5 = 13 + 5

2x² = 18

Divide both the sides of the equation by 2,

2x² / 2 = 18 / 2

x² = 9

Taking the square root on both the sides of the equation,

√x² = √9

x = ±3

x = -3, 3

Hence, the value of x in the given equation 2x² - 5 = 13 is -3 and 3.

Learn more about Square Root here:

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Answer:

x = 8.9 units

Step-by-step explanation:

We will use the theorem of intersecting tangent and secant segments.

"If secant and tangent are drawn to a circle from an external point, the product of lengths of the secant and its external segment will equal the square of the length of tangent."

8(8 + 2) = x²

x² = 80

x = √80

x = 8.944

x ≈ 8.9 units

Therefore, length of the tangent = 8.9 units

Answer:

y > -x/6 + 1

Step-by-step explanation:

Hope this can help

The graph of the inequality [tex]y > -(\frac{1}{6} )x+1[/tex]  is option "A" .

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line.

According to the question

The inequality : [tex]y > -(\frac{1}{6} )x+1.[/tex]  

now first we take out points to plot graph for that we will assume inequality to equation

i.e  

[tex]y = -(\frac{1}{6} )x+1[/tex]

x          y  

0          1

6          0

Now , as inequality have > sign

i.e according to the graph of inequality rules:

The boundary line is dashed for > and < and If the symbol ≥ or > is used, shade above the line.

Therefore,

Graph will be option "A" only .

Hence, the graph of the inequality [tex]y > -(\frac{1}{6} )x+1[/tex]  is option "A" .

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