Alma is estimating the proportion of students in her school district who, in the past month, read at least 1 book. From a random sample of 50 students, she found that 32 students read at least 1 book last month. Assuming all conditions for inference are met, which of the following defines a 90 percent confidence interval for the proportion of all students in her district who read at least 1 book last month?
a. [tex]32 \pm 1.645\sqrt{\frac{(32)(18)}{50}}[/tex]b. [tex]32 \pm 1.96\sqrt{\frac{(32)(18)}{50}}[/tex]c. [tex]0.64 \pm 1.282\sqrt{\frac{(0.64)(0.36)}{50}}[/tex]d. [tex]0.64 \pm 1.645\sqrt{\frac{(0.64)(0.36)}{50}}[/tex]e. [tex]0.64 \pm 1.96\sqrt{\frac{(0.64)(0.36)}{50}}[/tex]

Answer:

D. 4821 years

Step-by-step explanation:

A = A0e-0.000124t

A/A0 = e^-0.000124t

0.55 = e^-0.000124t

ln(0.55) = ln(e^-0.000124t)

ln(0.55) = -0.000124t × lne

t = ln(0.55)/-0.000124

4821.266135

Answer: y=  −3 /10 x +  2 /5

Step-by-step explanation:

Let's solve for y.

−3(x+y)+4=7y

Step 1: Add -7y to both sides.

−3x−3y+4+−7y=7y+−7y

−3x−10y+4=0

Step 2: Add 3x to both sides.

−3x−10y+4+3x=0+3x

−10y+4=3x

Step 3: Add -4 to both sides.

−10y+4+−4=3x+−4

−10y=3x−4

Step 4: Divide both sides by -10.

−10y /−10  =  3x−4 / −10

y=  −3 /10 x+  2 /5

Answer:

6 * [tex]\sqrt[3]{x}[/tex]

Step-by-step explanation:

6 x^1/3

The 1 means inside to the power of 1 and the 3 means to the cubed root

6 * [tex]\sqrt[3]{x}[/tex]

Answer:

(6/5,0)

(0, 6/8)

Step-by-step explanation:

[tex]5x=6-8y[/tex]

when y = 0 x-intercept

when x = 0 y-intercept

Answer:

x-intercepts- (1.2,0)

y-intercepts- (0,0.75)

Step-by-step explanation:

Answer:

x=40

Step-by-step explanation:

Since a circle has a total of a 360 degree angle the equation is

(x+40)+(2x+60)+(3x+20)=360

to simplify this we can bring all the variables(x) together and the numbers together.

(x+2x+3x)+(40+60+20)=360

6x+120=360

6x=360-120

6x=240

6x/6=240/6

x=40

The sum of all the degrees in a circle is 360 degrees. Knowing this you can make a equation:

(x + 40) + (2x + 60) + (3x + 20) = 360

x + 40 + 2x + 60 + 3x + 20 = 360

(x + 2x + 3x) + (40 + 60 + 20) = 360

Now you must combine like terms  This means the numbers with the same variables must be combined...

(x + 2x + 3x) + (40 + 60 + 20) = 360

x + 2x + 3x = 6x

(6x) + (40 + 60 + 20) = 360

Now combine the terms without variables (on the left side of the equation) together

(6x) + (40 + 60 + 20) = 360

40 + 60 + 20 = 120

(6x) + 120 = 360

Now we must isolate x. To do this first bring 120 to the right side by subtracting 120 to both sides (what you do on one side you must do to the other). Since 120 is being added on the left side, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.

6x + 120 - 120 = 360 - 120

6x + 0 = 240

6x = 240

To further isolate x  you must divide 6 to both sides. Since x is being multiplied by 6 you must divide 6 to both sides to make 6 one on the left side and bring it over to the right side

6x / 6 = 240 / 6

1x = 40

x = 40

Check:

(40 + 40) + (2(40) + 60) + (3(40) + 20)

(80) + (80 + 60) + (120 + 20)

80 + 140 + 140

360

Hope this helped! Let me know if you have any further questions or want anything clarified.

~Just a girl in love with Shawn Mendes

Answer:

Cecilia=£3.20

Dave=£2.40

Step-by-step explanation:

-The sum of the ratios is:

[tex]\sum{Ratios}=4+3\\\\=7[/tex]

#To find out how much each pay, your multiply the individuals ratio divide by the sum of the ratios times the cost;

[tex]Cecilia=\frac{4}[7}\times 5.60\\\\=\£3.20\\\\Dave=Total- Cecilia's\\\\=5.60-3.20\\\\=\£2.40[/tex]

Hence,Cecilia pays £3.20 and Dave pays £2.40

Answer:

The base charge = $18.5 and surcharge for each pound is = $1.75

Step-by-step explanation:

Solution:

- Denote:

     Base charge = $x   ...... For for Weight ≤ 1 lbs

     Additional charge = $y / unit pounds

- We are given that the customer is billed $29.00 for shipping a 7​-pound package. We can express this statement in terms of "x" and "y".

- The 1-pound out of 7 pounds will be charged with $x and remaining 6 additional pounds of weight will be charged "$y" for each unit of weight.

                         $x + ( 7 - 1 )*$y = $29.00    .... Eq1

- Similarly for a receipt of $64.00 for a 27​-pound package. The 1-pound out of 27 pounds will be charged with $x and remaining 26 additional pounds of weight will be charged "$y" for each unit of weight.      

                         $x + ( 27 - 1 )*$y = $64.00   .... Eq2

- Now solve the two equations simultaneously by subtracting Eq1 from Eq2:

                        (26 - 6 )*$y = $(64 - 29)

                        20*$y = $35

                         y = 1.75

                        $x = 29 - 6*1.75

                        x = 18.5    

- The base charge = $18.5 and surcharge for each pound is = $1.75

Given:

Given that the diameter of the circle is 10 kilometers.

We need to determine the area of the circle.

Radius of the circle:

The radius of the circle can be determined using the formula,

[tex]r=\frac{d}{2}[/tex]

Substituting d = 10, we get;

[tex]r=\frac{10}{2}[/tex]

[tex]r=5[/tex]

Thus, the radius of the circle is 5 kilometers.

Area of the circle:

The area of the circle can be determined using the formula,

[tex]A=\pi r^2[/tex]

Substituting r = 5, we get;

[tex]A=(3.14)(5)^2[/tex]

[tex]A=(3.14)(25)[/tex]

[tex]A=78.5[/tex]

Thus, the area of the circle is 78.5 square kilometers.

Determine the radius, which is 5 kilometers, before calculating the area of a circle with a diameter of 10 kilometers. Next, find the area, or roughly 78.54 km², using the formula Area = π × (radius)².

How to Calculate a Circle's Area

You can use the following formula to get the area of a circle with a given diameter:

π × (radius)² equals area.

Consequently, 78.54 km² is the approximate size of the circle with a diameter of 10 km.

Answer:

Its is just 0

Step-by-step explanation:

Answer:

Then it would be on a line

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that the regression equation for a set of paired data is = -23.8 + 2x. The values of x run from 100 to 400.

A new data point, P(194, 364.2), is added to the set.

From the given we can write it as y = -23.8+2x

Put x=194 in the above equation we get,

[tex]y(194) = -23.8+2\times 194[/tex]

[tex]=-23.8+ 388[/tex]

= 364.2

Hence, point P(194,364.2) is on regression line and it is not outlier.

Answer:

6

Step-by-step explanation:

The outlier is 67.

The mean with the outlier is: 115

(112+ 118 + 120 +67 + 128 + 119 + 121 + 124 + 126) ÷ 9

The mean without he outlier is: 121

(112+ 118 + 120 + 128 + 119 + 121 + 124 + 126) ÷ 8

So, 121 - 115 = 6

Answer:

Step-by-step explanation:

Answer:

Brian has $776 more account in his account than Chris.

Step-by-step explanation:

Compound interest Formula:

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

[tex]I[/tex]= A-P

A= Amount after t years

P= Initial amount

r= Rate of interest

t= Time in year

Given that,

Brian invests $10,000 in an account earning 4% interest, compounded annually for 10 years.

Here P = $10,000 , r= 4%=0.04, t=10 years

The amount in his account after 10 years is

[tex]A=10000(1+0.04)^{10}[/tex]

   =$14802.44

  ≈$14802

Five years after Brian's investment,Chris invests $10,000 in an account earning 7% interest, compounded annually for 5 years.

Here P = $10,000 , r= 7%=0.07, t=5 years

The amount in his account after 5 years is

[tex]A=10000(1+0.07)^{5}[/tex]

   =$14025.51

  ≈$14026

From the it is cleared that Brian has $(14802-14026)=$776 more account in his account than Chris.

Answer:

B) Brian has $766 more in his account than Chris

Step-by-step explanation:

Compound interest formula is [tex]A = P(1+r)^{2}[/tex]

P - principal amount

r - rate of interest

t - number of years

Brian invests $10,000 in an account earning 4% interest, compounded annually for 10 years

P = 10,000  

r= 4% = 0.04

t = 10

Plug in all the factors

[tex]Brian = 10000(1+0.04)^{10}= $14,802[/tex]

Chris invests $10,000 in an account earning 7% interest, compounded annually for 5 years.

P = 10,000  

r= 7% = 0.07

t =5

Plug in all the factors

[tex]Chris = 10000(1+.07)^{5 } = $14,026[/tex]

$14,802 - 14,026 = $776

Answer:

D. There are zeros between x = 1 and x = 2, x = 0 and x = –1.

Step-by-step explanation:

A zero point is inside an interval where value of y changes from positive to negative or viceversa. The curve is evaluated in the given points hereafter:

f(-3) = - 909, f(-2) = -192, f(-1) = -9,f(0) = 18, f(1) = 3, f(2) = -204, f(3) = -1017

There two zero, one between x = -1 and x = 0 and other between x = 1 and x = 2. Hence, the answer is D.

Final answer:

To calculate the mean number of push-ups Justin did each weekday, add up the total push-ups for the week and divide by 5. Justin did a mean of 186.8 push-ups per day.

Explanation:

To find the mean number of push-ups Justin did each weekday, we need to add the number of push-ups he did each day and then divide by the number of days. The steps are:

Therefore, the mean number of push-ups Justin did on a weekday is 186.8 push-ups.

Final answer:

The mean number of push-ups Justin did each weekday is calculated by adding the total push-ups for all the days and dividing by the number of days, resulting in 186.8 push-ups.

Explanation:

To find the mean number of push-ups, Justin did over the weekdays, you need to sum up the total push-ups and then divide by the number of days.

Add the number of push-ups for each day: 888 (Monday) + 14 (Tuesday) + 18 (Wednesday) + 6 (Thursday) + 8 (Friday) = 934 push-ups in total.

Divide the total number of push-ups by the number of days: 934 ÷ 5 days = 186.8 push-ups.

Therefore, the mean number of push-ups Justin did each weekday is 186.8 push-ups.

Answer: [tex]7.29[/tex]

Order the numbers

[tex]Before: 8,9,5,1,3,19,6\\After: 1, 3, 5, 6, 8, 9, 19[/tex]

Add

[tex]1+3+5+6+8+9+19=51[/tex]

Divide

[tex]51/7=7.28571428571[/tex]

Round

[tex]7.28571428571=7.29[/tex]

Final Answer

[tex]7.29[/tex]

Answer:

Step-by-step explanation:

Given that:

R(x) = [tex]\frac{17}{2x+1}[/tex] + 34x − 17

As we know that derivative of revenue function is marginal revenue function .

We will use following rules of derivative

=> dR/ dx = [tex]\frac{-17*2}{(2x+1)^{2} } + 34[/tex]

=> R' (x) =   [tex]\frac{-34}{(2x+1)^{2} } + 34[/tex]

=> R '(2000) =  [tex]\frac{-34}{(2*2000+1)^{2} } + 34[/tex] = 34

The revenue when 2000 units are sold is:

R(2000) = [tex]\frac{17}{2*2000+1}[/tex] + 34*2000 − 17 = $69,783

The marginal revenue be "34" and revenue change be "$69,783".

The increase throughout income caused by the acquisition of one more unit of production, is a Marginal revenue. Although marginal income can stay unchanged at a predetermined interval, it's indeed subject to the regulations of decreasing returns as well as will ultimately slow as outcome level grows.

According to the question,

Revenue function,

R(x) = [tex]\frac{17}{2x+1}[/tex] + 34x - 17

Units sold = 2000

(a) The marginal revenue be:

→ [tex]\frac{dR}{dx}[/tex] = [tex]-\frac{17\times 2}{(2x+1)^2}[/tex] + 34

R'(x) = [tex]- \frac{34}{(2x+1)^2}[/tex] + 34

By substituting "x = 2000",

R'(2000) = [tex]- \frac{34}{(2\times 2000+1)^2}[/tex] + 34

              = 34

(b) The revenue change be:

→ R(2000) = [tex]\frac{17}{2\times 2000+1}[/tex] + 34 × 2000 - 17

                 = 69,783 ($)

Thus the above response is appropriate.

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Answer:

fylinh rhthkrjehtegjhgjebjbebkbkbkertgbgrbkrt

Answer:

50(115-y) + 25y = 4125             [from eq2]

    5750 - 50y  + 25y = 4125           [distribute]

    5750 - 25y = 4125

     -25y = -1625

        y = 65             [divide both sides by (-25)]

There are 65 small boxes.

Put that value into either equation (now, which is easier?) to solve for x:

 x = 115 - y

 x = 115 - 65

 x = 50

 There are 50 large boxes.

- Mring0506

The required number of boxes that the truck contain is 55 small boxes and 65 large boxes.  

Given that, the large boxes weigh 45 pounds each, and the small boxes weigh 25 pounds each. There are 120 boxes in all, the truck is carrying a total of 4300 pounds.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Let the number of large boxes will be l and the number of small boxed be s,

According to the question,
l + s = 120
l = 120 - s - - - - - (2)
Again,
45l + 25s = 4300
put l in the above equation,
45[120 - s] + 25s = 4300
5400 - 45s + 25s = 4300
20s = 1100
s = 1100/20
s = 55
Now,
l = 120 - 55
l = 65

Thus, the required number of boxes that the truck contain is 55 small boxes and 65 large boxes.  

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The objective function in this scenario is minimizing the cost of shipping goods from the plant to the store.

The goal of the Linear Programming Problems (LPP) is to determine the best value for a given linear function. The ideal value may be either the highest or lowest value. The specified linear function is regarded as an objective function in this situation.

The most likely goal function, if we were to create a linear programme for this situation, would be to reduce the cost of shipping from the plants to the stores. This is important since it can become an expensive bottleneck.

Despite the fact that there are three factories and three stores, the costs will not be minimized if the same amount of goods are produced in each plant and carried to a specific store. In fact, the likelihood that each facility generates a distinct volume of items further exacerbates the issue.

Finding the optimal distribution of shipping commodities from each facility to each retailer is important as a result.

Hence, the objective function is minimizing the cost of shipping goods from the plant to the store.

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The options are missing in the question, which are as follow:

a. minimizing the quantity of goods distributed across the stores

b. minimizing the cost of shipping goods from the plant to the store

c. decreasing the cost of their raw material sourcing

d. increasing the number of goods manufactured at the plant

Answer:

Step-by-step explanation:

Answer:

0.5 meters per second

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

the first one

Answer:

24/5                                               (Nothing wrong with that.)

Step-by-step explanation:

Dividing is multiplying with the second fraction flipped.

4/5 / 2/12 ----> 4/5 x 12/2

Multiply across. 4 x 12 = 48. 5 x 2 = 10.

Combine. 48/10.

Simplify (divide both sides by 2) . 24/5.

Answer:

[tex] \frac{24}{5} [/tex]

Step-by-step explanation:

To divide two fractions we turn the second fraction upside down and multiply two fractions afterwards

[tex] \frac{4}{5} \div \frac{2}{12} = \\ \frac{4}{5} \times \frac{12}{2} [/tex]

now multiply 4 by 12 and 5 by 2

[tex] \frac{48}{10} [/tex]

now simplify fraction if needed

[tex] \frac{24}{5} [/tex]

Answer:

Answer is below

Step-by-step explanation:

Use 3 as the y-intercept. Factor the equation to find the solutions

(x - 1) (x - 3) so 1 and 3 are the x-intercepts. The vertex of the graph is at (2,-1).

I also graphed the equation below.

If this answer is correct, please make me Brainliest!

The graph of [tex]y = x^2 - 4x + 3[/tex] is a parabola that opens upward with its vertex at (2, -1). It intersects the x-axis at x = 3 and x = 1 and the y-axis at y = 3.

The equation is [tex]y = x^2 - 4x + 3.[/tex]

Use the formula x = -b / (2a) to find the x-coordinate of the vertex. In this case, a = 1, b = -4.

x = -(-4) / (2*1)

= 4 / 2

= 2.

So, the x-coordinate of the vertex is 2.

Subtitute x = 2 into the equation:

[tex]y = (2)^2 - 4(2) + 3[/tex]

= 4 - 8 + 3

= -1.

The y-coordinate of the vertex is -1.

The vertex is at (2, -1).

The y-intercept, we will set x = 0 in the equation:

[tex]y = (0)^2 - 4(0) + 3[/tex]

= 0 - 0 + 3

= 3.

The get x-intercepts, we set y = 0 in the equation:

[tex]0 = x^2 - 4x + 3.[/tex]

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

x = 3 or x = 1.

The x-intercepts are 3 and 1.

Now, we will plot the y-intercept and x-intercepts. The y-intercept is at (0, 3), and the x-intercepts are at (3, 0) and (1, 0).

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Answer:

  y = -3/4x +1

Step-by-step explanation:

Parallel lines have the same slope, so the slope of the line you want is -3/4. The point-slope form of the equation of a line is useful when you have this information:

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -(-2) = -3/4(x -4)

If you want slope-intercept form, you can rearrange this ...

  y +2 = -3/4x +3

  y = -3/4x +1 . . . . . . subtract 2 from both sides

Answer:

Answer: b. 20.8 ft-lb

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

That is the definition of a asymptote.  It is approached but will never get to the line.

Answer: True!

Step-by-step explanation:

An asymptote for a function f(x) is a straight line which is approached but never reached by f(x)

Answer:

20.4°C

Step-by-step explanation:

Initial temperature 't1'= -4.8°C

Final temperature 't2'= 15.6°C

In order to find change in temperature, take the difference of above two temperatures. So,

Change in temperature 'ΔT' = t2 - t1

ΔT= 15.6 - (-4.8)

ΔT= 20.4 °C

Therefore, the change in temperature was 20.4°C

Answer:

5789 pages

Step-by-step explanation:

9+180+2700+2900=5789