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Answer:

77.5% probability that this ball traveled fewer than 216 feet.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 247 feet and a standard deviation of 41 feet.

This means that [tex]\mu = 247, \sigma = 41[/tex]

What is the probability that this ball traveled fewer than 216 feet?

The probability as a decimal is the p-value of Z when X = 216. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{216 - 247}{41}[/tex]

[tex]Z = 0.756[/tex]

[tex]Z = 0.756[/tex] has a p-value of 0.775

0.775*100% = 77.5%

77.5% probability that this ball traveled fewer than 216 feet.

9514 1404 393

Answer:

  5y = 5

Step-by-step explanation:

  -2(x -2y) +(2x +y) = -2(-1) +(3) . . . . -2 times [eq2] + [eq1]

  -2x +4y +2x +y = 2 +3 . . . . eliminate parentheses

  5y = 5 . . . . . . . . collect terms

Answer:

92 dB

Step-by-step explanation:

Use the mean formula, mean = sum of elements / number of elements.

Since it is a 8 hour work day, there are 8 elements.

mean = sum of elements / number of elements

mean = (98 + 98 + 98 + 98 + 98 + 82 + 82 + 82) / 8

mean = 736 / 8

mean = 92

So, the average noise level is 92 dB

Answer:

(a) [tex]f(2) = 81[/tex]

(b) [tex]g(2) = 83[/tex]

(c) Test average for maths class after test 2 is greater

Step-by-step explanation:

Given

[tex]f(x) = 0.5x + 80[/tex]

[tex]x \to g(x)[/tex]

[tex]1 \to 81[/tex]

[tex]2 \to 83[/tex]

[tex]3 \to 85[/tex]

Solving (a): f(2)

We have:

[tex]f(x) = 0.5x + 80[/tex]

[tex]f(2) = 0.5*2+80[/tex]

[tex]f(2) = 1 + 80[/tex]

[tex]f(2) = 81[/tex]

Solving (b): g(2)

From the table:

[tex]g(x) = 83[/tex] when [tex]x = 2[/tex]

So:

[tex]g(2) = 83[/tex]

Solving (c): Which is greater f(2) or g(2)

In (a) and (b),

[tex]f(2) = 81[/tex]

[tex]g(2) = 83[/tex]

Hence, test average for maths class is greater

9514 1404 393

Answer:

  C.  Rhombus

Step-by-step explanation:

The symmetry of the coordinates tells you the figure has equal-length sides, but the angles are not right angles. Such a figure is a rhombus.

Answer:

A = 30 units²

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

Here b = 12 and h = 5 , then

A = [tex]\frac{1}{2}[/tex] × 12 × 5 = 6 × 5 = 30 units²

Answer:

4! = 24

Step-by-step explanation:

4! = 4 * 3 * 2 * 1

4! = 24

The number of patients chose chicken on Monday is 90.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Given that, there were 240 patients in total.

1/3 of these patients chose pasta.

Number of patients chose pasta

= 1/3 ×240

= 60

3/8 of these patients chose beef stew.

Number of patients chose beef stew

= 3/8 ×240

= 90

Number of patients chose chicken

= 240-(60+90)

= 240-150

= 90

Therefore, the number of patients chose chicken on Monday is 90.

To learn more about the fraction visit:

brainly.com/question/1301963.

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18.9% is the answer

Step-by-step explanation:

volume of a cylinder = πd²/4 x h

where d is diameter and h is height of cylinder.

thus

vol of A is

[tex]vol \: of \: a \: = \pi \times \frac{ {d}^{2} }{4} \times h \\ = \pi \times \frac{ {16}^{2} }{4} \times 19 \\ = \pi \times 4 \times 16 \times 19 \\ = 3818.24[/tex]

and

[tex]vol \: of \: b = \pi \times \frac{ {20}^{2} }{4} \times 15 \\ = \pi \times 5 \times 20 \times 15 \\ = 4710[/tex]

difference in vol of a and b is

[tex]diff \: = vol \: of \: b \: - vol \: of \: a \\ = 4710 - 3818.24 \\ = 891.76[/tex]

this volume will remain empty after container A is pumped into container B.

this volume as a percentage of total volume of B is

[tex]\% = \frac{diff \: vol}{total \: vol} \times 100 \\ = \frac{891.76}{4710} \times 100 \\ = 18.9\%[/tex]

a diameter is a line that starts from the circumference to the other part of the circumference

Answer:

Equation: [tex]y=-\frac{5}{4} x[/tex]

Slope: [tex]-\frac{5}{4}[/tex]

Point: [tex](-4,5)[/tex]

Step-by-step explanation:

To find the slope, you need two points [tex](-4,5)[/tex] and [tex](0,0)[/tex].

Then use the Slope Formula to Identify the slope.

M = Slope

M = [tex]\frac{y2-y1}{x2-x1}[/tex]         Second y being subtracted by the first y / the second x being subtracted by the first x.

M = [tex]\frac{0-5}{0--4}[/tex]          Plot the x and y values (In order) Then subtract

M = [tex]\frac{-5}{4}[/tex]             Move the negative sign

M = [tex]-\frac{5}{4}[/tex]

Slope = [tex]-\frac{5}{4}[/tex]

Then the Equation has to be written in Slope-Intercept Form (y=mx+b)

y = [tex]-\frac{5}{4} x[/tex]

Answer:

Vertex: (3,16)

Axis of symmetry: x = 3

Step-by-step explanation:

The vertex is the minimum or maximum of the graph.

The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.

Answer:

100%  probability that the loss in nominal dollars is less than 1000, given that the loss in nominal dollars is greater than 200.

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

The probability of finding a value between c and d is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

The probability of finding a value above x is:

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

Uniformly distributed on [0, 1000].

This means that [tex]a = 0, b = 1000[/tex]

Given that the loss in nominal dollars is greater than 200.

This means that [tex]a = 200[/tex]

Calculate the probability that the loss in nominal dollars is less than 1000

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

[tex]P(X < 1000) = \frac{1000 - 200}{1000 - 200} = 1[/tex]

100%  probability that the loss in nominal dollars is less than 1000, given that the loss in nominal dollars is greater than 200.

Answer:

Step-by-step explanation:

12. To find the carpet needed. Find the area :

   The figure is combination of semi circle and a rectangle.

   So Area = Area of semi circle + Area of rectangle

      [tex]Area \ of \ semi \ circle = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi \times 25 = 39.25 \ ft^2 \\\\Area \ of \ rectangle = Length \times Breadth = 15 \times 10 =150 \ ft^2[/tex]

     Area = 150 + 39.25 = 189.25 sq ft

13.   Cost per square feet = $$9.95

     Therefore cost for 189.25 square feet = 9.95 x 189.25 = $1883.04

Answer:

Larger angle= 73, smaller angle= 17

Step-by-step explanation:

I wrote an equation, and x is the measure of one of the angles

90=2x-56

90+56=2x-56+56

146=2x

73=x

One of the angles is 73, so subtract 53 from 73 to find the second angle. 73+56=17

You can make sure it adds up to a complementary angle by seeing if 17+73=90

Answer:

If the null hypothesis is rejected, the interpreatation is that there is significant evidence at the desired significance level to conclude that the mean time the students study at her university is of more than 4.9 hours.

Step-by-step explanation:

The dean of a major university claims that the mean number of hours students study at her University (per day) is at most 4.9 hours.

At the null hypothesis, we test if the mean is of at most 4.9 hours, that is:

[tex]H_0: \mu \leq 4.9[/tex]

At the alternative hypothesis, we test if the mean is more than 4.9 hours, that is:

[tex]H_1: \mu > 4.9[/tex]

Accepting the null hypothesis:

If the null hypothesis is accepted, the interpretation is that there is not significant evidence to conclude that the mean time the students study at her university is of more than 4.9 hours.

Rejecting the null hypothesis:

As is the case in this question, if the null hypothesis is rejected, the interpreatation is that there is significant evidence at the desired significance level to conclude that the mean time the students study at her university is of more than 4.9 hours.

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Answer:

 1.60

Step-by-step explanation:

The growth factor is 1 more than the growth rate:

  1 + 60% = 1 + 0.60 = 1.60 = growth factor

Solution :

Given data :

[tex]c_{in}[/tex] = 1 g/L

[tex]r_{in}[/tex] = 5 L/min

[tex]r_{out}[/tex] = 5 L/min

[tex]$v_0$[/tex] = 250 L

[tex]A_0[/tex] = 20 g

∴ [tex]r_{net} = r_{in}- r_{out}[/tex]

         = 5 - 5

          = 0

[tex]c_{out} = \frac{A}{250} \ g/L[/tex]

Now, [tex]\frac{dA}{dt}=(r_{in} \times c_{in}) - (r_{out} \times c_{out})[/tex]

[tex]$\frac{dA}{dt} = 5-5\left(\frac{A}{250}\right)$[/tex]

[tex]\frac{dA}{dt}+5 \left(\frac{A}{250}\right) = 5[/tex]

[tex]\frac{dA}{dt}+5 \left(\frac{A}{250}\right) = 5 \text{ with} \ A_0 = 20[/tex]

Integrating factor = exp(5 t/250)

Therefore,

[tex]A \times \exp (5t \ /250) = \text{integral of}\ 5 \times \exp (5t / 250) + C[/tex]

Put [tex]A_0=250+C[/tex]

C = -230

[tex]A \times \exp(5t/250) = 250 \exp(5t/250) + (-230)[/tex]

[tex]A(t) = 250-230 \exp(-5t/250)[/tex]

[tex]A(t) = 250-230e^{\left(\frac{-t}{50}\right)} \ g[/tex]

Answer:

(-1.5, 0.5)

Step-by-step explanation:

x = -1.5

y = 0.5

(-1.5, 0.5)

Answer:

53 1/3

Step-by-step explanation:

200×4/5=160

160×2/3=106 2/3

106 2/3×1/2=53 1/3

Step-by-step explanation:

200×1/2=100

100×2/3=66.6666666667

so, the question is wrong

Answer:

Step-by-step explanation:

divide the cost to the students.

use x

x+15= 17250

move 15 other side. which becomes negative

Answer: it is 1,150 per student

Step-by-step explanation: simple 17,250 divided by 15 = 1,150 now double check by 1,150 times 15 =17,250 so I am correct it is 1,150 per student

Answer:

equation 1or 2 divide

3x+y=7

2x+5y=22

or, equation 1 multiple 5

15x+5y=35

2x+5y=22

or,13x=13

therefore x=1 again

value of x put the y in equation 2

2.1 + 5y=22

5y=11

therefore y=11/5

b and c will be reduced

Step-by-step explanation:

exterior angle= sum of other two angles

in the pic the sum is 152 so the exterior angle should've been 152 but it has been decreased so b and c will also decrease........

Answer:

The plumber worked 50 hours, and his assistant worked 25 hours.

Step-by-step explanation:

Since a plumber and his assistant work together to replace the pipes in an old house, and the plumber charges $ 30 an hour for his own labor and $ 20 an hour for his assistant's labor, and the plumber works twice as long as his assistant on this job, and the labor charge on the final bill is $ 2000, to determine how long did the plumber and his assistant work on this job the following calculation must be performed:

40 x 30 + 20 x 20 = 1200 + 400 = 1600

50 x 30 + 25 x 20 = 1500 + 500 = 2000

Therefore, the plumber worked 50 hours, and his assistant worked 25 hours.