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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.

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]

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:

T = k * (A/W)

Step-by-step explanation:

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:

(-1.5, 0.5)

Step-by-step explanation:

x = -1.5

y = 0.5

(-1.5, 0.5)

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:

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

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

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

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:

[tex]\frac{11}{12} - \frac{1}{3} = \frac{7}{12}[/tex]

Step-by-step explanation:

Given

See attachment for question

Required

Solve

We have:

[tex]\frac{11}{12} - \frac{1}{3}[/tex]

Take LCM and solve

[tex]\frac{11}{12} - \frac{1}{3} = \frac{11 - 4}{12}[/tex]

[tex]\frac{11}{12} - \frac{1}{3} = \frac{7}{12}[/tex]

Answer:

1

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Find the sum. Write your answer in simplest form.

Step-by-step explanation:

Answer:

4equal to plus 5 eul is to be 9

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:

They are not in the same location

Step-by-step explanation:

Well because we have x axis and y axis, x always has to go first. In (2, 5) 2 is first and has to start from the x axis and 5 is the y axis. And the (5,2) is the opposite and the places would be in totally different places on the coordinate plane.

Answer: No

Step-by-step explanation: The order of coordinates for a given point is very important. For example, (2, 5) and (5, 2) represent two very different points on a coordinate system, as shown in the picture below.

A given point, such as (2, 5), is often reffered to as

an ordered pair because the order of coordinates is very important.

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:

2.6 2.6 2.8 2.9 2.9

Step-by-step explanation:

used median for the five numbers.

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.

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:

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.

Answer:

4! = 24

Step-by-step explanation:

4! = 4 * 3 * 2 * 1

4! = 24

Answer:

11. (a) 3/4+1/2=5/4

   (b) 4/5= 8/10 , 16/20

12. 8 children don't like choc ice cream

Step-by-step explanation:

11. 3/4 +2/4=5/4(change 1/2 by making it the same as the one next to it)

12. 3/5 of 20 = 12

     20-12=8