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[tex]\large\boxed{y = 12, x = 3}[/tex]

The two trapezoids are similar, so we can determine a common scale factor:

OL/UR = NM/TS

9/3 = 6/2

3 = 3

Trapezoid ONML is 3x larger than UTSR, so:

RS = 4, LM = y

3RS = LM

3 · 4 = y = 12.

Find x using the same method:

3UT = ON

3(2x+1) = 4x + 9

6x + 3 = 4x + 9

2x = 6

x = 3.

A sample size of approximately 9909 components is needed to estimate the true proportion of defective components within 2.5 percentage points with 99% confidence.

To estimate the true proportion of defective components with a desired level of confidence and precision, we can use the formula for sample size determination in a proportion estimation problem.

The formula is given by:

n = (Z²  p  (1-p)) / E²

Where:

- n is the required sample size,

- Z is the Z-value corresponding to the desired confidence level (in this case, 99% confidence),

- p is the estimated proportion of defective components from the initial sample (20/300 = 0.0667),

- (1-p) is the estimated proportion of non-defective components,

- E is the desired margin of error (2.5 percentage points = 0.025).

Determine the Z-value corresponding to a 99% confidence level. The Z-value can be obtained from a standard normal distribution table or using statistical software. For a 99% confidence level, the Z-value is approximately 2.576.

Substitute the values into the formula:

n = (2.576² * 0.0667 * (1-0.0667)) / (0.025²)

n = (6.641 * 0.9333) / 0.000625

n = 6.194 / 0.000625

n ≈ 9908.8

Therefore, a sample size of approximately 9909 components is needed to estimate the true proportion of defective components within 2.5 percentage points with 99% confidence.

More can be learned about proportions at;

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Answer:

72 cm

Step-by-step explanation:

Find the radius using the given information

308=1/2(πr^2)

r^2=616/π

r=14

The perimeter is πr + 2r so plug in 14

π(14) + 2(14)

43.96+28=71.96

Answer:

1/8

Step-by-step explanation:

   (5/6) × (3/20)

=  (5*3) / (6*20)

= 15/120

= 3/24

= 1/8

Answer:

Step-by-step explanation:

cos θ=8/17

sin θ=√(1-cos²θ)=√(1-(8/17)²)=√(1-64/289)=√((289-64)/289)=√(225/289)=15/17

Answer:

12.94

Step-by-step explanation:

5.75x125%=7.19

7.19+5.75=12.94

Answer:

The Standard Deviation is a measure of how spread out numbers are.

Its symbol is σ (the greek letter sigma)

The formula is easy: it is the square root of the Variance. So now you ask, "What is the Variance?"

Variance

The Variance is defined as:

The average of the squared differences from the Mean.

To calculate the variance follow these steps:

Work out the Mean (the simple average of the numbers)

Then for each number: subtract the Mean and square the result (the squared difference).

Then work out the average of those squared differences. (Why Square?)

Step-by-step explanation:

Answer:

Every book is 8 dollars but you have to subtract 10, so like this:

Step-by-step explanation:

p(x) = 8x - 10 Lets say you sell 2 books

p(2) = 8(2) - 10

p(2) = 16 - 10

p(2) = 6  You would make 6 dollars.

Question:

A number cube with faces labeled from 1 to 6 will be rolled once.  The number rolled will be recorded as the outcome.

Give the sample space describing all possible outcomes.  Then give all of the outcomes for the event of rolling a number greater than 2.

If there is more than one element in the set, separate them with commas.

Answer:

[tex]S = \{1,2,3,4,5,6\}[/tex]

[tex]Greater2 = \{3,4,5,6\}[/tex]

Step-by-step explanation:

Given

A roll of a 6 sided number cube

Solving (a): The sample space

This implies that we list out all number on the number cube.

So:

[tex]S = \{1,2,3,4,5,6\}[/tex]

Solving (b): Outcomes greater than 2

This implies that we list out all number on the number cube greater than 2 i.e. 3 to 6.

So:

[tex]Greater2 = \{3,4,5,6\}[/tex]

Answer:

I need help in math too so

Answer:

120 units²

Step-by-step explanation:

A= [tex]\frac{a+b}{2}[/tex]×h

A= [tex]\frac{15+15}{2}[/tex]×8

A= [tex]\frac{30}{2}[/tex]×8

A= 15×8

A= 120

Answer:

75%

Step-by-step explanation:

[tex] \frac{27}{36} \times 100\%[/tex]

Answer:

35 and 13

Step-by-step explanation:

Sum: 35 + 13 = 48

Difference: 35 - 13 = 22

Answer:

v = 196.25

Step-by-step explanation:

v = 3.14*r^2*h

v = 3.14*5^2*2.5

v = 196.25

Answer:

a) 0.1496 = 14.96% probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day.

b) Capacity of 252.6 cubic feet per second

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second).

This means that [tex]m = 100, \mu = \frac{1}{100} = 0.01[/tex]

(a) Find the probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.)

We have that:

[tex]P(X > x) = e^{-\mu x}[/tex]

This is P(X > 190). So

[tex]P(X > 190) = e^{-0.01*190} = 0.1496[/tex]

0.1496 = 14.96% probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day.

(b) What water-pumping capacity, in cubic feet per second, should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only 0.08?

This is x for which:

[tex]P(X > x) = 0.08[/tex]

So

[tex]e^{-0.01x} = 0.08[/tex]

[tex]\ln{e^{-0.01x}} = \ln{0.08}[/tex]

[tex]-0.01x = \ln{0.08}[/tex]

[tex]x = -\frac{\ln{0.08}}{0.01}[/tex]

[tex]x = 252.6[/tex]

Capacity of 252.6 cubic feet per second

Answer:

obj

Step-by-step explanation:

Answer:

send money and i gotchu

Step-by-step explanation:

Answer:

it is a

Step-by-step explanation:

its 72 sq. units igdoug

The area of the triangle is 36 square units, option C is correct.

A triangle is a three-sided polygon that consists of three edges and three vertices.

We have to find the area of triangle whose base is 4 units and height is 18 units

Area of triangle = 1/2 base ×height

Plug in the values of base and height in the above formula

=1/2×4×18

Divide numerator and denominator by 2

=36 square units

Hence, the area of the triangle is 36 square units, option C is correct.

To learn more on Triangles click:

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Answer:

1. 16

2. 36.62 in

Step-by-step explanation:

For the first one:

If you don't want to read the explanation go to the next section in bold

We are told that the triangles are similar.

We are told that the side lengths of the smaller triangle measure 7,4 and 9

And we are told that the longest side of the similar triangle measures 36

Given this information we need to find the other side lengths.

Because the triangles are similar each side length will share similar ratios. Note that the ratios must be between the two longest side, the two medium length sides and the two shorter sides

Because we are given the longest side length of the similar triangle and the longest side length of the smaller triangle we can set up a proportion to find the other side lengths.

The proportion can be found by dividing the longest side length of the larger triangle (36) by the longest side length of the smaller triangle (9)

proportion = [tex]\frac{36}{9} or4[/tex]

So the ratio to the side lengths of the triangle is 4 to 1

Now that we have created a proportion we can find the other side lengths.

Once again this information is not needed. If you don't want to read it go to the next section in bold.

For the medium length side:  [tex]\frac{4}{1} =\frac{x}{7}[/tex] ( remember x = missing side length)

multiply each side by 7

4 * 7 = 28

x/7 * 7 = x

x = 28

For the shorter side: [tex]\frac{4}{1} =\frac{x}{4}[/tex] ( once again x = missing side length )

multiply each side by 4

4 * 4 = 16

x/4 * 4 = x

x = 16

So we can conclude that the side length of the shortest side is 16

For the second one

This problem is like the other one.

The only difference is we are already given the ratio

( note that the ratio is width to height )

16 : 9

Given the proportion and the height (20.6) of the other flat screen tv we need to find the width

To do so we set up an equation using the ratio:

let x = width

[tex]\frac{16}{9} =\frac{x}{20.6}[/tex]

using cross multiplication

16 * 20.6 = 329.6

9 * x = 9x now we have 9x = 329.6

step 2 divide each side by 9

9x / 9 = x

329.6/9 = 36.62

we're left with x = 36.62

Meaning that the width of the other flat screen tv is 36.62 in

Answer:

d. 40

Step-by-step explanation:

The number of faces, edges and vertices is related by the following formula:

[tex]V - E + F = 2[/tex]

In which V is the number of vertices, E is the number of edges and F is the number of faces.

In this question:

[tex]F = 25, V = 17[/tex]

We want to find E. So

[tex]V - E + F = 2[/tex]

[tex]17 - E + 25 = 2[/tex]

[tex]E = 42 - 2 = 40[/tex]

The correct answer is given by option D.

Answer:

[tex](a)\ c = \frac{1}{15}[/tex]

[tex](b)\ 40\%[/tex]

[tex](c)\ 60\%[/tex]

Step-by-step explanation:

The given parameters can be represented as:

[tex]P_Y(y) \ge 0, y =1,2,3,4,5[/tex]

[tex]P_y(y) = cy, y=1,2,3,4,5[/tex]

Solving (a): The value of c

To do this, we make use of the following rule;

[tex]\sum\limit^5_{y=1}P_Y(y_i) = 1[/tex]

Given that:

[tex]P_y(y) = cy, y=1,2,3,4,5[/tex]

This is translated to:

[tex]c*1 + c * 2 + c * 3 + c * 4 + c * 5 = 1[/tex]

[tex]c + 2c + 3c + 4c + 5c = 1[/tex]

[tex]15c = 1[/tex]

Solve for c

[tex]c = \frac{1}{15}[/tex]

(b) The proportions of applications that requires at most 3 forms

This implies that: y = 1,2,3

So, we make use of:

[tex]P(Y \le 3) = P(Y=1) + P(y=2) + P(Y=3)[/tex]

Recall that:

[tex]P_y(y) = cy, y=1,2,3,4,5[/tex]

Substitute [tex]c = \frac{1}{15}[/tex]

[tex]P_y(y) =\frac{1}{15}y[/tex]

So:

[tex]P(Y \le 3) = P(Y=1) + P(y=2) + P(Y=3)[/tex]

[tex]P(Y\le 3) = \frac{1}{15} * 1 +\frac{1}{15} * 2 +\frac{1}{15} * 3[/tex]

[tex]P(Y\le 3) = \frac{1}{15} +\frac{2}{15} +\frac{3}{15}[/tex]

Take LCM

[tex]P(Y\le 3) = \frac{1+2+3}{15}[/tex]

[tex]P(Y\le 3) = \frac{6}{15}[/tex]

[tex]P(Y\le 3) = 0.4[/tex]

Express as percentage

[tex]P(Y\le 3) = 0.4*100\%[/tex]

[tex]P(Y\le 3) = 40\%[/tex]

(c) The proportions of applications that requires between 2 and 4 forms (inclusive)

This implies that: y = 2,3,4

So, we make use of:

[tex]P(2 \le Y \le 4) = P(Y=2) + P(Y=3) + P(Y=4)[/tex]

[tex]P(2 \le Y \le 4) = 2 * \frac{1}{15} + 3 * \frac{1}{15} + 4 * \frac{1}{15}[/tex]

[tex]P(2 \le Y \le 4) = \frac{2}{15} + \frac{3}{15} + \frac{4}{15}[/tex]

Take LCM

[tex]P(2 \le Y \le 4) = \frac{2+3+4}{15}[/tex]

[tex]P(2 \le Y \le 4) = \frac{9}{15}[/tex]

[tex]P(2 \le Y \le 4) = 0.6[/tex]

Express as percentage

[tex]P(2 \le Y \le 4) = 0.6 * 100\%[/tex]

[tex]P(2 \le Y \le 4) = 60\%[/tex]

Answer:

24

Step-by-step explanation:

12 + 4(3)

24

Answer:

[tex]4 \times {3}^{3} + 4 \times 3 \\ 108 + 12 \\ = 120[/tex]

9514 1404 393

Answer:

  sometimes

Step-by-step explanation:

4 + 7 = 11 . . . not a multiple of 7

28 + 7 = 35 . . . a multiple of 7

If you add a multiple of 4 and a multiple of 7, the sum is sometimes a multiple of 7.

__

It will be a multiple of 7 when the multiple of 4 used is a multiple of 7, such as 4×7 or 4×14 or 4×21, for example.

Answer:

An equation in standard form is -x^2-15=0.

Step-by-step explanation:

-x^2=15

-x^2-15=0

ax^2+bx+c=0

-x^2-15=0

Answer:

search up demos graphing calculator and plug in the numbers there.

Step-by-step explanation:

its super easy to use try it :)

Answer:

b

Step-by-step explanation:

Answer:

1209 square meters

Step-by-step explanation:

2(1/2*16*15)+3(17*19)=1209

Answer:

Simple=$14.80 Compound=$16.14

Step-by-step explanation:

Simple=A=P(1+rt)

10.00(1+0.08×6)

Compound-A=P(1+r/n)^nt

10.00(1+0.08/6)^12*6

Answer:

The midpoint of this line segment is (-1.5, -4.5).

Step-by-step explanation:

In finding the midpoint of a line segment we are actually averaging the x- and y-coordinates of the endpoints:

                                             -2 -1

x-coordinate of midpoint = --------- = -3/2 = -1.5

                                                 2

                                              -4 -5

y-coordinate of midpoint = ---------- = -4.5

                                                   2

The midpoint of this line segment is (-1.5, -4.5).

Answer:

938 millibars

Step-by-step explanation:

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Answer:

W=A/L

Step-by-step explanation:

If the area of the rectangle is L*W, you can just rearrange the equation A=L*W to get W=A/L, an equivalent equation.