A sample of 3 different calculators is randomly selected
from a group containing 13 that are defective and 15 that
have no defects. Assume that the sample is taken with
replacement. What is the probability that at least one of
the calculators is defective? Express your answer as a
percentage rounded to the nearest hundredth without
the % sign.

the expression describing all the angles that are coterminal with 8° is: θ = 8° + 360°k, where k is an integer.

How to solve and what is angle?

An angle of 8° has an initial side on the positive x-axis and rotates counterclockwise by 8°.

Any angle coterminal with 8° can be expressed as:

θ = 8° + 360°k

where k is an integer.

Therefore, the expression describing all the angles that are coterminal with 8° is:

θ = 8° + 360°k, where k is an integer.

An angle is a geometric figure formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles are typically measured in degrees or radians and are used to measure the amount of rotation or turn between two intersecting lines or planes.

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Answer:

Step-by-step explanation:

To calculate unadjusted cost of goods sold, sum the beginning inventory value and the cost of goods manufactured, then subtract the ending inventory value.

Answer:

2/3

Step-by-step explanation:

A six sided number cube :

Sample space = 1,2,3,4,5,6

Non composite numbers on a six sided number cube = 1,2,3,5

Probability of an event = required outcome / Total possible outcomes

Required outcome = number of non composite number = 4

Total possible outcomes = sample space = 6

P(not composite)= 4/6 = 2/3

The following sets of numbers could represent the three sides of a

triangle is {7, 15, 20}.

The set of numbers {7, 15, 20} could represent the three sides of a triangle, but the other sets of numbers do not satisfy the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side. Checking the sets of numbers:

For {7, 15, 20}, 7 + 15 > 20, 7 + 20 > 15, and 15 + 20 > 7, so they satisfy the triangle inequality theorem and could represent the sides of a triangle.

For {7, 16, 23}, 7 + 16 < 23, so they do not satisfy the triangle inequality theorem and cannot represent the sides of a triangle.

For {11, 22, 35}, 11 + 22 < 35, so they do not satisfy the triangle inequality theorem and cannot represent the sides of a triangle.

For {5, 17, 22}, 5 + 17 < 22, so they do not satisfy the triangle inequality theorem and cannot represent the sides of a triangle.

Therefore, the answer is {7, 15, 20}.

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Using a z-table, the probability of a z-score less than 1.58 is 0.9429 (rounded to 4 decimal places).

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. It is used in various fields such as mathematics, statistics, science, and finance to make predictions and analyze data.

Here,

1. The z-score for a sample mean of $75 is calculated as:

z = (75 - 76) / (6 / √(40)) = -2.36

Using a z-table, the probability of a z-score less than -2.36 is 0.0099 (rounded to 4 decimal places).

2. The z-score for a sample mean of $75 is calculated as:

z1 = (75 - 76) / (6 / √(40))

= -2.36

The z-score for a sample mean of $77 is calculated as:

z2 = (77 - 76) / (6 / √(40))

= 0.79

Using a z-table, the probability of a z-score between -2.36 and 0.79 is 0.8669 (rounded to 4 decimal places).

3. The z-score for a sample mean of $77 is calculated as:

z1 = (77 - 76) / (6 / √(40))

= 0.79

The z-score for a sample mean of $78 is calculated as:

z2 = (78 - 76) / (6 / √(40))

= 1.57

Using a z-table, the probability of a z-score between 0.79 and 1.57 is 0.0823 (rounded to 4 decimal places).

4. The standard error of the mean (SEM) is calculated as:

SEM = standard deviation / sqrt(sample size)

SEM = 6 / √(40) = 0.9487

The z-score for a sampling error of $1.50 is calculated as:

z = 1.50 / 0.9487 = 1.58

Using a z-table, the probability of a z-score less than 1.58 is 0.9429 (rounded to 4 decimal places).

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Answer:

6 weeks and 840 hours

Step-by-step explanation:

There are 168 hours in one week.

24 hrs/day * 7 days = 168 hours

1008 hours ÷ 24 hours(1 day) = 42 days ÷ 7 days in a week = 6 weeks

168 hours/week * 5 weeks = 840 hours

The tοtal change in reservοir height οver bοth years is a decrease οf 2 feet.

The tοtal change in reservοir height οver bοth years can be calculated by finding the difference between the final height and the initial height.

Let's assume that the initial height οf the reservοir was H.

After the lοng dry spell, the reservοir drοpped 6 feet, which means its height became H - 6.

Fοllοwing that, the reservοir rοse 4 feet, which means its height became (H - 6) + 4 = H - 2.

Therefοre, the tοtal change in reservοir height οver bοth years can be calculated as:

Tοtal change = Final height - Initial height

= (H - 2) - H

= -2

Sο the answer is C) -0+. The tοtal change in reservοir height is a decrease οf 2 feet.

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In the given angles the required value of x is 17° respectively.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.

Angles created by two rays are in the plane where the rays are located.

The meeting of two planes also creates angles. We refer to these as dihedral angles.

Based on the measurement, there are many kinds of angles in geometry.

The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation.

So, we know that:

2x+5 + 8x+5 = Straight angle

2x+5 + 8x+5 = 180

Now, solve for x as follows:

2x+5 + 8x+5 = 180

10x+10 = 180

10x = 170

x = 17

Therefore, in the given angles the required value of x is 17° respectively.

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The values of the variables in the semicircle shown are:

x = 63 degrees; y = 90 degrees.

A semi-circle is exactly half of a full circle and has a measurement of 180 degrees; the two endpoints of the diameter form the endpoints of the semi-circle. If an angle is enclosed inside a semi-circle, the angle formed measures 90 degrees.

Therefore, it means the value of the variable, y = 90 degrees.

Thus, using the triangle sum theorem, we have:

x = 180 - 90 - 27

x = 63 degrees.

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After solving the given expression, the value of x is 5.

What exactly are expressions?

An expression in mathematics is a set of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that may be evaluated to generate a value. Expressions can be simple or complicated, with one or more variables involved.

Now,

To solve the equation 6x+14x+5=5(4x+1), we first need to simplify both sides of the equation using the distributive property of multiplication:

6x + 14x + 5 = 20x + 5

Now we can simplify further by subtracting 20x and 5 from both sides of the equation:

6x + 14x - 20x = 0 - 5

Simplifying again:

x = -5

Finally, we can solve for x by multiplying both sides by -1:

x = 5

Therefore, the solution to the equation 6x+14x+5=5(4x+1) is x=5.

Word problem:

A clothing store sells two types of shirts: T-shirts and polo shirts. The store makes a profit of $6 on each T-shirt sold and a profit of $14 on each polo shirt sold. Last week, the store sold a total of 5 shirts and made a total profit of $25. If x represents the number of T-shirts sold, write an equation to represent the situation.

Solution:

Let x be the number of T-shirts sold, then the number of polo shirts sold is 5 - x (since a total of 5 shirts were sold). The total profit from selling x T-shirts and (5-x) polo shirts can be calculated as:

Profit = (profit per T-shirt x number of T-shirts) + (profit per polo shirt x number of polo shirts)

Profit = (6x) + (14(5-x))

Profit = 6x + 70 - 14x

Profit = -8x + 70

Since the total profit is given as $25, we can write the equation:

-8x + 70 = 25

Simplifying:

-8x = -45

x = 5.625

Since we can't sell a fraction of a shirt, we need to round down to the nearest integer. Therefore, the store sold 5 T-shirts.

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Answer: i think its A and B

Step-by-step explanation: 33 divided by 2 is 16.5

                                             50 divided by 3 is 16.6667

                                             72 divided by 4 is 18 so that would be to much

                                             89 divided by 5 is 17.8 which is also to much

By circle , 15 is the length of x .

What is a circle, exactly?

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by each line that traverses the circle.

                                Moreover, every angle has rotational symmetry around the center. With no sides or edges, a circle is a figure with a round shape. A circle can be characterized in geometry as a closed shape, a two-dimensional shape, or a curved shape.

AE² = EC . CD

10² = 5 * x

100 = 5 * x

100/5 = x

 20 = x

ED = 20 - 5   = 15

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Note that,
the encrypted message for "OK" is the pair of numbers (616, 2385).
and the final encrypted message for "HELP" is the sequence of numbers (738, 1277, 1479, 2252).

To encrypt a message using RSA, we need to first represent the message as numbers using a suitable encoding scheme. For simplicity, we can use the ASCII code for each character, which is a standard encoding scheme for text.

a) To encrypt "OK", we first convert each letter to its corresponding ASCII code:

"O" = 79

"K" = 75

Next, we use the RSA encryption formula:

C ≡ [tex]M^{e}[/tex] (mod n)

For "O", we have C ≡ 79¹¹ (mod 2911) ≡ 616 (mod 2911)

For "K", we have C ≡ 75¹¹ (mod 2911) ≡ 2385 (mod 2911)

Therefore, the encrypted message for "OK" is the pair of numbers (616, 2385).

b) To encrypt "HELP", we break it up into two blocks:

Block 1: "HE"

Block 2: "LP"

For block 1, we have:

"H" = 72

"E" = 69

Using the RSA encryption formula, we get:

C1 ≡ 72¹¹ (mod 2911) ≡ 738 (mod 2911)

C2 ≡ 69¹¹ (mod 2911) ≡ 1277 (mod 2911)

Therefore, the encrypted message for "HE" is the pair of numbers (738, 1277).

For block 2, we have:

"L" = 76

"P" = 80

Using the RSA encryption formula, we get:

C3 ≡ 76¹¹ (mod 2911) ≡ 1479 (mod 2911)

C4 ≡ 80¹¹ (mod 2911) ≡ 2252 (mod 2911)

Therefore, the encrypted message for "LP" is the pair of numbers (1479, 2252).

The final encrypted message for "HELP" is the sequence of numbers (738, 1277, 1479, 2252).

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A. The length of the cord needed to reach corner C is 17.6 m

B. The distance between the electrical outlet and corner N is 14.3 m

The length of the cord needed can be obtained as follow:

Sine θ = opposite / hypotenuse

Sine 27 = 8 / Length of cord

Cross multiply

Length of cord × sine 27 = 8

Divide both sides by sine 27

Length of cord = 8 / sine 27

Length of cord = 17.6 m

First, we shall determine the length OB. Details below:

Tan θ = Opposite / Adjacent

Tan 27 = 8 / Length OB

Cross multiply

Length OB × tan 27 = 8

Divide both sides by tan 27

Length OB = 8 / tan 27

Length OB = 15.7 m

Finally, we shall determine the distance between the electrical outlet and corner N. Details below:

Length BN = Length OB + Length ON

30 = 15.7 + Distance

Collect like terms

Distance = 30 - 15.7

Distance = 14.3 m

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by simplifying the expression, option d ,sec θ is the correct answer.

how can we solve this expression?

We can simplify the given expression as follows:

(tan θ - [tex]sec^2[/tex] θ) / tan θ

= (tan θ / tan θ) - ([tex]sec^2[/tex] θ / tan θ) ,

by diving it by tan θ

= 1 - (1/[tex]cos^2[/tex] θ)([tex]sin^2[/tex] θ / cos θ),

since sec = 1/cos and tan=sin/cos

placing the value in expression and solving it , we get

= 1 - ([tex]sin^2[/tex] θ / ([tex]cos^3[/tex] θ))

= [tex]cos^3[/tex] θ / [tex]cos^3[/tex] θ - [tex]sin^2[/tex] θ

= [tex]cos^3[/tex]θ / [tex]cos^2[/tex] θ (1 - [tex]tan^2[/tex] θ)

We can simplify the given expression as follows:

= cos θ ( [tex]cos^2[/tex]θ -  [tex]sin^2[/tex]θ) / ([tex]cos^2[/tex] θ)

= cos θ (cos θ / [tex]cos^2[/tex]θ)

= 1/cos θ is equal to sec θ

Therefore, the simplified expression is sec θ.

Hence, the answer is option (d) sec θ.

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Answer:

To solve 2^x = 32, we need to find the value of x that satisfies the equation.

We can rewrite 32 as a power of 2 by noting that 2^5 = 32. Therefore, we have:

2^x = 2^5

Since the bases of the powers are equal, we can equate the exponents:

x = 5

So the solution to 2^x = 32 is x = 5.

To rewrite this equation in a logarithmic form, we can use the definition of logarithms:

log(base 2)32 = x

Here, the logarithm with base 2 of 32 is equal to x.

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Answer:

Step-by-step explanation:

yes since they are both divisible by their denominators and equal the same thing

Answer:

yes, they are equivalent

Step-by-step explanation:

2/2 = (2/2)x(4/4) = 8/8 = 1

Answer: To solve the problem, we can use Bayes' theorem. Let D be the event that a device is defective, and let A be the event that the quality assurance check concludes that a device is defective.

We want to find P(A and not D) + P(not A and D), which represents the probability of an incorrect conclusion.

We know that P(D) = 1 - P(not D) = 1 - 0.84 = 0.16, and that P(A | not D) = 0.03 and P(A | D) = 0.97.

Using Bayes' theorem, we can compute:

P(not A | not D) = 1 - P(A | not D) = 1 - 0.03 = 0.97

P(not A | D) = 1 - P(A | D) = 1 - 0.97 = 0.03

Therefore,

P(A and not D) = P(not D) * P(A | not D) = 0.84 * 0.03 = 0.0252

P(not A and D) = P(D) * P(not A | D) = 0.16 * 0.03 = 0.0048

So the probability of an incorrect conclusion is:

P(A and not D) + P(not A and D) = 0.0252 + 0.0048 = 0.03

Therefore, the probability of an incorrect conclusion is 0.03, or 3% (rounded to the nearest tenth of a percent).

Why was this answer deleted prior?

The answer is (B) 45 feet

Step-by-step explanation:

We can use proportions to solve this problem.

Let x be the length of the shadow cast by the telephone pole. Then we have:

(42 / 31.5) = (60 / x)

We can cross-multiply to get:

42x = 31.5 * 60

Simplifying this equation, we get:

x = (31.5 * 60) / 42

x = 45 feet

Therefore, the length of the shadow that the telephone pole casts is 45 feet.

Answer: x=2 is the answer

Answer:

Step-by-step explanation

Rearrange terms

-16=(- 4)- 6 x

-16=-6x - 4

Add 4 to both sides

-16= - 6x - 4

-16 + 4=  -6x  - 4 + 4

Simplify the expression

-16+4=6x - 4+4

-12=6x

Divide both sides by the same factor

-12=6x

-12/-6= -6x/-6

so

x=2

Answer: 12 times

Step-by-step explanation:

165-20=145

12.5x11=137.5

12.5x12=150

Answer:   12.5x+20≥165

  x≥11.6

Step-by-step explanation:

Answer:

2/5 of the cookie

Step-by-step explanation:

12 friends need to split 4 cookies

4 cookies needs to divided by 10 people

[tex]\frac{4cookies}{10 people}[/tex] = [tex]\frac{4}{10}[/tex]

simplify: [tex]\frac{4}{10} = \frac{2}{5}[/tex]

Answer:

2.83333 pounds of flour in each container

Answer:

396 in²

Step-by-step explanation:

To answer this question we need to use pythagorean theorem (a² + b² = c²)

In our case, a would be 14 and b would be 17

Now we have to multiply this by 18

Which rounded would be 396

Hope this helps, have a lovely day! :)

Part 1: a. A. The sample size needs to be greater than or equal to 30.

Part 2: The probability is approximately 0.0013.

Part 3: There is a 10% chance of being at or below a mean oil-change time of 14.9 minutes.

The number of individuals or items in a population that are selected for study.

A. The sample size needs to be greater than or equal to 30.

This is due to the Central Limit Theorem, which states that the sample size of a normal distribution must be 30 or more to produce reliable results.

If a sample size is less than 30, the results may be skewed and not accurately represent the true population mean and standard deviation.

B. The probability is approximately 0.0013.

This probability can be calculated by using the z-score formula and plugging in the mean, standard deviation, and sample size.

The z-score for a sample mean of 15 minutes =-3.3,

which translates to a probability of 0.0013 using the z-score table.

C. There is a 10% chance of being at or below a mean oil-change time of 14.9 minutes.

This can be calculated by using the z-score formula and plugging in the mean, standard deviation, and sample size.

The z-score for a 10% chance= -1.28,

which translates to a mean oil-change time of 14.9 minutes.

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Simultaneous equations are a set of equations that are solved together to determine the values of the variables that satisfy both equations.

1) 4x + 5y = 3 ---(1)

y - 3x = -7 ----(2)

Using the substitution method;

y = -7 + 3x ----(3)

Thus

4x + 5(-7 + 3x) = 3

4x -35 +15x = 3

19x - 35 = 3

19x = 3 + 35

x = 2

Then

4(2) + 5y = 3

8 + 5y = 5

y = 13/5

y = 2 3/5

2) 2x - 4y = 24 ----- x 3

  -3x + 2y = -48 ----- x 2

   6x - 12 y = 72 ---- (3)

  -6x + 4y = -96 ---- (4)

Add 3 and 4

         16y = -24

y = -24/16

Substitute y = -24/16 into (1)

2x - 4(-24/16) = 24

2x + 6 = 24

x = 15

3) -x + y = 13 --- 1

  3x - 4y = 46 ---- 2

y = 13 + x ---- 3

Substitute 3 into 2

3x - 4(13 + x) = 46

3x - 52 - 4x = 46

-x - 52 = 46

x = 98

Substitute x = 98 into (1)

-98 + y = 13

y = 13 + 98

y = 111

Let C be x and D be y

x + y = 180

x = 33 + 6y

x - 6y = 33

x = 180 - y

Substitute and obtain;

180 - y - 6y = 33

180 - 7y = 33

y = 33 - 180/-7

y = 21

Then

x + 21 = 180

x = 180 - 21

x = 159

Lastly

Let small = x , medium = y

x + y = 150

4x + 6y = 764

x = 150 - y

4(150 - y) + 6y = 764

600 - 4y + 6y = 764

600 + 2y = 764

2y = 764 - 600

y = 82

Then;

x + 82 = 150

x = 68

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The solutions to the simultaneous equations are:

1) x = 2 and y = -1

2) x = 18 and y = 3

3) y = -7 and x = 6

There are three main methods in solving simultaneous equations and they are:

1) Elimination Method

2) Substitution Method

3) Graphical Method

1) 4x + 5y = 3

y = 3x - 7

Substitute 3x - 7 for y in the first equation to get:

4x + 5(3x - 7) = 3

4x + 15x - 35 = 3

19x - 35 = 3

19x = 35 + 3

19x = 38

x = 38/19

x = 2

Thus:

y = 3(2) - 7

y = -1

2) 2x - 4y = 24

-3x + 2y = -48

Multiply eq 2 by 2 and eq 1 by 1 to get:

2x - 4y = 24    -----(3)

-6x + 4y = -96   -----(4)

Add eq 3 to eq 4 to get:

-4x = -72

x = 18

2(18) - 4y = 24

36 - 4y = 24

36 - 24 = 4y

4y = 12

y = 3

3) -x + y = -13

3x - 4y = 46

From eq 1, x = y + 13

Thus:

3(y + 13) - 4y = 46

3y + 39 - 4y = 46

39 - y = 46

y = 39 - 46

y = -7

x = -7 + 13

x = 6

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Answer:

Below

Step-by-step explanation:

3.15 can be read as  3 and 15 hundredths =   3   15/100  = 3  3/20

Answer:  63/20

Step-by-step explanation:

Answer: D. 9.68

Step-by-step explanation:

145.2 oz/ 15 cups = 9.68 oz per cup