Dakota is a quality control manager for a manufacturing plant that produces batteries for tablet computers. Based on prior history, Dakota knows that 0.6% of all tablet computer batteries produced are defective. He selects a random sample of n=1,200 tablet computer batteries from a recently produced lot and tests each battery to determine whether it is defective. What is the probability that Dakota finds 5 or fewer defective batteries? Use a TI-83, TI-83 plus, or TI-84 calculator to find the probability.

Round your answer to four decimal places.

Answer:

  47.5%    (rounds to 48%)

Step-by-step explanation:

You want the probability that a tree has between 240 and 300 apples, given the distribution of numbers of apples is normal with mean 300 and standard deviation 30.

The given diagram shows the center 95% of numbers of apples lies between 240 and 360. The number between 240 and 300 is half that symmetical distribution, so is ...

  95%/2 = 47.5%

The probability a tree will have between 240 and 300 apples is about 47.5%.

__

Additional comment

The figure "95%" is an approximation. A closer value is 95.45%. Hence, a closer value to the probability is 47.7%.

No rounding requirement is shown. To the nearest whole percentage point, the probability would be 48%.

<95141404393>

ABC forms a right-angled triangle

Let the distance between AB = x

Using Pythagoras theorem

Sin 30 = Opposite / Hypoteneuse

Sin 30 = 12 in/ x

However, From the equilateral triangle, all sides are = 2 and the angles are all = 60 degrees. Then we take a right-angled triangle out of it. This means that the base equals 1, and the top side is halved and equals 30 degrees.

Using Pythagoras' theorem, Sin 30 = 1/ 2

Substituting back into the equation, we get:

1/ 2 = 12 in / x

Cross multiplying, we get:

x = 24 in

Recall x = AB

AB = 24 inches

To remember the angles and their respective formula, use SOHCAHTOA

Where sin x = Opposite / Hypoteneuse

Cos x = Adjacent / Hypoteneuse

Tan x = Opposite / Adjacent

Tamara should expect the sum of the two cubes to be equal to 7 around 30 times when rolling the two number cubes 180 times.

To determine how many times Tamara should expect the sum of the two number cubes to be equal to a certain value, we need to analyze the chart and calculate the probabilities.

Let's examine the chart and count the number of times each sum occurs:

Sum: 2, Occurrences: 1

Sum: 3, Occurrences: 2

Sum: 4, Occurrences: 3

Sum: 5, Occurrences: 4

Sum: 6, Occurrences: 5

Sum: 7, Occurrences: 6

Sum: 8, Occurrences: 5

Sum: 9, Occurrences: 4

Sum: 10, Occurrences: 3

Sum: 11, Occurrences: 2

Sum: 12, Occurrences: 1

Now, let's calculate the probabilities of each sum occurring.

Since there are 36 possible combinations when rolling two number cubes, the probability of each sum is the number of occurrences divided by 36:

Probability of sum 2 = 1/36

Probability of sum 3 = 2/36

Probability of sum 4 = 3/36

Probability of sum 5 = 4/36

Probability of sum 6 = 5/36

Probability of sum 7 = 6/36

Probability of sum 8 = 5/36

Probability of sum 9 = 4/36

Probability of sum 10 = 3/36

Probability of sum 11 = 2/36

Probability of sum 12 = 1/36

To find out how many times Tamara should expect a certain sum when rolling the two number cubes 180 times, we can multiply the probability of that sum by 180.

For example, to find the expected number of times the sum is 7:

Expected occurrences of sum 7 = (6/36) [tex]\times[/tex] 180 = 30

Similarly, we can calculate the expected occurrences for all other sums.

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The value of the expression [tex]n^2 - 11n + 10[/tex] is equivalent to (n - 1)(n - 10).

To find the value of the expression [tex]n^2 - 11n + 10[/tex], we can follow these steps:

Start with the given expression: [tex]n^2 - 11n + 10.[/tex]

Look for any like terms that can be combined. In this case, there are no like terms.

Since there are no like terms, we can simplify further by factoring the expression. We need to find two numbers that multiply to give 10 (the constant term) and add up to -11 (the coefficient of the middle term, which is -11n).

The numbers that satisfy these conditions are -1 and -10, because

(-1) × (-10) = 10 and (-1) + (-10) = -11.

Now we can rewrite the expression using these numbers:

[tex]n^2 - 11n + 10 = (n - 1)(n - 10).[/tex]

So the factored form of the expression is (n - 1)(n - 10).

Therefore, the value of the expression [tex]n^2 - 11n + 10[/tex] is equivalent to (n - 1)(n - 10).

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The area of the required shaded portion is 123 ft²

Given is figure having some shaded portion we need to find the area of the same,

So, the shaded portion is two right isosceles triangles with equal side measuring 14 ft and 7 ft,

So, to find the same, we will calculate the area of the triangles and add them,

Area of a triangle = 1/2 x base x height

Area of the shaded portion = 1/2 x 7 x 7 + 1/2 x 14 x 14

= 122.5 ft²

≈ 123 ft²

Hence the area of the required shaded portion is 123 ft²

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Answer:

5.85

Step-by-step explanation:

Answer:

y=3x+5

Step-by-step explanation:

you do 4 times 3 then subtract that from 17

The length of FE is equal to 35 units.

In Mathematics and Geometry, the triangle midpoint theorem states that the line segment which connects the midpoints of two (2) sides of a triangle must be parallel to the third side, and it's congruent to one-half of the third side.

By applying the triangle midpoint theorem to the triangle, we have the following:

AE = 1/2(FE)

BD ≅ FE (midpoints of AC and CE)

BD = FE = 35 units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The given picture with Midpoints B, D, and F, AC is 50 units, CE is 60 units, and BD is 35 units. The length of segment FE is determined to be 35 units.

In the given picture, let's label the points as A, B, C, D, E, and F. It is mentioned that points B, D, and F are midpoints.

Given information:

AC = 50

CE = 60

BD = 35

Since B, D, and F are midpoints, we know that BD is equal to half of AC and half of CE. Therefore, BD = AC/2 and BD = CE/2.

We are given that BD = 35, so we can set up the equations:

35 = AC/2    ...(Equation 1)

35 = CE/2    ...(Equation 2)

Let's solve Equation 1 for AC:

AC = 35 * 2

AC = 70

Similarly, solving Equation 2 for CE:

CE = 35 * 2

CE = 70

Now, let's consider triangle AFE. Since B and D are midpoints, we know that BD is parallel to FE, and FD is parallel to AE. Therefore, triangle AFE is similar to triangle ADC.

In similar triangles, corresponding sides are proportional. Hence, we can write the following ratios:

FE/AC = FD/AD

Substituting the known values, we get:

FE/70 = 35/AC

Cross-multiplying, we have:

FE * AC = 70 * 35

Since we know AC is 70, we can solve for FE:

FE = (70 * 35) / 70

FE = 35

Therefore, the length of FE is 35 units.

the given information, in the given picture with midpoints B, D, and F, AC is 50 units, CE is 60 units, and BD is 35 units. The length of segment FE is determined to be 35 units.

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The graph shows the solution set for -4.4 ≥ 1.6x - 3.6 is Graph I.

To solve the inequality -4.4 ≥ 1.6x - 3.6, we can follow these steps:

Add 3.6 to both sides of the inequality to isolate the term with x:

-4.4 + 3.6 ≥ 1.6x - 3.6 + 3.6

-0.8 ≥ 1.6x

Divide both sides of the inequality by 1.6

-0.8 / 1.6 ≥ 1.6x / 1.6

-0.5 ≥ x

So, the solution to the inequality is x ≤ -0.5.

Now, from the solution the graph for the inequality start with closed dot from 0.5 and move towards the points -0.6, -0.7, -0.8, ....

Thus, the graph shows the solution set for -4.4 ≥ 1.6x - 3.6 is Graph I.

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Given statement solution is :- The Inverse line that represents [tex]f^(-1[/tex]) is [tex]f^(-1)[/tex] (x) = 3x + 4.

To find the inverse function of f(x) = (x - 4)/3, we need to swap the roles of x and y and solve for y. Let's start by writing the equation with y instead of f(x):

y = (x - 4)/3

Now, let's interchange x and y:

x = (y - 4)/3

To solve for y, we can isolate it by multiplying both sides of the equation by 3:

3x = y - 4

Next, let's add 4 to both sides:

3x + 4 = y

Finally, we can write the inverse function as:

[tex]f^(-1)(x)[/tex] = 3x + 4

So, the Inverse line that represents [tex]f^(-1[/tex]) is [tex]f^(-1)[/tex] (x) = 3x + 4.

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The numerical value of x in the dimensions of the rectangle is 9.

A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.

Area of a rectangle is expressed as;

A = length × width

From the diagram:

Wdith of the rectangle = x - 2

Length of the rectangle = x + 5

Area = 98 ft²

Since area of a rectangle =  length × width:

98 = ( x - 2 )( x + 5 )

Simplify

( x - 2 )( x + 5 ) = 98

Apply distributive property:

x² + 3x - 10 = 98

x² + 3x - 10 - 98 = 0

x² + 3x - 108 = 0

Factor using AC method:

( x - 9 )( x + 12 ) = 0

Hence:

x - 9 = 0 or x + 12 = 0

x = 9 or x = -12

Since, we are dealing with dimensions, we take the positive value.

Hence, the value of x is 9.

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Answer:

The surface area of the hexagonal pyramid is 313.13 square inches.

Step-by-step explanation:

Hexagonal pyramid,

Surface Area = Area of hexagon base + areas of six triangles

b = 6

h = 12.2 (height of the triangle)

A = [tex]\frac{3\sqrt{3} }{2}b + 6(\frac{1}{2} bh)[/tex]

A = [tex]\frac{3\sqrt{3} }{2}b +3bh[/tex]

A = [tex]\frac{3\sqrt{3} }{2}6 +3*6*12.2\[/tex]

A = 93.53 + 219.6

A = 313.13 square inches

Answer:

  x = 2

Step-by-step explanation:

You want the value of x that satisfies x|x| = 4.

The absolute value function splits the domain of the equation into two parts.

For x < 0, the equation is ...

  x(-x) = 4

  x² = -4

There are no real solutions in this domain.

For x ≥ 0, the equation is ...

  x² = 4

  x = √4 = 2

The only solution is x = 2.

__

Additional comment

In the attachment, we have rewritten the equation to ...

  x|x| -4 = 0

The graphing calculator readily identifies x-intercepts, so this is a convenient way to find the solution. You will notice that for x < 0, the graph is of -x²-4, which is never zero.

<95141404393>

The function to model the amount remaining after t hours is:

[tex]A(t) = 500 \times e^{-0.045t}[/tex]

We have,

To model the amount remaining after t hours for the substance sodium-24, which decays at a rate of 4.5% per hour compounded continuously, we can use the formula for continuous exponential decay:

[tex]A(t) = A(0) \times e^{-rt}[/tex]

Where:

A(t) is the amount remaining after t hours,

A(0) is the initial amount,

e is the base of the natural logarithm (approximately 2.71828),

r is the decay rate (expressed as a decimal).

In this case,

The initial amount A(0) is 500 grams, and the decay rate r is 4.5% per hour, which can be expressed as 0.045 (decimal form).

Thus,

The function to model the amount remaining after t hours is:

[tex]A(t) = 500 \times e^{-0.045t}[/tex]

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The area of the slice of pizza is 25.1 inches squared.

The circular pizza has a diameter of 16 inches. Each slice of pizza have a angle of 45 degrees.

Therefore, the area of the slice of pizza can be calculated as follows:

area of the slice of pizza = ∅ / 360 × πr²

where

Therefore,

r = 16  /2

r = 8 inches

area of the slice of pizza = 45 / 360 × 3.14 × 8²

area of the slice of pizza = 45 / 360 × 3.14 × 64

area of the slice of pizza = 9043.2 / 360

area of the slice of pizza = 25.12 inches²

area of the slice of pizza = 25.1 inches²

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The solution of the given equations is: (3,-1).

Here, we have,

from the given graph we get,

1st line passes through ( 0,2 ) and (2,0)

so, equation: y = -x+2 .....1

2nd line passes through ( 0,-4 ) and (4,0)

so, equation: y = x-4 .....2

now, from 1 and 2 we get,

-x + 2 = x -4

or, 2x = 6

or, x = 3

so, we have, y = -1

so, the point of intersection is (3, -1)

Hence, The solution of the given equations is: (3,-1).

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The percentage of scores that fall between 65 and 75 is approximately [tex]2 \times 34 = 68%.[/tex]%

To determine the percentage of scores that fall between 65 and 75, we can use the properties of the normal distribution.

Mean score = 75

Standard deviation = 5

We know that the normal distribution is symmetric around the mean, and approximately 68% of the data falls within one standard deviation from the mean.

This means that about 34% of the scores fall between the mean and one standard deviation above the mean.

To calculate the percentage of scores between 65 and 75, we need to determine how many standard deviations away from the mean 65 and 75 are.

For 65:

(65 - 75) / 5 = -2

For 75:

(75 - 75) / 5 = 0

From the calculations, we can see that 65 is 2 standard deviations below the mean, and 75 is at the mean.

Since the distribution is symmetric, we can consider the percentage of scores between the mean and one standard deviation above the mean (34%) and double it to account for the scores between the mean and one standard deviation below the mean.

Therefore, the percentage of scores that fall between 65 and 75 is approximately 2 [tex]\times[/tex] 34% = 68%.

However, none of the given answer options match the calculated result. Therefore, none of the provided answer options accurately represent the percentage of scores between 65 and 75 based on the given information.

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Answer:

Step-by-step explanation:

ll hypothesis The critical value for this test is 9.488. Based on the test statistic of 1.358, we fail to reject the null hypothesis that the amount of smoking is independent of seat belt use. In other words, there is not enough evidence to support the claim that seat belt use and smoking habits are related.

Personal Note:

You really need to study, or you will end taking summer courses. trust me school isn't that easy and one time I failed I took summer courses but then I passed these summer courses with god's help. so please focus on your studys.

The Triangle Inequality Theorem holds for these values, and only one triangle is possible with these side lengths. Lucas' claim is false.

According to the Triangle Inequality Theorem, any two triangle sides' sums must be greater than the length of the third side. In other words, the following three inequalities must hold for any three positive numbers, a, b, and c:

a+b>c

a+c>b

b+c>a

In this case, a=9, b=13, and c=15. Let's check if the Triangle Inequality Theorem holds for these values:

9+13>15 (true)

9+15>13 (true)

13+15>9 (true)

Therefore, the Triangle Inequality Theorem holds for these values, and only one triangle is possible with these side lengths.

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If we know that <C is congruent to <E, we can say that: (a). the two triangles are similar by SAS.

from the question, we have the following parameters that can be used in our computation:

The triangles (see attachment)

Two triangles are similar when the ratio of their corresponding sides are equal and their corresponding angles are congruent.

So, we have

Ratio = BC/AC = 6/3 = 2.

Ratio = FE/DE = 4/2 = 2.

Since we know that <C is congruent to <E, we can say that the two triangles are similar by side, angle, side (SAS) criterion.

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Answer:

It maybe 12,000/120,000

Step-by-step explanation:

12months a year

12+12=24 so,

500×24=12,000

or 120,000

Autumn's bank registry will be :

Transaction Amount Balance

Paycheck $1275.00 $1275.00

Rent $400.00 $875.00

Utilities $75.00 $800.00

Cell Phone $80.00 $720.00

Subway Pass $120.00 $600.00

Groceries $200.00 $400.00

Work Clothes $100.00 $300.00

Entertainment $100.00 $200.00

Savings $200.00 $0.00

As you can see, Autumn has $0.00 left over at the end of the month. This means that she is spending more money than she is earning. In order to create a budget that works for her, Autumn will need to find ways to cut back on her expenses. Some possible areas where she could cut back include:

Autumn could look for a cheaper apartment or move in with more roommates. Autumn could turn off lights and appliances when she's not using them and seal up any cracks or holes in her apartment to keep the heat in during the winter and the cool air in during the summer.

By cutting back on her expenses, Autumn can create a budget that works for her and save money for the future.

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Step-by-step explanation:

1 qt = 2 pts     multiply both sides by two

2 qt = 4 pints

Answer:

A. mBC = 71

B. mAB = 142

C. AD = 30

D. BD = 30

E. YD = 16

F. DC = 18

Step-by-step explanation:

A. mBC = mAC = 71

B. mAB = mBC + mAC = 71 + 71 = 142

C. AD = AB/2 = 60/2 = 30

D. BD = AD = 30

E. YA^2 = YD^2 + AD^2

YD^2 = YA^2 - AD^2 = 34^2 - 30^2 = 1156 - 900 = 256

YD = √256 = 16

F. DC + YD = YC

DC = YC - YD = 34 - 16 = 18

Answer: the question doesn't give that much information but you would have 7/4 or 1.75 green counters.

Step-by-step explanation: 7/4 as a decimal is 1.75

Below are the right probabilities for each scenario;

8. P(red, then green) [tex]\frac{1}{32}[/tex]; P(yellow, then blue) = [tex]\frac{1}{16}[/tex] and P(blue both times) [tex]\frac{1}{4}[/tex]

9. The probability of choosing a boy then rolling a number that is at most 4 is [tex]\frac{5}{14}[/tex]

10. The probability that both flights will be delayed is [tex]\frac{2}{7}[/tex].

11. P(nickel, then quarter) [tex]\frac{1}{20}[/tex];  P(penny, then not a dime) [tex]\frac{1}{10}[/tex]; P(both dimes)[tex]\frac{3}{20}[/tex]; P(both nickels) [tex]\frac{1}{20}[/tex]

For the compounded probability, we can solve them the following way;

8. a) P(red, then green) = P(red) × P(green) = (2/8) × (1/8) = 1/32

b) P(yellow, then blue) = P(yellow) × P(blue) = (1/8) ×(4/8) = 1/16

c) P(blue both times) = P(blue) × P(blue) = (4/8) ×(4/8) = 1/4

9. There are 28 total students and 6 total outcomes on a standard die.

P(boy, then a number at most 4) = (15/28) × (4/6) = 5/14

10. The probability of the first flight being delayed is 6/14, and the probability of the second flight being delayed is 8/12.

P(both flights delayed) = 6/14 × 8/12 = 2/7

11. There are 25 total coins: 4 pennies, 6 nickels, 10 dimes, and 5 quarters.

a) P(nickel, then quarter)  = (6/25) × (5/24) = 1/20

b) P(penny, then not a dime)  = (4/25) × (15/24) = 1/10

c) P(both dimes) = (10/25) × (9/24) = 3/20

d) P(both nickels) = (6/25) × (5/24) = 1/20

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Answer:

A.  19.8

B.  15.9

Step-by-step explanation:

A.  

To find the geometric mean between two numbers, you multiply them together and then take the square root of the product.

28 × 14 = 392

[tex]\sqrt{392}[/tex] = 19.799 ≈ 19.8

B.

7 x 36 = 252

[tex]\sqrt{252}[/tex] = 15.8745 ≈ 15.9

Answer:

-6

Step-by-step explanation:

Because two lines that are parallel have the same slope