need help ASAP! Pls+Ty

Answer:

0

Step-by-step explanation:

The given statement "the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring." is False.

The union of two events A and B represents the event that at least one of the events A or B occurs. The probability of the union of two events can be calculated using the formula:

P(A or B) = P(A) + P(B) - P(A and B)

On the other hand, the intersection of two events A and B represents the event that both events A and B occur. The probability of the intersection of two events can be calculated using the formula:

P(A and B) = P(A) * P(B|A)

where P(B|A) is the conditional probability of B given that A has occurred.

It is possible for the probability of the union of two events to be greater than the probability of the intersection of two events if the two events are not mutually exclusive.

In this case, the probability of both events occurring together (the intersection) may be relatively small, while the probability of at least one of the events occurring (the union) may be relatively high.

In summary, the probability of the union of two events occurring can sometimes be greater than the probability of the intersection of two events occurring, depending on the relationship between the events.

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The probability of each event is as follows: (a) P(red) = 5/8 (b) P(odd) = 1/2 (c) P(red or odd) = 9/16 (d) P(blue or even) = 3/4.

(a) The probability of drawing a red marble is given by the number of red marbles divided by the total number of marbles:

P(red) = number of red marbles / total number of marbles

P(red) = 10 / (10 + 6) = 10/16 = 5/8

(b) The probability of drawing an odd-numbered marble can be calculated by considering the number of odd-numbered marbles (5 red marbles + 3 blue marbles) divided by the total number of marbles:

P(odd) = number of odd-numbered marbles / total number of marbles

P(odd) = (5 + 3) / (10 + 6) = 8/16 = 1/2

(c) To find the probability of drawing a red or odd-numbered marble, we need to consider the marbles that satisfy either condition. There are 5 red marbles and 5 odd-numbered marbles (1, 3, 5, 7, 9). However, we need to subtract the number of marbles that satisfy both conditions (red and odd) to avoid double-counting (1 red marble). Therefore:

P(red or odd) = (number of red marbles + number of odd-numbered marbles - number of marbles that satisfy both conditions) / total number of marbles

P(red or odd) = (5 + 5 - 1) / (10 + 6) = 9/16

(d) To find the probability of drawing a blue or even-numbered marble, we need to consider the marbles that satisfy either condition. There are 6 blue marbles and 7 even-numbered marbles (2, 4, 6, 8, 10). Again, we need to subtract the number of marbles that satisfy both conditions (blue and even) to avoid double-counting (1 blue marble). Therefore:

P(blue or even) = (number of blue marbles + number of even-numbered marbles - number of marbles that satisfy both conditions) / total number of marbles

P(blue or even) = (6 + 7 - 1) / (10 + 6) = 12/16 = 3/4

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Answer:

for -9x+2>18 its x<-16/9 and for 13x+15≤-4 its x<-19/13

Step-by-step explanation:

The expected value in a binomial situation with n = 18 and π = 0.60 is E(X) = np = 18 * 0.60 = 10.8.

In a binomial situation, the expected value, denoted as E(X), represents the average or mean outcome of a random variable X. It is calculated by multiplying the number of trials, denoted as n, by the probability of success for each trial, denoted as π.

In this case, we are given n = 18 and π = 0.60. To find the expected value, we multiply the number of trials, 18, by the probability of success, 0.60.

n = 18 (number of trials)

π = 0.60 (probability of success for each trial)

To find the expected value:

E(X) = np

Substitute the given values:

E(X) = 18 * 0.60

Calculate the expected value:

E(X) = 10.8

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Answer:

8 to 7

Step-by-step explanation:

5/7 to 5/8 = 40/56 to 35/56

We then have:

5/7 to 5/8 = 40 to 35

Now...

40 to 35 = 8 to 7

P.S: These colons ':' mean the same as 'to' in ratios

Answer:

154

Step-by-step explanation:

180-26=154

Answer:

  about 840.4 ft²

Step-by-step explanation:

You want the surface area of a regular pentagon with a side length of 16 ft and a slant height of 10 ft.

The area of the 5-sided base is ...

  A = 1/4(√(5(5 +2√5))s² . . . . for side length s

The area of the 5 triangular faces is ...

  A = 5×(1/2)sh

Using s = 16 ft and h = 10 ft, we find the total surface area to be ...

  SA = 1/4(√(5(5 +2√5))(16 ft)² +5/2(16 ft)(10 ft) ≈ 840.4 ft²

The surface area of this pentagonal pyramid is about 840.4 square feet.

__

Additional comment

The problem statement says the figure has a hexagonal base. We only count five sides, so have worked the problem as though it has a pentagonal base.

Either way, the figure cannot exist. The lateral area of such a figure must exceed the base area. In this figure, the base area is about 10% greater than the lateral area, meaning the points of the triangular faces cannot meet to form a pyramid.

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Answer:

Mean: 5

Median: 4

Mode: 3

Step-by-step explanation:

Therefore ,there are 158,184,000 ways to create a license plate in this system.

A selection from a group of separate items is called a combination in mathematics, and the order in which the elements are chosen is irrelevant (unlike permutations). An apple and a pear, an apple and an orange, or a pear and an orange are three combinations of two fruits that can be chosen from a set of three fruits, such as an apple, an orange, and a pear. Formally speaking, a set S's k-combination is a subset of S's k unique components. Two combinations are therefore equal if and only if they have the same elements in both combinations.

According to the counting principle, the total number of ways to obtain a license plate is calculated by multiplying the number of times each of these events might occur together.

The first number (the digits 1 through 9) can be obtained in nine different ways.

There are 26 methods to obtain the first letter. There are 26 ways to obtain the following letter (repetition is acceptable).

There are 26 methods to get the third letter, 10 ways to get the next number (zero is acceptable), and 10 ways to get the following number with repetitions.

How many ways are there to get the next number? 10 ways\s.

Thus ,total options for obtaining a license plate:

9 x 26 x 26 x 26 x 10 x 10=158184000

Therefore ,there are 158,184,000 ways to create a license plate in this system.

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The perimeter of a semi-circle with a 20cm diameter is approximately 31.4cm.

To find the perimeter of a semi-circle with a 20cm diameter, we first need to find the circumference of the full circle.

We can do this by using the formula:
C = πd

Where C is the circumference, π is a mathematical constant (approximately equal to 3.14), and d is the diameter. Plugging in the given diameter of 20cm, we get:
C = π(20cm) = 62.8cm

Next, we need to find half of the circumference since we only have a semi-circle. This can be done by dividing the full circumference by 2:
C/2 = 62.8cm/2 = 31.4cm

Therefore, the perimeter of a semi-circle with a 20cm diameter is approximately 31.4cm.

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To find the scalar projections, uv and vu, we must first find the magnitude of each vector and the angle between the vectors.

The magnitude of vector u is sqrt\((2^2 + 1^2) = sqrt(5)\) and the magnitude of vector v is \(sqrt(4^2 + (-1)^2) = sqrt(17)\). The angle between the vectors is given as 40 degrees.Using the formula for the scalar projection of u onto v, we get: uv = (u . v)/|v|, where u . v is the dot product of u and v.u . v = (2)(4) + (1)(-1)

= 8 - 1

= 7uv

= \((7)/(sqrt(17))\)

≈ 1.33Using the formula for the scalar projection of v onto u, we get: vu = (v . u)/|u|, where v . u is the dot product of v and u.v . u

= (4)(2) + (-1)(1)

= 8 - 1

= 7vu

= (7)/(sqrt(5))

≈ 3.16

Therefore, uv = 1.33 and

vu = 3.16

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The probability of having 7 boys in a family with 7 children is 1 out of 128, as there is only one favorable outcome out of 128 total possible outcomes.

To find the probability, we need to calculate n(E) and n(S).

In this case, event E represents the scenario where all 7 children are boys. The sample space S consists of all possible permutations of boys and girls for the 7 children, which is 2^7 = 128.

This is because each child has 2 possibilities (boy or girl), and we multiply these possibilities for all 7 children.

Since event E includes only one specific outcome (all boys), n(E) is equal to 1. Therefore, both n(E) and n(S) are 1 and 128, respectively. The probability of having 7 boys is given by n(E)/n(S) = 1/128.

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Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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The candy store will use 103 grams of sugar in 10 hours.

To find out how many grams of sugar the store will use in 10 hours, we can simply multiply the amount of sugar used in one hour (10.3 grams) by the number of hours (10).

To solve the problem, we use a simple multiplication formula: the amount used per hour (10.3 grams) multiplied by the number of hours (10) to find the total amount of sugar used in 10 hours.

We can interpret this problem using a rate equation: the rate of sugar usage is 10.3 grams/hour, and the time period is 10 hours. Multiplying the rate by the time gives the total amount of sugar used.

So the calculation would be:

10.3 grams/hour x 10 hours = 103 grams

Therefore, the candy store will use 103 grams of sugar in 10 hours.

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Answer:

239 miles per gallon for a round trip.

Step-by-step explanation:

you'd need to achieve 238,900 / 2000 = 119.5 miles per gallon for a one way trip,

Answer:

Mean:  76

Median:  69

Mode:  63

Range: 46

Standard deviation: 15.5

Step-by-step explanation:

Given:

If each value in the data set is increased by a constant k, the mean, median, and mode will be increased by k.  

The range and standard deviation will remain unchanged.

Therefore, if each value in the data set is increased by 14:

___________

\( \: \)

16.8 - v = 6v

128 - v = 6v

-v - 6v = -128

-7v = -128

7v = 128

v = 128 ÷ 7

v = 18 2/7

For situation 1, the z-value is approximately 1.96, and for situation 2, the z-value is approximately 0.84.

To find the value of z for each situation, we need to use the standard normal distribution table or a calculator. The standard normal distribution has a mean of 0 and a standard deviation of 1.

1. Situation 1: To find z for a given probability, we can use the cumulative distribution function (CDF). For example, if we want to find the z-value for a probability of 0.95, we can find it on the table or use a calculator. The z-value for a probability of 0.95 is approximately 1.96.

2. Situation 2: To find z for a given percentile, we can use the inverse cumulative distribution function (ICDF). For example, if we want to find the z-value for the 80th percentile, we can find it on the table or use a calculator. The z-value for the 80th percentile is approximately 0.84.

Remember to round your answers to two decimal places as requested.

In conclusion, for situation 1, the z-value is approximately 1.96, and for situation 2, the z-value is approximately 0.84.

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By applying Pythagoras' theorem, the length of x is equal to 10 units.

In Mathematics and Geometry, Pythagorean's theorem is modeled or represented by the following mathematical equation (formula):

x² + y² = z²

Where:

x, y, and z represents the length of sides or side lengths of any right-angled triangle.

Based on the information provided about the side lengths of this right-angled triangle, we have the following equation:

x² = y² + z²

x² = 8² + 6²

x² = 64 + 36

x = √100

x = 10 units.

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Answer:

x = -5

Step-by-step explanation:

3x + 1 = 2x - 4

x + 1 = -4

x = -5

Answer:

7y^2

Step-by-step explanation:

The number of F ratios which calculated in a 3 way ANOVA is 7.

So, the correct answer is C.

In a three-way ANOVA, which involves three independent variables, a total of 7 F ratios are calculated.

This includes the main effect of each independent variable (3 F ratios), the two-way interactions between the independent variables (3 F ratios), and the three-way interaction between all three independent variables (1 F ratio).

Thus, the correct answer is c. 7 F ratios.

These F ratios help in determining the significance of each factor and interaction effect on the dependent variable in the analysis.

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The probability that the average score of the golfers exceeded 62 = 0.0228

Given the mean score of all golfers, μ = 72

and the Standard Deviation, σ = 4

Number of golf players, n = 64

We have to find the probability that the average score of the golfers exceed 73. i.e., x = 73

This follows the Normal Distribution.

Hence the z-score, Z = (x - μ)/(σ/√n)

                                   = (73 - 72)√64/4

                                   = 2

Probability that the average score of the golfers exceeded 73 = P(Z > 2)

                                                                                                        = 0.0228 [from the z-tables]

The question is incomplete. Find the complete question below:

t\The average score of all golfers for a particular course has a mean of 72 and a standard deviation of 4. Suppose 64 golfers played the course today. Find the probability that the average score of the golfers exceeded 73 .

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Answer:

The linear equation is y = 450 - 30 x, where y is the number of pages

Lourdes has left to read after x days

Step-by-step explanation:

Each day, Lourdes reads 30 pages of a 450-page book

- We need to write a linear equation to represent the number of pages

 Lourdes has left to read after x days

∵ Lourdes reads 30 pages each day

∵ Lourdes will read for x days

∴ The number of pages Lourdes will read in x day = 30 x

- The left pages will be the difference between the total pages of the

 book and the pages Lourdes read

∵ The book has 450 pages

∵ Loured will read 30 x in x days

∴ The number of pages left = 450 - 30 x

- Assume that y represents the number of pages Lourdes has left

 to read after x days

∴ y = 450 - 30 x

The linear equation is y = 450 - 30 x, where y is the number of

pages Lourdes has left to read after x days

The answer is correct, we can plot both triangles on a Coordinate plane and visually inspect the result. If we plot triangle ABC with vertices A(-3, 3), B(0, 4), and C(-3, 0), and then plot the image triangle A'B'C' with vertices A'(-3, -1), B'(0, 0), and C'(-3, -4), we can see that the image is a translation of the original triangle down by 4 units.

To determine the coordinates of the vertices of the image of triangle ABC after being translated 4 units down, we need to subtract 4 from the y-coordinates of each vertex. This is because a translation is a type of transformation that moves each point of a figure a certain distance in a certain direction.

So, starting with the preimage of triangle ABC with vertices at A(-3, 3), B(0, 4), and C(-3, 0), we can find the image by subtracting 4 from the y-coordinates:

A'(-3, 3 - 4) = A'(-3, -1)

B'(0, 4 - 4) = B'(0, 0)

C'(-3, 0 - 4) = C'(-3, -4)

Therefore, the coordinates of the vertices for the image after the translation are A'(-3, -1), B'(0, 0), and C'(-3, -4).

So, the correct option is A) A′(−3, −1), B′(0, 0), C′(−3, −4).

To check if the answer is correct, we can plot both triangles on a coordinate plane and visually inspect the result. If we plot triangle ABC with vertices A(-3, 3), B(0, 4), and C(-3, 0), and then plot the image triangle A'B'C' with vertices A'(-3, -1), B'(0, 0), and C'(-3, -4), we can see that the image is a translation of the original triangle down by 4 units.

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The probability that the sample mean would be greater than 148.6 millimeters is 0.017

The spread of all the data points in a data collection is taken into account by the variance, which is a measure of dispersion.

Given  Population mean μ= 147

Population Variance σ^2 = 25

So, population SD = 5

Size of sample = n = 44 Sample mean = x

To find P( y > 148.6) :

SE =σ/√n =

5/√44= 0.7538

Transforming to Standard Normal Variate:

Z = (x - μ )/SE    

= (148.6 - 147)/0.7538    

= 2.1226

From Table of Area Under Standard Normal Curve, corresponding to Z = 2.1226, area = 0.4830.

So, required probability = 0.5 - 0.4830 = 0.017

The probability that sample mean would be greater than 148.6 millimeters is 0.017

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Answer:

C is the  answer

Step-by-step explanation:

The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. The measure of side DE is 12.3.

The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,

\(c =\sqrt{a^2 + b^2 -2ab\cdot Cos\theta}\)

where

c is the third side of the triangle

a and b are the other two sides of the triangle,

and θ is the angle opposite to the third side, therefore, opposite to side c.

In the given triangle the length of the side DE can be found using the law of cosine. Therefore, the length of the side DE can be written as,

DE² = DF² + EF² - 2(EF)(DF)(Cos 59°)

DE² = 144 + 169 - 2(12 × 13 × Cos 59°)

DE² = 144 + 169 - 160.6918

DE² = 152.30812

DE = 12.3413 ≈ 12.3

Hence, the measure of side DE is 12.3.

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The inequality that can be used to represent the number of miles, x, Jaime could bicycle on the 4th week to meet his goal is 240 + 310 + 320 + x ≥ 4 (280).

What is inequality?

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other.

For the next four weeks, Jaime wants to log at least 280 miles per week on average. Jamie's objective can be graphically expressed by the inequality: T4, or alternatively T 4 if T is the total number of miles he will pedal his bicycle for four weeks (280).

The sum of the distances Jamie has covered and has yet to cover is the total number of miles Jamie will cycle during this time. Hence,  T = 240 + 310 + 320 + x. Replacing this term into the inequality T ≥ 4(280) gives 240 + 310 + 320 + x ≥ 4(280). Therefore, choice D is the correct answer.

Thus, the correct answer is  240 + 310 + 320 + x ≥ 4 (280).

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