If P (A) = 0. 5, P(B) = 0. 1, and A and B are mutually exclusive, find P(A or B).

(2x + 5)² in the denominator represents the total number of gallons of gas purchased in the whole trip squared.

Annabella spends $2.25 per gallon on gas at the gas station. After driving a certain distance, she stops at a second gas station and spends $2.15 per gallon on gasoline.

Annabella can express her average cost per gallon of gasoline as 2.25 × 2.15(x + 5)/(2x + 5)²

The meaning of the parts of this rational expression in the context of the situation are as follows: 2.25 and 2.15 are the cost per gallon of gas at the two different gas stations.

x represents the number of gallons of gas bought at the first station.

5 is the number of miles driven between the first and second gas stations. And 2x + 5 is the total number of gallons of gas used in the entire trip (from the first gas station to the second).

Therefore, (x + 5) is the amount of gasoline bought from the second gas station, and 2x is the amount of gasoline bought from the first gas station.

The expression (x + 5)/(2x + 5) represents the weighted average of the cost per gallon of gas at the two gas stations.

Finally, (2x + 5)² in the denominator represents the total number of gallons of gas purchased in the whole trip squared.

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Answer:

x = 2

Step-by-step explanation:

19x - 7x + 8x = 48 - 8

20x = 40

20x/20 = 40/20

x =2

Answer:

x=2

Step-by-step explanation:

\(19x + 8 - 7x = 48 - 8x \\ ⟹ 12x + 8 = 48 - 8x \\ ⟹ 12x + 8x = 48 - 8 \\ ⟹20x = 40 \\ ⟹ x = \frac{40}{20} \\ ⟹x = 2\)

Answer

Model:

Equation:

Solution:

Step-by-step explanation

The problem presents 3 variables:

• number of miles Julie jogs per time

• number of times she jogs per day

• total number of miles she jogs per day

The model that relates these variables is:

She jogs 3/4 miles at a time and she jogs a total of 6 miles per day. Calling x to the unknown number of times she jogs per day, we get:

She jogs 8 times per day.

Answer:

D

Step-by-step explanation:

u are correct

To determine whether I is a necessary condition for II, a sufficient condition for II, or both, we need to understand the definitions of the terms.

I. Two angles are acute: Acute angles are angles that measure less than 90 degrees.

II. Two angles are complementary: Complementary angles are angles that add up to 90 degrees.

Now, let's consider the relationship between the two conditions.

If two angles are acute (condition I), it means that each angle measures less than 90 degrees. However, this does not necessarily mean that the two angles are complementary (condition II). There are many possibilities for two acute angles that are not complementary. For example, two acute angles could both measure 45 degrees, which would not add up to 90 degrees.

Therefore, I is not a necessary condition for II.

On the other hand, if two angles are complementary (condition II), it means that their measures add up to 90 degrees. In this case, we can say that the two angles must both be acute. This is because if one angle is obtuse (measuring more than 90 degrees), the other angle would have to be negative in order to add up to 90 degrees, which is not possible.

Therefore, II is a sufficient condition for I.

In conclusion, I is not a necessary condition for II, but II is a sufficient condition for I.

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He have to pay $3.25.

Let the number of miles traveled by a driver be x

The toll paid by the driver is then represented as y. (in dollar)

Linear equation : an equation in which there is only one variable present. It is of the form Ax + B = 0, where A and B are any two real numbers and x is an unknown variable that has only one solution.

Since there is a linear relation between the two, we can assume the equation can be written as:

y = mx + c

From the given data, we get

0.24 = m(0) + c

c = 0.25

Using the second point:

1 = m(1) + 0.25

m = 1 − 0.25 = 0.75

Hence, the equation is y = 0.75x + 0.25.

If  x = 4, then:

y = 0.75 × 4 + 0.25

y = 5.50

Hence, He have to pay $3.25.

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Total price paid by Michael for the basket of mangoes is $4.48.

For the calculation of total price, price of sales tax will be added with selling price. Forming the equation -

Total price = 4 + 12%×4

Calculating the percentage of sales tax on Right Hand Side of the equation

Total price = 4 + 12×4/100

Solving the percentage part on Right Hand Side of the equation

Total price = 4 + 0.48

Performing addition on Right Hand Side of the equation

Total price = $4.48

Hence, Michael has to pay $4.48 after addition of sales tax for the basket of mangoes.

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Learn more

Answer:

ti is 20

Step-by-step explanation:

ti's cuz I got 52 and I did was - 52 with 32 and I got 20

Answer:

(x+1)²

(m-n)²

Step-by-step explanation:

Answer: 2 Quarters and 6 dimes

Step-by-step explanation:

2 quarters = 50 Cents
6 Dimes = 60 Cents
2 Quarters + 6 Dimes = $1.10

hope it really helps......!!!!!!

Answer:

56, 72, and 198.

Step-by-step explanation:

Hope this helped! :)

The original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

To show that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves, we need to take the derivative of the equation and set it equal to -1/b^2, the slope of the orthogonal line.

First, we take the derivative of the equation with respect to x:

2x/a^2 = -2y/b^2 * dy/dx

Simplifying, we get:

dy/dx = -b^2*x/a^2*y

Now, we set this equal to -1/b^2:

-b^2*x/a^2*y = -1/b^2

Cross-multiplying and simplifying, we get:

x/a^2*y = 1/b^2

Finally, we can rearrange this equation to get:

y = b^2*x/a^2

This equation represents the orthogonal family of curves to the original family of conics. Since the original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

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(y2-y1)/(x2-x1)

3-2=1

4-2=2

slope: 1/2

y-int: 1

y=1/2x+1

Answer:

Slope=1/2, y-intercept=(0,1)

Step-by-step explanation:

Slope is written in the format of Y/X. If you look at the pattern, you'll notice that every time Y goes up 1, X goes up 2.

So, 1/2.

The y-intercept is where the line crosses the y-axis and is therefore when X is equal to 0. Following the pattern, this would be when Y is equal to 1.

(0,1)

Answer:

x=6

Step-by-step explanation:

4.3 + 3.2x = 23.5​

-4.3 on both sides

3.2x=19.2

divided by 3.2

x=6

Answer:

16 sides and 157.5°

Step-by-step explanation:

If two hundred liters of a punch that contains 35% fruit juice is mixed with 300 liters of another punch and the resulting fruit punch is 20% fruit juice, then the percent of fruit juice in 300 liters of punch is calculated to be 10%.

The percentage of fruit juice in 300 liters of punch can be calculated by forming a linear equation.

A linear equation also termed a first-degree equation is an equation with one or more variables that have the highest power of one.

A linear equation for this problem can be given as:

the volume of the first punch × percentage of fruit juice in the first punch + the volume of the second punch × percentage of fruit juice in the second punch = total volume × total percentage of fruit juice

Consider x = percentage of unknown fruit juice

Now add the given values in the equation:

200 × 35 + 300(x) = 500 × 20

7000 + 300(x) = 10000

300(x) = 10000 - 7000

300(x) = 3000

x = 3000 / 300

x = 10%

Hence, the percentage of fruit juice in 300 liters of punch is calculated to be 10%.

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The binomial sampling distribution for counts can be used when the population is at least 20 times as large as the sample. Each time we take a random sample from a population, we are likely to get a different set of individuals and calculate a different statistic.

The sample is a subset of the population, and is the set of values you actually use in your estimation. Let’s think 1000 individual you have selected for your study to know about average height of the residents of India. This sample has some quantity computed from values e.g. mean (x), Standard deviation (s) , sample proportion etc. This is called sample distribution. The mean and standard deviation are symbolized by Roman characters as they are sample statistics.

The Binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1 - p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process; for a single trial, i.e., n = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance.

Point Estimate of the Population Proportion, p,  is:

p = # of successes in the sample of size n

We know the sampling distribution of the sample proportion under certain conditions. We can use this information to construct a confidence interval for the population proportion.

If np and n (1-p) are greater than five, then p is approximately normal with mean, p , standard error \(\sqrt\frac{p(1-p)}{n}\)

Under these conditions, the sampling distribution of the sample proportion, p , is approximately Normal. The multiplier used in the confidence interval will come from the Standard Normal distribution.

Check all conditions before using the sampling distribution of the sample proportion.

We previously used np and n (1-p) . But p is not known. Therefore, for the confidence interval, we will use

For a confidence interval for a proportion, there is a technique called exact methods. These methods can be used if the software offers it. These exact methods are more complicated and are based on the relationship between the binomial and F-distribution. The Z-method is much simpler and fairly easy to compute. In fact if you ever come across a published random survey (e.g. a Gallup poll) you can use the methods in this lesson to construct a reliable proportion confidence interval rather quickly.

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Answer:

0.48911

Step-by-step explanation:

The formula for calculating a z-score is is z = (x-μ)/σ,

where x is the raw score, = 27.21 Ib

μ is the population mean = 26.86 lb

σ is the population standard deviation. = 12.82 lb

z = 0.027301

Probability value from Z-Table:

P(x<27.21) = 0.51089

P(x>27.21) = 1 - P(x<27.21) = 0.48911

The proportion of weeks in which the waste disposal facility is overloaded is

0.48911

The given statement "In performing a lower-tailed z-test for one mean, the value of the test statistic was z=0.51, which would yield a p-value of 0.695." is true because we perform null hypothesis.

In a lower-tailed z-test for one mean, we test a null hypothesis that the population mean (μ) is greater than or equal to a certain value, against an alternative hypothesis that the population mean is less than that value.

To perform the test, we calculate the z-test statistic using the sample mean, sample standard deviation, sample size, and the hypothesized population mean. If the calculated z-test statistic falls in the rejection region (below the critical value), we reject the null hypothesis and conclude that the population mean is less than the hypothesized value.

In this case, the calculated z-test statistic is 0.51, which falls in the non-rejection region (above the critical value) for a lower-tailed test with a significance level of 0.05. Therefore, the p-value is greater than 0.05, and we do not reject the null hypothesis. The statement that the p-value is 0.695 is consistent with this conclusion.

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Answer:

y ≈ -0.667x -1.333

Step-by-step explanation:

Answer:

slope=-2/3

Step-by-step explanation:

Use the slope formula to find the slope  m .

Answer:

The answer is 26.

An equation is formed of two equal expressions. The given number is 3.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the unknown number be represented by x.

The given statement "Nine less than 4 times a number equals that number" can be written in the form of an equation as,

4x - 9 = x

Solving the given equation,

4x - 9 = x

4x - x = 9

3x = 9

x = 9/3

x = 3

Hence, the given number is 3.

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Answer:

look below i promise its the answer

Answer:

a) 896 ways

c) 910 ways

Step-by-step explanation:

The question is a combination problem since it has to do with selection. In combination, if r object is selected from a pool of n objects, this can be done in nCr ways.

nCr = n!/(n-r)!r!

If from a group of 8 women and 6 men, a committee consisting of 3 men and 3 women is to be formed, we need to first calculate the total committee formed without any condition.

8C3 × 6C3

= 8!/5!3! × 6!/3!3!

= 8×7×6×5!/5!×6 × 6×5×4×3!/3!×6

= 56×20

= 1120ways

Now if;

a) two of the men refuse to serve together.

Since two men refuse to serve together, we will select 1 man from remaining 4 men since two has already been selected then select 3 from 8 women as shown.

4C1×8C3

= 4×56

= 224ways

Number of ways this can be done will be 1120-224 = 896ways

b) 1 man and 1 woman refuse to serve together

We need to choose 2 men from remaining 5 and 2 women from the rest of the men which is 7 as shown:

= (8-1)C(3-1) × (6-1)C(3-1)

= 7C2 × 5C2

= 7!/5!2! × 5!/3!2!

= 7×6×5!/5!×2 × 5×4×3!/3!×2

= 21×10

= 210ways

The number of ways this can be done will be 1120-210 = 910ways

The equation Q = -L³ + 15 represents the production function of Plainfield Electronics, where Q is the quantity of industrial control panels produced and L is the level of labor input.

In this production function, the term -L³ indicates that there is diminishing returns to labor. As the level of labor input increases, the additional output produced decreases at an increasing rate. The term 15 represents the level of output that would be produced with zero labor input, indicating that there is some fixed component of output. To maximize production, the firm would need to determine the optimal level of labor input that maximizes the quantity of industrial control panels produced. This can be done by taking the derivative of the production function with respect to labor (dQ/dL) and setting it equal to zero to find the critical points. dQ/dL = -3L². Setting -3L² = 0, we find that L = 0.

Therefore, the critical point occurs at L = 0, which means that the firm would need to employ no labor to maximize production according to this production function. However, this result seems unlikely and may not be practically feasible. It's important to note that this analysis is based solely on the provided production function equation and assumes that there are no other factors or constraints affecting the production process. In practice, other factors such as capital, technology, and input availability would also play a significant role in determining the optimal level of production.

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There are 4 quarts in a gallon, so there are 2 x 4 (8) quarts

To find price per quart, divide by number of quarts.

36.24/ 8 = $4.53 per quart

Hope this helps,

Jeron

:- )

(p.s., maybe brainliest if I really helped??  :))))    )

Answer:

$4.53

Step-by-step explanation:

Using the given information (that a 2-gallon container of laundry detergent costs $36.24), we can construct the equation:

\(p =\dfrac{2\, \text{gal}}{ \$36.24}\)

where \(p\) is the ratio of the detergent's price to its volume.

There are 4 quarts in 1 gallon. We can represent this using the equation:

\(4\, \text{qt} = 1\, \text{gal}\)

Then, we can substitute the quarts value for the gallons in the uppermost equation.

\(p =\dfrac{2\cdot (1\, \text{gal})}{ \$36.24}\)

\(p =\dfrac{2\cdot (4\, \text{qt})}{ \$36.24}\)

\(p =\dfrac{8\, \text{qt}}{ \$36.24}\)

Finally to solve for the price per one quart, we can divide the ratio by

\(\frac{8}{8}\). (We can do this because \(\frac{8}{8} = 1\), so we aren't changing the value of the ratio)

\(p =\dfrac{8\, \text{qt}}{ \$36.24} \div \dfrac{8}{8}\)

\(p =\dfrac{8\, \text{qt} \div 8}{ \$36.24 \div 8}\)

\(p =\dfrac{1\, \text{qt}}{ \$4.53}\)

So, the price for one quart of laundry detergent is $4.53.

The precision of the estimate decreases when standard error of an estimate when the sample size in a SRS decreases. So, the correct answer is D).

The standard error of an estimate measures the variability of sample means around the population mean. As the sample size in a simple random sample (SRS) decreases, the sample mean becomes less representative of the population mean, resulting in more variability or less precision in the estimate.

The standard error increases as the sample size decreases because there is more uncertainty in the estimate due to the smaller sample size. Therefore, decreasing the sample size will increase the margin of error and decrease the precision of the estimate. So, the correct option is D).

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Question 10a) According to the normal approximation, the percentage of metacritic critic scores that are greater than 70 and less than or equal to 95 is: (Solution)The normal distribution function, denoted by N(μ, σ) is described as:

N (μ, σ2) = (1/σ√2π) e^-((x-μ)/σ)^2

We will use the following formula to determine the percentage of metacritic critic scores that are greater than 70 and less than or equal to 95:

P (70 < x ≤ 95) = P (x < 95) – P (x < 70) = N (95) – N (70) = N (1.6) – N (0.7) (z = (x - μ)/σ)Where

,μ = Mean of metacritic critic scoreσ = Standard deviation of metacritic critic scoreP (70 < x ≤ 95) = N (1.6) – N (0.7)= 0.4452 – 0.2420= 0.2032

Therefore, the percentage of metacritic critic scores that are greater than 70 and less than or equal to 95 is 0.2032 or 20.32%.Question 11b) Using the actual data, the percentage of metacritic critic scores that are greater than 70 and less than or equal to 95 is: (Solution)We will use the following formula to determine the percentage of metacritic critic scores that are greater than 70 and less than or equal to

95:% (70 < x ≤ 95) = (Number of scores between 70 and 95 inclusive /

Total number of scores) × 100%Where,Number of scores between 70 and 95 inclusive = 85

Total number of scores = 147% (70 < x ≤ 95) = (85 / 147) × 100%= 0.5782 × 100%= 57.82%

Therefore, the percentage of metacritic critic scores that are greater than 70 and less than or equal to 95 using the actual data is 57.82%.Question 12c) Is it likely these critic scores follow a normal curve? The answer is No. (Solution)We can observe that the actual distribution of the data has the shape that is not like a bell-shaped normal curve. Therefore, it is less likely that these critic scores follow a normal curve.

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Answer:

x ( > or = ) 5/9

Step-by-step explanation:

● 2(1 + x) ( > or = ) 11 - 3x

● 2 + 2x ( > or = ) 11 - 3x

Add 3x to both sides

● 2 + 2x + 3x ( > or = ) 11 - 3x + 3x

● 2 + 5x (> or = ) 11

Substract 2 from both sides

● 2 + 5x -2 ( > or = ) 11 -2

● 5x (> or =) 9

Divide both sides by 5

● 5x/5 ( > or = ) 5/9

● x ( > or = ) 5/9

Answer:

5/6= 10/12

12/100<10/12