Nine more than the product of 21 and Victor's savings Use the variable v to represent Victor's savings.

The proof by contrapositive of the theorem is "For every real number x, if x is rational, then -3x - 8 is rational."

Assume x is rational, meaning x can be expressed as a ratio of two integers a and b, where b is not equal to zero. Thus, x = a/b.

We want to prove that -3x - 8 is rational. Substituting x = a/b, we get -3(a/b) - 8 = (-3a - 8b)/b.

Since a and b are integers, -3a and 8b are also integers. Thus, the numerator (-3a - 8b) is an integer.

We know that a/b is rational, so b is not equal to zero. Therefore, (-3a - 8b)/b is a ratio of two integers and is therefore rational.

Thus, we have shown that if x is rational, then -3x - 8 is rational, which is the contrapositive of the original theorem.

Therefore, the original theorem is true since its contrapositive is true.

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Answer:

the first option, I believe is correct

Step-by-step explanation:

a. To double at a rate of 4% per year, we can use the formula for compound interest:

A=P(1+r/n)

where A is the final amount, P is the principal amount (initial investment), r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the number of years.

In this case, we have P = $300, r = 4% = 0.04, and we compound interest once a year (n = 1). We want to find the time it takes for the amount to double, so we need to solve for t.

Doubling the principal means the final amount will be 2P = 2 * $300 = $600. Plugging in these values into the formula, we have:

$600 = $300(1 + 0.04/1)^(1*t).

Simplifying the equation:

2 = (1.04)^t.

Taking the logarithm of both sides:

log(2) = t * log(1.04).

Solving for t:

t = log(2) / log(1.04).

Using a calculator, we find t ≈ 17.67 years.

Therefore, it will take approximately 17.67 years for $300 to double at a 4% annual interest rate with compounding once a year.

To calculate the time it takes for an amount to double, we use the compound interest formula and solve for the exponent. In this case, we set the initial amount to be $300 and the final amount to be $600 (twice the initial amount). The annual interest rate is given as 4%, so we convert it to a decimal (0.04) to use in the formula. Since compounding occurs once a year, the value of n is 1. We plug these values into the formula and solve for t, which represents the number of years it takes for the amount to double. By applying logarithms, we isolate t and find that it takes approximately 17.67 years for the amount to double at a 4% interest rate with annual compounding.

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The best point estimate for the population mean score on the nationwide examination in psychology is the sample mean of 492.

When we take a sample from a population, the sample mean is a point estimate of the population mean. A point estimate is an estimate of a population parameter based on a single value or point in the sample. In this case, the sample mean of 492 is the best point estimate for the population mean, because it is an unbiased estimator.

An estimator is unbiased if it is expected to be equal to the true population parameter. In this case, the expected value of the sample mean is equal to the population mean. This means that if we were to take many different samples from the population and calculate the sample mean for each sample, the average of all these sample means would be equal to the population mean.

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The given question is incomplete, the complete question is:

You would like to construct a 95% confidence interval to estimate the population mean score on a nationwide examination in psychology, and for this purpose we choose a random sample of exam scores. The sample we choose has a mean of 492 and a standard deviation of 78. What is the best point estimate, based on the sample, to use for the population mean?

Based on the information provided, we can conduct a hypothesis test to determine if a majority of all students at Ohio University believe the academics are 'very strong'.

Let's set up the null and alternative hypotheses:

Null hypothesis (H₀): The proportion of all students who believe the academics are 'very strong' is equal to 50% or less.

Alternative hypothesis (H₁): The proportion of all students who believe the academics are 'very strong' is greater than 50%.

To test these hypotheses, we can use a one-sample proportion test. We will compare the sample proportion (55%) to the hypothesized proportion (50%) and assess if the difference is statistically significant.

Using appropriate statistical methods, such as calculating the test statistic and obtaining the p-value, we can evaluate the evidence against the null hypothesis. If the p-value is less than the chosen significance level (e.g., 0.05), we would reject the null hypothesis and conclude that a majority of all students at Ohio University believe the academics are 'very strong'. Otherwise, if the p-value is greater than the significance level, we would fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim of a majority belief.

Please note that without the actual test results or the p-value, we cannot make a definitive conclusion in this particular case.

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Answer:

Hi

Step-by-step explanation:

the answer is :

\(4 \sqrt{7} + 8 = x \\ aproximatly \: 18.58\)

with phithaghoreth law you can find the base of the two triangles

and then you sum

if you need more explanation tell me

Answer:

22.5 cm^2

Step-by-step explanation:

Amount of paper is going to be measured in area, so we want the surface area of the cone.  Since it is a cub it doesn't have a base, so we don't need to count it.  

Area of the cone without the base, or what is called the lateral area is pi*r*s where r is the radius and s is the slant height.  and of course radius is d/2 where d is the diameter.  so let's plug it in.  We know diameter is 6 and slant height is 7.5

SA = pi * r * s

SA = pi * d/2 * s

SA = pi * 6/2 * 7.5

SA = 22.5 cm^2

So you will need 22.5 square centimeters of paper.

Answer:

soo abcdefghigklmnopqrstuvwzyz

its 50 with Fahrenheit

Step-by-step explanation:

becauze 4+5÷6=71

Probability that the mean number of pieces of food will be less than 200 is -0.543.

In mathematics, probability is the ratio of any favorable outcome to the total possible outcome of an event. Standard deviation is the measure of how far the data values far from the mean value of a sample.

What is the probability that mean number of pieces be less than 200?

Mean number of pieces in one cup scoop = 205

Standard deviation = 9.2

Random sample, n = 15 scoop

let X = 200,

Mean Xi = 205

SD = 9.2

For a normally distributed sample the probability for P(X<200)

 z = (X - Xi)/ SD

z = (200-205) / 9.2

 z = - 0.543

Hence, the probability is z = -0.543

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Answer: x=32, y=45, z=45

Step-by-step explanation:

Now, x is cut in half on a flat plane which is a supplementary angle (2 angles that add up to 180 degrees) so just subtract 148 from 180 and you get 32.

Since a line cuts y and z equally in half and the line it is connected to is perpendicular (right angle), we can safely say both angles are equal to 45 degrees.

Answer:

She bought 11 stickers

Step-by-step explanation:

20 - 12.85

7.15

then

7.15/0.65

11

Answer:

the answer is 11 :D

Step-by-step explanation:

Im not sure but please correct me if im wrong!

The company will continue to produce the same quality of candy, and not be able to take advantage of the extra 2% production rate.

The p-value of 0.12 indicates that the null hypothesis (H0: p = 0.96) is not rejected, meaning that the machine is producing more than the required 96% high-quality candy. However, since the actual production rate of the machine is higher than the required rate, the false negative hypothesis (Ha: p > 0.96) is also not accepted. Thus, the company will not be able to make any changes to the machine to improve its performance, even though they could have if the p-value was lower than the predetermined α = 0.05. As a result, the company will continue to produce the same quality of candy, and not be able to take advantage of the extra 2% production rate.

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To factor a 7 from the numerator and a 6 from the denominator of f(x) = 7/6 - x, we can rewrite the expression as f(x) = 7/(6(1 - x/6)).

To factor out a common factor from a fraction, we need to find the greatest common factor of the numerator and denominator. In this case, the greatest common factor of 7 and 6 is 1, so we cannot factor it out. However, we can factor out a 6 from the denominator by dividing both the numerator and denominator by 6, which gives us f(x) = 7/6(1 - x/6). Then, we can simplify this expression by factoring out a 7 from the numerator, which gives us f(x) = 7/(6(1 - x/6)).

We can factor a 7 from the numerator and a 6 from the denominator of f(x) = 7/6 - x by rewriting the expression as f(x) = 7/(6(1 - x/6)). This is useful for simplifying the expression and solving equations involving it.

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Answer:

m = \(\frac{2-p}{n}\)

Step-by-step explanation:

Given

mn + p = 2 ( subtract 2 from both sides )

mn = 2 - p ( isolate m by dividing both sides by n )

m = \(\frac{2-p}{n}\)

Answer:

25 a week.

Step-by-step explanation:

100+25= 125

125÷5 = 25

Answer:

\(\left \{ {{x=0} \atop {y=2}} \right.\)

Step-by-step explanation: \(\left \{ {{4x-y=-2} \atop {2x+y=2}} \right.\)

Add the two equations

\(4x-y+(2x+y)=-2+2\)

Remove parentheses

\(4x-y+2x+y=-2+2\)

Cancel one variable

\(4x+2x=-2+2\)

Apply the Inverse Property of Addition

\(4x+2x=0\)

Combine like terms

\(6x=0\)

Divide both sides by the equation by the coefficient of variable

\(x=0\)

Substitute into one of the equations

\(2\times0+y=2\)

Apply Zero Property of Multiplication

\(y=2\)

The solution of the system is

\(\left \{ {{x=0} \atop {y=2}} \right.\)

I hope this helps you

:)

Answer:

70

Step-by-step explanation:

Answer:

k=70

Step-by-step explanation:

x=-5

k=6x+100

6X-5=-30

k=-30+100

100-30=100+-30=70

k=70

Also I did it on Khan :)

Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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Answer:

x = 1

Step-by-step explanation:

Given

\(\frac{x}{2}\) - \(\frac{4}{5}\) + \(\frac{x}{5}\) + \(\frac{3x}{10}\) = \(\frac{1}{5}\)

Multiply through by 10 ( the LCM of 2, 5 and 10 ) to clear the fractions

5x - 8 + 2x + 3x = 2 , that is

10x - 8 = 2 ( add 8 to both sides )

10x = 10 ( divide both sides by 10 )

x = 1

answer

answer in picture.

☺☺☺☺☺☺☺

Answer:

8:00 am his temperature was 86 at 1 pm it was 76 it went down 10 in the 5 hours of time so it went down 2 every hour I hope this helps                                                                                                                                                                                                                                                                                                                                          

Step-by-step explanation:

Answer:

the answer is 20

Step-by-step explanation:

20+0=20

Answer:

The number after reversing the digits is \(\bold{6y}\)

Step-by-step explanation:

First of all, let us try to learn about representing a 2 digit number.

28 can be written as 20 + 8 OR 2 \(\times\) 10 + 8

79 can be written as 70 + 9 OR 7 \(\times\) 10 + 9

17 can be written as 10 + 7 OR 1 \(\times\) 10 + 7

i.e. if we are given the unit's and ten's digits as U and T, we can write the two digit number as: T \(\times\) 10 + U

Now, it is given that ten's digit is \(y\).

Unit's digit is half of that i.e. \(\frac{y}{2}\).

So, the number is

\(y \times 10 +\frac{y}{2}\\\Rightarrow 10 y +\frac{y}{2}\\\Rightarrow \dfrac{21}{2}y\)

Now, the digits are reversed:

Unit's digit = \(y\)

Ten's digit = \(\frac{y}{2}\)

So, the number after reversing the digits:

\(\dfrac{y}{2}\times 10+y\\\Rightarrow 5y+y = \bold{6y}\)

The number after reversing the digits is \(\bold{6y}\).

To determine the proportion of z-scores that fall outside the interval from z = -2.65 to z = 2.65, we need to calculate the area under the standard normal curve outside this interval. This can be done by subtracting the area under the curve between -2.65 and 2.65 from 1. The resulting value represents the proportion of z-scores that are outside the given interval.

The standard normal distribution has a mean of 0 and a standard deviation of 1. The interval from z = -2.65 to z = 2.65 represents a range of 2.65 standard deviations to the left and right of the mean.

To calculate the proportion of z-scores outside this interval, we need to find the area under the standard normal curve between -2.65 and 2.65. This area represents the proportion of z-scores within the interval.

We can use a standard normal distribution table or statistical software to find the area under the curve between -2.65 and 2.65. Once we have this value, we subtract it from 1 to obtain the proportion of z-scores that fall outside the interval.

Therefore, the proportion of z-scores outside the interval from z = -2.65 to z = 2.65 is 1 minus the area under the standard normal curve between -2.65 and 2.65.

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The given vectors have a dot product of 10, cross product of ⟨-8, -12, 24⟩, and magnitude of √20.

Dot product of vector u and vector v: u · v = 10

Cross product of vector u and vector v: u × v = ⟨-8, -12, 24⟩

Magnitude of vector u: ||u|| = √20

To clarify, the dot product of two vectors is calculated by multiplying the corresponding components and summing them. In this case, u · v = (2)(6) + (-4)(-1) = 10.

The cross product of two vectors is determined by taking the determinant of a matrix formed by the vectors and the unit vectors (i, j, k). In this case, u × v = ⟨-8, -12, 24⟩.

The magnitude of a vector is found by taking the square root of the sum of the squares of its components. Here, ||u|| = √(2^2 + (-4)^2) = √20.

These calculations provide the numerical values associated with the dot product, cross product, and magnitude of the given vectors.

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Answer:

B

Step-by-step explanation:

You can see B has the points kind of clustered around it.

At 22nd percentile in the distribution of ages of homeless Floridians, an 18 year old would be considered.

Given that 78% of the ages are greater than or equal to 18 years. Hence.

18 years will be (100 - 78)th percentile

i.e. 22nd percentile.

Historically, policymakers and practitioners at every level of government have focused special attention on specific subpopulations.

Decision-makers are often concerned about children and young people due to their vulnerability. People in families with children make up 30 percent of the homeless population. Unaccompanied youth (under age 25) account for six percent of the larger group.

Finally, due to their service to our country, veterans are often analyzed separately from the larger group. They represent only six percent of people experiencing homelessness.

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sin^2(4x) cos^2(4x) can be written in terms of first powers of the cosines of multiple angles as: 1/4 [cos^2(4x) - cos^3(4x) - cos(4x) + 1].

Using the power-reducing formula for cosine:

cos(2x) = cos²(x) - sin²(x)

We can write:

cos²(x) = 1/2 [cos(2x) + 1]

sin²(x) = 1/2 [1 - cos(2x)]

Using these formulas, we can rewrite the expression:

sin^2(4x) cos^2(4x) = [sin²(2(2x))] [cos²(2(2x))]

= [1/2 (1 - cos(4x))] [1/2 (cos(4x) + 1)]

= 1/4 [cos^2(4x) - cos^3(4x) - cos(4x) + 1]

= 1/4 [cos^2(4x) - cos^3(4x) - cos(4x) + cos^2(0)]

= 1/4 [cos^2(4x) - cos^3(4x) - cos(4x) + 1]

Therefore, sin^2(4x) cos^2(4x) can be written in terms of first powers of the cosines of multiple angles as: 1/4 [cos^2(4x) - cos^3(4x) - cos(4x) + 1]

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The cosine of angle J is given as follows:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the rules presented as follows:

For the angle J in this problem, we have that:

Hence the cosine of angle J is given as follows:

\(\cos{J} = \frac{4}{\sqrt{98}} \times \frac{\sqrt{98}}{\sqrt{98}}\)

\(\cos{J} = \frac{4\sqrt{98}}{98}\)

\(\cos{J} = \frac{2\sqrt{98}}{49}\)

As 98 = 2 x 49, we have that \(\sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}\), hence:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

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Answer:

the graph of f(x)= -2-10x+16

Answer:

the vertex would be (-5,41)

Step-by-step explanation:

You just plug the -5 back into the equation to get 41

hello

any quadrilateral that has four right angle triangles with congurent diagonal is a rectangle

the answer to this question is option B