C. Subtract the following.
5x - 8xy + 4y + 13 from 13x - 10xy + 6y - 4​

The price of the Motorcycle, not including the tax, is $11,500

The price of the motorcycle before the tax, we need to subtract the tax amount from the total price, including the tax. Let's denote the price of the motorcycle before tax as P.

Given:

Tax rate = 12.5%

Tax amount = $1437.50

We know that the tax amount is equal to 12.5% of the price of the motorcycle:

Tax amount = 0.125 * P

We can set up the equation and solve for P:

0.125 * P = $1437.50

To isolate P, divide both sides of the equation by 0.125:

P = $1437.50 / 0.125

Performing the calculation:

P = $11,500

Therefore, the price of the motorcycle, not including the tax, is $11,500.

Tax amount = 0.125 * $11,500 = $1437.50

The tax amount matches the given information, confirming that the price of the motorcycle before tax is indeed $11,500.

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The given variance of a population equals 3,600. the answer probability  is (a) 7.84 or less.

There is a 0.95 probability that the sample mean will provide a margin of

Variance

(σ²) = 3600

Sample size

(n) = 225

Confidence interval = 0.95

Probability = 0.95.

For a 0.95

probability,

α = 1 - 0.95

= 0.05/2

= 0.025

(using the Z-table)

Now, z0.025 = 1.96

Margin of error (E) = z0.025 *

(σ/√n)E = 1.96 * (60/15

)E = 7.84

(a) 7.84 or less

Since we have calculated the margin of error (E) by using the formula of margin of error

.E = 1.96 * (σ/√n)

= 1.96 * (60/15)

= 7.84 or less.

Therefore, the answer is (a) 7.84 or less.

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The completed work breakdown structure (WBS) and It is marked as follows: Baseline

A work breakdown structure (WBS) has been a diagram that depicts project elements. It additionally serves as a hierarchical and goal-oriented project.

It has a three-tiered work breakdown structure:

Deliverables that may nevertheless be broken down, Major deliverables We can delegate the project to the team to finish by the third level about deliverables.

This demonstrates how each of them is related to one another and to the overall project goals.

A Work Breakdown Structure (WBS) has become a hierarchical breakdown of the tasks that must be completed to complete a project. The work breakdown structure (WBS) "falls down" a project's structure through manageable deliverables.

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Answer:

48

Step-by-step explanation:

2x + 3 = 15

2x = 15-3

2x = 12

x = 12 ÷ 2

x = 6

8x = 6 × 8

8x = 48

Answer:

I think it might be option 3

Step-by-step explanation:

sorry if I’m wrong

Answer:

The average value of the function over its domain

Its speed of Rachel would be 30 meters per second.

Given that,

Stunt driver Rachel is trying to get out of a building that is going to blow up.

Here, the equation is,

\(d = - 38t + 220\)

Where, variable d models Rachel's distance from her exit (in meters) t seconds after the cameras began recording the stunt.

Now, Velocity is the rate at which a distance changes over time.

\(d = - 38t + 220\)

\(\dfrac{d(d)}{dt} = - 38\)

Hence, Speed is the magnitude of velocity.

\(|- 38| = 38\)

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Answer:

The slope of the line is -8/5. The graph should be shown below

Step-by-step explanation:

The side PQ of triangle ΔPQS is a tangent of the circle C₂, given that

point Q is on the surface of circle C₂.

Correct response:

QS is not perpendicular to tangent PQ, therefore, QS is not a diameter of circle C₂

Here, we have,

Methods used to prove the property of QS

The given parameters are;

Points on the circle are; Q, P, and S

Tangent to circle, C₁ = RST

Point through which circle C₂ passes = Center O

Required:

To prove that SQ is not a diameter of circle C₂

Solution:

Given that RST is a tangent, we have;

OS is perpendicular to RST by definition of a tangent to a circle

Therefore;

90° = ∠OSQ + ∠QST

Which gives;

∠OSQ = 90° - 46° = 44°

ΔQOS is an isosceles triangle, by definition of isosceles triangles

Therefore;

∠QOS = 180° - 2 × 44° = 92°

∠QPS = 0.5 × 92° = 46° Angle at center is twice angle at the circumference

∠SOP =  × ∠SQP

Let x represent the base angles of ΔSOP, we have;

∠SOP = 180° - 2·x

Therefore;

∠SQP = 90° - x

Which gives;

∠SQP = 90° - x < 90°

PQ is a tangent to circle, C₂, by definition of a tangent (number of points circle C₂ intersect PQ is one)

PQ is not perpendicular to QS, which gives;

QS is not made up of two radii, and therefore, QS is not a tangent of circle, C₂

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Answer:

take the 4

-4 -x = -4 12

-x = 8

Step-by-step explanation:

Answer:

4=8

Step-by-step explanation:

because you have to minus - 4 and then to the other side to get 8 so your final answer will be x=8

Answer:

hello pero no hablo inglés ._.

When two events are independent, their joint probability is computed by multiplying their individual probabilities.

When events are independent, it means that the occurrence of one event does not affect the probability of the other event happening. In such cases, the joint probability of both events occurring is calculated by multiplying their individual probabilities.

Let's consider two events, A and B, and assume they are independent. The probability of event A happening is denoted as P(A), and the probability of event B happening is denoted as P(B). To find the joint probability of both events occurring (P(A ∩ B)), we multiply their individual probabilities: P(A ∩ B) = P(A) * P(B).

This multiplication rule applies to any number of independent events. If there are more than two independent events, you would continue multiplying their individual probabilities to calculate the joint probability.

Note that this rule holds true only for independent events. If the events are dependent, the joint probability calculation becomes more complex and requires considering the conditional probability of one event given the occurrence of another event.

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Answer: D

Step-by-step explanation: because I said so

Answer:

D: price before tip + tip = total price

Step-by-step explanation:

The price of the meal, say $10 is the before tip price.

The tip of the meal, say $2, is the tip price.

The total price is when the before-tip (meal) price and tip price are added together for a total price or total cost.

The probability that three or more defective bowling balls are found in the first 25 examined can be calculated using the binomial distribution formula, specifically P(X ≥ 3) = 1 - P(X < 3).

To calculate the probability that three or more defective bowling balls are found in the first 25 examined, we would use the binomial distribution formula. This formula calculates the probability of a certain number of successes (in this case, finding a defective bowling ball) in a given number of trials (25 examinations) with a known probability of success (the overall proportion of defective bowling balls).

The mathematical expression we would use is:

P(X ≥ 3) = 1 - P(X < 3)

Where X is the number of defective bowling balls found in the first 25 examinations. To calculate P(X < 3), we would use the binomial probability formula:

P(X = x) = (n choose x) * p^x * (1-p)^(n-x)

Where n is the number of trials (25), p is the probability of success (the proportion of defective bowling balls), and x is the number of successes (in this case, 0, 1, or 2).

Once we have calculated P(X < 3), we can subtract this value from 1 to find P(X ≥ 3), which is the probability of finding three or more defective bowling balls in the first 25 examinations.

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Answer:

107%

Step-by-step explanation:

Beginning:

32.7kg

2 months later:

87.4kg

Difference:

87.4-32.7 = 54.7

Percentage increase:

54.7/32.7 = 1.7

The hippopotamus's mass increased by approximately 167% over the two-month period from birth to two months old.

To calculate the percentage increase in mass over the two-month period, we need to find the difference between the initial and final masses and then express it as a percentage of the initial mass.

Given that the mass at birth was 32.7 kg and the mass at two months old was 87.4 kg, we can calculate the difference in mass:

Mass increase = Final mass - Initial mass

Mass increase = 87.4 kg - 32.7 kg

Mass increase = 54.7 kg

To find the percentage increase, we divide the mass increase by the initial mass and multiply by 100:

Percentage increase = (Mass increase / Initial mass) * 100

Percentage increase = (54.7 kg / 32.7 kg) * 100

Percentage increase ≈ 167.18%

Rounding to the nearest 1%, we can say that the hippopotamus's mass increased by approximately 167% over the two-month period.

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Answer:

the solution points for the system of equations are (3, 25) and (-7/2, -7).

Step-by-step explanation:

We can solve this system of equations using substitution or elimination. Here, we will use the substitution method:

Substitute y = 2x^2 + 5x - 10 into the second equation:

4x - (2x^2 + 5x - 10) = -11

Simplifying the left side of the equation:

4x - 2x^2 - 5x + 10 = -11

Rearranging the terms:

2x^2 - x + 21 = 0

Using the quadratic formula:

x = (-(-1) ± sqrt((-1)^2 - 4(2)(21))) / 2(2)

x = (1 ± sqrt(169)) / 4

x = (1 ± 13) / 4

Simplifying:

x = 3 or x = -7/2

Now, substitute each value of x back into one of the original equations to find the corresponding value(s) of y:

For x = 3:

y = 2(3)^2 + 5(3) - 10 = 25

So one solution point is (3, 25).

For x = -7/2:

y = 4(-7/2) + 11 = -7

So the other solution point is (-7/2, -7).

Therefore, the solution points for the system of equations are (3, 25) and (-7/2, -7).

Step-by-step explanation:

We need to find the value of x for all problems if Y is between X and Z.

For all cases, XZ = XY+YZ

4. XY = 5x, YZ=x, and XZ=25

Putting all values

25 = 5x + x

25 = 6x

\(x=\dfrac{25}{6}\)

5. XY = 12, YZ=2x, and XZ = 28

28 = 12 + 2x

x = 8

6.  XY = 4x. YZ=3x, and XZ = 42

XZ = XY+YZ

42 = 4x + 3x

42 = 7x

x = 6

7. XY=2x + 1. YZ = 6x, and XZ=81

XZ = XY+YZ

81 = 2x + 1 + 6x

80 = 8x

x = 10

a) The 95% confidence interval for a sample size of 12 is approximately (71.61, 109.39).

(b) The 95% confidence interval for a sample size of 20 is approximately (74.36, 106.64).

(c) The 99% confidence interval for a sample size of 20 is approximately (69.99, 111.01).

(a)To calculate the 95% confidence limits for a sample size of 12, we need to use the t-distribution. The formula to calculate the confidence interval is:

Confidence interval = sample mean ± (t-value * standard deviation / √sample size)

First, we need to find the t-value for a 95% confidence level with n-1 degrees of freedom (n-1 = 11). From the t-distribution table, the t-value is approximately 2.201.

Calculating the expression:

Confidence interval = 90.5 ± (2.201 * 28.5 / √12)

Confidence interval = 90.5 ± 18.89

Plain language summary: Based on a sample size of 12 soil samples taken from the golf course, we can be 95% confident that the true mean soil potassium concentration falls within the range of 71.61 mg/kg to 109.39 mg/kg.

b) To calculate the 95% confidence limits for a sample size of 20, we follow the same steps as in part a but with a different sample size.

Using the t-distribution table, the t-value for a 95% confidence level with n-1 degrees of freedom (n-1 = 19) is approximately 2.093.

Calculating this expression:

Confidence interval = 90.5 ± (2.093 * 28.5 / √20)

Confidence interval = 90.5 ± 16.14

c) To calculate the 99% confidence limits for a sample size of 20, we use a different critical value from the t-distribution table.

Using the t-distribution table, the t-value for a 99% confidence level with n-1 degrees of freedom (n-1 = 19) is approximately 2.861.

Calculating this expression:

Confidence interval = 90.5 ± (2.861 * 28.5 / √20)

Confidence interval = 90.5 ± 20.51

Plain language summary: Based on the given sample size, we can be 95% confident that the true mean soil potassium concentration falls within the range of 74.36 mg/kg to 106.64 mg/kg. With a larger sample size of 20, we can be 99% confident that the true mean falls within the range of 69.99 mg/kg to 111.01 mg

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Answer:

3:7 = 42.86% (hope this helps) ;)

Step-by-step explanation:

Ratios are often expressed in the form m:n or m/n. To convert a ratio into the form of a percentage, simply divide m by n and then multiply the result by 100.

Follow the following steps for converting a ratio to a percentage:

Step 1: (Rewrite as fraction)

3:7 = 37 = 0.4286

Step 2: (Multiply the fraction by 100)

0.4286 x 100% = 42.86%

Have a great day ;D

The needed sample size Smaller if the margin of error .

Given,

In the question:

This question in the form of: Fill in the blanks.

So, You want to estimate the proportion of students at your university in favor of a longer spring break. changing the confidence level from 95% to 90% will decrease the needed sample size_____ if the margin of error.

Hence, The answer is smaller the margin of error.

Let's Know:

What is Confidence level?

The confidence level is the percentage of times you expect to get close to the same estimate if you run your experiment again or resample the population in the same way. The confidence interval consists of the upper and lower bounds of the estimate you expect to find at a given level of confidence.

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Answer:

Step-by-step explanation:

Given costs:

Sum of the costs:

Average cost is sum divided by number:

On solving the provided question, by properties of parallel lines we got to know that -  1 - A  2 - C  3 - B  4 - D

When two or more lines cross the intersection line, alternate exterior angles result. These angles are created on a number of sides outside the transverse lines. Any two parallel lines that cross one another create two angles with the horizontal line. In the area between the parallel lines, interior angles are formed, while alternate exterior angles are formed in the area outside the parallel lines.

Matches are -

1 - A

2 - C

3 - B

4 - D

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You slept for 9 hours in those three days, calculated by multiplying 12.5% of the total hours (72) by 72, which equals 9.

To calculate the number of hours slept in three days, we first need to determine how many hours there are in three days.

As given, 1 day has 24 hours. So, three days will have 3 x 24 = 72 hours.

Now, we are told that you slept for 12.5% of those 72 hours. To calculate this, we multiply the percentage by the total number of hours:

12.5% x 72 hours = (12.5/100) x 72 = 0.125 x 72 = 9 hours

Therefore, you slept for 9 hours in those three days.

Percentage is a way to express a proportion or ratio as a fraction of 100. The sign "%" is widely used to represent it. For example, if you had 20 apples and you ate 5 of them, you would have consumed 25% of the apples (5 out of 20).

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The size of angle DCA is 480°.

In the given figure, ABCD is a rhombus with angle ABE as a straight line and BCE as an isosceles triangle. We are asked to find the measure of angle DCA.

Since ABCD is a rhombus, opposite angles are congruent. Therefore, angle ACD is equal to angle ABC.

Since BCE is an isosceles triangle, angle BEC is equal to angle BCE.

From the given information, we know that angle ABC + angle BCE + angle ECD = 180 degrees.

Let's denote the measure of angle BCE as "x." Therefore, angle ABC is also "x."

Substituting these values into the equation, we have:

x + x + angle ECD = 180

2x + angle ECD = 180

Since angle ECD is denoted as 480 degrees in the question, we can solve for "x" as follows:

2x + 480 = 180

2x = 180 - 480

2x = -300

x = -150

However, angles cannot have negative measures. Therefore, there is no valid measure for angle DCA given the information provided.

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We need to determine whether an 8x8 matrix A exists that satisfies three conditions:

(i) having zeros below the main diagonal,

(ii) having a non-zero entry in the first row and eighth column, denoted as a18

(iii) being diagonalizable. In the second paragraph.

we will either provide an example of such a matrix and prove that it satisfies the conditions, or prove that no such matrix exists.

To provide an example of an 8x8 matrix A that satisfies the given conditions, we need to construct a matrix that satisfies each condition individually.

Condition (i) requires that all entries below the main diagonal of A are zero. This condition can easily be satisfied by constructing a matrix with zeros in the appropriate positions.

Condition (ii) states that a18, the entry in the first row and eighth column, must be non-zero. By assigning a non-zero value to this entry, we can fulfill this condition.

Condition (iii) requires that the matrix A is diagonalizable. This condition means that A must have a complete set of linearly independent eigenvectors. If we can find eigenvectors corresponding to distinct eigenvalues that span the entire 8-dimensional space, then A is diagonalizable.

If we are able to construct such a matrix that satisfies all three conditions, we can provide it as an example and prove that it fulfills the given conditions. However, if it is not possible to construct such a matrix, we can prove that no such matrix exists by showing that the conditions are mutually exclusive and cannot be satisfied simultaneously.

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T test is used to compute the confidence interval, when the mean and standard deviation is given.

What is Standard Deviation?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be very close to the set mean. The lower case Greek letter (sigma), again for population standard deviation, or even the Latin letter s, again for sample standard deviation, are most frequently used in mathematical texts and equations to represent standard deviation. Standard deviation may be abbreviated as SD. A random variable, specimen, statistical population, data set, as well as probability distribution's standard deviation is equal to the square root of its variance. When the number in a sample, sample mean and sample standard deviation is given, the test statistic that should be used when computing a confidence interval is t test

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To answer this question, we'll use the exponential distribution and the concept of the probability density function (pdf). Let X be the time until failure of a single device, with a mean lifetime of 20 months. The exponential distribution has the following pdf:

f(x) = (1/μ) * e^(-x/μ),

where μ is the mean lifetime (20 months in this case).

Now, let's find the probability that the first failure occurs at w months among the 5 independent devices. For this, we need to calculate the probability that none of the other 4 devices fail before w months and that the first device fails at w months.

The probability that a single device does not fail before w months is given by the complementary cumulative distribution function (ccdf) of the exponential distribution:

P(X > w) = e^(-w/μ).

Since the devices are independent, the probability that all 4 devices do not fail before w months is:

P(All 4 devices survive > w) = (e^(-w/μ))^4.

Now, the probability that the first device fails at w months is given by the pdf of the exponential distribution:

P(X = w) = (1/μ) * e^(-w/μ).

Finally, we multiply the two probabilities to find the chance that the first failure occurs at w months:

P(First failure at w) = P(All 4 devices survive > w) * P(X = w)
= (e^(-w/μ))^4 * (1/μ) * e^(-w/μ)
= (1/20) * e^(-5w/20).

Thus, the chance that the first failure will occur at w months is given by the expression (1/20) * e^(-5w/20).

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