Greg earned $45 dollars for washing cars this month. He earned twice as much for washing cars than he did for mowing lawns. Write an equation to determine how much he earned for mowing lawns. m over

m over 2 equals 45
2m = 45
m + 2 = 45
m − 2 = 45

Answer:

0+10i

Step-by-step explanation:

sqrt(-100)

sqrt(-1) * sqrt(100)

The sqrt(-1) = i

i ( 10)

There is no real component and the imaginary part is 10

0 + 10i

The given statement is "There are 16 grapes for every 3 peaches in a fruit cup.

" We have to find out the ratio of the number of grapes to the number of peaches.

Given that there are 16 grapes for every 3 peaches in a fruit cup.

To find the ratio of the number of grapes to the number of peaches, we need to divide the number of grapes by the number of peaches.

Ratio = (Number of grapes) / (Number of peaches)Number of grapes = 16Number of peaches = 3Ratio of the number of grapes to the number of peaches = Number of grapes / Number of peaches= 16 / 3

Therefore, the ratio of the number of grapes to the number of peaches is 16:3.

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Answer:

7/-6

Step-by-step explanation:

y2-y1/x2-x1

6--1/-2-4

6+1/-2-4

7/-6

Hope This Helps!!

If the sample is genuinely random, the mode of the sample may or may not be equal to the mode or mean of the population. The population size must always be equal to the sample size.

A sample's mode is the most common value in the sample. Depending on the variables specified, it might be greater, lower, or equal to the population mode. In general, when the sample size is high enough, the sample mode is assumed to be identical to the population mode. Nevertheless, this is not always the case. The chance of picking any one item in a genuinely random sample is the same throughout the whole population. This means that the mode of the sample may not always be the same as the mode or mean of the population. The sample mode might be greater or lower than the population mode. The population size must always be equal to the sample size. If the population size is 500, the sample size must be 500 as well. Any sample size less than that of the population will not correctly reflect the population.

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Answer:

1:(1/6) where n = 1/6

Answer:

.3636 repeating

infinitly

Answer: 0.3636

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Answer: 5 hours

Step-by-step explanation:

She has already read 50 pages so we need to deduct that to calculate the answer:

= 175 - 50

= 125 pages left

She can read at a speed of 25 pages per hour. The number of hours it would take to read the remainder of the book would therefore be:

= 125 pages / 25 pages per hour

= 5 hours

Answer:

5

Step-by-step explanation:

The lowest and greatest values in the dataset, divided by two, make up the Mid-range. Thus, this provides us with the midrange value.

The mid-range or mid-extreme is the arithmetic mean of the highest and minimum values of the data set and is used in statistics as a measure of a sample's central tendency.

The difference between the greatest and minimum values, which is a measure of statistical dispersion, is strongly related to the mid-range.

The two measurements are complementary in that one can determine the sample's maximum and minimum values by knowing the range and the midpoint.

Therefore, the lowest and greatest values in the dataset, divided by two, make up the Mid-range. Thus, this provides us with the midrange value.

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Answer:

60,000

Step-by-step explanation:

So if you make 45,000 a year and you get a 2,500 raise all you need to do is add 45,000 and 2,500. Your answer for the first year is 47,500. Then you add another 2,500 to 47,500 which you will get 50,000 for your second year. The third year process is the same which is 52,500. You do this process until you get to the sixth year.

The set is linearly dependent because at least one of the vectors is a multiple of another vector. So, the correct answer is C.

The given vectors are:

v1 = 2v2 = 4v3 = 78 -2 3

To determine whether the vectors V1, V2, and V3 are linearly independent or linearly dependent, we'll use the following method:

We'll create a linear combination of the vectors that has a non-zero answer.

v1 * a + v2 * b + v3 * c = 0

Where a, b and c are scalars that are not all equal to zero.

If the answer is zero, the set of vectors is linearly independent; otherwise, it is linearly dependent.

Therefore, we'll substitute the given values in the above equation.

2a + 4b + 7c = 0

8a - 2b + 3c = 0

If we multiply the first equation by -4 and add it to the second equation, we obtain:-

34c = 0c = 0

This implies that 2a + 4b = 0.

If we divide the first equation by 2, we get: a + 2b = 0

If we multiply the first equation by 3 and subtract it from the third equation, we obtain:

-5a + 5b = 0a = b

Thus, v1 = 2v2.

Since one of the vectors is a multiple of the other, the given set of vectors is linearly dependent.

Therefore, the correct answer is C.

The set is linearly dependent because at least one of the vectors is a multiple of another vector.

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The median for the given sample of data is A. 20.

To find the median for the given sample of data, we need to arrange the numbers in ascending order and then find the middle value.

Arranging the numbers in ascending order: 16, 17, 18, 18, 19, 19, 21, 22, 22, 23, 25

There are 11 numbers in the sample, so the middle value is the (11 + 1) / 2 = 6th value.

The 6th value in the ordered list is 19.

Therefore, the median for this sample of data is A. 20.

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Answer:  A. $970

Step-by-step explanation:

An individual earning $60,000 would pay 10% on the first $9,700 they earned then pay for remaining amount earned depending on which tax brackets the amount falls within.

Answer:

x=2

Step-by-step explanation:

36=18x

x=36/18

x=2

Answer:

\(x = 2\)

Step-by-step explanation:

\(36 = 18x \\ divide \: both \: sides \: by \: 18\\ \\ 2 = x\)

Answer:

Step-by-step explanation:

y = 2.5  sin \(\frac{2}{3}\) x  

a = 2.5

b = \(\frac{2}{3}\)

Using the normal distribution, the 98th percentile of the distribution of scores is of 2084.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is given by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The mean of the scores is given as follows:

\(\mu = 1468´\)

The 20th percentile is of 1216, meaning that when X = 1216, Z = -0.84, hence the standard deviation is calculated as follows:

\(Z = \frac{X - \mu}{\sigma}\)

\(-0.84 = \frac{1216 - 1468}{\sigma}\)

\(0.84\sigma = 252\)

\(\sigma = \frac{252}{0.84}\)

\(\sigma = 300\)

The 98th percentile is X when Z = 2.054, hence it is calculated as follows:

\(Z = \frac{X - \mu}{\sigma}\)

2.054 = (X - 1468)/300

X - 1468 = 300 x 2.054

X = 2084.

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Answer:

C.

Step-by-step explanation:

It would cost approximately 0.897 cents to run your laptop for 2.6 hours, assuming a cost of 15 cents per kWh.

To calculate the cost of running your laptop for 2.6 hours, we need to determine the energy consumed in kilowatt-hours (kWh) and then multiply it by the cost per kWh.

Power of the laptop (P) = 23 Watts

Time (t) = 2.6 hours

Cost per kWh (C) = 15 cents

First, let's convert the power from Watts to kilowatts:

P = 23 Watts = 23/1000 = 0.023 kilowatts

Next, we calculate the energy consumed in kilowatt-hours using the formula:

Energy (E) = P * t

Substituting the values:

E = 0.023 kilowatts * 2.6 hours = 0.0598 kilowatt-hours (kWh)

Finally, we calculate the cost using the formula:

Cost = E * C

Substituting the values:

Cost = 0.0598 kWh * 15 cents/kWh

Calculating this, we find:

Cost = 0.897 cents

Therefore, it would cost approximately 0.897 cents to run your laptop for 2.6 hours, assuming a cost of 15 cents per kWh.

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When switched on, your laptop recuires a power of 23 Watts. How many cents does it cost to run it for 2.6 hours, if a kWh costs you 15 cents?

Answer: X = -20

Step-by-step explanation:

-12 + x/5 = -16 ( What you do to one side you do to the other )

+12             +12 ( adding 12 to both sides)

x/5 = -4 ( gives us this )

5 (x/5 = -4)    ( I multiplied by 5 to remove the denominator of x )

x =  -20 ( get the answer )

Overall, the graphs would differ in their rate of growth or decay and damping, with the k2 > k1 case exhibiting faster growth or decay and damping.

An equation is a mathematical statement that shows that two expressions are equal. It typically contains variables, constants, and mathematical operators (such as +, -, *, /) and can be solved to determine the values of the variables that make the equation true. Equations are used extensively in mathematics, science, engineering, and other fields to model relationships between quantities and make predictions about their behavior. Some common types of equations include linear equations, quadratic equations, and differential equations.

Here,

The damped equation with terms e2k1t and e2k2t can be written as:

y(t) = Aeⁿ₁⁺ⁿ₂*ˣ + Beⁿ₁⁻ⁿ₂*ˣ

where A and B are constants.

The graph of this function would have an initial exponential growth or decay phase determined by the sign of (k1 + k2), followed by a damping effect determined by the sign of (k1 - k2).

If k2 > k1, then (k1 + k2) is positive, which means that the initial phase of the function would have a faster growth or decay than the case where k2 < k1. The damping effect would also be faster, since (k1 - k2) would be negative, causing the exponential terms to decay more rapidly.

In other words, if k2 > k1, the function would approach zero more quickly and the oscillations would be damped out faster compared to the case where k2 < k1. The amplitude of the oscillations would also be smaller in the k2 > k1 case.

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Answer:

C.

Step-by-step explanation:

(I MAY BE WRONG) srry if I was

Answer:

Step-by-step explanation:

The function f(x) = 15x² is increasing over the interval x > 0.

To see why, we can look at the values of f(x) as x increases from left to right. We can see that when x is negative, f(x) is positive and increasing. When x is zero, f(x) reaches its minimum value of zero. And as x becomes positive, f(x) continues to increase without bound. Therefore, we can conclude that f(x) is increasing over the interval x > 0.

The function f(x) is decreasing over the interval x < 0.

To see why, we can again look at the values of f(x) as x increases from left to right. We can see that when x is negative, f(x) is positive and increasing. But as x approaches zero from the left, f(x) begins to decrease, reaching its minimum value of zero at x = 0. And as x becomes positive, f(x) continues to increase without bound. Therefore, we can conclude that f(x) is decreasing over the interval x < 0.

Answer:

259.5

Step-by-step explanation:

8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5

The correct option for calculating the degrees of freedom for the between-group estimate in ANOVA is: c. k - 1

Here's a step-by-step explanation:

1. ANOVA, or Analysis of Variance, is a statistical method used to compare the means of multiple groups to determine if there are significant differences between them. In this context, "k" represents the number of groups being compared, and "N" represents the total number of observations.

2. Degrees of freedom (df) are used in statistical tests to account for variability in the data. They are essentially the number of values that can vary independently in the calculation of a statistic.

3. In ANOVA, there are two types of degrees of freedom: between-group (df_between) and within-group (df_within).

4. To calculate the between-group degrees of freedom (df_between), we use the formula: df_between = k - 1. This is because there are k groups being compared, and each group contributes one degree of freedom, minus one since we are comparing the groups against each other.

5. The within-group degrees of freedom (df_within) would be calculated using the formula: df_within = N - k, which accounts for the total number of observations minus the number of groups.

In summary, to compute the degrees of freedom for the between-group estimate in ANOVA, you would use the formula df_between = k - 1.

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Part a: Kinko's income is $280.

Part b: Kinko's optimal consumption will change due to the increased price of leather jackets, but the specific values cannot be determined without further calculations.

To find Kinko's income, we need to determine his budget line based on his current consumption and the price of whips. Kinko is consuming 4 whips and 16 leather jackets, and the price of whips is $6.

The budget line equation is given by: Px * x + Py * y = I, where Px is the price of whips, Py is the price of leather jackets, x is the consumption of whips, y is the consumption of leather jackets, and I is the income.

Since Kinko spends all his money on whips and leather jackets, his income equals the total expenditure on these goods. Thus, the budget line equation becomes: 6x + 16y = I.

We can substitute Kinko's consumption values into the equation: 6 * 4 + 16 * 16 = I.

Simplifying, we have: 24 + 256 = I.

Therefore, Kinko's income is $280.

To visualize this, we can plot Kinko's indifference curves and the budget line on a graph with whips (x) on the horizontal axis and leather jackets (y) on the vertical axis.

The budget line represents all the affordable combinations of whips and leather jackets given Kinko's income and the prices. The indifference curves represent Kinko's preferences, showing the combinations of whips and leather jackets that provide him with the same level of utility.

Part b:

If the price of leather jackets increases by 16 times, the new price of leather jackets becomes $16 * Py = $16 * 1 = $16.

To determine Kinko's optimal consumption, we need to find the new tangency point between an indifference curve and the new budget line. Since Kinko's utility function is non-standard, we need to use calculus to find the optimal consumption bundle.

Using the Lagrange multiplier method, we set up the following optimization problem:

Maximize U(x, y) = min{x½ + y½, x/4 + y}

Subject to the constraint: Px * x + Py * y = I, where Px = $6 and Py = $16.

By solving the optimization problem, we can find the new optimal consumption bundle in terms of whips (x) and leather jackets (y).

However, without the specific values for x and y, it is not possible to provide the exact optimal consumption bundle in one line.

The solution would involve finding the tangency point between the new budget line (with the increased price of leather jackets) and the indifference curves, and determining the corresponding values of x and y.

Therefore, without further information, we can only state that Kinko's optimal consumption will change due to the change in the price of leather jackets, but we cannot provide the specific values without additional calculations.

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Answer:

10?

Step-by-step explanation:

There are 4 ways the rectangle can consist of 2 squares, 3 ways the rectangle can consist of 3 squares, 2 ways it can consist of 4 squares, and 1 way it can consist of 5.

4+3+2+1= 10. I could be wrong but I am pretty sure this is how you do it.

In the expansion of (2a+4b)⁸ the possible variable terms are a⁸, a⁵b³, a³b⁵, a⁷b, and b⁸.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expansion is given by the following formula: \(\left(a + b\right)^{n} = \sum_{k=0}^{n} {\binom{n}{k}} a^{n - k} b^{k}\), where \({\binom{n}{k}} = \frac{n!}{\left(n - k\right)! k!}\)

As given to us, a = 2a, b = 4 b, and n = 8.

Therefore, \(\left(2 a + 4 b\right)^{8} = \sum_{k=0}^{8} {\binom{8}{k}} \left(2 a\right)^{8 - k} \left(4 b\right)^{k}(2a+4b)\).

Thus, \(\left(2 a + 4 b\right)^{8} = 256 a^{8} + 4096 a^{7} b + 28672 a^{6} b^{2} + 114688 a^{5} b^{3} + 286720 a^{4} b^{4} + 458752 a^{3} b^{5} + 458752 a^{2} b^{6} + 262144 a b^{7} + 65536 b^{8}.\)

Hence, In the expansion of (2a+4b)⁸ the possible variable terms are a⁸, a⁵b³, a³b⁵, a⁷b, and b⁸.

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Answer:

127.3

Step-by-step explanation:

​

T≈127.333≈127.3

∘

The solution to the system of equations is x = -3 and y = 2. The y-value of the solution is 2

To find the y-value of the solution to the system of equations, we can solve the system using any suitable method such as substitution or elimination.

Given system of equations:

3x + 5y = 1

7x + 4y = -13

Let's use the method of elimination to solve the system:

Multiply equation 1 by 4 and equation 2 by 5 to make the coefficients of y in both equations equal:

4(3x + 5y) = 4(1) --> 12x + 20y = 4

5(7x + 4y) = 5(-13) --> 35x + 20y = -65

Now, subtract equation 1 from equation 2 to eliminate the y term:

(35x + 20y) - (12x + 20y) = -65 - 4

35x - 12x = -69

23x = -69

x = -69/23

x = -3

Substitute the value of x into equation 1 to find y:

3(-3) + 5y = 1

-9 + 5y = 1

5y = 1 + 9

5y = 10

y = 10/5

y = 2

Therefore, the solution to the system of equations is x = -3 and y = 2. The y-value of the solution is 2.

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Based on the given information, a survey of 50 high school students was conducted to determine the number of students in favor of forming a new rugby team. The school will form the team if at least 20% of the students at the school want the team to be formed.

Out of the 50 students surveyed, only 3 said they wanted the team to be formed. A simulation was then conducted to test the significance of the survey, assuming that 20% of the students wanted the team. The simulation was repeated 100 times.

The conclusion that can be drawn from the simulation results is that there is not enough evidence to support the formation of a new rugby team.

Since the simulation was repeated 100 times, it can be inferred that the sample size was adequate to accurately represent the entire school. If the simulation results had shown that at least 20% of the students wanted the team to be formed, then it would have been safe to say that the school should form the team.

However, since the simulation results did not show this, it can be concluded that there is not enough support from the students to justify the formation of a new rugby team.

It is important to note that this conclusion is based on the assumption that the simulation accurately represents the school's population. If there are factors that were not considered in the simulation that could affect the number of students in favor of forming the team, then the conclusion may not be accurate.

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