Your friend has $100 when he goes to the fair. He spends $10 to enter the fair and $20 on food.
Rides at the fair cost $2.00 per ride.
The function f(x) = -2x + 70 can be used to determine how much money he has left over after x
rides? What does f(17) represent?
O Your friend paid for 17 rides and had $36 left over.
O Your friend paid for 17 rides and had $64 left over.
O Your friend paid for 17 rides and spent $36.
O Your friend paid for 17 rides and spent $64

Answer:

70 x 4

Step-by-step explanation:

To round to one significant figure we have to round each numbers to the first numbers greater than 0

To round 74.5 to 1sf we have to round it to the nearest 10. As the number next to it (4) is less than 5 we will round down to 70

To round 3.6 to 1sf we have to round to the nearest whole number. As the number next to it (6) is greater than 5 we will round up to 4

Hope this helps, have a great day!

Answer:

Step-by-step explanation:

Remember that the median represents the value at the middle, literally.

So, if 12 is the median, it means is the value at the center of the data set.

Now, according to the problem, there are 10 kids older than 12 and 10 kids younger than 12. That means there are 24 kids who doesn't have 12 years old.

Therefore, there are 25 kids in total.

Answer: 0.4

Step-by-step explanation:

The number of way in which bride can rank the three Djs out of 6 is 120.

There are several different ways we might rank the three DJs.

Therefore, we must identify the permutation P. (6,3).

ⁿPₓ = n!/(n - x)!

⁶P₃ = 6!(6-3)!

⁶P₃ = 6×5×4

⁶P₃ = 120

Thus, the number of way in which bride can select the three Djs out of 6 is 120.

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Answer:

1 : 4

Step-by-step explanation:

Triangles : Total Shapes

3 : 12

1  : 4

*reduce as if it was the fraction \(\frac{3}{12}\), because fractions are ratios, and ratios are fractions. They're the same thing written in different ways*

Answer: False

Step-by-step explanation:

Researchers typically report the adjusted R-squared value in addition to the regular R-squared value, not because they lack confidence in the actual R-squared, but because the adjusted R-squared provides additional information about the goodness of fit of a statistical model. The regular R-squared value measures the proportion of the variance in the dependent variable that is explained by the independent variables in the model. However, it can be biased and increase as more predictors are added to the model, even if the additional predictors do not contribute significantly to the prediction.

The adjusted R-squared, on the other hand, takes into account the number of predictors in the model and penalizes the addition of irrelevant predictors. It provides a more conservative measure of the goodness of fit by adjusting for the number of predictors and the sample size. Researchers often use the adjusted R-squared to evaluate and compare different models with varying numbers of predictors or to assess the overall explanatory power of a model while considering its complexity.

In summary, researchers report the adjusted R-squared value to address the limitations of the regular R-squared and to provide a more accurate assessment of the model's goodness of fit.

The appropriate sample size for the researcher's study would be approximately 385.

To determine the appropriate sample size for the researcher's study, we can use the formula for sample size calculation for a proportion:

\(\[n = \left(\frac{Z^2 \cdot p \cdot (1-p)}{E^2}\right)\]\)

where:

- \(n\) is the required sample size

- \(Z\) is the Z-score corresponding to the desired confidence level (\(95\%\) confidence level corresponds to a Z-score of approximately 1.96)

- \(p\) is the estimated proportion of the target market in favor of the proposal (\(20\%\))

- \(E\) is the desired margin of error (\(2.5\%\))

Substituting these values into the formula, we have:

\(\[n = \left(\frac{(1.96)^2 \cdot 0.2 \cdot (1-0.2)}{(0.025)^2}\right)\]\)

Simplifying the equation, we get:

\(\[n \approx 384.16\]\)

Therefore, the appropriate sample size for the researcher's study would be approximately 385.

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The probability of one or more catastrophes in the next two missions, assuming the proposed changes are made and the mission catastrophe probability is 1 in 120, is approximately 0.0083.

This can be calculated using the Poisson distribution, which models the probability of a certain number of events occurring in a fixed interval of time or space, given the expected rate of occurrence. In this case, the expected rate of mission catastrophes is 1/120 per mission, or approximately 0.00833, and the interval of interest is two missions.

Therefore, the probability of one or more catastrophes in two missions is 1 - P(X=0), where X is the number of catastrophes in two missions, and P(X=0) is the probability of no catastrophes in two missions, which is

P(X = 0) = e^(-0.00833) = 0.9917

P(X >=1) = 1 - 0.9917 = 0.0083

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--The question is incomplete, answering to the question below--

"For about $1 billion in new space shuttle expenditures, NASA has proposed to install new heat pumps, power heads, heat exchangers, and combustion chambers. these will lower the mission catastrophe probability to 1 in 120. assume that these changes are made. calculate the probability of one or more catastrophes in the next two missions."

\(-x^4-\dfrac{1}{7}x+1\)

Answer:

1/3

Step-by-step explanation:

10 students have a brother.

12 students have a sister.

4 students have a brother and a sister.

6 students have only a brother.

8 students have only a sister.

4 students have a brother and a sister.

Given that a student has a sister, there are 12 such students (8 with only a sister and 4 with a brother and a sister).

Of those 12 with a sister, there are 4 with a brother and a sister, so there are 4 out of 12 with a sister who also have a brother.

p = 4/12 = 1/3

You took out approximately 3.63 ounces of peanut butter from the container.

To calculate the amount of peanut butter taken out of the container, we need to determine the weight of the pear butter used for the sandwich.

Given that the jar contains 1.31 kg of peanut butter and you used 7.85% of the peanut butter for the sandwich, we can calculate the weight of the peanut butter used as follows:

Weight of peanut butter used = 1.31 kg × 7.85% = 0.103 kg

To convert the weight from kilograms to ounces, we can use the conversion factor: 1 kg = 35.27396 ounces.

Weight of peanut butter used = 0.103 kg × 35.27396 ounces/kg ≈ 3.638 ounces

Therefore, you took out approximately 3.638 ounces of peanut butter from the container. Rounded to two significant figures, the amount is approximately 3.63 ounces.

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Answer:

Step-by-step explanation:

1)  12

The mean of any number series is all of them added together and divided by the amount of numbers there are, when you add all the numbers together you get 96, and you divide it by 8 because that's how many numbers there are.

2)  5

Range is the distance between the smallest and largest number in the series, there is a difference of 5 between 10 and 15.

3) mean: 12  mode: 13, the mode is larger

The median is found by writing the numbers down in order and ticking off the number on each side back and forth until you come to the middle, if the number sequence has an even amount of values like it is here, you split the difference of the two middle numbers. The two middle numbers this time are 11 and 13 so you find the middle which is 12. The mode is the number that appears most frequently, which is 13, which means that the mode is greater than the mean.

4) Joanne's dance class' youngest student(s) are 13 years old, but the difference between the youngest and the oldest student will still be 5 so the oldest member(s) of the dance class are 18.

hope this helped

Answer:

Step-by-step explanation:

Use Pythagorean's theorem. The two shorter sides (6+x) and 20 are apart of a right triangles of a hypotenuse of (18+6). Therefore:

\((6+x)^2+20^2} =(18+6)^2\)

\((6+x)^2+400 =576\)

\((6+x)^2=176\)

Take the square root of both sides:

\(6+x=\sqrt{176}\)

\(x=\sqrt{176} -6\)

Moving on to the smaller triangle, we can find the value of 'y' to be:

\(6^2+y^2=18^2\)

\(y^2+36=324\)

\(y^2=288\)

\(y=\sqrt{288}\)

Answer:23

Step-by-step explanation:

:)

Additive inverse of 23 will be -23

Its the opposite which is negative on the number line

Among the given options, (C) The maximum of the 9 measurements is less than the maximum of the 10 measurements must be true about the 9 measurements, excluding the outlier, when compared with the 10 measurements.

An outlier is defined as a measurement that significantly deviates from the other measurements in a data set.

In this case, one of the measurements among the 10 is identified as an outlier.

When comparing the remaining 9 measurements with the entire set of 10 measurements, the maximum value of the 9 measurements cannot exceed the maximum value of the 10 measurements because the outlier, by definition, exceeds the upper quartile or lower quartile by at least 1.5 times the interquartile range.

It is important to note that the median of the 9 measurements can be either greater than or less than the median of the 10 measurements, depending on the specific values of the measurements.

The presence of the outlier does not necessarily determine the relationship between the medians of the two sets.

Similarly, the standard deviation of the 9 measurements may or may not be less than the standard deviation of the 10 measurements.

The inclusion or exclusion of the outlier can have an impact on the standard deviation calculation, but it is not guaranteed to be lower or higher in either case.

Therefore, among the given options, the only statement that must be true is (C) The maximum of the 9 measurements is less than the maximum of the 10 measurements.

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Answer:

36 / (1 - |2 - 7|) = -9

Step-by-step explanation:

Answer:

-9

Step-by-step explanation:

Explanation

Add the components of the vectors

u+v = (4,2) + (-3,2)

u+v = (4+(-3),  2+2)

u+v = (1,4)

Then to evaluate the length of vector u = (a,b), we use this formula

|u| = sqrt(a^2+b^2)

Which is derived from the pythagorean theorem. We're looking for the hypotenuse of the right triangle formed. In this case a = 1 and b = 4.

So,

|u+v| = sqrt(1^2 + 4^2)

|u+v| = sqrt(17)

Jana's sole day off from work is Friday of the second week. According to the Fair Labor Standards Act, Jana is entitled to overtime pay because she works more than 40 hours per week.

A minimum wage and "time-and-a-half" overtime pay are guaranteed under the Fair Labor Standards Act of 1938, 29 U.S.C. 203 (FLSA), a piece of labor legislation in the United States.

Additionally, it forbids using children for "oppressive child labor."

Jana, for instance, has a two-week timetable.

She puts in nine hours a day, or 8 to 5, throughout the first week of work. She works 8.75 hours per day, Monday through Thursday, from 8 to 4:45 during the second workweek.

The second week's Friday is her only day off from work. Because Jana works more than 40 hours each week, she is entitled to overtime pay under the Fair Labor Standards Act.

Therefore, Jana's sole day off from work is Friday of the second week. According to the Fair Labor Standards Act, Jana is entitled to overtime pay because she works more than 40 hours per week.

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Correct question:

Jana has a two-week work schedule. During week one, she works from 8 to 5, or nine hours a day. During week two, she works Monday through Thursday from 8 to 4:45, or 8.75 hours a day. She does not work at all the Friday of week two. The Fair Labor Standards Act requires that Jana be paid overtime:

Answer:

Step-by-step explanation:

The the terms be x and y

The sum of the terms = x+y

Difference of terms = x-y

Product of the sun and differences will be expressed as:

(x-y)(x+y) = x²-xy+xy-y²

(x-y)(x+y) = x²-y²

Hence the product of the terms is equivalent to the difference of two squares of the terms

After making a $150 deposit in the bank in one year, two years, and three years, Homer will have a total of $689 in the bank in four years, considering the interest rate of 5.6%.

Let's break down the problem step by step. In one year, Homer makes a $150 deposit. After one year, his initial deposit will earn interest at a rate of 5.6%. Therefore, after one year, his account balance will be $150 + ($150 * 0.056) = $158.40.

After two years, Homer makes another $150 deposit. Now, his initial deposit and the first-year balance will both earn interest for the second year. So, after two years, his account balance will be $158.40 + ($158.40 * 0.056) + $150 = $322.46.

Similarly, after three years, Homer makes another $150 deposit. His account balance at the beginning of the third year will be $322.46 + ($322.46 * 0.056) + $150 = $494.62.

Finally, after four years, Homer's account balance will be $494.62 + ($494.62 * 0.056) = $689.35, which rounds down to $689. Therefore, Homer will have $689 in the b in four years, considering the interest rate of 5.6%.

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Answer:

its x=32.80244

Answer:

It took 32 days into the puppy was 16 ounces

Step-by-step explanation:

i hope this was helpful

Answer:

32 days to gain 16 ounce

Step-by-step explanation:

I. If y = \(\frac{1}{2}x\)

when y is total weight, x is day

Perform 16 = 1/2x

16 * 2 = x

x = 32

\(-7x-9y=-8\)

\(5x+6y=4\)

\(-35x-45y=-40\)

\(35x+42y=28\)

\(-3y=-12\)

\(y=4\)

\(5x+6(4)=4\)

\(5x+24=4\)

\(5x=-20\)

\(x=-4\)

\((-4,4)\)

Hope this helps.

頑張って!

The equation y' = x + y + 1  is not seperable. Therefore the statement is false.

In mathematics, an ordinary differential equation (also known as an ODE) is an equation made up of one or more functions of a single independent variable and its derivatives. A function having one or more derivatives is a component of a differential equation.

Common differential equations are used in everyday life to compute the flow of electricity, the motion of an item back and forth like a pendulum, and to illustrate the principles of thermodynamics. Additionally, in medical terminology, they are employed to graphically monitor the progression of illnesses.

If you can express a differential equation as y′=f(x)g(y), where f(x) is only a function of x and g(y) is only a function of y, then the problem is separable. Here, it is not the situation.

But we are not limited to solving separable differential equations. We frequently use integrating factors to solve linear first-order differential equations, such as this one. Using the product rule, multiply your differential equation by an integrating factor—in this example, e—and you get (eyy)′=eyy+eyy′=eyx,

which you may integrate to get your differential equation's solution. Finding integrating factors for generic linear first-order differential equations of the type y′+p(x)y=q may be done in a general way (x).

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Answer:

0.6 or \(\frac{3}{5}\)

Step-by-step explanation:

Using the Pythagorean theorem (\(a^{2} +b^{2} =c^{2}\)) we get that the hypotenuse is 5.

so the cos V is adjacent over the hypotenuse. so if adjacent is 3 and hypotenuse is 5, the answer is \(\frac{3}{5}\) which equals 0.6 in decimal form.

1. True statements about nonparametric tests: Nonparametric tests do not assume data follows a specific distribution and require fewer assumptions than parametric tests.

2. False statements about nonparametric tests: Nonparametric tests do not use means to compare underlying distributions and are not necessarily less powerful than parametric tests.

1. One true statement is that nonparametric tests do not assume data follows a specific distribution. They are distribution-free tests, meaning they do not make assumptions about the shape or parameters of the population distribution from which the data is sampled. This makes nonparametric tests robust and applicable in situations where the distributional assumptions are violated or unknown.

Another true statement is that nonparametric tests generally require fewer assumptions than parametric tests. Parametric tests often assume specific distributions, equal variances, or linearity, which may not hold true in many real-world scenarios. Nonparametric tests provide an alternative that relies on weaker assumptions, making them more versatile and applicable to a broader range of data.

2. However, it is not true that nonparametric tests use means to compare underlying distributions. Nonparametric tests focus on ranking or ordering the data rather than comparing means. They are designed to assess differences or relationships based on the order or ranks of the observations, making them suitable for ordinal or non-normally distributed data.

Lastly, it is false to claim that nonparametric tests are generally less powerful than parametric tests. The power of a statistical test depends on various factors such as sample size, effect size, and the specific test used.

While nonparametric tests might be slightly less powerful in some situations, they can often perform similarly or even outperform parametric tests, especially when distributional assumptions are violated or the data is skewed or contains outliers.

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\(x \times (x - 3) = 0 \\this \: means \: that \: \\ either \: x = 0 \: or \: (x - 3) = 0\)

\(so \: x = 0\)

\(x - 3 = 0\)

\(x = 3\)

so,

\(x = 0 \: or \: 3\)

The numerical expression to find the diver's current depth is: -150 + 17.5 + 122.2.

To find the diver's current depth, we need to calculate the total change in depth by taking into account both the descent and the ascent.

The initial depth is 150 feet below sea level, and the diver descends at a rate of 5 feet per minute for 3.5 minutes. So, the total descent can be calculated as:

Descent = Rate × Time = 5 ft/min × 3.5 min = 17.5 ft.

After the descent, the diver then ascends 122.2 feet.

To find the current depth, we need to add the descent and the ascent:

Current Depth = Initial Depth + Descent + Ascent

Substituting the given values:

Current Depth = -150 ft + 17.5 ft + 122.2 ft = -10.3 ft.

The diver's current depth is approximately 10.3 feet below sea level.

To write a numerical expression to find the answer, we can represent the initial depth, descent, and ascent as variables:

Initial Depth = -150 ft

Descent = 5 ft/min × 3.5 min

Ascent = 122.2 ft

Current Depth = Initial Depth + Descent + Ascent

Current Depth = -150 ft + (5 ft/min × 3.5 min) + 122.2 ft

Simplifying the expression:

Current Depth = -150 ft + 17.5 ft + 122.2 ft

Therefore, the numerical expression to find the diver's current depth is: -150 + 17.5 + 122.2.

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