Laurie is designing a type of candy dispenser for use at grocery stores. When pressure is applied to a lever by the customer, candy will fall into a container. As pressure on the lever increases, so will the amount of candy that is dispensed. For each pound per square inch of pressure placed on the lever, the amount of candy dispensed will triple.

Which of the following does this situation represent?

Answer:

-∞ < x<∞

Step-by-step explanation:

The domain is the input values or in this case the x values

Assuming that the graph goes to the left of the -2 line

We can have all values of x

Both Option C and Option D are both correct.

We have distance from the Earth to the moon.

We have to write it in scientific notation.

Scientific notation is a way of writing very large or very small numbers in the powers of 10.

According to the question -

Distance = 238000 miles

In scientific notation, we can write it as -

2.38 x \(10^{5}\) and   23.8 x \(10^{4}\).

Hence, both Option C and Option D are both correct.

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Combinations and sequences are widely used in mathematics to explain and assess situations in which the order or selection of components might influence the final result.

A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant. A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant. You can choose the components in any order in combinations. A combination is a method of picking elements from a collection when the order of selection is irrelevant. Assume we have three integers P, Q, and R. Combination defines how many possibilities we may choose two numbers from each set.

Here,

A combination is a grouping of things from a bigger set in which the order of the components is irrelevant. A sequence is a collection of elements that are ordered in a precise order. Combinations and sequences are frequently used in mathematics to describe and evaluate situations where the order or selection of components might impact the final outcome, such as in combinatorics, probability, and statistics.

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Complete question:

A combination of values that, when arranged correctly, result in a final value. true/false

The bank loaned out $4600 at B% interest.

Let's assume that the amount loaned at 8% interest is x dollars, and the amount loaned at 18% interest is $13,000 - x dollars.

The interest earned from the amount loaned at 8% interest can be calculated as (8/100) * x, which is 0.08x dollars.

The interest earned from the amount loaned at 18% interest can be calculated as (18/100) * ($13,000 - x), which is 0.18 * ($13,000 - x) dollars.

According to the given information, the total interest earned in one year is $1500. Therefore, we can set up the equation:

0.08x + 0.18 * ($13,000 - x) = $1500

Simplifying the equation:

0.08x + 2340 - 0.18x = $1500

Combine like terms:

-0.10x + 2340 = $1500

Subtracting 2340 from both sides:

-0.10x = -840

Dividing by -0.10:

x = 8400

So, $8400 was loaned out at 8% interest.

To find the amount loaned out at B%, we know that the total loan amount is $13,000. Since $8400 was loaned out at 8%, the remaining amount at B% can be calculated as:

$13,000 - $8400 = $4600

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The interquartile range (IQR) formula is: IQR = Q3 - Q1, where Q1 is the first quartile and Q3 is the third quartile of a dataset.

The interquartile range (IQR) is a measure of variability in a dataset that represents the range between the first quartile (Q1) and the third quartile (Q3). The first quartile (Q1) is the value that separates the lowest 25% of the data from the rest of the dataset, and the third quartile (Q3) is the value that separates the highest 25% of the data from the rest of the dataset.

Therefore, the IQR formula is simply the difference between the third and first quartiles: IQR = Q3 - Q1. The IQR is commonly used to identify outliers in a dataset, where any data points that fall outside of the range Q1 - 1.5IQR to Q3 + 1.5IQR are considered outliers.

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The median number of newspapers sold over seven weeks is 223.

The median is the middle score for a data set arranged in order of magnitude. The median is less affected by outliers and skewed data.

The formula for the median is as follows:

Find the median number of newspapers sold. (87, 87, 215, 154, 288, 235, 231)

We'll first arrange the data in ascending order.87, 87, 154, 215, 231, 235, 288

The median is the middle term or the average of the middle two terms. The middle two terms are 215 and 231.

Median = (215 + 231)/2

= 446/2

= 223

In statistics, the median measures the central tendency of a set of data. The median of a set of data is the middle score of that set. The value separates the upper 50% from the lower 50%.

Hence, the median number of newspapers sold over seven weeks is 223.

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If 1 > 0, then the linear function of time e(yt) = 0 + 1t displays an upward trend.

In the given linear function of time e(yt) = 0 + 1t, the coefficient of the time variable (t) is positive (1), and it is stated that 1 > 0. This indicates that as time increases, the value of yt also increases. This pattern signifies an upward trend.

An exponential trend would require an exponential function with a positive exponent, which is not the case here. Similarly, a downward trend would require a negative coefficient for time, which is also not the case. A quadratic trend would involve a time variable raised to the power of 2, but the given function is a simple linear function with only a first-degree time variable.

Hence, based on the condition that 1 > 0, the linear function of time e(yt) = 0 + 1t displays an upward trend.

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The total time taken by machine A and B working together to produce x amount of peanut butter is 7.2 minutes.

What is the concept of time and work?

Time and work defines the way how the particular work is done in the given time. It gives an exact relationship between the work and the number of days required to complete it.

Calculation of the total time taken by the machines A and B working together

Given that Machine A completes the entire job in 12 minutes.

So, machine A completes 1/12 of the job in one minute.

Machine B takes 18 minutes to complete the entire job.

So, machine B completes 1/18 of the job in one minute

When we combine their work, they will complete (1 / 12 + 1 / 18) job in one minute i.e.  (3 + 2) / 36 = 5/36 job in one minute     —---- 1

To find the time taketaken by them to produce x amount of peanut butter, we will reciprocate the result obtained in equation 1

i.e. 36 / 5 minutes to complete the entire job

i.e. 7.2 minutes

Hence, the time taken by machine A and B working together to produce x amount of peanut butter is 7.2 minutes.

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a) 4p+2p-3p

=> 6p-3p

=> 3p

b) 9s-5s+2s-s

=> 4s+1s

=> 5s

c) 8t+3r-7t-9r

=>8t-7t-9+3

=> t-6r

Hope it helps!

Answer:

3p , 5s , t - 6r

Step-by-step explanation:

(a)

4p + 2p - 3p ← add the first 2 terms

= 6p - 3p

= 3p

(b)

9s - 5s + 2s - s

= 4s + 2s - s

= 6s - s

= 5s

(c)

8t + 3r - 7t - 9r ← collect like terms

= (8t - 7t) + (3r - 9r)

= t - 6r

To achieve an 8% margin of error at a 95% confidence level in determining the percentage of people supporting the political candidate, the required sample size can be determined using the formula for sample size calculation.

To calculate the required sample size:

Sample Size (n) = \(\frac{Z^{2} X p X (1 - p))}{E^{2} }\)

Z is the Z-score corresponding to the desired confidence level

(95% confidence level corresponds to Z ≈ 1.96).

p is an estimate of the proportion of people who support the candidate.

E is the desired margin of error (8% in decimal form, which is 0.08).

Substituting the values into the formula,

n =   \(\frac{(1.96^{2} X 0.5 X (1 - 0.5))}{0.08^{2} }\)  ≈ 384.16

Therefore, the required sample size is 385 people.

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The choir booster club started the school year with a budget of $1,300.00. After spending $225.30 on t-shirts, $482.25 on lost uniforms, and $135.68 on a holiday party, they have $456.77 left in their budget.

Explanation: To calculate the amount left in the booster club's budget, we need to subtract the total expenses from the initial budget.

The total expenses are $225.30 + $482.25 + $135.68 = $843.23. Subtracting this amount from the initial budget of $1,300.00 gives us $1,300.00 - $843.23 = $456.77.

Therefore, the choir booster club has $456.77 left in their budget after spending on t-shirts, lost uniforms, and a holiday party.

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Answer:

41, 28

Step-by-step explanation:

x+x-13=69

2x=69+13=82

x=82/2=41

41-13=28

The portobello mushroom was growing faster.

Given that, Andrew has two mushrooms, he recorded their height, enoki mushroom was 3.9 centimeters tall, after 5 days, it was 4.8 centimeters tall.

Also, the height of the portobello mushroom is given by equation,

y = 0.2x + 4.1, where y is the height of the portobello mushroom in centimeters and x is the number of days since he brought it,

So,

Considering the portobello mushroom height, after 5 days,

y = 0.2(5) + 4.1 = 5.1 cm

And the enoki mushroom was 4.8 cm tall on its 5th day,

Since, the height of portobello mushroom is more than enoki mushroom on 5th day.

Hence, the portobello mushroom was growing faster.

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At least 15/16 or 15 out of 16 numbers in the data set must lie within 4 standard deviations from the mean.

Chebyshev's Theorem states that for any set of numbers, the fraction that will lie within k standard deviations of the mean is at least\(1 - 1/k^2\).

In this case, we are interested in finding the fraction of numbers that must lie within 4 standard deviations from the mean. Therefore, k = 4.

Using the formula from Chebyshev's Theorem, we can calculate the fraction:

\(1 - 1/k^2 = 1 - 1/4^2 = 1 - 1/16 = 15/16.\)

Hence, at least 15/16 or 15 out of 16 numbers in the data set must lie within 4 standard deviations from the mean.

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Question

Chebyshev's Theorem states that for any set of numbers, the fraction that will lie within k standard deviations of the mean is at least 1 - 1/k2. Use this theorem to find the fraction of all the numbers of a data set that must lie within 4 standard deviations from the mean. At least of all numbers must lie within 4 standard deviations from the mean. (Type an integer or a fraction.)

Based on the tree diagram, there are a total of 12 possible dinner combinations for Leila.

Define combinations?

In mathematics, combinations are a way to count the number of ways to choose a subset of items from a larger set, where the order of the chosen items does not matter. The number of combinations is often denoted using the symbol "n choose k", where n is the total number of items and k is the number of items being chosen.

To see why, we can count the number of paths through the tree diagram. Starting at the top, there are 2 choices for the type of dips: Guacamole dip or Cheese dip. For each of these choices, there are 2 choices for the dessert : Burrito and Enchilada. Finally, for each main course, there are 2 choices for the main course: Chicken and Beef.

Multiplying the number of choices at each step, we get:

2 (choices for dips) x 2 (choices for dessert) x 2 (choices for main course) = 8 possible dinner combinations.

Therefore, there are 3 possible dinner combinations for Leila.

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a) the terminal point is 2.4 radii to the left of the circle's center. b) the terminal point is 6 cm to the left of the circle's center.

a. To find the terminal point of the angle, we need to rotate the initial ray counterclockwise by an angle of 2.4 radians. Since 1 radian is equal to the angle subtended by an arc of length equal to the radius of the circle, the angle of 2.4 radians will subtend an arc of length:

\(2.4 * 2.5= 6\) cm

So, the terminal point of the angle will be 6 cm to the left of the initial ray, since the angle is measured counterclockwise. Since the radius of the circle is 2.5 cm, the terminal point is located:

\(\frac{6}{2.5}\) = 2.4 radii

to the left of the center of the circle. Therefore, the terminal point is 2.4 radii to the left of the circle's center.

b. To find the distance in cm from the circle's center to the terminal point, we can use the same approach as in part a. The terminal point is 2.4 radii to the left of the circle's center, so the distance from the center to the terminal point is:

\(2.4 * 2.5 = 6 cm\)

Therefore, the terminal point is 6 cm to the left of the circle's center.

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Correct question:

An angle measures 2.4 radians and the initial ray of the angle points in the 3-o'clock direction. A circle with a radius 2.5 cm long is centered at the angle's vertex.

a. The terminal point is how many radii to the right of the circle's center?  b. The terminal point is how many cm to the right of the circle's center?

a. The equation of a line is that depicts the relationship between distance and time is: y = mx + b. b. The graph is a straight line. c.  A car will drive 0 miles for 0 hours (s). It will pass through the point (0,0).

A line's slope serves as a gauge for its steepness. The ratio of the vertical change (rise) to the horizontal change (run) between any two locations on the line is what is referred to as the slope.

The rate of change of the dependent variable (y) in relation to the independent variable can also be calculated from the slope of a line (x). In the problem above, for instance, the slope of the line indicates the car's speed, which is the rate at which the distance travelled with regard to time changes.

a. The formula for the equation of a line can be used to express the equation of the line that depicts the relationship between distance and time is: y = mx + b.

b. The graph of the relationship between distance and time is a straight line.

Here, y = (144 miles / 3 hours) x

y = 48x

c. A car will drive 0 miles if it travels for 0 hours (s). This implies that it will pass through the point (0,0). Move 3 units to the right of the origin using the slope and 144 unit(s) up to locate the spot (3,144), which can be used to graph the connection.

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Answer:

It stands for like top quality, the best of the best

Step-by-step explanation:

first rate or excellent/first class

Answer:

a 90

b 90

a 8x+40

b 4y-36

c -6n-3

d 7x+7

e -10x+30

f 4/1x+2/1

Answer:

(0.25x, 0.25y)

Step-by-step explanation:

Since the origin is the center of the scale factor of dilation, we don't need to add or subtract anything

Multiplying the x and y values of the ordered pair by 0.25 represents what the value would be with the scale factor, meaning multiplication.

Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .

The distribution of candy colors in both years is not uniform. The hypothesis tests reveal significant differences in the distribution of colors for each year and indicate that last year's data does not fit this year's data.

To test the hypothesis of equal color distribution for each year, we can use a chi-square goodness-of-fit test. The null hypothesis states that the observed frequencies of candy colors follow an expected uniform distribution, while the alternative hypothesis suggests otherwise.

For last year's bag, we calculate the expected frequencies assuming a uniform distribution: 63/5 = 12.6 for each color. Using a chi-square test, we compare the observed frequencies (63, 60, 59, 61, 53) with the expected frequencies (12.6, 12.6, 12.6, 12.6, 12.6).

The chi-square test statistic is calculated by summing the squared difference between the observed and expected frequencies, divided by the expected frequencies. In this case, the chi-square value is found to be significant, indicating that the distribution of colors in last year's bag is not uniform.

In this year's bag, we again calculate the expected frequencies assuming a uniform distribution: 59/5 = 11.8 for each color. Performing the chi-square test using the observed frequencies (59, 60, 51, 50, 72) and expected frequencies (11.8, 11.8, 11.8, 11.8, 11.8), we find a significant chi-square value. Hence, the distribution of colors in this year's bag is also not uniform.

Comparing the two bags, we can use a chi-square test for independence. The null hypothesis assumes that the distribution of colors in the two bags is independent of each other, while the alternative hypothesis suggests a dependence.

By creating a contingency table with the observed frequencies from both years, we perform the chi-square test and find a significant chi-square value. Therefore, we reject the null hypothesis and conclude that last year's data does not fit this year's data.

In summary, the hypothesis tests indicate that neither last year's nor this year's distribution of candy colors is uniform. Furthermore, the comparison between the two bags suggests a significant difference in their color distributions.

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Answer:

The shaded area is 35

Step-by-step explanation:

Big rectangle area: 7 * 10 = 70

Small rectangle area: 5 * 7 = 35

Difference: 35

If derivative of \(f(x)=ln(x+4+e^{(-3x)})\), then f '(0) = -2/5.

What is derivative?

In calculus, the derivative of a function is a measure of how the function changes as its input changes. More specifically, the derivative of a function at a certain point is the instantaneous rate of change of the function at that point.

To find f'(0), we first need to find the derivative of f(x) with respect to x. Using the chain rule, we get:

\(f'(x) = 1 / (x+4+e^{(-3x)}) * (1 - 3e^{(-3x)})\)

Now we can find f'(0) by substituting the value x=0:

\(f'(0) = 1 / (0+4+e^{(-3(0))}) * (1 - 3e^{(-3(0))})\)

f'(0) = 1 / (4+1) * (1 - 3)

f'(0) = -2/5

Therefore, f'(0) = -2/5.

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To determine the percentile corresponding to 0.97 kgW in the radiation levels, you need to follow these steps:
1. Sort the radiation levels in ascending order from lowest to highest.
2. Calculate the rank of the value 0.97 kgW in the sorted list.
3. Use the formula (rank / n) * 100, where n is the total number of data points, to calculate the percentile.

To find the percentile corresponding to 0.97 kgW in the given radiation levels, you need to determine how many values in the dataset fall below or equal to 0.97 kgW and express it as a percentage of the total number of data points.

First, sort the radiation levels in ascending order. Then, find the position or rank of the value 0.97 kgW in the sorted list. The rank represents the number of values that are smaller than or equal to the target value.

Once you have the rank, divide it by the total number of data points and multiply by 100 to get the percentile. Round the calculated percentile to the nearest whole number as requested. This will give you the percentile corresponding to 0.97 kgW in the given radiation levels of the cell phones.

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Answer:

red box       5, 3, 0, -9, 4, 0, 2, -37

Step-by-step explanation:

Answer:

One of it culd be -3 or 3

Step-by-step explanation:

Answer:

4

Step-by-step explanation: