A rectangle has a length that is increasing at a rate of 10 mm per second with the width being held constant. What is the rate of change of the area of the rectangle if the width is 8 mm? (Do not include the units in your answer.)
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Question 15
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Owners of a boat rental company that charges customers between $95 and $475 per day have determined that the number of boats rented per day n can be modeled by the linear function n(p)=950−2p, where p is the daily rental charge. How much should the company charge each customer per day to maximize revenue? Do not include units or a dollar sign in your answer.

Answer:

The vertical line test is a test to determine if a relation or its graph is a function or not. For a relation or graph to be a function, it can have at most a single y-value for each x-value. Thus, a vertical line drawn at any x-position on the graph of a function will intersect the graph at most once.

Step-by-step explanation:

(winks and runs off)

Answer:

Option (C)

Step-by-step explanation:

Formula to get the scale factor of any image from it's preimage,

Scale factor of an image = \(\frac{\text{Dimension of the image}}{\text{Dimension of the preimage}}\)

From the figure attached,

F' is the image of preimage F after dilation.

Scale factor = \(\frac{\text{Length of A'B'}}{\text{Length of AB}}\)

                    = \(\frac{4}{6}\)

                    = \(\frac{2}{3}\)

Therefore, Figure F has been dilated by a scale factor of \(\frac{2}{3}\) to form F'.

Option (C). will be the answer.

Answer:

container A

Step-by-step explanation:

In Container A, we can plot the points (0,60) adn (2, 35)

The slope is :

\(m_A = \frac{y_2-y_1}{x_2-x_1} \\\\= \frac{35-60}{2-0} \\\\= \frac{-25}{2}\\ \\m_A = -12.5\\\)

For container B, the slope is:

\(m_B = \frac{y_2-y_1}{x_2-x_1} \\\\= \frac{32-54}{3-1} \\\\= \frac{-22}{2}\\ \\m_B = -11\\\)

The negative sign of the slope indicates the direction of the slope

\(|m_A| = 12.5\\\\|m_B| = 11\)

12.5 > 11

The slope of container A is steeper than container B

Therefore, the water is draining out of container A at a faster rate than container B

Answer:

2x +110= 180

2x=70

x=35

Step-by-step explanation:

Answer:

x=-6

Step-by-step explanation:

Divide both sides by -4

You will get an answer of x=-6.

Answer: B

Step-by-step explanation:

Answer:

Slope is 2/3 I think

Step-by-step explanation:

Assume all of the statistics used have a normal sampling distribution. Use 3 decimal places. Below are the steps of calculation:(a) For a 98% confidence interval for a population mean based on n = 11 observations with known: We know that margin of error formula = Zα/2 σ/√n, Where Zα/2 is the quantile of the normal distribution at α/2, σ is the population standard deviation and n is the sample size. In this case, α = 0.02, n = 11 and Zα/2 = 2.326. The sample size is small, and therefore we assume a normal distribution. Using the formula above, we obtain: margin of error = Zα/2 σ/√n = 2.326 σ/√11(b) For a 98% confidence interval for a population mean based on n = 11 observations with unknown. We know that margin of error formula = tα/2 s/√n. Where tα/2 is the quantile of the t-distribution at α/2, s is the sample standard deviation and n is the sample size. In this case, α = 0.02, n = 11 and tα/2 = 2.718. The sample size is small, and therefore we assume a normal distribution.

Using the formula above, we obtain: margin of error = tα/2 s/√n = 2.718 s/√11(c) For a 90% confidence interval for a population proportion, p, based on n = 11 observations. We know that margin of error formula = Zα/2 √((p(1-p))/n)Where Zα/2 is the quantile of the normal distribution at α/2, n is the sample size, and p is the sample proportion. In this case, α = 0.1, n = 11 and Zα/2 = 1.645.Using the formula above, we obtain: margin of error = Zα/2 √((p(1-p))/n) = 1.645 √((p(1-p))/11)(d) For a 92% confidence interval based on n = 14 observations for the slope parameter. We know that margin of error formula = tα/2 * SE. Where tα/2 is the quantile of the t-distribution at α/2, and SE is the standard error of the estimate. In this case, α = 0.08, n = 14 and tα/2 = 1.771.

Using the formula above, we obtain: margin of error = tα/2 * SE = 1.771 * SE. Therefore, the correct quantile for the margin of error of each confidence interval is as follows:(a) 2.670(b) 2.570(c) 0.512(d) 1.564.

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Answer:

Tyler. Because the temperature dropped at a faster °/hr rate then Mai's did

Step-by-step explanation:

                \(\frac{temp.drop}{hours}\)

Tyler

from 4-6 it dropped 8° in a course of 2 hours. averaging a 4°/Hr drop

\(\frac{8}{2hrs}\)= 4°/hr

Mai

from 6-10 it dropped 9° in a course of 4 hours. averaging a 2.25°/hr drop

\(\frac{9}{4hrs}\)= 2.25°/hr

Therefore Tyler is correct

The system of linear equations is 8x + 15y = 193 and 3x + 12y = 117. Then, the cost of each pair of jeans is $11, and the cost of each t-shirt is $7.

To find the cost of each t-shirt, we need to write a system of linear equations and solve it by elimination. Let's use the variables x to represent the cost of each pair of jeans and y to represent the cost of each t-shirt.

The first equation comes from Monyne's purchase: 8x + 15y = 193
The second equation comes from Steven's purchase: 3x + 12y = 117

Now we can use the elimination method to solve the system of equations. First, we'll multiply the first equation by -3 and the second equation by 8 to eliminate the x variable:
-24x - 45y = -579
24x + 96y = 936

Adding the two equations together gives us:
51y = 357

Dividing both sides by 51 gives us the cost of each t-shirt:
y = 7

Now we can plug this value back into one of the original equations to find the cost of each pair of jeans:
8x + 15(7) = 193
8x + 105 = 193
8x = 88
x = 11

So the cost of each pair of jeans is $11 and the cost of each t-shirt is $7.

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Answer:

y = -1x + 9

Step-by-step explanation:

y=mx+c

Find the gradient: (m)

gradient = change in y ÷ change in x

so, 3 ÷ -3 = -1

Substitute any coordinate into the equation y= -1x + c

eg. (6,3) (x,y)

x=6 and y=3

3 = -1(6) +c

3= -6 + c

Rearrange to make c the subject

C= 3+6 = 9

so y= -1x +9

Answer:

h = 61.83 feet

Step-by-step explanation:

length of string from Hector to kite = c = 86 feet.

and 4 feet off the ground.

angle A = 42° 15' 30"

req'd:  how high is the kite?

angle A = 42° + 15' (1° / 60') + 30"(1° / 3600'')

angle A = 42.26

to get the side a (height of kite) 4 feet above ground: use Sin(A) = opp / hyp

Sin(A) = a / c

Sin(42.26) = a / 86

a = Sin(42.26) * 86

a = 57.83 feet

therefore, the height of the kite from the ground = h = 57.83 + 4

h = 61.83 feet

Answer:

Ricardo spends $14 on the backpack and $11 o the binder.

Step-by-step explanation:

First, you have to calculate 56% of the amount Ricardo has to spend on school supplies to find the money he spends on the backpack:

$25*56%=$14

Now, you have to subtract 56% from 100% to find the percentage that he spent on a large binder:

100%-56%=44%

Finally, you have to calculate the 44% of the amount Ricardo has to spend on school supplies to find the money he spends on a large binder:

$25*44%=11

According to this, the answer is that Ricardo spends $14 on the backpack and $11 o the binder.

The probability that the baseball player has exactly 3 hits in his next 7 at-bats, given a batting average of 0.235, is approximately (rounded to four decimal places).

To calculate the probability, we can use the binomial probability formula. In this case, the player has a fixed probability of success (getting a hit) in each at-bat, which is represented by the batting average (0.235). The number of successes (hits) in a fixed number of trials (at-bats) follows a binomial distribution.

Using the binomial probability formula P(x; n, p) = C(n, x) * p^x * (1-p)^(n-x), where x is the number of successes, n is the number of trials, and p is the probability of success, we can calculate P(3; 7, 0.235).

Plugging in the values x = 3, n = 7, and p = 0.235, we can calculate the probability.

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Certify Completion Icon Tries remaining: 3 A high school has 52 players on the football team. The summary of the players' weights is given in the box plot. The median weight of the players on the football team is 160 pounds.

The box plot shows that the median weight of the players is the middle value of the distribution. In this case, the median weight is halfway between the 26th and 27th players, which is 160 pounds.

The box plot also shows that the minimum weight of the players is 150 pounds and the maximum weight is 212 pounds. The interquartile range, which is the range of the middle 50% of the data, is 20 pounds.

In conclusion, the median weight of the players on the football team is 160 pounds. This means that half of the players on the team weigh more than 160 pounds and half of the players weigh less than 160 pounds.

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The probability of drawing a red marble, putting it aside, and then drawing another red marble is about 0.133 or 13.3%.

To solve this problem, we can use the multiplication rule of probability which states that the probability of two independent events occurring together is equal to the product of their individual probabilities.

The probability of drawing a red marble on the first draw is 4/10 or 2/5 since there are 4 red marbles out of 10 total marbles. After drawing a red marble and putting it aside, there are now 3 red marbles and 9 total marbles remaining in the bag. So the probability of drawing a second red marble is 3/9 or 1/3.

By the multiplication rule of probability, the probability of drawing a red marble, putting it aside, and then drawing another red marble is:

(2/5) * (1/3) = 2/15 or approximately 0.133.

Therefore, the probability of drawing a red marble, putting it aside, and then drawing another red marble is about 0.133 or 13.3%.

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Answer:

Step-by-step explanation:

1/4

Answer:

  f(x) = -x^2 +8x -16

Step-by-step explanation:

With the given data, we can write the factored function as ...

  f(x) = -1(x -4)^2 . . . . . -1 is the leading coefficient; exponent of 2 gives root multiplicity

  f(x) = -x^2 +8x -16

The measure of dispersion is a statistical term that refers to the degree of variability in a set of data. The extent to which the data in the set deviate from the mean or the central value is referred to as the measure of dispersion. There are several measures of dispersion, and some of them are more suitable for certain types of data than others. The following is not a measure of dispersion:

Mode. Mode is not a measure of dispersion, but rather a measure of central tendency. It represents the most frequent value in a data set. In statistics, the mode is the most common value in a data set, which is usually the highest peak of a frequency distribution graph. In summary, mode is not a measure of dispersion, but rather a measure of central tendency. Standard deviation, range, and interquartile range are all measures of dispersion. Standard deviation is a measure of how spread out the data is from the mean, while range and interquartile range are measures of how much the data is spread out from the minimum and maximum values or the median, respectively.

Therefore, if you want to find the amount of variability in a data set, you should use one of these three measures of dispersion. To summarize, the mode is not a measure of dispersion, while standard deviation, range, and interquartile range are measures of dispersion.

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Answer:

V = (4/3)π(5.5³) = about 696.91 cm³

Answer:

The entrance to Sovngarde can be found, where the dead heroes of Skyrim await their final resting place.

Step-by-step explanation:

It seems like a sentence inspired by the video game "The Elder Scrolls V: Skyrim," which features a storyline that includes dragons and the afterlife realm of Sovngarde.

The sentence suggests that a dragon should be ridden to the top of a mountain called "Scalda Fin," where the skies are filled with the sounds of the dragon Alduin's cries.

Once there, the entrance to Sovngarde can be found, where the dead heroes of Skyrim await their final resting place.

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The solution set to the inequality is option (b)  (-∞, 8).

To find the solution set to the inequality 0.35x - 4.8 < 5.2 - 0.9x, we can start by simplifying the inequality:

0.35x - 4.8 < 5.2 - 0.9x

Next, we can combine like terms:

1.25x - 4.8 < 5.2

Then, we can isolate the variable by adding 4.8 to both sides:

1.25x < 10

Finally, we divide both sides by 1.25 to solve for x:

x < 10/1.25

x < 8

Therefore, the solution set to the inequality is (-∞, 8). This means that any value of x less than 8 will satisfy the inequality.

So option (b) is correct (-∞, 8)

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a) Possible sources of bias include human error in reading the tape measure, tape measure stretching or shrinking over time, and the angle of the tape measure affecting the measurement. b) A cloth tape is more subject to bias. c) The bias in a cloth tape may change over time due to stretching or shrinking.

a) Possible sources of bias when using a tape measure could include: inaccurate or worn markings on the tape, parallax error due to viewing the tape at an angle, inconsistent tension on the tape, or user error in lining up the tape measure with the object being measured.

b) A cloth tape is generally more subject to bias than a steel tape because it is more likely to stretch or shrink with use and temperature changes, leading to inaccuracies in measurement.

c) Yes, the bias in a cloth tape may change over time due to stretching, shrinking, or wear and tear. It is important to regularly check and calibrate tape measures to ensure accurate measurements.

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a) Causal, memoryless, linear, time-invariant.

b) Causal, memoryless, linear, time-invariant.

c) Causal, memoryless, nonlinear, time-invariant.

d) Causal, has memory, nonlinear, time-invariant.

a) The system described by y[n] = x[n] + 2x[n+1] is causal because the output value at any time index n only depends on the current and past input values. It is memoryless since the output at a given time index n does not depend on any past or future inputs. The system is linear because the output is a linear combination of the input values. It is also time-invariant because the system's behavior remains unchanged over time.

b) The system y[n] = u[n]x[n] is causal since the output at any time index n only depends on the current and past input values. It is memoryless because the output at a given time index n does not depend on any past or future inputs. The system is linear because the output is a product of the input signal and a constant. It is also time-invariant because the system's behavior remains unchanged over time.

c) The system y[n] = |x[n]| is causal since the output at any time index n only depends on the current and past input values. It is memoryless because the output at a given time index n does not depend on any past or future inputs. The system is nonlinear because the absolute value operation is a nonlinear operation. It is time-invariant because the system's behavior remains unchanged over time.

d) The system y[n] = ∑(0.5)^n x[i] for i=0 to n is causal since the output at any time index n only depends on the current and past input values. It has memory because the output at a given time index n depends on all past input values up to the current time index. The system is nonlinear because the output is a sum of terms raised to a power, which is a nonlinear operation. It is time-invariant because the system's behavior remains unchanged over time.

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Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.

Based on the given information, the amount of capital this year (K1) could be something less than 25 (option c).

To determine the amount of capital this year based on the given information, we can use the investment and depreciation rates.

Let's denote the amount of capital this year as K1.

According to the information provided:

People invest 55% of income, but we don't have any information about income. Therefore, we cannot determine the exact investment amount.

10% of capital depreciates. Based on this, the capital at the beginning of this year (K1) can be calculated as follows:

K1 = K - 0.1K

= 0.9K

Since we know that the capital last year was equal to 25, we substitute K = 25 into the equation above:

K1 = 0.9 * 25

= 22.5

Therefore, based on the given information, the amount of capital this year (K1) could be something less than 25 (option c).

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Answer:

its 5

Step-by-step explanation:

Answer:

You are calculating the constant speed

Answer:

r=6

Step-by-step explanation:

(r-(-3))/(2-(-1)) = (r+3)/3

r+3/3 = 3/1

cross-multiply:

r+3 = 9

r = 6

Check:

6-(-3)/2-(-1) should equal 3

9/3 = 3

checks out correctly

Answer:

r = 6

Step-by-step explanation:

Formula

m = (y2 - y1)/(x2 - x1)

Givens

x1 = - 1

x2 = 2

y1 = - 3

y2 = r

m = 3

Solution

3 = (r - -3) / (2 - - 1)         Combine

3 = (r + 3) / 3                 Multiply both sides by 3

9 = r + 3                       Subtract 3 from both sides

6 = r + 3 - 3

6 = r