An item was marked down 60% from its original price. The amount of the discount was $30. Fill in the numbers that belong in the diagram to find the original price a = b = c =

Answer:

its basically just x=4

Step-by-step explanation:

The important to consider the time frame when averaging data and examining the correlation between variables.

False, it does matter whether or not you average the data over every month versus every year; the correlation may not be the same. When you average the data over a longer period of time, such as a year, you are smoothing out any fluctuations that may occur within that time frame. This can result in a different correlation than if you were to average the data over a shorter period of time, such as a month.
For example, if you were looking at the correlation between temperature and ice cream sales, you may find a strong positive correlation when averaging the data over every month, as higher temperatures typically lead to higher ice cream sales. However, if you were to average the data over every year, you may find a weaker correlation, as there may be other variables, such as seasonal changes, that impact ice cream sales.
In conclusion, it is important to consider the time frame when averaging data and examining the correlation between variables.

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Option B (22,16,18,36)

Mean- Mean is an average of the data collected in the data set. It can be found by dividing the sum of the values by the number of values. Median is the middle value of the data set when the values are placed in order from least to greatest.

It is easy to calculate: add up all the numbers, then divide by how many numbers there are.

Add all the numbers (22+16+18+36) = 92

Avarage = sum of the all given numbers/ total numbers

total numbers =4

so avarage= mean= 92/4 =23

(22,16,18,36) has the most spread because one number as low as 16 and one as high as 36. Our mean is 23, so that means that the spread is huge.

Hence the answer is (22,16,18,36).

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in either case, the series Σ(1/n^(m²+6)) converges, and by the Limit Comparison Test, the given series also converges.

For the first series, we can use the Comparison Test.

First, note that all terms of the series are positive.
Then, we can compare the given series to the p-series with p = 3/4, which is convergent.

To see this, note that for n ≥ 2, we have:

n^8 - 1 ≤ n^8

and

7/8 - 1/n ≤ 7/8

Therefore, we can write:

0 ≤ 1/n^(3/4) ≤ (n^8 - 1)/(n^8)(7/8 - 1/n)

Taking the sum over all n, we get:

0 ≤ Σ(1/n^(3/4)) ≤ Σ[(n^8 - 1)/(n^8)(7/8 - 1/n)]

The right-hand series is a product of two convergent series, therefore it converges.
By the Comparison Test, the left-hand series also converges.

Hence, the series  Σ(1/n^(3/4)) is convergent.


For the second series, we can use the Limit Comparison Test.

We have:

lim n → ∞ (n²(m² + 6))/(n²) = m² + 6

Since the limit is positive and finite, we can conclude that the given series and the series Σ(1/n^(m²+6)) either both converge or both diverge.

Therefore, by the Limit Comparison Test, if we show that the series Σ(1/n^(m²+6)) converges, then the given series also converges.

Note that if m ≥ 1, then we have:

1/n^(m²+6) ≤ 1/n^7

and Σ(1/n^7) is a convergent p-series with p = 7.

If m < 1, then we have:

1/n^(m²+6) ≤ 1/n^2

and Σ(1/n^2) is also a convergent p-series with p = 2.

Therefore, in either case, the series Σ(1/n^(m²+6)) converges, and by the Limit Comparison Test, the given series also converges.

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Answer:

24÷3+12 would be 20

Step-by-step explanation:

You do 24÷3 which is 8 and then you add 12. I hope this helps!

Answer:

L = 15 and W = 15. Hence, the dimensions of the rectangle with the smallest perimeter and area of 225 sq.ft. are 15 ft x 15 ft (i.e. a square).

Step-by-step explanation:

Let's assume the length of the rectangle is L and the width is W. The area of the rectangle is given as 225 sq.ft. Therefore, we have:

L x W = 225

The perimeter of the rectangle is given by:

2L + 2W

We need to find the dimensions of the rectangle that will give the smallest possible perimeter. To do this, we need to minimize the expression for the perimeter subject to the constraint that the area is 225 sq.ft. We can use the method of Lagrange multipliers to solve this problem.

Let f(L, W) = 2L + 2W be the expression for the perimeter and g(L, W) = L x W - 225 be the expression for the area. We want to minimize f(L, W) subject to the constraint g(L, W) = 0.

The Lagrange function is given by:

L(L, W, λ) = f(L, W) - λg(L, W)

= 2L + 2W - λ(LW - 225)

Taking partial derivatives and setting them equal to zero, we get:

∂L/∂λ = W = 0

∂W/∂λ = L = 0

∂L/∂λ = -λW = 0

∂W/∂λ = -λL = 0

∂L/∂λ = 2 - Wλ = 0

∂W/∂λ = 2 - Lλ = 0

Solving these equations, we get:

λ = 2/L = 2/W

Substituting λ in the expression for the area, we get:

L^2 = 225

Therefore, L = 15 and W = 15. Hence, the dimensions of the rectangle with the smallest perimeter and area of 225 sq.ft. are 15 ft x 15 ft (i.e. a square).

Answer:

width = 15 ft

length = 15 ft

Step-by-step explanation:

Let x = length and y = width.

area = length × width

A = xy

perimeter = 2(length + width)

P = 2(x + y)

P = 2x + 2y

A = 225

xy = 225

y = 225/x

P = 2x + 2(225/y)

P = 2x + 450/x

P = 2x + 450x^-1

dP/dx = 2 + 450(-1)(x^-2)

dP/dx = 2 - 450/x²

2 - 450/x² = 0

2x² - 450 = 0

x² - 225 = 0

x = ±√225

x = ±15

Discard x = -15.

width = 15 ft

length = 15 ft

Answer:

What is the question?

Step-by-step explanation:

...

Answer:

unfortunately, I couldn't give you the answer because I can't see all of the number values provided in this problem, but hopefully with the explanation you'll be able to solve it : )

Step-by-step explanation:

1. To find the mean absolute deviation of the data, start by finding the mean of the data set.

2. Find the sum of the data values, and divide the sum by the number of data values.

3. Find the absolute value of the difference between each data value and the mean: |data value – mean|.

4. Find the sum of the absolute values of the differences.

5. Divide the sum of the absolute values of the differences by the number of data values.

Answer:

A transparent solid body, often having triangular bases,used for dispering light into a spectrum or for reflecting rays of light is prism.

A three dimensional figure with at least two parallel, congruent faces is called cylinder.

There are 9000 4-digit numbers from 1000 to 9999. There are 10,000 5-digit numbers that end in I. There are 1,000 5-digit numbers that end in 0. There are 10,000 5-digit numbers that are multiples of 10.

(a) To determine the number of 4-digit numbers from 1000 to 9999, we subtract the starting point (1000) from the ending point (9999) and add 1 since we're including both endpoints. Therefore, the number of 4-digit numbers is:

9999 - 1000 + 1 = 9000.

(b) To count the number of 5-digit numbers that end in I, we need to determine the possible values for the other four digits. For each of the other four digits, there are 10 possible choices (0-9). Therefore, the number of 5-digit numbers ending in I is:

10^4 = 10,000.

(c) To count the number of 5-digit numbers ending in 0, we again need to determine the possible values for the other four digits. For each of the other four digits, there are 10 possible choices (0-9). However, for the last digit, it must be 0. Therefore, the number of 5-digit numbers ending in 0 is:

10^3 = 1,000.

(d) To count the number of 5-digit numbers that are multiples of 10, we need to determine the possible values for the other four digits. For each of the other four digits, there are 10 possible choices (0-9). Again, the last digit must be 0 since it is a multiple of 10. Therefore, the number of 5-digit numbers that are multiples of 10 is:

10^4 = 10,000.

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Answer:

Step-by-step explanation:

it is 2x

The given statement "spearman's rho describes a linear relationship between two quantitative variables." is False, because it is a correlation coefficient that measures the strength of a monotonic relationship.

In particular, Spearman's rho is used to measure the degree of association between two variables when the relationship between them is not linear. It works by ranking the values of the two variables and then computing the correlation between the ranks.

If the variables have a monotonic relationship, the Spearman's rho will be close to 1 or -1, depending on the direction of the relationship. If there is no relationship, the Spearman's rho will be close to 0.

For example, consider a dataset where the number of hours studied and the grade obtained in an exam are recorded for a group of students.

If the relationship between the two variables is non-linear, such as a U-shaped or inverted U-shaped curve, then the Spearman's rho would be more appropriate than the Pearson correlation coefficient, which measures the strength of a linear relationship.

In summary, Spearman's rho is used to measure the strength of a monotonic relationship between two variables, which can be non-linear.

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If you sell eight bundles of seven, which also implies you get 8 hot dogs' earnings.

Thus the above response is right.

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The tip of the minute hand on a clock travels approximately 26.4 cm in 11 minutes if the minute hand is 23 cm long.

What is Circle?

A circle is a two-dimensional geometric shape that is defined as the set of all points in a plane that are a fixed distance away from a given point, called the center of the circle. This distance is known as the radius of the circle.

A circle can also be defined as the locus of a point that moves in a plane in such a way that its distance from a fixed point is constant. The constant distance is the radius of the circle.

The minute hand on a clock makes a full rotation in 60 minutes, which means it travels the circumference of a circle with a radius of 23 cm in 60 minutes. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14.

Therefore, the circumference of the circle traced by the tip of the minute hand is:

C = 2πr = 2 × 3.14 × 23 cm ≈ 144.44 cm

To find out how far the minute hand travels in 11 minutes, we need to calculate what fraction of the circumference it covers in that time. Since 11 minutes is about 18.3% of an hour (60 minutes), the minute hand travels 18.3% of the circumference of the circle in that time:

Distance traveled = 0.183 × 144.44 cm ≈ 26.4 cm

Therefore, the tip of the minute hand on a clock travels approximately 26.4 cm in 11 minutes if the minute hand is 23 cm long.

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2.622e+14

                                                    OR

262200000000000x^2

Answer:

2.622e+14

Step-by-step explanation:

10^8=100000000

100000000x3.8=380000000

10^5=100000

100000x6.9= 690000

380000000x690000= 2.622e+14

a)  8 is even, the remainder when 3,678 is divided by 2 is 0.

b) The remainder when 3,678 is divided by 5 is 3.

c) The remainder when 3,678 is divided by 7 is 1.

d) 9 is a multiple of 9, the remainder when 3,678 is divided by 9 is 0.

To find the remainder of 3,678 when divided by a certain number, we can use modular arithmetic. In modular arithmetic, we take the remainder of a number when divided by a modulus.

(a) To find the remainder when 3,678 is divided by 2, we simply need to look at the last digit of 3,678, which is 8. Since 8 is even, the remainder when 3,678 is divided by 2 is 0.

(b) To find the remainder when 3,678 is divided by 5, we need to look at the last digit of 3,678 again, which is 8. We then check if 8 is a multiple of 5. Since it is not, we need to subtract the nearest multiple of 5 less than 8, which is 5. So we have 8 - 5 = 3. Therefore, the remainder when 3,678 is divided by 5 is 3.

(c) To find the remainder when 3,678 is divided by 7, we can use the fact that 10 is congruent to 3 modulo 7. This means that if we take the last digit of 3,678 and subtract three times the next-to-last digit, we will get a number that is congruent to 3,678 modulo 7. So we have:

8 - 3 × 7 = -13

Since -13 is negative, we add 7 to it to get:

-13 + 7 = -6

Since -6 is still negative, we add 7 to it again to get:

-6 + 7 = 1

(d) To find the remainder when 3,678 is divided by 9, we can again use the fact that 10 is congruent to 1 modulo 9. So we have:

8 + 7 - 6 = 9

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Answer:

y - 1 = 7(x + 4)     (Answer C)

Step-by-step explanation:

Learn (or recall) the point-slope form y - k = m(x - h).

Substitute the givens m = 7 and point:  (-4, 1) into this framework (form):

y - 1 = (7)(x + 4), or y - 1 = 7(x + 4)  (Answer C)

Answer: 6 miles is 9.656064km

It should be noted that to obtain the graph of g(x) = |3x| from one of the basic graphs, we can start with the graph of y = |x|, which is the basic graph for the absolute value function.

First, we need to take the original function g(x) = |3x| and replace x with x/3 to get g(x/3) = |x|. This transformation stretches the graph horizontally by a factor of 1/3, making it narrower.

Next, we need to apply the vertical stretch by a factor of 3 to the graph of y = |x|. This involves multiplying all the y-coordinates of the points on the graph by 3. This transformation will make the graph taller.

Finally, we combine these two transformations by graphing the transformed function g(x/3) = |x| with the vertical stretch by a factor of 3. The resulting graph of g(x) = |3x| will be a taller, narrower version of the basic graph of y = |x|, with the vertex at the origin and the slope changing from negative to positive at x = 0.

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The solution of the statement is,

⇒ - 6, - 5, - 4, - 4, 5 , 6

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The algebraic statement is,

''All numbers with an absolute value greater than 3 but less than 7''.

Now,

The mathematical expression of the given statement is,

⇒ 3 < |x| < 7

Thus, All the possible values are;

⇒ |x| = 4, 5, 6

⇒ x = - 6, - 5, - 4, - 4, 5 , 6

Thus, All the solution of the given statement is,

⇒ x = - 6, - 5, - 4, - 4, 5 , 6

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Answer:

A. To find a linear equation that models the temperature T when crickets are chirping at x chirps per minute, we need to use two points that are known. In this case, we are given that a cricket produces 120 chirps per minute at 70 degrees F and 168 chirps per minute at 80 degrees F. We can use these two points to find the slope and y-intercept of the line.

The slope of a line can be found using the formula: m = (y2 - y1) / (x2 - x1)

In this case, we can substitute the given values to get:

m = (168 - 120) / (80 - 70) = 48/10 = 4.8

The y-intercept of a line can be found using the formula: b = y - mx

We can use the point (70, 120) and the slope that we found to get:

b = 120 - (4.8 * 70) = -264

So the linear equation that models the temperature T when crickets are chirping at x chirps per minute is:

T = 4.8x - 264

B. If the crickets are chirping at 150 chirps per minute, we can substitute this value for x in the equation we found above to estimate the temperature:

T = 4.8x - 264

T = 4.8(150) - 264 = 720 - 264 = 456

So the estimated temperature is 456 degrees F.

C. The y-intercept of the line is -264, it represents the temperature when x (chirps per minutes) is zero. In this case it represents the temperature when the cricket is not chirping which is impossible, so it doesn't have any physical meaning.

Answer:

top right graph

Step-by-step explanation:

because on every side of 0 the values are the same

Answer:

top right set

Step-by-step explanation:

The probability that the entire system works is approximately 0.52, rounded off to the second decimal place.

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

Let A, B, and C represent the events that components A, B, and C work, respectively. Then, the probability that a component works is given as P(A) = P(B) = P(C) = p.

The probability that the entire system works is the probability that either A and B work and C does not, or A and C work and B does not. This can be expressed as:

P(system works) = P((A and B and C') or (A and B' and C))

Using the distributive property of probability, we can rewrite this as:

P(system works) = P(A and B and C') + P(A and B' and C)

Since the components work independently, we can apply the product rule of probability to each term:

P(system works) = P(A) * P(B) * (1 - P(C)) + P(A) * (1 - P(B)) * P(C)

Substituting P(A) = P(B) = P(C) = p, we get:

P(system works) = p² * (1 - p) + p * (1 - p)²

Simplifying this expression, we get:

P(system works) = p * (2p - 3p² + 1)

Substituting the given value of p, we get:

P(system works) = 0.8 * (20.8 - 30.8² + 1) ≈ 0.52

Therefore, the probability that the entire system works is approximately 0.52, rounded off to the second decimal place.

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To find dz/dt using the chain rule, we need to calculate the derivatives of z with respect to x and y separately, and then multiply them by the derivatives of x and y with respect to t.

Given:

z =  \(cosh^{2} (xy)\)

x = (1/2)t

y = \(e^{t}\)

Let's start by finding the partial derivatives of z with respect to x and y:

∂z/∂x = \(2cosh(xy) * sinh(xy) * y\)  (using the chain rule)

∂z/∂y = \(2cosh(xy) *sinh(xy)*x\)    (using the chain rule)

Next, let's find the derivatives of x and y with respect to t:

dx/dt = 1/2

dy/dt = \(e^{t}\)

Finally, we can use the chain rule to find dz/dt:

dz/dt = (∂z/∂x)(dx/dt) + (∂z/∂y)(dy/dt)

      = \(2cosh(xy) *sinh(xy)*y*(1/2) + 2cosh(xy)*sinh(xy)*x*e^{t}\)

Now, substitute the given expressions for x and y:

\(dz/dt = 2cosh((1/2)t*e^{t} * sinh((1/2)t*e^{t} *(1/2)* + 2cosh((1/2)t*e^{t} *sinh((1/2)t*e^{t} *((1/2)t)\)

Simplifying further, we have:

\(dz/dt = cosh((1/2)t*e^{t} *sinh((1/2)t*e^{t})* e^{t} + cosh((1/2)t* e^{t}*sinh((1/2)t*e^{t}* ((1/2)t)\)

This is the expression for dz/dt using the chain rule with the given values of x and y.

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Answer:

can be fourth one cause it starts at 2 on y axis. ( fourth option)

Step-by-step explanation:

can't be the first one cause it starts at origin

can't be second one cause it starts at -2 on x axis

can't be third on cause it starts on 2 on x axis

can't be fifth cause it starts on -2 on y axis.

Answer:

179 + 49+ 139 = 367

Step-by-step explanation:

Answer:

0.45

Step-by-step explanation:

You divided 2.25 by 5

Answer:

y = -2 -5

Step-by-step explanation:

x - 2y = 14

-2y = -x + 14

y = 1/2x - 7

-3 = -2 (-1) + b

-3 = 2 + b

-5 = b

y = -2 -5