Find the midpoint of the line segment with the given endpoints.
(-10,-4), (6,-5)

Answer:

theres is no solution

Step-by-step explanation:

The line-integral of ∇f along C is \(\frac{e^{cos(2)} [ln(2)]^3 }{2}\)  .

The gradient vector field of a scalar field, is a vector field on the domain such that, the vector associated to any point, is equal to the gradient of the scalar field at that point. By the definition of gradient, ∇f . (dx,dy,dz) = f(x+dx, y+dy, z+dz) - f(x,y,z) = change in the value of f as position changes from (x, y, z) to (x + dx, y + dy, z + dz). so the line integral of  ∇f  along the curve C, is

\(\int\limits_C {\nabla f} \,.\, dC = f(\textrm{final point}) - f(\textrm{initial point}) = f(C(1)) - f(C(0))\)

if the curve C is defined on the interval [0,1].

in our question: \(f = xy^3z^2,\)

\(\textrm{and the curve C is } \{ r(t) = \, < e^{tcos(t^2+1)},\ln (t^2 + 1), \frac{1}{\sqrt{t^2 + 1}} > , | \, 0\leq t\leq 1\}\)

So the line integral along the curve C is

\(\int\limits_C {\nabla f} \, .\,dC = f(\textrm{final point}) - f(\textrm{initial point}) = f(C(1)) - f(C(0))\)

\(\textrm{C}(1) = < e^{cos(2)},\ln(2),\frac{1}{\sqrt{2}} > . \textrm{ So }f(\textrm C}(1)) = \frac{e^{cos(2)}{(\ln(2))}^3}{2}\)

\(\textrm{C}(0) = < 1,0,1 > . \textrm{ So }f(\textrm C}(0)) = 1(0^3)1^2 = 0\)

So the line integral is equal to \(\frac{e^{cos(2)}{(\ln(2))}^3}{2} - 0 = \frac{e^{cos(2)}{(\ln(2))}^3}{2}\)

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As asked, the question is incomplete:

The complete question is:

let  \(f = xy^3z^2,\) and

\(\textrm{and the curve C is } \{ r(t) = < e^{tcos(t^2+1)},\ln (t^2 + 1), \frac{1}{\sqrt{t^2 + 1}} > , | \, 0\leq t\leq 1\}\)

In this case compute the line integral of ∇f along c.

The line-integral of ∇f along C is \(\frac{e^{cos(2)} [ln(2)]^3 }{2}\)  .

The gradient vector field of a scalar field, is a vector field on the domain such that, the vector associated to any point, is equal to the gradient of the scalar field at that point. By the definition of gradient, ∇f . (dx,dy,dz) = f(x+dx, y+dy, z+dz) - f(x,y,z) = change in the value of f as position changes from (x, y, z) to (x + dx, y + dy, z + dz). so the line integral of  ∇f  along the curve C, is

\(\int\limits_C {\nabla f} \,.\, dC = f(\textrm{final point}) - f(\textrm{initial point}) = f(C(1)) - f(C(0))\)

if the curve C is defined on the interval [0,1].

in our question: \(f = xy^3z^2,\)

\(\textrm{and the curve C is } \{ r(t) = \, < e^{tcos(t^2+1)},\ln (t^2 + 1), \frac{1}{\sqrt{t^2 + 1}} > , | \, 0\leq t\leq 1\}\)

So the line integral along the curve C is

\(\int\limits_C {\nabla f} \, .\,dC = f(\textrm{final point}) - f(\textrm{initial point}) = f(C(1)) - f(C(0))\)

\(\textrm{C}(1) = < e^{cos(2)},\ln(2),\frac{1}{\sqrt{2}} > . \textrm{ So }f(\textrm C}(1)) = \frac{e^{cos(2)}{(\ln(2))}^3}{2}\)

\(\textrm{C}(0) = < 1,0,1 > . \textrm{ So }f(\textrm C}(0)) = 1(0^3)1^2 = 0\)

So the line integral is equal to \(\frac{e^{cos(2)}{(\ln(2))}^3}{2} - 0 = \frac{e^{cos(2)}{(\ln(2))}^3}{2}\)

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As asked, the question is incomplete:

The complete question is:

let  \(f = xy^3z^2,\) and

\(\textrm{and the curve C is } \{ r(t) = < e^{tcos(t^2+1)},\ln (t^2 + 1), \frac{1}{\sqrt{t^2 + 1}} > , | \, 0\leq t\leq 1\}\)

In this case compute the line integral of ∇f along c.

Considering that the two lines intersect at only one point, the system of equations described by them is consistent.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

According to the number of solutions, the system is classified as follows:

In this graph, each equation is described by a line, and they intersect once, meaning that there is one solution and the system is consistent.

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The number of cups of vinegar that Mike used lies between the whole numbers 2 and 4

If Mike used one cup of vinegar for each salad dressing recipe, then he used a total of 3 cups of vinegar (1 cup x 3 recipes = 3 cups).

However, the question states that he used "a cup of vinegar" in each recipe, which could mean that he used slightly less than one cup, exactly one cup, or slightly more than one cup.

Assuming that Mike used at least 3/4 cup of vinegar in each recipe (which is still close to "a cup"), then he used a minimum of 2 and 1/4 cups of vinegar in total (3/4 cup x 3 recipes = 2 and 1/4 cups).

Assuming that Mike used at most 1 and 1/4 cups of vinegar in each recipe (which is still close to "a cup"), then he used a maximum of 3 and 3/4 cups of vinegar in total (1 and 1/4 cups x 3 recipes = 3 and 3/4 cups).

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To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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Reading a list of data and answering questions related to comparisons, percentages, and proportions involves analyzing the given information and calculating relevant metrics based on the data.

To determine "how many more" or the difference between two values, you subtract one value from the other. For example, if you are comparing the sales of two products, you can subtract the sales of one product from the other to find the difference in sales.

To calculate "what percentage of" a specific value, you divide the specific value by the total and multiply it by 100. This will give you the percentage. For instance, if you want to find the percentage of customers who rated a product positively out of the total number of customers, you divide the number of positive ratings by the total number of customers and multiply it by 100.

To determine "what proportion of" a group falls into a specific category, you divide the number of individuals in that category by the total number of individuals in the group. This will give you the proportion. For example, if you want to find the proportion of customers who prefer a certain brand out of the total number of customers surveyed, you divide the number of customers preferring that brand by the total number of customers.

By applying these calculations to the given data, you can provide accurate answers to questions regarding comparisons, percentages, and proportions.

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After traveling 16 miles east and 18 miles north, you would be approximately 23.4 miles away from your starting point by using Pythagorean theorem.

To find the distance from your starting point, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the distance traveled east and north form the legs of the right triangle, and the distance from the starting point to the final position is the hypotenuse.

Using the Pythagorean theorem, we can calculate the distance as follows:

Distance^2 = (16 miles)^2 + (18 miles)^2

Distance^2 = 256 miles^2 + 324 miles^2

Distance^2 = 580 miles^2

Distance ≈ √580

Distance ≈ 24.083 miles

Rounding to the nearest tenth, the distance from the starting point would be approximately 23.4 miles.

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The number line representing the above situation is attached accordingly. Note that the function graphed is: t < 13, where "t" is the time taken by a runner to complete the 100-meter race.

A number line is a visual representation of numbers placed in order on a straight line. It is used to perform various mathematical operations.

In the above condition, Let's use the variable "t" to represent the time taken by a runner to complete the 100-meter race.

According to the track coach's requirement, a runner needs to be able to run 100 m in less than 13 s. This can be represented algebraically as:

t < 13

In other words, the time "t" taken by a runner to complete the 100-m race should be less than 13 seconds for them to be considered for the race.

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If you test for the difference between the means of two independent samples, there is  n1 + n2 - 1 degrees of freedom.

When testing for the differences between the means that exist between two independent populations that has the variances in all of their population which is still unknown but said to be equal, the degrees of freedom will be:

n1 + n2 - 1.

Therefore, If you test for the difference between the means of two independent samples, there is  n1 + n2 - 1 degrees of freedom.

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Answer:

$1935

Step-by-step explanation:

Part a

Rewrite tan x in terms of sin x and cos x

Part b

\(\sin x \tan x+\frac{\sin x}{\tan x}\\\\=\sin x \cdot \frac{\sin x}{\cos x}+\frac{\sin x}{\frac{\sin x}{\cos x}}\\\\=\sin x \cdot \frac{\sin x}{\cos x}+\frac{1}{\frac{1}{cos x}}\\\\=\frac{\sin^2 x}{\cos x}+\cos x\\\\=\frac{\sin^2 x+\cos^2 x}{\cos x}\\\\=\frac{1}{\cos x}\)

Answer:

Natural numbers are all numbers 1, 2, 3, 4… They are the numbers you usually count and they will continue on into infinity. Whole numbers are all natural numbers including 0 e.g. 0, 1, 2, 3, 4… Integers include all whole numbers and their negative counterpart

Answer:

Step-by-step explanation:

Therefore, the researcher cannot conclude that the growth hormone had an effect on the rats in the sample. To make a definitive conclusion, the researcher would need to repeat the experiment and compare the results to a control group that did not receive the hormone.

Based on the results of the study, the researcher cannot conclusively conclude that the growth hormone had an effect on the rats in the sample. The difference between the sample average and the population average could be explained by random variation in the population sample, or by other factors that the researcher was unaware of. It is also possible that the growth hormone did have an effect, however, to make a definitive conclusion, the researcher would need to repeat the experiment and compare the results to a control group that did not receive the hormone.

The difference in the sample average and the population average of 510 grams could be due to many factors, such as genetic differences in the rats in the sample. Additionally, environmental factors such as the quality of food or the amount of light in the laboratory can have an effect on the growth rate of rats. Without a control group, the researcher has no way of knowing whether the growth hormone had an effect or not.

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Answer:

x= amount of subscriptions

y= total amount

m= $5 rate of change

b= $15 a starting point....

Eq: y=5x+15

There are 2(24!) - 23! arrangements of the 26-letter alphabet that contain "the" or "of."

To find the number of arrangements of the 26-letter alphabet that contain "the" or "of," we can use the principle of inclusion-exclusion.

First, we find the total number of arrangements of the 26-letter alphabet, which is 26! (26 factorial).

Next, we find the number of arrangements that contain "the." To do this, we treat "the" as a single letter and arrange the remaining 24 letters along with it. Since there are 24 letters to arrange, the number of arrangements that contain "the" is 24! (24 factorial).

Similarly, we find the number of arrangements that contain "of" by treating it as a single letter and arranging the remaining 24 letters along with it. The number of arrangements that contain "of" is also 24!.

However, if we simply add the number of arrangements that contain "the" and "of," we will be double-counting the arrangements that contain both "the" and "of." To correct for this, we subtract the number of arrangements that contain both "the" and "of."

To find the number of arrangements that contain both "the" and "of," we treat "the of" as a single letter and arrange the remaining 23 letters along with it. Since there are 23 letters to arrange, the number of arrangements that contain both "the" and "of" is 23! (23 factorial).

Using the principle of inclusion-exclusion, the total number of arrangements that contain "the" or "of" is:

24! + 24! - 23! = 2(24!) - 23!

Therefore, there are 2(24!) - 23! arrangements of the 26-letter alphabet that contain "the" or "of."

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Answer:

dont have question

Step-by-step explanation:

Answer:

161.557- so the second one

Step-by-step explanation:

The Length of the conjugate axis is equal to 2b. The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola.

In a hyperbola, the name of the green segment is called the transverse axis. The transverse axis is the longest distance between any two points on the hyperbola, and it passes through the center of the hyperbola. It divides the hyperbola into two separate parts called branches.

The transverse axis of a hyperbola lies along the major axis, which is perpendicular to the minor axis. Therefore, it is also sometimes called the major axis.

The other axis of a hyperbola is called the conjugate axis or minor axis. It is perpendicular to the transverse axis and passes through the center of the hyperbola. The length of the conjugate axis is usually shorter than the transverse axis.In the hyperbola above, the green segment is the transverse axis, and it is represented by the letters "2a". Therefore, the length of the transverse axis is equal to 2a.

The blue segment is the conjugate axis, and it is represented by the letters "2b".

Therefore, the length of the conjugate axis is equal to 2b.The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola. In particular, the distance between the two branches of the hyperbola is determined by the length of the transverse axis.

If the transverse axis is longer, then the branches of the hyperbola will be further apart, and the hyperbola will look more stretched out. Conversely, if the transverse axis is shorter, then the branches of the hyperbola will be closer together, and the hyperbola will look more compressed.

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Answer:

But it not a prime number :( maybe divide

Step-by-step explanation:

We can Long Division method to solve quotients step by step

What is long division method and its steps ?

When splitting huge numbers, the task is divided into several sequential parts using the long division approach. The dividend is divided by the divisor, just as in conventional division problems, and the result is known as the quotient; occasionally, it also produces a remainder.

We need to comprehend a few stages in order to divide. A vinculum or right parenthesis separates the dividend from the quotient, while a vertical bar separates the divisor from the dividend. Let's now go through the long division stages listed below to comprehend the procedure.

1. Take the dividend's first digit starting from the left . Verify if this digit exceeds or is equal to the divisor.

2. Next, divide it by the divisor, and write the result as the quotient on top.

3. Subtract the outcome from the digit, and then put the difference below.

Step 4: Decrease the dividend's subsequent digit (if present).

Step 5: Carry out Step 4 again.

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Answer:

39.76

Step-by-step explanation:

8 x 8.3 = 66.4

2640/66.4 = ( when rounded to the nearest tenth) 39.76

The equation for her total cost y would be:

y = 45x

Let's use x to represent the number of months and y to represent the total cost.

For George from Acme TV:

The set-up fee is a one-time payment of \($50\), so it does not depend on the number of months.

For each month, he pays \($35\).

The equation for his total cost y would be:

y = 35x + 50

For Gwen from Metro TV:

There is no set-up fee, so her cost only depends on the number of months.

For each month, she pays \($45\).

The equation for her total cost y would be:

y = 45x

It's worth noting that these equations assume that the monthly fees remain constant over time, which may not necessarily be the case in real life.

Additionally, these equations do not take into account any potential taxes or additional fees that may be added to the cost of the memberships.

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Answer:

its octagon. first and last one it has total 8 sides

Answer:

b

Step-by-step explanation:

its a negative slope, so you can eliminate c and d. even though the scale is 2, the slope always pertains to $1 increase and not $2 increase.

Answer:

2

Step-by-step explanation:

Answer:

\(P(Not\ 2019) = \frac{2}{7}\)

Step-by-step explanation:

Given

\(n(2019)= 3\)

\(n(2001)= 2\\\)

\(n(2008)= 2\)

\(n = 7\) --- total

Required

\(P(Not\ 2019)\)

When two quarters not minted in 2019 are selected, the sample space is:

\(S = \{(2001,2001),(2001,2008),(2008,2001),(2008,2008)\}\)

So, the probability is:

\(P(Not\ 2019) = P(2001,2001)\ or\ P(2001,2008)\ or\ P(2008,2001)\ or\ P(2008,2008)\)

\(P(Not\ 2019) = P(2001,2001) + P(2001,2008) + P(2008,2001) + P(2008,2008)\)

\(P(2001,2001) = P(2001) * P(2001)\)

Since it is a selection without replacement, we have:

\(P(2001,2001) = \frac{n(2001)}{n} * \frac{n(2001)-1}{n - 1}\)

\(P(2001,2001) = \frac{2}{7} * \frac{2-1}{7 - 1}\)

\(P(2001,2001) = \frac{2}{7} * \frac{1}{6}\)

\(P(2001,2001) = \frac{1}{7} * \frac{1}{3}\)

\(P(2001,2001) = \frac{1}{21}\)

\(P(2001,2008) = P(2001) * P(2008)\)

Since it is a selection without replacement, we have:

\(P(2001,2008) = \frac{n(2001)}{n} * \frac{n(2008)}{n - 1}\)

\(P(2001,2008) = \frac{2}{7} * \frac{2}{7 - 1}\)

\(P(2001,2008) = \frac{2}{7} * \frac{2}{6}\)

\(P(2001,2008) = \frac{2}{7} * \frac{1}{3}\)

\(P(2001,2008) = \frac{2}{21}\)

\(P(2008,2001) = P(2008) * P(2001)\)

Since it is a selection without replacement, we have:

\(P(2008,2001) = \frac{n(2008)}{n} * \frac{n(2001)}{n - 1}\)

\(P(2008,2001) = \frac{2}{7} * \frac{2}{7 - 1}\)

\(P(2008,2001) = \frac{2}{7} * \frac{2}{6}\)

\(P(2008,2001) = \frac{2}{7} * \frac{1}{3}\)

\(P(2008,2001) = \frac{2}{21}\)

\(P(2008,2008) = P(2008) * P(2008)\)

Since it is a selection without replacement, we have:

\(P(2008,2008) = \frac{n(2008)}{n} * \frac{n(2008)-1}{n - 1}\)

\(P(2008,2008) = \frac{2}{7} * \frac{2-1}{7 - 1}\)

\(P(2008,2008) = \frac{2}{7} * \frac{1}{6}\)

\(P(2008,2008) = \frac{1}{7} * \frac{1}{3}\)

\(P(2008,2008) = \frac{1}{21}\)

So:

\(P(Not\ 2019) = P(2001,2001) + P(2001,2008) + P(2008,2001) + P(2008,2008)\)

\(P(Not\ 2019) = \frac{1}{21} + \frac{2}{21} +\frac{2}{21} +\frac{1}{21}\)

Take LCM

\(P(Not\ 2019) = \frac{1+2+2+1}{21}\)

\(P(Not\ 2019) = \frac{6}{21}\)

Simplify

\(P(Not\ 2019) = \frac{2}{7}\)

Answer:

If the population was 4,580,000 in 2000, and it increased by 18%, the population in 2015 would be `4,580,000 + (4,580,000 x 0.18) = 5,394,400`.

Answer:

5404400

Step-by-step explanation:

4580000×18%=424400

4580000+424400=5404400

Answer:

c = 0.17w + 0.42

$1.10

Step-by-step explanation:

Let total cost = c.

Let number of ounces = w.

total cost = fixed cost + cost per ounce

fixed cost = $0.42

cost per ounce = $0.17

cost for w ounces = $0.17w

total cost = fixed cost + cost per ounce

     c         =       0.42    +        0.17w

The expression is:

c = 0.17w + 0.42

For 4 ounces, w = 4.

c = 0.17 × 4 + 0.42

c = 1.1

Answer:

c = 0.17w + 0.42

$1.10

Answer:

Step-by-step explanation:

(179 * 40) + (179 * 4) = 179 *(40 + 4) = 179 * 44

YES

(100 * 4) + 70*4 + 9*4 =  4 * ( 100 +70 + 9) = 4 * 179

No

4000 + 2800 + 360 + 280 +36 = 7876 = 179 *44

YES

(100 *44) + (70*44) + (9*44) = 44 * (100 + 70 +9) = 44 * 179

YES

179 *(4 +4) = 179 * 8

NO