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Answer: x=2x +14

Step-by-step explanation:

1) subtract 8x from both sides: -4x= -8x -56

2) divide both sides by -4: x=2x +14

(a) The distance traveled by motorcycle is 1548 ft.

(b) The distance traveled by motorcycle is 1512 ft.

(c) (b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t.

What is velocity?

The primary indicator of an object's position and speed is its velocity. It is the distance that an object travels in one unit of time. The displacement of the item in one unit of time is the definition of velocity.

Given table is:

t (s)        0       12      24     36     48      60

v (ft/s)   30      28     25     21      25      27

The distance traveled by motorcycle during this time period using the velocities at the beginning of the time intervals is:

12(30 + 28 + 25 + 21 + 25)

=12 × 129

= 1548 ft

The distance traveled by motorcycle during this time period using the velocities at the end of the time intervals is:

12(28 + 25 + 21 + 25 + 27)

=12 × 126

= 1512 ft

The distance traveled by motorcycle at the end of the time intervals is greater than the distance traveled by motorcycle at the beginning of the time intervals.

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The solution to the mathematical statement is x ≤ -5/8

From the question, we have the following parameters that can be used in our computation:

The sum of a number times 8 and 25 is at most 20

Represent the number with x

So, we have the following representation

The sum of x times 8 and 25 is at most 20

Represent x times 8 with 8x

So, we have the following representation

The sum of 8x and 25 is at most 20

Represent The sum of 8x and 25  with 8x + 25

So, we have the following representation

8x + 25 at most 20

at most means less than or equal to

So, we have

8x + 25 ≤ 20

Subtrat 25 from both sides

8x ≤ -5

Divide by 8

x ≤ -5/8

Hence, the solution is x ≤ -5/8

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When the second derivative of a function equals zero, it indicates a possible point of inflection or a critical point where the concavity of the function changes. It is a significant point in the analysis of the function's behavior.

The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero at a particular point, it suggests that the function's curvature may change at that point. This means that the function may transition from being concave upward to concave downward, or vice versa.

Mathematically, if the second derivative is zero at a specific point, it is an indication that the function has a possible point of inflection or a critical point. At this point, the function may exhibit a change in concavity or the slope of the tangent line.

Studying the second derivative helps in understanding the overall shape and behavior of a function. It provides insights into the concavity, inflection points, and critical points, which are crucial in calculus and optimization problems.

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When the second derivative of a function equals zero, it indicates a critical point in the function, which can be a maximum, minimum, or an inflection point.

The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero, it indicates a critical point in the function. A critical point is a point where the function may have a maximum, minimum, or an inflection point.

To determine the nature of the critical point, further analysis is required. One method is to use the first derivative test. The first derivative test involves examining the sign of the first derivative on either side of the critical point. If the first derivative changes from positive to negative, the critical point is a local maximum. If the first derivative changes from negative to positive, the critical point is a local minimum.

Another method is to use the second derivative test. The second derivative test involves evaluating the sign of the second derivative at the critical point. If the second derivative is positive, the critical point is a local minimum. If the second derivative is negative, the critical point is a local maximum. If the second derivative is zero or undefined, the test is inconclusive.

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The variables on a scatter plot are related using the equation of a straight line graph; y = mx + c.

Since the options are unclear, I will try to help you as much as possible. A scatter plot is an arrangement in which one variable is plotted on the vertical axis and another is plotted on the horizontal axis.

The variables on a scatter plot are related using the equation of a straight line graph; y = mx + c. Using this relation, we can establish the equation of the scatter plot.

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Hideki should use coupon 2 to get a better deal.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, Hideki buys 2 sweaters for $18 each.

Coupon 1: Buy one, get one 40% off

Here, 40% of 18

= 40/100 ×18

= 0.4×18

= $7.2

So, cost of entire purchase 2(18)-7.2

= 36-7.2

= $28.8

Coupon 2: 25% off entire purchase

25% of 2(18)

= 25/100 ×36

= 0.25×36

= $9

Now, 36-9 =$27

Therefore, Hideki should use coupon 2 to get a better deal.

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1) The fraction is given as,

c) The fraction is given as,

d) The fraction is given as,

Tthe inequality that describes this graph is y ≤ 1/3x - 4/3

The graph that completes the question is added as an attachment

From the attached graph, we have the following points

(0, -1.3) and (3, -0.3)

The slope is calculated as:

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

Substitute the known values in the above equation

m = (-0.3 + 1.3)/(3 - 0)

Evaluate

m = 1/3

The equation is then calculated as:

y = m(x - x1) + y1

This gives

y = 1/3(x - 0) - 1.3

Evaluate

y = 1/3x - 4/3

From the graph, we have the following highlights:

The first highlight above implies, the inequality can be any of ≥ and ≤

While the second highlight above implies, the inequality is ≤

Hence, the inequality that describes this graph is y ≤ 1/3x - 4/3

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Answer:

y = 3x - 2

Step-by-step explanation:

The equation of a line is y = mx + c where m is the slope of the line and c is the y-intercept. I will be calculating the slope of the line using the points (1, 1) and (2, 4).

Slope = \(\frac{rise}{run}\)

          = \(\frac{4-1}{2-1}\)

          = 3

Based on the graph, the y-intercept is (-2) so the equation of the line is:

y = 3x - 2

Answer:

Step-by-step explanation:

The GCF is x^2 so

x^2(4x^3+3)

Answer:

8x^7

Step-by-step explanation:

2x^2 multiply by 4x^5 (reminder! multiply the numbers and the not the powers!)

then multiply the terms with the same base by adding their exponents

2+5= 7

8x^7

Answer:

Step-by-step explanation:

i thinks its 6 (im sorry if im wrong)

Answer:

qcrit ≈ 3.04.

Step-by-step explanation:

The tukey hsd test, if there are 16 df associated with mswithin, and α = .05 and the number of groups = 3, qcrit = 3.842.

To determine the value of qc rit for the Tukey HSD (Honestly Significant Difference) test, we need to use the Studentized range distribution with the appropriate degrees of freedom and significance level.

In this case, the number of groups is 3, which means we have 3 - 1 = 2 degrees of freedom associated with the numerator of the F-ratio.

The denominator degrees of freedom for mswithin is 16, which will be the denominator degrees of freedom for the F-distribution.

To find the value of qcrit, we can use a statistical table or a statistical software. For α = 0.05, with 2 and 16 degrees of freedom, the value of qcrit is approximately 3.842.

Therefore, qcrit = 3.842.

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∂g/∂u is equal to 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v)).

To find the indicated derivative, we need to use the chain rule. Let's differentiate step by step:

Given:

g(u, v) = f(x(u, v), y(u, v))

f(x, y) = 7x³y³

x(u, v) = ucos(v)

y(u, v) = usin(v)

To find ∂g/∂u, we differentiate g(u, v) with respect to u while treating v as a constant:

∂g/∂u = (∂f/∂x) * (∂x/∂u) + (∂f/∂y) * (∂y/∂u)

To find ∂f/∂x, we differentiate f(x, y) with respect to x:

∂f/∂x = 21x²y³

To find ∂x/∂u, we differentiate x(u, v) with respect to u:

∂x/∂u = cos(v)

To find ∂f/∂y, we differentiate f(x, y) with respect to y:

∂f/∂y = 21x³y²

To find ∂y/∂u, we differentiate y(u, v) with respect to u:

∂y/∂u = sin(v)

Now, we can substitute these partial derivatives into the equation for ∂g/∂u:

∂g/∂u = (21x²y³) * (cos(v)) + (21x³y²) * (sin(v))

To find the simplified form, we substitute the given values of x(u, v) and y(u, v) into the equation:

x(u, v) = ucos(v) = u * cos(v)

y(u, v) = usin(v) = u * sin(v)

∂g/∂u = (21(u * cos(v))²(u * sin(v))³) * (cos(v)) + (21(u * cos(v))³(u * sin(v))²) * (sin(v))

Simplifying further, we get:

∂g/∂u = 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v))

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If Niki correctly cut the mirror, the adjacent angle should measure 82 degrees. To verify this, we can measure the adjacent angle using a protractor or ruler. If the measured angle is indeed 82 degrees, then Niki has correctly cut the mirror. However, if the measured angle is different, then Niki made an error in cutting the mirror. In conclusion, we need to measure the adjacent angle to determine if Niki correctly cut the mirror.

The given figure shows a rhombus-shaped side mirror for a car, and the question asks if Niki correctly cut the mirror, with the lower right corner supposed to be 98 degrees. To determine if Niki made a correct cut, we need to examine the properties of a rhombus.

A rhombus is a quadrilateral with four equal sides and opposite angles that are congruent. In a rhombus, the sum of any two adjacent angles is 180 degrees.

Since the given angle is 98 degrees, we can subtract it from 180 to find the measure of the opposite angle.

180 - 98 = 82 degrees

If the opposite angle measures 82 degrees, it means that the adjacent angle (the one next to the given angle) must also measure 82 degrees since the angles in a rhombus are congruent.

Therefore, if Niki correctly cut the mirror, the adjacent angle should measure 82 degrees. To verify this, we can measure the adjacent angle using a protractor or ruler. If the measured angle is indeed 82 degrees, then Niki has correctly cut the mirror. However, if the measured angle is different, then Niki made an error in cutting the mirror.

In conclusion, we need to measure the adjacent angle to determine if Niki correctly cut the mirror.

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Answer:

Step-by-step explanation:

6*(x-3) yeah that is it.

Answer:

\(6x-18\)

Step-by-step explanation:

Step 1: Distribute

\(2x-6+4x-12\)

Step 2: Add like terms

\(2x+4x\)

\(-6-12\)

Step 3: Consolidate

\(6x-18\)

As per the survey of 400 students, 60 of them bring their lunch everyday.

A percentage is a figure or ratio that may be stated as a fraction of 100 in mathematics. If we need to compute a percentage of a number of students, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Percent signifies for every 100. The sign "%" is used to denote it.

Examples

10% is the fraction 1/10.

20% is the same as the 15 fraction.

25% translates to a 1/4 fraction.

50% is the same as a half fraction.

75% corresponds to a 1/4 fraction.

90% is the same as the proportion (9)/10.

No dimension exists for percentages. Thus, it is referred to as a dimensionless number. If we say 50% of a number, we mean 50% of its total.

How to solve ?

15% of 400 = 15 * 400/100 = 60

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Answer:

C

Step-by-step explanation:

It’s convenient that there are only two x values you need to check, -2 and 2. Just insert it to see what y is appropriate.

x = -2: y > 6 + 3 = 9 (and y > -2 + 2 = 0 which is redundant here)

x = 2: y > 2 + 2 = 4 (and y > -6 + 3 = -3 which is redundant here)

So, neither B nor D is in the solution set with 5 < 9 and -5 < 9.

A isn’t in the solution set either with -5 < 4.

C is in the solution set with 5 > 4.

Answer:

c

Step-by-step explanation:

Answer:

option (d)

Step-by-step explanation:

Answer:

143880000 people have dogs and b.

Step-by-step explanation:

327,000,000 * .44(44 percent) = 143880000

the sample of 437 is much smaller than the entire state of texas, so it is incorrect to assume that the small amount of people is representative of the entire state.

Answer:

Step-by-step explanation:

3)

327 Million → 100%

x → 44%

100x = 44×327

100x = 14388

x = 14388/100

x = 143.88 Million people

4) D

I hope I've helped you.

Answer:

875

Step-by-step explanation:

lets assume the original amount X

the new amount = X - ( X × 40% )

525 = (60 × X) ÷ 100

X = ( 525 × 100 ) ÷ 60

X = 875

Answer:

The number is 875

Step-by-step explanation:

Step One:

Convert 40% to a decimal --> .40

Step Two

525 = n - .40n

(525 is equal to a number minus forty percent of a number )

Step Three

Isolate the variable by dividing each side by factors that don't contain the variable.

N = 875

The zeros of the function f(s) = 3s^7 - 4s^2 + 8s + 8 are s = -1, s = 0, and s = 2. The polynomial can be written as a product of linear factors as f(s) = 3s(s + 1)(s - 2).

To find the zeros of the function, we can factor the polynomial. We can do this by first grouping the terms as follows:

```

f(s) = (3s^7 - 4s^2) + (8s + 8)

```

We can then factor out a 3s^2 from the first group and an 8 from the second group:

```

f(s) = 3s^2(s^3 - 4/3) + 8(s + 1)

```

The first group can be factored using the difference of cubes factorization:

```

s^3 - 4/3 = (s - 2/3)(s^2 + 2/3s + 4/9)

```

The second group can be factored as follows:

```

s + 1 = (s + 1)

```

Therefore, the complete factorization of the polynomial is:

```

f(s) = 3s(s - 2/3)(s^2 + 2/3s + 4/9)(s + 1)

```

The zeros of the polynomial are the values of s that make the polynomial equal to 0. We can see that the polynomial is equal to 0 when s = 0, s = -1, or s = 2. Therefore, the zeros of the function are s = -1, s = 0, and s = 2.

The function has three zeros, which correspond to the points where the graph crosses the x-axis. These points are at s = -1, s = 0, and s = 2.

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Answer:

Step-by-step explanation:

a.

To solve this system of equations, we can substitute the value of x from the second equation into the first equation:

x = 3y - 5

x + y = 3

Substituting x:

3y - 5 + y = 3

4y - 5 = 3

4y = 8

y = 2

Now, we can substitute y = 2 back into either equation to find x:

x + 2 = 3

x = 1

So the solution to the system of equations is (x, y) = (1, 2).

To confirm this solution, we can graph both equations on the same coordinate plane and see where they intersect:

x + y = 3 is a line with a y-intercept of 3 and a slope of -1.

x = 3y - 5 is a line with a y-intercept of -5/3 and a slope of 3.

Graphing these lines, we can see that they intersect at the point (1, 2), confirming our solution.

b.

To solve this system of equations, we can substitute the value of y from the second equation into the first equation:

y = -2x - 4

x - y = -5

Substituting y:

x - (-2x - 4) = -5

x + 2x + 4 = -5

3x = -9

x = -3

Now, we can substitute x = -3 back into either equation to find y:

y = -2(-3) - 4

y = 2

So the solution to the system of equations is (x, y) = (-3, 2).

To confirm this solution, we can graph both equations on the same coordinate plane and see where they intersect:

y = -2x - 4 is a line with a y-intercept of -4 and a slope of -2.

x - y = -5 is a line with a y-intercept of 5 and a slope of 1.

Graphing these lines, we can see that they intersect at the point (-3, 2), confirming our solution.

Answer:

\(\boxed{=2x(x^2+6y^2)}\)

Step-by-step explanation:

Remember:

\((a+b)(a-b)=a^2-b^2\\\\a^3+b^3=(a+b)(a^2-ab+b^2)\\\\\\(x+2y)^3+(x-2y)^3\\\\=(x+2y+x-2y)((x+2y)^2-(x+2y)(x-2y)+(x-2y)^2)\\\\=2x(x^2+4xy+4y^2-(x^2-4y^2)+x^2-4xy+4y^2)\\\\=2x(x^2+6y^2)\\\)

The sample means are Mean(Y) = 61.4 and Mean(X) = 15, the sample variances are Variance(Y) ≈ 1124.89 and Variance(X) ≈ 2.67, the sample standard deviations are Standard deviation(Y) ≈ 33.56 and Standard deviation(X) ≈ 1.63, the sample covariance is Covariance(X, Y) ≈ -131.69, and the sample correlation is Correlation(X, Y) ≈ -0.77.

a. To find the sample means, variances, and standard deviation, we can use the following formulas:

Sample mean of income (Y):

Mean(Y) = (100 + 65 + 47 + 112 + 34 + 85 + 92 + 83 + 67 + 29) / 10 = 614 / 10 = 61.4

Sample mean of education (X):

Mean(X) = (18 + 14 + 14 + 16 + 12 + 16 + 18 + 14 + 16 + 12) / 10 = 150 / 10 = 15

Sample variance of income (Y):

Variance(Y) = [(100 - 61.4)^2 + (65 - 61.4)^2 + (47 - 61.4)^2 + (112 - 61.4)^2 + (34 - 61.4)^2 + (85 - 61.4)^2 + (92 - 61.4)^2 + (83 - 61.4)^2 + (67 - 61.4)^2 + (29 - 61.4)^2] / 9 ≈ 1124.89

Sample variance of education (X):

Variance(X) = [(18 - 15)^2 + (14 - 15)^2 + (14 - 15)^2 + (16 - 15)^2 + (12 - 15)^2 + (16 - 15)^2 + (18 - 15)^2 + (14 - 15)^2 + (16 - 15)^2 + (12 - 15)^2] / 9 ≈ 2.67

Sample standard deviation of income (Y):

Standard deviation(Y) = √Variance(Y) ≈ √1124.89 ≈ 33.56

Sample standard deviation of education (X):

Standard deviation(X) = √Variance(X) ≈ √2.67 ≈ 1.63

b. To find the sample covariance and correlation, we can use the following formulas:

Sample covariance:

Covariance(X, Y) = [(18 - 15)(100 - 61.4) + (14 - 15)(65 - 61.4) + (14 - 15)(47 - 61.4) + (16 - 15)(112 - 61.4) + (12 - 15)(34 - 61.4) + (16 - 15)(85 - 61.4) + (18 - 15)(92 - 61.4) + (14 - 15)(83 - 61.4) + (16 - 15)(67 - 61.4) + (12 - 15)(29 - 61.4)] / 9 ≈ -131.69

Sample correlation:

Correlation(X, Y) = Covariance(X, Y) / (Standard deviation(X) * Standard deviation(Y)) ≈ -131.69 / (1.63 * 33.56) ≈ -0.77

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Correct question-

Consider the following random sample of income and education: Income(Y) Education(X) 100 18 65 14 47 14 112 16 34 12 85 16 92 18 83 14 67 16 29 12 a. Find sample means, variances and standard deviation. b. Find sample covariance and correlation.

No, I do not agree that non-random sampling technique is equivalent to quota sampling, which appears to be similar to stratified random sampling.

While quota sampling and stratified random sampling both involve dividing the population into subgroups or strata, they differ in terms of the sampling process.

In quota sampling, the researcher sets specific quotas or targets for each subgroup based on certain characteristics, such as age, gender, or occupation. The sampling process involves non-random selection within each subgroup until the quotas are fulfilled. Quota sampling does not involve a random selection of participants within each subgroup, making it a non-random sampling technique.

On the other hand, stratified random sampling is a true random sampling technique. It also involves dividing the population into strata based on certain characteristics, but in stratified random sampling, the selection of participants within each stratum is done randomly. This random selection ensures that every member of the population has an equal chance of being included in the sample, which helps to reduce bias and increase the representativeness of the sample.

So, while both quota sampling and stratified random sampling involve dividing the population into subgroups, the key difference lies in the selection process. Quota sampling involves non-random selection within each subgroup, whereas stratified random sampling involves random selection within each stratum.

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Part A

2 white, 5 red, 7 total

P(1st white) = 2/7

P(1st white, 2nd white) = P(1st white)*P(2nd white)

P(1st white, 2nd white) = (2/7)*(4/9)

P(1st white, 2nd white) = 8/63

Let m = 8/63

---------------

P(1st red) = 5/7

P(1st red, 2nd red) = P(1st red)*P(2nd red)

P(1st red, 2nd red) = (5/7)*(7/9)

P(1st red, 2nd red) = 5/9

Let n = 5/9 = 35/63

---------------

m+n = P(both are same color)

m+n = 8/63+35/63

m+n = 43/63

========================================

Part B

m = P(first white then red)

m = (2/7)*(5/9)

m = 10/63

n = P(first red then white)

n = (5/7)*(2/9)

n = 10/63

r = P(second bead isn't same color as first)

r = m+n

r = 10/63+10/63

r = 20/63

========================================

Part C

m = P(1st white, 2nd white)

m = (2/7)*(4/9)

m = 8/63

n = P(1st red, 2nd white)

m = (5/7)*(2/9)

m = 10/63

m+n = P(2nd is white)

m+n = 8/63+10/63

m+n = 18/63

m+n = 2/7

========================================

Part D

If we withdraw 1 white bead, but we add it back in, then the probability of selecting white has not changed on the second selection.

The same can be said if we picked a red bead as well. This is because we simply replace the red bead with a copy of some other red bead.

Nick's statement is another way of saying replacement is happening.

Answer:

exponent

Step-by-step explanation:

cuz that s what it is called

Answer:

expo

Step-by-step explanation:

give them brain, they're correct.

Answer:

What is not a property of all parallelograms?

Yes, opposite sides look congruent, and that's a property. But adjacent sides don't look congruent, and that's not a property. Do the sides appear to be parallel? Yes, opposite sides look parallel (and of course, you know this property if you know the definition of a parallelogram)

Step-by-step explanation: