write the equation of a line in slope-intercept form that is parallel to the line y=7x-8

Answer: Choice C) \(\sqrt{85} \text{ units}\)

Work Shown:

B = (4,3)

D = (-2,-4)

Use the distance formula to get:

\(d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(4-(-2))^2 + (3-(-4))^2}\\\\d = \sqrt{(4+2)^2 + (3+4)^2}\\\\d = \sqrt{(6)^2 + (7)^2}\\\\d = \sqrt{36 + 49}\\\\d = \sqrt{85}\\\\d \approx 9.21954446\\\\\)

You can also use the pythagorean theorem as a slight alternative method.

Step-by-step explanation: The answer is D. The quality a design has if it maintains all of its characteristics when it is reflected over an axis lying in its plane. This is the definition of reflectional symmetry. A and B are examples of reflectional symmetry over a vertical or horizontal axis, but not the general case. C is the definition of rotational symmetry.

The solution to the problem is as follows:Given that 80% of teenagers aged 12-17 own smartphones. A random sample of 250 teenagers is drawn.

The probability is calculated by using the Central Limit Theorem and the TI-84 calculator, and the answer is rounded to at least four decimal places.PC <0.11)-0 Х $P(X<0.11)To find the probability of less than 75% of the sampled teenagers owned smartphones, convert the percentage to a proportion.75/100 = 0.75

This means that p = 0.75. To find the sample proportion, use the given formula:p = x/nwhere x is the number of teenagers who own smartphones and n is the sample size.Substituting the values into the formula, we get;$$p = \frac{x}{n}$$$$0.8 = \frac{x}{250}$$$$x = 250 × 0.8$$$$x = 200$$Therefore, the sample proportion is 200/250 = 0.8.To find the probability of less than 75% of the sampled teenagers owned smartphones, we use the standard normal distribution formula, which is:Z = (X - μ)/σwhere X is the random variable, μ is the mean, and σ is the standard deviation.

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Therefore, the intersection of the arcs that Victor drew must be the midpoint of segment XY.

the midpoint is the point that is exactly halfway between two other points. It is the point that divides the line segment into two equal halves.

The midpoint of a line segment can be found by taking the average of the x-coordinates and the y-coordinates of the two endpoints of the segment. For example, if the endpoints of a line segment are (x1, y1) and (x2, y2), then the midpoint of the segment is\(((x_1 + x_2)/2,(y_1+y_2)/2).\)

by the question.

If Victor drew an arc centered at X and then drew an arc of the same radius centered at Y, the intersection of these arcs will be equidistant from X and Y. This is because the points on the arcs are all a fixed distance away from their respective centers.

Since Victor is drawing a perpendicular segment to XY, the intersection of the arcs he drew will be the midpoint of XY. This is because the perpendicular segment will divide XY into two equal segments, and the intersection of the arcs is equidistant from X and Y.

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what is the question???

Step-by-step explanation:

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Step-by-step explanation:

Circumference = pi * diameter = pi * 13.8 in = 43.354 = 43.4 in

Circumference of circle (formula) = pi × diameter of circle

So,

circumference of circle: 13.8 × pi ~ 43.4 inches (rounded to nearest tenth)

a)The value of f f(5) is  6

b) The third derivative of the Taylor polynomial is  -5

c)  The value of f(5.1) using the Taylor polynomial is T₄(5.1) ≈ 5.8252

d) The value of f'(4.9) using the Taylor polynomial T₄ is f'(4.9) ≈ -5.158

a) To find the value of f(5), we need to look at the constant term in the Taylor polynomial T₄(x). We see that the constant term is 6, so f(5) = 6.

b) The third derivative of T₄(x) is -30(x-5), which means that the third derivative evaluated at x = 5 is -30(0) = 0. This means that the correct choice is 3. f ⁽³⁾(5) = 30.

c) To estimate f(5.1) using T₄(x), we plug in x = 5.1 into the expression for T₄(x) and simplify. The calculation is as follows:

T₄(5.1) = 6 − 4(0.1) + 3(0.1)² − 5(0.1)³ + 2(0.1)⁴

= 6 - 0.4 + 0.03 - 0.0005 + 0.00008

= 5.6252 (rounded to four decimal places)

Therefore, the correct choice is 5. f(5.1) ≈ 5.6252.

d) To estimate f'(4.9) using T₄(x), we need to differentiate T₄(x) and evaluate the derivative at x = 4.9. The derivative of T₄(x) is as follows:

T'₄(x) = -4 + 6(x-5) - 15(x-5)² + 8(x-5)³

To evaluate T'₄(4.9), we substitute x = 4.9 into the expression for T'₄(x) and simplify:

T'₄(4.9) = -4 + 6(4.9 - 5) - 15(4.9 - 5)² + 8(4.9 - 5)³

= -4 - 0.6 + 0.25 - 0.008

= -5.158

Therefore, the correct choice is 1. f'(4.9) ≈ -5.158.

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Answer:

b

Step-by-step explanation:

Based on the given information, the conclusion of the t-test with a p-value of 0.03 and a significance level (α) of 0.05 is that we reject the null hypothesis. If the significance level is changed to α = 0.01, the decision remains the same.

In hypothesis testing, the p-value represents the probability of obtaining results as extreme as the observed data, assuming that the null hypothesis is true. The significance level (α) is the predetermined threshold used to make a decision about the null hypothesis.

When α = 0.05, it means that we are willing to accept a 5% chance of making a Type I error, which is rejecting the null hypothesis when it is actually true. In this case, since the p-value (0.03) is less than the significance level (0.05), we have sufficient evidence to reject the null hypothesis. Thus, we conclude that there is a statistically significant difference between the groups being compared.

If the significance level is changed to α = 0.01, it means we are now requiring stronger evidence to reject the null hypothesis. However, since the p-value (0.03) is still less than α, the decision remains the same. We would still reject the null hypothesis and conclude that there is a statistically significant difference between the groups.

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Answer:

see explanation

Step-by-step explanation:

Given 2 sides of a triangle then the third side x is in the range

difference of 2 sides < x < sum of 2 sides

(11)

given 2 sides 2, 6 , then

6 - 2 < x < 6 + 2

4 < x < 8

(12)

Given 2 sides 4, 12 , then

12 - 4 < x < 12 + 4

8 < x < 16

(13)

Given 2 sides 2, 11 , then

11 - 2 < x < 11 + 2

9 < x < 13

Answer:

if it a worksheet search the question online and the answer key comes up

Step-by-step explanation:

Answer:

perseveration

Step-by-step explanation:

The term you are looking for is "perseveration."

The z-score of an appliance that failed after 64 months is 2.

To find the z-score:

The given parameters are:

The z-score is then computed as follows:

We have the following for an appliance that stopped working after 64 months:

So, the equation becomes:

Compare and contrast the differences:

Calculate the quotient:

Therefore, the z-score of an appliance that failed after 64 months is 2.

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Tn = a + ( n- 1 ) d

T 26 = -33 + ( 26 - 1 ) 4

T 26 = -33 + ( 25 x 4 )

= -33 + 100

= 67.............. Option D

Let's denote the radius of the spherical balloon by r, and let's assume that the volume of the balloon is increasing at a rate of 10 cubic centimeters per second. We want to find an expression for the rate at which the radius of the balloon is increasing, which we'll denote by dr/dt.The volume of a sphere is given by the formula:V = (4/3)πr^3Differentiating both sides of this equation with respect to time t, we get:dV/dt = d/dt [(4/3)πr^3]where dV/dt is the rate at which the volume of the balloon is increasing, and dr/dt is the rate at which the radius of the balloon is increasing. Using the chain rule of differentiation, we get:dV/dt = (dV/dr) x (dr/dt)where dV/dr is the derivative of the volume V with respect to the radius r, which is given by:dV/dr = 4πr^2Substituting this expression into the previous equation, we get:10 = (4πr^2) x (dr/dt)Solving for dr/dt, we get:dr/dt = 10 / (4πr^2)Therefore, the expression for the rate at which the radius of the balloon is increasing is given by:dr/dt = 10 / (4πr^2)

In this kind of exercise, the first step is to define variables (the things you want to find) tagging them by a letter:

x := # of nickels in the purse,

y := # of quarters in the purse.

The next step is to translate the relationship between the variables into equations. In this case, the expression: "There are 15 coins" means

Besides, the expression: "... contains $1.55 in nickels and quarters" means

In summary, we have a 2x2 system of linear equations (don't worry about the name):

To solve it, we need to get rid of one variable. Let's eliminate y. Multiplying the second equation by -4, we get

Adding the equation we just obtained with the first in the system, we get

The number of nickels in the purse is 11.

The single equation we need to solve the problem is

Answer:

\( \displaystyle {r}^{} = 6\)

Step-by-step explanation:

remember that,

\( \displaystyle V _{ \rm sphere} = \frac{4}{3} \pi {r}^{3} \)

given that,

thus substitute:

\( \displaystyle \frac{4}{3} \pi {r}^{3} = 288\pi\)

divide both sides by 4/3π:

\( \displaystyle {r}^{3} = 216\)

cubic root both sides:

\( \displaystyle {r}^{} = 6\)

and we are done!

Answer:

Step-by-step explanation:

\(\bold{\dfrac{3m}4-\dfrac m{12}\ =\ \dfrac78}\\\\{}\qquad\cdot12\qquad\ \cdot12\\\\\bold{9m-m\ =\ \dfrac{21}2}\\\\{}\quad \ \bold{8m\ =\ \dfrac{21}2}\\\\{}\quad\div8\qquad\div8\\\\\bold{m\ =\ \dfrac{21}{16}}\)

Answer:

9

Step-by-step explanation:

6 ÷ 2(1+2) = ?

Parenthesis first:

6 ÷ 2(3) = ?

Then do the multiplication and division:

3(3) = ?

9 = ?

Answer:

It got colder by 9 degrees

Step-by-step explanation:

The inequality, and we can't find a number of days that Michelle must read in order to read more pages than Jill.

What is inequality?

An inequality is a mathematical statement that compares two values, expressing that they are not equal.

Let "x" be the number of days that Michelle must read in order to read more pages than Jill.

The total number of pages Michelle reads can be represented as:

33 + 19x

The total number of pages Jill reads can be represented as:

45 + 23x

To write an inequality to represent the number of days that Michelle must read in order to read more pages than Jill, we need to compare the two expressions:

33 + 19x > 45 + 23x

Simplifying the inequality, we get:

-12 > 4x

Dividing both sides by 4 (and flipping the inequality because we're dividing by a negative number), we get:

x < -3

However, this solution doesn't make sense in the context of the problem because we can't have negative days of reading.

Hence, there is no solution to the inequality, and we can't find a number of days that Michelle must read in order to read more pages than Jill.

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The mean absolute deviation of the data set is 2.5.  

It is defined as the measure to show the variation in data set in other words between the mean and every data value, the distance known as the MAD.

Given data:

10, 8, 10, 6, 6, 2, 10, 4

Using mean absolute deviation formula:

MAD = ∑ (xi - x)/n

So,

X = (10+8+10+6+6+2+10+4)/9

X = 56/8 = 7

Now, substituting the values in MAD formula

MAD = 20/8

MAD = 2.5

Hence, the mean absolute deviation of the data set is 2.5.

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The decrease in the number of pirates in the world correlates with an increase in mean global temperature is an example of a spurious correlation.

While there might be a statistical relationship between these two variables, it is not a causative one, and the correlation is likely coincidental.This is the importance of distinguishing between correlation and causation. In this case, the decrease in the number of pirates and the increase in mean global temperature are unrelated factors that happen to show a correlation when observed over time.

This is often used humorously to demonstrate the fallacy of assuming causation based solely on a correlation. It underscores the need for careful analysis and consideration of other relevant factors before making conclusions about causal relationships. In reality, factors such as greenhouse gas emissions, deforestation, and industrialization have a more significant impact on global temperature trends than the number of pirates in the world.

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The function \(\(f(x, y) = \frac{x^2y^5}{x^2 + 6y^2}\)\) is continuous at \(\((0, 0)\)\) because the limit of \(\(f(x, y)\) as \((x, y)\)\) approaches \(\((0, 0)\)\) exists and is equal to 0.

To determine if the function \(\(f(x, y)\)\) is continuous at \(\((0, 0)\),\) we need to evaluate the limit of \(\(f(x, y)\) as \((x, y)\)\) approaches \(\((0, 0)\)\) and check if it exists and is equal to the function value at \(\((0, 0)\).\)

Let's consider the limit of \(\(f(x, y)\) as \((x, y)\)\) approaches \(\((0, 0)\):\)

\(\[\lim_{(x, y) \to (0, 0)} f(x, y) = \lim_{(x, y) \to (0, 0)} \frac{x^2y^5}{x^2 + 6y^2}\]\)

To simplify the expression, we can use the fact that \(\(|xy^3| \leq x^2 + 6y^2\)\)for all \(\((x, y)\).\) This inequality ensures that the function is well-defined and bounded near \(\((0, 0)\).\)

Applying the Squeeze Theorem, we have:

\(\[\lim_{(x, y) \to (0, 0)} |f(x, y)| \leq \lim_{(x, y) \to (0, 0)} \frac{|x^2y^5|}{x^2 + 6y^2} \leq \lim_{(x, y) \to (0, 0)} \frac{x^2 + 6y^2}{x^2 + 6y^2} = 1\]\)

Since the limit of the absolute value of \(\(f(x, y)\)\) is bounded by 1, we can conclude that the limit of \(\(f(x, y)\) as \((x, y)\)\) approaches \(\((0, 0)\)\) exists and is equal to 0 (the function value at \(\((0, 0)\)\)).

Therefore, the function \(\(f(x, y)\)\) is continuous at \(\((0, 0)\).\)

In summary, the function \(\(f(x, y) = \frac{x^2y^5}{x^2 + 6y^2}\)\) is continuous at \(\((0, 0)\)\) because the limit of \(\(f(x, y)\) as \((x, y)\)\) approaches \(\((0, 0)\)\) exists and is equal to 0.

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Answer:

(a)\(20+(-9)+8+(-7)\)

(b)\(4x+(-7y)+(-5z)+6\)

Step-by-step explanation:

We are required to write an equivalent expression that uses only addition for each of the given term.

Note that the product of + and - is always -.

Therefore:

(a)20−9+8−7

\(20-9+8-7 \\=20+(-9)+8+(-7)\)

(b)4x−7y−5z+6

\(4x-7y-5z+6\\=4x+(-7y)+(-5z)+6\)

Step-by-step explanation:

The 90% confidence interval for the difference in the population means is -2.51 to 0.31

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

xˉ₁ = −17.1

s₁² = 8.4

n₁ = 22

​xˉ₂ = −16.0

s₂² = 8.7

n₂ = 24

Calculate the pooled variance using

P = (df₁ * s₁² + df₂ * s₂²)/df

Where

df₁ = 22 - 1 = 21

df₂ = 24 - 1 = 23

df = 22 + 24 - 2 = 44

So, we have

P = (21 * 8.4 + 23 * 8.7)/44

P = 8.56

Also, we have the standard error to be

SE = √(P/n₁ + P/n₂)

So, we have

SE = √(8.56/22 + 8.56/24)

SE = 0.86

The z score at 90% CI is 1.645, and the CI is calculated as

CI =  (x₁ - x₂) ± z * SE

So, we have

CI = (-17.1 + 16.0) ± 1.645 * 0.86

This gives

CI = -1.1 ± 1.41

Expand and evaluate

CI = (-2.51, 0.31)

Hence, the confidence interval is -2.51 to 0.31

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Answer: 24 T-shirts

Step-by-step explanation:

8 x t = 192

192/8 = 24

8 x 24 = 192