Compare the functions shown below: f(x) = (x + 3)2 − 2 g(x) linear graph with y intercept of negative 3 over 2 and x intercept of 3 h(x) x y −3 2 −2 7 −1 14 0 23 1 34 2 47 3 62 What is the correct order of the functions from least to greatest according to the average rate of change on the interval from x = −1 to x = 3?

Answer:

150

Step-by-step explanation:

Knowledge

Answer:

$18.50

Step-by-step explanation:

In the example before 61 messages = $6.10 or rounding to the tenths place 6.1. If you do the same with 185, you get 18.5 or 18.50

Answer:

$18.50

Step-by-step explanation:

6.10 times 10 = 61

185 divided by 10 = 18.5

The total amount of space taken up on the sign by the letters in Hannah's name is between 3 and 4 whole numbers.

If each letter takes up 5/8 inch of space, then the total amount of space taken up by all 6 letters in Hannah's name is:

6 letters × 5/8 inch per letter = 30/8 inches = 3 6/8 inches = 3 3/4 inches

To find the range of whole numbers between which 3 3/4 inches falls, we can convert 3 3/4 to an improper fraction:

3 3/4 = (4 × 3 + 3)/4 = 15/4

Now we can find the two whole numbers that 15/4 is between by dividing 15 by 4:

15 ÷ 4 = 3 with a remainder of 3

So 15/4 is between 3 and 4, specifically:

3 < 15/4 < 4

Therefore, the total amount of space taken up on the sign by the letters in Hannah's name is between 3 and 4 whole numbers.

A fraction is a mathematical concept that represents a part of a whole. It is typically written in the form of one number (the numerator) over another number (the denominator), separated by a horizontal line. For example, 3/4 is a fraction where the numerator is 3 and the denominator is 4.

The numerator represents how many parts of the whole we are referring to, and the denominator represents the total number of equal parts that make up the whole. So, 3/4 represents 3 out of 4 equal parts of a whole. Fractions are used to represent quantities that are not whole numbers, such as 1/2, 3/5, and 7/8.

Fractions are used in many different areas of math and everyday life, such as in measurement, cooking, and finance. They are also an important concept in understanding other mathematical ideas like decimals and percentages.

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Answer:

A

Step-by-step explanation:

We can solve this problem by eliminating wrong answers

It can be b because there is no 3

It can be c because the equation would be 4+3

And it can be d because the equation would be 3x+4

so it must be a

Answer:

option A is correct

as additional page costs is not fixed so there will be any value of x with multiply by 4

and the fixed remain only one time so it remains fixed and 3 is also fixed.

Answer:

12.56

Step-by-step explanation:

I'm 99% sure the answer is 12.57ft²

Answer:

Yes, they are correct.

Step-by-step explanation:

\( \frac{4}{10} = \frac{2}{5} \)

\( \frac{6}{15} = \frac{2}{5} \)

Hope it helps :)

The value of x for the same angle based on the information is 13.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle

Since angles 5 and 10 are the same, we can set them equal to each other:

91 - 2x = 5x

Simplifying this equation, we can add 2x to both sides:

91 = 7x

Then, we can divide both sides by 7 to solve for x:

x = 13

Therefore, the value of x for the same angle is 13.

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(8 x 47) - (5 x 47)

Also The difference is 141

In linear equation, y ≥ x + 12/3 is simple version .

What in mathematics is a linear equation?

y ≥ 1/3 x + 4

y ≥ x/3 + 4

y ≥ x + 12/3

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I'm guessing that you want to simplify \(67.6^2\)

The two above the 67.2 is a square or a power.

Usually when you take something to a power, you mutiply the number of time by the power:

Examples:   \(78^2\) would be 78*78

                   \(23^5\) would be 23*23*23*23*23

Questions?

67.6² would simply be 67.6*67.6.

So therefore it is 4569.76

Answer:

we need the graph in order to find the answer.

Step-by-step explanation:

Answer:

A, 1,2

Step-by-step explanation:

we translate it first into language of math

we use n for the number

n² = 3n - 2

then, do some algebra things

n² - 3n + 2 = 0

then factorize it

(n - 2)(n - 1) = 0

first n

n - 2 = 0

n = 2

2nd n

n - 1 = 0

n = 1

so n can be 1 or 2

The missing angle of the diagram is expressed as; x = 70°

An angle is usually measured with reference to a circle with its center at the common endpoint of the rays. Hence, the sum of angles at a point is always 360 degrees

Now, we are given a point with three angles where one is unknown and the other two are known. Thus, by the sum of angles about a point, they will sum up to 360 degrees.

Thus;

x + 160 + 130 = 360

x + 290 = 360

x = 360 - 290

x = 70°

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a. w is not in {v1, v2, v3}. b. There are infinitely many vectors in Span{v1, v2, v3}. c. No, w is not in the subspace spanned by {v1, v2, v3} because it is not a linear combination of these three vectors.

a. To determine if w is in {v₁, v₂, v₃}, we need to check if w is equal to a linear combination of v₁, v₂, and v₃. That is, we need to check if there exist constants c1, c₂, and c₃ such that:

c₁v₁ + c₂v₂ + c₃v₃ = w

Substituting the given values, we get:

c₁(1) + c₂(4) + c₃(11) = 50

Solving this system of equations, we find that there are no values of c₁, c₂, and c₃ that satisfy the equation. Therefore, w is not in {v₁, v₂, v₃}.

b. The set {v₁, v₂, v₃} has three vectors, and any linear combination of these vectors will be in the span of {v₁, v₂, v₃}. Therefore, to find the number of vectors in Span {v₁, v₂, v₃}, we need to determine how many linear combinations of these vectors are possible. Each vector in the span can be written as a linear combination of v₁, v₂, and v₃, so there are infinitely many vectors in Span {v₁, v₂, v₃}.

c. Since w is not in {v₁, v₂, v₃}, we need to check if w can be written as a linear combination of {v₁, v₂, v₃}. If w is in the subspace spanned by {v₁, v₂, v3}, then there exist constants c₁, c₂, and c₃ such that:

c₁v₁ + c₂v₂ + c₃v₃ = w

As we found in part (a), there are no values of c₁, c₂, and c₃ that satisfy this equation. Therefore, w is not in the subspace spanned by {v₁, v₂, v₃}.

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Answer:

32

Step-by-step explanation:

4 ÷ 1/8

4/1 · 8/1 = 32/1

32

I hope this helps & God bless!

For Pearson correlation the most common purpose to examine is given by option a. The relationship between 2 variables.

The Pearson correlation is a statistical measure that indicates the extent to which two continuous variables are linearly related.

It measures the strength and direction of the relationship between two variables.

Ranging from -1 perfect negative correlation to 1 perfect positive correlation.

And with 0 indicating no correlation.

It is commonly used in research to examine the association between two variables.

Such as the relationship between height and weight, or between income and education level.

Therefore, the most common purpose of a Pearson correlation is to examine the relationship between 2 variables.

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The above question is incomplete, the complete question is:

The most common purpose for a Pearson correlation is to examine,

a. The relationship between 2 variables

b. Relationships among groups

c. Differences between variables

d. Differences between two or more groups

False. Randomization distributions are centered at the value where the null is false. This distinction is important in hypothesis testing as it helps determine the statistical significance of observed differences or effects.

Randomization distributions are generated through permutation tests, which involve random shuffling of data points between groups. In hypothesis testing, the null hypothesis assumes that there is no difference between groups or no effect of a treatment. The alternative hypothesis suggests otherwise.

The randomization distribution is created by repeatedly shuffling the data and calculating a test statistic based on the null hypothesis. This distribution represents the expected outcomes if the null hypothesis is true. Therefore, the randomization distributions are centered at the value where the null is false, as they capture the potential differences or effects between groups.

In summary, randomization distributions are not centered at the value where the null is true; rather, they are centered at the value where the null is false. This distinction is important in hypothesis testing as it helps determine the statistical significance of observed differences or effects.

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Intro:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

Solve x−4y=−7 for x...

\(x-4y=-7\\x=4y-7\)

Substitute 4y−7 for x in −x+2y=3...

\(-x+2y=3\\-(4y-7)+2y=3\\-4y+7+2y=3\\-2y+7=3\\-2y=-4\\y=2\)

Substitute 2 for y in x=4y−7...

\(x=4y-7\\x=4(2)-7\\x=8-7\\x=1\)

So the solution of these equations is (1,2).

The margin of error at the 99% confidence interval is 0.018 or 1.8%.

Interpretation: This means that if we were to repeat the survey many times, about 99% of the intervals calculated from the samples would contain the true proportion of viewers under 30 in the population, and the margin of error for each interval would be no more than 1.8%.

The margin of error is the amount by which the sample statistic (in this case, the proportion of viewers under 30) may differ from the true population parameter.

Using the given formula for margin of error:

Margin of error = z* * sqrt(p*(1-p)/n)

Where:

- z* is the z-score corresponding to the confidence level (99% in this case), which is 2.576

- p is the proportion of viewers under 30, which is 0.3

- n is the sample size, which is 5000

Substituting these values, we get:

Margin of error = 2.576 * sqrt(0.3*(1-0.3)/5000) = 0.018

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The probability that a srs of 20 students will spend an average of between 600 and 700 dollars is 0.92081.

We need to find the probability that a simple random sample of 20 students will spend an average of between 600 and 700 dollars.

To solve this problem, we will use the central limit theorem, which states that the sampling distribution of the sample means will be approximately normally distributed with a mean of μ and a standard deviation of σ/√(n), where n is the sample size.

Thus, the mean of the sampling distribution is μ = 650 and the standard deviation is σ/sqrt(n) = 120/√(20) = 26.83.

We need to find the probability that the sample mean falls between 600 and 700 dollars. Let x be the sample mean. Then:

Z1 = (600 - μ) / (σ / √(n)) = (600 - 650) / (120 / √t(20)) = -1.77

Z2 = (700 - μ) / (σ / √(n)) = (700 - 650) / (120 / √(20)) = 1.77

Using a standard normal distribution table or calculator, we can find the area under the standard normal distribution curve between these two Z-scores as:

P(-1.77 < Z < 1.77) = 0.9208

Therefore, the probability that a simple random sample of 20 students will spend an average of between 600 and 700 dollars is 0.9208, or approximately 0.92081 when rounded to five decimal places.

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Prove the third angle theorem is the sum of the angles in each triangle is 180 degree by the Triangle Sum Theorem

What is Third angle theorem?

A triangle's outside angle has a measure greater than either of the distant interior angles. Because the parallel postulate is not required for its proof, this is a fundamental conclusion in absolute geometry.

Concept:

You're undoubtedly rather familiar with triangles by this point. You've been using triangular building blocks since you were in preschool, and you already know a lot about their length, area, and perimeter. What about those annoying angles, though? Would it really matter if they were all triangles, say 45-45-90 or 30-60-90? At least then you'd be able to recall everything you've ever needed to deal with them.

According to the third angle theorem, the third set of angles must likewise be congruent if two angles in one triangle are congruent with two angles in another triangle. What more details would you need to be aware of in order to establish that the triangles are congruent?

You require some knowledge of the side information for the triangles to be congruent. The triangles will be congruent if you are aware of two pairs of congruent angles and at least one pair of corresponding sides.

Using the Triangle Sum Theorem, demonstrate that the third angle theorem states that the sum of the angles in each triangle is 180 degrees.

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Answer:

312,480 downloads in one day

Step-by-step explanation:

There are different ways to approach this problem, but one possible method is to use unit conversions and basic arithmetic operations.

Here's how:

First, we need to know how many minutes are in a day. Since there are 24 hours in a day and 60 minutes in an hour, we can multiply those numbers:

24 x 60 = 1440 minutes

Next, we can use the given rate of downloads per minute (217) and multiply it by the total number of minutes in a day:

217 x 1440 = 312,480

Therefore, there are 312,480 downloads in one day.

ANOVA is a more appropriate and efficient method for evaluating mean differences when an experiment consists of three or more treatment conditions, as it provides a more robust and reliable analysis than multiple t-tests, while also reducing the risk of Type I errors.

The principal reason why you should use ANOVA (Analysis of Variance) instead of several t-tests to evaluate mean differences when an experiment consists of three or more treatment conditions is that multiple t-tests accumulate the risk of a Type I error.

A Type I error is the rejection of a true null hypothesis, which means that you have falsely concluded that there is a significant difference between the treatment groups when there is actually no difference. When conducting multiple t-tests, the probability of making a Type I error increases with the number of tests performed. In other words, if you perform multiple t-tests, the overall probability of making at least one Type I error increases, and this can lead to incorrect conclusions.

ANOVA is a statistical technique that allows you to compare the means of three or more treatment groups simultaneously while controlling the probability of making a Type I error. ANOVA compares the variance between groups to the variance within groups to determine if the differences between the treatment groups are statistically significant. By using ANOVA instead of multiple t-tests, you can reduce the overall risk of making a Type I error while still evaluating the mean differences between the treatment groups.

Therefore, ANOVA is a more appropriate and efficient method for evaluating mean differences when an experiment consists of three or more treatment conditions, as it provides a more robust and reliable analysis than multiple t-tests, while also reducing the risk of Type I errors.

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The error involved in approximating the sum of the given series by the sum of the first five terms of the series is `R5 = 1/6³ + 1/7³ + ...`.

To estimate the error that is made by approximating the sum of the given series by the series the first 5 terms 1/k³, we can use the remainder term of a convergent series.

The given series is ∑ 1/k³ from k = 1 to infinity.We have to find the error involved in approximating the sum of the given series by the sum of the first five terms of the series.

That is, we need to find the difference between the actual sum of the series and the sum of the first five terms of the series.

The sum of the series is given by: `S = 1/1³ + 1/2³ + 1/3³ + 1/4³ + ... + 1/n³ + ...` We can use the remainder term of the series to find the error in approximation.

The remainder term `Rn` is given by: `Rn = Sn - S` where `Sn` is the sum of the first `n` terms of the series. Thus, we have to find the remainder term for `n = 5`.

The remainder term `Rn` is given by: `Rn = S - Sn = 1/6³ + 1/7³ + ...` Since the given series is convergent, the remainder term `Rn` tends to zero as `n` tends to infinity.

So, if we take the sum of the first five terms of the series, the error involved in approximation is given by the remainder term `R5`.

The error involved in this approximation is very small and can be neglected.

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Answer:

34 child tickets

Step-by-step explanation:

let c = # child tickets

let a = # adult tickets

System of equations:

6.20c+9.50a=1179.80

a=3c

substitute 3c for a:

6.20c +9.50(3c) = 1179.80

34.7c=1179.80

c=34

Answer:

34 child tickets were sold that day.

Step-by-step explanation:

Let's use C to represent the number of child tickets sold and A to represent the number of adult tickets sold.

From the problem, we know that:

We can set up an equation based on the information given:

\(\qquad\large\rm{6.2C + 9.5A = 1179.8}\)

Substitute A with 3C:

\(\qquad\large\rm{6.2C + 9.5(3C) = 1179.8}\)

Simplify:

\(\qquad\large\rm{6.2C + 28.5C = 1179.8}\)

\(\qquad\qquad\large\rm{34.7C = 1179.8}\)

\(\qquad\qquad\quad\large\boxed{\boxed{\bold{\:\:C \approx 34\:\:}}}\)

\(\therefore\) 34 child tickets were sold that day.

Given:

The equations of a system of equations are

\(y=-2x^2+3x-1\)

\(x+y=-1\)

To find:

The solution of the given system of equations.

Solution:

We have,

\(y=-2x^2+3x-1\)           ...(i)

\(x+y=-1\)                      ...(ii)

Using (i) and (ii), we get

\(x+(-2x^2+3x-1)=-1\)

\(x-2x^2+3x-1+1=0\)

\(-2x^2+4x=0\)

Taking out the common factors.

\(2x(-x+2)=0\)

Using zero product property,we get

\(2x=0\) and \(-x+2=0\)

\(x=0\) and \(2=x\)

For x=0, we have

\(0+y=-1\)

\(y=-1\)

For x=2, we have

\(2+y=-1\)

\(y=-1-2\)

\(y=-3\)

Therefore, the two solutions of the given system of equations are (0,-1) and (2,-3).

Step-by-step explanation:

x² + (2x)² = (√180)²

x² + 4x² = 180

5x² = 180

x² = 180/5

x² = 36

x = √36 (and no - √36 because x ≥ 0)

x = 6

Inverse variation is the relationship that occurs between two quantities in which one decreases as the other increases.

The types of variation which exists are;

For instance;

The relationship between John's speed and distance is inversely proportional. If John's speed is 5km/h, his distance is 6km. Find John's distance when his speed increases to 6km/h.

s = k / d

where,

k = constant of proportionality

s = k / d

5 = k/6

30 = k

s = k / d

6 = 30/d

6d = 30

d = 30/6

d = 5 km

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