Enter the correct answer in the box. Write your answer in the form y = mx + b, using the appropriate inequality symbol in place of the equal sign.

What inequality is shown in the graph?

Answer:

27

Step-by-step explanation:

When solving complicated equations like this, we need to remember the order of operations (PEMDAS), which is the order that we solve an equation

P arentheses

E xponents

M ultiplication

D ivision

A ddition

S ubtraction

now, here's the thing: we actually to multiplication/division at the same time, and the same thing with addition/subtraction

(as in, adding -4 is the same thing as subtracting 4, so we can't truly make a distinction between the two)

so, when we have multiple instances of multiplication/division , we solve left to right

(and then the same thing for addition/subtraction)

8 × 3 + 70 ÷ 7 - 7

so, we first need to multiply 8 by 3

8 × 3 = 24

next, we move to the right:

and we divide 70 by 7

70 ÷ 7 = 10

let's rewrite our equation:

(24) + (10) - 7

24 + 10 - 7 = 27

so, the answer to this expression is 27

hope this helps!! have a lovely day :)

Answer:

x = 1/4p

y = 3/2p

Step-by-step explanation:

2x + 3y =5p__________________equ 1

y = 2x + p____________________equ 2

sub equ 2 for y in equ 1

2x + 3(2x + p) = 5p_______________open brackets

8x = 2p______________________divide both sides by 8

x = 1/4p

sub 1/4p for x in equ 2

y = 2(1/4p) + p___________________open brackets

y = 3/2p

The expression is equivalent to the given expression is 5x²+12x-7: Option C

You should understand that  simplification means making an expression more simpler for better understanding

The given expression is

-2x²+8x-9+4x+7x²+2

The first thing to do is to rearrange the expression in the following ways by collecting the like terms

7x²-2x²+8x+4x-9+2

This implies that

5x²+12x-7

Conclusively the simplest form of the expression is 5x²+12x-7

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Answer:

Step-by-step explanation:

Answer:

61.25

Step-by-step explanation:

The of cubic units which hat occupies having a radius of 3 inches and a height of 6.5 inches is 61.26 cubic inches.

Volume of cone is the amount of quantity, which is obtained it in the 3 dimensional space.

The volume of the cone can be given as,

\(V=\dfrac{1}{3}\pi r^2h\)

Here, (r) is the radius of the base of the cone and (h) is the height of the cone.

A cone-shaped party hat has a radius of r=3 inches and a height of h=6.5 inches. The amount of cubic units it occupies is equal to the volume of hat.

Thus, put the values in the above formula as,

\(V=\dfrac{1}{3}\pi (3)^2(6.5)\\V=\dfrac{1}{3}\pi (3)^2(6.5)\\V=61.26\rm\; in^3\)

Thus, the of cubic units which hat occupies having a radius of 3 inches and a height of 6.5 inches is 61.26 cubic inches.

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Answer:

3x12=36

Step-by-step explanation:

I'm pretty sure this is right

Answer:

Step-by-step explanation:

It is assumed you are looking for the value of x.

According the diagram, we have:

Property of exterior angle - it is same as the sum of remote interior angles.

Set equation:

It is easy to calculate the unknown angle measures if needed:

Answer:

Angle 1= 54 degrees

Step-by-step explanation:

Complementary angles are two angles whose sum is 90 degrees. Since on is 36 degrees, you juts need to subtract 90-36 to get the other angle

The notations x→∞⁻, x→∞⁺, x→-∞⁻, and x→-∞⁺ are not used in limits because they are ambiguous and can lead to confusion.

What are Limits?

In calculus, limits are used to describe the behavior of a function as the input values approach a certain value, usually infinity or a specific point. The concept of limits is essential in calculus and is used to define derivatives and integrals.

The notations x→∞⁻, x→∞⁺, x→-∞⁻, and x→-∞⁺ are not used in limits because they are ambiguous and can lead to confusion. In the limit notation lim x→a, the variable x is approaching the value a from both sides, meaning it can approach a from either the left or the right.

The notations x→∞⁻, x→∞⁺, x→-∞⁻, and x→-∞⁺ suggest that x is only approaching infinity or negative infinity from a specific direction, which is not the case in limit notation. Therefore, the notations x→∞⁻, x→∞⁺, x→-∞⁻, and x→-∞⁺ are not used in limits to avoid confusion and ensure clarity in mathematical expressions.

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Answer:

16 cubic units

Step-by-step explanation:

\(\displaystyle V=\int^b_aA(x)\,dx\\\\V=\int^6_2(\sqrt{x})^2\,dx\\\\V=\int^6_2x\,dx\\\\V=\frac{1}{2}x^2\biggr|^6_2\\\\V=\frac{1}{2}(6)^2-\frac{1}{2}(2)^2\\\\V=\frac{1}{2}(36)-\frac{1}{2}(4)\\\\V=18-2\\\\V=16\)

A(x) represents the area of the cross-section, so in this case, we square \(\sqrt{x}-0\) which is just \(\sqrt{x}\)

Answer:

Yes

Step-by-step explanation:

If we need to find the distance between two points on a number line, we subtract one of the points from the other. We then take the absoulte value of the difference. You done this right.

1/5 or -1/9 would both be correct

The height of the flagpole is 27 feet.

Given,

If two triangles are similar, sides of these triangles will be proportional.

Height of the flagpole  = h feet

Shadow castes by the flagpole  = 72 feet

Height of the person  = 6 feet

Shadow casted by the person = 16 feet

By using the property of similar triangles,

Hence, h/6 = 72/16

h = (6×72)/ 16

h = 27 feet

Therefore, The height of the flagpole is 27 feet.

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Answer:

\((f + g)(x) = 7 - 6x\) --- (1)

\((f - g)(x) = 6x - 1\) -- (2)

\((f . g)(x) =4(5^x)\) ---- (3)

\((f / g)(x) = \frac{4}{5^x}\) ----- (4)

\((f + g)(x) = -7x-7\) --- (5)

\((f - g)(x) = 9x+ 9\) --- (6)

\((f . g)(x) = (-8)(x+1)^2\) --- (7)

\((f / g)(x) = -\frac{1}{8}\) ----- (8)

\(F(t) = \frac{9}{5}t^2 + 32\) ---- (9)

\(T(t) = (t - 2)^2 - 4\) --- (10)

Step-by-step explanation:

Given

\(f(x) = 3\)

\(g(x) = 4 - 6x\)

Solving (1): (f + g)(x)

\((f + g)(x) = f(x) + g(x)\)

So, we have:

\((f + g)(x) = 3 + 4 - 6x\)

\((f + g)(x) = 7 - 6x\)

Solving (2): (f - g)(x)

\((f - g)(x) =f(x) - g(x)\)

So, we have:

\((f - g)(x) =3 - (4 - 6x)\)

\((f - g)(x) =3 - 4 + 6x\)

\((f - g)(x) =-1 + 6x\)

\((f - g)(x) = 6x - 1\)

Given

\(f(x) = 4\)

\(g(x) = 5^x\)

Solving (3): (f . g)(x)

\((f . g)(x) =f(x) * g(x)\)

So, we have:

\((f . g)(x) =4 * 5^x\)

\((f . g)(x) =4(5^x)\)

Solving (4): (f / g)(x)

\((f / g)(x) = \frac{f(x)}{g(x)}\)

So, we have:

\((f / g)(x) = \frac{4}{5^x}\)

Given

f(x) = x + 1

g(x) = -8 - 8x

Solving (5): (f + g)(x)

\((f + g)(x) = f(x) + g(x)\)

So, we have:

\((f + g)(x) = x + 1 -8-8x\)

Collect Like Terms

\((f + g)(x) = x -8x+ 1 -8\)

\((f + g)(x) = -7x-7\)

Solving (6): (f - g)(x)

\((f - g)(x) = f(x) - g(x)\)

So, we have:

\((f - g)(x) = x + 1 -( -8-8x)\)

\((f - g)(x) = x + 1 +8+8x\)

Collect Like Terms

\((f - g)(x) = x +8x+ 1 +8\)

\((f - g)(x) = 9x+ 9\)

Solving (7): (f . g)(x)

\((f . g)(x) = f(x) . g(x)\)

So, we have:

\((f . g)(x) = (x+1) . (-8 - 8x)\)

Factorize

\((f . g)(x) = (x+1) .(-8) (1 + x)\)

Rewrite as:

\((f . g)(x) = (x+1) .(-8) (x+1)\)

\((f . g)(x) = (-8)(x+1) (x+1)\)

\((f . g)(x) = (-8)(x+1)^2\)

Solving (8): (f / g)(x)

\((f / g)(x) = \frac{f(x)}{g(x)}\)

So, we have:

\((f / g)(x) = \frac{(x+1)}{(-8-8x)}\)

Factorize

\((f / g)(x) = \frac{(x+1)}{-8(1+x)}\)

\((f / g)(x) = \frac{1}{-8}\)

\((f / g)(x) = -\frac{1}{8}\)

Solving (9):

From the question, we have that:

\(F(c) = \frac{9}{5}c + 32\)

\(C(t) = t^2\)

Required

Determine function F in terms of c

The implication of this question is to solve for \(F(c(t))\)

If \(F(c) = \frac{9}{5}c + 32\) and \(C(t) = t^2\),

Then

\(F(c(t)) = \frac{9}{5}*t^2 + 32\)

\(F(c(t)) = \frac{9}{5}t^2 + 32\)

This can be rewritten as:

\(F(t) = \frac{9}{5}t^2 + 32\)

Solving (10):

\(T(h) = h^2 - 4\)

\(h(t) = t - 2\)

Required

Find \(T(h(t))\)

If \(T(h) = h^2 - 4\)  and   \(h(t) = t - 2\), then

\(T(h(t)) = (t - 2)^2 - 4\)

This is gotten by substituting t -2 for h

The solution can be rewritten as:

\(T(t) = (t - 2)^2 - 4\)

This analysis assumes that you have the mean cost for Kentucky and additional data from both states. The sample size is also an important consideration for the reliability of the statistical analysis.

To determine if there is a significant difference between the average costs of housing prisoners in North Carolina and Kentucky, we would need the mean cost for both states and additional data from each state. However, let's assume we have the mean cost for North Carolina, denoted as x1, from your random sample.

To evaluate the significance of the difference between North Carolina and Kentucky, we would typically perform a statistical test, such as an independent samples t-test or a non-parametric test like the Mann-Whitney U test, depending on the characteristics of the data.

Here's a step-by-step approach you can follow to analyze the data:

1. Obtain the mean cost for Kentucky: To conduct a meaningful comparison, we need the mean cost for Kentucky as well. If you have this information, let's denote it as x2.

2. Define the null hypothesis (H0) and alternative hypothesis (H1): In this case, the null hypothesis would state that there is no significant difference in the average costs of housing prisoners between North Carolina and Kentucky. The alternative hypothesis would state that there is a significant difference.

3. Select an appropriate statistical test: Depending on the nature of the data and its distribution, you can choose between the independent samples t-test or the Mann-Whitney U test. The t-test assumes normality and requires equal variances, while the Mann-Whitney U test is a non-parametric test that does not make any assumptions about the data distribution.

4. Calculate the test statistic: Using the selected statistical test, calculate the test statistic based on the provided data (mean cost for North Carolina and Kentucky) and the additional data you have.

5. Determine the p-value: From the test statistic, determine the p-value associated with the observed difference between the two states. The p-value represents the probability of obtaining such a difference or more extreme under the assumption that the null hypothesis is true.

6. Compare the p-value to the significance level (alpha): Choose a significance level (e.g., α = 0.05) to assess the statistical significance. If the p-value is less than the significance level, we reject the null hypothesis and conclude that there is a significant difference between the average costs of housing prisoners in North Carolina and Kentucky.

7. Interpret the results: If the null hypothesis is rejected, you can conclude that there is a significant difference in the average costs of housing prisoners between North Carolina and Kentucky. However, if the p-value is greater than the chosen significance level, we fail to reject the null hypothesis and conclude that there is not enough evidence to support a significant difference.

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If bx = by in the cross product or vector product, the unit-vector notation of the resulting vector would be (0, 0, 1) or simply k-hat.

In the cross product or vector product of two vectors, the resulting vector is perpendicular to both of the original vectors. The direction of the resulting vector is determined by the right-hand rule, where the thumb represents the direction of the cross product.

If bx = by, it means that the x-component of the first vector is equal to the y-component of the second vector. In this case, the resulting vector will have an x-component and y-component of zero.

Since the resulting vector must be perpendicular to both vectors, its z-component must be non-zero. Therefore, the unit-vector notation of the resulting vector would be (0, 0, 1), where the z-component (k-component) is 1.

If bx = by in the cross product, the resulting vector in unit-vector notation would be (0, 0, 1) or simply k-hat. This indicates that the resulting vector has zero components in the x and y directions and a non-zero component in the z direction.

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The sample mean is X[bar]=$1500

The sample standard deviation is S=$100

The sample size is n=70

The data set has a bell shaped distribution

The empirical rule states that

The values $1400 and $1600 are within one standard deviation away from the mean:

X[bar]+S=$1500+$100=$1600

X[bar]-S=$1500-$100=$1400

Following the rule you can expect 68% of the sample to be between them.

Whats left to do is to calculate the 68% of the sample

Around 47.6 of the farms have values per acre are between $1400 and $1600

The vertex of the graph of f(x) = |x - 5| - 6 is (5, -6). It lies in the fourth quadrant.

Therefore the answer is (5, -6).

The graph f(x) = |x - 5| - 6 is symmetrical about the axis  x = 5.

A vertex of a graph is a node of a graph. For a graph of the form f(x) = a|x - h| + k, the vertex is (h, k). So in this case where f(x) = |x - 5| - 6, a = 1, h = 5 and k = -6. Therefore the vertex of the given graph f(x) is

(5, -6)

--The question is incomplete, answering to the question --

"What is the vertex of the graph of f(x) = |x - 5| - 6?"

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The value of the expression "true && !false" can be determined by evaluating each part separately and then combining the results.

1. The "!" symbol represents the logical NOT operator, which negates the value of the following expression. In this case, "false" is negated to "true".

2. The "&&" symbol represents the logical AND operator, which returns true only if both operands are true. Since the first operand is "true" and the second operand is "true" (as a result of the negation), the overall expression evaluates to "true".

Therefore, the value of the expression "true && !false" is "true".

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Answer:

126 :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

first find angle ∠U,

As sum of angle in triangle = 180°

Now ∠U+∠V+∠W=180°

88°+38°+∠U=180°

∠U=54°

Now total horizontal line = 180°

∠NUV=180°-54°=126°

You have a total of six different ways to select a snack and a beverage at the amusement park.

To determine the number of different ways you can select a snack and a beverage, we can use the concept of combinations.

Let's analyze the options:

Snack: You can choose either a chili dog or popcorn. This gives us 2 choices for the snack.

Beverage: You can choose either lemonade, an energy drink, or water. This gives us 3 choices for the beverage.

To calculate the total number of combinations, we multiply the number of choices for the snack by the number of choices for the beverage. Therefore, the number of different ways to select a snack and a beverage is 2 (choices for snack) multiplied by 3 (choices for beverage), which equals 6.

In other words, there are six different combinations possible:

Chili dog and lemonade

Chili dog and energy drink

Chili dog and water

Popcorn and lemonade

Popcorn and energy drink

Popcorn and water

So, when considering all the options, you have a total of six different ways to select a snack and a beverage at the amusement park.

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The arithmetic sequence with a first term of 14, a common difference of 3, and the 14th term being 42 can be described by the formula: aₙ = 14 + (n - 1) * 3.

In an arithmetic sequence, each term is obtained by adding a constant difference to the previous term. The general formula for the nth term of an arithmetic sequence is given as aₙ = a₁ + (n - 1) * d, where aₙ represents the nth term, a₁ is the first term, n is the position of the term in the sequence, and d is the common difference.

Given that a₁₄ = 42 and d = 3, we can substitute these values into the formula to find the nth term. Plugging in the values, we have a₁₄ = 14 + (14 - 1) * 3, which simplifies to 14 + 13 * 3, resulting in a₁₄ = 14 + 39 = 53. Therefore, the 14th term of the arithmetic sequence is 42.

To graph the first six terms of the sequence, we can substitute n = 1, 2, 3, 4, 5, and 6 into the formula. The corresponding terms are as follows:

a₁ = 14 + (1 - 1) * 3 = 14

a₂ = 14 + (2 - 1) * 3 = 17

a₃ = 14 + (3 - 1) * 3 = 20

a₄ = 14 + (4 - 1) * 3 = 23

a₅ = 14 + (5 - 1) * 3 = 26

a₆ = 14 + (6 - 1) * 3 = 29

Plotting these values on a graph, we would have the following points: (1, 14), (2, 17), (3, 20), (4, 23), (5, 26), and (6, 29). Connecting these points would result in a straight line with a positive slope, representing the arithmetic sequence.

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We are 99% confident that the true average stance duration among elderly individuals lies within the range of 744.56 ms to 857.44 ms.

To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test. The null hypothesis (H0)

Using the t-test, we compare the means and standard deviations of the two samples and calculate the test statistic

a) To calculate a 99% confidence interval for the true average stance duration among elderly individuals, we can use the sample mean, sample standard deviation, and the t-distribution.

Given:

Older adults: n = 28, sample mean = 801, sample standard deviation = 117

Using the formula for a confidence interval for the mean, we have:

Margin of error = t * (sample standard deviation / √n)

Since the sample size is relatively large (n > 30), we can use the z-score instead of the t-score for a 99% confidence interval. The critical z-value for a 99% confidence level is approximately 2.576.

Calculating the margin of error:

Margin of error = 2.576 * (117 / √28) ≈ 56.44

The confidence interval is then calculated as:

Confidence interval = (sample mean - margin of error, sample mean + margin of error)

Confidence interval = (801 - 56.44, 801 + 56.44) ≈ (744.56, 857.44)

b) To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test.

The null hypothesis (H0): The true average stance duration among elderly individuals is equal to or less than the true average stance duration among younger individuals.

The alternative hypothesis (Ha): The true average stance duration among elderly individuals is larger than the true average stance duration among younger individuals.

. With the given data, perform the t-test and obtain the p-value.

c) To construct a 95% confidence interval for the difference in means between older and younger adults, we can use the formula for the confidence interval of the difference in means.

Given:

Older adults: n1 = 28, sample mean1 = 801, sample standard deviation1 = 117

Younger adults: n2 = 16, sample mean2 = 780, sample standard deviation2 = 72

Calculating the standard error of the difference in means:

Standard error = √((s1^2 / n1) + (s2^2 / n2))

Standard error = √((117^2 / 28) + (72^2 / 16)) ≈ 33.89

Using the t-distribution and a 95% confidence level, the critical t-value (with degrees of freedom = n1 + n2 - 2) is approximately 2.048.

Calculating the margin of error:

Margin of error = t * standard error

Margin of error = 2.048 * 33.89 ≈ 69.29

The confidence interval is then calculated as:

Confidence interval = (mean1 - mean2 - margin of error, mean1 - mean2 + margin of error)

Confidence interval = (801 - 780 - 69.29, 801 - 780 + 69.29) ≈ (-48.29, 38.29)

Comparison with part (b): In part (b), we performed a one-tailed test to determine if the true average stance duration among elderly individuals is larger than among younger individuals. In part (c), the 95% confidence interval for the difference in means (-48.29, 38.29) includes zero. This suggests that we do not have sufficient evidence to conclude that the true average stance duration is significantly larger among elderly individuals compared to younger individuals at the 95% confidence level.

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Answer:

The answer to the question is 603.186

The z-score corresponding to Anastasia's test score is -0.5. This indicates that her score is 0.5 standard deviations below the mean.

To calculate the z-score corresponding to Anastasia's test score of 110, we can use the formula:

z = (x - mean) / standard deviation

where x is Anastasia's score, mean is the mean of the test scores (120), and standard deviation is the standard deviation of the test scores (20).

Substituting the values into the formula, we get:

z = (110 - 120) / 20 = -0.5

Therefore, the z-score corresponding to Anastasia's test score is -0.5. This indicates that her score is 0.5 standard deviations below the mean. A negative z-score implies that her score is below the mean, while a positive z-score would indicate a score above the mean. In this case, Anastasia's z-score of -0.5 suggests that her score is below average relative to the distribution of scores on the standardized test.

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The amount of the apple pie that was left will be 3/4.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

From the information, Bert found 2 1/2 of an apple pie in the refrigerator. He shared 1 3/4 of the pie with his friends.

The amount of the apple pie that was left will be:

= 2 1/2 - 1 3/4

= 3/4

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Complete question

Bert found 2 1/2 of an apple pie in the refrigerator. He shared 1 3/4 of the pie with his friends. How much of the apple pie was left?

Answer:

I hope this helps!