5. Solve for x.
(9x - 16)
(3x + 11)
(7x - 5)
X=

Answer:

15 and 47

Step-by-step explanation:

62/2=31

31-16=15

31+16=47

15+47=62.

I apologise if I'm wrong

Answer:

23 and 39

Step-by-step explanation:

x+y=62

x-y=16

2x=78

x=39

y=23

The addition inequality 37 + x ≥ 42 can be used to determine how much taller William must be to ride the coaster, where x represents the additional height he needs to meet the height requirement.

To write an addition inequality to determine how much taller William must be to ride the coaster, we first need to convert his height to inches. Since he is 3 feet 1 inch tall, his height is (3 x 12) + 1 = 37 inches.

Let x be the amount of additional height William needs to ride the roller coaster. The inequality can be written as:

37 + x ≥ 42

This inequality ensures that William's total height after adding x must be greater than or equal to the required height of 42 inches to ride the roller coaster.

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Using the graph, we can find the following:

a) The gymnast stays 4 seconds in the air.

b) The maximum height that the gymnast reaches is 10 ft.

c) After 2 seconds the gymnast starts to descend.

d) The quadratic function that models this situation is:

y = mx + c

Quantitative data can be represented and analysed graphically. In a graph, variables representing data are drawn over a coordinate plane. Analysing the magnitude of one variable's change in light of other variables' changes became simple.

Here in the question,

a. We can see from the graph that the curve above x-axis starts from the origin (0,0) and ends at (4,0) on the x-axis.

So, the gymnast stays 4 seconds in the air.

b. As we can see from the graph that it rises and then at point (2,10) it starts to descend.

So, the maximum height that the gymnast reaches is 10 ft.

c. As we can see from the graph that it rises and then at point (2,10) it starts to descend.

So, after 2 seconds the gymnast starts to descend.

d. The quadratic function that models this situation is:

y = mx + c

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Based on the description of the problem,the measure of ∠BTX is 60°.

A circle is a two-dimensional geometric shape made up of all the points that are equally spaced apart from the circle's centre.

The radius of the circle is the distance measured from any point on the circle to its centre.

The circumference is the collection of all the points on the circle.

Based on the description of the problem, we can conclude that triangle BOX is an isosceles triangle with OB = OX. This is because both OB and OX are radii of the same circle centered at O.

Since m/BOX = 120°, we can find the measure of angle B by dividing this angle in half, since angle B is the base angle of the isosceles triangle BOX.

∠BO = (180° - 120°)/2 = 30°

Now, since TX and TB are tangent to the circle at points X and B respectively, we know that angle BTX is equal to the sum of angles BOY and OXT, since angle BOY and OXT are both in the same quadrant and add up to 90°.

∠BTX = ∠BOY + ∠OXT>

Since triangle BOX is an isosceles triangle with angle BOY equal to 30°, we can find the measure of angle OXT as follows:

∠OXT = 180° - ∠BOX - ∠BOY

= 180° - 120° - 30°

= 30°

Therefore,

∠BTX = ∠BOY + ∠OXT

= 30° + 30°

= 60°

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The completely factored form of the quadratic expression 3x²- 30x - 72 is (x - 4)(3x + 6).

To find the completely factored form of the quadratic expression 3x² - 30x - 72, we can use the factoring method.

Look for the common factor (if any) among the coefficients of the quadratic expression. In this case, there is no common factor among 3, -30, and -72.

We need to find two numbers whose product is -72 (the constant term) and whose sum is -30 (the coefficient of the linear term). The two numbers are -12 and 6.

Rewrite the middle term -30x as the sum of -12x and 6x:
3x² - 12x + 6x - 72

Group the terms:
(3x² - 12x) + (6x - 72)

Factor out the common factor from each group:
3x(x - 4) + 6(x - 4)

Notice that we now have a common binomial factor of (x - 4):
(x - 4)(3x + 6)

Therefore, the completely factored form of the quadratic expression 3x² - 30x - 72 is (x - 4)(3x + 6).

The completely factored form of the quadratic expression 3x^2 - 30x - 72 is (x - 4)(3x + 6). To find this form, we used the factoring method, which involves finding two numbers whose product is equal to the constant term (-72 in this case) and whose sum is equal to the coefficient of the linear term (-30 in this case).

By rewriting the middle term as the sum of two terms and grouping them, we were able to factor out the common factors. In this case, the common binomial factor was (x - 4). Once we factored out this common factor, we were left with (3x + 6). Therefore, the completely factored form of the quadratic expression 3x² - 30x - 72 is (x - 4)(3x + 6).

The completely factored form of the quadratic expression 3x² - 30x - 72 is (x - 4)(3x + 6).

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After riding for 10 hours, she is 72 miles away. So, Fatema's rate was 7.2 miles per hour.

We can use the formula:

rate = distance / time

Fatema's speed is shown in miles per hour (mph), the distance she has traveled, and the time it took her to complete that distance.

Let x represent Fatema's speed in mph. Then, using the above data, we can construct the following two equations:

First, when Fatema rides for 3 hours, she travels 23 miles, so:

3x = 23

⇒ x = 23/3

Second, when Fatema rides for 10 hours, she travels 72 miles, so:

10x = 72

⇒ x = 7.2

Given that x has two different values, we should make sure that they are consistent. The first number of x that we discovered (x = 23/3) is consistent with the speed at which Fatema was moving during the first three hours of her voyage. The rate at which Fatema was moving for the whole of the 10-hour voyage is represented by the second number of x that we discovered (x = 7.2). We can assume that Fatema's average speed for the entire 10-hour voyage was 7.2 mph since the second value of x, which considers the full journey, is a more accurate rate.

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The y-intercept is the initial value of the investment is $400.

If an investment is compounded annually, it means that both the initial amount invested and the interest that is accrued increases in value once a year. The equation that is used to determine the future value of the investment that earns a compound interest is an exponential function.

The form of the exponential function is:

FV = P (1 + r)^nm

Where:

The y-intercept of an exponential function is the point where the graph touches the y-axis. It is the point where the value of x is zero. The y-intercept is the initial value of the investment. The initial value of the investment is $400.

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The equation of a line in slope-intercept form is y = 2x + 1.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of a line is y = m(1)x + c.

The equation of a line passes through (3,7).

The equation of a line is parallel to the line y = 2x + 4.

This means,

y = 2x + 4

y = m(2)x + 4

m(2) = 2

So,

m(2) = m(1) = 2

And,

(3, 7) = (x, y)

7 = m(1) x 3 + c

7 = 2 x 3 + c

7 = 6 + c

c = 7 - 6

c = 1

Now,

y - m(1)x + c

y = 2x + 1

Thus,

The equation of a line is y = 2x + 1.

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The number of non-isomorphic trees that can be drawn with four vertices can be calculated using the concept of labeled trees. In this case, each vertex is labeled with a distinct number from 1 to 4.

To count the number of non-isomorphic trees, we can use the Cayley's formula, which states that the number of labeled trees with n vertices is equal to n^(n-2). Substituting n=4, we have 4^(4-2) = 4^2 = 16.

Now, we need to account for isomorphic trees. Isomorphic trees have the same structure but differ only in the labeling of the vertices. To eliminate the isomorphic trees, we need to identify the distinct structures that can be formed with four vertices.

By examining the different possible arrangements, we find that there are three distinct structures for trees with four vertices: the path graph (line), the star graph, and the tree with one vertex as the parent of the other three vertices. Therefore, the number of non-isomorphic trees with four vertices is 3.

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Math SAT scores explain about 98.7% of the variation in the total SAT scores.

In statistics, correlation or dependence exists as any statistical relationship, whether causal or not, between two random variables or bivariate data.

A correlation exists as a statistical measure (expressed as a number) that defines the size and direction of a relationship between two or more variables. A correlation between variables, however, does not automatically mean that the change in one variable exists as the cause of the change in the values of the other variable.

Since r² exists = (0.9935)² = 0.9870, we interpret r² as 98.7% of the variation in the y variable exists explained by the x variable.

In context, math SAT score explains about 98.7% of the variation in total SAT score.

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The height in meters of a lava rock that falls for 5 seconds will be 122.5 meters.

The missing function is y = 1/2 gt².

A function is a remark, tenet, or regulation that establishes a relationship between the two parameters.

The height of lava fountains spewed from volcanoes cannot be measured directly.

Instead, their height in meters can be found using the equation is given as

y = 1/2 gt²

where y represents the height, g is 9.8, and t represents the falling time of the lava rocks.

Then the equation will be

y = 1/2 × 9.8 × t²

y = 4.9t²

Then the height in meters of a lava rock that falls for 5 seconds will be

y = 4.9 x 5²

y = 122.5 meters

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Answer:

Step-by-step explanation:

\( \frac{2}{ \sqrt{3} - 1 } \\ \frac{2}{ \sqrt{3 } - 1} \times \frac{ \sqrt{3} + 1}{ \sqrt{3} + 1} \\ \frac{2 \times ( \sqrt{3} + 1)}{( \sqrt{3} - 1)( \sqrt{3 } + 1) } = \frac{2 \sqrt{3} + 2}{( \sqrt{3} )^{2} - {1}^{2} } \\ \frac{2 \sqrt{3} + 2 }{3 - 1} = \frac{2 \sqrt{3} + 2 }{2} = \frac{2( \sqrt{3} + 1)}{2} \\ \sqrt{3 } + 1 = 1.732 +1 = 2.732\)

\( \frac{2}{ \sqrt{3 - 1} } \\ \frac{2}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{2 \sqrt{2} }{( \sqrt{2} ) ^{2} } = \frac{2 \sqrt{2} }{2} \\ \sqrt{2} = 1.4142\)

I hope I helped you^_^

We need a sample size of at least 62 to detect the alternative hypothesis with power of at least 0.80 at a 5% significance level.

To answer this question, we need to use power analysis. Power is the probability of rejecting the null hypothesis when it is false. In this case, the null hypothesis is m = 0 and the alternative hypothesis is m > 0. We want to detect the alternative hypothesis with power of at least 0.80 at a 5% significance level.

Assuming that s is 20 and we want to detect the alternative m > 4, we can use the following formula to calculate the sample size:

n = (Zα/2 + Zβ)² * σ² / δ²

where:
- Zα/2 is the critical value for the significance level α/2 (α = 0.05, so Zα/2 = 1.96)
- Zβ is the critical value for the power (power = 0.80, so Zβ = 0.84)
- σ is the standard deviation (σ = 20)
- δ is the difference between the null hypothesis and the alternative hypothesis (δ = 4)

Substituting these values into the formula, we get:

n = (1.96 + 0.84)² * 20² / 4²
n = 61.61

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The value of E is \((-2)^{\frac{n-1}{8n} }\).

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

\(E^{8n}\) = 1 x \((-2)^{n -1}\)

8n root on both sides.

E = \(((-2)^{n -1})^\frac{1}{8n}\)

E = \((-2)^{(n-1)\times\frac{1}{8n}}\)

E = \((-2)^{\frac{n-1}{8n} }\)

Thus,

E = \((-2)^{\frac{n-1}{8n} }\).

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Given an arithmetic sequence -1, -2, -3, …So, the common difference is d = -1 - (-2) = 1. The 23rd term of the given sequence is 21.

Step by step answer:

The given arithmetic sequence is -1, -2, -3, ….The common difference is d = -1 - (-2) = 1. To find the nth term of this sequence, we can use the formula: a_n = a_1 + (n - 1) * d where a_n is the nth term and a_1 is the first term of the sequence. In this sequence, a_1 = -1.

Substituting the values in the formula, a_n = -1 + (n - 1) * 1

= -1 + n - 1

= n - 2

Therefore, to find the term 23 in the sequence, we put

n = 23.a_23

= 23 - 2

= 21Hence, the 23rd term of the sequence is 21.

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Answer:

Step-by-step explanation:

Hello,

For each survey that Gwen completes she earns 10 points.

So the number of points Gwen earns for completing each survey is 10 and there is only one value.

If x is the number of surveys Gwen completed, her number of points is 10 multiplied by x.

The number of surveys Gwen completes can have several values.

And then, the total number of points Gwen earns can have several values too.

So you need to choose

The number of surveys Gwen completes.

and

The total number of points Gwen earns.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

9.14 servings

Step-by-step explanation:

The question is asking how many servings of cereal does the box contain, or in other words, how many groups of 56 grams can you make from 512 grams.

To find out how many groups of 56 you can make, you need to divide 512 by 56:

512 ÷ 56 = 9.14

D

__________________________________

\((\frac{1}{2^3})^2\)

\((\frac{1}{8})^2\)

\(\frac{1}{64}\)

__________________________________

\(Determine\ whether\ (\frac{2^0}{2^3})^2\ and\ \frac{1}{64}\ are\\ equivalent:\)

\(True\)

I hope this helps you

:)

In each scenario, the choice between mean and median as a representative measure of central tendency depends on the nature of the data and the specific context..

1. Scenario: Income distribution of a population

- If the income distribution is skewed or contains extreme values (outliers), the median would be a better representation of the central tendency. This is because the median is not influenced by outliers and provides a more robust estimate of the "typical" income level. However, if the income distribution is approximately symmetric without outliers, the mean can also be an appropriate measure.

2. Scenario: Exam scores in a class

- If the exam scores are normally distributed without significant outliers, the mean would be a suitable measure as it takes into account the value of each score. However, if there are extreme scores that deviate from the majority of the data, the median may be a better representation. This is especially true if the outliers are indicative of errors or exceptional circumstances.

3. Scenario: Housing prices in a city

- In this case, the median would be a more appropriate measure to represent the central tendency of housing prices. This is because the housing market often exhibits a skewed distribution with a few high-priced properties (outliers). The median, being the middle value when the data is sorted, is not influenced by these extreme values and provides a better understanding of the typical housing price in the city.

Ultimately, the choice between mean and median depends on the specific characteristics of the data and the objective of the analysis. It is important to consider the distribution, presence of outliers, and the context in which the data is being interpreted.

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Answer:

33000

Step-by-step explanation:

this is because you have to look at 2 then look at the number next to 2 if it is 5 or above make the 2 a 3.. then the answer is 33000

Hope this helped! <3

Divide the number of micrometers by 10,000 to get the equivalent number of centimeters.

To convert micrometers to centimeters, you need to use the conversion factor between the two units. There are 10,000 micrometers in a centimeter.

Here are the steps to convert micrometers to centimeters:

1. Start with the number of micrometers you want to convert.
2. Divide the number of micrometers by 10,000 to get the equivalent number of centimeters.
3. The result is the number of centimeters equivalent to the given number of micrometers.

For example, if you want to convert 50,000 micrometers to centimeters, you would divide 50,000 by 10,000 to get 5 centimeters.

So, the conversion formula is:

centimeters = micrometers ÷ 10,000

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The total number of red marbles in the vase are 10.

A ratio is described as a comparison between two amounts with the same unit to determine the amount of 1 quantity is contained in the other. Ratios are divided into two sorts.

The first is a part-to-part ratio, and the second is a part-to-whole ratio. The part-to-part ratio expresses the relationship between 2 separate entities or groupings.

Now, according to the question;

Let 'x' be the red marbles in the vase.

Let 'y' be the orange marbles in the vase.

The total number of marbles in the vase are 60

x  + y = 60 (equation 1)

The ratio of red marbles to orange ones is 1:5.

Thus, x/y = 1/5

cross multiplying;

5x = y

or y = 5x

substitute the value of y in equation 1;

x  + y = 60 (equation 1)

x  + 5x = 60

6x = 60

x = 10  (red marbles)

Thus, the number of red marbles in the vase are 10.

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Answer:

The second choice.

Step-by-step explanation:

A linear functions graph is a straight line.

The linear regression model can be extended to accommodate certain forms of non-linear relationships between the response and predictor(s).  Polynomial regression is one specific method for incorporating non-linear associations within the linear regression framework.

It involves understanding the flexibility of the linear regression model and the techniques available to address non-linear relationships. While the linear regression model assumes a linear relationship between the response variable and predictors, it can still be useful in accommodating certain types of non-linear relationships.

By applying appropriate transformations to the predictor variables, such as taking their squares, logarithms, or other non-linear functions, we can introduce non-linear associations into the linear regression model. This allows the model to capture curvature or other non-linear patterns in the data.

Polynomial regression is a specific approach to incorporating non-linear relationships within the linear regression framework. It involves adding polynomial terms of the predictor variables to the model, such as squared or cubed terms. By including these polynomial terms, the model can account for non-linear relationships and capture more complex patterns.

It's important to note that while linear regression can be extended to accommodate some non-linear relationships, there may be cases where more advanced non-linear regression techniques or alternative models are necessary to adequately capture complex non-linear associations. Nonetheless, the inclusion of transformed predictor variables and the use of polynomial regression are valuable approaches to address non-linear relationships within the linear regression framework.

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\(x + 85 + x + 64 + 45 = 180°\)

\((x + x) + (85 + 64 + 45)= 180\)

\(2x + 194= 180\)

\(2x = 180 - 194\)

\(2x = - 14\)

\(x = \frac{ - 14}{ \: \: \: \: 2} \)

\(x = - 7\)

\(∴ \: the \: value \: of \: x \: = - 7\)

The distance from point A to point C and the bearing from point A to point C is 229.5 miles.

Given that:

AB = 370 miles

angle A = 24 degrees

BC = 240 miles

angle B = 37 degrees 

To determine the distance from point A to C, we can use the cosine law since we are given two angles and two sides of a regular triangle. 

The angle opposite side AC is angle B which is equal to 37 degrees. 

(AC)^2 =(AB)^2 + (BC)^2 - 2(AB)(BC)cos(B)

Now we have to solve for AC:

(AC)^2 =(370)^2 + (240)^2 - 2(370)(240)cos(37) 

AC = 229.48 miles.

Hence the answer is, the distance from point A to point C and the bearing from point A to point C is 229.5 miles. 

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Marginal relative frequency of customers liking hamburgers is 53.66%, calculated by dividing 110 customers by 205, resulting in a value of 0.5366.

To find the marginal relative frequency of all customers that like hamburgers, we need to divide the number of customers who like hamburgers by the total number of customers.

According to the given data, there are 110 people who like hamburgers out of a total of 205 people.

Marginal relative frequency of customers who like hamburgers = (Number of customers who like hamburgers) / (Total number of customers)
= 110 / 205

To calculate the exact value, we divide 110 by 205:
Marginal relative frequency of customers who like hamburgers = 0.5366

Therefore, the marginal relative frequency of all customers who like hamburgers is approximately 0.5366 or 53.66%.

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Population  is an entire group under study as specified by the objectives of the research project.

In research methodology, a population refers to the entire group of individuals or elements that are of interest to the researcher and are under study as specified by the objectives of the research project. It represents the larger group from which a sample is drawn. The population is the target group to which the research findings are intended to be generalized.

When conducting research, it is often impractical or impossible to study an entire population due to constraints such as time, cost, and accessibility. Therefore, researchers typically select a subset of the population called a sample. The sample is a smaller representative group that is selected from the population and is used to draw inferences and make generalizations about the population.

The selection of a sample is based on the principle of randomization and aims to ensure that the sample is representative of the population. By studying the sample, researchers can make statistical inferences about the population as a whole.

In summary, the population refers to the entire group under study, while a sample is a subset of the population that is selected for research purposes. The population is the broader target group of interest, and the sample is used to draw conclusions about the population.

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Answer:

The negative square root of -49 is -7