Find the domain and range of the function without graphing. Explain how you found your answers.
\(y = \frac{1}{3}\sqrt{x - 4}\)

Answer:

7.2£

Step-by-step explanation:

I used pencil and paper for this so I am sure

Hope this helps!!! If so please give brainliest!!!

Answer:

7 miles

Step-by-step explanation:

Let x be the number  of hours he rides away from home at 28 mph.

Then, since the speed of the automobile is 7 times his walking speed, the number of hours he spends walking is 7x.

Then, the total time, which is 2 hours, is equal to x plus 7x, or 8x.

8x=2-->x=1/4

So the amount of time he spends in the automobile is x=1/4 hour.

The distance he travels in 1/4 hour at 28 mph is 7 miles.

Avg speed of the round trip= 2*28*4/(28+4)= 7 mi/hr

RT=7*2=14 miles

--> 7 miles each way.

The initial value problem x^2y'' - 2xy' + 2y = ln(x), y(1) = 1, y'(1) = 0 is a second-order linear differential equation with variable coefficients. The equation involves the second derivative of the unknown function y, its first derivative, and the function itself. The initial conditions are specified at the point (1, 1) with a given value for y and its derivative.

The equation x^2y'' - 2xy' + 2y = ln(x) represents a second-order linear differential equation. It contains the unknown function y and its derivatives up to the second order. The variable coefficients in the equation, x^2, -2x, and 2, introduce dependence on the independent variable x.

The initial conditions y(1) = 1 and y'(1) = 0 specify the values of y and its derivative at x = 1. These initial conditions provide the starting point for solving the differential equation and finding a particular solution that satisfies both the equation and the given initial conditions.

Solving this initial value problem involves finding the general solution to the differential equation and applying the initial conditions to determine the specific solution that satisfies the given conditions. The solution to this problem will be a function y(x) that meets both the differential equation and the initial conditions y(1) = 1 and y'(1) = 0.

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Answer:

25

Step-by-step explanation:

1000≥150+33(s)

1000-150=850

850≥33(s)

850/33=25.(numbers that don't matter because you can't have a decimal of a student)

You can take at most 25 students because you cant have a half a student.

Answer:

−3x+ −3/5y

Step-by-step explanation:

The standard deviation is best described as a measure of the spread of a distribution around its mean or expected value.

What is standard deviation?

Standard deviation (SD) is a numerical measurement of how spread out or dispersed a set of data is. It can be expressed as the square root of variance (s²), which is the average deviation of a data point from the mean.

What is the formula for standard deviation?

The formula for standard deviation can be written as:

s = √(Σ (Xi - µ)² / (n - 1))

where:s = standard deviation

           Σ = sum

           Xi = each data point

           µ = the mean of the data points

           n = number of data points

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9.5137534 is value of the exponential smoothing coefficient "a" that results in the smallest MSE

Trial and error can be used to find the value of the exponential smoothing coefficient "a" that minimizes the Mean Squared Error (MSE). By calculating the forecasted values for different values of "a" and comparing the squared differences between the actual and forecasted values, the value of "a" that results in the smallest MSE can be determined.

However, without performing the calculations, a specific value of "a" cannot be provided.

To find the value of the exponential smoothing coefficient "a" that results in the smallest Mean Squared Error (MSE), we can perform trial and error by calculating the MSE for different values of "a" and selecting the one with the smallest MSE.

Let's calculate the MSE for different values of "a" using the given data:Month: 1 2 3 4 5 6 7

Value: 23 15 20 12 18 22 15

We'll start by assuming a value of "a" and calculate the forecasted value for each month using exponential smoothing. Then, we'll calculate the squared difference between the actual value and the forecasted value for each month and average them to obtain the MSE.

Here's an example calculation for "a" = 0.3:

Month: 1 2 3 4 5 6 7

Value: 23 15 20 12 18 22 15

Forecast: 23 18.8 19.16 16.912 15.2384 17.96668 18.276676

Squared Difference: 0 23.04 0.4356 16.134544 5.6236096 17.770278 4.0636256

MSE = (0 + 23.04 + 0.4356 + 16.134544 + 5.6236096 + 17.770278 + 4.0636256) / 7 = 9.5137534

Performing similar calculations for different values of "a" and comparing the MSE values, we can determine the value of "a" that results in the smallest MSE.

Note: Since the trial and error process involves calculating the MSE for different values of "a," it is not possible to provide a specific value without performing the calculations.

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The equation of the line that passes through the point; (-4, 8) and is parallel to x + y = 6 is; x + y = 4.

By expressing the given linear equation in slope-intercept form; it follows that we have;

x + y = 6

y = -x + 6

Hence, the slope of the equation by comparison with; y = mx + c is; -1.

Therefore, the slope of the required equation is same as the two lines are said to be parallel.

Therefore, the required equation from point-slope form of an equation is;

( y - 8) = -1 ( x - (-4))

y - 8 = -x - 4

x + y = -4 +8

x + y = 4.

Ultimately, the required equation is; x + y = 4.

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Answer:

b.

Step-by-step explanation:

6 times 1/2 is the same thing as 6/1 times 1/2, which is 6/2.

Hope this helps.

The equation of l1 in the form y = mx + c is:

y = 2x - 3.

We can find the slope of the line passing through points (3,3) and (5,7) using the slope formula:

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

= (7 - 3) / (5 - 3)

= 2

Now we can use the point-slope form of the equation of a line to find the equation of l1:

y - y1 = m(x - x1)

y - 3 = 2(x - 3)

Simplifying this equation, we get:

y - 3 = 2x - 6

y = 2x - 3

Therefore, the equation of l1 in the form y = mx + c is:

y = 2x - 3.

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The probability of landing on red is 4/11, the probability of landing on blue is 5/11, and the probability of landing on green is 2/11.

Since the spinner is divided into three sections, the sum of the areas of these sections must equal the total area of the spinner, which we can consider to be 1.

Let R be the area of the red section, B be the area of the blue section, and G be the area of the green section. We know that:

R = (2/5) * 1 = 2/5 (since the red section is 2/5 of the total area)

B = (1/2) * 1 = 1/2 (since the blue section is 1/2 of the total area)

To find the area of the green section, we can subtract the areas of the red and blue sections from the total area:

G = 1 - R - B = 1 - 2/5 - 1/2 = 1/10

Now, we can find the probability of each outcome by dividing the area of each section by the total area:

Probability of red = R / (R + B + G) = (2/5) / (2/5 + 1/2 + 1/10) = 4/11

Probability of blue = B / (R + B + G) = (1/2) / (2/5 + 1/2 + 1/10) = 5/11

Probability of green = G / (R + B + G) = (1/10) / (2/5 + 1/2 + 1/10) = 2/11

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Answer:

The cost for 20 students would be $120

Step-by-step explanation:

We know that 4x5=20 therefore we will multiply 30x4 which will give us 120.

Our final answer would be $120

Exploratory data analysis (EDA) is an approach to examining and analyzing data to generate insights, ideas, and hypotheses. It involves a variety of data visualization methods, such as plotting, which help to quickly identify patterns, trends, and outliers in the data.

When we do exploratory data analysis, we rely heavily on plotting the data. Exploratory data analysis (EDA) is an approach to examining and analyzing data in order to generate insights, ideas, and hypotheses that may guide subsequent research.

Exploratory data analysis is a crucial first step in most data analytics tasks, whether in scientific research or business applications. EDA methods are used to gain a better understanding of data characteristics such as distribution, frequency, and outliers. Exploratory data analysis typically involves a variety of data visualization methods, such as plotting, which help to quickly identify patterns, trends, and outliers in the data. EDA techniques can also help to identify important variables, relationships, and potential correlations among data points. By visualizing data in different ways, we can often discover patterns that we might not have seen otherwise, or that we might have overlooked with other techniques.

Therefore, when we do exploratory data analysis, we rely heavily on plotting the data to help us gain insights, find patterns, and identify relationships and correlations among variables.

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Answer:

40 unit^2.

Step-by-step explanation:

Area = 1/2 * base * altitude

= 1/2 * 8 * 10

= 40 unit^2.

To find the points (x, y) on the graph of f(x) = 2x^2 - 3x with tangent lines parallel to the line y = 5x + 6, we need to find the values of x where the derivative of f(x) is equal to the slope of the given line (which is 5).

The derivative of f(x) is f'(x) = 4x - 3.

Setting f'(x) equal to 5, we have:

4x - 3 = 5

Solving for x, we get:

4x = 8

x = 2

Substituting x = 2 into the equation f(x) = 2x^2 - 3x, we can find the corresponding y-value:

f(2) = 2(2)^2 - 3(2) = 8 - 6 = 2

Therefore, the point where the tangent line to the graph of f(x) is parallel to y = 5x + 6 is (2, 2).

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Answer:

Area

Step-by-step explanation:

When you are deciding how much of something is needed to cover something, in this case a table, you need to know everything. Including the inner part of the circle. Not just the outside.

Answer:

A

Step-by-step explanation:

Answer:

1. area
2. multiply
3. 2
4. circumference
5. multiply
6. height
7. add

Step-by-step explanation:

The formula for surface area of a cylinder is 2πrh + 2π\(r^{2}\), which consists of the formula for curved surface area, 2πrh, and 2 bases for the top and bottom of the cylinder, which is the formula 2π\(r^{2}\).

Answer:

0, 1, 2, 3

Step-by-step explanation:

-1 < x < 4 means that x has to be an integer (whole number aka no fractions)  between -1 and 4. Note that the < and > means that x cannot be -1 or 4 since it has to be greater than -1, or smaller than 4.

Answer: 7-i√3

Step-by-step explanation:

√36+ √-75+ √1-√-108

6 + √75i + 1 - √108i

7 + 5i√3 - 6i√3

7-i√3

The probability that a randomly chosen young adult has at least a high school education can be found using the rule of probability called the "complement rule".

To find the answer, we need to subtract the probability that a randomly chosen young adult does not have at least a high school education from 1. In other words:

Probability of having at least a high school education = 1 - Probability of not having at least a high school education.

By using this rule, we can calculate the probability.

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Answer:

The answer is C, (12, -1).

Step-by-step explanation:

With the help of given table of data of travelling time to work for 50 people, the estimated mean travelling time is 24.8 minutes.

To estimate the mean travelling time from the given frequency table, we can use the midpoint method, where we calculate the midpoint of each class interval and multiply it by the frequency of that interval. We then sum up the products and divide by the total frequency to get the estimate of the mean travelling time. The midpoint of each interval can be calculated as the average of the lower and upper bounds of the interval. Using this method, we get:

Class interval 0 < t < 10 | 10 < t < 20 |  20 < t < 30 | 30 < t < 40 |  40 < t < 50

Midpoint (m)    5                     15               25                 35                  45

Frequency (f)    5                    15               13                  10                   7

Midpoint x Frequency 25      225            325               350               315

Total | | 50 | 1240

To estimate the mean travelling time, we can now calculate the sum of the products of the midpoint and frequency for each interval, which is 1240. We then divide this by the total frequency, which is 50. Therefore, the estimate of the mean travelling time for these 50 people is: Mean  travelling time = Sum of (midpoint x frequency) / Total frequency

Mean travelling time = 1240 / 50 = 24.8

Thus, the estimated mean travelling time is 24.8 minutes.

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Complete Question

The table shows the travelling time to work of 50 people.

-Travelling time (t)  in minutes- -Frequency-

0 <t<10                                           5

10 < t < 20                                     15  

20 < t < 30                                    13

30 < t < 40                                    10

40 < t < 50                                    7

Calculate an estimate of the mean travelling time

Answer:

34

Step-by-step explanation:

Substitute the values.

s = 3 and t = -2

8s-5t

8 (3) - 5(-2)

( 8 x 3 ) - ( 5 x -2 )

24 + 10 [ - x - = + ]

= 34

The correct answer is that 13 students who spend more than 12 hours a week on screens were surveyed.

The provided data represents the number of students based on their screen time and whether their grade average is above or below 80.

To find the total number of students who spend more than 12 hours a week on screens, we need to look at the "Screen Time" category that corresponds to "more than 12 hours" and sum up the corresponding counts.

Looking at the data:

Screen Time:

less than 4 hours: 6 students

4-8 hours: 15 students

8-12 hours: 9 students

more than 12 hours: 13 students

If we consider only the "more than 12 hours" category, we find that there were 13 students.

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Answer:

15

Step-by-step explanation:

Answer:

15

Explanation:

If p=5 then 3p=3(5)

3*5=15

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