The necessary condition for creating confidence intervals for the population mean is that the sample mean is normally distributed or that the sample size is large enough to satisfy the central limit theorem.
Thus, a necessary condition for creating confidence intervals for the population mean is that the sample data should follow a normal distribution, or the sample size should be sufficiently large (usually n ≥ 30) to apply the Central Limit Theorem.
This condition ensures that the confidence interval accurately estimates the population mean with a specified level of confidence.
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The clients who get haircuts at Cameron's salon have a variety of hair colors.
brown 7
black 7
blond 4
What is the experimental probability that the next client to get a haircut Cameron's salon will have blond hair?
Write your answer as a fraction or whole number.
The experimental probability that the next client to get a haircut at Cameron's salon will have blond hair is 2/9.
To find the experimental probability of a client having blond hair, we need to divide the number of clients with blond hair by the total number of clients.
In this case, we know that there are a total of 7 + 7 + 4 = 18 clients who get haircuts at Cameron's salon.
Out of these 18 clients, only 4 have blond hair.
So, the experimental probability of the next client having blond hair is:
Experimental probability of having blond hair = Number of clients with blond hair / Total number of clients
Experimental probability of having blond hair = 4 / 18
Experimental probability of having blond hair = 2 / 9
Experimental probability is based on observation and is not necessarily an accurate representation of the true probability. To get a more accurate estimate of the probability, a larger sample size would be needed.
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Find the volume of each rectangular prism from the given parameters.
height: 14; area of the base: 88
best answer get 41 points
A T-shirt stand on the boardwalk recently sold 6 purple shirts and 9 shirts in other colors. What is the experimental probability that the next shirt sold will be purple?
Write your answer as a fraction or whole number.
The experimental probability that the next shirt sold will be purple is [tex]2/5[/tex].
What is experimental probability on purple shirt?The experimental probability means ratio of the number of times the event occurs to the total number of trials or observations.
In this case, the event is the sale of a purple shirt and the trials are the total number of shirts sold.
So, total number of shirts sold is:
= 6 purple shirts + 9 other color shirts
= 15 shirts
The number of purple shirts sold is 6.
The experimental probability of selling a purple shirt on the next sale will be:
= Number of purple shirts sold / Total number of shirts sold
= 6 / 15
= 2 / 5.
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Translate the quotient of x and 9 is greater than 27
The English statement "the quotient of x and 9 is greater than 27" can be represented mathematically as x/9 > 27.
This inequality indicates that the value of x divided by 9 is greater than 27. In other words, x is a number that is more than 27 times 9.
For example, let's say we want to find all the values of x that satisfy this inequality. We can begin by dividing both sides by 9, which gives us:x > 243 So any value of x that is greater than 243 will satisfy the inequality.
For instance, x could be 300 or 500 or any other number larger than 243. Alternatively, we can subtract 27 from both sides to get: x/9 - 27 > 0 This form shows that the difference between x divided by 9 and 27 is positive.
We can then find the range of x that satisfies this inequality by multiplying both sides by 9: x - 243 > 0 This tells us that any value of x that is greater than 243 will satisfy the inequality.
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How many points of inflection will f(x) = 3x^7 + 2x^5 - 5x - 12 have
a 4
b 5
c 2
d 3
There is only one point of inflection. Answer: d) 3
The second derivative of the function f(x) is:
[tex]f''(x) = 126x^5 + 40x^3 - 5[/tex]
The second derivative of a function is the derivative of its first derivative. It is denoted represents the rate of change of the slope of the function.
In other words, if the first derivative f'(x) represents the slope of the function, the second derivative f''(x) represents the rate at which the slope is changing.
The points of inflection occur where the concavity changes, that is where the second derivative changes sign or equals zero.
Setting f''(x) = 0, we have:
[tex]126x^5 + 40x^3 - 5 = 0[/tex]
This equation has only one real solution, which can be found numerically:
x ≈ 0.357
Therefore, there is only one point of inflection. Answer: d) 3
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Residual standard error: 21.38 on 145 degrees of freedom
Multiple R-squared: 0.2242, Adjusted R-squared: 0.2189
F-statistic: 41.91 on 1 and 145 DF, p-value: 1.384e-09
Which answer is correct?
(1 Point)
no difference between R2 and the adjusted R2 is good aspect
22.42% from the variation of the independent variables is explained through the variation of the dependent one
p-value of the model is very high
R2 is very high
The correct interpretation of the given results is that 22.42% of the variation in the dependent variable is explained by the independent variable, the model as a whole is significant, and the p-value is very small.
The output is from a linear regression model. Here are the interpretations of the given results:
The residual standard error is a measure of the variability of the errors in the model. It tells us how much the actual responses deviate from the predicted responses on average. In this case, the residual standard error is 21.38, which means that the typical prediction error is about 21.38 units.
The multiple R-squared is a measure of how well the model fits the data. It represents the proportion of the variance in the dependent variable (y) that is explained by the independent variable(s) (x). The R-squared value ranges from 0 to 1, where 0 means the model does not explain any variation in the dependent variable, and 1 means the model explains all the variation. In this case, the R-squared value is 0.2242, which means that 22.42% of the variation in the dependent variable is explained by the independent variable.
The adjusted R-squared value is similar to the R-squared value, but it takes into account the number of independent variables in the model. It penalizes the model for including unnecessary variables. In this case, the adjusted R-squared value is 0.2189, which is slightly lower than the R-squared value, indicating that the model may have some unnecessary variables.
The F-statistic is a test of the overall significance of the model. It tests whether at least one of the independent variables in the model is significantly related to the dependent variable. The F-statistic value is compared to the F-distribution with degrees of freedom (1, 145) to calculate a p-value. In this case, the F-statistic is 41.91, which means that the model as a whole is significant, and the p-value is very small (1.384e-09), indicating strong evidence against the null hypothesis that all the regression coefficients are zero.
Therefore, the correct interpretation of the given results is that 22.42% of the variation in the dependent variable is explained by the independent variable, the model as a whole is significant, and the p-value is very small.
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The sum of two numbers is 32 and their difference is 13. What are the two numbers? Let's start by calling the two numbers we are looking for x and y.
The sum of x and y is 32. In other words, x plus y equals 32 and can be written as equation A:
x + y = 32
The difference between x and y is 13. In other words, x minus y equals 13 and can be written as equation B:
x - y = 13
The two numbers are x = 22.5 and y = 9.5. To find the two numbers, x and y, we will solve the given equations (A and B) simultaneously.
Equation A: x + y = 32
Equation B: x - y = 13
Step 1: Add Equation A and Equation B together to eliminate the 'y' variable.
(x + y) + (x - y) = 32 + 13
2x = 45
Step 2: Divide both sides by 2 to isolate 'x'.
2x / 2 = 45 / 2
x = 22.5
Step 3: Substitute the value of 'x' in Equation A to find the value of 'y'.
22.5 + y = 32
Step 4: Subtract 22.5 from both sides to isolate 'y'.
y = 32 - 22.5
y = 9.5
The two numbers are x = 22.5 and y = 9.5.
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If H is the circumcenter of triangle BCD find each measure
We have found the measures of CD, CE, HD, GD, HG, and HF in triangle BCD, given that H is the circumcenter of the triangle.
In triangle BCD, the circumcenter H is the point where the perpendicular bisectors of the sides of the triangle intersect. This point is equidistant from the three vertices of the triangle.
Using the properties of the circumcenter, we can find the measures of various sides and angles of the triangle:
CD = 2FD, where FD is the foot of the perpendicular from H to CD.
CE = BE = 26, since H is equidistant from B and C.
HD = HC = 33, since H is equidistant from D and C.
GD = 1/2BD = 1/2(58) = 29, since H is equidistant from B and D.
HG = √HD² - GD² = √33² - 29² = 2√62 ≈ 15.75, using the Pythagorean theorem.
HF = √HD² - FD² = √33² - 32² = √65 ≈ 8.06, using the Pythagorean theorem.
Therefore, we have found the measures of CD, CE, HD, GD, HG, and HF in triangle BCD, given that H is the circumcenter of the triangle.
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A random survey of 460 students was conducted from a population of 2,800 students to estimate the proportion who had part time jobs. The sample showed that 207 had part-time jobs Calculate the 90 percent confidence interval for the true proportion of students who had part-time jobs (Round your answers to 3 decimal places) The 90% confidence interval is from ____ to ____
The 90% confidence interval for the true proportion of students who had part-time jobs is from 0.374 to 0.526.
We have,
1. First, calculate the sample proportion (p) by dividing the number of students with part-time jobs (207) by the total number of students surveyed (460): p = 207/460 ≈ 0.450
2. Calculate the standard error (SE) using the formula SE = √(p (1 - p)/n), where n is the sample size:
SE ≈ √(0.450(1 - 0.450)/460) ≈ 0.046
3. Find the critical value (z) for a 90% confidence interval, which is 1.645.
4. Calculate the margin of error (ME) using the formula ME = z x SE:
ME ≈ 1.645 x 0.046 ≈ 0.076
5. Find the lower and upper limits of the confidence interval by adding and subtracting the margin of error from the sample proportion:
Lower limit ≈ 0.450 - 0.076 ≈ 0.374,
Upper limit ≈ 0.450 + 0.076 ≈ 0.526
Thus,
The 90% confidence interval for the true proportion of students who had part-time jobs is from 0.374 to 0.526.
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1. The table shows the numbers of points scored and numbers of rebounds for players
in a basketball game.
Player
Number of Points
Number of Rebounds
Number of Rebounds 10
11
9
7
5
A
3
18
1
B
0 1 3 5 7
7
4
C
D
11 28
4
6
E
5
3
F
16
Number of Points
6
G
a. Construct a scatter plot of the numbers of points scored and the numbers of rebounds.
Players in a Basketball Game
9
3
H
5
2
I
12
1
9 11 13 15 17 19 21 23 25 27 29
b. Do you notice an association between the number of points scored and the number
of rebounds? Explain.
J
0
2
c. Based on the scatter plot, can you conclude that greater numbers of points scored cause
greater or lesser numbers of rebounds?
TA
EXI
CKE
50
Note that this prompt examines the given data using scatter plot whose details is analyzed below.
What is the analysis of the scatter plot?1) The scatter plot showing the relationship between the numbers of points scored and the numbers of rebounds is attached.
2) The association between the numbers of points scored and the numbers of rebounds is a positive one. This means that generally, there is a tendency to get more points when the number of rebounds is high.
3) No, we cannot conclude that greater numbers of points scored cause
greater or lesser numbers of rebounds. This would be an inverse relationship which contradicts our findings above.
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ORRELATION
Please complete the following quiz. Use the data set attached. Please upload your Word doc for your submission. Include your SPSS output in this document as part of Step 3.
Test for the significance of the correlation coefficient at the .05 level using a two-tailed test between hours of studying and grade.
Hours of Study Grade
0 80
5 93
8 97
6 100
5 75
3 83
4 98
8 100
6 90
2 78
Sheet 1, Sheet 2, Sheet 3
We can reject the null hypothesis and conclude that there is a significant correlation between hours of studying and grades at the .05 level.
To test for the significance of the correlation coefficient at the .05 level using a two-tailed test between hours of studying and grade, we can perform a Pearson correlation analysis in SPSS.
Step 1: Open SPSS and import the data set provided.
Step 2: Click on Analyze > Correlate > Bivariate.
Step 3: In the Bivariate Correlations dialog box, select "Hours of Study" and "Grade" as the two variables to be analyzed. Click on Options and select "Two-tailed" under the "Significance" section. Click OK.
Step 4: Click OK again to run the analysis.
The output will provide the Pearson correlation coefficient (r) and the p-value.
In this case, the Pearson correlation coefficient is 0.871, indicating a strong positive correlation between hours of studying and grades. The p-value is 0.002, which is less than the alpha level of 0.05. Therefore, we can reject the null hypothesis and conclude that there is a significant correlation between hours of studying and grades at the .05 level.
In conclusion, the correlation between hours of studying and grades is statistically significant.
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i am confused and need help!
Answer:
Step-by-step explanation:
I used to do these as a kid! theyre pretty fun :)
for the first one:
the sum has to be 9. (as we can see from the first row).
the middle box in the last row will be -1. (since two boxes fill to be 10, you subtract 1 to get to 9)
and so on. it solves itself. use similar tactics for all others.
1:
0 7 2
5 3 1
4 -1 6
2:
1 2 6
8 3 -2
0 4 5
3:
3 -2 5
4 2 0
-1 6 1
Find volume of the solid
The volume of the cylinder is 803.9 ft².
Given is oblique cylinder, we need to find it volume,
Volume = π × radius² × height
The radius = 8 ft
The height = 4 ft
So,
The volume = 3.14 × 8² × 4
= 803.9 ft²
Hence, the volume of the cylinder is 803.9 ft².
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A rectangle has a length of 9.6 cm and a width of 6.5 cm. What is the area, in square centimeters, of the rectangle?
The area of the rectangle is 62.4 square centimeters.
The area of a rectangle is a measure of the amount of space enclosed by the rectangle in two-dimensional (2D) space. It is the product of the length and width of the rectangle, and is usually expressed in square units.
The area of a rectangle will be given by the formula;
Area = Length × Width
where "Length" represents the length of one side of the rectangle, and "Width" represents the length of the other side of the rectangle.
Given that the length of the rectangle is 9.6 cm and the width is 6.5 cm, we can substitute these values into the formula;
Area = 9.6 cm × 6.5 cm
Calculating the area using these values;
Area = 62.4 cm²
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Hello, can someone answer this for me?
If Amy wants to go to the place that has the highest typical temperature and the least variability, she should visit C. Destin.
Why should she visit Destin?Destin has one of the highest temperatures as it reaches about 95 degrees. This is the second highest of all the places and so can be one of the places to visit.
Destin has a variability (using range) of :
= 95 - 83
= 12 degrees
Pensacola Beach on the other hand, is:
= 98 - 80
= 18 degrees
Destin has the lower variability.
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Which graph shows the solution to the inequality shown below?
The solution to the inequality 15 ≤ 5x + 20 < 35 is -1 ≤ x < 3.
Option C is the correct answer.
We have,
To solve the inequality 15 ≤ 5x + 20 < 35,
We need to isolate the variable x by performing the same operation on all three parts of the inequality.
15 ≤ 5x + 20 < 35
Subtract 20 from all three parts:
-5 ≤ 5x < 15
Divide all three parts by 5:
-1 ≤ x < 3
Therefore,
The solution to the inequality 15 ≤ 5x + 20 < 35 is -1 ≤ x < 3.
This means that any value of x between -1 (inclusive) and 3 (exclusive) will satisfy the inequality
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Previously, 12.1% of workers had a travel time to work of more than 60 minutes. An urban economist believes that the percentage has increased since then. She randomly selects 80 workers and finds that 18 of them have a travel time to work that is more than 60 minutes. Test the economist's belief at the a= 0.1 level of significance. What are the null and alternative hypotheses?
The null hypothesis assumes that there is no change in the percentage, while the alternative hypothesis suggests an increase in the proportion of workers with a travel time exceeding 60 minutes.
We have,
The null and alternative hypotheses for testing the economist's belief can be defined as follows:
Null hypothesis (H₀): The percentage of workers with a travel time to work of more than 60 minutes is still 12.1%.
Alternative hypothesis (H₁): The percentage of workers with a travel time to work of more than 60 minutes has increased.
In mathematical notation:
H₀: p = 0.121 (p represents the proportion of workers with a travel time > 60 minutes)
H₁: p > 0.121
Thus,
The null hypothesis assumes that there is no change in the percentage, while the alternative hypothesis suggests an increase in the proportion of workers with a travel time exceeding 60 minutes.
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Participants in a study of a new medication received either medication A or a placebo. Find P(placebo and improvement). You may find it helpful to make a tree diagram of the problem on a separate piece of paper.
Of all those who participated in the study, 70% received medication A.
Of those who received medication A, 56% reported an improvement.
Of those who received the placebo, 52% reported no improvement.
According to the concept of probability, there is a 48% chance that a participant who received a placebo will report an improvement.
Of those who received medication A, 56% reported an improvement. This means that the probability of a participant receiving medication A and reporting an improvement is 0.56.
On the other hand, of those who received the placebo, 52% reported no improvement. We can use this information to find the probability of a participant receiving a placebo and reporting an improvement.
To do this, we can use the complement rule of probability, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, the event we are interested in is a participant receiving a placebo and reporting an improvement. So, the probability of this event happening is equal to 1 minus the probability of a participant receiving a placebo and not reporting an improvement, which is 0.52.
Therefore, the probability of a participant receiving a placebo and reporting an improvement is:
P(placebo and improvement) = 1 - P(placebo and no improvement)
= 1 - 0.52
= 0.48 or 48%.
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Simplify the following expression. 3x^4+2x^3-5x^2+4x^2+6x-2x-3x^4+7x^5-3x^3
The simplified form of the expression is [tex]7x^5 - 3x^4 - x^3 - x^2 + 4x.[/tex]
The given expression is a polynomial expression, which can be simplified by combining the like terms. The like terms have the same variable and the same exponent. The given expression can be rearranged and combined as follows:
To simplify the given expression, we need to combine the like terms.
Starting with the x^5 term, we see that there is only one term with [tex]x^5[/tex]which is [tex]7x^5.[/tex]
Moving on to the[tex]x^4[/tex]terms, we have two terms with[tex]x^4,[/tex] namely [tex]3x^4[/tex]and [tex]-3x^4[/tex], which add up to 0. Therefore, we can eliminate the[tex]x^4 t[/tex]erms from the expression.
[tex]7x^5 + 2x^3 - 5x^2 + 4x^2 + 6x - 2x - 3x^4 - 3x^3[/tex]
[tex]= 7x^5 - 3x^4 + 2x^3 - 3x^3 - 5x^2 + 4x^2 + 6x - 2x[/tex] (rearranging the terms)
[tex]= 7x^5 - 3x^4 - x^3 - x^2 + 4x[/tex] (combining the like terms)
Therefore, the simplified form of the expression is [tex]7x^5 - 3x^4 - x^3 - x^2 + 4x.[/tex]
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A figure undergoes a translation, reflection, and dilation. Will the image be similar to the original figure? Why or why not?
O A No; a dilation is not a rigid transformation, so the image is not similar to the preimage.
OB. Yes; any number of rigid transformations and dilations will always produce an image similar to the preimage.
OC. No, when more than one transformation is applied, the image is not similar to the preimage.
OD. Yes; since only 3 transformations were applied, the image will be similar to the preimage.
The image will be similar to the original figure. The correct answer is OB) Yes; any number of rigid transformations and dilations will always produce an image similar to the preimage.
A translation, reflection, and dilation are all examples of rigid transformations, which means that they preserve the shape and size of the figure.
A dilation is also a similarity transformation, which means that it scales the figure uniformly in all directions from a fixed center. The result of applying these three transformations to a figure will be a figure that is similar to the original, but possibly rotated or reflected.
Therefore, the correct option is OB).
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I'm
curious about why dx/dy becomes -e^-y.
how should I calculate this??
dx/dy = d/dy(-e^(-y)) = -(-e^(-y)) * 1 = e^(-y). Therefore, dx/dy is equal to e^(-y).
The derivative of a function tells you the rate at which the function is changing with respect to its independent variable. In the case of dx/dy = -e^(-y), x is a function of y, and you're trying to find the derivative of x with respect to y.
To find dx/dy, you need to use the chain rule of differentiation. The chain rule states that if y is a function of t and x is a function of y, then dx/dt = dx/dy * dy/dt.
In this case, you have x as a function of y given by x = -e^(-y). So, you can rewrite dx/dy as d/dy(-e^(-y)).
To differentiate -e^(-y) with respect to y, you can use the chain rule again. The derivative of e^(-y) with respect to y is -e^(-y) (since the derivative of e^u with respect to u is e^u), and then you need to multiply by the derivative of -y with respect to y, which is -1.
So, dx/dy = d/dy(-e^(-y)) = -(-e^(-y)) * 1 = e^(-y). Therefore, dx/dy is equal to e^(-y).
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PLS HELP QUICK
A geologist has a rock that is shaped like a rectangular pyramid that she would like to give as a gift. A model of the rock is shown.
A rectangular pyramid with base dimensions of 5 inches by 4 inches. The large triangular face has a height of 5.8 inches. The small triangular face has a height of 6 inches.
How much wrapping paper is needed without overlapping?
53 in2
73 in2
93 in2
146 in2
Answer:
146in2
Step-by-step explanation:
i dont like explaining but im in the test to
For the system of equations shown, what is the value of x+y? 3x+y=−6−3x−4y=−12
Answer:
x + y = -12 + 30 = 18
Step-by-step explanation:
To solve this system of equations, we can use the elimination method. Multiplying the first equation by 3, we get:
9x + 3y = -18
Adding this to the second equation, we eliminate the x terms:
9x + 3y = -18
-3x - 4y = -12
-----------------
-y = -30
Solving for y, we get y = 30. Substituting this back into either equation, we can solve for x:
3x + 30 = -6
3x = -36
x = -12
Therefore, x + y = -12 + 30 = 18.
You must study for your test in one of three periods, t = 0, 1, 2. The instantaneous utility cost of studying at t = 0 is 8, at t = 1 is 10, and at t = 2 is 12. You are a naive quasi-hyperbolic discounter with β = 0.75 and δ = 1.
a) In which period will you study? [1 mark]
b) You like to reward yourself with a chocolate cake when you finish study. Your instantaneous utility from eating this cake is equal to 6. Discuss whether binding the unpleasant task to a pleasant task overcome procrastination in this example? [1 mark]
c) After completing this unit you learn about your present bias and become a sophisticated quasi-hyperbolic discounter. Does being sophisticated change the period in which you study? (Assume that there is no cake.)
Since the utility cost is lowest at t=0, you will conduct your research during period 0 as a quasi-hyperbolic discounter. Procrastination may be beaten if the painful job was linked to an enjoyable task.
a) As a naive quasi-hyperbolic discounter, you must choose the period to study based on your discount factors (β = 0.75, δ = 1) and the utility costs. To determine this, you must compare the present value of the utility costs of studying in each period:
At t = 0: Utility cost = 8 (since you're studying now, no discounting is applied)
At t = 1: Utility cost = 10 x β = 10 x 0.75 = 7.5
At t = 2: Utility cost = 12 x β x δ = 12 x 0.75 x 1 = 9
Since the utility cost is lowest at t=0 (8), you will study during period 0.
b) By binding the unpleasant task (studying) with the pleasant task (eating chocolate cake with utility of 6), it may help overcome procrastination if the combined utility is less than the utility cost of studying in later periods. In this case:
At t = 0: Combined utility cost = 8 - 6 = 2
Since the combined utility cost at t=0 (2) is lower than the utility costs of studying in periods 1 and 2 (7.5 and 9), binding these tasks could help overcome procrastination.
c) As a sophisticated quasi-hyperbolic discounter, you're now aware of your present bias. However, since there is no cake involved, the utility costs remain the same as in part (a):
At t = 0: Utility cost = 8
At t = 1: Utility cost = 7.5
At t = 2: Utility cost = 9
Even though you're now sophisticated, the period in which you study does not change. You will still study during period 0, as it has the lowest utility cost.
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I don't understand this problem
Answer:
1. a
2. a
3. b
Step-by-step explanation:
Q1. The equation is 3x+6=30. b c d are all good answers so it has to be a. If you want more details on why a is wrong, if you expand it becomes 3x+18=30 which is wrong
Q2. This one is 4(x+6) = 40 because you have x+6 4 times and it tells you the total is 40. So the one that matches is a.
Q3.
You have 6 plus 4 x which makes a total of 40.
So 6 + 4x = 40. The equation that matches is b.
Hmu if you need more explanation
[tex]9x^2 -7 \\-4x^{2} -20x+25[/tex]
Consider the curve defined by x2 - y2 – 5xy = 25. A. Show that dy – 2x–5y dx 5x+2y b. Find the slope of the line tangent to the curve at each point on the curve when x = 2. C. Find the positive value of x at which the curve has a vertical tangent line. Show the work that leads to your answer. D. Let x and y be functions of time t that are related by the equation x2 - y2 – 5xy = 25. At time t = 3, the value of x is 5, the value of y is 0, and the value of sy is –2. Find the value of at at time t = 3
A.Hence proved dy/dx = (2x - 5y)/(5x + 2y). B. The slope of the tangent line at any point on the curve when x=2 is given by (4-5y)/(10+2y). C. The curve has a vertical tangent line at x = 5/√29. D. The x-axis is increasing at a rate of 60 square units per unit time at time t=3. D. The value of da/dt at time t=3 is 60.
A. To show that dy/dx = (2x-5y)/(5x+2y), we differentiate the given equation with respect to x using implicit differentiation:
2x - 2y(dy/dx) - 5y - 5x(dy/dx) = 0. Simplifying and solving for dy/dx, we get:
dy/dx = (2x - 5y)/(5x + 2y)
B. To find the slope of the line tangent to the curve at each point when x=2, we substitute x=2 into the expression we derived in part A:
dy/dx = (2(2) - 5y)/(5(2) + 2y) = (4-5y)/(10+2y)
C. To find the positive value of x at which the curve has a vertical tangent line, we need to find where the slope dy/dx becomes infinite. This occurs when the denominator of dy/dx equals zero, which is when: 5x + 2y = 0
Solving for y in terms of x, we get:
y = (-5/2)x
Substituting this into the equation for the curve, we get:
[tex]x^2 - (-5/2)x^2 - 5x(-5/2)x = 25[/tex]
Simplifying and solving for x, we get:
[tex]x = 5/√29[/tex]
or
[tex]x = -5/√29[/tex]
D. To find the value of da/dt at time t=3, we first use the chain rule to get:
2x(dx/dt) - 2y(dy/dt) - 5y(dx/dt) - 5x(dy/dt) = 0. We are given that x=5, y=0, and dy/dt=-2 when t=3. Substituting these values into the equation above and solving for dx/dt, we get:
dx/dt = (5dy/dt)/(2x-5y) = -10/25 = -2/5 Substituting these values into the expression for da/dt, we get:
[tex]da/dt = 2(5)^2 - 2(0)^2 - 5(0)(-2/5) - 5(5)(-2) = 60[/tex]
So the value of da/dt at time t=3 is 60. This means that the area enclosed by the curve.
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The average salary of an accountant is $ 71,000 a year. He just finished and his training which will increase his salary by 20%. How much more money he will make in next 10 years as compared to what he was earning without the training?
Answer:
After 10 years he will make 142 000$ more compared to what was earning without training
Show your calculation steps dearly Correct you answer to 4 decimal places and report the measurement unit when applicable. Question 1 (10 marks) A salad shop is selling fruit cups. Each fruit cup consists of two types of fruit, strawberries and blue berries. The weight of strawberries in a fruit cup is normally distributed with mean 160 grams and standard deviation 10 grams. The weight of blue berries in a fruit cup is normally distributed with mean u grams and standard deviation o grams. The weight of strawberries and blue berries are independent, and it is known that the weight of a fruit cup with average of 300 grams and standard deviation of 15 grams. (a) Find the values of u and o (b) The weights of the middle 96.6% of fruit cups are between (300 - K. 300 + K) grams. Find the value of K.
C) The weights of the middle 96.6% of fruit cups are between (L1, L2) grams. Find the values of LI and L2.
(a) The values of u is 140 g and o is 13.42 g. (b) The value of K in (300 - K. 300 + K) grams is 27.15 g. C) The weights of the middle 96.6% of fruit cups are between (L1, L2) grams. The values of LI is 272.85 g and L2 is 327.15 g.
(a) The mean weight of blueberries is:
300 g - 160 g = 140 g
The standard deviation of the weight is:
Var(X + Y) = Var(X) + Var(Y)
Adding the variances:
15^2 = 10^2 + o^2
Solving for o:
o = sqrt(15^2 - 10^2) = 13.42 g
Therefore, the values of u and o are u = 140 g and o = 13.42 g.
(b) Since the distribution is normal, we can use the standard normal distribution to find K.
The middle 96.6% of a standard normal distribution corresponds to the interval (-1.81, 1.81) (using a table or calculator). Therefore,
K = 1.81 * 15 = 27.15 g
Therefore, the weights of the middle 96.6% of fruit cups are between 300 - 27.15 = 272.85 g and 300 + 27.15 = 327.15 g.
(c) Using the standard normal distribution to find the corresponding interval on the standard normal scale:
(-1.81, 1.81)
We can then scale this interval to the distribution of the weight of fruit cups by dividing by the standard deviation and multiplying by 15 g:
L1 = 300 + (-1.81) * 15 = 272.85 g
L2 = 300 + 1.81 * 15 = 327.15 g
Therefore, the weights of the middle 96.6% of fruit cups are between 272.85 g and 327.15 g.
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A particular fruit's weights are normally distributed, with a mean of 438 grams and a standard deviation of 17 grams. If you pick one fruit at random, what is the probability that it will weigh between 443 grams and 492 grams
_____
The probability that a fruit picked at random weighs between 443 grams and 492 grams is approximately 0.3695 or 36.95%.
To find the probability that a fruit picked at random weighs between 443 grams and 492 grams, we need to standardize these values using the formula:
z = (x - μ) / σ
where x is the weight of the fruit, μ is the mean weight (438 grams), σ is the standard deviation (17 grams), and z is the standardized score.
For the lower end of the range (443 grams), we have:
z = [tex]\frac{(443 - 438)}{17} = 0.29[/tex]
For the upper end of the range (492 grams), we have:
z = [tex]\frac{(492 - 438)}{17} = 3.18[/tex]
Using a standard normal distribution table or calculator, we can find the probability that a standardized score falls between these values.
The probability of a z-score between 0.29 and 3.18 is approximately 0.3695.
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