Solve each literal equation for the indicated variable.
11. For h: V = (1/3)bh ​

[tex]f(x)=\frac{2x^2-7x+6}{x^2-9x+20}\\ f(x)=\frac{(2x-3)(x-2)}{(x-5)(x-4)}\\\\[/tex]

Therefore, the value of x must not be either 5 or 4 which will give the undefined answer.

Therefore, the domain is x<4, x>5 or R - {4,5}

Answer:

2d

Step-by-step explanation:

Since Pete has double what Leo has, we need to multiply Leo's number of stamps by 2. But because we don't know how many he actually has, and the amount is represented by "d", we multiple "d" by 2

Answer:

Step-by-step explanation:

The difference is

Pete had d more stamps than Leo

Answer:

I think it's C.

Step-by-step explanation:

A. and D. don't make any sense so I assume they're incorrect. B. just seems wrong also by a small margin.

Answer:

1. 678.58 in^2

2. 59.08 m^2

Step-by-step explanation:

Answer:

3)

[tex](-4^{6})^{-2} \\=-4^{-12} \\=\frac{1}{-4^{12} }[/tex]

4)

[tex](-12^{3})^{4} \\= -12^{12}[/tex]

6)

[tex](-x^{-13})^{2} \\= -x^{-26}\\= \frac{1}{-x^{26} }[/tex]

Answer:

Step-by-step explanation:

its A

Answer:

c

Step-by-step explanation:

answer is c    u have to divide

1. When the population mean shifts to 7.8, the probability of detecting the change is approximately 0.0495 (or 4.95%).

2.  The probability of detecting the change is 0.0495 or 4.95%.

To solve this problem, we'll use the concept of control limits and the sampling distribution of the sample means.

When the population mean shifts to 7.8: First, let's calculate the standard deviation of the sampling distribution, also known as the standard error (SE). The formula for SE is given by SE = σ / sqrt(n), where σ is the standard deviation of the population (1.0 ounce) and n is the sample size (47).

SE = 1.0 / sqrt(47) ≈ 0.145

Next, we need to determine the z-score corresponding to the lower and upper tails of the sampling distribution that capture 5% each. Since the total probability in both tails is 10%, each tail will have a probability of 5%. We can find the z-scores using a standard normal distribution table or calculator.

The z-score corresponding to the lower tail of 5% is approximately -1.645.

The z-score corresponding to the upper tail of 5% is approximately 1.645.

Now, let's calculate the lower and upper control limits:

Lower Control Limit (LCL) = Population Mean - (z * SE)

Upper Control Limit (UCL) = Population Mean + (z * SE)

LCL = 7.8 - (-1.645 * 0.145) ≈ 8.026

UCL = 7.8 + (1.645 * 0.145) ≈ 9.574

To find the probability of detecting the change, we need to calculate the area under the sampling distribution curve that falls beyond the control limits. In this case, we're interested in the area above the upper control limit.

Since the distribution is assumed to be normal, we can use the standard normal distribution's cumulative distribution function (CDF) to calculate this probability.

Probability of detecting the change = 1 - CDF(z-score for UCL)

Using the z-score for the upper control limit (UCL), we can calculate the probability.

Probability of detecting the change ≈ 1 - CDF(1.645) ≈ 0.0495

Therefore, when the population mean shifts to 7.8, the probability of detecting the change is approximately 0.0495 (or 4.95%).

When the population mean shifts to 8.6: We'll follow the same steps as before.

SE = 1.0 / sqrt(47) ≈ 0.145

The z-score corresponding to the lower tail of 5% is still approximately -1.645.

The z-score corresponding to the upper tail of 5% is still approximately 1.645.

LCL = 8.6 - (-1.645 * 0.145) ≈ 8.926

UCL = 8.6 + (1.645 * 0.145) ≈ 10.274

Probability of detecting the change = 1 - CDF(z-score for UCL)

Probability of detecting the change ≈ 1 - CDF(1.645) ≈ 0.0495

Therefore, when the population mean shifts to 8.6, the probability of detecting the change is also approximately 0.0495 (or 4.95%).

In both cases, the probability of detecting the change is 0.0495 or 4.95%.

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Answer:

Richard: 35 years old

Teo: 10 years old

Step-by-step explanation:

Let the ages of Richard and Teo be R and T years old respectively.

R +T= 45 -----(1)

R= 2T +15 -----(2)

Substitute (2) into (1):

2T +15 +T= 45

3T +15= 45

3T= 45 -15 (-15 on both sides)

3T= 30

T= 30 ÷3

T= 10

Substitute T= 10 into (2):

R= 2(10) +15

R= 20 +15

R= 35

Thus, Richard is 35 years old and Teo is 10 years old.

Answer:

X = -7

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

8x-2= -9 +7x

+9. +9

8x+7= 7x

-8x. -8x

7 = -x or -1x

÷ -1 to both sides

x = -7

hope this helps

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Number of booths = 29

Food booth = 12

Cost of food booth = 175 + $4 per day

Game booth = (29 - 12) = 17

Cost of game booth = $50 + $10 per day

Number of days for which fair lasts (d) = 40 days

Total cost of food booth:

Number of booths * cost per booth

12($175 + 4d) ----(1)

Total cost of game booth:

Number of booths * cost per booth

17($50 + 10d) - - - (2)

(1) + (2)

12($175 + 4d) + 17($50 + 10d)

2100 + 48d + 850 + 170d

2950 + 218d

d = 40

2950 + 218(40)

2950 + 8720

= 11,670

Answer:

They are both functions, linear equations, and they both have a constant rate if that is what you are asking.

Step-by-step explanation:

Constant rate is k in y=kx. For the equation on the left, 2 is the constant rate and for the equation on the right is 0.5. They are both linear equations because if you line them up on a graph, it will show a straight line. And for every input should give one output. Hope this helps! Have a great day!

Answer:

[tex]y = \frac{x}{3} [/tex]

Step-by-step explanation:

divide both sides by 3 to get the answer

Answer: 7

Step-by-step explanation:

You would have to set it up like a Variables on Both Sides Equation:

95+40m = 25+50m

Solve the equation correctly, just like any other, and biggidy-boom.

Answer:

...

Step-by-step explanation:

Answer:

4.8 months

Step-by-step explanation:

First, let's write down the information that we are given.

Plant A:

Initial Height: 3 in.

Constant Rate of Growth (CRG): 2in/month (2 inches per month)

Plant B:

Initial Height: 1 in.

CRG: 29in/year (29 inches per year)

We can see that Plant B grows 29 inches per year, so lets convert Plant B's 'CGR' to months.

Plant B - Divide by 12 (12 months in a year)

29/12 in/year

Now, Lets put these into equations:

Plant A: y = 2x + 3

Plant B: y = 29/12 x + 1

Now, set these two equations together and solve for x.

2x + 3 = 29/12 x + 1

2 = 5/12 x

4.8

So, after 4.8 months, the plants will be the same height.

Answer:

144

Step-by-step explanation:

Using the Method Of LCM

Find and list multiples of each number until the first common multiple is found. This is the lowest common multiple.

Multiples of 16:

16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176

Multiples of 18:

18, 36, 54, 72, 90, 108, 126, 144, 162, 180

Multiples of 24:

24, 48, 72, 96, 120, 144, 168, 192

Therefore,

LCM(16, 18, 24) = 144

Answer:

The answer is - 8

......

Answer:

x=3

Step-by-step explanation:

Covert to decimals

5x+.25=15.25

5x=15.25-.25

5x= 15

x= 3

Answer:

7x+9

Step-by-step explanation:

Because 6+3=9-2=7 and 5+4=9

Answer:

Explained below.

Step-by-step explanation:

A correlation coefficient is a mathematical measure of certain kind of correlation, in sense a statistical relationship amid two variables

Negative correlation is a relationship amid two variables in which one variable rises as the other falls, and vice versa.  

Values amid 0.7 and 1.0 (-0.7 and -1.0) implies a strong positive (negative) linear relationship amid the variables.

It is provided that Warren noticed a strong negative linear relationship between the success rate and putt distances.

This implies that as the putt distances are increasing the success rates are decreasing and as the putt distances are decreasing the success rates are increasing.

Answer:

16.85

Step-by-step explanation:

This answer is if the question asks, "Use this model to predict the success rate of putts from 5 meters".  When you create your equation, 84.05-13.44(x), plug 5 into x and you get 16.85.

To determine which location yields the higher profit per year, we need the specific data for the annual profit in each location. Please provide the annual profit values for the locations in question, and I will be able to calculate and compare the profit per year.

Without the necessary information regarding the annual profits of the locations, it is not possible to determine which location yields the higher profit per year. To make a meaningful comparison, we need the specific profit figures for each location. Once the annual profit values are provided, we can calculate the profit per year by dividing the total profit by the number of years.

Once the profit per year is calculated for each location, we can compare the values to determine which location has the higher profit per year. However, as the specific data regarding the annual profit in each location is missing, it is not feasible to provide a conclusive answer at this time. Please provide the annual profit figures for the locations in question, and I will be able to assist you further in determining which location yields the higher profit per year.

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Answer:

5 hours

Step-by-step explanation:

(53-13)÷8

53-13=40

40÷8=5

She worked 5 hours I hope this helped. :)

The three consecutive integers are 21, 22, and 23 respectively.

Given that the sum of the squares of three consecutive integers is 1454.

We need to find out what the numbers are.

Let's assume the first integer as x, then the next two consecutive integers can be represented as x + 1 and x + 2 respectively.

Hence we can write the given statement as

x² + (x + 1)² + (x + 2)² = 1454

We can expand the terms of the equation and then simplify it to find the value of x.

After getting the value of x, we can find the next two consecutive integers by adding 1 and 2 to it.

Let's solve the above equation:

x² + (x + 1)² + (x + 2)² = 1454

⇒ x² + x² + 2x + 1 + x² + 4x + 4 = 1454

⇒ 3x² + 6x - 1449 = 0

⇒ x² + 2x - 483 = 0

By solving the above quadratic equation, we can get the value of x as follows:

x = (-2 + √(2² + 4×1×483))/2×1

(We ignore the negative value of x here)

⇒ x = (-2 + 44)/2

⇒ x = 21

Hence the three consecutive integers are 21, 22, and 23 respectively.

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The false statement about statistical analysis is: 3) Observational studies can determine cause and effect relationships. Option 3

Observational studies are a type of study in which researchers observe and collect data on individuals or groups without any intervention or manipulation of variables. These studies are often used to explore relationships and associations between variables but cannot establish cause and effect relationships.

In observational studies, researchers do not have control over the variables being studied, which means that they cannot manipulate or assign treatments to participants.

On the other hand, experiments are designed to investigate cause and effect relationships. In an experiment, researchers actively manipulate independent variables and control other variables to determine the effects on the dependent variable.

While observational studies are valuable in identifying patterns and associations, they cannot establish causality on their own. To establish cause and effect relationships, controlled experiments with random assignment are needed.

option 3

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Answer:

no

Step-by-step explanation:

.25 is first

All of the above factors - confidence level, required precision (margin of error), and the degree of variation in the population as measured by its standard deviation - are used to determine sample size.

When determining the sample size for a study or survey, several factors need to be considered: confidence level, required precision (margin of error), and the degree of variation in the population as measured by its standard deviation. Let's break down each factor and understand how they contribute to determining the sample size:

Confidence Level: The confidence level represents the degree of certainty or confidence desired in the results. It is typically expressed as a percentage (e.g., 95% or 99%). The higher the confidence level, the more confident we can be that the estimated result falls within a certain range. For example, a 95% confidence level means that if the study were repeated 100 times, we would expect the true population parameter to fall within the estimated range in 95 out of those 100 times.

Required Precision (Margin of Error): The required precision, also known as the margin of error, defines the acceptable amount of uncertainty or error allowed in the estimation. It represents the maximum difference between the estimated result and the true population parameter that is considered acceptable. A smaller margin of error indicates higher precision and vice versa. For instance, if you want to estimate the proportion of people supporting a particular political candidate with a margin of error of ±3%, it means that the estimated proportion should be within 3% of the true proportion.

Degree of Variation (Standard Deviation): The degree of variation in the population, quantified by its standard deviation, reflects how much the values within the population differ from the population mean. If the population has a high standard deviation, it suggests a larger spread of values, indicating greater heterogeneity. Conversely, a low standard deviation implies less variability and more homogeneity in the population. The standard deviation helps determine how much information is needed from the sample to make accurate estimates of the population parameters.

These factors are interrelated in determining the sample size. As the confidence level increases, the margin of error becomes smaller, requiring a larger sample size to achieve the desired precision. Similarly, a higher degree of variation in the population (larger standard deviation) necessitates a larger sample size to capture that variability accurately.

In summary, the confidence level, required precision (margin of error), and degree of variation (standard deviation) are essential factors used in determining the appropriate sample size for a study or survey. The balance between these factors ensures that the sample is representative enough to provide reliable estimates of the population parameters with the desired level of confidence and precision.

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Answer:

variable is ( x )

∆product of 8 :

8 x

∆the number increased by 2 :

8 x + 2

And we're done ♥️

Answer:

The sentence can be interpreted in two ways: 8x+2 or 8(x+2).

The first one would be the product of 8 and a number, increased by 2.

The second one would be the product of 8, and a number increased by 2.

Hope that helps.

Answer:

???

Step-by-step explanation:

Answer: X=-7

Step-by-step explanation: