find the equation of a line perpendicular to 2x+2y=-2 that passes through the point (9,8)

Answer:

(1,0)

Step-by-step explanation:

\(\boxed{midpoint = ( \frac{x1 + x2}{2}, \frac{y1 + y2}{2}) }\)

Thus, midpoint of the line segment is

\( = ( \frac{3 - 1}{2} , \frac{1 - 1}{2} ) \\ = ( \frac{2}{2} , \frac{0}{2} ) \\ = (1,0)\)

Answer:

4(3 + 20)

Step-by-step explanation:

The largest GCF of 12 and 80 is 4. Factor out 4 to get your answer in distributive form.

Answer:

4(3+20)

Step-by-step explanation:

First you should find the gcm factor because that is the number we will place outside of the parentheses in order to distribute. The GCM of 12 and 80 is 4. So, we place 4 outside of the grouping symbol. Now, we have to form what will be inside of the parentheses. When we use distributive property, we take the inner number and multiply it by the outside number. So, that means if we have 12 the inner number should be 3 since 4*3=12. Now, we move onto the number 80. Same thing here. This time it's going to be 20 since 4*20=80

So, we're left with this expression: 4(3+20)

Answer:

the answer is 42. hope this helped

First turn 15% into a decimal.

You get .15

Then multiply .15 by 280

You get 42

Answer:

128 <33

Step-by-step explanation:

6 ÷ 3 + 32 • 4 - 2 = 128

▪︎▪︎▪︎▪︎▪︎▪︎

Answer:

3 2/3 * 5 1/4 = 19 1/4

the answer would be:19 5/9

Answer: 360 bacteria

Step-by-step explanation: if it triples every hour, you would need to triple the amount of hours, and multiply that by 40 since 40 was the initial bacterial count. Hope this helps:)

Answer:

x+1

Step-by-step explanation:

Since it's a consecutive integer it's 1 added to the smaller integer, which is x.

Answer:

39 Minutes

Step-by-step explanation:

Given data

Total time for the car trip= 56minutes

Stoppage time= 17 minutes

Hence the time left for the trip

=Total time- Stoppage time

= 56-17

=39 Minutes

Answer:

120

Step-by-step explanation:

Answer:

118/125

Step-by-step explanation:

We can find first the probability that there isn’t suitable weather:

60/100 * 60/100 * 60/100 = 3/5 * 3/5 * 3/5 = 27/125

now we have just to do this operation

125/125 - 27/125 = 118/125

The probability of drawing a head card of diamonds and then a head card of hearts is:

P = 0.003

Here we assume that we have a deck of 52 cards, and we want to find:

P(Head, Diamond AND Head, Heart)

This is the probability of drawing a head of diamonds and then a head of hearts.

Remember that for each suit has 3 head cards, J, Q, and K.

Then for the first card, the probability of getting a head of diamonds is equal to the quotient between the number of cards with these properties (3) and the total number of cards (52).

P = 3/52

Then we need to draw a head of hearts, the probability is computed in the same way, but before we drew a card, so now the total number of cards is 51, so we get:

Q = 3/51

Then the joint probability is:

p = (3/52)*(3/51) = 0.003

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The expected weekly bonus for the workers is $20.

Given that each worker gets a bonus every Friday with an amount of probabilities $10-0.75, $50-0.25. We are to determine the expected weekly bonus.

Expected value is the weighted average of all possible values. The formula to find the expected value is as follows:

Expected Value = ∑ (value × probability)

Thus, the expected value of the weekly bonus can be calculated as follows:

Expected weekly bonus = (10×0.75) + (50×0.25) = 7.5 + 12.5 = $20

Therefore, the expected weekly bonus for the workers is $20.

Note: Expected value helps to determine the average value of a random variable. It is a theoretical value that represents the average amount one can expect to win or lose on an average on a given bet if it were repeated many times.

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tThe population in this scenario refers to the entire group of policyholders of the large automobile insurance company.

Set up the hypotheses ; Null hypothesis (H0): The mean age in the population of policyholders is 50.  Alternative hypothesis (Ha): The mean age in the population of policyholders is different from 50. Determine the significance level: The significance level is given as 5%.  Calculate the test statistic: The test statistic for a two-sample t-test is given by:
    t = (sample mean - hypothesized mean) / (standard error)

 In this case, the sample mean is 47.2, and the hypothesized mean is 50. The standard error can be calculated using the formula: standard error = sqrt(variance / sample size).  In this case, the variance is 121 and the sample size is 361. Calculate the degrees of freedom:  For a two-sample t-test, the degrees of freedom is calculated as the sum of the sample sizes minus 2.  In this case, the sample size is 361.  Determine the critical value:  Since the alternative hypothesis is two-tailed (different from 50), we divide the significance level by 2 (5% / 2) to get the critical value for each tail.

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The slope of the linear equation, \(C = 22.5 - (\frac{1}{160}) m\), is: \(-\frac{1}{160}\)

Recall:

Thus, given the linear equation:

\(C = 22.5 - (\frac{1}{160}) m\),

C represents y

m represents x

\(-\frac{1}{160}\) represents the slope (m)

22.5 represents b.

Therefore, the slope of the linear equation, \(C = 22.5 - (\frac{1}{160}) m\), is: \(-\frac{1}{160}\)

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Data collected over several time periods are called time series data.

Time series data refers to data that is collected over several time periods. It captures a sequence of observations of a variable of interest over time, such as sales figures, stock prices, temperature, and so on. The observations are usually taken at regular intervals, such as daily, weekly, monthly or yearly, and the data reflects the changes in the variable over time.

Time series data is useful for identifying trends, patterns, and seasonality in the data, and for making predictions about future values. It's often used in economic forecasting, weather forecasting, and other fields where understanding how a variable changes over time is important.

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The probability of rolling a sum of 10 is \(\frac{1}{18}\)

as we know that total number of outcomes for a dice is equal to six raised to the power times the dice is rolled

that is,  total number of outcomes = \(6^{2} = 36\)

also, the sum can be equal to 10 in only two cases, (6,4) and (5,5)

according to the formula

Probability = \(\frac{favorable events}{ total number of outcome} = \frac{2}{36} = \frac{1}{18}\)

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Question:

You roll a fair six-sided die and record the result X. You roll the die again and record the result Y. What is the probability of rolling a sum of 10?

Answer:

sorry if wrong

Step-by-step explanation:

Probability and statistics are related areas of mathematics which concern themselves with analyzing the relative frequency of events. ... Probability deals with predicting the likelihood of future events, while statistics involves the analysis of the frequency of past events.

When a question asks for an exponential model, the answer should have at least two variables, typically denoted as y and x.

The exponential model is a type of mathematical equation that represents the relationship between two variables, where one variable (y) changes exponentially with respect to changes in the other variable (x).

In its general form, an exponential model can be written as:

y = ab^x

where y is the dependent variable, x is the independent variable, a is a constant (representing the value of y when x=0), and b is the base of the exponential function (representing the rate of change of y with respect to x).

It is important to note that there can be variations of this general form of the exponential model, depending on the specific context of the problem and the type of data being analyzed.

For example, some exponential models may have additional parameters or modifications to better fit the data. However, the fundamental characteristic of an exponential model is that it represents an exponential relationship between two variables.

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Answer:

The answer is True.

Step-by-step explanation:

-3x - 10 > -31

-3(5) - 10 > -31

-15 - 10 > -31

-25 > -31

True.

Answer: the value of n = 1.5

Step by Step Solution: to figure this out, you can just substitute the number in for the variable and solve. hope this helps

Answer:

x= -3 and y= -3

Step-by-step explanation:

first, use elimination or substitution method for simplify the system

Answer:

Below

Step-by-step explanation:

x-8y = 21

3x-8y = 15       <==== multiply THIS equation by -1 to get

-3x+8y = -15     now add THIS equation to the TOP equation

-2x = 6

x =  -3    use this value of x in one of the equations to calculate the 'y' value

x- 8y = 21

-3 -8 y = 21

y = -3            

The proportion of babies have a birthweight over 4,00 grams is 0.62% and the proportion of babies have a birthweight between 3,200 and 3,800 is 86.64%.

How to calculate proportion?

Assumed,

mean = μ = 3500

standard deviation = σ = 200

For proportion over 4,000 grams, use this formula

P(x>4,000) = P(z>\(\frac{x-\mu}{\sigma}\))

P(x>4,000) = P(z>\(\frac{4000-3500}{200}\))

= P(z>2.5)

Look z score table for 2.5. So, z = 0.9938. Since is over so 1 - the result

= 1 - 0.9938

= 0.0062 or 0.62%

For proportion between 3,200 and 3,800 grams, use this formula

P(3,200<x<3,800) = P(\(\frac{x-\mu}{\sigma}\)<z<\(\frac{x-\mu}{\sigma}\))

P(3,200<x<3,800) = P(\(\frac{3200-3500}{200}\)<z<\(\frac{3800-3500}{200}\))

= P(-1.5<z<1.5)

= P(z<1.5) - P(z<-1.5)

Look z score table for 1.5 and -1.5. So, z for 1.5 = 0.9332 and z for -1.5 = 0.0668

= 0.9332 - 0.0668

= 0.8664 or 86.64%

Your question is incomplete, but this answer uses assumptions and general formulas that can be used.

Thus, the proportion of babies have a birthweight over 4,00 grams is 0.62% and the proportion of babies have a birthweight between 3,200 and 3,800 is 86.64%.

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∂g/∂u is equal to 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v)).

To find the indicated derivative, we need to use the chain rule. Let's differentiate step by step:

Given:

g(u, v) = f(x(u, v), y(u, v))

f(x, y) = 7x³y³

x(u, v) = ucos(v)

y(u, v) = usin(v)

To find ∂g/∂u, we differentiate g(u, v) with respect to u while treating v as a constant:

∂g/∂u = (∂f/∂x) * (∂x/∂u) + (∂f/∂y) * (∂y/∂u)

To find ∂f/∂x, we differentiate f(x, y) with respect to x:

∂f/∂x = 21x²y³

To find ∂x/∂u, we differentiate x(u, v) with respect to u:

∂x/∂u = cos(v)

To find ∂f/∂y, we differentiate f(x, y) with respect to y:

∂f/∂y = 21x³y²

To find ∂y/∂u, we differentiate y(u, v) with respect to u:

∂y/∂u = sin(v)

Now, we can substitute these partial derivatives into the equation for ∂g/∂u:

∂g/∂u = (21x²y³) * (cos(v)) + (21x³y²) * (sin(v))

To find the simplified form, we substitute the given values of x(u, v) and y(u, v) into the equation:

x(u, v) = ucos(v) = u * cos(v)

y(u, v) = usin(v) = u * sin(v)

∂g/∂u = (21(u * cos(v))²(u * sin(v))³) * (cos(v)) + (21(u * cos(v))³(u * sin(v))²) * (sin(v))

Simplifying further, we get:

∂g/∂u = 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v))

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Using the properties of rational exponents, the value of y is 7/3.

Solve the equation using the properties of rational exponents. We are given the equation: (x^(4/3))^2 / x^(1/3) = x^y, and we need to find the value of y.

Step 1: Apply the power rule of exponents to (x^(4/3))^2.
The power rule states that (a^m)^n = a^(m*n).

So, in our case, (x^(4/3))^2 = x^((4/3)*2) = x^(8/3).

Step 2: Rewrite the equation with the result from step 1.
Now, our equation is x^(8/3) / x^(1/3) = x^y.

Step 3: Apply the quotient rule of exponents.
The quotient rule states that a^m / a^n = a^(m-n).

In our case, x^(8/3) / x^(1/3) = x^((8/3) - (1/3)) = x^(7/3).

Step 4: Compare the resulting expression to x^y.
Now our equation is x^(7/3) = x^y.

Since the bases (x) are the same, we can conclude that the exponents must be equal. Therefore, y = 7/3.

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Answer: the domain is -3. 1, 0, 1, and 5 and range is, 3. 1, -2, -4, and-1 I dont know the function but I hope this helped

Step-by-step explanation:

The argument can be used to adjust the size of the two tick labels B and 0 on the x-axis is cex.axis of the boxplot. Option D is the correct choice.

To create a boxplot of rear width (RW) by species (sp) using the boxplot function in R, you can use the following R code:
```R
boxplot(RW ~ sp, data = your_data)
```

In this code, replace 'your_data' with the name of your data frame containing the variables RW and sp.

Regarding the options for adjusting the size of the tick labels (B and 0) on the x-axis, the correct argument is (D) cex.axis. You can use this argument to set the size of the tick labels as follows:
```R
boxplot(RW ~ sp, data = your_data, cex.axis = desired_size)
```

Replace 'desired_size' with a numerical value to set the size of the tick labels.

The answer is: (D) cex.axis

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