The temperature dropped 14.4 over a period
of 4.5 hours. What was the average change in
temperature each hour?

Answer:

x< -11/2

Step-by-step explanation:

Let's solve your inequality step-by-step.

2(4x+1)<3(2x−3)

Step 1: Simplify both sides of the inequality.

8x+2<6x−9

Step 2: Subtract 6x from both sides.

8x+2−6x<6x−9−6x

2x+2<−9

Step 3: Subtract 2 from both sides.

2x+2−2<−9−2

2x<−11

Step 4: Divide both sides by 2.

2x/2<−11/2

x< −11/2

The regression equation for predicting Y from X based on the given data is Y = 3.5X + 13. The SSresidual is 56.125, and the standard error of estimate for the equation is approximately 4.73.

To find the regression equation for predicting Y from X, we can use the least squares method. By fitting a line to the data points, we determine the equation in the form of Y = aX + b, where 'a' is the slope and 'b' is the y-intercept. Using the given data points (X, Y), we can calculate the regression equation. The calculations result in the equation Y = 3.5X + 13, indicating that for every unit increase in X, Y is expected to increase by 3.5 units.

To calculate the Pearson correlation coefficient, we need to determine the strength and direction of the linear relationship between X and Y. The Pearson correlation coefficient ranges from -1 to +1, where +1 represents a perfect positive correlation, 0 indicates no correlation, and -1 indicates a perfect negative correlation. In this case, the Pearson correlation coefficient is calculated as 0.819, suggesting a strong positive correlation between X and Y.

Using the residuals (the differences between the actual Y values and the predicted Y values from the regression equation), we can calculate the sum of squares of the residuals (SSresidual). By using the rand SSy (the sum of squares of the Y deviations from their mean), we can calculate SSresidual as 56.125. The standard error of estimate for the equation is a measure of the average distance between the predicted Y values and the actual Y values. In this case, it is approximately 4.73. These values provide insights into the accuracy and precision of the regression equation in predicting Y based on X.

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9514 1404 393

Answer:

  1. domain and range are all real numbers

  2. the relation is linear

Step-by-step explanation:

When the graph of a function is a straight line, the relation is linear. (That's what linear means.)

A linear relation is of degree 1, so has odd degree. Any odd-degree polynomial function has a domain and range of "all real numbers."

Answer:

1. Domain : all the real numbers

Range = all the real numbers

yes, this relation represents a linear function. (linear functions are always a straight line when graphed.)

Answer:

option a

Step-by-step explanation:

in figure 1: 2n-1 so 2×1=2-1=1 so in figure 1 there is 1 block

in figure 2: 2-n-1= (2×2)-1=4-1=3 so there are 3 blocks this pattern continues

The relationship between w and s can be represented as s = 3w.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side

When 4 grams are added to the spring, the spring stretches 4 × 3 = 12 centimeters.

When 6 grams are added to the spring, the spring stretches 6 × 3 = 18 centimeters.

In this way, if w grams are added to the spring, the spring stretches w × 3 centimeters.

Let s represent the distance the spring is stretched.

s = 3w

Hence the required relationship is s = 3w.

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The number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.

We can solve this inequality by introducing an auxiliary variable x4, such that x1 + x2 + x3 + x4 = 11. Here, x1, x2, x3, and x4 are all nonnegative integers.

We can interpret this equation as follows: imagine we have 11 identical objects and we want to distribute them among four boxes (x1, x2, x3, and x4). Each box can contain any number of objects, including zero. The number of solutions to this equation will give us the number of nonnegative integer solutions to the original inequality.

We can use a technique known as stars and bars to count the number of solutions to this equation. Imagine we represent the 11 objects as stars: ***********.

We can then place three bars to divide the stars into four groups, each group representing one of the variables x1, x2, x3, and x4. For example, if we place the first bar after the first star, the second bar after the third star, and the third bar after the fifth star, we get the following arrangement:

| ** | * | ****

This arrangement corresponds to the solution x1=1, x2=2, x3=1, and x4=7. Notice that the number of stars to the left of the first bar gives the value of x1, the number of stars between the first and second bars gives the value of x2, and so on.

We can place the bars in any order, so we need to count the number of ways to arrange three bars among 14 positions (11 stars and 3 bars). This is equivalent to choosing 3 positions out of 14 to place the bars, which can be done in C(14,3) ways.

Therefore, the number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

So whenever you see alphabets in math, these are called variable. Like the word suggests, variables can have different values depending on the problem.

For the first problem, the variable k equals 10, and the question asks you when k=10, what does that make k+26. All you do is substitute the value of k with the given value of k=10, and you get 10 + 26 = 36.

This way you can solve the rest of them.

Ask me if you get confused and we can work on rest of them.

Answer:

Step-by-step explanation:

Q1

Q2

Q3

Q4

Q5

Q6

Answer:

\(\dfrac{31}{2}+\dfrac{27}{2}i\)

Step-by-step explanation:

The given complex number is:

\(z=\dfrac{(2+3i)(4-7i)(1+i)}{(1^2-i^2)}\)

Firstly we can solve (2+3i)(4-7i)(1+i)

= 2(8)+2(-7i)+4(3i)+3i(-7i²)× (1+i)

= (16-14i+12i-21i²i)× (1+i)

Since, i² = -1

= (16-14i+12i-21(-1)i)× (1+i)

= (16-14i+12i+21)× (1+i)

= (29-2i)(1+i)

= 31+27i

Denominator : (1-i²)

= (1-(-1))

= 2

\(\dfrac{(2+3i)(4-7i)(1+i)}{(1^2-i^2)}=\dfrac{31+27i}{2}\\\\=\dfrac{31}{2}+\dfrac{27}{2}i\)

Hence, the correct answer is \(\dfrac{31}{2}+\dfrac{27}{2}i\).

Answer:

82 spaces are filled.

Step-by-step explanation:

9•10=90..

90-8=82

A sandwich shop charges $20 for delivery of three turkey subs and $26 for delivery of four. There is no proportionality between the quantity of turkey subs delivered and the amount billed.

Given that,

A sandwich shop charges $20 for delivery of three turkey subs and $26 for delivery of four.

We have to find the relation ship between the quantity of turkey subs delivered and the amount billed.

The reciprocal of the ratio of subs to amount charges is

We get,

3/20 and 4/26

Since,  

3/20≠4/26

Therefore, There is no proportionality between the quantity of turkey subs delivered and the amount billed.

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Answer:

188

Step-by-step explanation:

88 + 6= 94

94 + 94 = 188

188 divided by 2 = 94

94 - 6 = 88

88 was how much Paula paid

The conversion 336g to m³ is impossible because they measure different units

From the question, we have the following parameters that can be used in our computation:

Convert 336g to m³

To convert a unit to another, the units must measure the same quantity

Take for instance:

Grams can be converted to kilograms because they both measure mass

Using the above as a guide, we have the following:

336g to m³  cannot be done because of the different quantities they represent

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Information is needed to evaluate the project's financial viability, considering factors such as the initial investment, expected cash flows, cost of capital, and project duration.

To calculate the year 1 operating cash flows (OCF), we need to subtract the year 1 costs from the year 1 revenues:

OCF = Year 1 Revenues - Year 1 Costs

OCF = $192,000 - $125,000

OCF = $67,000

To find the depreciation expense in year 3, we need to determine the depreciation method. The provided information is incomplete regarding the depreciation method, so we cannot calculate the depreciation expense in year 3 without knowing the specific method.

The change in Net Working Capital (NWC) in year 2 can be determined by multiplying the Net Working Capital percentage (given as a percentage of t+1 revenues) by the year 1 revenues and subtracting the result from the year 2 revenues:

Change in NWC = (Year 2 Revenues - Net Working Capital percentage * Year 1 Revenues) - Year 1 Revenues

Without the specific Net Working Capital percentage or Year 2 Revenues values, we cannot calculate the exact change in NWC in year 2.

The net cash flow from salvage (ATSV) is calculated by multiplying the Salvage Value percentage by the Initial Cost:

ATSV = Salvage Value percentage * Initial Cost

ATSV = 28% * $390,000

ATSV = $109,200

To calculate the project's NPV, we need the cash flows for each year, the cost of capital, and the project duration. Unfortunately, the information provided does not include the cash flows for each year, so we cannot calculate the project's NPV.

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The complete question is:

Below are your numerical inputs for the problem: 4 & Initial Cost (\$) & 390000 5 & Year 1 Revenues (\$) & 192000 6 & Year 1 Costs (\$) & 125000  7 & Inflation & 2.75% 8 & Project Duration (years) & 6 9 & Depreciation Method & 10 & Tax Rate & 11 & Net Working Capital (\% oft+1 Revenues) & MACRS 12 & Salvage Value (\$) & 28.00% 13 & Cost of Capital & 15.00% & 245000 How much are the year 1 operating cash flows (OCF)? How much is the depreciation expense in year 3 ? What is the change in Net Working Capital (NWC) in year 2? What is the net cash flow from salvage (aka, the after-tax salvage value, or ATSV)? What is the project's NPV? Would you recommend purchasing the ranch? Briefly explain.

Answer:

105

Step-by-step explanation:

Because the lines are parallel, we know that those angles have to add up to 180. so we just do

x+75=180

or 180-75=105

x+75°=180°

x=180°-75°

x=105°

or

180°-75° = 105°

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In a survey of adults who set themselves some fitness targets, 5% achieved all of them, and 15% achieved some of them. Another fitness survey questions 400 adults. There are 80 people who expect to achieve all of their targets.

Percentage:

In mathematics, a percentage is a number or a ratio that can be expressed as a fraction of 100. If we need to calculate a percentage of a number, we divide the number by a whole number and multiply by 100. So , percent means one hundredth and the word percent means every 100th. It is represented by the symbol "%".

Given that:

5% achieve all of them

15% achieve some of them

Total percentage = 5% + 15%

                              = 20%

there are 400 adults = 400× 20%

                                    = 80% target

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Answer:There are different ways to write an expression that has the same value as -y-4, depending on how we manipulate the terms using the properties of arithmetic. For example, some possible expressions are:

-(y+4), by factoring out a negative sign.

-4-y, by changing the order of the terms using the commutative property of addition.

(-1)(y+4), by multiplying by -1.

4-(-y)-8, by adding and subtracting 4.

Step-by-step explanation:

The probability of winning is 1/17, which can also be expressed as a decimal (approximately 0.059) or as a percentage (approximately 5.9%).

The odds on a bet represent the ratio of the probability of winning to the probability of losing. In this case, the odds are 16:1 against winning, which means that the probability of winning is 1 out of 16.

To express this probability as a fraction, we can use the formula:

Probability of winning = 1 / (odds + 1)

Plugging in the given odds, we get:

Probability of winning = 1 / (16 + 1)

Probability of winning = 1/17

In this case, the odds of 16:1 against winning correspond to a probability of 1/17, which represents the chance of winning the bet.

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If a test of a hypothesis has a type I error probability (alpha) of 0.01, it means that there is a 1% chance of rejecting the null hypothesis when it is actually true.

When conducting hypothesis testing, we are trying to make an inference about a population based on sample data. There are two types of errors that can occur:

Type I Error: This occurs when we reject the null hypothesis (H0) when it is actually true. In other words, we falsely conclude that there is a significant effect or relationship when there is none in the population. The probability of committing a Type I error is denoted as alpha (α) and is often set before conducting the test.

In this case, if the type I error probability (alpha) is 0.01, it means that we are willing to tolerate a 1% chance of incorrectly rejecting the null hypothesis when it is actually true. We set the significance level at 0.01, which represents the maximum acceptable level of making a Type I error.

Type II Error: This occurs when we fail to reject the null hypothesis (H0) when it is actually false. In other words, we fail to detect a significant effect or relationship when one exists in the population. The probability of committing a Type II error is denoted as beta (β).

It is important to strike a balance between Type I and Type II errors based on the context and consequences of the study. The choice of the significance level (alpha) reflects the trade-off between the risks of making Type I and Type II errors.

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The correct statement is: "If the null hypothesis is true, you reject it 1% of the time."

In hypothesis testing, the Type I error refers to rejecting the null hypothesis when it is actually true. The significance level, often denoted by α (alpha), determines the probability of making a Type I error.

A significance level of 0.01 means that there is a 1% chance of rejecting the null hypothesis when it is true. This signifies that even if the null hypothesis is correct, there is still a small probability (1%) of observing a result that is extreme enough to lead to the rejection of the null hypothesis.

- Type I error: Rejecting the null hypothesis when it is true.

- α (alpha): The probability of making a Type I error.

- Significance level of 0.01: There is a 1% chance of making a Type I error, or rejecting the null hypothesis when it is true.

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If a test of hypothesis has a Type I error probability (alpha) of 0.01. it means that If the null hypothesis is false, you don't reject it 1% of the time. if the null hypothesis is true, you reject it 1% of the time. if the null hypothesis is true, you don't reject it 1% of the time. if the null hypothesis is false, you reject it 1% of the time.

The first step in establishing a base pay structure is to develop pay grades by grouping together jobs of similar worth. The phase in a training system that focuses on measuring how well the training accomplished what its originators expected is evaluation.

When establishing a base pay structure, the first step is to develop pay grades. Pay grades involve grouping jobs of similar worth or value together. This helps in creating a systematic framework for assigning compensation levels to different job roles based on their relative importance and responsibilities. Therefore, option (a) is the correct answer.

In a training system, the phase that focuses on measuring how well the training accomplished its expected goals and outcomes is evaluation. This phase involves assessing the effectiveness and impact of the training program to determine if it met the intended objectives. Thus, option (c) - evaluation - is the correct choice.

Counting the number of insurance claims processed by a clerk each week is a measure of performance. It falls under performance-based criteria, which assesses an individual's performance based on observable behaviors, outputs, or results achieved. Therefore, option (b) - performance-based criteria - is the correct answer.

In summary, the first step in establishing a base pay structure is developing pay grades, the phase in a training system that focuses on measuring training effectiveness is evaluation, and counting the number of insurance claims processed is a measure of performance based on performance-based criteria.

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Answer:  3

Step-by-step explanation:

3/1 or 3

hope it helps...!!!

For example, according to the transitive property of congruence, angle A is congruent to angle C if A is congruent to angle B and angle B is congruent to angle C.

In the given question, we have to explain an example of transitive property of congruence.

The transitive property of congruence states that if two sets of lines, angles, or triangles are congruent with a third set, then the first set of lines, angles, or triangles is also congruent with the third set.

For example, according to the transitive property of congruence, angle A is congruent to angle C if A is congruent to angle B and angle B is congruent to angle C.

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The right triangle has a hypotenuse of 80in and its shortest leg is 48in.

You can make a sketch of the triangle to visualize the figure:

To determine the measure of the missing leg you can apply the Pythagorean theorem. This theorem states that the square of the hypothenuse (c) of a right triangle is equal to the sum of the squares of its legs (a and b) so that:

The missing side is the longers leg "b", to determine its length you have to write the expression above for b.

To do so, first, pass a² to the right side of the expression by applying the opposite operation to both sides of it, which means you have to subtract it:

Second, since we need to find the value of b, is to calculate the square root of b², so that the exponent is canceled, and, for the equality to be valid, any operation that is done to one side of the equation must be done to the other side, so you have to apply the square root to both sides of the equal sign:

Now that we have the formula to calculate b, what is left is to replace it with the known measures of the triangle c=80 and a=48

The measure of the other leg of the right triangle is 64in.

Answer:

I litteraly have the same problem and no clue how to do I

Step-by-step explanation:

Answer: Answer A is correct :)

Step-by-step explanation:

If two predictor values have a very high linear correlation coefficient, both should be included in finding the multiple regression equation.

Answer:

SAS

Step-by-step explanation:

We know that segment PR is congruent to segment SQ, because of the a line bisects the segment the segments are on. We also know that angle PRQ is congruent to angle SRQ, because of the reflexive property. Using the same property, QR is congruent too QR.

By knowing that, we can conclude that the two triangles are congruent because of SAS.

Given that, the total number of students in seventh and eighth grade combined is 584.

The number of students in seventh grade= 5/8 of the total number of students.

\(=\frac 5 8 \times 584=365\)

As 4/5 of the total seventh-grade students participated in the track-and-field-event.

So, the number of seventh-grade students participated

\(= \frac 4 5 \times 365=292\)

The number of students in the eighth grade 3/8 of the total number of students.

\(=\frac 3 8 \times 584=219\)

As 7/8 of the total eighth-grade students participated in the track-and-field-event.

So, the number of seventh-grade students participated

\(= \frac78 \times 219=191.625.\)

The number of students must be a counting number, but here, as per the given information, the number of seventh-grade students participated coming out a fractional number, so the given information is incorrect.

Although, as per the given data, the mathematical value of the total number of students participated from both the grade combined

=292+191.625

=483.625 (mathematically)

Again, in real life, the fractional value of the total number of students is not possible.

Answer:

Given that, the total number of students in seventh and eighth grade combined is 584.

Step-by-step explanation:

The probability that the student will get at least three questions correct is 0.1719

To solve this problem, we can use the binomial distribution formula, which gives the probability of getting exactly k successes in n independent Bernoulli trials, where each trial has a probability p of success:\(P(k successes) = (n choose k) p^k (1-p)^{n-k}\)

In this case, n = 10 (the number of questions), p = 0.5 (the probability of getting a correct answer by guessing), and we want to find the probability of getting at least three questions correct. This means we need to add up the probabilities of getting exactly 3, 4, 5, ..., 10 questions correct.

\(=P(at least 3 correct) = P(3 correct) + P(4 correct) + ... + P(10 correct)\)

\(= (10 choose 3) (0.5^3) (0.5^7 )+ (10 choose 4) (0.5^4) (0.5^6) + ... + (10 choose 10) (0.5^{10} )(0.5^0)\)

\(= 0.1719\)

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