9.2 less than 3 times a number is the same as 2114.What is the number?

Answer:

$0.76 per serving of pumpkin pie

Step-by-step explanation:

the total cost of the ingredients needed to prepare a pumpkin pie = $1.50 + ($2.59 / 6) + ($5.99 / 6) + $1.25 + ($3.79 / 2) = $6.075

if we cut 8 servings per pie, then the cost per serving = total cost of the pie / number of servings = $6.075 / 8 = $0.759375 ≈ $0.76 per serving of pumpkin pie

We want to find the cost of each slice of a pie given that we know the price of the ingredients that we use to make the whole pie. We will see that the cost of a single slice is $0.75.

First, we must get the cost of the whole pie. We have:

The total cost is then:

C = $1.50 + $0.43 + $0.89 + $1.25 + $1.90 = $5.97

Now we know the total cost of the pie, and it has 8 slices, then each slice costs: $5.97/8 = $0.75

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Answer: 12

Step-by-step explanation:

4 x 3 =12

The length of an arc swept out by an angle of θ radians on a circle with radius r is given by L = rθ.

So, in this case, the length of the arc swept out by 5 radians on a circle with radius 1 is L = 1 x 5 = 5.

Therefore, the answer is (d) 5 radians.

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The t-test has 15 degrees of freedom when testing the null hypothesis H₂ = 50.

To determine the degrees of freedom for the t-test, we need to use the formula:

Degrees of freedom = n - 1

In this case, the sample size is n = 16. Therefore, the degrees of freedom for the t-test would be:

Degrees of freedom = 16 - 1 = 15

So, the t-test has 15 degrees of freedom when testing the null hypothesis H₂ = 50.

The degrees of freedom in a t-test represent the number of independent pieces of information available for estimating the population parameters. In the case of a t-test, the degrees of freedom are determined by the sample size.

In this scenario, the sample size is given as n = 16. When conducting a t-test, we estimate the population parameters based on the sample data. However, since we are estimating the population mean from the sample mean, we lose one degree of freedom in the estimation process.

Therefore, the degrees of freedom for the t-test in this case is calculated as:

Degrees of freedom = n - 1 = 16 - 1 = 15

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Answer:

67

Step-by-step explanation:

Each time the number goes up by 7. After 9 moretimes 4 will increase by 63.

4+63=67.

The 10th term should be 67

The statement "Any first order linear autonomous ODE is an exponential model ODE, and all exponential model ODEs are first order linear autonomous ODEs" is false.

The statement is false.

A first order linear autonomous ODE has the form:

y' + p(x)y = q(x)

where p(x) and q(x) are continuous functions of x. This ODE can be solved using the integrating factor method, which involves multiplying both sides of the equation by an integrating factor, which is an exponential function. Thus, the solution to a first order linear autonomous ODE may involve an exponential function, but not necessarily.

On the other hand, an exponential model ODE has the form:

y' = ky

where k is a constant. This is a special case of a first order linear autonomous ODE where p(x) = -k and q(x) = 0. The general solution to this ODE is y(x) = Ce^(kx), where C is a constant. However, not all first order linear autonomous ODEs are of this form.

Therefore, the statement "Any first order linear autonomous ODE is an exponential model ODE, and all exponential model ODEs are first order linear autonomous ODEs" is false.

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Two reasons that multiple regression designs cannot completely establish causation are: 1) correlation does not imply causation, and 2) the presence of confounding variables.

1) Correlation does not imply causation: Multiple regression designs can help identify correlations between variables, but correlation alone does not prove causation. There could be other factors at play, or the observed relationship could be due to chance.

2) Presence of confounding variables: Confounding variables are variables that affect both the independent and dependent variables, leading to a spurious association. In multiple regression designs, it is possible that not all confounding variables are accounted for, which can lead to inaccurate conclusions about the causal relationship between variables.

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That means that each hour it drops about 0.0625 inches

Divide the decrease in water level by the length of the time interval.

decrease = 7/12 inches ≅ 0.583 inches

Time interval: From 11 pm to 8:20 am you have 9:20 hours = (9 + 20/60) hours ≅ 9.33 hours

So the water drops at a rate of about

0.583/9.33 inches/hour ≅ 0.0625 inches/hour

Therefore, each hour it drops about 0.0625 inches.

The rate constant, or the specific rate constant, is the proportionality constant in the equation that expresses the relationship between the rate of a chemical reaction and the concentrations of the reacting substances.The rate constant is a proportionality factor in the rate law of chemical kinetics that relates the molar concentration of reactants to reaction rate. It is also known as the reaction rate constant or reaction rate coefficient and is indicated in an equation by the letter k.

Rate constant is dependent on the temperature. For zero-order reaction, rate constant's unit is mol L - 1 s - 1 . For first-order reaction, rate constant's unit is . For second-order reaction, rate constant's unit is mol - 1 L s - 1 .

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With plan A and B John will save 2800 and 2000 $ respectively.

Savings are the funds left over after subtracting a person's consumer spending from their disposable income during a certain time period. After all expenses and responsibilities have been met, savings signifies a net excess of funds for a person or household.

plan A formula is y = 800 + (200 * x)

plan B formula is y = 1500 * 15% * x

when x = 10, you get:

plan A = 2800

plan B = 2000

plan A has 800 dollars more than plan B.

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The statistical technique used to estimate future values by successive observations of a variable at regular intervals of time that suggest patterns is called trend analysis.

Trend analysis is a statistical technique that helps identify patterns and tendencies in a variable over time. It involves analyzing historical data collected at regular intervals to identify a consistent upward or downward movement in the variable.

By examining the sequential observations of the variable, trend analysis aims to identify the underlying trend or direction in which the variable is moving. This technique is particularly useful when there is a time-dependent relationship in the data, and past observations can provide insights into future values.

Trend analysis typically involves plotting the data points on a time series chart and visually inspecting the pattern. It helps in identifying trends such as upward or downward trends, seasonality, or cyclic patterns. Additionally, mathematical models and statistical methods can be applied to quantify and forecast the future values based on the observed trend.

This statistical technique is widely used in various fields, including finance, economics, marketing, and environmental sciences. It assists in making informed decisions and predictions by understanding the historical behavior of a variable and extrapolating it into the future.

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Answer:

-0.5

Step-by-step explanation:

y=-3x+2.5

y=-3 (1) +2.5

y=-3+2.5

y=-0.5

The solution is y = -0.5

The value of y from the equation when x = 1 is y = -0.5

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

y = -3x + 2.5   be equation (1)

On simplifying the equation , we get

when x = 1

Substitute the value of x in the equation , we get

y = -3 ( 1 ) + 2.5

y = -3 + 2.5

y = -0.5

Therefore , the value of y = -0.5

Hence , the value of the equation is y = -0.5

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The area of the triangle in the image is 10 square units, thus, option C is the correct one.

For a triangle of height H and a base B, the area is given by:

A = H*B/2.

In the image we can see that the base of the triangle goes from (0, 0) to (5, 0), then the length of the base is 5 units.

While the height goes from (0, 0) to (0, 4), so the height is 4 units.

Then the area will be:

A = (4 units)*(5 units)/2 = (20 square units)/2 = 10 square units.

The area is 10 square units.

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The use of this approximation is justified when both m and n are large enough, typically greater than 30, where the CLT holds reasonably well and the sample means can be considered approximately normally distributed.

(a) To find a confidence interval for μ1 - μ2 with a coverage probability of 1 - α, we can use the following approach:

1. Given that σ1 and σ2 are known, we can use the properties of the normal distribution.

2. The difference of two independent normal random variables is also normally distributed. Therefore, the distribution of (xbar) -  ybar)) follows a normal distribution.

3. The mean of (xbar) -  ybar)) is μ1 - μ2, and the variance is σ1^2/m + σ2^2/n, where m is the sample size of X observations and n is the sample size of Y observations.

4. To construct the confidence interval, we need to find the critical values zα/2 that correspond to the desired confidence level (1 - α).

5. The confidence interval can be calculated as:

  (xbar) -  ybar)) ± zα/2 * sqrt(σ1^2/m + σ2^2/n)

  Here, xbar) represents the sample mean of X observations, ybar) represents the sample mean of Y observations, and zα/2 is the critical value from the standard normal distribution.

(b) When both m and n are large, we can apply the Central Limit Theorem (CLT), which states that the distribution of the sample mean approaches a normal distribution as the sample size increases.

Based on the CLT, the sample mean xbar) of X observations and the sample mean ybar) of Y observations are approximately normally distributed.

Therefore, we can approximate the confidence bounds for μ1 - μ2 as:

  (xbar) -  ybar)) ± zα/2 * sqrt(SX^2/m + SY^2/n)

  Here, SX^2 represents the sample variance of X observations, SY^2 represents the sample  of Y observations, and zα/2 is the critical value from the standard normal distribution.

Note that in this approximation, we replace the population variances σ1^2 and σ2^2 with the sample variances SX^2 and SY^2, respectively.

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Answer:

The coordinates of the image B' is;

Explanation:

Given the figure in the attached image.

The coordinate of the Preimage B is;

Then rotating it 90 degrees in the counter-clockwise direction;

Applying the transformation to the given coordinate, we have;

Therefore, the coordinates of the image B' is;

Answer:

11

Step-by-step explanation:

lets suppose the number is x

twice the number would be 2x and 15 more than that will be

2x + 15

and this is equal to 37

2x + 15 = 37

2x = 37 - 15

2x = 22

x = 22/2

x = 11

Answer:

1482

Step-by-step explanation:

2n+5

1) when n= 1

2(1)+5

= 7

2) when n=12

2(12)+5

=29

3) when n=29

2(29)+5

=63

4) when n=36

2(36)+5

=77

5) when n=216

2(216)+5

=437

6) when n=433

2(432)+5

=869

therefore, 7+29+63+77+437+869 = 1482

Answer:

The 32 electricians are expected to finish the job in 27 days.

Step-by-step explanation:

In this case we can apply a rule of three to calculate the time it'll take for the 32 electricians to finish the job. This is done below:

24 electricians -> 36 days

32 electricians -> x days

We have to be careful here, since the variables are inversely proportional, since if there are more electricians working on the same job, we expect the job to be finished in fewer days, therefore we need to invert one of the fractions as shown below:

\(\frac{24}{32} = \frac{x}{36}\\32*x = 36*24\\x = \frac{864}{32}\\x = 27\)

The 32 electricians are expected to finish the job in 27 days.

Answer:

27

Step-by-step explanation:

Critical probability is the essentially cut-off value. The critical probability when the confidence level of 58% is 0.79.

Critical probability is the essentially cut-off value that defines the region where the test statistic is unlikely to lie.

As it is given that the confidence level is 58%. therefore, in order to calculate the critical probability, we need to calculate the margin of error within a set of data, and  it is given by the formula

\(\rm Critical\ Probability, (P*) = 1-\dfrac{\alpha }{2}\)

where the value of the α is expressed as,

\(\alpha= 1 -\dfrac{\rm Confidence\ interval}{100}\)

Now, as the confidence interval is given to us, therefore, the value of the alpha can be written as,

\(\alpha= 1 -\dfrac{\rm 58\%}{100} = 0.42\)

Further, the critical probability, assuming a confidence level of 58% is,

\(\rm Critical\ Probability, (P*) = 1-\dfrac{\alpha }{2}\\\\\rm Critical\ Probability, (P*) = 1-\dfrac{0.42}{2} = 0.79\)

Hence, the critical probability is 0.79.

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Answer:

x = 3

Step-by-step explanation:

5(x-1)+3=13

Distribute the 5

(5x - 5) + 3 = 13

5x - 5 + 3 = 13

x = 3

Answer:

x = 3

Step-by-step explanation:

5(x-1)+3=13

5(x - 1) + 3 = 13

5(x - 1) = 10

5x - 5 = 10

5x = 15

x = 3

The angular velocity of link CD when angle BAD = 60° is 21.16 rad/s.

The given values are:

AD = 150 mm

AB = 40 mm

CD = 80 mm

The crank AB rotates at 120 r.p.m. clockwise.

BC and AD are of equal length.

To find:

The angular velocity of link CD when angle BAD = 60°.

From the given data, we have to first find the value of angle BCD.

Angle BCD can be calculated as follows:

AB = 40 mm

BC = AD

= 150 mm

In ΔABC,

By using Cosine rule;

AC² = AB² + BC² - 2 × AB × BC × Cos ∠ABC∴ AC² = (40)² + (150)² - 2 × 40 × 150 × Cos 180°

∴ AC = 160.6 mm

In ΔBCD,

By using Cosine rule;

BD² = BC² + CD² - 2 × BC × CD × Cos ∠BCD

∴ BD² = (150)² + (80)² - 2 × 150 × 80 × Cos ∠BCD

In ΔABD,By using Cosine rule;

BD² = AB² + AD² - 2 × AB × AD × Cos ∠BAD

∴ BD² = (40)² + (150)² - 2 × 40 × 150 × Cos 60°

∴ BD = 184.06 mm

In ΔABD,By using Sine rule;

AB / Sin ∠BAD = BD / Sin ∠ABD

∴ Sin ∠ABD = BD × Sin ∠BAD / AB

∴ ∠ABD = Sin⁻¹ [BD × Sin ∠BAD / AB]

∴ ∠ABD = Sin⁻¹ [184.06 × Sin 60° / 40]

∴ ∠ABD = 87.2°∠ACD = ∠ABD - ∠ACB

∴ ∠ACD = 87.2° - 180°

∴ ∠ACD = - 92.8°∠BCD

= 180° - ∠ACD

∴ ∠BCD = 180° - (- 92.8°)

∴ ∠BCD = 272.8°

As we know that for four-bar mechanism, we have a formula for finding the angular velocity of link CD.

ωCD / Sin ∠BCD = ωAB / Sin ∠BADωCD / Sin 272.8°

= ωAB / Sin 60°

Substituting the values, ωCD / Sin 272.8° = ωAB / Sin 60°ωCD

= ωAB × Sin 272.8° / Sin 60°

But, ωAB = 2 × π × N / 60

= 2 × π × 120 / 60

= 4 × π rad/s

∴ ωCD = 4 × π × Sin 272.8° / Sin 60°ωCD

= 21.16 rad/s

Therefore, the angular velocity of link CD when angle BAD = 60° is 21.16 rad/s.

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Answer:

domain = 0,1,2,3

range= 5,7,15,44

Answer:

\(b=\frac{r}{9} +a\)

Step-by-step explanation:

To solve this problem, we have to isolate b. The steps are shown below:

Given - \(9(b-a)=r\)

Divide both sides by 9 - \(\frac{9(b-a)}{9}=\frac{r}{9}\)  → \((b-a)=\frac{r}{9}\)

Add a to both sides - \((b-a+a)=\frac{r}{9}+a\)  → \(b=\frac{r}{9} +a\)

So after doing these steps, we are left with our answer of  \(b=\frac{r}{9} +a\).

\(b=\dfrac{r}{9}+a\)

Main Concepts:

Concept 1. Solving for a variable

Concept 2. Undoing a multi-step equation

Concept 1. Solving for a variable

To solve any equation ever in mathematics, there are two main steps:

In this case, the variable already appears exactly once, so we can skip ahead to Step 2.

Concept 2. Undoing a multi-step equation

To "Isolate the variable", one must undo the things that are done to it.

To undo something, things must be undone in the reverse order in which they are done.

Looking at the equation, "b" appears on the left side of the equation.  Focusing on the left side, if everything were a number and we were trying to simplify it, Order of Operations would require us to take the "b" and do the following:

1. subtract  by "a" in the parentheses

2. then multiply by 9

To undo these things, we'll need to use the opposite operation of what would have been done in the first place.

To undo the steps above, we undo them in reverse order, so

1. Undo multiplication by 9

2. Then undo the subtraction by "a".

\(9(b-a)=r\)

To undo the multiplication, divide both sides by 9

\(\dfrac{9(b-a)}{9}=\dfrac{r}{9}\)

simplifying the left side gives

\(b-a=\dfrac{r}{9}\)

To undo the subtraction by "a", add "a" to both sides

\(b-a+a=\dfrac{r}{9}+a\)

simplifying the left side gives

\(b=\dfrac{r}{9}+a\)

Gabe is lacking in Equity model of job satisfaction.

Equity theory in job satisfaction is outlined by John Stacey Adams, which states that a continuous evaluation of the job in the "give and take" policy is to be involved between employee and employer in a job.

The equity models that there is a relationship between the job satisfaction and the output of the employer which results from the fair balance in the inputs (support by colleagues, hard work, etc.) and outputs (praise, financial compensation, etc.) of the employer.

So a certain sense of fairness must be included to boost an employer's motivation.

If the imbalance increases, then the productivity and strength of the job decreases.

Here, Gabe is not getting a fair salary compared to those with the same job description and experience level.

He has also feeling that he is contributing more inputs than his colleagues.

So this is an equity model of job satisfaction.

Hence the model is equity.

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Answer:

Mr. Ramirez purchased 20 concert tickets for a total of $225. The concert tickets cost $15 for adults and $10 for children under the age of 12. Part A: Write a system of equations to represent the given scenario. Use the variable "a" for adults and "c" for children. 1.

Step-by-step explanation:

Hope this helps

The remainder from the division of p(x) = (x + √3)^16 by q(x) = x^2 + 1 is a polynomial of degree less than 2.

We perform polynomial long division by dividing (x + √3)^16 by x^2 + 1. The first step is to divide the leading term of the dividend by the leading term of the divisor, which gives us (x + √3)^16 / x^2. We obtain x^14√3 + x^12(3√3) + x^10(9√3) + ... + x^2(216√3) + x^0(648√3).

Next, we multiply the divisor, x^2 + 1, by x^14√3 and subtract it from the dividend. This cancels out the x^14√3 term. We repeat this process for each subsequent term, multiplying the divisor by the highest power of x in the dividend and subtracting it from the dividend.

Eventually, after all the terms have been canceled, we are left with a polynomial that does not contain x^2 or any higher powers of x. This remaining polynomial is the remainder. Since the degree of the divisor is 2, the remainder will have a degree less than 2.

Therefore, the remainder from the division of p(x) = (x + √3)^16 by q(x) = x^2 + 1 is a polynomial of degree less than 2.

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Answer:

74 °

Step-by-step explanation:

the sum of every angle from a triangle is 180

so to find b is add 80 with 26 which is 106

then subtract 180 with 106

the final answer is 74

Answer:

sorry, not for certain

Step-by-step explanation:

id love to help tho... ill comment this if not saw...

Answer:

a = 30°

b = 11°

Step-by-step explanation:

JK = 360 - 110 - 130 - 54 = 66°

Inscribed angles = 1/2 their arc

∠K = 1/2(130 + 54) = 92°

∠J = 1/2(110 + 130) = 120°

∠M = 1/2(66 + 110) = 88°

8b = 88°

b = 11°

∠L = 1/2(54 + 66) = 60°

2a = 60°

a = 30°

Answer:

I suggest that you use Socratic to solve this.

Step-by-step explanation:

Answer:

\(x=\frac{-3}{2}\)

Step-by-step explanation:

\(2 + 4 ( x + 1 ) = 0\)

\(2 + 4x + 4 = 0\)

\(6 + 4x = 0\)

\(4x = -6\)

\(x = \frac{-3}{2}\)