Regression Analysis: Write formula from the following summary statistics. Make predictions of yhat. 1. SSxy = 151 SSxx = 28 Σx = 30 Σv= 420 n=6 a) Write equation - use 3 decimals b) Using the equation, solve for x = 50 2. SSxy = 66.233 SSxx = 64.817 x = 46.5 y = 45.5 n=15 a) Write equation-use 3 decimals b) Using the equation, solve for x = 2 3. a) SSE = 126 SST = 490 Solve for r^2
b) Write the definition of the Coefficient of Determination.

Answer:

SSS

Step-by-step explanation:

if two of the sets of angles show they are congruent then the third set of angles must be congruent too. There are no sides showing they are congruent either.

Answer:

Hello

Step-by-step explanation:

Al' Kashi theorem:

189²=123²+215²-2*123²215²cos(P)

cos(P)=(123²+215²-189²)/(2*123*215)=0.48464...

P=61.01062...°≈61.01°

Answer:

8x^2y

Step-by-step explanation:

Subtract 2x^2y from 10x^2y

Step-by-step explanation:

the difference of 10x²y and 2x²y

Answer:

Sorry I took so long, I hope I helped though

3) 2.428

5) 5.414

6) 8.29

10) 3.34

11) 42.35

12) 24.276

14) 6.777

17) 17

18) 19

19) 50.6

20) 17

26) basically add them all, I got the answer 1

27) 0.29+0.24 is 0.53

28) your answer is right, one fourth of 1 is .25, so the answer is 0.15+0.08+0.02

95% confidence that the sample mean for the bio/total carbon ratio of blended fuels will fall within the interval is 0.9390 ± 0.002696, which is (0.9364, 0.9416).

We can use the formula for the margin of error for a 95% confidence interval for the population mean, given by:

the margin of error = 1.96 × standard deviation / √(sample size)

where the standard deviation of the sampling distribution of the sample mean is given by:

standard deviation = population standard deviation / sqrt(sample size)

Substituting the given values, we have:

standard deviation = 0.0080 / √(34) = 0.001375

margin of error = 1.96 × 0.001375 = 0.002696

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The question is -

Concerns about climate change and CO2 reduction have initiated the commercial production of blends of biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). Random samples of 34 blended fuels are tested in a lab to ascertain the bio/total carbon ratio.

If the true mean is .9390 with a standard deviation of .0080, within what interval will 95 percent of the sample mean to fall? (Round your answers to 4 decimal places.)

What is Compound Interest rate?

Compound interest is interest on interest. This is the addition of interest to the principal amount of the loan or deposit. It is created by reinvesting interest instead of paying it out. In the next period, the principal plus the previously accrued interest accrues interest.

Alice invests some money at an annually compounded interest rate of r%. Bob invests the same amount at a simple interest rate of s%. If their investsments are worth the same after 10 years, then which of their investments is worth more after 11 years?

ChatGPT

To compare the worth of Alice's and Bob's investments after 11 years, we need to consider the formulas for compound interest and simple interest.

Compound Interest Formula:

A = P(1 + r/100)^n

Simple Interest Formula:

A = P(1 + s/100 * n)

Where:

A is the final amount

P is the principal amount (initial investment)

r is the annual compound interest rate

s is the annual simple interest rate

n is the number of years

Given that their investments are worth the same after 10 years, we can equate the final amounts for Alice and Bob:

For Alice:

A_Alice = P(1 + r/100)^10

For Bob:

A_Bob = P(1 + s/100 * 10)

To compare the worth of their investments after 11 years, we need to calculate the final amounts for Alice and Bob after 11 years:

For Alice:

A_Alice_11 = P(1 + r/100)^11

For Bob:

A_Bob_11 = P(1 + s/100 * 11)

To determine which investment is worth more after 11 years, we need to compare A_Alice_11 and A_Bob_11. However, without knowing the specific values of r and s, we cannot determine which investment is worth more after 11 years. The comparison depends on the specific interest rates chosen by Alice and Bob.

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Answer:

C. 5, because I-5I =5

Have a beautiful day!

The equation that relates M to R is M = 13 - R

From the question, we have the following parameters:

The total number of new magazines is the sum of the number of magazines read and the number of magazines left

This is represented as

Total number of new magazines = Number of magazines read + Number of magazines left

Substitute the known values in the above equation

13 = R +M

Make M the subject

M = 13 - R

Hence, the equation is M = 13 - R

See attachment for the graph

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So the slope of the scenario is $28 per hour, which indicates that the expense of the tour increases by $28 for every extra hour spent on it.

The slope of a line indicates its steepness. Slope is computed mathematically as "rise over run" (change in y divided by change in x). The slope-intercept form of an equation occurs when the equation of a line is stated in the form y = mx + b. The slope of the line is given by m. And b is the value of b in the y-intercept point (0, b). For example, the slope of the equation y = 3x - 7 is 3, while the y-intercept is (0, 7).

Here,

In this situation, the slope represents the rate of change in the cost of the tour with respect to the time spent on the tour. The slope of the situation can be calculated as the change in cost divided by the change in time.

Since the one-time fee is a fixed cost, it does not change with respect to the time spent on the tour. Therefore, the slope can be calculated as the rate of change in the cost due to the hourly fee of $28.

The slope can be represented as:

slope = Δcost/Δtime = $28/hour

So, the slope of the situation is $28 per hour, which means that for every additional hour spent on the tour, the cost of the tour increases by $28.

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Answer:

\(23\)

Step-by-step explanation:

\(g+\frac{h}{7}\)

First, divide 36 by 7:

Add 14 and 9:

________________________

Answer:8

Step-by-step explanation:

no can do

Substitute \(x=e^t\). By the chain rule,

\(\dfrac{dy}{dx} = \dfrac{dy}{dt}\cdot\dfrac{dt}{dx}\)

Now \(t=\ln(x)\implies\frac{dt}{dx}=\frac1x\), so

\(\dfrac{dy}{dx} = \dfrac1x \dfrac{dy}{dt} \\\\ ~~~~~~~~ \iff \dfrac{dy}{dt} = x\dfrac{dy}{dx}\)

Differentiate both sides again to recover the second and third derivatives.

\(\dfrac{d^2y}{dx^2} = -\dfrac1{x^2}\dfrac{dy}{dt} + \dfrac1x \dfrac{d\frac{dy}{dt}}{dx} \\\\ ~~~~~~~~ = -\dfrac1{x^2}\dfrac{dy}{dt} + \dfrac1x \left(\dfrac{d\frac{dy}{dt}}{dt}\cdot\dfrac{dt}{dx}\right) \\\\ ~~~~~~~~ = -\dfrac1{x^2} \dfrac{dy}{dt} + \dfrac1{x^2}\dfrac{d^2y}{dt^2} \\\\ ~~~~~~~~ \iff \dfrac{d^2y}{dt^2} - \dfrac{dy}{dt} = x^2 \dfrac{d^2y}{dx^2}\)

\(\dfrac{d^3y}{dx^3} = \dfrac2{x^3}\dfrac{dy}{dt} - \dfrac1{x^2}\dfrac{d\frac{dy}{dt}}{dx} - \dfrac2{x^3} \dfrac{d^2y}{dt^2} + \dfrac1{x^2}\dfrac{d\frac{d^2y}{dt^2}}{dx} \\\\ ~~~~~~~~ = \dfrac2{x^3} \dfrac{dy}{dt} - \dfrac1{x^2}\left(\dfrac{d\frac{dy}{dt}}{dt}\cdot\dfrac{dt}{dx}\right) - \dfrac2{x^3} \dfrac{d^2y}{dt^2} + \dfrac1{x^2}\left(\dfrac{d\frac{d^2y}{dt^2}}{dt}\cdot\dfrac{dt}{dx}\right) \\\\ ~~~~~~~~ = \dfrac2{x^3} \dfrac{dy}{dt} - \dfrac1{x^3} \dfrac{d^2y}{dt^2} - \dfrac2{x^3} \dfrac{d^2y}{dt^2} + \dfrac1{x^3}\dfrac{d^3y}{dt^3} \\\\ ~~~~~~~~ \iff \dfrac{d^3y}{dt^2} - 3 \dfrac{d^2y}{dt^2} + 2 \dfrac{dy}{dt} = x^3 \dfrac{d^3y}{dx^3}\)

The ODE then transforms to a linear one,

\(3\left(\dfrac{d^3y}{dt^2} - 3 \dfrac{d^2y}{dt^2} + 2 \dfrac{dy}{dt}\right) + 28\left(\dfrac{d^2y}{dt^2} - \dfrac{dy}{dt}\right) + 55\dfrac{dy}{dt} + 9 y = 0\)

or using Lagrange's prime notation,

\(3(y''' - 3y'' + 2y') + 28(y'' - y') + 55y' + 9y = 0\)

\(3y''' + 19y'' + 33y' + 9y = 0\)

The characteristic equation is

\(3r^3 + 19r^2 + 33r + 9r = (r + 3)^2 \left(r + \dfrac13\right) = 0\)

with roots at \(r=-3\) and \(r=-\frac13\), so the general solution is

\(y(t) = C_1 e^{-1/3\,t} + C_2 e^{-3t} + C_3 t e^{-3t}\)

Back in terms of \(x\), we get

\(\boxed{y(x) = C_1 x^{-1/3} + C_2 x^{-3} + C_3 x^{-3}\ln(x)}\)

Answer:

a

Step-by-step explanation:

Answer:

4(3.30)+ 6(1.25)

Step-by-step explanation:

because you would multiply 4 and 3.30 and 6 ×1.25 :)

Answer:

Sorry, it's gonna be 0.97, and you just add 0.12 to 0.25 7 times. This is the right answer.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

8 hours were spent in CPR training and 16 hours were spent in first aid training so the ratio of hours of CPR to hours of first aid training is 8: 16.

(a) The values of x that satisfy y = -√2/2 in the interval [0, 4π] are: x = π/4, 3π/4, 5π/4, 7π/4, 9π/4, 11π/4, 13π/4, 15π/4.

(b) All x-values except those listed in part (a) satisfy y > -√2/2 in the interval [0, 4π].

(c) All x-values except those listed in part (a) satisfy y < -√2/2 in the interval [0, 4π].

To find the values of x that satisfy the given conditions, we need to examine the graph of the equation y = sin(x) on the interval [0, 4π].

(a) For y = -√2/2:

Looking at the unit circle or the graph of the sine function, we can see that y = -√2/2 corresponds to two points in each period: -π/4 and -3π/4.

In the interval [0, 4π], we have four periods of the sine function, so we need to consider the following values of x:

x₁ = π/4, x₂ = 3π/4, x₃ = 5π/4, x₄ = 7π/4, x₅ = 9π/4, x₆ = 11π/4, x₇ = 13π/4, x₈ = 15π/4.

Therefore, the values of x that satisfy y = -√2/2 in the interval [0, 4π] are:

x = π/4, 3π/4, 5π/4, 7π/4, 9π/4, 11π/4, 13π/4, 15π/4.

(b) For y > -√2/2:

Since -√2/2 is the minimum value of the sine function, any value of x that produces a y-value greater than -√2/2 will satisfy the condition.

In the interval [0, 4π], all x-values except those listed in part (a) will satisfy y > -√2/2.

(c) For y < -√2:

Again, since -√2/2 is the minimum value of the sine function, any value of x that produces a y-value less than -√2/2 will satisfy the condition.

In the interval [0, 4π], all x-values except those listed in part (a) will satisfy y < -√2/2.

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Answer:

perfect square therefore rational

non perfect square therefore irrational

cuberoot

5

Step-by-step explanation:

the topic is about perfect squares and rationality of numbers

Since μ≥0, if the calculated μ_MLE is negative, set the MLE to 0 as the final answer: μ_MLE = max(0, Σ(xi) / n).

Based on the given information, we have a sample (x1, ..., xn) from a normal distribution N(μ, 1) with an unknown mean μ≥0 and a known variance of 1. To determine the Maximum Likelihood Estimator (MLE) of μ, we follow these steps:
1. Write down the likelihood function, which is the product of the probability density functions (PDF) for the normal distribution: L(μ) = ∏[1/(√(2π)) * exp(-(xi - μ)² / 2)]
2. Take the natural logarithm of the likelihood function to get the log-likelihood function: log L(μ) = Σ[-(xi - μ)² / 2 - log(√(2π))]
3. Differentiate the log-likelihood function with respect to μ and set the result to zero to find the maximum: d(log L(μ))/dμ = Σ[2(xi - μ)] = 0
4. Solve for μ: μ_MLE = Σ(xi) / n
The MLE of μ is the sample mean, which is the sum of the xi values divided by the sample size n. However, since μ≥0, if the calculated μ_MLE is negative, set the MLE to 0 as the final answer: μ_MLE = max(0, Σ(xi) / n)

To determine the maximum likelihood estimator (MLE) of μ in this scenario, we need to first calculate the likelihood function. Since (x1, . . . , xn) is a sample from an n(μ, 1) distribution, the likelihood function can be expressed as:
L(μ|x1, . . . , xn) = (2π)^(-n/2) exp(-(1/2)Σ(xi - μ)^2)
To find the MLE of μ, we need to maximize this likelihood function with respect to μ. To do so, we take the derivative of the likelihood function with respect to μ and set it equal to zero:
d/dμ L(μ|x1, . . . , xn) = Σ(xi - μ) = 0
Solving for μ, we get:
μ = (1/n)Σxi
Therefore, the MLE of μ in this scenario is the sample mean, (1/n)Σxi. Note that since we do not know the true value of μ, we cannot substitute it into the likelihood function to obtain a numerical value for the maximum likelihood. Rather, we can only determine the MLE in terms of the sample and the distribution.

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The volume of the rectangular bird feeder is 300 in³.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length

Given that;

Plug the given values into the above formula and solve for the volume.

V = w × h × l

V = 5 in × 12 in × 5 in

V = 300 in³

Therefore, the volume of the prism is 300 cubic inch.

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Answer:

The radius of the base of the cylinder is half of its diameter, so the radius is:

r = 18 cm / 2 = 9 cm

The height of the cylinder is 2.5 times the radius:

h = 2.5r = 2.5(9 cm) = 22.5 cm

The volume of a cylinder is given by the formula:

V = πr^2h

Substituting the values we have found, we get:

V = π(9 cm)^2(22.5 cm)

V = π(81 cm^2)(22.5 cm)

V = 1822.5π cm^3

So the volume of the cylinder is approximately 5713.77 cubic centimeters, or 5713.77 cm^3.

Step-by-step explanation:

18 triangles area unit required to compose a vicinity that's one square meters.

A square with a locality of one square metre is rotten into nine identical little squares. every little sq. is rotten into 2 identical triangles.

1 square metre is rotten into nine identical little squares.

So there area unit nine little squares in one square metre.Each little sq. is rotten into 2 identical triangles therefore nine little squares is rotten into 9(2) = eighteen identical triangles

Hence, one square metre is rotten into eighteen identical triangles.

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Answer:

Thus: a7=-1

Step-by-step explanation:

Arithmetic Sequences

The arithmetic sequences are identified because each term is obtained by adding or subtracting a fixed number to the previous term.

The equation to calculate the nth term of an arithmetic sequence is:

\(a_n=a_1+(n-1)r\)

We know: a12=29, a16=53, thus

\(a_1+(12-1)r=29\)

\(a_1+(16-1)r=53\)

Simplifying:

\(a_1+11r=29\)

\(a_1+15r=53\)

Subtracting both equations:

\(4r=53-29=24\)

Solving:

\(r=24/4\)

r=6

The 7th term can be found as 5 terms before the 12nd:

\(a_7=a_{12}-5r\)

\(a_7=29-5*6=29-30=-1\)

Thus: a7=-1

Using the Pythagorean Theorem, it is found that the base of the pole should be set 10 feet from the end of the wire.

The Pythagorean Theorem relates the length of the legs \(l_1\) and \(l_2\) of a right triangle with the length of the hypotenuse h, according to the following equation:

\(h^2 = l_1^2 + l_2^2\)

In this problem, the distance is \(l_2\), while the other measures are \(l_1 = 24, h = 26\), hence:

\(24^2 + l_2^2 = 26^2\)

\(l_2 = \sqrt{26^2 - 24^2}\)

\(l_2 = 10\)

The base of the pole should be set 10 feet from the end of the wire.

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Answer:

9 cm^2

Step-by-step explanation:

Area of a square = a^2, where a is the length of a side

Area = 3^2 = 3*3 = 9 cm^2

The mean, median, mode and range by adding the data point and removing the data point are found.

Consider a data set which shows the ages of children in a park.

4, 5, 5, 6, 7, 7, 9

Mean = (4 + 5 + 5 + 6 + 7 + 7 + 9) / 7 = 6.143

Median = 6

Mode = 5 and 7

Range = 9 - 4 = 5

Part C :

Consider the data set by adding a data value.

4, 5, 5, 6, 6, 7, 7, 9

Mean = 6.125

Median = (6 + 6) / 2 = 6

Mode = 5, 6, 7

Range = 9 - 4 = 5

Part D :

Consider the data set by removing a data value.

4, 5, 5, 6, 7, 9

Mean = 6

Median = (5 + 6) / 2 = 5.5

Mode = 5

Range = 5

Hence the age is added and removed and thus found the median, mean, mode and range.

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Among all the topics of mathematics , The topic of probability and statistics fascinates me the most.

As contrast to methods for gathering statistical data, mathematical statistics is the application of probability theory, a branch of mathematics, to statistics. The gathering, characterization, analysis, and drawing of inferences from quantitative data are all tasks that fall under the purview of statistics, a subfield of applied mathematics. Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Probability and statistics fascinates me the most in mathematics.

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Answer:

62 degrees

Step-by-step explanation:

the total angle of a straight line like this hypotenuse would be 180. So it's 180-118=62

Explanation:

A markup of 45% means we involve the multiplier 1.45

100% + 45% = 1.00 + 0.45 = 1.45

The selling price is 1.45*45 = 65.25

This is the price before tax.

Given:

The equation is:

\(\sqrt{x+7}+5=x\)

To find:

Whether \(x=2\) and \(x=9\) both are solutions or one/both of them extraneous solutions.

Solution:

We have,

\(\sqrt{x+7}+5=x\)

Subtract 5 from both sides.

\(\sqrt{x+7}=x-5\)

Taking square on both sides, we get

\(x+7=(x-5)^2\)

\(x+7=x^2-10x+25\)

\(0=x^2-10x+25-x-7\)

\(0=x^2-11x+18\)

Splitting the middle term, we get

\(x^2-2x-9x+18=0\)

\(x(x-2)-9(x-2)=0\)

\((x-2)(x-9)=0\)

\(x=2,9\)

Now, substitute \(x=2\) in the given equation.

\(\sqrt{2+7}+5=2\)

\(\sqrt{9}+5=2\)

\(3+5=2\)

\(8=2\)

This statement is false because \(8\neq 2\). So, 2 is an extraneous solution.

Substitute \(x=9\) in the given equation.

\(\sqrt{9+7}+5=9\)

\(\sqrt{16}+5=9\)

\(4+5=9\)

\(9=9\)

This statement is true. So, 9 is a solution of given equation.

Therefore, 2 is an extraneous solution and 9 is a solution of given equation.