Which of the following has 2 as a root a x2 4x 5 0 B x2 3x 12 0 C 2x2 7x 6 0 D 3x2 6x 2 0?

Approximately the correlation coefficient of the scatter plot below: .: mr. O +1 O +0.5 O -0.9 O +0.2 is +1.

As per the given scatter plot below: .: Mr. O +1 +0.5 -0.9 +0.2, the approximate correlation coefficient can be calculated as follows:

The correlation coefficient is the measure of the strength and direction of the linear relationship between two quantitative variables. It takes values between -1 and 1. If the value is negative, it indicates that as one variable increases, the other decreases, and if the value is positive, it indicates that as one variable increases, the other also increases.

Here, we can see that the scatter plot has a roughly linear relationship with a positive slope. Therefore, the approximate correlation coefficient of the scatter plot below is +1.

The correlation coefficient is +1.

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Time taken by Matilda on each project is \(5\frac{7}{12}\) hours.

According to the question we have been given that,

Total time taken by Matilda to complete the consulting projects = \(16\frac{3}{4}\) hours

First we will convert it into simple fraction which is

         \(16\frac{3}{4} = \frac{67}{4} \\\) hours

Number of consulting projects = 3

And Matilda spends same amount of time to each of the project.

To find the time she spend on each project is by using unitary method

that is,            3 projects = \(\frac{67}{4}\) hours

                      1 project = \(\frac{67}{4} / 3\)

                                     = 67/12

                                     = \(5\frac{7}{12}\) hours

Hence time taken by Matilda on each project is \(5\frac{7}{12}\) hours.

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Given:

The scores on a standardized test are normally distributed with a mean of 115 and standard deviation of 10.

Required:

What test score is 0.8 standard deviations below the mean?

Explanation:

Answer:

answered the question.

Answer:C. 17,280

Step-by-step explanation:It this way because it cant be 3k obv or 6k. And it says 72% down not up so not d either :D

he residual value of the car be after three year is mathematically given as

R=17280

Option C

Question Parameters:

A car with a MSRP of $24,000 for three years.

After three years, the leasing company expects the car to have a value of 72%

Generally the equation for the  residual value  is mathematically given as

R=percentage of drop *original price

R=0.72*24000

R=17280

Therefore, the residual value of the car be after three years is R=17280

Option C

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Answer:

first graph the y-intercept start at 0 and go up 2 plot that. Then, go up 7 from 2 and to the right 1

Step-by-step explanation:

Both conditions of the alternating series test are satisfied, so the series ∑ (-1)^n a_n converges.

To apply the alternating series test, we need to verify the following two conditions:

The sequence {a_n} = 1/(n^2 - 5) is positive, decreasing, and approaches 0 as n approaches infinity.

The series ∑ (-1)^n a_n = ∑ (-1)^n/(n^2 - 5) converges.

To check the first condition, we can take the derivative of a_n:

a'_n = -2n/(n^2 - 5)^2

Since n ≥ 3, we have n^2 - 5 ≥ 4, so (n^2 - 5)^2 ≥ 16. This implies that a'_n ≤ 0 for n ≥ 3. Therefore, the sequence {a_n} is decreasing.

To check that the sequence approaches 0, we can use the limit comparison test with the convergent p-series ∑ 1/n^2:

lim n→∞ a_n/(1/n^2) = lim n→∞ n^2/(n^2 - 5) = 1

Since the limit is finite and positive, we conclude that {a_n} approaches 0 as n approaches infinity.

Thus, both conditions of the alternating series test are satisfied, so the series ∑ (-1)^n a_n converges.

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the second option is more profitable

if she sells more than $ 18000 per month

Explanation

Step 1

let's check the options we have

a)

one paying ​$3,000 per month

it means, in a month , she will receive 3.000

b)$2,100 per month plus a​ 5% commission on all sales made during the month

if x represents the sales, then the formula would be

Step 2

now, to make the option 2 more profitable

solve for x

therefore, the second option is more profitable

if she sells more than $ 18000 per month

I hope this helps you

The forecast for May using a five-month moving average is 39 (Option E).

Moving average is used for smoothing out time series data to find any trends or cycles within the data. A five-month moving average is the average of the past five months. To calculate the moving average, add up the sales for the previous five months and divide it by five.

According to the question, the sales for the previous five months are: Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47

We have to add the sales of these five months, which gives:

27 + 40 + 42 + 41 + 47 = 197

To find the moving average for May, we divide this sum by 5:

197 / 5 = 39.4

Since we have to round the answer to the nearest whole number, we round 39.4 to 39, which is option E.

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Answer:

Is it Khan Academy? You do 5.8 - 2.7 = 3.1

Step-by-step explanation:

Hope that helps!

Answer:

675 (6913)

\( \div \)

\( + \)

Answer:1999000

Step-by-step explanation:

1²-2²=(1-2)(1+2)=-1*3=-3

3²-4²=(3-4)(3+4)=-7

5²-6²=(5-6)(5+6)=-11

7²-8²=(7-8)(7+8)=-15

...

1997²-1998²=(1997-1998)(1997+1998)=-3995

1²-2²+3²-4²+....+1997²-1998²+1999²=1999²-(3+7+11+15+...+3995)

Number of terms in the parenthesis: =(3995-3)/(7-3)+1=998+1=999

Parenthesis=

\(\dfrac{(3995+3)*999}{2} =\dfrac{3998*999}{2} =1997001\)

1²-2²+3²-4²+....+1997²-1998²+1999²==1999²-1997001=1999000

Answer:

Below

Step-by-step explanation:

Actually....NONE of those answers would show the total amount after 3 years

the correct option would be   2000 + (2000*.02 *3)     a PLUS sign rather than a multiplication sign  ....so the answer MIGHT be B if you transcribed it incorrectly

Answer:

whoa this is a lot of math what level would thus be mate

Answer: I think it's 36 ft.

Step-by-step explanation:

The probability that he makes exactly 3 sales is 0.3087 and  the probability that he makes exactly 4 sales is 0.2401

Gary schwartz is the top salesman for his company. records indicate that he makes a sale on 70% of his sales calls.

p = 70/100 = 0.7

q = 30/100 = 0.3

Probability of exactly 3 sales

P(X = 3) = ⁴C₃ (0.7)³(0.3)¹

= 3 x 0.343 x 0.3

= 0.3087

P(X =4) = ⁴C₄ (0.7)⁴

= 0.2401

Therefore,  the probability that he makes exactly 3 sales is 0.3087 and  the probability that he makes exactly 4 sales is 0.2401

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If the resistance is 0.1 ohm, the impressed voltage is e(t) = 5, and i(0) = 0. The current i(t) is 50t.

The equation of the circuit is given as;v = L di/dt + R iThe initial current is zero, and the capacitor has no charge. As a result, the total voltage is equal to the impressed voltage.

e(t) = L di/dt + R i

Differentiate both sides with respect to time.

t(e(t)) = d(L di/dt)/dt + d(R i)/dt

t(e(t)) = L d²i/dt² + R di/dt + i(dR/dt)

Substituting the given values,R = 0.1, L = 0.02

Therefore;e(t) = 0.02(d²i/dt²) + 0.1(di/dt)

The equation is a second-order linear homogeneous differential equation. The auxiliary equation is given by;0.02m² + 0.1m = 0m(0.02m + 0.1) = 0m = 0 or -5

Taking m = 0;

Let i(t) = A + Bt

Substituting in equation (1);

e(t) = 0.02(d²i/dt²) + 0.1(di/dt)0 = 0.02d²i/dt² + 0.1di/dt

Substituting i(t) = A + Bt0 = 0.02B0 + 0.1A5 = 0.1B0.1B = 5B = 50

Using the values of A and B, i(t) can be calculated as;i(t) = 50t

Hence, the current i(t) is 50t.

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The solution basis for the provided differential equation is:

{ y1 = e^(6x), y2 = e^(-2x)}. None of the provided options match the solution, hence the correct answer is (e) none of the above.

To obtain a solution basis for the differential equation y'' - 4y' - 12y = 0, we can assume a solution of the form y = e^(rx), where r is a constant.

Substituting this into the differential equation, we have:

(r^2)e^(rx) - 4(re^(rx)) - 12e^(rx) = 0

Factoring out e^(rx), we get:

e^(rx)(r^2 - 4r - 12) = 0

For a non-trivial solution, we require the expression in parentheses to be equal to 0:

r^2 - 4r - 12 = 0

Now, we can solve this quadratic equation for r by factoring or using the quadratic formula:

(r - 6)(r + 2) = 0

From this, we obtain two possible values for r: r = 6 and r = -2.

Therefore, the solution basis for the differential equation is:

y1 = e^(6x)

y2 = e^(-2x)

Comparing this with the options provided:

(a) {y1 = e^(4x), y2 = e^(-3x)}

(b) {y1 = e^(-6x), y2 = e^(2x)}

(c) {y1 = e^(-4x), y2 = e^(3x)}

(d) {y1 = e^(6x), y2 = e^(-2x)}

None of the provided options match the correct solution basis for the provided differential equation. Therefore, the correct answer is (e) none of the above.

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The provided system is controllable and the rank of C = 2.

To determine the controllability of the system, we will use the controllability matrix and check its rank.

Provided system dynamics:

\(\[\dot{\bar{x}}(t) = \begin{bmatrix} 3 & 1 \\ 0 & -2 \end{bmatrix} \bar{x}(t) + \begin{bmatrix} 0 \\ 1 \end{bmatrix} u(t)\]\)

\(\[y(t) = \begin{bmatrix} 1 & 0 \end{bmatrix} \bar{x}(t) + [0] u(t)\]\)

(a) Controllability analysis:

The controllability matrix is defined as:

\(\[C = \begin{bmatrix} B & AB \end{bmatrix}\]\)

where:

\(\[A = \begin{bmatrix} 3 & 1 \\ 0 & -2 \end{bmatrix}\]\)

\(\[B = \begin{bmatrix} 0 \\ 1 \end{bmatrix}\]\)

Calculating the controllability matrix:

\(\[C = \begin{bmatrix} B & AB \end{bmatrix} = \begin{bmatrix} 0 & 3 \\ 1 & -2 \end{bmatrix}\]\)

Now, we check the rank of the controllability matrix C.

If the rank is equal to the dimension of the state space (2 in this case), then the system is controllable.

Using the rank function, we obtain that the rank of C is 2.

Since the rank of C is equal to the dimension of the state space, the system is controllable.

(b) Finding the left eigenvectors:

To obtain the left eigenvectors, we need to calculate the eigenvectors of the transpose of the system matrix A.

The transpose of A is:

\(\[A^T = \begin{bmatrix} 3 & 0 \\ 1 & -2 \end{bmatrix}\]\\\)

Calculating the eigenvectors of \(A^T\), we obtain the eigenvalues and eigenvectors:

Eigenvalue λ1 = 3:

Eigenvector v1 = \(\[\begin{bmatrix} 0 \\ 1 \end{bmatrix}\]\)

Eigenvalue λ2 = -2:

Eigenvector v2 = \(\[\begin{bmatrix} 1 \\ -1 \end{bmatrix}\]\)

(c) Eigenvector-Controllability test:

To verify controllability using the Eigenvector-Controllability test, we need to check if the matrix M is invertible, where:

\(\[M = \begin{bmatrix} v1 & A*v1 \end{bmatrix}\]\)

In this case:

\(\[M = \begin{bmatrix} 0 & 3 \\ 1 & -2 \end{bmatrix}\]\)

Calculating the determinant of M, we obtain that |M| = -3.

Since the determinant of M is non-zero (-3 ≠ 0), M is invertible, which confirms the controllability of the system.

Therefore, the system is controllable.

Since the system is controllable, it is also stabilizable.

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Answer:

f(2)= -3

Step-by-step explanation:

f(x)= 2 [x-3.5]

f(2)= 2[2-3.5]                         substitute all of your "x" for the number "2"     f(2)=2[ -1.5]                                                2-3 is -1.5

f(2)= -3                                                 2 times -1.5 is -3

The value of f(2)= -3

Since f(x) = 2[[X-3.5]

So,,

f(x)= 2 [x-3.5]

f(2)= 2[2-3.5]                      

f(2)=2[ -1.5]                                  

f(2)= -3                  

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Answer:

6

cuz 6*3=18 and 6*4=24

Answer:

18: 2x9 3x6

24: 12x2 6x4  8x3

So 2

Step-by-step explanation:

Is that what you mean?

To determine the correct probability, we need additional information about the specific event or condition for which the probability is being calculated.

The given information provides the counts of elements within the circles and their overlaps but does not specify the event or condition of interest.Probabilities are calculated by dividing the favorable outcomes by the total possible outcomes. Without knowing the specific event or condition, we cannot determine the favorable outcomes or the total possible outcomes, and hence cannot calculate the probabilities accurately.Please provide additional context or specify the event for which the probability is required, and I will be glad to assist you further in calculating the correct probability using the given Venn diagram information.

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The product of 2 odd numbers will be odd and any number that is a multiple of 2 is even.

Odd numbers are those numbers that cannot be divided into two equal parts, whereas even numbers are those numbers that can be divided into two equal parts

let the odd number be 2x+ 1

and the even number be 2x

Now, the product of two odd numbers

=(2x + 1)(2x + 1)

= 4x² + 4x + 1.

Here, 4x² is even because 4x² can be expressed as multiple of 2.

Also, 4x is even because 4x can be expressed as multiple of 2.

So, the expression 4x² + 4x + 1 is odd because an even number + 1 is odd.

Hence, the product of 2 odd numbers will be odd.

and any number that is a multiple of 2 is even.

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Answer:

1) 2 × 2 × 5 × 7 + 9 -7×1 = 142

2) 9 × 7 × 2 + 5 × 2 + 7 - 1 = 142

3) 2 × 9² - 7 - 7 - 5 - 1 = 142

4) 2 × 7² + 9 + 7 × 5 × 1 = 142

Step-by-step explanation:

1) 2 × 2 × 5 × 7 + 9 -7×1 = 142

Multiply 2 by 2 by 5 by 7 add to 9 then subtract 7 multiplied by 1

2) 9 × 7 × 2 + 5 × 2 + 7 - 1 = 142

Multiply 9 by 7 by 2 by 7 add to 5 multiplied by 2 then add to 7 and subtract 1

3) 2 × 9² - 7 - 7 - 5 - 1 = 2 × 9² - (7 + 7 + 5 + 1) = 142

Multiply 2 by 9 raised to the power of 2 then subtract  the sum of 7, 7, 5 and 1

4) 2 × 7² + 9 + 7 × 5 × 1 = 142

Multiply 2 by 7 raised to the power of 2 then add 9 and add 7 multiplied by 5 multiplied by 1.

Answer:

0.9y

Step-by-step explanation:

Answer:

its not a complete problem

Step-by-step explanation:

Answer:

42cm^2

Step-by-step explanation:

9+12= 21

21/2=10.5

The four criteria that can be used to prove triangles are congruent and can be used to prove the triangles are congruent.

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and all three of their corresponding angles have the same measurements. These triangles can be moved around, rotated, flipped, and turned to have a same appearance. They match up with one another when moved.

The four criteria that can be used to prove triangles are congruent are SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and SSS (Side-Side-Side). Additionally, CPCTC (Corresponding Parts of Congruent Triangles are Congruent) can be used to prove the triangles are congruent.

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Answer:

Step-by-step explanation: go to the x axis that goes left to right and go to the #4 and then go down 3

the sales tax is 8% because there was a $6.32 increase

hope this helps :))

Answer: The number of miles increases as time increases.

The number of hours causes a change in the number of miles ridden.

The variable h is the independent variable.

The variable m is the dependent variable.

Step-by-step explanation:

Answer:

Rational

Step-by-step explanation:

It is a rational number because any number that can be rewritten as a simple fraction is a rational number. This means that natural/counting numbers, whole numbers and integers, like 5, are all part of the set of rational numbers as well because they can be written as fractions, as are mixed numbers such as 1 ½.