f(t)=14+40/t+1 velocity m/s,speed m/s

The standard deviation of the value of the variable at the end of 3 years is 3√3.

a) To find the expected value of the variable x after 3 years, we can use the properties of the Wiener process. The expected value of the variable at any given time t is given by:

E[x(t)] = x(0) + a * t

Given that x(0) = 10 and a = 2, we can substitute these values into the equation:

E[x(3)] = 10 + 2 * 3 = 10 + 6 = 16

Therefore, the expected value of the variable x after 3 years is 16.

b) The standard deviation of the value of the variable at the end of 3 years can be calculated using the formula:

σ = √(b^2 * t)

Given that b = 3 and t = 3, we can substitute these values into the formula:

σ = √(3^2 * 3) = √(9 * 3) = √27 = 3√3

Therefore, the standard deviation of the value of the variable at the end of 3 years is 3√3.

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Answer:

12%

Step-by-step explanation:

Take 69.44 and subtract 62.

You should get 7.44.

If you take the original 62 & multiply by .12, you get the 7.44 tip.

The standard normal probability density function is represented by its formula, 1 /σ√2π(e^(-z²/2))

What is standard normal variate?

A standard normal variate is defined as a variate whose mean is equal to 0, i.e. µ=0 and standard deviation is equal to 1, σ =1. Its probability density function is given by:

f(x) = 1/√2π(e^(-z²/2))

Explanation

The standard normal probability density function is a bell-shaped curve that can be represented by using the given formula:

1 /σ√2π(e^(-z²/2))

Hence, the standard normal probability density function is represented by using its formula..

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Answer:

Total cost is $177.50.

Step-by-step explanation:

Rackets:

Divide the cost for racket by 6 to find the cost per racket.

186÷6=31

Multiply 31 by 5 to find the cost for 5 rackets.

31×5=155

$155

Tubes of balls:

Divide 27 by 6 to find the cost per a tube of balls.

27÷6=4.50

Multiply 4.50 by 5 to find the cost for 5 tubes of balls.

4.50×5=22.50

$22.50

Add the amounts for rackets and tubes of balls to find the total cost.

155+22.50=177.50

The total cost is $177.50.

Hope this helps!

Answer:

18 and 21

Step-by-step explanation:

Let the smaller number = 3x

Let the larger number =  3x + 3

The three and the plus 3 insure that the numbers are multiples of 3 and are consecutive.

3* (3x + 3) = 7/10 * 5 (3x)       Multiply both sides by 10

30*(3x + 3) = 7 * 5 * 3x          Remove the brackets

90x + 90 = 7 * 5 * 3x             Combine the right

90x + 90 = 105x                    Subtract 90x from both sides.

-90x             -90x

           90 = 15x                     Divide by 15

x = 90/15

x = 6

Let's see if it works.

3*(3x + 3) = 3*(18 + 3) = 3 * 21 = 63

7/10 * 5 *3x = 7/10 * 5 * 3*6 = 630 / 10 = 63

Answer:

C. Evaluate f - 6g

1. 4

2. 45

3. -35

4. 0

D. Evaluate \(\frac{18}{m}\)+ p

1. 7

2. 0

3. 2

4. -3

Step-by-step explanation:

Answer and Explanation:

We can solve for the value of expressions given the variable values by plugging the given values into the expression.

If \(f = 10\) and \(g=1\) ...   \(10 - 6(1) = \boxed{4}\)

If \(f=33\) and \(g=-2\) ...   \(33-6(-2) = 33+12 = \boxed{45}\)

If \(f = -5\) and \(g=5\) ...   \(-5 - 6(5) = -5-30=\boxed{-35}\)

If \(f = -42\) and \(g=-7\) ...   \(-42 - 6(-7) = -42 + 42 = \boxed{0}\)

If \(m=3\) and \(p=1\) ...   \(\dfrac{18}{3} + 1 = 6 + 1 = \boxed{7}\)

If \(m=-2\) and \(p=9\) ...   \(\dfrac{18}{-2} + 9 = -9 + 9 = \boxed{0}\)

If \(m=6\) and \(p=-1\) ...   \(\dfrac{18}{6} + (-1) = 3-1 = \boxed{2}\)

If \(m=-9\) and \(p=-5\) ...   \(\dfrac{18}{-9} + (-5) = -2 -5 = \boxed{-7}\)

The output of 0.7326 represents the test statistic (Z-score) computed from the 1-sample Z-test in Excel.

It tells you how many standard deviations the sample mean is from the population mean under the null hypothesis.

A test statistic (Z-score) is a numerical value used in statistical hypothesis testing to assess the evidence against the null hypothesis.

A test statistic measures the difference between a sample statistic (eg sample mean) and the corresponding population parameter (eg population mean) assuming the null hypothesis is true.

For the Z-test, the test statistic is computed as

z = (x - μ) / (σ / √n)

where x = sample mean,

μ = population mean,

σ= population standard deviation,

and n = sample size.

The resulting Z-score indicates how many standard deviations the sample mean is from the population mean, assuming the null hypothesis is true.

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Answer:

9. 15b + 4

10. 4y + 6

11. 15r+72

12. 130n + 20

Step-by-step explanation:

9. Combine Like terms

10. Combine Like terms

11. Distribute the 8 into (r + 9) then combine like terms

12. Distribute 10 into (3n + 2 + 10n) then combine like terms

Answer:

\(\mathsf {9) 15b + 4}\\\mathsf {10) 4y + 6}\\\mathsf {11) 15r + 72}\\\mathsf {12) 130n + 20}\)

Step-by-step explanation:

\(\textsf {Question 9}\)

\(\mathsf {3 + 8b + 4 + 7b - 3}\)

\(\mathsf {8b + 7b + 4 + 3 - 3}\)

\(\mathsf {15b + 4}\)

\(\textsf {Question 10}\)

\(\mathsf {8 + 7y - 3y + 2 - 4}\)

\(\mathsf {7y - 3y + 8 + 2 - 4}\)

\(\mathsf {4y + 6}\)

\(\textsf {Question 11}\)

\(\mathsf {8(r + 9) + 7r}\)

\(\mathsf {8r + 8(9) + 7r}\)

\(\mathsf {8r + 7r + 72}\)

\(\mathsf {15r + 72}\)

\(\textsf {Question 12}\)

\(\mathsf {10(3n + 2 + 10n)}\)

\(\mathsf {10(13n + 2)}\)

\(\mathsf {10(13n) + 10(2)}\)

\(\mathsf {130n + 20}\)

Answer:

Yasmin will spend $6

Nadia will spend $5.9

Step-by-step explanation:

Step one:

the cost of 5 jars at Central market is $3

the cost of 1 jar = 3/5= $0.6

60 cents per jar

we are told that Valley Market sells jars of jam at 59 cents per jar.

$0.59

Step two:

If Yasmin buys 10 jars from Central Market,

Yasmin will spend = 10*0.6= $6

If Nadia buys 10 jars from Valley Market.

Nadia will spend = 10*0.59= $5.9

The market difference is 6-5.9= $0.1

The region satisfying both |z| ≥ 1 and Re(z) ≥ 0 consists of all complex numbers z that lie on or outside the unit circle centered at the origin, including the positive real axis.

To sketch the region satisfying both |z| ≥ 1 and Re(z) ≥ 0, let's consider the conditions separately. First, |z| ≥ 1 represents all complex numbers with a distance of 1 or more from the origin. This includes all points on or outside the unit circle centered at the origin. Therefore, the region satisfying |z| ≥ 1 consists of the entire complex plane except for the interior of the unit circle.

Next, Re(z) ≥ 0 represents all complex numbers with a real part greater than or equal to zero. In other words, it includes all points to the right of or on the imaginary axis. Combining this condition with the previous one, the region satisfying both conditions includes all complex numbers that lie on or outside the unit circle and have a real part greater than or equal to zero. In summary, the region satisfying both |z| ≥ 1 and Re(z) ≥ 0 consists of all complex numbers that lie on or outside the unit circle centered at the origin, including the positive real axis.

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If particular shipment of thousands of components actually has a 7% rate of defects, there is a 54.29% probability that this whole shipment will be accepted.

According to the company's acceptance sampling plan, 25 components are randomly chosen and tested from a shipment before the entire batch is accepted if there are no more than three defects. The probability of choosing a defective component from a sample of 25 is computed as follows, assuming that the shipment genuinely has a 7% defect rate:

P(defective) = 0.07

P(non-defective) = 0.93

Using the binomial distribution, we can calculate the probability of having 0, 1, or 2 defectives in a sample of 25:

P(X ≤ 2) = P(X=0) + P(X=1) + P(X=2)

= (0.93)²⁵ + 25(0.07)(0.93)²⁵ + (0.07)²(0.93)²³

= 0.5429

This means that there is a 54.29% chance of having 2 or fewer defectives in a sample of 25. Since the whole shipment will be accepted if there are fewer than 3 defectives in the sample, this is the probability that the whole shipment will be accepted. Therefore, there is a 54.29% chance that the company will accept the shipment based on their acceptance sampling plan.

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The exact value of arcos is \(\( \frac{\pi}{3} \)\). Therefore, the given statement is True.

The value of

\(\( \cos ^{-1}\left(-\frac{1}{2}\right) \)\)

is equal to \(\( \frac{\pi}{3} \).\)

The given statement is, therefore, True.

In mathematics, arccos is the inverse function of cosine and is also known as cos -1. In other words, for a given angle x, arccos(x) returns the angle whose cosine is x. It's expressed as:

cos(arccos(x)) = x

where -1 ≤ x ≤ 1 and 0 ≤ arccos(x) ≤ π.

Rewriting the above equation by replacing x with -1/2,

cos(arccos(-1/2))

= -1/2cos(arccos(-1/2))

= π/3

Arccos can return values between 0 and π, and it gives the value of the angle in radians.

Thus, the answer is \( \frac{\pi}{3} \). Therefore, the given statement is True.

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The coefficients of the transformed basis vectors in this linear combination are the components of the matrix product Ax. That is, [t a (x)]i = ai1x1 + ai2x2 + … + ainxn, where the aij are the entries of the transformation matrix A.

It would have been easier for me to assist you with your question if you had provided the specific instructions for exercises 19-20. Nevertheless, I will provide you with a general explanation of how to find t a (x) and express the answer in matrix form.

For a linear transformation, t a (x), the transformation of a vector x equals the product of the vector and a matrix. The matrix is called the transformation matrix. The transformation matrix is equal to the matrix formed by putting the transformed basis vectors in the columns.

For example, suppose you have the linear transformation, t a (x), and you want to find the transformation matrix of this linear transformation. You can find the matrix by performing the following steps:

Choose a basis for the domain vector space of the linear transformation t a (x). Let the basis vectors be e1, e2, …, en.Apply the linear transformation t a (x) to each basis vector. Let the transformed basis vectors be f1, f2, …, fn.

Form the matrix, A, by putting the transformed basis vectors in the columns. That is, A = [f1 f2 … fn].

The matrix A is the transformation matrix of the linear transformation t a (x).To express t a (x) in matrix form, multiply the matrix A by the vector x. That is, t a (x) = Ax.Note that if x is written as a linear combination of the basis vectors, x = c1e1 + c2e2 + … + cnen, then t a (x) can be written as a linear combination of the transformed basis vectors. That is,

t a (x) = c1f1 + c2f2 + … + cnfn.

The coefficients of the transformed basis vectors in this linear combination are the components of the matrix product Ax. That is, [t a (x)]i = ai1x1 + ai2x2 + … + ainxn, where the aij are the entries of the transformation matrix A.

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Answer: 108

Step-by-step explanation:

The sum of squared residuals form of the f statistic can be computed easily even when many independent variables are involved; this particular f statistic is usually called the Chow statistic in econometrics.

What is Chow statistic?

In order to determine whether the coefficients in two distinct regression models on two separate datasets are similar, statisticians utilise the Chow test, which was created by economist Gregory Chow.

In situations where the disturbance term is believed to be the same in both periods, the Chow test is frequently used to examine whether any of a model's parameters have structurally changed.

In situations where the disturbance term is believed to be the same in both periods, the Chow test is frequently used to examine whether any of a model's parameters have structurally changed.

Hence, the sum of squared residuals form of the f statistic can be computed easily even when many independent variables are involved; this particular f statistic is usually called the Chow statistic in econometrics.

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Answer:

5 hours

Step-by-step explanation:

let the time she baby sat be x.

4x= 20

x= 5

Answer:

The image is not clear but get the idea

a) The mean of the sampling distribution of the sample proportion is given as follows: p = 0.18.

b) The standard deviation of the sampling distribution of the sample proportion is given as follows: s = 0.14.

The sampling distribution of p is defined according to the Central Limit Theorem, which states that the sampling distribution of a proportion p in a sample of size n has mean and standard deviation defined as follows:

The sample size and the proportion for this problem are given as follows:

n = 8, p = 0.18.

Then the standard deviation of the sampling distribution of the sample proportion is calculated as follows:

s = square root (0.18 x 0.82/8) = 0.14.

(0.1358 is rounded to 0.14 as 5 is the third digit).

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1. The total area of the picture and frame is 60 + 24x + 4x².

2. A solution to this equation is a value of x that makes the total area of the picture and frame equal to 110 square inches

1. The area of the picture is 12 x 5 = 60 square inches. The frame has thickness x, so the total width of the picture and frame is 12 + 2x and the total height is 5 + 2x. The total area of the picture and frame is therefore:

= (12 + 2x)(5 + 2x)

= 60 + 24x + 4x²

2. A solution to this equation is a value of x that makes the total area of the picture and frame equal to 110 square inches. In other words, a solution to the equation is a thickness for the frame that will make the picture and frame fit within a 110 square inch frame.

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Answer:

840

Step-by-step explanation:

1600 people total

21 out of 40 favorite is sausage pizza

1600 = 40 * 40

x = 21 * 40

x = 840

Hope this helps

Answer:

x = 5

y = 0

Step-by-step explanation:

add both equations so the y-terms are eliminated and you get:

5x = 25

x = 5

substitute 5 into 'x' in one of the equations:

3(5) + 8y = 15

15 + 8y = 15

8y = 0

y = 0

Answer:

1/2

Step-by-step explanation:

It will be either heads of tails equally likely.

It’s still 1/2. Flipping a coin is an independent event. In other words, the outcome of the next flip is uninfluenced by what has happened previously. It’s as if it were the first time you ever flipped the coin. The probability is unaltered.

Answer:

24.584...

Step-by-step explanation:

2x4(6.5x9.5) power of 12

2x4 x 61.75 power of 12

2x4 x 3.073...

8 x 3.073...

24.584...

Step-by-step explanation:

To multiply rational expressions, simply multiply the numerators together (the tops) and the denominators together (the bottoms).

For example:

\(\frac{x+a}{y+b}\times\frac{x+c}{y+d}\)

\(= \frac{(x+a)(x+c)}{(y+b)(y+d)}\)

\(=\frac{x^{2}+ax+cx+ac}{y^{2}+by+dy+bd}\)

To divide by a rational expression, multiply by its reciprocal.  In other words, flip the fraction, then multiply.

For example:

\(\frac{x+a}{y+b}\div\frac{x+c}{y+d}\)

\(=\frac{x+a}{y+b}\times\frac{y+d}{x+c}\)

\(=\frac{(x+a)(y+d)}{(x+c)(y+b)}\)

\(=\frac{xy+dx+ay+ad}{xy+bx+cy+bc}\)

Answer:9m=17n

Step-by-step explanation:

The number of real roots found are-

1. (x-4)(x+3)^2(x-1)^3=0 ; 6 real roots.

2. X^2(x^3-1)=0 ; 3 real roots.

3. X(x+3)(x-6)^2=0 ; 4 real roots.

4. 3x(x^3-1)^2=0 ; 3 real roots.

5. (x^3-8)(x^4+1)=0​ ; 1 real roots.

Consider the given cases-

1. (x-4)(x+3)^2(x-1)^3=0,

Put each equals zero.

x – 4 = 0 or (x + 3)^2 = 0 or (x – 1)^3 = 0,

Thus,

x = 4

x = –3 twice

x = 1 thrice

All are real numbers, thus given polynomial has 6 real roots.

2. x^2(x^3-1)=0

Put each equals zero.

x² = 0

x³ – 1 = x³ – 1³ = (x – 1)(x² + x + 1) = 0

The quadratic expressions has 2 imaginary roots.

Use the discriminant formula to find-

D = b² – 4ac = 1² – 4(1)(1) = 1 – 4 = –3 < 0.

Thus, roots that are not real.

So, the real roots of this polynomial : 0(twice) and 1.

Hence, thus given polynomial has 3 real roots.

3. x(x+3)(x-6)^2=0

Put each equals zero.

x = 0

x = 3

x = 6 twice

Hence, thus given polynomial has 4 real roots.

4. 3x(x^3-1)^2=0

Put each equals zero.

3x = 0 and  x = 0

(x^3 – 1)² = [(x – 1)(x² + x + 1)]² = (x – 1)²(x² + x + 1)² = 0,

Here, only two roots are real

The quadratic expression do have unreal roots, thus 1 twice are the real roots.

Hence, thus given polynomial has 3 real roots..

5. (x^3-8)(x^4+1)=0

Put each equals zero.

x³ – 8 = x³ – 2³ = (x – 2)(x² + 2x + 4) = 0

There is only one real root i.e, 2, the quadratic expression do have imaginary roots

Check using the discriminant formula

D = b² – 4ac = 2² – 4(1)(4) = 4 – 16 = – 12 < 0.

x⁴ + 1 = 0 has imaginary roots.

Hence, thus given polynomial has 1 real roots..

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