Jerry uses an exercise program to help him eventually do 100 push-ups. He started with 17 push-ups in Week 1 and planned to increase the number of push-ups by 2 each week. Show your work. a) In which week does Jerry expect to reach his goal? b) What is the total number of push-ups he will have done when he reaches his goal?

The rank of a matrix is equal to the number of non-zero rows in its row echelon form. The value of x for which the given matrix is singular is `19 ± 2√190`.

Given matrix is, A =  [-x  9;  -7  x - 38]

We have to find the value of x for which the given matrix is singular. A matrix is singular if its determinant is zero. Therefore, the determinant of the given matrix must be zero for it to be singular. \(|A| = (-x * (x-38)) - (9 * (-7))|A|\)

\(= -x² + 38x + 63\).

Now, the determinant of the matrix A must be zero as it is a singular matrix. |A| = -x² + 38x + 63

= 0

=> x² - 38x - 63

= 0On solving the quadratic equation, we get; \(x = \frac{38 \pm \sqrt{(-38)^2 - 4(1)(-63)}}{2(1)}\)\(x = 19 \pm 2\sqrt{190}\).

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Area under the normal curve to the right of μ = 0.5.

A normal distribution curve has a 1.0, or 100%, area under it. The curve of a normal distribution is symmetrical about the mean. Therefore, half of the total area under a normal distribution curve is located on the left side of the mean, and half is located on the right side of the mean.

The normal curve is divided into two equal parts with the mean lying in the center. The area of the normal curve is equal to 1 and it is divided into two equal parts which means that area on either side of the mean is 0.5.

Final answer: Hence, the area under the normal curve to the right of

μ = 0.5.

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he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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38

Step-by-step explanation:

2+2+2+2+7+7+10+6= 38

count up all of the sides of the shape then you get your answer :)

The value of x in quadrilateral JKLM is 29

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points. The sum of interior angles of quadrilaterals is always equal to 360 degrees.

The sum of the interior angles in a quadrilateral is 360°

∠J + ∠K + ∠L + ∠M = 360

3X + 90 + 2X + 8 + 4X + 1 = 360

9x + 99 = 360

9x = 360 - 99

9x = 261

x = 261/9

x = 29

In conclusion 29 is the value of x in the quadrilateral.

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Answer:

15$

Step-by-step explanation:

The probability distribution of X follows a binomial distribution since there are a fixed number of trials (10 vehicles) and each trial is independent with a constant probability of success (exceeding the speed limit). The parameters of this distribution are n = 10 and p = 0.6, where p is the probability of exceeding the speed limit.

To find P(X = 10), we can use the binomial probability formula:
P(X = 10) = (10 choose 10) * 0.6^10 * 0.4^0 = 0.006
To find P(4 < X < 9), we need to sum the probabilities of X = 5, 6, 7, 8, and 9:
P(4 < X < 9) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)
Using the binomial probability formula for each value of X, we get:
P(4 < X < 9) = 0.323 + 0.202 + 0.088 + 0.026 + 0.005 = 0.644
Suppose a highway patrol officer can obtain radar readings on 500 vehicles during a typical shift. Using the same probability of exceeding the speed limit (p = 0.6), we can find the expected number of traffic violations:
E(X) = np = 500 * 0.6 = 300
Therefore, we can expect to find 300 traffic violations during a typical shift.

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Answer:

Step-by-step explanation:

For example, we have 8, which is not a perfect square

square root of(8)

we divide 8 by prime numbers, until it gets to 1

8/2

4/2

2/2

1

We have divided our number 8 with 2 by 3 times.

Now we pair the numbers.

2 with 2, and the third 2 remains.

the pairs will be in front of the squareroot, and what remains will remain in the squareroot.

squareroot(8) = 2\(\sqrt{2}\)

Let's take another number

32

Divide it in prime numbers

32/2

16/2

8/2

4/2

2/2

1

We have 2 pairs of 2 and on remaining 2

We multiply the pairs together, and we get 4 in front of the squareroot.

squareroot(32) = 4\(\sqrt{2}\)

Let's take 21

21/7

3/3 (3 is a prime number also 5,7,11,13,17 etc)

1

-This one doesn't have a short answer that could be written.

take 80

80/2

40/2

20/2

10/2

5/5

1

We have 2 pairs of 2 and a 5

squareroot(80) = 4\(\sqrt{5}\)

Given the class width of 6 and the minimum value of 12, the maximum value in the first class would be 12 + 6 - 1 = 17. The maximum value in the 6th and last class would be 17 + (6 x 5) = 42. Hence, the largest possible value in the data set is '42'.

A frequency table is used to organize and represent the distribution of a set of data. In this case, the data set has 6 classes and a class width of 6. This means that the range of values in each class is 6 units. The minimum value in the data set is 12, so the first class starts at 12 and ends at 12 + 6 - 1 = 17. This is because the class width is 6, so the end value of the first class would be the starting value plus the class width minus 1.

For the last class, the end value would be 17 + (6 x 5) = 42. This is because the end value of the first class is 17 and each subsequent class increases by 6 units. The largest possible value in the data set would be the end value of the last class, which is 42. This means that any value greater than 42 would not be part of the data set and would not be included in the frequency table.

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Answer:

729

Step-by-step explanation:

because the square of 27 gives 729

I can check this through long division

Answer:

Average Acceleration = (change in speed) / (time for the change)

Change in speed = (ending speed) - (starting speed)

                            =   15 m/s - 24 m/s  =  -9 m/s

Acceleration =  (-9 m/s) / (12 sec) =  - 0.75 m/s² .

Step-by-step explanation:

Hope this helps UwU

Answer:

32-18= 14

14m/s

14 divided by 12= 1.16666666667

1.16666666667

Step-by-step explanation:

I think, though I may be wrong and I wish to fix my mistake if wrong. Also, hey Jace

Answer:The vertex is

(0,7)

Sometimes we have problems with the easier questions because it's not exactly in the form we're used to. Normally for a quadratic, you would complete the square to find the vertex. But this quadratic is already in vertex or standard form:

f(x)=−(x−0)2+7

Step-by-step explanation: Hope this helps

Answer:

add

Step-by-step explanation:

The correct option is D. the number of sweatshirts for which cost and income are equal.

Any equation that contains only one element which squares the variable and none that raises it to a higher power.

The general form form of quadratic equation is-

ax² + bx + c = 0

According to the question;

Use the substitute method to get the quantity of sweatshirts in which cost and earnings are equal.

Step 1: Write the following system of equations as the first step.

\(\begin{aligned}&y=35 x \\&y=-0.05(x-400)^{2}+9492\end{aligned}\)

Step 2: Replace the value of "y" in the equation (2).

\(35 x=-0.05(x-400)^{2}+9492\)

Step 3: Make the equation above simpler.

\(35 x=-0.05 x^{2}-8000+40 x+9492\)

Step 4: Write the preceding equation in generalised quadratic form.

\(0.05 x^{2}-5 x-1492=0\)

The processes above lead to the conclusion that option D provides the proper statement.

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The complete question is-

In the first equation in the system of equations, y represents the money collected from selling sweatshirts. In the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league. What does the solution of the system represent in this context?

y=35x

y=-0.05(x-400)^2+9,492

A. the number of sweatshirts that generate the maximum income

B. the number of sweatshirts that generate the minimum cost

C. the number of sweatshirts for which the difference between cost and income is greatest.

D. the number of sweatshirts for which cost and income are equal

Answer:

D

Step-by-step explanation:

He said so

The probability of flipping two tails and rolling an even number is 1/8.

Probability is the possibility of getting an event. We are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Suppose you flip a coin.

Total number of outcomes = 2

Number of outcomes getting a tail = 1

The probability of getting a tail = 1/2

Now, suppose you flip two coins.

Probability of getting two tails = 1/2 × 1/2 = 1/4

Suppose you roll a die.

Total number of outcomes = 6

Number of outcomes which are even number = 3

Probability of getting an even number = 3/6 = 1/2

The probability of flipping two tails and rolling an even number is,

P = 1/4 × 1/2 = 1/8

Hence the required probability is 1/8.

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Answer:

11 ounces

Step-by-step explanation:

It is not possible to make a prediction about the number of items purchased by someone who paid $35 without more information.

Addition is a mathematical operation that combines two or more numbers to create a new, larger number. The result of an addition operation is called the sum. Addition is typically denoted by the plus sign (+), and the numbers being added are called addends. Addition is a basic arithmetic operation and is used extensively in mathematics. It is one of the four basic operations, along with subtraction, multiplication, and division. Addition is commutative, meaning that the order in which the addends are added does not affect the sum.

Here,

In order to make a reasonable prediction about the number of items purchased, we would need to know the cost of each item, any discounts or promotions applied, and any additional fees or taxes. Without this information, any prediction about the number of items purchased would be purely speculative.

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Answer:

\(m\widehat{VU}=120^{\circ}\)

Step-by-step explanation:

The angle \(\angle TUV\) forms arc \(\widehat{TV}\). The measure of this arc is twice the measure of angle \(\angle TUV\), since \(U\) is a point on the circle. Since \(\overline{TU}\) forms an arc \(\widehat{TU}\), we can set up the following equation:

\(\widehat{TV}+\widehat{VU}=\widehat{TU}\).

Since arc TU represents half of a circle and there are 360 degrees in a circle, we can substitute the following values and solve for the measure of arc VU:

\(\\2\cdot 30^{\circ}+\widehat{VU}=180^{\circ},\\60^{\circ}+\widehat{VU}=180^{\circ},\\m\widehat{VU}=\boxed{120^{\circ}}\)

The results from the given data,

Mean = 0

Median = 0

Mode = 0

To find the mean, median, and mode of the given data set {-4, -3, -2, -1, 0, 0, 1, 2, 3, 4},

we'll calculate each of these measures step by step:

Mean, To find the mean, we sum up all the values in the data set and divide by the total number of values:

Mean = (-4 + -3 + -2 + -1 + 0 + 0 + 1 + 2 + 3 + 4) / 10

Mean = 0 / 10

Mean = 0

Median, The median is the middle value when the data set is arranged in ascending order.

Since we have 10 values, the median will be the average of the fifth and sixth values:

Arranged data set: -4, -3, -2, -1, 0, 0, 1, 2, 3, 4

Median = (0 + 0) / 2

Median = 0

Mode, The mode is the value(s) that appear(s) most frequently in the data set. In this case, the mode is 0 since it appears twice, more than any other value in the data set.

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Answer:

N=6

Step-by-step explanation:

−3(

Answer:

96

Step-by-step explanation:

100%-60%=40%

40% of x = 64 students (X=Total no. of students)

(40/100)*x=64

x=64*(100/40)

x=160

Missing no. of students=160-64=96

Answer:

96 students

Pls mark me brainliest!

Step-by-step explanation:

If an unknown amount of students is 60% of the students, the 64 of the students must be 40% of the students because 40+60 = 100.

You want to find what 1% equals, so we will divide 64 by 40 because 40% divided by 40 = 1% and whatever you do to one side you do to the other.

64/40 = 1.6

Assuming that the ? number of students that equals 60% will be a whole number, lets go with 1.6.

If 1.6 = 1%, and we want 60%, then multiply both sides by 60, because 1*60 = 60.

1.6*60 = 96

96 students

(1x - 3) - 5 > 4

Simplify the left side:

1x - 3 - 5 > 4

1x - 8 > 4

Add 8 to both sides:

1x - 8 + 8 > 4 + 8

1x > 12

Simplify:

x > 12

The solution to the inequality is all values of x that are greater than 12. On a number line, this would be all values to the right of 12, but not including 12. We can represent this graphically by shading the region to the right of 12 on a number line and using an open circle to indicate that 12 is not included in the solution.

Answer:

1/2

Step-by-step explanation:

options in a 6 sided die= 1,2,3,4,5,6

greater than 3 = 4,5,6

so three  sides  out of a 6 sided die is greater than three

P(not greater than 3) = \(\frac{6-3}{6} = \frac{1}{2}\)

Answer:

1/2 or 0.5

Step-by-step explanation:

The probability of rolling a number greater than 3 on a six-sided die is 3/6 or 1/2, since there are three numbers (4, 5, 6) out of six that are greater than 3.

To find the probability of not rolling a number greater than 3, we can subtract the probability of rolling a number greater than 3 from 1:

P(not greater than 3) = 1 - P(greater than 3)

P(not greater than 3) = 1 - 1/2

P(not greater than 3) = 1/2

Therefore, the probability of not rolling a number greater than 3 is 1/2 or 0.5.

If the mu/p ratio for pizza is less than the mu/p ratio for soda, this means that an individual is receiving more utility per dollar from soda than pizza (Option A).

In other words, the marginal utility of spending one more dollar on soda is greater than spending one more dollar on pizza. This doesn't necessarily mean that the price of pizza is lower than the price of soda (Option B) or that the price of pizza is lower than the price of coke (Option C), as the prices of the two goods could be equal or have different relative prices. It also doesn't mean that the MU of pizza is lower than the MU of soda (Option D), as the MU of each good could be different regardless of their price ratios.

The final answer is: Option A

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The Taylor polynomial of degree 2 for f(x) = sin(x) around x = 0 is P2(x) = x. The Maclaurin series for f(x) = xe^2x is x^2.  Therefore, the Maclaurin series for f(x) = xe^2x converges for all values of x, and its radius of convergence is infinite. The interval of convergence is (-∞, +∞).

To find the Taylor polynomial of degree 2 for f(x) = sin(x) around x = 0, we can use the Taylor series expansion formula, which states that the nth-degree Taylor polynomial is given by:

Pn(x) = f(a) + f'(a)(x - a) + (f''(a)/2!)(x - a)^2 + ... + (f^n(a)/n!)(x - a)^n

In this case, a = 0 and f(x) = sin(x). We can then evaluate f(a) = sin(0) = 0, f'(a) = cos(0) = 1, and f''(a) = -sin(0) = 0. Substituting these values into the Taylor polynomial formula, we get:

P2(x) = 0 + 1(x - 0) + (0/2!)(x - 0)^2 = x

Therefore, the Taylor polynomial of degree 2 for f(x) = sin(x) around x = 0 is P2(x) = x.

Moving on to the Maclaurin series for f(x) = xe^2x, we need to find the successive derivatives of the function and evaluate them at x = 0.

Taking derivatives, we get f'(x) = e^2x(1 + 2x), f''(x) = e^2x(2 + 4x + 2x^2), f'''(x) = e^2x(4 + 12x + 6x^2 + 2x^3), and so on.

Evaluating these derivatives at x = 0, we find f(0) = 0, f'(0) = 0, f''(0) = 2, f'''(0) = 0, and so on. Therefore, the Maclaurin series for f(x) = xe^2x is:

f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ...

Simplifying, we have:

f(x) = 0 + 0x + 2x^2/2! + 0x^3/3! + ...

Which further simplifies to:

f(x) = x^2

The Maclaurin series for f(x) = xe^2x is x^2.

To find the radius and interval of convergence of the Maclaurin series, we can apply the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is L as n approaches infinity, then the series converges if L < 1, diverges if L > 1, and the test is inconclusive if L = 1.

In this case, the ratio of consecutive terms is |(x^(n+1))/n!| / |(x^n)/(n-1)!| = |x/(n+1)|.

Taking the limit as n approaches infinity, we find that the limit is |x/∞| = 0, which is less than 1 for all values of x.

Therefore, the Maclaurin series for f(x) = xe^2x converges for all values of x, and its radius of convergence is infinite. The interval of convergence is (-∞, +∞).

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Answer:

5s + 0.65 = 14.4

      - 0.65  - 0.65

______________

5s = 13.75

___.   ___

5          5

s = 2.75 meters of string for each pennant

Explanation:

s represents the length of string required for each pennant.

We know that Ingrid is using a total of 14.4 meters of string to hang a banner and 5 pennants.

We also know that out of that 14.4 meters, 0.65 meters is used to hang the banner. The rest of the string left is equally distributed among the 5 pennants.

So, therefore, we have a constant of 0.65 and a coefficient of 5 with variable, s.

Next, we solve this by first isolating the constant by subtracting 0.65 on both sides.

Then. we isolate the variable by dividing 5 into both sides.

So, s = 2.75 meters of string for each pennant