30 points!!!!

- Part A: Explain why x = 5 makes 4x - 13 19 true but not 4x -1 < 19. (5 points)

Part B: What value from the set (6,7,8,9,10} makes the equation 5x + 2 = 47 true? Show your work (5 points)
​

The vector parametric equation for the line through the point (4, -1) that is perpendicular to the line (-2 - 5t, -5 - 2t) is L(t) = <4 - (2/5)t, -1 + (5/2)t>.

To find a vector parametric equation for the line through the point (4, -1) that is perpendicular to the line (-2 - 5t, -5 - 2t), we need to determine the direction vector of the perpendicular line.

The given line (-2 - 5t, -5 - 2t) has a direction vector <5, 2>. To obtain a direction vector perpendicular to this, we can take the negative reciprocal of the components, giving us a direction vector of <-2/5, 5/2>.

Now, we can write the vector parametric equation for the line:

L(t) = <4, -1> + t<-2/5, 5/2>

Expanding the equation, we have:

L(t) = <4, -1> + <-2/5, 5/2>t

Simplifying, we get:

L(t) = <4 - (2/5)t, -1 + (5/2)t>

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The correct form of a particular solution of the differential equation y" + 4y = cos (2x) is y_p = A cos (2x) + B sin (2x).

The complementary function of the differential equation is y_c = C_1 cos (2x) + C_2 sin (2x), where C_1 and C_2 are constants determined by the initial conditions.

To find the particular solution, we assume that y_p has the same form as the forcing function, which is cos (2x). Since the equation is linear, we can superimpose the particular solution on top of the complementary function, so we have:

y_p = A cos (2x) + B sin (2x)

Taking the first and second derivatives of y_p, we get:

y'_p = -2A sin (2x) + 2B cos (2x)

y''_p = -4A cos (2x) - 4B sin (2x)

Substituting these expressions into the differential equation, we have:

(-4A cos (2x) - 4B sin (2x)) + 4(A cos (2x) + B sin (2x)) = cos (2x)

Simplifying, we get:

(4B - 4A) sin (2x) + (4A + 4B) cos (2x) = cos (2x)

We can solve for A and B by equating coefficients of sin (2x) and cos (2x) on both sides of the equation. This leads to:

A = 0

B = 1/4

Therefore, the particular solution is y_p = A cos (2x) + B sin (2x) = 1/4 sin (2x).

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Answer:

the asnwer is 15

Step-by-step explanation:

firts add sevent in both sides

7x=105

Then divide by 7

105/7=x

x=15

Answer

x=15

Step-by-step explanation:

first step 7x=98+7 second step 7x=105 third step x=105/7 fourth step is your answer which is x=15

check it =

7x15-7=98

105-7=98

98=98

After six years, the population will grow to 586,455 if compounded annually at a rate of 7.5%.

This is exactly like a compound interest problem where the interest rate is 7.5% compounded annually for 6 years.

If we use the compound interest formula A = P(1+r/n)nt where A is the end amount to be found, p = initial amount (p= 380,000), n = number of times the interest is compounded annually (n= 1) and t is the time in years (t=6)

A = 380,000(1 + .075/1)1(6)

A = 380,000(1.075)6

A = 586,454.58 people

Rounded to the nearest whole number

the population after 6 years should be

586,455 people

Hence we get the required answer.

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Your question is incomplete. Please find the missing content below.

A city has a population of 380,000 people. suppost that each year the population grows by 7.5%. what will be the population after 6 years.

7h-15h+40=-72

40+72=15h-7h

112=8h

h=14

We can calculate probability when coin is flipped by \(C(n, k) / 2^n\)

To calculate the probability of getting an equal number of heads and tails when a fair coin is flipped n times, we'll use the binomial coefficient formula. Here's a step-by-step explanation:

1. Ensure that n is an even number, as an equal number of heads and tails is only possible with an even number of flips.

2. Divide n by 2 to find the number of heads (or tails) required for an equal outcome. Let's call this k.

3. Calculate the binomial coefficient, which is the number of ways to choose k heads (or tails) from n flips. This is represented as C(n, k) or "n choose k" and can be calculated using the formula:

  C(n, k) = \(n! / (k!(n-k)!)\)

  where n! is the factorial of n (n*(n-1)*...*1), and similarly for k! and (n-k)!.

4. Calculate the total possible outcomes for n coin flips. Since there are 2 possible outcomes (heads or tails) for each flip, there are \(2^n\)total outcomes.

5. Calculate the probability of getting an equal number of heads and tails by dividing the number of favorable outcomes (C(n, k)) by the total possible outcomes (2^n):

  Probability =\(C(n, k) / 2^n\)

By following these steps with your given value of n, you can find the probability of getting an equal number of heads and tails when flipping a fair coin n times.

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The equation\(2^2 = 3^2\) does not define any of the given shapes, as it is simply a false statement. The equation \(y^{2/2 }= x^{2/2\) does define a hyperbolic paraboloid.

On the other hand, the equation \(y^{2/2 }= x^{2/2\) defines a hyperbolic paraboloid. A hyperbolic paraboloid is a three-dimensional surface that has a saddle-like shape, with two opposing parabolic curves that cross each other. It is also known as a "saddle surface" due to its shape.

The equation \(y^{2/2 }= x^{2/2\) can be rewritten as \(y^{2/2 }= x^{2/2\), which is in the form of a hyperbolic paraboloid equation. This surface can be obtained by taking a parabolic curve and sweeping it along a straight line in a perpendicular direction. This creates a surface with a hyperbolic cross-section in one direction and a parabolic cross-section in the other direction.

Hyperbolic paraboloids have a wide range of applications in architecture, engineering, and design. They are often used in the construction of roofs, shells, and other structures that require strong and lightweight materials. They can also be used to create interesting and unique shapes in art and sculpture.

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The equation 2x^2 = 3y^2 does not define any of the given three-dimensional shapes.

This is because it does not contain a z variable, which is necessary to define these shapes in three dimensions. Therefore, the equation cannot represent any of the given shapes.

On the other hand, the equation y^2 = 2x defines a hyperbolic paraboloid. This is a three-dimensional shape that resembles a saddle. It is formed by taking a hyperbola and rotating it around its axis. In this case, the hyperbola is oriented along the x-axis, and the parabolic cross-sections occur in the y-direction.

The equation can be rewritten as y^2 = 2(x - 0)^2, which is the standard form of a hyperbolic paraboloid. This equation can be graphed in a three-dimensional coordinate system, with the x-axis and y-axis forming the base and the z-axis representing the height of the surface above the base.

The shape is characterized by its saddle-like appearance, with two opposing hyperbolic curves along the x-axis and two opposing parabolic curves along the y-axis.

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The test used to determine whether or not first-order autocorrelation is present is the Durbin-Watson test.

1. Fit a regression model to the data.

2. Obtain the residuals, which represent the differences between the observed values and the predicted values from the regression model.

3. Calculate the Durbin-Watson statistic, which is a ratio of the sum of squared differences between adjacent residuals to the sum of squared residuals.

4. Compare the calculated Durbin-Watson statistic to critical values from a Durbin-Watson table or use statistical software to determine if there is significant autocorrelation.

5. The Durbin-Watson statistic ranges from 0 to 4, where a value around 2 suggests no autocorrelation, a value below 2 indicates positive autocorrelation, and a value above 2 indicates negative autocorrelation.

6. By analyzing the Durbin-Watson statistic, researchers can make conclusions about the presence or absence of first-order autocorrelation in the regression model.

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the total amount of money that jayden made when both paychecks were the same is $99.45

To determine the number of hours Jayden worked the week his paycheck was the same for both jobs, we can solve an equation. The equation we'll use is 14.86h + 17.10 = 99.45. We can subtract 17.10 from both sides, leaving 14.86h = 82.35. Then we cane b divide both sides of the equation by 14.86, which will give us the result of h = 5.55 hours. The total amount of money that Jayden made when both paychecks were the same is 99.45. This can be confirmed by combining his earnings for both jobs, which would be 9.64h + 82.35 + 14.86h + 17.10 = 99.45.

Jayden worked 5.55 hours in the week his paycheck was the same for both jobs, and he earned a total of $99.45.

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Answer:

-7.8n+7.9

Step-by-step explanation:

Answer:

well if you have 10 and you subtract 2 you get 8 it really simple  

Step-by-step explanation:

if its in slope intercept witch I expect then,

Y=Mx+b

Y=1/5+4

There are 20 different combinations of colors possible in a 6-pack of lacrosse balls.

What is the combination?

A combination is a choice of items from a group of different items where the order of the choices is irrelevant. Either the process of combining or the condition of combining. a combination of several things a mixture of thoughts. something created through fusion: A chord is made up of several notes.

Here, we have

Given: lacrosse balls come in 3 colors: red, yellow, and blue.

We have to find the different combinations of colors that are possible in a 6-pack of lacrosse balls.

We apply here combination formula and we get

= ⁶C₃

= (6×5×4×3!)/(3!×3×2×1)

= 20

Hence, there are 20 different combinations of colors possible in a 6-pack of lacrosse balls.

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The combined mass of Kylie's quarters is 11.863 g.

The quarter, also known as one-fourth is an English units based on ¼ sizes of some base unit.

To get combined mass of Kylie's quarters, we will add the mass of the modern quarter and the mass of the older silver quarter together.

The combined mass of Kylie's quarters is:

= 5.623 g + 6.24 g

= 11.863 g

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a) The 90% confidence interval for the population mean is approximately (21.52, 23.48).

b) The 95% confidence interval for the population mean is approximately (21.322, 23.678).

c) The 99% confidence interval for the population mean is approximately (20.926, 24.074).

To develop confidence intervals for the population mean, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard error)

where the standard error is equal to the sample standard deviation divided by the square root of the sample size.

a) For a 90% confidence interval, we need to find the critical value corresponding to a confidence level of 90%. The critical value can be obtained from the t-distribution table with (n-1) degrees of freedom. Since the sample size is 56, the degrees of freedom is 56-1 = 55.

From the t-distribution table, the critical value for a 90% confidence interval with 55 degrees of freedom is approximately 1.671.

The standard error can be calculated as:

Standard Error = sample standard deviation / sqrt(sample size)

Standard Error = 4.4 / sqrt(56)

Standard Error ≈ 0.5882

Now we can calculate the confidence interval:

Confidence Interval = 22.5 ± (1.671 * 0.5882)

Confidence Interval = 22.5 ± 0.9816

Confidence Interval ≈ (21.52, 23.48)

b) For a 95% confidence interval, the critical value for 55 degrees of freedom is approximately 2.004 (obtained from the t-distribution table).

Standard Error = 4.4 / sqrt(56) ≈ 0.5882

Confidence Interval = 22.5 ± (2.004 * 0.5882)

Confidence Interval = 22.5 ± 1.178

Confidence Interval ≈ (21.322, 23.678)

c) For a 99% confidence interval, the critical value for 55 degrees of freedom is approximately 2.678 (obtained from the t-distribution table).

Standard Error = 4.4 / sqrt(56) ≈ 0.5882

Confidence Interval = 22.5 ± (2.678 * 0.5882)

Confidence Interval = 22.5 ± 1.574

Confidence Interval ≈ (20.926, 24.074)

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Answer:

Step-by-step explanation:

The cabinet is rectangular shaped. Using the formula for calculating the surface area of a reactangular bos to solve the problem.

Surface area = 2(LW+WH+LH) where;

L is the length of the cabinet

W is the width of the cabinet

H is the height of the cabinet.

If the entire outside of the cabinet is being painted, except for the bottom, then the surface area of the painted area will be expressed as;

S = LW+2WH+2LH

Given L = 2 feet, W = 3 feet and H = 6 feet

S = 2(3)+2(3*6)+2(2*6)

S = 6+2(18)+2(12)

S = 6+36+24

S = 66 feet²

Hence the surface area of the painted part is 66ft²

Answer and Step-by-step explanation:

For the first part

Tara is incorrect as she practices the softball in 4 days in a week and she do each practice of minimum one hour

So we can conclude that she practices minimum hours in a week  

For the second part

Also in 4 days, she does practice \(1 \frac{1}{3}\) hours per day i.e \(5 \frac{1}{3}\)

Now convert \(1 \frac{1}{3}\) this into a fraction which comes \(\frac{4}{3}\)

For four days, it is

= \(4 \times \frac{4}{3} \\\\ \frac{16}{3} \\\\ 5 \frac{1}{3}\)

Step-by-step explanation:

Without multiplying, explain how you know Tara is incorrect.

How long will Tara have softball practice this week? Write your answer as a mixed number.  

Each practice is \(1\frac{1}{3}\) hours

Each practice is more than 1 hour. so 4 days of practice is more than 4 hours.

So Tara is incorrect

Practice for 4 days

\(1\frac{1}{3}+1\frac{1}{3}+1\frac{1}{3}+1\frac{1}{3}=4\frac{4}{3}=5\frac{1}{3}\)

More than 5 hours .

Tara will have \(5\frac{1}{3}\) softball practice this week

Answer:

Tara will have \(5\frac{1}{3}\)  hours softball practice this week

The acutal width of the picnic area by using proportion if the scale used is 3 inches : 2 yards will be 60 yards.

Let the actual width of the picnic area be x yards.

According to the given question.

Laura measured a picnic area near the river and made a scale drawing.

The scale she used was 3 inches : 2 yards.

⇒ The scale is 3 inches : 2 yards

The width of the picnic area in the drawing is 90 inches.

As we know that, a proportion is a fraction of a total amount, and the measures are related using a rule of three.

Thereofore, the acutal width of the picnic area by using proportion if the scale used is 3 inches : 2 yards is given by

3inches : 2 yards = 90inches : x

⇒ 3x = 180

⇒ x = 60yards

The acutal width of the picnic area by using proportion if the scale used is 3 inches : 2 yards will be 60 yards.

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The approximate increase in Area of the parking lot is about 133%

Area of a rectangle = Length × width

Initial Area of parking lot :

New Area of parking lot :

Width = 75 + 100 = 175 feets

Length = 150 feets

Area = 175 × 150 = 26250 ft²

Percentage increase in Area of lot :

((16250 - 11250) / initial Area) × 100%

(15000 / 11250) × 100% = 133.33%

Therefore, the approximate increase on area of lot is 133%

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Autumn's volunteer rate is 2 1/4 hours. It is greater than the challenge rate.

In order to determine her volunteer rate, divide the total number of hours by the total number of weeks.

Volunteer rate = total hours / number of weeks

63/4÷ 3

27 / 4 x 1/3 = 9/4 = 2 1/4

Autumn's volunteer rate exceeds the minimum rate they are advised.

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The projected balance of cash at the end of August is $38,000. The correct option is D.

To calculate the projected balance of cash at the end of August, we need to consider the cash balance at the beginning of the month, cash collections, and cash payments for August.

Given that the cash balance on July 31 was $32,000.00, we start with this amount.

Cash collections for August are $52,000.00, which means this amount is added to the cash balance.

Next, we consider cash payments for August, which include purchases of direct materials and operating expenses. The total cash payments for August are $20,000 (purchases of direct materials) + $26,000 (operating expenses) = $46,000.00. This amount is subtracted from the cash balance.

Finally, we calculate the projected balance of cash at the end of August by adding the cash collections and subtracting the cash payments from the beginning cash balance:

Projected cash balance at the end of August = Beginning cash balance + Cash collections - Cash payments

= $32,000 + $52,000 - $46,000

= $38,000

Therefore, correct option is D.

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Complete question is:

Berman Company is preparing its budget for the third quarter. Cash balance on July 31 was $32,000.00. Assume there is no minimum balance of cash required and no borrowing is undertaken. Additional budgeted data are provided here:

                                         July           Aug             Sep

Cash collections       $51,000.00 $52,000.00 $50,000.00

Cash payments

Purchases of direct materials     23,000     20,000        24,000

Operating expenses       32,000      26,000    22,000

Capital expenditures      7,000       9,000      13,000

Calculate the projected balance of cash at the end of August.

A. $23000

B. $29000

C. $107000

OD. $38000

Answer:

39

Step-by-step explanation:

Answer:

You would distribute 7 to the numbers inside the parentheses.

Step-by-step explanation:

7(-4p + 3) ---> -28p + 21.

The Hall's Marriage Theorem holds, and there exists a perfect matching of the men and women on the island so that everyone is matched with someone they are willing to marry.

The Hall's Marriage Theorem.

Let there be m men and w women on the island.

It is possible to match them so that everyone is matched with someone they are willing to marry.

First, we need to prove that for any subset S of men on the island, the number of women that they are collectively willing to marry is at least |S|k.

Let S be any subset of men on the island.

Since every man is willing to marry exactly k women, the number of women that any single man is willing to marry is k.

The number of women that S collectively is willing to marry is at least |S|k.

Next, we need to prove that for any subset T of women on the island, the number of men that they are collectively willing to marry is at least |T|k.

Let T be any subset of women on the island.

Since every woman is willing to marry exactly k men, the number of men that any single woman is willing to marry is k.

The number of men that T collectively is willing to marry is at least |T|k.

Now, we need to show that the Hall's Marriage Theorem holds.

That is, we need to show that for any subset S of men on the island, the number of women that they are collectively willing to marry is at least |S|, and for any subset T of women on the island, the number of men that they are collectively willing to marry is at least |T|.

Suppose, for the sake of contradiction, that there exists a subset S of men on the island such that the number of women that they are collectively willing to marry is less than |S|.

Then, by the first proof, the number of women that they are collectively willing to marry is at least |S|k. Since |S|k < |S|, this leads to a contradiction.

Similarly, suppose there exists a subset T of women on the island such that the number of men that they are collectively willing to marry is less than |T|.

Then, by the second proof, the number of men that they are collectively willing to marry is at least |T|k. Since |T|k < |T|, this leads to a contradiction.

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We want to solve the proportion:

For doing so, we remember that solving a proportion equivals to find the variable x. We will multiply means and extremes:

This means that the value of x is 8, which is the solution of the proportion.

The total number of different lists is \(10^3\), which equals 1000. Therefore, there are 1000 different possible lists.

To explain why there are 1000 different possible lists, we can break down the process.

Joe chooses a ball from a bin and records the number. Since there are 10 balls in the bin, he has 10 choices for the first number.

After recording the number, Joe puts the ball back in the bin, so for the second number, he again has 10 choices. The same process repeats for the third number, giving Joe another 10 choices.

Since each selection is independent and there are 10 choices for each selection, we can multiply the number of choices together to find the total number of different lists.

Therefore, the total number of different lists is 10 * 10 * 10, which equals 1000.

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By taking the quotient between the total volume of paint and the volume needed to fill a container we can see that 16 containers can be filled.

We know that the art teacher has 12 + 4/5 gallons of paint, and we know that it requires 4/5 gallons to fill a single container.

Then the number of containers that can be filled is equal to the quotient between the total volume of paint and the volume needed fill a single container, it gives:

(12 + 4/5)/(4/5) = 16

So 16 containers can be totally filled.

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After solving the equation the value of x is -12. So the option b is correct.

The first step to solving an equation is to identify the unknown variable(s). Once the unknown variable(s) is identified, the next step is to isolate the variable(s) on one side of the equation. After isolating the variable(s), you can then use inverse operations to solve the equation. Finally, check your answer to make sure it makes sense in the context of the equation.

The equation is −10x + 1 + 7x = 37.

To solve that equation we first simplify the equation.

After simplifying the equation we isolate the variable of x.

−10x + 1 + 7x = 37

-3x + 1 = 37

Subtract 1 on both side, we get

-3x = 36

Divide by -3 on both side, we get

x = -12

So the option b is correct.

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The complete question is:

Solve the equation.

−10x + 1 + 7x = 37

a. x = -15

b. x = -12

c. x = 12

d. x = 15