3). AFTER PAYING HER BILLS CAROL HAS -$45 IN HER CHECKING
ACCOUNT. SHE RECEIVES A $150 PAYCHECK. HOW MUCH MONEY
DOES SHE HAVE IN HER ACCOUNT NOW?

The correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3)

For the first question:

The table shows a proportional relationship between x and y. To describe what the graph of this proportional relationship would look like, we can examine the given data points.

The data points are (12, 3), (8, 26), and (24, ?). We can observe that as x increases, y also increases. This indicates a positive correlation between the variables. Additionally, we can see that the ratio of y to x remains constant for each data point.

Now, let's analyze the answer options:

A. A line passes through the point (0, 0) and continues through the point (3, 12).

This answer option does not align with the given data because there is no data point with an x-value of 3 and a corresponding y-value of 12.

B. A line passes through the point (0, 0) and continues through the point (2, 8).

This answer option aligns with the given data because (2, 8) is a valid data point from the table, and the line passes through the origin (0, 0).

C. A line passes through the point (0, 0) and continues through the point (6, 24).

This answer option does not align with the given data because there is no data point with an x-value of 6 and a corresponding y-value of 24.

D. A line passes through the point (0, 0) and continues through the point (12, 3).

This answer option aligns with the given data because (12, 3) is a valid data point from the table, and the line passes through the origin (0, 0).

Based on the analysis, the correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3). This accurately represents the graph of the proportional relationship given in the table.

For the second question, I'm sorry, but you didn't provide the multiple-choice options or the complete question. Could you please provide the question and options so that I can assist you further?

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Answer: 0.0208

Step-by-step explanation:

Given: The length of time to find a parking spot on the UW campus is normally distributed with a mean of 4.75 minutes and a standard deviation of 1.35 minutes.

Let x = time taken to find parking spot

The probability that a randomly selected driver takes less than 2 minutes to find a parking spot on the UW campus will be :

\(P(x<2)=P(\dfrac{x-\mu}{\sigma}<\dfrac{2-4.75}{1.35})\\\\=P(Z<-2.037)\ \ \ [z=\dfrac{x-\mu}{\sigma}]\\\\=1-P(Z<2.037)\\\\=1- 0.9792=0.0208\ \ \ \text{[By p-value table]}\)

Hence, the probability than a randomly selected driver takes less than 2 minutes to find a parking spot on the UW campus.= 0.0208

The dot product of vectors a and b is option D. 30.

To find the dot product of two vectors, you need to multiply their corresponding components and then sum the results.

Let's calculate the dot product of vectors a = <5, 2> and b = <4, 5>:

a • b = (5 x 4) + (2 x 5)

= 20 + 10

= 30

Therefore, the dot product of vectors a and b is 30.

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Answer:

Step-by-step explanation:

To show that the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\), we can simplify both sides of the equation using the properties of logarithms. Here are the steps:

Step 1: Simplify the expression on the left side:

\(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\)

Step 2: Apply the logarithmic property \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\) to combine the logarithms:

\(\ln\left(\frac{\sqrt{2} + 1}{\frac{1}{\sqrt{2}}}\right)\)

Step 3: Simplify the expression within the logarithm:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)}\right)\)

Step 4: Simplify the denominator by multiplying by the reciprocal:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)} \cdot \sqrt{2}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{\left(\frac{1}{\sqrt{2}}\right) \cdot \sqrt{2}}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

Step 5: Simplify the numerator:

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

\(\ln\left(\sqrt{2}(\sqrt{2} + 1)\right)\)

\(\ln\left(2 + \sqrt{2}\right)\)

Now, let's simplify the right side of the equation:

Step 1: Simplify the expression on the right side:

\(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\)

Step 2: Simplify the expression within the logarithm:

\(-\ln\left(\frac{\sqrt{2} - 1}{\sqrt{2}}\right)\)

Step 3: Apply the logarithmic property \(\ln\left(\frac{a}{b}\right) = -\ln\left(\frac{b}{a}\right)\) to switch the numerator and denominator:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

Step 4: Simplify the expression:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

\(-\ln\left(\frac{\sqrt{2}(\sqrt{2} + 1)}{1}\right)\)

\(-\ln\left(2 + \sqrt{2}\right)\)

As we can see, the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) simplifies to \(\ln(2 + \sqrt{2})\), which is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\).

Answer:

B

Step-by-step explanation:

6x -8y = - 16y

6x = -8y

8y = 17x + 4

-8y = -17x - 4

6x = -17x - 4

23x = -4

x = -4/23

Answer:

hello ok I will share u the link where u can find step by step answers

Answer:

The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.

A Let tower be AB

Let point be C

Distance of point C from foot of tower = 30m Hence,

BC = 30m

Angle of elevation = 30°

So < ACB = 30°

Since tower is vertical,

< ABC = 90°

The acceleration of the collar at point A is 5 ft/s^2.

A) To determine the normal force on the collar at point A, we need to consider the forces acting on the collar. The only force acting on the collar in the vertical direction is the weight of the collar (5 lb), which is balanced by the normal force exerted by the rod. Therefore, we can write:

N - 5 = 0

where N is the normal force. Solving for N, we get:

N = 5 lb

B) To determine the acceleration of the collar at point A, we need to use Newton's second law, which states that the net force acting on an object is equal to its mass times its acceleration. The net force on the collar is given by the force exerted by the spring, which is equal to the spring constant times the displacement of the collar from its unstretched length. At point A, the displacement of the collar is:

x = L - y = 3 - 0 = 3 ft

where L is the length of the rod and y is the position of the collar on the rod. Therefore, the force exerted by the spring is:

F = kx = 10 lb/ft × 3 ft = 30 lb

The weight of the collar is:

W = mg = 5 lb

where g is the acceleration due to gravity. The net force on the collar is therefore:

Fnet = F - W = 30 - 5 = 25 lb

Using Newton's second law, we can write:

Fnet = ma

where a is the acceleration of the collar. Solving for a, we get:

a = Fnet / m = 25 lb / 5 lb = 5 ft/s^2

Therefore, the acceleration of the collar at point A is 5 ft/s^2.

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You can just cross out the Xs. Hope this helps.

Answer:

65.9734457254 (65.97 =2dp)

Step-by-step explanation:

equation

diameter x pi = circumference

21 x pi = 65.9734457254

Answer:

69.08

Step-by-step explanation:

circumference= πd

3.14×21= 69.08

9514 1404 393

Answer:

  B

Step-by-step explanation:

To find the graph of the inverse function, swap the labels x and y on the axes of the given graph.

There are no x-values common to all the tables, but you can make a determination of the correct one by looking at x=1 and x=-1.

After you swap the axis labels you see that the points ...

  (x, y) = (1, -2) or (-1, -3)

are on the graph. These points are only found in the table of selection B.

The table contains points from the inverse of the graphed function is B. Table 2.

A graph simply means a diagram that represents the variation of a variable when being compared with other variables.

In this case, the inverse of the graphed function will simply be done by switching all the values of x and y in each point. This is clearly illustrated in the second table.

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Answer:

a) yes

The point ( 1,-3) lie on the given line y = 5x-8

b) No

 The point ( -2,-7) does not lie on the given line y = -3 x +1        

Step-by-step explanation:

Step(i):-

a)   Given line  y = 5 x - 8 ...(i)

   Point ( 1, -3 )

 substitute  ( 1,-3 ) in equation (i)

           -3 = 5(1) - 8

         -3 = 5 -8

         -3 = -3

∴ The point ( 1,-3) lie on the given line y = 5x-8

b)

Given line  y = -3 x +1 ...(i)

   Point ( -2, -7 )

 substitute  (-2, -7 ) in equation (i)

           -7 = -3(-2) +1

         -7 ≠ 7

 The point ( -2,-7) does not lie on the given line y = -3 x +1        

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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From the directory for her state, Haylee randomly chooses 10 small firms. Assume that the binomial variable BBBB represents the number of the firms she chooses that have websites.

The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and having its own Boolean-valued outcome: success (with probability p) or failure (with probabilitq=1-pq=1-p).

This distribution is used in probability theory and statistics.

A Bernoulli trial, or experiment, is another name for a single success-or-failure experiment, and a Bernoulli process is another name for a series of results. For a single trial, or n = 1, the binomial distribution is a Bernoulli distribution.

The popular binomial test of statistical significance is based on the binomial distribution.

A sample of size n drawn with replacement from is widely used to model the number of successes using the binomial distribution.

Hence, From the directory for her state, Haylee randomly chooses 10 small firms. Assume that the binomial variable BBBB represents the number of the firms she chooses that have websites.

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Answer:

2007

Step-by-step explanation:

If the number of visitors was, say, 100 people in 2003, then in 2005 that number would have gone up to 300 people, which is a 200% increase. And that number would have gone up to 900 people in 2007, which is an 800% increase.

Answer:

2007

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The length of line x in the figure of the cube given is 19.

Calculate the length of the base of the cube, which is the diagonal of the lower sides :

base length = √10² + 6²

base length = √136

The length of x is the diagonal of the cube

x = √(√136)² + 15²

x = √136 + 225

x = √361

x = 19

Therefore, the length of line x in the figure given is 19.

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The correct graph of the relationship is shown in Option D.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Mr. Mole left his burrow that lies below the ground and started digging his way at a constant rate deeper into the ground.

Now, Let y represent Mr. Mole's altitude (in meters) relative to the ground after x minutes.

Hence, The graph of line goes down with constant rate.

Thus, The correct graph of the relationship is shown in Option D.

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Answer:

the length of the line is 7

Step-by-step explanation:

it is b. 7

Answer:

Option 2

Step-by-step explanation:

The first statement is false because the price for 10 gallons is about $37 from the graph. Using this same reasoning, the third statement is also false. The last statement doesn't make sense because the graph has nothing to do with the amount of miles driven. Therefore, the answer is the second statement. We can prove it by looking at the point (4, 15). This means that it costs $15 for 4 gallons, so then the price for one gallon will be 15 / 4 = $3.75.

The solution of the geometric system is (x, AB, BC, AC) = (10, 14, 19, 33).

In accordance with geometry, three points are collinear if and only if these points lie on the same line. Then, the geometric system is represented by the following model:

AC = AB + BC

If we know that AB = x + 4, BC = 2 · x - 1 and AC = 4 · x - 7, then the value of x and the lengths of the line segments are, respectively:

4 · x - 7 = (x + 4) + (2 · x - 1)

4 · x - 7 = 3 · x + 3

x = 10

AB = 10 + 4

AB = 14

BC = 2 · 10 - 1

BC = 20 - 1

BC = 19

AC = 4 · 10 - 7

AC = 40 - 7

AC = 33

The solution of the geometric system is (x, AB, BC, AC) = (10, 14, 19, 33).

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The length of BD is 18.5 units.

In the given right triangle ABC, with altitude BD drawn to hypotenuse AC, we are given the lengths AD = 22 and DC = 15. We need to find the length of BD.

Let's consider triangle ABD. Since BD is the altitude, it divides the right triangle ABC into two smaller right triangles: ABD and CBD.

In triangle ABD, we have the following sides:

AB = AD = 22 (given)

BD = ?

Now, let's consider triangle CBD. In this triangle, we have the following sides:

BC = DC = 15 (given)

BD = ?

Since triangles ABD and CBD share the same base BD, and their heights are the same (BD), we can say that the areas of these triangles are equal.

The area of triangle ABD can be calculated as:

Area(ABD) = (1/2) * AB * BD

Similarly, the area of triangle CBD can be calculated as:

Area(CBD) = (1/2) * BC * BD

Since the areas of ABD and CBD are equal, we can equate their expressions:

(1/2) * AB * BD = (1/2) * BC * BD

We can cancel out the common factor (1/2) and solve for BD:

AB * BD = BC * BD

Dividing both sides of the equation by BD (assuming BD ≠ 0), we get:

AB = BC

In triangle ABC, the lengths AB and BC are equal, which implies that triangle ABC is an isosceles right triangle. In an isosceles right triangle, the leg's length are congruent, so AB = BC = AD = DC.

BD is equal to half of the hypotenuse AC:

BD = (1/2) * AC

Substituting the given values, we have:

BD = (1/2) * (AD + DC) = (1/2) * (22 + 15) = (1/2) * 37 = 18.5

Therefore, the length of BD is 18.5 units.

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The required value of x is  135° in the given polygon. which is the correct answer would be an option (A).

A polygon is given in the figure

According to the given question, the required solution would be as:

Number of sides = 8

The required value of x is the equal to measure of one Interior angle in the given polygon.

Interior angles of a polygon = (sides - 2) × 180°

In this case, the number of sides is 8

Sum of Interior angles = (8 - 2) × 180

Sum of Interior angles = (6) × 180

Sum of Interior angles = 1080°

the measure of one Interior angle = 180°/8

the measure of one Interior angle = 135°

Thus, the required value of x is  135°.

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Hi! I'd be happy to help you. However, there is not enough information here for us to help, as there is no way to tell which graph is correct without the equations of f(x) and g(x). They'd look something like:

"f(x) = x-2," or "g(x) = 7x+3."

Are you able to provide the equations of of f(x) and g(x)? I would be more than happy to help.

----------------------------------------------------------------------------------------------------------------

UPDATE: I did not realize that you could solve this problem without the original equations. Please refer to the other user's response for an amazing and detailed explanation of this problem! :)

Answer:

The first graph.

Step-by-step explanation:

We want to find the graph that shows:

\(h(x)=f(x)g(x)\)

Notice that g(x) is a line and f(x) is a quadratic.

So, their product must be a cubic.

Also, g(x) and f(x) is the same across all four graphs. The only difference is h(x).

Notice that our quadratic f(x) is curving upwards. Therefore, the leading coefficient of f(x) is positive.

Notice that the line g(x) is sloping downwards. Therefore, the leading coefficient of g(x) is negative.

So, this means that the leading coefficient of our cubic h(x) must be negative since a positive times a negative yields a negative.

Remember that the parent cubic function has a positive leading coefficient and it rises from left to right.

So, if our leading coefficient is negative, the cubic will fall from left to right.

Therefore, we can eliminate the 2nd and 3rd graphs since in those two, h(x) has a positive leading coefficient.

Now, we can just pick a test point and determine whether our graph is the first or the fourth.

Let's let x = -2. So, we have the equation:

\(h(x)=f(x)g(x)\)

Substitute all Xs for -2s:

\(h(-2)=f(-2)g(-2)\)

Looking at the graphs, we can see that f(-2) is 8. g(-2) is 0.5. Substituting this back, we get:

\(h(-2)=8(.5)=4\)

So, h(-2) should be 4.

For the first graph, h(-2) is indeed 4.

For the second graph, h(-2) is 6.

So, the correct graph that represents f(x)g(x) is the first graph.

And we're done!

The graph that represents the function y= tanx is Option A.

The graph of y =tan (x) is a periodic function that has vertical asymptotes at x = (n + 1/2)π, where n is an integer.

It oscillates between positive and   negative infinity, creating a wave-  like pattern.

It has a repeating pattern of sharp peaks and valleys, exhibiting both positive and negative slopes.

Thus, option A is the correct answer.

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The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Answer: 1.To find the mean, we sum up all the scores and divide by the number of scores:

Mean = (5 + 12 + 8 + 14 + 11) / 5 = 50 / 5 = 10

To find the variance, we first find the deviation of each score from the mean:

5 - 10 = -5

12 - 10 = 2

8 - 10 = -2

14 - 10 = 4

11 - 10 = 1

We square each deviation and sum them up:

(-5)^2 + 2^2 + (-2)^2 + 4^2 + 1^2 = 26

Then, we divide by the number of scores to find the variance:

Variance = 26 / 5 = 5.2

Finally, we find the standard deviation by taking the square root of the variance:

Standard deviation = √5.2 = 2.28

2. To construct a simple random sample of size 2, we can choose any two scores from the population. The number of ways to do this is given by the combination formula:

C(5,2) = 5! / (2! * (5 - 2)!) = 10

Therefore, there are 10 simple random samples of size 2 that can be constructed.

3.The mean of the sampling distribution of the sample means is equal to the population mean, which we found to be 10. The variance of the sampling distribution is equal to the population variance divided by the sample size:

Variance of sampling distribution = Variance / Sample size = 5.2 / 2 = 2.6

The standard error of the sampling distribution is the square root of the variance:

Standard error = √2.6 = 1.61

4.The variance of the sampling distribution is 2.6, as we found in part

5. Since this is considered to be data from a simple random sample, we can use the sample mean as a point estimate of the population mean. Therefore, the point estimate of the population mean is 10.

Similarly, we can use the sample variance as a point estimate of the population variance. However, we need to correct for the bias in the sample variance by dividing by (n-1) instead of n:

Point estimate of population variance = Variance * (n / (n-1)) = 5.2 * (5 / 4) = 6.5

Step-by-step explanation:

The fraction of magazines that were delivered to families who were home written as a decimal is 0.4

Difference between fraction and decimal?

Total number of families = 25

Number of families in home = 10

Then, number of families away = 25 - 10 = 15

Fraction of magazines that were delivered to families who were home

= Number of families in home/ Total number of families

= 10 / 25

= 0.4

Hence, the fraction of magazines that were delivered to families who

were home written as a decimal is 0.4

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Answer:

use this info to help answer it

Measure the distance between the two end points, and divide the result by 2. This distance from either end is the midpoint of that line. Alternatively, add the two x coordinates of the endpoints and divide by 2. Do the same for the y coordinates.