Keep getting this answer wrong please help!!

The charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation.

To determine the number of miles at which the charges for the two car services, A and B, are equal, we can set up an equation based on the given information.

Let's represent the charge for car service A as y_A and the charge for car service B as y_B. We can set up the following equations:

For car service A: y_A = 0.60x + 300 (in cents)

For car service B: y_B = 0.75x (in cents)

To find the number of miles at which the charges are equal, we set y_A equal to y_B and solve for x:

0.60x + 300 = 0.75x

Subtracting 0.60x from both sides:

300 = 0.15x

Dividing both sides by 0.15:

x = 300 / 0.15

x = 2000

Therefore, the charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation. Let's use the equation for car service A:

y_A = 0.60(2000) + 300

y_A = 1200 + 300

y_A = 1500 cents or $15.00

So, when each car travels 2000 miles, the charges will be equal at $15.00.

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In polar coordinates, the inequality changes to

\(x^2+y^2\le4x\implies r^2\le4r\cos\theta\implies r\le4\cos\theta\)

which is a circle of radius 2 and centered at (2, 0). The set D is then

\(D=\left\{(r,\theta)\mid0\le r\le4\cos\theta\land0\le\theta\le\pi\right\}\)

The integral is then

\(\displaystyle\iint_D\frac{y^2}{x^2+y^2}\,\mathrm dx\,\mathrm dy=\int_0^\pi\int_0^{4\cos\theta}\frac{r^2\sin^2\theta}{r^2}r\,\mathrm dr\,\mathrm d\theta\)

\(=\displaystyle\int_0^\pi\int_0^{4\cos\theta}r\sin^2\theta\,\mathrm dr\,\mathrm d\theta\)

\(=\displaystyle\frac12\int_0^\pi((4\cos\theta)^2-0^2)\sin^2\theta\,\mathrm d\theta\)

\(=\displaystyle8\int_0^\pi\cos^2\theta\sin^2\theta\,\mathrm d\theta\)

There are several ways to compute the remaining integral; one would be to invoke the double-angle formula,

\(\sin(2\theta)=2\sin\theta\cos\theta\)

so that the integral is

\(=\displaystyle8\int_0^\pi\frac{\sin^2(2\theta)}4\,\mathrm d\theta\)

\(=\displaystyle2\int_0^\pi\sin^2(2\theta)\,\mathrm d\theta\)

Then invoke another double-angle formula,

\(\sin^2\theta=\dfrac{1-\cos(2\theta)}2\)

to change the integral to

\(=\displaystyle\int_0^\pi1-\cos(4\theta)\,\mathrm d\theta\)

\(=(\pi-\cos(4\pi))-(0-\cos0)=\boxed{\pi}\)

The limits for the 95% confidence interval are given as follows:

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

The parameters for this problem are given as follows:

\(n = 225, \pi = \frac{159}{225} = 0.7067\)

Then the lower bound of the interval is given as follows:

\(0.7067 - 1.96\sqrt{\frac{0.7067(0.2933)}{225}} = 0.65\)

The upper bound of the interval is given as follows:

\(0.7067 + 1.96\sqrt{\frac{0.7067(0.2933)}{225}} = 0,77\)

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The value of k in g(x) = 5^x + k is -7

The complete question is added as attachment

The functions are given as:

f(x) = 5^x

g(x) = 5^x + k

From the attached graph, we can see that:

f(x) is shifted down by 7 units to form g(x)

This means that:

g(x)= f(x) - 7

This gives

g(x) = 5^x - 7

Substitute g(x) = 5^x - 7 in g(x) = 5^x + k

5^x + k = 5^x - 7

This gives

k = -7

Hence, the value of k in -7

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Answer:

it would probably be t series

The plane is most likely taking off.The two vectors provided, position and velocity, indicate that the plane is moving eastward with a velocity of 150 m/s and is ascending with a vertical velocity of 21m/s.

This indicates that the plane is taking off, and not just touching down, ascending, or in level flight.

The position and velocity vectors of the plane indicate that the plane is moving in an eastward direction with a velocity of 150 m/s, and is also ascending with a vertical velocity of 21 m/s. This indicates that the plane is taking off, and not just touching down, ascending, or in level flight. This means that the plane is most likely taking off from the origin and is in the process of gaining altitude.

the complete question is :

( figure attached below )

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The research explores the various factors that may influence the learning choices of first-year undergraduates, such as the family and educational background of the student, their socioeconomic status and the availability of resources, among others.

Factor is a mathematical quantity which is multiplied with another quantity to give a product. Factors can also be defined as the numbers that divide a given number exactly. Factors are used in everyday life to calculate many different types of problems, such as compound interest, speed, distance and time, and more. Factors are also used in statistics and probability to determine the likelihood of certain events occurring.

The paper will also examine the various types of postgraduate courses that are available to undergraduates, including those offered by universities and other institutions, such as professional courses or distance learning programmes.

The research adopts a qualitative approach, and will use semi-structured interviews with first-year undergraduates to gain an understanding of their learning choices, and the factors that influence them. Interviews will be conducted with students in different disciplines, in order to gain an insight into how the different disciplines shape students' learning preferences. The research will also use questionnaires to obtain data on the socioeconomic background, family background and educational background of students.

In addition, the research will use documentary analysis of university prospectuses and websites, and information from other sources, such as employers and professional bodies, to gain an understanding of the various postgraduate courses that are available to undergraduates. This data will be used to compare and contrast the learning choices of undergraduates from different disciplines and economic backgrounds.

Finally, the research will use an interpretive approach to analyse the data collected and develop a theory of the factors that influence the learning choices of first-year undergraduates. The theory will be used to inform the design of initiatives to help undergraduates make informed decisions about their learning choices.

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Answer:

\(\boxed {\tt 20 \ movies}\)

Step-by-step explanation:

The equation given represents the number of movies, \(r\), that must be rented to spend the same amount at each store.

We want to find the number of movies, so we should solve for \(r\). To solve for \(r\)we must isolate it on one side of the equation.

\(1.5r+15=2.25r\)

First, let's get all the terms with a variable on one side. Subtract 1.5r from both sides of the equation.

\(1.5r-1.5r+15=2.25r-1.5r\)

\(15=2.25r-1.5r\)

\(15=0.75r\)

0.75 and \(r\) are being multiplied. The inverse of multiplication is division. Divide both sides of the equation by 0.75

\(\frac{15}{0.75}=\frac{0.75r}{0.75}\)

\(\frac{15}{0.75} =r\)

\(20=r\)

20 movies must be rented to spend the same amount at each store.

Answer:

Because it helps you to graph quickly, having both equations in Y= form makes this method useful. In contrast, if neither equation has Y isolated, you are better off using substitution or elimination.

Step-by-step explanation:

Mrs. Grubbs would get more cookie to eat by choosing the 4 smaller cookies with diameter 5 cm each rather than the single cookie with diameter 14 cm.

To compare the amount of cookie Mrs. Grubbs would get by eating a single cookie with diameter 14 cm and 4 smaller cookies with diameter 5 cm each, we need to consider the total area of the cookies.

The area of a cookie with diameter 14 cm can be calculated as follows:

A = πr^2 = π(7 cm)^2 = 49π cm^2

where r is the radius of the cookie.

On the other hand, the area of a single small cookie can be calculated as follows:

A1 = \(πr^2\) = \(π(2.5 cm)^2\)= \(6.25π cm^2\)

where r is the radius of the small cookie.

Therefore, the total area of 4 small cookies is:

A2 = 4A1 = \(4(6.25π cm^2)\) = \(25π cm^2\)

Comparing the two options, we see that the total area of the 4 small cookies is greater than the area of the single large cookie:

A2 > A

\(25π cm^2 > 49π cm^2\)

It's worth noting that this comparison assumes that the thickness or volume of the cookies is the same for both options. If the cookies have different thicknesses, then the comparison would need to take into account the volume of the cookies instead of just the area.

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The missing values are

<UTQ = 41 degree

x= 1

<UQT = 47 degree

We have a parallelogram QRST.

We know that the opposite sides of the parallelogram is equal and parallel then

QR || ST

QT || SR

Then, <SRT = <RTQ (<UTQ) (alternate Interior Angle)

<UTQ = 41

Similarly, <UQT = <SRQ = 47

Now, RU = UT

2x + 1= 3

2x = 2

x= 1

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The loaded die appears to behave differently from a fair die.Based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

To test the claim that the outcomes of the loaded die are not equally likely, we can use the chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the outcomes are equally likely, while the alternative hypothesis (H₁) assumes that they are not equally likely.

Step 1: Set up hypotheses

H₀: The outcomes of the die are equally likely.

H₁: The outcomes of the die are not equally likely.

Step 2: Select the significance level

The significance level is given as 0.025, which means we have a two-tailed test and an alpha level of 0.025 for each tail.

Step 3: Compute the test statistic

We calculate the chi-square test statistic using the observed frequencies and the expected frequencies assuming equal probabilities for each outcome.

Expected frequencies (fair die):

1: 200/6 = 33.33

2: 200/6 = 33.33

3: 200/6 = 33.33

4: 200/6 = 33.33

5: 200/6 = 33.33

6: 200/6 = 33.33

Applying the chi-square formula, we get the test statistic:

χ² = ∑((observed - expected)² / expected)

Calculating this value, we get χ² ≈ 13.97.

Step 4: Determine the critical value

Since the significance level is 0.025 and the test is two-tailed, we divide the significance level by 2 to find the critical value associated with each tail. With 5 degrees of freedom (6 categories - 1), the critical value is approximately 11.07.

Step 5: Make a decision

The test statistic (13.97) is greater than the critical value (11.07), which leads us to reject the null hypothesis. Thus, we have evidence to suggest that the outcomes of the loaded die are not equally likely.

The loaded die appears to behave differently from a fair die.

In conclusion, based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

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Information about concavity is contained in the second derivative of a function. Given f(x) = ax² + bx + c, we have

f'(x) = 2ax + b

and

f''(x) = 2a

Concavity changes at a function's inflection points, which can occur wherever the second derivative is zero or undefined. In this case, since a ≠ 0, the function's concavity is uniform over its entire domain.

(i) f is concave up when f'' > 0, which occurs when a > 0.

(ii) f is concave down when f'' < 0, and this is the case if a < 0.

In Mathematica, define f by entering

f[x_] := a*x^2 + b*x + c

Then solve for intervals over which the second derivative is positive or negative, respectively, using

Reduce[f''[x] > 0, x]

Reduce[f''[x] < 0, x]

The number of pounds of type A coffee used is 20 pounds.

Let's assume the number of pounds of type A coffee used is 'x'.

According to the given information, the number of pounds of type B coffee used is twice the number of pounds of type A coffee, so it would be '2x'.

The cost of type A coffee per pound is $4.30, and the cost of type B coffee per pound is $5.45.

The total cost of the blend is given as $304.00.

To determine the solution, we can set up the equation:

Cost of type A coffee + Cost of type B coffee = Total cost

(x * $4.30) + (2x * $5.45) = $304.00

Now, let's solve the equation to find the value of 'x':

4.30x + 2 * 5.45x = 304.00

4.30x + 10.90x = 304.00

15.20x = 304.00

x = 304.00 / 15.20

x = 20

Therefore, the number of pounds of type A coffee used is 20 pounds.

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Answer:

30/48

Step-by-step explanation:

Hi there!

We can begin by splitting the data into two equal parts, ignoring the median.

The median is simply the number in the middle of the data, or 5.

Now, we can split the data, taking the three left numbers and the three right numbers.

We have:
Left: 1, 3, 4

Right: 5, 7, 9

Find the medians of these sections. These are the middle numbers again, so:
Left: 3

Right: 7

These are our 1st and 3rd quartiles, respectively. The IQR is the difference between these, so:
7 - 3 = 4 = IQR.

The length of AB which is the missing length side of the similar triangles would be = 28 cm.

To calculate the missing length of the triangle = AB , the scale factor should be determined.

The scale factor that exists between two similar object shows the number of times the original object can be found in the new formed one.

The scale factor = dimensions of new object/ dimensions of original object.

A side of original = EF =22cm

A side of the new triangle = BC = 44

Scale factor = 44/22 = 2

Therefore the missing length of the new triangle = 14×2 = 28cm

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Answer:

11.75, 2.9375

12, 3

12.48, 3.12

Step-by-step explanation:

First, let's go over what they want us to do.

Boring but brief history lesson of geometry:

In the beginning of the history of geometry and circles, mathematicians would find the approximate circumference of circles by drawing polygons inside of circles and finding the perimeter of that polygon. In other words, the approximate circumference of the circle about the perimeter of the shape. The more side lengths there are, the smaller each side is, and the closer the perimeter is to the actual circumference (more on this later)

Problem 1:

The pentagon has a side length of 2.35, so the perimeter is 5 * 2.35 = 11.75

Thus, the approximate circumference is 11.75.

The diameter of a circle is r * 2, or 4, so the ratio of the circumference to the diameter is 11.75 / 4, or 2.9375

Problem 2:

The hexagon has a side length of 2, so the perimeter is 6 * 2 = 12. Thus, the approximate circumference is 12.

The ratio of the circumference to the diameter is 12 / 4, or 3.

Problem 3:

The dodecagon (12 sided shape) has a side length of 1.04, so the perimeter is 12 * 1.04 = 12.48.

The ratio of the circumference to the diameter is 12.48 / 4 = 3.12

Although we are done, let's ~circle~ back (sorry for the pun) to the idea that this exercise is trying to tell us.

The circumference of a circle is 2πr (which is also equal to the diameter times pi). So in this example, the circumference should be 2 * π * 2, or 4π. π is approximately 3.14159, so 4π is about 12.56636. And the ratio of this to the diameter (which is 4) is, if you look at how we got 4π, should be π no matter what.

Note: the definition of π is the ratio of a circles circumference to its diameter, so this makes sense.

Do you see how the approximate circumferences are slowly getting closer to the actual circumference of 12.56?:      11.75, 12, and 12.48

Look at the progression of approximate circumferences / diameter:  2.9375, 3, 3.12. These are slowly getting closer to π (3.14)

As you can see, the more sides, and the more "circular" the shape becomes, the closer the polygon/approximate circumference is to an actual circle.

I hope this helps! Feel free to ask any questions! :)

An inequality to represent the cost of Jason’s food for the party is

An inequality to represent this situation "Jason knows that he will be buying at least 5 packages of hot dogs" is

The two options for buying wings and hot dogs include the following:

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of packages of hot dogs and number of packages of wings respectively, and then translate the word problem into algebraic equation as follows:

Since one package of wings costs $7 and Hot dogs cost $5 per package, and he must spend no more than $40, a linear inequality which represents this situation is given by;

7x + 5y ≤ 40

Additionally, since Jason knew he would buy at least 5 packages of hot dogs, a linear inequality which represents this situation is given by;

y ≥ 5

Next, we would use an online graphing calculator to plot the above system of linear inequalities as shown in the graph attached below.

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Answer:

see explanation

Step-by-step explanation:

using the tangent ratio in the right triangle

tan A = \(\frac{opposite}{adjacent}\) = \(\frac{BC}{AB}\) = \(\frac{5}{11}\) , then

∠ A = \(tan^{-1}\) ( \(\frac{5}{11}\) ) ≈ 24.4° ( to 1 decimal place )

tan C = \(\frac{opposite}{adjacent}\) = \(\frac{AB}{BC}\) = \(\frac{11}{5}\) , then

∠ C = \(tan^{-1}\) ( \(\frac{11}{5}\) ) ≈ 65.6° ( to 1 decimal place )

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

AC² = AB² + BC² = 11² + 5² = 121 + 25 = 146 ( take square root of both sides )

AC = \(\sqrt{146}\) ≈ 12.08 ( to 2 decimal places )

Answer:

Step-by-step explanation:

1. Let's see. One time $10 and $3.50 per hour. So $10+$3.50x(where x represents number of hours)

2. Put in the value of x(substitute it).

$10+$3.50x

$10+$3.50(5)

$10+$17.50

Answer-$27.50

Hope it helps!

The point representing 4/5 would be located to the left of the point representing 7/8 on a number line.

what are fractions?

Fractions are a way of representing a part of a whole or a portion of a quantity. A fraction consists of two numbers separated by a horizontal or diagonal line. The number above the line is called the numerator, and the number below the line is called the denominator.

To compare the fractions 4/5 and 7/8 using number lines, we need to draw two number lines, one for each fraction, and then compare the position of the points representing the fractions on the number lines.

Using the drop-down menus to complete the statement:

The point representing 4/5 would be located to the left of the point representing 7/8 on a number line.

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Answer: x≤-6 or 0<x≤6.Option D.

Step-by-step explanation:

Given:

Subtract   from both sides,

0

Simplifying by taking common denominator:

0

Factoring numerator:

0

Computing the signs and selecting that one satisfies ≤ 0:

x≤ -6,0<x≤6.

Option D is the right answer.

❥\(\Large\pmb{ \underline {\tt Answer}}\)

\( \rm V = \tt\pi {r}^{2} h\)

\( \\ \\ \)

\( \dashrightarrow \rm V = \tt \pi \times {12}^{2} \times 17\)

\( \\ \\ \)

\( \dashrightarrow \rm V = \tt \pi\times 1 44 \times 17\)

\( \\ \\ \)

\( \dashrightarrow \boxed{ \bf V = \bf2,448 \pi{ \{unit \}}^{3} }\)

━━━━━━━━━━━━━━━

Wallah! and all we are done. :)

Using Trigonometry, tan O can be expressed in simple terms as: \(tan (O) = \frac{10}{5} = 2\)

(See image of the referred problem in the attachment below.)

\(MN = 10\\NO = 5\)

Reference angle = \(\angle O = \theta\)

Recall: SOHCAHTOA

\(tan(O) = \frac{Opposite}{Adjacent} (TOA)\)

Where,

\(Opposite = MN = 10\\Adjacent = NO = 5\)

\(tan(O) = \frac{10}{5} \\tan(O) = 2\)

Therefore the tan O is expressed as 2.

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Answer:

3rd option

Step-by-step explanation:

(1/2)^-2t

= (2^-1)^-2t

= 2^2t

= (2^2)^t

Answered by GAUTHMATH

The form of association that would be found in the variables would be:

As the number of hours spent playing a video game increases, the player is likely to reach higher levels within the game. So positive association.

The number of letters in a person's name and the last digit of their phone number are likely to be unrelated and randomly distributed. There is no association.

As the temperature of the drink decreases, the number of ice cubes in the drink is likely to increase, and vice versa. This is therefore negative association.

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