Lily bought a car for $13500. She paid for it in 36 equal monthly payments. Calculate the amount she paid each month.

Answer:

(x - 4)(x + 4)

Step-by-step explanation:

x² - 16 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

x² - 16

= x² - 4²

= (x - 4)(x + 4)

The particular antiderivative that satisfies the given condition is: C(x) = (4/9)x^4 - (9/8)x^3 + K1x + 2000

To find the particular antiderivative (or integral) of the given derivative \(C''(x) = 4x^2 - 3x\)  that satisfies the condition C(0) = 2000, we need to integrate the given function twice.

First, we integrate C''(x) to find C'(x):

\(C'(x) = ∫ (4x^2 - 3x) dx\)

To find the antiderivative of \(4x^2\), we use the power rule for integration: the power of x increases by 1 and is divided by the new power. Similarly, the antiderivative of -3x is \(-(3/2)x^2\).

\(C'(x) = ∫ (4x^2 - 3x) dx = (4/3)x^3 - (3/2)x^2 + K1\)

Here, K1 is the constant of integration. Next, we integrate C'(x) to find C(x):

\(C(x) = ∫ (C'(x)) dx = ∫ ((4/3)x^3 - (3/2)x^2 + K1) dx\)

To find the antiderivative of \((4/3)x^3\), we again use the power rule for integration. Similarly, the antiderivative of \(-(3/2)x^2\) is \(-(3/2)(1/3)x^3\).

The constant of integration K1 will also be integrated with respect to x, resulting in another constant of integration, K2.

\(C(x) = (1/3)(4/3)x^4 - (1/2)(3/2)x^3 + K1x + K2\)

Simplifying further, we have:

\(C(x) = (4/9)x^4 - (9/8)x^3 + K1x + K2\)

Now, we can apply the initial condition C(0) = 2000 to find the particular solution for K2:

\(C(0) = (4/9)(0)^4 - (9/8)(0)^3 + K1(0) + K2 = 2000\)

Since all the terms involving x become zero when x = 0, we have:

K2 = 2000

Therefore, the particular antiderivative that satisfies the given condition is: \(C(x) = (4/9)x^4 - (9/8)x^3 + K1x + 2000\)

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The estimated change in yy using differentials is -0.00679. This means that if xx is increased by 0.005, then yy is estimated to decrease by 0.00679. The differential of yy is dy=-5sin(5x)dxdy=−5sin⁡(5x)dx. We are given that y=cos(5x)=π/30y=cos⁡(5x)=π/30 and x=0.055x=0.055.

We want to estimate ΔyΔy, which is the change in yy when xx is increased by 0.005. We can use the differential to estimate ΔyΔy as follows:

Δy≈dy≈dy=-5sin(5x)dx

Plugging in the values of y, x, and dxdx, we get:

Δy≈-5sin(5(0.055))(0.005)≈-0.00679

Therefore, the estimated change in yy using differentials is -0.00679.

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Answer:

$3.23 per pound.

Step-by-step explanation:

First, you need to find what 12.5% of $3.69 is.

To do so, you multiply 3.69 by 0.125 which equals to 0.46125.

Then you subtract 0.46125 from 3.69 which gives you 3.22875.

Then I just rounded the answer to $3.23 per pound.

Answer:

  9/4

Step-by-step explanation:

You want to know the value required to complete the square in the equation 1 = x² -3x.

Your picture shows the required value: (-3/2)² = 9/4.

<95141404393>

Answer:

Step-by-step explanation:

First, since they have the same base, you can join them. Because it is division, you have to subtract the exponents.

4^(-11/3 -(-2/3)) = 4^-9/3 = 4^-3

Negative exponents turn the base into a fraction and 4^3= 64

so the answer is C. 1/64

Answer:

360=297+(x-36)+25

360=297+25-36+x

360=286+x

360-286=x

74=x

Answer:

x = 74 degree

Step-by-step explanation:

All those angles must add up to 360 degrees:

360 degrees  =  (297 + x - 36 + 25) deg, or

360 = 297 - 36 + 25 + x, or

x = 74 degrees

Answer:

x=3

Step-by-step explanation:

14x= 5(2x-4) - 12

14x= 10x - 20 - 12

14x= 10x -8

24x= 8

x= 3

Based on the given temperature data, the forecasted high temperature for today using a three-day moving average is 93°F, and using a two-day moving average is 89°F. The mean absolute deviation for the two-day moving average is 1°F, and the mean squared error is 1. The mean absolute percent error for the two-day moving average is approximately 1.13%.

These metrics provide a way to assess the accuracy of the temperature forecasts and the variability of the actual temperatures from the moving averages.

a) To forecast the high temperature today using a three-day moving average, we take the average of the temperatures from the last three days. So, (95 + 96 + 88) / 3 = 93°F.

b) To forecast the high temperature today using a two-day moving average, we take the average of the temperatures from the last two days. So, (88 + 90) / 2 = 89°F.

c) The mean absolute deviation (MAD) based on a two-day moving average is calculated by finding the absolute difference between each temperature and the two-day moving average, summing up those differences, and then dividing by the number of observations.

The two-day moving average is 89°F. The deviations from the moving average are: |88 - 89| = 1 and |90 - 89| = 1. The sum of these deviations is 1 + 1 = 2. Since we have two observations, the MAD is 2 / 2 = 1°F.

d) The mean squared error (MSE) for the two-day moving average is calculated by squaring the differences between each temperature and the two-day moving average, summing up those squared differences, and then dividing by the number of observations.

The differences are: (88 - 89)^2 = 1 and (90 - 89)^2 = 1. The sum of squared differences is 1 + 1 = 2. Since we have two observations, the MSE is 2 / 2 = 1.

e) The mean absolute percent error (MAPE) for the two-day moving average is calculated by finding the absolute difference between each temperature and the two-day moving average, dividing that difference by the actual temperature, summing up those absolute differences, and then dividing by the number of observations.

The two-day moving average is 89°F. The absolute percent differences are: |88 - 89| / 88 = 0.0114 and |90 - 89| / 90 = 0.0111. The sum of these absolute differences is 0.0114 + 0.0111 ≈ 0.0225. Since we have two observations, the MAPE is 0.0225 / 2 ≈ 0.0113 or 1.13%.

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The probable question may be:

A Canadian tourist travelling to Miami learned that the local temperatures in Fahrenheit for the last week were as follows: 93, 94, 93, 95, 96, 88, 90 (yesterday).

a) Forecast the high temperately today, using a three-day moving average.

b) Forecast the high temperature today, using a two-day moving average.

c) Calculate the mean absolute deviation based on a two-day moving average.

d) Compute the mean squared error for the two-day moving average.

e) Calculate the mean absolute percent error for the two-day moving average.

The slope of the line, m = -3

The equation passes through the point (-2, 5)

That is x₁ = -2, y₁ = 5

Substitute x₁ = -2, y₁ = 5, and m = -3

The point-slope form of the equatio of a line is:

y - y₁ = m(x - x₁)

y - 5 = -3(x - (-2))

y - 5 = -3(x + 2)

y - 5 = -3x - 6

y = -3x - 6 + 5

y = -3x - 1

The graph of the equation y = -3x - 1 is plotted below

The instructor can conclude that the class performed around the average and that the distribution of grades is likely to be symmetrical. This can also imply that there is no skewness or bias in the data. Answer more than 100 words:When an instructor notes that the mean, median, and mode are all exactly 76.00, it can be inferred that the distribution of grades in the class is roughly symmetrical. This indicates that there are nearly equal numbers of students above and below the average grade.

The mean, median, and mode are three measures of central tendency that are used to summarize the distribution of a dataset. The mean is calculated by adding all the values in the dataset and dividing by the number of observations, while the median is the middle value when the dataset is ordered from smallest to largest. The mode is the value that occurs most frequently in the dataset. When all three measures of central tendency are equal, as in this case, it means that the dataset is roughly symmetrical and there is no skewness or bias. This can also indicate that the dataset is normally distributed, which means that it follows a bell-shaped curve.The instructor can conclude that the class performed around the average, as the mean, median, and mode are all 76.00.

However, it is important to note that this does not give any information about the spread of the dataset. In other words, the instructor cannot tell from this information alone whether the grades were tightly clustered around the average or widely dispersed. For this reason, it may be useful to calculate additional measures of spread, such as the range or standard deviation, to get a better understanding of the distribution.

The instructor can conclude that the class performed around the average and that the distribution of grades is likely to be symmetrical, with no skewness or bias. However, it is important to remember that this information alone does not provide any insight into the spread of the dataset. Additional measures of spread would need to be calculated to determine the degree of variability in the grades.

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The coordinates of triangle U'V'W' include U'(8, 3), V'(4, -8) and W'(-8, -6) and this is represented by graph A shown in the image attached below.

A transformation can be defined as the movement of a point on a cartesian coordinate from its original (initial) position to a new location.

In Geometry, there are different types of transformation and these include the following:

Based on the information provided, triangle UVW would be rotated counterclockwise through an angle of 270 degree at origin to produce triangle U'V'W', we have:

\(\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]\)

Therefore, the image of triangle UVW would be given by this matrix:

\(\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]\) \(\left[\begin{array}{ccc}-3&8&6\\8&4&-8\end{array}\right]\)

Image = \(\left[\begin{array}{ccc}8&4&-8\\3&-8&-6\end{array}\right]\)

Based on the image above, we can logically deduce that the coordinates of triangle U'V'W' include U'(8, 3), V'(4, -8) and W'(-8, -6) and this is represented by graph A shown in the image attached below.

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Answer:

hi friend

Step-by-step explanation:

Answer:

It is still 549.5

Step-by-step explanation:

Rounding to 1 decimal place is just rounding by the tenth place

So it is still 549.5

Hope this helps!

Answer:

ABCD is a rhombus => AC is perpendicular with BD

=> AC = 2(2n + 5) = 30

<=> 2n + 5 = 15

=> n = 5

with n = 5 => AC/2 = 15

BD/2 = 4.5 - 3 = 17

BC² = (AC² + BD²)/4 = 514/4 = 128.5

=> BC = 11.34

Answer:

Step-by-step explanation:

The question is what does 2n + 5 represent? Is it 1/2 the line or all of AC. There seems to be a run on ambiguous questions. I'm going to assume that 2n + 5 is AC -- all of it. And 4n-3 is all of BD.

AC = 30

2n + 5 = 30      Subtract 5 from both sides.

2n = 30 - 5

2n = 25            Divide by 2

n = 25/2

n = 13.5

====================

BD = 4n - 3

BD = 4*13.5 - 3

BD = 54 - 3

BD = 51

The water level will rise by V2/ (length x width) = (cm^3)/ (cm x cm) = cm.

Let's call the dimensions of the base of the aquarium "length," "width," and "height," and represent them by the variables L, W, and H, respectively. Similarly, let's call the dimensions of the base of the brick "length," "width," and "height," and represent them by the variables l, w, and h, respectively. Finally, let's call the height by which the water level rises "x."

Since the aquarium is rectangular, its volume can be calculated as V_aquarium = L * W * H. Similarly, the volume of the brick can be calculated as V_brick = l * w * h.

When the brick is placed in the aquarium, it displaces an amount of water equal to its own volume, so the water level rises by an amount equal to the volume of the brick divided by the area of the base of the aquarium:

x = V_brick / (L * W)

Substituting the given values, we get:

x = (cm * cm * cm) / (cm * cm) = cm

Therefore, the water level in the aquarium rises by cm when the brick is placed in it.

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Answer:

B.) \(6^{\frac{1}{2}}\)

Step-by-step explanation:

Use the exponent rule that states \(a^{\frac{1}{m}}=\sqrt[m]{a}\).  For this problem, let

a=6

m=2

So,

\(\sqrt6=6^{\frac{1}{2}}\)

There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

The multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).

where n is the total number of men and r is the number of men chosen

so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.

Similarly, we evaluate the number of ways to choose 2 women from the 8 women

as = ⁸C₂ = 14

Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.

220 x 14 = 3080

Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

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Answer:

y = 2x -4

Step-by-step explanation:

-10x + 5y = -20

+10x           +10x

         5y = 10x -20

         5      5       5

         y = 2x - 4

The probability that X, which follows a normal distribution with a mean (u) of 15.2 and a standard deviation (a) of 0.9, falls between 14.3 and 16.1 is approximately 0.6826, or 68.26%.

In a normal distribution, the area under the curve represents probabilities. To find the probability that X falls between 14.3 and 16.1, we need to calculate the area under the curve between these two values.

First, we convert the values to z-scores by subtracting the mean and dividing by the standard deviation. For 14.3, the z-score is (14.3 - 15.2) / 0.9 = -1. The z-score for 16.1 is (16.1 - 15.2) / 0.9 = 1.

Using a standard normal distribution table or a calculator, we can find that the cumulative probability for a z-score of -1 is 0.1587, and the cumulative probability for a z-score of 1 is 0.8413.

To find the probability between these two z-scores, we subtract the cumulative probability for the lower z-score from the cumulative probability for the higher z-score: 0.8413 - 0.1587 = 0.6826.

Therefore, the probability that X falls between 14.3 and 16.1 is approximately 0.6826, or 68.26%.

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The complete question is :

Assume that X has a normal distribution. The mean is u= 15.2 and the standard deviation is a=0.9. Find the probability that X is between 14.3 and 16.1

Using the cosine law, the measure of angle R is calculated as approximately: a. 44.5°.

The cosine law is expressed as follows:

cos R = [s² + q² – r²]/2sq

Given the following side lengths of triangle QRS:

Side q = 11,

Side r = 17,

Side s = 23.

Plug in the values into the cosine law formula:

cos R = [23² + 11² – 17²]/2 * 23 * 11

cos R = 361/506

Cos R = 0.7134

R = cos^(-1)(0.7134)

R ≈ 44.5°

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All your answers are correct already.

However, an equation has an Equal sign in it so I think you might want to think about what you have for equation.

Hope this helps and have a nice day.

-R3TR0 Z3R0

You did it! I suppose check the equal sign like said in the "other answer" but other than that, you did a great job! Pat yourself on the back and get yourself a cookie or something. Also possibly maybe make brainliest if you want... if i get one more I get ~Virtuoso~

Check the picture below.

Let, speed of car B is -x.

So, speed of car A is x + 10.

Relative speed of A w.r.t B is ,

\(v_{ab}=(x+10)-(-x)\\\\v_{ab}=2x+10\ mph\)

So, time taken by A to travel 300 miles relative to B given by 3 hours .

\(v_{ab}=2x+10\\\\\dfrac{300}{3}=2x+10\\\\x = 45 \ mph\)

Therefore, speed of car A is 45 + 10 = 55 mph.

Hence, this is the required solution.

Answer: The first one is a. the second is b. The third is c and the fourth is d. All of the answers are correct

Step-by-step explanation:

Answer:

T = 55 + 6w and $103

Step-by-step explanation:

We have already saved $55, so that is our constant. We gain $6 per week, so that will be our w value

T = 55 + 6w

Solving for T when w = 8 weeks

T = 55 + 6(8)

T= 55 + 48

T = $103

Answer:

sqrt(2) =x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp/ hyp

sin 45 = x/2

2 sin 45 =x

2 ( sqrt(2)/2) =x

sqrt(2) =x

The distance between points A and B is 11785.2 ft.

In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations.

Given is that the plane maintains a constant altitude of 6350 feet. Mei Mei initially measures an angle of elevation of 17° to the plane at point A. At some later time, she measures an angle of elevation of 36° to the plane at point B.

We can write -

tan (17°) = 6350/AC

tan (36°) = 6350/BC

Now, we can write -

AC = 6350/tan (17°)                                ... { 1 }

AC = 20483.9 ft

&

BC = 6350/tan (36°)                              ... { 2 }

BC = 8698.7 ft

We can write -

AB = AC - BC                                        ... { 3 }

AB =  20483.9 - 8698.7

AB = 11785.2 ft

Therefore, the distance between points A and B is 11785.2 ft.

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0.75x+0.8(x + 10) = 101

Answer:

0.75x+0.8(x+10)=101

Step-by-step explanation:

Jared attempted x shots and made 75% of them, or 0.75x. Zach attempted 10 more shots than Jared did, which is represented as x + 10. He made 80% of them, or 0.8(x + 10). Together, they made 101 shots. So, add the two expressions and set the sum equal to 101:

0.75x + 0.8(x + 10) = 101.

Answer:

sorry

Step-by-step explanation: im am no good at math