Mr. Kestor drives 24,000 miles per year and pays an average of $3,30 per gallon of gasoline. His car gets 25 miles per gallon. He estimates his repairs and maintenancecosts to be st 5675 for the year. How much should he budget monthly for car expenses?$333.77$320.25$315.641312.00None of these choices are correct

The population grows by approximately 0.43% each month. To calculate the monthly growth rate, we could also use the formula for compound interest, which is often used in finance and economics.

To find out how much the population grows each month, we need to first divide the annual growth rate by 12 (the number of months in a year).
So, we can calculate the monthly growth rate as follows:
5.2% / 12 = 0.4333...
We need to round this to two decimal places, so the final answer is that the population grows by approximately 0.43% each month.

The formula is:
A = P (1 + r/n)^(nt)
In our case, we have:
Plugging these values into the formula, we get:
A = 1 (1 + 0.052/12)^(12*1)
Simplifying this expression, we get:
A = 1.052
So, the population grows by 5.2% in one year.
To find out how much it grows each month, we need to take the 12th root of 1.052 (since there are 12 months in a year).
Using a calculator, we get:
(1.052)^(1/12) = 1.00434...

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{yearly, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases} \\\\\\ A = 2000\left(1+\frac{0.08}{1}\right)^{1\cdot 10}\implies A=2000(1.08)^{10} \implies A \approx 4317.85\)

Answer:

What would you like to know?

Step-by-step explanation:

The perimeter is 28 yds

The area is 24 yds

Answer:

The perimeter is 28 yds

The area is 24 yds

Step-by-step explanation:

Answer:

63, 15, 90

Step-by-step explanation:

The yearly deposit needed to achieve the retirement goal is approximately $17,650.23. None of the given options match this amount, so the correct answer is not provided in the given options.

To calculate the yearly deposits needed, we can use the concept of future value of an annuity. The future value formula for an annuity is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV = Future value of the annuity

P = Yearly deposit amount

r = Interest rate per period

n = Number of periods

In this case, the future value needed is $2 million, the interest rate is 8% (0.08), and the number of periods is 30 years. We need to solve for the yearly deposit amount (P).

Using the given formula:

2,000,000 = P * [(1 + 0.08)^30 - 1] / 0.08

Simplifying the equation:

2,000,000 = P * [1\(.08^3^0 -\) 1] / 0.08

2,000,000 = P * [10.063899 - 1] / 0.08

2,000,000 = P * 9.063899 / 0.08

Dividing both sides by 9.063899 / 0.08:

P = 2,000,000 / (9.063899 / 0.08)

P ≈ 2,000,000 / 113.298737

P ≈ 17,650.23

Therefore, the yearly deposit needed to achieve the retirement goal is approximately $17,650.23. None of the given options match this amount, so the correct answer is not provided in the given options.

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Using concepts of Mean, we got Paired samples test for the difference between two means is the type of test researcher is using.

The test procedure, called the two-sample t-test, is correct when the following conditions are met:

If the sample findings are not in favour, given the null hypothesis, the researcher rejects the null hypothesis. Typically, this will involves comparing the P-value to the significance level, and rejecting null hypothesis when the P-value is smaller than the significance level.

Hence, the test type which researcher is using Paired samples test for the difference between two means.

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The value of m in the proportion is given as follows m = 3.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The proportion is defined as follows:

3/4 = (1/4)m.

As the values have a proportional relationship, the value of m can be obtained applying cross multiplication, as follows:

3/4 = (1/4)m

cross multiplication;

3/4 x 4 = m

m = 3

Hence m =3 is the value that satisfies the proportion in this problem.

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Answer:

I think it's 19 I'm pretty sure

Answer:

20

Step-by-step explanation:

The first step would be to divide 351 by 18 to see what score he would need to tie his previous record. The answer to that would be 19.5, so if you round to the nearest whole, you would get 20.

The iterated integral that expresses the surface area of the given surface over the triangle is:

\(S = \int\limits^1_2 { \int\limits^{(y-1)}_{(1/2-y)} \sqrt(1 + 16y^6 cos^6 x sin^2 x + 9y^4 cos^8 x) dxdy\)

What is surface area?

The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area.

To express the surface area of the given surface over the triangle with vertices (-1,1), (1,1), (0,2), we can use the formula for surface area:

S = ∫∫ √(1 + (fx)² + (fy)²) dA

where fx and fy are the partial derivatives of z with respect to x and y, and dA is an infinitesimal area element.

In this case, we have:

z = y³ (cos⁴ x)

fx = -4y³ cos³ x sin x

fy = 3y² cos⁴ x

So,

(1 + (fx)² + (fy)²) = 1 + 16y⁶ cos⁶ x sin² x + 9y⁴ cos⁸x

The triangle is bounded by the lines y = 1, y = 2, and the line joining (-1,1) and (1,1):

y = 1: -1 ≤ x ≤ 1

y = 2: -1/2 ≤ x ≤ 1/2

y = x + 1: -1 ≤ x ≤ 0

Therefore, the iterated integral that expresses the surface area of the given surface over the triangle is:

\(S = \int\limits^1_2 { \int\limits^{(y-1)}_{(1/2-y)} \sqrt(1 + 16y^6 cos^6 x sin^2 x + 9y^4 cos^8 x) dxdy\)

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Answer:

Probably the first one because the other two questions would be un-reliable

Step-by-step explanation:

a. Based on the sample data, the mean price in dollars for a gallon of unleaded gasoline in San Francisco is $3.72.

b. The sample standard deviation in dollars is $0.3589.

Standard deviation,

Mean (the simple average of the numbers

Data and Calculations:

Average price of a gallon of unleaded gasoline in U.S. = $3.28

Number of gasoline and convenience stores for the U.S. average price = 90,000

Sample of San Francisco gasoline and convenience stores = 20

Prices of a gallon of gasoline in 20 San Francisco stores are as follows:

S/N.     Prices Difference in Mean  Difference Squared

1.          $3.59             -$0.13                     0.0169

2.           3.39                -0.33                     0.1089

3.           4.79                 1.07                      1.1449

4.           3.56               -0.16                      0.0256

5.           3.35              -0.37                      0.1369

6.           3.71               -0.01                     0.0001

7.           3.85              0.13                     0.0169

8.           3.40              -0.32                     0.1024

9.           3.55              -0.17                      0.0289

10.         3.76             0.04                      0.0016

11.          3.77             0.05                        0.0025

12.         3.39             -0.33                      0.1089

13.         3.75              0.03                       0.0009

14.         3.79              0.07                      0.0049

15.         4.19              0.47                       0.2209

16.        4.15             0.43                      0.1849

17.        3.66              -0.06                      0.0036

18.        3.93              0.21                       0.0441

19.        3.41              -0.31                       0.0961

20.      3.57              -0.15                       0.0225

Total $74.40                                          2.5765

Mean = $3.72 ($74.40/20)                 $0.12885 ($2.27394/20)

Standard deviation = square root of $0.12885

= $0.3589

Thus, in San Francisco, the price per gallon of unleaded gasoline is $0.03589 .

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To find the average price of unleaded gasoline in San Francisco, add up all the given prices and divide by the total number of prices. The standard deviation, indicating spread around this average price, is computed by finding the square root of the average of the squared deviations from the mean.

To estimate the mean price of a gallon of unleaded gasoline in San Francisco, you need to add up all the 20 given prices, then divide by the number of terms (20) in this case. The mean gives us the average value of the data set.

The standard deviation is a measure of how spread out the prices are from the mean. It is calculated by finding the square root of the variance, which is the average of the squared differences from the mean.

Remember, these calculations provide estimates, as the sample might not represent the entire population of gasoline prices in San Francisco. It's also important to note that external factors, such as changes in crude oil prices or regional taxes, can impact the cost of unleaded gasoline in diverse regions.

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Answer:

es la b) Oscar es más bajos que todos

Step-by-step explanation:

espero y te ayude

Answer:

18

Step-by-step explanation:

24=8×3

If F=24 when A=8 then F is directly proportional to A•3

In the equation 12x+33=93, the value of x is 5.

The given equation is 12x+33=93.

Twelve times of x plus thirty three equal to ninety three.

x is the variable in the equation.

We need to solve for x:

Subtract 33 from both sides of the equation:

12x=93-33

12x=60

Divide both sides of the equation by 12:

x=60/12

x=5

Hence, the value of x in the equation is 5.

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The probability of Stephen Curry making exactly three of his next five free throws is 0.3264 or 32.64%.

\(p(x) = nCx * p^x * q^(n-x)\)

where:

n = total number of attempts (5 in this case)

x = desired number of successes (3 in this case)

p = probability of success (0.92 in this case)

q = probability of failure (1 - p, or 0.08 in this case)

Plugging these numbers into the equation gives us:

p(3) = 5C3 * 0.92^3 * 0.08^2 = 0.3264

Stephen Curry is a professional basketball player in the NBA who is known for his incredibly accurate shooting ability. He made 92% of his free throws during the 2018-2019 regular season with the Golden State Warriors. We can calculate the probability of Curry making exactly three of his next five free throws using the binomial probability formula. This formula takes into account the probability of the event (Curry making the free throw) and the number of attempts (five). In this case, the probability of success (Curry making the free throw) is 0.92 and the number of attempts is five. Plugging these numbers into the equation gives us a probability of 0.3264 or 32.64%. This means that Curry has a 32.64% chance of making exactly three of his next five free throws.

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Answer:

y = 42 and/or x = 36

Step-by-step explanation:

y + 48 = 90
y = 42 (subtracted 48 from 90)

3x + 2x = 180 (angles are linear pairs)
5x = 180 (combine like terms)
x = 36 (divided by 5 on both sides)

I didn't know which question you needed help with, I hope this makes sense :)

❄ Hi there,

the sum of complementary angles is always 90°.

If we know one of these angles, we can set up an equation –

\(\triangleright\sf{y+48=90}\)

and then solve for y...

\(\triangleright \ \sf{y=42}\)

That's it!

❄

Answer:

a) 45° cause tan = sin/cos and sin 45 and cos 45 both give square root 2/2

b) 120°

c) sin = -1/2 = -30° or 330° both are same

Use the trig circle which i have included in the answer to better understand trig angles

hope that answers your question

I want to let you know that each angle has sets of coordinates the left number is cos and right is sin. Ex) sin of 30 is 1/2 and cos of 30 is square root 3/2 In case you dont fully understand dont hesitate to comment.

good luck!!

Answer:

From top to bottom: 1/8, 2 1/2, 3

Step-by-step explanation:

The first number means that it take 8 quarters to equal a toonie and you don't have a toonie with 1 quater

brainliest please

Answer:

x = -2 to x = 1

Step-by-step explanation:

A function is constant when the y value does not change (i.e. the graph is a horizontal line). This is true between x = -2 and x = 1.

Answer:The Funcation is Constact from x=-5 to x=8

Step-by-step explanation:

\(\qquad\qquad\huge\underline{{\sf Answer}}\)

By squaring the sum of two variables identity ~

\(\qquad \sf  \dashrightarrow \:(a + b) {}^{2} = {a}^{2} + {b}^{2} + 2ab\)

Now, plug in the given values ~

\(\qquad \sf  \dashrightarrow \:( - 6) {}^{2} = 20 + 2ab\)

\(\qquad \sf  \dashrightarrow \:36 = 2(10 + ab)\)

\(\qquad \sf  \dashrightarrow \:10 + ab = 36 \div 2\)

\(\qquad \sf  \dashrightarrow \:10 + ab = 18\)

\(\qquad \sf  \dashrightarrow \:ab = 18 - 10\)

\(\qquad \sf  \dashrightarrow \:ab = 8\)

I hope it was clear through my steps ~

Answer:

8

Step-by-step explanation:

(a+b)^2 = (-6)^2

a^2 + 2ab + b^2 = 36

a^2 + b^2 = 36 - 2ab

Equating 36 - 2ab with 20

36 - 2ab = 20

2ab = 16

ab = 8

Hope this helps out, feel free to mark this answer as brainliest :)

The probability that at least one will have a defect if if 10 items are chosen at random is  0.65132.

binomial distribution is given as :

\(P(X=x) = (_{x} ^{n}) p^{x}q^{n-x} ; x = 0,1,2,3,........n\\q = 1 - p ;\)

where

x = number of times for a specific outcome within n trials

{n  x}=      number of combinations

p = probability of success on a single trial

q = probability of failure on a single trial

n = number of trials

Let D be a random variable represents the number of defected items out of 10.

i.e., D(0,1,2,3,4,5,6,7,8,9,10)

probability that given items is defected is :

p = 0.1

q = 1 - p

q = 1 - 0.1 = 0.9

where

p = probability of defected items

q = probability of non-defective

then

D- bin(10,0.1)

P(D=0) = \(^{10} C_{0}{(0.1)^0}{(0.9)^{10}}\)

\(= \frac{10!}{0!(10-0)!} * (0.9)^{10}\)

= 0.3486784401

\(P(D\geq 1) = 1-P\)

1 - = 0.3486784401

= 0.65132

The probability that at least one will have a defect if if 10 items are chosen at random is  0.65132.

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Answer:

$409.15

Step-by-step explanation:

The finance charge for September is $10.

Unpaid Balance at End of Month: $665.49 + $38.45 + $10.00 + $16.67 - $321.54 - $38.92 = $409.15.

Answer:

it is the 2nd option

Step-by-step explanation:

To find the selling price that will yield the maximum profit, we need to find the vertex of the quadratic function given by the profit equation y = -5x² + 286x - 2275.The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -5 and b = 286.

x = -b/2a

x = -286/(2(-5))

x = 28.6

So, the selling price that will yield the maximum profit is $28.60 (rounded to the nearest cent).

Therefore, the widgets should be sold for $28.60 to maximize the company's profit.

Hope I helped ya...

Answer:

29 cents

Step-by-step explanation:

The amount of profit, y, made by the company selling widgets, is related to the selling price of each widget, x, by the given equation:

\(y=-5x^2+286x-2275\)

The maximum profit is the y-value of the vertex of the given quadratic equation. Therefore, to find the price of the widgets that maximises profit, we need to find the x-value of the vertex.

The formula to find the x-value of the vertex of a quadratic equation in the form y = ax² + bx + c is:

\(\boxed{x_{\sf vertex}=\dfrac{-b}{2a}}\)

For the given equation, a = -5 and b = 286.

Substitute these into the formula:

\(\implies x_{\sf vertex}=\dfrac{-286}{2(-5)}\)

\(\implies x_{\sf vertex}=\dfrac{-286}{-10}\)

\(\implies x_{\sf vertex}=\dfrac{286}{10}\)

\(\implies x_{\sf vertex}=28.6\)

Assuming the value of x is in cents, the widget should be sold for 29 cents (to the nearest cent) to maximise profit.

Note: The question does not stipulate if the value of x is in cents or dollars. If the value of x is in dollars, the price of the widget should be $28.60 to the nearest cent.

The line that maximizes the margin in the associated SVM classification problem is given by B₀ + B₁x + B₂y = 0, where B₀ = 1, B₁ = -1/3, and B₂ = -1/3.

(a) To draw the three points in the Cartesian plane, we plot them according to their respective coordinates:

Point X₁: (2, 1)

Point X₂: (5, 1)

Point X₃: (4, 5)

Now, we label the points as follows:

- X₁ (2, 1) with label y₁ = 1

- X₂ (5, 1) with label y₂ = 1

- X₃ (4, 5) with label y₃ = -1

The graph will show these three points on the plane, with different labels assigned to each point.

Intuitively, the line that maximizes the margin in the associated support vector machine (SVM) classification problem is the line that separates the two classes (y = 1 and y = -1) with the largest possible gap or margin between them. This line should aim to be equidistant from the closest points of each class, maximizing the separation between the classes.

(b) To prove that the guess in part (a) is the unique solution of the optimization problem:

  min ||B||² subject to yᵢ(xᵢB + B₀) ≥ 1

We can use the Karush-Kuhn-Tucker (KKT) conditions to derive the solution. The KKT conditions for SVM can be stated as follows:

1. yᵢ(xᵢB + B₀) - 1 ≥ 0 (for all i, the inequality constraint)

2. αᵢ ≥ 0 (non-negativity constraint)

3. αᵢ[yᵢ(xᵢB + B₀) - 1] = 0 (complementary slackness condition)

4. Σ αᵢyᵢ = 0 (sum of αᵢyᵢ equals zero)

Now let's solve the optimization problem for the given dataset and prove that the guess from part (a) is the unique solution.

We have the following points and labels:

X₁: (2, 1), y₁ = 1

X₂: (5, 1), y₂ = 1

X₃: (4, 5), y₃ = -1

Assume the solution for B and B₀ as (B₁, B₂) and B₀.

For point X₁:

y₁(x₁B + B₀) = 1[(B₁ * 2 + B₂ * 1) + B₀] = B₁ * 2 + B₂ + B₀ ≥ 1

This implies: B₁ * 2 + B₂ + B₀ - 1 ≥ 0

For point X₂:

y₂(x₂B + B₀) = 1[(B₁ * 5 + B₂ * 1) + B₀] = B₁ * 5 + B₂ + B₀ ≥ 1

This implies: B₁ * 5 + B₂ + B₀ - 1 ≥ 0

For point X₃:

y₃(x₃B + B₀) = -1[(B₁ * 4 + B₂ * 5) + B₀] = -B₁ * 4 - B₂ * 5 - B₀ ≥ 1

This implies: -B₁ * 4 - B₂ * 5 - B₀ - 1 ≥ 0

Now we can write the Lagrangian function for this optimization problem:

L(B, B₀, α) = (1/2) ||B||² - Σ αᵢ[yᵢ(xᵢB + B₀) - 1]

Using the KKT conditions, we have:

∂L/∂B₁ = B₁ - Σ αᵢyᵢxᵢ₁ = 0

∂L/∂B₂ = B₂ - Σ αᵢyᵢxᵢ₂ = 0

∂L/∂B₀ = -Σ αᵢyᵢ = 0

Substituting the values of xᵢ and yᵢ for each point, we have:

B₁ - α₁ - α₂ = 0

B₂ - α₁ - α₂ = 0

-α₁ + α₂ = 0

Simplifying these equations, we get:

B₁ = α₁ + α₂

B₂ = α₁ + α₂

α₁ = α₂

This implies B₁ = B₂, which means the decision boundary is perpendicular to the vector (1, 1).

Substituting B₁ = B₂ and α₁ = α₂ into the equation ∂L/∂B₀ = -Σ αᵢyᵢ = 0, we get:

-α₁ + α₂ = 0

α₁ = α₂

So, we have α₁ = α₂, which implies that the guess in part (a) is the unique solution for the given optimization problem.

Therefore, the line B₀ + B₁x₁ + B₂x₂ = 0 that maximizes the margin in the associated SVM classification problem is the line perpendicular to the vector (1, 1), passing through the mid-point of the closest points between the two classes.

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- 17 woule be the correct answer for the equation being simplified

Answer:

For edge

Step-by-step explanation:

The first one is -3

The second one is -6

The last one is -17

The graph of x(t) can be drawn by substituting the values of C1 and C2 into the equation

The second-order linear differential equation can be written as follows:x''(t) - x'(t) = 0To verify that x(t) = C1et + C2 is a solution, we need to differentiate the given function twice and substitute the resulting values back into the equation.x(t) = C1et + C2Differentiating x(t) = C1et + C2 with respect to t once,x'(t) = C1e tDifferentiating x'(t) = C1e t with respect to t once,x''(t) = C1e tSince the resulting values for x''(t) and x'(t) are equal, we can state that x(t) = C1et + C2 is indeed a solution to x''(t) - x'(t) = 0.For x(t) = C1et + C2 to satisfy x(0) = 10 and x'(0) = 100, the following conditions must be satisfied:x(0) = C1e0 + C2 = 10⇒ C1 + C2 = 10andx'(0) = C1e0 = 100⇒ C1 = 100We can solve the two equations above to obtain C1 and C2:C1 + C2 = 10, C1 = 100∴ C2 = - 90Therefore, C1 = 100 and C2 = - 90.The graph of x(t) can be drawn by substituting the values of C1 and C2 into the equation x(t) = C1et + C2 and plotting the resulting function on a graph. This will yield a rising exponential curve that levels off as it approaches the x-axis.

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The mean, µ = 100

The standard deviation, σ = 15

At X = 90, the z-score is calculated below

At X = 109

P(90 < X < 109) = P(-0.67 < z < 1.27)

From the standard normal

P(-0.67

The proportion of the population with IQ from 90 to 109 = 0.64653 x 100% = 64.65%