The firt time larry play a video game, he i knocked out in 30 econd. The next time he play 30 econd longer than the econd. Larry i able to play 30 econd longer each game. It cot him 25 cent to play each game. How much will it cot Larry to lat 4 minute before he i knocked out?

The required probability of the given exponential distribution with mean of 10 minutes is equal to 0.39 rounded to two decimal places.

The amount of time spent at a bank follows an exponential distribution with a mean of 10 minutes,

The probability density function (PDF) of the time spent at the bank is given by,

f(x) = (1/10)e^(-x/10), where x ≥ 0

The probability of spending less than 5 minutes at the bank,

Evaluate the cumulative distribution function (CDF) of the exponential distribution up to x=5 minutes,

P(X < 5) = \(\int_{0}^{5}\) f(x) dx

=\(\int_{0}^{5}\)(1/10)e^(-x/10) dx

= [-e^(-x/10)]\(|_{0}^{5}\)

= -e^(-1/2) + 1

≈ 0.393

Therefore, the probability of spending less than 5 minutes at the bank is approximately 0.39, rounded to two decimal places.

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Answer:

\(y=\frac{-3}{4} x+2\)

Step-by-step explanation:

First, we can find the slope using the slope equation and two of the points.

Slope equation:

\(m=\frac{y2-y1}{x2-x1}\)

I'm going to use the first two points just so I can avoid the fraction... Substitute the x and y values into the equation.

\(m=\frac{2-5}{0--4}\)

Simplify:

\(m=\frac{-3}{4}\)

Now that we have the slope, all we need is the y-intercept. Luckily, it gives it to us in the table. The x value of y-intercepts will always be 0. Looking at the table, we see that the point where x=0 is (0,2). Thus, the y-intercept is 2. Your final equation is

\(y=\frac{-3}{4} x+2\)

Answer:

y = -3/4x + 2

Step-by-step explanation:

we will choose any two points: (-4,5) and (0,2)

an linear equation should be like this y=ax+b

a is the slope, b is the y intercept

to find the slope we will use this formula: y1 - y2/x2 - x1

2-5/0-(-4) = -3/4

y = -3/4x + b

now you can find the answers by putting the values of x and y from the table

Answer:

Length: 20, Width: 14

Step-by-step explanation:

(x-12)(x-18)

x^2-30x+216=280

x^2-30x-64=0

x=32,-2

Plug 32 into x, and see if it equals 280

Answer:

Can you repeat the question?

Step-by-step explanation:

Answer:

thanks for the points haha

Let's see

#a

Take 28

#2

Take 9,10

Answer:

Two-digit number greater than 25:   32

Rewrite 32 as the difference of 2 numbers: 40 - 8

Therefore, x = 40  and  y = 8

\(\begin{aligned}\implies (40-8)^2 & =40^2-2(40)(8)+8^2\\ & = (4 \cdot 10)^2-(80)(8)+64\\ & = 4^2 \cdot 10^2-640+64\\ & = 16 \cdot 100-640+64\\ & = 1600-640+64\\ & = 960+64\\ & = 1024\end{aligned}\)

Let a = 10

Let b = 11

\(\begin{aligned}\implies 10^3+11^3 & =(10+11)(10^2-10 \cdot 11+11^2)\\& = 21(100-110+121)\\ & = 21(-10+121)\\ & = 21(111)\\& = 21 (100 + 10 + 1)\\ & = (21 \cdot 100)+(21 \cdot 10)+(21 \cdot 1)\\ & = 2100 +210+21\\ & = 2310 + 21\\ & = 2331\end{aligned}\)

Therefore, the mean temperature for the recorded week is approximately 29.9°F.

To calculate the mean temperature, we need to sum up all the recorded temperatures and divide the total by the number of days.

Given the daily temperatures for the week:

Monday: 35.5°F

Tuesday: 30.8°F

Wednesday: 27.3°F

Thursday: 32.1°F

Friday: 23.8°F

Saturday: 29.9°F

To find the mean temperature, we sum up all the temperatures and divide by the total number of days (which is 6 in this case):

Mean temperature = (35.5 + 30.8 + 27.3 + 32.1 + 23.8 + 29.9) / 6

Calculating the sum:

Mean temperature = 179.4 / 6

Mean temperature ≈ 29.9°F

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The mean temperature for the week is calculated to be 29.9 degrees Fahrenheit.

To calculate the mean temperature, we need to find the average temperature over the course of the week. This is done by summing up the temperatures recorded on each day and then dividing the total by the number of days.

In this case, the temperatures recorded on each day are 35.5, 30.8, 27.3, 32.1, 23.8, and 29.9 degrees Fahrenheit.

By adding these temperatures together:

35.5 + 30.8 + 27.3 + 32.1 + 23.8 + 29.9 = 179.4

We obtain a sum of 179.4.

Since there are 6 days in a week, we divide the sum by 6 to find the average:

Mean temperature = 179.4 / 6 = 29.9 degrees Fahrenheit

Therefore, the mean temperature for the week is calculated to be 29.9 degrees Fahrenheit. This represents the average temperature over the recorded days.

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Answer:

1/11

Step-by-step explanation:

Given:

Bonnie has 4 sharpened and 8 unsharpened pencils in her pencil case. she randomly selects 2 of the pencils from the box without replacement.

Question to Answer:

what is the probability that both pencils will be sharpened?

Solve:

Probability is possibility of an event being equal to the ratio of the number of outcomes and the total number of outcomes.

Thus we known that,

Bonnie has 4 sharpened and 8 unsharpened pencils.

Hence, the total numbers of pencils is 12.

Let, the probability first one is sharpened be P(E₁) and  probability second one is sharpened be P(E₂)

Simplify - P(E₁) = 4/12 = 1/3       and      P(E₂) = 3/11

Therefore we have;

P(E) = P(E₁)×P(E₂)

P(E) = 1/3 × 3/11

P(E) = 3/33

P(E) = 1/11

As a result, the probability is 1/11 that both pencils will be sharpened.

Kavinsky

Check the picture below.

\(\textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left( ~~ \cfrac{\pi \theta }{180}-\sin(\theta ) ~~ \right) \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =60 \end{cases} \\\\\\ A=\cfrac{8^2}{2}\left( ~~ \cfrac{\pi (60) }{180}-\sin(60^o ) ~~ \right)\implies A=32\left( ~~ \cfrac{\pi }{3}-\sin(60^o ) ~~ \right) \\\\\\ A=32\left( ~~ \cfrac{\pi }{3}-\cfrac{\sqrt{3}}{2} ~~ \right)\implies A=\cfrac{32\pi }{3}-16\sqrt{3}\implies A\approx 5.8~in^2\)

Given:

Suzanne has purchased a car with a list price of$23,860.

She traded in her previous car, which was a Dodge in good condition, and financed the rest of the cost for five years at a rate of 11.62, compounded monthly. The dealer gave her 85 of the listed trade-in price for her car. She was also responsible for 8.11 sales tax, a $1695 vehicle registration fee, and a $228 documentation fee. If Suzanne makes a monthly payment of $455.96, then we need to calculate the original cost of the car.

Method of Solution:

We need to apply the following formula to get the original cost of the car:

\($$A=P(1+\frac{r}{n})^{nt}$$\)

Where, A is the future value, P is the principal amount, r is the rate of interest, t is the time, n is the number of times the interest is compounded per year.

Using the given data,Let the original cost of the car be ‘P’.

Then, she financed the rest of the cost of the car after the trade-in,

So,

the amount financed = $P − Trade-in value

Rate of interest = 11.62% compounded monthly

= 0.1162/12 = 0.00968 per month

Time period = 5 years

Number of times interest is compounded per year = 12

Sales tax = 8.11%

Registration fee = $1,695

Documentation fee = $228

Trade-in value = 85% of the listed trade-in price for her car = 0.85LTP

Now, we have to calculate the value of ‘P’ as per the formula stated above

.Step-by-step Solution:

Amount financed = $P − Trade-in value principal

amount = $PInterest rate

= 0.1162/12 per monthTime

= 5 yearsNumber of times interest is compounded per year

= 12Sales tax

= 8.11%

Registration fee = $1,695

Documentation fee = $228

Trade-in value = 85% of the listed trade-in price for her car = 0.85LTP

Now, we have, Monthly payment = $455.96

Using the formula,

Future value (A) = $455.96*60

= $27,357.6.$A

\(= P(1 + $\frac{r}{n}$)$^{nt}$\)

∴ $27,357.6

=\((P – 0.85 LTP)(1 + \frac{0.1162}{12})^{12*5}$∴ $27,357.6\)

= \((P – 0.85LTP)(1.01082)^{60}$\)

Now, we can add the sales tax, registration fee, and documentation fee to get the value of ‘P

.∴ P – 0.85LTP

\(= $\frac{27,357.6}{1.01082^{60}}$ + 0.0811P + 1,695 + 228\)

∴\(P – 0.7225 LTP = 23,860.01 + 0.0811P + 1,695 + 228\)

∴ \(P – 0.0811P + 0.7225 LTP = 23,860.01 + 1,695 + 228\)

∴ \(0.9189 P = 25,783.01 + 0.7225 LTP --- (i)\)

Now, let's calculate the monthly payment if LTP

(listed trade-in price) = $16,000.

First, let’s calculate the amount Suzanne paid for the car:

Amount financed = $P − Trade-in value amount financed

= $P − 0.85LTP

Amount financed = P − 0.85(16,000)

Amount financed = P − 13,600

Now, we can add the sales tax, registration fee, and documentation fee to get the amount financed.

∴ Amount financed = P – 13,600 + 0.0811P + 1,695 + 228

∴ Amount financed = 1.0811 P – 11,677 --- (ii)

Now, we can calculate the monthly payment:

\(Monthly payment = $\frac{A*r}{n*(1 + \frac{r}{n})^{nt}}$\)

\($$A=P(1+\frac{r}{n})^{nt}$$\\\\Future value (A) = $455.96*60= $27,357.6.$A = P(1 + $\frac{r}{n}$)$^{nt}$∴ $27,357.6 = (P – 0.85 LTP)(1 + \frac{0.1162}{12})^{12*5}$∴ $27,357.6 = (P – 0.85LTP)(1.01082)^{60}$\\\\∴ P – 0.85LTP = $\frac{27,357.6}{1.01082^{60}}$ + 0.0811P + 1,695 + 228∴ P – 0.7225 LTP = 23,860.01 + 0.0811P + 1,695 + 228∴ P – 0.0811P + 0.7225 LTP = 23,860.01 + 1,695 + 228∴ 0.9189 P = 25,783.01 + 0.7225 LTP --- (i)\\\\Monthly payment = $\frac{A*r}{n*(1 + \frac{r}{n})^{nt}}$\\\\\)

therefore

$ Monthly payment = 455.96

Using a graphing calculator, we can find that P = $22,328.44

Therefore, the original cost of the car was $22,328.44. Therefore, option (a) is the correct answer.

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False. The statement is not entirely accurate. While significantly different sample variances can impact the assumptions of a t-test, it does not necessarily mean that a t-test cannot be conducted.

In traditional t-tests, there is an assumption of equal variances between the compared groups or populations. This assumption is known as the assumption of homogeneity of variances. If the sample variances are significantly different, it violates this assumption.

However, there are alternative versions of the t-test that can be used when the variances are not equal, such as the Welch's t-test or the modified t-test. These tests do not assume equal variances and can be applied when the variances are significantly different.

Therefore, it is possible to conduct a t-test even when the sample variances are significantly different, using appropriate modifications to the test. However, it is essential to consider the validity and appropriateness of the chosen test based on the specific circumstances and assumptions of the data.

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Answer:

s

\(4x {}^{2} + 3x - 11 = 0\)

Step-by-step explanation:

Hope it helps :)

Answer: 36mm

Step-by-step explanation:

All sides are multiplied by a factor of 9. 9 x 4 = 36

We have disproved the second implication, we can conclude that the statement "S = T if and only if S - T ⊆ T" is not true in general.

The "logical result or consequence that follows from a particular policy, idea, or action" is called a "implication" and it can be used to forecast how a particular action or decision will turn out.

To prove or disprove the statement "S = T if and only if S - T ⊆ T," we need to show two implications:

1. If S = T, then S - T ⊆ T.

2. If S - T ⊆ T, then S = T.

Let's consider each implication separately:

1. If S = T, then S - T ⊆ T:

If S = T, it means that every element in S is also in T, and every element in T is also in S. In this case, when we subtract T from S, the result will be an empty set since all elements of S are also in T. Therefore, S - T = ∅ (empty set). And since an empty set is a subset of any set, we can say that S - T ⊆ T.

2. If S - T ⊆ T, then S = T:

To disprove this implication, we need to find a counterexample. Let's consider the following example:

S = {1, 2, 3}

T = {1, 2}

In this case, S - T = {3}. And we can see that {3} is a subset of T because all elements in {3} (which is only 3) are also in T. However, S is not equal to T because S contains an element (3) that is not in T.

Therefore, we have shown a counterexample where S - T ⊆ T, but S is not equal to T. This disproves the implication.

Since we have disproved the second implication, we can conclude that the statement "S = T if and only if S - T ⊆ T" is not true in general.

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To find a vector v orthogonal to the plane through the points p(4, 0, 0), q(0, 3, 0), and r(0, 0, 5), we can use the cross product of two vectors that lie in the plane.

Let's first find two vectors that lie in the plane. We can take the vectors p to q and p to r.

Vector p to q can be calculated as q - p, which is (0 - 4, 3 - 0, 0 - 0) = (-4, 3, 0).

Vector p to r can be calculated as r - p, which is (0 - 4, 0 - 0, 5 - 0) = (-4, 0, 5).

Now, we can find the cross product of these two vectors.

To calculate the cross product, we take the determinant of a 3x3 matrix.

The cross product is given by:

(i  j  k)
(-4  3  0)
(-4  0  5)

Using the determinant formula, we get:

(3 * 5 - 0 * 0)i - (-4 * 5 - 0 * -4)j + (-4 * 0 - 3 * -4)k

Simplifying, we have:

15i - (-20)j - (-12)k

Which gives us:

15i + 20j - 12k

Therefore, a vector v orthogonal to the plane through the points p, q, and r is given by 15i + 20j - 12k.

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Answer:

In 10 months the amount will be the same, $570 paid

Answer (12,5). In this example, the value "5" is the Y Coordinate.

Step-by-step explanation:

The vertical value in a pair of coordinates. How far up or down the point is. The Y Coordinate is always written second in an ordered pair of coordinates (x,y) such as (12,5). In this example, the value "5" is the Y Coordinate.

9514 1404 393

Answer:

  y = 24

Step-by-step explanation:

The line marked 'x' is a midline of the triangle, hence half the length of the parallel base line marked '4x-7'. This lets us solve for x and find the lengths of the sides of the triangle.

  2x = 4x -7

  7 = 2x . . . . . add 7-2x

  3.5 = x

Then the horizontal side of the triangle is ...

  4x -7 = 4(3.5) -7 = 7

The hypotenuse of the triangle is ...

  6x +4 = 6(3.5) +4 = 25

The Pythagorean theorem can be used to find y:

  y^2 +7^2 = 25^2

  y^2 = 625 -49 = 576

  y = √576

  y = 24

The annual percentage yield, or the effective interest rate, for $1200 invested at 6.63% over 8 years compounded daily is approximately 64.04%.

To determine the annual percentage yield, or the effective interest rate, for $1200 invested at 6.63% over 8 years compounded daily, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (6.63%)
n = the number of times interest is compounded per year (365 for daily compounding)
t = the number of years (8)
Plugging in the values, we have:
A = 1200(1 + 0.0663/365)^(365*8)
Calculating this, we get A ≈ $1,968.49.
To find the annual percentage yield, we need to find the interest earned:
Interest = A - P = $1,968.49 - $1200 = $768.49
Now, we can find the annual percentage yield using the formula:
Annual percentage yield = (Interest / P) * 100
Plugging in the values, we have:
Annual percentage yield ≈ ($768.49 / $1200) * 100 ≈ 64.04%
Therefore, the annual percentage yield, or the effective interest rate, for $1200 invested at 6.63% over 8 years compounded daily is approximately 64.04%.

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The image of the coordinates after a dilation of (9, −7) by a scale factor of 4 centered at the origin include the following: (36, -28).

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

Next, we would have to dilate the coordinates of the preimage (9, -7) by using a scale factor of 4 centered at the origin as follows:

Coordinate A (9, -7) → Coordinate A' (9 × 4, -7 × 4) = Coordinate A' (36, -28).

In conclusion, the coordinates of the image after a dilation are  (36, -28).

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Answer:

The answer is x = -13/4

Step-by-step explanation:

-13/4 + 2  /  -13/4 +3 = 5

The solution to the differential equation y''(t) = 1 - t^17 with initial condition y(1) = 12 is:

y(t) = (1/2)t^2 - (1/342)t^19 + (217/18)t + (19805/342)

None of the provided options (a, b, c, d) match the correct solution.

To solve the given differential equation y''(t) = 1 - t^17 with the initial condition y(1) = 12, we can integrate the equation twice.

Integrating the equation once will give us y'(t):

y'(t) = ∫(1 - t^17) dt

y'(t) = t - (1/18)t^18 + C₁

Now, we need to apply the initial condition y(1) = 12 to determine the value of the constant C₁:

12 = 1 - (1/18) + C₁

C₁ = 12 + (1/18) - 1

C₁ = 217/18

Next, we integrate y'(t) to find y(t):

y(t) = ∫(t - (1/18)t^18 + 217/18) dt

y(t) = (1/2)t^2 - (1/342)t^19 + (217/18)t + C₂

Finally, we apply the initial condition y(1) = 12 to determine the value of the constant C₂:

12 = (1/2) - (1/342) + (217/18) + C₂

C₂ = 12 - (1/2) + (1/342) - (217/18)

C₂ = (20619 - 1 + 6 - 819)/(342)

C₂ = 19805/342

Therefore, the solution to the differential equation y''(t) = 1 - t^17 with initial condition y(1) = 12 is:

y(t) = (1/2)t^2 - (1/342)t^19 + (217/18)t + (19805/342)

None of the provided options (a, b, c, d) match the correct solution.

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the time required for an investment of $5000 to grow to $\(7200\) at an interest rate of  \(7.5\) percent per year, compounded quarterly, is approximately  \(3.79\) years.

o find the time required for an investment of $5000 to grow to $7200 at an interest rate of 7.5 percent per year, compounded quarterly, we can use the formula for compound interest:

\(A = P(1 + r/n)^(nt)\)

where:

A = the final amount (in this case, $7200)

P = the principal amount (in this case, $5000)

r = the annual interest rate (in decimal form, so 7.5% = 0.075)

n = the number of times the interest is compounded per year (in this case, quarterly, so n = 4)

t = the number of years (which we need to find)

Plugging in the values, we get:

\(7200 = 5000(1 + 0.075/4)^(4t)\)

Now we can solve for t by isolating it on one side of the equation.

Dividing both sides by 5000:

Taking the natural logarithm of both sides:

\(ln(7200/5000) = ln((1 + 0.075/4)^(4t))\)

Using the property of logarithms that ln(a^b) = b * ln(a):

\(ln(7200/5000) = 4t\times ln(1 + 0.075/4)\)

Dividing both sides by \(4 \times ln(1 + 0.075/4):\)

\(t = ln(7200/5000) / (4 * ln(1 + 0.075/4))\)

Using a calculator, we can find the value of t to be approximately 3.79 years (rounded to two decimal places).

Therefore, the time required for an investment of $5000 to grow to $7200 at an interest rate of 7.5 percent per year, compounded quarterly, is approximately 3.79 years.

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Answer:

3:4

Step-by-step explanation:

36 inches = 3 feet and 4 ft = 48 inches

And there are 12 inches in a foot so then:

36/12= 3 & 48/12 = 4 so 3:4 is the ratio

The type of sampling used in this scenario is B. Stratified sampling. Stratified sampling involves dividing the population into distinct subgroups or strata and then selecting samples from each subgroup.

In this case, Miranda divides her day into three parts: morning, afternoon, and evening. Each part of the day represents a stratum or subgroup.  Miranda measures her breathing rate at 4 randomly selected times during each part of the day. This means she is taking samples from each of the three strata (morning, afternoon, and evening) and collecting data from within those subgroups.

By using stratified sampling, Miranda ensures that her samples represent the different parts of her day in a proportional and systematic manner, allowing her to capture potential variations in her breathing rate throughout the day.

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Answer:

ranalllldooo

Step-by-step explanation:

suiiiiiii

Answer:

a

Step-by-step explanation:

because it's calculated by dividing AbM and that's how a is answer

Answer: To match the shapes produced by the slice through the triangular prism, we need to consider the orientation of the slice relative to the prism. Here are the matching options:

A. Perpendicular to the base: Rectangle

B. Parallel to the base: Triangle with dimensions equal to the base

C. Diagonal from vertex to vertex: Triangle with unknown dimensions

Answer: -6

Step-by-step explanation: y= 17x -6

y=17•0 -6

y= -6

Just multiply by zero to know where the line will cross

Apothem and perimeter of a regular pentagon the apothem and perimeter of a regular pentagon are given as 3.0 ft and 22.0 ft, respectively. The  the area of the pentagon is 33.0 square feet.

The area of the pentagon is required. The formula for calculating the area of a regular pentagon is given below:`Area = 1/2 x Perimeter x Apothem`Substituting the values of the apothem and perimeter in the above formula, we get:Area = 1/2 x 22.0 ft x 3.0 ft`= 33.0 ft²`Therefore, the area of the regular pentagon is 33.0 square feet.

The area of a regular polygon can be determined by multiplying the perimeter by the apothem and then dividing by 2. When solving problems about a regular pentagon, this formula is helpful.

Because the perimeter and apothem of a regular pentagon are supplied, this formula is used to calculate the area of a regular pentagon.

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