The life of Sunshine CD players is normally distributed with a mean of 4. 1 years and a standard deviation of 1. 3 years. A CD player is guaranteed for 3 years. We are interested in the length of time a CD player lasts. Find the probability that a CD player will break down during the guarantee period. Sketch the situation. Label and scale the axes. Shade the region corresponding to the probability

Answer:

B

Step-by-step explanation:

hope it helps man

The inverse of f is a function which takes any value x and divides it by 4, then adds 7 to the result.

The inverse of a function is the opposite of the original function, meaning that it takes the output of the original function and turns it back into the input. In this case, the original function is f(x)=1/4x+7. To find the inverse, we need to solve for x in the equation, which can be done by subtracting 7 from both sides and then multiplying both sides by 4. This gives us x=(x+7)/4, which is the inverse of the original function. To put it simply, the inverse of f takes any output of the original function, adds 7 to it, and then divides it by 4 to get the original input.

example;

If f(x)=1/4x+7 and x=3, then

f(3) = (1/4)3 + 7

7.75

The inverse of f is f^-1(x) = (x + 7) / 4.

If f^-1(7.75) = (7.75 + 7) / 4, then

f^-1(7.75) = 14.75 / 4

3.6875

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By greatest common divisor , we can say the most bags that may be produced are 12, and each of those 12 bags will include two pencils, three candy bars, and four erasers.

The biggest number that divides both of two integers is referred to as the greatest common divisor (gcd), or greatest common divisor. For instance, 5 is the largest common divisor of 20 and 15. This is so that 5 can divide both 20 and 15, which is a quality that higher numbers lack.

Since you have 36 candy bars, 24 pencils, and 48 erasers to divide among the gift bags and you want to divide the items evenly and not have any items left over, the calculation that follows must be done in order to determine, if you make the most gift bags possible, how many of each item would go in each bag:

It is necessary to find the three numbers' highest common divisor.

\(24 = 2, 3, 4, 6, 8, 12, 24\\36 = 2, 3, 4, 6, 9, 12, 18, 36\\48 = 2, 3, 4, 6, 8, 12, 24, 48\)

The maximum number of bags that may be produced is 12, as 12 is the largest common divisor of these integers.

Thus, there will be two pencils, three candy bars, and four erasers in each of the 12 bags.

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Answer:

-6, -4 , -3 , and - 1 only.

Step-by-step explanation:

−12x + 3 ≥  5

-12x  ≥  5 - 3

-12x  ≥  2

Divide both sides by -12:

x ≤ -1/6    (Note the inequality sign flips because we are dividing by a negative value).

So considering the given set, all the values except 0 and 2 fit this inequality.

The maximum earning is v(r,b)

Let v(r,b) be the expected value of the game for the player, assuming optimal play, if the remaining deck has r red cards and b black cards.

Then v(r,b) satisfies the recursion

and

The stopping rule is simple: Stop when v(r,b)=0.

To explain the recursion . . .

If r,b>0, and the player elects to play a card, then:

Thus, if r,b>0, electing to play a card yields the value f(r,b).

But the player always has the option to quit, hence, if r,b>0, we get v(r,b)=max(0,f(r,b)).

Implementing the recursion in Maple, the value of the game is

v(26,26)=41984711742427/15997372030584

v(26,26)  ≈2.624475549

and the optimal stopping strategy is as follows . . .

So, The maximum earning is v(r,b)

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We can find the orthogonal vector when we use the dot product.

Then, the result must be equal to zero.

The vector u is given by coordinates <-7,-4>

Then, we need to find a vector in which their dor product will be equal to zero:

<-7,-4>*<1/7,-1/4> =-7*1/7 +(-4)*-1/4 = -1+1 =0

Therefore, the orthogonal vector is <1/7,-1/4>

The correct answer is option B

Answer:

Step-by-step explanation:

1.c

2.c

3.a

4.d

5.d

6.c

7. they are equal

8 A.a

8 B.d

9 A. c

9 B. b

10 A.c

10 B. b

11.b

12.d

13.b

14.b

15. a

16.d

17.c

18. 26.56 degrees

The total drag coefficient of the rectangular wing can be calculated using lift-induced drag coefficient and the profile drag coefficient.   Without values, it is not possible to determine total drag coefficient.

The lift-induced drag coefficient is determined by the wing's lift distribution and the aspect ratio, while the profile drag coefficient accounts for the drag caused by the shape of the wing. Given the lift coefficient (Cl) of 2 and the aspect ratio, we can calculate the lift-induced drag coefficient (Cd,i) using the equation Cd,i = Cl^2 / (π * e * AR), where AR is the aspect ratio.

The aspect ratio (AR) of the wing is calculated as span^2 / wing area. The wing area can be determined by multiplying the span by the chord length. Next, we calculate the total drag coefficient (Cd) by adding the lift-induced drag coefficient (Cd,i) and the profile drag coefficient (Cd,p).  

In this case, the calculation of the total drag coefficient requires numerical values for the aspect ratio and the lift-induced drag coefficient, which are not provided in the question. Without these values, it is not possible to determine the total drag coefficient accurately.      

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Answer:

Option d, ln 54.6 = 4

Step-by-step explanation:

54.6 = e⁴

taking log both side (where base of log is e)

ln 54.6 = log e⁴

or, ln 54.6

or, ln 54.6 = 4×ln e

or, ln 54.6 = 4 (ln e = 1)

Answered by GAUTHMATH

Step-by-step explanation:

If water is being poured into a bucket, the amount of water inside the bucket would increase as time passes.

Hence the slope of the line should be increasing. The best answer is Graph C.

slope = 5/2

The points given: (3, 8)and (1, 3)

Using the slope formula:

Answer:

See below

Step-by-step explanation:

IN a right triangle , remember  S-O-H-C-A-H-T-O-A   <===memorize this!

sin z = O/H = opposite side/hypotenuse = 16/20

cos z = A/H = adjacent / hy[potenuse = 12/20

tan z  = O/A = 16/12

A manufacturer of compact fluorescent light bulbs advertises have a standard deviation of 1,000 hours so the values are:

A normal distribution with,

μ = 9000

σ = 1000

a) The standardized score is the value x decreased by the mean and then divided by the standard deviation.

x = 105000 - 9000 / 1000 ≈ 1.50

Determine the corresponding probability using the normal probability table in appendix,

P(X>10500) = P(Z>1.50) = 1 - P(Z<1.50)

= 1 - 0.9332 = 0.0668.

b) n = 15

The sampling distribution of the mean weight is approximately normal, because the population distribution is approximately normal.

The sampling distribution of the sample mean has mean μ and standard deviation σ/√n

μ = 1000/√15 = 258.19

c) The sampling distribution of the sample mean has mean μ and standard deviation σ/√n

The z-value is the sample mean decreased by the population mean, divided by the standard deviation:

z = x-u/σ/√n = 10500-9000/1000√15 = 5.81

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The minimum number of neckless needed to sell to make a profit is 18 thus option (A) is correct.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given,

12n > 135 + 4.50n

In order to make a profit and solve inequality,

12n - 4.50n > 135

7.5n > 135

n > 18

Thus, it needed to sell more than 18 to make a profit.

Hence "The bare minimum of necklaces that must be sold in order to turn a profit is 18".

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Answer:

The equation y = 10x + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

The equation y = 10x + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.Slope (m) = 10

The equation y = 10x + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.Slope (m) = 10Y-intercept (b) = 5

The equation y = 10x + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.Slope (m) = 10Y-intercept (b) = 5The slope represents the rate of change of the monthly rate with respect to the fee to join. For every increase of $1 in the fee to join, the monthly rate increases by $10.

The equation y = 10x + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.Slope (m) = 10Y-intercept (b) = 5The slope represents the rate of change of the monthly rate with respect to the fee to join. For every increase of $1 in the fee to join, the monthly rate increases by $10.The y-intercept represents the initial cost of joining the gym. It is the amount that the gym charges even if the fee to join is $0. In this case, the gym charges $5 to join.

The value of s on the right triangle is s = 4.

Here we can assume that the two triangles are similar triangles, then, the measures of the hypotenuses of the right triangles must be the same one.

Remember that the hypotenuse is the side that is opposite to the 90° angle, then we can write the equation:

s + 43 = 47

s = 47 - 43 = 4

That is the value of s.

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Answer:

25.5 feet because of some

Step-by-step explanation:

.,........

Answer:

Step-by-step explanation:

Answer:

C. 76.3%

Step-by-step explanation:

To find Korey's gross profit margin, we can use the formula:

Gross Profit Margin = (Gross Profit / Net Sales) x 100%

We are given that Korey's net sales were $4,350 and gross profit was $3,320. Plugging these values into the formula, we get:

Gross Profit Margin = ($3,320 / $4,350) x 100%

Gross Profit Margin = 0.763 x 100%

Gross Profit Margin = 76.3%

Therefore, Korey's gross profit margin is c. 76.3%

Answer:

c) 76.3%

\(\hrulefill\)

Step-by-step explanation:

Gross profit margin is a percentage that shows how much money a company keeps from its sales after taking away the costs of making the products they sell. It helps us understand how well the company is managing its expenses and making a profit.

To calculate Korey's gross profit margin, we can use the formula:

\(\boxed{\sf Gross \;Profit \;Margin =\dfrac{Gross\;profit}{Net\; Sales} \times 100}\)

Given information:

(Note: The net income of $1,850 is not related to the calculation of the gross profit margin).

Substitute the given values into the formula:

\(\begin{aligned}\sf Gross \;Profit \;Margin& =\sf \left (\dfrac{Gross\; Profit}{Net\; Sales}\right) \times 100}\\\\&=\sf \left (\dfrac{3320}{4350}\right) \times 100}\\\\&=\sf 0.76321839 \times 100}\\\\&=\sf 76.3\%\;(nearest\;tenth)\end{aligned}\)

Therefore, Korey's gross profit margin is approximately 76.3% (rounded to the nearest tenth).

The equation of the tangent to the curve at the given point. x = 7 sin(t), y = t2 t, (0, 0) is y = 0, To find the equation of the tangent to the curve at the given point (0, 0), we first need to find the derivative of x and y with respect to t, and then find the slope of the tangent at the given point.

Given: x = 7sin(t), y = t^2

Find dx/dt and dy/dt:
dx/dt = 7cos(t)
dy/dt = 2t

Now, find the slope of the tangent at the point (0, 0) by dividing dy/dt by dx/dt:

Slope = (dy/dt) / (dx/dt) = (2t) / (7cos(t))

At t = 0, the slope is:
Slope = (2*0) / (7cos(0)) = 0 / 7 = 0

Now we use the point-slope form of the equation to find the equation of the tangent line:

y - y1 = slope * (x - x1)

Since the point is (0, 0) and the slope is 0, the equation becomes:

y - 0 = 0 * (x - 0)

Simplifying, we get the equation of the tangent line as:

y = 0

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"The chance that A has occurred is not changed by knowing that B has occurred". If events A and B are independent, then it means that the chance that event A will occur is not affected by knowing whether event B has happened or not. This definition is known as the definition of independent events.

The correct answer is-B

If A and B are independent events, then the probability of event A happening is not altered by the occurrence of event B. In other words, when two events A and B are independent, they have no effect on each other, and the probability of the occurrence of one event does not change the probability of the other event occurring. Therefore, the chance that event A will occur is not changed by knowing that event B has occurred.

If the events A and B are independent, what does that mean? Neither "There are no events in common" nor "The chance that A has occured is not changed by knowing that B has occured." There are no events in common between events A and B. The chance that A has occured is not changed by knowing that B has occured. Both "There are no events in common" and "The chance that A has occured is not changed by knowing that B has occured. ".

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If the leading coefficient is positive, bigger inputs only make the leading term more and more positive

How do you tell if a graph has a positive or negative coefficient?

If the leading coefficient is positive, bigger inputs only make the leading term more and more positive. The graph will rise to the right. If the leading coefficient is negative, bigger inputs only make the leading term more and more negative. The graph will descend to the right.

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Answer:

h(x)

h(x)

f(x) g(x) h(x)

Step-by-step explanation:

Edge 2020

~theLocoCoco

h(x) , h(x) , and f(x) g(x) h(x)

The obtained value must be compared against the critical value. Hence, the correct option is b.

In hypothesis testing, the critical value is a threshold or cutoff point that is determined based on the chosen significance level (alpha level) and the distribution of the test statistic. It helps in determining whether to reject or fail to reject the null hypothesis.

After calculating the test statistic (such as z-score or t-statistic) from the observed data, it is compared to the critical value associated with the chosen significance level.

If the test statistic exceeds the critical value, it falls into the critical region, leading to the rejection of the null hypothesis.

If the test statistic is less than or equal to the critical value, it falls into the non-critical region, resulting in a failure to reject the null hypothesis.

Therefore, the obtained value must be compared against the critical value to make a decision in hypothesis testing. Hence, the correct answer is option b.

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At asymptote, pigeons make the correct choice on nearly 100% of the matching to sample trials exists true about matching to sample.

A random experiment has a result known as a sample. One particular value is chosen at random from a set of potential values when we sample a random variable. A sample is that specific value. The probability distribution of the random variable specifies the possible values and their probabilities.

An easier-to-manage portion of a larger group is referred to as a sample. A larger population's traits are contained in this subset. When populations are too big for a statistical test to include every potential participant or observation, samples are used.

Therefore, the correct answer is option a) at asymptote, pigeons make the correct choice on nearly 100% of the matching to sample trials

The complete question is:

Which is TRUE about matching to sample?

a) at asymptote, pigeons make the correct choice on nearly 100% of the matching to sample trials

b) it is a very difficult task for pigeons

c) the training procedure for organisms such as pigeons is complex and extensive

d) all of the above are true

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a) Using the Euclidean algorithm, we can find gcd (707,413) as follows:707 = 1 · 413 + 294413 = 1 · 294 + 119294 = 2 · 119 + 562119 = 2 · 56 + 71356 = 4 · 71 + 12 71 = 5 · 12 + 11 12 = 1 · 11 + 1

Thus, gcd (707,413) = 1.

We can find the coefficients s and t that solve the equation 707s + 413t

= 1 as follows:1 = 12 - 11 = 12 - (71 - 5 · 12) = 6 · 12 - 71 = 6 · (119 - 2 · 56) - 71

= - 12 · 56 + 6 · 119 - 71

= - 12 · 56 + 6 · (294 - 2 · 119) - 71 = 18 · 119 - 12 · 294 - 71

= 18 · 119 - 12 · (413 - 294) - 71 = 30 · 119 - 12 · 413 - 71

= 30 · (707 - 1 · 413) - 12 · 413 - 71 = 30 · 707 - 42 · 413 - 71

Thus, s = 30, t = -42. So we have found that 707(30) + 413(−42) = 1.

b) Since 707s + 413t = 1 and 9 does not divide 1, the equation 707x + 413y = 9 has no integer solutions. Therefore, we can conclude that there are no such integers x and y.

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Answer:

5x + 15

Step-by-step explanation:

3(2x + 5)-x

6x + 15 - x

5x + 15

Hope this Helps!!!

Answer:

I think it is

24.6

Answer:

Step-by-step explanation:

\(x\times(x+ 28) = 20\times (20+32)\\\\x^2+28x-1040=0\\\\\ x=\dfrac{-28\pm\sqrt{28^2-4\cdot1\cdot(-1040)}}{2\cdot1}= \dfrac{-28\pm\sqrt{4944}}{2}\\\\x\approx21.2\quad or\quad x\approx-49.2\)

x has to be >0 so the answer is 21.2

It calculates the fine by taking 200 times the square root of 40d and subtracting 325.

Part a) To write a linear equation that represents the fine for speeding, F, as a function of the speed in mph on the state highway, we need to determine the equation of the line passing through the two given points: (70, $25) and (85, $100).

Let's first identify the input and output variables:

Input variable: Speed in mph (denoted as x)

Output variable: Fine for speeding in dollars (denoted as y or F)

Using the two given points, we can find the slope (m) of the line:

m = (change in y) / (change in x) = (100 - 25) / (85 - 70) = 75 / 15 = 5

Now that we have the slope, we can use the point-slope form of a linear equation:

y - y₁ = m(x - x₁)

Using the point (70, $25):

y - 25 = 5(x - 70)

Expanding and simplifying:

y - 25 = 5x - 350

y = 5x - 325

Therefore, the linear equation that represents the fine for speeding, F, as a function of the speed in mph on the state highway is:

F(x) = 5x - 325

Part b) To find (F∘S)(d), we need to substitute the function S(d) = 40√(40d) into the equation F(x) = 5x - 325. Here, d represents the length of a skid mark in feet, and we want to find the fine for speeding based on the speed calculated using the skid mark length.

Substituting S(d) into F(x):

(F∘S)(d) = F(S(d)) = 5S(d) - 325

S(d) = 40√(40d)

(F∘S)(d) = 5 * 40√(40d) - 325

Simplifying:

(F∘S)(d) = 200√(40d) - 325

In the context of the problem, the function (F∘S)(d) represents the fine for speeding based on the speed of the car, which is approximated using the skid mark length (d) as determined by the function S(d).

It calculates the fine by taking 200 times the square root of 40d and subtracting 325.

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Answer:

KR

Step-by-step explanation:

First, you can see the right angle and the 30 degrees. Those are the same, so we can flip the triangle on the right to match the one on the left. The line that is similar is KR.

To test if there is a difference between the means of the two populations, we can perform a two-sample t-test. The null hypothesis is that there is no difference between the mean number of hours per week that a family with no children participates in recreational activities and a family with children participates in recreational activities.

Let's assume that the researcher has collected the following data:

Sample of families with no children: n1 = 30, sample mean = 4.5 hours per week, sample standard deviation = 1.2 hours per week.

Sample of families with children: n2 = 40, sample mean = 3.8 hours per week, sample standard deviation = 1.5 hours per week.

Using the critical value method, we need to calculate the t-statistic and compare it to the critical value from the t-distribution table with n1+n2-2 degrees of freedom and a significance level of α = 0.05.

The formula for the t-statistic is:

t = (x1 - x2) / sqrt(s1^2/n1 + s2^2/n2)

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Plugging in the numbers, we get:

t = (4.5 - 3.8) / sqrt((1.2^2/30) + (1.5^2/40)) = 2.08

The degrees of freedom for the t-distribution is df = n1 + n2 - 2 = 68.

Using a t-distribution table, we find the critical value for a two-tailed test with α = 0.05 and df = 68 is ±1.997.

Since our calculated t-statistic of 2.08 is greater than the critical value of 1.997, we can reject the null hypothesis and conclude that there is a statistically significant difference between the mean number of hours per week that a family with no children participates in recreational activities and a family with children participates in recreational activities.

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