Madelyn has 4 pairs of red socks, 6 times as many pairs of blue socks 1 as white pairs of socks, and I as many white pairs as red pairs. How many pairs of socks does she have in all? How many socks does Madelyn have?​

Answer:

\({ \tt{ {a}^{8} - {12a}^{4} + 36}} \\ = { \tt{ {a}^{4} ( {a}^{2} - 12) + 36 }} \\ = ( {a}^{2} - 12)( {a}^{4} + 36) \\ \)

Answer:

a) 19/20

b) 1/20

Step-by-step explanation:

a) calculate the fraction of the attendants time will be spent servicing cars

l / L > 0 =  Ц / [ Ц -  λ ] = 20 --- ( 1 )

Ц (service )  = 15 hour

∴ λ ( arrival rate )  = 14.25

P = λ / Ц  = 14.25 / 15 = 0.95 = 19/20

b) Fraction of potential customers lost

Ls = P / ( 1 - P )

where ; P = 19/20

Ls ( fraction of potential customers lost ) = 19/20 / ( 1 - 19/20 )  = 19

hence proportion of customers lost = 1 - 19/20 = 0.05 = 1/20

Answer:

the tool is the compass

Step-by-step explanation:

It affors a high quality circles with precise mesurements

The probability that the cause is problem A given that the caller reports a lock-up is 0.25, or 25%.

We have,

We can use Bayes' theorem to solve this problem, which states:

P(A | B) = P(B | A) * P(A) / P(B)

where:

P(A | B) is the probability of event A given that event B has occurred (in this case, the probability that the cause is problem A given that the caller reports a lock up)

P(B | A) is the probability of event B given that event A has occurred (in this case, the probability that the caller reports a lock up given that the cause is problem A)

P(A) is the prior probability of event A (in this case, the probability that the cause is problem A)

P(B) is the prior probability of event B (in this case, the probability that the caller reports a lock up)

We are given that:

P(B) = 0.8 (the probability that the caller reports a lock up)

P(B | A) = 0.5 (the probability that the caller reports a lock up given that the cause is problem A)

We want to find P(A | B) (the probability that the cause is problem A given that the caller reports a lock up)

We don't have the value of P(A), but we can use the fact that the sum of the probabilities of all possible causes (A, B, C, and D) is 1:

P(A) + P(B) + P(C) + P(D) = 1

We also know that the lock up symptom is present in some of the problems, so we can write:

P(B) = P(B | A) * P(A) + P(B | C) * P(C) + P(B | D) * P(D)

Substituting the values we have, we get:

0.8 = 0.5 * P(A) + P(B | C) * P(C) + P(B | D) * P(D)

We don't have the values of P(C) and P(D), but we know that they are not given in the problem statement, so we can assume that they are not relevant for this calculation and that P(C) + P(D) = 0. This allows us to simplify the equation to:

0.8 = 0.5 * P(A) + 0

which gives us:

P(A) = 0.8 / 0.5 = 0.4

Now we can use Bayes' theorem to calculate the probability that the cause is problem A given that the caller reports a lock up:

P(A | B) = P(B | A) * P(A) / P(B) = 0.5 * 0.4 / 0.8 = 0.25

Therefore, the probability that the cause is problem A given that the caller reports a lock up is 0.25, or 25%.

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complete question:

A computer software company receives hundreds of support calls each day. There are several common installation problems, call them A, B, C, and D. Several of these problems result in the same symptom, lock up after initiation. Suppose that the probability of a caller reporting the symptom lock up is 0.80.8 and the probability of a caller having problem A and a lock up is 0.50.5.

Step 1 of 2 :

Given that the caller reports a lock up, what is the probability that the cause is problem A? Round your answer to four decimal places, if necessary.

The equivalent expression of -14 - 6 is -14 - (+6)

Equivalent expressions are expressions that have the same value when evaluated

The expression is given as:

-14 - 6

Put the terms of the expression in brackets

-14 - (6)

Rewrite 6 as +6

-14 - (+6)

Hence, the equivalent expression of -14 - 6 is -14 - (+6)

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Answer:

The answer is 4y

Step-by-step explanation:

6×2y-6×1-2×2y=6y

Answer:

Step-by-step explanation:

Sample scores : 105, 98, 101, 110, 96, 103, 104, 101, 98, 105, 112, 95, 105, 100, 108

Sample mean, xbar = 102.73

Standard deviation, s = 4.98

H0: μ = 98ttt

H1 : μ ≠ 98

Test statistic :

(xbar - μ) ÷ s/sqrt(n)

(102.73 - 98) ÷ 4.98 / sqrt(15)

t = 3.655

Pvalue from t score = 0.002599

When. Pvalue < α ; We reject the Null

We can conclude that significant evidence exists that average performance of students is not

Answer:

Triangle C and D

Is your correct answer

Triangle A have 3 sides equal so it is equilateral triangle

Triangle B have 2 sides equal so it is isosceles triangle

Triangle C have no equal sides so it is scalene triangle

Triangle D have no equal sides so it is scalene triangle

Triangles C and D are scalene triangles.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Triangle A has three sides each measuring 7 units.

Triangle B has two sides that are equal in length, and the base is longer than the two sides.

Triangle C has no sides of equal length.

Triangle D has sides of length seven, three, and six.

Now, We know that;

A scalene triangle have different sides.

Hence, Triangles C and D are scalene triangles.

Thus, We get;

Triangles C and D are scalene triangles.

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Answer:

The critical points are 0,2,4

0 is semi-stable, 2 is stable, 4 is unstable.

Check the phase line and the solution curves in the files attached below

Step-by-step explanation:

\(dy/dx = y^{4} - 6y^{3} + 8y^{2}\)

To get the critical points, dy/dx = 0

\(y^{4} - 6y^{3} + 8y^{2} = 0\\y^{2} ( y^{2} - 6y + 8) = 0\\y^{2} ( y-2)(y-4) = 0\\y = 0, 2, 4\)

To classify the stability, the interval \((-\infty, \infty)\) is divided into \((-\infty, 0), (0,2), (2,4),(4, \infty)\)

\(f(y) = y^{4} - 6y^{3} +8y^{2}\)

If y = -1, f(-1) = 15 > 0

If y = 1, f(1) = 3 > 0

If y = 3, f(3) = -9 < 0

If y = 5, f(5) = 75 > 0

The phase line is drawn in the file attached.

By critically observing the phase line:

The point y = 4 is unstable because the arrows are moving away from it

The point y = 2 is stable because the arrows are moving towards it

The point y = 0 is semi-stable because one arrow is moving towards it while the other moves away from it.

The typical solution curves are sketched in the file attached below.

Answer: Just look it up on goo gle

Step-by-step explanation:

The rate per annum compound interest is approximately 11.5%.

To find the rate per annum compound interest, we can use the formula for compound interest:

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

Where:

A = the final amount (N5353 in this case)

P = the principal amount (N4000 in this case)

r = the annual interest rate (what we want to find)

n = the number of times interest is compounded per year (assuming once per year)

t = the number of years (5 years in this case)

Now, we can plug in the values:

\(N5353 = N4000(1 + r/1)^{1*5}\)

Divide both sides by N4000:

\(1.33825 = (1 + r)^5\)

Now, isolate (1 + r) by taking the fifth root of both sides:

\(1 + r = (1.33825)^{1/3}\\1 + r \approx 1.115\)

Now, subtract 1 from both sides to find the interest rate (r):

r ≈ 1.115 - 1

r ≈ 0.115

Finally, convert the interest rate to a percentage:

r ≈ 0.115 * 100

r ≈ 11.5%

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Answer:

Step-by-step explanation:

Traingle 72 LN

Twenty standard cartons of octal boxes weigh a total of 1,100 pounds. The weight per carton is 55 pounds.

Given that twenty standard cartons of octal boxes weigh a total of 1,100 pounds. We need to find the weight per carton.

How to find the weight per carton? To find the weight per carton, we need to divide the total weight of twenty standard cartons of octal boxes by 20.Let's assume the weight of each carton be x.

Therefore, the equation can be formed asx * 20 = 1,100 Solving the above equation for x, x = 1,100/20 Therefore, the weight per carton is 55 pounds. So, twenty standard cartons of octal boxes weigh a total of 1,100 pounds.

The weight per carton is 55 pounds.

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The square root of 138 lies between 11 and 12, as 11²=121 and 12²=144.

Number is a mathematical object used to count, measure, and label. Numbers are used in almost every field of mathematics and science, including algebra, calculus, geometry, physics, and computer science. Numbers can also be used to represent data, such as population, income, temperature, or time. In addition, numbers are used to represent abstract concepts, such as love, truth, beauty, and justice.

This is because the square root of a number is the number that, when multiplied by itself, produces the original number. Therefore, to find the square root of 138, we need to identify two consecutive integers such that one of them squared is smaller than 138 and the other squared is larger than 138.

To do this, we can work our way up from the integer closer to 0, in this case 11. 11 squared is 121, which is smaller than 138, so we know that the square root of 138 must be between 11 and a larger integer. Then, if we square 12, we get 144, which is larger than 138. Therefore, we can definitively say that the square root of 138 lies between 11 and 12.

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The square root of 138 lies between 11 and 12, as 11² is 121 and 12² is 144.

Number is a mathematical object used to count, measure, and label. Numbers are used in almost every field of mathematics and science, including algebra, calculus, geometry, physics, and computer science. Numbers can also be used to represent data, such as population, income, temperature, or time. In addition, numbers are used to represent abstract concepts, such as love, truth, beauty, and justice.

To calculate this, we can divide 138 by 11 and 12, and see which integer is closer to the answer.

138 divided by 11 is 12.545454545454545454545454545455.
138 divided by 12 is 11.5.

Since 11.5 is closer to the answer, the square root of 138 lies between 11 and 12.

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Answer:

2.5 days

Step-by-step explanation:

To solve this problem, we can use the concept of work rate. The work rate is defined as the amount of work done per unit of time.

Given:

15 people working 5 hours per day can make 30 units of the product in 10 days.

From this information, we can calculate the work rate of these 15 people:

Work rate = Total units of the product / (Number of people × Number of hours × Number of days)

Work rate = 30 units / (15 people × 5 hours × 10 days)

Work rate = 0.04 units per person per hour

Now, we need to find how many days it will take for 10 people, working 10 hours per day, to make 10 units of the product.

Using the work rate formula:

Number of days = Total units of the product / (Number of people × Number of hours × Work rate)

Number of days = 10 units / (10 people × 10 hours × 0.04 units per person per hour)

Number of days = 2.5 days

Therefore, 10 people, working 10 hours per day, can make 10 units of the product in 2.5 days.

The correct answer is:

2.5 days

Answer: C

she donates a for 12 months, the 12 in the a * 12=300. the a is the fixed amount, meaning she will donate a 12 times in a year.

Since the Johns snowmobile weighs 600 pounds, the weight difference between the two vehicles is 100 pounds.

The term "proportionate" refers to relationships that always have the same ratio. For instance, the average number of apples per tree influences how many trees there are in an orchard and how many fruits there are in a harvest of apples. A linear relationship between two numbers or variables is referred to in mathematics as being proportionate. In the same way as the first quantity doubles, so does the other. The other decreases as well when one of the variables is reduced to 1/100th of its previous value.

When two quantities are proportional, it means that when one rises, the other rises as well and that the ratio between the two quantities is constant at all values. As an example, consider a circle's diameter and circumference.

given

2000 pounds make up a ton.

Snowmobile owned by John weighs 600 pounds or 0.3 tons.

The difference between Mike's snowmobile's 500 and 600 pound weights is 100 pounds.

= 600 - 500 = 100 pounds

Since the Johns snowmobile weighs 600 pounds, the weight difference between the two vehicles is 100 pounds.

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Answer:

12

Step-by-step explanation:

You do 6+6, or 2+2+2+2+2+2=12

Answer:

The height of the triangle would be

5

√

15

c

m

or

19.36

c

m

Step-by-step explanation:

The graph of g(x) is obtained from the graph of f(x) by the following transformations:

- A horizontal stretch by a factor of 9. This is because the graph of g(x) is 9 times wider than the graph of f(x).

- A vertical translation down by 2 units. This is because the graph of g(x) is 2 units lower than the graph of f(x).

In other words, to obtain the graph of g(x) from the graph of f(x), we stretch the graph horizontally by a factor of 9 and then translate it down by 2 units.

Here is a more detailed explanation of the transformations:

- Horizontal stretch by a factor of 9: To stretch the graph horizontally by a factor of 9, we multiply all of the x-coordinates by 9. This means that every point on the graph of f(x) will be moved 9 units to the right on the graph of g(x).

- Vertical translation down by 2 units: To translate the graph down by 2 units, we subtract 2 from all of the y-coordinates. This means that every point on the graph of f(x) will be moved 2 units down on the graph of g(x).

Answer:selecting 6 or 7 in the first draw and 8 or 9 in the second draw, no replace?

Step-by-step explanation:What is the probability of selecting a king from the first card and a queen from the second ... Originally Answered: Two cards are drawn successively from a pack of 52 cards. ... I. With replacement : Probability that the first card drawn is a king is . ... of selecting 6 or 7 in the first draw and 8 or 9 in the second draw, no replace?

Answer:

$872.29

Step-by-step explanation:

to do a 8.25 percent sales tax you do $803.95*1.085 and you get the above number

The z-score for an age of 30 years is 0.43.

A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level.

To convert an age to a z-score, we use the formula:

z = (x - μ) / σ

where:

x = the age we want to convert to a z-score

μ = the mean age

σ = the standard deviation of the ages

For example, if we want to convert an age of 30 years to a z-score using the given information with μ = 28.5 and σ = 3.5, we have:

z = (30 - 28.5) / 3.5

z = 0.43

So the z-score for an age of 30 years is 0.43.

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Complete question:

Pre-paid interest = $405,225 * 0.0138888888888889 * 22

To calculate the amount of pre-paid interest the Smiths must pay at closing, we need to determine the daily interest rate and then multiply it by the number of days between the closing date and the first mortgage payment date.

Given:

- Sales price of the home: $450,250

- LTV (Loan-to-Value) ratio: 90%

- Loan term: 15 years

- Interest rate: 5.00%

First, let's calculate the loan amount. Since the LTV is 90%, the loan amount will be 90% of the sales price:

Loan amount = 0.9 * $450,250 = $405,225

Next, we need to calculate the daily interest rate. The annual interest rate is 5.00%, so the daily interest rate can be obtained by dividing the annual interest rate by the number of days in a year (assuming a 360-day calendar year):

Daily interest rate = 5.00% / 360 = 0.0138888888888889

Now, we need to determine the number of days between the closing date (January 10, 2011) and the first mortgage payment date. Let's assume the first mortgage payment is due on February 1, 2011. The number of days between these two dates is 22 days.

Finally, we can calculate the pre-paid interest amount by multiplying the loan amount by the daily interest rate and the number of days:

Pre-paid interest = Loan amount * Daily interest rate * Number of days

Pre-paid interest = $405,225 * 0.0138888888888889 * 22

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Answer:

\(54\pi \: {cm}^{2} \)

Step-by-step explanation:

Given:

A cone

l = 15 cm

r (radius) = 3 cm

Find: A (surface area) - ?

\(a(surface) = \pi {r}^{2} + \pi \times r \times l\)

\(a(surface) = \pi \times {3}^{2} + \pi \times 3 \times 15 = 9\pi + 45\pi = 54\pi \: {cm}^{2} \)