PT=3x-7 and TQ=5x-5
( find the value of PT. )

Answer:

Volume of Cylinder X = 712 cm³

Step-by-step explanation:

Given:

Volume of Cylinder Y = 89 cm³

Radius of cylinder Y = 2 cm

Radius of cylinder X = 4 cm

Find:

Volume of Cylinder X

Computation:

We know that, Cylinder X and Cylinder Y are similar

So,

Volume of Cylinder X / Volume of Cylinder Y = [Radius of cylinder X / Radius of cylinder Y]³

Volume of Cylinder X / 89 = [4/2]³

Volume of Cylinder X / 89 = [2]³

Volume of Cylinder X / 89 = 8

Volume of Cylinder X = 8 x 89

Volume of Cylinder X = 712 cm³

Answer:

23.3

Step-by-step explanation:

(a) The nonvanishing connection coefficients for the given metric are Γ¹_111 = Γ¹_112 = Γ¹_221 = Γ¹_122 = Γ²_111 = Γ²_112 = Γ²_221 = Γ²_122 = 0. (b) The geodesic equation simplifies to d\(^{(2x)}\)\(^{(i)}\)/ds² = 0, which implies that the coordinates x\(^{(i)}\) move along straight lines with constant velocities.

(a) To calculate the nonvanishing connection coefficients Γ¹_11 and Γ²_22, we can use the formula for the Christoffel symbols:

Γ\(^{(i)}\)_jk = (1/2) g\(^{(im)}\) [(∂g_mj/∂x\(^{(k)}\)) + (∂g_mk/∂x\(^{(j)}\)) - (∂g_jk/∂x\(^{(m)}\))]

where g\(^{(im)}\)is the inverse metric tensor and g_mj is the metric tensor.

In this case, the metric tensor components are:

g_11 = c

g_22 = y

g_12 = g_21 = 0 (since there are no mixed terms)

The inverse metric tensor components are:

g¹¹ = 1/c

g²² = 1/y

g¹² = g²¹ = 0

Using these values, we can calculate the connection coefficients:

Γ¹_111 = (1/2) (1/c) [(∂g_11/∂x¹)+ (∂g_11/∂x¹) - (∂g_11/∂x¹)] = 0

Γ¹_112 = (1/2) (1/c) [(∂g_11/∂x²) + (∂g_12/∂x¹) - (∂g_21/∂x¹)] = 0

Γ¹_221 = (1/2) (1/c) [(∂g_22/∂x¹) + (∂g_21/∂x²) - (∂g_21/∂x²)] = 0

Γ¹_122 = (1/2) (1/c) [(∂g_22/∂x²) + (∂g_12/∂x²) - (∂g_12/∂x²)] = 0

Γ²_111 = (1/2) (1/y) [(∂g_11/∂x¹) + (∂g_11/∂x¹) - (∂g_11/∂x¹)] = 0

Γ²_112 = (1/2) (1/y) [(∂g_11/∂x²) + (∂g_12/∂x¹) - (∂g_21/∂x¹)] = 0

Γ²_221 = (1/2) (1/y) [(∂g_22/∂x¹) + (∂g_21/∂x²) - (∂g_21/∂x²)] = 0

Γ²_122 = (1/2) (1/y) [(∂g_22/∂x²) + (∂g_12/∂x²) - (∂g_12/∂x²)] = 0

Therefore, all the nonvanishing connection coefficients are equal to zero.

(b) Since all the connection coefficients are zero, the geodesic equation simplifies to:

d²x\(^{(i)}\)/ds² + 0 + 0 = 0

This means that the second derivative of the coordinates x^i with respect to the affine parameter s is zero. In other words, the geodesic equation for this metric is:

d²x\(^{(i)}\)/ds² = 0

This implies that the coordinates x\(^{(i)}\) move along straight lines with constant velocities.

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This is a Type II error.

a) The test statistic is given by:

z = (x - μ) / (σ / sqrt(n))

z = (51.8 - 52.3) / (2.92 / sqrt(40))

z = -1.15 (rounded to 2 decimal places)

b) At α = 0.02, the rejection region is z < -2.33 or z > 2.33. Since -1.15 is not in this rejection region, we fail to reject the null hypothesis.

c) The decision is to fail to reject the null hypothesis.

d) If we mistakenly fail to reject the null hypothesis, that means we accept the null hypothesis when it is actually false. This is a Type II error.

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Answer:

185 dimes and 73 quarters

Step-by-step explanation:

q + d = 258

25(q) + 10(d) = 3675

1) The magic sum for this magic square is 75.

2) The missing numbers are: 2, 3, 4, 7, and 8.

1)The magic square provided has 5 rows, 5 columns, and 2 diagonals that must add up to the same number. To find the magic sum, we need to determine the number that all these lines should add up to.
To find the magic sum, we can calculate the sum of any of the rows, columns, or diagonals. Let's choose one of the rows for simplicity. Adding up the numbers in the first row, we get:
17 + 24 + 1 + 23 + 10 = 75
Therefore, the magic sum for this magic square is 75.

2) The missing numbers are the ones that have not been included in the given set of numbers from 1 to 25. To find the missing numbers, we need to identify the numbers that are not present in the given set.
The given set includes the numbers 1 to 25. Therefore, the missing numbers are the ones that are not included in this set. By subtracting the given set from the complete set of numbers from 1 to 25, we can find the missing numbers.
The missing numbers are: 2, 3, 4, 7, and 8.

3) To construct a 5 x 5 magic square, we need to fill in the missing numbers in the provided empty boxes. The goal is to ensure that all 5 rows, 5 columns, and 2 diagonals add up to the magic sum of 75.
Here is one possible arrangement of the missing numbers in the 5 x 5 magic square:
17   24   1   23   10
11    5     6  18    18
14   16   13  20  22
19   21   25  9    4
8     2     7   3    12
Please note that there can be multiple valid arrangements for the missing numbers, as long as the resulting square satisfies the condition of all lines adding up to the magic sum of 75.

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Answer:

Let 'l' be the side length of the decagon. Then its perimeter is given by:

P = 10l

or, 788m = 10l

or, l = 78.8m

So, the length of one of its sides is 78.8m

Bayes' rule, also known as Bayes' theorem or Bayes' law, is a mathematical formula used in probability theory and statistics. It provides a way to update our belief or probability of an event occurring, given new evidence.

The formula for Bayes' rule is:

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

where P(A|B) is the probability of event A occurring given that event B has occurred, P(B|A) is the probability of event B occurring given that event A has occurred, P(A) is the prior probability of event A occurring, and P(B) is the prior probability of event B occurring.

An example of how Bayes' rule can be used is in medical diagnosis.

Let's say a patient has a positive test result for a certain disease.

The probability of having the disease (event A) can be calculated using Bayes' rule, taking into account the sensitivity and specificity of the test.

The sensitivity is the probability of a positive test result given that the patient has the disease, and the specificity is the probability of a negative test result given that the patient does not have the disease.

By applying Bayes' rule, we can update the probability of having the disease based on the test result and the sensitivity and specificity values.

In short, Bayes' rule is a useful tool for updating probabilities based on new evidence. It is commonly used in various fields, including medicine, finance, and machine learning.

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Answer:

The probability of C appearing in two adjacent positions is the product of the probability of C appearing in the first position and the probability of C appearing in the second position given that C appeared in the first position:

P(CC) = P(C in first position) * P(C in second position | C in first position)

Using the given information, we know that P(C in first position) = 0.341 and P(C in second position | C in first position) = 0.368. Therefore:

P(CC) = 0.341 * 0.368 = 0.125488

So the probability of a randomly chosen pair of adjacent nucleotides being CC is approximately 0.125.

The probability that the next position is C given that the current position is not C is the conditional probability:

P(C in next position | not C in current position) = P(C in next position and not C in current position) / P(not C in current position)

The numerator is the probability of C in the next position and not C in the current position, which is equal to the probability of not C in the current position times the probability of C in the next position given that the current position is not C:

P(C in next position and not C in current position) = (1 - 0.341) * P(C in next position | not C in current position)

The denominator is the probability of not C in the current position, which is equal to 1 minus the probability of C in the current position:

P(not C in current position) = 1 - 0.341

Using the given information, we know that P(C in next position | not C in current position) = 0.159. Therefore:

P(C in next position | not C in current position) = [(1 - 0.341) * 0.159] / (1 - 0.341) = 0.159

So the probability that the next position is C given that the current position is not C is approximately 0.159.

If a position n along the strand is C, then the probability that position n + 2 is also C is:

P(C in n + 2 position | C in n position) = P(C in n + 2 position and C in n position) / P(C in n position)

The numerator is the probability of C in both position n and position n + 2, which is equal to the probability of C in position n times the probability of C in position n + 2 given that C appeared in position n:

P(C in n + 2 position and C in n position) = 0.341 * 0.368

The denominator is the probability of C in position n, which is equal to 0.341:

P(C in n position) = 0.341

Therefore:

P(C in n + 2 position | C in n position) = (0.341 * 0.368) / 0.341 = 0.368

So the probability that position n + 2 is also C given that position n is C is approximately 0.368.

Similarly, the probability that position n + 4 is also C given that position n is C is:

P(C in n + 4 position | C in n position) = P(C in n + 4 position and C in n position) / P(C in n position)

The numerator is the probability of C in both position n and position n + 4, which is equal to the probability of C in position n times the probability of not C in position n + 1 times the probability of not C in position n + 2 times the probability of C in position n + 3 times the probability of C in position n + 4 given that C appeared in position n + 3:

P(C in n + 4 position and C in n position) = 0.341 * 0.659 * 0.632 * 0.368

The denominator is still the probability of C in position n, which is equal to 0.341:

P(C in n position) = 0.341

Therefore:

P(C in n + 4 position | C in n position) = (0.341 * 0.659 * 0.632 * 0.368) / 0.341 = 0.158

So the probability that position n + 4 is also C given that position n is C is approximately 0.158.

If C appeared independently in any one position with probability 0.341, then the probabilities calculated in parts (a)-(c) would be different. In particular:

(a) The probability of C in two adjacent positions would be the product of the probability of C in each position, since the positions are independent:

P(CC) = 0.341 * 0.341 = 0.116281

So the probability of a randomly chosen pair of adjacent nucleotides being CC is approximately 0.116.

(b) The probability that the next position is C given that the current position is not C would be the same as the overall probability of C, since the positions are independent:

P(C in next position | not C in current position) = P(C) = 0.341

(c) The probability that position n + 2 is also C given that position n is C would be the same as the overall probability of C, since the positions are independent:

P(C in n + 2 position | C in n position) = P(C) = 0.341

Similarly, the probability that position n + 4 is also C given that position n is C would also be the same as the overall probability of C:

P(C in n + 4 position | C in n position) = P(C) = 0.341

Answer:

17

Step-by-step explanation:

both m's substitute for 4

4+4+9

8+9

17

Ans .: The dimensions of the container that will minimize the cost are a base with sides of length 16.7 cm and a height of 8.35 cm.

To minimize the cost of the container, we need to find the dimensions that will use the least amount of material. Let's call the length of one side of the square base "x" and the height of the container "h".

The volume of the container is given as 2000 cm^3, so we can write:

V = x^2h = 2000

We need to find the dimensions that will minimize the cost, which is determined by the amount of material used. We know that it costs twice as much per square centimeter to make the top and bottom as it does the sides.

Let's call the cost per square centimeter of the sides "c", so the cost per square centimeter of the top and bottom is "2c". The total cost of the container can then be expressed as:

Cost = 2c(x^2) + 4(2c)(xh)

The first term represents the cost of the top and bottom, which is twice as much as the cost of the sides. The second term represents the cost of the four sides.

To minimize the cost, we can take the derivative of the cost function with respect to "x" and set it equal to zero:

dCost/dx = 4cx + 8ch = 0

Solving for "h", we get:

h = -0.5x

Substituting this into the volume equation, we get:

x^2(-0.5x) = 2000

Simplifying, we get:

x^3 = -4000

Taking the cube root of both sides, we get:

x = -16.7

Since we can't have a negative length, we take the absolute value of x and get:

x = 16.7 cm

Substituting this into the equation for "h", we get:

h = -0.5(16.7) = -8.35

Again, we can't have a negative height, so we take the absolute value of "h" and get:

h = 8.35 cm

Therefore, the dimensions of the container that will minimize the cost are a base with sides of length 16.7 cm and a height of 8.35 cm.

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The answer of Area and perimeter will be 60 and 37.2. of that given triangle.

What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle. Triangles can be divided into three types based on the lengths of their sides, and these are: Scalene. Isosceles. Equilateral.

The perimeter will be P = sum of all three side.
Side a = \(\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\) = 10√2side b = 4√5side c = 10√2height = 6√5Area is = 1/2 (base * height) = 60 cm²Perimeter = a+b+c = 37.2 cm
Hence the Area and perimeter will be 60 and 37.2 respectively.

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After 10 years, Debora's investment of $5000 in the savings account with a 5% annual interest rate, compounded yearly, will grow to approximately $6,633.16.

To calculate the value of Debora's investment after 10 years, we can use the formula for compound interest:

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

Where:

A is the final amount (the value of the investment after the given time period)

P is the principal amount (the initial deposit)

r is the annual interest rate (expressed as a decimal)

n is the number of times interest is compounded per year

t is the number of years

In this case, Debora deposits $5000 into the savings account with an annual interest rate of 5%, compounded yearly. Plugging in the values into the formula:

\(A = 5000(1 + 0.05/1)^(1*10)\)

Simplifying the calculation:

\(A = 5000(1.05)^10\)

Using a calculator or computing the value iteratively, we find:

A ≈ 5000 * 1.628895

A ≈ 6,633.16

Therefore, after 10 years, Debora's investment of $5000 in the savings account will grow to approximately $6,633.16. This means that the investment will accumulate approximately $1,633.16 in interest over the 10-year period, given the 5% annual interest rate compounded yearly.

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The total amount the girls spend altogether is $ 15.

Let the cost of barrettes be a.

Let the cost of the comb be b.

Shelby buys 3 barrettes and a comb. So the expression of the amount Shelby buys = 3a+b

Ashley buys 2 barrettes and 4 combs. So the expression of Ashley's purchase = 2a+4b

The purchase the girls did altogether = 3a+b+2a+4b

                                                               = 5a+5b.

Here cost of barrettes, a = 2

        cost of comb, b = 1

Substituting the expression of the total purchase

         5a+5b = 5×2+5×1

                     = 10+5

                     = 15

So the total amount spent by both girls = $15

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C'(56) represents the rate of change of carbon dioxide concentration in the atmosphere at 56 years since 1960, in parts per million per year.

What C'(56) represents?

The atmospheric carbon dioxide levels in Barrow, Alaska can be modeled using the function

C(t) = 0.04t^2 + 0.6t + 330 + 7.5 sin(2 pi t),

where C(t) represents the concentration of carbon dioxide in parts per million, and t is measured in years since 1960. The function C is the sum of a quadratic function and a sine function.

The physical significance of each function is as follows:

The quadratic function (0.04t^2 + 0.6t + 330) represents the btrend of increasing carbon dioxide levels over time. This increase is due to factors such as human activities and natural processes.

The sine function (7.5 sin(2 pi t)) represents the seasonal fluctuations in carbon dioxide levels due to the natural carbon cycle, which includes processes like photosynthesis and respiration.

To estimate C'(56) using points close to t = 56, we can use the difference quotient method:

C'(56) ≈ (C(56.01) - C(55.99)) / (56.01 - 55.99)

Calculate C(56.01) and C(55.99) using the given function:

C(56.01) = 0.04(56.01)^2 + 0.6(56.01) + 330 + 7.5 sin(2 pi (56.01))
C(55.99) = 0.04(55.99)^2 + 0.6(55.99) + 330 + 7.5 sin(2 pi (55.99))

Now, plug these values into the difference quotient:

C'(56) ≈ (C(56.01) - C(55.99)) / (56.01 - 55.99)

Finally, interpret the value C'(56) in terms of rate of change:

C'(56) represents the rate of change of carbon dioxide concentration in the atmosphere at 56 years since 1960, in parts per million per year. If the value is positive, it means the concentration is increasing at that point in time, while if the value is negative, the concentration is decreasing.

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The inequality that describes the calories burned is 7x + 9y ≥ 441

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depends on other variable while a dependent variable is a variable that depends on other variable.

let x represent the number of minutes of running and y represent the number of minutes of swimming, hence:

7x + 9y ≥ 441

The inequality that describes the calories burned is 7x + 9y ≥ 441

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Answer:

no idea my friend sorry

Step-by-step explanation:

Solving a simple linear equation we can see that the value of b is 7.

Here we have the point (5, b - 7) and we want to find the value of b such that the point lies on the x-axis.

Remember that a point lies on the x-axis only if the y-value is zero, so we need to solve the linear equation:

b - 7 = 0

Adding 7 in both sides we get:

b - 7+ 7 = 0 + 7

b = 7

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Answer:

$45,800

Step-by-step explanation:

$8000 + 14.5%= 9160

9160 x 5= $45,800

Answer:

-38h-30

4h+(−6)(5)+(−6)(7h)

=4h+−30+−42h

=(4h+−42h)+(−30)

=−38h+−30

Answer:

It's point B

Step-by-step explanation:

I did it on USA Testprep and got it correct so yea hope this helps :)

P.S sorry 'bout being 2 weeks late.

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The expression 2^2020+2^2022=5.2^2020​ is proved below

From the question, we have the following parameters that can be used in our computation:

2^2020+2^2022=5.2^2020​

Express 2022 as 2020 + 2

So, we have the following representation

2^2020+2^(2020 + 2) = 5.2^2020​

When expanded, we have

2^2020+2^(2020) * 2^2 = 5.2^2020​

Factor out 2^2020

2^2020 * (1 + 2^2) = 5.2^2020​

Evaluate

2^2020​ * 5 = 5. 2^2020​

This implies that

5.2^2020​ = 5.2^2020​

HEnce, the expression has been proved

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To ensure that you have at least two cards with the same denomination, you would need to draw five cards.

This problem is a variation of the pigeonhole principle, also known as the birthday paradox. There are 13 denominations in a standard deck of cards (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King), and drawing five cards creates five pigeonholes. Since there are more pigeonholes than there are denominations, it is guaranteed that at least two of the cards will have the same denomination. To see this, note that drawing six cards will also guarantee two cards with the same denomination, since there would be six pigeonholes and only 13 denominations.

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Answer:

$1.10

Step-by-step explanation:

What we know:

Emilio has 2 quarters, 4 dimes, 3 nickels, and 5 pennies.

Quarters = 0.25 * 2

Dimes = 0.1 * 4

Nickels = 0.05 * 3

Pennies = 0.01 * 5

$0.50 + $0.40 + $0.15 + $0.05

$0.90 + $0.20 = $1.10 in total

The range is 31

Step-by-step explanation:

The range is the difference between the smallest and highest numbers in a list or set. To find the range, first put all the numbers in order. Then subtract (take away) the lowest number from the highest. The answer gives you the range of the list.

Answer:

The skateboard will be $60

Step-by-step explanation:

$75 x 0.2 = $15

$75 - $15 = $60

If all other factors are held constant, then the true parameter is farther from the value of the null hypothesis which is an increase in the probability of a Type II error.The correct option is A.

The true parameter is farther from the value of the null hypothesis.

When the true parameter is farther away from the value of the null hypothesis, it increases the probability of a Type II error. This is because the null hypothesis will have a harder time rejecting the true parameter.

The other factors - increasing sample size, decreasing significance level, and decreasing standard error - all result in a decreased probability of a Type II error.

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Answer:

1/2 x 1/5 = 1/10.

Step-by-step explanation:

Answer : fraction of the sheet of paper she use to make the flower is 1/10

Using compound interest, it is found that the coke will actually cost him $5.50.

Compound interest:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In this problem:

Then:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(A(5) = 1.85\left(1 + \frac{0.22}{12}\right)^{12(5)}\)

\(A(5) = 5.50\)

The coke will actually cost him $5.50.

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Ihis test is used when the population mean and standard deviation are known or when the sample size is large enough to estimate the population standard deviation from the sample standard deviation.

If a treatment effect increases both the mean and standard deviation of a measurement, a hypothesis test with z can be conducted if the population standard deviation is known, or the sample size is sufficiently large to enable an estimation of the population standard deviation from the sample standard deviation (using the sample standard deviation as an estimate of the population standard deviation).

A hypothesis test is a statistical tool for assessing the probability of a given hypothesis.

This entails comparing a hypothesis with an alternative hypothesis, as well as collecting data and determining whether the observed data falls within the range of values anticipated by the null hypothesis (also known as the default position)..

In other words, this test is used when the population means and standard deviation are known or when the sample size is large enough to estimate the population standard deviation from the sample standard deviation.

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