Write and solve an equation to calculate the measure of arc PQ (I'm not sure if my equation is correct)

Grams per cubic centimeter to kilograms per cubic meter is 1000.

1 g/cm³ = 1000 kg/m³

The conversion value:

1 gram = 1/1000 kg

1 cm³ = 1/1000000 m³

Find the conversion from grams per cubic centimeter to kilograms per cubic meter!

Grams per cubic centimeter = g/cm³

Kilograms per cubic meter = kg/m³

Multiply the number with the each conversion value!

See that the cubic centimeter is as a denominator. So, we reverse the fractional value.

1 g/cm³

= 1 × 1/1000 × 1000000/1 kg/m³

= 1000 kg/m³

Hence, the conversion value from grams per cubic centimeter to kilograms per cubic meter is 1000.

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To calculate the length of the curve defined by r(t) = 〈2 cos(t), 2 sin(t)〉 with the domain -π/2 ≤ t ≤ π/2, we need to find the arc length using the following formula:

Arc length = ∫(from a to b) ||r'(t)|| dt

First, let's find the derivative r'(t) of the given vector function r(t):

r(t) = 〈2 cos(t), 2 sin(t)〉
r'(t) = 〈-2 sin(t), 2 cos(t)〉

Next, find the magnitude ||r'(t)|| of the derivative vector:

||r'(t)|| = √((-2 sin(t))^2 + (2 cos(t))^2)
||r'(t)|| = √(4 sin^2(t) + 4 cos^2(t))

Factor out 4:

||r'(t)|| = √(4(sin^2(t) + cos^2(t)))

Since sin^2(t) + cos^2(t) = 1:

||r'(t)|| = √(4) = 2

Now, we can find the arc length by integrating ||r'(t)|| over the given domain:

Arc length = ∫(from -π/2 to π/2) 2 dt

To integrate, simply multiply the constant by the difference in t:

Arc length = 2(π/2 - (-π/2)) = 2(π) = 2π

So, the length of the curve is 2π.

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The standard deviations that would meet a 5-sigma capability for Cpk are  0.005, 0.015, and 0.025. (Options A, B and C).

To determine which standard deviations would meet a 5-sigma capability for Cpk, we need to use the following formula:

Cpk = minimum((USL - mean) / 3sigma, (mean - LSL) / 3sigma)

where USL is the upper specification limit, LSL is the lower specification limit, mean is the process mean, and sigma is the process standard deviation.

For a 5-sigma capability, we want Cpk to be at least 2.0, so we can set up the following inequality:

2.0 <= minimum((USL - mean) / 3sigma, (mean - LSL) / 3sigma)

Assuming the process mean remains unchanged, and the specification limits are at ±3 sigma from the mean (which is a common assumption), we can simplify the inequality to:

2.0 <= 1/3sigma

which can be rearranged as:

sigma <= 1/6

Therefore, the standard deviation should be less than or equal to 0.1667 to achieve a 5-sigma capability.

Now we can check which of the given standard deviations meet this criterion:

a. 0.005: Yes, this is less than 0.1667.

b. 0.015: Yes, this is less than 0.1667.

c. 0.025: Yes, this is less than 0.1667.

d. 0.035: No, this is greater than 0.1667.

e. 0.045: No, this is greater than 0.1667.

f. 0.055: No, this is greater than 0.1667.

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Answer:

-2x² - 8x + 15 = 0

Step-by-step explanation:

Given the following algebraic expression;

x² – 7x + 5

-3x² - x + 10

To add the equation together;

x² – 7x + 5 + (-3x² - x + 10) = 0

x² – 7x + 5 - 3x² - x + 10 = 0

Collecting like terms, we have;

(x² - 3x²) - (7x + x) + (5 + 10) = 0

-2x² - 8x + 15 = 0

Answer:

yes, both the numerator and denominator are polynomials, so it is a rational function.

Step-by-step explanation:

Answer:

It will take it 7 weeks

Step-by-step explantion

Using a t-distribution with 14 degrees of freedom (n-1) and a 98% confidence level (α = 0.02/2 = 0.01 for each tail), we have:

sample mean (x) = (2051+2061+2162+2167+2169+2171+2180+2183+2186+2195+2196+2198+2205+2210+2211)/15 = 2180.6

sample standard deviation (s) = 39

standard error of the mean (SEM) = s/√n = 39/√15 ≈ 10.077

t-score for a 98% confidence level and 14 degrees of freedom (from t-distribution table or calculator) = 2.977

Margin of error (ME) = t-score × SEM = 2.977 × 10.077 ≈ 30.05

Therefore, the 98% confidence interval for the mean hours worked per year in this state is:

(x- ME, x+ ME) = (2180.6 - 30.05, 2180.6 + 30.05) = (2150, 2211)

Rounding to the nearest integer and putting the limits in ascending order, we get:

(2150, 2211)

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Only matrices of the same size can be added or subtracted.

A matrix is a rectangular array of numbers and is composed of rows and columns. In order to add or subtract matrices, the matrices must have the same number of rows and columns. If the matrices do not have the same size, they cannot be added or subtracted.

For example, if one matrix is a 2x3 matrix, the other matrix must also be a 2x3 matrix. Similarly, if one matrix is a 3x2 matrix, the other matrix must also be a 3x2 matrix. The numbers in each matrix may vary, but the size of the matrices must be the same for the operation to be valid.

When adding or subtracting matrices, the numbers in the same position (row and column) are added or subtracted. For example, if one matrix is [[1,2,3], [4,5,6], [7,8,9]] and the other matrix is [[2,4,6], [8,10,12], [14,16,18]], the resulting matrix would be [[3,6,9], [12,15,18], [21,24,27]].

Adding and subtracting matrices is a useful tool in mathematics and is often used to solve equations and simplify complex problems. It is important to remember that only matrices of the same size can be added or subtracted.

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Answer:

Denver: 37%

Engle: 47%

Fido: 16%

Step-by-step explanation:

Denver eats 7/19 of the dog food.

There is 12/19 left for Engle and Fido.

The ratio of Engle to Fido is 6:2.

6x + 2x = 12/19

8x = 12/19

x = (12/19)/8

x = 0.0789

2x = 0.158

6x = 0.474

7/19 = 0.368

Denver: 37%

Engle: 47%

Fido: 16%

Answer: range

Step-by-step explanation:      

the angle between 0 and 2π that is coterminal with 17π/4 is π/4.

To find the angle between 0 and 2π that is coterminal with 17π/4, we need to find an equivalent angle within that range.

Coterminal angles are angles that have the same initial and terminal sides but differ by a multiple of 2π.

To determine the coterminal angle with 17π/4, we can subtract or add multiples of 2π until we obtain an angle within the range of 0 to 2π.

Starting with 17π/4, we can subtract 4π to bring it within the range:

17π/4 - 4π = π/4

The angle π/4 is between 0 and 2π and is coterminal with 17π/4.

what is equivalent'?

In mathematics, the term "equivalent" is used to describe two things that have the same value, meaning, or effect. When two mathematical expressions, equations, or statements are equivalent, it means that they are interchangeable and represent the same mathematical concept or relationship.

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The lengths of the two pieces of a wire will be 19,19.

A square is a closed, two-dimensional object with four equal sides and four vertices. On either side, it has parallel sides.

The square of a square's side determines its area.

Given data -

Length of a wire = 38 m

As the wire is divided into two pieces,

Let the length of two pieces of wire be x and y m respectively.

As per given data, x + y = 38

Therefore, y = 38 - x    

As each piece is bent into a square, area of squares will be

\((x/4)^{2}\)  and  \((y/4)^{2}\)

Therefore, the sum of areas of two squares will be A = \((x/4)^{2}\) +      \((y/4)^{2}\)

A = \(x^{2}\)/16 + \(y^{2}\)/16

A = \(x^{2}\)/16 + \((38-x)^{2}\)/16

By differentiating, we will get

A' = \(\frac{2x}{16}\) - \(\frac{2(38-x)}{16}\)

In order to minimize the the sum of the areas of the two squares, we will take A' = 0

0 = x - (38 - x)

2x = 38

x = 19

Therefore y = 19

The length of two pieces of a wire should be 19 m each.

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To cut the margin of error for a given confidence level in half, you would need to quadruple the sample size.

The margin of error is influenced by three factors: the desired confidence level, the standard deviation of the population, and the sample size. Assuming the confidence level and standard deviation remain constant, the margin of error decreases as the sample size increases.

The relationship between the sample size and the margin of error is approximately inversely proportional. Therefore, to cut the margin of error in half, you would need to double the sample size. However, this only reduces the margin of error by 50%, not 100%.

To achieve a reduction of 100% in the margin of error, you would need to quadruple the sample size. This is because if you double the sample size, you reduce the margin of error by 50%. Then, doubling it again reduces the remaining margin of error by another 50%, resulting in a total reduction of 75%. Doubling it for the third time reduces the remaining margin of error by another 50%, resulting in a total reduction of 87.5%. Finally, doubling it for the fourth time reduces the remaining margin of error by another 50%, resulting in a total reduction of 93.75%. Therefore, to achieve a reduction of 100% and cut the margin of error in half, you need to quadruple the sample size.

To cut the margin of error for a given confidence level in half, you would need to quadruple the sample size. Increasing the sample size helps to reduce the margin of error as it provides more data points, leading to more accurate estimates. However, it is important to note that increasing the sample size also incurs additional costs and efforts in data collection and analysis. Therefore, it is crucial to carefully consider the trade-off between the desired level of accuracy and the practical constraints of the study.

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Answer:

Step-by-step explanation:

The nth term of an exponential sequence is expressed as ar^n-1

The nth term of a linear sequence is expressed as Tn = a + (n-1)d

a is the first term

r is the common ratio

d is the common difference

n is the number of terms

Let the three consecutive terms  of an exponential sequence be a/r, a and ar

second term of a linear sequence = a +d

third term of a linear sequence = a + 2d

sixth term of a linear sequence = a + 5d

Now if the three consecutive terms  of an exponential sequence are  the second third and sixth terms  of a linear sequence, this is expressed as;

a/r = a + d ..... 1

a = a + 2d ..... 2

ar = a+ 5d .... 3

From 2: a = a + 2d

a-a= 2d

0 = 2d

d = 0/2

d = 0

Substitute d = 0 into equation 1:

From 1: a/r = a + d

a/r = a+0

a/r = a

Cross multiply

a = ar

a/a = r

1 = r

Rearrange

r = 1

Hence the common ratio of the exponential sequence is 1

Answer:

2/3

Step-by-step explanation:

you can set it up as x/y because it varies directly

so when y=6 x=72

72/6 = 12

so x will always be 12 times greater than y

x=12y

so if x=8

8=12y

y=8/12

y=2/3

The equation that can be factored and solved for the samller integer is x² + x - 72 = 0

The product of two consecutive integers is 72. The equation that represents the situation is as follows:

x(x + 1) = 72

where

Therefore,

x(x + 1) = 72

x² + x = 72

x² + x - 72 = 0

Therefore, the equation that can be factored and solved for the samller integer is x² + x - 72 = 0

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Answer:

$22

Step-by-step explanation:

So if a videotape was on a 40% discount, then the person who is buying it pays 60% of the original price (100 - 40 = 60)

call "x" the original price, then set up a proportion to explain the relationship

13.2/x = 60/100

simplify

13.2/x = 3/5

solve using cross products

13.2/x = 3/5

13.2 * 5 = 3 * x

66 = 3x

22=x

The probability of the total being less than or equal to 4 when rolling two six-sided fair dice is 1/12.

To calculate the probability, we need to determine the favorable outcomes and the total number of possible outcomes. The favorable outcomes are the combinations that result in a total less than or equal to 4: (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1). The total number of possible outcomes is 6 x 6 = 36, as each die has 6 sides. Therefore, the probability is calculated as the ratio of favorable outcomes to total outcomes: 6/36 = 1/6. However, since we want the total to be less than or equal to 4, we exclude (3, 3) from the favorable outcomes.

Hence, the final probability is 5/36. The probability of the total being less than or equal to 4 when rolling two six-sided fair dice is 1/12 or approximately 0.0833.

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The more that the ROC curve hugs the top left corner of the plot, the better the model does at classifying the data into categories

A true positive result is one in which the model accurately predicts the positive class. A true negative, on the other hand, is a result in which the model correctly predicts the negative class.

A false positive is an outcome in which the model forecasts the positive class inaccurately. A false negative is an outcome in which the model forecasts the negative class inaccurately.

The ROC curve is obtained by plotting the true positive rate (TPR) against the false positive rate (FPR) at various threshold values.

The true-positive rate is also known as sensitivity, recall, and likelihood of detection.

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The conversion of 29,333 CAD at a forward rate of 1.6 is approximately 47,132.8 USD.

Amount left = CAD 29,333Forward rate = 1.6To find:

Amount in some other currency using this forward rateSolution:

Forward rate is used to determine the future exchange rate based on the present exchange rate.

The forward rate is calculated on the basis of the spot rate and the interest rate differential.

The forward rate in foreign exchange markets indicates the exchange rate that will be applicable at a future delivery date.

the Canadian dollar is the domestic currency and we want to find out the amount of some other currency that can be obtained using this forward rate of 1.6.

Using the forward rate,1 CAD = 1.6

Another way of writing this can be:1/1.6 = 0.625So, using this we can calculate the amount in some other currency, Let us assume it to be USD.

The amount in USD will be = CAD 29,333 * 0.625= 18,333.125 USD (approx)

Hence, the amount in USD is 18,333.125 using the given forward rate of 1.6.

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Answer:

i wish i could help but i'm trynna figure that out myself

Step-by-step explanation:

Answer:

im pretty sure it might be 50

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

76.96902001

Step-by-step explanation:

We know that the area of a circle is \(pi * r^2\) so we can take that equation and divide it by two to get your answer. So in this case it would be \(\frac{pi*7*2}{2}\). Hope this helps!

The conversion of a fraction number with denominator 5 and numerator 2 , 2/5 in decimals is equals to the 0.4 value.

A decimal number can be defined as a number whose whole number part and fractional part are separated by a decimal point. Writing 2/5 as a decimal number by converting the denominator to powers of 10. We multiply the numerator and denominator by a number so that the denominator is a power of 10.

2/5 = (2 × 2) / (5 × 2) = 4/10

Now move the decimal point to the left as many places as there are zeros in the denominator, which is a power of 10.

The decimal moved one place to the left because the denominator was 10. Therefore, 4/10 = 0.4. Hence, required value is 0.4.

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To help account for variability, the pollster used a simple random sample.

Sampling is the selection of a subset (a statistical sample) of people from within a statistical population in statistics, assurance, and survey procedures. the population's characteristics that were sampled. Obtaining samples that are typical of the population being researched is the objective of statisticians.

In situations where it is not practical to evaluate the complete population, sampling offers insights and is more cost-effective and time-efficient than doing so.

Each observation gives a number for one or more characteristics of certain things or people, including their size, location, color, or weight.

In survey sampling, especially in stratified sampling, ratings can be added to the results to take into consideration the sample design. The practice is guided by conclusions from statistical theory and probability theory.

Since 1000 people are randomly selected , hence we can say that the preference is simple random sample.

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Answer:

Solve the following system for x and y:

{2 x + 53 = 53, 8 x + 3 = 42}

Check whether x and y are present in the given system:

Answer:  The variable y is not present. Therefore its value cannot be determined.

Step-by-step explanation:

Answer:  The cost of each chair is $1.5 and the cost of each table is $10

Step-by-step explanation:

We can represent the first statement by the equation 2x + 5y = 53  where x is the cost of a chair and y is the cost of a table.

The second statement can also be represented by the equation  

8x + 3y = 42

Using the equations

2x + 5y =53

8x + 3y = 42    solve for x and y  

Solve  by elimination. Eliminate the x variable by multiply the top equation by -4.

-4( 2x + 5y) = 53(-4)   =  -8x - 20y = -212    

-8x -20y = -212          Add the equations

8x  + 3y  = 42  

        -17y = -170      Divide both sides by -17

    y = 10    

So we know each table cost $10   now input the value for y and solve for x.

8x + 3(10) = 42

8x  + 30 = 42

       -30     -30

8x =  12

x = 1.5  

Each chair cost $1.5

Answer:

153

Step-by-step explanation:

You need to find the area of the triangle first which is 63. The you want to find the area of the trapezoid which is 90. Then add them together.

Answer:

About 9.2 units

Step-by-step explanation:

[8-(-1)^2]+[(5-3)^2]

81+4

sqrt(85)

9.2

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