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Answer: 5/2 divided by 20/5

Step-by-step explanation:

3/8 divided by 3/5 =

3/8 * 5/3 =

15/24 = 5/8

5/8 = 25/40

5/2 * 5/20 =

5/2 divided by 20/5

The shoulders contain approximately 4.3% of the bones in a typical human body.

To estimate the percentage of bones in the shoulders in a typical human body, we need to consider the total number of bones in the body and the number of bones in the shoulders. The human body has 206 bones on average.

The shoulders consist of the clavicle (collarbone), scapula (shoulder blade), and the humerus (upper arm bone). These three bones make up a small fraction of the total number of bones in the body.

Assuming the shoulders contain 9 bones (2 clavicles, 2 scapulae, and 2 humeri), we can calculate the percentage as follows:

Percentage of bones in the shoulders = (Number of bones in shoulders / Total number of bones) × 100

Percentage of bones in the shoulders = (9 / 206) × 100 ≈ 4.37%

To estimate the percentage of leg bones, we can apply a similar approach. By counting the number of bones in the legs (including the femur, tibia, fibula, and other smaller bones), we can calculate the percentage of leg bones using the same formula.

Therefore, by following a similar calculation, we can estimate the percentage of leg bones in a typical human body.

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Answer:

a₅ = 1701

Step-by-step explanation:

\(a_1=7\\\\a_n=-4a_{n-1} + n\\\\a_2 = -4*a_1 + 2\\\\\)

    = -4*7 + 2

    = -28 + 2

   = -26

a₃ = -4a₂ + 3

    = -4*(-26) + 3

    = 104 + 3

    = 107

a₄ = -4a₃ + 4

    = -4*107 + 4

   = -428 + 4

  = -424

a₅ = -4a₄ + 5

    = -4*(-424) + 5

    = 1696 + 5

   = 1701

Answer:

1.85

Step-by-step explanation:

equation will be 10(h+1.75)=36

hamburger price is $1.85

Given statement solution is :- The t-statistic associated with the test is approximately -0.28.

The t-statistic, which is used in statistics, measures how far a parameter's estimated value deviates from its hypothesised value relative to its standard error. Through the Student's t-test, it is utilised in hypothesis testing. In a t-test, the t-statistic is used to decide whether to accept or reject the null hypothesis.

To find the t-statistic associated with the test, we need to calculate the test statistic using the estimated slope coefficient, the null hypothesis, and the standard error.

The estimated slope coefficient is 4.93.

The null hypothesis is H₀: β₁ ≥ 5.14 (stating that the true slope coefficient is greater than or equal to 5.14).

The predicted slope's standard error is 0.74.

The formula to calculate the t-statistic is:

t = (estimated slope - hypothesized slope) / standard error

Plugging in the values:

t = (4.93 - 5.14) / 0.74

t = -0.21 / 0.74

t ≈ -0.28 (rounded to two decimal places)

Therefore, the t-statistic associated with the test is approximately -0.28.

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It would cost approximately $1.10 to use the clothes washer.

To calculate the cost of using the clothes washer, you'll need to multiply the energy usage (in kilowatts) by the duration (in hours) and the cost per kilowatt-hour. In this case, the clothes washer used 2.6 kilowatts for 0.9 hours and the electricity cost is $0.47 per kilowatt-hour.

To find the total cost, use the following formula:

Total cost = Energy usage (kilowatts) × Duration (hours) × Cost per kilowatt-hour

Plug in the given values:

Total cost = 2.6 kilowatts × 0.9 hours × $0.47 per kilowatt-hour

Total cost = $1.1046

To find the cost to the nearest penny, round the result to two decimal places:

Total cost = $1.10

So, it cost approximately $1.10 to use the clothes washer.

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Answer:

First one

Step-by-step explanation:

Look at the picture*

The rate at which the average revenue is changing when 175 belts have been produced and sold is approximately -0.0065 dollars per belt.

To find the rate at which the average revenue is changing when 175 belts have been produced and sold, we need to differentiate the revenue function with respect to x and then evaluate it at x = 175.

The revenue function is given as:

\(R(x) = 45x^(9/10)\)

To find the average revenue, we divide the total revenue by the number of belts produced and sold. So, the average revenue function, AR(x), can be expressed as:

AR(x) = R(x) / x

Differentiating the average revenue function with respect to x using the quotient rule:

\(AR'(x) = (R'(x) * x - R(x)) / x^2\)

Now, let's calculate the derivative of the revenue function R(x):

\(R(x) = 45x^(9/10)\)

Using the power rule, we differentiate R(x) with respect to x:

\(R'(x) = (9/10) * 45 * x^(-1/10)\)

Simplifying:

\(R'(x) = 405/10 * x^(-1/10)\\R'(x) = 40.5 * x^(-1/10)\)

Now, substitute the values into the average revenue derivative formula:

\(AR'(x) = (40.5 * x^(-1/10) * x - 45x^(9/10)) / x^2\)

Simplifying further:

\(AR'(x) = (40.5 * x^(9/10) - 45x^(9/10)) / x^2\\AR'(x) = (40.5 - 45x^(1/10)) / x^2\)

To find the rate at which average revenue is changing when 175 belts have been produced and sold, we substitute x = 175 into AR'(x):

\(AR'(175) = (40.5 - 45(175)^(1/10)) / (175)^2\)

Calculating the value:

AR'(175) ≈ -0.0065

Therefore, the rate at which the average revenue is changing when 175 belts have been produced and sold is approximately -0.0065 dollars per belt.

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Answer:

Step-by-step explanation:

Distance covered in 1 minute= 1.8x 10^7 kilometers

So, by unitary method,

distance covered in 8 minutes= 1.8 x 10^7 kilometers x 8

                                                  = 14.4 x 10^7 kilometers

Answer: 8 posters

Step-by-step explanation:

From the question, we are informed that Lincoln has 16 pins in one box and 17 pins in another box and that he uses 4 pins to hang each posters posted. The total number of posters he can hang with the pins goes thus:

We should first calculate the total number of pins he has.

= 16 + 17 = 33 pins

Since he uses 4 pins to hang a poster, we then divide 33 pins by 4.

= 33 ÷ 4

= 8.25

This means that he can hang 8 posters with the pin

The amount of the money after 7 years with a rate of 13% with an initial amount of $400 will be $ 941.04.

Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.

Tanvi opened a savings account and deposited $400.00 as principal.

The account earns 13% interest, compounded annually.

Then the balance after 7 years will be

We know the compound interest formula.

A = P (1 + r)ⁿ

We have

P = $ 400

r = 13%

n = 7 years

Then we have

A = 400 x (1 + 0.13)⁷

A = 400 x 1.13⁷

A = 400 x 2.3526

A = $ 941.04

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PART A:

In the expression -7 - (-9), we can combine both negative signals and create a positive signal, so the expression will be -7 + 9.

That means in the number line we start at the number -7 and go 9 units to the right.

So Karissa is not correct, because she said a different starting point and a different direction to add the 9 units.

PART B:

Let's solve the equation:

We can see that the equation is not true, since the final statement is false. So Hugo is not correct, because the final values of each side of the equation didn't match.

The words savage and savory are neither similar nor contradictory.

Contradiction is a term used to indicate mutually opposite things. It is commonly used in statements where both the statements cannot be true.

Savage is a word the meaning of which is wild or non cultivated in a context as an adjective. In another context, savage can be used as a noun to define an uncivilized or a brutal human.

On the other hand, savory is a completely different term which is used to define the taste of the dishes, typically in a positive way.

Hence the terms savage and savory are neither similar nor contradictory words.

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The constraints to represent the incoming students at the college are \(0<x \leq 200\) and \(0<y \leq 400\) and this can be determined by using the given data.

Given :

The following steps can be used in order to determine the constraints to represent the incoming students at the college:

Step 1 - The inequalities are formed in order to determine the constraints to represent the incoming students at the college.

Step 2 - The linear equation that represents the situation "two times as many in-state students as out-of-state" is:

\(y = 2x\)

Step 3 - The inequality that represents the situation "college only have space to accept 200 out-of-state students" is:

\(0<x \leq 200\)

Step 4 - So, the inequality that represents the maximum number of in-state students that college can take is:

\(0<y \leq 400\)

Therefore, the correct option is D).

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The explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

The given sequence is -4, 16, -64, 256,...

If we observe the sequence it is a geometric sequence

aₙ=a.rⁿ⁻¹

a is the first term and r is the common ratio

From the sequence the first term is -4 and common ratio is -4

aₙ=(-4).(-4)ⁿ⁻¹

Plug in the value n as 8

a₈=(-4).(-4)⁷

The value of minus four power seven is minus sixteen thousand three hundred eighty four

a₈=(-4)(-16384)

When four is multiplied with sixteen thousand three hundred eighty four we get sixty five thousand five hundred thirty six

a₈= 65536

Hence, the explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

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Answer:

60 is 61.2244897959% of 98

Step-by-step explanation:

60 + 98 = 158 so your total mass is 158g

Therefore, the Marginal Rate of Technical Substitution (MRTS) in this Cobb Douglas production function is (0.45/0.55) * (L/K), or approximately 0.818 * (L/K).

To determine the Marginal Rate of Technical Substitution (MRTS) in a Cobb Douglas production function, we need to calculate the ratio of the marginal product of labor (MP_L) to the marginal product of capital (MP_K). In this case, the MRTS can be calculated as MRTS = MP_L / MP_K, where MP_L is the partial derivative of the production function with respect to labor (L) and MP_K is the partial derivative of the production function with respect to capital (K).

Taking the partial derivatives of the Cobb Douglas production function, we have:

MP_L = 0.45 * L^(-0.55) * K^0.55

MP_K = 0.55 * L^0.45 * K^(-0.45)

Now we can calculate the MRTS:

MRTS = MP_L / MP_K

= (0.45 * L^(-0.55) * K^0.55) / (0.55 * L^0.45 * K^(-0.45))

= 0.45/0.55 * (L^(-0.55) * L^0.45) * (K^0.55 * K^(-0.45))

= (0.45/0.55) * (L/K)

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Answer:

Step-by-step explanation:

Choice

Answer:

Can you award me brainest

Simplify complex expressions, find matching pairs, determine moduli, identify minimum value and provide an example complex number.

A. Simplifying 4i(1+i)+(6+2i):

4i(1+i) = 4i + 4i\(^2\) = 4i - 4 = -4 + 4i

So the expression becomes: (-4 + 4i) + (6 + 2i) = 2 + 6i

B. Simplifying -3(5i)\(^2\):

(5i)\(^2\) = 5\(^2\) * i\(^2\) = 25 * (-1) = -25

So the expression becomes: -3 * (-25) = 75

C. Simplifying i\(^2\)43(1+3i):

i\(^243\) = i^(4*60 + 3) = (i\(^4\))\(^60\) * i\(^3\) = 1\(^2\) * i\(^3\) = 1 * (-i) = -i

So the expression becomes: -i * (1 + 3i) = -i - 3i^2 = -i - 3(-1) = -i + 3 = 3 - i

D. Simplifying -1/2 (1+i)(2i^10):

(1+i)(2i^10) = (1+i)(2i\(^2\))^5 = (1+i)(-4)^5 = (1+i)(1024) = 1024 + 1024i

So the expression becomes: -1/2 * (1024 + 1024i) = -512 - 512i

E. Simplifying 6(5+5i) / (-2i)(3i\(^5\)):

6(5+5i) = 30 + 30i

(-2i)(3i^5) = -6i * i^5 = -6i * (-i) = -6i * i = 6

So the expression becomes: (30 + 30i) / 6 = 5 + 5i

Matching pairs and their simplified responses:

A → 2 + 6i

B → 75

C → 3 - i

D → -512 - 512i

E → 5 + 5i

The modulus of each complex number:

|2 + 6i| = sqrt(2^2 + 6^2) = sqrt(40) = 2sqrt(10)

|75| = 75

|3 - i| = sqrt(3^2 + (-1)\(^2)\) = sqrt(10)

|-512 - 512i| = sqrt((-512)\(^2\)+ (-512)\(^2\)) = sqrt(2 * 512\(^2\)) = 512sqrt(2)

|5 + 5i| = sqrt(5^2 + 5^2) = sqrt(50) = 5sqrt(2)

Listing the moduli from smallest to largest:

C → sqrt(10)

E → 5sqrt(2)

A → 2sqrt(10)

D → 512sqrt(2)

B → 75

For the complex number n, the minimum value of the modulus is sqrt(10).

One example of the complex number n is n = sqrt(10).

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The nth term can be written as: 2 \(\times\) floor(n/2) + 2 / (2 + \((-1)^n\) \(\times\) (n mod 2))where floor(n/2) is the largest integer less than or equal to n/2, and (n mod 2) is the remainder when n is divided by 2.

a. To find the formula for the nth term in the sequence 19, -19/8, 19/27, -19/64, 19/125, we notice that the sequence alternates between positive and negative values, and the denominators of the fractions are perfect cubes.

The pattern seems to be that the signs alternate, and the denominators are the cubes of the natural numbers starting with 2. That is, the nth term can be written as:

\((-1)^{(n+1)\) \(\times\) 19 / \((n+1)^3\)

b. To find the formula for the nth term in the sequence 4/2, 8/6, 12/12, 16/20, 20/30, we can simplify each term by dividing the numerator and denominator by their greatest common factor. Doing so, we get:

2/1, 4/3, 1/1, 4/5, 2/3

We can notice that the numerator is increasing by 2 each time, and the denominator is increasing by 2 as well until it reaches the halfway point, and then it decreases by 2 each time. That is, the nth term can be written as:

2\(\times\) floor(n/2) + 2 / (2 + \((-1)^n\) \(\times\) (n mod 2))

where floor(n/2) is the largest integer less than or equal to n/2, and (n mod 2) is the remainder when n is divided by 2.

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The difference lies in the comparison made: critical values in the z-test using rejection region(s) and the P-value in the z-test using a P-value. The choice between the two approaches depends on the nature of the population and the specific hypothesis being tested.

The correct answer is (d): In the z-test using rejection region(s), the test statistic is compared with critical values. The z-test using a P-value compares the P-value with the level of significance alpha.

The z-test is a statistical test used to assess whether a sample mean or proportion significantly differs from a hypothesized population mean or proportion. The difference between the z-test for mu (population mean) using rejection region(s) and the z-test for p (population proportion) using a P-value lies in the approach used to make the inference.

In the z-test using rejection region(s), the test statistic (calculated from the sample) is compared with critical values based on the chosen level of significance alpha. The critical values are determined from the standard normal distribution or a z-table, and if the test statistic falls within the rejection region (beyond the critical values), the null hypothesis is rejected.

On the other hand, in the z-test for p using a P-value, the test statistic is compared with the P-value. The P-value represents the probability of observing a test statistic as extreme or more extreme than the one obtained, assuming the null hypothesis is true. If the P-value is smaller than the chosen level of significance alpha, the null hypothesis is rejected.

Therefore, the difference lies in the comparison made: critical values in the z-test using rejection region(s) and the P-value in the z-test using a P-value. The choice between the two approaches depends on the nature of the population and the specific hypothesis being tested.

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there are 55 red marbles in the jar

Answer:

There are 55 red marbles in the jar.

Step-by-step explanation:

Green marbles = 125 x 2/100 = 2.5

Blue marbles = 125 x 54/100 = 67.5

Red marbles = 125 - 67.5 - 2.5 = 55

The molarity of the KOH solution is approximately 0.1497 M.

To find the molarity of the potassium hydroxide (KOH) solution, we need to use the concept of stoichiometry and the balanced chemical equation for the reaction between KOH and HCl. The balanced equation is as follows:

KOH + HCl → KCl + H2O

From the balanced equation, we can see that 1 mole of KOH reacts with 1 mole of HCl to produce 1 mole of KCl and 1 mole of water. This means that the ratio of moles of KOH to moles of HCl is 1:1.

Given that the volume of the hydrochloric acid solution used is 27.1 mL and its molarity is 0.122 M, we can calculate the number of moles of HCl using the equation:

moles of HCl = molarity × volume (in liters)

= 0.122 mol/L × 0.0271 L

= 0.00331 mol

Since the stoichiometric ratio between KOH and HCl is 1:1, the number of moles of KOH is also 0.00331 mol.

Now, we can use the volume of the potassium hydroxide solution used in the titration, which is 22.1 mL, and the number of moles of KOH to calculate the molarity of the KOH solution.

molarity of KOH = moles of KOH / volume (in liters)

= 0.00331 mol / 0.0221 L

= 0.1497 M

Therefore, the molarity of the potassium hydroxide solution is approximately 0.1497 M.

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Complete Question:

An aqueous solution of potassium hydroxide is standardized by titration with a 0.122 M solution of hydrochloric acid. If 22.1 mL of base are required to neutralize 27.1 mL of the acid, what is the molarity of the potassium hydroxide solution?

Answer:

The correct answer is C.  As x approaches ±∞, p(x) approaches -∞

Step-by-step explanation:

The easiest way to see this is to consider the term with the largest power of x.  In this case that's the first term -5x⁶.  Because the exponent is an even number, the function will ultimately move in the same direction as x approaches infinity.  If the exponent was odd, like -5x⁷, then they'd be moving in opposite directions.

The next thing to consider is the coefficient.  If the coefficient is positive, then the left side of the curve goes downward, and the right side goes either downward or upward depending on the exponent.  If the coefficient is negative, then the left side goes upward, and the right side goes upward or downward depending on the coefficient.

In this case, we have a negative coefficient, so the left side goes downward, and an even power, so the right side goes the same way as the left side.

The correct answer is C.  As x approaches +∞, function p(x) approaches -∞and vice versa.

Polynomial is a combination of algebraic terms may be in addition, subtraction, multiplication, division.

In the case  the first term is -5x⁶.  Because the exponent is an even number, the function will move in the same direction as x approaches infinity.  If the exponent was odd, like -5x⁷, then they would  be moving in opposite directions.

The next thing to consider is the coefficient.  If the coefficient is positive, then the left side of the curve goes downward, and the right side shifts downward or upward and vice versa.

In our case case, we have a negative coefficient, so the left side goes downward, and an even power, so the right side goes the same way as the left side.

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The standard deviation of the given data can be calculated using the formula for the population standard deviation:

Standard deviation = √[∑(X - μ)² * f / N]

where X is the data value, μ is the mean, f is the frequency, and N is the total number of observations.

Given the data:

X: 3 4 5 6 7 8 9

f: 37 8 10 12 4 3 2

Assumed mean (μ) = 6

To calculate the standard deviation, we need to calculate the squared difference between each data value and the mean, multiply it by the frequency, and sum up these values. Then divide the sum by the total number of observations (N) and take the square root of the result.

Let's calculate it step by step:

(X - μ)² * f:

(3 - 6)² * 37 = 111

(4 - 6)² * 8 = 32

(5 - 6)² * 10 = 10

(6 - 6)² * 12 = 0

(7 - 6)² * 4 = 4

(8 - 6)² * 3 = 12

(9 - 6)² * 2 = 18

Sum of (X - μ)² * f = 187

Now divide the sum by the total number of observations (N = 37 + 8 + 10 + 12 + 4 + 3 + 2 = 76) and take the square root of the result:

Standard deviation = √(187 / 76) ≈ 1.82

Therefore, the standard deviation of the given data is approximately 1.82.

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