Identify the form of the following quadratic

The acceleration of the box is 0.4 m/s².

The magnitude of the force that Rory applies is 20.12 N.

(a)

The acceleration of the box can be calculated using the formula:

[tex]a = (v_f^2 - v_i^2) / (2d)[/tex]

where vf is the final velocity, vi is the initial velocity, and d is the distance traveled.

Substituting the given values, we get:

a = (1.2² - 0²) / (2 x 1.8)

a = 0.4 m/s²

(b)

To find the magnitude of the force that Rory applies, we can use Newton's second law, which states that the net force on an object is equal to its mass times its acceleration:

F(net) = ma

The resistance force is acting in the opposite direction to the force applied by Rory.

F(applied) - F(resistance) = ma

Substituting the given values.

F(applied) - 19 = 2.8 x 0.4

F(applied) = 19 + 1.12 = 20.12 N

Therefore, the magnitude of the force that Rory applies is 20.12 N.

Thus,

The acceleration of the box is 0.4 m/s².

The magnitude of the force that Rory applies is 20.12 N.

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Answer:3/10 or 30%

Step-by-step explanation:

the sectors are 1 through 10 meaning 1 2 3 4 5 6 7 8 9 10 out of all those numbers the only ones divisible by 3 is 3 6 9 meaning that 3 numbers out of 10 are divisible by 3. therefore being 3/10.

The probability of randomly drawing a vowel is two eighths

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

P, E, R, C, E, N, T, S

Using the above as a guide, we have the following:

Vowels = 2

Total = 8

So, we have

P(Vowel) = Vowel/Total

Substitute the known values in the above equation, so, we have the following representation

P(Vowel) = 2/8 = two eighths

Hence, the solution is two eighths

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Ha: difference in Apgar score between first-born and second-born twins is not equal to zero.

The most appropriate test for this scenario would be a paired t-test, as the researchers collected data from the same set of twins and are comparing the differences in Apgar score between the first-born and second-born twins.

The appropriate alternative hypothesis for this test would be "Ha: difference in Apgar score between first-born and second-born twins is not equal to zero."

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The hours and minutes elapsed from 8:00 a.m. to 2:30 p.m is 6 hours and 30 minutes.

The hours and minutes elapsed from 7:40 p.m. to 1:10 a.m. is 5 hours and 30 minutes.

The hours and minutes elapsed from 12:00 noon to 4:59 p.m is 4 hours and 59 minutes.

The hours and minutes that elapsed from 1:23 a.m. to 7:35 a.m is 6 hours and 12 minutes.

The hours and minutes that belapsed from 11:28 p.m. to 5:30 a.m is 6 hours and 2 minutes.

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The Multiplicative inverse of 47x = 1 mod 64 is 47 x 15 = 1 (mod 64) . Using Inverse GCD 50x = 63 mod 71 is 50 x 27 = 63 (mod 71).

The reciprocal of a particular integer is referred to as the multiplicative inverse. It is employed to make mathematical expressions simpler. The word "inverse" denotes an opposing or opposed action, arrangement, position, or direction. A number becomes 1 when it is multiplied by its multiplicative inverse.

When a number is multiplied by the original number, the result is 1, that number is said to be the multiplicative inverse of that number. A-1 or 1/a is used to represent the multiplicative inverse of the constant 'a'. In other terms, two integers are said to be multiplicative inverses of one another when their product is 1. The division of 1 by a number yields the multiplicative inverse of that number.

a) The Multiplicative inverse of 47x = 1 mod 64 is

x = 47⁻¹ mod 64

Mow,

Let (47)⁻¹ = y(mod64)

Then, 47y + 64k = 1

Now,

64 = 47 x 1 + 17

47 = 17 x 2 +13

17 = 13 x 1 + 4

13 = 4 x 3 + 1

Comparing with equation we get,

y = 15 and k = -11

Hence, 47 x 15 = 1 (mod 64)

b) The Multiplicative inverse of 50x = 63 mod 71 is

x = 50⁻¹ 63(mod 71)

Mow,

Let (50)⁻¹ = y(mod71)

Then, 50y + 71k = 1

Now,

71 = 50 x 1 + 21

50 = 21 x 2 + 8

21 = 8 x 2 + 5

8 = 5 x 1 + 3

5 = 3 x 1 + 2

3 = 2 x 1 + 1

Comparing with equation we get,

y = 27 and k = -19

Hence, 50 x 27 = 63 (mod 71)

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5. The multiplicative inverse of 47x = 1 mod 64 is 47 x 15 = 1 (mod 64)

6.  The value of 50x = 63 mod 71 using inverse GCD is 50 x 27 = 63 (mod 71).

Given that

47x = 1 mod 64

Divide both sides of the equation by 47

So, we have

47/47x = 1/47 mod 64

Evaluate the quotient

x = 47⁻¹ mod 64

Let (47)⁻¹ = y(mod64)

So, we have

47y + 64k = 1

Expand 64

64 = 47 x 1 + 17

Expand 47

47 = 17 x 2 +13

Expand 17

17 = 13 x 1 + 4

Expand 13

13 = 4 x 3 + 1

When the equations are compared, we have

y = 15 and k = -11

This means that, the multiplicative inverse is 47 x 15 = 1 (mod 64)

Here, we have

50x = 63 mod 71

Divide

50x/50 = 63/50 mod 71

So, we have

x = 50⁻¹ 63(mod 71)

Let (50)⁻¹ = y(mod71)

So, we have

50y + 71k = 1

Expand 71

71 = 50 x 1 + 21

Expand 50

50 = 21 x 2 + 8

Expand 21

21 = 8 x 2 + 5

Expand 8

8 = 5 x 1 + 3

Expand 5

5 = 3 x 1 + 2

Expand 3

3 = 2 x 1 + 1

When the equations are compared, we have

y = 27 and k = -19

This means that 50 x 27 = 63 (mod 71)

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As per the given triangle, the value of sin A in decimal form, rounded to three decimal places, is approximately 0.946.

We can use the definition of sine to find sin A:

sin A = opposite/hypotenuse

In this case, the opposite side is the height of the triangle, which is 35, and the hypotenuse is 37. Therefore:

sin A = 35/37

This fraction cannot be simplified any further, so the value of sin A in fraction form is 35/37.

To find the equivalent decimal, we can divide the numerator by the denominator:

sin A = 35/37 ≈ 0.946

Therefore, the value of sin A in decimal form, rounded to three decimal places, is approximately 0.946.

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Therefore, William needs to score a 97 on the third quiz to get an average of 90.

Average: The arithmetic mean is calculated by adding a set of integers, dividing by their count, and then taking the result. For instance, the result of 30 divided by 6 is 5, which is the average of 2, 3, 3, 5, 7, and 10.

The average test score is calculated by dividing the total score on an assessment by the total number of test-takers. As an illustration, if three students each obtained test scores of 69, 87, and 92, their combined scores would be totaled together and divided by three to yield an average of 82.6.

William needs to score "x" on the third quiz to get an average of 90.

The average of three quizzes can be calculated using the formula:

average = (sum of scores) / (number of scores)

To get an average of 90, William's total score on all three quizzes needs to be:

90 x 3 = 270

His current total score from the first two quizzes is:

85 + 88 = 173

So, to reach a total score of 270, William needs to score:

270 - 173 = 97

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The value of - (the point estimate of the difference of proportions) is 0.02. Option C (0.02) is the correct answer.

To find the value of the point estimate of the difference of proportions, we need to subtract the sample proportion of one group from the sample proportion of the other group.

Let's denote the sample proportion of group 1 as p1 and the sample proportion of group 2 as p2. Then, the point estimate of the difference of proportions can be calculated as:

^p1 - ^p2

where ^p1 = 0.12 and ^p2 = 0.1 (as given in the question).

Substituting the values, we get:

^p1 - ^p2 = 0.12 - 0.1 = 0.02


It is important to note that this is just a point estimate based on the given sample statistics, and the true difference of proportions in the population may differ. We can calculate a margin of error and construct a confidence interval to estimate the range in which the true difference of proportions may lie.

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we have shown that a positive integer is divisible by 3 if and only if the sum of its decimal digits is divisible by 3.

Let n be a positive integer and let d1, d2, ..., dm be its decimal digits, where dm is the leftmost (most significant) digit and d1 is the rightmost (least significant) digit. Then n can be written as:

n = [tex]d1 * 10^{(m-1)} + d2 * 10^{(m-2)} + ... + dm-1 * 10 + dm[/tex]

We want to show that n is divisible by 3 if and only if the sum of its decimal digits is divisible by 3.

First, suppose that n is divisible by 3. Then we have:

n = 3k

for some integer k. Substituting the expression for n, we have:

[tex]d1 * 10^{(m-1)} + d2 * 10^{(m-2)} + ... + dm-1 * 10 + dm = 3k[/tex]

Taking both sides modulo 3, we obtain:

d1 + d2 + ... + dm-1 + dm ≡ 0 (mod 3)

which means that the sum of the decimal digits of n is divisible by 3.

Conversely, suppose that the sum of the decimal digits of n is divisible by 3. Then we have:

d1 + d2 + ... + dm-1 + dm = 3k

for some integer k. Substituting this expression into the equation for n, we obtain:

n =[tex]d1 * 10^{(m-1)} + d2 * 10^{(m-2)} + ... + dm-1 * 10 + dm[/tex]

= [tex]d1 * (10^{(m-1)} - 1) + d2 * (10^{(m-2)} - 1) + ... + dm-1 * (10 - 1) + (d1 + d2 + ... + dm-1 + dm)[/tex]

= [tex]d1 * (10^{(m-1)} - 1) + d2 * (10^{(m-2)} - 1) + ... + dm-1 * (10 - 1) + 3k[/tex]

The first m-1 terms on the right-hand side are all divisible by 3, since 10^n - 1 is divisible by 3 for any positive integer n. Therefore, we have:

n ≡ dm + 3k (mod 3)

Since the sum of the decimal digits of n is divisible by 3, we have dm + d1 + d2 + ... + dm-1 ≡ 0 (mod 3). Therefore, we have:

n ≡ 0 (mod 3)

which means that n is divisible by 3.

Therefore, we have shown that a positive integer is divisible by 3 if and only if the sum of its decimal digits is divisible by 3.

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The probability that a continuous random variable takes a value less than zero is any number between zero and one.

The standard deviation of a normal distribution cannot be negative.

For any continuous random variable, the probability that it takes a value less than zero is given by the cumulative distribution function (CDF) at zero. Since the CDF is a monotonically increasing function that ranges from 0 to 1, the probability that the random variable takes a value less than zero is any number between 0 and 1, inclusive.

The standard deviation of a normal distribution is always a positive number since it is the square root of the variance, which is defined as the average of the squared deviations from the mean.

Since the deviations are squared, they are always non-negative, and their average (the variance) cannot be negative. Therefore, the standard deviation of a normal distribution cannot be negative.

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Math is not relevant to the research question as it is not directly related to smartphone ownership. Verbal, Credits, Year, Exercise, Sleep, Veg, and Cell are also not relevant to the research question as they do not provide information on smartphone ownership or the proportion of smartphone owners at a specific university. The relevant variable in this research question is smartphone ownership.

The relevant variable in this research question is smartphone ownership. This variable is quantitative as it involves measuring the proportion of smartphone owners at a specific university. The proportion of smartphone owners can be expressed as a percentage or a decimal value, which are both quantitative measurements.

Categorical variables are not relevant to this research question as they do not provide information on the proportion of smartphone owners. Categorical variables involve categorizing data into groups or categories, such as gender or race, which are not directly related to smartphone ownership.

In summary, the only relevant variable in this research question is smartphone ownership, which is a quantitative variable.

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The general solution to the original differential equation is:  

y(t) = [tex]C1 e^t cos t + C2 e^t sin t + (1/2)ex sin t + (1/4)ex sin(2t) + (1/4)ln|[/tex]

We first solve the associated homogeneous differential equation:

[tex]2y'' - 4y' + 4y[/tex] = 0

The characteristic equation is[tex]r^2[/tex] - 2r + 2 = 0, which has roots r = 1 ± i. Therefore, the general solution to the homogeneous equation is:

[tex]y_h(t) = e^t([/tex]C1 cos t + C2 sin t)

To use the method of variation of parameters to find the particular solution to the original equation, we assume that the solution has the form:

[tex]y_p(t) = u(t)e^t cos t + v(t)e^t sin t[/tex]

where u(t) and v(t) are functions to be determined.

[tex]y_p''(t) \\\\2u'(t)e^t cos t + 2v'(t)e^t sin t + 2u(t)e^t cos t - 2v(t)e^t sin t - 2u(t)e^t sin t - 2v(t)e^t cos t[/tex]

[tex]y_p'(t) = u'(t)e^t cos t + v'(t)e^t sin t + u(t)e^t cos t + v(t)e^t sin t[/tex]

Substituting these into the original equation and simplifying, we get:

[tex]2u'(t)e^t cos t + 2v'(t)e^t sin t = ex sec x[/tex]

We need to find u'(t) and v'(t) such that this equation holds for all t. To do this, we take the derivative of the assumed solution with respect to t and equate coefficients of cos t and sin t separately:

[tex]u'(t)e^t cos t + v'(t)e^t sin t + u(t)e^t cos t + v(t)e^t sin t = 0 (1)\\v'(t)e^t cos t - u'(t)e^t sin t + u(t)e^t sin t - v(t)e^t cos t = ex sec x (2)[/tex]

Solving equation (1) for u'(t) and v'(t) and substituting into equation (2), we get:

[tex]v(t) = ∫ [ex sec x / (e^(2t))] dt\\u(t) = -∫ [ex sec x / (e^(2t))] tan t dt[/tex]

Evaluating the integrals, we get:

[tex]v(t) = (1/2)ex tan x - (1/2)ln|cos x| + C1\\u(t) = (1/4)ex [sin(2t) - 2cos(2t)] + (1/4)ln|cos x| tan x + C2[/tex]

where C1 and C2 are arbitrary constants.

The general solution to the original differential equation is:  

y(t) = [tex]C1 e^t cos t + C2 e^t sin t + (1/2)ex sin t + (1/4)ex sin(2t) + (1/4)ln|[/tex]

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The cars will be 225 km from point A when they meet and it will take 5 hours for the cars to meet..

Let's denote the distance of the faster car from point A as "x" km. Therefore, the distance of the slower car from point B would be "400-x" km.

We can use the formula for distance, which is:

distance = rate × time

For the faster car, the distance it travels can be expressed as:

x = 45t

where t is the time it takes for the cars to meet.

For the slower car, the distance it travels can be expressed as:

400-x = 35t

Now, we can solve for t by setting these two expressions equal to each other:

45t = 400 - 35t

80t = 400

t = 5

We can then substitute t back into either expression to find the distance from point A:

x = 45t = 45(5) = 225 km

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The two main categories of sampling techniques are probability sampling and non-probability sampling.

Probability sampling includes simple random sampling, systematic sampling, stratified sampling, and cluster sampling.

Simple random sampling involves selecting random samples from the entire population.

Systematic sampling involves selecting every nth individual from a population list.

Stratified sampling involves dividing the population into subgroups and selecting samples from each subgroup.

Cluster sampling involves dividing the population into clusters and selecting entire clusters for sampling.

Non-probability sampling includes convenience sampling, quota sampling, purposive sampling, and snowball sampling.

Convenience sampling involves selecting samples that are easily accessible.

Quota sampling involves selecting samples based on predetermined characteristics.

Purposive sampling involves selecting samples based on specific criteria.

Snowball sampling involves selecting samples based on referrals from other participants.

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By using the formula for variance

[tex]varX= m*(n*(m-1)/m^n)(1 - n(m-1)/(m^n-1))[/tex]

To compute varX:

we first need to find the expected value of X, denoted as E(X).

We can approach this by using the linearity of expectation, which states that the expected value of the sum of random variables is equal to the sum of their individual expected values.

Let's define a random variable Xi as the number of bins with exactly one ball. Then, we have:

[tex]X = X1 + X2 + ... + Xm[/tex]

where m is the total number of bins.

By the definition of Xi, we know that Xi can only take on values between 0 and 1, since a bin can either have exactly one ball (Xi = 1) or not (Xi = 0).

To find E(Xi), we can use the probability of Xi being 1. The probability that a specific bin has exactly one ball is given by:

[tex]P(Xi = 1) = (n choose 1) * ((m-1) choose (n-1)) / (m choose n)[/tex]

The first term (n choose 1) represents the number of ways to choose one ball out of n balls to put into the bin. The second term ((m-1) choose (n-1)) represents the number of ways to choose (n-1) balls out of the remaining (m-1) bins. Dividing by (m choose n) gives us the probability that exactly one bin has one ball.

Therefore, we have:

E(Xi) = P(Xi = 1) * 1 + P(Xi = 0) * 0
     = P(Xi = 1)=[tex](n choose 1) * ((m-1) choose (n-1)) / (m choose n)[/tex]
Using the linearity of expectation, we can find E(X) as:

E(X) = E(X1) + E(X2) + ... + E(Xm)
    = [tex]m * (n choose 1) * ((m-1) choose (n-1)) / (m choose n)[/tex]

Now, to find varX, we need to find the variance of Xi and use the formula for variance of a sum of random variables.

The variance of Xi can be found as:

Var(Xi) = E(Xi^2) - (E(Xi))^2

Since Xi can only take on values 0 or 1, we have:

E(Xi^2) =[tex]0^2 * P(Xi = 0) + 1^2 * P(Xi = 1) = P(Xi = 1)[/tex]

Therefore, we have:

Var(Xi) = P(Xi = 1) - (E(Xi))^2
      = [tex]m*(n*(m-1)/m^n) + m*(m-1)(n(m-1)/m^n)^2 - (mn(m-1)/m^n)^2[/tex]

Using the formula for variance of a sum of random variables, we have:

varX = Var(X1 + X2 + ... + Xm)
    = Var(X1) + Var(X2) + ... + Var(Xm)      (since Xi's are independent)
    = [tex]m*(n*(m-1)/m^n)(1 - n(m-1)/(m^n-1))[/tex]

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The initial mortality rate in 1998 per 100,000 people is :

88.8 deaths

To find the initial mortality rate in 1998, you'll need to use the given relation :

M = 88.8(0.9418)^t, where M is the number of deaths per 100,000 people, and t is the number of years since 1998.

Identify the value of t for 1998. Since 1998 is the starting year, t = 0.

Substitute the value of t into the equation. M = 88.8(0.9418)^0

Calculate M. Since any number raised to the power of 0 is 1, the equation becomes M = 88.8(1), which simplifies to M = 88.8.

So, the initial mortality rate in 1998 is 88.8 deaths per 100,000 people.

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Step-by-step explanation:

Total cost will be

$ 73.56   + 7% of 73.56

$ 73.56 + .07 * $73.56

(1.07) ( 73.56) = $ 78 . 71

Answer: Perimeter: 60ft Area: 150ft^2

Step-by-step explanation:

Since the area of a triangle is equal to the (base*height)/2, you can take the values of each and turn it into an equation like this:

[tex]\frac{25\cdot12}{2}[/tex]

This comes out to be 150ft^2.

Next is the perimeter, which is all of the side lengths of a shape added together.

15+20 is equal to 35, then when you add 25 to it, you get 60.

This means the perimeter is 60 and the area is 150ft^2

Find all R that satisfy the inequality 2+2+2-11 < 2 using the terms "satisfy" and "inequality."

First, let's simplify the inequality:

2 + 2 + 2 - 11 < 2

Now, combine the like terms:

6 - 11 < 2

Next, subtract 6 from both sides:

-5 < 2

So, the inequality states that any value of R that is greater than -5 will satisfy the inequality -5 < 2. In this case, all real numbers R greater than -5 satisfy the given inequality.

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Answer:

The formula for the surface area, S, of a cube with edges of length 2x is:

S = 6(2x)^2

Simplifying the expression inside the parentheses gives:

S = 6(4x^2)

Multiplying 6 by 4x^2 gives:

S = 24x^2

Therefore, the formula for the surface area of a cube with edges of length 2x is S = 24x^2, which is option (B).

Step-by-step explanation:

(a) The number of ways that the event can occur is 6.

(b) Probabilities are :

1) 1/2, 2) 1/6 and 3) 1/3.

(a) Given a bag of different shapes.

Total number of shapes = 6

So, if we select one shape from random,

total number of ways that the event can occur = 6

(b) Number of squares in the bag = 3

Probability of choosing a square = 3/6 = 1/2

Number of circles in the bag = 1

Probability of choosing a circle = 1/6

Number of stars in the bag = 2

Probability of choosing a star = 2/6 = 1/3

Hence the required probabilities are found.

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The null hypothesis is H₀: p ≥ 0.2 (the return rate is greater than or equal to 20%). The alternative hypothesis is H₁: p < 0.2 (the return rate is less than 20%).

We will first identify the null hypothesis (H₀) and alternative hypothesis (H₁). The null hypothesis represents the assumption that there is no significant difference or effect. In this case, the return rate is assumed to be equal to 20%. The alternative hypothesis represents the claim we want to test, which is that the return rate is less than 20%. So, the null hypothesis and alternative hypothesis are: H₀: p = 0.2 H₁: p < 0.2 Based on the provided options,

The correct answer is: OB. H₀: p = 0.2 OC. H₁: p < 0.2

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After approximately 60.2 minutes, the pizza will reach a temperature of 150°F.

We can model the cooling of the pizza using Newton's law of cooling:

T(t) = T_room + (T_0 - T_room) e^(-kt)

where T(t) is the temperature of the pizza at time t, T_0 is the initial temperature of the pizza (300°F), T_room is the room temperature (70°F), and k is the cooling rate constant. We can solve for k using the fact that the pizza cools from 300°F to 100°F in M minutes:

100 = 70 + (300 - 70) e^(-kM)

e^(-kM) = 0.1

-kM = ln(0.1)

k = -ln(0.1)/M

Now we want to find the time t when the pizza's temperature is 150°F:

150 = 70 + (300 - 70) e^(-kt)

e^(-kt) = (150 - 70)/(300 - 70)

e^(-kt) = 4/13

-kt = ln(4/13)

t = -ln(4/13)/k

Substituting the expression for k derived earlier, we get:

t = M ln(4/13) / ln(0.1)

For example, if M = 30 (i.e., it takes 30 minutes for the pizza to cool from 300°F to 100°F), then:

t = 30 ln(4/13) / ln(0.1) ≈ 60.2 minutes

Therefore, after approximately 60.2 minutes, the pizza will reach a temperature of 150°F.

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The hexagon's apothem is approximately 13.856 inches long. The hexagon's perimeter is 96 inches. The hexagon has a surface area of approximately 665.088 square inches.

A hexagon is a six-sided polygon in geometry. The sum of any simple (non-self-intersecting) hexagon's internal angles is 720°.

Given that the length of a side is = 16 in

So half a side = 8 in

Using the Pythagorean theorem, calculate the area of the given right triangle.

Apothem = [tex]\sqrt{16^{2} - 8^{2} }[/tex]

= [tex]\sqrt{256 - 64}[/tex]

= √192

= 13.856 inches.

Now, we will calculate the perimeter of the hexagon. We have been given 6 sides of hexagon and each side length is 16 in, so

Perimeter = 16 × 6 = 96 inches

Area of hexagon = 1/2 × apothem × perimeter

= 1/2 × 13.856 × 96

= 665.088 inches

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Correct question:

Find the missing measures in this regular hexagon.

A regular hexagon has side lengths of 16 inches. The radius is 16 inches. An apothem is shown.

The length of the apothem of the hexagon is about ___inches.

The perimeter of the hexagon is ___ inches.

The area of the hexagon is about ___ square inches.

When x = 2, f(g(x)) is approximately equal to 187/9.

To solve for f(g(x)) when x = 2, we need to substitute the value of x into the function g(x) and then substitute the result into the function f(x). Let's calculate it step by step:

Step 1: Calculate g(x) when x = 2:

g(x) = x + 4/3

g(2) = 2 + 4/3

g(2) = 2 + 4/3

g(2) = 10/3

Step 2: Substitute the result from step 1 into f(x):

f(x) =[tex]x^2[/tex] + 2x + 3

f(g(x)) = f(10/3)

f(g(2)) = f(10/3)

Step 3: Calculate f(g(2)):

f(10/3) = (10/3[tex])^2[/tex] + 2(10/3) + 3

f(10/3) = 100/9 + 20/3 + 3

f(10/3) = 100/9 + 60/9 + 27/9

f(10/3) = 187/9

Therefore, when x = 2, f(g(x)) is approximately equal to 187/9.

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a) 27 business owners plan to provide a holiday gift to their employees.

b) Using a z-table, the p-value for z = -0.1583 is 0.4371 (rounded to four decimal places).

c) The smallest level of significance for which we could draw this conclusion would be equal to the calculated p-value, which is 0.4371 (rounded to four decimal places).

(a) In the survey of 60 business owners, 45% plan to provide a holiday gift to their employees. To find the number of business owners planning to give gifts, multiply the total number of business owners (60) by the percentage (0.45): 60 x 0.45 = 27 business owners plan to provide a holiday gift to their employees.

(b) To compute the p-value for a hypothesis test to determine if the proportion of business owners providing holiday gifts has decreased from last year, first, find the test statistic:

z = (p_sample - p_population) / sqrt((p_population * (1 - p_population)) / n)
z = (0.45 - 0.46) / sqrt((0.46 * (1 - 0.46)) / 60)
z = -0.01 / 0.0632 = -0.1583

Using a z-table, the p-value for z = -0.1583 is 0.4371 (rounded to four decimal places).

(c) Since the p-value (0.4371) is greater than the level of significance α=0.05, we fail to reject the null hypothesis. Thus, we cannot conclude that the proportion of business owners providing gifts has decreased based on the given level of significance.

The smallest level of significance for which we could draw this conclusion would be equal to the calculated p-value, which is 0.4371 (rounded to four decimal places).

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(a)  (AUB) \ (AnB) has a total of 4 elements.

(b) sin(pi/4) = 1/sqrt(2)

cos(pi/3) = 1/2

a) To find the elements in (AUB) \ (AnB), we first need to find AUB and AnB.
AUB is the set of all elements that are in A or B or both.

Therefore, AUB = {1,3,4,5,6,7,8}.

AnB is the set of all elements that are in both A and B.

Therefore, AnB = {3,5,7}.

To find (AUB) \ (AnB), we need to remove the elements in AnB from AUB.

Therefore, (AUB) \ (AnB) = {1,4,6,8}.
Thus, (AUB) \ (AnB) has 4 elements.

b) sin(pi/4) = 1/sqrt(2) and cos(pi/3) = 1/2.
We can remember these values using the unit circle.

At pi/4 radians, the point on the circlunit e is located at (sqrt(2)/2, sqrt(2)/2), which gives us a sine value of 1/sqrt(2) and a cosine value of 1/sqrt(2).

At pi/3 radians, the point on the unit circle is located at (1/2, sqrt(3)/2), which gives us a sine value of sqrt(3)/2 and a cosine value of 1/2.

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The integral ∫[0,6] 1/x dx is divergent, An integral is said to be divergent if it does not have a finite value.

The given integral is:

[tex]∫[0,6] 1/x dx[/tex]

We know that the integral of 1/x is ln(x), and the antiderivative of ln(x) is xln(x) - x.

So, applying the limits of integration, we get:

[tex]∫[0,6] 1/x dx = ln(x)|[0,6] = ln(6) - ln(0)[/tex]

The natural logarithm of zero is unclear, so the indispensably isn't characterized at x = 0. In this manner, the indispensability is unique.

An integral is said to be divergent in the event that it does not have limited esteem. In other words, on the off chance that the fundamentally does not meet a genuine number, it is said to be unique.

There are a few reasons why a fundamentally may be unique. A few common reasons incorporate:

The integrand gets to be unbounded at a few points inside the limits of integration.

The integrand does not approach zero as the constraint of integration approaches boundlessness.

The limits of integration are interminable, and the integrand does not merge to a limited esteem as the limits approach interminability.

When an indispensably is disparate, it implies that the zone beneath the bend is interminable or does not exist.

This could have imperative suggestions in ranges such as material science and designing, where integrands are utilized to calculate amounts such as work, energy, and a liquid stream. 

Thus, the answer is (b) Divergent. 

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The distance between the given coordinates  (−5, −19) and (−5, 32) is given by 51 units.

Let us consider the coordinates of two given points be,

(x₁ , y₁ ) = ( -5 , -19 )

(x₂ , y₂ ) = (-5 , 32 )

Distance formula between two points is equals to,

Distance = √ ( y₂ - y₁)² + ( x₂ - x₁ )²

Substitute the values of the coordinates we have,

⇒ Distance = √ ( 32 - (-19))² + ( -5- (-5) )²

⇒ Distance = √ (32 +19)² + (-5 + 5)²

⇒ Distance = √ 51² + 0²

⇒ Distance =  51 units.

Therefore, the distance between the two points is equal to 51 units.

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