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If the slope of a line is 1/2, find x when (-4, 12) and (x, 5) ?
Please show formula.

Answer:

(g o f)(8)

Step-by-step explanation:

First we find f(8).

f(8) = 8 - 1 or 7.

We now find g(f(8)), which means g(7).

g(7) = 7^3 or 343

The correct option A, "None of the associations listed are correct," is the appropriate response.To determine the association suggested by the two-way table, we need to calculate the relative frequency of the data.

The table provides information about whether individuals have a brother and a sister.

Based on the options given, let's calculate the relative frequencies to see which association is suggested:

Calculate the relative frequency for individuals who have a brother and a sister:Relative frequency = (Number of individuals with both a brother and a sister) / (Total number of individuals)

Calculate the relative frequency for individuals who have a brother but no sister:Relative frequency = (Number of individuals with a brother but no sister) / (Total number of individuals)

Calculate the relative frequency for individuals who have a sister but no brother:Relative frequency = (Number of individuals with a sister but no brother) / (Total number of individuals)

Calculate the relative frequency for individuals who have neither a brother nor a sister:Relative frequency = (Number of individuals with neither a brother nor a sister) / (Total number of individuals)

By comparing the relative frequencies, we can determine which association is suggested by the data.Unfortunately, the given two-way table is missing, so we cannot perform the necessary calculations to determine the association.

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Answer:

D

Step-by-step explanation:

if cosec is 13/5 then sin is 5/13

Answer:

25

Step-by-step explanation:

1/5× 150= 30

1/3× 150= 50

3/10×150= 45

30+50+45= 125

150-125= 25

25 are green

Answer:

16

Step-by-step explanation:

Tertiary consumers are one level above primary producers in a food chain. In a food chain, the transfer of energy and nutrients occurs from one trophic level to another.

The trophic levels are categorized into producers, primary consumers, secondary consumers, and tertiary consumers.

Primary producers, such as plants or algae, are the first trophic level in a food chain. They convert energy from sunlight into organic matter through photosynthesis. Primary consumers, also known as herbivores, are the organisms that feed directly on primary producers.

Secondary consumers are the next trophic level and they feed on primary consumers. They are usually carnivores or omnivores that consume herbivores.

Finally, tertiary consumers occupy the highest trophic level in a food chain. They are the top predators that feed on secondary consumers. These can include large carnivores or even apex predators.

Therefore, tertiary consumers are one level above primary producers in the food chain. They represent the organisms that obtain energy by consuming other organisms higher up in the trophic hierarchy.

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The percentage strength of neomycin in the final compounded product is approximately 2.5%.

To determine the percentage strength of neomycin in the final compounded product, we need to calculate the weight of neomycin in the cream and divide it by the total weight of the cream.

Neomycin (5%) cream: 30g

The neomycin content is 5% of the total cream weight. To find the weight of neomycin in the cream, we multiply the cream weight by the neomycin percentage:

Weight of neomycin = 30g × 0.05 = 1.5g

Now, to calculate the percentage strength of neomycin in the final compounded product, we divide the weight of neomycin by the total weight of the cream and multiply by 100:

Percentage strength of neomycin = (Weight of neomycin / Total weight of cream) × 100

Percentage strength of neomycin = (1.5g / 60g) × 100 ≈ 2.5

Therefore, the percentage strength of neomycin in the final compounded product is approximately 2.5%.

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We can compute various descriptive statistics such as the mean, median, mode, range, variance, standard deviation, sum of values, and sum of squared deviations.

The sample mean, also known as the average, provides information about the central tendency of the variable X. It represents the typical or average number of coupons used by the shoppers in the sample. In this case, calculating the mean of the given data would provide an estimate of the average number of coupons used over the 6-month period.

The sample standard deviation measures the dispersion or variability of the data points around the mean. It indicates how much the individual observations deviate from the mean value. A higher standard deviation implies greater variability, indicating a wider range of coupon usage among the shoppers in the sample.

By computing the sample mean and standard deviation, we can understand the average coupon usage and the degree of variability in the data. These statistics help us summarize and interpret the characteristics of the variable X, allowing us to make comparisons, identify outliers, assess the spread of the data, and make inferences about the larger population from which the sample was drawn.

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Answer:

16/81

Step-by-step explanation:

Answer:

Step-by-step explanation:

The explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹ where;

a is the first term of the geometric sequence

r is the common ratio

n is the number of terms

If a geometric sequence has a common ratio of 2 and the 12th term is −12,288, then;

T₁₂ = ar¹²⁻¹

T₁₂ = ar¹¹

Given T₁₂ = -12,288 and r = 2, we can calculate the first term a

-12,288 = a2¹¹

a = -12,288/2¹¹

a =  -12,288/2048

a = -6

Since the explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹, then for the sequence given, the explicit rule will be;

Tₙ = -6(2)ⁿ⁻¹

Tₙ = -6 * 2ⁿ * 2⁻¹

Tₙ = -6 * 2ⁿ * 1/2

Tₙ = -3(2)ⁿ

Hence the explicit rule that describes this sequence is Tₙ = -3(2)ⁿ

Answer:

WHEN YOU COMPARE THE TEMPERATURE ON MONDAY TO THE TEMPERATURE ON TUESDAY, THE TEMPERATURE ON TUESDAY IS COLDER.

Answer:

11 Tenths

Step-by-step explanation:

Withouth the tenths, the bottom number would be 1.05. So we need 1.10 or 11 more. 10 tenths is one whole plus the 1 tenth we need to put in the tenths place.

In this scenario, we have a budget constraint and an indifference curve representing preferences. By analyzing the given information, we can determine the optimal bundle of goods and how it changes with a decrease in income.

a. The budget constraint can be represented graphically. The X-intercept is found by setting Y = 0, giving us X = I/Px = 100/2 = 50. The Y-intercept is found by setting X = 0, giving us Y = I/Py = 100/4 = 25. The slope of the budget constraint is determined by the ratio of the prices, giving us -Px/Py = -2/4 = -1/2. Thus, the budget constraint line can be drawn connecting the X and Y intercepts with a slope of -1/2.

b. The optimal bundle of X and Y can be found by maximizing utility subject to the budget constraint. Given the marginal rate of substitution (MRS) of Y/(2X), we set the MRS equal to the slope of the budget constraint, -Px/Py = -1/2. Solving for X and Y, we can find the optimal bundle.

c. Labeling the optimal bundle found in part b as "A," we can draw an indifference curve passing through this point on the graph. The indifference curve represents the combinations of X and Y that provide the same level of utility.

d. If the income decreases to $80, the new budget constraint can be drawn with the same slope but a lower intercept. We can find the new optimal bundle, labeled "B," by maximizing utility subject to the new budget constraint. Similarly, we can draw another indifference curve passing through point B to represent the new optimal bundle.

If X is a normal good and Y is an inferior good, a decrease in income will generally lead to a decrease in the optimal amount of Y and an increase in the optimal amount of X. This is because as income decreases, the demand for inferior goods like Y tends to decrease, while the demand for normal goods like X remains relatively stable or may even increase. The specific changes in the optimal amounts of X and Y would depend on the specific preferences and income elasticity of the goods.

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Answer:

i-

Step-by-step explanation:

Answer:

The 4th graph.

Step-by-step explanation:

Answer:

The first one

Step-by-step explanation:

f(2)=4 means when x=2. F(x) or you may call it y, equals 4, so find the one that when x=2, y=4, then its your answer.

The expected area of a random square which has a side length that is uniform random variable is 1/3.

A family of symmetric probability distributions includes the continuous uniform distribution and rectangular distribution. The distribution describes an experiment with a random result that falls within predetermined bounds.

 The parameters, a and b, which represent the minimum and maximum values, define the bounds. The interval may be closed (for example, [a, b]) or open (for example, (a, b)). common abbreviation for the distribution is U (a, b), where U stands for uniform distribution. 

The length of the interval is defined by the difference between the bounds; intervals with the same length on the distribution's support are equally likely.

Let, side of the square = X

we know that the area of a square = side × side

                                                          =  X  ×  X

                                                          =  X^{2}

now, by using Continuous uniform distribution,

E[ X^{2} ] =  \(\int\limits^1_0 X^{2} \, dx\)    

                =  \([\frac{1^{3} }{3} - \frac{0^{3} }{3} ]\)

                =  \(\frac{1}{3}\)

Hence , the expected area of the square is \(\frac{1}{3}\).

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Answer:

17.

9x - 2 = 8x + 6 (opposite angles on the transversal)

9x - 8x = 6+2

x = 8

18.

-5 + 21x + 15x +5 = 180 (angles on the same side of transversal add up to 180)

36x = 180

x = 180/36

x = 5

19.

9x + 4 + 95 = 180  (angles on the same side of transversal add up to 180)

9x + 99 = 180

9x = 180-99

9x = 81

x = 81/9

x = 9

20.

16x - 2 = 110 (opposite angles on the transversal)

16x = 110 +2

16x = 112

x = 112/16

x = 7

21.

29x + 4 = 31x -4 (opposite angles on the transversal)

4 + 4 = 31x - 29x

2x = 8

x = 8/2

x= 4

22.

12x + 2 + 6x + 16 = 180(angles on the same side of transversal add up to 180)

18x +18 = 180

18x = 180-18

18x = 162

x = 162/18

x = 9

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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To set up this confidence interval, first identify the population parameter of interest, next select the appropriate estimator, then check the conditions for constructing the confidence interval that are: Randomization, Sample size and Distribution shape.

State:
Zachary wants to estimate the mean number of daily texts he sent over the past four years using a 90% confidence interval. He has an SRS of 50 days, with a daily average of 22.5 messages. The data is strongly skewed to the right with many outliers.

Plan:
1. Identify the population parameter of interest: The mean number of daily texts sent by Zachary over the past four years (µ).
2. Select the appropriate estimator: In this case, it's the sample mean = 22.5 messages.
3. Check the conditions for constructing the confidence interval:
  a. Randomization: Zachary used a simple random sample (SRS) of 50 days, which satisfies the randomization condition.
  b. Sample size: The sample size is n = 50, which is typically considered large enough for constructing a confidence interval.
  c. Distribution shape: Since the data is strongly skewed to the right with many outliers, the normality condition might not be satisfied. In this case, the Central Limit Theorem (CLT) may not apply, and the confidence interval might not be accurate.

Given the potential issue with the distribution shape, Zachary should consider either transforming the data to approximate normality or using a nonparametric method.

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Answer:64 students

Step-by-step explanation:

using the empirical rule, we know that 34% of a normal distribunion is below the mean but above 1 standard deviation. This means that 16% of the students enter before 9:55. Take 16% of 400 and you get the amount of students in before 9:55

The total time required to cook a 12-pound turkey in an oven preheated to 325 degrees would be 2 hours and 53 minutes.

Based on the given information, it takes 5 minutes to preheat the oven to 325 degrees, and for an oven preheated to 325 degrees, the recommended cooking time for a turkey is about 14 minutes per pound.

The amount of time it takes to cook the turkey depends on the weight of the turkey.

Therefore, to calculate the total time to cook a turkey, the following steps should be followed:

Step 1: Determine the weight of the turkey.The weight of the turkey is required to know the cooking time. Suppose the turkey weighs 12 pounds.

Step 2: Calculate the total cooking time using the given information.To calculate the total cooking time for a 12-pound turkey:

14 minutes per pound × 12 pounds = 168 minutes (or 2 hours and 48 minutes).

Step 3: Add the preheating time to the total cooking time.The total time to cook the turkey, including preheating the oven, would be:

168 minutes (total cooking time) + 5 minutes (preheating time) = 173 minutes (or 2 hours and 53 minutes).

Therefore, the total time required to cook a 12-pound turkey in an oven preheated to 325 degrees would be 2 hours and 53 minutes.

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To provide a solution for this problem, we can factor the polynomial or find its roots using the rational root theorem.

One possible factorization of the polynomial is:

3x^3 + 13x^2 + 18x - 12 = (x+1)(3x^2 + 10x - 12)

To obtain this factorization, we can start by trying factors of the constant term -12 that might work as roots of the polynomial.

One such factor is -1, so we can use synthetic division or long division to divide the polynomial by x+1. This gives us a quotient of 3x^2 + 10x - 12, which can be factored using the quadratic formula or other methods.

The roots of the polynomial can be found by setting each factor equal to zero and solving for x. This gives us:

x+1 = 0 or 3x^2 + 10x - 12 = 0

The first equation has a single root of x = -1. The second equation can be solved using the quadratic formula or factoring, giving us two more roots:

x = (-10 ± sqrt(100 + 4312)) / (2*3) = (-10 ± 2sqrt(19)) / 3

Therefore, the roots of the polynomial are -1, (-10 + 2sqrt(19))/3, and (-10 - 2sqrt(19))/3.

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The number of kilometres it can travel in 2 hours at the same speed is 120 km

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

Rate = 180 km in 3 hours

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

Speed = 180km/3 hours

So, we have

Speed = 60 km/hr

When it travels for 2 hours, we have

Distance = 60 km/hr * 2 hr

Evaluate

Distance = 120 km

Hence, the distance is 120 km

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Qualitative graphs depict the relationship between two quantities without including numerical values.

The benefit is that it only shows the overall trend of the effect. When we experiment with these variables, we can immediately see how the graph will look. This could validate our findings.

A quantitative relationship emerges as one variable influencing another, which can be seen with a graph. Examine how each variable is represented on the graph, as well as how quantitative relationships are stated using equations.

Quantitative data refers to data that's represented by numbers.

This is the result of graphing all of the data points. Look at that, our data points have formed a straight line! We can draw the line in using a ruler to make it more visible. We'll notice that the line passes through all of the points in our data, indicating that there is a definite relationship in our quantitative data.

Thus, qualitative graphs depict the relationship between two quantities without including numerical values.

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An equation of the plane through the point (-1, -5, 1) and perpendicular to the vector (5, 4, 2) can be -4x + 5y - 2z = 11.

First, the normal vector of the plane must be determined. The vector perpendicular to the given vector (5, 4, 2) is (-4, 5, -2).

Now, the equation of the plane can be determined using the given point and the normal vector. The standard form of the equation of a plane is Ax + By + Cz = D.

We can use the point (-1, -5, 1) and the normal vector (-4, 5, -2) to calculate the values of A, B, C, and D in the equation. To do this, we can use the point-normal form of the equation of a plane.

The point-normal form is (x - x1) × nx + (y - y1) × ny + (z - z1) × nz = 0. We can plug in the point and normal vector values into this equation to calculate A, B, C, and D.

Therefore, the equation of the plane is -4x + 5y - 2z = 11.

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Answer:

4\(\sqrt{10}\)

Step-by-step explanation:

side ('s') squared equals 160

s² = 160

so 's' = \(\sqrt{160}\) which can be broken down to \(\sqrt{4}\)· \(\sqrt{4}\) · \(\sqrt{10}\) which equals

2 · 2 · \(\sqrt{10}\) or 4\(\sqrt{10}\)

It akes 2.5 seconds for the football to reach its maximum height.

It should be noted that to find the initial height of the football, we need to determine the height when t=0. We can substitute t=0 into the equation:

h(0) = -16(0)² + 80(0) + 1

h(0) = 1

We can find the time at which the vertical velocity is zero by finding the vertex of the parabolic function. The vertex can be found using the formula:

t = -b/2a

where a = -16 and b = 80. Substituting these values into the formula gives:

t = -80/(2(-16)) = 2.5

Therefore, it takes 2.5 seconds for the football to reach its maximum height.

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Answer:

x=-3

Step-by-step explanation:

follow the PEMDAS method then see if the 2 equation equal each other after plugging in the x.

Answer:

x = - 3

Step-by-step explanation:

Given

- 3(7x - 5) = 87 + 3x ← distribute parenthesis on left side

- 21x + 15 = 87 + 3x ( subtract 3x from both sides )

- 24x = 72 ( divide both sides by - 24 )

x = - 3

If Shen produced and Manuel consumed one additional bottle of water, total surplus would be $2

The law of supply and demand combines two fundamental economic ideas that describe how changes in the price of a resource, commodity, or product affect its supply and demand.

Supply grows as the price rises, but demand drops. In contrast, as the price falls, supply is constrained and demand is increased.

Demand and supply levels for different prices can be displayed as curves on a graph. The intersection of these curves symbolizes the process of price discovery in the marketplace, as it indicates the balance, or market-clearing price, at which demand equals supply.

According to the law of demand, demand for a good or resource will decrease as its price increases and increase as its price decreases.

How to solve?

Price ------ Quantity Supplied ----- Quantity Demanded

2 --------------------- 1 ------------------------- 3

4 --------------------- 2 ------------------------ 2

6 --------------------- 3 ------------------------ 1

4 (quantity supplied = quantity demanded = 2)

4 ($7>$4 and $5>$4, $3<$4<$5, area above price line but under curve if price line was at $4, $7-$4=$3, $5-$4=$1, $3+$1=$4); 4 ($1<$4 and $3<$4, $3<$4<$5, area below price line and under curve if price line at $4, $4-$1=$3, $4-$3=$1, $3+$1=$4); 8 ($4 from consumer surplus + $4 from producer surplus)

fall (equilibrium = 2, 2-1=1, Shen: quantity supplied = 1 -> $2, Manuel: quantity demanded = 1 -> $6, total surplus = producer surplus + consumer surplus = ($4-$1)+($7-$4)=$6, $8>$6)

rise (equilibrium = 2, 2+1=3, Manuel: quantity demanded = 3 -> $2, Shen: quantity supplied = 3 -> $6, total surplus = consumer surplus + producer surplus = ($3-$2)+($7-$6)=$2, $8>$2, $6>$2)

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