Heights of 10-year-old girls (5th graders) follow an approximately normal distribution with mean = 54.4 inches and standard deviation of = 2.7 inches.
A. What proportion of 10-year-old girls are shorter than 48 inches (4 feet)? Report your answer with four decimal places.
B. What proportion of 10-year-old girls are taller than 60 inches (5 feet)? Report your answer with three decimal places.
C. What proportion of 10-year-old girls have heights between 50 and 55 inches? Report your answer with three decimal places.
D. The tallest 15% of 10-year-old girls are taller than what height? Report your answer with one decimal place.

Answer:

Well, as it turns out, when two figures are similar or congruent, they have certain properties, and these properties can be used to prove relationships between the figures. When two figures are similar figures, they have the following properties: Corresponding angles have equal measure.

Step-by-step explanation:

Answer:

q(s)=s³-3s²

s is replaced by 11

q(11)=(11)³-3(11)²

      =(11)²(11-3)

      =121×8

      =968

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Since T is at the midpoint of SU, then

ST = TU , substitute values

8x = 3x + 20 ( subtract 3x from both sides )

5x = 20 ( divide both sides by 5 )

x = 4

Thus

ST = 8x = 8(4) = 32

For each given point and axis, we need to determine the equation of the plane that is perpendicular to that axis. The correct equations are chosen from the given options. The correct equations are: a) z = 6, b) y = -2, c) x = -2.

a) To find the equation of the plane perpendicular to the z-axis at the point (9, 5, 6), we need to fix the z-coordinate and allow the x and y coordinates to vary. Since the z-axis is vertical and parallel to the z-coordinate, the equation that represents the plane is z = 6.

b) For the plane perpendicular to the x-axis at the point (-7, -2, 7), we fix the x-coordinate and allow the y and z coordinates to vary. Since the x-axis is horizontal and parallel to the x-coordinate, the equation that represents the plane is x = -7.

c) Similarly, for the plane perpendicular to the y-axis at the point (-2, -7, -9), we fix the y-coordinate and allow the x and z coordinates to vary. Since the y-axis is vertical and parallel to the y-coordinate, the equation that represents the plane is y = -7.

Therefore, the correct equations for the planes perpendicular to the given axes at the given points are a) z = 6, b) x = -7, and c) y = -7.

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Therefore , the solution of the given problem of percentage comes out to be invested now is $9,017.67. The response is (B).

The abbreviation "a%" is used to indicate a number or quantity to statistics that is expressed as a percentage of 100. Versions containing the characters "pct," "pct," and "pc" are also rare. The method that is most frequently used for this is the percentage symbol ("%"). Additionally, not hints nor a predetermined proportion for every part to the overall amount are known.

Here,

To calculate the present worth, we can use the compound interest formula:

=> P = A / (1 + r/n)^(n*t)

where P is the value in the present, A is the value in the future, r is the interest rate per year, n is the number of times the interest is multiplied annually, and t is the amount of time in years.

A = $12,868.21, r = 6.1%, n = 1 (compound annually), and t = 7 years in this instance. When these numbers are added to the formula, we obtain:

=>  P = 12,868.21 / (1 + 0.061/1)⁷

=>  P = 12,868.21 / (1.061)⁷

=>  P = $9,017.67

In order to amass $12,868.21 at a compound annual interest rate of 6.1% over a period of seven years,

the present value that should be invested now is $9,017.67. The response is (B).

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This person owns 50% of the money required for property B. But we cannot calculate a percentage without knowing the actual value of property B or how much money the person has.

The question asks what percentage of the money needed for Device B the person has. Without more information on the actual cost of Device B or how much money the person has, we cannot determine an exact percentage.

However, we can use a formula to calculate the percentage of money that the person has for Device B, given the cost of Device B and the amount of money the person has. The formula is:

Percentage = (Money for Device B ÷ Cost of Device B) x 100%

For example, if Device B costs $100 and the person has $50, the percentage of money the person has for Device B would be:

Percentage = ($50 ÷ $100) x 100% = 50%

Therefore, the person has 50% of the money needed for Device B. However, without knowing the actual cost of Device B or how much money the person has, we cannot calculate a specific percentage.

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Answer:

Moving 4 to the right on the x axis

1. The mean number of households that will have one or more cats is 15.

2. This means that getting 10 or fewer households with cats out of 50 is not extremely unusual, as there is a 5.3% chance of it happening by random chance alone.

The mean number of households that will have one or more cats can be calculated as:

Mean = (30/100) x 50 = 15

Therefore, the mean number of households that will have one or more cats is 15.

The standard deviation can be calculated using the formula:

Standard deviation = \(\sqrt{(npq)}\)

where n is the sample size (50), p is the probability of success (30/100 = 0.3), and q is the probability of failure (1 - p = 0.7).

Standard deviation = sqrt(50 x 0.3 x 0.7) = 3.08

Rounding to 1 decimal place, the standard deviation is 3.1.

If 10 of the 50 random households had one or more cats, we can calculate the z-score as:

z = (x - μ) / σ

where x is the observed number of households with cats (10), μ is the mean (15), and σ is the standard deviation (3.1).

z = (10 - 15) / 3.1 = -1.61

Looking up the z-score in a standard normal distribution table, we find that the probability of getting a z-score of -1.61 or lower is 0.053.

This means that getting 10 or fewer households with cats out of 50 is not extremely unusual, as there is a 5.3% chance of it happening by random chance alone.

However, it is somewhat lower than the expected value of 15, which suggests that the sample may not be fully representative of the population.

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The point (9, -7) is the only solution to the system of linear inequalities given.

To determine which point would be a solution to the system of linear inequalities, let's substitute the given points into the inequalities and see which point satisfies both inequalities.

The system of linear inequalities is:

y > -4x + 6

y > (1/3)x - 7

Let's test each given point:

For the point (9, -7):

Substituting the values into the inequalities:

-7 > -4(9) + 6

-7 > -36 + 6

-7 > -30 (True)

-7 > (1/3)(9) - 7

-7 > 3 - 7

-7 > -4 (True)

Since both inequalities are true for the point (9, -7), it is a solution to the system of linear inequalities.

For the point (-12, -2):

Substituting the values into the inequalities:

-2 > -4(-12) + 6

-2 > 48 + 6

-2 > 54 (False)

-2 > (1/3)(-12) - 7

-2 > -4 - 7

-2 > -11 (False)

Since both inequalities are false for the point (-12, -2), it is not a solution to the system of linear inequalities.

For the point (12, 1):

Substituting the values into the inequalities:

1 > -4(12) + 6

1 > -48 + 6

1 > -42 (True)

1 > (1/3)(12) - 7

1 > 4 - 7

1 > -3 (True)

Since both inequalities are true for the point (12, 1), it is a solution to the system of linear inequalities.

For the point (-12, -7):

Substituting the values into the inequalities:

-7 > -4(-12) + 6

-7 > 48 + 6

-7 > 54 (False)

-7 > (1/3)(-12) - 7

-7 > -4 - 7

-7 > -11 (True)

Since one inequality is true and the other is false for the point (-12, -7), it is not a solution to the system of linear inequalities.

In conclusion, the point (9, -7) is the only solution to the system of linear inequalities given.

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Answer:

0

Step-by-step explanation:

y = 1x + b

-3 = 1(-3) + b

-3 = -3 + b
+3   +3

0 = b

Answer:

Domain: (−∞,∞),{x|x∈R}

Range: (−∞,∞),{y|y∈R}

Step-by-step explanation:

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: (−∞,∞),{x|x∈R}

Range: (−∞,∞),{y|y∈R}

E

Step-by-step explanation:

The line stems from the vertex Q to the middle of R and S

I would greatly appreciate if you can give the brainliest answer crown!

Step-by-step explanation:

please mark me as brainlest

5. 4 + 8a - 13 + 7a

Collect like terms:

4 - 13 + 8a + 7a

= -9 + 15a

6. 8n - 32 + 5m + 33- 3

Collect like terms:

8n + 5m - 32 + 33 - 3

= 8n + 5m - 2

7. 7 + 13a - 3 - 20 + 2a

Collect like terms:

7 - 3 - 20 + 13a + 2a

= -16 + 15a

8. -5 - 2c + 7 - 60​

Collect like terms:

-5 + 7 - 60 - 2c

= -58 - 2c

The area to the right of the z-score 1.40 and to the left of the z-score 1.58 is the difference between the areas to the left of these two z-scores.

To find the area to the right of the z-score 1.40 and to the left of the z-score 1.58 under the standard normal curve,

we can use a standard normal distribution table or a calculator that provides the area under the normal curve.

The area to the right of a z-score is equal to 1 minus the area to the left of that z-score.

Therefore, the area to the right of the z-score 1.40 and to the left of the z-score 1.58 is the difference between the areas to the left of these two z-scores.

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Answer:

2, 10, 0, 4

Step-by-step explanation:

"regrouping 1 tenth into 10 hundredths" is taking one of those green tenth sticks and dividing it into 10 hundredth squares. That means that you have 2 wholes, 2 tenths (remaining green sticks), and 10 hundredths (because the only hundredths you have are the ones you got from that tenth you regrouped).

After crossing them out, you have 2 wholes, 0 tenths (because you only had 2 before), and 4 hundredths (because you crossed out 6 of the 10, 10-6=4).

Hope I could help you!

The distance across the river, if OC = 335 ft, RE = 245 ft, OR = 160 ft, is PR = 433.39 ft.

Comparing one quantity to another is what ratio is. For instance, the weight ratio is 1:3 if you weigh 30 kg and your father weighs 90 kg.

Given:

OC = 335 ft, RE = 245 ft, OR = 160 ft,

As you can see, the Δ PRE and Δ POC are similar to the AA similarity,

the ratio of the sides is also equal,

PR / PO = RE / OC

PR / PR + OR = 245 / 335

PR = 0.73PR + 0.73 × 160

PR = 117 / 0.27

PR = 433.39 ft

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Freezing point depression is directly proportional to the molality of a solution, which is determined by the concentration of solutes in the solvent. the correct option is (b)

The greater the number of particles in a solution, the more the freezing point is reduced. In this question, we must determine which of the given solutes would be expected to cause the smallest lowering of the freezing point of an aqueous solution. This is a question of the colligative properties of solutions.

According to colligative properties, the number of particles present in a solution determines its freezing point. The molar concentration of each solute present in a solution is related to its molality by the density of the solution. Hence, we can assume that the molality of each of the given solutes is proportional to its molar concentration. We can also assume that all solutes are completely ionized in solution. The correct option is (b) 0.2 M CH3COOH.

According to the Raoult's law of vapor pressure depression, the vapor pressure of a solvent in a solution is less than the vapor pressure of the pure solvent.

The reduction in the vapor pressure is proportional to the mole fraction of solute present in the solution. The equation for calculating the freezing point depression is ΔT = Kf m, where ΔT is the freezing point depression, Kf is the freezing point depression constant for the solvent, and m is the molality of the solution. We need to compare the molality of each of the solutes to determine the expected freezing point depression. The number of particles in solution determines the magnitude of freezing point depression. Here, all solutes are completely ionized in solution. For each of the options, we have: Option (a) NaCl produces two ions: Na+ and Cl-, for a total of two particles per formula unit. Therefore, the total number of particles in solution is (2 x 0.1) = 0.2. Option (b) CH3COOH is a weak acid. It is not completely ionized in solution.

However, we can assume that it is ionized enough to produce a small number of particles in solution. Each molecule of CH3COOH dissociates to form one H+ ion and one CH3COO- ion. Hence, the total number of particles in solution is approximately equal to (2 x 0.2) = 0.4. Option (c) MgCl2 produces three ions: Mg2+, and 2Cl-, for a total of three particles per formula unit.

Therefore, the total number of particles in solution is (3 x 0.1) = 0.3. Option (d) Al2(SO4)3 produces five ions: 2Al3+, and 3SO42-, for a total of five particles per formula unit. Therefore, the total number of particles in solution is (5 x 0.05) = 0.25. Option (e) NH3 is a weak base. It is not completely ionized in solution.

However, we can assume that it is ionized enough to produce a small number of particles in solution. Each molecule of NH3 accepts one H+ ion to form NH4+ ion and OH- ion. Hence, the total number of particles in solution is approximately equal to (2 x 0.25) = 0.5. Therefore, among the given options, the smallest freezing-point lowering is expected with 0.2 M CH3COOH.

Thus, we can conclude that  CH3COOH as it is expected to exhibit the smallest freezing-point lowering in aqueous solution.

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Answer:

39

Step-by-step explanation:

the interior angles of a triangle equal 180.

180-(51+90)

180- 141 = 39

hope this helps :)

An option that best approximates the percent decrease in consumption of wood power in the United States from 2000 to 2010 is (B) 11%.

To find an option that best approximates the percent decrease in consumption of wood power in the United States from 2000 to 2010:

Therefore, an option that best approximates the percent decrease in consumption of wood power in the United States from 2000 to 2010 is (B) 11%.

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Answer:

y = 13x -107

Step-by-step explanation:

(10 - -3) / (9-8) =13

10= 13* 9 + b

b = 10 - 117 = -107

The length of RS is 6.32 unit (B).

To find the length of RS, we can use the distance formula:

D = √[(x₂ - x₁)² + (y₂ - y₁)²]

where:

(x₁, y₁) = coordinate of point 1

(x₂, y₂) = coordinate of point 2

In this case, we have:

the coordinates of R: (-2, -4)

the coordinates of S: (-8, -6).

Plugging in these values into the distance formula, we get:

D = √[(-8 - (-2))² + (-6 - (-4))²]

D = √[(-6)² + (-2)²]

D = √[36 + 4]

D = √40

D = 6.32

Therefore, the length of RS is about 6.32 units.

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The critical value will be +- 1.96.

What is critical value?

A crucial value delimits areas of a test statistic's sampling distribution. Both confidence intervals and hypothesis tests take these values into account.

Main body:

sample size is 10.

if you use z-scores, and it appears that you have to, since you don't know the mean or standard deviation of your population, your mean is 0 and your standard deviation is 1.

at 95% confidence level, 100% - 95% is your alpha.

that makes it equal to 5%.

divide that by 2 and you have half your alpha on the left end of the confidence interval and half on the right end.

that makes it 2.5% on each end.

2.5% is the same as .025 in decimal form.

look up a z-score to the left of .025 to get a z-score of -1.959963986 which can be rounded to -1.96.

since the normal distribution is symmetric about the mean,

Therefore your critical z-score is plus or minus 1.96.

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Answer: 14 tons and $3,860.50

Step-by-step explanation:

Based on this information, we will calculate the probabilities for various scenarios: (a) exactly 34 people living in such cities, (b) at most 33 people living in such cities, (c) at least 32 people living in such cities, and (d) between 30 and 38 people (inclusive) living in such cities.

Given:

Probability of living in cities with population > 100,000 = 68% = 0.68

Number of Americans randomly selected (sample size) = 49

(a) Probability of exactly 34 people living in cities with population > 100,000:

Using the binomial probability formula:

P(X = 34) = (49 C 34) * (0.68^34) * (0.32^15) ≈ 0.0986

(b) Probability of at most 33 people living in cities with population > 100,000:

P(X ≤ 33) = P(X = 0) + P(X = 1) + ... + P(X = 33)

To calculate this, we can use cumulative binomial probability or subtract the probability of the complement event:

P(X ≤ 33) = 1 - P(X > 33) = 1 - P(X ≥ 34)

P(X ≤ 33) = 1 - (P(X = 34) + P(X = 35) + ... + P(X = 49)) ≈ 0.9124

(c) Probability of at least 32 people living in cities with population > 100,000:

P(X ≥ 32) = 1 - P(X < 32) = 1 - P(X ≤ 31)

P(X ≥ 32) = 1 - (P(X = 0) + P(X = 1) + ... + P(X = 31)) ≈ 0.9727

(d) Probability of between 30 and 38 people living in cities with population > 100,000:

P(30 ≤ X ≤ 38) = P(X = 30) + P(X = 31) + ... + P(X = 38)

P(30 ≤ X ≤ 38) = (P(X ≤ 38) - P(X ≤ 29)) ≈ 0.9663

Therefore, the probabilities are:

(a) P(X = 34) ≈ 0.0986

(b) P(X ≤ 33) ≈ 0.9124

(c) P(X ≥ 32) ≈ 0.9727

(d) P(30 ≤ X ≤ 38) ≈ 0.9663

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(d.) Each run of the simulation only provides a sample of the actual system's operation.

This assertion is right, not mistaken. Indeed, each simulation run is a sample of the actual system's operation. A single simulation run cannot account for all possible outcomes and variations in the real system because simulations are based on mathematical models and involve random variations.

In order to take into consideration various scenarios and variations, multiple simulation runs are typically carried out. By running numerous reenactments, specialists can assemble a scope of results and measurable data to acquire a superior comprehension of the framework's way of behaving and go with informed choices.

The analysis and confidence in the simulation study's conclusions increase with the number of simulation runs performed.

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well, since the y-intercept is at -5, or namely when the line hits the y-axis is at -5, that's when x = 0, so the point is really (0 , -5), and we also know another point on the line, that is (-1 ,6), to get the equation of any straight line, we simply need two points off of it, so let's use those two

\(\stackrel{y-intercept}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{-5})}\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{0}}} \implies \cfrac{6 +5}{-1} \implies \cfrac{ 11 }{ -1 } \implies - 11\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{- 11}(x-\stackrel{x_1}{0}) \implies y +5 = - 11 ( x -0) \\\\\\ y+5=-11x\implies {\Large \begin{array}{llll} y=-11x-5 \end{array}}\)

Answer:

The answer is 10.