Find the surface area of the sphere shown below.

the histogram is a visual representation of the data distribution and should be interpreted accordingly. It provides insights into the frequency and distribution of LSAT scores among accepted students at the law school

1. Set up the x-axis to represent the LSAT score range from 120 to 180. Divide the x-axis into appropriate intervals or bins based on the desired level of detail.

2. On the y-axis, represent the frequency or count of LSAT scores falling within each interval or bin.

3. Start by plotting the first quartile at 155 and the third quartile at 173. You can mark these values on the x-axis.

4. Now, consider the median score of 167. You can mark this value as a vertical line on the x-axis, indicating the point where half the scores are below and half are above.

5. Based on the given information, you can roughly estimate the distribution of LSAT scores within the bins. Consider that the data is likely to be skewed towards the higher end since the median (167) is closer to the third quartile (173) than the first quartile (155).

6. Sketch the bars of the histogram, ensuring that the height of each bar represents the frequency or count of LSAT scores falling within the corresponding interval.

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Answer:

a=-6

Step-by-step explanation:

2(a+5)=-2 Step 1 distribute

2a+10=-2 Step 2 minus 10 on both sides

2a=-12      Step 3 divide but 2 on both sides

a=-6

Answer:

a=-6

Step-by-step explanation:

In order to solve for a, we must isolate a on one side of the equation.

\(2(a+5)=-2\)

2 is being multiplied by (a+5). The inverse of multiplication is division. Divide both sides of the equation by 2.

\(2(a+5)/2=-2/2\)

\((a+5)=-2/2\)

\((a+5)=-1\)

5 is being added to a. The inverse of addition is subtraction. Subtract 5 from both sides of the equation.

\(a+5-5=-1-5\)

\(a=-1-5\)

\(a=-6\)

Let's check our solution. Plug -6 in for a and solve.

\(2(a+5)=-2\)

\(2(-6+5)=-2\)

\(2(-1)=-2\)

\(-2=-2\)

This checks out, so we know our solution is correct.

The solution to the equation 2(a+5)=-2 is a=-6

Answer:

One triangle could have one angle at 30 degrees and the other two angles at 75 degrees, while the other triangle could have two angles that are 30 degrees and one angle that is 120 degrees, therefore making them not similar.

Answer:

the third one

Step-by-step explanation:

all you have to do is multiply the exponents

The carbs that are in one glass of milk and

in one snack bar is 27 carbs

Since 4 glasses of milk and 3 snack bars have a total of 80 carbohydrates (carbs), this will be:

4m + 3b = 80

2 glasses of milk and 4 snack bars have a total of 70 carbs. This will be:

2m + 4b = 70

Collect both equations and solve

4m + 3b = 80 ..... i

2m + 4b = 70 ..... ii

m = milk

b = snack bars

Multiply equation i by 2

Multiply equation ii by 4

8m + 6b = 160

8m + 16b = 280

Subtract

10b = 80

Divide

b = 80/10 = 8

Snack bars = 8 carbs

Since 2m + 4b = 70

2m + 4(8) = 70

2m + 32 = 70

2m = 70 - 32

2m = 38

Divide

m = 38/2 = 19

Milk = 19 carbs

The total carbs will be:

= Milk + Snack

= 19 + 8

= 27 carbs

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Answer: 7/5 or 1 2/5

Step-by-step explanation:

Ok so the bakery uses 3 3/5 cups cups of oats for 2 4/7 POUNDS of cookies.

You need to find the unit price.

So to get from 2 4/7 to 1, you need to divide 2 4/7 by 2 4/7

You need to do the same thing to 3 3/5 cups.

3 3/5 as an improper fraction is 18/5

2 4/7 as an improper fraction is 18/7

Now to divide you need to keep, change, and flip

keep the 18/5, change the sign to multiplycation, and flip the 18/7 to 7/18

18/5*7/18=7/5

7/5 or 1 2/5 pounds of outs are required to make 1 pound of oatmeal cookies

The solution of given Expression without using the absolute value Symbol is  -(x/3), (x/3)

If x < 0, then -x > 0. Therefore, we can write:

|x/3| = |-x/3| = (-x)/3 = -(x/3)

So, the expression |x/3| can be written as -(x/3) when x < 0 and

(x/3) when x>0

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Answer:

i dont really know to be honest

Answer:

x=13

Step-by-step explanation:

The attached photo might help

Answer:

x ≈ 2.76

Step-by-step explanation:

The inscribed angle (34x + 4) is half the measure of its intercepted arc, then

34x + 4 = \(\frac{1}{2}\) × 196° = 98 ( subtract 4 from both sides )

34x = 94 ( divide both sides by 34 )

x ≈ 2.76 ( to the nearest hundredth )

The correct answer is a) Osmotic pressure.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

Osmotic pressure is indeed a colligative property, which means it depends on the concentration of solute particles in a solution and not on the nature of the solute itself. Osmotic pressure is the pressure required to prevent the flow of solvent molecules into a solution through a semipermeable membrane.

On the other hand, options b), c), and d) are all colligative properties:

b) Elevation of a boiling point: Adding a non-volatile solute to a solvent increases the boiling point of the solution compared to the pure solvent.

c) Freezing point: Adding a non-volatile solute to a solvent decreases the freezing point of the solution compared to the pure solvent.

d) Depression in freezing point: Adding a solute to a solvent lowers the freezing point of the solvent, causing the solution to freeze at a lower temperature than the pure solvent.

Therefore, the correct answer is a) Osmotic pressure.

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We need a sample size of at least 1536 to be 95% confident that our sample mean will be within 0.0005 inches of the true mean.

To determine how large a sample is needed, we can use the formula for the margin of error:
To determine the required sample size for a 95% confidence interval with a specified margin of error, we'll use the following formula:
n = (Z * σ / E)^2
where:
- n is the sample size
- Z is the Z-score for a given confidence level (1.96 for a 95% confidence interval)
- σ is the population standard deviation
- E is the margin of error (0.0005 inches in this case)

The margin of error = Z-score * (standard deviation / square root of sample size)

Since we want to be 95% confident, the Z-score will be 1.96. We are given that we want the sample mean to be within 0.0005 inches of the true mean, so the margin of error will be 0.0005.

Thus, we can rearrange the formula to solve for the sample size:

Sample size = (Z-score)^2 * (standard deviation)^2 / (margin of error)^2

Since we do not know the population standard deviation, we can use the sample standard deviation as an estimate. Let's assume the sample standard deviation is 0.001 inch.

Plugging in the values, we get:

Sample size = (1.96)^2 * (0.001)^2 / (0.0005)^2

Sample size = 1536

Therefore, we need a sample size of at least 1536 to be 95% confident that our sample mean will be within 0.0005 inches of the true mean.

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Answer: x=4+2i , x=4-2i hope this helps tho :>

Step-by-step explanation

The solutions to the equation x 2 −8x+20=0 are x= 10,-2.

The equation  x 2 −8x+20=0  can be written as (x-10) (x+2) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x-10=0

x+2=0

so, the solution to the equation x 2 −8x+20=0 are x=10 and x=-2.

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Once a model of reality is constructed around certain assumptions, it can be tested to determine its value in predicting outcomes.

Once a model of reality is constructed around certain assumptions, it can be tested to determine its value in predicting outcomes. This involves comparing the model's predictions with actual observed data or outcomes to assess its accuracy and reliability. By testing the model against real-world data, we can evaluate its validity and determine if it accurately represents the underlying reality or phenomenon being studied.

Producing data and graphing equations are related activities that can be part of the process of testing a model, but they are not the primary purpose of the model itself. Producing data involves collecting and generating empirical data that can be used to assess the model's predictions or outcomes. Graphing equations can be a way to visualize the relationships between variables in the model, but it is not the main purpose of the model itself. The primary purpose of constructing a model is to make predictions or generate hypotheses about how a system or phenomenon works, and testing these predictions against real-world outcomes is the key step in evaluating the model's value.

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Answer:

The answer to this is 1,256

The probability that the student competed in Rhythm given they had competed in Smooth or Standard: P(Rhythm |Smooth or Standard) or P ( A/( B or C)) is 0.6613 = 66.13%.

We have, A survey was conducted at a local ballroom dance studio asking students with three dance categories. The above Venn diagram shows the number of students in these three categories of dance.

Total number of students in all dance categories n(A or B or C) = 5 + 6 + 8 + 12 + 14 + 15 + 10 + 4

= 74

let us consider the events

A : students in Rhythm dance category

B : students in Standard dance category

C : students in Smooth dance category

Using the conditional probability,

Probability that student has competed in Rhythm and they have competed in Smooth, P(Rhythm/ smooth) = P(A/C) = P(A and C)/P(C)

= (12+14)/74 = 26/74 = 0.703

but we have to calculate probability that the student competed in Rhythm given they had competed in Smooth or Standard, P(Rhythm/Smooth or Standard) = P(Rhythm and (Smooth or Standard))/P(Smooth or Standard)

i.e., P( A/(B or C) )= P(A and (B or C))/P(B or C)

n(B or C) = n(B) + n(C) - n( B and C)

=> n(B or C) = 14 + 5 + 10 + 15 + 12 + 14 + 5 + 6 - 5 - 14 = 62

Now, P(B or C) =n(B or C)/n(A or B or C)

=> P(B or C) = 62/74 = 0.703 = 70.3%

P(A and (B or C)) = n(A and (B or C))/n(A or B or C)

n(A and (B or C)) = n(A) + n(B or C) - n(A or B or C)

= 12 + 14 + 15 + 8 + 62 - 70 +4 = 41

P(A and (B or C)) = 37/74

So, P( A/(B or C) )= P(A and (B or C))/P(B or C)

=> P( A/(B or C) )= 41/74/62/74 = 41/62

= 0.6613 = 66.13%

Hence, the required probability is 66.13%.

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Complete question:

A survey was conducted at a local ballroom dance studio asking students if they had ever competed in the following dance categories:

- Smooth

- Rhythm

- Standard

The results were then presented to the owner in the following Venn Diagram. Use the Venn Diagram to determine the following probabilities. Write your answers in percent form, rounded to the nearest tenth .If a student is chosen at random; what is the probability that the student competed in Rhythm GIVEN they had competed in Smooth or Standard: P(Rhythm |Smooth or Standard)

Answer:

The constant of proportionality is 2.

Step-by-step explanation:

z^2 = kW   where k is a constant.

When z = 4 , W = 8 so

4^2 = 8k

k = 4^2/8

= 16/8

= 2.

Answer:

z² = 2W

Step-by-step explanation:

Assuming you require the equation of proportionality

Given z² is directly proportional to W then the equation relating them is

z² = kW ← k is the constant of proportion

To find k use the condition z = 4 when W = 8

4² = 8k

16 = 8k ( divide both sides by 8 )

2 = k

z² = 2W ← equation of proportionality

In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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The minimized SOP expression for F(A,B,C,D,E) using a five-variable Karnaugh map is D'E' + BCE'. A five-variable Karnaugh map is a graphical tool used to simplify Boolean expressions.

The map consists of a grid with input variables A, B, C, D, and E as the column and row headings. The cell entries in the map correspond to the output values of the logic function for the respective input combinations.

To find the minimized SOP expression, we start by marking the cells in the Karnaugh map corresponding to the minterms given in the function: 2m(4,5,6,7,9,11,13,15,16,18,27,28,31). These cells are identified by their binary representations.

Next, we look for adjacent marked cells in groups of 1s, 2s, 4s, and 8s. These groups represent terms that can be combined to form a simplified expression. In this case, we find a group of 1s in the map that corresponds to the term D'E' and a group of 2s that corresponds to the term BCE'. Combining these groups, we obtain the expression D'E' + BCE'.

The final step is to check for any remaining cells that are not covered by the combined terms. In this case, there are no remaining cells. Therefore, the minimized SOP expression for the given logic function F(A,B,C,D,E) is D'E' + BCE'.

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Answer:

8 miles per hour

Step-by-step explanation:

First find the slope. The slope is the unit rate/constant of proportionality.

To find slope use the points given and formula y2-y1 / x2-x1

(32-16) / (4-2)

= 16 / 2

= 8

Thus the unit rate is 8 miles per hour.

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Answer:

No

Step-by-step explanation:

Answer:

0.342

Step-by-step explanation:

round to the given amount of significant figures