if the probability that a portfolio outperforms its benchmark in any quarter is 0.75, the probability that the portfolio outperforms its benchmark in three or fewer quarters over the course of a year is closest to: 0.26 0.42 0.68

Factor of the expression are,

⇒ (x - 1) (x - 12) (x - 10)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ x³ - 23x² + 142x - 120 = 0

Now, Put x = 1;

⇒ x³ - 23x² + 142x - 120 = 0

⇒ 1 - 23 + 142 - 120 = 0

⇒ 0 = 0

Thus, One factor of the equation is,

⇒ (x - 1)

Now, After divide we get;

⇒ (x³ - 23x² + 142x - 120 ) ÷ (x - 1)

⇒ x² - 22x + 120

⇒ x² - (12 + 10)x + 120

⇒ x² - 12x - 10x + 120

⇒ x (x - 12) - 10 (x - 12)

⇒ (x - 12) (x - 10)

Thus, Factor of the expression are,

⇒ (x - 1) (x - 12) (x - 10)

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The ratio of the areas of the two similar figures is 9 : 16.

We can use comparisons or ratios to compare the size of an object with other objects. The quantity of an object can be in the form of length, speed, mass, time, number of objects, and so on.

For example, penguins have 2 legs, while dogs have 4 legs. We say that the ratio of the number of legs above can be written in three ways, namely:

2 to 4, 2 to 4, or 2/4.

The writing above is read: a comparison of 2 to 4, a comparison between 2 and 4, or a comparison of 2 to 4.

The order of the numbers in the comparison is important and should receive special attention. The first number in the comparison must be written as a numerator, if the comparison is written in fractional form.

Example:

The ratio of the number of penguin and dog legs is 2: 4 or 2/4

The ratio of the number of dog and penguin legs is 4 : 2 or 4/2

According to the question above:

Side figure 1 : side figure 2

6 : (6+2)

6 : 8

3 : 4

The ratio of the areas of two similar figure is equal to the square of the ratio of the corresponding sides.

Squaring the ratio 3 : 4, gives us:

3² : 4² = 9 : 16

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Answer:

Step-by-step explanation:

50%. 24 is half of 48. So, 50% of 48 if 24.

Answer: To convert miles per gallon to kilometers per liter, we can use the conversion factor 1 mile = 1.60934 kilometers and 1 gallon = 3.78541 liters.

54 miles per gallon is equivalent to:

54 * 1.60934 km/mile / (1 gallon * 3.78541 liters/gallon) = 21.63 km/liter.

Rounding to the nearest hundredth, the equivalent rate is 21.63 km/liter.

Step-by-step explanation:

The Board of Trustees can choose a president and a provost in 1000 different ways because there are 1000 professors on the college's faculty. The concept used in this is permutations and combinations.

What are combinations?

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant (unlike permutations). Three fruits, such as an apple, an orange, and a pear, for instance, can be combined into three different pairs: an apple and a pear, an apple and an orange, or a pear and an orange. A k-combination of a set S is officially defined as a subset of S's k unique elements. So, if and only if each combination contains the same elements, two combinations are said to be identical.

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Correct question:

Suppose that a college has 1000 professors.

a) In how many ways can the Board of Trustees pick a president? The president should be one of the 1000 professors.

The interval equivalent to each range is given below

     x = 3 - 5

    x' = 7,8,9

What exactly is interval notation?

Which section of the number line, from left to right, is included in the answer can be determined using interval notation (i.e., which part of the number line is shaded).

                           Endpoints not included in the solution are denoted by parentheses, whereas endpoints that are included are denoted by brackets.

We have that

The  interval equivalent to each range is given below

     x = 3 -5

     x' = 7,8,9

From the Question we are told that

2  <  x  ≤  5   or   x  >7

Generally the interval equivalent is given as follow from the number line

(...-1,0,1...)

For 2  <  x  ≤  5  

Here  this means x is less than 2 and less than or equal to 5

Therefore

A range of numbers

  x = 3 - 5

For  x  >7

Here x is greater than 7  i.e

  x' = 7,8,9

in conclusion

The  interval equivalent to each range is given below

     x = 3 - 5

    x' = 7,8,9

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For 5 batches, 65 cups of chocolate chips are needed.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that Marie’s recipe for one batch of chocolate chip cookies calls for 13 cup of chocolate chips. If Marie is making 5 batches of cookies.

For 1 batch - 13 cups of chocolate chips are needed.

For 5 batches - (13 x 5) = 65 cups of chocolate chips are needed.

Therefore, for 5 batches, 65 cups of chocolate chips are needed.

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The length of the fencing will be 92 feet. And the total cost of the fencing will be $92.

Let W be the rectangle's width and L its length.

The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be

Perimeter of the rectangle = 2(L + W) units

Judith's vegetable patch is 21 feet wide and 25 feet long. Judith wants to build a fence around the vegetable patch. The length of fencing is given as,

P = 2(21 + 25)

P = 2 x 46

P = 92 feet

The fencing material costs $1.00 per foot. Then the total cost of the fencing is given as,

Total cost = $1 x 92

Total cost = $92

The length of the fencing will be 92 feet. And the total cost of the fencing will be $92.

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Answer:

I wasn't sure if you had wanted decimals or remainder so here is both.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Step:Start by setting it up with the divisor 93 on the left side and the dividend 478 on the right side .

The divisor (93) goes into the first digit of the dividend (4), 0 time(s). Therefore, put 0 on top:

Step 3:

Multiply the divisor by the result in the previous step (93 x 0 = 0) and write that answer below the dividend.

Step 4:

Subtract the result in the previous step from the first digit of the dividend

Move down the 2nd digit of the dividend (7) like this:

The divisor (93) goes into the bottom number (47), 0 time(s). Therefore, put 0 on top:

Step 7:

Multiply the divisor by the result in the previous step (93 x 0 = 0) and write that answer at the bottom:            

Answer:?=-9

Step-by-step explanation:

9x+3x-4-5=12x-9

The relative frequency for the event tails is given as follows:

53.64%.

The expected relative frequency should be closed to the theoretical probability of 0.5.

The relative frequency is given by the division of the number of desired outcomes by the number of total outcomes.

The relative frequency for all the throws is obtained as follows:

132/(114 + 132) = 132/146 = 53.64%.

Considering a fair coin, it is equally as likely to come up heads or tails, hence increasing the number of trials, the relative frequency of each outcomes is expect to be closer to 50%.

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The percent of change is -1/15 which represent a decrease. percentage of change is 6.7%

Percentage change is  the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage. Generally, to convert a fraction into a percent, we multiply it by 100.

From the question,

The old amount is 2/5

The new amount is 1/3

We substract the new amount from the old amount

1/3 - 2/5

= -1/15

The percent of change is -1/15 which represent a decrease

To calculate the percentage change

1/15 x 100

= 6.7%

hence, the percentage of change is 6.7%

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Answer: To divide 9x³ - 18x² - x + 2 by 3x + 1 using long division, we can follow the following steps:

Step 1: Divide the first term of the dividend 9x³ by the first term of the divisor 3x. The result is 3x².

Step 2: Multiply the divisor 3x + 1 by 3x². The result is 9x³ + 3x².

Step 3: Subtract 9x³ + 3x² from 9x³ - 18x² - x + 2. The result is -18x² - 4x + 2.

Step 4: Repeat the division and multiplication process by dividing the first term of the new dividend, -18x², by the first term of the divisor, 3x. The result is -6x.

Step 5: Multiply the divisor 3x + 1 by -6x. The result is -18x + 6.

Step 6: Subtract -18x + 6 from -18x² - 4x + 2. The result is -4x² + 10.

Step 7: Repeat the division and multiplication process by dividing the first term of the new dividend, -4x², by the first term of the divisor, 3x. The result is -4/3 x.

Step 8: Multiply the divisor 3x + 1 by -4/3 x. The result is -4/3 x + 4/3.

Step 9: Subtract -4/3 x + 4/3 from -4x² + 10. The result is 10 - 4/3.

Thus, the final answer is:

(9x³ - 18x² - x + 2) / (3x + 1) = 3x² - 6x - 4/3 x + 4/3 + 10

Step-by-step explanation:

The ingredient you need to serve, round the amount of an ingredient instead of using an exact amount, is vanilla extract.

Rounding is a process to estimate a particular number in a context.

Given that, a recipe serving 10 persons, but you need to serve 30, we need to multiply the amount of each ingredient by to adjust the recipe

Here we have a recipe that works for 10 serves.

Then, if we want to make 30 servings, we need to use that recipe 3 times. (because x·10 = 30, then x = 30/10 = 3)

This would be equivalent to multiply each ingredient by 3.

for 30 cupcakes, we need:

3 cups of vegetable oil.

3 cups of all-purpose flour

(because for each one of these ingredients, we needed only 1 cup to make 10 cupcakes).

for 10 cupcakes, we need 1 teaspoon of vanilla.

for 30 cupcakes we need 3 teaspoons of vanilla, the difference is 3 - 1 = 2.

So the difference is 2 teaspoons.

About which quantities we should round are those where we may have mixed numbers or big numbers.

For example, we have 4 tablespoons of sour cream for 10 servings, then for 30 servings we should have:

3×4 = 12 tablespoons.

We could round this down to 10 tablespoons.

Hence, the ingredient you need to serve, round the amount of an ingredient instead of using an exact amount, is vanilla extract.

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This years tuition is $1900

Let us assume that the next year tuition fee be x dollars.

The next year's tuition will be $2000 which is $600 more than this year's tuition fee.

Chana will pay $2000 which is 80 percent of her college tuition.

Using percentage formula we get an equation,

x × (80/100) = 2000

we solve this equation for x.

x = (2000 × 100)/80

x = 2500

If the next year's tuition fee is $600 more than this year's tuition fee, then this year's tuition fee would be,

2500 - 600 = 1900 dollars

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Answer:

-1/2 is the answer of this question

110 miles/hr is the interval with highest average speed. Option C is correct.

The given diagram is a graph with different rate of change. According to the graph, we are to determine which interval has the highest average speed.

Average speed = change in distance/time

Considering the change between t = 4 and t = 5;

Average speed = 270 - 160/5 - 4
Average speed= 110/1

Average speed = 110 miles/hr

Hence the interval that has the highest average speed is 110 miles/hr

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Answer: h=12  r=√12

Step-by-step explanation:

volume of cone=πr^2 h/3

πr^2 h/3=48π

πhr^2=144π

hr^2=144

h=12  r=√12

Answer:

The formula for the future value of a single sum is:

F = P * (1 + r/n)^(nt)

Where:

F is the future value

P is the principal (the initial deposit)

r is the annual interest rate

n is the number of compounding periods per year

t is the number of years

For our calculation, we have:

P = £7000

r1 = 3% = 0.03

r2 = 1.5% = 0.015

n = 1 (annual compounding)

t1 = 1 (first year)

t2 = 1 (second year)

So, the future value of Ella's investment at the end of the first year is:

F1 = £7000 * (1 + 0.03/1)^(1 * 1) = £7000 * (1.03)^1 = £7,210

And the future value of Ella's investment at the end of the second year is:

F2 = £7,210 * (1 + 0.015/1)^(1 * 1) = £7,210 * (1.015)^1 = £7,333.15

So, at the end of 2 years, the value of Ella's investment is £7,333.15.

Step-by-step explanation:

Answer: a) i) The width of the floor can be expressed in terms of c as: w = c - 2 cm.

ii) The area of the floor can be expressed in terms of c as: A = c * (c - 2) cm^2.

b) If the area of the room is 15 cm^2, then we can write the equation as:

c * (c - 2) = 15.

c) Solving for c, we get:

c^2 - 2c - 15 = 0.

Using the quadratic formula, we find that:

c = 5 or c = -3.

Since the length of the room cannot be negative, we choose c = 5.

Therefore, the length of the room is 5 cm and the width of the room is 3 cm.

Step-by-step explanation:

Answer:

1.77777777778

Answer:

23°

Step-by-step explanation:

As We All Know Sum Of Angles In A Straight Line is 180° so,

157° + a = 180°

or, a = 180° - 157°

or, a = 23°

A regular frequency distribution table provides more detailed and accurate information about the scores in a dataset than a grouped frequency distribution table.

In a regular frequency distribution table, individual scores and their corresponding frequencies are listed, whereas in a grouped frequency distribution table, the scores are grouped into intervals and the frequencies of the intervals are listed.

The following information can be obtained from a regular frequency distribution table but not from a grouped table:

Individual Scores: A regular frequency distribution table lists individual scores, providing a clear understanding of the exact values that make up the data.

Accuracy: A regular frequency distribution table provides a more accurate representation of the data as it doesn't involve grouping the scores into intervals, which can lead to loss of information.

Outliers: In a regular frequency distribution table, outliers (unusual or extreme values) can be easily identified as they stand out from the other scores.

Shape of Distribution: A regular frequency distribution table provides a more detailed representation of the distribution, allowing for easier evaluation of the shape of the distribution, such as whether it is symmetrical, skewed, etc.

Measures of Central Tendency: Measures of central tendency, such as the mean, median, and mode, can be more accurately calculated from a regular frequency distribution table as the exact values of the scores are available.

In conclusion, a regular frequency distribution table provides more detailed and accurate information about the scores in a dataset than a grouped frequency distribution table.

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2. The mean score is 80.6

3.The missing term is 32.

The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.

Given:

2. A student receives test scores of 62, 83, and 91.

Test A is 0.20 of the total and scores 62.

Test B is 0.20 of the total and scores 83.

Test C is 0.20 of the total and scores 91.

Test F is 0.25 of the total and scores 88.

Work H is 0.15 of the total and scores 76.

Now, Multiply the scores:

= 0.2 x 62 = 12.4

= 0.2 x 83 = 16.6

= 0.2 x 91 = 18.2

= 0.25 x 88 = 22

= 0.15 x 76 = 11.4

Now, add the scores to get the

= 12.4 + 16.6 + 18.2 + 22 + 11.4

= 80.6

3. let the missing term or 4th term be x.

So, The median is sum of 3rd and 4th term.

27.5 = 23 + x/ 2

55 = 23+ x

x= 32

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The length of chord BC is 3 cm

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

The angle in a semicircle is 90 degrees

This means that

B = 90 degrees

Using the pythagorean theorem, we have

AC^2 = AB^2 + BC^2

This gives

5^2 = 4^2 + BC^2

So, we have

BC^2 = 9

This gives

BC = 3

Hence, the length s 3 units

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Yes, it is appropriate to calculate the probability of a sample mean being more than $0.32 using an approximately normal model, under certain assumptions.

What is Probability?

Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Yes, it is appropriate to calculate the probability of a sample mean being more than $0.32 using an approximately normal model, under certain assumptions.

The central limit theorem states that the distribution of the sample means approaches a normal distribution, as the sample size increases, regardless of the shape of the population distribution. So, for large enough sample sizes, the sample mean is approximately normally distributed, even if the population distribution is not normal.

In this case, a sample size of 50 is considered large enough to use the normal approximation. Therefore, we can assume that the distribution of the sample mean is approximately normal, with mean equal to the population mean of $0.29, and standard deviation equal to the standard deviation of the sample mean, which can be calculated as the standard deviation of the population divided by the square root of the sample size.

The standard deviation of the sample mean is given by the formula:

[tex]$\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{0.1164}{\sqrt{50}} \approx 0.039$[/tex]

Using this information, we can calculate the desired probability as the area under the normal curve to the right of $0.32$. This can be done using a standard normal table or a normal probability calculator.

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Answer:

The ratio of flies to all insects is 1:5

For every 1 bee, there are 10 insects

Step-by-step explanation:

give brainlist please

Answer: 345 + n

For finding the total, we have to add 345 with n.

Answer:

△ABC ~ △MLN

Step-by-step explanation:

Because the sum of all the angles in a triangle equals 180, we can find the missing angle in both triangles

△ABC

c + 90 + 51 = 180

c = 39

△MLN

[tex]l[/tex] + 90 + 39 = 180

[tex]l[/tex] = 51

Because <C has the same angle degree as <N,  <B has the same angle degree as <L, and  <A has the same angle degree as <M, then △ABC must be similar to △MLN