A student reading the results stated that more than half of the study participants are taking vitamins. determine if the student is correct. yes, because 23.5% take one vitamin and 48.2% take more than one vitamin, which is a total of 71.7% taking vitamins. yes, because 27.4% take one vitamin and 49.5% take more than one vitamin, which is a total of 76.9% taking vitamins. no, because 11.4% take one vitamin and 23.5% take more than one vitamin, which is a total of 34.9% taking vitamins. no, because 16% take one vitamin and 26% take more than one vitamin, which is a total of 42% taking vitamins.

Answer:

A.) x=16

Step-by-step explanation:

-5/6-4/6e=-24 (Given)

-9/6e=-24 (Add)

e=16 (Simplify)

Hope this helps

When two painters work together to paint the roof of a big house, they can complete the task in approximately 2.4 days.

The first painter estimates that it will take him 12 days to complete the job alone, while the second painter estimates it will take him 4 days alone. To determine how long it will take them to paint the roof together, we can use the concept of their individual work rates.

Let's denote the first painter's work rate as "P1" (amount of work done per day) and the second painter's work rate as "P2". The formula for their combined work rate when working together is given by:

1/(P1 + P2) = 1/12 + 1/4.

To simplify the equation, we can find a common denominator:

1/(P1 + P2) = 1/12 + 3/12 = 4/12 = 1/3.

Now, we can solve for the combined work rate:

P1 + P2 = 3.

Since we know that the first painter can complete the job alone in 12 days, his work rate is 1/12. Substituting this value into the equation, we can solve for the second painter's work rate:

1/12 + P2 = 3,

P2 = 3 - 1/12,

P2 = 35/12.

Now that we have the individual work rates, we can determine how long it will take them to complete the job together:

1/(1/12 + 35/12) = 1/(36/12) = 12/36 = 1/3.

Therefore, when the two painters work together, they can paint the roof of the big house in approximately 2.4 days.

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Nolan stops reading at time 2:05 am.

To calculate this,  first, calculate the amount of time elapsed since he began reading. Since he started reading at a quarter to 11, then subtract 11:45 pm (a quarter to 12) from the time he began reading, which was 11:45 pm. This gave me an elapsed time of 0 hours and 15 minutes.  then added this elapsed time to the total time Nolan read, which was 3 hours and 5 minutes. This gave us a total elapsed time of 3 hours and 20 minutes. Finally, then added this total elapsed time to the start time of 11:45 pm. This gave me the result of 2:05 am as the time Nolan stopped reading.

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The time taken for the water level in the tank to drop from 3 to 0.5 meters above the bottom cannot be determined without additional information.

To calculate the time taken, we need to know the flow rate or discharge rate of the water from the tank. This information is not provided in the question. The time taken to drain the tank depends on factors such as the diameter of the outlet pipe, the pressure difference, and any restrictions or obstructions in the flow path.

If we assume a known discharge rate, we can use the principles of fluid mechanics to calculate the time. The volume of water that needs to be drained is the difference in the volume of water between 3 meters and 0.5 meters above the bottom of the tank. The flow rate can be determined using the pipe diameter and other relevant factors. Dividing the volume by the flow rate will give us the time taken.

However, since the discharge rate is not given, we cannot perform the calculation and determine the time taken accurately.

Without knowing the discharge rate or additional information about the flow characteristics, it is not possible to calculate the time taken for the water level in the tank to drop from 3 to 0.5 meters above the bottom.

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The number of possible outcomes in the sample space of a wireless garage door opener with 16 switches can be determined using the concept of combination is 1.

Combination is a mathematical concept that refers to the number of ways that a set of objects can be selected from a larger set without regard to their order.

To determine the number of possible outcomes in the sample space, we can use the concept of combination. In this case, the objects are the 16 switches, and the larger set is the set of all possible settings for these switches (up or down).

To calculate the number of possible combinations, we can use the formula for combination, which is:

ⁿCₓ = n! / (x! * (n - x)!)

where n is the total number of objects (16 switches), and x is the number of objects selected (in this case, also 16 switches). The exclamation mark (!) represents the factorial function, which is the product of all positive integers up to and including the given integer.

Using this formula, we can calculate the number of possible combinations as follows:

=> 16! / (16! x (16 - 16)!)

=> 16! / (16! x 0!)

=> 1

Therefore, the sample space of possible codes for a wireless garage door opener with 16 switches is 1.

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We are given that 25% of the students at Lincoln High School play on a sports team, and 13% of the students play on a sports team and take a music class. The probability that a randomly chosen student who plays on a sports team also takes a music class is 52%.

We are given that 25% of the students at Lincoln High School play on a sports team, and 13% of the students play on a sports team and take a music class. To find the probability that a student who plays on a sports team also takes a music class, we need to calculate the conditional probability.

The conditional probability of taking a music class given that the student plays on a sports team can be calculated using the formula:

P(Music class | Sports team) = P(Music class and Sports team) / P(Sports team)

In this case, P(Music class and Sports team) is given as 13% (0.13) and P(Sports team) is given as 25% (0.25). Plugging these values into the formula, we get:

P(Music class | Sports team) = 0.13 / 0.25 = 0.52

Therefore, the probability that a randomly chosen student who plays on a sports team also takes a music class is 52%.

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Answer:

230

Step-by-step explanation:

If you simply add the numbers step by step. You will end up with 230.

Answer:

(X - 10, y - 5)

Step-by-step explanation:

Just like walking

Answer:

1) The equation of the line is y =  \(\frac{-1}{2}\) x + 4

2) The equation of the line is y = -12x + 8

Step-by-step explanation:

The slope-intercept form of the linear equation is y = m x + b, where

Let us solve the two questions

1)

∵ points (-2, 5) and (2, 3) lie on the same line

→ Find the slope m

∵ Δ x = 2 - (-2) = 2 + 2 = 4

∵ Δ y = 3 - 5 = -2

∴ m = \(\frac{-2}{4}=\frac{-1}{2}\)

∴ The slope of the line is \(\frac{-1}{2}\)

→ Substitute the value of m in the form of the equation above

∴ y =  \(\frac{-1}{2}\) x + b

→ To find b substitute the x and y in the equation by the coordinates

   of a point on the line

∵ Point (-2, 5) lies on the line

∴ x = -2 and y = 5

∵ 5 =  \(\frac{-1}{2}\)(-2) + b

∴ 5 = 1 + b

- Subtract 1 from both sides

∴ 5 - 1 = 1 - 1 + b

∴ 4 = b

→ Sustitute it in the equation

∴ y =  \(\frac{-1}{2}\) x + 4

The equation of the line is y =  \(\frac{-1}{2}\) x + 4

2)

∵ The slope of the line is -12

∴ m = -12

∵ The line passes through point (0, 8)

∵ b is the value of y at x = 0

∴ b = 8

→ Substitute the values of m and b in the form of the equation above

∴ y = -12x + 8

The equation of the line is y = -12x + 8

Answer:

72

Step-by-step explanation:

5a = 540            [ all interior angles r equal to 540 as "(n-2)x 180  (Interior                                           ____________________________________________angle poperty )]

a= 540/5 = 108   (one interior angle)

x + a = 180                      (linear pair)

x= 180 - a

x = 180 - 108 = 72

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Another way ::

Sum of Exterior angle = 360                 (exterior angle property)

One exterior angle = x = 360 / 5 = 72        ( 360 by the number of sides )

I hope im right!1 Sorry if im wrong :((

Answer: (a)  $ 36  (b) $ 236

Step-by-step explanation:

Simple interest = Principal x rate x Time

Given: Principal = $200 . rate = 6% = 0.06 ,

(a )Time = 3 years

Simple interest = 200 x 0.06  x 3

= $ 36

So,  the interest earned after 3 years  = $ 36

(b)  Balance in account after 3 years =  Principal  + Simple interest

= $ (200+36) = $ 236

So,  the balance after 3 years =  $ 236

We can prove that the product of three consecutive positive integers is divisible by 6 using mathematical induction, without assuming that one of the integers must be divisible by 3.

Base case: Let the first positive integer be 1. Then the product of the three consecutive positive integers is 1 x 2 x 3 = 6, which is divisible by 6.

Inductive step: Assume that the product of three consecutive positive integers, n(n+1)(n+2), is divisible by 6 for some positive integer n.

We need to prove that the product of the next three consecutive positive integers, (n+1)(n+2)(n+3), is also divisible by 6.

Expanding the product, we get:

(n+1)(n+2)(n+3) = (n(n+1)(n+2)) + 3(n+1)(n+2)

By the inductive hypothesis, n(n+1)(n+2) is divisible by 6. Since 3(n+1)(n+2) is the product of two consecutive integers, it is divisible by 2. Thus, the sum of the two terms is divisible by 6 + 2 = 8.

Since 6 and 8 are relatively prime, their least common multiple is 24. Therefore, the sum of the two terms is divisible by 24. Thus, (n+1)(n+2)(n+3) is divisible by 24, which means it is also divisible by 6.

By the principle of mathematical induction, the statement is true for all positive integers.

Therefore, we have shown that the product of three consecutive positive integers is always divisible by 6, even if we do not assume that one of the integers must be divisible by 3.

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The standard deviation and proportion value is obtained as 0.02 and 0.05 respectively.

What is standard deviation?

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.

To find the standard deviation of the sample proportion, we can use the formula -

σp = √(p(1-p)/n)

where p is the population proportion (0.045) and n is the sample size (400).

σp = √(0.045(1-0.045)/400) ≈ 0.0208

To find the value of p that corresponds to a 40% chance of the sample proportion being no greater than that value, we can use the z-score formula -

z = (\(\hat{\rho}\) - p) / σp

where \(\hat{\rho}\) is the sample proportion and p is the population proportion.

For a 40% chance, the corresponding z-score is 0.25 (since 0.40 is halfway between 0.25 and 0.50 on the standard normal distribution).

So we have -

0.25 = (\(\hat{\rho}\) - 0.045) / 0.0208

\(\hat{\rho}\) - 0.045 = 0.0208 × 0.25

\(\hat{\rho}\) ≈ 0.0517

Therefore, the value of p is 0.05, and the value of σp is 0.02.

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We have demonstrated the definition of an isosceles triangle.

What is an isosceles triangle?

An isosceles triangle is a triangle with at least two equal-length sides in geometry. It is sometimes specified as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter version including the equilateral triangle as a special case.

The isosceles triangle has both two equal sides and two equal angles. The name derives from the Greek iso (same) and Skelos (leg). A triangle with all sides equal is called an equilateral triangle, and a triangle with no sides equal is called a scalene triangle.

The given diagram shows an isosceles triangle.

Hence, we have demonstrated the definition of an isosceles triangle.

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The equation of the line in slope-intercept form is y = -2x+8

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system

The slope-intercept form of  the equation of a line is y = mx+b,

where m is the slope and b is the y-intercept

Given the table, pick any two points in order to find the slope:

point 1: x₁ = 0, y₁ = 8

point 1: x₂ = -2, y₂ = 12

slope (m) =  (y₂-y₁) / (x₂-x₁)

slope (m) = (12-8)/(-2-0) = 4/(-2) = -2

Using y = mx+b and x₁ = 0, y₁ = 8:

8 = -2(0) + b

b = 8

y = -2x+8

Thus, the equation of the line is y = -2x+8

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Answer:

what is the question?

Step-by-step explanation:

#MASTER GROUP

# FIRST MASTER

# PHILIPPINES

The probability value of (m, n) is (1, 2^1005).

Let n be a positive odd integer. We are asked to find the probability that its reciprocal gives a terminating decimal. This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.

If n is less than 2010, then its only possible prime factors are 3, 7, 11, ..., 2009, since all primes greater than 2009 are greater than n. We want n to have no prime factors other than 2 and 5. There are 1005 odd integers less than 2010.

We want to count how many of these have no odd prime factors other than 3, 7, 11, ..., 2009. This is equivalent to counting how many subsets there are of {3, 7, 11, ..., 2009}. There are 1004 primes greater than 2 and less than 2010. Each of these primes is either in a subset or not in a subset. Thus, there are 2^1004 subsets of {3, 7, 11, ..., 2009}, including the empty set.

Thus, the probability is:

P = (number of subsets with no odd primes other than 3, 7, 11, ..., 2009) / 2^1004

We can count this number using the inclusion-exclusion principle. Let S be the set of odd integers less than 2010. Let Pi be the set of odd integers in S that are divisible by the prime pi, where pi is a prime greater than 2 and less than 2010. Let Pi,j be the set of odd integers in S that are divisible by both pi and pj, where i < j.

Then, the number of odd integers in S that have no prime factors other than 2 and 5 is:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...|

where the union is taken over all sets of primes with at least one element and less than or equal to 1005 elements.

By the inclusion-exclusion principle:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...| = ∑ (-1)^k ⋅ (∑ |Pi1,i2,...,ik|)

where the outer summation is from k = 0 to 1005, and the inner summation is taken over all combinations of primes with k elements.

This simplifies to:

(1/2) ⋅ (2^1004 + (-1)^1005)

Thus, the probability is: P = (1/2^1004) ⋅ (1/2) ⋅ (2^1004 + (-1)^1005) = 1/2 + 1/2^1005. Hence, (m, n) = (1, 2^1005).

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Complete question:

If m/n is the probability that the reciprocal of a randomly selected positive odd integer less than 2010 gives a terminating decimal, with m and n being relatively prime positive integers. what is probability value of m and n?

The probability value of (m, n) is (1, 2^1005).This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.

Let n be a positive odd integer. We are asked to find the probability that its reciprocal gives a terminating decimal. This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.

If n is less than 2010, then its only possible prime factors are 3, 7, 11, ..., 2009, since all primes greater than 2009 are greater than n. We want n to have no prime factors other than 2 and 5. There are 1005 odd integers less than 2010.

We want to count how many of these have no odd prime factors other than 3, 7, 11, ..., 2009. This is equivalent to counting how many subsets there are of {3, 7, 11, ..., 2009}. There are 1004 primes greater than 2 and less than 2010. Each of these primes is either in a subset or not in a subset. Thus, there are 2^1004 subsets of {3, 7, 11, ..., 2009}, including the empty set.

Thus, the probability is:

P = (number of subsets with no odd primes other than 3, 7, 11, ..., 2009) / 2^1004

We can count this number using the inclusion-exclusion principle. Let S be the set of odd integers less than 2010. Let Pi be the set of odd integers in S that are divisible by the prime pi, where pi is a prime greater than 2 and less than 2010. Let Pi,j be the set of odd integers in S that are divisible by both pi and pj, where i < j.

Then, the number of odd integers in S that have no prime factors other than 2 and 5 is:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...|

where the union is taken over all sets of primes with at least one element and less than or equal to 1005 elements.

By the inclusion-exclusion principle:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...| = ∑ (-1)^k ⋅ (∑ |Pi1,i2,...,ik|)

where the outer summation is from k = 0 to 1005, and the inner summation is taken over all combinations of primes with k elements.

This simplifies to:

\((1/2) * (2^{1004} + (-1)^1005)\)

Thus, the probability is: P = \((1/2)^{1004}* (1/2) *(2^{1004} + (-1)^{1005}) = 1/2 + 1/2^{1005}.\)

Hence, (m, n) = (\(1, 2^{1005\)).

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The value of k that makes the function f(x) = k(8 - x) a probability density function (PDF) over the interval [0, 8] is k = 1/32. The probability density function is f(x) = (1/32)(8 - x).

To determine the value of k that makes the function a probability density function (PDF) over the given interval [0, 8], we need to satisfy two conditions:

Let's proceed with the calculations:

Condition 1: Non-negativity

For the function to be non-negative, we have k(8 - x) ≥ 0.

This condition holds true as long as k ≥ 0 and 8 - x ≥ 0.

Condition 2: Integral equals 1

To determine the value of k, we need to find the integral of the function over the interval [0, 8] and set it equal to 1.

∫[0,8] k(8 - x) dx = 1

Now let's evaluate the integral:

∫[0,8] k(8 - x) dx = k ∫[0,8] (8 - x) dx

= k [8x - (x^2/2)] from 0 to 8

= k [8(8) - (8^2/2) - (0 - 0^2/2)]

= k [64 - 32 - 0]

= k * 32

Setting this equal to 1:

k * 32 = 1

Dividing both sides by 32:

k = 1/32

Therefore, the value of k that makes the function a probability density function over the interval [0, 8] is k = 1/32.

The probability density function is:

f(x) = k(8 - x) = (1/32)(8 - x)

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The square of a binomial, the value of the constant \(c\) should be equal to half the coefficient of the linear term squared, which in this case is \(c = \left(\frac{22}{2}\right)^2 = 121\). Therefore, the constant that needs to be filled in is 121.

To express the quadratic expression \(x^2 + 22x + c\) as the square of a binomial, we need to find a binomial of the form \((x + a)^2\) that expands to \(x^2 + 22x + c\). Expanding \((x + a)^2\) gives \(x^2 + 2ax + a^2\). Comparing the coefficients of the expanded binomial and the given quadratic expression, we can equate the linear terms to find \(2ax = 22x\), which gives \(a = 11\). Substituting this value of \(a\) back into the expanded binomial, we have \(x^2 + 22x + 121\). Therefore, the constant that needs to be filled in is 121.

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The meaning of the graph is that the value of x is no less than -1

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

x ≥ − 1

The above expression is an inequality that implies that

The value of x is no less than -1

Next, we plot the graph

See attachment for the graph of the inequality

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Question

What does the graph of x ≥ −1 mean?

Approximately 47.72% of the students scored between 167 and 253 on the exam. To find the percentage of students who scored between 167 and 253 on the exam, we can use the properties of the normal distribution.

Given that the scores are normally distributed with a mean of 253 and a standard deviation of 43, we can calculate the z-scores for the two given scores and then use the z-table to find the corresponding probabilities. First, let's calculate the z-score for the lower score of 167:

z1 = (167 - 253) / 43

z1 ≈ -2

Next, let's calculate the z-score for the upper score of 253:

z2 = (253 - 253) / 43

z2 = 0

Using the z-table, we can find the area under the normal curve between z1 and z2, which represents the percentage of students who scored between 167 and 253 on the exam.

Since the z-score of z1 is -2, we look up the area to the left of -2 in the z-table, which is approximately 0.0228. This represents the percentage of students who scored below 167.

Since the z-score of z2 is 0, we look up the area to the left of 0 in the z-table, which is 0.5000. This represents the percentage of students who scored below 253.

To find the percentage of students who scored between 167 and 253, we subtract the percentage below 167 from the percentage below 253:

Percentage = 0.5000 - 0.0228 ≈ 0.4772

Therefore, approximately 47.72% of the students scored between 167 and 253 on the exam.

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Answer: x(-1.8-6y)  =  -1.8*x -6*y*x

Step-by-step explanation:

The distributive property says that if we have:

A*(B + C) where A, B and C can be any numbers, we can expand the equation as:

A*(B + C) = A*B + A*C.

So, in this case, we have the equation:

x*(-1.8 - 6y)

so we can expand this as:

x*(-1.8 - 6y) = x*(-1.8) + x*(-6*y) = -1.8*x -6*y*x

Yes we need that value which is equidistant from -1 and 1 both.

So the answer is -1/2=-0.5

If x has a normal distribution with mean 80 and standard deviation 5 then the 90th percentile of x is 70.

A normal distribution with mean 80 and standard deviation 5

We need to find the  90th percentile of x

Computing values to standard deviation from mean,

Lower limit = mean - 2s

                 = 80 - 2(5)

                 = 80 - 10

Lower limit = 70

Hence, if x has a normal distribution with mean 80 and standard deviation 5 then the 90th percentile of x is 70.

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Zach will need 19 feet of string to make his lanyard.

Zach and Jessica have 114 feet of string to make lanyards.

According to the given information, for every one foot Zach uses, Jessica needs 5 feet.

Let's assume that Zach uses x feet of string. Since Jessica needs 5 feet for every 1 foot Zach uses, she will need 5x feet of string.

The total length of string used by both Zach and Jessica should equal the total length of string they have, which is 114 feet.

So, we can set up an equation to represent this:
x + 5x = 114

Simplifying the equation:
6x = 114
Divide both sides by 6:
x = 19

Therefore, Zach will need 19 feet of string to make his lanyard.

Zach will need 19 feet of string to make his lanyard.

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Answer: In mathematics, the method of equating the coefficients is a way of solving a functional equation of two expressions such as polynomials for a number of unknown parameters. It relies on the fact that two expressions are identical precisely when corresponding coefficients are equal for each different type of term.

.

Answer:

You tutor for 4 hours

Step-by-step explanation:

If you count all the boxes, there are 6

12/6 is 2

You have 2 boxes so you do 2*2 which is 4

THE ANSWER IS 4

Answer:

24

Step-by-step explanation:

i added the time frame of you both tutoring ig.

Answer: 94.2 square inches

Step-by-step explanation:

Answer:

B

Step-by-step explanation: