Suppose X1, . . . , X64 are independent and identically distributed continuous uniform random variables on the interval (0,12). Recall that if X Unif (0,12), then f(x) = 1/12 for 0 < x < 12 (and otherwise), μ = E(X) = 6, and σ^2 = Var(X) = 12 (there is no need to verify this). Approximate the probability that the sample mean X is less than 5.5. i.e. approximate P(X < 5.5). a. 0.1251 b. 0.0548 c. 0.1446
d. 0.2420

Answer:

-4r+2s-15

Step-by-step explanation:

collect like terms

r-5r= -4r

-6s+8s= 2s

therefore -4r+2s-15

Therefore, the mean of the sampling distribution of the proportion is 0.076 and the standard deviation is approximately 0.0189.

To be able to approximate the sampling distribution with a normal model, we need the following conditions to be met:

Random Sampling: The 240 loans should be randomly selected from the population of all loans. This ensures that the sample is representative of the population.

Independence: The loans should be independent of each other. This means that the default status of one loan does not affect the default status of another loan.

Success-Failure Condition: The number of successes (people who do not make payments on time) and failures (people who make payments on time) in the sample should each be at least 10. This ensures that the sampling distribution can be approximated using a normal model.

Now, let's calculate the mean and standard deviation of the sampling distribution of the proportion:

The mean of the sampling distribution of the proportion is equal to the population proportion, which is 7.6% or 0.076.

The standard deviation of the sampling distribution of the proportion can be calculated using the formula:

σ = √((p * (1 - p)) / n)

where p is the population proportion and n is the sample size.

In this case, p = 0.076 and n = 240.

σ = √((0.076 * (1 - 0.076)) / 240)

= √(0.07095 / 240)

≈ 0.0189

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The box plot that represents the data-set is given as follows:

Option B.

From left to right, the five features of the box and whisker plot are listed as follows

The data-set in this problem has 11 elements, hence:

The quartiles are the mean of each half, hence:

Meaning that the second plot is correct.

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The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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A. The ball will be in the air for approximately 8.623 seconds on Mars.

B. The ball will reach a maximum height of approximately 138.17 meters on Mars.

To approximate the time the ball will be in the air on Mars, we can use the kinematic equation:

v = u + at

where:

v = final velocity (0 m/s when the ball reaches its maximum height)

u = initial velocity (32 m/s)

a = acceleration (gravity on Mars, -3.711 m/s²)

t = time

Setting v = 0, we can solve for t:

0 = 32 - 3.711t

3.711t = 32

t ≈ 8.623 seconds

Therefore, the ball will be in the air for approximately 8.623 seconds on Mars.

To approximate the maximum height the ball will reach, we can use the kinematic equation:

v² = u² + 2as

where:

v = final velocity (0 m/s when the ball reaches its maximum height)

u = initial velocity (32 m/s)

a = acceleration (gravity on Mars, -3.711 m/s²)

s = displacement (maximum height)

Setting v = 0, we can solve for s:

0 = (32)² + 2(-3.711)s

1024 = -7.422s

s ≈ -138.17 meters

The negative sign indicates that the displacement is in the opposite direction of the initial velocity, which means the ball is moving upward.

Therefore, the ball will reach a maximum height of approximately 138.17 meters on Mars.

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Answer:

( X - 2 )(3x + 5)  For 3x^2-x-10

Step-by-step explanation:

The range would be needed to label the subjects correctly is 000-210.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given that a researcher is comparing the effectiveness of three devices.

There are 210 people who snore participating in the experiment

The researcher will randomly place the participants into three equally sized treatment groups suitable for comparison.

We need to find the range which would be needed to label the subjects correctly.

210 people are participating in experiment

We need to label subjects from 001 to 210

Since there is no value in using 000 to indicate someone.

Hence, 000–210 is the range would be needed to label the subjects correctly.

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Answer:

$20.64

Step-by-step explanation:

When you take 40% of 33, you are left with 19.8. You then translate the sales tax into 84 cents and add it to 19.8. That will give you $20.64 as the after tax price.

Answer:

-4

Step-by-step explanation:

Parallel lines are lines that run across from each other but never intersect. For this to work, they must change at the same rate and have the same slant. This means parallel lines must have equal slopes; therefore, the slope of the parallel line is -4. It is also important to note that parallel lines must have different y-intercepts, or they would just be the same line.

SOLUTION

We want to find (A ∩ B)’ we have to first find (A ∩ B), that is elements that are common to both A and B, elements seen in A and also seen in B

So

Now (A ∩ B)’ are elements seen in the universal set U that are not in (A ∩ B). These are

Hence the answer is c) {1, 3, 4, 5, 6, 7}

The answer is 18 ounces of salt in 20% solution should be mixed with 27 ounces of 10% solution to produce 45 ounces of 14% salt solution.

let x and y be the amount of 20% and 10% solutions respectively:

x + y = 45 ____eq.1

20%x + 10%y = 14% (45)

20/100x + 10/100 y = 14/100 (45)

0.2x + 0.1y = 0.14 (45)____eq.2

Rewrite eq.1 to (x=45-y) and plug that value into that of eq.2

0.2(45-y) + 0.1y = 6.3

9 - 0.2y + 0.1y = 6.3

-0.1y = -2.7

y = (-2.7) ÷ (-0.1)

y = 27

put the value of y in eq. 1

x + y = 45

x + 27 = 45

x = 45 - 27

x = 18

Therefore, 18 ounces of salt in 20% solution should be mixed with 27 ounces of 10% solution to produce 45 ounces of 14% salt solution.

Full Question:

How many ounces of a 20% salt solution should be mixed with a 10% salt solution to produce 45 ounces of a 14% salt solution?

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Answer:

.........................................

Step-by-step explanation:

.............................................................................................................................................................................................

Answer:

15% of $67.50 is $10.125 lets round it up to $10.13

Tip: $10.13

Total meal cost: $77.63

Brainly plz :))

Answer:

the waiter 10.13

your parents will pay 77.63

Step-by-step explanation:

67. 50 x 0.15 = 10.13

67.50 + 10.13 = 77.63

hope this helps

Answer:

51

Step-by-step explanation:

15% of 60 = 9

60 - 9 = 51

Given:

Area and altitude PS of ∆PQR are ar(∆PQR) = 180cm² and PS = 15​.

To find:

The measure of side QR.

Solution:

According to the given information, PS is an altitude of ∆PQR. It means QR is the base of ∆PQR.

We know that, the area of a triangle is

\(Area=\dfrac{1}{2}\times Base\times Height\)

\(ar(\Delta PQR)=\dfrac{1}{2}\times QR\times PS\)

Substituting the given values, we get

\(180=\dfrac{1}{2}\times QR\times 15\)

\(180\times 2=QR\times 15\)

\(360=QR\times 15\)

Divide both sides by 15.

\(\dfrac{360}{15}=QR\)

\(24=QR\)

Therefore, the measure of side QR is 24 cm.

Using fractions, if year boys built 3/14 of an igloo and year 3 girl have built 3/7 of the same igloo. The total amount of igloo built is 18/28.

Given that, Year 2 boys built 3/14 of an igloo, Year 3 girls have built 3/7 of the same igloo.

To find the total amount of the igloo built, we need to find the common denominator of 14 and 7 which is 14.

Let us convert 3/14 into 6/28 and 3/7 into 12/28.

So, total igloo built,

= 6/28 + 12/28= 18/28

Therefore, the total amount of the igloo built is 18/28.

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Answer:

26

Step-by-step explanation:

AB=CB so

3x+8=7x-16

-4x=-24

x=6

then plug that x value into the length which is 3x+8

so 3(6)+8=18+8=26

The angles are x is 35° and y is 17° when the angles on protractor ∠QUT=74°, ∠RUS=22° and ∠QUS=57°.

Given that,

The angles are given ∠QUT=74°, ∠RUS=22° and ∠QUS=57°.

We have to find the angles.

An angle is formed when two straight lines or rays meet at a single terminal. The vertex of an angle is the point at which two points converge. ​The name "angle" comes from the Latin word "angulus," which meaning "corner." ​

The ∠QUS = ∠QUR + ∠RUS

57°=x+22°

x=57°-22°

x=35°

Now, ∠QUT = ∠QUR + ∠RUS + ∠SUT

74°=35°+22°+y
y=74-35-22

y=17°

Therefore, The angles are x is 35° and y is 17° when the angles are given ∠QUT=74°, ∠RUS=22° and ∠QUS=57°.

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Answer:

0.18

Step-by-step explanation:

100 has two zeros, so you move the decimal point from the back to two places forward and put zero before it.

The covariance between the total scores X1 = X2 and Y1 + Y2 is 16.

a. To show that Cov(X, Y + Z) = Cov(X, Y) + Cov(X, Z), we need to use the properties of covariance.

The covariance between two random variables X and Y is defined as:

Cov(X, Y) = E[(X - E[X])(Y - E[Y])],

where E[X] represents the expected value of X.

Let's calculate Cov(X, Y + Z) using the definition of covariance:

Cov(X, Y + Z) = E[(X - E[X])(Y + Z - E[Y + Z])].

Expanding the expression:

Cov(X, Y + Z) = E[(X - E[X])(Y + Z - E[Y] - E[Z])].

Distributing the terms:

Cov(X, Y + Z) = E[(X - E[X])(Y - E[Y]) + (X - E[X])(Z - E[Z])].

Now, let's calculate Cov(X, Y) + Cov(X, Z):

Cov(X, Y) + Cov(X, Z) = E[(X - E[X])(Y - E[Y])] + E[(X - E[X])(Z - E[Z])].

Expanding and rearranging the terms:

Cov(X, Y) + Cov(X, Z) = E[(X - E[X])(Y - E[Y]) + (X - E[X])(Z - E[Z])].

As we can see, Cov(X, Y + Z) = Cov(X, Y) + Cov(X, Z).

Therefore, we have shown that Cov(X, Y + Z) = Cov(X, Y) + Cov(X, Z).

b. To find the covariance between the total scores X1 = X2 and Y1 + Y2, we can use the properties of covariance and the given covariances:

Cov(X1, Y1 + Y2) = Cov(X1, Y1) + Cov(X1, Y2) + Cov(X1, Y2) + Cov(X1, Y2).

Since Cov(X1, Y2) = Cov(X2, Y1), we can simplify the expression:

Cov(X1, Y1 + Y2) = Cov(X1, Y1) + Cov(X1, Y2) + Cov(X2, Y1) + Cov(X2, Y2).

Plugging in the given covariance values:

Cov(X1, Y1 + Y2) = 5 + 1 + 2 + 8 = 16.

Therefore, the covariance between the total scores X1 = X2 and Y1 + Y2 is 16.

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Answer:

d. 2.0

Step-by-step explanation:

i hope this helps :)

Answer:

D

Step-by-step explanation:

√2π / √5 (expand the expression)

√2π / √5  x  √5 / √5 (multiply the fractions)

√2π√5 / √5/√5 (calculate and multiply)

solution is √10π/5 so 1.98 round it to the nearest 10 and it'll be 2 so the answer is D

Using Algebraic expression , Tebogo will pay R52 200 after a year if Tebogo pays R4 350 a month for a house that she is ranting.

A combination of variables and constants is an algebraic expression.

A mathematical expression known as an algebraic expression can include exponents, parenthesis, variables, integers, and arithmetic operators (such as addition, subtraction, multiplication, and division).

Tebogo's payment after a year will be determined by multiplying the monthly payment by the 12 months that make up a year.

Amount Tebogo will pay in a year = 12 x R4 350 = R5 2200

Therefore, Tebogo will pay R52 200 after a year if Tebogo pays R4 350 a month for a house that she is ranting.

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Answer:

It is not possible to determine the percentage of samples that pass without additional information.

The point where he  buried his treasure is (6.28,9.84)

First of all, we are going to find the equation of the line which describes the first path crossed by the horseman.  In order to find it we have to take into account that the vector V  provides us with the direction of this path. We can associate the direction with the slope of the line. The slope is defined by the ratio of vertical changes to horizontal changes between two points.  

According to the V=6i+5j, we can determine that:

Vertical change (y)= 5

Horizontal change (x)=6

Slope=\frac{5}{6}

Now, using the point-slope form:

y-y₁=m(x-x₁)

The chosen point is the point where the horseman began riding (-2,5). Therefore:

m=5/6

y1=5

x1=-2

y-5=5/6(x+2)

y=5x/6-10/3

Since the horseman at some point turned at a right angle towards village B  and he unchanged his direction until arrived in village B, the second path must be described by a line perpendicular to the first path.  

We should know that two lines are perpendicular if and only if their slopes are negative reciprocals This means m1*m2=-1

m₁=5/6

m₂=-1/m₁=-6/5

In order to find the equation of the second path, we will use again the point-slope form.

The chosen point is the point where is located Village B (2,11)

y-11=-6/5(x-2)

y=-6x/5+13.4

The coordinates of the point where the horseman buried a jar full of silver coins correspond to the intersection of path 1 and path 2. Therefore we are going to equal the two equations of each path.

5x/6-10/3=-6x/5+13.4

Solving this equality for x

X=6.28

Replacing this value in any of the equations of the paths

Y=9.84.

Finally, the point where he buried his treasure is (6.28,9.84).

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Answer:

The correct answer is – 1/2

Answer:

The answer is -1/2

Step-by-step explanation:

If we compare this with y = mx + c, we can do a comparison. m is the slope and c is the added constant.

Since y = -1/2 x + 1/4,

m = -1/2

Since m is the slope, the slope is -1/2.

The law that establishes the equality of the two sets (A ⋂ B) ⋃ (A ⋂ B) and A ⋂ B is the Absorption law.

The Absorption law states that for any sets A and B, the union of the intersection of A and B with itself is equal to the intersection of A and B. Mathematically, it can be written as (A ⋂ B) ⋃ (A ⋂ B) = A ⋂ B.

This law can be understood by considering the properties of intersections and unions of sets. When we take the intersection of A and B, we consider the elements that are common to both sets. By taking the union of this intersection with itself, we are essentially including the common elements twice. However, since the union operation removes duplicates, we end up with the same set A ⋂ B.

Therefore, the Absorption law is the one that establishes the equality between (A ⋂ B) ⋃ (A ⋂ B) and A ⋂ B, making option c, Absorption law, the correct choice.

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The pet will need 3 tablets of Albon for the treatment. This can be answered by the concept of Simple mathematics.

To calculate the required dosage, we need to convert the pet's weight from pounds to kilograms, which gives us 11.36 kg. On day 1, the pet requires 5 mg/kg of Albon, which amounts to 56.8 mg. Since each tablet contains 125 mg, we need to give the pet 0.454 tablets (56.8/125) which we will round up to 1 tablet. For the next 5 days, the pet requires 2.5 mg/kg of Albon, which amounts to 28.4 mg.

Therefore, we will give the pet 0.227 tablets (28.4/125) which we will round up to 1/4 of a tablet (0.25 tablets) each day. So, over the course of 6 days, the total number of tablets needed will be 1 + (0.25 x 5) = 2.25, which we will round up to 3 tablets.

Therefore, the owner will need to be dispensed with 3 tablets of Albon for the pet's treatment.

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24 people

Number of people that can be served with 6 cups of rice = 14

Number of people that can be served with 1 cup of rice = 14/6 = 7/3

Number of people that can be served with 21/2 cups of rice = 21/2 x 7/3

Number of people that can be served with 21/2 cups of rice = 147/6

Number of people that can be served with 21/2 cups of rice = 24.5

24 people can be served with 21/2 cups of rice