Estimate the measure of

Answer: 64.95

Step-by-step explanation: The formula is (3√3 s2)/2 so using that we can find the answer which is, 64.95

Answer:

These lines are neither parallel nor perpendicular.  

Step-by-step explanation:

Parallel lines are lines that never intersect and perpendicular intersect at a ninety degree angle.

Using desmos, you can find your solution.

I hope this helps

-No one

An example of experiment is B. Researchers working for a company test their new sneaker design to see if it helps athletes run faster.

An experiment simply means a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. It should be noted that experiments provide insight into cause-and-effect as they demonstrate what outcome occurs when a particular factor is manipulated

Experiments have a vital place in the development of science because experiments are used to test the reality of a thought, an axiom, or a phenomenon with a theoretical basis and to turn it into a law or a theorem.

In this case, testing the new sneakers is an experiment.

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The expression that represents the statement "the product of a number and eight" is 8x.

Expression:

Expression means the mathematical statement that consists of  minimum of two numbers/variables and at least one math operation(addition, subtraction, multiplication and division) in it.

Given,

The given statement is "the product of a number and eight".

Now, we have to find the suitable expression for this statement.

In order to find the suitable expression, we have to divide the given statement and then we have to identify the keyword in it.

By using those keywords, we have to solve it.

In the given statement we have identify the following:

product

number

eight

Here the product refers the multiplication

number is any unknown number that is x.

eight refers the number 8.

When we combine these keywords we can get the expression 8x.

Therefore, the resulting expression is 8x.

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[tex]\fbox{7.07...}[/tex]

First, we need the square of both numbers (8 and 18)

square of 8:

[tex]\sqrt{8}[/tex]

[tex]=2.828[/tex]

square of 18:

[tex]\sqrt{18}[/tex]

[tex]=4.242[/tex]

Now, let's add both numbers:

[tex]2.828+4.242[/tex]

[tex]=7.07[/tex]

Answer:

11.6666666 (infinitely)

The first five terms of the given sequence are a₁ = 50, a₂ = 25, a₃ = 12.5, a₄ = 6.25 and a₅ = 3.125.

In a geometric sequence the ratio of any two consecutive terms are equal. This ratio is known as the common ratio of the sequence.

Given that,

a₁ = 50 and aₙ = aₙ₋₁ ÷ 2

The first five terms are a₁, a₂, a₃, a₄  and a₅.

All the terms can be written using  aₙ = aₙ₋₁ ÷ 2 as follows,

a₂ = a₁ ÷ 2

⇒ a₂ = 50 ÷ 2

⇒ a₂ = 25

a₃ = a₂ ÷ 2

⇒ a₃ = 25 ÷ 2

⇒ a₃ = 12.5

a₄ = a₃ ÷ 2

⇒ a₄ = 12.5 ÷ 2

⇒ a₄ = 6.25

a₅ = a₄ ÷ 2

⇒ a₅ = 6.25 ÷ 2

⇒ a₅ = 3.125

Hence, the first five terms are 50, 25, 12.5, 6.25 and 3.125 respectively.

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It will take 6 days for the sister to earn as much as the brother.

Two or more expressions with an equal sign are defined as an equation.

Given that, the sister earns $30 per day and pays a $60 license fee and the brother earns$20 per day.

The income of the sister in x days is:

30x - 60

The income of the brother in x days is:

20x

The income of the sister and the brother is equal when:

30x - 60 = 20x

30x - 20x = 60

10x = 60

x = 6

Hence, It will take 6 days for the sister to earn as much as the brother.

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a) The mean distribution is 5.295.

b) The standard deviation is 0.1026

c) The probability that the child will be older than 5 years old is 0.7657

d) The probability that the child's age is between 4.84 and 5.34 is  0.4504

e) At the 9th percentile, the age of the child is 5.739 years old.

Given interval distribution is

4.74 - 5.85.

a) Firstly, we will find the mean distribution,

Mean distribution = Sum of intervals / Number of intervals

= 4.74+5.85 / 2

= 5.295.

Hence, the mean distribution is 5.295.

b) Now, we will find the standard deviation,

We use the formula:

SD = [tex]\sqrt{\frac{(b-a)^{2} }{12} }[/tex]

b = 5.85

a = 4.74

SD = [tex]\sqrt{\frac{(5.85-4.74)^{2} }{12} }[/tex]

SD = [tex]\sqrt{\frac{(1.11)^{2} }{12} }[/tex]

SD = 0.1026

Hence, the standard deviation is 0.1026

c) The probability that the child will be older than 5 years will be

p(older than 5) = 5.85 - 5 / 5.85 - 4.74

= 0.85 / 1.11

= 0.7657

Hence, the probability that the child will be older than 5 years old is 0.7657

d) The probability that the child will be between 4.84 and 5.34 years old will be

p(between 4.84 and 5.34) = 5.34 - 4.84 / 5.85 - 4.74

= 0.5 / 1.11

= 0.4504

Hence, the probability that the child's age is between 4.84 and 5.34 is  0.4504

e) If the child is at the 9th percentile, the age will be

At the 9th percentile = 4.74 + 9/100 ×(5.85 - 4.74)

= 4.74 +(0.9)(1.11)

= 4.74 + 0.999

= 5.739

Hence, at the 9th percentile, the age of the child is 5.739 years old.

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Dario cuts the lasagna into 15 equal slices.

Given,

Quantity of Parmesan cheese = 2/3 pounds

Quantity of Ricotta cheese = 1 3/4 = 7/4 pounds

Quantity of Mozzarella cheese = 1 1/3 = 4/3 pounds

The quantity of cheese in each pieces when the lasagna is cut = 1/4 pounds

We have to find the number of slices of cheese.

Here,

Total quantity of cheese;

2/3 + 7/4 + 4/3 = 2 + 7/4 = 15/4 pounds

Number of slices = total cheese / quantity of cheese in pieces

= (15/4) / (1/4) = 15 slices

That is,

Dario cuts the lasagna into 15 equal slices.

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50 would be the reliability of that measure  by standard error.

What is the standard deviation?

A measure that has no random error and no true score (i.e., is only random error) has zero reliability. A measure that has random error.

50 would be the reliability of that measure .

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If 1/5 of Joanna's monthly savings is $55 the equation of her savings is

The solution to the equation is $275

information from the question include

Joanna saves $55 each month from her part-time job

She saves 1/5 of her earnings

let x represent the Joanna's earnings

The equation of Joanna savings is represented in the form

1/5 of x = 55

This equation deals with multiplication and the term 'of' as used in math represents multiplication

Hence 1/5 of x = 1 / 5 * x = x/5

x/5 = 55

multiplying both sides by 5

x = 275

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Amount of water after x minutes is more in pool B.

Two or more expressions with an Equal sign is called as Equation.

Given,

Pool A started with 5000 liters of water, and 50 liters per minute are being.

Pool B started with 4800 liters of water, and 30 liters per minute are being.

5000-50x=4800-30x

Add 30x on both sides

5000-50x+30x=4800-30x+30x

5000-20x=4800

5000-4800=20x

200=20x

Divide both sides by 20

20=x

Now substitute x in pool A equation

5000-50x

5000-50(20)=5000-1000

Pool A =4000

Now substitute x in pool B equation

4800-30x

4800-30(20)

4800-600

Pool B =4200

4200>4000

Pool B> Pool A

Hence amount of water after x minutes is more in pool B.

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Answer:

the slope of the line is undefined

Considering the expression of a line, the equation of the line that passes through the pair of points (-5,-4) and (0,4) is y=8/5x + 4.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, the value of the ordinate to the origin b can be obtained.

Being (x₁, y₁)= (-5, -4) and (x₂, y₂)= (0,4), the slope m can be calculated as:

m= (4 - (-4))÷ (0 - (-5))

m= (4 + 4)÷ (0 +5)

m= 8÷ 5

m= 8/5

Considering point 2 and the slope m, you obtain:

4= 8/5×0 + b

4= 0 +b

4= b

Finally, the equation of the line is y=8/5x + 4.

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Answer:

see explanation

Step-by-step explanation:

(a)

given y is inversely proportional to x² then the equation relating them is

y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation

to find k use any ordered pair from the table

using (2, 4 ) , then

4 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )

16 = k

y = [tex]\frac{16}{x^2}[/tex] ← equation of variation

(b)

when y = 25 , that is

25 = [tex]\frac{16}{x^2}[/tex] ( multiply both sides by x² )

25x² = 16 ( divide both sides by 25 )

x² = [tex]\frac{16}{25}[/tex] ( take square root of both sides )

x = ± [tex]\sqrt{\frac{16}{25} }[/tex] = ± [tex]\frac{4}{5}[/tex]

the positive value of x is then [tex]\frac{4}{5}[/tex]

The domain is x [tex]\geq[/tex] 0. interval notation:  [0,[tex]\infty[/tex])

the range is f(x)≤0, interval notation:  (-[tex]\infty[/tex],0 ]

What are the domain and range of a function?

The domain is the set of all x-values that can be used to make the function "work" and produce actual y-values.

A function's range is the variety of conceivable y-values (minimum y-value to maximum y-value)

Find domain:

Set the term under the square root [tex]\geq[/tex]0

So, the domain is x [tex]\geq[/tex] 0. interval notation:  [0,[tex]\infty[/tex])

Find range:

The range of a radical function of the form -c√(ax+b) +k is f(x)≤k

So, the range is f(x)≤0

interval notation:  (-[tex]\infty[/tex],0 ]

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Answer:

-22 1/3

Step-by-step explanation:

We should start by subtracting both sides of the equality by 21.

After doing this, we get that -67=3m.

Furthermore, we can divide both sides by 3 and get -67/3=m.

However, this is an improper fraction, not a mixed number.

If we divide -67 by 3, we get -22 1/3.

Therefore, m= -22 1/3

The measure of ∠MCJ is 130° because ∠MCJ and ∠CMB are alternate interior opposite angles.

According to the question,

We have the following information:

We have a figure where angle MCJ is 130°.

Now, we can extend the two given lines as imaginary lines. After extending the lines, we will find that these lines are parallel and the lines are being cut by another line.

We know that in this case the alternate interior opposite angles are equal and the sum of consecutive alternate interior angles is 180°.

Now, ∠MCJ and ∠CMB are alternate interior opposite angles and thus they are equal.

Hence, the measure of ∠MCJ is 130° because ∠MCJ and ∠CMB are alternate interior opposite angles.

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Answer:

16 and 12

Step-by-step explanation:

A.1 IN=2FT

8IN =2(8)FT

= 16

B.1 IN=2FT

6IN=2(6)FT

=12 FT

Answer:

Step-by-step explanation:

Ok;

1. Area is base times height.

Here shown, the base is 18cm and the height is 11cm. Don't be fooled by the 14cm for it is just the leg of a triangle not full height!!

18*11=198cm^2

2. Divide by two. We just caculated the area of the rectangle. Now we know a triangle is half of a rectangle's area so divide by 2!

198/2= 98cm^2

Answer:

Step-by-step explanation:

there is probably a way to do this w/o calculus,  but I cheated and used that.

A = Length * Width

A = x * ( 650 -2x)

A = 650x -2[tex]x^{2}[/tex]

d/dx ( A = 650x -2[tex]x^{2}[/tex])

0=650 -4x

4x = 650

x = 135 m

A= 650*135 -2*[tex]135^{2}[/tex]

A = 51,300  [tex]m^{2}[/tex]

The scale factor of a figure with a shape with a side length of 12 and is dilated to a shape with 4 is 1/3.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Given that a figure with side length of 12 units is being dilated in a figure with side length of 4.

In this case, the scale factor = 4/12 = 1/3

Hence, The scale factor of a figure with a shape with a side length of 12 and is dilated to a shape with 4 is 1/3.

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1) Probability that exactly 4 flights are selected is; P(X = 4) = 0.11469

2) The probability that at most 3 flights are on time is; P(X ≤ 3) = 0.99533

3) The probability that at least 6 flights are on time is; P(X ≥ 6) = 0.57672

The formula for binomial probability distribution is;

P(r) = nCr * p^(r) * (1 − p)^(n − r)

Where;

n = Number of events

r = Number of successful events in the trials

p = Probability of success in the single trial of the events

We are given;

p = 80% = 0.8

n = 7

1) Probability that exactly 4 flights are selected is;

P(X = 4) = ⁷C₄ * 0.8⁴ * (1 − 0.8)^(7 − 4)

P(X = 4) = ⁷C₄ * 0.8⁴ * 0.2³

P(X = 4) = 0.11469

2) The probability that at most 3 flights are on time is;

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

Solving using online binomial calculator gives;

P(X ≤ 3) = 0.99533

3) The probability that at least 6 flights are on time is;

P(X ≥ 6) = P(X = 6) + P(X = 7)

P(X ≥ 6) = 0.57672

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Answer:

x = 1

Step-by-step explanation:

Given exponential equation:

[tex]3^{2x}-9=0[/tex]

Add 9 to both sides of the equation:

[tex]\implies 3^{2x}-9+9=0+9[/tex]

[tex]\implies 3^{2x}=9[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]

[tex]\implies \left(3^2\right)^{x}=9[/tex]

[tex]\implies9^{x}=9[/tex]

[tex]\textsf{Apply exponent rule} \quad a=a^1:[/tex]

[tex]\implies9^{x}=9^1[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]

[tex]\implies x=1[/tex]

The standard error for the sample was 0.13 when "for the 25 students, the standard deviation of grade points was 0.65 and the mean was 2.89."

The standard deviation of a statistic's sampling distribution, or an estimate of that standard deviation, is the statistic's standard error. The term "standard error of the mean" is used when referring to a statistic that is the sample mean. By dividing the standard deviation by the square root of the sample size, the standard error is determined. By taking into account the sample-to-sample variability of the sample means, it provides the precision of a sample mean.

Here,

The standard error=standard deviation/√number of samples

=0.65/√25

=0.65/5

=0.13

When "for the 25 students, the standard deviation of grade points was 0.65 and the mean was 2.89," the standard error for the sample was 0.13.

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The probability of selecting a blonde is 0.40

Probability is the likelihood that something will occur.

In this case, from the twenty students, it should be noted that the number of blondes are 8.

Black hair = 5

Blonde hair = 8

Brown hair = 5

Red hair = 2

Therefore, the probability of choosing a blonde will be:

= Number of blonde / Total students

= 8/20

= 0.40

The probability is 0.40

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Complete question

Of the 20 students in Kendra's class 5 have black hair eight have blonde hair 5 have brown hair 2 have red hair.kendra used the spinner to blonde hair. What's the experimental probability that the student will have blonde hair?

Answer:

(f+g)(x) = x - 7

Step-by-step explanation:

(f+g)(x) tells you to add the functions together. It means

f(x) + g(x)

= -3x - 5 + 4x - 2

combine like terms.

= 4x-3x - 5 - 2

= x - 5 - 2

simplify.

= x - 7

(f+g)(x) means

f(x) + g(x)

= x - 7