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Using the normal distribution, there is a 0.6826 = 68.26% probability that the sample mean will be within 2 points of the population mean.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, the parameters are given as follows:

[tex]\mu = 40, \sigma = 8, n = 16, s = \frac{8}{\sqrt{16}} = 2[/tex]

The probability that the sample mean will be within 2 points of the population mean is the p-value of Z when X = 40 + 2 = 42 subtracted by the p-value of Z when X = 40 - 2 = 38, hence:

X = 42:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (42 - 40)/2

Z = 1

Z = 1 has a p-value of 0.8413.

X = 38:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (38 - 40)/2

Z = -1

Z = -1 has a p-value of 0.1587.

0.8413 - 0.1587 = 0.6826 = 68.26% probability that the sample mean will be within 2 points of the population mean.

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Answer:

The total surface area of the the cylinder is 640.56cm², surface are is always give in cm² not in cm³ b/c cm³ indicates the volume of the cylinder not the surface area.

Step-by-step explanation:

Hello!

. SA=2πr(r+h) ,or 2πr²+h(2πr)

Answer:

204π cm^2

which is 640.88 cm^2 to the nearest hundredth.

Step-by-step explanation:

Surface area = 2 * area of the base + area of the curved side.

= 2*π *r^2  + 2*π*r*h

= 2π(6)^2 + 2π(6)(11)

= 72π + 132π

= 204π cm^2.

The  statements that are correct  about right triangle QRS are:

A right triangle posses  a right angle which is in opposite direction to the  hypotenuse.

Considering the right angle triangle, it can be deduced that Side opposite ∠Q is RS not RQ,  and  Adjacent side to ∠Q is QS.

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Explanation:

The proof can be had by making use of the AAS congruence postulate (twice) and CPCTC.

We start by showing ΔPQY≅ΔPRX, then by showing ΔXQN≅ΔYRN. The proof is then a result of CPCTC.

1. PQ≅PR, ∠Q≅∠R . . . . given

2. ∠P≅∠P . . . . reflexive property of congruence

3. ΔPQY≅ΔPRX . . . . AAS congruence postulate

4. PX≅PY . . . . CPCTC

5. PX+XQ=PQ, PY+YR=PR . . . . segment sum theorem

6. PX+XQ = PY +YR . . . . substitution property

7. PX +XQ = PX +YR . . . . substitution property

8. XQ = YR . . . . subtraction property of equality

9. ∠XNQ≅∠YNR . . . . vertical angles are congruent

10. ΔXNQ≅ΔYNR . . . . AAS congruence postulate

11. XN ≅ YN . . . . CPCTC

__

Additional comment

You probably did steps 1-3 in part (a) of the problem.

A mortgage payment is typically made up of four components: principal, interest, taxes, and insurance. The Principal portion is the amount that pays down your outstanding loan amount. Interest is the cost of borrowing money. The amount of interest you pay is determined by your interest rate and your loan balance.

The term “loan” can be used to describe any financial transaction where one party receives a lump sum and agrees to pay the money back. A mortgage is a type of loan that's used to finance a property. A mortgage is a type of loan, but not all loans are mortgages. Mortgages are “secured” loans.

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The population mean is symbolized as μ. The sample mean is symbolized M.

A population in statistics, is a the total number of people of a group that shares similar characteristics that are of interest to a researcher. Example of population a researcher can understudy include:

A sample is a subset of a population, which is drawn using any sampling technique. An example of a sample is 100 randomly selected persons who patronize a shopping mall.

The population mean can be defined as the average data value of a particular group characteristics that is measured by the researcher. The symbol for population mean is: μ.

The sample mean can be defined as the average data value of the sub-group of an entire population that having characteristics that are of interest to a researcher. The symbol for sample mean is: M.

In summary, the population mean is symbolized as μ. The sample mean is symbolized M.

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Using the Fundamental Counting Theorem, it is found that:

a) 256 codes are possible.

b) The probability is [tex]\frac{1}{256}[/tex].

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

There are 4 keys, each with 4 options, hence the parameters are:

[tex]n_1 = n_2 = n_3 = n_4 = 4[/tex].

Then the number of codes is:

[tex]N = 4^4 = 256[/tex]

And the probability is:

[tex]p = \frac{1}{256}[/tex].

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Answer:

B

Step-by-step explanation:

Finding the area of the trapezoid using the lengths in the diagram, we get (c)(2d+a+b)/2.

This is equal to c(d+b), so:

(1/2)(c)(2d+a+b)=c(d+b)

(1/2)(2d+a+b)=d+b

d+0.5a+0.5b=d+b

0.5a+0.5b=b

0.5a=0.5b

a=b

Considering that the value of 126.07 is valid for the population, it is a parameter.

In this problem, the mean blood pressure is calculated for all employees, which means that it is valid for the population, hence it is a parameter.

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Answer:

60:1

Step-by-step explanation:

60:1 = 366:x

60x = 366

x = 6.1

366 minutes is equivalent to 6.1 hours.

Convert 366 minutes to hours.

[tex]\boldsymbol{\sf{Therefore \ \to \ 366 \not{m}*\dfrac{1 \ hr}{60\not{m}}=6.1 \ hr }}[/tex]

We conclude that a time of 366 minutes is equal to 6.1 hours

There are 60 minutes in 1 hour. To convert from minutes to hours, divide the number of minutes by 60. For example, 120 minutes equals 2 hours because 120/60=2.

Answer:

  the equation is no longer quadratic

Step-by-step explanation:

A quadratic equation is a polynomial equation in which the highest-degree term has degree 2.

The value a=0 makes the squared term disappear. If 'a' is zero, the equation becomes a linear equation, not a quadratic equation:

  bx +c = 0

The value of the constant of variation include 8, 3.2, and 1.25

From the information given, when x = -0.5, y = -4.0. The constant will be:

y = kx

-4 = -0.5k

k = -4.0/-0.5

k. = 8

When x = 2.5, y = 8

y = kx

8 = 2.5k

k = 8/2.5

k = 3.2

When x = 4, y = 5

y = kx

5 = 4k

k = 5/4

k = 1.25

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The solution to the equation is 2

Given the equation

4 + 4(x-2) = 2(x+1) - x

First, we expand the bracket

4 + 4x - 8 = 2x + 2 - x

collect like terms

4x - 2x + x = 2 - 4 + 8

Add like terms

3x = 6

Make 'x' the subject

x = 6/3

x = 2

Thus, the solution to the equation is 2

The complete question is

What is the solution to the equation of 4 + 4(x-2) = 2(x+1) - x? show your work

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Answer:

$13.20

Step-by-step explanation:

A dozen consists of 12 items. If you have 3 you must multiply the current amount by 4 to get 12. Therefore you must also multiply the price by 4.

3.30*4=13.20

The probability that a kid who goes to the doctor has a sore throat given that he has a fever is 30%

The given parameters are:

P(Fever) = 70%

P(Fever and sore throat) = 21%

The probability that a kid who goes to the doctor has a sore throat given that he has a fever is calculated as:

P = P(Fever and sore throat)/P(Fever)

So, we have:

P = 21%/70%

Evaluate

P = 30%

Hence, the probability is 30%

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Answer:

Meena age = 5 yrs Meenas father = 30

Step-by-step explanation:

let,

meena's age = x

meena's father's age = 6x

Five years from now

meena's age will be 1/3(6x)

meena's father's age will be 6x+5

A/Q

x+5+6x+5=2x+6x+5

=x+6x-2x-6x=5-5-5

= -x =-5

= x =5

meena's age = 5

meena's father's age = 6x

= 6×5

= 30

The center of the circle = (8, -4)

The radius of the circle =  [tex]\sqrt{76}[/tex]

The given equation of the circle is:

[tex]x^2+y^2-16x+8y+4=0[/tex]

The equation can be expressed and simplified as:

[tex]x^2-16x+y^2+8y=-4\\\\x^2-16y+8^2+y^2+8y+4^2=-4+8^2+4^2\\\\(x-8)^2+(y+4)^2=-4+64+16\\\\(x-8)^2+(y+4)^2=76[/tex]

The general equation of a circle is:

[tex](x-a)^2+(y-b)^2=r^2[/tex]

Comparing the two equations:

The center, (a, b) = (8, -4)

The radius, r = [tex]\sqrt{76}[/tex]

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Answer: R: {f(x) ∈ ℝ | f(x) ≥ 4}

Step-by-step explanation:

[tex]|x-3| \geq 0[/tex] for all real x, so the range is [tex]f(x) \geq 4[/tex].

[tex] \frac{(6x - 4)(3 - 2x)}{(4x - 6)} = \frac{2(3x - 2)(3 - 2x)}{2(2x - 3)} [/tex]

[tex] \frac{2(3x - 2)(3 - 2x)}{2(2x - 3)} = \frac{(3x - 2)(3 - 2x)}{(2x - 3)} [/tex]

[tex] \frac{(3x - 2)(3 - 2x)}{(2x - 3)} = \frac{ - (3x - 2)(2x - 3)}{(2x - 3)} [/tex]

[tex] \frac{ - (3x - 2)(2x - 3)}{(2x - 3)} = - (3x - 2)[/tex]

[tex] - (3x - 2) = 2 - 3x[/tex]

Average speed of Alishia is 19 kilometers per hour

Average speed is calculated by dividing the total distance that something has traveled by the total amount of time it took it to travel that distance. Speed is how fast something is going at a particular moment. Average speed measures the average rate of speed over the extent of a trip

Given :

Distance = 45.3 km

Time taken = 143 minutes = 143/60 =2.384 hours

∴ Average speed = 45.3/2.384 = 19 kilometers per hour

Thus the average speed of Alishia is 19 kilometers per hour.

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Using the z-distribution, it is found that the 95% confidence interval for the proportion of college students who work to pay for tuition and living expenses is: (0.4239, 0.5161).

If we had increased the confidence level, the margin of error also would have increased.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96. Increasing the confidence level, z also increases, hence the margin of error also would have increased.

The sample size and the estimate are given as follows:

[tex]n = 450, \pi = 0.47[/tex].

The lower and the upper bound of the interval are given, respectively, by:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.47 - 1.96\sqrt{\frac{0.47(0.53)}{450}} = 0.4239[/tex]

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.47 + 1.96\sqrt{\frac{0.47(0.53)}{450}} = 0.5161[/tex]

The 95% confidence interval for the proportion of college students who work to pay for tuition and living expenses is: (0.4239, 0.5161).

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Answer:

see explanation

Step-by-step explanation:

(a)

(the side required )² = sum of squares of other 2 sides - ( 2 × product of other 2 sides and cos(angle opposite side required ) )

x² = 12² + 15² - (2 × 12 × 15 × cos71°)

(b)

x² = 144 + 225 - 360cos71°

   = 369 - 360cos71° ( take square root of both sides )

x = [tex]\sqrt{369-360cos71}[/tex]

  ≈ 16 cm ( to the nearest integer )

The factorise form of the two expression are as follows:

b. (x - 3)(2 / 3 x - 6) = 0

Therefore, let's open the brackets

2 / 3 x² - 6x -2x + 18 = 0

2 / 3 x²  - 8x + 18 = 0

multiply through by 3

2x² - 24x + 54 = 0

Hence,

 2 (x - 3)  (x - 9)

c.

(-3x - 15)(x + 7)  = 0

Therefore,

-3x² - 21x - 15x - 105 = 0

-3x² - 36x - 105 = 0

-3(x + 5)(x + 7)

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Answer:

the following 3 equations are equivalent :

• x + 1 = 4

• 2 + x = 5

• -5 + x = -2

Step-by-step explanation:

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

-5 + x = - 2

Let’s take this equation :

x + 1 = 4

=======

By Adding 1 to both sides of the equation we get :

x + 1 + 1 = 4 + 1

⇔ x + 2 = 5

⇔ 2 + x = 5

Then the equations x + 1 = 4  and 2 + x = 5 are equivalent.

…………………………………………………………………

On the other hand ,if we subtract 6 from both sides

of the equation x + 1 = 4  we get :

x + 1 - 6 = 4 - 6

⇔ x - 5 = -2

⇔ -5 + x = -2

Then the equations x + 1 = 4  and -5 + x = -2 are equivalent.

Answer:

A. 2 + x = 5

B. x + 1 = 4

E. -5 + x = -2

Step-by-step explanation:

right on edg, hope it helps ya'll.

Answer:

X multiplied by 2 is 8

X divided by 2 is 4

Step-by-step explanation:

This is the quickest thing i can give you

Joel spent 72.5% of his time exercising after playing soccer on Tuesda

The given parameters are

Minutes spent on Tuesday = 27 more minutes than Monday

Total minutes spend = 60

This means that

Tuesday = Monday + 27

Monday + Tuesday = 60

Make Monday the subject in Tuesday = Monday + 27

Monday = Tuesday - 27

Substitute Monday = Tuesday - 27 in Monday + Tuesday = 60

Tuesday - 27 + Tuesday = 60

Evaluate

2 * Tuesday = 87

Divide by 2

Tuesday = 43.5

The percentage of time spent exercising on Tuesday is then calculated as

Percentage = 43.5/60 * 100%

Evaluate the expression

Percentage = 72.5%

Hence, Joel spent 72.5% of his time exercising after playing soccer on Tuesday

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The percentage of this plane that's enclosed by the pentagons is closest to: D. 56.

Since the side of the small square is a, then the area of the tile is

given by:

Area of tiles = 9a²

Note: With an area of 9a², 4a² is covered by squares while 5a² by pentagons.

This ultimately implies that, 5/9 of the tiles are covered by pentagons and this can be expressed as a percentage as follows:

Percent = 5/9 × 100

Percent = 0.555 × 100

Percent = 55.5 ≈ 56%.

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Complete Question:

The plane is tiled by congruent squares of side length a and congruent pentagons of side lengths a and a²/a, as arranged in the diagram below. The percent of the plane that is enclosed by the pentagons is closest to (A) 50 (B) 52 (C) 54 (D) 56 (E) 58

The relationship which best defines a function, for the houses on Katrina's street exists appraised value, property tax.

Table exists a form to describe the data of the two or more variables.

To read the data from the table, examine for the value of one variable, and obtain the resultant value of other variables from the related block.

The table below details some of the characteristics of the houses on Katrina’s street. Let's estimate the most suitable choice whose relationship defines a function.

The relationship which nicely illustrates the function, of the houses on Katrina's street exists between the appraised value and property tax.

Therefore, the correct answer is option d) (appraised value, property tax).

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Answer: D

Step-by-step explanation: Appraised Value , Property Tax

Answer:A or C

Step-by-step explanation: i guessed plus 19 hours ago