In a study of 24 criminals convicted of antitrust offenses, the average age was 60 years, with a standard deviation of 7.4 years. Construct a 95% confidence interval on the true mean age. (Give your answers correct to one decimal place.)___ to____ years

Answer:

B. x=2, x=-3

Step-by-step explanation:

Hello,

We are given this system of equations:

y=4-x²

x-y=2

And we want to solve it for x.

There are a couple ways to solve systems of equations, but let's use substitution in this problem, which we will set one variable equal to an expression containing the other variable, use that expression to solve for the variable the expression contains in the other equation, then use the value of the solved variable to find the value of the other variable.

But in this case, we just need to find x, which is just one of the variables, so there's no need to find the values of y.

In x-y=2, subtract x from both sides.

-y=-x+2

Multiply both sides by -1.

y=x-2

Substitute y as x-2 in y=4-x².

x-2=4-x²

Add x² to both sides.

x²+x-2=4

Subtract 4 from both sides.

x²+x-6=0

Now factor using FOIL.

1 (coefficient in front of x) is the sum of the numbers used in the binomials, while -6 is their product.

Two numbers that add up to 1 but multiply to get -6 are -2 and 3.

So now factor:

(x-2)(x+3)=0

Split and solve:

x-2=0

x=2

x+3=0

x=-3

The solutions for x are x=2 and x=-3, which means the answer is B.

Hope this helps!

that's what I got, you can confirm if it's correct or not... I'm not sure

have a nice dayʘ‿ʘ

Answer:

Option 4) The area of the flower bed is smaller than 4 square feet.

Step-by-step explanation:

Let’s solve for the area of the flower bed.

Consider that the flower bed is a rectangle.

The area of a recrangle is given by the formula:

A = length x width

The area of the flower bed is:

4 ft x 4/6 ft = 2 2/3 ft^2

2 2/3 ft ^2 < 4 ft^2

Therefore option 4 is the correct answer.

9514 1404 393

Answer:

  c = a - b

Step-by-step explanation:

Subtract b from both sides of the equation.

  a = b + c

  a - b = b + c - b . . . . . show the subtraction

  a - b = c . . . . . . . . . . simplify

  c = a - b . . . . . . write with c on the left

Answer:

y = 2(x - 3)² + 5

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (3, 5), thus

y = a(x - 3)² + 5

To find a substitute (1, 13) into the equation

13 = a(1 - 3)² + 5 ( subtract 5 from both sides )

8 = 4a ( divide both sides by 4 )

a = 2, then

y = 2(x - 3)² + 5 ← equation of parabola in vertex form

Complete Question

In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year later. A sample of 64 one-year-old cars revealed that only 24 met the particulate emission standard. The test statistic to see whether the proportion is below the requirement is:

A -1.645

B -2.066

C -2.000

D-1.960

Answer:

The  correct option is C

Step-by-step explanation:

From the question we are told that

   The  population mean is  [tex]p = 0.50[/tex]

    The sample size is  [tex]n = 64[/tex]

     The  number that met the standard is  [tex]k = 24[/tex]

Generally the sample proportion is mathematically evaluated   as

             [tex]\r p = \frac{24}{64}[/tex]

             [tex]\r p =0.375[/tex]

Generally the standard error is mathematically evaluated as  

       [tex]SE = \sqrt{ \frac{p(1- p )}{n} }[/tex]

=>    [tex]SE = \sqrt{ \frac{0.5 (1- 0.5 )}{64} }[/tex]

=>   [tex]SE = 0.06525[/tex]

The  test statistics is evaluated as

        [tex]t = \frac{ \r p - p }{SE}[/tex]

        [tex]t = \frac{ 0.375 - 0.5 }{0.0625}[/tex]

        [tex]t = -2[/tex]

Answer:

[tex]\large \boxed{\mathrm{-3w + 5(2w + 1)}}[/tex]

Step-by-step explanation:

-2w + 3 + 5w - 2

Combine like terms.

3w + 1

-3w + 5(2w + 1)

Expand brackets.

-3w + 10w + 5

Combine like terms.

7w + 5

Answer:

The answer is C.

-3w +5(2w +1)

Step-by-step explanation:

Answer:

  A.  1,162.5

Step-by-step explanation:

Write the next two terms and add them up:

  S5 = 600 +300 +150 +75 +37.5 = 1162.5 . . . . matches choice A

================================================

Explanation:

{600, 300, 150, ...} is a geometric sequence starting at a = 600 and has common ratio r = 1/2 = 0.5, this means we cut each term in half to get the next term. We could do this to generate five terms and then add them up. Or we could use the formula below with n = 5

Sn = a*(1-r^n)/(1-r)

S5 = 600*(1-0.5^5)/(1-0.5)

S5 = 1,162.5

-----------

Check:

first five terms = {600, 300, 150, 75, 37.5}

S5 = sum of the first five terms

S5 = 600+300+150+75+37.5

S5 = 1,162.5

Because n = 5 is relatively small, we can quickly confirm the answer. With larger values of n, a spreadsheet is the better option.

Answer:

Consider the following identity:

Let a = 2, b = 1/2

Use the algebraic identity given below

[tex]\boxed{\sf a^3-b^3=(a+b)(a^2-ab+b^2)}[/tex]

[tex]\\ \sf\longmapsto (2+\dfrac{1}{2})(2^2-1+\dfrac{1}{4})[/tex]

[tex]\\ \sf\longmapsto (2+\dfrac{1}{2})(2^2-2\times \dfrac{1}{2}+\dfrac{1}{2}^2)[/tex]

[tex]\\ \sf\longmapsto 2^3-\dfrac{1}{2}^3[/tex]

[tex]\\ \sf\longmapsto 8-\dfrac{1}{8}[/tex]

Answer: Its everthing except irrational

Step-by-step explanation:

Answer:

15 units

Step-by-step explanation:

Point D is at 8

Point A is at -7

D - A

8 - -7

8+7

15 units

Answer:

the answer is 15

you can just count the number of steps going forward from -7 to 8.

Answer:

18 - 8 * n = -6 * n

The number is 9

Step-by-step explanation:

Let n equal the number

Look for key words such as is which means equals

minus is subtract

18 - 8 * n = -6 * n

18 -8n = -6n

Add 8n to each side

18-8n +8n = -6n+8n

18 =2n

Divide each side by 2

18/2 = 2n/2

9 =n

The number is 9

━━━━━━━☆☆━━━━━━━

▹ Answer

n = 9

▹ Step-by-Step Explanation

18 - 8 * n = -6 * n

Simple numerical terms are written last:

-8n + 18 = -6n

Group all variable terms on one side and all constant terms on the other side:

(-8n + 18) + 8n = -6n + 8n

n = 9

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

The correlation of X and Y is 1.006

Step-by-step explanation:

Given

X: 2, 3, 5, 6

Y: 1, 2, 4, 5

n = 4

Required

Determine the correlation of x and y

Start by calculating the mean of x and y

For x

[tex]M_x = \frac{\sum x}{n}[/tex]

[tex]M_x = \frac{2 + 3+5+6}{4}[/tex]

[tex]M_x = \frac{16}{4}[/tex]

[tex]M_x = 4[/tex]

For y

[tex]M_y = \frac{\sum y}{n}[/tex]

[tex]M_y = \frac{1+2+4+5}{4}[/tex]

[tex]M_y = \frac{12}{4}[/tex]

[tex]M_y = 3[/tex]

Next, we determine the standard deviation of both

[tex]S = \sqrt{\frac{\sum (x - Mean)^2}{n - 1}}[/tex]

For x

[tex]S_x = \sqrt{\frac{\sum (x_i - Mx)^2}{n -1}}[/tex]

[tex]S_x = \sqrt{\frac{(2-4)^2 + (3-4)^2 + (5-4)^2 + (6-4)^2}{4 - 1}}[/tex]

[tex]S_x = \sqrt{\frac{-2^2 + (-1^2) + 1^2 + 2^2}{3}}[/tex]

[tex]S_x = \sqrt{\frac{4 + 1 + 1 + 4}{3}}[/tex]

[tex]S_x = \sqrt{\frac{10}{3}}[/tex]

[tex]S_x = \sqrt{3.33}[/tex]

[tex]S_x = 1.82[/tex]

For y

[tex]S_y = \sqrt{\frac{\sum (y_i - My)^2}{n - 1}}[/tex]

[tex]S_y = \sqrt{\frac{(1-3)^2 + (2-3)^2 + (4-3)^2 + (5-3)^2}{4 - 1}}[/tex]

[tex]S_y = \sqrt{\frac{-2^2 + (-1^2) + 1^2 + 2^2}{3}}[/tex]

[tex]S_y = \sqrt{\frac{4 + 1 + 1 + 4}{3}}[/tex]

[tex]S_y = \sqrt{\frac{10}{3}}[/tex]

[tex]S_y = \sqrt{3.33}[/tex]

[tex]S_y = 1.82[/tex]

Find the N pairs as [tex](x-M_x)*(y-M_y)[/tex]

[tex](2 - 4)(1 - 3) = (-2)(-2) = 4[/tex]

[tex](3 - 4)(2 - 3) = (-1)(-1) = 1[/tex]

[tex](5 - 4)(4 - 3) = (1)(1) = 1[/tex]

[tex](6-4)(5-3) = (2)(2) = 4[/tex]

Add up these results;

[tex]N = 4 + 1 + 1 + 4[/tex]

[tex]N = 10[/tex]

Next; Evaluate the following

[tex]\frac{N}{S_x * S_y} * \frac{1}{n-1}[/tex]

[tex]\frac{10}{1.82* 1.82} * \frac{1}{4-1}[/tex]

[tex]\frac{10}{3.3124} * \frac{1}{3}[/tex]

[tex]\frac{10}{9.9372}[/tex]

[tex]1.006[/tex]

Hence, The correlation of X and Y is 1.006

Answer:

D

Step-by-step explanation:

[tex]4(x^2+3)-2y\\\\=4((-6)^2+3)-2(\frac{-1}{2} )\\\\=4(36+3)+1\\\\=4(39)+1\\\\=156+1\\\\=157[/tex]

The value of the expression 4(x² + 3) - 2y is 157, when x = -6 and y = -1/2.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expression is,

4(x² + 3) - 2y

Substitute x = -6 and y = -1/2 to find the value of expression,

= 4 ((-6)² + 3) - 2(-1/2)

= 4 (36 + 3) + 1

= 4 x 39 + 1

= 156 + 1

= 157

The required value of the expression is 157.

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Answer:

Below

Step-by-step explanation:

If d is a positive number then the greatest common factor is 108d.

To get it isolate d and d^2 from the numbers.

108 divides 216. (216 = 2×108)

Then the greatest common factor of 216 and 108 is 108.

For d^2 and d we will follow the same strategy

d divides d^2 (d^2 = d*d)

Then the greatest common factor of them is d.

So the greatest common factor will be 108d if and only if d is positive. If not then 108 is the answer

Answer:

[tex]\boxed{108d}[/tex]

Step-by-step explanation:

Part 1: Find GCF of variables

The equation gives d ² and d as variables. The GCF rules for variables are:

The GCF for the variables is d.

Part 2: Find GCF of bases (Method #1)

The equation gives 108 and 216 as coefficients. To check for a GCF, use prime factorization trees to find common factors in between the values.

Key: If a number is in bold, it is marked this way because it cannot be divided further AND is a prime number!

Prime Factorization of 108

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 108 is 2 * 2 * 3 * 3 * 3, or simplified as 2² * 3³.

Prime Factorization of 216

216 ⇒ 108 & 2

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 216 is 2 * 2 * 2 * 3 * 3 * 3, or simplified as 2³ * 3³.

After completing the prime factorization trees, check for the common factors in between the two values.

The prime factorization of 216 is 2³ * 3³ and the prime factorization of 108 is 2² * 3³.  Follow the same rules for GCFs of variables listed above and declare that the common factor is the factor of 108.

Therefore, the greatest common factor (combining both the coefficient and the variable) is [tex]\boxed{108d}[/tex].

Part 3: Find GCF of bases (Method #2)

This is the quicker method of the two. Simply divide the two coefficients and see if the result is 2. If so, the lesser number is immediately the coefficient.

[tex]\frac{216}{108}=2[/tex]

Therefore, the coefficient of the GCF will be 108.

Then, follow the process described for variables to determine that the GCF of the variables is d.

Therefore, the GCF is [tex]\boxed{108d}[/tex].

Answer:

(a) The probability that a study participant has a height that is less than 67 inches is 0.4013.

(b) The probability that a study participant has a height that is between 67 and 71 inches is 0.5586.

(c) The probability that a study participant has a height that is more than 71 inches is 0.0401.

(d) The event in part (c) is an unusual event.

Step-by-step explanation:

The complete question is: In a survey of a group of​ men, the heights in the​ 20-29 age group were normally​ distributed, with a mean of 67.5 inches and a standard deviation of 2.0 inches. A study participant is randomly selected. Complete parts​ (a) through​ (d) below. ​(a) Find the probability that a study participant has a height that is less than 67 inches. The probability that the study participant selected at random is less than inches tall is nothing. ​(Round to four decimal places as​ needed.) ​(b) Find the probability that a study participant has a height that is between 67 and 71 inches. The probability that the study participant selected at random is between and inches tall is nothing. ​(Round to four decimal places as​ needed.) ​(c) Find the probability that a study participant has a height that is more than 71 inches. The probability that the study participant selected at random is more than inches tall is nothing. ​(Round to four decimal places as​ needed.) ​(d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.

We are given that the heights in the​ 20-29 age group were normally​ distributed, with a mean of 67.5 inches and a standard deviation of 2.0 inches.

Let X = the heights of men in the​ 20-29 age group

The z-score probability distribution for the normal distribution is given by;

                          Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean height = 67.5 inches

            [tex]\sigma[/tex] = standard deviation = 2 inches

So, X ~ Normal([tex]\mu=67.5, \sigma^{2}=2^{2}[/tex])

(a) The probability that a study participant has a height that is less than 67 inches is given by = P(X < 67 inches)

      P(X < 67 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{67-67.5}{2}[/tex] ) = P(Z < -0.25) = 1 - P(Z [tex]\leq[/tex] 0.25)

                                                                 = 1 - 0.5987 = 0.4013

The above probability is calculated by looking at the value of x = 0.25 in the z table which has an area of 0.5987.

(b) The probability that a study participant has a height that is between 67 and 71 inches is given by = P(67 inches < X < 71 inches)

    P(67 inches < X < 71 inches) = P(X < 71 inches) - P(X [tex]\leq[/tex] 67 inches)

    P(X < 71 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{71-67.5}{2}[/tex] ) = P(Z < 1.75) = 0.9599

    P(X [tex]\leq[/tex] 67 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{67-67.5}{2}[/tex] ) = P(Z [tex]\leq[/tex] -0.25) = 1 - P(Z < 0.25)

                                                                = 1 - 0.5987 = 0.4013

The above probability is calculated by looking at the value of x = 1.75 and x = 0.25 in the z table which has an area of 0.9599 and 0.5987 respectively.

Therefore, P(67 inches < X < 71 inches) = 0.9599 - 0.4013 = 0.5586.

(c) The probability that a study participant has a height that is more than 71 inches is given by = P(X > 71 inches)

      P(X > 71 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{71-67.5}{2}[/tex] ) = P(Z > 1.75) = 1 - P(Z [tex]\leq[/tex] 1.75)

                                                                 = 1 - 0.9599 = 0.0401

The above probability is calculated by looking at the value of x = 1.75 in the z table which has an area of 0.9599.

(d) The event in part (c) is an unusual event because the probability that a study participant has a height that is more than 71 inches is less than 0.05.

The 2 triangles are congruent

41.9 mi

Step-by-step explanation:

First, we convert the angle from degree measure to radian measure:

[tex]\theta = 240°×\left(\dfrac{\pi}{180°}\right)= \dfrac{4\pi}{3}\:\text{rad}[/tex]

Using the definition of an arc length [tex]s[/tex]

[tex]s = r\theta[/tex]

[tex]\:\:\:\:=(10\:\text{mi})\left(\dfrac{4\pi}{3}\:\text{rad}\right)[/tex]

[tex]\:\:\:\:= 41.9\:\text{mi}[/tex]

The decimal number is 0.9

Answer:

The equation for a unit radius circle, centered at the origin is:

x^2 + y^2 = 1

Now, if we want to move it horizontally, you can recall to the horizontal translations:

f(x) -----> f(x - a)

Moves the graph to the right by "a" units.

A vertical translation is similar.

Then, if we want a circle centered in the point (a, b) we have:

(x - a)^2  + (y - b)^2 = 1.

Now, if you want to change the radius, we can actually write the unit circle as:

x^2 + y^2 = 1^2

Where if we set x = 0, 1 = y, this is our radius

So if we have:

x^2 + y^2 = R^2

And we set the value of x = 0, then R = y.

So our radius is R.

Then:

"A circle of radius R, centered in the point (a, b) is written as:

(x - a)^2 + (y - b)^2 = R^2

Answer:

-4, -1/7,0.09,π/2,√3 ,√225,17

Step-by-step explanation:

π/2, is approx 1.5

-4,

0.09,

17,

√3 is approx 1.7

,-1/7, is approx -.143

√225 = 15

From most negative to greatest

-4, -1/7,0.09,π/2,√3 ,√225,17

Answer:

[tex]-4, -1/7, 0.09, \pi/2, \sqrt3, \sqrt{225}, 17[/tex]

Step-by-step explanation:

So we have the numbers:

[tex]\pi/2, -4, 0.09, 17, \sqrt3, -1/7, \sqrt{225}[/tex]

(And without using a calculator) approximate each of the values.

π is around 3.14, so π/2 is around 1.57.

17 squared is 289, so 1.7 squared is 2.89. Thus, the square root of 13 is somewhere between 1.7 and 1.8.

-1/7 can be divided to be about -0.1429...

And the square root of 225 is 15.

Now, use the approximations to place the numbers:

[tex]\pi/2\approx1.57; -4; 0.09;17;\sqrt3 \approx1.7; -1/7\approx-0.14;\sqrt{225}=15[/tex]

The smallest is -4.

Next is -1/7 or about -0.14

Followed by the first positive, 0.09.

And then with π/2 or 1.57

And then a bit bigger with the square root of 3 or 1.7.

And then with the square root of 225 or 15.

And finally the largest number 17.

Thus, the correct order is:

[tex]-4, -1/7, 0.09, \pi/2, \sqrt3, \sqrt{225}, 17[/tex]

Answer:

.15

Step-by-step explanation:

Answer:

∠PQR =  67.36° (Approx)

Step-by-step explanation:

Given:

PRQ is a right triangle

∠R = 90°

PQ = 13 cm

QR = 5 cm

PR = 12 cm

Find:

∠PQR = ?

Computation:

Using trigonometry application.

SinФ = 12 / 13

SinФ = 0.92

Sin 67.36° = 0.92

So,

∠PQR =  67.36° (Approx)

Answer:

30×5=150

so 150+10=160

thus his payment in the 30th installment is

rs.160

Answer: (7, 20)

Concept:

There are three general ways to solve systems of equations:

Since the question has specific requirements, we are going to use substitution to solve the equations.

Solve:

Given equations

y = 3x - 1

2x + 6 = y

Substitute the y value since both equations has isolated [y]

2x + 6 = 3x - 1

Add 1 on both sides

2x + 6 + 1 = 3x - 1 + 1

2x + 7 = 3x

Subtract 2x on both sides

2x + 7 - 2x = 3x - 2x

[tex]\boxed{x=7}[/tex]

Find the value of y

y = 3x - 1

y = 3(7) - 1

y = 21 - 1

[tex]\boxed{y=20}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

a negative integer

Step-by-step explanation:

Answer:

Base = 21 while Height = 16

Answer:

0.0618

Step-by-step explanation:

z = (x - μ)/σ, where

x is the raw score = 69

μ is the sample mean = population mean = 65

σ is the sample standard deviation

This is calculated as:

= Population standard deviation/√n

Where n = number of samples = 25

σ = 13/√25

σ = 13/5 = 2.6

Sample standard deviation = 2.6

z = (69 - 65) / 2.6

z = 4/2.6

z = 1.53846

Approximately to 2 decimal places = 1.54

Using the z score table to determine the probability,

P(x = 69) = P(z = 1.54)

= 0.93822.

The probability that the sample mean is greater than 69 is

P(x>Z) = 1 - 0.93822

P(x>Z) = 0.06178

Approximately to 4 decimal places = 0.0618

Answer:

If we put x=17/4

f(4×17/4-15)=8×17/4-27

f(2x=34-27

f(x)=7.

Hope i helped you.

The guidance director is conducting a sample poll in this experimental design.

Sample is a part of population. It does not comprises whole population. It is representatitive of whole population.

We are required to fill the blank with appropriate term among the options.

The correct option is sample poll because the guidance director collects data in his school only.

Census collects the whole population of the country.

Sample poll means collecting data from small population.

Random sample means collecting data from a part of popultion without identifying any variable.

Hence we found that he was doing sample poll.

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