Evaluating function expressions

-1•f(-8)-4•g(4)=

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:

3[x + 3(4x – 5)] = (39x-15)

Step-by-step explanation:

The given expression is : 3[x + 3(4x – 5)]

We need to find the equivalent expression for this given expression. We need to simplify it. Firstly, open the brackets. So,

[tex]3[x + 3(4x -5)]=3[x+12x-15][/tex]

Again open the brackets,

[tex]3[x+12x-15]=3x+36x-45[/tex]

Now adding numbers having variables together. So,

[tex]3[x + 3(4x - 5)]=39x-15[/tex]

So, the equivalent expression of 3[x + 3(4x – 5)] is (39x-15).

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.

Answer:

Paula will travel 234 miles in 4.5 hours

Step-by-step explanation:

Step 1: We first find the speed Paula is going in hours, we divide 130 mile by 2.5 hours to get 52 miles per hour

Step 2: We multiple 52 miles per hour with 4.5 hours to get 234 miles

Therefore Paula will travel 234 miles in 4.5 hours

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]

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]

Answer:

Simple Interest : $ 4400

Step-by-step explanation:

We want to calculate the interest on $ 10,000, at 5.5% interest rate per year, over a course of 8 years.

We can use the simple interest formula here, or :

I = P × r × t,

Where P is the principle amount, $ 10,000, r is the interest rate, 5.5% each year, or in decimal form 5.5 / 100 = 0.055. t is the time, 8 years.

Simple Interest : 10000 × 0.055 × 8 =  $4400.00

Then again the interest can be added to the principal amount ( $10,000 ) to receive some new amount after 8 years, which is $ 14,000. However the simple interest earned in 8 years at a rate of 5.5% should be $4400.

The simple interest earned on the amount is $4,400

Interest is the total amount that would be paid or earned from making an investment or taking a loan over a period of time.

Simple Interest  = principal x time x interest rate

principal = amount borrowed = $10,000

time = 8 years

Interest rate = 5.5%

10,000 x 0.055 x 8 = $4,400

To learn more about simple interest, please check: https://brainly.com/question/9352088?referrer=searchResults

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:

t= 0.4933

t ≥ t ( 0.025 ,8 ) = 2.306

Since the calculated value of t= 0.4933 is less than t ( 0.025 ,8 ) = 2.306 therefore we accept the null hypothesis at 5 % significance level . On the basis of this we conclude that the book had no effect on their scores.

Step-by-step explanation:

We state our null and alternative hypotheses as

H0: ud= 0 Ha: ud≠0

The significance level is set at ∝= 0.05

The test statistic under H0 is

t= d`/ sd/√n

which has t distribution with n-1 degrees of freedom

The critical region is t ≥ t ( 0.025 ,8 ) = 2.306

Computations

Student       Scores before      Scores after    Difference           d²

                        reading book                    ( after minus before)

1                          720                   740             20                       400

2                        860                   860              0                           0

3                        850                   840             -10                       100

4                        880                   920             40                       1600

5                        860                   890             30                        900

6                        710                    720              10                         100

7                       850                    840              -10                       100

8                      1200                  1240             40                        1600

9                      950                    970              20                           40

∑                    6930                  8020           140                         4840

d`= ∑d/n= 140/9= 15.566

sd²= 1/8( 4840- 140²/9) = 1/8 (4840 - 2177.778) = 2662.22/8= 332.775

sd= 18.2422

t= 3/ 18.2422/ √9

t= 0.4933

Since the calculated value of t= 0.4933 is less than t ( 0.025 ,8 ) = 2.306 therefore we accept the null hypothesis at 5 % significance level . On the basis of this we conclude that the book had no effect on their scores.

Answer:

1300 and 700 respectively.

Step-by-step explanation:

Let x be invested in first account and y be invested in second account.

ATQ, x+y=2000 and 101=(4)*x/100+7*y/100. Solving it will give us x=1300 and y=700

Let numbers be a and b

Adding both

[tex]\\ \qquad\quad\sf\longmapsto 2a=24[/tex]

[tex]\\ \qquad\quad\sf\longmapsto a=\dfrac{24}{2}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto a=12[/tex]

[tex]\\ \qquad\quad\sf\longmapsto 12-b=9[/tex]

[tex]\\ \qquad\quad\sf\longmapsto b=12-9[/tex]

[tex]\\ \qquad\quad\sf\longmapsto b=3[/tex]

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.

To know more about Algebraic expression on:

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(i) False. If two lines are parallel, then they never intersect.

(ii) True. We can draw infinitely many different lines through a single point. We can think of rotating a line around a single point to form a circular fan of lines.

(iii) True. Any line is defined uniquely by two distinct points.

Answer:

4x^2-22x+30

=2(2x^2 - 11x + 15)

=2(2x^2 -6x -5x +15)

= 2 { 2x(x-3) - 5(x-3) }

= 2 (x-3) (2x - 5)

Step-by-step explanation:

Hey, there!!!

The answer is option B

here, we have;

=4x^2-22x+30

=4x^2-(10+12)x+30

= 4x^2-10x-12x+30

now, taking common,

=2x(2x-5) -6(2x-5)

= 2(x-3)(2x-5).

Hope it helps

Answer:

490000000

Step-by-step explanation:

For every exponent of 10, move the decimal point one place to the right.

Answer:

Base = 21 while Height = 16

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:

Rounded: -5.5

Step-by-step explanation:

Work above :)

Answer:

Step-by-step explanation:

Assuming the gravel reaches the top of the walls and no higher, the volume is 7×4×16 = 448 m³

Answer:

hello thereee

now vol of truck = l b h = 7 * 4 * 16 = 448 m^3

( 448m^3 is final ans...

glad for brainliest.... hope that helps <3

Answer:

2.952755906 ft

Step-by-step explanation:

We need to convert 90 cm to inches

90 cm * 1 inch / 2.54 cm =35.43307087 inches

Now convert inches to ft

12 inches = 1ft

35.43307087 inches * 1 ft/ 12 inches =2.952755906 ft

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.  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:

  C.  As x → –∞, y → +∞, and as x → +∞, y → +∞

Step-by-step explanation:

The leading coefficient of this even-degree function is positive, so y goes to +∞ when the magnitude of x gets large.

_____

When the function is even degree, its value for large magnitude x heads toward the infinity with the same sign as the leading coefficient.

When the function is odd degree, its value for large magnitude x will head toward the infinity with the sign that matches the product of the sign of x and the sign of the leading coefficient.

Answer:

[tex]\large\boxed{\frac{3}{2}a^{8}}[/tex]

Step-by-step explanation:

([tex]a^{8}[/tex]) * [tex]\frac{3}{2}[/tex]

Remove the parenthesis by multiplying

[tex]\frac{3}{2}[/tex][tex]a^{8}[/tex]

This expression cannot be simplified further

[tex]\large\boxed{\frac{3}{2}a^{8}}[/tex]

Hope this helps :)

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.

Answer:

It more complex .Try to take help toggely

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:

m<2= 148.4

Step-by-step explanation:

A linear pair means that both angles add to 180.

m<2 = 4*m<1 +22

Together

m1 + m2 = 180

Put the value for m<2 into the above equation

m<1  + 4*m<1 + 22 = 180         Combine like terms\

5m<1 + 22 = 180                      Subtract 22

5m<1 = 180 - 22

5m<1 = 158                              Divide by 5

m<1 = 158/5

m<1 = 31.6

m<2 = 4*31.6 + 22

m<2 = 138.4

Answer:

-3

Step-by-step explanation:

[tex]8+3y = -1\\3y = -9\\y = -3[/tex]

Answer:

y = -3

Step-by-step explanation:

-1=3y+8

3y+8=-1

3y=-9

y=-3

Answer:

a negative integer

Step-by-step explanation: