Given
f(x) = 3x + 10 and g(x) = x - 2, find f (g(5))
-10
23
None of these.

Answer:

y= -207

Step-by-step explanation:

61 = 268 + y

Collect like terms

y= 61 - 268

Simplify

= -207

y= -207

Alternatively,

61 = 268 + y

Subtract 268 from both sides

61 - 268 = 268 + y - 268

-207 = y

Therefore,

y= -207

Answer: y = 3x + 7

Step-by-step explanation:

Since we are given the slope and y intercept we could write the equation in slope intercept form as y=mx +b .Only m and b are needed to write the equation.M is the slope and B is the y intercept.

Answer:

y=3x+7

Step-by-step explanation:

The equation of a line in slope-intercept form is:

y=mx+b

where m is the slope and b is the y-intercept.

We know the slope is 3, so we can substitute 3 in for m.

y=3x+b

We also know the y-intercept is (0,7). When writing the equation of a line in this form, we can ignore the x-coordinate of 0. Therefore, the y-intercept is also just 7. Substitute 7 in for b.

y=3x+7

The equation of a line with a slope of 3 and a y-intercept of (0,7) is y=3x+7

Answer:

probability that the sample mean will be between 166.75 and $170.50 = 0.42816

Step-by-step explanation:

We are given;

Mean; μ = $178

Standard deviation; σ = $50

Now, we want to find the probability that the sample mean will be between $166.75 and $170.50.

Thus, we'll use the z-score formula;

z = (x - μ)/σ

So;

Lower limit of z is;

z = (166.75 - 178)/50

z = -0.225

Upper limit of z is;

z = (170.50 - 178)/50

z = -0.15

From the z-distribution table attached, the area between -0.225 and -0.15 is;

0.44038 - 0.01222 = 0.42816

Answer:

£11564.54

Step-by-step explanation:

100 + 3.3 = 103.3%

103.3% = 1..013

£11125 x 1.013^3 = £11564.54

I hope this helped you!

Answer:

7

Step-by-step explanation:

Given the following data:

Average speed : 60.5, 63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4

To construct a one-sample t - statistic, the value of the degree of freedom will be ;

In a one sample test of known mean, if the number of observations are 4, one can choose to vary at most three of the observations and still obtain the mean, that is the 4th observation must remain fixed.

Degree of freedom = Number of observations (n) - 1. This is the maximum number of independent variables which can be varied.

Nunber of observations or sample size in the data above is 8

Hence,

Degree of freedom = (8 - 1) = 7

Answer:the anwser is 7

Step-by-step explanation:

Answer:

RU = 9

ST = 3

Step-by-step explanation:

RT = 6

RS = ST = (1/2)RT = (1/2)(6) = 3

ST = 3

RU = 3ST = 3 * 3 = 9

Answer:

The answer is

Step-by-step explanation:

To find an equation of a line given a point and slope we use the formula

y - y1 = m(x - x1)

where

m is the slope

(x1 , y1) is the point

From the question

slope = 4

point = ( 3 , - 2)

Substitute the values into the above formula

We have

Hope this helps you

Answer:

y+

Step-by-step explanation:

Point-Slope form- (y − y 1) = m ⋅ (x − x 1)

Slope: m = 4

Point: (x1, y1) = (3, -2)

Answer: y + 2 = 4 ⋅ (x - 3)

Answer:

[tex]\frac{-8 +2\sqrt{3} }{3}[/tex]

Step-by-step explanation:

When working with surds we need to take note of the roots present there.

To expand this equation we can do it the following way noting that √3 X √3 = 3

Expanding (1-√3)(⅓+√3)

1 X 1/3 = 1/3

1 X √3 = √3

-√3 X 1/3 =-√3/3

√3 X √3 = 3

hence, expanding the equation, we have

1/3 + √3 -√3/3 + 3

We can simply group the like terms and add them up.

[1/3 +3] +[√3-√3/3]

10/3 + [tex]\frac{2\sqrt{3} }{3}[/tex]

= [tex]\frac{-8 +2\sqrt{3} }{3}[/tex]

Answer: -2

Step-by-step explanation:

-2 - 7 = -9

Answer:

[tex]\Huge \boxed{c=-2}[/tex]

Step-by-step explanation:

[tex]c-7=-9[/tex]

We need to isolate the [tex]c[/tex] variable on one side of the equation.

Adding 7 to both sides of the equation.

[tex]c-7+7=-9+7[/tex]

Simplifying the equation.

[tex]c=-2[/tex]

Answer:

c. 48 packages

d. Possibilities:

1 x 28 = 28

2 x 14 = 28

4 x 7 = 28

7 x 4 = 28

14 x 2 = 28

28 x 1 = 28

Possible combinations:

17, 1, 28

17, 2, 14

17, 4, 7

17, 7, 4

17, 14, 2

17, 28, 1

Step-by-step explanation:

c. 127 employees get 3 uniforms each, meaning a total of 127 * 3 = 381 uniforms

The uniforms come in packs of 8, so dividing 381 by 8, we get:

381/8 = 47.625

However, you probably can't order a portion of a package, so you must round up to 48 packages. There will be 3 uniforms left over.

d. The divisors of 28 are 1, 2, 4, 7, 14, and 28. All I did was enumerate the six possibilities.

Answer:

[tex] {\sqrt[ 3 ]{x^{2} } }•{ \sqrt[4] {{y}^{3}} }[/tex]

Explanation-

As,

[tex]a^{\frac{1}{n} } = \sqrt[n]{a} [/tex]

and

[tex]a^{-n}=1/a^n[/tex]

Answer to part (a) is: 33 degrees

Answer to part (b) is: 5 meters

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

Explanation:

Check out the diagram below.

For now, focus only on triangle ABC. The ladder is segment AC = 10. We first need to find the length of [tex]AB = h_1[/tex] which is the initial height of the ladder.

sin(angle) = opposite/hypotenuse

sin(70) = h/10

h = 10*sin(70)

h = 9.396926 approximately

Subtract off 4 since the ladder slips 4 meters down the wall

h-4 = 9.396926-4

h-4 = 5.396926

which is the new height the ladder reaches. The hypotenuse stays the same

sin(angle) = opposite/hypotenuse

sin(theta) = 5.396926/10

theta = arcsin(5.396926/10)

theta = 32.662715

theta = 33 degrees when rounding to 2 significant figures

This is the value of [tex]\theta_2[/tex] in the diagram below.

---------------------------------

We'll use the cosine rule with the old theta value [tex]\theta_1[/tex]

cos(angle) = adjacent/hypotenuse

cos(70) = x/10

x = 10*cos(70)

x = 3.420201 is the approximate distance the foot of the ladder is from the wall. This is before the ladder slips.

After the ladder slips, we use the new angle value [tex]\theta_2[/tex]

cos(angle) = adjacent/hypotenuse

cos(32.662715) = x/10

x = 10*cos(32.662715)

x = 8.418622

Subtract the two x values

8.418622-3.420201 =  4.998421

which gives the approximate distance the foot of the ladder moved (the distance from point C to point E in the diagram)

This rounds to 5.0 or simply 5 when rounding to 2 significant figures.

Answer:

45

Step-by-step explanation:

m<1 and m<2 are complementary angles because the sum of two angles = 90° and since m<1 = m<2

90 ÷ 2 = 45

Answer:

24,300

Step-by-step explanation:

So on Thursday you have 300 next day it's 900 bc 300x3=900

Friday: 900x3=2,700

Saturday: 2,700x3=8,100

Sunday: 8,100x3=24,300

Answer:

tan (thita) = 35/13

Step-by-step explanation:

Tan( angle) = opposite/ adjacent

Tan( angle) = 35/13

Angle = arc tan 35/13

Angle = 69.624 degrees

Round the answer as needed.

Answer:

x = 100

Step-by-step explanation:

All you need is contained in the sheet attached

Answer:

x = 100

Step-by-step explanation:

3 log2(x) - 2 log2(5x) = 2

We know that a log(c) = log c^a

log2(x)^3 - log2(5x)^2 = 2

log2(x^3) - log2(25x^2) = 2

We know that log a - log b = log a/b

log2(x^3 /25x^2) = 2

Simplify

log2(x /25) = 2

Raise each side to  base 2

2^log2(x /25) = 2^2

x/25 = 4

Multiply each side by 25

x = 4*25

x = 100

Answer:

y = 10x, which is the relationship between two 7 in the number 3772

Step-by-step explanation:

In the given number 3772

3 is at thousandth position its value is 3000 numerically

7 is at the hundredth position its value is 700 numerically

next 7 is at tens position its value is 70 numerically

and 2 is at unit position its value is 2 numerically

thus, 3772 can also be written as sum  of number based on its position

3000

+700

+  70

+    2

___-

= 3772

Thus,

since Third 7 from left  has value of 70

and Second 7  from left  has value of 700

we know 70*10 = 700

Thus, 70 is 10 times to that 700

Thus, we can say that

value of Second 7  from left = 10*value of Third 7  from left

Thus,

let value of Second 7  from left be y

value of Third 7  from left  be x

then

y = 10x, which is the relationship between two 7 in the number 3772

Answer:

2

Step-by-step explanation:

-7 - (-8) = 1

1 + (-3) = -2

-2 + 6 = 4

4 - 2 = 2

Answer:

2

Step-by-step explanation:

Start by removing the parentheses appropriately:

-(-8) = +8, and

+(-3) = -3

Then

-7 - (-8) + (-3) + 6 - 2  =  -7 + 8 - 3 + 6 - 2

Now, working from left to right, we perform the indicated operations:

-7 + 8 comes out to 1, and so we have 1 - 3 + 6 - 2.

Continuing, we get -2 + 6 - 2, or 4 - 2, or 2

Answer:

14.74%

Step-by-step explanation:

The formula for ANNUAL PERCENTAGE YIELD (APY) for an account that is COMPOUNDED CONTINUOUSLY is given as

APY = Pe^rt - 1

Where P = Principal

e = exponential

r = rate

t = time

Since Principal and Time was not given in the question,

APY = e^r - 1

r = 13.75% = 0.1375

APY = e^0.1375 - 1

APY = 1.147401706 - 1

APY = 0.147401706

Converting to percentage

= 0.147401706 × 100

= 14.7401706%

Approximately to 2 decimal places: 14.74%

Therefore, the annual percentage yield is 14.74%

Answer: Find answer in the attached file

Answer:

b = [tex]\frac{ln190}{ln200}[/tex]

Step-by-step explanation:

Using the rule of logarithms

log [tex]x^{n}[/tex] ⇔ nlogx

Given

190 = [tex]200^{b}[/tex] ( take the natural log ln of both sides )

ln190 = ln[tex]200^{b}[/tex] = bln200 ( divide both sides by ln200 )

[tex]\frac{ln190}{ln200}[/tex] = b

Answer:

hexagon; not regular

Step-by-step explanation:

hope this helps

Answer:

B. 0.58 + 1.48h

Step-by-step explanation:

h+0.48h+0.58

=(1h+0.48h)+0.58

=1.48h +0.58

Answer:

That's my slovings for your question

Answer:

first option is right

Step-by-step explanation:

Answer:

Option D.

Step-by-step explanation:

We need to find the circumstances that would likely make factoring the best method for solving a quadratic equation.

A quadratic equation is prime if its factors can not possible. So, option A is incorrect.

In a quadratic equation leading coefficient can not be zero. So, option B is incorrect.

For large numbers (coefficient or constant), quadratic formula is best method. So, option C is incorrect.

The difference of 2 perfect squares is:

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

In this case factoring is the best method.

Therefore, the correct option is D.

Answer:

the probability that a randomly chosen test-taker will score 142 or lower = 0.8643

Step-by-step explanation:

We are given;

Data point; x = 142

Mean; μ = 153

Standard deviation; σ = 10

So,let's find the z-score using;

z = (x - μ)/σ

z = (142 - 153)/10

z = -1.1

From the z-distribution table attached, the probability is;

P(z < -1.1) = 1 - 0.13567 ≈ 0.8643

Answer:

C

Step-by-step explanation:

Note that the right triangle has two tick marks.

This means that the sides are equivalent.

Therefore, this is a 45-45-90 triangle.

In a 45-45-90 triangle, the side lengths are n, and the hypotenuse is n√2

Since n is 5√2, then the hypotenuse x is n√2. Thus:

[tex]x=n\sqrt2\\x=(5\sqrt2)\sqrt2[/tex]

Simplify:

[tex]x=5(2)=10[/tex]

The answer is C :)

Answer:

  -7

Step-by-step explanation:

As x increases by 1, y decreases by 7, so the "rise"/"run" is ...

  slope = rise/run = -7/1 = -7