School a has graduated 1700 students and graduates 50 students each year school b has graduated 600 students but 150 each year how many years will it be before school b has as many graduates as school a

Answer:

Step-by-step explanation:

Given the domain and target set of functions f and g expressed as;

f(x) = 2x+3 an g(x) = 5x+7 we are to find the following;

a) f◦g

f◦g = f[g(x)]

f[g(x)] = f[5x+7]

To get f(5x+7), we will replace the variable x in f(x) with 5x+7 as shown;

f(x) = 2x+3

f(5x+7) = 2(5x+7)+3

f(5x+7) = 10x+14+3

f(5x+7) = 10x+17

Hence f◦g = 10x+17

b) g◦f

g◦f = g[f(x)]

g[f(x)] = g[2x+3]

To get g(2x+3), we will replace the variable x in g(x) with 2x+3 as shown;

g(x) = 5x+7

g(2x+3) = 5(2x+3)+7

g(2x+3) = 10x+15+7

g(2x+3) = 10x+22

Hence g◦f = 10x+22

c) For (f◦g)−1 (inverse of (f◦g))

Given (f◦g) = 10x+17

To find the inverse, first we will replace (f◦g) with variable y to have;

y = 10x+17

Then we will interchange variable y for x:

x = 10y+17

We will then make y the subject of the formula;

10y = x-17

y = x-17/10

Hence the inverse of the function

(f◦g)−1 = (x-17)/10

d) For the function f−1◦g−1

We need to get the inverse of function f(x) and g(x) first.

For f-1(x):

Given f(x)= 2x+3

To find the inverse, first we will replace f(x) with variable y to have;

y = 2x+3

Then we will interchange variable y for x:

x = 2y+3

We will then make y the subject of the formula;

2y = x-3

y = x-3/2

Hence the inverse of the function

f-1(x) = (x-3)/2

For g-1(x):

Given g(x)= 5x+7

To find the inverse, first we will replace g(x) with variable y to have;

y = 5x+7

Then we will interchange variable y for x:

x = 5y+7

We will then make y the subject of the formula;

5y = x-7

y = x-7/5

Hence the inverse of the function

g-1(x) = (x-7)/5

Now to get )f−1◦g−1

f−1◦g−1 = f-1[g-1(x)]

f-1[g-1(x)] = f-1(x-7/5)

Since f-1(x) = x-3/2

f-1(x-7/5) = [(x-7/5)-3]/2

= [(x-7)-15/5]/2

= [(x-7-15)/5]/2

= [x-22/5]/2

= (x-22)/10

Hence f−1◦g−1 = (x-22)/10

e) For the composite function g−1◦f−1

g−1◦f−1 = g-1[f-1(x)]

g-1[f-1(x)] = g-1(x-3/2)

Since g-1(x) = x-7/5

g-1(x-3/2) = [(x-3/2)-7]/5

= [(x-3)-14)/2]/5

= [(x-17)/2]/5

= x-17/10

Hence g-1◦f-1 = (x-17)/10

Answer:

the answer is c: 44

hope it helps

:)

The value of m in the equation one-half m minus three-fourths n equals 16, when n equals 8 is 44.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

The equation form;

1/2m - 3/ 4n = 16

Substituting the value of n in the equation, we have;

½m - ¾n = 16

½m - (¾×8) = 16

½m - 6 = 16

½m = 16 + 6

½m = 22

m = 44

Hence, The value of m in the equation one-half m minus three-fourths n equals 16, when n equals 8 is 44.

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Answer:

D

Step-by-step explanation:

The total annual FICA tax for an annual salary of $38,480 is D $2,943.72.

FICA tax comprise of Social security tax + Medicare tax

Where:

Hence:

FICA tax=($38,480×6.2%)+($38,480×1.45%)

FICA tax=$2,385.76+$557.96

FICA tax= $2,943.72

Inconclusion the  total annual FICA tax for an annual salary of $38,480 is D $2,943.72.

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Answer:

C. [tex] z = 82 [/tex]

Step-by-step explanation:

To find z, find x first:

[tex] 105 = \frac{1}{2}(x + 120) [/tex] (angle of intersecting chord theorem)

Solve for x

[tex] 105*2 = \frac{1}{2}(x + 120)*2 [/tex]

[tex] 210 = x + 120 [/tex]

[tex] 210 - 120 = x + 120 - 120 [/tex]

[tex] 90 = x [/tex]

[tex] x = 90 [/tex]

Find z:

Full circle = 360°

Therefore,

[tex] x + z + 68 + 120 = 360 [/tex]

[tex] 90 + z + 68 + 120 = 360 [/tex]

[tex] z + 278 = 360 [/tex]

[tex] z + 278 - 278 = 360 - 278 [/tex]

[tex] z = 82 [/tex]

Answer:

Test is Left tailed test

Parameter tested is standard deviation

Step-by-step explanation:

We are given the hypothesis as;

Null hypothesis; H0: σ = 8.6

Alternative hypothesis; H1: σ < 8.6

Where;σ is a constant generally known in statistics as the standard deviation.

Now, it's the alternative hypothesis that will let us know whether this is left tailed, right tailed or two tailed.

Alternative hypothesis says σ < 8.6.

This means that the values of σ that satisfy this hypothesis are less than 8.6 and thus are on the left hand side of 8.6 on a number line. Thus, the shaded region in a normal distribution curve will be on the left.

Thus, it's a left tailed test

Answer:

it is this graph

Step-by-step explanation:

it is this graph

Answer:

B

Step-by-step explanation:

Answer:

{3, 4, 5, 6, 7, 8} and {8, 7, 6, 5, 3}

Step-by-step explanation:

The sets {3, 4, 5, 6, 7, 8} and {3, 4, 5, 6, 7, 8} will be constraint through {x | x < 9 and x >2} so option (A) and (C) will be correct.

A set is a combination of specific quantities in which the meaning of each variable must be the same.

For example {1,2,3,4,5,6...} is a set of natural numbers in which each variable is representing a natural number so the overall meaning is the same among all.

Another example could be a set of the whole number like that.

Given the constraint

{x | x < 9 and x >2}

It means x should be greater than 2 and less than  9

So all possible values are

3,4,5,6,7,8

Now set associated with these number is {3, 4, 5, 6, 7, 8} and {8, 7, 6, 5, 3}.

Hence "The sets {3, 4, 5, 6, 7, 8} and {3, 4, 5, 6, 7, 8} will be constraint through {x | x < 9 and x >2}".

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Answer:

The length of each side is 10.5

Step-by-step explanation:

If you mean h as in the hypotenuse:

perimeter= 45    side h= 24    find x

45 - 24 = 2x

21 = 2x

/2     /2

10.5 = x

Answer:

The answer in standard form to the given expression is 6x⁵ - 5x⁴ + 6x³ - x² + 12x - 31

Step-by-step explanation:

(-5x⁴ + 6x³ - 43) + (6x⁵ - x² + 12x + 12)

Combine like terms. When the problem says to put the equation in standard form, it means that the terms will go in order from greatest to least exponential number.

6x⁵ - 5x⁴ + 6x³ - x² + 12x - 31

Answer:

6/36 (16.667%)

Step-by-step explanation:

Answer:

5/36

Step-by-step explanation:

Answer:

  see below

Step-by-step explanation:

The cube of something to the 1/3 power is the original something. The cube of a cube root of something is the original something. Since the cube of a cube root is the same as the cube of a 1/3 power, the 1/3 power is equivalent to the cube root.

The applicable rules of exponents are ...

  (a^b)^c = a^(bc)

Answer:

yes

Step-by-step explanation:

Answer:

Step-by-step explanation:

14. 2

15. 3

16. -5

17. -11

Answer:

8.9 is the answer i just took the test

Answer:

325/3

Step-by-step explanation:

[tex]48+4^2+\frac{3}{5}\\\\\mathrm{Convert\:element\:to\:fraction}:\quad \:48=\frac{48\cdot \:5}{5}\\\\=\frac{48\cdot \:5}{5}+\frac{3}{5}\\\\\mathrm{Since\:the\:denominators\:are\:equal,\\\\\:combine\:the\:fractions}:\\\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\=\frac{48\cdot \:5+3}{5}\\\\48\cdot \:5+3=243\\\\=4^2+\frac{243}{5}\\\\=16+\frac{243}{5}\\\\=\frac{16\cdot \:5}{5}+\frac{243}{5}\\\\=\frac{16\cdot \:5+243}{5}\\\\16\cdot \:5+243=323\\\\=\frac{323}{5}[/tex]

Answer:

Explained below.

Step-by-step explanation:

Consider the variables height and weight.

It is usually seen that taller people are heavier than shorter people.

So a regression analysis can be used to specify this belief.

The statistical questions that are being asked here are:

The variable Y is considered as the dependent variable and the variable Y is considered as the independent variable.  And the main purpose of the regression analysis is to predict the value of Y when the value of X is given.

The linear regression model can be used to predict the past and future value of the dependent variables provided that the independent variables for those times are provided.

Answer:

75°

Step-by-step explanation:

In a parallelogram, any two adjacent angles are supplementary. In other words, they total 180.

Angle D and Angle E are adjacent. Thus, they are supplementary. In other words:

[tex]\angle D +\angle E =180[/tex]

Substitute them for the equations:

[tex]7x+21+15+5x=180[/tex]

Combine like terms and add on the left:

[tex]12x+36=180[/tex]

Subtract 36 from both sides:

[tex]12x=144[/tex]

Divide both sides by 12:

[tex]x=12[/tex]

Thus, the value of x is 12.

Note that Angle D and Angle C are also adjacent. Thus, their angles also equal 180.

So:

[tex]\angle D+\angle C =180[/tex]

Substitute the equation for D:

[tex]7x+21+\angle C=180[/tex]

Plug in 12 for x:

[tex]7(12)+21+\angle C =180[/tex]

Simplify:

[tex]84+21+\angle C =180\\105+\angle C =180[/tex]

Subtract 105 from both sides:

[tex]\angle C =75\textdegree[/tex]

Thus, Angle C is 75 degrees.

Complete Question

A biologist reports a confidence interval of (3.5,4.9) when estimating the mean height (in centimeters) of a sample of seedlings. What is the estimated margin of error and the sample mean?

Answer:

The  margin of error is  [tex]E = 0.7[/tex]

The  sample mean is  [tex]\= x = 4.2[/tex]

Step-by-step explanation:

from the question we are told that

   The  upper limit is  [tex]k = 4.9[/tex]

    The  lower limit is  [tex]r = 3.5[/tex]

Generally the margin of error is mathematically represented as

      [tex]E = \frac{k - r}{ 2}[/tex]

      [tex]E = \frac{ 4.9 - 3.5 }{2}[/tex]

     [tex]E = 0.7[/tex]

Generally the sample mean is mathematically evaluated as

        [tex]\= x = k - E[/tex]

=>    [tex]\= x = 4.9 - 0.7[/tex]

=>    [tex]\= x = 4.2[/tex]

Answer:

Your coordinates would be:

(1,8) (1,5) (5,8)

Hope this helps!

Answer:

Actually its (1,8) (1,5) (6,8)

Step-by-step explanation:

The red part is incorrect, the orange is the correct one. I got it wrong.

Answer:

options a is correct

4/7 likely

Probability = Favourable outcomes/ Total outcomes

All outcomes that we have are = 1,2,3,4,5,6,7,8

→ Total outcomes are 8 .

Favourable outcomes are = 1,3,5,7

→ Favourable outcomes are 4.

P(odd) = 4 divided by 8

→ P( odd) is 1/2 , 50% , equally likely.

So option 2nd is correct .

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

Explanation:

The domain is the set of all real numbers. This is because the graph goes on forever to the left and right. We can use any x value we want as an input. There are no restrictions to worry about such as to prevent dividing by zero errors.

To say "all real numbers" in interval notation, we write [tex](-\infty, \infty)[/tex] which is another way of saying [tex]-\infty < x < \infty[/tex]

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

The range in interval notation is [tex][3, \infty)[/tex] since y = 3 is the smallest y output possible, and we could have larger y values as well. So basically [tex]y \ge 3[/tex] can be used to describe the range without saying much else.

Note the use of a square bracket to include 3 as part of the interval.

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

There are no x intercepts because this graph does not cross the x axis. The lowest point is at (-2,3) so there's no way we could reach y = 0. Put another way, y = 0 is not part of the range so we cannot have any x intercepts.

There is one y intercept and it is at (0,7) where the graph crosses the y axis. For any function, the max number of y intercepts is 1.

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

When it says "interval positive", its asking "which part(s) of the graph are above the x axis?". That would be the entire graph meaning we have the interval [tex](-\infty, \infty)[/tex]. Every point on this V shaped curve is of the form (x,y) where y is positive.

So this means that we do not have any points with a negative y value, and therefore the answer to "interval negative" is none.

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

Now onto the "interval increasing". This is similar to the previous section, but now we're looking when the graph is going uphill as we read from left to right. This happens on the interval [tex](-2, \infty)[/tex] or put another way when x > -2.

The graph goes downhill whenever x < -2. So that's why the answer for the "interval decreasing" is [tex](-\infty, -2)[/tex]

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

Note the points (-2,3) and (0,7) are on the V shaped graph. These points have x coordinates of x = -2 and x = 0, which are the endpoints of the interval we're focusing on.

Compute the slope of the line through those two points

m = (y2-y1)/(x2-x1)

m = (7-3)/(0-(-2))

m = (7-3)/(0+2)

m = 4/2

m = 2

The positive slope means the line goes uphill as we read from left to right

The average rate of change on the interval [-2, 0] is the value 2

In other words, we go up 2 units each time we move to the right 1 unit.

Answer:

Value of LN = 19 units

Step-by-step explanation:

Given:

LN = 3 + 8x

Find:

Value of LN

Computation:

We know that LM + MN = LN

So,

8 + 6x - 1 = LN

So,

3 + 8x = 8 + 6x - 1

3 + 8x = 7 + 6x

8x - 6x = 7 - 3

2x = 4

x = 2

So,

LN = 3 + 8x

LN = 3 + 8(2)

LN = 3 + 16

LN = 19

Value of LN = 19 units

Question:

Approximately 30% of the calls to an airline reservation phone line result in a reservation being made.  Suppose that an operator handles 10 calls. What is the probability that none of the 10 calls result in a reservation?

Answer:

[tex]Probability = 0.028[/tex]

Step-by-step explanation:

Given

Represent probability of reservation with p and Number of calls  with n

[tex]n= 10[/tex]

[tex]p = 30\%[/tex]

First, we need to convert p to decimal

[tex]p = \frac{30}{100}[/tex]

[tex]p = 0.30[/tex]

In probability; opposite probability add up to 1;

In other words,

[tex]p + q = 1[/tex]

Where q represents probability of no reservation

Substitute 0.30 for p

[tex]0.30 + q = 1[/tex]

[tex]q = 1 - 0.30[/tex]

[tex]q = 0.70[/tex]

The probability that out of the 10 calls, no reservation is made is calculated as;

[tex]Probability = q^n[/tex]

[tex]Probability = 0.70^{10}[/tex]

[tex]Probability = 0.0282475249[/tex]

[tex]Probability = 0.028[/tex]  (Approximated)

Answer:

7.8

Step-by-step explanation:

Answer:

The answer is 3.6

Step-by-step explanation:

d=[tex]\sqrt{(2-0)^{2}+(3-0)^{2} }[/tex]

d=[tex]\sqrt{(2)^{2}+(3)^{2} }[/tex]

d=[tex]\sqrt{4+9}[/tex]

d=[tex]\sqrt{13}[/tex]

d=3.6

Answer:

$243.375

Step-by-step explanation:

multiply 8.25 by 29.5

Answer:

5/6

Step-by-step explanation:

you must flip 3 over 5 and multiply

Answer:

The third one

Step-by-step explanation:

600-225 (the weight of Terrell and his equipment)

=375

375/25(weight of each box)

=15

the circle is close because it can be exactly 15 or or less.

Answer:

actually is 2

Step-by-step explanation:

its not 1 or 3, its 2 I did clicked 3 got it wrong then I clicked one and got it wrong, its 2