Step by step of how to find f(g(x)) and g(f(x))

Answer:

m∠1 = 40°

Step-by-step explanation:

Measures of angle 1 and angle 2 are examples alternate exterior angles. Alternate exterior angles are basically a pair of angles that are outside the parallel lines and are on opposite sides of the transversal. In other words, alternate exterior angles are congruent to each other.

Since we are given that measure of angle 2 is 40°. Measure of angle 1 has to be 40° because both angle 1 and angle 2 are alternate exterior angles.

Answer:

p=-5

Step-by-step explanation:

3p-49+9 -49+9=-40

3p-40=8p 3p-3p=0 8p-3p=5p

-40=5p p=5

Answer:

Enlargement rate is 24

Step-by-step explanation:

Divide 8 by one third to get the enlargement rate. I hope this helps:)

Answer:

Which side of the original parallelogram corresponds to the 6 ft side of the enlarged parallelogram? ITS IS  x ft

What is the second step in solving the proportion? IT IS  cross multiply

What is the value of the missing measure? IT IS  1/4

Step-by-step explanation:

i got this right

Answer:

she has 4 quarters and 18 dimes

Answer:

16 dimes and 8 quarters

Step-by-step explanation:

.25x8=2

.05x16=.8

$2+$.8=$2.80

Step-by-step explanation:

Answer:

(a) The probability that the student made the​ Dean's list is 0.1655.

(b) The probability that the student came from a private high school, given that the student made the Dean's list is 0.2411.

(c) The probability that the student was not home schooled, given that the student did not make the Dean's list is 0.9185.

Step-by-step explanation:

The complete question is:

Of the entering class at a college, 71% attended public high school, 21% attended private high school, and 8% were home schooled. Of those who attended public high school, 16% made the Dean's list, 19% of those who attended private high school made the Dean's list, and 15% of those who were home schooled made the Dean's list.

a) Find the probability that the student made the Dean's list.

b) Find the probability that the student came from a private high school, given that the student made the Dean's list.

c) Find the probability that the student was not home schooled, given that the student did not make the Dean's list.

Solution:

Denote the events as follows:

A = a student attended public high school

B = a student attended private high school

C = a student was home schooled

D = a student made the Dean's list

The provided information is as follows:

P (A) = 0.71

P (B) = 0.21

P (C) = 0.08

P (D|A) = 0.16

P (D|B) = 0.19

P (D|C) = 0.15

(a)

The law of total probability states that:

[tex]P(X)=\sum\limits_{i} P(X|Y_{i})\cdot P(Y_{i})[/tex]

Compute the probability that the student made the​ Dean's list as follows:

[tex]P(D)=P(D|A)P(A)+P(D|B)P(B)+P(D|C)P(C)[/tex]

         [tex]=(0.16\times 0.71)+(0.19\times 0.21)+(0.15\times 0.08)\\=0.1136+0.0399+0.012\\=0.1655[/tex]

Thus, the probability that the student made the​ Dean's list is 0.1655.

(b)

Compute the probability that the student came from a private high school, given that the student made the Dean's list as follows:

[tex]P(B|D)=\frac{P(D|B)P(B)}{P(D)}[/tex]

             [tex]=\frac{0.21\times 0.19}{0.1655}\\\\=0.2410876\\\\\approx 0.2411[/tex]

Thus, the probability that the student came from a private high school, given that the student made the Dean's list is 0.2411.

(c)

Compute the probability that the student was not home schooled, given that the student did not make the Dean's list as follows:

[tex]P(C^{c}|D^{c})=1-P(C|D^{c})[/tex]

               [tex]=1-\frac{P(D^{c}|C)P(C)}{P(D^{c})}\\\\=1-\frac{(1-P(D|C))\times P(C)}{1-P(D)}\\\\=1-\frac{(1-0.15)\times 0.08}{(1-0.1655)}\\\\=1-0.0815\\\\=0.9185[/tex]

Thus, the probability that the student was not home schooled, given that the student did not make the Dean's list is 0.9185.

Answer:

mulitply

Step-by-step explanation:

PEMDAS

mutiply

divide

add

and subtract

Answer:

The coordinates of Bodega is B(1,-2)

The coordinates of OWL Barbershop is O(3,-1)

Step-by-step explanation:

Coordinates of House H = (-3,-4)

Coordinates of Job J= (5,0)

His first stop is at the bodega to get something to eat. The bodega is exactly halfway between his house and the school.

Let B to represent the Bodega

Now to find coordinates of Bodega we will use use mid point formula since  bodega is exactly halfway between his house and the school.

[tex]x=\frac{x_1+x_2}{2} , y = \frac{y_1+y_2}{2}\\(x_1,y_1)=(-3,-4)\\(x_2,y_2)=(5,0)\\x=\frac{-3+5}{2} , y = \frac{-4+0}{2}\\x=1, y = -2[/tex]

So, The coordinates of Bodega is B(1,-2)

Now we are given that The OWL Barbershop location partitions the way from Wilfred’s house and job in the ratio 3:1.

Le O to represent OWL Barbershop.

We will use section formula

[tex]x=\frac{mx_2+nx_1}{m+n} , y =\frac{my_2+ny_1}{m+n}\\(x_1,y_1)=(-3,-4)\\(x_2,y_2)=(5,0)\\m:n=3:1\\x=\frac{3(5)+1(-3)}{3+1} , y =\frac{3(0)+1(-4)}{3+1}\\x=3,y=-1[/tex]

So, The coordinates of OWL Barbershop is O(3,-1)

Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

8=6 2/5

50=40

100=80

Step-by-step explanation:

8x4/5=6 2/5

4x10=40 so 5x10=50 (I got this from the second row)

5x20=100 so 4x20=80 (also from second row)

Answer:

D

Step-by-step explanation:

just flip the fraction

Answer:

D

Step-by-step explanation:

The reciprocal is just the fraction flipped.

Answer:

The largest three-digit number divisible by 24 and 54 is:

Step-by-step explanation:

To identify the largest number what I did was dividing 999 (the largest whole three-digit number of all) in the first number given (24):

With this number, you know that you must multiply 24 by a number like 41 or less until you find a number that can be divisible by 54 and obtain a whole number, so:

Now, you have identified that the number 864, you can prove it by dividing this in 24 and 54:

Answer: Mathematical distance is defined as the amount of space between two points. This distance can be calculated using the distance formula, which is just a derivation of the Pythagorean theorem, which is used to find the length of any one side of a right triangle when you know the other two sides

Step-by-step explanation:

Answer:

-3/2, -2, 0, 2.1, 7/3

Step-by-step explanation:

Please correct me if I am wrong. Thank you.

Answer:

1. x > 9

2. n < 5

3. b > 2

4. p < 4

5. p < -2

6. m > 0

Step-by-step explanation:

1.

x - 2 - 2 > 5

x - 4 > 5

x > 5 + 4

x > 9

2.

5 + n < 2 x 5

n < 10 - 5

n < 5

3.

50b > 100

b > 100 : 50

b > 2

4.

-5 + p + 2 < 1

p < 1 + 3

p < 4

5.

p + 6 + 8 < 12

p + 14 < 12

p < 12 - 14

p < -2

6.

80m - 64 - 2 > -66

80m > -66 + 66

m > 0:80

m > 0

Answer: 2

Step-by-step explanation: ( l + w )

Answer:

A, D ,E

Step-by-step explanation:

18/30

Divide the top and bottom by 6

3/5

A.15/25  Divide top and bottom by 5  = 3/5

B.6/11  cannot be simplified

C.3/4 cannot be simplified

D.3/5 cannot be simplified

E. 9/15​  divide top and bottom by 3 = 3/5

Answer: $24

Step-by-step explanation: if you divide $120 by 5 then you get $24

Answer:

m∠WXZ = 38°

m∠ZXY = 52°

Step-by-step explanation:

In the question

∵ ∠WXY is a right angle

→ That means its measure is 90°

∴ m∠WXY = 90°

∵ m∠WXZ + m∠ZXY = m∠WXY

∵ m∠WXZ = (5x + 3)°

∵ m∠ZXY = (8x - 4)°

∵ m∠WXY = 90°

→ Substitute their values in the equation above

∴ (5x + 3) + (8x - 4) = 90

→ Add the like terms in the left side

∵ (5x + 8x) + (3 - 4) = 90

∴ 13x + (-1) = 90

∴ 13x - 1 = 90

→ Add 1 to both sides

∴ 13x - 1 + 1 = 90 + 1

∴ 13x = 91

→ Divide both sides by 13

∴ [tex]\frac{13x}{13}=\frac{91}{13}[/tex]

∴ x = 7

→ To find the measure of each angle substitute x by 7 in their measures

∵ m∠WXZ = 5x + 3

∴ m∠WXZ = 5(7) + 3

∴ m∠WXZ = 35 + 3

∴ m∠WXZ = 38°

∵ m∠ZXY = 8x - 4

∴ m∠ZXY = 8(7) - 4

∴ m∠ZXY = 56 - 4

∴ m∠ZXY = 52°

Answer:

(0,3)

Step-by-step explanation [0,3] indicates that the numbers are greater or equals to 0 and less than or equals to 3; while (0,3) leaves out the equal sign

Answer:  6g2−9g+4

Step-by-step explanation: 3g2+−g+3g2+−8g+4

=(3g2+3g2)+(−g+−8g)+(4)

=6g2+−9g+4

Answer:

x=3

Step-by-step explanation:

We are given the equation, 6x-2=x+13.

1. 6x=x+15

2. 5x=15

3. x=3

Hope this helps! Good luck on your assignment!

Answer: x=3

Step-by-step explanation:

6x-2=x+13

First get both x’s on one side

We are going to subtract x from both sides

5x-2=13

Now we want to get 5x alone

We are going to add 2 to both sides

5x=15

Now we want to get x alone

We are going to divide by 5

x=3

Answer:

1 1/2 kilometers

Step-by-step explanation:

She ran 1/4 of a kilometer and then ran another 10/8 kilometer.

The 5 minute rest is to throw people off, so ignore it.

10/8 can simplify to 5/4 kilometers, so you can add that to the first quarter of a kilometer she already traveled.

5/4 plus 1/4 equals 6/4.

6/4 can be simplified to 3/2 which is equal to one and one half.

1   1/2

Hope this helps!

Answer:

no solution

Step-by-step explanation:

[1]    6x - 9y = 16

  [2]    2x - 3y = 7

// Solve equation [2] for the variable  x  

 [2]    2x = 3y + 7

 [2]    x = 3y/2 + 7/2

// Plug this in for variable  x  in equation [1]

  [1]    6•(3y/2+7/2) - 9y = 16

  [1]    0 = -5 =>  NO solution

No solution

Answer:

(-1,0)

Step-by-step explanation:

Answer:

(-1, 0)

Step-by-step explanation:

The x-axis is the horizontal line in bold. It's basically asking what points in the form (x,y) are touching said line.

So we use our eyes and determine that the line intercepts the x-axis at -1 because that vertical bold line is the y-axis and it determines that the left side of the graph is negative and the right side is positive.  

Since it is an x-intercpet, when the y-value is 0 the y-term in

(x,y) is 0

and the x-term would be the -1

Answer:

3

Step-by-step explanation:

Usually, when there is contamination the smallest amount can have huge ramifications in the data collected. In this scenario, if in a "clean" environment the trait is found in 2/10 frogs then anything above this number should be considered contaminated. This is because data above this ratio would be considered uncommon or rare and this unique occurrence can be most likely tied to the only new factor which would be the contamination. Therefore the minimum number of frogs with this trait in the sample would be 3.

Answer:  y = 5

Step-by-step explanation:

If the slope is 0, the graph of the line is a horizontal line (parallel to the x-axis).   0 slope means it is flat.

Here it passes through the y-axis  at +5 and passes through every value of x.

Answer:

See below

Step-by-step explanation:

(a) the equation

(b) If f(t) = 1000000