choose a number between 67 and 113 as a multiple of 3, 5 and 10

Answer:

9

Step-by-step explanation:

we know by definition that

[tex]f^{-1}(f(x))=x\\\\f^{-1}(\frac{2x}{3})=x\\\\f^{-1}(x)=ax\\\\f^{-1}(\frac{2x}{3})=a(\frac{2x}{3})=x\\\\f^{-1}(x)=\frac{3x}{2}[/tex]

so now we evaluate

[tex]f^{-1}(6)=\frac{3*6}{2}\\\\=3*3\\\\f^{-1}(6)=9[/tex]

and if we want to do an extra step

[tex]f^{-1}(f(6))=6\\\\f^{-1}(\frac{2*6}{3})=f^{-1}(4)=\frac{3*4}{2}=6[/tex]

which works.

Answer:

The slope is 3

The y-intercept is -2

The linear equation is y = 3x - 2

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

∵ A line passes through points (2, 4) and (6, 16)

∴ x1 = 2 and y1 = 4

∴ x2 = 6 and y2 = 16

→ Substitute them in the rule of the slope above to find it

∵ m = [tex]\frac{16-4}{6-2}[/tex] = [tex]\frac{12}{4}[/tex] = 3

∴ m = 3

→ Substitute it in the form of the equation above

∴ y = 3x + b

→ To find b substitute x and y in the equation by the coordinates of

   a point on the line

∵ Point (2, 4) is on the line

∴ x = 2 and y = 4

∵ 4 = 3(2) + b

∴ 4 = 6 + b

→ Subtract 6 from both sides to find b

∵ 4 - 6 = 6 - 6 + b

∴ -2 = b

→ Substitute its value on the equation above

∵ y = 3x + (-2)

∴ y = 3x - 2

→ Let us answer the questions

The slope is 3

The y-intercept is -2

The linear equation is y = 3x - 2

Answer:

The answer is switched.

Step-by-step explanation:

Given that John's bank account is $10 which is a constant (fixed) amount and he make $120 per day.

In the equation, x act as number of days so if you wants to find how much he earn after few days, you have to multiply $120 with the number of days.

The correct equation will be y = 120x + 10, 120 is the slope value and 10 is the y-intercept.

Answer:

f(x)=-[tex]\frac{5}{2}\\[/tex]x+9

Step-by-step explanation:

Use the slope formula and slope intercept formula form y=mx + b to find the equation

yes

no

no

yes

hope it help!!!

Yes, no, no, yes I believe

Answer:

ΔABD is an obtuse triangle

Step-by-step explanation:

The type of a triangle according to its angle measures

In triangle ABD

∵ m∠ABD = 100°

∵ m∠BAD = 50°

→ The sum of the interior angles of a triangle is 180°

∴ m∠ABD + m∠BAD + m∠BDA = 180°

∴ 100 + 50 + m∠BDA = 180

∴ 150 + m∠BDA = 180

→ Subtract 150 from both sides

∴ m∠BDA = 30°

∵ m∠ABD = 100°

∴ ∠ABD is an obtuse angle

∵ m∠BAD = 50° and m∠BDA = 30°

∴ ∠BAD and ∠BDA are acute angles

∵ ΔABD has 1 obtuse angle and 2 acute angles

∴ ΔABD is an obtuse triangle

Answer:

3 shirts, 6 shorts

Step-by-step explanation:

A total of $264 is spent during shopping on shirts and shorts

Each shirt costs $24

Each shorts cost $32

Therefore the quantity of shirts and shorts bought can be calculated as follows

24× 3= 72

32×6= 192

192+72= 264

Hence 3 shirts and 6 shorts were bought

Step-by-step explanation:

2.6% b/c 1820×2.6/100

Answer:

1164 are the total number of miles he rode in 6 months.

Step-by-step explanation:

It means:

Thus,

Thus, the number of miles he rode in 6 months would be = 194×6 = 1164 miles

Therefore, 1164 are the total number of miles he rode in 6 months.

Answer:

A

Step-by-step explanation:

took test on edge

Answer:

A

Step-by-step explanation:

Just took the test

Answer:

Janet uses less than 4 cups of flour because is less than 4.

Step-by-step explanation:

She is using 3/8 of 4 so less than. Then you use 4 not 1 because there is 4 cups.

Answer:

She uses less than four cups because 3/8 (1.5) is less than 4.

Step-by-step explanation:

Answer:

what I think this question has mistake

Answer:

9

Step-by-step explanation:

we just replace n with 15

A(n) =16 + (N - 1) (-0.5)

      =16 + (15 - 1) (-0.5)

      =16-7.5+0.5

       =9

hope it helps

Answer:

-3.82

Step-by-step explanation:

You are going up the line of negative numbers so you have to add o.o2 to 3.8 (3.80).

Answer:

y=79/73x+644/73

theres the equation, enjoy <3

Answer:

She practiced a total of 64.5 hours

Step-by-step explanation:

Here, we need to know the number of hours practiced on both per day

Mathematically, that will be;

0.75 + 1.4 = 2.15 hours per day

So in 30 days ; the total number of hours will be

30 * 2.15 = 64.5 hours

Answer:

The type of function the equation represents is "directly proportional" ⇒ B

Step-by-step explanation:

Let us solve the question using the rules above

∵ The equation of the function is y = -8x

→ Compare it with the two forms above

∵ The equation is in the form of y = kx, where k = -8

∴ The equation represents directly proportional

∴ The type of function the equation represents is "directly proportional"

Answer:

D.20

Step-by-step explanation:

4*5=20

Answer: 45.65 is incorrect.

Step-by-step explanation: it’s a place value problem; right of the decimal is ones, tens, hundredths, thousandths which is 4 place values so 45.065 shows the correct placement

Answer:

Yes, he got the correct quotient

Step-by-step explanation:

1.5 divided by 1/3 is 4.5, and 4.5 is equal to 4 1/2

Answer:

Sage did it right.

your work:

1 1/2 ÷ 1/3

3/2 ÷ 1/3

3/2 × 3/1

9/2

4 1/2

Step-by-step explanation:

first convert 1 1/2 into an improper fraction:

multiply the 2 and 1, you get 2, than add that to the current numerator to get a new one. You get 3/2 as your improper fraction

you now have: 3/2 ÷ 1/3

then turn the division sign into a multiplication sign by flipping the divisor:

you get 3/2 × 3/1

solve this:

multiply the numerators together, you get 9 as a new numerator

multiply your denominators, you get 2 as your new denominator

so now you have 9/2

next turn this into a mixed fraction, you get 4 1/2

so Sage did it right.

Answer:

If Susan bought 12 ounces that would equal to .75 pounds

Step-by-step explanation:

Answer:

I think u kept option incorrect but the correct answer is 1/4

Step-by-step explanation:

Let x represent the number.

We have 8x - 6 = 7.

Therefore 8x = 13 and x = 1.625.

tan(2A) + sin(2A) = sin(2A)/cos(2A) + sin(2A)

• rewrite tan = sin/cos

… = 1/cos(2A) (sin(2A) + sin(2A) cos(2A))

• expand the functions of 2A using the double angle identities

… = 2/(2 cos²(A) - 1) (sin(A) cos(A) + sin(A) cos(A) (cos²(A) - sin²(A)))

• factor out sin(A) cos(A)

… = 2 sin(A) cos(A)/(2 cos²(A) - 1) (1 + cos²(A) - sin²(A))

• simplify the last factor using the Pythagorean identity, 1 - sin²(A) = cos²(A)

… = 2 sin(A) cos(A)/(2 cos²(A) - 1) (2 cos²(A))

• rearrange terms in the product

… = 2 sin(A) cos(A) (2 cos²(A))/(2 cos²(A) - 1)

• combine the factors of 2 in the numerator to get 4, and divide through the rightmost product by cos²(A)

… = 4 sin(A) cos(A) / (2 - 1/cos²(A))

• rewrite cos = 1/sec, i.e. sec = 1/cos

… = 4 sin(A) cos(A) / (2 - sec²(A))

• divide through again by cos²(A)

… = (4 sin(A)/cos(A)) / (2/cos²(A) - sec²(A)/cos²(A))

• rewrite sin/cos = tan and 1/cos = sec

… = 4 tan(A) / (2 sec²(A) - sec⁴(A))

• factor out sec²(A) in the denominator

… = 4 tan(A) / (sec²(A) (2 - sec²(A)))

• rewrite using the Pythagorean identity, sec²(A) = 1 + tan²(A)

… = 4 tan(A) / ((1 + tan²(A)) (2 - (1 + tan²(A))))

• simplify

… = 4 tan(A) / ((1 + tan²(A)) (1 - tan²(A)))

• condense the denominator as the difference of squares

… = 4 tan(A) / (1 - tan⁴(A))

(Note that some of these steps are optional or can be done simultaneously)

Answer:

a) The class interval containing the median is the interval 2 ≤ h <  3

b) The mean number of hours the children spent on their tablets is 2.2 hours.

Step-by-step explanation:

a) The given parameters are;

The number of students that spent 0 ≤ h < 1 hour = 4

The number of students that spent 1 ≤ h < 2 hours = 8

The number of students that spent 2 ≤ h < 3 hours = 11

The number of students that spent 3 ≤ h < 4 hours = 7

The median is given by the location of the 15th child which is located in the interval given as follows;

We note that the total number of children is obtained by adding the  frequencies of the intervals together, as follows;

The number of children = 4 + 8 + 11 + 7 = 30

The frequency of the first interval = 4

The sum of the first + Second intervals = 4 + 8 = 12

The sum of the first + Second + Third intervals = 4 + 8 + 11 = 23

Therefore, the class interval containing the median is the interval 2 ≤ h <  3

b) We use the midpoint of each class interval to find the mean as follows;

The mean = ∑fh/∑h

∴ The mean = (4 × 0.5 + 8 × 1.5 + 11 × 2.5 + 7 × 3.5)/(4 + 8 + 11 + 7) = 2.2

The mean number of hours the children spent on their tablets = 2.2 hours.