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stepladder [879]

3 years ago

5

An arts academy requires there to be 6 teachers for every 144 students and 3 tutors for every 27 students. How many students doe

s the academy have per teacher? Per tutor? How many tutors does the academy need if it has 63 students?

1 answer:

Nataliya [291]3 years ago

3 0

-There would be 24 students per teacher.
-If there were 63 students the academy would need 7 tutors.

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during Sonia's trip across the country that she travel 2884 miles her trip took 7 Days find a unit rate to represent the average

wolverine [178]

You could find the unit rate by dividing 2884 miles by 7 days to get 412 miles/ day

6 0

4 years ago

Two linear functions are shown. Which function has the greater initial value?

tangare [24]

Answer:

Function A has the greater initial value because the initial value for Function A is 6 and the initial value for Function B is 3.

Step-by-step explanation:

✔️Function A:

Initial value = y-intercept (b)

y-intercept is the value of y, when the corresponding value of x = 0

From the table, y = 6 when x = 0.

The y-intercept of function A = 6

Therefore, initial value for Function A = 6

✔️Function B:

y = 4x + 3 is given in the slope-intercept form, y = mx + b.

b = y-intercept = initial value.

Therefore

Initial value for Function B = 3

✔️Function A has the greater initial value because the initial value for Function A is 6 and the initial value for Function B is 3.

4 0

3 years ago

A milk container capacity is one gallon. How many cups would that equal ?

nekit [7.7K]

<span>1 gallon = 4 quarts = 8 pints = 16 cups </span>

6 0

3 years ago

Which is the inverse of the function a(d)=5d-3? And use the definition of inverse functions to prove a(d) and a-1(d) are inverse

Drupady [299]

Answer:

$a'(d) = \frac{d}{5} + \frac{3}{5}$

$a(a'(d)) = a'(a(d)) = d$

Step-by-step explanation:

Given

$a(d) = 5d - 3$

Solving (a): Write as inverse function

$a(d) = 5d - 3$

Represent a(d) as y

$y = 5d - 3$

Swap positions of d and y

$d = 5y - 3$

Make y the subject

$5y = d + 3$

$y = \frac{d}{5} + \frac{3}{5}$

Replace y with a'(d)

$a'(d) = \frac{d}{5} + \frac{3}{5}$

Prove that a(d) and a'(d) are inverse functions

$a'(d) = \frac{d}{5} + \frac{3}{5}$ and $a(d) = 5d - 3$

To do this, we prove that:

$a(a'(d)) = a'(a(d)) = d$

Solving for $a(a'(d))$

$a(a'(d)) = a(\frac{d}{5} + \frac{3}{5})$

Substitute $\frac{d}{5} + \frac{3}{5}$ for d in $a(d) = 5d - 3$

$a(a'(d)) = 5(\frac{d}{5} + \frac{3}{5}) - 3$

$a(a'(d)) = \frac{5d}{5} + \frac{15}{5} - 3$

$a(a'(d)) = d + 3 - 3$

$a(a'(d)) = d$

Solving for: $a'(a(d))$

$a'(a(d)) = a'(5d - 3)$

Substitute 5d - 3 for d in $a'(d) = \frac{d}{5} + \frac{3}{5}$

$a'(a(d)) = \frac{5d - 3}{5} + \frac{3}{5}$

Add fractions

$a'(a(d)) = \frac{5d - 3+3}{5}$

$a'(a(d)) = \frac{5d}{5}$

$a'(a(d)) = d$

Hence:

$a(a'(d)) = a'(a(d)) = d$

7 0

3 years ago

You have $814 that you want to share equally between 5 charities.

kifflom [539]

Answer:

give each charity $60

Step-by-step explanation:

$814 to divide equally to 5 charities.

From 814 if we give -100, -100, -100, -100, -100, we have left 314 to split in 5

the most useful next step is to give each charity $60

From $814 if we give -100, -100, -100, -100, -100

-60, -60, -60, -60, -60

we have left now:

814 -5*100 -5*60 = 814-500-300 = $14 left to split among the 5 charity.

6 0

3 years ago