1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
WITCHER [35]
3 years ago
10

An instructor wants to write a test with 25 questions where each question is worth 3, 4, or 5 points based on difficulty. He wan

ts the number of 3-point questions to be 4 less than the number of 4-point questions, and he wants the quiz to be worth a total of 100 points. How many 3, 4, and 5 point questions could there be?
Mathematics
1 answer:
irakobra [83]3 years ago
3 0

ANSWER

Find out the how many 3, 4, and 5 point questions could there be.

To proof

Let us assume that the 3 points based question be = x

Let us assume that the 4 points based question be = y

Let us assume that the 5 points based question be = z

As given

An instructor wants to write a test with 25 questions

than the equation become in the form

x + y + z = 25

he quiz to be worth a total of 100 points.

than the equation is becomes

3x + 4y + 5z =100

As given

He wants the number of 3-point questions to be 4 less than the number of 4-point questions

x = y -4

Than the three equation are

x + y + z = 25 ,3x + 4y + 5z =100 and x = y -4

put  x = y -4 in the x + y + z = 25 ,3x + 4y + 5z =100

than

2y + z = 29, 7y +5z= 112

multiply 2y + z = 29 by 5 and subtracted 7y +5z= 112

10 y -7y + 5y -5y = 145 -112

3y = 33

y = \frac{33}{3}

y =11

put in the  x = y -4

x = 11-4

x= 7

put the value of x ,y in the x + y + z = 25

7 + 11 +z =25

18 +z = 25

z = 25 -18

z=7

therefore

numbers of the 3 point question be = 7

numbers of the 4 point question be = 11

numbers of the 5 point question be = 7

Hence proved



You might be interested in
What is the measure of angle 4?​
LUCKY_DIMON [66]

Answer: Where is angle 4?? Not enough info

8 0
3 years ago
In the diagram below, the angle of depression from the top of the lighthouse to a speed boat is 27 degrees.  The base of the lig
elixir [45]

Answer:

=

412

feet

Step-by-step explanation:

The angle of depression is always measured from the horizontal.

A triangle is formed by the lighthouse, the ground and the boat. The angle of depression is not in the triangle, but it is equal to the angle of elevation at the boat. (Alternate angles on parallel lines)

The angle at the top of the lighthouse, inside the triangle is:

90°−27°

=63°

The distance to the boat is the side opposite the angle of

63°

while the height of the lighthouse is the adjacent side.

opposite

adjacent

=tan 63°

distance

210=tan 63°

distance=210×tan 63°=412 feet

7 0
3 years ago
Read 2 more answers
Jamie has 7/10 of a pound of chicken to cook for dinner if she is going to split the chicken between 3 people how much chicken w
Arisa [49]

7/10÷3=7/10×1/3=7/30

8 0
3 years ago
Read 2 more answers
What the answer to this equation X/8+4=5 ?
V125BC [204]

Answer:

The answer to this equation is 8

Step-by-step explanation:

\frac{x}{8} +4=5\\

<u>First: Subtract</u>

8-4=4

5 > 4 meaning that 5 is greater than 4.

You still need another number to make it equal than or greater than or equal to five.

5-4=1

Since 5 minus 4 does equal 1

You need somewhere to divide it from to get 1 so you can add up the 4 to it and get the answer to the equation.

<u>Lastly: Divide</u>

\frac{8}{8} =1

1+4=5\\5=5\\4\neq 5

Now, if you do 8/8 which equals 1, 1+4 = 5; Now everything is, <u>equaled</u> up!

<u>So in conclusion...</u>

\frac{x}{8} +4=5\\x=8\\\frac{8}{8}=1\\1+4=5\\5\neq5

3 0
3 years ago
Read 2 more answers
I need help with this problem
cupoosta [38]
\bf \begin{cases}&#10;(n^4)^p=n^{12}\to &n^{4\cdot p}=n^{12}\to 4p=12&#10;\\&#10;&\qquad \uparrow \\&#10;&\textit{same bases, thus}\\&#10;&\qquad \downarrow &#10;\\&#10;n^3\cdot n^q=n^6\to &n^{3+q}=n^6\to 3+q=6&#10;\end{cases}&#10;\\\\\\&#10;thus\implies &#10;\begin{cases}&#10;4p=12\implies p=\frac{12}{4}&#10;\\\\&#10;3+q=6\implies q=6-3&#10;\end{cases}&#10;\\\\&#10;&#10;\\\\&#10;then\implies p\cdot q=\boxed{?}
7 0
3 years ago
Other questions:
  • Can someone check if this is right? simple probability but i am unsure if my answer
    7·1 answer
  • PLEASE HELP ASAP STUCK HELP PLEASE
    8·1 answer
  • Which measurement is the best estimate for the thickness of a phone book?
    6·2 answers
  • What is 50% of 20 in a fraction?
    14·2 answers
  • The weight of water is 62 1/2 lb per cubic foot. what is the weight of 20 1/2 cubic feet of water? How much does 20 1/2 cubic fe
    6·1 answer
  • Which expression is equivalent to 3(10-4y)
    6·1 answer
  • What is the value of x in the equation 3(4x-) - 2x+1=3 - (3x-6)?​
    9·1 answer
  • Help me! The question is in the image
    14·1 answer
  • What function would reveal the minimum of f(x) = 2x^2 + 8x + 6
    7·2 answers
  • There were 340 shoppers at an electronics store on opening day. The specials that day allowed 21% of shoppers to receive a free
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!