Answer:
(a) 7 essays and 29 multiple questions
(b) Your friend is incorrect
Step-by-step explanation:
Represent multiple choice with M and essay with E.
So:
[tex]M + E= 36[/tex] --- Number of questions
[tex]2M + 6E = 100[/tex] --- Points
Solving (a): Number of question of each type.
Make E the subject of formula in [tex]M + E= 36[/tex]
[tex]E = 36 - M[/tex]
Substitute 36 - M for E in [tex]2M + 6E = 100[/tex]
[tex]2M + 6(36 - M) = 100[/tex]
[tex]2M + 216 - 6M = 100[/tex]
Collect Like Terms
[tex]2M - 6M = 100 - 216[/tex]
[tex]-4M = - 116[/tex]
Divide both sides by -4
[tex]M = \frac{-116}{-4}[/tex]
[tex]M = 29[/tex]
Substitute 29 for M in [tex]E = 36 - M[/tex]
[tex]E = 36 - 29[/tex]
[tex]E = 7[/tex]
Solving (b): Can the multiple questions worth 4 points each?
It is not possible.
See explanation.
If multiple question worth 4 points each, then
[tex]2M + 6E = 100[/tex] would be:
[tex]4M + xE = 100[/tex]
Where x represents the number of points for essay questions.
Substitute 7 for E and 29 for M.
[tex]4 * 29 + x * 7 = 100[/tex]
[tex]116 + 7x = 100[/tex]
Subtract 116 from both sides
[tex]116-116 + 7x = 100 -116[/tex]
[tex]7x = 100-116[/tex]
[tex]7x = -16[/tex]
Make x the subject
[tex]x = -\frac{16}{7}[/tex]
Since the essay question can not have worth negative points.
Then, it is impossible to have the multiple questions worth 4 points
Your friend is incorrect.
The test contained 29 multiple choice questions and 7 essay questions.
Let x represent the number of multiple questions and y represent the number of essay questions.
Given that there are a total of 36 questions, hence:
x + y = 36 (1)
Also, the test is worth a total of 100 points, hence:
2x + 6y = 100 (2)
Solving equation 1 and 2 simultaneously gives:
x = 29, y = 7
Therefore the test contained 29 multiple choice questions and 7 essay questions.
Find out more at: https://brainly.com/question/16763389
Which is the coefficient in the expression 7pie+ 142
Answer:
7pie
Step-by-step explanation:
On average, Carter can get ready in 25 minutes but, depending on the day, his time can vary from the average by 15 minutes.
Which absolute value equation can be used to calculate Carter's maximum and minimum time to get ready?
Let x represent the maximum and minimum time.
|x−15|=25
|x+15|=25
|x+25|=15
|x−25|=15
Answer:
x-25=15 or D
Step-by-step explanation:
I promise that is the answer
3kg of meat costs £54
Nina buys 2 kg of the meat.
Work out how much Nina pays
Answer:
£36
Step-by-step explanation:
3kg = 54
÷ 3
1kg = 18
18 × 2 = 36
hope this helps...
Which statements are true? Select all that apply.
A. m∠WZX = 34°
B. m∠WXY = 123°
C. m∠XYZ = 46°
D. m∠WPZ = 90°
Answer:
C. and D.
Step-by-step explanation:
C.) Angle sum property, as XY = ZY
3.
%.
Paul says that the grids show 150%.
Rebecca says that they show 75%
How could each be correct?
9514 1404 393
Answer:
Paul is using 1 grid = 100%; Rebecca is using 2 grids = 100%
Step-by-step explanation:
We assume that a full grid and half of another are shaded.
If 1 grid is taken to be 100%, then the total amount shaded is 100% +50% = 150%, as Paul says.
__
If the two full grids are taken to be 100%, then the full shaded grid is 50% of the total, and the additional half-shaded grid is 25% of the total. That makes a total of 50% +25% = 75% of the total being shaded, as Rebecca says.
A customer bought 8.5 pounds of apples from a local produce market. If 1 pound = 16 ounces, how many ounces of apples did
the customer buy?
112 ounces
112 ounces
128 ounces
128 ounces
120 ounces
120 ounces
136 ounces
136 ounces
Answer:
136 ounces
Step-by-step explanation:
8.5*16=136
So 136 ounces
Which expression doe
11/15-1/6
Answer:
Exact Form:
17/30
Decimal Form:
0.56
Step-by-step explanation:
Answer:
0.56 i think
Step-by-step explanation:
Work out the percentage change to 2 decimal places when a price of £8.95 is increased to £10.
Answer:
12% increase
Step-by-step explanation:
Divide the difference between the two prices by the original price:
1.05/8.95
= 0.12
So, the percent change is 12%
What is the measure of XYZ?
State the equation of the line which has the y-intercept :
a) 2 and slope 7 .
b) -1 and is parallel to y= 5x - 7.
c) 2 and is inclined at 45 degree to the x- axis.
Answer:
A general line is written as:
y = a*x + b
where:
a is the slope
b is the y-intercept.
a) y-intercept = 2 and slope = 7.
This line is:
y = 7*x + 2
b) y-intercept = -1 and is parallel to y= 5x - 7.
Now, if two linear equations are parallel if they have the same slope and different y-intercept. Then if we want a line parallel to y= 5x - 7, this means that the slope of this line must also be equal to 5.
y = 5*x + (-1)
c) y-intercept 2 and is inclined at 45° to the x- axis.
When we have an inclination of A degrees from the x-axis, the slope of the equation is given by: a = Tan(A)
In this case, we have A = 45°
Then the slope is a = Tan(45°) = 1
Then the equation of this line is:
y = 1*x + 2
please help me on this.
Answer:
here
Step-by-step explanation:
so most of the time it would land on brown only 5% of the time would it land on red and the other there is a 0% chance
Solve. y −3 = 1 6 y =
Step-by-step explanation:
y - 3 = 16y original problem
y - 3 - y = 16y - y grouping variables
-3 = 15y Simplification
-3÷15 = 15y÷15 Isolating the variable
-1/5 = y the answer
I hope this helps!!!!!!
a local restaurant purchased 10 pounds of flour at a total cost of $40. what is the cost for one pound of flour?
Answer:
4 dollars a pound
Step-by-step explanation:
4x 10 = 40
Identifying the Rate of Change
Warm-Up
Which statements are correct? Check all that apply.
The graph shows the linear relationship between the
height of a plant (in centimeters) and the time in
weeks) that the plant has been growing.
The rate of change is 4.
The rate of change is 1.
24
y
20
The rate of change is 4.
16
Height (cm)
The plant grows 4 cm in 1 week.
o me plant grows 1 cm in 4 weeks.
12
Time (weeks)
Answer:
Data collected shows that the more you water, the larger your plant will grow. If you use the following Equation, y = 1/2x + 2 How tall will a plant be at 25 weeks if x is the number of weeks watered and y represents the height of the plant? Show your work.
Step-by-step explanation:
A total of 559 tickets were sold for the school play. They were either adult tickets or student tickets. There were 59 more student tickets than adult tickets. How many adult tickets were sold?
Answer: The answer is 500 hope this helps!
Step-by-step explanation:
WILL GIVE BRAINLIEST
3. Determine the amount of an investment of $500.00 is invested at an interest rate of 4.75% compounded quarterly for 20 years.
Step-by-step explanation:
Use the compound interest formula:
A = P( 1 + r/n)^nt
A is the amount at the end
P is the principal or original amount.
R is annual rate as a decimal (you have to convert)
N is the # of compounding periods in a year (quarterly means 4)
T is time in years
A = 500( 1 + 0.0475/4)^(4×20)
This would be $1285.64 when fully computed.
please help me please will give brainliest to
can yall help me with this one
Answer:
The answer for the dropdown section in x section is 5 and the answer for the dropdown section in the y section is 75
Step-by-step explanation:
Answer:
2 Pumpkins / 15 Dollars
5 Pumpkins / 37.5 Dollars
10 Pumpkins / 75 Dollars
Step-by-step explanation:
2 pumpkins for 15 dollars
that is what we have to work with here
the first step would probably be to figure out how much one pumpkin is, so we should divide the amount that we spent by the amount of pumkins that we got, which would look like
15 / 2 = 7.5
so 1 pumpkin = 7.5 dollars
now, to figure out how many pumpkins you can buy with 37.5 dollars, you would divide the amount of money spent by the amount that each pumpkin costs, which turns out to be
37.5 / 7.5 = 5
Now, to figure out how much money you would need for 10 pumpkins, you would multiply the number of pumpkins by the cost of a single pumpkin, which ends up being
10 x 7.5 = 75
8 x 6 = (4 x 6) (__x 6)
= 24 + __
=
Answer:
8x6= (4x6) + (4x6)
= 24+24
= 48
Step-by-step explanation:
Hope this helps :)
Answer:
8×6=48
4×6=24 and 24×2=48
So I'm guessing 4,24,48
what information is necessary to prove two triangles are similar by SAS similarity thereom?
Answer:
two sides and an angle of the triangle should be equal
PLEASE HELP!! WILL MARK BRAINLIEST!!!!
Answer:
Choice A (-18.75 or -75/4)
At a fundraiser, a school group charges $6 for tickets for a "grab bag." You choose one bill at random from a bag that contains 39 $1 bills, 19 $5 bills, 3 $10 bills, 7 $20 bills, and 3 $100 bills. Is it likely that you will win enough to pay for your ticket?
Answer:
no, the probability is only about 18%
Step-by-step explanation:
there are total of 71 bills of varying denominations in the bag
you need to select a bill that is $10 or more to cover your $6 expense; therefore, P($ ≥ 10) = 3 + 7 + 3 / 71 or 13 /71, about 18%
Evaluate the expression if p = 1,1=-7, and s= -2.
-3p-21
6+4s
Plzz hurry!!
Convert 40.64 centimeters to inches.
1 Inch = 2.54 centimeters
PLS HELP!!!
help me nowwwww!!!!!!
Answer:
its the second one
Step-by-step explanation:
it's the only one where the x number dosent repeat
6x-8y-x+3y please this is hard
6x-8y-x+3y
= (6x-x)+(-8y+3y)
= 5x+(-5y)
=5x-5y
Answer:
5x-5y
Step-by-step explanation:
Equation;
6x-8y-x+3y(Group like terms)
Which is going to be;
6x-x-8y+3y
Then you proceed to simplify;
5x-5y
This is the final answer
Triangle A C D is shown. A line is drawn from point D to point B on side A C to form a right angle. Line A D is labeled s. The length of A B is 8, the length of B C is 5, and the length of B D is 15.
What is the value of s
Answer:
17 units
Step-by-step explanation:
just took the quiz
Answer:
17 units.
Step-by-step explanation:
Hope it helps!!!
1.8 to 1 decimal place
Step-by-step explanation:
1.8
8 is 1 decimal place
1./8
8 > 5
1 change to 2
2.0
Solve the system of equations by using the substitution method. 4x - 5y = 25 y=x-6
Answer:
x=5
Step-by-step explanation:
substitute y to the first expression
4x-5(x-6)=25
4x-5x+30=25
-x=25-30
-x=-5
times left and right hand side with minus youll get
x=5
A method for solving 5(x - 2) = 10 is shown below. Which step shows
distributive property?
A. 5x+2=10
B.5x-2=10
C.5x+10=10
D.5x-10=10
Answer:
D
Step-by-step explanation: