Your math teacher tells you that the next test is worth 100 points and contains 38 problems. Multiple-choice questions are worth 2 points each and word problems are worth 5 points. How many of each type of question are there?
Answers
x isthe number of multiple choice questions, and y is the number of word problems, we can write a system of equations like:
{ x + y = 38
{ 2x + 5y = 100
If we multiply the first equation by -2 we get:
{ -2x-2y = -76
{ 2x + 5y = 100
Now if we add both equations we get only equation with 1 unknown (y) :
3y = 24 ⇒ y = 8
Substituting the calculated value to the first equation we get:
x + 8 = 38 ⇒ x = 30
The solution:
{ x = 30
{ y = 8
means that:
The test had 30 multiple choice questions, and 8 word problems.
Related Questions
13/16 - 1/4.¿ using 5th grade work
Answers
Answer:
[tex]\frac{9}{16}[/tex]
Step-by-step explanation:
Answer:
9/16
Step-by-step explanation:
1/4x4=4/16 13/16-4/16=9/16
Lisa is making ethernet cables for Mrs. Houston in the computer lab. The spool of wire that she is creating the cables from is 40ft long. She creates 5 equal cables and has 12ft remaining. What was the length of each cable? (HOW DID YOU GET YOUR ANSWER PLEASE SHOW ME YOUR WORK!!)
A. 16.6%
B. 50%
C. 20%
D. 5.6FT
E. $29.40
F. $30.40
G. 6.3FT
H. 25%
Answers
Answer:
D. 5.6 ft
Step-by-step explanation:
40 ft - 12 ft = 28 ft (You subtract the leftover wire(12 ft) from the total amount(40 ft) so you can see how much wire was used to make the 5 cables. There was 28 ft of wire in total used to create the 5 cables.) 28 ÷ 5 = 5.6 ft (You divide 28 by 5 so that you can see how much wire was used for each cable.)Final Answer: The length of each cable was 5.6 ft or just 5.6 ft.“The length of the unknown side has to be greater than ___ and less than ___.” PLEASE HELP, WILL GIVE BRAINLIEST
Answers
Answer:
7< 8
Step-by-step explanation:
Centerpieces are normally distributed with mean of 30 ounces and standard deviation of 2 ounces. The weights of the shipping boxes are normally distributed with mean of 12 ounces and standard deviation of 1 ounce. Suppose that centerpieces are chosen at random and packed into randomly chosen shipping boxes.If a package exceeds 45 ounces, an additional charge is incurred. What is the proportion of packages will incur such a charge
Answers
Answer:
0.0901 = 9.01% of packages will incur such a charge
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Sum of normal variables:
When we add normal variables, the mean will be the sum of the means, while the standard deviation is the square root of the sum of the variances.
Centerpieces are normally distributed with mean of 30 ounces and standard deviation of 2 ounces.
This means that [tex]\mu_C = 30, \sigma_C = 2[/tex]
The weights of the shipping boxes are normally distributed with mean of 12 ounces and standard deviation of 1 ounce.
This means that [tex]\mu_S = 12, \sigma_S = 1[/tex]
Suppose that centerpieces are chosen at random and packed into randomly chosen shipping boxes.
The shipment is given by the centerpice plus the shipping box. So the mean and the standard deviation of the weight are given by:
[tex]\mu = \mu_C + \mu_S = 30 + 12 = 42[/tex]
[tex]\sigma = \sqrt{\sigma_C^2 + \sigma_S^2} = \sqrt{2^2 + 1^2} = \sqrt{5} = 2.236[/tex]
If a package exceeds 45 ounces, an additional charge is incurred. What is the proportion of packages will incur such a charge
This proportion is 1 subtracted by the pvalue of Z when X = 45. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{45 - 42}{2.236}[/tex]
[tex]Z = 1.34[/tex]
[tex]Z = 1.34[/tex] has a pvalue of 0.9099
1 - 0.9099 = 0.0901
0.0901 = 9.01% of packages will incur such a charge
12 is 3 more than 7
True or False?
Answers
Answer:
false
Step-by-step explanation:
It is 5 more 7+3 is 10 and 5+7 is 12
Answer:
false
Step-by-step explanation:
false coz 12 is 5 more than 7 not 3
a discount of 15% is given on all t-shirt how much less is paid on such a T-shirt which ordinary cost $85
Answers
Answer:
$72.25
Step-by-step explanation:
85 x 15/100
85 x 0.15= 12.75
85- 12.75=
72.25
PLZ HELP! Sorry about the terrible picture but I had to take it quick cuz I need an answer fast.
Answers
Answer:
it will 90° because it is making right angle at C
Answer:
40 digree is the answer
brooo I think it will help u
Solve
2
X = 6.
x =
Help would be greatly appreciated
Answers
Answer:
x=3
Step-by-step explanation:
A coin will be tossed three times, and each toss will be recorded as heads (H) or tails (7). Give the sample space describing all possible outcomes. Then give all of the outcomes for the event that the second toss is heads. Use the format HTH to mean that the first toss is heads, the second is tails, and the third is heads. If there is more than one element in the set, separate them with commas. Sample space: Event that the second toss is heads: 0 Х ?
Answers
Answer:
A). {HHH, HHT, HTH, THH, TTH,THT,HTT,TTT}
(B). {HHH, HHT, THH, THT}
Step-by-step explanation:
Given:
A coin is to be tossed three times and each tossed will be recorded as Head(H) and Tails(T).
To Find:
(a). Sample Space
(b). Event that the second toss is Heads
Explanation:
(A). Sample Space: When a coin is tossed 3 times
{HHH, HHT, HTH, THH, TTH,THT,HTT,TTT}
(B). Event that second toss is Head
{HHH, HHT, THH, THT}
What is the degree of ADB
1.112°
2.86°
3.65°
4.68°
Answers
Answer:
I think it’s 1
Step-by-step explanation:
Because it’s a right triangle and it’s equal to 90° So
and 2,3,4 is less than 90 so
Atatürk ordular ilk hedefimiz Akdeniz ileri emrini aşağıdaki savaşlardan hangisinde vermiştir a Sakarya savaşı b 1. İnönü c 2. İnönü d büyük taarruz
Answers
Answer:
D şıkkı Büyük tarruz olmalı
Which of the fractions is equivalent to 3/8?
A. 2/7
B. 8/3
C. 9/24
D. 5/10
Answers
Answer:
I think its C. 9/24
Step-by-step explanation:
Holly shipped a 5-pound package for $4. She shipped a 3-pound package for $3.60 and a l-pound l package for $3.20. A 10-pound package cost $5 to ship. The cost follows a pattern based on the
weight. Which expression could be used
to find the shipping cost for a package
of p pounds?
Answers
Answer:
the answer would be A
Step-by-step explanation:
The cost seems to start at 3 and increase by each pound times .20 cents. Ex: 1 x .20 =.20 + 3 =3.20
What is the end behavior of the graph of the polynomial function y = 10x9 – 4x?
Answers
Answer:
The value of the highest degree ( x^9) is 9 - odd.
So this well rise from negative infinity on the left and rise to positive infinity on the right - or, putting it in a different way, fall to the left and rise to the right.
Answer:
Step-by-step explanation:
-4x-2y=-10
3x+y=4
Using substitution
Answers
Let get x from the first equation
-4x=+2y-10
x=-1/2y + 5/2
Now substitute the x in the second equation
3(-1/2y+5/2)+y=4
-3/2y + 15/2 + y =4
Move the terms without the y to the other side
-3/2y + y = -15/2 +4
Now multiple both side by 2
-3y +2y = -15+8
-y = -7
Y = 7 (ANSWER)
Now we substitute the y in the first equation so we can get the x
x = -1/2 (7) + 5/2
x = -7/2 + 5/2
x = -2/2
X = -1 (SECOND ANSWER)
Which values are solutions to the inequality square root of x is less than 8? A. 55 B. 8 C. -8 D. 4 E. 65 F. -64
Answers
9514 1404 393
Answer:
A. 55
B. 8
Step-by-step explanation:
We want ...
√x < 8
x < 8² . . . . . square both sides
x < 64
In order for the inequality to make any sense, we must also have ...
0 ≤ x
So, the solution space is ...
0 ≤ x < 64
Only answer choices A (55) and B (8) are in that range.
If someone can help me with this question i’ll thank them forever!!
Answers
Answer:
[tex]-\frac{3}{2}[/tex] < x or x > 4
Step-by-step explanation:
Convert the inequality to an equation.
2x² - 5x = 12
2x² - 5x - 12 = 0
Factor by grouping.
(2x + 3)(x - 4) = 0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
2x + 3 = 0
x - 4 = 0
Solve for x.
x = -3/2
x = 4
Use each root to create test intervals.
The solution consists of all of the true intervals.
[tex]-\frac{3}{2}[/tex] < x or x > 4
good luck, i hope this helps :)
What is true about (0, 5)
Answers
Answer:
0/5 equals zero as anything divided by zero gives zero. However 5/0 is an undetermined form which gives infinity.
Step-by-step explanation:
A company charges $60 per day plus $0.50
per mile for truck rentals. If Greg rents a
truck for 3 days and drives it a total of 150
miles, what will the company charge?
Answers
Answer:
$225
Step-by-step explanation:
$60 ×3=$180
150 ×$0.50 = $75
$180+ $75= $225
the company will charge $225
How could
you re-write the number 330 using the 4, 82 and the
remainder of 2 ?
Answers
Step-by-step explanation:
the answer for ur question is:
82(4)+2
एक कार की गति 92.4 किमी प्रति घंटा है यह 20 मिनट मे कितना दुरी तय करेगी
Answers
Answer:
mate I will surely help if nut pls translate it in English as I can barely read hindi
Can someone help me? I'd appreciate it
Answers
You can see the curve is at 5
IWHDHDNDJBFJDNX HELP!!!!!
Answers
Answer:
The answer should be B.
Step-by-step explanation:
I got the answer before. Can't remember if I was right. Also A can also be correct.
The line plot shows the amount of water collected after seven days of an experiment. Tina decides to evenly divide the water into 3 glas
Amount of Water
X
X
X X
+ +
1 1 3
0
2 4
Measurement (in cups)
1
How much water should go into each glass?
cup
O
1 cup
2 cups
3 cups
Answers
Answer: my brother did it and it's 1 cup
Step-by-step explanation:
Answer:
1 cup
Step-by-step explanation:
ive done this test in class if you need further explionation let me know
The students measured length during a science experiment,they got 12 cm.But the actual measurement was 14.25cm.what was the percent error?
Answers
Answer:
Percent error = 15.79%
Step-by-step explanation:
Given the following data;
Experimental value = 12cm
Actual value = 14.25cm
To find the percentage error;
Percent error can be defined as a measure of the extent to which an experimental value differs from the theoretical value.
Mathematically, it is given by this expression;
[tex] Percent \; error = \frac {experimental \;value - actual \; value}{ actual \;value} *100[/tex]
Substituting into the equation, we have;
[tex] Percent \; error = \frac {12 - 14.25}{14.25} *100[/tex]
[tex] Percent \; error = \frac {2.25}{14.25} *100[/tex]
[tex] Percent \; error = 0.1579 *100[/tex]
Percent error = 15.79%
Find the difference.
34(3x+6)−14(5x−24)
I need help
Answers
Answer:
I believe the answer is 32x+24 correct me if im wrong
Step-by-step explanation:
someone pls answer this i’ll mark u as brainleist.
Answers
la diferencia entre un numero y ocho
Answers
Answer:
hzyuzj ahuaaia hs7w8aijw. hu7sisj. shususijs bhsusj
Answer:
lo siento, no lo sé
Step-by-step explanation:
Find a solution to the linear equation 13x+y=26
Answers
Answer:
y = -13x+26
Step-by-step explanation:
13x+y=26
y= -13x+26
A construction worker drops a hammer while building the Grand Canyon skywalk 4,000ft above the Colorado River. Use the formula t=h‾√4 to find how many seconds it takes for the hammer to reach the river. Round your answer to the nearest tenth of a second.
Answers
Answer:
The hammer reaches the river after 15.8 seconds.
Step-by-step explanation:
The formula to find for how long it takes for the hammer to reach the ground is given by:
[tex]t = \frac{\sqrt{h}}{4}[/tex]
In which h is the initial height.
A construction worker drops a hammer while building the Grand Canyon skywalk 4,000ft above the Colorado River.
This means that [tex]h = 4000[/tex].
So
[tex]t = \frac{\sqrt{4000}}{4}[/tex]
[tex]t^2 = \frac{4000}{16}[/tex]
[tex]t^2 = 250[/tex]
[tex]t = \sqrt{250}[/tex]
[tex]t = 15.8[/tex]
The hammer reaches the river after 15.8 seconds.