Let x represent the number of math problems that you completed.
Let y represent the number of biology problems that you completed
From the information given,
You completed a total of 15 problems. This means that
x + y = 15
If each math problem takes 5 minutes to complete, it means that the time to complete x math problems is 5 * x = 5x
If each biology problem takes 3 minutes to complete, it means that the time to complete y biology problems is 3 * y = 3y
If you spent 51 minutes working on your homework problems for math and
biology, it means that
5x + 3y = 51
Thus, the system of equations is
x + y = 15
5x + 3y = 51
A group of friends traveled at a constant rate. They traveled 2/5 of a mile in 1/4 of an hour.Which of the following statements are true about this unit rate? Select all that apply.A divide 2/5 by 1/4 to find the unit rate per hour B The average speed will be less than 1 mile per hour because the group travels less than a fourth of a mile in1/4 of an hour C The group traveled at an average speed of 1 3/5 miles per hour.D The average speed will be greater than 1 mile per hour because the group travels more than a fourth of a mile in1/4 of an hour .E The group traveled at an average speed of 2 1/4 of a miles per hour.
The distance traveled, d = 2/5 miles = 0.4 miles.
The time taken to travel 0.4miles is given as, t = 1/4 hr = 0.25 hr.
Thus, the average speed, s = distance traveled divided by time taken.
i.e.
[tex]\begin{gathered} \text{average speed = }\frac{distance\text{ traveled}}{\text{time taken}}\text{ = }\frac{0.4}{0.25}\text{ } \\ \text{average sp}eed\text{ = 1.6 miles/hr} \end{gathered}[/tex]we can now go through the options and see the correct answers:
option A is correct because unit rate per hour is the same thing as average speed
option B is wrong because average speed is greater than 1mile/hr from our calculation above
option C is wrong because 13/5 gives us 2.6 miles/hr
option D is correct because the average speed is indeed greater than 1
option E is wrong because average speed is 1.6 miles/hr not 2 1/4 miles/hr
Thus, the answers are:
Option A and Option D
Victor received an 8-year subsidized student loan of $24,000 at an annual interest rate of 4.55%. If victor qualifies for an income-adjusted repayment plan of $500 per month, how long (in months) will it take him to repay the loan?
Time taken by Victor to repay the subsidized student loan of $24,000 at an annual interest rate of 4.55% is equal to 59 months.
As given in the question,
Principal = $24000 (given)
Rate of interest = 4.55% (given)
Time duration of subsidized loan = 8 years (given)
Repayment (equated monthly instalment) rate = $500 per month
To find: time for Victor to repay loan
We know that Principal + Simple Interest = Amount
Let t be the expected time duration for repayment of the subsidized student loan for Victor
24000+[tex]\frac{(24000).(4.55).t}{100}[/tex] = 500x12t (Simple Interest = Principal x Rate x Time)/100
=> 24000 + 1092t = 6000t
=> 4908t = 24000
=> t = 4.89 years ≈ 59 months
Therefore, it will take 59 months for Victor to repay the subsidized student loan of $24,000 at an annual interest rate of 4.55%.
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Find a formula for the general term a n of the sequence assuming the pattern of the first few terms continues. { 8 , 6 , 4 , 2 , 0 , ... } Assume the first term is a 1
The general term aₙ of the sequence is aⁿ = 10 - 2n
How to find the general term of a sequence?The sequence follows a arithmetic patterns.
Therefore, arithmetic pattern is described by the following formula,
aₙ = a + (n - 1)d
where
a = first term of the sequencen = number of termsd = common difference of the sequenceTherefore,
a = 8
d = 6 - 8 = -2
Hence, the general term of the sequence is as follows;
aₙ = 8 + (n - 1)-2
aₙ = 8 + (-2n + 2)
aₙ = 8 - 2n + 2
aⁿ = 10 - 2n
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SAT scores are normed so that, in any year, the mean of the verbal or math test score should be 500 and the standard deviation 100. Assuming this is true, answer the following question.
What percentage of students score between 400 and 600 on the verbal SAT? Please round to a whole number.
The percentage of students that score between 400 and 600 on the verbal SAT is 11%.
How to calculate the percentage?It should be noted that from the information, SAT scores are normed so that, in any year, the mean of the verbal or math test score should be 500 and the standard deviation is 100.
Therefore, the percentage of students score between 400 and 600 on the verbal SAT will be:
Z = (625 - 500) / 100
Z = 125 / 100
Z = 1.25.
We will then look at the z table. This will be:
P(Z > 1.25) = 0.11
The percentage is 11%.
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Evaluate the expression when x = 6. (- 2 ) * (-3 x )-4x
noah is running a portion of a marathon at a constant speed of 6 miles per hour.
The miles he ran in 4/3 hours at a constant speed of 6 miles per hour is 8 miles.
What is the average speed?The average speed is the ratio of total length traveled to total time taken to travel that length. Average speed is the total distance travelled per time.
Average speed = the total distance / total time
Given that Noah's average speed is 6mph
From the above formula, to determine miles run is average speed x time
The Total miles he ran in 1 hour = 6 x 1 = 6 miles
Total miles he ran in 1/2 hours = 6 x 1/2 = 3 miles
Total miles he ran in 1 and 1/3 hours = 6 x 4/3 = 8 miles
The formula for the total time: total distance / average speed
The Time it took Noah to run 1 and 1/2 miles = 3/2 ÷ 6 = 1/4
Time it took Noah to run 9 miles = 9 ÷ 6 = 1 1/2
Time it took Noah to run 4 and 1/2 miles = 9/2 ÷ 6 = 3/4
The miles he ran in 4/3 hours at a constant speed of 6 miles per hour is 8 miles.
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The complete question is
Noah is running a portion of a marathon at a constant speed of 6 mph. Complete the table to predict how long it would take him to run different distances at that speed and how far he would run in different time intervals.
Time in hours Miles traveled at 6mph
1.
1/2
1 1/3
1 1/2
9
4 1/2
Translate the sentence into an equation.
Eight less than the product of 4 and a number is 9
Use the variable w for the unknown number
Answer:
8-(w x4)=6
Step-by-step explanation:
all you have to do is just follow the words and plug the number in
The radius of a circle is 36 cm. A second circle has a radius of
6 cm. What is the ratio of the area of the larger circle to the area
of the smaller circle?
Answer:
36 : 1
Step-by-step explanation:
Hello!
Let's find the area of each circle in it's exact value, and then compare it.
Circle 1A = πr²A = π(36)²A = 1296πCircle 2A = πr²A = π(6)²A = 36πSince the values of pi are equal , we can compare the ratio of 1296 and 36.
Compare1296 : 3636:1The ratio is 36:1.
Describe the transformation of f(x)=x2 represent by g
G(x) = [tex]x^{2}[/tex] + 4 is the transformation of f(x)=[tex]x^{2}[/tex] represented by g.
The change mentioned comes from f(x)=[tex]x^{2}[/tex], g(x) = x² + 4
The value of h determines the horizontal shift. The formula for the horizontal shift is g(x)=f(x+h). The graph has been moved left by h units.
g(x)=f(x-h)
The graph is moved right by h units.
The graph is not moved left or right in this instance because h=0.
No Horizontal Shift
The value of k determines the vertical shift. The formula for the vertical shift is g(x)=f(x)+k. The graph has been raised k units.
g(x)=f(x)-k The graph is moved k units downward.
Shift vertically up four units.
When g(x)=-f, the graph is mirrored on the x-axis (x)
No reflection on the x-axis
When g(x)=f, the graph is mirrored on the y-axis (x)
No reflection on the y-axis
Depending on the value of a, compressing and expanding.
When an exceeds 1, the line is extended vertically.
In the range 0 to 1, an is vertically compressed.
Vertical Stretch or Compression: None
Compare the transformations and make a list.
No Horizontal Shift
Shift vertically up four units.
No reflection on the x-axis
No reflection on the y-axis
Vertical Stretch or Compression: None
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Add (7x^3-2x^2-5x+6) and (2x^3+3x^2-x-1)
Answer:
(9x^3+x^2-6x+5) is the answer to algebra equation
What is 321 x 21398?
The multiplication of the given values of 321 x 21398 is 6868758.
What is multiplication operation?Multiplication operation can be described as the operation which involves the addition of numbers that are of equal groups which is been performed using the sign *.
When performing a multiplication operation a value will be used to multiply another values, for instance the given question, where 321 was given to multiply 21398, which can be represented as (321 x 21398 ) then we now have 6868758 as the result of the multiplication operation.
Therefore, after performing the multiplication operation on the given values the result will be 6868758.
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I went to Old Navy and found a pair of pants on sale for $24. This price was 15% off the original price. What was the original price?
An individual with $36,000 in taxable
income pays $970 for the 10% tax
bracket, and $3,156 for the 12% bracket.
What is the overall federal income tax
payment for this individual?
A. $32,900
C. $4,126
B. $2,136
D. $3,656
The federal income tax is levied against the yearly profits of people, companies, and other legal entities. The overall federal income tax payment of this individual will be $4126.
What is federal Income tax?The federal income tax is levied against the yearly profits of people, companies, and other legal entities. Federal income taxes are due on all compensation, including salaries, monetary gifts from employers, business profits, tips, winnings from gaming, bonuses, and unemployment benefits.
Income taxes are levied by the federal government and the majority of states in the US. Income taxes, which may be incurred as income increases, are produced by applying a tax rate to taxable income, which is the total income less allowable deductions.
The overall federal income tax payment of this individual exists $970 + $3,156 = $4126.
The taxable income of the individual will be $4126.
Therefore, the correct answer is option C. $4,126.
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1. Tim wants air conditioning in his room. The air conditioner costs $40. Each day the
electricity costs $1. Write an expression that can be used to find the cost to run the air
conditioner for d days.
Answer:
the answer/expression you require is 40 - 1 = 1 day x - 1 = day 2 (repeat day 2 forever
Step-by-step explanation:
i say this because - 40 for the air conditioner and if it’s - 1 for electricity a day then unless your buying an air conditioner every day i don’t think you,l be repeating day 1 every day
:D
Send answers please and thanks. ILL GIVE BRAINLIEST
a. The approximation of each population written in scientific notation is
China : 1.4 × 10⁹ people
United States : 3.2 × 10⁸ people
b. 1.06 × 10⁹ people live in China than in the United States
Writing Scientific NotationFrom the question, we are to write the approximation of each population in scientific notation
From the given information,
China has a population of approximately 1,382,323,332 people
The United States has a population of about 324,118,787 people
Using scientific notation, the population of
China is 1.382323332 × 10⁹
United States is 3.24118787 × 10⁸
Approximately,
China : 1.4 × 10⁹
United States : 3.2 × 10⁸
To determine how many more people live in China than in the United States
1,382,323,332 - 324,118,787
= 1,058,204,545
= 1.058204545 × 10⁹
≈ 1.06 × 10⁹
Hence, the number of people that live in China than in the United States is 1.06 × 10⁹
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I NEED HELP ASAP ILL PAY YOU
The translation T₁: (x,y) → (x+7, y - 5) is applied to rectangle JKLM.
Next, the translation T₂: (x,y) → (x − 1, y +9) is applied to the rectangle.
What is the image of L(-9, -9) after the two translations are applied?
-
6-Mr. Lofters has 7/8 of a gallon of blue paint. He needs to distribute the blue paint out equally to his students. If Mr. Lofters pours 1/16 of a gallon of blue paint into each cup, how many cups of blue paint can he get? IMAGINE WHAT IS HAPPENING IN THE PROBLEM. WHAT OPERATION WILL BE INVOLVED? WHICH NUMBER WILL GO FIRST? LOOK FOR KEYWORDS. DO YOU REMEMBER THE FISH SONG?? YOU'LL REALLY FLIP IF YOU DON'T GET THIS ONE RIGHT.
We need to distribute 7/8 of a gallon into cups of 1/16 of a gallon. It means that to know the number of cups, we need to divide 7/8 into 1/16.
So, let's remember how to make a division between two fractions:
[tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c}[/tex]Then, the division of 7/8 into 1/16 is equal to:
[tex]\frac{\frac{7}{8}}{\frac{1}{16}}=\frac{7\cdot16}{8\cdot1}=\frac{112}{8}=14[/tex]Therefore, he gets 14 cups of blue paint.
Answer: 14 cups
find the difference between 289.6 and 99.9
Answer:
189.7
Step-by-step explanation:
Hope it helps! =D
Please help me get the anwser im not sure if im right.
we have the expression
[tex]2(y-z)(r-s)[/tex]Applying distributive property
[tex]\begin{gathered} 2(y-z)(r-s) \\ 2(yr-ys-zr+zs) \\ 2yr-2ys-2zr+2zs \\ \end{gathered}[/tex]therefore
There are 4 terms
The answer is option BA chicken soup recipe calls for 13 cups of chicken stock. How much is this in quarts?Write your answer as a whole number or a mixed number in the simplest form. Include the correct unit in your answer.
ANSWER
[tex]3\frac{1}{4}qt[/tex]EXPLANATION
We want to find how much chicken stock will be needed in quarts.
To convert a value from cups to quarts, we have to divide it by 4.
Therefore, the amount of chicken stock needed, in quarts, is:
[tex]\begin{gathered} \frac{13}{4} \\ \Rightarrow3\frac{1}{4}qt \end{gathered}[/tex]That is the answer.
Compute the requested average.
Tim Worker received a statement. It showed 3 payments totaling $158.14.
In dollars and cents, the average payment was $
The average payment of Tim worker is $52.71 .
The Average of n numbers can be defined as sum of n numbers divided by n .
For Example : Average of 2,4,5,9 is
=(2+4+5+9)/4
=20/4
=5
In the question ,
it is given that
Sum of amount Tim Worker received = $158.14
number of payments received = 3
So the Average payment for Tim worker can be calculated using the formula
Average = (Sum of payment)/(number of payment)
Substituting the values of Sum of payment and number of payment , we get
Average = 158.14/3
= 52.71
The average payment of Tim worker is $52.71 .
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Answer:
$52.71
Hope It Helps. (HIP).
Identify the parent function for the function g (x) = x + 4 based on its function rule. Then graph g and identify the transformation of the parent function that it represents.Linear; translation up 4 unitsConstant; translation up 4 unitsLinear; translation down 4 unitsConstant; translation down 4 units
linear; translation up 4 units
Explanation:The given function is:
g(x) = x + 4
This is of the form:
y = mx + c
where m is the slope and c is the y-intercept
Therefore, g(x) is a linear function
The parent function is:
g(x) = x
g(x) = x + 4 means that the function is translated up 4 units
lve the inequalityr divided by negative 3.2 is greater than or equal to 7.6 for r.
r ≥ −24.32
r ≤ −24.32
r ≥ 2.375
r ≤ −2.375
The solution for r of the inequality as described in the task content; r divided by negative 3.2 is greater than or equal to 7.6 is; r ≤ −24.32.
What is the solution for r of the inequality given?It follows from the task content that the inequality given is required to be solved for r.
Since the given inequality according to the task content is;
( r / -3.2 ) ≥ 7.6
Then, by multiplying both sides of the inequality given by; -3.2 in which case the inequality sign is reversed, we have;
r ≤ ( -3.2 × 7.6)
r ≤ -24.32.
Therefore, the solution of the inequality for the variable, r as required is; r ≤ −24.32.
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Suppose you have a $60000 loan with an annual percentage rate of 8% for 25 years? Requires monthly payment?
The required monthly payment is $ 180,000
How to calculate SI?Simple interest is the cost of borrowing money that does not take compounding into consideration. In other words, just the principal is affected by simple interest. Simple interest is calculated by multiplying the principal by the time, interest rate, and time period. "Simple Interest = Principal x Interest Rate x Time" is the written formula.
Given: Principal= $60000
Rate= 8% and time= 25 years
To calculate the monthly payment use the formula:
Simple interest=PRT/100
= 60,000×8×25/100
=120,000
And total amount accrued will be $180,000.
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hey can someone help me with this problem? please I’m really stuck :/
Answer:13x+150<400
Step-by-step explanation:
13(19)+150<400
247+150<400
397<400
Answer:
I think is c but I'm not sure
D
Let a be a number such that 15 < a < 50, and let b be
a number such that 40 < b < 70. Which of the
following represents all possible values of a - b?
A. -55 < a - b < 10
B. 20
C. -55 < a - b <-20
D. -25 < a - b < 10
Answer:
A
Step-by-step explanation:
PLS HELP MEEEEEEEEEEEEEEEEEEEEE PLS I BEG U
how could you use a graph of a proportional relationship to find any ratio in the the proportional relationship why does this work?
When the graph of a proportional connection passes through the origin, the ratio in the proportional relationship can be found.
How to illustrate the information?The connection is proportional if the graph is a line through the origin. This relationship is non-proportional unless the line or ray is non-proportional. K = y/x is the formula for the constant of proportionality. The formula for the slope of a straight line with respect to the origin is the same as this.
If the graph is a line or lines through the origin, the relationship is proportional. If the line or ray does not pass through the origin, it will not be proportional. Also, anything that is not linear is not proportional
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10.
A container has 20 ½ cups of pancake mix. A serving uses exactly 2½ cups.
Part A
How many full servings are in the container?
Part B
How many cups of pancake mix are left over?
full serving
If D = 1 + 4p – 6p2 and C =1-p, find an expression that equals 2Dstandard form.
Find the perimeter of ABO. A) 90 u B) 60 u C) 75 u D) 55 u E) 80 u
Answer:
Step-by-step explanation:
is the base of the triangle 30?