The classroom had 25 glue sticks. If the ratio of glue sticks to glue bottles was 5 : 2, how many glue bottles did the classroom have?
5 sticks / 2 bottles
25 sticks / x bottles
10 bottles
Answer: 10 bottles
A student finished 8 of her homework problems in class. If the ratio of problems she finished to problems she still had left was 4 : 1, how many homework problems did she have total?
8 finished
4 finished / 1 left
8 finished / 2 left
10 total
Answer: 10 total problems
A recipe called for the ratio of sugar to flour to be 7 : 3. If you used 63 ounce of sugar, how many ounces of flour would you need to use?
7 sugar / 3 flour
63 oz sugar / x oz flour
27 oz flour
Answer: 27 oz flour
Write an equation for each using the variables provided.
For each pound there are 16 ounces.
Write an equation to express the total number of ounces (Z) in (Y) pounds.
1 lb / 16 oz
Z = 16Y
Equation: Z = 16Y
Every dollar is 4 quarters.
Write an equation to express the total number of quarters (Q) in dollars (D).
1 dollar = 4 q
Q = 4D
Equation: Q = 4D
Word Problems. You must show your work and answer to get full credit.
Henry and Grace had the same amount of money. After Henry spent $28 and Grace spent $16, the ratio of the amount of money Henry had to the amount of money Grace had was 2 : 5. How much money did each of them have at first?
You may create a tape diagram to help you.
(copy & paste)
( H - 28 ) / ( G - 16 ) = 2 / 5
H - 28 = 2
H = 30
G - 16 = 5
G = 21
Henry: 30
Grace: 21
Three clerks can type six documents in 12 days. At this rate, how long will it take for two clerks to type three such documents?
3 clerks take 12 days to write 6 docs
1 clerk takes 4 days to write 2 docs
2 clerks take 8 days to write 4 docs
8 : 4
3/4 * ( 8 ) : ( 4 ) * 3/4
6 : 3
6 days
You are assigned 32 math questions for homework. You complete 87.5% of these before dinner. How many questions do you have left to do after dinner?
Answer:
4 questions
Step-by-step explanation:
To find a percentage of a number, you move the decimal mark all the way to the left.
87.5% becomes 0.875
Next you multiply 32 by 0.875 to find the percentage of questions that are completed
32 x 0.875 = 28
28 out of 32 questions have been solved, so now you subtract 28 from 32
32 - 28= 4
There are 4 questions to complete
How do you do this question?
Answer:
Diverges
Step-by-step explanation:
3/(4ⁿ) = 3 (¼)ⁿ is a geometric series with r = ¼, which converges.
7/n is a harmonic series, which diverges.
The sum of a convergent series and a divergent series is divergent.
what value for x makes this equation true? 0.6x-5=0.1x+7
Translate the sentence into an equation.
Twice the difference of a number and 2 equals 6.
Use the variable b for the unknown number.
Answer:
2(b-2)=6
Step-by-step explanation:
Twice the difference means multiply the difference by two
It explains the difference being between the unknown number(b) and 2
The answer is said to be six
So you put the difference (b-2)
Multiply it 2(b-2)
and finally, add the answer: 2(b-2)=6
The equation for the given sentence is 2(b-2)=6 and the unknown number is 5.
Given that, twice the difference of a number and 2 equals 6.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Use the variable b for the unknown number.
2(b-2)=6
⇒ b-2=3
⇒ b=5
Therefore, the equation for the given sentence is 2(b-2)=6 and the unknown number is 5.
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What are the coefficients of this expression 7a+23b +2c + 16
Answer:
Step-by-step explanation:
A coefficient is basically the number infront of a variable or term.
E.g. the coefficient in 7x is 7
The coefficient in 23y is 23
The coefficient in 43a is 43.
So for your question: 7a + 23b + 2c + 16,
The coefficients are 7, 23 and 2
What is an equation of the line that passes through the points (0, -2) and (6,6)
Answer:
y= 4/3x -2 or y=1[tex]\frac{1}{3}[/tex] -2
Step-by-step explanation:
d+fg=h (solve for the variable “g”)
Answer:
g = h/f - d/f
Step-by-step explanation:
what is the range of y= square root of x+5
Answer:
Range: [5,∞),{y|y≥5}
Step-by-step explanation:
Set the radicand in √x greater than or equal to 0 to find where the expression is defined.
x≥0
the domain is all values of X that make the expression defined.
Interval Notation:
[0,∞)
Set-Builder Notation:
{x|x≥0}
The range of an even indexed radical starts at its starting point (0,5) and extends to infinity.
Interval Notation:
[5,∞)
Set-Builder Notation:
{y|y≥5}
Determine the domain and range.
Domain: [0,∞),{x|x≥0}
Range: [5,∞),{y|y≥5}
I hope this helps you. Sorry if it doesn’t!!!!
A triangle has vertices on the coordinate grid at points A(2, 4), B(2, 9) and C(5, 6) . What is the length, in units, of AB ?
Answer:
5 units long
Step-by-step explanation:
If you graph it, it is a simple straight line 5 units long between A and B.
You could also use the distance formula if you had to do more advanced distance calculations.
The distance formula is d=√((x2-x1)²+(y2-y1)²)
If you multiply a matrix and its inverse together, you will always get the identity
matrix.
True
False
Answer:
True
Step-by-step explanation:
If you multiply a matrix (such as A) and its inverse (in this case, A–1), you get the identity matrix I. And the point of the identity matrix is that IX = X for any matrix X (meaning "any matrix of the correct size", of course).
Answer:
Yes
Step-by-step explanation: And 1 is the identity, so called because 1x = x for any number x. It works the same way for matrices. If you multiply a matrix (such as A) and its inverse (in this case, A–1), you get the identity matrix I.
Cheryl read for 30 minutes twice yesterday.Today she read for twice as long as she did yesterday.choose the expression that is a correct translation of the problem.
Answer:
(30x2)x2
Step-by-step explanation:
Answer:
Step-by-step explanation:
O
A food scientist determine the new type of orange is 15.38 mg of vitamin c/oz how much vitamin C is in orange that weighs 6 3/5 oz in your answer as a decimal to the nearest 10th in the box
Answer:
(Sorry this is a late response) This fraction 6 3/5 would equal 6.6 so 6 3/5=6.6 Then you will do 6.6 times 15.38=101.508 or 101.5
Step-by-step explanation:
You would divide 3 and 5 or 5 and 3 because 3 and 5 equals the fraction 3/5. The dividend is 3 and the 5 is the divisor. The quotient of this is 0.6. So the next step would be to add the 6 from 6 3/5 so this is the whole number so add it in front of 0.6 so it would turn into 6.6. The last step is to multiply the weight of the orange by the mg of vitamin C/oz that is 15.38 so multiply 6.6 by 15.38 this would equal 101.508 so you would just round this to a better answer and that would make it 101.5. I hope this helps :0
Add and subtract the rational expressions.
Which statements are true about the process for adding and subtracting the rational expressions? Check all that apply. The expression is not defined when t = 0. The first step is to use the order of operations and simplify the expression inside the parentheses. The denominator will be simplified to 15t. The numerator will be simplified to 13t 8. The numerator will be simplified to 13t 2
Answer:
The numerator will simplified to 13t-2
Step-by-step explanation:
After you write the numerators with the common denominator, you collect like terms and then calculate.
Answer:
A , B , E
Step-by-step explanation:
Correct on edge 2021. Just did the assignment.
Have a good day <3
Find the polynomial function of degree 3 such that f(2)=24 and x-1, x and x+2 are factors of the polynomial
Answer:
f(x) = 3x^3 + 3x^2 - 6x.
Step-by-step explanation:
Let:
f(x) = x(x - 1)(x + 2)
= x(x^2 + x - 2)
= x^3 + x^2 - 2x - this might be the answer or it might be some multiple of this.
Now f(2) = 24 so
24 = a(2^3 + 2^2 - 2(2)) where a is a constant.
24 = 8a
a = 3
So the function is
3( x^3 + x^2 - 2x)
= 3x^3 + 3x^2 - 6x.
which value of x is the solution of the equation 2/3x + 1/2 = 5/6?
Answer:
2
Step-by-step explanation:
2/3(2) + 1/2 = 5/6
If it's 2/3 * X then x is equal to 1/2.
priya changed the rate at which flowed through the faucet. write an equation that represents the relationship w of t and when it takes 3 minutes to fill the cooler with 1 gallon of water. Which of the following equations represent the relationship between w and t? select all that apply.
Answer:
i love you sm
Step-by-step explanation:
The cost of renting a car is $20 to take the car and $4 for every hour that it is rented. The total amount Lucie paid was 546. For how many hours did Lucie have the car?
a. Define your variable.
b. Write an equation and solve.
c. Write a sentence to interpret your results.
h = time in hours
20 + 4h = 546
4h = 526
h = 131.5
131.5 hours
Solve the following inequality. Graph the solution.
4b + 3 < 19
Answer:
b<4 , I am not 100% sure on the graphing part and I have done this in 7th grade but I think it is A, not 100% sure.
15 ounces
2.5 servings
Answer:
6 ounces per serving
Step-by-step explanation:
If you divide 15 ounces by 2.5 servings, you get 6 ounces per serving. I guess this is what you are trying to find, and hopefully it helps!
(45 points!)
Line n contains points (3, 4) and (-6, -2). What is the slope of a line perpendicular to the given line?
Answer: -3/2
Step-by-step explanation:
Answer:
y=nx−2+6n
Step-by-step explanation:
I have used the slope-intercept form to find the answer.
Hope this helps :)
Evaluate −b2−2bx2−x when x=−2.
An expression is defined as a set of numbers, variables, and mathematical operations. The value of −b²−2bx²−x when the value of x=-2 is −b²−8b + 4.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The value of the expression −b²−2bx²−x will be,
−b² − 2bx² − x
= − b² − 2b(-2)² − (-2)
= − b² − 8b + 4
Hence, the value of −b²−2bx²−x when the value of x=-2 is −b²−8b + 4.
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Your paycheck is 500. If you want to save 2,000 dollars in one year, how much should you set aside from your paycheck each week
Answer:
how many weeks are in a year? 52 so 2000 / 52 = ?
Step-by-step explanation:
the question asks how many WEEKS to save 2000.... so just divide the weeks of one year into 2000 that you want to save for that year
my calculator says 2000/52=38.46
so save $ 38.46 each week
the sum and twice the number and 18 is greater than 25
Answer:
Step-by-step explanation:
45
can someone find the inverse and explain it step to step please!!!!!!! (FOR QUESTION 3)
Answer:
f^-1(x) = 4(x+5)/3
Step-by-step explanation:
Let f(x) = y
So, y = (3/4)x - 5
y + 5 = (3/4)x
4(y+5)/3 = x
The steps are first to make a variable that holds the same value as the function, then from there you simplify and eventually make x the subject of the equation.
Round 1,439 to the nearest ten
Answer:
1,440.
Step-by-step explanation:
39 is closer to 40.
1,400 is unchanged.
Maple tree diameters in a forest area are normally distributed with mean 10 inches and standard deviation 2.2 inches. Find the proportion of trees having a diameter less than 9 inches.
Answer:
0.32472
Step-by-step explanation:
Maple tree diameters in a forest area are normally distributed with mean 10 inches and standard deviation 2.2 inches. Find the proportion of trees having a diameter less than 9 inches.
The formula for calculating a z-score is z = (x-μ)/σ
where x is the raw score
μ is the population mean
σ is the population standard deviation
z = (9 - 10)/2.2
z = -1/2.2
= -0.45455
Probability value from Z-Table:
P(x ≤ 9) = P(x < 9)
= 0.32472
Therefore, the proportion of trees having a diameter less than 9 inches is
0.32472
The proportion of trees having a diameter less than 9 inches is 32.64%
z score is used to determine by how many standard deviations the raw score is above or below the mean.
It is given by:
[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x\ is\ raw\ score.\mu\ is\ mean,\sigma\ is \ standard \ deviation[/tex]
Given that μ = 10, σ = 2.2, hence:
[tex]For\ x<9:\\\\z=\frac{9-10}{2.2} =-0.45[/tex]
From the normal distribution table, P(x < 9) = P(z < -0.45) = 0.3264 = 32.64%
The proportion of trees having a diameter less than 9 inches is 32.64%
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Find the unknown value in the proportion.
4/7=?/14. please help
Answer:
8
Step-by-step explanation:
4/7 = ?/14
Multiply the numerator and denominator of the left fraction by 2.
8/14 = ?/14
That means that ? = 8
Answer: 8
Answer:
8
Step-by-step explanation:
Step 1:
4/7 = x/14 Proportion
Step 2:
7x = 56 Multiply
Step 3:
x = 56 ÷ 7 Divide
Answer:
x = 8
Hope This Helps :)
2d + 7 = 9
Hellllllpppppp
Answer:
Doesn't 2+7 = 9 itself?
Step-by-step explanation:
For a statistics project a community college student at Diablo Valley College decides to investigate cheating in two popular majors at DVC: business and nursing. She selects a random sample of nursing and business courses and convinces the professors to distribute a short anonymous survey in their classes. The question about cheating is one of many other questions about college life.
When the student summarizes the data, she finds that 42 of the 50 business students and 38 of the 70 nursing students admitted to cheating in their courses. Can the student proceed with the calculation of the confidence interval for the difference in population proportions?
Answer:
The student can proceed with the calculation of the confidence interval for the difference in population proportions. This is because, from the data she has, 3/4 of the Business students admitted to cheating while 1/2 of the Nursing students admitted to cheating also.
This is above the average number of students in her given sample size which is valid for extrapolation to the College Majors being investigated.
Step-by-step explanation:
Spencer is 10 years old. His age is two years less than three times his sister's age. How old is Spencer's sister?
The age of Spencer's sister is 4 years old.
What is an Equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, Spencer is 10 years old. His age is two years less than three times his sister's age.
Let the age of Spencer's sister be x
According to the question,
3x - 2 = 10
3x = 10 +2
3x = 12
x = 12/3
x = 4
Hence, The age of Spencer's sister is 4 years old.
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