Answers
The products of the fractions given are:
1. (-3/4)(7/8) → -21/32
2. (2/3)(-4)(9) → -24
3. (5/16)(-2)(-4)(-4/5) → -2
4. (2 3/5)(7/9) → 91/45
How to Multiply Fractions?To multiply two or more fractions, multiply the denominators of both fractions together, and their numerators together.
1. (-3/4)(7/8)
Multiply the denominators of the fractions together, and also multiply their numerators:
= (-3 × 7) / (4 × 8)
= (-21) / (32)
(-3/4)(7/8) → -21/32
2. (2/3)(-4)(9)
Multiply the denominators of the fractions together, and also multiply their numerators:
= (2 × -4 × 9) / (3)
= -72/3 = -24
(2/3)(-4)(9) → -24
3. (5/16)(-2)(-4)(-4/5)
= (5 × -2 × -4 × -4) / (16 × 5)
= -160/80 = -2
(5/16)(-2)(-4)(-4/5) → -2
4. (2 3/5)(7/9)
= (13/5)(7/9)
= (13 × 7)/(5 × 9) = 91/45
(2 3/5)(7/9) → 91/45
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Related Questions
Mr. Mole left his burrow and started digging his way down. A represents Mr. Mole's altitude relative to the ground (in meters) after t minutes.
Answers
Based on the model that shows the altitude of Mr. Mole relative to the ground, the rate at which Mr. Mole was digging was 2.3 meters down per minute.
How to find the rate?When given a linear function, the rate that the model progresses is given by the slope. The slope in a linear function can be found as:
y = mx + b
m = slope
b = y-intercept
In the model given for Mr. Mole's digging, which is -2.3t - 7, the slope is -2.3.
This means that Mr. Mole is digging downwards at 2.3 meters per minute.
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253 x 67 using the turtle method
Answers
The value of the expression 253×67 using the turtle method is given by 16951.
The turtle method of multiplication was designed in order to make the multiplication of larger numbers easier. The larger numbers can be multiplied imagining them as the form of a turtle's head and neck. It involves mainly three steps of multiplication. The first step includes the multiplication of the numbers lying on the neck of a turtle. The next step includes making the collar of the turtle, taking care of the carryovers, and laying the egg of the turtle. The last step involves the multiplication of the other numbers. In the question, we are given the expression 253×67. We multiply this expression in the turtle method as attached in the figure.
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twice the diffrence of a number and 2 equals 8
Answers
Answer:
2(x - 2) = 8
x = 6
Step-by-step explanation:
2(x - 2) = 8
2(x - 2) = 8
2x - 4 = 8
+4 +4
-----------------
2x = 12
÷2 ÷2
----------
x = 6
I hope this helps!
6b³ +16b² -15b-40
Factor
Answers
Answer:
(2[tex]b^{2}[/tex] - 5) (3b + 8)
Step-by-step explanation:
First factor out 2[tex]b^{2}[/tex] from the first set of parentheses and -5 from the second
2[tex]b^{2}[/tex] ( 3b + 8) - 5 (3b + 8)
Next factor out (3b + 8)
(2[tex]b^{2}[/tex] - 5) (3b + 8)
Julie is flying to New York. She has budgeted $200 to
rent a car for 3 days while she is there. If the car rental
is $44 per day plus $0.25 per mile, what is the
maximum number of miles Julie can drive the car?
Answers
The maximum number of miles Julie can drive the car is 272 miles.
Let's check how:
Julie's budget for renting a car is $200.
number of days she'll rent a car is 3.
car rental per day is $44 + $0.25 per mile.
so to know maximum no. of miles she can drive
we'll first subtract the 3 days rent from Julie's budget = $200 - ( 3 x $44 )
= $200 - $132
= $132
Now, the left money is $68.
so, we will divide $68 by $0.25 to know how much miles she can drive.
= $68 ÷ $0.25
= 272 miles
Hence, the maximum number of miles Julie can drive the car for 3 days is 272 miles.
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Answer:
Step-by-step explanation:
Create an Equivalent expression for 18^-7*18^5
Answers
Help, this is Math.
Dividing fractions
Answers
Step-by-step explanation:
don't panic. just breathe and then use common sense.
1.
1 math question in 1/200 second
2 minutes have 2×60 seconds = 120 seconds.
each of the seconds has 200 1/200 seconds.
so, in 2 minutes we have
120 × 200 time units to finish math questions.
in each time unit 1 math question can be answered.
120×200 = 24,000
the computer can answer 24,000 math questions in 2 minutes.
2.
it can run for 15 minutes.
15 minutes have
15×60 = 900 seconds (as every minute has 60 seconds)
it can vacuum 1/2 ft² in 1 seconds.
in 900 seconds it can then vacuum 900×1/2 = 450 ft².
so, yes, it can clean 400 ft² without recharging.
What is the percentage of 150 out of 329.5 million?
Answers
The number 150 is 0.0000455 % out of 329.5 million
How to determine the percentage?The statement is given as
the percentage of 150 out of 329.5 million
The percentage can be calculated as
Percentage = 150 out of 329.5 million *100%
Express as fraction
So, we have
Percentage = 150/329.5 million *100%
Rewrite as
Percentage = 150 *100/329.5 million %
Evaluate the product
Percentage = 15000/329.5 million %
Evaluate the quotient
Percentage = 0.0000455 %
Hence, the percentage of 150 out of 329.5 million is 0.0000455 %
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Mia is factoring the polynomial
x^2+4x−12. She uses the steps shown.
x^2+4x−12
Step 1
x^2+6x−2x−12
Step 2
(x^2+6x)−(2x+12)
Step 3
x(x+6)−2(x+6)
Step 4
(x+6)(x+2)
In which step did Mia make an error?
Answers
Answer:
Step 4
Step-by-step explanation:
Mia made a mistake in step 4.
Step3: x(x + 6) -2(x + 6)
In both terms, (x + 6) is common.
Step 4: When we take (x + 6) out, it will be (x + 6 ) (x - 2)
(9) 0.5= A. 3 B. 4.5 C. 1/81
Answers
The expression is 0.5=[tex]\frac{a\times3+b\times4.5+c\times1}{81}[/tex]. The evaluated expression is 3a+4.5b+c=40.5
Given that,
The expression is 0.5=[tex]\frac{a\times3+b\times4.5+c\times1}{81}[/tex]
We have to evaluate the expression
Evaluating an algebraic expression involves determining its value when a particular integer is substituted for a variable. We use the given number to replace the expression's variable before applying the order of operations to simplify the expression.
Take,
0.5=[tex]\frac{a\times3+b\times4.5+c\times1}{81}[/tex]
0.5×81=a×3+b×4.5+c
40.5=3a+4.5b+c
The expression can be written in 4 ways
1st- 3a+4.5b+c=40.5
2nd- a=[tex]\frac{40.4-4.5b-c}{3}[/tex]=13.4-1.5b-c (this is the expression with subject a)
3rd- b= [tex]\frac{40.5-3a-c}{4.5}[/tex]=9-1.6a-c (this is the expression with subject b)
4th- c= 40.5-3a-4.5b (this is the expression with subject c)
Therefore, The evaluated expression is 3a+4.5b+c=40.5
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Sandy is buying t shirts for her school. The company she called charges $5.75 per shirt plus a $35 set up fee. Write an expression that represents the total cost for x number of shirts?
Answers
The expression that represents the given condition is given by
5.75x + 35.
In mathematics, an expression that was created using integer variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)
However, since they are not produced from integer constants and algebraic operations, transcendental numbers such as such and e are not algebraic. The production of is often done as a geometric expression, but the definition of e requires an infinite number of algebraic operations. An expression is considered rational if it can be reduced to a rational fraction using the properties of arithmetic operations (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).If x shirts are bought, cost of x shirts at $5.75 = 5.75x
Set up fee $ 35
Total cost of x shirts = 35 + 5.75x
Therefore the required expression = 35 + 5.75 x
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Hello, please I need the right answer for this:
Answers
Answer: (4) [tex]y=2x[/tex]
When you look at the table, you can see that the y values are double the x values they are associated with. Therefore, to get to the y value, the x values must be multiplied by 2, which would be the equation [tex]y=2x[/tex]
On a plane, 2 men had 135 kilograms of luggage added together. The first paid $1.35 for his excess luggage and the second paid $2.70 for his excess luggage. The charge was at a flat rate. If all of the luggage belonged to one person, the ecess luggage charge would have been $8.10. At most, how many kilograms of luggag is each person permitted to bring onto the plane free of an additional charge?A. 55 kilogramsB. 50 kilogramsC. 45 kilogramsD. 40 kilograms
Answers
Let's call the amount of lugagge the first men had as x, and the amount of lugagge the second men had as y.
Since both had to pay for excess of luggage, both had the permitted amount of luggage plus an extra amount. Let's call the permitted amount as a, the extra the first men had as z, and the extra the second man had as w. Then, our total amounts of luggage can be rewritten as
[tex]\begin{gathered} x=a+z \\ y=a+w \end{gathered}[/tex]Since their total amount of luggage added together was 135 kg, this gives to us the following equation
[tex]x+y=135[/tex]The charge for the extra luggage is a flat rate, let's call it r, then, the price you pay for the extra luggage is given by the product between this rate and the amount of extar luggage. The first paid $1.35 for his excess luggage and the second paid $2.70 for his excess luggage, therefore
[tex]\begin{gathered} zr=1.35 \\ wr=2.70 \end{gathered}[/tex]If we divide one equation by the other, we can write the excess of luggage of one as a function of the other.
[tex]\begin{gathered} \frac{zr}{wr}=\frac{1.35}{2.70} \\ \frac{z}{w}=\frac{1}{2} \\ w=2z \end{gathered}[/tex]If all of the luggage belonged to one person, this person would have to pay $8.10 for the excess. If we call the excess of this person as p, the amount of luggage this person had would be
[tex]a+p=135[/tex]Using the "rate formula" we created before, we can also write p as a function of z.
[tex]pr=8.10\Rightarrow\frac{pr}{zr}=\frac{8.10}{1.35}\Rightarrow p=6z[/tex]Rewritting all the total amounts, we have
[tex]\begin{gathered} a+6z=135 \\ a+2z=y \\ a+z=x \end{gathered}[/tex]If we add the equations for x and y together, we have
[tex]\begin{gathered} (a+z)+(a+2z)=(x)+(y) \\ a+z+a+2z=x+y \\ 2a+3z=x+y \end{gathered}[/tex]From the first equation, we know that the sum between both total amounts of luggage is equal to 135.
[tex]\begin{cases}x+y=135 \\ 2a+3z=x+y\end{cases}\Rightarrow2a+3z=135[/tex]Now, we have two equations for our two variables.
[tex]\begin{cases}2a+3z=135 \\ a+6z=135\end{cases}[/tex]If we multiply the first equation by 2, and subtract the second equation, we're going to get a new equation only for a(the amount in kilograms of permitted luggage).
[tex]\begin{gathered} 2\cdot(2a+3z)-(a+6z)=2\cdot(135)-135 \\ 4a+6z-a-6z=270-135 \\ 3a=135 \\ a=45 \end{gathered}[/tex]The amount of luggage permitted to bring onto the plane for free is 45 kilograms.
he function y=f(x)y=f(x) is graphed below. What is the average rate of change of the function f(x)f(x) on the interval −1≤x≤0?
Answers
The estimate of the average rate of change f is -2
How to estimate the average rate of change f?The possible graph that completes the question is added as an attachment
The interval is given as
-1 ≤ x ≤ 0
This can be rewritten as
x = -1 to x = 0
This can also be represented as
(a, b) = (-1, 0)
From the attached graph, we have
f(-1) = 7
f(0) = 5
The estimate (to one decimal place) of the average rate of change f is
Rate = [f(b) - f(a)]/[b - a]
This gives
Rate = [f(-1) - f(0)]/[-1 - 0]
So, we have
Rate = [7 - 5]/[-1 - 0]
Evaluate
Rate = -2
Hence, the average rate of change f is -22
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Suppose you have a population with mean 25 and standard deviation 20. You take samples of size 100 and consider the distribution of the means of those samples. What is the mean of the sample means?.
Answers
The value obtained for z-score for the given sample mean is 0.5.
What is described as the z-score?A Z-score is a numerical quantification that describes the relationship of a value to the mean of a set of values. The Z-score is expressed in standard deviations of the mean. A Z-score of 0 signifies that the data point's points tally is the same as the mean score.For the given question;
The formula for finding the z-score is;
z = (x - μ)/σ
x = sample size
μ = population mean
σ = standard deviation population.
The given values are-
μ = 25σ = 20x = 35Put the value in the z-score.
z = (35 - 25)/20
z = 10/20
z = 0.5
Therefore, the value obtained for z-score for the given sample mean is 0.5.
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The correct question is-
Suppose you have a population with mean 25 and standard deviation 20. You take samples of size 100 and consider the distribution of the means of those samples. What is the z-score for the of the sample means for the sample less than 35?.
help me i need help.
Answers
Answer:108 inches
Step-by-step explanation:
to find the area of one of the right triangles you do.
base = 6/2 =3
3x6=18
18/2=9
there are 8 right triangles so you would do
9x8 = 72.
then you would add 72 and the area of the square in the middle
6x6=36
36+72= 108
so Area of SA = 108 inches ^2
the ratio as a fraction in simplest form, 26.1 miles : 3.6 hours ?
Answers
Answer:8.7:1.2
Step-by-step explanation: divide both by 3
evaluate log49 base 1/7
Answers
Answer:
Step-by-step explanation:
Exact Form:
1/2
Decimal Form:
-0.5
Answer:
- 2
Step-by-step explanation:
using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
given
[tex]log_{\frac{1}{7} }[/tex] 49 = n , then
49 = [tex](\frac{1}{7}) ^{n}[/tex]
49 = [tex](7^-1)^{n}[/tex] , that is
7² = [tex]7^{-n}[/tex]
since bases on both sides are equal then equate exponents
- n = 2 ( multiply both sides by - 1 )
n = - 2
Which of the contexts below represents exponential growth?
The amount of a certain medication in a person's bloodstream decreases by
every hour.
Snow was falling at a rate of 1.75 inches per hour.
A population of 200 bacteria quintuples every week.
A car depreciates at a rate of 5.3% per year.
Answers
Answer:
I believe it would be "A population of 200 bacteria quintuples every week"
Step-by-step explanation:
If it is quintupling each week then the number is getting larger and larger exponentially.
Fill in the blank to make a perfect square trigeminal x^+18x+
Answers
The number that fills in the blank to make a perfect square trigeminal of the given expression is 81.
Given expression:
[tex]x^2+18x +[/tex] _
We have to find the number that will fill the blank.
A perfect square trigeminal is an algebraic expression that is of the form ax 2 + bx + c, which has three terms. It is obtained by the multiplication of a binomial with itself.
Let the number that fills the blank be a.
Hence, the expression becomes:-
[tex]x^2+18x +a[/tex]
To make it a perfect square geminal, the expression must be a perfect square of a binomial.
We know that,
[tex](x+y)^2=x^2+2xy+y^2[/tex]
Comparing it with given expression, we get
2xy = 18x and,
[tex]y^2=a[/tex]
Hence,
y = 9
a = [tex]9^2[/tex] = 81
Hence, the number that fills the blank is 81.
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Elyse uses 42 gallons of water for a 10-minute
shower. Write and solve a prediction problem that uses this information.
Answers
Water used in three minutes in the shower is 12.6 gallons.
What is unit rate?An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.
Given Data
Elyse uses 42 gallons of water for a 10-minute shower,
Let
the time in minutes at position x
y=the quantity of water in gallons
The fact that
[tex]\frac{y}{x}[/tex] = [tex]\frac{42}{10}[/tex] = 4.2x
The unit price equals
The slope of the linear equation is equal to the unit rate.
then
y=4.2x
Problem
How much water will Elyse use in her shower for three minutes?
x = 3 minutes
substituting in the previous equation
y = 4.2x
y = 4.2(3)
y = 12.6
Water used in three minutes in the shower is 12.6 gallons.
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-(8-²)=
Evaluate the expressions
Answers
After evaluating the given expression -(8⁻²), the resultant expression is - 1/64.
What are expressions?An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules. A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.2x + 3 is an illustration of a mathematical expression with a variable. Each and every variable needs to have a coefficient or a value multiplied by the variable. The number 2 is the coefficient of x in the expression 2x + 3, which means 2 times x plus 3.So, -(8⁻²):
Now, evaluate -(8⁻²) as follows:
-(8⁻²)-(1/64)- 1/64Therefore, after evaluating the given expression -(8⁻²), the resultant expression is - 1/64.
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Sum of 8 consecutive numbers is 124. Find the numbers
i will mark you as brainliest for giving breif explanation step by step
Answers
Answer:
x = 12
Step-by-step explanation:
Be the 8 consecutive numbers like this:
x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) = 124
8x + 28 = 124
8x = 124 - 28
8x = 96
x = 12
State all integer values of x in the interval 3 ≤ x ≤ 9 that satisfy the following
inequality:
-4x+10> -7
Answers
The integer values of x in the interval 3 ≤ x ≤ 9 that will satisfy the inequality include 3, 4, 5, 6, 7, 8, and 9.
How to illustrate the information?It should be noted that an integer is simply used to represent a given number which can be positive.
From the information, we are given the information 3 ≤ x ≤ 9. This means that 3 is less than or equal to x and x is less than or equal to 9.
Therefore, the number that fits are from 3 to 9.
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The assets and liabilities of a credit union banker are listed below.
What is the total net worth is the banker pays off the student loans?
A. $219,869
B. $247,517
C. $233,693
D. $252,304
Answers
Given the credit union banker's assets and liabilities, their total net worth is C. $233,693.
What is the net worth?The net worth of an individual is the difference between their assets (long-term and short-term) and their liabilities (long-term and short-term).
The net worth is equivalent to the equity of a business, which refers to the net assets owned by the stockholders after paying off all debts.
Assets:Car Value = $29,850
Savings Accounts = $12,409
Treasury Bonds = $10,000
Checking Account Balance = $19,419
Home Value = $194,450
Total assets = $266,128
Liabilities:Car loan = $10,560
Student Loans = $13,824
Credit Card Balance = $8,051
Total liabilities = $32,435
Net worth = $233,693 ($266,128 - $32,435)
Thus, the banker's net worth is not $219,869, $247,517, or $252,304 but Option C.
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Answer:
$247,517
Step-by-step explanation:
ITS RIGHT ON THE TEST GUYS ! :)
The height of square room is Sm and volume is 180m³. Find the length.
Answers
Answer:
length = 6m
Step-by-step explanation:
H=5m
V=180m^3
Here
V=l^2 ×H ( being a square)
180=a^2×5
a^2=36
a=6m
By what number should you multiply $3\frac{1}{3}$ to get a product of $4$? Express your answer as a mixed number.
Answers
The number you should multiply 3 1/3 to get a product of 4 is 1 1/5
How to determine the number?From the question, the statement is given as
What number should you multiply 3 1/3 to get a product of 4
Let the number be x
So, we have the following representation
3 1/3 * x = 4
Express 3 1/3 as an improper fraction
So, we have the following representation
10/3 * x = 4
Multply both sides by 3
So, we have
10 * x = 12
Divide both sides by 10
This gives
x = 12/10
Express as mixed numbers
x = 1 1/5
Hence, the number is 1 1/5
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A line has a slope of 1/4 and includes the points (-6, -7) and (z, -5) what is the value of z
Answers
Slope is rise divided by run, which is (change in y) divided by (change in x).
See details:
Find the area of square plot of land whose each side measures 17/2
Answers
The area of the land is 289/4 square units
What are areas?The area of a shape is the amount of space on the shape
For most regular quadrilaterals, you multiply the side lengths to determine the area
How to determine the area of the shape?The given parameters are
Shape = Square
Side length = 17/2
The area of a square shape is
Area = Side length^2
So, we have
Area = (17/2)^2
Evaluate the exponent
Area = 289/4
Hence, the area of square plot of land whose each side measures 17/2 is 289/4 square units
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The table shows information about the
masses of some dogs.
a) Work out the minimum number of
dogs that could have a mass of more than 27 kg.
b) Work out the maximum number of
dogs that could have a mass of more than 27 kg.
Answers
a) The minimum number of dogs that could have a mass of more than 27 kg is 4.
b) The maximum number of dogs that could have a mass of more than 27 kg is 17.
The given table shows information about the masses of some dogs.
a) Because we need the minimum number of dogs,
Let's assume all dogs present in the interval 20 to 40 have a mass of more than 27kg so the minimum value out of 13 and 4 is 4.
b) Because we need the maximum number of dogs,
Let's assume all dogs present in the interval 20 to 40 have a mass of more than 27kg so the maximum of the values present in the interval 20 to 40 is 13 + 4 = 17
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Answer:
Step3
-by-step explanation: