The weight of both books when put on the scale together is [tex]\frac{37}{24}=1\frac{13}{24}[/tex].
The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm), lowest common multiple (lcm), or smallest common multiple of two numbers a and b in mathematics and number theory.
Let the weight of the two books Paulette had be x and y.
The weight of one of the books is x = 7/8 pounds.
The weight of the other book is y = 2/3 pound.
If the books are put on the scale then the total weight of the books will be:
[tex]x+y=\frac{7}{8}+\frac{2}{3}[/tex]
The least common multiple or LCM of 8 and 3 is 24.
[tex]x+y=\frac{21+16}{24}[/tex]
[tex]x+y=\frac{37}{24}[/tex]
The correct option is (B) [tex]\frac{37}{24}=1\frac{13}{24}[/tex].
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• perform operations
on functions.
• perform
.
operations on
functions.
Use f(x) = -4x + 1, g(x)=x²-8x + 21, and h(x) = 19-3x]
1. Find f(-6)
Find h(8)-f(-7)
the graph of the function to answer each part.
on functions.
2.
y = f(x)
f(x)=-4x+1
h(x)=19-3x
Using the concept of function we can solve the question
What is a function?A function can be defined as an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
f(-6) can be found out by substituting x=-6 in f(x)
f(-6)=-4×(-6)+1
f(-6)=24+1
f(-6)=25
The question h(8)-f(-7) can be solved by first finding value of 8 in h(x)
h(8)=19-(3×8)
h(8)=19-24
h(8)=5
Now lets find f(-7)
f(-7)=-4×(-7)+1
f(-7)=28+1
f(-7)=29
Now we can find h(8)-f(-7) by substituting the values of h(8) and f(-7), which was found earlier
h(8)-f(-7)=5-29
h(8)-f(-7)=-24
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The correct question is " f(x)=-4x+1,h(x)=19-3x then find f(-6) and h(8)-f(-7)."
A bicycle is traveling at 22 miles per hour. How many feet will it cover in 40 seconds? Round your answer to the nearest tenth of a foot.
Savannah went into a bakery and bought 9 cookies and 3 brownies, costing a total of $18. Serenity went into the same bakery and bought 5 cookies and 2 brownies, costing a total of $10.75. Write a system of equations that could be used to determine the price of each cookie and the price of each brownie. Define the variables that you use to write the system.
9x+3y=18 and 5x+2y=10.75
where x is price of 1 cookie and
y is price of 1 brownie.
steps for writing Systems of Linear Equations from Word Problems:
Understand the problem. Understand all the words used in stating the problem. Translate the problem to an equation. take some variable to represent them.Carry out the plan and solve the problem.Savannah and Serenity were goes to the bakery for purchasing some cookies and brownies .
We have to write a system of linear equations for the given condition .
Let the cost of 1 cookie be $x and
cost of 1 brownie be $y
Savannah bought 9 cookies and 3 brownies at $18
so, linear equation for this situation is
9x+3y=18
Serenity bought 5 cookies and2 brownies at $10.75
so, linear equation for this situation is
5x+2y=10.75
Hence, System of equations for the given situation is
9x+3y=18 and
5x+2y=10.75
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Enola needs to order some new supplies for the restaurant where she works. The restaurant needs at least 767 spoons. There are currently 263 spoons. If each set on sale contains 12 spoons, use the drop-down menu below to write an inequality representing ss, the number of sets of spoons Enola should buy.
The number of sets of spoons Enola should buy is given by this inequality: ss ≥ 42.
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).Based on the information provided, the total number of sets of spoons after ss sets are purchased is given by:
T(ss) = 263 + 12ss
The number of sets of spoons needed by the restaurant is given by this inequality:
T(ss) ≥ 767
Substituting the value of T(ss) into the inequality above, we have;
263 + 12ss ≥ 767
12ss ≥ 767 - 263
12ss ≥ 504
ss ≥ 504/12
ss ≥ 42
In conclusion, the number of sets of spoons Enola should buy is 42.
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Which expression is equivalent to 16.8 - 18.6?
A. 18.6 - 16.8
B. -18.6 + (-16.8)
C. 16.8 + (18.6)
D. 16.8 - (-18.6)
The expression is equivalent to 16.8 - 18.6 is 16.8 + (-18.6)
How to determine which expression is equivalent to 16.8 - 18.6?The expression is given as
16.8 - 18.6
The additive inverse property states that:
a - b = a + (-b)
Using the above as a guide, we have the following expression that is equivalent
16.8 - 18.6 = 16.8 + (-18.6)
Hence, the expression is equivalent to 16.8 - 18.6 is 16.8 + (-18.6)
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What is the sum of 6 cups and 4 pints?
Answer:
14 us cups
Step-by-step explanation:
what is the mode of this?
Answer:
There is no mode for this distribution.
Step-by-step explanation:
The mode is the value that appears most frequently in a data set. If there are no repeating numbers in a given list, there is no mode existing for that particular list.
Write the slope-intercept form of the equation that goes with the following chart:
40123
V
6
18
30
42
Answer:
The slope intercept of a line is given by y=mx+c, where:
m=slope, c=y-intercept.
Thus the slope-intercept form of our equation will be:
-6+2y≤42
adding 6 in both sides we get:
-6+6+2y≤42+6
2y≤6
dividing both sides by 2 we get:
(2y)/2≤6/2
y≤3
the answer is y≤3
Step-by-step explanation:
The disposable income from your part-time job in 2019 was $17,000. In 2018, you borrowed $560 at 15 percent interest. You repaid
your loan with interest in 2019. How much would you have available for spending in 2019? (Do not round intermediate calculations.)
Spending amount available in 2019
If my disposable income from a part-time job in 2019 was $17,000, and I repaid a loan of $560 at 15 percent interest, borrowed in 2018 from my income of 2019, then I will have $ available for spending in 2019.
As per the question statement, my disposable income from a part-time job in 2019 was $17,000, and I repaid a loan of $560 at 15 percent interest, borrowed in 2018 from it.
We are required to calculate the amount I will be left with, to spend in 2019.
To solve this question, first, let us calculate the amount we had to pay to close our loan of 2018, along with it's 1 year's interest.
Since the loan was repaid in a year, hence, it does not matter if the interest was simple or compound as the magnitude of simple and compound interest on the same principle and at same rate of interest for a year is equal.
Let us proceed with the consideration that the interest was compounded annually at the rate of 15% per annum.
As per the basic formula of Compound Interest,
[tex]A=[P*(1+\frac{R}{100})^n][/tex]
Where, A = Final Amount i.e., (Principle + Interest).
P = Principle on which Interest in compounded
R = Rate of Compound Interest per annum
n = Time period of interest .
Here, (P = $560), (R = 15%) and (n = 1).
Therefore, total amount to be repaid to close the loan in 2019
[tex]=[560*(1+\frac{15}{100})^1]\\\\=[560*(1+\frac{3}{20})]\\=[560*(\frac{20+3}{20})]\\ =(560*\frac{23}{20})\\ =(28*23)\\=644[/tex]
Hence, my left-over balance after paying $644 from my disposable income of $17,000 which I earned from a part time job in 2019, will be $(17000 - 644) = $16356.
Loan: In Business, a loan is a lended a sum of money that is expected to be paid back with interest.Interest: Interest is the amount, paid regularly at a particular rate of the main principle borrowed, for the use of money lent, or for delaying the repayment of a debt.To learn more about Loans and Interest, click on the link below.
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Help me this is due tomorrow
Pls help me
find the midpoint of the segment with the given endpoints.
(2,-6) and (-4,-4)
Answer:
Midpoint: (-1,-5)
Step-by-step explanation:
In this circle, 26 of the total area is shaded.
A circle is divided into 6 equal parts with 2 parts shaded. The circle is labeled 2 sixths shaded.
In which circles is the shaded area equivalent to 26 of the total area?
Select each correct answer.
A circle is divided into 3 equal parts with 1 parts shaded. The circle is labeled 1 third shaded.
Image with alt text: A circle is divided into 3 equal parts with 1 parts shaded. The circle is labeled 1 third shaded.
A circle is divided into 5 equal parts with 2 parts shaded. The circle is labeled 2 fifths shaded.
Image with alt text: A circle is divided into 5 equal parts with 2 parts shaded. The circle is labeled 2 fifths shaded.
A circle is divided into 10 equal parts with 4 parts shaded. The circle is labeled 4 tenths shaded.
Image with alt text: A circle is divided into 10 equal parts with 4 parts shaded. The circle is labeled 4 tenths shaded.
A circle is divided into 12 equal parts with 4 parts shaded. The circle is labeled 4 twelfths shaded.
Image with alt text: A circle is divided into 12 equal parts with 4 parts shaded. The circle is labeled 4 twelfths shaded.
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The circles whose shaded area is equivalent to 2/6 of the total area are:
a. The circle which is labeled 1/3 shaded.
b. The circle which is labeled 4/12 shaded.
Given, a circle is 2/6 shaded.
Six equal halves of a circle are separated, two of which are darkened. The circle is marked as shaded by two-sixths.
= 2/6
which means that the fraction can be simplified furthermore.
= 1/3
which means for every 3 parts, one part is shaded.
Therefore, we need to find the circle which has the shaded area equivalent to 2/6 of the total area, that is for every 3 parts of the parts, there should be one part shaded.
a. A circle is divided into 3 equal parts with 1 parts shaded
The circle is labeled 1 third shaded.
= 1/3 which is equivalent to the area of the circle 2/6.
b. A circle is divided into 5 equal parts with 2 parts shaded.
The circle is labeled 2 fifths shaded.
= 2/5 which is not equivalent to 2/6.
c. A circle is divided into 10 equal parts with 4 parts shaded.
The circle is labeled 4 tenths shaded.
= 4/10
= 2/5 which is again not equivalent to 2/6.
d. A circle is divided into 12 equal parts with 4 parts shaded.
The circle is labeled 4 twelfths shaded.
= 4/12
after simplifying it furthermore, we get:
= 1/3 which is equivalent to the area of the circle 2/6.
hence we get the desired results.
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done earned 97.50 for 10 hours of work Amy earned $120 for 12 hours of work how much did each person earn per hour how can you use this information to compare their earnings?
Answer:
Done: $9.75 an hour
Amy: $10 an hour
Amy makes more than Done per hour
Step-by-step explanation:
[tex]Done:\\97.50/ 10 = 9.75\\Amy:\\120/12=10\\[/tex]
9v2-1=-77 I need help solving this equation.
Given Expression
[tex]9v^2-1=-77[/tex]
Step-By-Step Process.
________________
1. Add 1 to both sides of the equation.
[tex]9v^2-1+1=-77+1[/tex]
________________
2. Simplify.
[tex]9v^2=-76[/tex]
________________
3. Divide both sides by 9.
[tex]\frac{9v^2}{9} =\frac{-76}{9}[/tex]
________________
4. Simplify.
[tex]v^2=-\frac{76}{9}[/tex]
For [tex]x^2=f(a)[/tex] the solutions are [tex]x=\sqrt{f(a),} - \sqrt{f(a)} \\[/tex].
[tex]v=\sqrt{-\frac{76}{9} }, v=-\sqrt{-\frac{76}{9} }[/tex]
_________________
[tex]\sqrt{-\frac{76}{9}}=\frac{2\sqrt{19} }{3}i[/tex]
[tex]-\sqrt{-\frac{76}{9} } =-\frac{2\sqrt{19} }{3}i[/tex]
_________________
Solution:
[tex]v=\frac{2\sqrt{19} }{3}i,v=-\frac{2\sqrt{19} }{3}i[/tex]
Hope this helps!
Linda bought 35 yards of fencing at $4.88 a yard. How much did she spend? $
Answer:
$170.80
Step-by-step explanation:
Since it's $4.88 per yard, you could times that by 35, because she bought 35 yards of fencing.
Equation:
4.88(35)
or
4.88x x=35
I hope this helped! <3
b-2. If long-term financing at 12 percent had been utilized throughout the six months, would the total-dollar interest payments be larger or smaller than with the short-term financing plan?
a) The total dollar interest payments for the six months using the short-term financing interest rates is $377.73.
b.1) The total dollar interest payments for the six months using the long-term financing interest rate is $442.00.
b.2) If long-term financing at 12 percent had been utilized throughout the six months, the total-dollar interest payments would be larger than with the short-term financing plan by $64.27.
Data and Calculations:Month Amount Interest Rate Interest Long-Term
Annual Month Amount Rate Amount
January $9,700 6% 0.50% $48.50 1% $97.00
February $3,700 7% 0.58% 21.46 1% 37.00
March $4,700 10% 0.83% 39.01 1% 47.00
April $9,700 13% 1.08% 104.76 1% 97.00
May $10,700 12% 1.00% 107.00 1% 107.00
June $5,700 12% 1.00% 57.00 1% 57.00
Total interest amount = $377.73 $442.00
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Question Completion:Carmen's Beauty Salon has estimated monthly financial requirements for the next six months as follows:
Month Amount Interest Rate
January $9,700 6%
February $3,700 7%
March $4,700 10%
April $9,700 13%
May $10,700 12%
June $5,700 12%
a) Compute total dollar interest payments for the six months.
b.1) Compute the total dollar interest payments if the long-term financing at 12% had been used throughout the six months.
Joyce saved $180 on an item that was 40
%
off. What was the original price?
Write answer to the nearest cent.
Answer: 450
Step-by-step explanation:
x is the original price.
40 percent times x = 180
or [tex]\frac{40}{100}[/tex] times x= 180
multiplying both sides by 100 and dividing by 40
x=180 times [tex]\frac{100}{40}[/tex]
now just do 180 times 100 divided by 40
which gives you 450
Solve the compound inequality. 1/2x -4< 3 and 7≤ 3x +5
In Compound inequality the value of the x is 1/14 < x and 2/3≤ x.
According to the statement
We have to find that the value of the compound inequality.
So, For this purpose, we know that the
A compound inequality consists of two inequalities that are joined together by the word "and" or the word "or".
From the given information:
The equations are:
1/2x -4< 3 and 7≤ 3x +5
Now solve these equations then
1/2x -4< 3
1/2x < 3+4
1/2x < 7
1 < 14x
The value becomes 1/14 < x.
And then take second equation:
7≤ 3x +5
7-5 ≤ 3x
2≤ 3x
The value becomes 2/3≤ x.
So, In Compound inequality the value of the x is 1/14 < x and 2/3≤ x.
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Vijay's family is leaving for Galactic Gardens Resort once his parents get home from work on Friday. Their house is 544 miles from the resort. They plan to stop and spend the night at a hotel after 3 hours of driving, then complete the rest of the trip on the second day. If their average speed is 64 miles per hour, how long will they drive on the second day?
Write your answer as a whole number or a decimal
The time taken by Vijay's family to drive on the second day is 5.5 hours.
What is Distance?
Distance is the total movement of an object without any regard to direction.
Given that;
Vijay's family house is 544 miles from the resort.
Vijay's family plan to stop and spend the night at a hotel after 3 hours of driving.
Average speed = 64 miles per hour.
Now, For 3 hours of driving at an average speed of 64 miles per hour, the distance covered is,
⇒ d = 64 x 3 = 192 miles
And, Remaining distance for the second day is,
⇒ 544 - 192 = 352 miles
Hence, Time taken for distance 352 miles second day is,
T = 352 / 64 = 5.5 hours
So, The time taken by Vijay's family to drive on the second day is 5.5 hours.
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in how many minutes does the hand nake 1/6 of a rotation
The minute hand moves a full circle in 60 minutes (1 hour); so 360 degrees.
10 minutes is 1/6 of an hour so the hour hand has also moved 1/6 of the distance between the 3 and the 4, which adds 5° (1/6 of 30°). The total measure of the angle, therefore, is 35°.
Since a clock is a circle and circles have 360 degrees, and there are 60 seconds in one minute, the answer can be derived by using the equation:
360°/60 minutes = 6° per minute
Edited to replace 60 seconds with 60 minutes in the formula.
Therefore,
Answer is 60 minutes the hand make 1/6 of a rotation.
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Write your answer as a fraction or as a whole or mixed number
2 6/8 + 3 5/8 =
Answer:
6 3/8
Step-by-step explanation:
2 6/8 + 3 5/8
= (2 + 3) + ( 6/8 + 5/8)
= 5 + (6 + 5)/8
= 5 + 11/8
= 5 + 1 3/8
= 6 3/8
Kosanga lives in San Mateo. He bought an item for $844.29 and when the clerk calculated the sales tax it came out to exactly $88.87287. Round the sales tax to the nearest
The sales tax to the nearest dollars is $89 whereas it is $88.87 to the nearest cents.
How many figures after decimal is cents?The cents is normally expressed to 2 decimal places, in other words, the sales in cents in this case is to express the sales tax amount to 2 figures after the decimal which is $88.87 since the 2 before 7 is insignificant and cannot be rounded to 1 because it is less than 5.
In dollars, the sales tax is $89 because the 8 after the decimal when rounded to 1 and added to 8 gives 9.
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Full question: Kosanga lives in San Mateo. He bought an item for $844.29 and when the clerk calculated the sales tax it came out to exactly $88.87287. Round the sales tax to the nearest:(a) dollars(b) cents
The sales tax when rounded to the nearest dollars is $89 whereas it is $88.87 to the nearest cents.
How many figures after decimal is cents?The cents is normally expressed to 2 decimal places, in other words, the sales in cents in this case is to express the sales tax amount to 2 figures after the decimal which is $88.87 since the 2 before 7 is insignificant and cannot be rounded to 1 because it is less than 5.
In dollars, the sales tax is $89 because the 8 after the decimal when rounded to 1 and added to 8 gives 9.
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Full question:
Kosanga lives in San Mateo. He bought an item for $844.29 and when the clerk calculated the sales tax it came out to exactly $88.87287. Round the sales tax to the nearest:
(a) dollars
(b) cents
Eva is saving up to buy a computer.
The computer costs £690
Eva has £429
How much more does Eva need to save?
Answer: £261
Step-by-step explanation: Subtracting 429 from 690 will give you 261 which is the remaining amount needed to purchase the computer.
g(x)=5x+2, find g(-4)g(−4).
The value of g(-4) is (-18)
What is function?A function is defined as a relation between a set of inputs having one output each. A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
Given function:
g(x)=5x+2
So, the value of g(-4)
g(-4) = 5(-4) +2
g(-4) = -20+2
g(-4) = -18
Hence, the value of g(-4) is -18.
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If two angles are vertical angles, then they are congruent.
Which is the conclusion of the conditional?
OA. Two angles are not vertical angles.
O
O
B. The angles are congruent.
C. The angles are not congruent.
OD. Two angles are vertical angles.
The conclusion of the conditional statement is that; D) The angles are congruent.
What are vertical angles?
Vertical angles are also called opposite angles and they are formed when two lines meet each other at a point.
Now, we are given the conditional statement "If two angles are vertical angles, then they are congruent."
Now, we can say that the conditional statement is always true according to the definition of vertical angles. Thus, we can say that the conclusion of the conditional is that The angles are congruent.
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find the pattern write a rule for the table
Larry Mitchell invested part of his $32,000 advance at 4% annual simple interest and the rest at 6% annual simple interest. If his total yearly interest from both accounts was $1,340, find the amount invested at each rate
The amount invested at each rate is $30,000 at 4%, and $2000 at 6%.
Given that;
Larry Mitchell invested part of his $32,000 advance at 4% annual simple interest and the rest at 6% annual simple interest.
If his total yearly interest from both accounts was $1,340.
To find;
The amount invested at each rate.
Let x is the amount at 4%, therefore the amount at 6% is 32000 - x.
The total interest is:
0.04x + 0.06(32000 - x) = 1320
0.04x - 0.06x + 1920 = 1320
0.02x = 1920 - 1320
0.02x = 600
x = 600/0.02
x = 30,000
The amount at 6% is:
$32,000 - $30,000 = $2000
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which number is greater -4.2 or -4.2???. sorry don't have to much points
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Module 4 Lesson 2 - Application
A student loan needs to be paid off
beginning the first year after
graduation. Beginning at Year 1, there
s $52,000 remaining to be paid. The
graduate makes regular payments of
58000 each year
Write an explicit rule.
According to the solving the explicit rule:
y = 52000 - 58000 * x
What is the explicit formula rule?The explicit formula for an arithmetic sequence is a = a + (n - 1)d, and each term of the sequence may be computed without knowing the previous terms of the sequence. In general, the explicit formula is the nth term of an arithmetic, geometric, or harmonic sequence.
What exactly is the difference between implicit and explicit function?An implicit function is a function containing numerous variables, one of which is a function of the other set of variables. An explicit function is one in which the dependent variable may be clearly stated in terms of the independent variable.
According to the given data:Initial = 52000
Rate = 58000 each year
Determine the equation of the graph:
The equation can be used:
Amount = initial - rate * years
We used minus (-) because, the amount reduces as the student pays.
So,
y = amount
x = years
we have:
y = initial - rate * x
putting the values we get:
y = 52000 - 58000 * x
According to the solving the explicit rule:
y = 52000 - 58000 * x
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Can you please help me
Answer:
25 and 6
Step-by-step explanation: