Answer:
It would take the apprentice 14 hours to make the fireplace on his own.
Step-by-step explanation:
Let x represent the hours it takes the bricklayer to make a fireplace on his own and x + 10 represent the hours it takes the bricklayer's apprentice to make a fireplace on his own.
7/(x + 10) + 2/x = 1
7/(x+10) represents the fraction of the fireplace the bricklayer's apprentice made (total amount of time the bricklayer's apprentice worked on the fireplace/time it takes the bricklayer's apprentice to make a fire place on his own) while 2/x represents the fraction of the fireplace the bricklayer made (total amount of time the bricklayer worked on the fireplace/time it takes the bricklayer to make a fire place on his own). The 1 on the right side of the equation represents the number of fireplaces they made in that time.
Multiply both sides of the equation by x(x + 10) to get rid of the denominators:
x(x + 10)[7/(x + 10) + 2/x] = x(x + 10)1
x(x + 10)[7/(x + 10)] + x(x + 10)(2/x) = x(x + 10)
7x + 2(x + 10) = x² + 10x
7x + 2x + 20 = x² + 10x
Gather all the terms to one side of the equation:
x² + 10x - 7x - 2x - 20 = 0
x² + x - 20 = 0
Factoring the simplified equation:
(x + 5)(x - 4) = 0
Solving for each factor:
When x + 5 = 0,
x = -5
When x - 4 = 0,
x = 4
Since a negative solution wouldn't make sense for this question, it would take the bricklayer 4 hours to complete the fireplace on his own.
Substituting x = 4 into x + 10 to find out how long it would take the apprentice to make the fireplace on his own:
x + 10 = 4 + 10 = 14
Therefore, it would take the apprentice 14 hours to make the fireplace on his own.
HELP ASAP Which set of statements explains how to plot a point at the location (Negative 3 and one-half, negative 2)?
Start at the origin. Move 3 and one-half units right because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between 3 and 4. Move 2 units down because the y-coordinate is -2.
Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units left because the y-coordinate is -2.
Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units right because the y-coordinate is -2.
Start at the origin. Move 3 and one-half units left because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units down because the y-coordinate is -2.
Answer:
The last one: Start at the origin. Move 3 and one-half units left because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units down because the y-coordinate is -2.
Step-by-step explanation:
To get to (-3 1/2, -2), you would have to go left 3 1/2 units, and down 2 units.
Write an equation for the nth term of
the arithmetic sequence:
15,28,41 ....
Answer:
The equation for the nth term of the given arithmetic sequence is: [tex]\mathbf{a_n=13n+22}[/tex]
Step-by-step explanation:
We need to write an equation for the nth term of the arithmetic sequence:
15,28,41 ....
The equation for arithmetic sequence is: [tex]a_n=a_1+(n-1)d[/tex]
Where [tex]a_n[/tex] is the nth term, [tex]a_1[/tex] is first term and d is common difference
In the given sequence we have:
a₁ = 15
a₂ = 28
We can find common difference using the formula:
[tex]a_n=a_1+(n-1)d\\Put\: n=2, a_2=28\: and\: a_1=15\\a_2=a_1+(2-1)d\\28=15+d\\d=28-15\\d=13[/tex]
So, the common difference d is 13
Now, equation for nth term will be:
[tex]a_n=a_1+(n-1)d\\Put\:a_1=15, d=13\\a_n=15+(n-1)13\\Solving:\\a_n=15+13n-13\\a_n=13n+2[/tex]
So, the equation for the nth term of the given arithmetic sequence is: [tex]\mathbf{a_n=13n+22}[/tex]
where n=1,2,3..
solve the literal equation
6/p=x+a for p
a forest covers 58,000 acres. A survey finds that 0.2 of the forest is old-growth trees. how many acres of old-growth trees are there?
15y + (x + 9y) = ? someone halp
Answer:
x = -24ySimplifying
15y + (x + 9y) = 0
Remove parenthesis around (x + 9y)
15y + x + 9y = 0
Reorder the terms:
x + 15y + 9y = 0
Combine like terms: 15y + 9y = 24y
x + 24y = 0
Solving
x + 24y = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-24y' to each side of the equation.
x + 24y + -24y = 0 + -24y
Combine like terms: 24y + -24y = 0
x + 0 = 0 + -24y
x = 0 + -24y
Remove the zero:
x = -24y
Simplifying
x = -24y
Step-by-step explanation:
is a spray bottle a gallon pint quart or cup
Answer:
most bottles are
about 2 pints
Step-by-step explanation:
Plz mark brainliest!
Answer:
I depends on the size a big can have 2 cups ,a medium can have 1 cup and the small has 2 pints
Step-by-step explanation:
I NEED HELP NOW!!!!what is 5+5?!?!?!!
Answer: its 20 bro i got you
Step-by-step explanation:
An opera singer teaches singing classes to teens. She teaches 96 teens in all. One-third of her
students are boys. How many boys are in the singing?
Answer:
32
Step-by-step explanation:
1/3x96= 31.999
Step-by-step explanation:
There are 96 students in total.
1/3 of total students = 96 * (1/3) = 32.
Since 1/3 of total students are boys,
there are 32 boys in the singing.
what is X decreased by 61%
Find the slope of the linear function.
12x = -10 + 2y
Slope =
Blank 1:
Pls help extra points.
How many buttons are there in a Fionas Fashion shirt , and how many buttons are there in a jacket ?
Answer:
842
Step-by-step explanation:
Fiona's Fashion Store is world renowned for its buttoned uniforms. A collection of 36 shirts and 42 jackets contains 842 buttons. Additionally, a collection of 6 shirts and 7 jackets contains 137 buttons.
Hi everyone! I have a question!
Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of pi (no approximations.) THANKS!!!!!!
Answer:
7π
Step-by-step explanation:
SO first find the area of the whole circle
which has a radius of 3
a=πr^2
So 3^2=9
9π
Now the two circles which are the same in area due to having the same radius
so if you plug in the 1 for radius the answer would just be π or 1π
now multiply that by 2 becuase there are 2 identical circles
π*2=2π
Now subtract
9π-2π=7π
Answer:
Step-by-step explanation:
area of unshaded circle:
A=π*r^2=π*1=π
we have 2 circles so the area of both circles are 2π
area of the large circle is A(l)=Π*3^2=Π*9=9Π
area of the shaded region: A(s)=9Π-2Π=7Π
HERRRRRRRRRRRRRRRREEEEEEEEEEeee pt3
Help me please!! And have a good day
Let f(x) = 5x +1.
Find f(2)
Answer:
f(2) =11
Step-by-step explanation:
Explanation:-
Given the function f(x) = 5x+1
Put x = 2
f(2) = 5(2)+1
⇒ f(2) = 10 +1
⇒ f(2) =11
Please Help
2/3(9x−15)−4x −5
c) x 3
Answer:
2/3 . 9x-2/3. 15-4x-5
=2 .3x -2 .5-4x-5
=6x-10-4x-5
=2x-5
pls help!
15 boxes of apples weighs 840 pounds. If the weight of the apples is proportional to the number of boxes then how many pounds does 28 boxes weigh?
Answer:
4,704 pounds
Step-by-step explanation:
make a ratio
boxes of apples:pounds
15:840
28:x
cross multiply:
15x = 23520
x = 4,704
hope this helps!
In ΔFGH, f = 83 inches, g = 11 inches and ∠H=60°. Find the length of h, to the nearest inch.
Answer: 78
Step-by-step explanation:
The length of h to the nearest inch is 78 inches.
What is Law of Cosines?Law of cosines of triangle states that for three length of sides of the triangle, a, b and c opposite to the angles A, B and C respectively can be related as,
a² = b² + c² - 2bc cos(A)
Given that, In ΔFGH,
f = 83 inches, g = 11 inches and ∠H = 60°.
Using the law of cosines,
h² = f² + g² - 2fg cos(H)
Substituting,
h² = 83² + 11² - (2 × 83 × 11) cos (60°)
= 7010 - (1826 × 1/2)
= 7010 - 913
= 6097
h = √6097 = 78.083 inches ≈ 78 inches
Hence the length of h is 78 inches.
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PLEASE I NEED THIS ANSWER AND IM OUT OF SCHOOL FOR THE WEEKEND
Answer:
11
Step-by-step explanation:
A triangle has 180 degrees, and two of them are given, so you subtract them from 180 to 110. But since it is 10x, you have to divide by 10 to get your answer.
(hope this helps!)
Simplify the expression by combining like terms.
2x + 4y + 6 + 2y - 5 + 3x 
Use the distributive property to solve: 5(x – 2)
Answer:
5x-10
Step-by-step explanation:
Answer:
5x-10
Step-by-step explanation:
5(x-2)
5(x)=5x
5(-2)=-10
5x-10
Write the expression with fewer terms.
10−2
Answer:
8
Step-by-step explanation:
（10-2 is 8)
Hope this helps!
A homeowner is mixing vinegar with water to dissolve calcium deposits
around a bathroom sink. The original formula calls for 10 ounces of vinegar
mixed with 30 ounces of water. The homeowner wants to make a stronger
mixture by adding more vinegar (variable v). Which equation will show
"total water / total vinegar"
30/(10 + v)
(30 + v) / 10
(30 + v) / (10 + v)
30/10
Answer:
get good buddy
Step-by-step explanation:
Answer:
30/(10 + v)
Step-by-step explanation:
The original formula calls for 30 ounces of water and 10 ounces of vinegar. To make it stronger they are only adding an unknown amount of vinegar (v).
What is the answer to this?
Answer:
Since 5 tenths is 5 over ten, 5 tenths as a Fraction is 5/10. If you divide 5 by ten you get 5 tenths as a decimal which is 0.50.
Step-by-step explanation:
if im right Brainliest?
x is 4 more than
thrice of y
Answer:
x is 4 more than thrice of y[tex] \huge \boxed{x = 3y + 4}[/tex]
Max delivers 8,520 pieces of mail in one year. If he delivers the same number of pieces of mail each month, about how many pieces of mail does he deliver in 2 months? Solve the problem and explain the steps you took to solve.
Answer:
Because there are 12 months in a year the ratio of the number of pieces of mail Max delivers in 12 months can be written as: 852012 or 7101 (720 pieces of mail per month).
Answer:
He would deliver 1420 mails in 2 month's
Step-by-step explanation:
First, I divided 8,520 by 12 because 12 month's in one 1 year
Then, I get 710, that is the amount he delivers each month
Lastly, I multiply 710 by 2 because that is the amount for 2 month's and it equals 1,420 so, the answer is 1,420 :)
Write an algebraic expression for
the verbal expression:
"5 times the sum of a squared and
b minus 3 times the sum of
a and b".
Answer:
"5 times the sum of a squared and b minus 3 times the sum of
a and b".
5(a²+b) - 5(a+b)which can be simplified such as:
[tex]5\left(a^2+b\right)-5\left(a+b\right)=5a^2-5a[/tex]
Step-by-step explanation:
Given the verbal expression
"5 times the sum of a squared and b minus 3 times the sum of
a and b".
BREAKIN DOWN THE STATEMENT:
The sum of 'a' Squared and 'b' = a²+b
5 times the sum of a squared and b = 5(a²+b)The sum of a and b = a+b
3 times the sum of a and b = 5(a+b)Now, "5 times the sum of a squared and b minus 3 times the sum of
a and b".
5(a²+b) - 5(a+b)Let us simplify the algebraic expression
[tex]5\left(a^2+b\right)-5\left(a+b\right)[/tex]
[tex]=5a^2+5b-5a-5b[/tex]
simplify
[tex]=5a^2-5a[/tex]
Thus,
[tex]5\left(a^2+b\right)-5\left(a+b\right)=5a^2-5a[/tex]
Jim is a 60-year-old Anglo male in reasonably good health. He wants to take out a $50,000 term (that is, straight death benefit) life insurance policy until he is 65. The policy will expire on his 65th birthday. The probability of death in a given year is provided by the Vital Statistics Section of the Statistical Abstract of the United States (116th Edition).
x = age 60 61 62 63 64
P(death at this age) 0.01030 0.01357 0.01609 0.01981 0.02362
Jim is applying to Big Rock Insurance Company for his term insurance policy.
(a) What is the probability that Jim will die in his 60th year? (Round your answer to five decimal places.)
Using this probability and the $50,000 death benefit, what is the expected cost to Big Rock Insurance?
$
(b) Repeat part (a) for years 61, 62, 63, and 64.
Year Expected Cost
61 $
62 $
63 $
64 $
What would be the total expected cost to Big Rock Insurance over the years 60 through 64?
$
(c) If Big Rock Insurance wants to make a profit of $700 above the expected total cost paid out for Jim's death, how much should it charge for the policy?
$
(d) If Big Rock Insurance Company charges $5000 for the policy, how much profit does the company expect to make?
$
The probabilities are solved and:
a) The expected cost at the age 60 is $ 515.
b)
Year Expected Cost
61 $678.50
62 $804.50
63 $990.50
64 $1181
c) The policy should be priced at $4869.50.
d) The company expects to make a profit of $830.50.
Given data:
(a)
The probability that Jim will die in his 60th year is given as 0.01030.
The expected cost to Big Rock Insurance can be calculated by multiplying the probability of death at age 60 by the death benefit of $50,000:
Expected Cost at age 60 = (0.01030) * ($50,000)
Expected Cost at age 60 = $515
(b)
Expected Cost at age 61 = (0.01357) * ($50,000) = $678.50
Expected Cost at age 62 = (0.01609) * ($50,000) = $804.50
Expected Cost at age 63 = (0.01981) * ($50,000) = $990.50
Expected Cost at age 64 = (0.02362) * ($50,000) = $1181
Year Expected Cost
61 $678.50
62 $804.50
63 $990.50
64 $1181
(c)
The total expected cost to Big Rock Insurance over the years 60 through 64 can be obtained by summing up the individual expected costs:
Total Expected Cost = $515 + $678.50 + $804.50 + $990.50 + $1181 = $4169.50
To make a profit of $700 above the expected total cost, Big Rock Insurance should charge:
Policy Price = Total Expected Cost + Profit
= $4169.50 + $700
= $4869.50
Therefore, the policy should be priced at $4869.50.
(d)
If Big Rock Insurance charges $5000 for the policy, the expected profit can be calculated as:
Expected Profit = Policy Price - Total Expected Cost
= $5000 - $4169.50
= $830.50
Hence, the company expects to make a profit of $830.50.
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The probabilities are solved and
a) The expected cost at the age 60 is $ 515.
b)
Year/Age Expected Cost
61 $678.50
62 $804.50
63 $990.50
64 $1181
c) The policy should be priced at $4869.50.
d) The company expects to make a profit of $830.50.
How to compute the probability, expected cost, policy price and expected profit.(a) The probability that Jim will die in his 60th year is given as 0.01030.
The expected cost to Big Rock Insurance can be calculated by multiplying the probability of death at age 60 by the death benefit of $50,000 -
Expected Cost at age 60 = (0.01030) * ($50,000)
= $515
(b)
Expected Cost at age 61 = (0.01357) * ($50,000) = $678.50
Expected Cost at age 62 = (0.01609) * ($50,000) = $804.50
Expected Cost at age 63 = (0.01981) * ($50,000) = $990.50
Expected Cost at age 64 = (0.02362) * ($50,000) = $1181
Thus,
Year/Age Expected Cost
61 $678.50
62 $804.50
63 $990.50
64 $1181
(c)
The total expected cost to Big Rock Insurance over the years 60 through 64 can be obtained by summing up the individual expected costs:
Total Expected Cost = $515 + $678.50 + $804.50 + $990.50 + $1181
= $4169.50
To make a profit of $700 above the expected total cost, Big Rock Insurance should charge -
Policy Price = Total Expected Cost + Profit
= $4169.50 + $700
= $4869.50
Thus it is correct to state that the policy should be priced at $4869.50.
(d) If Big Rock Insurance charges $5000 for the policy, the expected profit can be calculated as:
Expected Profit = Policy Price - Total Expected Cost
= $5000 - $4169.50
= $830.50
Hence, the company expects to make a profit of $830.50.
Learn more about probability at:
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Read the problem and examine the diagram.
Of all the students in the school band, 6 play the trumpet. They represent 10% of the
total number of students in the band. How many students are in the band?
Which choice is NOT a correct way to check your answer?
A. The answer should be 10% of 6.
B. The answer multiplied by 10% should be 6.
C. 10% of the answer should be 6.
D. 6 should be 10% of the answer.
Answer:
Option A: The answer should be 10% of 6 is the correct answer.
Step-by-step explanation:
Given that:
6 students play trumpet. As they represent 10% of the total students.
Let,
x represent the number of students in the band.
10% of x = 6
By solving this, we will get the value for number of students in the band.
As x will be our answer,
The choices B, C and D are correct in the given scenario.
However,
10% of 6 cannot be the solution to the problem.
Hence,
Option A: The answer should be 10% of 6 is the correct answer.