Michael has $96 in savings and makes $12.00 an hour at his job. Greg has $128 in savings and makes $10.00 an hour his job. They both save all their earned money. How many hours they both have to work to have the same amount of money saved?
Answers
The computation shows that the hours that they both have to work to have the same amount of money saved is 16 hours.
How to calculate the function?Based on the information given, let the number of hours be represented by h
Therefore, the first function for Michael will be:
96 + 12h
The second function for Greg will be:
= 128 + 10h
Therefore, we'll equate both equations. This will be:
96 + 12h = 128 + 10h
12h - 10h = 128 - 96.
2h = 32.
h = 32/2
h = 16 hours.
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Related Questions
The denominator of a rational number is greater than the numerator by 10. If the numerator is
increased by 1 and the denominator is decreased by 1, then find the
original rational number.
answer with steps for more points
ANSWER ASAP
Answers
The expression for the original rational number is; x/(x + 10)
How to solve algebraic expressions?Let the numerator be x
Therefore, according to given condition, the denominator will be expressed as; (x + 10)
According to question If the numerator is increased by 1 and the denominator is decreased by 1, then new numerator is; x + 1
New denominator is (x + 10 - 1) = (x + 9)
Thus, the original rational number will be expressed as;
x/(x + 10)
The new rational number will be : (x + 1)/(x + 9)
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A human resource company performs employment screening for large companies in southern California. Recently, the company began working with a new client and formulated a new test just for this company. Thirty people were given the test. The data below reflect the scores of those 30 people. The human resource company has in the past issued a rejection letter with no interview to the lower 16% taking the test. They also send the upper 2.5% directly to the company without an interview. Everyone else is interviewed. Based on the data and assuming a bell-shaped distribution, what scores should be used for the two cutoffs?
79 79 7151 65 71 65 90 60 62 78 76 88 69 65
91 72 56 61 83 61 78 68 66 52 79 88 74 71 69
A score of ________should be used as the cutoff for the lower 16% and a score of________ (Round to the nearest integer as needed.)
Answers
Answer:
A score of 61 should be used as the cutoff for the lower 16% and a score of 92 should be used as the cutoff for the upper 2.5%.
Step-by-step explanation:
The data set for the scores of the 30 people are:
S = {79, 79, 71, 51, 65, 71, 65, 90, 60, 62, 78, 76, 88, 69, 65, 91, 72, 56, 61, 83, 61, 78, 68, 66, 52, 79, 88, 74, 71, 69}
Compute the mean and standard deviation:
\(\mu=\frac{1}{n}\sum X=\frac{1}{30}\times 2138=71.27\\\\\sigma=\sqrt{\frac{1}{n-1}\sum (X-\mu)^{2}}=\sqrt{\frac{1}{30-1}\times 3343.8667}=10.74\)
It is provided that in the past the company issued a rejection letter with no interview to the lower 16% taking the test.
That is the probability of no interview is, P (X > x) = 0.16.
That is, P (Z > z) = 0.16.
The z-score corresponding to this probability is, -1.
Compute the value of x as follows:
\(z=\frac{x-\mu}{\sigma}\\\\x=\mu+z\cdot \sigma\\\\=71.27+(-1\times 10.74)\\\\=60.53\\\\\approx 61\)
It is also provided that the upper 2.5% directly to the company without an interview.
That is the probability of no interview is, P (X < x) = 0.025.
That is, P (Z < z) = 0.025.
The z-score corresponding to this probability is, 1.96.
Compute the value of x as follows:
\(z=\frac{x-\mu}{\sigma}\\\\x=\mu+z\cdot \sigma\\\\=71.27+(1.96\times 10.74)\\\\=92.3204\\\\\approx 92\)
Thus, the complete sentence is:
A score of 61 should be used as the cutoff for the lower 16% and a score of 92 should be used as the cutoff for the upper 2.5%.
Find x round to the nearest whole number helpppp
Answers
Answer:
Below
Step-by-step explanation:
Instead of x , I assume you want the angle.
For RIGHT triangles, remember
cos (angle ) = adjacent leg / hypotenuse
cos ( angle ) = 5 /12
angle = arccos( 5/12) = 65 °
You could also use pythagorean theorem to calculate the misssing side....then use cos law to calculate the angle.
Solve the equation.
3(x - 5) = 18
X =
Reset
Sub
Please help me this is 80% of my grade please help
Answers
Answer:
X=11
Step-by-step explanation:
since x=11,11-5=6.
then 6*3=18
3(x-5)=18
x-5=6
x=6+5
x=11
A football team lost 9 yards on each of two consecutive plays. represent the total change as a product of sun numbers and then find the total loss.
Answers
Do the total list is -18 yards
Determine the correct inventory amount on December 31.
I am so lost and have no clue what to do. Any help is appreciated!
Answers
The adjusted balance of Blossom's inventory account is $214,680.
Define rate of interestThe rate of interest, also known as the interest rate, is the percentage amount charged by a lender or financial institution for the use of borrowed money or for the extension of credit. It is the cost of borrowing money, typically expressed as an annual percentage of the amount borrowed or owed.
Goods shipped FOB shipping point on December 28 to Splish Company for $53,940 were not included in the physical inventory count. Therefore, we need to add this amount to the year-end balance of inventory:$286,950 + $53,940 = $340,890Goods shipped FOB destination to Blossom for $97,100 were not included in the physical inventory count. Therefore, we need to subtract this amount from the year-end balance of inventory: $340,890 - $97,100 = $243,79Goods received FOB shipping point on January 2 for $26,120 were not included in the physical inventory count. Therefore, we need to add this amount to the year-end balance of inventory: $243,790 + $26,120 = $269,91Goods shipped FOB destination to Ehler of Canada for $55,230 were not included in the physical inventory count. Therefore, we need to subtract this amount from the year-end balance of inventory: $269,910 - $55,230 = $214,680Goods received FOB destination on January 2 for $38,960 were included in the physical inventory count. Therefore, we do not need to make any adjustments for this transaction.Therefore, the adjusted balance of Blossom's inventory account is $214,680.
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If there are penguins in the aquarium is full of fish, then this is an octopus write
this in Symbolic form
Answers
The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o
How to explain the informationLet's assign variables to represent the statements:
q: The aquarium is full of fish.
r: There are penguins.
The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o
∧ represents the logical operator "and" which connects the statements r and q.
→ represents the logical operator "implies" or "if...then".
o represents the statement "this is an octopus".
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8/12 as common factor
Answers
Answer: 2/3
Step-by-step explanation: Cancel the common factor of 8 and 12 which is 2/3. Divided by common denominator which is 4.
8 divided by 4 = 2
12 divided by 4 = 3
so 2/3 is the answer
56÷(7-9)^3 -24/23-5×4
Answers
Answer:
= −28.043478261
Step By Step Explanation
Answer From Gauth Math
Hope it helps
8.6w+2.2(2w-5)=54
help plz
8th grade math
Answers
8.6w + 2.2 (2w-5) = 54
8.6w + 4.4w - 11 = 54
13w - 11 = 54
13w = 65
w = 5
how Do you graph an
absolute valve function
Answers
Answer:
To graph the absolute value, you need to know where the vertex is, so the numbers will be going down, then turn and start going back up, or going up and then turn and start going down, the middle point will be the vertex and should be the center point of the table.
What is the number sentence for "1 less than N is the sum of Z and
2"?
Answers
Answer:
N–1=Z+2 should be the solution.
A couple lives in Florida for 1/3 of the year. Each year has 12 months. What fraction of a year, in twelfths, does the couple not live in Florida?
Answers
Answer:
4/12
Step-by-step explanation:
plz give me a brainlies
The couple did not live for 2/3 part of the year.
What is fraction?Fractions are used to represent smaller pieces (or parts) of a whole.
Given that, A couple lives in Florida for 1/3 of the year,
12*1/3 = 4
Therefore, they lived for 4 months there,
And, They did not live for 12 - 4 = 8 months.
8 months in fraction = 8/12 = 2/3
Hence, The couple did not live for 2/3 part of the year.
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A sports ball has a diameter of 25 cm. Find the volume of the ball
Answers
V = 8181.2cm^3
Step-by-step explanation:
Simplify.
Rewrite the expression in the form of 4^n.
(4^11)(4^-8)
Answers
Answer:
4^19
Step-by-step explanation:
Solve the following linear programming problem.
z = 5x + 4y
2x + 4y ≤8
5x + y ≤8
x ≥ 0, y ²0
Maximize:
subject to:
Answers
The maximum value of the objective function z = 5x + 4y is 12
Solving the linear programmingFrom the question, we have the following parameters that can be used in our computation:
z = 5x + 4y
2x + 4y ≤8
5x + y ≤8
x ≥ 0, y ²0
This means that the objective function is
Max z = 5x + 4y
And the constraints are
2x + 4y ≤8
5x + y ≤8
x, y ≥ 0
When solved graphically, we have
(x, y) = (4/3, 4/3)
Substitute (x, y) = (4/3, 4/3) in the objective function
So, we have
z = 5 * 4/3 + 4 * 4/3
Evaluate
z = 12
Hence, the maximum value of the objective function is 12
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Find the slope of the line tangent to the curve 3 x^2 y + cos(y) = (√3 + π)/2 at the point ( − 1 , π/6 ) .
Answers
Answer:
fuhghoierhfoqierhf
Step-by-step explanation:
NO LINKS!! URGENT HELP PLEASE!!!
Determine if the sequence is arithmetic. If it is, find the common difference, the 52nd term, and the explicit formula.
34. -11, -7, -3, 1, . . .
Given the explicit formula for an arithmetic sequence find the common difference and the 52nd term.
35. a_n = -30 - 4n
Answers
Answer:
#34. aₙ = 4n - 15; a₅₂ = 193#35. a₅₂ = -238; d = - 4-----------------
Question 34Find the differences in the sequence -11, -7, -3, 1, ...
1 - (-3) = 4,-3 - (-7) = 4,-7 - (-11) = 4The difference is common, so the sequence is an AP.
The nth term is:
\(a_n=a_1+(n-1)d\)\(a_n=-11+(n-1)*4=-11+4n-4=4n-15\)Find the 52nd term:
\(a_{52}=4*52-15=208-15=193\)Question 35Find the 52nd term using the given formula:
\(a_{52}=-30-4*52=-30-208=-238\)Find the previous term:
\(a_{51}=-30-4*51=-30-204=-234\)Find the common difference:
\(d=a_{52}-a_{51}=-238-(-234)=-4\)Answer:
\(\begin{aligned}\textsf{34)} \quad d&=4\\a_n&=4n-15\\a_{52}&=193\end{aligned}\)
\(\begin{aligned}\textsf{35)} \quad d&=-4\\a_{52}&=-238\end{aligned}\)
Step-by-step explanation:
Question 34An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.
Given sequence:
-11, -7, -3, 1, ...To determine if the given sequence is arithmetic, calculate the differences between consecutive terms.
\(a_4-a_3=1-(-3)=4\)
\(a_3-a_2=-3-(-7)=4\)
\(a_2-a_1=-7-(-11)=4\)
As the differences are constant, the sequence is arithmetic, with common difference, d = 4.
The explicit formula for an arithmetic sequence is:
\(\boxed{a_n=a+(n-1)d}\)
where:
a is the first term of the sequence.n is the position of the termd is the common difference between consecutive terms.To find the explicit formula for the given sequence, substitute a = -11 and d = 4 into the formula:
\(\begin{aligned}a_n&=-11+(n-1)4\\&=-11+4n-4\\&=4n-15\end{aligned}\)
To find the 52nd term, simply substitute n = 52 into the formula:
\(\begin{aligned}a_{52}&=4(52)-15\\&=208-15\\&=193\end{aligned}\)
Therefore, the 52nd term is a₅₂ = 193.
\(\hrulefill\)
Question 35Given explicit formula for an arithmetic sequence:
\(a_n=-30-4n\)
To find the common difference, we need to compare it with the explicit formula for the nth term:
\(\begin{aligned}a_n&=a+(n-1)d\\&=a+dn-d\\&=a-d+dn\end{aligned}\)
The coefficient of the n-term is -4, therefore, the common difference is d = -4.
To find the 52nd term, simply substitute n = 52 into the formula:
\(\begin{aligned}a_{52}&=-30-4(52)\\&=-30-208\\&=-238\end{aligned}\)
Therefore, the 52nd term is a₅₂ = -238.
solve for x
(look at photo)
Answers
By definition of proportion, the value of x is,
⇒ x = 80
We have to given that;
In a triangle,
Perpendicular = 60
Now, By Pythagoras theorem we get;
60² = 36² + y²
3600 = 1296 + y²
y² = 3600 - 1296
y² = 2304
y = 48
Hence, By definition of proportion;
⇒ x / 48 = 60 / 36
⇒ x = 80
Thus, By definition of proportion, the value of x is,
⇒ x = 80
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Need help wit num ur 16 please quick expalanation don’t got all day
Answers
A
-2+
Which graph represents the
function y = tan x?
B
2T
2T
D
-2+1
21
4+
ㅠ
2T
2πT
Answers
The graph that represents the function y= tanx is Option A.
What is the description of the above function?The graph of y =tan (x) is a periodic function that has vertical asymptotes at x = (n + 1/2)π, where n is an integer.
It oscillates between positive and negative infinity, creating a wave- like pattern.
It has a repeating pattern of sharp peaks and valleys, exhibiting both positive and negative slopes.
Thus, option A is the correct answer.
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A car is traveling at a rate of 108 kilometers per hour. What is the cars rate in meters per second? How many meters will the car travel in 20 seconds?
Answers
Answer:
\(\frac{30meters}{second}\)
600meters
Step-by-step explanation:
Use conversion factors that represent 1. You can cross cancel wods just like numbers.
\(\frac{108km}{1hour}\) · \(\frac{1hour}{60 minutes}\) · \(\frac{1minute}{60seconds}\) ·\(\frac{1000meters}{1 km}\)
\(\frac{108000meters}{3600seconds}\)
\(\frac{30meters}{second}\)
\(\frac{30meters}{second}\) ·\(\frac{20seconds}{1}\)
600 meters
Helping in the name of Jesus.
Please help!!
A jar contains 30 red marbles, 50 blue marbles, and 20 white marbles. You choose one marble from the jar at random. What is the theoretical probability of choosing a red marble?
Answers
Answer:
you have a 1/5 chance of choosing a red marble.
Step-by-step explanation:
Answer:
Your probability of choosing a red marble is 30%
Step-by-step explanation:
You'll need to start by adding all the marble's which will give you 100.
30 + 50 + 20 = 100
Then add up the non-red marbles, which is 70.
50 + 20 = 70
30 red marbles are left.
Now, you'll have the fraction 30 over 100.
As a percentage that would be 30%
Find the equation of a line that passes through the points (2,7) and (4,6). Leave your answer in the form y = m x + c
Answers
Answer:
I think the answer would be
y = 0.5x -8
tough this might be wrong?
Step-by-step explanation:
(2, 7) ( 4,6)
to find the gradient- mx
y2-y1/ x2 - x1
chose which would be 1/ 2
if I chose (2,7) as 1 then (4, 6) as 2
mx = 6- 7/ 4-2
= -0.5x
y = -0.5x + c
substitute
6 = -0.5(4) + c
6= -2+ c
c = -8
Sets A, B, and C are subsets of the universal set U.
These sets are defined as follows.
U= {f, g, h, p, q, r, x, y, z)
A={g, h, q, r, z
:}
B={q, r, x, y, z)
C = {h, p, q,y}
Find (An B)' U C'.
Write your answer in roster form or as Ø.
(An B)' UC' = []
Answers
As sets A, B, and C are subsets of the universal set U, the value of A’ ∪ B’ U C' = {f}.
What is De Morgans law?Demorgan's law can be utilised in set theory and boolean algebra to make mathematical formulations simpler. Let's say that the universal set U has two subsets, A and B. A' is A's complement, and B' is set B's complement.
Given that, (An B)' UC'.
Using the De Morgan's law we have:
(A ∩ B)’ = A’ ∪ B’.
Substituting this in (An B)' UC'. we have:
A’ ∪ B’ U C'
A' = {f, p, x, y}
B' = {f, g, h, p}
C' = {f, g, x, z}
A’ ∪ B’ U C' = {f}
As sets A, B, and C are subsets of the universal set U, the value of A’ ∪ B’ U C' = {f}.
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Consider
the polynomials given below.
P = 1125 + 924 - 42³ 72² + 5
Q = (22² + 1) (42² - 3)
Determine the operation that results in the simplified expression below.
1125 + - 42³ - 52² + 8
O P Q
O
Ο
O
P+Q
PO
Q-P
Answers
The polynomial 11x⁵ + x⁴ - 4x³ - 5x² + 8 denotes the expression P - Q. The correct option is option A.
What is an expression?
A mathematical expression is a phrase that contains a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: Expression is (Math Operator, Number/Variable, Number/Variable)
Given polynomials are:
P = 11x⁵ + 9x⁴ - 4x³ - 7x² + 5
Q = (2x² + 1) (4x² - 3)
Simplify the polynomial Q = (2x² + 1) (4x² - 3):
Q = (2x² + 1) (4x² - 3)
Q = 2x²(4x² - 3) + 1(4x² - 3)
Q = 8x⁴ - 6x² + 4x² - 3
Add like terms:
Q = 8x⁴ - 2x² - 3
Now calculate P + Q
P + Q = 11x⁵ + 9x⁴ - 4x³ - 7x² + 5 + 8x⁴ - 2x² - 3
Combine like terms:
P + Q = 11x⁵ + (9x⁴ + 8x⁴) - 4x³ + (- 7x² - 2x²) + 5 - 3
P + Q = 11x⁵ + 17x⁴ - 4x³ - 9x² + 2
Now calculate P - Q
P - Q = 11x⁵ + 9x⁴ - 4x³ - 7x² + 5 - (8x⁴ - 2x² - 3)
P - Q = 11x⁵ + 9x⁴ - 4x³ - 7x² + 5 - 8x⁴ + 2x² + 3
P - Q = 11x⁵ + (9x⁴ - 8x⁴) - 4x³ + (-7x² + 2x² )+ (5 + 3)
P - Q = 11x⁵ + x⁴ - 4x³ - 5x² + 8
Now calculate Q - P
Q - P = 8x⁴ - 2x² - 3 - (11x⁵ + 9x⁴ - 4x³ - 7x² + 5)
Q - P = 8x⁴ - 2x² - 3 - 11x⁵ - 9x⁴ + 4x³ + 7x² - 5
Combine like terms:
Q - P = - 11x⁵ + (8x⁴ - 9x⁴) + 4x³ + (- 2x² + 7x²) - 3 - 5
Q - P = - 11x⁵- x⁴ + 4x³ + 5x² - 8
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How many solutions does the system of equations below have?
x − 4y = 6
2x − 8y = 12
Answers
Answer: Infinitely many solutions.
Step-by-step explanation:
When looking at the system, it is immediately clear that the second equation is simply the first equation with all terms multiplied by 2. Therefore, there are infinite solutions because these are actually the same exact line when graphed and will always equal each other no matter what the values for x and y are.
find x and y
pls help
Answers
Step-by-step explanation:
(3x+6)= 48(Alternate angles)
3x=48-6
3x=42
x=14
2y+48=5y-9 (Sum of two opposite interior angles= exterior angle)
48+9=5y-2y
57=3y
y=19
t•t•t•t•t•t•t rewrite using exponents
Answers
Answer:
t^7
Step-by-step explanation:
there are 7 ts so it is t to the power of 7
What is the value of 7 in 52.703.?
Answers
7 = Tenth
7 is the first decimal of the number making it a tenth.