To find the number of hours Carla worked, we'll set up and solve equations based on the information given.
Explanation:To solve this problem, we'll set up an equation based on the information given.
Let x be the number of hours Carla worked last week and y be the number of hours she worked this week.
According to the problem, 15 more than twice the hours Carla worked last week is the same as three times the hours she worked this week decreased by 15:
2x + 15 = 3y - 15
Next, we'll set up another equation based on the fact that Carla worked the same number of hours each week:
x = y
We can now solve this system of equations to find the value of y, which represents the number of hours Carla worked this week:
Substituting y for x in the first equation: 2y + 15 = 3y - 15
Combining like terms: 15 = y - 15
Adding 15 to both sides: 30 = y
So, Carla worked 30 hours this week.
Graham uses a 10 by 10 grid to model a decreasing pattern. He cuts off a section representing a percent of the current area so that the remaining area represents the next term in the pattern, rounded to nearest whole centimeter. The area after each cut is shown on the graph.
After each cut, the remaining area is___% of the previous area
After the first cut, the remaining area represents 70% of the previous area.
How to calculate the areaLet's assume the initial area of the 10 by 10 grid is 100 square centimeters. After the first cut, a certain percentage of the current area is removed, leaving behind the remaining area. Let's say the remaining area after the first cut is 70 square centimeters.
To calculate the percentage of the remaining area compared to the previous area, we can use the formula:
(remaining area / previous area) * 100
In this case:
(70 / 100) * 100 = 70%
So, after the first cut, the remaining area represents 70% of the previous area.
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A classic counting problem is to determine the number of different ways that the letters of "balloon" can be arranged. Find that number.
The number is:
1260
Step-by-step explanation:We know that the number of ways of arranging n items is calculated by the method of permutation.
If n letters are to be arranged such that there are [tex]r_1,r_2[/tex] items each of the same type.
Then, the number of ways of arranging is:
[tex]\dfrac{n!}{r_1!\times r_2!}[/tex]
We are asked to find the number of ways of arranging the letters of "Balloon"
There are a total of 7 words such that 'l' occurs two times and 'o' occurs two times.
Hence, the number of ways of arranging them are:
[tex]=\dfrac{7!}{2!\times 2!}\\\\=\dfrac{7\times 6\times 5\times 4\times 3\times 2!}{2!\times 2}\\\\=1260\ ways[/tex]
Roger can run one mile in 8 minutes. jeff can run one mile in 6 minutes. if jeff gives roger a 1 minute head start, how long will it take before jeff catches up
Greg practiced playing his clarinet for 12 minutes He has practiced 40% of the amount of time he needs to practice today how many more minutes does Greg need to practice today?
An ounce of pine nuts cost $1.40 if Ellen buys 2.5 ounces of pine nuts, how much will she have to pay
Solve this quadratic equation using the quadratic formula. 3x2 + 4x = 6
Answer:
x= -2 + and - sqrt 22 /3
Step-by-step explanation:
is 0.142045454545 a repeating or terminating number??
kwei-twang kuo plans to make these online payments: store charge account $160; charitable donation, $40; rent $550; cable bill, $42.01. She began the day with a checking account balance of $16.83. Later that same day she estimated her online payments and transferred $800 into checking from savings to cover the expected payments. What will be the balance of her checking account after the online payments are made?
Final answer:
After making her online payments totaling $792.01, Kwei-Twang Kuo will have a balance of $24.82 in her checking account.
Explanation:
First, we'll calculate the total payments Kwei-Twang Kuo needs to make by adding up all of her expenses:
Store charge account: $160
Charitable donation: $40
Rent: $550
Cable bill: $42.01
Adding these amounts together gives us a total of $792.01 for the payments.
Let's calculate the balance of her checking account after she transfers $800 and makes the payments:
Begin with checking account balance: $16.83
Transfer into checking account: +$800.00
New balance before payments: $816.83
Total payments to be made: -$792.01
Final checking account balance: $24.82
Therefore, after Kwei-Twang Kuo makes her online payments, she will have a balance of $24.82 in her checking account.
what is greater 4 liter or 1 gallon
Which equation correctly applies the distributive property A. −2.5⋅(4⋅1.045)=(−2.5⋅4)⋅1.045 B. 50+1.015=(50⋅1)+(50⋅0.01)+(50⋅0.005) C. (0.5⋅0.5)+(0.5⋅0.3)+(0.5⋅0.2)=0.5⋅(0.5+0.3+0.2) D. −1.2⋅0.57⋅0.5=−1.2⋅0.5⋅0.57
By observing the given options we can conclude that equation
C. (0.5⋅0.5) + (0.5⋅0.3) + (0.5⋅0.2) = 0.5⋅(0.5 + 0.3 + 0.2) correctly applies the distributive property.
What are the other properties?The other two properties are commutative property and associative property.
We know the distributive property for four terms states,
a(b ± c± d ± e) = ab ± ac ± ad ± ae.
∴ From observing the given options we can conclude that
0.5⋅(0.5 +0.3 + 0.2) = (0.5⋅0.5) + (0.5⋅0.3 )+ (0.5⋅0.2).
Or
(0.5⋅0.5) + (0.5⋅0.3) + (0.5⋅0.2 ) = 0.5⋅(0.5 + 0.3 + 0.2).
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What number is 40% of 135?
Enter your answer in the box.
What is 1 4/9 of 9000 feet
A sports club plans to have its lawn mowed. The cost of mowing x square feet of lawn is given by the function f(x) = 0.04x + 3.5, where f(x) represents the cost in dollars. The total area that needs to be mowed is given by the function g(x) = 12x.
Which function best describes C(x), the total cost of mowing the lawn of the sports club?
A) C(x) = 0.48x + 3.5x
B) C(x) = 0.48x2 + 3.5
C) C(x) = 0.48x2 + 42x
D) C(x) = 0.48x2 + 42
D
This is the plato answer
Estimate 36472-32841
Find the area enclosed by the figure.
Shakira went bowling with her friends. She paid $3 to rent shoes and then $4.75 for each game of bowling. If she spent a total of $42, then how many games did Shakira bowl?
Shakira bowls about 8 games.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Let Shakira bowl x games.
Since Shakira has to pay $4.75 for each game, she would pay $4.75x for x games.
Shakira also paid $3 to rent shoes, therefore, the total money Shakira spent is:
4.75x + 3
Given that, the total spent is $42, therefore,
4.75x + 3 = 42
4.75x = 42 - 3
4.75x = 39
x = 39/4.75
x ≈ 8
Hence, Shakira bowls about 8 games.
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The distance between two cities is 145 miles. A truck can cover this distance in 2.5 hours. The speed of a car is 1.5 times faster than the speed of the truck. How long does it take them to meet, if they start moving towards each other simultaneously?
The speed at which the distance is covered by the two vehicles is the sum of their speeds:
... (truck speed) + 1.5×(truck speed) = 2.5×(truck speed)
The time required to cover the distance is inversely proportional to speed, so is
... (2.5 hours)/2.5 = 1.0 hours
It takes 1.0 hours for the vehicles to meet.
_____
The speed of the truck is (145 mi)/(2.5 h) = 58 mi/h
The speed of the car is 1.5 × 58 mi/h = 87 mi/h.
The speed at which they move toward each other is
... 58 mi/h + 87 mi/h = 145 mi/h
So, the time it takes to cover 145 miles is
... (145 mi)/(145 mi/h) = 1.0 h
In the figure, sin ∠MQP = ______.
A. Cos N and Sin R
B. Sin R and Sin N
C. Cos N and Sin M
D. Cos R and Sin N
I WILL MARK BRAINLIEST!!!!! 24 POINTS!!!!!
we know that
in the right triangle MNR
[tex]Sin(N\°)=Cos(R\°)[/tex]
[tex]Sin(56\°)=Cos(34\°)[/tex]
Because
[tex]N+R=90\°[/tex]
[tex]56\°+34\°=90\°[/tex] --------> by complementary angles
so
sin ∠MQP=[tex]Sin(56\°)[/tex]
therefore
the answer is the option
D. Cos R and Sin N
In the figure, AB¯¯¯¯¯ is parallel to DE¯¯¯¯¯ .
Select from the drop-down menu to correctly complete the statement.
Triangle ABC and triangle DEC are A.Similar B. Nonsimilar
Answer:
(A) Similar triangles
Step-by-step explanation:
It is given that AB is parallel to DE, therefore ∠CAB=∠DEC=65°(Alternate angles),
Then from ΔACB and ΔDCE, we have
∠CAB=∠DEC=65°(Alternate angles)
and ∠ACB=∠DCE=50°(Vertically opposite angles)
Thus, by AA similarity, ΔACB is similar to ΔDCE.
Hence, option A that is similar triangles is correct.
What is the locus of all points that are a fixed distance from a given point? A) angle B) circle C) triangle D) line segment
Evaluate the function for x = 8. f(x)=x^2/16-2x A. –15 B. 20 C. –12 D. –24
Line ET is a tangent to circle A at point T and the measure of ∠TNG is 25°
What is the measure of ∠NET?
A) 130°
B) 50°
C) 65°
D) 90°
Which situation could best be represented by this linear equation?
24x + 38y = 520
C. If x represents the number of bracelets sold at $24 each and y represents the number of rings sold at $38 each, the total sales were $520.
what is 1/5 of 80% this is worth 100 points soooo yes
plz solve correctly
Suppose that a person with a push mower can mow a large lawn in 2 hours, whereas the lawn can be mowed with a riding lawn mower in 1 hours. working together, how long will it take to mow the lawn
2/3 hours take to mow the lawn.
what is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
Time taken to mow by push mower= 2 hours
Time taken to mow by riding mower= 1 hours
So, if working together the time taken
= 1 / (1/2 + 1/1)
=1/ (3/2)
= 2/3
Hence, it will take 2/3 hours.
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which group contains numbers that all mostly round most closely to 1/2 A. 1/5 , 2/9 , 4/8 B. 3/5 , 2/4 , 4/6
Answer:
b
Step-by-step explanation:
As of this writing, the powerball lottery is run in 42 states. winning the jackpot requires that you select the correct five numbers between 1 and 59 and, in a separate drawing, you must also select the correct single number between 1 and 39. find the probability of winning the jackpot. 34.
Final answer:
The probability of winning the Powerball jackpot is 1 in 292,201,338.
Explanation:
To find the probability of winning the Powerball jackpot, we need to calculate the probability of selecting the correct five numbers between 1 and 59 and the correct single number between 1 and 39.
The probability for each part is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
For the five numbers, there are 59 possible choices and we need to select 5, so the probability is 1/59 × 1/58 × 1/57 × 1/56 × 1/55.
For the single number, there are 39 possible choices, so the probability is 1/39.
To find the overall probability, we multiply the probabilities of both parts together: (1/59 × 1/58 × 1/57 × 1/56 × 1/55) × (1/39) = 1/292,201,338.
what values of x make up f(x)=3x+1 equal to g(x)=3^x+1? 0, 1, 2, 3 select all that apply
Let us plug-in the values of x to know
> x = 0
f(0) = 3(0) + 1 = 1
g(0) = 3^0 + 1 = 2
> x = 1
f(1) = 3(1) + 1 = 4
g(1) = 3^1 + 1 = 4
> x = 2
f(2) = 3(2) + 1 = 7
g(2) = 3^2 + 1 = 10
> x = 3
f(3) = 3(3) + 1 = 10
g(2) = 3^3 + 1 = 28
Therefore the only answer is:
1
Mrs. Barlow's math class took a test yesterday. Out of 60 students, 70% of them passed. How many of Mrs. Barlow's students passed the test?
427 thousand conveted into scientific notation