Mitch completes the course and his boss promotes him. Mitch receives a 25% increase on his previous pay of $40 000 per year after tax.
However, Mitch took out a Study Assist loan from the government to pay his course fee. This means that 4% of his new after-tax salary goes towards repaying the loan.
How much extra pay does Mitch actually end up with for the year?
Mitch's salary increases by $10,000 but he has to repay $2,000 for his loan. Therefore, he ends up with an extra $8,000 per year.
Explanation:Mitch receives a 25% increase on his previous pay of $40,000 which equates to an additional $10,000 for the year (25% of $40,000 is $10,000), giving him a new salary of $50,000.
However, Mitch must pay 4% of his new salary towards his Study Assist loan. 4% of $50,000 equals $2,000. So he must repay $2,000 for his loan.
Therefore, the extra pay that Mitch actually keeps after paying his loan is $10,000 (rise in salary) minus $2,000 (loan repayment) which is $8,000 for the year. He ends up with $8,000 extra compared to his initial salary.
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what's the volume???
Which statement is true for the equation 4x − 4x − 5 = −5?
It has no solution.
It has one solution.
It has two solutions.
It has infinitely many solutions.
look at the following numbers -7 , 0 , 7 , 14 which pair of numbers has a sum of 0
Answer:-7, 7.
Step-by-step explanation:
-7+7= 0
Simple as that :) Plz mark brainliest
1. A package weighs 2.6 pounds. How much do 8 of some sized packages weigh?
It takes Maxine 0.3 hours to make a pat holder. How many pat holders can she make in 4.5 hours
3. A box of garss seed weighs 0.62 pounds. HOw much does a box containing 0.75times as grass seeds weigh?
4. A collection of nickels is worth 18.60$. how many nickels are in this collection?
5. Mrs.Anderson bought party flavors for the 24 studentsin ther class. Each flavor costs
$2.27. How much did all the party flavors cost.
6. Each prize for a carnival booth costs $0.32. How many prizes can you buy with $96?
7. Bob has a pack of 24 pencils, each pencil weighs 0.9 grams. How much does the pack of pencils weigh?
Aaron's hourly rate is $8 more than Rachel's if both of them work for 2 hours and received a total of $124 what is Rachel's hourly pay
the state fair is a popular field trip destination. This year the señior class at High school A and the señior class at High school B both planned trips there the señior class A rented and filled 8 vans and 8 buses with 240 students. High school B rented and filled 4 vans and 1 bus with 54 students. every van had the same number of students in it as did the buses. find the number of students in each van and each bus
Answer:
The number of student in each van is 8. The number of student in each bus is 22.
Step-by-step explanation:
Consider the provided information.
Let the number of student in each van is x.
The number of student in each bus is y.
School A rented and filled 8 vans and 8 buses with 240 students.
This can be written as:
[tex]8x+8y=240[/tex]......(1)
School B rented and filled 4 vans and 1 bus with 54 students.
[tex]4x+y=54[/tex]
[tex]y=54-4x[/tex]......(2)
Substitute the value of y in equation (1).
[tex]8x+8(54-4x)=240[/tex]
[tex]8x+432-32x=240[/tex]
[tex]8x-32x=240-432[/tex]
[tex]24x=192[/tex]
[tex]x=8[/tex]
Thus, the number of student in each van is 8.
Substitute the value of x in equation (2).
[tex]y=54-4(8)[/tex]
[tex]y=54-32[/tex]
[tex]y=22[/tex]
Thus, the number of student in each bus is 22.
A 150-unit apartment complex is infested with rats. The apartment caretaker checked 9 units and found the following number of rats {2, 5, 3, 1, 0, 3, 7, 2, 2}. If the sample data is representative of the rat population, how many units in the entire apartment complex have 3 rats?
To estimate the number of units in the entire apartment complex that have 3 rats, we can use the proportion of units in the sample that have 3 rats and apply it to the total number of units in the complex.
Explanation:To determine how many units in the entire apartment complex have 3 rats, we can use the concept of sampling. Since the apartment caretaker checked 9 units and recorded the number of rats in each, we can calculate the proportion of units with 3 rats in these 9 units. We can then apply this proportion to the entire apartment complex to estimate the number of units with 3 rats.
Out of the 9 units checked, there were 3 units with 3 rats. So the proportion of units with 3 rats in the sample is 3/9 = 1/3.
To estimate the number of units with 3 rats in the entire apartment complex, we can multiply the proportion of units with 3 rats in the sample (1/3) by the total number of units in the complex: 1/3 * 150 = 50. So, approximately 50 units in the entire apartment complex have 3 rats.
The Lions won 35 out of 40 games this season what fraction of the games played did the Lions won? Write your answer in a simplest form
What is the distance between the points (-4, 6) and (1, -6)?
1. 85
2. 13
3. 15
4. 29
1--4 = 5
-6 -6 = 12
5^2 = 25
12^2 = 144
144+25 = 169
sqrt(169) = 13
distance = 13
(08.03) Consider the following pair of equations:
y = 3x + 3
y = x − 1
Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form
NEED HELP FAST!!!
15.
(08.06 MC)
Abril and Alanis put some money into their money boxes every week. The amounts of money (y), in dollars, in their money boxes after certain amounts of time (x), in weeks, are shown by the equations below:
Abril
y = 50x + 10
Alanis
y = 30x + 70
After how many weeks will Abril and Alanis have the same amount of money in their money boxes, and what will that amount be? (1 point)
3 weeks, $160
3 weeks, $210
4 weeks, $160
4 weeks, $210
A pizza is cut into six unequal slices (each cut starts at the center). The largest slice measures 90 degrees
If Larry eats the slices in order from the largest to the smallest, then the number of degrees spanned by a slice decreases at a constant rate. (So the second slice is smaller than the first by a certain number of degrees, then the third slice is smaller than the second slice by that same number of degrees, and so on.)
What is the degree measure of the fifth slice Larry eats?
Which logarithmic function has x=5 as its vertical asymptote and (6,0) as the x-intercept?
Jamie unfolded a cardboard box. The figure of the unfolded box is shown below: Which expression can be used to calculate the area of cardboard, in square inches, that was used to make the box? 6 x 4 x 4 4 x 6 x 6 6 x 2 x 2 2 x 6 x 6
there are 6 sections and the sections are 4 x 4
so the correct expression can be 6x4x4
Answer:
6 x 4 x 4
Step-by-step explanation:
IN order to calculate the total area or the cardboard you just have to make a simple multiplication, the carboard is divided in equal sized squares, 6 equal sizd squares, and each one of them has a 4 inches side, so to calculate the area of the cardboard you just calculate the area of one square and then multiply it by the number of squares.
Area of one square= 4x4
Number of squares=6
Total area of the carboard= 6x4x4
because the angles in a rectangle are 90 degrees it is not a parallelogram true or false
A rectangle is a parallelogram because each pair of sides is parallel and the same length as each other
Properties of a parallelogramFor a parallelogram, the following are true
Two of the interior angles are equal
Only two o fits sides are parallel
A parallelogram is a quadrilateral figure with opposite parallel sides.
For a rectangle, all the interior angles are 90 degrees, a
Hence we can conclude that a rectangle is a parallelogram because each pair of sides is parallel and the same length as each other
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Two similar polygons are shown below:
Which transformation was performed on PQRS to form P′Q′R′S′?
A dilation factor of 2
A dilation factor of 4
A dilation factor of 1 over 2
A dilation factor of 1 over 4
Answer: The correct option is (A) A dilation factor of 2.
Step-by-step explanation: We are shown two similar polygons in the figure.
We are to select the transformation that was performed on PQRS to form P'Q'R'S'.
We can see clearly from the figure that two polygons have same shape but different sizes.
So, the only transformation possible from PQRS to P'Q'R'S' is dilation.
To find the dilation factor, we need the lengths of any two corresponding sides of PQRS and P'Q'R'S'.
From the graph, we note that
PQ = 2 units and P'Q' = 4 units.
Therefore, the dilation factor is given by
[tex]D_f\\\\\\=\dfrac{\textup{length of a side of the dilated figure P'Q'R'S'}}{\textup{length of the corresponding side of the original figure PQRS}}\\\\\\=\dfrac{P'Q'}{PQ}\\\\\\=\dfrac{4}{2}\\\\=2.[/tex]
Thus, the required transformation is a dilation with dilation factor of 2.
Option (A) is CORRECT.
In Coach Sullivan's gym class, there are 28 girls and 35 boys. Coach Sullivan plans to divide the students into teams so that each team has the same number of girls and the same number of boys. Coach Sullivan also wants to make as many teams as she possibly can.
How many teams will Coach Sullivan be able to make? How many girls will be on each team? How many boys will be on each team?
Simplify 5 square root of 11 end root minus 12 square root of 11 end root minus 2 square root of 11.
negative 33 square root of 9
negative 11 square root of 9
negative 9 square root of 11
negative 9 square root of 33
Question 5(Multiple Choice Worth 1 points)
Simplify square root of 5 open parentheses 10 minus 4 square root of 2 close parentheses.
14
15 square root of 2
5 square root of 2 end root minus 4 square root of 10
None of the above
Question 6(Multiple Choice Worth 1 points)
Simplify square root of 3 times square root of 21.
square root of 24
square root of 63
3 square root of 7
None of the above
Answer:
[tex]-9\sqrt{11}[/tex]; None of the above; [tex]3\sqrt{7}[/tex]
Step-by-step explanation:
For the first question:
[tex]5\sqrt{11}-12\sqrt{11}-2\sqrt{11}[/tex]
Treating the radicals as a variable, we combine like terms:
[tex]5\sqrt{11}-12\sqrt{11}-2\sqrt{11}\\\\=-7\sqrt{11}-2\sqrt{11}\\\\-9\sqrt{11}[/tex]
For the second question:
[tex]5(10-4\sqrt{2})[/tex]
We use the distributive property:
[tex]5(10-4\sqrt{2})\\\\5\times 10-5\times4\sqrt{2}\\\\50-20\sqrt{2}[/tex]
This is not one of the choices available.
For the third question:
[tex]\sqrt{3}\times \sqrt{21}[/tex]
We will first find the prime factorization of 21. 21 = 3*7:
[tex]\sqrt{3}\times \sqrt{3\times7}[/tex]
These can all be written under one radical:
[tex]\sqrt{3\times 3\times 7}[/tex]
For square roots, we want pairs of factors. We have a pair of 3s, so this comes out, giving us
[tex]3\sqrt{7}[/tex]
Answer: Answer of First Question is -9√11, answer of second Question is 'None of the above' and answer of third question is 3√7
Step-by-step explanation:
since, in first question, given expression is,
5√11-12√11-2√11
And, we can write, 5√11-12√11-2√11=-9√11
In other words, negative 9 square root of 11
Thus, option third is correct.
In second question, given expression is,
5(10-4√2),
And we can write, 5(10-4√2)=50-20√2
In other words, 50 minus 20 square root of 2.
Thus, Option fourth is correct.
In third question, given expression,
√3×√21,
And we can write, √3×√21=√3×√3×√7=3√7
Thus, third option is correct.
The sum of the first natural number and 0 is 1, the sum of the first two natural numbers and 0 is 3, the sum of the first three natural numbers and 0 is 6, and the sum of the first four natural numbers and 0 is 10. Which explicit formula generates the sum of the first n natural numbers and 0?
A) n(n+1)/2
B) 2n-1
C) n(n+4)/4
D) 3n-2
If the area of the following figure is 46 square centimeters, what is the height of the trapezoid?
Bottom: 15 cm
Top: 8 cm
Dotted line with a box right before the curve from the top. Which is H.
4 cm
2 cm
5.75 cm
3.1 cm
Answer:
4cm
Step-by-step explanation:
Area= 1/2(b1 +b2)(h)
46 = 1/2(8+15)(h)
46 = 1/2(23)(h)
46/11.5=11.5h/11.5
4 = h
What other information do you need to prove ΔABE is congruent to ΔEDA by SSS?
A) A= C
B) ΔEAC is isosceles triangle with base EC
C) E= C
D) EAC is equilateral triangle
Answer:
D) EAC is equilateral triangle
Step-by-step explanation:
Given :
AEC is a triangle in which B∈ AC and D∈EC
Such that,
∠ABE = 90°,
∠ADE = 90°,
Also, BC = CD
We have to prove that :
Δ ABE is congruent to Δ EDA
Proof :
If EAC is an equilateral triangle,
By the property of equilateral triangle,
EA = AC = EC
If AC = EC
⇒ AB + BC = ED + CD
⇒ AB + CD = ED + CD
⇒ AB = ED
Also, AE = AE ( common segment )
Now, if in two right triangles hypotenuse are equal and any corresponding legs are equal,
Then, the other legs must be equal,
That is, BE = DA,
Hence, by SSS postulate of congruence,
Δ ABE ≅ Δ EDA
Therefore, option D is correct.
Choose the correct simplification of (3x3 + 2x2 − 5x) − (8x3 − 2x2)
A.−5x3 + 4x2 − 5x
B. 5x3 + 2x2 + 5x
C.−5x3 − 4x2
D. 5x3 + 2x2
Answe
-5x³ + 4x² - 5x
Step-by-step explanation:
got it right on the quiz
I need help please!!
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Kendra rides her bike to school each day. It takes her 10 minutes to ride 30 blocks. What unit rate expresses the speed of Kendra's bike ride?
2 blocks per minute
3 blocks per minute
4 blocks per minute
10 blocks per minute
Answer:
3 blocks.
Step-by-step explanation:
The answer is 3 blocks
The cheerleading team lines up down the football field to rally the spectators. If there are 12 cheerleaders, which expression gives the number of ways can they line up down the field?
Final answer:
The number of ways 12 cheerleaders can line up is calculated using permutations, specifically 12!, which is the product of all positive integers from 1 to 12.
Explanation:
The number of ways the 12 cheerleaders can line up down the football field can be calculated using the concept of permutations. A permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement. For 12 cheerleaders, each of whom is distinct, the number of different ways they can line up is the same as the number of permutations of 12 objects, which is given by the factorial of the number of objects.
The formula for permutations of n objects is n! (n factorial), where n represents the total number of objects. Therefore, for 12 cheerleaders, the expression for the number of ways they can line up is:
12!
This is calculated as 12 × 11 × 10 × 9 × ... × 3 × 2 × 1. The value of 12! (12 factorial) gives us the total number of possible arrangements for the 12 cheerleaders.
The side of a square measures (4x − 7) units.
Part A: What is the expression that represents the area of the square? Show your work to receive full credit. (4 points)
Part B: What are the degree and classification of the expression obtained in Part A? (3 points)
Part C: How does Part A demonstrate the closure property for polynomials? (3 points)
help me solve this equation 3x-7=4x
Ten minutes after a plane leavesthe airport, it is reported to be 40 miles
away. What is the avarage speed in miles per hour of the plane?