The unit rate for this problem is how much Alyssa earns per hour
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Alyssa works 6.4-hour shifts at the donut shop each day.
Last week she earned $480 for working 32 hours.
Now, To determine her earnings per hour we have to divide her total earnings by the total no. of hours she worked which is,
= $(480/32).
= $15 per hour.
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In 2021, Sally Morris, a single taxpayer, pays $3,000 of interest on qualified student loans. Her AGI is $40,000. What is her qualified student loan interest deduction in 2021?
The qualified student loan interest deduction in 2021 is $37500.
What is adjusted gross income?Adjusted gross income is an individual's total gross income less specific deductions in the United States income tax system. It is used to compute taxable income, which is AGI minus personal exemption and itemized deduction allowances. AGI is more important than gross income for most individual tax purposes.
AGI is calculated by taking your gross income and subtracting certain "above the line" deductions. 401(k) contributions, health savings account contributions, and educator expenses are common examples of deductions
As per Law, a maximum of $2,500 will be allowed to be deducted from the Income. Thus the following would be the solution.
Income of Sally Morris = $40,000
Less: Qualified student loan interest $2,500
Modified Adjusted Gross Income $37,500
The deduction is $37500.
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the equation of the curve is y = x^2 + ax + b. The points (0,-5) and (5,0) lie on the curve. Find the coordinates of the turning point of the curve.
The turning point of the parabola is the point (2, - 9).
What is the turning point of a quadratic equation?
Quadratic equations represents parabolae and the vertex of the parabola represents the turning point as the slope of the curve changes its sign, from positive to negative or viceversa. The vertex can be derived by the vertex form of the equation of the parabola:
y - k = C · (x - h)²
Where:
(h, k) - Coordinates of the vertex.C - Vertex constantSince the quadratic equation has two real coefficients, we need the location of two points on Cartesian plane to find one solution. First, create the system of linear equations:
b = - 5 (1)
5 · a + b = - 25 (2)
Second, substitute b in (2) and clear a:
5 · a - 5 = - 25
5 · a = - 20
a = - 4
Third, write the quadratic equation:
y = x² - 4 · x - 5
Fourth, transform the equation into vertex form by completing the square:
y + 9 = x² - 4 · x + 4
y + 9 = (x - 2)²
Fifth, write the vertex of the parabola:
(h, k) = (2, - 9)
The point (2, - 9) represents the turning point of the parabola.
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Graph the piecewise function.
(6 points - 2 points for each piece)
Points of interval A (-1,-3) and (-2,-6)
Points of interval B is (1,1) and (2,-1)
How to find Piecewise function?
Determine which of the following intervals (or inequalities) the input belongs to before evaluating a piecewise function at any given input. The function specification for that specific interval can then simply be updated to reflect the new input.
[tex]f(x)=\left \{ {{3x, if x\leq -1} \atop {-2x+3, if 0 < x < 4}}\atop {2, if x\geq 4}\right.[/tex]
lets take 3x as Interval A
-2x+3 as interval B
and 2 as interval C
Now lets calculate the interval A
f(x)=3x
as x≤-1
∴f(-1) = 3(-1)
=(-3)
∴ point is (-1,-3)
∴f(-2) = 3(-2)
=(-6)
∴ point is (-2,-6)
Now lets calculate the interval B
f(x)=-2x+3
as 0<x<4
∴f(1) = -2(1)+3
=-2+3
=1
∴ point is (1,1)
∴f(2) = -2(2)+3
=-4+3
= -1
∴ point is (2,-1)
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solve the equation by elimination method 4x-2y=8,5x+3y=6
Solving the set of equation by elimination method gives
x = 1.64
y = -0.727
How to solve the equation by elimination methodThe given data
4x - 2y = 8 (1)
5x + 3y = 6 (2)
multiplying (1) by 3/2 and adding the result to (2)
6x - 3y = 12
5x + 3y = 6
6x + 5x - 3y + 3y = 12 + 6
11x = 18
x = 18/11
x = 1.64
substitute x = 18/11 into (1)
4 * 18/11 - 2y = 8
72/11 - 2y = 8
2y = 72/11 - 8
2y = -16/11
y = -8/11
y = -0.727
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If u can solve both the blanks that would be great
Find each probability if you spin the spinner and roll the number cube.
10. P(blue, 2)
12. P(not blue, 5)
11. P(red, even)
13. P(yellow, not 4)
red
blue
yellow
red
4
6
5
. The ratio of cups of almonds to cups of peanuts in a mixed nuts snack is 4 to 3.
How many cups of peanuts would be needed to make 49 cups of the mixed nuts
snack?
Number of cups of peanuts needed to make 49 cups of the mixed nuts snack is 21 cups
The ratio of cups of almonds to cups of peanuts in a mixed snack = 4 : 3
Number of of cups of almonds = 4x
Number of cups of peanuts = 3x
Total number of cups of mixed nuts snack = 49 cups
Then the equation will be
4x + 3x = 49
Add the like terms
7x = 49
x = 49 / 7
x = 7
Number of cups of almonds needed = 4x
= 4×7
= 28 cups
Number of cups of peanuts needed = 3x
= 3×7
= 21 cups
Hence, number of cups of peanuts needed to make 49 cups of the mixed nuts snack is 21 cups
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the number of hours spent watching television by students in the week before final exams has a normal distribution with a standard deviation of 4.5 hours. a random sample of 30 students is taken. is the probability that the sample standard deviation exceeds 3.5 hours more than 0.95?
The probability that the sample standard deviations exceeds 3.5 hours more than 0.95 is 0.23 < 0.95 ..
The numbers of hours spent on watching television by a student in a weak before is normally distributed.
We have provide the following details, standard
deviations of sample ( Number of hours in weak) (σ) = 4.5 hours
sample size (n) = 30
we shall compute the mean and variance of sample .
The E of s squared is equal to 4.5 squared. The variance of S squared is equal to twice the square of sigma divided by 1, which is 30 minus 1, which is 28.6, 28.2817. The chi-square distribution here has 29 degrees of freedom, which equals 29 squared to 4.5 squared. We want to find probabilities greater than 90 because the standard deviation of our sample is greater than 3.5 hours. The probability that S squared is greater than 3.5 is The probability that chi-square with 29 degrees of freedom is greater than
17. 54321 is very high. This is the same as zero.
This is equal to 1 minus the probability that 29 degrees of freedom chi-square is greater than 51 points 5556, which is what we want for part B. we are given one Probability will be zero.
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#Complete question
The number of hours spent watching television by students in the week before final exams has a normal distribution with a standard deviation of 4.5 hours. A random sample of 30 students was taken.a. Is the probability more than 0.95 that the sample standard deviation exceeds 3.5 hours?b. Is the probability more than 0.95 that the sample standard deviation is less than 6 hours?
Without calculating, order the quotients smallest to largest.
The order of the quotient from smallest to largest is given as follows:
42.6/70, 426/70, 42.6/0.07, 42.6/0.07.
What is a quotient?A quotient is given by the division of two terms a and b, that is:
a / b.
From this, we have that the dividend a and divisor b are inverse proportional, that is:
A large quotient is achieved when a is large and b is small.A small quotient is achieved when a is small and b is large.There are three divisions with the same term a, hence they are ordered, from smallest to largest, as follows:
42.6/70, 42.6/0.07, 42.6/0.07.
(the smallest the value of b, the largest the quotient).
The final quotient is:
426/70.
Dividing by 10 to have an equivalent value of a, we have that:
426/70 = 42.6/7.
Which is the second largest value of b, hence the second smallest quotient.
Missing InformationThe problem is given by the image shown at the end of the answer.
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What is another way to write (a6)(a²)?
a4
a8
a12
a36
At an elevation of 1221. 4 feet, lake mead will hold 28,945,000 acre-feet of water. Which number is the best estimate of this amount of water?.
The best estimate of this amount of water is [tex]3*10^{7}[/tex].
Given:
At an elevation of 1221. 4 feet, lake mead will hold 28,945,000 acre-feet of water.
So, the amount of water that is in the lake will be 28,945,000 acre-feet which is estimated to be 30000000 acre-feet of water.
Because the nearest estimate to 28945000 is 30000000.
= 30000000
= 300000*[tex]10^{2}[/tex]
= 30000*[tex]10^{3}[/tex]
= 3000*[tex]10^{4}[/tex]
= 3*[tex]10^{3} *10^{4}[/tex]
= 3*[tex]10^{7}[/tex]
Therefore The best estimate of this amount of water is [tex]3*10^{7}[/tex].
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Harry took a 5-hour trip on which he averaged 40 miles per hour. What distance did he travel?
Answer:
200 miles
Step-by-step explanation:
if its 40 miles per hour then multiply 5 with 40 and you'll end up with 200 miles
help me pls. i dont know how to do this
Answer:
k=f(x)-ab^x-h
h=x-ln(f(x)/a-k/a)/ln(b)
a=f(x)/b^x-h - k/b^x-h
Find the equation of the line passing through the given point and parallel to the given line.
( 7,-3) , 3y = 12x + 5
(-5, -2), y + 3x = 10
The equation of the lines passing the points and parallel to the equations ( 7,-3) , 3y = 12x + 5 (-5, -2), y + 3x = 10 is as follows:
y = 4x - 31y = -3x - 17.How to find the equation of a line?The equation of a line can be represented in different form such as standard form, general form, slope intercept form and point slope form. Therefore, let's represent the line in slope intercept form.
The equation of a line in slope intercept form is as follows:
y = mx + b
where
m = slopeb = y-interceptParallel line shave the same slope.
Hence,
( 7,-3) , 3y = 12x + 5
y = 4x + 5 / 3
slope is 4
The equation of the line is y = 4x + b. let's find the y-intercept using (7, -3).
-3 = 4(7) + b
b = -3 - 28
b = - 31
Hence, y = 4x - 31
(-5, -2), y + 3x = 10
y = -3x + 10
slope = -3
Therefore, let's find y-intercept using (-5, -2)
-2 = -3(-5) + b
-2 = 15 + b
b = -2 -15
b = - 17
Therefore, y = -3x - 17.
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The price of a dvd is $24. 00 plus 8% sales tax. What is the sales tax on this dvd in dollars and cents?.
Answer: $1.92
Step-by-step explanation:
This is the correct answer. Have a good day
Write the equation using function notation
x - y = -4
A) f(x) = x - 4
B) f(x) = x + 4
C) f(x) = -x + 4
D) f(x) = -x - 4
Answer:
C
Step-by-step explanation:
The owner of a bookstore buys used books from customers for $1. 50 each. The owner then resells the used books for 400% of the amount he paid for them. What is the price of a used book in this bookstore?.
Answer:
$7.50
Step-by-step explanation:
Bob’s employer covers 23% of his family’s annual health insurance premium. The balance of the premium is deducted in equal amounts from bob’s paycheck 26 times over the calendar year. If $185. 30 is withheld from each of bob’s paychecks, what is his family’s annual health insurance premium? a. $805. 65 b. $4,817. 80 c. $6,256. 88 d. $20,946. 96.
If $185.30 is withheld from each of Bob's paychecks, then his family's annual health insurance premium is $4817.80.
From the given information,
It was stated that the balance of the premium is deducted in equal amounts from Bob’s paycheck 26 times over the calendar year and $185.30 is withheld from each of Bob’s paychecks.
Therefore, the family’s annual health insurance premium will be calculated :
= $185.30 × 26
= $4,817.80
In conclusion, the correct option is $4,817.80.
therefore, his family's annual health insurance premium is $4817.80
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Yuson must complete a certain number of hours of community service. She does 2 hours of service each day. After 8 days, Yuson has completed half of her required community service.
Write a linear equation to represent the hours that Yuson has left to do after x days.
The linear equation to represent the hours that Yuson has left to do after x days is 16 - 2x.
How to calculate the equation?From the information, Yuson has to do Y hours of community service.
She works two hours every day, so service hours in x days = 2x
Remaining service hours after x days = y-2x
Also we have after 8 days , Yuson has completed half of her required community serivice. Therefore,
8 = y/2.
Cross multiply
y = 16
So the linear equation is 16-2x.
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Which fractions are equivalent to 0.63 repeating?
===============================================
Work Shown:
[tex]\text{x} = 0.\overline{63}[/tex]
x = 0.63636363...
100x = 63.63636363...
100x - x = (63.63636363...) - (0.63636363...)
99x = 63
x = 63/99
x = (7*9)/(11*9)
x = 7/11
This table shows a few fractions equivalent to 7/11
[tex]\begin{array}{|c|c|} \cline{1-2}\text{Multiply top} & \\ \text{and bottom by} & \text{Equivalent fraction}\\\cline{1-2}2 & 14/22\\\cline{1-2}3 & \boldsymbol{21/33}\\\cline{1-2}4 & \boldsymbol{28/44}\\\cline{1-2}5 & 35/55\\\cline{1-2}6 & 42/66\\\cline{1-2}\end{array}[/tex]
The terms in bold are the two answers
In other words, 7/11 = 21/33 when multiplying top and bottom by 3.
Also, 7/11 = 28/44 when multiplying top and bottom by 4.
To confirm those answers, use a calculator to find that
7/11 = 0.636363...
21/33 = 0.636363...
28/44 = 0.636363...
To rule out the non-answers, use the calculator to find that
14/21 = 0.667 approximately
7/12 = 0.5833 approximately
1. Is the game fair? We are flipping a coin twice. The first player wins if we get 2 tails, and the second player wins if we get 1 head and 1 tail. 2. Is the game fair? we are tossing two dice and the first player wins if the sum on the dice is 9 and the second player wins if the sum on the dice is 5.
For the given table of values for a polynomial function, where must the zeros of the function lie?.
The zero of the function lie between 2.5 and 3.0 and between 4.0 and 4.5
The given question is incomplete the complete question is
x 2.0 2.8 2.5 1.1 3.0 –0.8
f(x) 3.5 –1.2 4.0 –0.3 4.5 0.7
For the given table of values for a polynomial function, where must the zeros of the function lie?
A. between 2.0 and 2.5 and between 4.0 and 4.5
B. between 2.5 and 3.0 and between 4.0 and 4.5
C. between 2.0 and 2.5 and between 3.5 and 4.0
D. between 2.5 and 3.0 and between 3.5 and 4.0
answer : If a function is continuous and you have points on opposite sides of the x-axis, there must be a zero-crossing between those points. As evidenced by the table and graph,...
(3.0, 4.0) and (3.5, -0.2)
are points on the x-axis on opposite sides. As a result, between x=3.0 and x=3.5, there must be a zero crossing.
In the same way,...
(4.0, -0.8) and (4.5, 0.1)
are points on the x-axis on opposite sides. As a result, between x=4.0 and x=4.5, there must be a zero-crossing.
The correct answer option includes both of these possible zero crossings.
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Write the correct function and online represented in the table below
HELP ASAP
Answer:
y = 5x -2
Step-by-step explanation:
The 5 is the slope. It is the change in y over the change in x. As the x changes by 1, the y changes by 5.
The -2 is the y intercept. This is at the point (0,-2) The -2 is the y intercept.
HELP MEEEEEE PLEASEEEEE
Answer:
1000-400=600km
good luck i hope it helped, its all about reading the graph!
11/12+7/12 in simplest form
Answer:
The answer to your question could be either 3/2 (improper fraction), 1.5 (decimal), or 1 1/2 (mixed fraction).
Step-by-step explanation:
11/12 + 7/12 = 18/12
18/12 = 9/6
9/6 = 3/2
I WILL GIVE 30 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS
Answer:
third and last, can't promise that's right
Which does point A represent in this box plot?
A box plot is used to study the distribution and level of a set of a set of numbers. A box plot is made up of two lines and a box. The two lines are known as whiskers.
The end of the first whisker represents the minimum number. The minimum number is the smallest number in the dataset. The end of the second whisker represents the maximum number. The maximum number is the largest number in the dataset.
The first line to the left represents the lower (first) quartile. The second line on the box represents the median. The third line on the box represents the upper (third) quartile.
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1. Jorge used 2 7/8 packs of pencils in the first 1/3
of the year. At what rate is Jorge using
pencils
Answer:
Jorge is using pencils at a rate of 6 packs a year or a rate of 2 packs every four months.
Step-by-step explanation:
1/3 of a year is four months so that would be 2 packs every four months and if you multiply that by three you’d get 12 month, or one year, and 6 packs of pencils.
Identify the solution of the inequality |9m| + 40> 4 and the graph that represents it.
Answer:
can i have more info?
Step-by-step explanation:
If shown,
AB
and
CD
are straight lines. Find x in each case.
WILL MARK BRAINLISIT
Answer:
4x+x+x+90=360
6x+90=360
6x=270
x=45
good luck!
4x+x+x+90=360
6x+90=360
6x=270
x=45