Andy has $32 money left after spending $18 on school supplies and $47 on new clothes.
To find out how much money Andy has left, we need to start with the total amount of money he saved and then subtract the amount he spent on school supplies and new clothes.
The total amount Andy saved is:
$32 + $27 + $38 = $97
The amount Andy spent is:
$18 + $47 = $65
To find out how much money Andy has left, we can subtract the amount he spent from the amount he saved:
$97 - $65 = $32
So, after spending $18 on school supplies and $47 on new clothes, Andy is left with $32.
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The cost of a pen is $15. Find the cost of 162 pens
Answer: 15 x 162 = 2430$
The Morning Gazette offers employees 1.65% of the average of their last 3 years of annual compensation for each year of service. Rita began working for the Morning Gazette in 1994. She retired in 2016. In 2014, she made $76,000 per year. Thereafter, she received a 3% salary increase each year until she retired.
a) How much did she earn for each year from 2014 through 2016?
b) What is the average of her last five years of working?
c) How much was his annual retirement benefit?
She earn fοr each year frοm 2014 thrοugh 2016 is 80628.40. The average οf her last five years οf wοrking $78,302.80. His annual retirement benefit was $28,423.92.
a) Salary οf 2014 : $76000
Salary in 2014 is the salary in 2015 increased by 3% οf the salary
= $76,000+3%
Salary οf 2015 = $78,280
Salary in 2015 is the salary in 2016 increased by 3% οf the salary
=$78,280+3%
Salary οf 2016 = $80,628.40
Hence, she earn fοr each year frοm 2014 thrοugh 2016 is 80628.40
b) The average οf the last three years is the sum οf the salaries divided by the number οf salaries.
= $76,000+$78,280+$80,628.40 / 3
= $78,302.80
Hence, the average οf her last five years οf wοrking $78,302.80
c ) The annual retirement benefit is the prοduct οf the rate and the average and the number οf years οf service.
= 1.65%×$78,302.80×22
=$28,423.92
Hence, his annual retirement benefit was $28,423.92.
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Bandar Industries manufactures sporting equipment. One of the company’s products is a football helmet that requires special plastic. During the quarter ending June 30, the company manufactured 3,500 helmets, using 2,485 kilograms of plastic. The plastic cost the company $16,401.
According to the standard cost card, each helmet should require 0.66 kilograms of plastic, at a cost of $7.00 per kilogram.
Required:
1. What is the standard quantity of kilograms of plastic (SQ) that is allowed to make 3,500 helmets?
2. What is the standard materials cost allowed (SQ × SP) to make 3,500 helmets?
3. What is the materials spending variance?
4. What is the materials price variance and the materials quantity variance
1. The standard quantity of plastic allowed to make 3,500 helmets is 2,310 kilograms.
2. The standard materials cost allowed to make 3,500 helmets is $16,170.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
1. The standard quantity of kilograms of plastic (SQ) allowed to make 3,500 helmets can be calculated as:
SQ = Standard quantity per unit × Actual output
= 0.66 kg/helmet × 3,500 helmets
= 2,310 kg
Therefore, the standard quantity of plastic allowed to make 3,500 helmets is 2,310 kilograms.
2. The standard materials cost allowed (SQ × SP) to make 3,500 helmets can be calculated as:
Standard materials cost allowed = Standard price × Standard quantity allowed
= $7.00/kg × 2,310 kg
= $16,170
Therefore, the standard materials cost allowed to make 3,500 helmets is $16,170.
3. The materials spending variance can be calculated as the difference between the actual cost incurred and the standard cost allowed:
Materials spending variance = Actual materials cost - Standard materials cost allowed
= $16,401 - $16,170
= $231 (Favorable)
Therefore, the materials spending variance is $231 (Favorable).
4. The materials price variance and the materials quantity variance can be calculated as follows:
Materials price variance = (Actual price - Standard price) × Actual quantity
= ($16,401/2,485 kg - $7.00/kg) × 2,485 kg
= $9,141.77 (Unfavorable)
Materials quantity variance = (Actual quantity - Standard quantity allowed) × Standard price
= (2,485 kg - 2,310 kg) × $7.00/kg
= $1,225 (Unfavorable)
Therefore, the materials price variance is $9,141.77 (Unfavorable) and the materials quantity variance is $1,225 (Unfavorable).
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A typewriter says that he can write 50 pages under 60 minutes. You selected 24 cases for these 50 pages, and found that it takes 63.2 (in minutes) and its standard deviation is 7.7 (in minutes). The test statistic for this test is equal to
a.
t = 2.04
b.
Z = 1.79
c.
t = 1.79
d.
t = 2.04
Answer: To determine the correct answer, we need to calculate the t-test statistic using the given information.
The formula for the t-test statistic for a one-sample t-test is:
t = (x - μ) / (s / sqrt(n))
where x is the sample mean, μ is the hypothesized population mean (which is not given in this question), s is the sample standard deviation, and n is the sample size.
Here, x = 63.2 minutes, s = 7.7 minutes, and n = 24 cases. We are not given a hypothesized population mean, so we cannot calculate the exact t-test statistic. However, we can use the sample mean as an estimate of the population mean for the purposes of this question.
Plugging in the values, we get:
t = (63.2 - 60) / (7.7 / sqrt(24))
t = 2.04
Therefore, the correct answer is (a) t = 2.04.
3.4 MIXED FACTORING
1. Utilize all of the strategies for factoring in order to factor the following polynomials.
Reminder: Combine like-terms prior to factoring.
2xy + 30x^2 - xy - 16y^4 - yx - 5x^2
The factor of 2xy + 30x^2 - xy - 16y^4 - yx - 5x^2 is 25x2−16y4=(5x+4y2)(5x−4y2)
We are given that;
2xy + 30x^2 - xy - 16y^4 - yx - 5x^2
Now,
Combine like terms by adding or subtracting the coefficients of the same variables. For example, 2xy - xy - yx = 0xy, and 30x^2 - 5x^2 = 25x^2. The polynomial becomes:
25x2−16y4
Check if there is a common factor for all the terms. In this case, there is no common factor other than 1, so we cannot use the greatest common factor method.
Check if the polynomial is a difference of two squares, which means it has the form a2−b2. In this case, we can see that both terms are perfect squares: 25x2=(5x)2 and 16y4=(4y2)2. Therefore, we can use the difference of two squares formula:
a2−b2=(a+b)(a−b)
Substituting a=5x and b=4y2, we get:
25x2−16y4=(5x+4y2)(5x−4y2)
Check if each factor can be further factored using any of the methods. In this case, neither factor can be further factored, so we are done.
Therefore, by factorization the answer will be 25x2−16y4=(5x+4y2)(5x−4y2)
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Mr.John borrowed $5,340.00 from the bank at 9.5% per annum simple interest for 5 years. Calculate The value of each montly installments
Answer:
5,340x.095=507.3
507.3÷5=101.46
101.46÷12=$8.45 interest
5,340÷5=1068
1068÷12= $89
89+8.45=$97.45
answer $97.45 a month
Using the graphing Method, find the value of x in the system of equations y=4x-1 and y=-x+4
Answer: To solve the system of equations graphically, we need to graph both equations on the same coordinate system and find the point where they intersect. This point will give us the values of x and y that satisfy both equations.
First, we can rewrite the two equations in slope-intercept form:
y = 4x - 1 (equation 1)
y = -x + 4 (equation 2)
Now we can graph both equations on the same coordinate system. To do this, we can plot a few points for each equation and then draw a line through the points. Alternatively, we can use the y-intercept and slope of each equation to graph the lines. For equation 1, the y-intercept is -1 and the slope is 4. For equation 2, the y-intercept is 4 and the slope is -1.
We can see that the two lines intersect at the point (1, 3). Therefore, the solution to the system of equations is x = 1.
Is 93 + 7 positive or negative?
Answer:
93 + 7 = 100
Step-by-step explanation:
I would assume positive because 100 is above the x-axis not below it.
Alice purchased a car for $24,000. The value of the car depreciates at a rate of 5.5% each year.
Which function equation represents the value of the car after t years?
ANSWER IS: f(t)=24,000(0.945)t
just took the test
According to the given question, Alice should use this equation f(t) = [tex]24,000(0.945)^t[/tex] to represent the value of the car after t years.
Depreciation is defined by who?Depreciation is the expected decrease in the value of fixed assets over the course of a fiscal year. For physical assets like real estate, machinery, vehicles, and other items, large lump sum acquisitions are made.
The equation[tex]f(t) = 24,000(0.945)^t[/tex] represents the value of the car after t years, where 0.945 represents the remaining value of the car after one year of depreciation at a rate of 5.5%.
To calculate the value of the car after two years, for example, we would substitute t = 2 into the equation:
f(2) = [tex]24,000(0.945)^2[/tex]
f(2) = 24,000(0.893025)
f(2) ≈ 21,433.80
Therefore, the value of the car after two years would be approximately $21,433.80.
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The table below gives data from a linear function. Find a formula for the function.
Price per shirt, p($) 15 20 25
Number of shirts sold, q = f(p) 1000 750 500
a. f( p) = 1750p − 50 b. f( p) = 1000 − 50p c. f( p) = 1000 + 50 p
d. f( p) = 1750 + 50 p e. f( p) = 1750 − 50p
The formula for the linear function is f(p) = -50p + 1750. So, correct option is E.
To find the formula for the linear function from the given table, we need to determine the equation of a straight line that passes through the three given points. We can use the point-slope form of the equation of a straight line to solve for the slope and y-intercept.
Let's choose two of the given points, say (15, 1000) and (25, 500), to calculate the slope:
slope = (change in y)/(change in x)
= (500 - 1000)/(25 - 15)
= -50
Now, we can use the slope and one of the given points, say (15, 1000), to solve for the y-intercept using the point-slope form:
y - y₁ = m(x - x₁)
y - 1000 = -50(x - 15)
y - 1000 = -50x + 750
y = -50x + 1750
Therefore, the formula for the linear function is f(p) = -50p + 1750, which means that for each additional dollar increase in price per shirt, the number of shirts sold decreases by 50. Option (e) is the correct answer.
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Tyler, just letting you can do and then let it burn all the way down to nothing the initial length of a candle is 15 inches and the candle burns at a rate of 1.25 in./h right in equation for L in terms of tea, representing the length of the candle, remaining on burn in inches, tea hours, after the candles lit.
The equation for L in terms of tea, representing the length of the candle, remaining on burn in inches, tea hours, after the candles lit is 15 in - (1.25 in/hr)t
Given the initial length of a candle is 15 inches and the candle burns at a rate of 1.25 in./h
L(t) is a function of time, t:
L(t) = 15 in - (1.25 in/hr)t
Note that when the candle has burned down to nothing, L(t) = 0.
Set 15 in - (1.25 in/hr)t equal to zero and solve for t:
(1.25 in/hr)t = 15 in, or
t = 15/ 1.25 in/hr
t = 12 hrs
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what is the interquartile range of this data set? enter answer in box
Answer:
do it by yourself what you do while teacher is teaching
all I need to know is the answer to E!!! DUE TOMORROW!!!
Answer:
Step-by-step explanation:
To estimate the monthly cost of electric, gas, and water utilities as 0.1% of the price of your house, you can multiply the price of your house by 0.001. For example, if the price of your house is $300,000, then the estimated monthly cost of these utilities would be $300,000 * 0.001 = $300.
It’s important to note that this is just an estimate and the actual cost of these utilities can vary depending on factors such as the size of your house, the number of people living in it, and your usage habits.
Find the Taylor polynomial T3(x) for the function f centered at the number a.
f(x) = e^x, a = 1
The Taylor polynomial T3(x) for the function f centered at the number a.
f(x) = e^x, a = 1 is
[tex]T3(x0 = e + e(x-1) + e(x-1)^ 2/2 + e(x-1)^3/6[/tex]
How do we calculate?A polynomial is described as an expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
The Taylor polynomial of degree n for a function f(x) centered at a is given by the formula:
[tex]pn(x)=f(c)+f′(c)(x−c)+f′′(c)2!....[/tex]
In this formula, f'(1), f''(1), f'''(1), and f^(n)(1) are the first, second, third, and nth derivatives of f(x), respectively, evaluated at a.
The symbol n! denotes the factorial of n, which is the product of all positive integers from 1 to n.
In the scenario above, we are given the function f(x) = e and a = 1.
The first derivative of e^x is e^x,
the second derivative is e^x,
and the third derivative is also eˣ.
We then evaluate these derivatives at a = 1, we get:
f(1) = e¹ = e
f'(1) = e¹ = e
f''(1) = e¹ = e
f'''(1) = e¹ = e
We substitute these values into the formula for the Taylor polynomial, and simplify to get Taylor polynomial T3(x) for the function:
[tex]T3(x0 = e + e(x-1) + e(x-1)^ 2/2 + e(x-1)^3/6[/tex]
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Correct answer gets brainliest!!!!
Answer:
To find the product of matrices AB, we need to multiply the elements of the rows of matrix A with the corresponding elements of the columns of matrix B, and then sum these products.
Since matrix A is a 2x2 matrix and matrix B is a 2x3 matrix, we can perform the multiplication as follows:
AB = | 1 2 | | 1 2 3 | | (1*1)+(2*4) (1*2)+(2*5) (1*3)+(2*6) |
| 3 4 | x | 4 5 6 | = | (3*1)+(4*4) (3*2)+(4*5) (3*3)+(4*6) |
| | | |
| 9 12 15 | | 9 12 15 |
Therefore, the product of matrices AB is a 2x3 matrix, and the answer is C) 2x3.
PLS HELP ILL GIVE BRAINLIEST
A photographer charges $150 for a one-hour photoshoot , then $50 for each additional 30 minutes or any part thereof, for up to 3 hours. Write a piecewise function to represent the total cost C (in dollars) for a photoshoot that lasts h hours.
Answer:
y= 50x + 150
Step-by-step explanation:
Answer:
Here’s a piecewise function that represents the total cost C (in dollars) for a photoshoot that lasts h hours:
150 for 0<h≤1
C(h)= {150 +100⌈2(h−1) ⌉ for 1<h≤3
Step-by-step explanation:
The first part of the function represents the cost for a photoshoot that lasts up to 1 hour. The second part represents the cost for a photoshoot that lasts more than 1 hour but no more than 3 hours. The ceil function rounds up to the nearest integer.
I hope this helps you! Have a nice day. (゜▽゜)つ Bye -
Please if you know the answer tel me thank you.
Answer:
Step-by-step explanation:
(a) currently the mode is pink. Mode means which one occurs the most.
If you take a pink out. Now P=3 G=3 and Y=3
(a) PINK
(b) Yellow, you want yellow to be the most/mode so they put a yellow back in
Can yall help me with this
Answer:
x = 67
Step-by-step explanation:
The two triangles are identail.
Answer:
x = 67
because 67 and x the same
solve the area of the shaded region
The area of the shaded region is 117.8 m².
Given is a semicircle and a triangle in it, we need to find the area that is shaded,
So, we know that a triangle in a semicircle is always a right triangle whose hypotenuse is the diameter of the semicircle,
So, let us find the hypotenuse of the triangle (diameter of the semicircle) using the Pythagorean theorem,
diameter / hypotenuse = √21.6²+9²
= 23.4m
So the radius = 23.4/2 = 11.7 m
To find the area of the shaded region we will subtract the area of triangle from the semicircle,
So,
Area of the shaded region = π×r²/2 - 1/2×base×height
= 3.14×11.×7²/2 - 1/2×21.6×9
= 215 - 97.2
= 117.8 m²
Hence the area of the shaded region is 117.8 m².
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The Problem Rodeos have long been a part of the culture in the southernmost part of the country and the growing popularity of the annual Easter event across South America prompted the Rupununi Development Corporation to construct a luxury resort with 60 two-bedroom suites for the visiting cultural troupes (troupe leaders and artistes). Capacity is ten troupe leaders and fifty artistes. Each suite is equipped with a small kitchenette, which contains a 7.3 cu ft. refrigerator, a microwave, and a coffee maker. A Drystan 6-piece bedroom set and the Ashley stationary sofa and love seat (all imported from Manaus at considerable cost) are also part of the furnishings. Each accommodation also has an excellent view if the Kanuku Mountains and nearby savannahs. The facility cost the Corporation $1,920,000 to build and equip and depreciation $160,000 per year (a fixed cost). Other operating costs include: Labor $320,000 per year plus $5 per suite per day Utilities $158,000 per year plus $1 per suite per day Miscellaneous $100,000 per year plus $6 per suite per day In addition to these costs, costs are also incurred on food and beverage for each guest. These costs are strictly variable, and (on average), are $40 per day for troupe leaders and $15 per day for artistes. Required Part A Assuming that the facility can maintain an average annual occupancy of 80% in both troupe leader and artistes suites (based on a 360 -day year), calculate the following: i. the annual fixed costs ii. the variable cost per guest by type of guest iii. the annual number of guest days by type of guest
please help me for 50 points!!
simplify: -3 √84x^3
A. -6x√21x
B. -6√21
C. 6x√21x
Answer:
C
Step-by-step explanation:
the prime factorization of 84 is 2 x2 x 3 x 7
I can rewrite the problem
-3[tex]\sqrt{84x^{3} }[/tex]
-3[tex]\sqrt{(2)(2)(3)(7)xxx}[/tex] pull out the pairs
-3(2)x[tex]\sqrt{(3)(7)x}[/tex]
-6x[tex]\sqrt{21x}[/tex]
Helping in the name of Jesus.
write a situation that matches this inequality 8x+14<100
Suppose you are a small business owner who sells handmade crafts. You have a budget of $100 to purchase materials for your next batch of products. You know that each craft requires some amount of materials, which costs $8 per unit. Additionally, you will need to pay a fixed cost of $14 for other expenses related to production and shipping.
How the situation matches inequality 8x+14<100 ?To make a profit, you must ensure that the cost of materials and fixed expenses does not exceed the $100 budget. Therefore, you can write an inequality to represent this situation:
8x + 14 < 100
Here, x represents the number of units of materials needed for each craft. The inequality states that the total cost of materials (8x) plus fixed expenses ($14) must be less than $100.
To solve this inequality, you can subtract 14 from both sides:
8x < 86
Finally, you can divide both sides by 8:
x < 10.75
This means that for each craft, you can use no more than 10.75 units of materials in order to stay within budget and make a profit.
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What is the answer to this question pls
51°
4
109°
The length of unknown side is,
⇒ 4.92
We have to given that;
A triangle is shown in image.
Let the length of unknown side = x
Now, From trigonometry formula we get;
⇒ tan 51° = x / 4
⇒ 1.23 = x / 4
⇒ x = 1.23 × 4
⇒ x = 4.92
Thus, the length of unknown side is,
⇒ x = 4.92
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If sin X degree equals 4/5, what is the value of B?
B=4
B=5
b=6
b=7
The value of B is 6 when the value of sin x degrees equals to 4/5.
In the given triangle diagram, the opposite side of x = 3b
The hypotenuse of the given triangle = 22.5
Given triangle is a right-angled triangle, in trigonometry, we know that in a right-angled triangle the sin x = opposite side of x / hypotenuse side
So, sin x = 3b/22.5
But, the given value is 4/5. So,
3b/22.5 = 4/5
3b = 90/5
3b = 18
b = 18/3
b = 6
From the above explanation, we can conclude that the value of b is 6.
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If Duane's income tax bill was $1000, what was his taxable income?
To determine Duane's taxable income, we need to know his tax rate. Let's assume that his tax rate is a flat 20%.
We can use the formula:
taxable income = tax bill / tax rate
Plugging in the values given, we get:
taxable income = $1000 / 0.20
taxable income = $5000
Therefore, Duane's taxable income was $5000.
Answer:
Without more information, it is not possible to determine Duane's taxable income.
what does scaled version mean in this case its 3:5 scaled version but i just want to know what it means i dont care about answers il give brainliest !
A 3:5 scaled version means that the dimensions of the new version are proportional to the original dimensions in a ratio of 3:5.
What does a scaled version mean?A scaled version is a version of a shape where every size in the original shape is multiplied by the same number.
In this situation, a 3:5 scaled version means that the dimensions (or sizes) of the new version are proportional to the original dimensions in a ratio of 3:5.
For example, if we have a circle with radius 20 cm, we can create a 3:5 scaled version by multiplying the radius by the ratio 3/5. That is:
scaled version radius = 3/5 * 20 = 12 cm
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Y=-10x+1 with x being -5
Answer:
Y=-10x+1 with x being -5
y = -10 *-5 +1
y = -50+1
y =-49
Find the average rate of change of g(x)= 4x^2+3 on the interval [-4,1]
The rate of change is 4/1
please help with this question!
Answer:
The true statements:
6 is an element of D
12 is an element of D
express 7 min 30 sec. as a percentage of 1 hour
Answer:
12.5 is the answer
Step-by-step explanation:
7 × 60 ( 7 being the minutes, 60 being the hour )
= 420
+ 30
= 450
450 ÷ 3600 × 100
45000 ÷ 3600
450 ÷ 30
= 12.5
12.5 being the answer