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Work Shown:
x = number of windows purchased
The cost expression is 145.50x+3150 because the "145.50x" portion represents the $145.50 per window charge, then we tack on the fixed fee of $3150. Set this cost expression equal to the total charge ($5769) and solve for x.
\(145.50x+3150 = 5769\\\\145.50x = 5769-3150\\\\145.50x = 2619\\\\x = 2619/(145.50)\\\\x = 18\\\\\)
They bought 18 windows.
A company charges $60 per day plus $0.50 per mile for truck rentals. If Greg rents a truck for 3 days and drives 150 miles, how much will the company charge?
Answer:
$255
Step-by-step explanation:
Equation would be
60x+0.5y= $ charged
x= days
y = per mile
60 * 3 + 0.5 * 150 = $
180+75=
=255
Greg would have to pay $255
Hope this helps!
(Pls mark brainiest)
Thanks!
Which equation represents the total number of black and white squares on the chess board?
The equation that represents the total number of black and white squares on the chess board is 8 * 2² = 32
How to determine the equation of the black and white squaresFrom the question, we have the following parameters that can be used in our computation:
The chess board
From the chess board, we have
Black squares = 32
White squares = 32
When factorized, we have
Black squares = 32 = 8 * 2²
White squared = 32 = 8 * 2²
Hence, the equation that represents the squares on the chess board is 8 * 2² = 32
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There is a box of 45 markers. Of the markers, 20 are black and the rest are red. What fraction of the
total marbles is red? Write your answer in simplest form.
Answer:
5/9 of the marbles are red
Step-by-step explanation:
Of the 45 marbles, 20 are black, and the other 25 are red. So 25/45, or 5/9, of the marbles are red.
The path of a race will be drawn on a coordinate grid like the one shown below. The starting point of the race will be at (−5.3, 1). The finishing point will be at (1, −5.3).
Part A: For the -5.3, 1 it would be located in Quadrant Q because even though it just goes to -4 and 4 I can extend the grid in my head and that's how I was able to figure out.
Step-by-step explanation:
please help on numbers 7-11 im having a lot of trouble thank you!
Answer:
Questions?
Step-by-Step Explanation:
Answer:
What is the questions or share a picture of the questions
Find the absolute value of x: (x+8)=-2
Given that the absolute value of a function is its positive value and the value of x is -10, hence the absolute value of x is 10
How to find the absolute value of a function?The absolute value is the positive value of any given value.
Given the equation
x + 8 = -2
Determine the value of x
x = -2 - 8
x = -10
Since x is -10, hence the absolute value of x is 10
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(a) The number of terms in an arithmetic progression is 40 and the last is -54. Given that the sum of the 15 terms added to the sum of the first 30 terms is zero. Calculate (1) The first term and common difference, (ii) the sum of the progression.
(i) The first term (a) is 24 and the common difference (d) is -2.
(ii) The sum of the progression is 2520.
i) Finding the first term and common difference:
Given that the number of terms in the arithmetic progression is 40 and the last term is -54, we can use the formula for the nth term of an arithmetic progression to find the first term (a) and the common difference (d).
The nth term formula is: An = a + (n-1)d
Using the given information, we can substitute the values:
-54 = a + (40-1)d
-54 = a + 39d
We also know that the sum of the first 15 terms added to the sum of the first 30 terms is zero:
S15 + S30 = 0
The sum of the first n terms of an arithmetic progression can be calculated using the formula:
Sn = (n/2)(2a + (n-1)d)
Substituting the values for S15 and S30:
[(15/2)(2a + (15-1)d)] + [(30/2)(2a + (30-1)d)] = 0
Simplifying the equation:
15(2a + 14d) + 30(2a + 29d) = 0
30a + 210d + 60a + 870d = 0
90a + 1080d = 0
a + 12d = 0
a = -12d
Substituting this value into the equation -54 = a + 39d:
-54 = -12d + 39d
-54 = 27d
d = -2
Now we can find the value of a by substituting d = -2 into the equation a = -12d:
a = -12(-2)
a = 24
Therefore, the first term (a) is 24 and the common difference (d) is -2.
ii) Finding the sum of the progression:
The sum of the first n terms of an arithmetic progression can be calculated using the formula:
Sn = (n/2)(2a + (n-1)d)
Substituting the values:
S40 = (40/2)(2(24) + (40-1)(-2))
S40 = 20(48 - 39(-2))
S40 = 20(48 + 78)
S40 = 20(126)
S40 = 2520
Therefore, the sum of the arithmetic progression is 2520.
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can anyone help me with 5 and 7
Answer:
4) add 5x and 9x
answer: 14x - 30
7) subtract 28 from 15
answer: x - 13
Step-by-step explanation: sorry if it is wrong I try my best
whats the second step of calculating the present value of an ordinary annuity by table lookup
The second step of calculating the present value of an ordinary annuity by the table lookup is to look up the periods and rates in the PV annuity table.
What is the present value of an ordinary annuity?The present value of an ordinary annuity is the current value based on future cash inflows of the annuity, given a specified discount rate.
The present value is higher when the discount rate is lower, and vice versa.
The present value of an ordinary annuity, which discounts the annuity to the current time, is computed as Annuity Payment x Present value of the ordinary annuity table.
In conclusion, an annuity simply means a series of periodic payments and may involve payment at the beginning (annuity due) or at the end of the period (ordinary annuity).
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A researcher was interested in the impact of listening to different types of music on learning. She designed an extensive maze for rats and after she taught rats how to get through the maze, she randomly assigned each rat to run the maze while (a) listening to classical music, (b) listening to heavy metal music, or (c) in a quiet room (i.e., no music). The researcher measured the amount of time it took each rat to get through the maze and the number of errors made.
a. Independent Variable ? _________________ What are the levels? ________________________________
b. Dependent Variable ? _____________________________
c. What might be an extraneous variable?: ___________________________________
d. Control group? _________________ Experimental Group(s)?____________________
a.) The independent variable is the different types of music
b.) The dependent variable is the impact of listening felt by the rats
c.)An extraneous variable is the length of the maze.
d.) The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.
What is an independent and dependent variables?An independent variable is defined as the type of variable that cannot be manipulated by a researcher and isn't affected by what is being measured.
A dependent variable is the variable that can be manipulated by a researcher and is affected by what is being measured.
For question a.)
The independent variable is the different types of music
For question b.)
The dependent variable is the impact of listening felt by the rats
For question c.)
An extraneous variable is the length of the maze.
For question d.)
The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.
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Hey guys please help me with my quiz its about finding the values of letters in angles!!
The value of x is given as follows:
x = 24.
The measure of angle DFE is given as follows:
<DFE = 62º.
How to obtain the measures?To obtain the measures, we consider that the sum of the measures of the internal angles of a triangle is of 180º.
The internal angle measures for this problem are given as follows:
180 - (5x - 14) -> each angle is supplementary with it's external.44º.3x - 10.Hence the value of x is obtained as follows:
180 - 5x + 14 + 44 + 3x - 10 = 180
228 - 2x = 180
2x = 48
x = 24.
The measure of angle DFE is obtained as follows:
<DFE = 3(24) - 10
<DFE = 72 - 10
<DFE = 62º.
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Canada has a population of 1/10 as large as the United States and Canada population is about 32 million about how many people live in United States explain how many zeros in your answer
Answer:
Step-by-step explanation: If Canada(C) is 32,000,000 and America is A and C x 10 = A then 32,000,000 x 10 = A
And to multiply any whole number by 10 you just add a zero to the end so
320,000,000 is the answer which is pronounced "Three hundred twenty million" And there is 7 zeros in the answer
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The lengths of a certain species of beetles are normally distributed with a mean of 1.9 centimeters and a standard deviation of 0.2 centimeters.
What is the z-score of a beetle of this species with a length of 2.38 centimeters?
Enter your answer in the box.
Enter your answer, rounded to the nearest tenth, in the box.
Answer:
The z-score of a beetle with a length of 2.38 centimeters is 2.4
Step-by-step explanation:
As we know,
z = (x - µ)/σ
x is the length of the beetle species.
µ is the mean length
σ is the standard deviation
Substituting the given values in above equation, we get
z = (2.38 - 1.9)/0.2
z = 0.48/0.2
z = 2.4
The length of a rectangle is 4 inches longer than it is wide. If the area is 32 square inches, what are the dimensions of the rectangle?
Answer:
width = 4in
length = 8in
Step-by-step explanation:
A = LxW = 32
L = W + 4
W(W+4) = 32
W² + 4W - 32 = 0
(W + 8)(W - 4) = 0
W ≠ -8 (dimensions cannot be negative)
W = 4in
L = W+4 = 4+4 = 8in
Having Problems With This Question
Answer:
f+g(2)=10
f-g(4)=-4
F/G(2)= 7/3
(f)(g)(1)=0
Step-by-step explanation:
1. (f+g)=2x+3+x^2-1 2(2)+2=10
2. (f-g)=(2x+3)-(x^2-1)=-x^2+2x+4= -16+8+4=-4
3. f/g= 2x+3/x^2-1 4+3/3= 7/3
4. f*g= (2x+3)(x^2-1)= 2x^3+3x^2-2x-3= 2(1)^3-2(1)+3(1)^2-3=0
Determine the value of y for the inequality 2 times the quantity y plus one third end quantity is greater than two thirds. y is greater than negative 1 over 36 y is less than negative 1 over 36 y > 0 y < 0
The value of y for the inequality is y > 0
How to determine the value of y for the inequality?
An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.
The inequality 2 times the quantity y plus one third end quantity is greater than two thirds can be written as:
2(y + 1/3) > 2/3
To determine the value of y in the inequality, you need to solve for y. That is:
2(y + 1/3) > 2/3
y + 1/3 > 1/3 (Divide both sides by 2)
y > 1/3 - 1/3 (Collect like terms)
y > 0
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-2 3/4, -1 3/4, -3/5 < o > -2 3/4, -3/5, -1 3/4 cual es menor?
Therefore , the solution of the given question of fractions comes out to be 5th option -3/5.
What is fraction?An element of a fraction or ratio is a piece of a whole. The number of equally sized pieces into which the whole has been divided is represented by the denominator b, and the number of parts that are included is represented by the numerator a. The LCM of two fractions' denominators is the least common multiple (LCD) of those denominators.
Here,
Given:
2 \(\frac{3}{4}\), -1 \(\frac{3}{4}\), 3/5 , -2 \(\frac{3}{4}\), -3/5, -1 , \(\frac{3}{4}\),
Therefore , by seeing the above given numbers ,
We compare above number
and we get to know ,
The 5th number 3/5, comes out to be smallest number from the following given numbers.
Therefore , the solution of the given question of fractions comes out to be 5th option -3/5.
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Determine the amount of money you need to invest to accumulate $7,000 dollars in 4 years if you invest it at 2.5% annual interest, compounded quarterly.
An initial investment of $5,951.71 is needed to accumulate $7,000 in 4 years with 2.5% annual interest compounded quarterly.
To determine the amount of money needed to accumulate $7,000 in 4 years with 2.5% annual interest compounded quarterly, we need to use the formula for compound interest.
The formula is A = P(1+r/n)^(nt), where A is the final amount, P is the initial investment, r is the interest rate, n is the number of times compounded per year, and t is the number of years.
Using the given information, we can plug in the values and solve for P. A = $7,000, r = 0.025, n = 4, and t = 4.
A = P(1+r/n)^(nt)
A = P(1+0.025)^4
$7,000 = P(1+0.025/4)^(4*4)
$7,000 = P(1.00625)^16
P = $5,951.71
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The correlation coefficient rbetween an employee's age, x, and yearly salary, y, is0.547.What percent of the variation in yearly salaries can be explained by differences inthe employees' ages?(Make answer a percent then rounded to the tenths place
When given the correlation coefficient of two variables, you can find out how much of the variation in the dependent variable can be explained by the independent variable by the formula:
\((correlationcoefficient)^2\times100\)Where correlation coefficient is 0.547, so
\((0.547)^2\times100=29.9\)Answer: 29.9% of the variation in salary can be explained by age
what is 7/8 x 4/7 in simplest form?
The expression (7/8) x (4/7) simplified to its simplest form is 1/2.
To simplify the expression (7/8) x (4/7), you can multiply the numerators together and the denominators together, and then simplify the resulting fraction if possible.
(7/8) x (4/7)
= (7 x 4) / (8 x 7)
= 28 / 56
To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 28:
28 / 56
= (28 ÷ 28) / (56 ÷ 28)
= 1 / 2
Therefore, (7/8) x (4/7) simplified to its simplest form is 1/2.
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udy Guide
The difference between 3 times a number x and 2 is 19. What is the value of x?
What is the product?
(ay3)2 + 3y - 5)
Ghana van company invested P45 700 for two years at a rate of 12%per annum compounded for quarter year. Work out the compound interest over the two years
\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$45700\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &2 \end{cases}\)
\(A = 45700\left(1+\frac{0.12}{4}\right)^{4\cdot 2}\implies A=45700(1.03)^8 \implies A \approx 57891.39 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{earned interest}}{57891.39~~ - ~~45700} ~~ \approx ~~ \text{\LARGE 12191.39}\)
Please please solve this right now!! Find the perimeter of a rectangle. that is 5 1/3 inches wide by 10 1/6 inches long.
Answer:
31
Step-by-step explanation:
Step 1
5 1/3 + 5 1/3 + 10 1/6 + 10 1/6
Step 2
5 1/3 + 5 1/3 = 10 2/3
Step 3
10 1/6 + 10 1/6 = 20 2/6 or 20 1/3
Step 4
20 1/3 + 10 2/3 = 30 3/3 or 31
Megan earns $8 per hour babysitting write and solve an inequality that can be used to find how many hours she must work in a week to earn at least $120 interpret the solution
Which of the following ordered pairs represents a solution to the equation graphed below?
A. (-2, -1)
B. (-1, -1)
C. (0, -4)
D. (1, -2)
E. (2, -6)
B. (-1,-1)
Reason:
Evidently shown in the graph.
which expression is equivalent to 7(d+3)-3
expression is
\(\begin{gathered} 7(d+3)-3 \\ 7d+21-3 \\ 7d+18 \end{gathered}\)Given: B is the midpoint of AC. AB = 9x and AC = 13x + 25.9xFind the value of x.X=
we have the following:
\(AC=AB+BC\)replacing:
\(\begin{gathered} AC=AB+BC \\ AB=BC \\ 13x+25=9x+9x \\ 18x-13x=25 \\ 5x=25 \\ x=\frac{25}{5} \\ x=5 \end{gathered}\)c) Evaluate: 3√11x√2
Answer:
\(3\sqrt{22}\)
Step-by-step explanation:
The product of roots with the same index is equal to the root of the product \(3\sqrt{11*2}\)
Multiply
There are four rational numbers which are listed smallest to largest, A, B, C, and D. If the numbers are 5/3 7/15 6/10 and 25/5 , identify which is A, which is B, which is C, and which is D. brainly
The rational numbers are given as follows:
A = 7/15.B = 6/10.C = 5/3.D = 25/5.How to order the rational numbers?To order the rational numbers, we must convert the fractions to decimal, dividing the numerator of the fraction by the denominator.
The conversion of each number is given as follows:
5/3 = 1.67.7/15 = 0.47.6/10 = 0.6.25/5 = 5.Hence they are ordered as follows:
7/15, 6/10, 5/3, 25/5.
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