68.5% of Colton's gross pay is take-home pay. To find the percentage of Colton's gross pay that is take-home pay, we need to divide his net pay by his gross pay and then multiply by 100 to convert the resulting decimal to a percentage.
To find the percentage of Colton's gross pay that is take-home pay, we need to divide his net pay by his gross pay and multiply the resulting decimal by 100 to express it as a percentage. Colton's gross pay is $1421.50 and his net pay is $973.48. Dividing the net pay by the gross pay gives a result of 0.685, or 68.5% when converted to a percentage. This means that 68.5% of Colton's gross pay is take-home pay, or the amount of money that he receives after deductions are made. Therefore, Colton's take-home pay is $973.48, which is 68.5% of his gross pay.
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In a group of 62 people 27 like cold tea while 42 like hot tea how many people like neither of the two
SOMEBODY PLEASE LOOK AT THE PICTURE AND HELP MEEEE
The equation that represent the graph is C = 1.5m + 200.
How to represent linear equation?A moving company charges a one time fee and cost per miles of it service. Therefore, the relationship is between the total cost and the number of miles.
Therefore, let's use equation to represent the relationship between the total cost C and number of miles travelled, m.
Hence, using slope intercept form
y = mx + b
where
m = slopeb = y-interceptHence,
using (0, 200) (200, 500)
m = 500 - 200 / 200 - 0
m = 300 / 200
m = 1.5
Hence,
y-intercept = 200
Therefore, the equation is C = 1.5m + 200
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i need help with pleaseee
The points are plotted on the graph below.
What are the Coordinates?Coordinates are the set of points in a geometrical plane or space, which is used to denote the exact point in the coordinate plane or space.
Given a coordinate plane.
We have to plot the points given.
(0, 1/2) is a point on the Y axis, since the x coordinate is zero. y coordinate will be in the middle of 0 and 1.
(1, 1 1/2) is a point at a distance of 1 to the right from the origin and at a distance of 1 1/2 to the up from the origin.
(2, 2 1/2) is a point at a distance of 2 to the right from the origin and at a distance of 2 1/2 to the up from the origin.
These points are plotted in the graph below.
Hence the graph is shown below.
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y=3x+2
-4x+2y=8
elimination method
Answer:
Step-by-step explanation:
Leo Gandolfi takes out a short-term loan of $1,800 at 12 percent
for 6 months. The monthly payment is $310.50. The balance of the loan after 4 payments is
$612.34. How much does he save by paying off the loan when the next payment is due?
A. $6.12 B. $18.00 C. $2.54 D. $618.46
Leo Gandolfi would save $54.34 by paying off the loan when the next payment is due.
What is percentage ?
Percentage can be defined as product of ratio of given value, total value and hundred.
To find out how much Leo Gandolfi saves by paying off the loan early, we need to first calculate how much interest he would pay if he were to continue making payments for the full 6-month term of the loan.
The total interest on the loan for the full 6 months can be calculated as:
Total interest = Total payments - Loan amount
We know the loan amount is $1,800, and the monthly payment is $310.50, so the total payments for the full 6 months would be:
Total payments = Monthly payment x Number of payments
Total payments = $310.50 x 6 = $1,863
Therefore, the total interest paid over the 6-month term of the loan would be:
Total interest = $1,863 - $1,800 = $63
Now, we need to calculate how much interest Leo Gandolfi would pay if he were to pay off the loan after making 4 payments.
The remaining balance on the loan after 4 payments is $612.34, so if Leo were to make one more payment, the remaining balance would be:
Remaining balance = $612.34 - $310.50 = $301.84
To calculate the interest paid on this remaining balance, we need to calculate the interest for one month:
Monthly interest rate = Annual interest rate / 12
Monthly interest rate = 12% / 12 = 1%
Monthly interest = Monthly interest rate x Remaining balance
Monthly interest = 1% x $301.84 = $3.02
Therefore, if Leo were to make one more payment, he would pay $310.50, which includes both the principal and the interest. So, the amount of interest he would pay if he were to pay off the loan after 4 payments is:
Interest paid = Total payment - Remaining balance
Interest paid = $310.50 - $301.84 = $8.66
So, by paying off the loan early, Leo Gandolfi would save:
Savings = Total interest - Interest paid
Savings = $63 - $8.66 = $54.34
Therefore, Leo Gandolfi would save $54.34 by paying off the loan when the next payment is due.
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A 6
6
-foot ribbon is cut into 4
4
equal pieces.
Which equation shows how to find the length of each piece?
The equation shows how to find the length of each piece is L = R / N and the length of each piece is 1.5 feet.
To find the length of each piece, we can use the following equation:
Length of each piece = Total length of the ribbon / Number of pieces
In mathematical terms, we can represent this equation as:
L = R / N
Where,
L is the length of each piece
R is the total length of the ribbon (66 feet in this case)
N is the number of pieces (44 in this case)
In this problem, we are given a 66-foot ribbon and we are asked to cut it into 44 equal pieces. We need to find out the length of each piece.
Using this equation, we can easily find the length of each piece:
L = 66 / 44
L = 1.5 feet
Therefore, each piece of the ribbon is 1.5 feet long.
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What is the value of x?
first to answer brainliest
Answer:
99
Step-by-step explanation:
We can set up and solve this equation:
X + X - 50 = X + 49
X = 99
Give an example of a matrix A and a vector b such that the solution set of Ax = b is a line in R^3 that does not contain the origin.
x = k - 2, y = 8 - 2k, z = k is the general solution of the given system, where k is an arbitrary, if k = 1
x = -1, y = 6, z = 1 is the solution.
Ax = [tex]\left[\begin{array}{ccc}1&1&1\\1&2&3\\1&4&7\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]
and b = [tex]\left[\begin{array}{ccc}6\\14\\30\end{array}\right][/tex]
the augmented matrix is [A:B] = [tex]\left[\begin{array}{ccc}1&1&1:6\\1&2&3:14\\1&4&7:30\end{array}\right][/tex]
we need to reduce the augmented matrix [A:B] to row echelon form by applying elementary row transformations only.
operating R₂→R₂-R₁ , R₃→R₃-R₁
[A:B] = [tex]\left[\begin{array}{ccc}1&1&1:6\\0&1&2:8\\0&3&6:24\end{array}\right][/tex]
operating, R₃→R₃-3R₃
~ [tex]\left[\begin{array}{ccc}1&1&1:6\\0&1&2:8\\0&0&0:0\end{array}\right][/tex]
which is the row echelon, form of the matrix [A:B]
we have rank of [A:B] = the number of the non zero rows in echelon form = 2
also by the same elementary transformation we get,
A ~ [tex]\left[\begin{array}{ccc}1&1&1\\0&1&2\\0&0&0\end{array}\right][/tex]
∴ rank of A = 2
since rank A = rank [A:B] = 2 < number of unknowns
therefore, the given equation are consistent and will have an infinite number of solutions.
We see that the given system of equations is equivalent to the matrix equation
[tex]\left[\begin{array}{ccc}1&1&1\\0&1&2\\0&0&0\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}6\\8\\0\end{array}\right][/tex]
which gives the equations x + y + z = 6 ........(1)
and y + 2z = 8 .......(2)
from (2), y = 8 - 2z, putting the value of y in (1) we get,
x = 6 - y - z = 6 (8 - 2z) z = z - 2
taking z = k, we get x = k - 2, y = 8 - 2k, z = k is the general solution of the given system, where k is an arbitrary,
if k = 1
x = -1, y = 6, z = 1 is the solution.
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A new image that is formed after a transformation is called an ________
A new image that is formed after a transformation is called reflection.
What is a reflection?A sort of symmetry known as reflective symmetry occurs when one half of an object mirrors the other half. For instance, both the left and right sides of a human face are typically the same. Most butterflies have identical wings on their left and right sides.
From the question, it is asked what we call a new image that is formed after a transformation. Reflection is the name given to the new picture that results from a change.
Therefore, the new image will be called a reflection after transformation.
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What value of n makes the equation true? 7^7 multiplied by 7^5 equals (7^n)^4 over 7^4
From power rules, the value of n is 4.
Power Rules
The main power rules are presented below.
Multiplication with the same base: you should repeat the base and add the exponents. Division with the same base: you should repeat the base and subtract the exponents. Power. For this rule, you should repeat the base and multiply the exponents. Exponent negative - For this rule, you should write the reciprocal number with the exponent positive. Zero Exponent. When you have an exponent equal to zero, the result must be 1.For solving this question, you should convert the given text into a math expression. See below.
7^7 multiplied by 7^5 equals (7^n)^4 over 7^4 = [tex]7^7 * 7^5 =\frac{ (7^n)^4 }{7^4}[/tex]
After that, you should apply the power rules. Using the rule for the multiplication with the same base, you have: [tex]7^{12} =\frac{ (7^n)^4 }{7^4}[/tex].
Next step, you should apply the rule Power, then: [tex]7^{12} =\frac{ (7^{4n})}{7^4}[/tex]. One more time, you should apply the rule for the multiplication with the same base, and you will have:
[tex]7^{12} =\frac{ (7^{4n})}{7^4}\\ \\ 7^{16}=7^{4n}[/tex]
Thus,
16=4n
n=16/4
n=4
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€-grade10
mathematics
Answer:
29/5
Step-by-step explanation:
hope this helps
Can some one help sovle this?
-
By using the graph of the piecewise function we can see that:
f(0) = 0.
How to find the value of f(0)?Here we have the graph of a piecewise function, and we want to find the function when x = 0.
Remember that on a graph, an open circle means that the value does not belong to the graph, while a closed circle means taht the value belongs to the graph.
Here we can see that the closed circle at x = 0 is on the line at the middle, then we can conclude that f(0) = 0.
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Find a polynomial function of degree 3 such that f(10)=17 and the zeros of f are 0, 5 and 8
Please help giving brainliest answer
To find a polynomial function of degree 3 such that f(10) = 17 and the zeros of f are 0, 5, and 8, we can use the factored form of the polynomial. The polynomial can be written as f(x) = (17/20)x(x - 5)(x - 8).
If the zeros of a polynomial function are 0, 5, and 8, then the factored form of the polynomial can be written as: f(x) = k(x - 0)(x - 5)(x - 8)
To find a polynomial function of degree 3 such that f(10) = 17 and the zeros of f are 0, 5, and 8, we can use the factored form of a polynomial. The factored form of a polynomial is the product of its factors, which are its linear binomials that correspond to its zeros.
For example, if a polynomial has zeros of 1, 2, and 3, then its factored form can be written as (x - 1)(x - 2)(x - 3). We can use this concept to find the factored form of the polynomial with zeros of 0, 5, and 8, which is:
f(x) = k(x - 0)(x - 5)(x - 8)
where k is a constant coefficient that we need to determine. We can use the given condition that f(10) = 17 to solve for k. When we plug in x = 10, we get:
f(10) = k(10 - 0)(10 - 5)(10 - 8) = 2k * 5 * 2 = 20k
Since f(10) = 17, we can set 20k = 17 and solve for k:
k = 17/20
Therefore, the polynomial function of degree 3 with the given conditions is:f(x) = (17/20)x(x - 5)(x - 8)
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If an 8-pound turkey takes 150
minutes to cook, how long would
it take a 16-pound turkey to cook?
_____ minutes
Answer:
just 150x2 = 300 minutes or just 150 minutes to cook
Step-by-step explanation:
The cooking time of a turkey depends on its weight, so a 16-pound turkey will take longer to cook than an 8-pound turkey. However, without additional information such as the cooking method, temperature, and the shape and size of the turkeys, it's not possible to determine the exact cooking time for the 16-pound turkey.
In Exercises 1-4, tell whether the ordered pair is a solution of the inequality.
1. x - y > 2; (5, 4)
2. x + y ≤ -3; (−1, −4)
3. 5x + y ≤ 12; (2, 2)
4. x-3y > 6; (3, −1)
Hence, or otherwise, find the two consecutive integers whose squares have a difference of 279
The two consecutive integers whose squares have a difference of 279 is 140 and 139.
What are consecutive integers?The uninterrupted series of integers is represented by consecutive meaning in mathematics. It implies that the numbers are continuously following one another in a series. First, we must comprehend the idea of predecessors and successors in order to comprehend the consecutive meaning of consecutive numbers in mathematics. The number that is written immediately before the number is referred to as the predecessor. As opposed to successors, which refer to the number that follows the number. Think about the range 4, 5, 6, and 7. In this case, 4 comes before 5, while 6 comes after 5.
Let us suppose a number = x.
The consecutive number is given as (x - 1)
Two consecutive integers whose squares have a difference of 279, is given as:
x² - (x - 1)² = 279
x² - x² + 2x - 1 = 279
2x - 1 = 279
2x = 280
x = 140
x - 1 = 140 - 1 = 139
Hence, the two consecutive integers whose squares have a difference of 279 is 140 and 139.
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W^2+2+48 divided by 28
Key: w=5
X=3
Y=4
Z=8
Step by step?
The solution to the algebraic expression w² + 2 + 48 ÷ 28 is 2.68
How to solve algebra?w² + 2 + 48 ÷ 28
Where,
w=5
X=3
Y=4
Z=8
w² + 2 + 48 ÷ 28
substitute w = 5 into the expression
= 5² + 2 + 48 ÷ 28
= 25 + 2 + 48 ÷ 28
Add
= 75 ÷ 28
divide
= 2.678571428571428
Approximately,
2.68
In conclusion, 2.68 is the solution to the given expression.
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Mr. Herman compare his students score for two class periods for a social studies final
Based on the information in the graph, it can be stated that the median test score of period 2 was less than the median test score of period 1.
How to identify the median?The median is identified by locating the value that lies in the middle, in the case of a whisker plot, the median corresponds to the value shown by the vertical line.
The median for period 1: 84
The median for period 2: 82
Based on this information, it can be stated that the median test score of period 2 was less than the median test score of period 1.
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Frodo ran 2 4/5 in 7/12 of an hour. How many miles can Frodo run in one hour?
Answer:
In 1 hour run:
4 4/5 miles
Step-by-step explanation:
2 4/5 = 2 + 4/5 = 10/5 + 4/5 = (10+4)/5 = 14/5
Proportions:
14/5 miles ⇒ 7/12 hour
A miles ⇒ 1 hour
A = (14/5 miles)(1hour) / (7/12 hour)
A = (14/5)/(7/12)
A = (14*12) / (5*7)
A = 168 / 35
A = 140/35 + 28/35
A = 4 + 28/35
A = 4 + 4/5
A = 4 4/5 Miles
If a = 6 and B = 40 degrees,
find c.
Answer: My guess is 90 degrees if we're looking at the uppercase C
Step-by-step explanation: Because of the square in the corner
A picture 6 1/2 feet long is to be centered on a wall that is 21 feet long. How much space is there from edge of the wall to the picture
On solving the provided question, we can say that by fractions, the space from the edge of the wall to the picture = 17/4*1/2 = 17/8
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
Simply subtract the length of the image from the length of the wall to get the total area below and above the picture from the edge of the wall. So.
[tex]14\frac{1}{2} - 10\frac{1}{4}[/tex]
29/2 - 41/2
17/2
the space from the edge of the wall to the picture = 17/4*1/2 = 17/8
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what is the meaning of square?
Answer:
Step-by-step explanation:
A square is a 4 sided polygon in which all of its side lengths are equal and the diagonals are also be
an army regiment with 400 soldiers has provision for 80 days. if 80 soldiers moved out of the regiment, how long would the food last at the same rate?
Answer: If the army regiment had 400 soldiers with provisions for 80 days, the food would last each soldier for 80 days / 400 soldiers = 0.2 days per soldier.
If 80 soldiers moved out, the number of soldiers remaining in the regiment would be 400 soldiers - 80 soldiers = 320 soldiers.
Since the amount of provisions has not changed, the food would last for 80 days / 320 soldiers = 0.25 days per soldier.
Therefore, the food would last the 320 soldiers for 0.25 days * 320 soldiers = 80 days.
Step-by-step explanation:
consider the equation 4(10^-3x)=18, solve the equation for x. Express the solution as a logarithm in base-10.
The solution of the exponent equation [tex]\rm 4 \times (10^{-3x})=18[/tex] will be negative 0.2177.
What is the solution to the equation?In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.
The equation is given below.
[tex]\rm 4 \times (10^{-3x})=18[/tex]
Simplify the equation, then we have
[tex]\begin{aligned} \rm 4 \times (10^{-3x}) &=18\\\\\rm (10^{-3x}) &=4.5 \end{aligned}[/tex]
Take a log with base 10 on both sides, then we have
- 3x log₁₀ 10 = log₁₀ 4.5
- 3x = 0.6532
x = -0.2177
The solution of the exponent equation [tex]\rm 4 \times (10^{-3x})=18[/tex] will be negative 0.2177.
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question 10
What is the length of segment LN?
21.93
27.57
30.36
55.14
For the given matrix A find a 3x2 matrix B such that AB=I, where I is the 2x2 identity matrix. [Hint: If B1 and B2 are the columns of B, then ABj = Ij.]A =1 2 11 1 1
We can solve this equation by setting B2 = [c d], so that AB2 = [c+d 1] = [0 1]. This gives us the system of equations c + d = 0 and c = 1. Solving this system, we have c = 1, where I is the 2x2 identity matrix
Let A be the given 2x2 matrix A = [1 2 ; 1 1]. To find a 3x2 matrix B such that AB = I, where I is the 2x2 identity matrix, we can use the hint provided: If B1 and B2 are the columns of B, then ABj = Ij. This means that for each column j of B, we need to solve the equation ABj = Ij. For j = 1, we have AB1 = I1 = [1 0]. We can solve this equation by setting B1 = [a b], so that AB1 = [a+b 1] = [1 0]. This gives us the system of equations a + b = 1 and a = 0. Solving this system, we have a = 0 and b = 1, so B1 = [0 1].For j = 2, we have AB2 = I2 = [0 1]. We can solve this equation by setting B2 = [c d], so that AB2 = [c+d 1] = [0 1]. This gives us the system of equations c + d = 0 and c = 1. Solving this system, we have c = 1.
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3. find the 95% confidence interval for the mean number of hours of tv watched each day by adults in the us. report the upper and lower bounds of the interval:
The lower and upper bounds of the given confidence interval of 95% with sample size= 1,555 , sample mean = 2.938 and standard deviation 2.837 is equal to ( 2.797 , 3.079 ).
Upper and lower bounds of the confidence interval is :
= Sample mean ± Margin of error
And Margin of error is :
= Z-critical × ( σ/√(n ) )
Standard deviation 'σ ' = 2.837
Sample size 'n' = 1,555
Sample mean 'μ' = 2.938
Z-critical for 95% confidence interval
= Zα/2
= 1.96
Margin of error
= 1.96 × (2.837/√1,555)
= 1.96 × (2.837/ 39.43 )
= 0.1410
Confidence interval:
Upper boundary
= 2.938 + 0.1410
= 3.079
Lower boundary
= 2.938 - 0.1410
= 2.797
Therefore, for the given confidence interval of 95% the lower and upper bounds of the interval are ( 2.797 , 3.079 ).
The above question is incomplete , the complete question is:
find the 95% confidence interval for the mean number of hours of tv watched each day by adults in the us. report the upper and lower bounds of the interval:
Sample size Sample mean Standard deviation
1,555 2.938 2.837
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What is the number 9.88 x 10-5 in standard notation?
What is BD?
please help!!
The length of BD in the triangle is 24 units.
How to find the side of a triangle?The triangles are similar by angle bisector theorem. The angle bisector theorem states that the angle bisector of an angle of a triangle divides the opposite side into two parts that are proportional to the other two sides of the triangle.
Therefore, let's find BD.
Hence, using the proportion,
12 / 20 = x / x + 6
cross multiply
12(x + 6) = 20x
12x + 72 = 20x
72 = 20x - 12x
72 = 8x
divide both sides by 8
x = 72 /8
x = 9
Therefore,
BD = x + x + 6 = 2x + 6
BD = 2(9) + 6
BD = 18 + 6
BD = 24 units
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3. The scatter plot represents the age x of a driver in years and the monthly cost of insurance y
in dollars for a specific car model. The equation of the line of best fit for this data is
y=474.34-7.445x
Cost (dollars)
A
350
300
250
200
150
100
50
increases
decreases
0
5
10
Monthly Auto Insurance Costs
Write the values that complete each sentence.
Part A
The slope of the line of best fit is
The y-intercept of the line of best fit is
Part B
Circle an answer choice in each box to make each statement true.
The slope of the line of best fit means that as the age of the driver (A), the predicted monthly
cost of insurance (B)
B
15
20
Age of Driver (years)
The value of the y-intercept (C) make sense in this context. The predicted monthly cost of
surance for a driver who is 0 years old (D) possible for this situation.
25
decreases
30
increases
stays the same
35
does
40
does not
D
is
is not
NEED HELP NOWWWWW
