The dimensions of the rug that Cynthia Besch should buy are 11 ft wide and 25 ft long, which gives an area of 275 ft².
How are the dimensions determined?The dimensions of the rug include the width and the length.
Cynthia is budget-constrained to buy 275 ft² only.
When we factorize 275, we have 1, 5, 11, 25, 55, and 275.
The possible combinations of width and length to get 275 ft² and also ensure that a uniform strip of the floor is left around the rug are 11 ft and 25 ft. This width and length are less than the room's width and length and satisfy the requirement for a uniform strip.
The strip from the room's width and length must be 8 ft each (from all sides).
Data and Calculations:Width of room = 19 ft
Length of room = 33 ft
Area of room = 627 ft²
Dimensions:Width of rug = 11 ft(19 - 8)
Length of rug = 25 ft (33 - 8)
Area = 275 ft² (11 x 25)
Thus, the dimensions of the rug that Cynthia Besch should buy are 11 ft wide and 25 ft long.
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Question content area top Part 1 Zachary purchased a computer for $1,500 on a payment plan. Five months after he purchased the computer, his balance was $975. Ten months after he purchased the computer, his balance was $450. What is an equation that models the balance y after x months?
The equation that models the balance y after x months is given by y = 1500 -150x,
Apparently, we have to assume that the balance is a linear function of the number of months that the payment is boing made.
We are given 3 points:
(0, 1500), (6, 600) and (8, 300)
Any two of these can be used to write the equation of the line :
y = (y₂ - y₁) / (x₂ - x₁) (x - x₁) + y₁
y = (600 - 1500) / (6 - 0) (x - 0) + 1500
y = - 900 / 6 x + 1500
y = 1500 - 150 x
where x is the number of months.
Therefore, the equation that models the balance y after x months is given by y = 1500 -150x,
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Find the value of x.
130°
(2x)
Answer:
Step-by-step explanation:
Vertical opposite angles are equal to each other so
2x = 130
x = 65 (divide both sides by 2)
The points I, J, K and L all lie on the same line segment, in that order, such that the ratio IJ:JK:KL is equal to 2:5:5 IfIL=60, find KL.
The length of KL with the given ratio is 25 units
How to determine the length of KL?The given parameters are:
IJ : JK : KL is equal to 2 : 5 : 5
IL = 60
Rewrite properly as:
IJ : JK : KL = 2 : 5 : 5
This means that the length of KL
KL = KL ratio/Sum of ratios * IL
So, we have
KL = 5/(2 + 5 + 5) * 60
Evaluate the sum
KL = 5/12* 60
Divide 60 by 12
So, we have
KL = 5 * 5
Evaluate the product
KL = 25
Hence, the length of KL with the given ratio is 25 units
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Let f(x) = -10x-18 and g(x) = -3x, find (f-g)(x).
Answer:
[tex]{ \tt{f(x) = - 10x - 18}} \\ { \tt{g(x) = - 3x}} \\ \\ { \tt{(f - g)(x) = ( - 10x - 18) -( - 3x) }} \\ \\ { \tt{(f - g)(x) = ( - 10x + 3) - 18}} \\ \\ { \tt{(f - g)(x) = - 7x + (3 - 18)}} \\ \\ { \tt{(f - g)(x) = - 7x - 15}}[/tex]
The sum of x and its square is equal to y times z.
Answer:
x + [tex]x^{2}[/tex] = yz
Step-by-step explanation:
what is -11 + l-5l - l-15l
Answer: -21
Step-by-step explanation: abs(-5) and abs (-15) just makes it positive, so the equation becomes -11 + (5) - (15), which equals -21.
Which system of equations is represented by the matrix below?
[2 3| 2]
[12 0| -24]
System of equations is represented by the matrix below is 2x + 3y = 2 and 12x = -24
[2 3 2]
[12 0 -24]
This means 2x + 3y = 2 and 12x = -24
How matrix is used to solve system of equation?
The matrix can be used to solve system of equation. it can be 3 by 3 matrix or 2 by 2 matrices.
The first rows of the matrix above represent the coefficient of the first equation and second row represents the second equation of the system of equations.
Matrices is the plural form of matrix, which is a rectangular array or table with rows and columns of numbers or elements. They can have as many columns and rows as they want. Matrix operations include addition, scalar multiplication, multiplication, transposition, and others.
Matrices, the plural form of matrix, are the arrangements of numbers, variables, symbols, or expressions in a rectangular table with varying rows and columns. They are rectangular arrays with defined operations such as addition, multiplication, and transposition. The elements of the matrix are the numbers or entries in it. The horizontal entries of matrices are referred to as rows, while the vertical entries are referred to as columns.
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A sample of ore is found to be 0.0022% gold and 0.059% diamond. What is the percentage of matter in the ore that is neither gold nor diamond? Round your answer to the nearest ten thousandth.
The percentage of matter in the ore that is neither gold nor diamond is 99.9388%.
In the question, we are given that a sample of ore is found to be 0.0022% gold and 0.059% diamond.
We are asked for the percentage of matter in the ore that is neither gold nor diamond.
We know that in any quantity, the total is shown as 100%.
If we assume the percentage of matter in the ore that is neither gold nor diamond to be x%, then using the above theory, we can say that;
x% + 0.0022% + 0.059% = 100%.
This can also be shown as:
x + 0.0022 + 0.059 = 100, which can be simplified as:
x + 0.0612 = 100, which can be solved by subtracting 0.0612 from both sides to get:
x = 100 - 0.0612 = 99.9388.
Thus, the percentage of matter in the ore that is neither gold nor diamond is 99.9388%.
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656 divded by 9 and 3.6 divded by 17
Answer: 72.8 and 0.21
Answer:
72.8888888889
and
0.5142857143
A store gathers some demographic information from their customers. The following chart summarizes the age-related information they collected:
Age Number of Customers
<20 78
20-30 58
30-40 53
40-50 77
50-60 52
>60 91
One customer is chosen at random for a prize giveaway.
What is the probability that the customer is at least 30 but no older than 60?
What is the probability that the customer is either older than 60 or younger than 40?
What is the probability that the customer is at least 60?
The probability that the customer is at least 30 but no older than 60 is o.45, that the customer is either older than 60 or younger than 40 is 0.68 and that the customer is at least 60 is 0.22.
We have the data:
Age Number of Customers
< 20 78
20 - 30 58
30 - 40 53
40 - 50 77
50 - 60 52
> 60 91
The probability that the customer is at least 30 but no older than 60 will be:
P = 182 / 409
P = 0.45
The probability that the customer is either older than 60 or younger than 40 will be:
P = 280 / 409
P = 0.68
The probability that the customer is at least 60 will be:
P = 91 / 409
P = 0.22
Therefore we get the probability that the customer is at least 30 but no older than 60 is o.45, that the customer is either older than 60 or younger than 40 is 0.68 and that the customer is at least 60 is 0.22.
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What is the difference when 54.89 is subtracted from 235.987?
29.0877
1,810.97
290.877
181.097
ill brainlist the right answer
[tex]{ \blue{ \tt{option(d)}}} \: { \boxed{ \red{ \sf{181.097}}}}[/tex]
Step-by-step explanation:
[tex] \: \: \: \: 235.987[/tex]
[tex] - \: \: \: 54.89[/tex]
_______________
[tex]{ \boxed{ \red{ \sf{= 181.097}}}}[/tex]
Which of the following are factors of 96? Select ALL that apply.
018
6
04
012
014
Answer:04,6and 12
Explation:factors are numbers which divide the original number without leaving a remainder.The factors are:1,2,3,4,6,8,12,16,32,48and 96
Consider a circle whose size can vary. The circumference of the circle is always
2
π
times as large as its radius. Let
r
represent the radius of the circle (in feet) and let
C
represent the circumference of the circle (in feet).
Answer:
The circumference of the circle is always 2π times as large as its radius. Let r represent the radius of the circle (in feet) and let C represent the circumference of the circle (in feet).
Step-by-step explanation:
hopes this helps
answer 2
π
times as large as its radius.
The table below shows the assets and liabilities of the Tanner family.
Assets and Liabilities Amount
Checking account $17,532
Car (paid off) $12,225
Retirement Savings $43,675
Credit Card Debt $7,876
Home Loan Balance $65,225
What is the net worth of the Tanner family?
If checking account has $17,532,car (paid off) is $12,225,retirement savings are $43,675,credit card debt is $7,876,home loan balance has $65,225, the the net worth of the Tanner family is $331.
Given that checking account has $17,532,car (paid off) is $12,225, retirement savings are $43,675,Credit Card Debt is $7,876,Home Loan Balance has $65,225.
We are required to find the net worth of the Tanner family.
Net worth is basically the value of the assets a person or corporation owns, minus the liabilities they owe.
Net worth=Checking account+Car +Retirement savings-credit card debt-Home loan balance
=17532+12225+43675-7876-65225
=$331
Hence if checking account has $17,532,Car (paid off) is $12,225 ,retirement Savings are $43,675,credit card debt is $7,876,home loan balance has $65,225, the the net worth of the Tanner family is $331.
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which of the following 5-digit numbers can be rounded to 20,000?
Suppose that approximately 273,000,000 people live in the United States. Of these people, 31,200,000 speak a language other than English at home. Of those who speak another language at home, over 50 percent speak Spanish.
• E = speak English at home
• E' = speak another language at home
• S = speak Spanish at home
Finish each probability statement by matching the correct answer.
P(E' )
Part (b)
P(E)
Part (c)
P(S)
Part (d)
P(S | E' )
The required probability is given by P(E') =4/35 .
Probability is the study of chance. It can also be defined as the ratio of the favorable outcomes to an event to the total number of outcomes of the event.
Given the total number of people in the USA = 273000000
Let E be the number of people who speak English at home.
Therefore the number of people who don't speak English at home is E'.
∴ E' = 31200000
S speak Spanish in their homes.
∴ S = 50% of 31200000 = 15600000
Now let us find the required probabilities.
We know that probability = favorable outcome ÷ total outcome
total outcome = 273000000
a) favorable outcome(E') = 31200000
P(E')=31200000/273000000
P(E') =4/35
b)favorable outcome(E) = 273000000 - 31200000 = 241800000
P(E) = 241800000/273000000
P(E)={31}/{35}
c)favorable outcome = 15600000
P(S)={15600000}/{273000000}
P(S)={2}/{35}
Therefore the required probability is given by P(E') =4/35 , [tex]P(E)=\frac{31}{35}[/tex] P(E)=31/35 and P(E)=2/35and .
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Write algebraic expressions for two numbers with a sum of -17. Let one of the number be represented by x.
The algebraic expression is x + y = -17
Given,
The sum of two numbers = -17
One number = x
We have to write an algebraic expression for the above condition:
Algebraic expression
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.).
You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.
So, let’s find the algebraic expression:
Given that one number is x. We can take other number as y.
So, the expression will be like:
x + y = -17
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K(2, 7), L(6, 12), M(13, 13), N(9.8) (Slope Formula) is it a parallelogram?
angles and sides opposite one another on a parallelogram are congruent, we can say this is a parallelogram because there are congruent.
What in mathematics is a parallelogram?
A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus.Slope Formula: y2-y1/x2-x1
KL: 12-7/6-2 = 5/4
LM; 13-12/13-6 = 1/7
MN: 8-13/9-13 = 5/4
KN: 7-8/9-2 = 1/7
Since angles and sides opposite one another on a parallelogram are congruent, we can say this is a parallelogram because there are congruent.
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Given the graph of the function f(x) below, estimate the slope of the tangent line to the curve at x=0. Select the answer that is closest.
Since f(x) appears to admit a local minimum at the point of abscissa zero, then the tangent drawn at that point must admit a slope equal to zero.
Option 3“Some friends ordered two cinnamon sugar pizzas cut into 12 pieces each for dessert. Each person had 2 slices and there were four slices leftover. How many friends were at the dinner?
Write out an equation that will go with the problem and then solve it.”
Answer: 4 People were at the dinner.
Equation: 2x + 4 = 12
Step-by-step explanation: We know that there are 4 pieces left. So we can just take away 4 from 12. When that's done, we're left with 8 eaten slices. Then divide the 8 slices by the number of pieces per person. Therefore, 8/2 gives us 4.
I took algebra last year and loved it! I hope this helps!
ln(3) - ln(2) + ln(1/x) =
A. 3 / (2x)
B. 3x/2
C. 1 + 1/x
D. 3/2 - 1/x
The required simplified solution for the given logarithm expression is y = 3 / 2x.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
To simplify the given expression,
ln(3) - ln(2) + ln(1/x) = ln (y)
ln(3) + ln(1/x) = ln(2) + ln(y)
By the property of logarithm,
3/x = 2y
y = 3 / 2x
Thus, the required simplified solution for the given logarithm expression is y = 3 / 2x
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61% of 407
rounding pls <3
Answer:
Step-by-step explanation:
61.407
Answer:
248.3
Step-by-step explanation:
61% of 407
61% = 0.61
0.61 * 407 = 248.27
248.27 = 248.3
248.3
Need help I ready pls help me
Answer:
(9+b)+(10+s)
Step-by-step explanation:
please help
please hury
the one you highlighted is right!
Answer:
The highlighted one is correct!
The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using 14 HCF of water is $32.62 , and the cost for using 48 HCF is $78.52 . What is the cost for using 40 HCF of water?
The cost for using 40 HCF of water is $67.72
What is the cost for using 40 HCF of water?To solve this question, we use the following representations
x represents HCFy represents the amountUsing the above representations, we have the following points
(x, y) = (14, 32.62), (48, 78.52)
For 40 HCF of water, we have
(x, y) = (40, y)
The slope of a linear equation is calculated using
m = (y2 - y1)/(x2 - x1)
So, we have
m = (78.52 - 32.62)/(48 - 14) = 1.35
m = (78.52 - y)/(48 - 40)
Substitute m = 1.35 in m = (78.52 - y)/(48 - 40)
So, we have:
1.35 = (78.52 - y)/(48 - 40)
Evaluate the difference
1.35 = (78.52 - y)/8
Multiply both sides by 8
10.8 = 78.52 - y
This gives
y = 78.52 - 10.8
Evaluate the difference
y = 67.72
Hence, the cost for using 40 HCF of water is $67.72
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In the figure below, mz1 = (4x + 50)° and
mz3 = (2x + 66)°.
3
a. What is the value of x?
b. What is the measure of m<3?
c. What is the measure of m22?
the measure of m22 = 98° by linear pair .
What is linear pair?
When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°.
Given , mz1 = (4x + 50)°
mz3 = (2x + 66)°.
a) mz1 = mz3
(4x + 50)° = (2x + 66)°
4x - 2x = 66 - 50
2x = 16°
x = 8°
b) mz3 = (2x + 66)°.
put value of x
2x + 66 = 2 * 8 + 66
= 16 + 66 ⇒ 82°
c) mz2 = ∠ 1 + ∠ 2 = 180° { linear pair }
4x + 50 + ∠2 = 180°
4 × 8 + 50 + ∠2 = 180°
82° + ∠2 = 180°
∠2 = 180° - 82°
∠2 = 98°
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The sum of the measures of two complementary angles is 90°. If one angle measures
15° more than twice the measure of the other, find the measure of the smaller angle.
The smaller angle measures: ?
Answer: 75°
Step-by-step explanation:
Solution;
Here:. let, one angle be x
From the question ,
x+15=90(Being sum of complementary angle)
x=90-15
x=75
Given f(x) = x^2 - 3x + 5, what is f(-2)?
A. f(-2) = 3
B. f(-2) = -5
C. (-2) = 15
Using the ratio 49N:5kg calculate the force needed to lift an object that is 365 kg
The force needed to lift an object that is 365 kg is calculated as; 3577 N
How to solve ratio problems?
We are given the ratio as;
49N : 5 kg
This ratio means that 49 newtons of force represents 5 kg of mass. Now, we want to find the force required to lift an object with a mass of 365 kg.
Using the given ratio, we can say that the force that can lift a mass of 365 kg is calculated as;
(365 * 49)/5 = 3577 N
Thus, we conclude that the force needed to lift an object that is 365 kg is calculated as 3577 N.
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Pllzzzzzz help
What number should be placed in the box to help complete the division calculation?
Answer:
160
Step-by-step explanation:
1 is in 10s place 16x10=160
