Rectangle with the given ratio of length to diagonal has measure of the width equals to 27.35 feet.
Actual length of the rectangle = 6 feet
Ratio of the length to diagonal = 3 : 14
⇒Length/ diagonal = 3:14
⇒6/ diagonal = 3:14
⇒Diagonal = (14×6)/3
⇒Diagonal = 28 feet
Let 'x' be the width of the rectangle.
Length , width , and diagonal forms a right angle triangle in a rectangle.
Using Pythagoras theorem ,
Width² = Diagonal² - length²
⇒x² = 28² - 6²
⇒ x = √784 -36
⇒x = 27.35 feet ( nearest hundredth )
Therefore, the width of the given rectangle with the given ratios and dimensions is equal to 27.35 feet.
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the 20th term in a sequence is x 25. the 40th term in a sequence is x 105. write an equation for the arithmetic sequence by filling in the blanks
The arithmetic sequence is x+4n -55.
Given that,
20th term is = x + 25
a20 = a +19d = x + 25,
40th term is = x + 105
a40 = a +39d = x + 105,
now subtract a20 by a40,
a40 - a20
a + 19d - (a + 39d) = x + 25 - (x + 105)
20d = x + 25 -x - 105
20d = 80
d= 4.
a1 = a20 - 19d
a1 = x+ 25 - 19 x 4
a1 = x -51
so,
an = a1 + (n-1)d
an = x- 51 + (n-1)4
an = x- 51 + 4n - 4
an = x + 4n -55.
so, The arithmetic sequence is x+4n -55.
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Divide 3x^2 + 6 by 3x – 3.
Which expression represents the quotient and remainder?
because i couldn't find it anywhere
the answer is c
The quotient and remainder on dividing 3x² + 6 by 3x – 3 are (x - 1) and 9 respectively.
Division of Polynomials :To divide polynomials by a polynomial, we use the long division method.
When there is no common factor in both the numerator and the denominator, we can use the long division.
It may be used to find reminders and quotients while dividing.
Here we have
Divide 3x² + 6 by 3x – 3
On dividing 3x² + 6 by 3x – 3 in long division method
we get the remainder as 9 and the quotient as (x - 1)
For more understanding understand the long division in the given picture.
Therefore,
The quotient and remainder on dividing 3x² + 6 by 3x – 3 are (x - 1) and 9 respectively.
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58 2/3 as a fraction in simplest form
Answer:
176/3
Step-by-step explanation:
58 2/3 = 58 + 2/3 = 58/1 + 2/3 = 174/3 + 2/3 = 176/3
Juwan makes 12 baskets in 40 minutes. If he continues making baskets at this rate, how many baskets will he make in 90 minutes?
The required number of baskets made in 90 minutes are 27 baskets.
It is given that Juwan makes 12 baskets in 40 minutes and continues to make the baskets for 90 minutes.
Number of baskets made in 90 minutes = ?
So, let us calculate the number of baskets made in 1 minute.
40 min - 12 baskets
1 min - 12/40 baskets
Now, we need to find out the number of baskets made in 90 minutes.
90 min - ?
1 × 90 min - 90 × 12/40 = 27 baskets
Thus, the required number of baskets made in 90 minutes are 27 baskets.
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Valentino is a patient in a nursing home for 61 days of 2020. While in the nursing home, he incurs total costs of $27,816. Medicare pays $16,690 of the costs. Valentino receives $30,598 from his long-term care insurance policy, which pays while he is in the facility. Assume that the Federal daily excludible amount for Valentino is $380.
Of the $30,598, what amount may Valentino exclude from his gross income?
A person who purchases his/her own policy can exclude the benefits from gross income. It's also good to note that statutory limitations exist for the following amounts:
Benefits that have been collected under the employer's plan
Premiums that have been paid by the employer
benefits that have been collected from the individuals' policy. Therefore the amount Valentino may exclude will be calculated as follows;
Daily statutory amount in 2020 (380 * 61)
= $23180.
Actual cost of care $27816 $23180
Less: Amount received from Medicare ($16690)
Equal amount of exclusion ($6490)
Thus:
Valentino must include (30598 - 6490)=$6800 of the long-term care benefits received in his gross income.
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1. Express 40 1/4% as a fraction (simplest form)
2. Express 65 5/8% as a fraction (simplest form)
Answer: To express 40 1/4% as a fraction, we can convert the percentage to a fraction with a denominator of 100: 40 1/4% = 40.25/100.
To simplify this fraction we can divide both the numerator and denominator by the greatest common factor (GCF) which is 25.
So, (40.25/100) = (4025/10000) = (161/400)
To express 65 5/8% as a fraction, we can convert the percentage to a fraction with a denominator of 100: 65 5/8% = 65.625/100.
To simplify this fraction we can divide both the numerator and denominator by the greatest common factor (GCF) which is 625.
So, (65.625/100) = (65625/10000) = (261/400)
Therefore, the simplest form of 40 1/4% as a fraction is 161/400, and 65 5/8% as a fraction is 261/400
Step-by-step explanation:
A triangle has two sides of length 18.1 and 16.6. What compound inequality describes the possible lengths for the third side, x?
Answer:
1.5 < x < 34.7
Step-by-step explanation:
You want a compound inequality describing possible lengths (x) for the third side of a triangle with sides 18.1 and 16.6.
Triangle inequalityThe shortest side cannot be any shorter than the difference of the two known sides:
18.1 -16.6 = 1.5
The longest side cannot be any longer than the sum of the two known sides:
18.1 +16.6 = 34.7
The possible lengths of the third side are given by ...
1.5 < x < 34.7
__
Additional comment
If the third side is exactly equal to the sum or the difference, then the "triangle" looks like a line segment. It has zero area. That possibility is usually disallowed. If you want to allow it, then change < to ≤ in the inequality.
Find the dimensions of the figure. Round your answer to the nearest thousandth.
The Dimension of parallelogram is 7.57 inches . A special type of quadrilateral known as a parallelogram has opposite sides that are parallel and equal.
What is the area of the parallelogram?A parallelogram is a two-dimensional shape with four sides. The sides of this particular example of a quadrilateral are parallel and equal. The area of a parallelogram is the space enclosed by its four sides. The area of a parallelogram is calculated by multiplying its height by its length.
Given:Area of Parallelogram = b × h
area is 63.9 in x in.
Area of Parallelogram = b × h 63.9
= x+6.5 × x 63.9-6.5
= 57.4 x
= 7.57 inches x
height = dimension = 7.57 inches
Why is the height multiplied by the base area of a parallelogram?
Because it can be rearranged into a rectangle with the same area, the area of a parallelogram is the base times the height. A particular kind of parallelogram is a rectangle.
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RS bisects MO at N. If MN= 5x + 8 and NO= 10 + 3x find the value of x.
Answer:
Given that RS bisects MO at N, we know that:
RN = RO (by definition of a bisector)
MN + NO = MO (by the angle bisector theorem)
Given that MN = 5x + 8 and NO = 10 + 3x, we can substitute these values into the second equation to find the value of x.
MN + NO = MO
(5x + 8) + (10 + 3x) = MO
8x + 18 = MO
Now we can use the first equation to find the value of x.
RN = RO
5x + 8 = 10 + 3x
3x = 2
x = 2/3
Therefore, the value of x is 2/3.
a baseball player went up to bat 250 times in a season. he hit the ball times. find the rate of balls hit to times at bat. express as a simplified fraction.
If the baseball player went up to bat 250 times in a season and hits the ball 100 times then the rate of balls hits to times at bat is 2/5 .
the number of times the player went up to bat is = 250 times ;
the number of times he hits the ball is = 100 times ;
So , the rate of balls hit to times at bat is calculated as :
= (number of times he hits the bat)/(number of times player went to bat)
substituting the required values in formula ,
we get ;
= 100/250 ;
writing the fraction in the simplified form ,
we have ⇒ 2/5 .
Therefore , the rate of balls hit to times at bat in simplified fraction is 2/5 .
The given question is incomplete , the complete question is
A baseball player went up to bat 250 times in a season. he hit the ball 100 times. find the rate of balls hit to times at bat. express as a simplified fraction.
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amy needs to mail a usb drive to a friend. she uses 41-cent stamps and 7-cent stamps to pay $1.79 in postage. how many of each stamp did amy use?
So, Amy used 30 stamps of 41-cent stamps and 17 stamps of 7-cent stamps.
This is a system of equations problem. We can call the number of 41-cent stamps x and the number of 7-cent stamps y.
The two equations are:
x + y = total number of stamps used
0.41x + 0.07y = 1.79 (the total cost of the postage in dollars)
We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for y in terms of x:
y = total number of stamps used - x
Then we can substitute this into the second equation:
0.41x + 0.07(total number of stamps used - x) = 1.79
Solving for x,
x = (1.79 - 0.07*total number of stamps used) / 0.41
We can substitute this into the first equation to solve for total number of stamps used.
x + y = total number of stamps used
x + (total number of stamps used - x) = total number of stamps used
2x = 1.79/0.41 + 0.07/0.41
x = (1.79/0.41 + 0.07/0.41)/2
x = (1.79 + 0.07)/(0.41*2)
So, x = 30 stamps of 41-cent stamps
and y = (total number of stamps used - x) = (total number of stamps used - 30) = (1.79/0.48 - 30) = 17 stamps of 7-cent stamps
So, Amy used 30 stamps of 41-cent stamps and 17 stamps of 7-cent stamps.
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HELP ME PLEAE ASAP!!!!!!!!!!!!
what metric unit would be best to measure the amount of spices put into a batch of cookies? responses
Grams are the ideal unit for calculating the quantity of spices in a batch of cookies (g).
A system of measurements is called the metric system. It is employed in calculations and research across the globe. Here are some instances of measurements made with the metric system:
The unit used to measure lengths and distances is the meter. In daily life, we use this unit to measure things like the length of a piece of clothing, the distance from school to home, etc.
You may have noticed that the bag of your favorite food has a weight listed on it. 250 grams of potato chips, as an illustration. The unit of weight used here is the gram.
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A sample of bacteria begins with 38 cells and triples in size every 40 minutes.
Approximately how many minutes will it take for there to be 100,000 bacteria
in the sample?
It will take approximately 197.36 minutes for the sample to reach 100,000 bacteria.
Calculate the growth rate of bacteria in each 40 minute interval by dividing 3 (the amount of growth) by 40 (the time interval):
Growth rate = 3/40 = 0.075
Calculate the number of growth periods necessary to get from 38 to 100,000 bacteria. To do this, divide the desired number of bacteria (100,000) by the initial number of bacteria (38):
Growth Periods = 100,000/38 = 2,631.57
Calculate the total time required for the sample to reach 100,000 bacteria by multiplying the growth rate (0.075) by the number of growth periods (2,631.57):
Total Time = 0.075 x 2,631.57 = 197.36 minutes
Therefore, it will take approximately 197.36 minutes for the sample to reach 100,000 bacteria.
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Find the 9th term of the geometric sequence9,−18,36,
The 9th term of the geometric sequence is 2304.
What is a geometric sequence?A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.
Example:
2, 4, 8, 16 is a geometric sequence.
We have,
9, -18, 36
First term = 9
Common difference = -18/9 = -2
Now,
The nth term of a geometric sequence.
= a[tex]r^{n-1}[/tex]
For n = 9,
= 9 [tex](-2)^{9 - 1}[/tex]
= 9 x [tex](-2)^8[/tex]
= 9 x 256
= 2304
Thus,
The 9th term is 2304.
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Rhonda and Shalene live together in an apartment, so they combine their income each week to pay for
their rent and bills. Rhonda's paycheck is modeled by the function r(x) = 22x + 50, where x is the
number of hours worked. Shalene's paycheck is modeled by the function s(x) = 30x – 25, where x is the
number of hours worked.
Which function represents their household income if they work the same number of hours?
A. (s - r)(x) = -8x + 75
B. (r + 3)(x) = 52x + 25
C. (r + s)(x) = 52x + 75
D. (r - 5)(x) = 8x - 75
The function that represents their household income if they work the same number of hours is 52x + 25.
Therefore the answer is B. (r + s)(x) = 52x + 25
Rhonda's paycheck is modeled by the function r(x) = 22x + 50, where x is the number of hours worked.
Shalene's paycheck is modeled by the function s(x) = 30x – 25, where x is the number of hours worked.
The function that represents their household income if they work the same number of hours can be determined by adding their individual income
(r + s)(x) = 22x + 50 + 30x - 25
(r + s)(x) = 52x + 25
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Helppppp!!!! Question: Jimmy’s friend Tom also wants to save money to buy concert tickets. He draws up the following savings plan. Each week Tom will raise $4 to the number of weeks he has been working and add that amount to his savings during the first 3 weeks of his new job. Use summation notation to write the sum and find the total amount Tom will save in three weeks.
The summation notation of the sum is:
[tex]Sum = \[ \sum_{n=1}^{3} (4^{n})\][/tex]
The total amount is $84.
How to use summation notation to write the sum?Summation notation, also known as sigma notation, is a mathematical notation used to represent the sum of a sequence of numbers. The notation typically uses the Greek letter sigma (∑) to represent the operation of summation.
Since each week Tom will raise $4 to the number of weeks he has been working and add that amount to his savings during the first 3 weeks of his new job.
Let n represent the number of weeks
Thus, this can be written using summation notation as:
[tex]Sum = \[ \sum_{n=1}^{3} (4^{n})\][/tex]
Thus, the total amount = 4¹ + 4² + 4³ = $84
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If you were to sketch a circle graph for the data shown in the table below approximately what fraction of the circle would represent food
-----------------------------------------
vacation expenses budget
expense | amount budgeted
activities | $600
food | $450
souvenirs| $270
35% of the circle would represent the food budget.
What is a radian?The radian is the unit of angle in the International System of Units and is the standard unit of angular measure used in many areas of mathematics
Given are the vacation expenses budgets labeled in a circle graph.
We can write the total budget as equivalent to the Area of the circle as -
${600 + 450 + 270} → πr²
$1320 → πr²
$1 → πr²/1320
$450 → πr²/1320 x 450 = 0.35 πr²
Therefore, 35% of the circle would represent the food budget.
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PLEASE HELP Select the correct answer.
Simplify the following expression.
The simplified form of the expression is option C. (3)^5/12 * (4)^2/3.
Simplification of an exponential expression.An exponential expression is one which has the value of the power of one of its terms to be greater than 1 or in a fraction form. Thus some laws are required to simplify a given exponential expression. These laws are sometimes referred to as the law of indices.
Considering the given question;
(3^2/3 * 3^3/2)^5/12 x (4^2/3)
Simplifying this expression requires applying required laws, so that;
(3^2/3 * 3^3/2)^5/12 = (3^6/6)^5/12
= (3^1)^5/12
= 3^5/12
(3^2/3 * 3^3/2)^5/12 = 3^5/12
Therefore, we have;
(3^2/3 * 3^3/2)^5/12 x (4^2/3) = (3)^5/12 x (4)^2/3
Thus the simplified form is option C.
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what is the domain of the function shown in the graph below?
The domain of the function shown in the graph above include the following: D. {x|x ≥ -4}.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.
In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
By using set builder notation, the domain of this function shown in the graph above can be written as follows;
Domain = {-4, ∞}
Domain = {x|x ≥ -4}
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Need help solving this question
Answer: Billy drives 171 miles in 3 hours, so he could drive 256.5 miles in 4.5 hours.
Step-by-step explanation:
Speed = Distance/Time
The number of miles driven varies directly with the number of hours in the car. Billy drives 171 miles in 3 hours. Then the number of miles he can drive in 4.5 hours will be. This meas that x will be the number of miles covered in 4.5 hours.
x / 4.5 = 171 / 3
x = 256.5 miles
I hope this helps!
Find the missing side length of the following right triangle. x
Answer24
Step-by-step explanation:
When Landon moved into a new house he planted two trees in his backyard. At the time of planting tree a what 24 inches tall and tree B was 40 inches tall. Each year there after three A grew by 9 inches per year and tree B grew by 5 inches per year. Let A represent the height of tree A t years after being planted and let B represent the heights of tree B t years after being planted. Write an equation for each situation in terms of t, and determine the height of both trees at the time when they have an equal height.
Answer:
A=24+9t
B=40+5t
Step-by-step explanation:
see attached
A can of soda can be modeled as a right cylinder. Levi measures its radius as 2.4 cm and volume as 152 cubic centimeters. Find the height of the can in centimeters. Round your answer to the nearest tenth if necessary. Answer: \text{ cm} cm
The height of right circular cylinder is 8.4 cm.
Given that,
The radius = r = 2.4 cm
Volume = 152 cubic cm
Let height of right circular cylinder = h
We know that,
The right circular cylinder is a cylinder with circular bases that are parallel to each other. It's a three-dimensional form. The axis of the cylinder connects the centres of the cylinder's two bases. This is the most frequent sort of cylinder encountered in daily life. The oblique cylinder, on the other hand, does not have parallel bases and resembles a skewed construction.
And we know that,
Volume of right circular cylinder = πr²h
152 = 3.14 x 2.4 x 2.4 x h
⇒ h = 8.4 cm
Hence, height is 8.4 cm.
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5 2/5 divided by 7 =?? Whats the answer?
Answer:189/2
Step-by-step explanation:
janine speds 1/10 hour making the bed, 1/5 hour getting dressed, 1/2 hour eating breakfast. what is the total fraction of an hour
The total fraction of an hour that Janine spends making the bed, getting dressed, and eating breakfast is 4 / 5 hour.
The total fraction of an hour that Janine spends making the bed, getting dressed, and eating breakfast can be calculated by adding the fractions of time she spends on each activity:
1/10 hour + 1/5 hour + 1/2 hour
= (2 + 1 + 5) / 10 hour
= 8 / 10 hour
= 4 / 5 hour
The addition of two or more fractions with the same denominator is straightforward.
Simply add the numerators and keep the same denominator. For example:
(1/5) + (2/5) = (1 + 2) / 5 = 3/5
If the fractions have different denominators, you will need to find a common denominator before adding the numerators. The common denominator is the least common multiple of the denominators. Once you have found the common denominator, convert each fraction to an equivalent fraction with the common denominator and then add the numerators.
For example:
(1/5) + (2/3) = (3/15) + (10/15) = (3 + 10) / 15 = 13/15
So the addition of two or more fractions is performed by finding a common denominator, converting the fractions to equivalent fractions with the common denominator, and then adding the numerators.
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- 10x + 2y = 4
.-9x + 3y = 18
Solved by substitution
Answer:
To solve a system of equations by substitution, we can use one equation to solve for one variable in terms of the other variable, and then substitute that expression into the other equation.
Given the system of equations:
10x + 2y = 4
.-9x + 3y = 18
We can start by isolating y in one of the equations. For example, we can use the first equation:
10x + 2y = 4
To solve for y, we can divide both sides by 2:
y = -5x + 2
Now we can substitute this expression for y into the second equation:
-9x + 3(-5x + 2) = 18
-9x - 15x + 6 = 18
-24x + 6 = 18
-24x = 12
x = -0.5
Now that we know x = -0.5, we can substitute this value back into the original expression we found for y:
y = -5(-0.5) + 2
y = 2.5
So the solution of the system of equations is (x, y) = (-0.5, 2.5).
Pt.2 Can someone review my answers please? Thank you!
Answer:
Step-by-step explanation: Whats you answer? cant see it.
consider the 12 face diagonals of a rectangular block. how many pairs of them are skew lines? (two lines in space are skew if they do not intersect and they are not parallel.)
Considering the 12-face diagonals of a rectangular block, 30 pairs of these diagonals are skew lines.
In a rectangular block, there are a total of 12 face diagonals. These diagonals are formed by connecting the opposite vertices of each face of the block. To determine the number of pairs of skew lines among these diagonals, we can consider the following:
There are 6 faces in a rectangular block, each with 2 diagonals.
Every diagonal on one face is unique and does not intersect with any other diagonal on the same face.
However, diagonals on opposite faces are parallel to each other and therefore, do not form skew lines.
So, we will be selecting one diagonal from one face, so we have 6 options, then we select another diagonal from another face, which would be 5 options, and we repeat this process until we exhaust all the diagonals. This will give us 6*5 = 30 pairs of skew lines.
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here is an equation: 4x - 4 = 4x + _. What could you write in the blank so the equation would be true for:
a. No values of x
b. All values of x
c. One value of x
The value to write in the blank so the equation would be true is -4. Option A. no values of x
How to determine the valueIt is important to note that an algebraic expression is an expression comprising of coefficients, terms, factors, constants and variables.
These algebraic expression also consist of mathematical operations, such as;
MultiplicationDivisionFloor divisionSubtractionAdditionParenthesesBracketFrom the information given, we have the equation;
4x - 4 = 4x + _
To make the equation true, then, the values must be the same on both sides, the value to add is (-4) because expanding the bracket would give the same value. We have;
4x - 4 = 4x + (-4)
expand the bracket
4x - 4 = 4x - 4
0 = 0
Hence, the value is -4
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