Answers
The dimensions are 7 inches by 17 inches.
What is the area of rectangle?
Let the length be l inches
Let the breadth be b inches
Area = l*b
We can find dimensions as shown below:
Let the length be x inches
Let the width be y inches
Area = 119 square inches
x=3+2y (1)
Area = l*w
119 = x*y
Putting value of x
119 = (3+2y) *y
119 = 3y+2y^2
2y^2+3y-119=0
2y^2-14y+17y-119=0
2y(y-7) +17(y-7) =0
(y-7) (2y+17) =0
y=7, -17/2
y cannot be negative
so, y = 7
Putting in equation (1)
x=3+2(7)
= 3+14
= 17
Hence, the dimensions are 7 inches by 17 inches.
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Related Questions
Find the sum of the first 20 arithmetic progression 2, 7, 12, 17, 22
Answers
Answer: 5
Step-by-step explanation: 2 + 5 = 7, 7 + 5 = 12, 12 + 5 = 17, 17 + 5 = 22
Solve the logarithmic equation by writing in exponential form or by
graphing.
log (5-2x) = 0
Answers
Answer:
Hello,
Step-by-step explanation:
[tex]log(5-2x)=0\\\\\ \Longleftrightarrow\ 10^{log(5-2x)}=10^0\\\\\\\Longleftrightarrow\ 5-2x=1\\\\\Longleftrightarrow\ 2x=5-1\\\\\\\Longleftrightarrow\ x=\dfrac{4}{2}\\\\\\\Longleftrightarrow\ \boxed{x=2}\\[/tex]
a) A furniture store can sell 40 chairs per week at a price of sh. 80 each. The manager estimates that for each and sh. 5 price reduction, she can sell five more chairs per week. The chairs cost the store sh. 30 each. If x stands for the number of sh. 5 per price reduction, find price of the chairs and the quantity that maximize profit.
Answers
The price of the chairs and the quantity that maximizes profit is to sell 45 chairs at $75 each.
ProfitGiven that a furniture store can sell 40 chairs per week at a price of $80 each, and the manager estimates that for each and $5 price reduction, she can sell five more chairs per week, and the chairs cost the store $30 each, to determine the price of the chairs and the quantity that maximize profit, the following calculation must be made:
40 x (80-30) = 200045 x (75-30) = 202550 x (70-30) = 200055 x (65-30) = 1925Therefore, the price of the chairs and the quantity that maximizes profit is to sell 45 chairs at $75 each.
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10 - 13x + 2 in words
Answers
The simplification of the equation above in words is = Twelve minus thirteen X.
Simplification of an equationIn mathematics, coefficients are those numbers that multiplies a variable. For example in 13x, the coefficient is 13 which multiplies a variable known as X.
The equation given is,
10 - 13x + 2
Arrange the digits without a coefficient together.
That is ,
10+2 -13x
12 - 13x
Therefore the simplification of the given equation in words is Twelve minus thirteen X.
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The median household in the United States increased by a rate of 0.25% each year between 1980 and 1985. If the median household income was $42,050 in 1980, what was the median household income after 5 years? Round answer to the nearest whole dollar.
Answers
Using an exponential function, the median household income after 5 years was of $42,578.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.For this problem, the parameters are:
A(0) = 42050, t = 5, r = 0.0025[/tex]
Hence:
[tex]A(t) = A(0)(1 + r)^t[/tex]
[tex]A(t) = 42050(1.0025)^t[/tex]
[tex]A(5) = 42050(1.0025)^5 = 42578[/tex]
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5·(3+6)x^{2} -6x^{2}
[tex]5·(3+6)x^{2} -6x^{2}[/tex]
Answers
[tex]\large\displaystyle\text{$\begin{gathered}\sf 5(3+6)x^{2} -6x^{2} \end{gathered}$}[/tex]
Add 3 and 6 to get 9.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 5\times9x^{2} -6x^{2} \end{gathered}$}[/tex]Multiply 5 and 9 to get 45.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 45x^{2} -6x^{2} \end{gathered}$}[/tex]Combine 45x² and −6x² to get 39x².
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \red{39x^{2} } \end{gathered}$} }[/tex]You get a raise of 3.5% each year.
a. What is the approximate doubling time of your salary?
b. If you are currently 25 years old and are making $40,000 per year, use the approximate doubling time to find your annual salary when you retire at the age of 65.
Answers
Using an exponential function, it is found that:
a) The doubling time of the salary is of approximately 20 years.
b) The salary will be of $160,000.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.The growth rate for this problem is:
r = 0.035.
The doubling time is t for which A(t) = 2A(0), hence:
[tex]A(t) = A(0)(1 + r)^t[/tex]
[tex]2A(0) = A(0)(1.035)^t[/tex]
[tex](1.035)^t = 2[/tex]
[tex]\log{(1.035)^t} = \log{2}[/tex]
[tex]t\log{1.035} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{\log{1.035}}[/tex]
t = 20 years.
You retire in 40 years, which is 2 doubling periods, hence the salary will be of:
40000 x 2 x 2 = $160,000.
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What is an equation of the line that passes through the points (6, 4) and(6,−6)?
Answers
Answer:
Step-by-step explanation:
A shopkeeper sold 20 mobile sets of same brand for Rs 3,00.0000 at the same rate in a week What is the selling price of each mobile set
Answers
Answer:
15
Step-by-step explanation:
cost of 20 mobile set=300
cost of 1 mobile set
=cost of mobile set/number of mobile set
=300/20
=15
The cost of each mobile set is ₹1,50,000.
What is the unit rate?Unit rate can be defined as the ratio between two measurements with the second term as 1. It is considered to be different from a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity.
Given that, a shopkeeper sold 20 mobile sets of same brand for ₹3,000,000.
The selling price of each mobile set = Total cost of mobile sets/Number of mobile sets
= 3,000,000/20
= ₹1,50,000
Therefore, the cost of each mobile set is ₹1,50,000.
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A company's cost formula for its salaries and wages cost is $2,850 per month plus $317 per job. For the
month of February, the company planned for activity of 16 jobs, but the actual level of activity was 14
jobs. The actual salaries and wages cost for the month was $7,640. The spending variance for salaries
and wages cost in February would be closest to:
$352 F
$352 U
O $282 F
$282 U
Answers
The spending variance for salaries and wages cost in February would be closest to; $282 F.
What is the spending variance in February?The spending variance as the name implies is the difference between the budgeted cost and actual cost paid for an item. It therefore follows from the definition above that for the month of February;
Spending variance = $7,640 - (2850 + (16×317))
Spending variance = $7,640 - (7922)
Spending variance is therefore; $282 F.
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the set of all months that contain less than 31 years
Answers
The set of all months that contains less than 31 days is; {February, April, June, September, November}.
What is the set of all months that contain less than 31 days?It follows from the task content that the set whose elements are to be determined is characterized by containing less than 31 days.
On this note, it follows that the elements of the set are; February (28/29 days), April (30 days), September (30 days), June (30 days) and November (30 days).
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In the year 2000, The U.S. Budgeted $25,003 million for Natural Resources and Environment. In 2014, they budgeted $40,156 million. What was the absolute and relative change in environmental spending from 2000 to 2014?
Answers
Using it's concepts, we have that:
The absolute change was of $15,153 million.The relative change was of 60.60%.What is the absolute change of two values?The absolute change between two values is given by the absolute value of the difference between two values.
In this problem, the values are of $40,156 million, which is the final value, and $25,003 million, which is the initial value, hence the absolute change is:
A = 40,156 - 25,003 = $15,153 million.
What is the relative change?The relative change is the absolute change multiplied by 100% and divided by the initial value, hence:
(15,153/25,003) x 100% = 60.60%.
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how can i got 24.8 show your work
Answers
What are the fourth roots of -3+3√3i?
Enter your answer by filling in the boxes. Enter the roots in order of increasing angle measure in simplest form.
Answers
By De Moivre's formula, we have the following four roots: [tex]z_{1} = 1.565 \cdot \left(\cos \frac{\pi}{6} + i\,\sin \frac{\pi}{6} \right)[/tex], [tex]z_{2} = 1.565\cdot \left(\cos \frac{2\pi}{3} + i\,\sin \frac{2\pi}{3} \right)[/tex], [tex]z_{3} = 1.565\cdot \left(\cos \frac{7\pi}{6}+i\,\sin \frac{7\pi}{6} \right)[/tex] and [tex]z_{4} = 1.565\cdot \left(\cos \frac{5\pi}{3} + i\,\sin \frac{5\pi}{3} \right)[/tex].
How to determine a fourth root of a complex numberAccording to complex analysis, the fourth roots of a complex number can be found by De Moivre's formula:
[tex]\sqrt[n]{z} = \sqrt[n]{r}\cdot \left[\cos \left(\frac{\theta + 2\pi\cdot i}{n} \right)+ i\,\sin \left(\frac{\theta + 2\pi\cdot i}{n} \right)\right][/tex], for [tex]i = \{0, 1, ..., n - 1\}[/tex] (1)
Where:
r - Magnitude of the complex number.θ - Direction of the complex number, in radians.First, we find the magnitude and direction of the complex number:
[tex]r = \sqrt{(-3)^{2}+(3\sqrt{3})^{2}}[/tex]
r = 6
[tex]\theta = \tan^{-1} \left(\frac{3\sqrt{3}}{-3} \right)[/tex]
[tex]\theta = \frac{2\pi}{3} \,rad[/tex]
Now we find the four quartic roots of the complex number:
[tex]z_{1} = 1.565 \cdot \left(\cos \frac{\pi}{6} + i\,\sin \frac{\pi}{6} \right)[/tex]
[tex]z_{2} = 1.565\cdot \left(\cos \frac{2\pi}{3} + i\,\sin \frac{2\pi}{3} \right)[/tex]
[tex]z_{3} = 1.565\cdot \left(\cos \frac{7\pi}{6}+i\,\sin \frac{7\pi}{6} \right)[/tex]
[tex]z_{4} = 1.565\cdot \left(\cos \frac{5\pi}{3} + i\,\sin \frac{5\pi}{3} \right)[/tex]
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32) Find the cost of linoleum flooring for a floor that is 15 feet by 10 feet if it costs $9.00 to cover 12 square feet.
O a.) $110.50
Ob.) $132.50
Oc.) $122.50
Od.) $112.50
Answers
Answer:
d.) $112.50
Step-by-step explanation:
Area of floor:
15 ft × 10 ft = 150 ft²
150 ft² is how many times 12 ft²?
It is 150 ft² / 12 ft² = 12.5.
150 ft² is 12.5 times 12 ft².
12 ft² cost $9.00, so 12.5 times 12 ft² costs 12.5 times $9.00.
12.5 × $9.00 = $112.5
Answer: d.) $112.50
The Square foot flooring is calculated by doing 15ft x 10ft = 150ft^2. Since it cost $9.00 to cover 12ft^2, you would do 150ft^2/12ft^2 to find out how many times you have to pay 9 dollars. This gives you 12.5 times you have to pay 9 dollars. Therefore, you do $9.00x12.5 which gives you $112.50
BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
B.) (1, -5)
Given, equation:
[tex]\sf \dfrac{(x-1)^2}{25} -\dfrac{(y+5)^2}{49} =1[/tex]
Comparing it with standard formula of hyperbola:
[tex]\sf \dfrac{(x-h)^2}{a^2} -\dfrac{(y-k)^2}{b^2} =1[/tex]
where (h, k) is center
The given equation in standard form:
[tex]\sf \dfrac{(x-1)^2}{5^2} -\dfrac{(y-(-5))^2}{7^2} =1[/tex]
Determined:
(h, k) = (1, -5)
a = 5, b = 7
So, here (1, -5) is the center of the given hyperbola.
If John has pairs of red, orange, yellow, blue, green, white and black socks, how many orders can he wear them in over 7 days? Repetition is allowed because John is alright with wearing dirty socks.
Answers
The order in which he can wear the socks with repetition in 7 days is 823, 543 orders
How to determine the order
The formula for calculating permutation with repetition is given as;
Permutation = [tex]n^r[/tex]
Where n = 7
r = 7
Substitute into the formula
Permutation = [tex]7^7[/tex]
Permutation = [tex]823, 543[/tex] ways
Thus, the order in which he can wear the socks with repetition in 7 days is 823, 543 orders
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HELP PLEASE
2. You are making necklaces for your friends. You have 72 blue beads and 42 red beads. Each friend will receive an identical necklace, and all beads must be used.
(A) What is the greatest number of friends who can receive a necklace? Explain your reasoning.
(B) How many of each color bead will each friend receive on the necklace? Explain your reasoning.
Answers
A. The greatest number of friends who can receive a necklace made from a combination of 72 blue and 42 red beads is 6.
B. Each friend will receive a necklace with 12 blue beads and 7 red beads.
How is this determined?The solution to this problem can be determined by considering the highest common factors of 72 and 42.
The common factors of 72 and 42 are 2 and 3.
The factors of 72 are 2, 3, and 12.
The factors of 42 are 2, 3, and 7.
2 x 3 = 6
When 6 divides 72 = 12
When 6 divides 42 = 7
Data and Calculations:Number of blue beads = 72
Number of red beads = 42
The highest number that can divide 72 and 42 without a remainder is 6.
Thus, each friend's necklace will contain 19 beads (12 blue beads and 7 red beads).
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What is the domain of the function given below
Answers
Answer:
c. [-1, infinity)
Step-by-step explanation:
the domain the interval or set of valid x values (while the range is the same for the valid y values).
what is the smallest value of x we see for the graph ?
for x values we need to look left and right.
and the more left the value, the smaller it is.
so, in other words, what is the left-most x value e can find ?
x = -1
that is the "starting point" of the function. there is no functional value for any smaller x.
and then clearly, the function goes on and on to the right without any boundary in sight. so, it keeps going to the right in all eternity, that means it goes to infinity.
therefore the answer.
keep in mind that "infinity" is not a number, only a concept. so, when writing "infinity" at an interval end, it is not included (and we use a round bracket).
A national chain of department stores ranks its 1,000,000 salespeople by the monetary value of their sales. Karen's sales are at the 26th percentile. Brian's sales
are at the 33rd percentile.
(If necessary, consult a list of formulas.)
(a) Which of the following must be true about Karen's sales?
The value of Karen's sales were about 26% of the chain's total.
O The value of Karen's sales was in the top half of all of the salespeople.
O Karen sold $2600 in merchandise.
O Karen had sales lower in value than about 74% of the salespeople.
(b) Which of the following must be
true about Karen's and Brian's sales?
The value of Brian's sales were $700 more than Karen's.
O The value of Karen's sales were $700 more than Brian's.
O Both Karen and Brian had sales higher in value than the median.
O Both Karen and Brian had sales lower in value than the median.
Answers
(a) The truth about Karen's sales is that Karen had sales lower in value than about 74% of the salespeople. So, the correct option is D.
(b) The truth about Karen's and Brian's sales is that both Karen and Brian had lower sales in value than the median. So, the correct option is D.
Given that department stores rank their 1,000,000 salespeople by the monetary value of their sales. Karen's sales are at the 26th percentile and brian's sales are at the 33rd percentile.
A percentile is a measure used in statistics that indicates the value below which a certain percentage of observations in a group of observations falls.
(a) Karen had sales lower in value than about 74% of the salespeople because the 26% percentile represents his relative position among all the employees in terms of sales.
(b) Both Karen and Brian had sales lower in value than the median because the Median represents the 50th percentile. Since Karen's sales are at the 26th percentile and Brian's sales are at the 33rd percentile it implies their sales are less than the median value.
Hence, the truth about Karen's sales is Karen had sales lower in value than about 74% of the salespeople, and true about Karen's and Brian's sales is both Karen and Brian had lower sales in value than the median.
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If n = 140 and X = 112, construct a 95% confidence interval for the population proportion, p.
Give your answers to three decimals
Answers
The confidence interval for the population proportion, p is (0.766, 0.833)
Confidence intervalThe formula for calculating the confidence interval for proportion is expressed as:
CI = p±√pq/n
Given the following
p = 112/140 = 0.8
q = 1-p = 0.2
Substitute
CI = 0.8±√(0.8)(0.2)/140
CI = 0.8±0.0338
CI = (0.766, 0.833)
Hence the confidence interval for the population proportion, p is (0.766, 0.833)
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Please help I’m unsure
Answers
Step-by-step explanation:
3 answer.....
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Students at a high school were polled to determine the type of music they preferred. There were students who completed the poll. Their responses are represented in the circle graph.
What percent of students preferred music?
A circle graph titled Music Preferences consists of a circle divided into 6 regions with labels and sizes as follows: rap, 945; alternative, 462; rock and roll, 275; country, 168; jazz, 15; other, 85.
Music Preferences
Rap 945
Alternative 462
Rock and Roll 275
Country 168
Jazz 15
Other 85
Answers
The percent of students that preferred alternative music is 23.7%
How to determine the percentage?The music type and the preference are given as:
Music Preferences
Rap 945
Alternative 462
Rock and Roll 275
Country 168
Jazz 15
Other 85
From the above table, we have:
Alternative = 462
Total = 945 + 462 + 275 + 168 + 15 + 85
Total = 1950
The percentage is then calculated as:
Percentage = Alternative/Total * 100%
This gives
Percentage = 462/1950 * 100%
Evaluate
Percentage = 23.7%
Hence, the percent of students that preferred alternative music is 23.7%
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Find the area of the figure.
Answers
Need help with that I don’t understand it
Answers
The answer is no. b.
Step-by-step explanation:
The answer is no b. u just take common
How do the y-values in the table grow? The y-values increase by a factor of 49 for each x increase of 1. The y-values increase by 49 for each x increase of 1. The y-values increase by a factor of 7 for each x increase of 1. The y-values increase by 7 for each x increase of 1.
Answers
From the table, we can deduce that The y-values increase by a factor of 7 for each x increase of 1 and is denoted as option C.
What is a Factor?
This is defined as a number which divides another without leaving a remainder afterwards.
From the table, we can deduce that the y-values are divisible by 7 thereby making it a factor of it and confirming that it increase by a factor of 7 for each x increase of 1.
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If cot theta = 3/2, what is the value of csc theta?
Answers
The value of csc theta is [tex]\frac{3. 61}{2}[/tex]
How to determine the valueIt is important to note that the ratio for cot is given as;
Cot theta = adjacent/opposite
cosec theta = hypotenuse/opposite
If cot theta = 3/2, then
Adjacent = 3
Opposite = 2
Using Pythagoras theorem, we have
Hypotenuse square = opposite + adjacent square
[tex]H = \sqrt{2^2 + 3^2}[/tex]
[tex]H = \sqrt{4 + 9}[/tex]
[tex]H = 3. 61[/tex]
Cosec theta = [tex]\frac{3. 61}{2}[/tex]
Thus, the value of csc theta is [tex]\frac{3. 61}{2}[/tex]
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Answer:
3.16/2
Step-by-step explanation:
Have a great day
Linear functions f(x) and g(x) have been combined by addition and multiplication. The table shows values for the sum, s(x), and product, p(x).
Which statements correctly compare the sum and product? Check all that apply.
Both functions have a constant rate of change.
The sum is linear and the product is quadratic.
The x-intercepts are the same.
The sum has one y-intercept and the product has two x-intercepts.
Both functions decrease for x ≥ 2.
Answers
The statements that correctly compare the sum and product of the function are:
The sum is linear and the product is quadratic.The sum has one y-intercept and the product has two x-intercepts.What is a linear function?A linear function simply means a function that represents a straight line on the coordinate plane.
In this case, the sum is linear and the product is quadratic while the sum has one y-intercept and the product has two x-intercepts.
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A jar contains 100ml of a mixture of oil and water in the ratio 1:4. Enough oil is added to make the ratio of oil to water 1:2. How much water must be added to make the ratio oil to water 1:3?
Answers
Answer:
40 ml of water must be added.Step-by-step explanation:
Initial volume of mixture is 100 ml with oil to water ratio of 1 : 4.
First, let's find the volume of each component.
If the oil is x then water is 4x according to ratio and their sum is 100 ml:
x + 4x = 1005x = 100x = 20So, we have 20 ml of oil and 80 ml of water.
Now, let's added volume of oil be y. Then we have the ratio:
(20 + y)/80 = 1/220 + y = 40y = 20So, we have 40 ml of oil and 80 ml of water.
Lastly, let's added water be z. Then we have the ratio:
40/(80 + z) = 1/380 + z = 120z = 40We must add 40 ml of water.
Gcf of 12h3,36h3,12h6
Answers
The greatest common factor from the given information is 12h³.
What is the greatest common factor?The greatest common factor (GCF) of a given set of whole numbers is the largest value that can be divided by the set of numbers.
From the information given, we are to find the GCF of:
12h³ = (1 , 2, 3, 4, 6 , 12 )h³
36h³ = (1, 2, 3, 4, 6, 9, 12, 18, 36)h³
12h⁶ = (1, 2, 3, 4, 6, 12)h³ * h³
Therefore, we can conclude that the greatest common factor is 12h³.
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