The values of x and the side length are as follows:
a. x = 6 ; RS = 15; ST = 19; RT = 34;
b. x = 5 ; RS = 20; ST = 1; RT = 21;
How to write equation in terms of x?Point S is between R and T.
Therefore, the equation in terms of x can be represented as follows:
RT = RS + ST
a.
RS = 4x - 9
ST = 19
RT = 8x - 14
Hence,
8x - 14 = 4x - 9 + 19
8x - 14 = 4x - 9 + 19
8x - 14 = 4x + 10
8x - 4x = 10 + 14
4x = 24
x = 24 / 4
x = 6
RS = 4x - 9 = 4(6) - 9 = 24 - 9 = 15
ST = 19
RT = 8x - 14 = 8(6) - 14 = 48 - 14 = 34
b.
RS = 2x + 10
ST = x - 4
RT = 21
Therefore,
21 = 2x + 10 + x - 4
21 = 3x + 6
21 - 6 = 3x
15 = 3x
divide both sides by 3
x = 15 / 3
x = 5
RS = 2x + 10 = 2(5) + 10 = 10 + 10 = 20
ST = x - 4 = 5 - 4 = 1
RT = 21
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The researcher meets with one participant and asks a series of pre-determined questions using a topic guide. What type of qualitative data collection is this
The qualitative data collection method described, where the researcher meets with one participant and asks pre-determined questions using a topic guide, is commonly known as an "interview." Interviews are a form of qualitative data collection where the researcher engages in a direct conversation with the participant to gather information and insights related to the research topic. The questions are typically structured or semi-structured, allowing for flexibility and deeper exploration of the participant's experiences, perspectives, and opinions.
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simplify the following expression -2a- (-3+a^2)
Answer is in the image
Step-by-step explanation:
Sorry if wrong or blurry
If each of the 4 shelves holds 14 movies, how many movies does Betty have on her shelving unit?
Answer:
Step-by-step explanation:
4 x 14= 56
6
How many solutions does the system of linear equations represented in the graph below have?
Infinitely many solution
One solution
No Solution
None of the above
pls help me I need this
Answer:
150x÷×÷320y
Step-by-step explanation:
it's hard to tell in writing I can speak it but
write 17/20 as a fraction decimal percent.
Written as a fraction, the amount is 17/20 .
But a fraction actually means "division". When you see "17/20", it means "17 divided by 20".
If you actually go ahead and DO the division problem (with a pencil or on your calculator) that the fraction is talking about, the answer you get is the same amount as the fraction, but written as a decimal.
The same amount as 17/20, written as a decimal, is 0.85 .
The same amount as 17/20, written as a percent, is 85% .
In the given problem, find a similar relationship to the given relationship. Support the answer with an explanation.
Notice that the relation between the first two figures is that the outside figure becomes the inside figure, and the inside figure becomes the outside figure.
Therefore the triangle inside the square corresponds to the square inside the triangle.
Answer: Option A.
Find the least common denominator (LCD) of
4/9 and 5/3
HELP ME BRU
If number of electricity power failures occur according to a Poisson distribution with an average of 4 failures per 5 months. 12. What is the probability that there will be at least one failure during the coming month
Answer:
123
Step-by-step explanation:
3(x–6)–1/2(8x+10)=–25
The solution to the equation 3(x-6) - 1/2(8x+10) = -25 is x = 2.
To simplify the equation 3(x-6) - 1/2(8x+10) = -25, we can start by applying the distributive property and then combining like terms.
First, let's distribute the 3 and the -1/2 to the terms inside the parentheses:
3(x-6) - 1/2(8x+10) = 3x - 18 - (4x + 5)
Now, let's simplify further by combining like terms:
3x - 18 - 4x - 5 = -x - 23
So, the simplified equation is -x - 23 = -25.
To solve for x, we can isolate the variable by adding 23 to both sides of the equation:
-x - 23 + 23 = -25 + 23
This simplifies to:
-x = -2
Finally, we can solve for x by multiplying both sides of the equation by -1:
(-1)(-x) = (-1)(-2)
This gives us:
x = 2
Therefore, the solution to the equation 3(x-6) - 1/2(8x+10) = -25 is x = 2.
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A girl weight increased by 12% between her tenth and four teen birthdays . If she weighed 45kg on her tenth birthday. What did she weigh on her fourteenth birthday
What is the sum and classification of StartFraction 3 Over 20 EndFraction + StartRoot 10 EndRoot?
3.31227766..., irrational
3.31227766..., rational
18.16227766..., irrational
18.16227766..., rational
9514 1404 393
Answer:
3.31227766..., irrational
Step-by-step explanation:
3/20 +√10 = 0.15 + 3.16227766017...
The root of 10 is irrational, so adding that to a rational number will give an irrational sum.
The sum is about 3.31227766017..., an irrational number.
Answer:
A
Step-by-step explanation:
find the angle between the vectors. f(x) = 2x, g(x) = 4x4, f, g = 1 f(x)g(x) dx −1
Answer:
The angle between f and g is approximately 53.13 degrees.
Net Present Value (6 points total) The city of Corvallis is deciding whether or not to undertake a project to improve the quality of the city's drinking water. The project would require an immediate payment of $20,000 to install a new filtration system. This filtration system will require yearly maintenance costs of $1,000 after the initial period. The filtration system will be operational for 5 years. The benefits in first year are $500. At the end of year 2, the benefit received is $4000. For years 3, 4, and 5, the benefit received is $7,000. Assume that the discount rate is 6%. a. Write out the general mathematical formula you would use to determine the net present value (NPV) of this project. (2 points) b. Plug-in the appropriate numbers into the formula from above. You DO NOT need to calculate the answer, simply plug in the values in the appropriate places. (2 points) c. What criteria should the city use to decide if they should install the filtration system or not?
a. The formula for NPV is NPV = (Benefits - Costs) / (1 + Discount Rate)^n.
b. Plugging in the appropriate values, Benefits: $500 (Year 1), $4,000 (Year 2), and $7,000 (Years 3-5); Costs: $20,000 (initial payment), $1,000 (yearly maintenance from Year 2); Discount Rate: 6%.
c. The city should use a positive NPV as a criterion to decide whether to install the filtration system or not.
a. The general mathematical formula to determine the net present value (NPV) of this project is as follows:
NPV = (Benefits - Costs) / (1 + Discount Rate)^n
Where:
Benefits represent the cash inflows or benefits received from the project in each period.
Costs refer to the initial investment or cash outflows required to undertake the project.
Discount Rate is the rate used to discount future cash flows to their present value.
n represents the time period (year) when the cash flow occurs.
b. Plugging in the appropriate numbers into the formula:
Benefits: $500 in Year 1, $4,000 at the end of Year 2, and $7,000 for Years 3, 4, and 5.
Costs: Initial payment of $20,000 and yearly maintenance costs of $1,000 from Year 2 onwards.
Discount Rate: 6%.
n: 1 for Year 1, 2 for Year 2, and 3, 4, and 5 for Years 3, 4, and 5, respectively.
c. The city should use the criteria of positive net present value (NPV) to decide whether to install the filtration system or not. If the NPV is greater than zero, it indicates that the present value of the benefits exceeds the costs, suggesting that the project is financially favorable and would generate a positive return.
Conversely, if the NPV is negative, it implies that the costs outweigh the present value of the benefits, indicating a potential financial loss. Therefore, a positive NPV would indicate that the city should proceed with installing the filtration system, while a negative NPV would suggest not undertaking the project.
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Note this question belongs to the subject Business.
find each value of k for which the lines y=9kx-1 and kx 4y=12 are perpendicular
The value of k in the equations is 2/3
How to determine the value of kFrom the question, we have the following parameters that can be used in our computation:
y = 9kx - 1
kx + 4y = 12
This can be expressed as
y = 9kx - 1
y = -kx/4 + 3
The slopes of perpendicular lines are opposite reciprocal
This means that
9k * -k/4 = -1
So, we have
k^2 = 4/9
Evaluate
k = 2/3
Hence, the value of k is 2/3
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a body’s weight varies inversely with the square of its distance from the center of the earth; if a chicken weighs 12 pounds when it is 5,000 miles from the earth’s center, how much will the chicken weigh when it is 10,000 miles from the earth’s center ?
The chicken will weigh 3 pounds when it is 10,000 miles from the earth's center.
There are two types of proportions.
1) Direct Proportion - shows the direct relationship between two quantities. It can be represented by the equation y = kx. As one quantity increases, the other quantity also increase.
2) Inverse Proportion - describes the indirect relationship between two quantities. It can be represented by the equation y = k/x. As one quantity increases, the other quantity decreases.
According to the problem, a body’s weight varies inversely with the square of its distance from the center of the earth.
y = k/x
let y = a body's weight
x = square of its distance from the center of the earth
Solving for the proportionality constant, k.
y = k/x
12 = k / (5000^2)
k = 12 x 25, 000, 000
k = 300, 000, 000
The equation for the relationship in the problem can now be represented by:
y = 300,000,000/x
where
y = a body's weight
x = square of its distance from the center of the earth
Evaluating the new equation where x = square of 10,000:
y = 300,000,000/x
y = 300,000,00/(100,000,000)
y = 3
Hence, the chicken will weigh 3 pounds when it is 10,000 miles from the earth's center.
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Brainly to whomever solves these proportion questions! I will give brainly to whomever has the most detailed answer, but I WILL report unrelated and unhelpful questions ( the more reports you get, the quicker you get kicked of brainly - SO DON'T TRY ME)
Answer:
a.) terry didn't line up the triangle correctly. 4/y = 20/18
b.) (20+16)/18
Step-by-step explanation:
for part a, you have to make sure the angles line up correctly (the angle with one tick mark lining up with the angle with one tick mark, the angle with two tick marks lining up with the angle with two tick marks, etc.)
for part b.) you just put the proportional lengths of the bigger triangle in for the lengths of the smaller triangle.
Factor the polynomial
below completely:
10m5n² + 25m³n³
(Show work please)
Answer:
\(5mn^{2} (2+ 5m^{2} n)\)
Step-by-step explanation:
I assumed the polynomial is \(10mn^{2} +25m^{3}n^{2}\)
FIRST: Highlight the common factors{ 5 , m and\(n^{2}\))
\(5mn^{2} (2+ 5m^{2} n)\)
how many ways are there to select 12 countries in the united nations to serve on a council if 2 are selected from a block of 45, 4 are selected from a block of 57, and the others are selected from the remaining 69 countries
By combination, there are 2346953264 ways to do so.
What is the example of combination?
Without regard to the sequence in which the things are chosen, a combination is the selection of all or a portion of a collection of objects. Consider a group of three letters, such as A, B, and C.Total number of selected countries = 12
Number of selected countries from a block of 45 = 3
Number of selected countries from a block of 57 = 4
So, remaining number of selected countries from a block of 69.
So, 12-(3+4)=12-7=5
= ⁴⁵C₃ × ⁵⁷C₄ × ⁵⁷C₅
= 14190 × 395010 × 4187106
= 2346953264
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Translate the sentence into an equation.
Nine more than the product of a number and 7 is 5.
Use the variable w for the unknown number.
Answer:
5=9+7w
Step-by-step explanation:
We know that the final solution will be 5, so that can be on a side by itself.
The keyword to see is a product, which means multiplication. It says "a number (w) and 7" which means it is the unknown number multiplied by 7.
Lastly, we add 9 to 7(w) because it says "nine more than the product," which means you add 9
\(\frac{1}{3} + \frac{2}{k} =\frac{13}{3k}\)
Answer:
\(k = 1 - \frac{ \sqrt{313} }{26} \)
\(k = \frac{ \sqrt{313} }{26} + 1\)
the figure below is made of two triangular prisms. what is the volume of the figure
Answer:
896 cubic inches
Step-by-step explanation:
V (Δ prism) = 1/2 · height · base · length
V (top prism) = 1/2(6)(12)(14)
V (top prism) = 504 in³
V (bottom prism) = 1/2(7)(8)(14)
V (bottom prism) = 392 in³
504 + 392 = 896
Please help fast! 25 points and brainliest!! Let f(x) = 36x5 − 44x4 − 28x3 and g(x) = 4x2. Find f of x over g of x
Answer:
fx/gx=10
Step-by-step explanation:
fx= (36x5)-(44x4)-(28x3)
fx=80
gx= 4x2
gx=8
To work out fx/gx:
fx/gx=80/8
fx/gx=10
In a level-C confidence interval about the proportion p of some outcome in a given population, the margin of error, m, is o the maximum distance between the sample statistic and the population parameter in any random sample of the same size from that population. the minimum distance between the sample statistic and the population parameter in C% of random samples of the same size from that population. o the maximum distance between the sample statistic and the population parameter in C% of random samples of the same size from that population. O the minimum distance between the sample statistic and the population parameter in any random sample of the same size from that population.
The margin of error in a level-C confidence interval is the maximum distance between the sample statistic and the population parameter in any random sample of the same size from that population
In a level-C confidence interval about the proportion p of some outcome in a given population, the margin of error (m) represents the maximum distance between the sample statistic and the population parameter in any random sample of the same size from that population.
The margin of error is a measure of the precision or uncertainty associated with estimating the true population proportion based on a sample. It reflects the variability that can occur when different random samples are taken from the same population.
When constructing a confidence interval, a level-C confidence level is chosen, typically expressed as a percentage. This confidence level represents the probability that the interval contains the true population parameter. For example, a 95% confidence level means that in repeated sampling, we would expect the confidence interval to contain the true population proportion in 95% of the samples.
The margin of error is calculated by multiplying a critical value (usually obtained from the standard normal distribution or t-distribution depending on the sample size and assumptions) by the standard error of the sample proportion. The critical value is determined by the desired confidence level, and the standard error accounts for the variability in the sample proportion.
The margin of error provides a range around the sample proportion within which we can confidently estimate the population proportion. It represents the uncertainty or potential sampling error associated with our estimate.
To summarize, the margin of error in a level-C confidence interval is the maximum distance between the sample statistic and the population parameter in any random sample of the same size from that population. It accounts for the variability and uncertainty in estimating the true population proportion based on a sample, and it helps establish the precision and confidence level of the interval estimation.
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A helicopter landing pad has a length of 80 ft and a width of 50 ft. A safety zone
of uniform width, which is not to be entered during landing, surrounds the landing
pad. The landing pad and safety zone together have a combined area of 10800 ft2,
what is the uniform width (safety zone) around the landing pad?
Answer:
uniform width around the landing pad = 9.41 feet
Step-by-step explanation:
Length of landing pad = 80 ft
width of landing pad = 50 ft
Length of safety zone = (80 + 2w)
width of safety zone = (50 + 2w)
Total area = 10800 \(ft^{2}\)
Area of landing pad = length x width
= 80 x 50
= 4000 \(ft^{2}\)
Area of landing pad = 4000 \(ft^{2}\)
Thus,
area of safety zone = total area - area of landing pad
= 10800 - 4000
= 6800
area of safety zone = 6800 \(ft^{2}\)
But,
area of safety zone = length x width
6800 = (80 + 2w) x (50 + 2w)
6800 = 4000 + 160w + 100w + 4\(w^{2}\)
divide through by 4,
1700 = \(w^{2}\) + 65w + 1000
⇒ \(w^{2}\) + 65w + 1000 - 1700 = 0
\(w^{2}\) + 65w -700 = 0
Applying the quadratic formula,
w = (-b ± \(\sqrt{b^{2} -4ac}\)) ÷ 2a
a = 1, b= 65 and c = -700
w = (-65 ± \(\sqrt{(65)^{2}-(4*1*-700) }\)) ÷ 2
= (-65 ± \(\sqrt{7025}\)) ÷ 2
= (-65 ± 83.82)÷ 2
w = (-65 + 83.82) ÷ 2 OR (-65 - 83.82) ÷ 2
= 18.82 ÷ 2 OR -148.82 ÷ 2
= 9.41 OR -74.41
Thus, w = 9.41 ft.
A certain music box has the shape of a cube. Each side of the music bos is 15 cm long. What is the surface area of the box
The music box has a surface area of 1350 square cm.
A cube has six square faces that are all the same size. The length of each side of the cube is given as 15 cm. Therefore, the surface area of the cube can be found by calculating the area of one square face and then multiplying it by 6:
Area of one square face = (15 cm) x (15 cm) = 225 square cm
The surface area of the cube = 6 x (Area of one square face)
= 6 x 225 square cm
= 1350 square cm
As a result, the music box has a surface area of 1350 square cm.
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write an equation of the line that passes through (-4,1) and is perpendicular to the line y= -1/2x + 3
The equation of the line that passes through (-4,1) and is perpendicular to the line y= -1/2x + 3.
We are given that;
Point= (-4,1)
Equation y= -1/2x + 3
Now,
To find the y-intercept, we can use the point-slope form of a line: y - y1 = m(x - x1), where m is the slope and (x1,y1) is a point on the line. Substituting the values we have, we get:
y - 1 = 2(x - (-4))
Simplifying and rearranging, we get:
y = 2x + 9
Therefore, by the given slope the answer will be y= -1/2x + 3.
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a rectangular parking lot is 67.5 ft wide and 148 ft long. what is the area of the parking lot in square meters?
The area of the rectangular parking lot is 929.03 square meters.
Use the formula for the area of a rectangle to calculate the area of the rectangular parking lot, which is given as:
Area = length × width
We know that the parking lot is 67.5 ft wide and 148 ft long, the area can be calculated as follows:
Area = 67.5 ft × 148 f
t= 9990 sq. ft
However, the question asks for the area in square meters, so we need to convert square feet to square meters. 1 square foot is equal to 0.092903 square meters, so we can use this conversion factor to convert square feet to square meters.
Area in square meters = Area in square feet × 0.092903
= 9990 sq. ft × 0.092903
= 929.03 sq meters
Therefore, the area is 929.03 square meters.
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John is deciding between three different
apartments. The table below shows the
monthly rental price and size for three
apartments.
Apartment
A
B
C
Size
(m²)
75
84
92
830 75 11.1
1,05084 = 12.5
Monthly rental price (in
euros)
1,10092 12
John tried to order the apartments by their
price per square meter from least to
greatest, but he made a mistake. Here's his
work.
Least
12
11.1
Apartment C Apartment A
<
830
What was John's mistake?
1,050
1,100
Greatest
12.5
Apartment B
The price per square meter from least to greatest is 1.07, 12.01, 12.50.
What is Area of Rectangle?The area of Rectangle is length times of width.
The table shows the monthly rent of each apartment.
Apartment Size(m²) Monthly rent
A 75 830
B 84 1050
C 102 1225
Now we have find the rent per square meter of each apartment.
To find rate per square meter, we have to divide the rent by the number square meters rented out.
Apartment A = 830/75 = 11.07
Apartment B = 1050/84 =12.50
Apartment C = 1225/102 = 12.01
From least to greatest is 11.07, 12.01, 12.50
Hence, 11.07, 12.01, 12.50 is the price per square meter from least to greatest.
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The complete question is given in the attachment.
Instructions to the teacher:
You can give partial credit for partial solutions. The total is 36 points, so divide the student's score by 36 and
multiply by 100 to get a percent score. For example, if the student scores 30, divide 30 = 36 to get 0.8333. The
percent score is 83%.
Question Max. points Student score
1
2 points
2 1 point
3
4 points
Question Max. points Student score
8 1 point
9 3 points
10
3 points
11 4 points
12
3 points
13
3 points
TOTAL 36 points
36
4
4 points
5
2 points
6
2 points
4 points
7
Answer:
It’s 3,1 pretty sure
Step-by-step explanation: