(I need help asap)
There are a total of 15 apartments in two buildings. The difference of two times the number of apartments in the first building and three times the number of apartments in the second building is 5.
(a) Write a system of equations to model the relationship between the number of
apartments in the first building 2 and the number of apartments in the second building.
(b) How many apartments are in each building?
Answers
(a) The system of equations for the first building and the second building is x + y = 15 and 2x - 3y = 5.
(b) There are 10 and 5 apartments in each building.
Given that,
There is a total of 15 apartments in two buildings. Also, the difference is of the two times the no of apartments in the first building and three times the no of apartments in the second building is 5.Let us assume the first building is x and the second building be y.Now based on the above information, the following equations are as follows:
x + y = 15 ...........(1)
2x - 3y = 5 ............(2)
Now
y = 15-x
Now put the y value in equation (2)
2x -3(15-x) = 5
2x - 45 + 3x = 5
5x = 50
x = 10,
And, y = 5
Therefore we can conclude that
(a) The system of equations for the first building and the second building is x + y = 15 and 2x - 3y = 5.
(b) There are 10 and 5 apartments in each building.
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Related Questions
using traditional methods, it takes 99 hours to receive a basic driving license. a new license training method using computer aided instruction (cai) has been proposed. a researcher used the technique with 260 students and observed that they had a mean of 98 hours. assume the standard deviation is known to be 7 . a level of significance of 0.1 will be used to determine if the technique performs differently than the traditional method. is there sufficient evidence to support the claim that the technique performs differently than the traditional method? what is the conclusion?
Answers
Answer:
There is enough sufficient evidence to support the claim.
Step-by-step explanation:
There is sufficient evidence to support the claim that the new CAI training method performs differently than the traditional method. The conclusion is that utilizing the new CAI training approach, it takes much less time on average to obtain a basic driving license than it does using the conventional method.
To determine if the new license training method using computer aided instruction (CAI) performs differently than the traditional method, we need to conduct a hypothesis test. Let's define the null and alternative hypotheses as follows:
Null hypothesis (H0): The mean time to receive a basic driving license using the new CAI training method is equal to the mean time using the traditional method, i.e., μ = 99.
Alternative hypothesis (Ha): The mean time to receive a basic driving license using the new CAI training method is different from the mean time using the traditional method, i.e., μ ≠ 99.
We are given that the sample size is 260, the sample mean is 98, and the population standard deviation is 7. We can use a z-test to test the hypothesis since the sample size is large (n > 30).
The test statistic can be calculated as:
z = (x - μ) / (σ / √n) = (98 - 99) / (7 / √260) = -2.475
where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
The corresponding p-value for a two-tailed test is 0.013, which is less than the level of significance of 0.1. Therefore, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the new CAI training method performs differently than the traditional method.
In other words, the mean time to receive a basic driving license using the new CAI training method is significantly different from the mean time using the traditional method.
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Find the demand function for the marginal revenue function. Recall that if no items are sold, the revenue is 0. R'(x) = 0.06x2 – 0.05x + 152 p(x) = 0
Answers
The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 152 when R'(x) = 0.06x² - 0.05x + 152.
Given that,
We have to find for the marginal revenue function, locate the demand function.
Remember that the income is zero if no things are sold:
R'(x) = 0.06x² - 0.05x + 152
p(x) is what.
We know that,
MR = dTR/dx = 0.06x² - 0.05x + 152
Integrating the marginal revenue function , we get total revenue function,
MR = TR
= (0.06x²⁺¹)/(2+1) - (0.05x¹⁺¹)/(1+1) + 152x
= (0.06x³)/3 - (0.05x²)/2 + 152 x
TR = 0.02 x³ - 0.025 x² + 152 x
TR = (P)(Q) = (P)(x) = 0.02 x³ - 0.025 x² + 152 x
P = ( 0.02 x³ - 0.025 x² + 152 x)/x
P = 0.02x² -0.025x + 152
Therefore, The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 152 when R'(x) = 0.06x² - 0.05x + 152.
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Yahira orders a sweater priced at $40.00. Shipping and handling are an additional 6% of the price. How much shipping and handling will Yahira pay?
A. $37.60
B. $24.00
C. $2.40
D. $42.40
Answers
Answer:
the answer would be c I did this one yesterday
Using a table of values, determine the solution to the equation below to the nearest fourth of a unit.
2x-4=3^x+1
A.
x ≈ 3.25
B.
x ≈ 1
C.
x ≈ 2
D.
x ≈ 2.5
Answers
Answer: D. x ≈ 2.5
Step-by-step explanation: I circled the intersection in green in this attachment I provided.
As you can see, it's near 2.5 which is correct.
I really hope this is correct. I answered this one with confidence. Good luck on your test btw.
Answer:
D. x ≈ 2.5
Step-by-step explanation:
Fill in the blank. I NEED AN ANSWER FASTTT
Answers
Answer:
It is =
Step-by-step explanation:
Because (6 x 1 = 6 ) + 1 x 1/100 = 6.1
Carter wants to use the model above to solve 273 ÷ 13. Explain how he would find parts A, B, and C of the model.
Answers
Using the model Carter will find parts A, B and C b to be
Part A = 26 tens
Part B = 13
Part C = 13 ones
What is a model?A model is a representation in form of shape used for to achieve a desired aim. Models are choose with respect to the importance
How to determine parts A. part B, and part C using the modelThe given model is a rectangle
Subtracting 13 from 273 to give 260. This can be arranged in tens by doing
= 260 / 10
= 26
Hence, A is 26 tens
Representing the C part in place value we have 13 ones
Since B = C, we have B = 13
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can somebody help me ?
Answers
Answer:
0.21.......
Step-by-step explanation:
Your welcome
Answer:
0.21
Step-by-step explanation:
$5.25 divided by 25 is $0.21 per trading card
Evaluate 4y - 5x + 10m
y=2 x=3 m=5
Answers
Answer:
43
Step-by-step explanation:
4(2)-5(3)+10(5)
8-15+50
-7+50
43
hopes this helps please mark brainliest
Answer:
17/54,x=3 m=5
Step-by-step explanation:
Hello! I'm really having trouble with this problem,if you can't see the image clearly here is the directions.
Determine if the two figures shown below are congruent,similar,or neither. Prove your answers using the transformations.
The transformations are Translation, Rotation,and Reflection.
Here's the words for the bottom part if you can't read it
Josiah believes the scale factor from ABC to FED is 1.5 since AB=2 and FE=3 (you can multiply by 1.5) why is he incorrect?
Please take your time with this, I know this is a lot.
Answers
The two given figures are neither similar nor congruent
How to determine if a figure is similar or congruent?Congruent figures are geometric figures that have the same shape and size. That is, if you can transform one figure into another figure by a sequence of translations , rotations , and/or reflections , then the two figures are congruent.
Similar triangles are defined as triangles that have the same shape, but their sizes may vary. Therefore, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
Now, it is clear that both shapes are not congruent because the lengths are not congruent.
Similarly, the ratio of the two corresponding sides are not the same. Thus:
We can say neither of both are similar or congruent.
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Will two students using the same piece of glassware have the exact same measurement? Explain your answer
Answers
Two students using the same piece of glassware may not have the exact same measurement.
Is it possible for two students to obtain identical measurements using the same glassware?While the same glassware provides a consistent measuring tool, variations in the students' measurement techniques, environmental conditions, and inherent limitations of the glassware can lead to differences in the obtained measurements.
Factors such as parallax errors, variations in reading techniques, and differences in the precision of the measuring instrument can all contribute to variations in measurements.
Additionally, small imperfections in the glassware, such as scratches or irregularities, can affect the accuracy of the measurement. These imperfections may cause slight variations in the volume or capacity being measured.
To minimize discrepancies, it is important for students to follow proper measurement techniques, ensure accurate calibration of the glassware, and consider potential sources of error.
By adhering to standardized procedures and using precise measurement techniques, students can aim to obtain measurements that are as consistent and reliable as possible.
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a) A circular channel section has diameter of 6m and it is running half. Calculate the discharge through the channel if the bed slope is 1 in 600 and manning’s co efficient is equal to 0.014.
Answers
To calculate the discharge through the circular channel, we can use Manning's equation, which relates the flow rate (Q) to the channel properties and flow conditions. Manning's equation is given by:
Q = (1/n) * A * R^(2/3) * S^(1/2)
where:
Q is the discharge (flow rate)
n is Manning's coefficient (0.014 in this case)
A is the cross-sectional area of the channel
R is the hydraulic radius of the channel
S is the slope of the channel bed
First, let's calculate the cross-sectional area (A) of the circular channel. The diameter of the channel is given as 6m, so the radius (r) is half of that, which is 3m. Therefore, the area can be calculated as:
A = π * r^2 = π * (3m)^2 = 9π m^2
Next, let's calculate the hydraulic radius (R) of the channel. For a circular channel, the hydraulic radius is equal to half of the diameter, which is:
R = r = 3m
Now, we can calculate the slope (S) of the channel bed. The given slope is 1 in 600, which means for every 600 units of horizontal distance, there is a 1-unit change in vertical distance. Therefore, the slope can be expressed as:
S = 1/600
Finally, we can substitute these values into Manning's equation to calculate the discharge (Q):
Q = (1/0.014) * (9π m^2) * (3m)^(2/3) * (1/600)^(1/2)
Using a calculator, the discharge can be evaluated to get the final result.
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1.sundaybought10pens,andapencost$5dollars.whatisthecostof15pensinnaira,if$1is30naira?
Answers
Answer:
Step-by-step explanation:
gnag dsewhqjhnqrhjwqkhjqrkhwq
Ama's income has just risen from ¢940 per month to ¢1060 per month. As a result, she decides to purchase 12 % more shoes per month. The income elasticity of Ama's demand for shoes is?
Answers
Ama's demand for shoes does not increase by a proportionate amount to her increase in income.
To calculate the income elasticity of Ama's demand for shoes, we need to know how much the quantity demanded of shoes changes in response to a change in income. In this case, we know that Ama's income has increased by (1060 - 940) = ¢120 per month, which is a percentage change of:
(120/940) x 100% = 12.77%
We also know that Ama has decided to purchase 12% more shoes per month in response to this increase in income.
So, the income elasticity of demand can be calculated as:
% Change in Quantity Demanded / % Change in Income
= (12% / 12.77%)
= 0.94
Since the income elasticity of demand is less than 1, we can say that Ama's demand for shoes is income inelastic. This means that the percentage change in the quantity demanded of shoes is less than the percentage change in income.
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Lyle and Shaun open savings accounts at the same time. Lyle deposits $100 initially and adds $20 per week. Shaun deposits $500 initially and adds $10 per week. Lyle wants to know when he will have the same amount in his savings account as Shaun.
Part A: Write two equations to represent the amounts of money Lyle and Shaun have in their accounts
f(x=
g(x)=
Part B: to solve the system you will make f(x)=g(x)
Answers
A. The equations for the amounts of money Lyle and Shaun have in their accounts are represented as:
f(x) = 20x + 100
g(x) = 10x + 500
B. When f(x) = g(x), x = 40.
How to Write the Equation of a System?A linear equation can be written in slope-intercept form y = mx + b. Here, the value of m is the unit rate or slope, while the value of b is its y-intercept or initial value.
Part A:
Equation for Lyle:
y-intercept / initial value (b) = $100
Slope / unit rate (m) = $20
To write the equation, substitute m = 20 and b = 100 into f(x) = mx + b:
f(x) = 20x + 100.
Equation for Lyle:
y-intercept / initial value (b) = $500
Slope / unit rate (m) = $10
To write the equation, substitute m = 10 and b = 500 into g(x) = mx + b:
g(x) = 10x + 500.
Part B: To solve the system, we would do the following:
20x + 100 = 10x + 500
20x - 10x = -100 + 500
10x = 400
x = 400/10
x = 40
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Check all the equations that apply to meet the Segment Addition
Postulate in segment OQ. OP=6X+5,PQ=4x and OQ=45
Answers
Answer:
Options (2) and (5)
Step-by-step explanation:
Given in the question,
Length of OQ = 45
OP = (6x + 5)
PQ = 4x
By segment addition postulate,
Length of a segment OQ = length of segment OP + length of segment PQ
45 = 6x + 5 + 4x
10x + 5 = 45
10x = 45 - 5
10x = 40
x = \(\frac{40}{10}\)
x = 4
Therefore, Option (2) and Option (5) are the correct options.
consider the following geometric series. [infinity] (−3)n − 1 7n n = 1
Answers
The given series is an infinite geometric series with a common ratio of -3 and a first term of (-3)^0 * 7^1 = 7. To determine the sum of this series, we can use the formula for the sum of an infinite geometric series, given by S = a / (1 - r).
The given series is an infinite geometric series with a common ratio of -3 and a first term of (-3)^0 * 7^1 = 7. In this case, a = 7 and r = -3. Plugging these values into the formula, we get S = 7 / (1 - (-3)). To simplify the expression, we can rewrite it as S = 7 / (1 + 3) = 7 / 4.
Therefore, the sum of the infinite geometric series is 7/4, or 1.75. The sum of the given infinite geometric series is 1.75. This result is obtained by using the formula for the sum of an infinite geometric series with a first term of 7 and a common ratio of -3.
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160 bananas;20%decrease
Answers
Answer:
128 banana's... I would work it all out for u but the teacher just came in my room and had a go
Answer: 128
Step-by-step explanation:
Percent (%)' means 'out of one hundred':
p% = p 'out of one hundred',
p% is read p 'percent',
p% = p/100 = p ÷ 100.
20% = 20/100 = 20 ÷ 100 = 0.2.
100% = 100/100 = 100 ÷ 100 = 1.
What is the numerical solution to the equation five less than three times a number equals four more than eight times rhetorical number?
Answers
Answer:
3n-5=8n+4
Step-by-step explanation:
20 The rectangle ABCD represents a park.
B
Not to scale
40m
A
D
60m
The lines show all the paths in the park.
The circular path is in the centre of the rectangle and has a diameter of 10m.
Calculate the shortest distance from A to C across the park, using only the paths shown.
Answers
Answer: 33
Step-by-step explanation:
Cold weather is hard on Ava’s grandmother, so she is knitting her a striped scarf for her birthday. As Ava was knitting the scarf she made a mistake. She has to 0.75 feet of the scarf, and now the remaining part is only 4.75 feet long. Which equation will help find the total length of the scarf, s, before it was unraveled?
Answers
Answer:
4.75+0.75
Step-by-step explanation:
The equation that help find length of scarf is l = 0.75 + 4.75
What is a sum?The result of adding two or more numbers is called a sum.
Given,
Length of striped scarf = 0.75 feet
Length of remaining scarf = 4.75 feet
Total length = Length of striped scarf + Length of remaining scarf
Hence, l = 0.75 + 4.75
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A 5.0 µC point charge is moved within an electric field and has an electric potential energy change of 10.0 J. What is the electric potential difference before and after the charge was moved? Show work. (µC = 1.0 × 10–6)
Answers
For a 5.0 µC point charge moved within an electric field, the electric potential difference is mathematically given as
du=2*10^6
What is the electric potential difference before and after the charge was moved?Generally, the equation for the change in potential energy is mathematically given as
dV=qdu
Therefore
10=5*10^{-6}*du
du=2*10^6
In conclusion, the electric potential difference
du=2*10^6
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A spinner has 17 equal-sized sections marked 1 through 17. Find the probability. Enter your answer as a simplified fraction.
You spin once and land on an odd number.
The probability that you land on an odd number is
Answers
Answer:
9/17 or 52.9% or likely
Step-by-step explanation:
Equation 1
A linear relationship crosses the y-axis at (0,0) and the x-axis at (0, 0)
with a rate of change of -3.
Equation 2
y=x
Answers
Wouldn’t y =x be a straight line from the origin with a slope of 1?
Find an equation of the line with the given slope that passes through the given point Write the equation in the form Ax + By = C
m= -8 (-6-4)
(Simplify your answer Use integers or fractions for any numbers in the equation )
Answers
Answer:
\(8x + y = - 52\)
Step-by-step explanation:
m= -8
p (-6,-4)
Formula for equation of a logbook passing through to points:
\(y - y1 = m(x - x1)\)where y1= -4 and x1= -6\(y - ( - 4) = - 8(x - ( - 6)) \\ y + 4 = - 8(x + 6) \\ y + 4 = - 8x - 48 \\ 8x + y = - 52\)Express each question as a single power. Then state the Exponent law used.
A) 2^4 x 2^7
Exponent Law(s)
B) (-3)^9 divided (-3)^5
Exponent Law(s)
C) (5^2)^-3 x 5^0
Exponent Law(s)
Please answer this math problem asap. Thanks!
Answers
Answer:
A) 2^4 x 2^7 = 2^(4 + 7) = 2^11
Exponent Law(s): Product Law
B) (-3)^9 divided (-3)^5 = (-3)^(9 - 5) = (-3)^4
Exponent Law(s): Quotient Law
C) (5^2)^-3 x 5^0 = 5^(-6) × 1 = 5^(-6)
Exponent Law(s): Power of a power rule; zero exponent rule
f(x)=|x| to g(x) = |x + 1| + 3
Answers
should start at point (-1,3) and it’s a V since it’s absolute value
What is the domain of the function Y = 3 In x graphed below?
Answers
The given function is
\(\sf y=3ln(x)\)
Which is a logarithm function. An important characteristic of logarithms is that their domain cannot be negative, because the logarithm of a negative number is undefined, the same happens for x = 0.
Therefore, the domain of this function is all real numbers more than zero.
The image attached shows the graph of this function, there you can notice its domain restriction.
So, the right answer is the first choice: x greater than 0
If Line LK = 16, find the length of Line JK.
Answers
Answer:
JK = 16√2
Step-by-step explanation:
This triangle is a special case right triangle, where you have 1 90-degree angle and 2 45-degree angles. The sides that correspond to the 45-degree angles are scalable by 1 and the hypotenuse is scalable by √2. Sometimes these are called 1-1-√2 triangles, describing the measurements of the sides.
Since this has a side of 16, the hypotenuse will be 16√2.
Cheers.
A jar contains "q" quarters and "d" dimes. There are 7 coins in the jar and the total value of the coins is $1.00
Which system of equations can be used to find how many of each type of coin is in the jar.
A. 0.25q + 0.10d = 1.00
q + d =7
B. 0.25q + 0.10d= 7.00
q + d = 1
C. 0.10q + 0.25d = 1.00
q + d = 7
D. 25q + 10d = 1
q + d = 7
Answers
Answer:
A. 0.25q + 0.10d = 1.00
q + d =7
Step-by-step explanation: Only logical choice I see. The others mix up values and units.
The system of equations is
0.25q + 0.10d = 1.00
q + d =7
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have,
A jar contains "q" quarters and "d" dimes.
There are 7 coins in the jar and the total value of the coins is $1.00.
As, 2 quarters and 5 dimes
= 2(.25) + 5(.10)
= $.50+ $.50
= $1
Now, according to question,
0.25q + 0.10d = 1
and, 0.10q + 0.10d = 0.7
Solving above equation we get
0.15q = 0.3
q = 2 quarter
Then, d= 7 -q = 7- 2 = 5 quarter
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Please help me out! Will mark brainliest!
Answers
Answer:
Add -3+8
Step-by-step explanation:
You would do this first because it is in the brackets. Usually you would do (*) first but those are just there because the 4 is negative and if they were not there it would get confusing and look like this::[-3+8]--4. So the next step would be the [*].
HOPE THIS HELPS!!!
Answer:
Use PEMDAS
Step-by-step explanation:
Parenthesis, If there are none move on to exponents if there are no exponents move to multiplication. No multiplication? use division. If you dont see division use addition and lastly if there is no addition use subtraction. In the equation, it looks like you have to make the -3 and 8 positive. So, since the -4 is in the parenthesis(P) multiply(M) 4 by 3 and 8 once the three is positive. So your final answer would be either C or D
Its the best i could do but good luck. I tried...