Answer: 3n - 1 = n + 5
Step-by-step explanation:
If needed to solve 3n-1=n+5
3n-n=5+1
2n=6
n=3
This is extra information. I hope this helped you
A used bookstore sells hardback books and paperback books.
· A hardback book costs $11, including tax.
· A paperback book costs $5, including tax.
· Jamal bought 3 more paperback books than hardback books.
· Jamal spent $47.
How many paperback books did Jamal buy?
2
3
4
5
Answer:
4 HOPE IM NOT WRONG O-O
Step-by-step explanation:
In a half hour, Sarah is meeting her friends at the lake, 6 miles from her house. At what average speed must
she ride her bike to get there on time?
Answer:
Divide 6 miles by 0.5 hour: 6/0.5 = 12 miles per hour.
Step-by-step explanation:
The average speed must she rides her bike to get there on time will be 12 miles per hour.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
In a half-hour, Sarah is meeting her friends at the lake, 6 miles from her house.
The average speed must she rides her bike to get there on time will be
S = 6 / (1/2)
S = 6 x 2
S = 12 miles per hour
The average speed must she rides her bike to get there on time will be 12 miles per hour.
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The sum of 3 times a number and 12 is 20
Answer:
3x+12=20 is the equation
Step-by-step explanation:
Answer:
x= 2.666
Step-by-step explanation:
3x+12=20 is the equation
Two cars start traveling in the same direction around a circular road that is 80 km long. The speed of one car is 92 km/h and the sped of the other is 68 km/h. How many minutes after the two cars start traveling will one car lap the other for the second time?
PLEASE HELP! I WILL AWARD BRAINLIEST IF THERE ARE TWO ANSWERS!
Answer:
400 minutes
Step-by-step explanation:
The speed for car 1 is 92 km/h and the speed for car two is 68 km/h. The time is unknown but we know it has to be converted into minutes so the time for both cars will be x/60. Now we multiply speed by time and get distance. The first car is 92 x/60 and the second car is 68 x/60. Cross multiply and you get 92x/60 and 68 x/60 now we can make an equation. 92x/60 - 68 x/60 = 80, x = 200. We multiply x by 2 to get the second time which is 400 minutes.
for tires with a lifetime below 30,000 miles, Grear will refund a customer $1 per 100 miles short of 30,000 . (a) For each tire sold, what is the average cost of the promotion (in $ )? (Use at least 1,000 trials. Round your answer to two decimal places.) $ (b) What is the probability that Grear will refund more than $25 for a tire? (Use at least 1,000 trials. Round your answer to three decimal places.)
(a) The average cost of the promotion per tire sold by Grear can be calculated by simulating the refund amounts for a large number of trials. (b) To determine the probability that Grear will refund more than $25 for a tire, we again simulate a large number of trials.
(a) The average cost of the promotion per tire sold by Grear can be calculated by simulating the refund amounts for a large number of trials. Assuming each trial represents a tire sold, we can calculate the refund amount for each trial based on the difference between the tire's lifetime and 30,000 miles. By averaging the refund amounts over the trials, we can determine the average cost of the promotion. Let's simulate at least 1,000 trials to obtain a reliable estimate.
(b) To determine the probability that Grear will refund more than $25 for a tire, we again simulate a large number of trials. For each trial, we calculate the refund amount as we did in part (a). Then, we count the number of trials where the refund amount exceeds $25 and divide it by the total number of trials. This will give us the probability of refunding more than $25. By simulating at least 1,000 trials, we can obtain a reasonably accurate estimation of the probability.
Due to the constraints of the current text-based interface, I'm unable to perform the simulations and calculations required to provide you with the specific numerical answers. However, you can apply the described methodology to conduct the simulations using programming or spreadsheet software to obtain the desired results.
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Fifteen items or less: The number of customers in line at a supermarket express checkout counter is a random variable with the following probability distribution. х 0 1 2 3 4 5 P(x) 0.10 0.20 0.30 0.20 0.15 0.05 (g) If each customer takes 3 minutes to check out, what is the probability that it will take more than 6 minutes for all the customers currently in line to check out? The probability that it will take more than 6 minutes for all the customers currently in line to check out is 0.15 Х s
The probability that it will take more than 6 minutes for all the customers currently in line to check out is 0.15 Х s.
The probability distribution of the number of customers in line at a supermarket express checkout counter is given as below: х 0 1 2 3 4 5
P(x) 0.10 0.20 0.30 0.20 0.15 0.05
Here, we have to find the probability that it will take more than 6 minutes for all the customers currently in line to check out if each customer takes 3 minutes to check out.
We know that time taken for one customer to check out is 3 minutes.
So, time taken for n customers to check out is 3n minutes.
The probability of more than 6 minutes is P(x>6) = P(x=4) + P(x=5)
On substituting the given probability distribution, we have: P(x>6) = 0.15 Х s
Therefore, the probability that it will take more than 6 minutes for all the customers currently in line to check out is 0.15 Х s.
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Find the average rate of change in the simplest form
(a) A type of lightbulb is labeled as having an average lifetime of 1,000 hours. It's reasonable to model the probability of failure of these bulbs by an exponential density function with mean μ=1,000. Recall than an exponential probability density function looks like f(t)={0μ−1e−t/μ if t<0 if t≥0′ where μ is the mean. (i) Use this model to find the probability that a bulb fails within the first 300 hours. (Round your answer to three decimal places.) x (ii) Use this model to find the probability that a bulb burns for more than 600 hours. (Round your answer to three decimal places.) x (b) What is the median lifetime of these lightbulbs? (Round your answer to one decimal place.) hr
(a) We can use the exponential probability density function to calculate the probabilities:
(i) The probability that a bulb fails within the first 300 hours can be found by integrating the density function from 0 to 300:
P(failure within 300 hours) = ∫[0 to 300] (1/1000) * e^(-t/1000) dt
This integral can be solved to get the probability.
(ii) The probability that a bulb burns for more than 600 hours can be found by subtracting the probability of failure within 600 hours from 1:
P(burns for more than 600 hours) = 1 - P(failure within 600 hours)
Again, this probability can be calculated by integrating the density function from 600 to infinity.
(b) The median lifetime of the lightbulbs is the value of t for which the cumulative distribution function (CDF) equals 0.5. In other words, we need to find the value of t such that ∫[0 to t] (1/1000) * e^(-x/1000) dx = 0.5.
Solving this equation will give us the median lifetime of the lightbulbs.
Note: To provide specific numerical answers for parts (i), (ii), and (b), the exact values and calculations need to be performed using the given exponential probability density function.
(a) P(t > 600) = 1 - P(t < 600) = 1 - 0.00368 = 0.99632
(b) t = 1000 ln(2) = 693.14 hours
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Triangle DEF has vertices D ( − 4 , 1 ) D-4, 1, E ( 2 , 3 ) E2, 3, and F ( 2 , 1 ) F2, 1 and is dilated by a factor of 3 using the point ( 1 , 1 ) 1, 1 as the point of dilation. The dilated triangle is named Δ D ' E ' F ' ΔD'E'F'. What are the coordinates of the vertices of the resulting triangle?
Answer:
D'(-14,1), F'(4,1) and E'(4,7)
Step-by-step explanation:
Let's take each point and dilate about the point (1,1) using rule (x,y)--->(kx,ky). Where 'k' is dilation factor
Find the equation of the line parallel to line h that passes through (–4, 2). y = one-third x + StartFraction 10 Over 3 Endfraction y = negative one-third x + two-thirds y = 3x + 14 y = –3x – 10
Answer:
y = 1/3x + 10/3
I hope this helped
Step-by-step explanation:
Answer:y = 1/3x + 10/3
Step-by-step explanation: got it right on edge
Dan and David win some money and share it in the ratio 5:4. Dan gets £8 more than David. How much did David get
An automatic filling machine is used to fill 2-litre bottles of cola. The machine’s output is known to be approximately Normal with a mean of 2.0 litres and a standard deviation of 0.01 litres. Output is monitored using means of samples of 5 observations.
Determine the upper and lower control limits that will include roughly 95.5 percent of the sample means.
If the means for 6 samples are 2.005, 2.001, 1.998, 2.002, 1.995 and 1.999, is the process in control?
The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.
Now let's check if the process is in control using the given sample means:
To determine the upper and lower control limits for the sample means, we can use the formula:
Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))
Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))
In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.
For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.
Given:
Mean = 2.0 litres
Standard Deviation = 0.01 litres
Sample size (n) = 5
Using the formula, we can calculate the upper and lower control limits:
UCL = 2.0 + (1.96 * 0.01 / sqrt(5))
LCL = 2.0 - (1.96 * 0.01 / sqrt(5))
Calculating the values:
UCL ≈ 2.0018 litres
LCL ≈ 1.9982 litres
Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.
Now let's check if the process is in control using the given sample means:
Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997
Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.
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<3=3x
<6=9x+4
x=
PLEASEEE HELPPP
ill make brainiest
Answer: x=no solution
Step-by-step explanation:
HELPPP PLEASE ITS DUE TODAY!!!!!!
Answer:
B, look at the size compared to the others, it's DEFINITLY not d or c
Can you please help me
Answer:
x = 23
Step-by-step explanation:
The marked angles are "corresponding," hence congruent:
8x -27 = 7x -4
x = 23 . . . . . . . . . add 27-7x to both sides
Two runners start the race at the same time. The first runner's speed is 4/5 of the speed of the second runner. After 30 minutes, the runners are 2 miles apart. What is the speed of each runner?
The speed of the second runner is x = 40/9 miles per hour. The speed of the first runner is (4/5)x = (4/5)*(40/9) = 16/9 miles per hour.
Let the second runner's speed be x. Then the first runner's speed is 4/5 * x = (4/5)x.Therefore, the speed of the first runner is (4/5)x and the speed of the second runner is x.After running for 30 minutes, the first runner would have covered a distance of (4/5)x * 1/2 = (2/5)x miles.
The second runner would have covered a distance of x * 1/2 = (1/2)x miles. Since the runners are 2 miles apart, we can write an equation:(2/5)x + (1/2)x = 2. Multiplying both sides of the equation by 10 to eliminate fractions, we get: 4x + 5x = 40.
Simplifying the equation, we get: 9x = 40. Dividing both sides of the equation by 9, we get: x = 40/9. Therefore, the speed of the second runner is x = 40/9 miles per hour. The speed of the first runner is (4/5)x = (4/5)*(40/9) = 16/9 miles per hour.
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The black graph is the graph of
y = f(x). Choose the equation for the
red graph.
Answer:
C
Step-by-step explanation:
The equation for the red graph is,
⇒ 2y = f (x)
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
We have to given that;
The black graph is the graph of,
⇒ y = f (x)
Now,
The red graph is spread out the function of blk graph.
Hence, We get;
The equation for the red graph is,
⇒ y = f (x) / 2
⇒ 2y = f (x)
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PLEASE HELP
Evaluate the expression when x= 7 and y=13.
63
y-
X
Answer:
6Step-by-step explanation:
x = 7
y = 13
[tex]y - x[/tex]
Substitute values into the given equation
[tex]13 - 7 = 6[/tex]
rewrite using a single positive exponent 4^9/4^3
Answer:
4⁶
Step-by-step explanation:
Exponent Rule: [tex]\frac{b^m}{b^n} =b^{m-n}[/tex]
4⁹/4³ = 4⁹⁻³ = 4⁶
Which expression is equivalent to (a^8)^4
?
Answer:
=a^32
Step-by-step explanation:
(a^8)^4= a^8.4
=a^8.4
On Monday, Jan made withdrawals of $15, $55, and $95 from her savings account. On the same day, her twin sister Julie made withdrawals of $25, $65, and $75 from her savings account. Julie and Jan's brother also withdrew money from his savings account on Monday. He made three withdrawals and withdrew $20 more than Julie did. What are three possible amounts he could have withdrawn?
Answer:
Three possible amounts are: 35+73+77
Step-by-step explanation:
The total amount of money the brother withdrew is 185 because 185 is 20 more than 165 the total of money Julie withdrew. Any three numbers that add up to 185 are possible answers.
It's in the picture
Answer:
2nd, 3rd and 5 th
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = [tex]\frac{2}{3}[/tex] and (a, b) = (1, 2) , thus
y - 2 = [tex]\frac{2}{3}[/tex] (x - 1) ← 2 nd option
Using (a, b) = (4, 4), then
y - 4 = [tex]\frac{2}{3}[/tex] (x - 4) ← 3 rd option
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = [tex]\frac{2}{3}[/tex] , thus
y = [tex]\frac{2}{3}[/tex] x + c ← is the partial equation
To find c substitute (4, 4) into the partial equation
4 = [tex]\frac{8}{3}[/tex] + c ⇒ c = 4 - [tex]\frac{8}{3}[/tex] = [tex]\frac{4}{3}[/tex]
f(x) = [tex]\frac{2}{3}[/tex] x + [tex]\frac{4}{3}[/tex] ← 5 th option
Given = 7.6182 +0.08145X and Y = 29, X = 262.5. Use elasticity of expenditure to interpret the model above.
The elasticity of expenditure is given by;e = δY/δX * X/Ywhere δY/δX is the slope of the demand curve and can be obtained by taking the derivative of the demand curve. X/Y is the expenditure share of X.In the given equation:
Y = 7.6182 + 0.08145X, we can rearrange to give X in terms of Y; X = (Y - 7.6182) / 0.08145Hence, expenditure share of X (X/Y) = (262.5 - 7.6182) / 29 = 8.9743.
Now we need to find δY/δX, by taking the derivative of the demand equation above, we get;δY/δX = 0.08145*Hence, the elasticity of expenditure is;e = δY/δX * X/Y = 0.08145*(262.5/29) = 0.731Conclusion:The value of elasticity of expenditure obtained above is less than one (0.731 < 1). This implies that the demand for X is inelastic. Hence, a 1% increase in the price of X will cause less than 1% decrease in the quantity demanded. Conversely, a 1% decrease in the price of X will cause less than 1% increase in the quantity demanded.
The elasticity of expenditure (E) is a metric used to measure the sensitivity of the quantity demanded of a good or service to a change in the price of that good or service. If E > 1, then the good or service is considered elastic. This means that a small change in price can cause a significant change in the quantity demanded of the good or service.
If E = 1, then the good or service is considered to have unit elasticity. This means that a change in price will cause a proportional change in the quantity demanded. If E < 1, then the good or service is considered inelastic. This means that a change in price will cause a relatively small change in the quantity demanded. In the given model above, the elasticity of expenditure was computed as 0.731. Since this value is less than one, it implies that the demand for the good is inelastic. A 1% increase in the price of the good will cause a less than 1% decrease in the quantity demanded. Conversely, a 1% decrease in the price of the good will cause less than a 1% increase in the quantity demanded.
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Help ASAP !!!!!!!!!!!
any one help in the question
Answer:
here
Step-by-step explanation:
identify the slope. y = -x - 4
Answer:
-4 is the y intercept. You know this because it is the only one without a variable.
The slope is -1.
Step-by-step explanation:
Tom and Claire both like do short exercise that involve small breaks. Tom does a short
burst of exercise every 2 minutes, and Claire does hers every 3 minutes. If they start
doing their exercise at 9:00am, when do they both do their exercises again?
HELP!!! 15 points and marked brainliest
Answer:
35.8 I just used a calculator to find the answer
Subtract: 3l (l − 4m + 5n) from 4l (10n − 3m + 2l)
Answer:
5l² + 25ln
Step-by-step explanation:
Step 1: Write expression
4l(10n - 3m + 2l) - 3l(l - 4m + 5n)
Step 2: Distribute
40ln - 12lm + 8l² - 3l² + 12lm - 15ln
Step 3: Combine like terms
5l² + 25ln
In the Troubled Waters region, the delivery of water supply and waste water services is provided by Troubled Waters Utilities (TWU). The inverse demand curve is P(Q)=10−Q, where P is measured in dollars. Under normal conditions, the marginal cost (i.e. the marginal cost of supplying water and waste water service) is constant and equal to 5 dollars, MC(Q)=5. (a) Calculate the socially optimal level of output (assuming no externalities) and the corresponding price. Compute the corresponding consumer surplus. ( 5 marks) When the dam levels are high, however, the experts at TWU estimate that water consumption reduces costs of preventing floods and associated damage. It is estimated that each extra unit of water consumption reduces those costs by 1 dollar.
The socially optimal level of output in the Troubled Waters region is 7.5 units, and the corresponding price is $5. The consumer surplus at this level of output is $37.5.
To calculate the socially optimal level of output, we need to find the point where marginal cost (MC) equals the inverse demand curve (P). In this case, MC(Q) = 5 and P(Q) = 10 - Q. Setting these equal to each other, we have:
5 = 10 - Q
Solving for Q, we find Q = 5. The socially optimal level of output is thus 5 units.
To find the corresponding price, we substitute the value of Q into the inverse demand curve:
P = 10 - 5 = 5
So the socially optimal price is $5.
Consumer surplus is the difference between what consumers are willing to pay for a good and what they actually pay. To calculate consumer surplus, we need to integrate the area under the demand curve from 0 to the socially optimal quantity (Q = 5). Using the formula for the area under the curve, we find:
Consumer Surplus = ∫[0,5] (10 - Q) dQ
= [10Q - (Q^2/2)] [0,5]
= [(10*5) - (5^2/2)] - [(10*0) - (0^2/2)]
= (50 - 12.5) - (0 - 0)
= 37.5
Therefore, the consumer surplus at the socially optimal level of output is $37.5.
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