For a sample of radioactive material,
a) The half-life of the radioactive material with that it disintegrates to 90% of the original amountb is equals to the 6.58 years.
b) The time is 2.12 years, at which the material disintegrates to 80% of the original amount.
We have, a sample of radioactive material disintegrates to 90% of the original amount after one year. The term half-life is defined as the time it takes for one-half of the atoms of a radioactive material to disintegrate. Let the original/ initial amount of a sample of radioactive material = y₀ and after t year amount of material = y₀/2. After one year, amount of sample of radioactive material = 90% of y₀. Now, radioactive decay equation form is y(t) = y₀( 0.90)ᵗ ,
We have to calculate value of t when y = y₀/2.
=> [tex]\frac{ y_0}{2} = y_0( 0.90)^t[/tex]
=> 1/2 = (0.90)ᵗ
Taking natural logarithm both sides
=> ln( 1/2) = ln ( 0.90)ᵗ
=> ln( 1/2) = t ln ( 0.90)
=> t = ln(1/2)/ln(0.90)
=> t = 6.579 ~ 6.58 years
b) Now, we have to determine value of t when material disintegrates to 80% of the original amount. Let t years be required time here. So, 80% of y₀ = y₀ ( 0.90)ᵗ
=> 0.80y₀ = y₀( 0.90)ᵗ
Taking natural logarithm both sides
=> ln( 0.80 ) = ln( 0.90)ᵗ
=> ln( 1/2) = t ln( 0.90)
=> t = ln(0.80)/ln(0.90)
=> t = 2.117 ~ 2.12years
Hence, required value of time is 2.12 years.
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for the function graphed, determine the interval(s) where the derivative is (a) positive; (b) negative; and the x-value(s) at which the derivative is (c) equals zero; (d) does not exist.'
(a) Positive derivative interval: From x = -∞ to x = -4, and from x = 0 to x = 3.
(b) Negative derivative interval: From x = -4 to x = 0, and from x = 3 to x = ∞.
(c) x-value(s) where derivative equals zero: At x = -3 and x = 2.
(d) x-value(s) where derivative does not exist: At x = -4 and x = 3.
To find the intervals where the derivative of the function is positive, negative, or equals zero, we first need to find the critical points by setting the derivative equal to zero and solving for x. We can see from the graph that there is only one critical point at x = -2. We then test each interval between the critical points and endpoints to determine if the derivative is positive or negative.
From x = -infinity to x = -2, the derivative is negative. From x = -2 to x = 3, the derivative is positive. From x = 3 to x = infinity, the derivative is negative. Therefore, the answer is (a) the derivative is positive on (-2, 3); (b) the derivative is negative on (-infinity, -2) and (3, infinity); (c) the derivative equals zero at x = -2; (d) the derivative exists for all x.
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The diameter of a cone's circular base is 12 inches. The height of the cone is 12 inches.
What is the exact volume of the cone?
Enter your answer in the box.
in³
Answer: It is 144 but add pi symbol
Step-by-step explanation:
In conclusion the exact volume of the cone is 144π cubic inches.
How to solve and what does volume mean?
The radius of the circular base is half the diameter, which is 12/2 = 6 inches.
The volume of a cone can be found using the formula V = (1/3)πr²2h, where r is the radius and h is the height.
Substituting the given values, we get:
V = (1/3)π(6²2)(12)
V = (1/3)π(36)(12)
V = (1/3)(432π)
V = 144π
Therefore, the exact volume of the cone is 144π cubic inches.
Volume is a measure of the amount of space occupied by a three-dimensional object, such as a solid, liquid, or gas. It is typically measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³). The volume of an object can be determined by measuring its dimensions, such as length, width, and height, and applying the appropriate formula for the shape of the object.
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Write a rule for the translation.
(x-1, y + 2)
(x-2, y + 1)
(x+2, y - 1)
(x+1, y-2)
Answer: Step 1: Pick a pair of corresponding points: one point in the shape before the translation and the same point in the shape after the translation.
Step 2: Determine how many units, a, left or right the shape moved.
Step-by-step explanation:
A boxplot for a set of 80 scores is given below.
How many scores are represented in the blue section of the boxplot?
Answer: The number of scores represented in the blue section of the boxplot is 12.
Tickets for a raffle cost $8. There were 737 tickets sold. One ticket will be randomly selected as the winner, and that person wins $1800 and also the person is given back the cost of the ticket. For someone who buys a ticket, what is the Expected Value (the mean of the distribution)?
On average, someone who buys a ticket can expect to make a profit of $2.43 as the expected value for someone who buys a ticket is $2.43.
What is expected value?It is the average amount of money that an individual can expect to win or lose on an investment. It is calculated by multiplying the probability of each outcome by its payoff and then adding the expected values of all outcomes.
In this case, the probability of winning= 1/737
and the payoff = $1800 - $8
= $1792.
The expected value (EV) is calculated by multiplying the probability of each outcome by its payoff.
EV = (1/737) x (1792)
EV = $2.43
Therefore, the expected value for someone who buys a ticket is $2.43. This means that, on average, someone who buys a ticket can expect to make a profit of $2.43.
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Help? Not sure how to do this
The company bank account currently has a positive balance of R2195,00. You have to refund five clients an amount of R665,00 each, due to a sales discount not being applied to their recent purchases. What will the balance be on the company account after the refunds have been paid?
Step-by-step explanation:
The total amount to be refunded to the five clients is:
5 x R665,00 = R3325,00
To find the balance on the company account after the refunds have been paid, we need to subtract the total amount refunded from the current balance:
R2195,00 - R3325,00 = -R1130,00
Therefore, the balance on the company account will be negative and equal to -R1130,00 after the refunds have been paid.
A container holds 44 cups of water. How much is this in gallon? write your answer as a whole number or a mixed number
Answer:2.75 gallons of water
Step-by-step explanation:
Answer:
One gallon is equal to 16 cups of water.
To find out how many gallons are in 44 cups of water, we can divide 44 by 16:
44 cups ÷ 16 cups/gallon = 2.75 gallons
Therefore, 44 cups of water is equal to 2 and 3/4 gallons.
Step-by-step explanation:
1. Recall that 1 gallon is equal to 16 cups of water. Therefore, to find how many gallons are in 44 cups of water, we can set up a proportion:
1 gallon / 16 cups = x gallons / 44 cups
2. To solve for x, we can cross-multiply and simplify:
16x = 1 * 44
16x = 44
x = 44 / 16
x = 2.75
3. The result of 2.75 gallons represents the equivalent amount of water in gallons. To express this answer as a whole number or mixed number, we can observe that 2.75 is equal to 2 and 3/4:
2.75 = 2 + 0.75
2.75 = 2 + 3/4
Therefore, 44 cups of water is equal to 2 and 3/4 gallons.
51. For which of the following values of L will the lines whose equations are 2x+3y=8
and 8x+12y = L be parallel?
I. L = 0
II. L = 8
III. L = −8
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
PLEASE HELP!!! URGENT 60 POINTS!!!!!
1. Construct the 99% confidence interval estimate of the population proportion p if the sample size is n=100 and the number of successes in the sample is x=66.
Give your answers to 4 decimal places, and use at least 3 decimal places in your critical value.
______ < p < ______
2. In a random sample of 710 Americans, 37.2% indicated that they have a cat for a pet. Estimate with 95% confidence the proportion of all Americans that have cats as pets. Give the confidence interval in interval notation, (LCL,UCL) . Give your answer as percentages, to at least 2 decimal places, and use at least 3 decimal places in your critical value.
Confidence Interval:
3. Refer to the following scenario.
An epidemiologist is worried about the prevalence of the flu in East Vancouver and the potential shortage of vaccines for the area. She will need to provide a recommendation for how to allocate the vaccines appropriately across the city. She takes a simple random sample of 336 people living in East Vancouver and finds that 39 have recently had the flu.
Suppose that the epidemiologist wants to re-estimate the population proportion and wishes for her 95% confidence interval to have a margin of error no larger than 0.04. How large a sample should she take to achieve this? Please carry answers to at least six decimal places in intermediate steps, and use at least 3 decimal places in your critical value.
Sample size =
4. Refer to the following scenario.
A government official is in charge of allocating social programs throughout the city of Vancouver. He will decide where these social outreach programs should be located based on the percentage of residents living below the poverty line in each region of the city. He takes a simple random sample of 126 people living in Gastown and finds that 21 have an annual income that is below the poverty line.
Suppose that the government official wants to re-estimate the population proportion and wishes for his 90% confidence interval to have a margin of error no larger than 0.05. How large a sample should he take to achieve this? Please carry answers to at least six decimal places in intermediate steps, and use at least 3 decimal places in your critical value.
Sample size =
The 99% confidence interval estimate of the population proportion p is (0.5323, 0.7877) to 4 decimal places.
What is confidence interval?
A confidence interval is a range of values calculated from a sample of data that is used to estimate an unknown population parameter with a certain level of confidence.
1.To construct a 99% confidence interval estimate of the population proportion p, we can use the following formula:
CI=[tex]$\hat{p}$[/tex]±[tex]\item $z_{\alpha/2}$[/tex]×[tex]\sqrt{\frac{\hat{p}(1-\hat{p})}{n} }[/tex]
where:
[tex]$\hat{p}$[/tex] is the sample proportion (x/n)
[tex]\item $z_{\alpha/2}$[/tex] is the critical value of the standard normal distribution at the 99% confidence level, which is 2.576
n is the sample size
Substituting the given values, we have:
[tex]$\hat{p}$[/tex] = x/n = 66/100 = 0.66
[tex]\item $z_{\alpha/2}$[/tex] = 2.576 (from the standard normal distribution table or calculator)
n = 100
Plugging these values into the formula, we get:
CI = 0.66 ± 2.576 * [tex]\sqrt{(0.66)\frac{(1-0.66)}{100}}[/tex]
CI = 0.66 ± 0.1277
Therefore, the 99% confidence interval estimate of the population proportion p is (0.5323, 0.7877) to 4 decimal places.
2.To estimate the proportion of all Americans that have cats as pets with 95% confidence, we can use the following formula:
CI=[tex]$\hat{p}$[/tex]±[tex]\item $z_{\alpha/2}$[/tex]×[tex]\sqrt{\frac{\hat{p}(1-\hat{p})}{n} }[/tex]
where:
[tex]$\hat{p}$[/tex] is the sample proportion (0.372)
[tex]\item $z_{\alpha/2}$[/tex] is the critical value of the standard normal distribution at the 95% confidence level, which is 1.96
[tex]\item $n$[/tex] is the sample size (710)
Substituting the given values, we have:
CI=0.372±1.96×[tex]\sqrt{0.372\frac{(1-0.372)}{710} }[/tex]
CI=0.372±0.0325
Therefore, the 95% confidence interval estimate of the proportion of all Americans that have cats as pets is [tex]$(0.3395, 0.4045)$[/tex] to 4 decimal places.
Expressing this in interval notation, we get [tex](33.95$, $40.45$)$[/tex] to 2 decimal places as a percentage.
Thus, we can say with 95% confidence that the proportion of all Americans that have cats as pets is between 33.95% and 40.45%.
3.To determine the sample size required to estimate the population proportion with a margin of error no larger than 0.04 and a 95% confidence level, we can use the following formula:
[tex]n=(\frac{z_{\alpha/2}}{E} )^2[/tex]×[tex]\hat{p}$(1-$\hat{p}$)[/tex]
where:
[tex]\item $n$[/tex] is the required sample size
[tex]\item $z_{\alpha/2}$[/tex] is the critical value of the standard normal distribution at the 95% confidence level
[tex]\item $E$[/tex] is the margin of error
[tex]$\hat{p}$[/tex] is the sample proportion
Substituting the given values, we have:
[tex]n=(\frac{1.96}{0.04} )^2[/tex]×[tex]0.1161[/tex][tex](1-0.1161)[/tex]
Rounding up to the nearest whole number, we get:
n=476
Therefore, the required sample size to estimate the population proportion with a margin of error no larger than 0.04 and a 95% confidence level is 476.
4.To determine the sample size required to estimate the population proportion with a margin of error no larger than 0.05 and a 90% confidence level, we can use the following formula:
[tex]n=(\frac{z_{\alpha/2}}{E} )^2[/tex]×[tex]\hat{p}$(1-$\hat{p}$)[/tex]
where:
[tex]\item $n$[/tex] is the required sample size
[tex]\item $z_{\alpha/2}$[/tex] is the critical value of the standard normal distribution at the 90% confidence level, which is 1.645
[tex]\item $E$[/tex] is the margin of error, which is 0.05
[tex]$\hat{p}$[/tex] is the sample proportion, which is 21/126 = 0.1667
Substituting the given values, we have:
[tex]n=(\frac{1.645}{0.05} )^2[/tex]×[tex]0.1167[/tex][tex](1-0.1167)[/tex]
n=145.9198
Rounding up to the nearest whole number, the government official should take a sample size of 146 to achieve his desired margin of error.
Therefore, the required sample size to estimate the population proportion with a margin of error no larger than 0.05 and a 90% confidence level is 146.
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Pls help I will give 35 points
Answer: i believe its 10 if there no multiplication
Step-by-step explanation:
:o
In the year 2000, the number of snakes in a certain forest was 280.
Since that year the number of snakes in that forest has increased at a
rate of 12% per year. Write a function, f(x), that models the number of
snakes x years after the year 2000.
For the expression y + 6 − 3, determine the coefficient for the variable term. (2 points) a 0 b 1 c 3 d 6
The answer would probaly be 1
The first three terms of the geometric series are; x+5,x+1&x; Calculate the a) Value of x [2]
The value of x in the series given the first three terms x + 5, x + 1 and x is 1/3
Given that, we have
x + 5, x + 1 and x
Using the common ratio, we have
(x + 5)/(x + 1) = (x + 1)/x
So, we have
x² + 5x = x² + 2x + 1
Evaluating the like terms, we have
3x = 1
Divide by 3
x = 1/3
Hence, the value of x is 1/3
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Equal to which of the following?
The expression for the difference quotient is option C and the simplified form of the function f(x) when evaluated at x and x + h is 2x + 4 + 2h.
What is the expression of the difference quotient?We are asked to find the expression for the difference quotient of the function f(x) when evaluated at x and x + h. The difference quotient is given by:
[tex]$\frac{f(x+h) - f(x)}{h}$[/tex]
where h is a small nonzero number representing the change in the input.
Substituting f(x) with its expression, we get:
[tex]$\frac{(2(x+h)^2 + 4(x+h) - 3) - (2x^2 + 4x - 3)}{h}$[/tex]
Expanding and simplifying the numerator, we get:
[tex]$\frac{2x^2 + 4xh + 2h^2 + 4x + 4h - 3 - 2x^2 - 4x + 3}{h}$[/tex]
Simplifying further, we get:
[tex]$\frac{2x^2 + 4xh + 2h^2 + 4h}{h}$[/tex]
Canceling the common factors of h, we get:
[tex]$2x + 4 + 2h$[/tex]
Therefore, the expression for the difference quotient of the function f(x) when evaluated at x and x + h is 2x + 4 + 2h.
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Please help me answer these two questions!!!
in the alphabetical order A-B SO I THINK IT IS 10
A chain was calibrated to be of exact length 30.00 m at 200C. When this chain was used for chain surveying in field, the temperature was recorded to be 45oC. If the coefficient of linear expansion of steel used in chain is 8x 10-6 per oC, find the true total distance chained if measured distance on ground is 6000 m.
The true total distance chained if the measured distance on the ground is 6000 m would be 6001.8 m.
Linear expansivity problemThe measured distance on the ground is 6000 m. However, due to the increase in temperature during the surveying, the chain would have expanded, leading to an increase in the measured length.
The coefficient of linear expansion of steel is 8 x 10^-6 per oC. Therefore, for a temperature increase of 45 - 20 = 25 oC, the increase in length of the chain can be calculated as follows:
ΔL/L = αΔT
where ΔL is the increase in length, L is the original length (30.00 m), α is the coefficient of linear expansion (8 x 10^-6 per oC), and ΔT is the temperature increase (25 oC).Substituting the given values, we get:
ΔL/30.00 = (8 x 10^-6) x 25
ΔL = 0.006 m
This means that the actual length of the chain during the surveying was 30.006 m.
To find the true total distance chained, we need to correct the measured distance on the ground for the increase in chain length. Let D be the true total distance chained. Then we have:
D/30.006 = 6000/30.00
Solving for D, we get:
D = 6000 x 30.006 / 30.00
D = 6001.8 m
Therefore, the true total distance chained is 6001.8 m.
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You have a bag containing 14 red marbles numbered 1 – 14 and 3 green marbles numbered 15 – 17. 15. You choose a marble at random. What is the probability that you choose a red or an even-numbered green marble? 16. You randomly choose 2 marbles from the bag without replacement. What is the probability that you choose a red marble and a green marble?
The probability of choosing a red marble and a green marble is 21/136 or approximately 0.154.
We must combine the probability of each occurrence occurring in order to determine the likelihood of selecting a red or an even-numbered green marble. Given that there are 14 red marbles in total among the total of 17 marbles, the chance of selecting a red marble is 14/17. Given that there is only one even-numbered green marble among the other 17 marbles, the probability of selecting one is 1/17. The likelihood of selecting a red or an even-numbered green marble is therefore: 14/17 + 1/17 = 15/17.
The likelihood of selecting a red or an even-numbered green marble is therefore 15/17, or roughly 0.882.
We must multiply the likelihood of selecting a red marble by the likelihood of selecting a green marble in order to determine the likelihood of selecting both red and green marbles. There are 16 marbles left after selecting one, including 2 green marbles. The odds of selecting a red stone during the initial draw are 14/17. After a red marble has been selected and is not being changed, the likelihood of selecting a green marble on the subsequent draw is 3/16. The odds of selecting a red marble and a green marble are as follows: (14/17) x (3/16) = 21/136 = 0.154
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There are 3590 soldiers in a platoon in the commander of the Platoon. he wants to impress the visiting general by arranging his soldiers in such a manner that they are arranged in and rows and each row has and soldiers he finds that he cannot do this with the number of soldiers she has what is the minimum number of soldiers he needs additional to do this kind of a formation? a) 6 b) 10 c) 18 d) 2
Answer:
Step-by-step explanation: b) 10
A packaging employee making $14
per hour can package 200 items
during that hour. The direct
material cost is $.40 per item. What
is the total direct cost of 1 item?
Answer: the total direct cost of one item is $0.47.
Step-by-step explanation:
If the packaging employee makes $14 per hour and can package 200 items in one hour, the direct labor cost per item would be:
Direct labor cost per item = Hourly wage rate / Number of items packaged per hour
Direct labor cost per item = $14 / 200
Direct labor cost per item = $0.07
The direct material cost per item is given as $0.40.
Now we can calculate the total direct cost per item:
Total direct cost per item = Direct labor cost per item + Direct material cost per item
Total direct cost per item = $0.07 + $0.40
Total direct cost per item = $0.47
Peaceful Travel Agency offers vacation packages. Each vacation package includes a city, a month, and an airline. The agency has 2 cities, 5 months, and 1 airline to choose from. How many different vacation packages do they offer?
The number of vacation packages offered by Peaceful Travel Agency is 10
Calculating the Number of Vacation Packages offered by Peaceful Travel AgencyTo determine the number of different vacation packages offered by Peaceful Travel Agency, we need to use the multiplication principle of combination and counting.
Since the agency has 2 cities, 5 months, and 1 airline to choose from, we can multiply the number of options for each category to get the total number of vacation packages:
So, we have
vacation packages = 2 cities x 5 months x 1 airline
vacation packages = 10
Therefore, Peaceful Travel Agency offers 10 different vacation packages.
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tyler orders a meal thats 15$ if the tax rate is 6.6% how much will the sales tax be on tylers meal?
Answer : 0.99
Explanation : 15 * 6.6/100 For The Tax.
Total : 15.99
find the area of the arrow
Answer:
650
Step-by-step explanation:
It's simple
lodine-131, a radioactive substance that is effective in locating brain tumors, has a half-life of only eight days. A
hospital purchased 16 grams of the substance but had to wait six days before it could be used. How much of the
substance was left after six days?
...
The amount of substance left after six days was
9.
(Round the final answer to three decimal places as needed. Round all intermediate values to seven decimal places as
needed.)
The mass of substance left after 6 days is 9 g
The mass of substance left, N is given by
N = N₀exp(-λt) where λ = decay constant and N₀ = initial mass of substance present = 24 g and t = time
Also, λ = 0.693/t' where t' = half-life of iodine = 8 days
So, λ = 0.693/t'
λ = 0.693/8
λ = 0.086625/day
Since the mass of substance left is N = N₀exp(-λt) and we require the mass of substance after t = 6 days,
N = N₀exp(-λt)
N = 16 gexp(-0.086625/day × 7 days)
N = 16 gexp(-0.606375)
N = 16 g × 0.5453
N = 8.72 g
N = 8.72 → 9 g
So, the mass of substance left after 7 days is 9 g
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Suppose the probability of an IRS audit is 1.5 percent for U.S. taxpayers who file form 1040 and who earned $100,000 or more.
(a) What are the odds that such a taxpayer will be audited? (Round your answers to the nearest whole number.)
(b) What are the odds against such a taxpayer being audited? (Round your answers to the nearest whole number.)
(a) For every 100 taxpayers who file form 1040 and who earned $100,000 or more, about 2 of them will be audited. (b) for every 100 taxpayers who file form 1040 and who earned $100,000 or more, about 66 of them will not be audited.
(a) To calculate the odds that a taxpayer will be audited, we need to divide the probability of being audited by the probability of not being audited. The probability of being audited is given as 1.5 percent or 0.015. The probability of not being audited is the complement of the probability of being audited, which is 1 - 0.015 = 0.985. Therefore, the odds that a taxpayer will be audited are:
0.015/0.985 = 0.0152284264
To convert this to odds notation, we divide the probability of being audited by the probability of not being audited:
0.015/0.985 = 0.0152284264 = 0.0152 (rounded to four decimal places)
This means that for every 100 taxpayers who file form 1040 and who earned $100,000 or more, about 2 of them will be audited.
(b) The odds against a taxpayer being audited is the ratio of the probability of not being audited to the probability of being audited. We have already calculated the probability of not being audited to be 0.985, and the probability of being audited to be 0.015. Therefore, the odds against a taxpayer being audited are:
0.985/0.015 = 65.66666667
To convert this to odds notation, we divide the probability of not being audited by the probability of being audited:
0.985/0.015 = 65.66666667 = 66 (rounded to the nearest whole number)
This means that for every 100 taxpayers who file form 1040 and who earned $100,000 or more, about 66 of them will not be audited.
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On a normal day, 12 airplanes arrive at an airport every 15 minutes. Write a rate that represents this situation.
which gives us a rate of "4 airplanes per 5 minutes" or "4/5 airplanes per minute."
How to change minutes into hour?To change minutes into hours, you can use simple mathematical operations.
There are 60 minutes in one hour. Therefore, to convert minutes into hours, you can divide the number of minutes by 60.
For example, if you have 120 minutes, you can divide 120 by 60 to get 2 hours (120 ÷ 60 = 2). Similarly, if you have 90 minutes, you can divide 90 by 60 to get 1.5 hours (90 ÷ 60 = 1.5).
Here's the formula you can use:
Hours = Minutes ÷ 60
So, to change any number of minutes into hours, divide that number by 60
by the question.
On a normal day, 12 airplanes arrive at an airport every 15 minutes. Write a rate that represents this situation.
The rate of airplanes arriving at the airport can be expressed as "12 airplanes per 15 minutes" or "12/15 airplanes per minute."
We can simplify this fraction by dividing the numerator and denominator by 3,
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29. For which values of k would the product of ᵏ⁄3 × 12 be greater than 12?
A. for any value of k less than 1 but greater than 0
B. for any value of k less than 3 but greater than 1
C. for any value of k equal to 3
D. for any value of k greater than 3
The values of k that would make the product of ᵏ⁄3 × 12 be greater than 12 is: D. for any value of k greater than 3.
What is the Product of two Numbers?The product of two numbers is the result obtained when one number is multiplied by another.
A. For values of k that are less than 1 but greater than 0, i.e 1.5, we have:
0.5/3 * 12 > 12
2 > 12 [false]
B. For values of k that are less than 3 but greater than 1, i.e 2, we have:
2/3 * 12 > 12
8 > 12 [false]
C. For any value of k that is equal to 3, i.e. 3, we have:
3/3 * 12 > 12
12 > 12 [false]
D. For values of k that are greater than 3, i.e 6, we have:
6/3 * 12 > 12
24 > 12 [true]
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A glass of cold milk is sitting on the counter, warming up to room temperature. Currently, the milk is 16°C below room temperature. However, that temperature difference is shrinking by 7% every minute. What will the temperature difference be in 14 minutes? If necessary, round your answer to the nearest tenth.
Answer: it's 8.6 or 1.4
Step-by-step explanation:
Turn 10% into a decimal form... .10
.10 x 14 = 1.4
10 - 1.4 = 8.6
Pls help !! Find the equation of a line parallel to that passes y= 4/3x+4 through the point (3,-7).
The equation of the new line which is parallel to the given line of equation y= 4/3x+4 is found to be: y + 7 = 4/3(x - 3).
Explain about slopes of parallel lines?The amount by which a line is inclined towards the horizontal axis is known as its slope. The slope can also provide a measure of a line's steepness and is helpful in assessing if two lines remain parallel or perpendicular.
Standard equation of line:
y = mx + c
m is the slope and c is the y intercept.
equation of a line: y = 4/3x + 4
On comparing both equation:
m = 4/3 and c is 4
Now, we know that : slopes of parallel lines are equal.
m = 4/3 and passing point is given as: (3,-7).
Using the point slope form:
y - y1 = m(x - x1)
y - (-7) = 4/3(x - 3)
y + 7 = 4/3(x - 3)
Thus, the equation of the new line which is parallel to the given line of equation y= 4/3x+4 is found to be: y + 7 = 4/3(x - 3).
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Find the areas of the sectors formed by
Area of sector is 177.8cm².
Define area of sectorIn geometry, a sector is a region of a circle that is bounded by two radii and an arc, where the radii intersect at the center of the circle. The area of a sector is the fraction of the circle's total area that is enclosed by the sector.
where A is the area of the sector, θ is the central angle of the sector (measured in degrees), r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14159.
The formula for the area of a sector is:
A = (θ/360) x πr²
Angle made by sector=360-256=104
Radius of circle=14cm
Area of the sector DFE=∅/360×πr²
=104/360×π×14²
=177.8cm²
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