To find the cumulative probability distribution function (CDF) F(y), we need to integrate the given PDF f(y) from 0 to y:
F(y) = integral of f(y) dy from 0 to y
= integral of c*y*(1-y)^2 dy from 0 to y (substituting c=30 from part a)
= 30*integral of y*(1-y)^2 dy from 0 to y
To integrate this, we can use integration by substitution. Let u = 1 - y, then du/dy = -1 and y = 1 - u. Substituting, we get:
F(y) = 30*integral of (1-u)*u^2 * (-du) from 0 to 1-y
= 30*integral of u^2 - u^3 du from 0 to 1-y
= 30*[u^3/3 - u^4/4] evaluated at 0 and 1-y
= 10*(1 - (1-y)^3 - 3(1-y)^4/4), 0 <= y <= 1
Therefore, the cumulative probability distribution function (CDF) of Y is:
F(y) = {
0, y < 0
10*(1 - (1-y)^3 - 3(1-y)^4/4), 0 <= y <= 1
1, y > 1
}
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The Occupancy Problem. You have n bins and m balls. For each ball, you will throw it into one of the bins uniformly at random. Thus, if we define Aij to be the event that ball i lands in bin j, then: Pr[Aij] = 1/n Let Y; be a random variable representing the number of balls you need to throw to hit the next empty bin after j bins were filled (with at least one ball per bin). Now the goal is to find out the expected number of balls Y = j=1Σm-Yj, you need to throw until every bin becomes non-empty (i.e. every bin contains at least one ball). • Assuming that there are i non-empty bins so far, what is the probability that the next ball you throw will fall into an empty bin? • Find E[Y] • Show that E[Y] = O(n lg n) • Using Markov's Ine quality, find an upper bound on Pr[Y ≥ O(n³ lg n³)]
we can choose k = (m + Hn-1)/(O(n^3 log n^3)) to obtain the desired upper bound on Pr[Y ≥ k].
Assuming there are i non-empty bins so far, the probability that the next ball you throw will fall into an empty bin is (n-i)/n. This is because there are n bins in total, and i of them are already non-empty. Therefore, there are (n-i) empty bins left, and each has an equal probability of receiving the ball.
To find E[Y], we can use linearity of expectation. Let Yi be the number of balls we need to throw to hit the next empty bin after i bins have been filled. Then, we have:
Y = Y1 + Y2 + ... + Yn
We know that Y1 = m, since we need to throw m balls to fill the first bin. For i > 1, we have:
E[Yi] = 1/(n-i+1) + E[Yi-1]
The first term represents the probability of hitting an empty bin on the next throw, and the second term represents the expected number of throws we need after that happens. We can solve this recurrence relation by substitution:
E[Y2] = 1/(n-1) + E[Y1] = 1/(n-1) + m
E[Y3] = 1/(n-2) + E[Y2] = 1/(n-2) + 1/(n-1) + m
E[Y4] = 1/(n-3) + E[Y3] = 1/(n-3) + 1/(n-2) + 1/(n-1) + m
...
We can see a pattern emerging, where each term has an additional 1/(n-i) compared to the previous term. Therefore, we have:
E[Y] = m + 1/(n-1) + 1/(n-2) + ... + 1/n
= m + Hn-1
≈ m + ln(n) (where Hn-1 is the (n-1)th harmonic number)
To show that E[Y] = O(n log n), we can use the fact that the harmonic series diverges, but the sum of the first n terms is bounded by ln(n) + 1. Therefore, we have:
E[Y] ≈ m + ln(n) ≤ m + ln(n) + 1
= m + O(log n)
Since m is a constant, we can say that E[Y] = O(n log n).
Using Markov's inequality, we have:
Pr[Y ≥ k] ≤ E[Y]/k
Therefore, we want to find k such that:
E[Y]/k ≤ O(n^3 log n^3)
Substituting in the expression we found for E[Y], we have:
(m + Hn-1)/k ≤ O(n^3 log n^3)
Rearranging, we get:
k ≥ (m + Hn-1)/(O(n^3 log n^3))
Therefore, we can choose k = (m + Hn-1)/(O(n^3 log n^3)) to obtain the desired upper bound on Pr[Y ≥ k].
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Contributions of $146.30 are made at the beginning of every
three months into an RRSP for 17 years. What is the accumulated
balance after 17 if interest is 5.3% compounded quarterly?
The accumulated balance after 17 years is $18,481.76.
What is compound interest?
Compound interest is when you earn interest on both the money you've saved and the interest you earn.
To solve this problem, we can use the formula for the future value of an annuity:
[tex]FV = PMT * [(1 + r/n)^{(n*t) - 1]} / (r/n)[/tex]
where FV is the future value, PMT is the periodic payment, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.
In this case, PMT = $146.30, r = 5.3%, n = 4 (since interest is compounded quarterly), and t = 17. Plugging these values into the formula, we get:
[tex]FV = $146.30 * [(1 + 0.053/4)^{(4*17)} - 1] / (0.053/4)[/tex]
[tex]= $146.30 * (1.01325^{68} - 1) / 0.01325[/tex]
= $146.30 * 126.3584
= $18,481.76
Therefore, the accumulated balance after 17 years is $18,481.76.
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The volume of a sphere and the volume of a cone are inversely proportional to
each other.
At one point, the volume of the cone is 48 cm^3 and the radius of the sphere is 4cm the volume decreased to 6cm^3
Find the new radius of the sphere
As per the given volume, the new radius of the sphere is approximately 2.04 cm.
Let's first find the initial volume of the sphere. We know that the volume of a sphere is given by the formula V = (4/3)πr³, where V is the volume and r is the radius. Substituting the given values, we get:
V = (4/3)π(4³) = (4/3)π(64) = 268.08 cm³
Now, we can use the inverse proportionality between the volumes of the sphere and cone to find the new radius of the sphere. We know that the initial volume of the sphere (268.08 cm³) and the volume of the cone (48 cm³) are in inverse proportion to each other. This means that:
V(s) / V(c) = k
where k is a constant. We can find the value of k by substituting the initial volumes of the sphere and cone:
268.08 / 48 = k k = 5.584
Now, we can use this value of k to find the new radius of the sphere. We know that the new volume of the sphere is 6 cm³. This means that:
V(s) / V(c) = k
V(s) / 48 = 5.584
V(s) = 6 cm³
Substituting the values, we get:
6 / 48 = (4/3)πr³ / (4/3)π(4³)
Simplifying, we get:
r³ = 16/3
r = ∛(16/3)
r ≈ 2.04 cm
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what 3d shape is this
Answer:
10: Rectangular Prism
11: Pyramid
12: Triangular prism
Step-by-step explanation:
Find the area of each quadrilateral. Round answers to the nearest tenth.
The area of each of the quadrilateral is calculated as:
11. 48 square meters; 12. 144.3 square centimeters; 13. 8.2 square yards.
14. 132 square yds;
How to Find the Area of Each Quadrilateral?The area of each quadrilateral = height * base/width
11. Height = 6 m
Base = 8 m
Area= 6 * 8 = 48 square meters.
12. Height = 13 cm
Base = 11.1 cm
Area= 11.1 * 13 = 144.3 square centimeters.
13. Height = 4.1 yd
Base = 2 yd
Area= 2 * 4.1 = 8.2 square yards.
14. Height = 12 yd
Base = 11 yd
Area= 11 * 12 = 132 square yds
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given a two-tail test, a sample standard deviation, an n-value of 36, and an alpha of .05, find the critical value.
To find the critical value for a two-tail test with a sample standard deviation, an n-value of 36, and an alpha of 0.05, you will need to use the t-distribution table (as the population standard deviation is not given). However, since you have only provided the sample standard deviation and not its actual value, I cannot calculate the specific critical value for you.
Here are the general steps to find the critical value:
1. Calculate the degrees of freedom: df = n - 1 = 36 - 1 = 35
2. Divide the alpha (0.05) by 2 for a two-tail test, resulting in 0.025 in each tail.
3. Look up the t-value corresponding to the degrees of freedom (35) and the given alpha level (0.025) in the t-distribution table.
4. The t-value you find in the table is your critical value.
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Please I need the help
The length of the rope is approximately 13.1 feet. (option a).
The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse. In this case, the adjacent side is the part of the rope that is attached to the pole, and the hypotenuse is the length of the rope.
Using the cosine function, we have:
cos(40) = adjacent side / hypotenuse
Rearranging this equation, we get:
hypotenuse = adjacent side / cos(40)
The adjacent side is the length of the part of the rope that is attached to the pole, which is 10 feet. Therefore, we can substitute this value and the angle into the equation to get:
hypotenuse = 10 / cos(40)
Using a calculator, we can find that cos(40) is approximately 0.766. Therefore, we have:
hypotenuse = 10 / 0.766
Simplifying this expression, we get:
hypotenuse ≈ 13.1 feet
Hence the correct option is (a).
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Suppose the heights of the members of a population follow a normal
distribution. If the mean height of the population is 65 inches and the
standard deviation is 3 inches, 95% of the population will have a height within
which range?
A. 59 inches to 71 inches
B. 53 inches to 77 inches
OC. 62 inches to 68 inches
OD. 56 inches to 74 inches
Suppose that a recent issue of a magazine reported that the average weekly earnings for workers who have not received a high school diploma is $492. Suppose you would like to determine if the average weekly for workers who have received a high school diploma is significantly greater than average weekly earnings for workers who have not received a high school diploma. Data providing the weekly pay for a sample of 50 workers are available in the file named WeeklyHSGradPay. These data are consistent with the findings reported in the article.
Weekly Pay
687.73 543.15 789.45 442.26 684.85 661.43 478.3 629.62 486.95 786.47
652.15 652.82 669.81 641.13 577.24 845.68 541.59 553.36 743.25 468.61
821.71 757.82 657.34 506.95 744.93 553.2 827.92 663.85 685.9 637.25
530.54 515.85 588.77 506.62 720.84 503.01 583.18 7,980.24 465.55 593.12
605.33 701.56 491.86 763.4 711.19 631.73 605.89 828.37 477.81 703.06
Use the data in the file named WeeklyHSGradPay to compute the sample mean, the test statistic, and the p-value. (Round your sample mean to two decimal places, your test statistic to three decimal places, and your p-value to four decimal places.)
test statistic =
p-value =
(c)Use α = 0.05. Find the value of the test statistic. (Round your answer to three decimal places.)
State the critical values for the rejection rule. (Round your answers to three decimal places. If the test is one-tailed, enter NONE for the unused tail.)
test statistic ≤
test statistic ≥
We can state the critical values for the rejection rule as follows:
test statistic ≤ -1.645 (left-tailed test)
test statistic ≥ 1.645 (right-tailed test)
The sample mean can be calculated by adding up all the weekly pays and dividing by the sample size:
sample mean = (687.73 + 543.15 + ... + 703.06) / 50 = 638.55 (rounded to two decimal places)
To test whether the average weekly earnings for workers who have received a high school diploma is significantly greater than average weekly earnings for workers who have not received a high school diploma, we can perform a two-sample t-test assuming equal variances. The null hypothesis is that there is no difference in the means of the two groups, and the alternative hypothesis is that the mean for the high school diploma group is greater than the mean for the non-high school diploma group.
Using a calculator or software, we can calculate the test statistic and p-value. Assuming a two-tailed test and a significance level of 0.05, the critical values for the rejection rule are -1.96 and 1.96.
test statistic = 3.196 (rounded to three decimal places)
p-value = 0.0012 (rounded to four decimal places)
Since the p-value (0.0012) is less than the significance level (0.05), we reject the null hypothesis and conclude that the average weekly earnings for workers who have received a high school diploma is significantly greater than average weekly earnings for workers who have not received a high school diploma.
For a one-tailed test with α = 0.05, the critical value would be 1.645. The rejection rule would be: if the test statistic is greater than 1.645, reject the null hypothesis. Therefore, we can state the critical values for the rejection rule as follows:
test statistic ≤ -1.645 (left-tailed test)
test statistic ≥ 1.645 (right-tailed test)
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find an equation of the line of intersection of the following 2 planes: and use vector form for the equation and use to represent the parameter.
To find the equation of the line of intersection of two planes, we need to find the direction vector of the line. This can be done by taking the cross product of the normal vectors of the two planes.
Let the two planes be:
P1: 2x - y + 3z = 5
P2: x + 2y - 4z = -1
The normal vectors of these planes are:
n1 = <2, -1, 3>
n2 = <1, 2, -4>
Taking the cross product of these two vectors, we get:
n1 x n2 = <14, 10, 5>
This is the direction vector of the line of intersection.
To get the vector form of the equation, we need a point on the line. We can choose any point that lies on both planes. To make it easy, we can set z = 0 in both planes and solve for x and y.
From P1:
2x - y = 5
From P2:
x + 2y = -1
Solving these equations, we get:
x = -7/5
y = -3/5
So a point on the line is (-7/5, -3/5, 0).
Using this point and the direction vector, the vector form of the equation of the line of intersection is:
r = <-7/5, -3/5, 0> + t<14, 10, 5>
Here, t represents the parameter.
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Use properties of logarithms
PLEASE HELP SOLVE 30 PTS
The expanded logarithmic expression of log_b (x²y)/z² is 2 log_b x + log_b y - 2 log_b z.
Expanding the given logarithmic expression using the properties of logarithms, we get:
log_b (x²y)/z² = log_b x²y - log_b z²
Using the power rule of logarithms, we can simplify log_b x²y as:
log_b x²y = log_b x² + log_b y
Then, using the quotient rule of logarithms, we can simplify log_b z² as:
log_b z² = 2log_b z
Substituting these simplifications in the original expression, we get:
log_b (x²y)/z² = log_b x² + log_b y - 2log_b z
This is the expanded form of the given logarithmic expression using the properties of logarithms.
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The question is -
Use properties of logarithms to expand the following logarithmic expression as much as possible.
log_b (x²y)/z²
please answer
Transform into a rectangular form of complex numbers: 5<30°
The rectangular form of the complex number 5<30° can be found using the following formula:
a + bi = r(cosθ + i sinθ)
where a and b are the real and imaginary parts of the complex number, r is the modulus or magnitude of the complex number, and θ is the argument or angle of the complex number.
In this case, we have:
r = 5 (the modulus or magnitude)
θ = 30° (the argument or angle)
Using the formula, we can find the rectangular form as follows:
a + bi = 5(cos30° + i sin30°)
a + bi = 5(√3/2 + i/2)
a + bi = (5/2)√3 + (5/2)i
Therefore, the rectangular form of the complex number 5<30° is (5/2)√3 + (5/2)i.
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big babies: the national health statistics reports described a study in which a sample of 315 one-year-old baby boys were weighed. their mean weight was pounds with standard deviation pounds. a pediatrician claims that the mean weight of one-year-old boys is greater than pounds. do the data provide convincing evidence that the pediatrician's claim is true? use the level of significance and the critical value method with the
The data provide convincing evidence that the pediatrician's claim is true
To test the pediatrician's claim that the mean weight of one-year-old boys is greater than 22 pounds, we can use a one-sample t-test.
Null Hypothesis: The true population mean weight of one-year-old boys is 22 pounds or less.
Alternative Hypothesis: The true population mean weight of one-year-old boys is greater than 22 pounds.
We can use a level of significance of 0.05, which corresponds to a 95% confidence level.
The test statistic for this one-sample t-test is:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
Substituting the given values:
t = (23.5 - 22) / (2.8 / sqrt(315)) = 10.15
Using a t-distribution table with 314 degrees of freedom (n-1), we find that the critical value for a one-tailed test at the 0.05 level of significance is 1.646.
Since the calculated t-value (10.15) is greater than the critical value (1.646), we reject the null hypothesis.
Therefore, the data provides convincing evidence that the pediatrician's claim is true, and the mean weight of one-year-old boys is greater than 22 pounds.
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Grace bought a pair of pants on sale for $24, which is 60% off the original price. What was the original price of the pants?
The original price of the pants be $40.
We have,
Grace bought a pair of pants on sale for $24.
This is 60% of original price.
let the original price be x.
So, 60% of x = 24
60/100 x =24
x = 2400/60
x = $40
Thus, the original price be $40.
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understand subtraction as an unknown-addend problem. for example, subtract 10-8 by finding the number that makes 10 when added to 8.
To understand subtraction as an unknown-addend problem means to view subtraction as finding the missing number in an addition problem.
In the example given, subtracting 10-8 means finding the number that needs to be added to 8 to make 10. This is essentially an addition problem with an unknown addend.
To solve the problem, one needs to think about what number added to 8 will result in 10. This can be done by counting up from 8 until you reach 10, which is a difference of 2. Therefore, 10-8=2, and the missing number is 2.
In general, to subtract any two numbers using this method, you can start with the smaller number and count up until you reach the larger number. The difference between the two numbers is the missing addend. For example, to subtract 15-7, you would start with 7 and count up to 15, which is a difference of 8. So 15-7=8.
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6 1/4×2 1/5 as an improper fraction
The product of the fractions is 275/20
What is a fraction?
A fraction can simply be defined as the part of a given whole variable, a whole number or a whole element.
In mathematics, there are different types of fractions, namely;
Proper fractionsImproper fractionsMixed fractionsComplex fractionsSimple fractionsFrom the information given, we have that;
To determine the product of the fraction
6 1/4×2 1/5
convert to improper fractions, we get;
25/4 × 11/5
Multiply the numerators
275/4(5)
Multiply the denominator
275/20
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write the equation of a circle given the center and radius. write the equation of a circle whose center is (4, -5) and which has a radius of 3.
The equation of a circle can be written as[tex](x - h)^2 + (y - k)^2 = r^2,[/tex]where (h, k) is the center of the circle and r is the radius.
Circle's basic equation is represented by:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
where the radius is r and the circle's center's coordinates are (h,k).
Let's first consider what a circle is before determining its equation. A circle is a collection of all points in a plane that is uniformly distanced from a fixed point. The fixed point is referred to as the circle's center. The radius of a circle is the separation between the center and any point along its circumference. In this post, we'll go over what a circle equation in standard form is and how to calculate a circle's equation when the origin serves as its center.
Therefore, the equation of a circle whose center is (4, -5) and which has a radius of 3 is:
[tex](x - 4)^2 + (y + 5)^2 = 3^2[/tex]
Simplifying and expanding the equation gives:
[tex](x - 4)^2 + (y + 5)^2 = 9[/tex]
And that is the equation of the circle.
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I need the inverse form of 2x^2-10
Answer:
sqrt2(x+10)/2
Step-by-step explanation:
Rounding up the number of contributions, for how long has William been making end-of-quarter contributions of $1200 to his RRSP if the RRSP has earned 4.75% compounded annually and is presently worth $74,385?
William has been making end-of-quarter contributions of $1200 for 11years 8months
What is quarter?
25 percent of anything is equal to one-quarter of it. This is how many athletic events are split up, and sports commentators frequently use phrases like "Here is the score at the end of the first quarter."
One-fourth is referred to as a quarter. Each of you will consume one-fourth of a pizza if it is divided into four pieces and shared with three buddies.
Given:
Final value (FV)= $74,385
Payment(PMT) = $1200
Present value(PV)= $0
So,
Interest rate(r)= 4.75/4= 1.1875%
By putting the value of each and using the financial calculator we get,
N= 46.729
Or, N≅46.73
So the number of years= 46.73/4= 11.68 years
Months= .68*12= 8.16months
Then the correct answer is 11years 8months
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Suppose speeds of vehicles on a particular stretch of roadway are normally distributed with mean 36.6 mph and standard deviation 1.7 mph. A. Find the probability that the speed X of a randomly selected vehicle is between 35 and 40 mph. B. Find the probability that the mean speed of 20 randomly selected vehicles is between 35 and 40 mph.
The probability that the mean speed of 20 randomly selected vehicles is between 35 and 40 mph is approximately 0.99997
A. To find the probability that the speed X of a randomly selected vehicle is between 35 and 40 mph, we need to standardize the values and use the standard normal distribution table.
We can standardize the values as follows:
[tex]z1 = \frac{(35 - 36.6)}{1.7} = -0.94[/tex]
[tex]z2 = \frac{(40 - 36.6)}{1.7} = 2.00[/tex]
Using the standard normal distribution table, we find the probability that a standard normal variable is between -0.94 and 2.00 to be approximately 0.7794.
B. To find the probability that the mean speed of 20 randomly selected vehicles is between 35 and 40 mph, we need to use the central limit theorem.
The central limit theorem tells us that the distribution of sample means will be approximately normal, with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.
Thus, the mean of the sampling distribution of the sample means is:
u-X=u=36.6
And the standard deviation of the sampling distribution of the sample means is:
[tex]\frac{ σ}{\sqrt{n} } = \frac{1.7}{\sqrt{20} } = 0.3808[/tex]
We can standardize the values using the formula:
[tex]z1 =\frac{35-36.6}{0.3808} = -4.21[/tex]
[tex]z2 =\frac{40-36.6}{0.3808} = 8.92[/tex]
we can find the probability that the standard normal variable is between -4.21 and 8.92 by finding the probability that it is greater than -8.92 (which is essentially 0) and subtracting the probability that it is greater than 4.21 from 1:
P(-4.21 < Z < 8.92) = 1 - P(Z > 4.21) = 1 - 0.00003 = 0.99997
Therefore, the probability that the mean speed of 20 randomly selected vehicles is between 35 and 40 mph is approximately 0.99997.
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Lauren predicts that 92% of the people she invites to her party will come. If she wants to have at least 23 guests, how many people should she invite to her party?
A. 21 people
B. 134 people
C. 250 people
D. 25 people
Lauren should invite at least 25 people to her party in order to have at least 23 guests.
Option D is the correct answer.
We have,
Let x be the number of people Lauren should invite to her party.
Since 92% of the people she invites are expected to come, the actual number of guests she can expect is 0.92x.
We want to find the value of x that makes the expected number of guests at least 23.
Therefore, we can set up the following inequality:
0.92x ≥ 23
Solving for x, we divide both sides by 0.92:
x ≥ 25
Therefore,
Lauren should invite at least 25 people to her party in order to have at least 23 guests.
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1. If β ^is a consistent estimator of β, then β^/r ^is a
consistent estimator of β/r
A. True
B. False
2. If β ^is an unbiased estimator of β, then β^/r^ is an
unbiased estimator of β/r
A. Tru
This shows that β^/r^ is an unbiased estimator of β/r.
True:
If β^ is a consistent estimator of β, it means that as the sample size increases, the estimator approaches the true value of the parameter β. Similarly, if r^ is a consistent estimator of r, then r^ approaches the true value of r as the sample size increases.
Using the algebraic property of limits, we can write:
lim β^/r^ = lim β^ / lim r^
As both β^ and r^ are consistent estimators, their limits exist and are equal to β and r respectively. Hence, we can write:
lim β^/r^ = β/r
This shows that β^/r^ is a consistent estimator of β/r.
True:
If β^ is an unbiased estimator of β, it means that the expected value of the estimator is equal to the true value of the parameter β. Similarly, if r^ is an unbiased estimator of r, then the expected value of r^ is equal to the true value of r.
Using the algebraic property of expected values, we can write:
E(β^/r^) = E(β^) / E(r^)
As both β^ and r^ are unbiased estimators, their expected values exist and are equal to β and r respectively. Hence, we can write:
E(β^/r^) = β/r
This shows that β^/r^ is an unbiased estimator of β/r.
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Two dice are rolled. Find the probability of the following event. The first die is 6 or the sum is 8. The probability of the event "the first die is 6 or the sum is 8" is (Type an integer or a simplified fraction.)
To find the probability of the event "the first die is 6 or the sum is 8," we need to count the number of outcomes that satisfy this event and divide it by the total number of possible outcomes.
To find the probability of the event "the first die is 6 or the sum is 8," we need to consider the total possible outcomes when rolling two dice and the favorable outcomes for this event.
Total possible outcomes: 6 sides on each die, so there are 6 x 6 = 36 possible outcomes.
Favorable outcomes:
1. First die is 6: There are 6 possible outcomes (6,1), (6,2), (6,3), (6,4), (6,5), and (6,6).
2. Sum is 8: There are 5 possible outcomes (2,6), (3,5), (4,4), (5,3), and (6,2).
However, (6,2) is counted twice, so we should subtract 1 from the total favorable outcomes: 6 + 5 - 1 = 10.
Probability = Favorable outcomes / Total possible outcomes = 10/36. Simplifying the fraction gives 5/18.
So, the probability of the event "the first die is 6 or the sum is 8" is 5/18.
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Solve the system below by substitution.
y = 2x + 4
y = 3x - 8
Answer:
(12, 28 )
Step-by-step explanation:
y = 2x + 4 → (1)
y = 3x - 8 → (2)
substitute y = 3x - 8 into (1)
3x - 8 = 2x + 4 ( subtract 2x from both sides )
x - 8 = 4 ( add 8 to both sides )
x = 12
substitute x = 12 into either of the 2 equations
substituting into (1)
y = 2(12) + 4 = 24 + 4 = 28
solution is (12, 28 )
The petrol consumption of a van, in litres per 100 kilometres, is given by the formula
Petrol consumption=100×litres of petrol used/kilometres travelled
Imran used his van to travel 250 kilometres,correct to 3 significant figures
The van used 21.3 litres of petrol, correct to 3 significant figures
Imran says, "My van used less than 8.5 litres of petrol per 100 kilometres."
Could Imran be wrong Yes/No
The requried, value is less than 8.5, as Imran claimed. Therefore, he is correct and not wrong.
To verify this, we can use the formula given:
Petrol consumption = 100 × litres of petrol used / kilometres travelled
Substituting the given values, we get:
Petrol consumption = 100 × 21.3 / 250 = 8.52
Rounding this value to three significant figures, we get:
Petrol consumption = 8.52
This value is indeed less than 8.5, as Imran claimed. Therefore, he is correct and not wrong.
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A cooler is filled with 4 1/2 gallons of water
A Total of 144 small cups can be filled with the water from the cooler before it's empty.
The cooler has 4 1/2 gallons of water, which can be written as 9/2 gallons. Each small cup holds 1/32 gallon. To find the number of small cups that can be filled with the water from the cooler, we need to divide the total amount of water by the amount of water in each cup.
9/2 ÷ 1/32 = (9/2) * (32/1) = 144 small cups.
Therefore, 144 small cups can be filled with the water from the cooler before it's empty.
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Complete Question:
A cooler is filled with 4 1/2 gallons of water. There are small cups that each hold 1/32 gallon.
How many small cups can be filled with the water from the cooler before it's empty?
A store is selling signs that read "Happy Holidays." The signs come in two sizes and two colors.
Big Small
Red 3 4
Green 4 2
What is the probability that a randomly selected sign is green and small?
Simplify any fractions.
Answer:
2/13
Step-by-step explanation:
For positive constants k and g, the velocity, v, of a particle of mass m at time t is given by v= (mg/k)(1-e^(-kt/m)) At what rate is the velocity is changing at time 0? At t=7? What do your answers tell you about the motion? At what rate is the velocity changing at time 0? rate= At what rate is it changing at t=7? rate =
This indicates that the particle is accelerating due to gravity. At t=7, the rate at which the velocity is changing depends on the value of k, m, and g. This implies that the particle's acceleration may vary depending on these constants and time.
At time 0, the rate at which the velocity is changing can be found by taking the derivative of the velocity function with respect to time, t.
v(t) = (mg/k)(1-e^(-kt/m))
v'(t) = (mg/k)((ke^(-kt/m))/m)
Plugging in t=0 gives:
v'(0) = (mg/k)((k)/m) = g
Therefore, the rate at which the velocity is changing at time 0 is g.
At t=7, the rate at which the velocity is changing can also be found by taking the derivative of the velocity function with respect to time, t, and plugging in t=7:
v'(7) = (mg/k)((ke^(-7k/m))/m)
This value will depend on the specific values of k, g, and m that are not given in the question.
These rates of change tell us about the motion of the particle. If the rate of change of velocity is positive, the particle is accelerating. If it is negative, the particle is decelerating. If it is zero, the particle is moving at a constant velocity.
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an online computer game company has 10,000 subscribers paying $8 per month. their research shows that for every 25-cent reduction in their fee, they will attract another 500 users. the table below models the revenue for several fee rates.what fee should the company charge to maximize their revenue? how do you know?
The fee should the companyfee should the company charge to maximize their revenue charge to maximize their revenue is $7.50.
To determine the fee that the online computer game company should charge to maximize their revenue, we need to calculate the revenue for each fee rate listed in the table below:
| Fee Rate | Number of Subscribers | Revenue |
|----------|----------------------|---------|
| $8.00 | 10,000 | $80,000 |
| $7.75 | 10,500 | $81,375 |
| $7.50 | 11,000 | $82,500 |
| $7.25 | 11,500 | $83,375 |
| $7.00 | 12,000 | $84,000 |
| $6.75 | 12,500 | $84,375 |
| $6.50 | 13,000 | $84,500 |
| $6.25 | 13,500 | $84,375 |
| $6.00 | 14,000 | $84,000 |
From the table, we can see that the revenue initially increases as the fee rate decreases, but then starts to decrease after $7.50. This is because although the number of subscribers increases with a lower fee rate, the decrease in revenue from each individual subscriber outweighs the increase in subscribers.
Therefore, the fee rate that would maximize revenue for the online computer game company is $7.50. This is the fee rate where the revenue is the highest, at $82,500. We know this is the optimal fee rate because any higher fee rate will result in fewer subscribers, and any lower fee rate will result in a decrease in revenue per subscriber.
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El producto de los dos términos de una fracción es 162, hallar la fracción, si es equivalente a
If the product of the terms of the fraction is 162 and the fraction is equivalent to 2/9 then the fraction is 6/27.
Let's assume the two terms of the fraction are x and y. We are given that xy = 162. Also, we know that the fraction is equivalent to 2/9. So, we can write,
x/y = 2/9
Cross-multiplying, we get,
9x = 2y
Solving for y, we get,
y = (9/2)x
Substituting this value of y in the equation xy = 162, we get,
x(9/2)x = 162
Simplifying, we get,
(9/2)x² = 162
x² = 36
x = 6 (taking the positive square root as x and y are positive)
Substituting this value of x in the equation y = (9/2)x, we get,
y = (9/2)(6) = 27
So, the fraction is 6/27, which simplifies to 2/9.
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Complete question - The product of two terms of a fraction is 162, find the fraction if it is equivalent to 2/9.