The possible values of X and their associated probabilities are:
4: with probability 6/91
1: with probability 64/91
4: with probability 28/91
To determine the probabilities associated with each possible value of X (winnings), we need to consider all the possible combinations of selecting two balls from the urn:
Possible Cases:
Two Black Balls:
Probability = (4C2 / 14C2) * (4C2 / 14C2) = 6/91, where 4C2 represents choosing 2 balls from 4 black balls and 14C2 represents choosing 2 balls from a total of 14 balls.
Winnings (X) = $2 * 2 = $4.
One Black Ball, One White Ball:
There are two scenarios: Black-White and White-Black.
Probability (Black-White) = (4C1 * 8C1) / 14C2 = 32/91.
Probability (White-Black) = (8C1 * 4C1) / 14C2 = 32/91.
Combining both scenarios, total probability = 64/91.
Winnings (X) = $2 * 1 - $1 * 1 = $1.
Two White Balls:
Probability = (8C2 / 14C2) = 28/91.
Winnings (X) = $1 * 0 - $2 * 2 = -$4.
Therefore, the possible values of X and their associated probabilities are:
4: with probability 6/91
1: with probability 64/91
4: with probability 28/91
Final answer:
To determine the probabilities for X, the winnings from selecting two balls out of an urn with 8 white, 4 black, and 2 orange balls, one must calculate the probability of each possible combination of draws and the associated winnings.
Explanation:
To complete the explanation and provide accurate calculations for the probabilities associated with each possible value for X (the winnings from selecting two balls), we need to adjust and clarify the possible outcomes and their associated winnings based on the given scenario:
1. Two Black Balls:
- Winning: $4 (since each black ball is worth $2)
- Probability [tex]: \( \frac{4}{14} \times \frac{3}{13} \)[/tex] because there are 4 black balls out of 14 total, and then 3 out of 13 after the first is drawn.
2. One Black and One White Ball:
- Winning: $1 (since a black ball is +$2 and a white ball is -$1)
- Probability:[tex]\( 2 \times \frac{4}{14} \times \frac{8}{13} \)[/tex] because there are two ways this can happen (black then white or white then black).
3. Two White Balls:
- Winning: -$2 (since each white ball is -$1)
- Probability:[tex]\( \frac{8}{14} \times \frac{7}{13} \)[/tex] because there are 8 white balls initially, then 7 out of the remaining 13.
4. One Black Ball and One Orange Ball:
- Winning: $2 (since a black ball is +$2 and an orange ball has no change)
- Probability:[tex]\( 2 \times \frac{4}{14} \times \frac{2}{13} \)[/tex] because there are two ways this can occur (black then orange or orange then black).
5. One White Ball and One Orange Ball:
- Winning: -$1 (since a white ball is -$1 and an orange ball has no change)
- Probability: [tex]\( 2 \times \frac{8}{14} \times \frac{2}{13} \)[/tex] because there are two sequences for this outcome (white then orange or orange then white).
6. Two Orange Balls
- Winning: $0 (since orange balls have no change)
- Probability:[tex]\( 2 \times \frac{8}{14} \times \frac{2}{13} \)[/tex] because there are only 2 orange balls.
Marathon runner covered the whole distance in 4 hours running at a constant speed of 8.1 km per hour. How long would it take him to cover the same distance if he decreased the speed to 7.2 km per hour?
Answer: it will take him 4.5 hours to cover same distance
Step-by-step explanation:
Marathon runner covered the whole distance in 4 hours running at a constant speed of 8.1 km per hour.
Speed = distance / time
Distance = speed×time
Therefore, distance covered by the marathon runner in in 4 hours, running at a speed of 8.1 km per hour is
8.1 × 4 = 32.4 kilometers
if he decreased the speed to 7.2 km per hour, the distance remains 32.4 kilometers. Therefore,
At 7.2 km per hour, the time it would take him to cover the same distance would be
Distance/ speed = 32.4/7.2 = 4.5 hours
Determining null and alternative hypothesesA presidential candidate claims that the proportion of college students who are registered to vote in the upcoming election is at least 62% . Suppose that we want to sample a number of college students and carry out a hypothesis test to see if this claim may be refuted. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test.What is:H0_____.H1_____.
Answer:
[tex]H_0: p =0.62\\H_a: p\geq 0.62[/tex]
Step-by-step explanation:
Given that a presidential candidate claims that the proportion of college students who are registered to vote in the upcoming election is at least 62% .
Let p be the proportion of college students who are registered to vote in the upcoming election
we have to check the claim whether p is actually greater than or equal to 62%
For this a hypothesis to be done by drawing random samples of large size from the population.
The hypotheses would be the proportion is 0.62 against the alternate that the proportion is greater than or equal to 0.62
[tex]H_0: p =0.62\\H_a: p\geq 0.62[/tex]
(right tailed test at 5% level)
Affect or use is 1/8 of a barrel of raisins in each batch of granola bars yesterday the factory use 1/2 of a barrel of raisins how many batches of granola bars did the factory made yesterday?
Answer:
Factory made 4 batches of granola bars yesterday.
Step-by-step explanation:
Given:
1 batch of granola bar is made of 1/8 barrel of raisins.
1/8 barrels can be rewritten as 0.125 barrels.
Hence we can say 1 batch of granola bar is made of 0.125 barrels.
Also Given:
Yesterday Factory used 1/2 barrel of raisins.
1/2 barrels can be rewritten as 0.5 barrels.
Hence we need to find how much batches of granola bars were made using 0.5 barrels of raisins.
Now,
For 0.125 barrels raisins = 1 batch of granola bar
for 0.5 barrels of raisins = Batches of granola bar for 0.5 barrels of raisins
By Using Unitary method we get;
Batches of granola bar for 0.5 barrels of raisins = [tex]\frac{1\times 0.5}{0.125}=4[/tex]
Hence Factory made 4 batches of granola bars yesterday.
50 points
Kanna has 2 red pens, 4 black pens, 3 blue pens, 1 purple pen. What is the chance Kanna pulls one of her black pens. Write you answer in a fraction and percentage.
[Note:False answers will be reported]
Answer:
4 out of 10 or 4/10 is my answer
Answer:
The fraction will be 4/10, or 2/5.
The percentage will be 40%.
Step-by-step explanation:
The fraction and percentage will be the number of black pens divided by the total number of pens.
We can find the total number of pens by adding all the pens in each color together.
2 + 4 + 3 + 1 = 10
The total number of pens is 10. The number of black pens is 4.
The fraction will be 4/10, or 2/5.
The percentage will be 40%.
I hope this helps. Happy studying. :)
Suppose the scores of students on a Statistics course are Normally distributed with a mean of 563 and a standard deviation of 37. What percentage of the students scored between 563 and 637 on the exam?
Answer:
47.72% of students scored between 563 and 637 on the exam .
Step-by-step explanation:
The percentage of the students scored between 563 and 637 on the exam
= The percentage of the students scored lower than 637 on the exam -
the percentage of the students scored lower than 563 on the exam.
Since 563 is the mean score of students on the Statistics course, 50% of students scored lower than 563. that is P(x<563)=0.5
P(x<637)=P(z<z*) where z* is the z-statistic of the score 637.
z score can be calculated using the formula
z*=[tex]\frac{X-M}{s}[/tex] where
X =637M is the mean score (563)s is the standard deviation of the score distribution (37)Then z*=[tex]\frac{637-563}{37}[/tex] =2
P(z<2)=0.9772, which means that 97.72% of students scored lower than 637 on the exam.
As a Result, 97.72%-50%=47.72% of students scored between 563 and 637 on the exam
James is selling candy at a local marketplace. He needs to earn at least $200 to break even. He has already earned $11.25. If the price of one pound of candy is $2.50, how many more pounds of candy, x, does he have to sell to break even?
Answer:
75.5 pounds
Step-by-step explanation:
He needs 200
He already has 11.25
He needs:
200 - 11.25 = $188.75 more
1 pound of candy costs 2.50, so x pounds would cost 2.50x
This would need to equal 188.75 (the amount he needs to break even). We can write an equation in x and solve:
[tex]2.50x=188.75\\x=\frac{188.75}{2.50}\\x=75.5[/tex]
James needs 75.5 pounds more to break even
Final answer:
James needs to sell an additional 75.5 pounds of candy to break even, after taking into account the $11.25 he has already earned towards his $200 goal by dividing the remaining amount needed ($188.75) by the price per pound of candy ($2.50).
Explanation:
James is selling candy at a local marketplace and needs to earn at least $200 to break even. He has already earned $11.25. The price of one pound of candy is $2.50. To find out how many more pounds of candy, x, he has to sell to break even, we need to calculate the remaining amount he needs to earn and divide it by the price per pound of candy.
First, subtract the amount already earned from the total needed to break even:
$200 - $11.25 = $188.75
Then, divide this amount by the price per pound of candy to find out how many more pounds he needs to sell:
$188.75 / $2.50 = 75.5
Therefore, James needs to sell an additional 75.5 pounds of candy to break even.
Write down the quadratic equation whose roots are x = -7 and x = 1, and the coefficient of $x^2$ is 1. Enter your answer in the form "x^2 + bx + c = 0".
For this case we must write a quadratic equation of the form:
[tex]x ^ 2 + bx + c = 0[/tex]
We have two roots:
[tex]x_ {1} = - 7\\x_ {2} = 1[/tex]
Thus, we can rewrite the equation in a factored form as:
[tex](x + 7) (x-1) = 0[/tex]
If we apply distributive property we have:
[tex]x ^ 2-x + 7x-7 = 0[/tex]
Different signs are subtracted and the major sign is placed.
[tex]x ^ 2 + 6x-7 = 0[/tex]
Answer:
The quadratic equation is:
[tex]x ^ 2 + 6x-7 = 0[/tex]
An arch is 630 ft high and has 580=ft base. It can be modeled by the parabola =630\left [ 1-\left ( x/290 \right )^2 \right ]. Find the average height of the arch above the ground.
The average height of the arch is __??? ft above the ground.
Answer:
420 ft
Step-by-step explanation:
The given equation of a parabola is
[tex]y=630[1-\left(\frac{x}{290}\right)^{2}][/tex]
An arch is 630 ft high and has 580=ft base.
Find zeroes of the given function.
[tex]y=0[/tex]
[tex]630[1-\left(\frac{x}{290}\right)^{2}]=0[/tex]
[tex]1-\left(\frac{x}{290}\right)^{2}=0[/tex]
[tex]\left(\frac{x}{290}\right)^{2}=1[/tex]
[tex]\frac{x}{290}=\pm 1[/tex]
[tex]x=\pm 290[/tex]
It means function is above the ground from -290 to 290.
Formula for the average height:
[tex]\text{Average height}=\dfrac{1}{b-a}\int\limits^b_a f(x) dx[/tex]
where, a is lower limit and b is upper limit.
For the given problem a=-290 and b=290.
The average height of the arch is
[tex]\text{Average height}=\dfrac{1}{290-(-290)}\int\limits^{290}_{-290} 630[1-\left(\frac{x}{290}\right)^{2}]dx[/tex]
[tex]\text{Average height}=\dfrac{630}{580}[\int\limits^{290}_{-290} 1dx -\int\limits^{290}_{-290} \left(\frac{x}{290}\right)^{2}dx][/tex]
[tex]\text{Average height}=\dfrac{63}{58}[[x]^{290}_{-290}-\frac{1}{84100}\left[\frac{x^3}{3}\right]^{290}_{-290}][/tex]
Substitute the limits.
[tex]\text{Average height}=\dfrac{63}{58}\left(580-\frac{580}{3}\right)[/tex]
[tex]\text{Average height}=\dfrac{63}{58}(\dfrac{1160}{3})[/tex]
[tex]\text{Average height}=420[/tex]
Therefore, the average height of the arch is 420 ft above the ground.
The average height of the arch above the ground is approximately 420 feet.
To find the average height of the arch, we need to find the average value of this function over the interval x=0 to x=580 (the base of the arch).
[tex]\[ \text{Average height} = \frac{1}{580 - 0} \int_{0}^{580} 630 \left(1 - \left(\frac{x}{290}\right)^2\right) \, dx \]\[ = \frac{630}{580} \int_{0}^{580} \left(1 - \left(\frac{x}{290}\right)^2\right) \, dx \]\[ = \frac{630}{580} \left(x - \frac{1}{3} \cdot \frac{x^3}{290^2}\right) \Bigg|_{0}^{580} \]\[ = \frac{630}{580} \left(580 - \frac{1}{3} \cdot \frac{580^3}{290^2} - 0\right) \][/tex]
[tex]\[ = \frac{630}{580} \left(580 - \frac{1}{3} \cdot \frac{580^3}{290^2}\right) \]\[ = \frac{630}{580} \left(580 - \frac{1}{3} \cdot \frac{580^3}{290^2}\right) \]\[ \approx \frac{630}{580} \times 420 \]\[ \approx 420 \text{ ft} \][/tex]
A research firm conducted a survey to determine the mean amount Americans spend on coffee during a week. They found the distribution of weekly spending followed the normal distribution with a population standard deviation of $5. A sample of 64 Americans revealed that X¯¯¯=$20 . What is the 95% confidence interval estimate of μ?
Answer:
95% confidence Interval would be between $18.775 and $20.225.
Step-by-step explanation:
Confidence Interval can be calculated using M±ME where
M is the sample mean Americans spend on coffee during week. ($20)ME is the margin of error from the meanAnd margin of error (ME) around the mean calculated as
ME=[tex]\frac{z*s}{\sqrt{N} }[/tex] where
z is the corresponding statistic in 95% confidence level (1.96)s is the population standard deviation ($5)N is the sample size (64)Using the numbers, we get:
ME=[tex]\frac{1.96*5}{\sqrt{64} }[/tex] =1.225
Then 95% confidence Interval would be 20±1.225 or between $18.775 and $20.225
Answer:
The confidence interval is between 18.775 and 21.225.
Step-by-step explanation:
In a one-way ANOVA, the __________ is calculated by taking the squared difference between each person and their specific groups mean, while the ______________ is calculated by taking the squared difference between each group and the grand mean.
Answer:
In a one-way ANOVA, the [tex]SS_{within}[/tex] is calculated by taking the squared difference between each person and their specific groups mean, while the [tex]SS_{between}[/tex] is calculated by taking the squared difference between each group and the grand mean.
Step-by-step explanation:
The one-way analysis of variance (ANOVA) is used "to determine whether there are any statistically significant differences between the means of two or more independent groups".
The sum of squares is the sum of the square of variation, where variation is defined as the spread between each individual value and the mean.
If we assume that we have p groups and each gtoup have a size [tex]n_j[/tex] then we have different sources of variation, the formulas related to the sum of squares are:
[tex]SS_{total}=\sum_{j=1}^{p} \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2 [/tex]
A measure of total variation.
[tex]SS_{between}=\sum_{j=1}^{p} n_j (\bar x_{j}-\bar x)^2 [/tex]
A measure of variation between each group and the grand mean.
[tex]SS_{within}=\sum_{j=1}^{p} \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 [/tex]
A measure of variation between each person and their specific groups mean.
Find the missing side length
Answer:
Step-by-step explanation:
The triangle given is aright angle triangle. This is because one if its angles is 90 degrees. The other two angles add up to give 180 degrees. Looking at the right angle triangle, taking the 8 degree angle as the reference angle, the length of the adjacent side is 82, the length of the opposite side is t. Applying trigonometric ratio,
Tan # = opposite side / adjacent side.
# = 8 degrees
Tan 8 = t/82
t = 82 tan8
t = 82 × 0.1405
t = 11.521
A bottle contains a label stating that it contains pills with 500 mg of vitamin C, and another bottle contains a label stating that it contains pills with 325 mg of aspirin When testing claims about the mean contents of the pills, which would have more serious implications: rejection of the vitamin C claim or rejection of the aspirin claim? Is it wise to use the same significance level for hypothesis tests about the mean amount of vitamin C and the mean amount of aspirin? Rejection of the claim about________ is more serious because the wrong_________ dosage could cause more serious adverse reactions than a wrong_______dosage. It would be wise to use a__________ significance level for testing the claim about the aspirin.
Answer:
Step-by-step explanation:
Rejection of aspirin argument is more dangerous because the incorrect dosage of aspirin may cause more severe adverse reactions than the incorrect dosage of vitamin C. It would be prudent to use a lower level of significance to test the aspirin argument.
When to use chain rule and product rule?
How do I differentiate between these two. Thanks very much!!
Chain rule when it's one function inside another.
d/dx f(g(x)) = f’(g(x))*g’(x)
Product rule when two functions are multiplied side by side.
d/dx f(x)g(x) = f’(x)g(x) + f(x)g’(x)
Final answer:
The chain rule is used when you have a composite function, while the product rule is used when you have a product of two functions.
Explanation:
The chain rule and product rule are both rules used in calculus to differentiate functions.
Chain Rule:The chain rule is used when you have a composite function, where one function is inside another function. To differentiate a composite function, you multiply the derivative of the outer function by the derivative of the inner function.
For example, if you have y = f(g(x)), where f(x) and g(x) are functions, the chain rule states that dy/dx = f'(g(x)) * g'(x).
Product Rule:The product rule is used when you have a product of two functions. To differentiate a product, you take the derivative of the first function times the second function, plus the first function times the derivative of the second function.
For example, if you have y = f(x) * g(x), the product rule states that dy/dx = f'(x) * g(x) + f(x) * g'(x).
A line contains the points (a, b) and (a + 3, b + 3). Find the equation of the line in terms of a and b in point-slope form, and then convert it to slope-intercept form.
Answer:
y -b = x -ay = x + (b-a)Step-by-step explanation:
The slope is the ratio of the change in y to the change in x:
m = ((b+3) -b)/((a +3) -a) = 3/3 = 1
The point-slope form of the equation of a line through point (h, k) with slope m is ...
y -k = m(x -h)
Here, we have (h, k) = (a, b) and m=1, so the equation in point-slope form is ...
y -b = x -a
Adding b puts this in slope-intercept form:
y = x + (b-a)
The expected number of typographical errors on a page of a certain magazine is .2. What is the probability that an article of 10 pages contains (a) 0 and (b) 2 or more typographical errors? Explain your reasoning!
The probability of having 0 typographical errors on an article of 10 pages is approximately 0.8187. The probability of having 2 or more errors is approximately 0.0176.
Explanation:To find the probability of certain events happening, we can use the Poisson distribution. In this case, the Poisson distribution can be used to model the number of typographical errors on a page. The parameter of the Poisson distribution, lambda (λ), is equal to the expected number of errors on each page, which is 0.2.
(a) To find the probability of 0 errors on an article of 10 pages, we can use the Poisson distribution with λ = 0.2 and x = 0. We can plug these values into the formula:
P(X = x) = (e^-λ * λ^x) / x!
So for (a), the probability is:
P(X = 0) = (e^-0.2 * 0.2^0) / 0! = e^-0.2 ≈ 0.8187
(b) To find the probability of 2 or more errors on an article of 10 pages, we can calculate the complement of the probability of 0 or 1 errors. The complement is 1 minus the sum of the probabilities of 0 and 1 errors:
P(X ≥ 2) = 1 - P(X = 0) - P(X = 1) ≈ 1 - 0.8187 - (e^-0.2 * 0.2^1) / 1! ≈ 1 - 0.8187 - 0.1637 ≈ 0.0176
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Using the Poisson distribution with λ = 0.2, we find the probability of 0 errors on a page and 2 or more errors in a 10-page article, offering insightful predictions.
The given situation involves a Poisson distribution, as it deals with the number of events (typographical errors) occurring in a fixed interval of time or space. The expected number of errors per page is λ = 0.2, and the total number of pages is 10.
(a) To find the probability of 0 errors on a page, we use the Poisson probability mass function:
P(X = k) = (e^(-λ) * λ^k) / k!
For k = 0:
P(X = 0) = (e^(-0.2) * 0.2^0) / 0!
Solving this gives the probability of having 0 errors on a single page.
(b) To find the probability of 2 or more errors, we sum the probabilities for k = 2, 3, ..., up to the total number of pages (10):
P(X ≥ 2) = 1 - P(X = 0) - P(X = 1)
This accounts for the complement probability that there are 0 or 1 errors, leaving us with the probability of 2 or more errors on at least one page.
In summary, the Poisson distribution helps model the likelihood of different numbers of typographical errors on a page, providing a useful tool for analyzing such scenarios.
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Justin invested his savings in two investment funds. The $8000 he invested in Fund A returned a 10% profit. The amount he invested in Fund B returned a 3% profit. How much did he invest in Fund B, if both funds together returned a 7% profit?
Answer:
$6000
Step-by-step explanation:
Profit from the investment of $8000 in fund A
= 10% × $8000
= $800
Let the amount invested in fund B be $Y
Profit from the investment of $Y in fund B
= 3% × $Y
= $0.03Y
if both funds together returned a 7% profit
800 + 0.03Y = 7% (8000 + Y)
800 + 0.03Y = 560 + 0.07Y
Collect like terms
0.07Y - 0.03Y = 800 - 560
0.04Y = 240
Y = 240/0.04
Y = 6000
Amount invested in Fund B is $6000
he sum of two numbers is 58. The difference of the two numbers is 32.
What are the two numbers?
Let x be the larger number and y be the smaller number.
Write an equation that expresses the information in the sentence "The sum of two numbers is 58."
Answer:x+y=58
Step-by-step explanation:
Sum means addition
Which statement can be used to prove that a given parallelogram is a rectangle? A) The opposite sides of the parallelogram are congruent. B) The diagonals of the parallelogram are congruent. C) The diagonals of the parallelogram bisect the angles. D) The opposite angles of the parallelogram are congruent.
Answer:
B) The diagonals of the parallelogram are congruent.
Step-by-step explanation:
Since, If the diagonals of a parallelogram are equal in length, then is the parallelogram a rectangle.
For proving this statement.
Suppose PQRS is a parallelogram such that AC = BD,
In triangles ABC and BCD,
AB = CD, ( opposite sides of parallelogram )
AD = CB, ( opposite sides of parallelogram )
AC = BD ( given ),
By SSS congruence postulate,
[tex]\triangle ABC\cong \triangle BCD[/tex]
By CPCTC,
[tex]m\angle ABC = m\angle BCD[/tex]
Now, Adjacent angles of a parallelogram are supplementary,
[tex]\implies m\angle ABC + m\angle BCD = 180^{\circ}[/tex]
[tex]\implies m\angle ABC + m\angle ABC = 180^{\circ}[/tex]
[tex]\implies 2 m\angle ABC = 180^{\circ}[/tex]
[tex]\implies m\angle ABC = 90^{\circ}[/tex]
Since, opposite angles of a parallelogram are congruent,
[tex]\implies m\angle ADC = 90^{\circ}[/tex]
Similarly,
We can prove,
[tex]m\angle DAB = m\angle BCD = 90^{\circ}[/tex]
Hence, ABCD is a rectangle.
That is, OPTION B is correct.
Answer:
B
Step-by-step explanation:
I just took it
Find the cotangent of both angle A and angle B.
Thank you!
Answer: tangent of A = 2.4
Cotangent of B = 0.4167
Step-by-step explanation:
Answer:
[tex]\displaystyle \frac{5}{12} = cot∠B \\ 2\frac{2}{5} = cot∠A[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{OPPOSITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOSITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOSITE} = csc\:θ \\ \frac{ADJACENT}{OPPOSITE} = cot\:θ \\ \\ \frac{10}{24} = cot∠B → \frac{5}{12} = cot∠B \\ \\ \frac{24}{10} = cot∠A → 2\frac{2}{5} = cot∠A[/tex]
I am joyous to assist you anytime.
As part of a survey, 300 girls were asked to name their favorite sport. The results showed that 12 of the girls named bowling as their favorite sport. What percentage of the girls in the survey choose bowling as their favorite sport?
Answer:
4%
Step-by-step explanation:
1. Convert the problem to an equation using the percentage formula: P% * X = Y.
2. P is 10%, X is 150, so the equation is 10% * 150 = Y.
3. Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10.
You purchase a home for $253,600.00 with a mortgage rate of 3.75% APR. How much
interest is due after your first month?
(1 point)
$79.25
$660.42
$792.50
$951.00
Answer:
$792.50
Step-by-step explanation:
As the mortgage rate is 3.75% APR , One has to pay 3.75% of the amount of home in a year as Interest .
Amount of home = $253,600.00
One year interest one has to pay in a year = [tex]\frac{3.75}{100}[/tex]×253,600
= $9510.
So, In one month , he has to pay amount $[tex]\frac{9510}{12}[/tex] .
= $792.5.
love this called sketch a graph of the polynomial function f(x)=x^3-6x^2+3x+10. Use it to complete the following:
• increasing
• positive
• decreasing
• negative
f is ____ on the intervals (-∞, 0.27) and (3.73, ∞).
f is ____ on the intervals (-1,2) and (5, ∞).
f is ____ on the intervals (-∞, -1) and (2,5).
Answer:
increasingpositivenegativeStep-by-step explanation:
You can actually answer this question without graphing the equation, but a graph confirms the answers.
__
A cubic with a positive leading coefficient will be negative and increasing on any interval* whose left end is -∞. Similarly, it will be positive and increasing on any interval whose right end is +∞.
The answer choices tell you ...
there are zeros at -1, 2, 5there are turning points at 0.27, 3.73The function is increasing up to the first turning point and after the second one.
The function is negative up to the first zero and between the last two.
f is increasing on the intervals (-∞, 0.27) and (3.73, ∞).f is positive on the intervals (-1,2) and (5, ∞).f is negative on the intervals (-∞, -1) and (2,5)._____
* We say "any interval" but we mean any interval whose boundary is a zero or turning point, and which properly describes an interval where the function is one of increasing, decreasing, positive, or negative.
To graph the polynomial function f(x) = x^3 - 6x^2 + 3x + 10, we need to find the x-intercepts, y-intercept, and determine the behavior of the graph. Then, using test points, we can determine the intervals where the function is increasing or decreasing, and where it is positive or negative.
Explanation:Graphing the Function f(x) = x3 - 6x2 + 3x + 10To graph the polynomial function f(x) = x3 - 6x2 + 3x + 10, we can start by finding the x-intercepts, y-intercept, and identifying the behavior of the graph. The x-intercepts are the points where the graph intersects the x-axis, and they can be found by setting f(x) = 0 and solving for x using factoring or other methods. The y-intercept is the point where the graph intersects the y-axis, and it can be found by evaluating f(0). Finally, to identify the behavior of the graph, we can examine the signs of the coefficients of the polynomial.
Step 1: Finding the x-interceptsTo find the x-intercepts, we set f(x) = 0:
x3 - 6x2 + 3x + 10 = 0
At this point, we can either try factoring the polynomial or use more advanced methods like synthetic division or the rational root theorem. Let's use a graphing calculator to find the approximate x-intercepts. From the calculator, we find that the x-intercepts are approximately x = -1.01, x = 1.25, and x = 6.76.
Step 2: Finding the y-interceptThe y-intercept is the point where the graph intersects the y-axis, which occurs when x = 0. We can find the y-intercept by evaluating f(0):
f(0) = 03 - 6(0)2 + 3(0) + 10 = 10
The y-intercept is (0, 10).
Step 3: Identifying the behavior of the graphBy examining the signs of the coefficients of the polynomial, we can determine the behavior of the graph.
For x3, the coefficient is positive, which means the graph will be “up” on the left side and “down” on the right side. For -6x2, the coefficient is negative, which means the graph will be “down” on the left side and “up” on the right side. The positive coefficient of 3x indicates that the graph will have a “upward” trend on both sides. Finally, the constant term 10 does not have an effect on the overall behavior of the graph.
Step 4: Sketching the graphBased on the information gathered, we can sketch the graph of the polynomial function f(x) = x3 - 6x2 + 3x + 10. By plotting the x-intercepts (-1.01, 0), (1.25, 0), and (6.76, 0) and the y-intercept (0, 10), and considering the behavior of the graph, we can roughly sketch the shape of the graph.
Based on the sketch of the graph, we can now identify the intervals where the function f(x) is increasing or decreasing, and where it is positive or negative. We can use test points within each interval to determine the sign of the function. For example, to determine the sign of f(x) within the interval (-∞, 0.27), we can choose a test point like x = -1. Plugging in this value, we find that f(-1) = -11. Since f(-1) is negative, we can conclude that f(x) is negative within the interval (-∞, 0.27). Similarly, we can choose test points in the other intervals to determine the signs of f(x) and complete the statement.
Summary:The graph of the polynomial function f(x) = x3 - 6x2 + 3x + 10 has x-intercepts at approximately x = -1.01, x = 1.25, x = 6.76, and a y-intercept at (0, 10). The graph has a certain behavior, with an upward trend on both sides. Using test points, we can determine that f(x) is negative on the intervals (-∞, 0.27) and (3.73, ∞), positive on the intervals (-1, 2) and (5, ∞), and positive on the intervals (-∞, -1) and (2, 5).
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A flag post 10 meters long is fixed on top of a tower. From a point on horizontal ground, the angles of elevation of the top and bottom of the flag post are 40 degrees and 33 degrees respectively. Calculate:
a) The height of the tower
b) The shortest distance from the point on the ground to the top of the flag post
Answer:
Tan33=x/y
y= x/Tan33
Tan40=(10+x)/y
y= (10+x)/Tan40
Therefore
x/Tan33 = (10+x)/Tan40
xTan40-xTan33 =10Tan33
x= 10Tan33/(Tan40-Tan33)
x=34.2m
Step-by-step explanation:
Can someone explain this tree diagram for me? I understand why it’s 0.7 and why it’s 0.3 but what I don’t understand why it’s 0.4 shouldn’t it be 0.1? Shouldn’t it be 0.5 instead of 0.2?
Answer:
66% have graduated within five years.
Step-by-step explanation:
It is given that 70% of freshmen went to public schools. Then the rest 30% i.e., [tex]$ \frac{30}{100} = 0.3 $[/tex] should have gone to other schools.
Now, the number the freshmen in public schools is considered as 100% or 1.
60% of the freshmen from public schools have graduated means out of the total freshmen from public schools, 60% of them have graduated. That is why it is denoted as 0.6 and those not graduated as 0.4.
Note that 60% of total students have graduated.
Let us assume there were 100 students initially. Then 70 students went to public school. Number of students graduated = 60%
[tex]$ \implies \frac{60}{100} \times 70 = 42 $[/tex]
That is 42 students have passed from public school.
Now, the ones in other schools:
80% of them have graduated in other schools. That means out of total students 80% of them have graduated.
That means [tex]$ \frac{80}{100} \times 30 = 24 $[/tex]
24 students from other schools have passed.
Therefore, totally 66 students have passed. i.e., 66 percent have passed.
What is the area of a trapezoid with height 5 m and bases 8 m and 1 m?
A. 6.5 m^2
B. 22.5 m^2
C. 24 m^2
D. 45 m^2
If anyone has the answers to the rest, that would be great!
Answer:
B. 22.5m^2
Step-by-step explanation:
To find the area of a trapezoid, you must use the formula:
1/2 × height × (base 1+ base 2)
1. 1/2 × 5m × (8+1)
2. 1/2 x 5m x (9)
3. Switch it around to make it easier to solve
5m × 9× 1/2 (We can do this because of the commutative property.)
4. 45m × 1/2 = 45 ÷ 2 = 22.5m^2
In the context of the problem, this means that the area of the trapezoid is 22.5m^2.
How many pentagons can you make using five points as vertices?
Answer:
56 pentagon.
Step-by-step explanation:
Here is the complete question: Eight point lies on the circle. How many pentagons can you make using five points as vertices?
Given: Five points on vertices.
Using the combination formula to find the number of pentagon.
[tex]_{r}^{n}\textrm{C} = \frac{n!}{r!(n-r)!}[/tex]
⇒ [tex]_{8}^{5}\textrm{C}= \frac{8!}{5!(8-5)!}[/tex]
⇒[tex]_{8}^{5}\textrm{C}= \frac{8!}{5!\times 3!} \\\\_{8}^{5}\textrm{C} = \frac{8\times 7\times 6\times5\times4\times3\times2\times1}{5\times4\times3\times2\times1\times3\times2\times1} = \frac{336}{6}[/tex]
∴ [tex]_{8}^{5}\textrm{C}= 56[/tex]
∴ With eight point lies on circle, we can make 56 pentagons using five points as vertices
A company with a fleet of 150 cars found that the emissions systems of only 5 out of the 22 they tested failed to meet pollution control guidelines. The company initially believed that 20% of the fleet was out of compliance. Is this strong evidence the percentage of the fleet out of compliance is different from their initial thought? Your Question: State the null hypothesis and the alternative hypotheses they should use for completing a hypothesis test.
Answer: No, the percentage of the fleet out of compliance is not different from their initial thought.
Step-by-step explanation:
Since we have given that
n = 22
x = 5
So, [tex]\hat{p}=\dfrac{x}{n}=\dfrac{5}{22}=0.23[/tex]
he company initially believed that 20% of the fleet was out of compliance. Is this strong evidence the percentage of the fleet out of compliance is different from their initial thought.
so, p = 0.2
Hypothesis would be
[tex]H_0:p=\hat{p}\\\\H_a:p\neq \hat{p}[/tex]
So, the t test statistic value would be
[tex]t=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\\\t=\dfrac{0.23-0.20}{\sqrt{\dfrac{0.2\times 0.8}{22}}}\\\\\\t=\dfrac{0.03}{0.085}\\\\t=0.353[/tex]
Degree of freedom = df = n-1 = 22-1 =23
So, t{critical value} = 2.080
So, 2.080>0.353
so, we will accept the null hypothesis.
Hence, No, the percentage of the fleet out of compliance is not different from their initial thought.
Final answer:
A hypothesis test can be conducted to determine whether the percentage of the fleet out of compliance is different from the initial belief of 20% by using a null hypothesis of p = 0.20 and an alternative hypothesis of p ≠ 0.20, followed by a Z-test for proportions.
Explanation:
To determine whether there is strong evidence that the percentage of the fleet out of compliance is different from the company's initial belief of 20%, we should set up a hypothesis test. The null hypothesis (H₀) is that the true proportion of cars that are out of compliance is equal to 20% (H₀: p = 0.20). The alternative hypothesis (Ha) is that the true proportion of cars that are out of compliance is different from 20% (Ha: p ≠ 0.20).
Using the sample data of 5 failures out of 22 tested, a statistical test such as the Z-test for proportions can be conducted to determine if we should reject the null hypothesis. This would involve calculating the test statistic comparing the sample proportion to 0.20 and then finding the p-value to make a decision based on the chosen significance level, usually 0.05. If the p-value is below the significance level, we would reject the null hypothesis, indicating that there is evidence that the percentage of the fleet out of compliance is different from 20%.
Hey, can I please get some help with this? It shouldn’t be too hard, thanks!
Answer:
(x -3)(x+3)(2x +1)(x -1)(x +1)(x +3)(2x -1)(2x +1)(x -4)Step-by-step explanation:
A) 2x³ +x² -18x -9 = x²(2x +1) -9(2x +1) = (x² -9)(2x +1) = (x -3)(x+3)(2x +1)
__
B) x³ +3x² -x -3 = x²(x +3) -1(x +3) = (x² -1)(x +3) = (x -1)(x +1)(x +3)
__
C) 4x³ -16x² -x +4 = 4x²(x -4) -1(x -4) = (4x² -1)(x -4) = (2x -1)(2x +1)(x -4)
_____
In each case, the third-level factoring mentioned in step 4 is the factoring of the difference of squares: a² -b² = (a -b)(a +b).
_____
The step-by-step is exactly what you need to do. It is simply a matter of following those instructions. You do have to be able to recognize the common factors of a pair of terms. That will be the GCF of the numbers and the least powers of the common variables.
Maya charges $9.50 an hour for peertutoring. One week last mouth she worked 5 hours and the next week she worked 8 hours. How much did maya earn tutoring those two weeks?
The random variable X is normally distributed with mean 5 and standard deviation 25. The random variable Y is defined by Y = 2 + 4X. What are the mean and the standard deviation of Y ? The mean is 20 and the standard deviation is 102.
A) The mean is 20 and the standard deviation is 50.
B) The mean is 22 and the standard deviation is 102.
C) The mean is 22 and the standard deviation is 100.
D) The mean is 22 and the standard deviation is 50.
Answer:
C) The mean is 22 and the standard deviation is 100.
Step-by-step explanation:
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.
The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).
If [tex] X\ sim N(\mu_x =5, \sigma_x =25)[/tex]
And the random variable Y =2+4X.
If we are interested in find the mean and the standard deviation for this new variable we need to apply the concepts of expected value and Variance of random variables.
Using the concept of expected value we have:
[tex]E(Y) =E(2+4X) = E(2) +E(4X)= 2+ 4E(X) =2+4(5) =2+20=22[/tex]
So on this case the [tex]E(Y) =\mu_Y =22[/tex]
Using the concept of variance we have:
[tex]Var(Y)=Var(2+4x)=Var(2)+Var(4X)+2Cov(2,4X)[/tex]
But since 2 is a constant we don't have variance for this and the [tex]Cov(2,4x)=0[/tex] because the covariance of a random variable with a constant is zero. So applying these concepts we have:
[tex]Var(Y)= Var(4x)=4^2 Var (X)= 16 \sigma^2_x =16(25^2)=10000[/tex]
And then if we need the standard deviation we just need to take the square root:
[tex]sd(Y) = \sqrt{10000}=100[/tex]
So the best option for this case would be:
C) The mean is 22 and the standard deviation is 100.
Answer:
Option c) is correct.
Step-by-step explanation:
Given :
[tex]\mu_x = 5[/tex] and [tex]\sigma_x = 25[/tex]
Y = 2 + 4X
Calculation:
This problem can be solved by using concept of expected value and variance of random variables.
By expected value concept,
[tex]\rm E(Y) = E(2 + 4X)= E(2) + E(4X)= 2 + 4E(X)=2+4(5)=22[/tex]
Therefore, [tex]\mu_y = 22[/tex]
By variance concept,
[tex]\rm Var(Y)= Var(2+4X)=Var(2)+Var(4X)+2Cov(2,4X)[/tex]
[tex]\rm Cov(2,4X)=0[/tex]
Var(2) = 0
Therefore,
[tex]\rm Var(Y) = Var(4X)= 4^2Var(X)= 16\sigma_x^2=16(25^2)=10000[/tex]
Therefore,
Standard deviation(Y) = [tex]\sqrt{10000}[/tex] = 100
Hence, option c) is correct.
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