Answer:
By the Chebyshev Theorem, 75% probability of a randomly selected state having between 21 and 53 multi-million dollars
Step-by-step explanation:
We have no information about the distribution, so we use the Chebyshev's theorem to solve this question.
Chebyshev Theorem:
75% of the data within 2 standard deviations of the mean.
89% of the data within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 37
Standard deviation = 8
What is the probability of a randomly selected state having between 21 and 53 multi-million dollars
21 = 37 - 2*8
So 21 is 2 standard deviations below the mean.
53 = 37 + 2*8
So 52 is 2 standard deviations above the mean.
By the Chebyshev Theorem, 75% probability of a randomly selected state having between 21 and 53 multi-million dollars
Find the margin of error for a 95% confidence interval for estimating the population mean when the sample standard deviation equals 100, with a sample size of (i) 484 and (ii) 1521. What is the effect of the sample size? (i) Find the margin of error for a 95% confidence interval for estimating the population mean when the sample standard deviation equals 100 with a sample size of 484.
Answer:
i) the margin of error for a 95% confidence interval for estimating the population mean is
M.E = 8.909
ii) the margin of error for a 95% confidence interval for estimating the population mean is
M.E = 5.025
Step-by-step explanation:
Step:-(i)
i ) Given sample size n = 484
Given sample standard deviation 'S' = 100
Margin of error for 95% confidence interval for estimating the population mean is determined by
[tex]M.E = \frac{1.96 X 100}{\sqrt{484} } = 8.909[/tex]
ii) Given sample size n =1521
Given sample standard deviation 'S' = 100
Margin of error for 95% confidence interval for estimating the population mean is determined by
[tex]M.E = \frac{1.96 X 100}{\sqrt{1521} } = 5.025[/tex]
Because of the commutative property of multiplication, it is true that
3/4 × 4 = 4 × 3/4. However, these expressions can be calculated in different ways even though the solutions will be the same.
Below, show two different ways of solving this problem.
First, show how 3/4 x 4 can be solved using repeated addition.
Answer:
1. 3/4 + 3/4 + 3/4 +3/4
2. 0.75 * 4
Step-by-step explanation:
1. add 3/4 four times
3/4 + 3/4 + 3/4 +3/4
2. You can turn 3/4 into a decimal. 3/4 =0.75
0.75 * 4
Final answer:
3/4 × 4 can be solved through repeated addition by adding 3/4 to itself four times to get 9/4 or 2 1/4. Alternatively, by simplifying before multiplying, recognizing that 4 is the reciprocal of 1/4, we easily find that the product is 3.
Explanation:
When solving 3/4 × 4 using repeated addition, we use the concept that multiplying a number by a whole number is the same as adding that number to itself that many times. In this case, 3/4 is added to itself 4 times:
3/4 + 3/4 + 3/4 + 3/4We have four 3/4's, and when we add them up, we get:
3/4 + 3/4 = 3/2 (or 1 1/2)3/2 + 3/4 = 6/4 (or 1 1/2)When we add 3/2 (1 1/2) and 3/4, we can convert 1 1/2 into 6/4 to make it easier to add the fractions, obtaining:
6/4 + 3/4 = 9/4 (or 2 1/4)Therefore, 3/4 × 4 equals 9/4 or 2 1/4 through repeated addition.
Another way to approach the problem is by simplifying before multiplying. Since we are multiplying by 4, which is the reciprocal of 1/4, we can simplify by understanding that:
3/4 × 4/1 = (3 × 4) / (4 × 1) = 12/4 = 3Thus, by canceling out the common factors (4 in the numerator and 4 in the denominator), the multiplication becomes 3 × 1, which equals 3. This satisfies the condition that as long as we perform the same operation on both sides of the equals sign, the expression remains an equality.
ABCD is a trapezoid. Solve for x and y
Given:
The given figure ABCD is a trapezoid.
The measure of ∠A is (2x + 32).
The measure of ∠B is 112°
The measure of ∠C is y.
The measure of ∠D is 46°
We need to determine the value of x and y.
Value of x:
We know the property that the adjacent angles in a trapezoid are supplementary.
Thus, we have;
[tex]\angle A+\angle B=180[/tex]
Substituting the values, we get;
[tex]2x+32+112=180[/tex]
[tex]2x+144=180[/tex]
[tex]2x=36[/tex]
[tex]x=18[/tex]
Thus, the value of x is 18.
Value of y:
The value of y can be determined using the property that the adjacent angles of a trapezoid are supplementary.
Thus, we have;
[tex]\angle C+\angle D=180[/tex]
[tex]y+46=180[/tex]
[tex]y=134[/tex]
Thus, the value of y is 134.
Hence, Option c is the correct answer.
The density of people (number of people per mile) during the evening rush hour for the 5 mile stretch along a certain sidewalk in New York is given by f(x), where x is the distance in miles north of the subway station. Which of the following gives the number of people on this 5 mile stretch from the subway?
5
a. ∫ f(x). dx
0
x
b. ∫ f(x). dx
0
x
c. ∫ f(x). dx
5
5
d. ∫ f(x). dx
x
Answer:
a. [tex]\int\limits^5_0 {f(x)} \, dx[/tex]
Step-by-step explanation:
Since f(x) is the function for the populational density at a certain sidewalk for a 5 mile stretch, a definite integral of that function will yield the total number of people within the integration intervals. If we are interested in the number of people in the whole 5 mile stretch, we must integrate f(x) from x = 0 miles to x = 5 miles:
[tex]\int\limits^5_0 {f(x)} \, dx[/tex]
Therefore, the answer is alternative a.
7. Certain car manufacturers install a gauge that tells the driver how many miles they can drive
until they will run out of gas. A study was conducted to test the accuracy of these gauges.
Each driver was assigned a certain gauge reading until empty to watch for. When their car
announced it had that many miles remaining until empty, they began to measure their
distance traveled. After they ran out of gas, they reported the distance they were able to dove
(in miles) as well as the gauge reading they were assigned (in miles). Here is computer output
showing the regression analysis:
Regression Analysis: Distance versus Gauge Reading
Predictor Coef SE Coef
Constant -0.7928 3.2114
-0.2469 0.8060
Gauge 1.1889 0.0457
26.0310 0.0000
5 - 7.0032
R-Sq -0.9326 R-Sqladj) - 0.9312
Identify and interpret the slope of the regression line used for predicting the actual distance
that can be driven based on the gauge reading
(A) Slope - 1.1889. The predicted distance the drivers were able to drive increases by 1.1889
miles for each additional mile reported by the gauge.
(B) Slope - 0.0457. The predicted distance the drivers were able to drive increases by 0.0457
miles for each additional mile reported by the gauge.
(C) Slope - -0.7928. The predicted distance the drivers were able to drive decreases by
0.7928 miles for each additional mile reported by the gauge.
(D) Slope - 1.1889. For each additional mile reported by the gauge, the drivers were able to
drive an additional 1.1889 miles
(E) Slope -0.0457. For each additional mile reported by the gauge, the drivers were able to
drive an additional 0.0457 miles,
Answer:
A) Slope - 1.1889. The Predicted distance the drivers were able to drive increases by 1.1889
Step-by-step explanation:
Circle P has a circumference of approximately 75 inches.
What is the approximate length of the radius, m? Use 3.14 for
TT. Round to the nearest inch,
O 12 inches
O 24 inches
O 38 inches
46 inches
Answer: 12
Step-by-step explanation: To find the radius you have to do the opposite of 2r(pi). So you divide 75 by 2 and then by 3.14, getting 11.9, which rounds to 12
Answer:
1) 12in
Step-by-step explanation:
The circumference is 75, so to find the diameter you have to divide 75 by 3.14. You get 24 approximately. Then divide the diameter by 2, so 24/2=12.
In circle T, ZPTQ E ZRTS.
What is the length of PQ?
3 units
4 units
6 units
7 units
Since PQ = SR, hence the length of PQ is 4 units
Similar shapesFrom the given figure, w are told that triangle PTQ is similar to that of RTS, this means that;
PQ = SR
Given the following
Length of SR = 4 units
Since PQ = SR, hence the length of PQ is 4 units
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Find the minimum sample size when we want to construct a 90% confidence interval on the population proportion for the support of candidate A in the following mayoral election. Candidate A is facing two opposing candidates. In a preselected poll of 100 residents, 22 supported her. The desired margin of error is 0.08.
What is the distance between –5 and 2?
units
Answer:
it would be a distance of 7 units
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
the absolute value of -5 - 2 = 7
In recent years, the IRS has been inundated with taxpayer calls and has redesigned its phone service as well as posting answers to frequently asked questions on its website (The Cincinnati Enquirer, January 7, 2010). According to a report by a taxpayer advocate, callers using the new system can expect to wait on hold for an unreasonably long time of minutes before being able to talk to an IRS employee. Suppose you select a sample of callers after the new phone service has been implemented; the sample results show a mean waiting time of minutes before an IRS employee comes on line. Based upon data from past years, you decide is it reasonable to assume that the standard deviation of waiting times is minutes 11?
Answer:
The calculated p-value is greater than the significance level at which the test was performed, hence, we fail to reject the null hypothesis & conclude that there is no significant evidence to say that the actual mean waiting time turned out to be significantly less than the 15-minute claim made by the taxpayer advocate.
That is, the true mean waiting time is equal to or greater than the 15-minute claim by the taxpayer advocate.
Step-by-step explanation:
For hypothesis testing, we first clearly state our null and alternative hypothesis.
For hypothesis testing, the first thing to define is the null and alternative hypothesis.
In hypothesis testing, especially one comparing two sets of data, the null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the direction of the test.
The alternative hypothesis usually confirms the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the direction of the test.
For this question, we are to investigate that the actual mean waiting time turned out to be significantly less than the 15-minute claim made by the taxpayer advocate.
The null hypothesis would be that there is no significant evidence to say that the actual mean waiting time turned out to be significantly less than the 15-minute claim made by the taxpayer advocate. That is, the true mean waiting time is equal to or greater than the 15-minute claim by the taxpayer advocate.
The alternative hypothesis is that there is significant evidence to suggest that the actual mean waiting time turned out to be significantly less than the 15-minute claim made by the taxpayer advocate.
This is evidently a one tail hypothesis test (we're investigating only in one direction; less than the claim
Mathematically, the null hypothesis is
H₀: μ ≥ 15
The alternative hypothesis is
Hₐ: μ < 15 minutes
To do this test, we will use the z-distribution because the population standard deviation is known.
So, we compute the z-test statistic
z = (x - μ₀)/σₓ
x = sample mean = 13 minutes
μ₀ = the advocate's claim = 15 minutes
σₓ = standard error of the poll proportion = (σ/√n)
where n = Sample size = 50
σ = population standard deviation = 11 minutes.
σₓ = (σ/√n) = (11/√50) = 1.556
z = (13 - 15) ÷ 1.556 = -1.29
checking the tables for the p-value of this z-statistic
p-value (for z = -1.29, at 0.05 significance level, with a one tailed condition) = 0.098525
The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 5% = 0.05
p-value = 0.098525
0.098525 > 0.05
Hence,
p-value > significance level
This means that we fail to reject the null hypothesis & conclude that there is no significant evidence to say that the actual mean waiting time turned out to be significantly less than the 15-minute claim made by the taxpayer advocate.
That is, the true mean waiting time is equal to or greater than the 15-minute claim by the taxpayer advocate.
Hope this Helps!!!
A box is to be made where the material for the sides and the lid cost $0.20 per square foot and the cost for the bottom is $0.650.65 per square foot. Find the dimensions of a box with volume 1010 cubic feet that has minimum cost.
Answer:
the dimensions xyz of a box with volume 10 cubic feet that has minimum cost is;
x = 1.68 ft
y = 1.68 ft
z = 3.54 ft
Step-by-step explanation:
See attachment for the full explanation.
Is 100x^3 a perfect square
Answer:
No.
Step-by-step explanation:
This is not a perfect square because the exponent would need to be even, not odd. The 100 is a perfect square. If you were to simplify it, it would be (10x^2) * (10x). In order for it to be truly a perfect square, they both need to be the same.
Please help with this math question
Answer:
Im not 100% sure but i think its first row second
Answer: all the triangle are similar
Step-by-step explanation: ;)
Solve 2/5 (j + 40) = -4 *
Answer: j=-5 as long as you follow my steps you will also be able to show your work.
Combine multiplied terms into a single fraction
Distribute it then
Multiply all terms by the same value to eliminate fraction denominators.
Find the unit rate for the situation: Corrin has twin boys. She buys a box ot
10 toy cars to share evenly between the boys. *
(1) Given:
Given that Corrin has twin boys. She buys a box of 10 toy cars to share evenly between them.
We need to determine the unit rate of toy cars for one boy.
Unit rate:
The unit rate for toy cars for one boy can be determined by dividing the total number of cars by the total number of boys.
Thus, we have;
[tex]Unit \ rate=\frac{10}{2}[/tex]
[tex]Unit \ rate=5[/tex]
Thus, the unit rate is 5 cars per boy.
Hence, Option b is the correct answer.
(2) Given:
Given that the Belle works at a donut shop. They sell a box of donut holes for $1.80. There are 20 donut holes in the box.
We need to determine the unit rate.
Unit rate:
We need to determine the cost of one donut hole in the box.
The cost of one donut hole can be determined by dividing the cost of box of donut holes by the total number of donut holes in the box.
Thus, we have;
[tex]Unit \ rate=\frac{1.80}{20}[/tex]
[tex]Unit \ rate=0.09[/tex]
Thus, the unit rate is $0.09 per donut hole.
Hence, Option a is the correct answer.
A triangle has a base of 4 m and a height of 3 m. Find the area of the triangle in square millimeters.
Answer:
6000000 mm squared
Step-by-step explanation:
We first convert the meters to millimeters. We got 4000 and 3000. The area of a triangle is base times height divided by 2. So we get 12000000 divided by 2 or 6000000 mm squared
2y2(35 – 4y) in standard form
Step-by-step explanation:
[tex]2 {y}^{2} (35 - 4y) \\ = 2 {y}^{2} \times 35 - 2 {y}^{2} \times 4y \\ = 70 {y}^{2} - 8 {y}^{3} \\ = \red { \bold{ - 8 {y}^{3} + 70 {y}^{2} }} \\ is \: in \: the \: standard \: form.[/tex]
Ivan started the week on page 35 of his book and read 20 pages each night. What page would Ivan be on if he reads for 8 nights
Answer:
160 plus 35 = 185
Step-by-step explanation:
8×20
hopefully this helps you
If you were to create a histogram from the data shown in the stem-and-leaf plot, with each bar covering six values from 13 to 42, how many data points would be in the bar from 13 - 18?
Answer:
4
Step-by-step explanation:
4 data points are between 13 and 18 they are 13, 14, 15, and 18.
Answer:
4
Step-by-step explanation:
i took test
What is 0.68 expressed as a fraction in simplest form? Both the 6 and the 8 repeat.
Answer:
68/99
Step-by-step explanation:
.68686868686 repeating
Let x= .68686868668repeating
Multiply by 100
100x = 68.686868686repeating
Subtract x = .68686868repeating from this equation
100x = 68.686868686repeating
-x = .68686868repeating
------------------------------------------
99x = 68
Divide each side by 99
99x / 99 = 68/99
x = 68/99
Answer:
68/99 I agree with the other person
Step-by-step explanation:
Morgan can make 4 cupcakes (the y value) with one cup of flour (the x value). How many cupcakes can she make with 18 cups of flour?
Answer:
y = 18x
72 cupcakes = 18 cups of flour
Step-by-step explanation:
y= cupcakes
x=flour
4/1
72/18
18x4=72
Answer:
72 cupcakes
Step-by-step explanation:
Take 4 and multiply it by 18! Simple! :)
How do you get the answer to 54-200 divide by 4
Answer:
4
Step-by-step explanation:
use the order of operations- (parentheses, exponets, multiply, divide, add, subtract...)
54-200/4
-200/4=-50
54-50=4
a car was valued at $41,000 in the year 2009 by 2013 the car value has depreciated to 19,000 if the car value continues to by the same percentage what will it be worth in 2019?
Answer:
$6,376.92
Step-by-step explanation:
-Let d be the rate of depreciation per year.
-Therefore, the value after n years can be expressed as:
[tex]A=P(1-d)^n\\\\A=Value \ after \ n \ years\\P=Initial \ Value\\d=Rate \ of \ depreciation\\n=Time \ in \ years[/tex]
#We substitute for the years 2009-2013 to solve for d:
[tex]A=P(1-d)^n\\\\19000=41000(1-d)^4\\\\0.475=(1-d)^4\\\\d=1-0.475^{0.25}\\\\d=0.1698[/tex]
#We then use the calculated depreciation rate above to solve for A after 10 yrs:
[tex]A=P(1-d)^n\\\\=41000(1-0.1698)^{10}\\\\=\$6,376.92[/tex]
Hence, the value of the car after 10 yrs is $6,376.92
To find the future value of a car in 2019, we calculate the percentage decrease in value from 2009 to 2013 and apply it for 6 years.
Explanation:To find the future value of the car in 2019, we need to determine the percentage decrease in value each year. From 2009 to 2013, the car depreciated from $41,000 to $19,000.
This is a decrease of $22,000. To find the percentage decrease, divide this by the initial value: 22,000 / 41,000 = 0.5366 (approximately).
To find the future value in 2019, we need to apply this percentage decrease continuously for 6 years. Multiply the current value by the percentage decrease repeatedly.
= 19,000 * 0.5366 * 0.5366 * 0.5366 * 0.5366 * 0.5366 * 0.5366
= $5,862.54 (approximately).
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A researcher is interested in seeing if negative political ads against an opponent (group one) are more effective than positive ads for the original candidate (group two). If the mean for group one is 7.00, the mean for group two is 10.00, the n for group one is 20, the n for group two is 20, the variance for group one is 2.50, and the variance for group two is 4.5.
What is the correct write up for this study in a results section?A. t(40) = 5.07, p < .01B. t(38) = .592, p > .05C. t(19) = 5.07, p < .01D. t(38) = 2.59, p > .05E. None of the above (it should be t(38) = 5.07, p < .01)
Answer:
[tex]t=\frac{10-7}{\sqrt{\frac{1.581^2}{20}+\frac{2.121^2}{20}}}}=5.07[/tex]
The first step is calculate the degrees of freedom, on this case:
[tex]df=n_{1}+n_{2}-2=20+20-2=38[/tex]
Since is a one side test the p value would be:
[tex]p_v =P(t_{(38)}>5.07)=5.33x10^{-6}[/tex]
And the best option for this case would be:
None of the above (it should be t(38) = 5.07, p < .01)
Step-by-step explanation:
Data given and notation
[tex]\bar X_{1}=7[/tex] represent the mean for the sample 1
[tex]\bar X_{2}=10[/tex] represent the mean for the sample 2
[tex]s_{1}=\sqrt{2.5}= 1.581[/tex] represent the sample standard deviation for the sample 1
[tex]s_{2}=\sqrt{4.5}= 2.121[/tex] represent the sample standard deviation for the sample 2
[tex]n_{1}=20[/tex] sample size selected for 1
[tex]n_{2}=20[/tex] sample size selected for 2
[tex]\alpha[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean for the group 1 is higher than the mean for group 2, the system of hypothesis would be:
Null hypothesis:[tex]\mu_{2} \leq \mu_{1}[/tex]
Alternative hypothesis:[tex]\mu_{2} > \mu_{1}[/tex]
If we analyze the size for the samples both are less than 30 so for this case is better apply a t test to compare means, and the statistic is given by:
[tex]t=\frac{\bar X_{2}-\bar X_{1}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]t=\frac{10-7}{\sqrt{\frac{1.581^2}{20}+\frac{2.121^2}{20}}}}=5.07[/tex]
P-value
The first step is calculate the degrees of freedom, on this case:
[tex]df=n_{1}+n_{2}-2=20+20-2=38[/tex]
Since is a one side test the p value would be:
[tex]p_v =P(t_{(38)}>5.07)=5.33x10^{-6}[/tex]
And the best option for this case would be:
None of the above (it should be t(38) = 5.07, p < .01)
(1.64x10^0)/(2.0x10^2) answers in scientific notation
Answer:
8.2*10^-3
Step-by-step explanation:
Answer:
0.0082
(scientific notation)-step explanation:
People's Software Company has just set up a call center to provide technical assistance on its new software package. Two technical representatives are taking the calls, where the time required by either representative to answer a customer's questions has an exponential distribution with a mean of 5 minutes. Calls are arriving according to a Poisson process at a mean rate of 10 per hour. By next year, the mean arrival rate of calls is expected to decline to 5 per hour, so the plan is to reduce the number of technical representatives to one then. a-) Assuming that service rate μ will stay the same for next year's queueing system, determine L, Lq, W, and Wq for both the current system and next year's system. For each of these four measures of performance, which system yields the smaller value? b-) Now assume that μ will be adjustable when the number of technical representatives is reduced to one. Solve algebraically for the value of μ that would yield the same value of W as for the current system.
The question revolves around calculating queueing system performance measures for a software company's call center and adjusting the service rate to maintain consistent service levels during an operational change. Calculations would apply queue theory but specifics require further details about the model type, such as M/M/1 or M/M/2. Algebraic methods would be needed to adjust the service rate to keep waiting times consistent.
Explanation:The question deals with determining key performance measures (L, Lq, W, Wq) for a queueing system at People's Software Company call center, under two different operational scenarios, and solving for the service rate (μ) that equates waiting times between these scenarios. The system initially with two representatives and an arrival rate of 10 calls per hour, transitioning to one representative and a decreased arrival rate of 5 calls per hour, is examined assuming exponential service times with a mean of 5 minutes.
For the current system with two technical representatives and ten calls arriving per hour, assuming the call arrival rate follows a Poisson process and service times are exponentially distributed, key performance measures could be calculated utilizing formulas from queueing theory. However, these formulas depend highly on the specifics of the queueing model used, such as M/M/1, M/M/2, etc., and are not directly provided here.
For next year's system with a reduction in technical representatives and a halved arrival rate, similar analytical methods could be applied to predict performance based on the adjusted arrival rate and the assumption of unchanged service time distributions.
Regarding the adjustment of μ to maintain the same waiting time (W), algebraic solutions involving the exponential service time distribution and Poisson arrival processes must be derived, factoring in the reduction of workers and the change in arrival rate, to find the new service rate (μ) that would ensure continuity in service level expectations.
What is the midpoint of AC ?
A: (m + p, n + r)
B: (p – m, r – n)
C: (m – p, n – r)
D: (m + n, p + r)
Answer:
A: (m + p, n + r)
Step-by-step explanation:
[tex]Midpoint \: of \: AC \\ = \bigg( \frac{2m + 2p}{2} \: \: \frac{2n + 2r}{2} \bigg) \\ \\ = \bigg( m + p, \: \: n + r \bigg)[/tex]
A pro basketball player is a poorâ free-throw shooter. Consider situations in which he shoots a pair of free throws. The probability that he makes the first free throw is 0.48. Given that he makes theâ first, suppose the probability that he makes the second is 0.62. Given that he misses theâ first, suppose the probability that he makes the second one is 0.38.
1. Find the probability that he makes one of the two free throws using the multiplicative rule with the two possible ways he can do this.
Answer:
The probability that he makes one of the two free throws is 0.38
Step-by-step explanation:
Hello!
Considering the situation:
A pro basketball player shoots two free throws.
The following events are determined:
A: "He makes the first free throw"
Ac: "He doesn't make the first free throw"
B: "He makes the second free throw"
Bc: "He doesn't make the second free throw"
It is known that
P(A)= 0.48
P(B/A)= 0.62
P(B/Ac)= 0.38
You need to calculate the probability that he makes one of the two free throws.
There are two possibilities, that "he makes the first throw but fails the second" or that "he fails the first throw and makes the second"
Symbolically:
P(A∩Bc) + P(Ac∩B)
Step 1.
P(A)= 0.48
P(Ac)= 1 - P(A)= 1 - 0.48= 0.52
P(Ac∩B) = P(Ac) * P(B/Ac)= 0.52*0.38= 0.1976≅ 0.20
Step 2.
P(A∩B)= P(A)*P(B/A)= 0.48*0.62= 0.2976≅ 0.30
P(A)= P(A∩B) + P(A∩Bc)
P(A∩Bc)= P(A) - P(A∩B)= 0.48 - 0.30= 0.18
Step 3
P(Ac∩B) + P(A∩Bc) = 0.20 + 0.18= 0.38
I hope this helps!
The probability that the player makes one of the two free throws using the multiplicative rule is 0.4952 or 49.52%.
Explanation:To find the probability that the player makes one of the two free throws using the multiplicative rule, we need to consider the two possible ways he can do this:
The player makes the first free throw (probability of 0.48) and misses the second (probability of 0.62).The player misses the first free throw (probability of 0.52) and makes the second (probability of 0.38).We can calculate the probability for each case and sum them up to find the total probability:
p(make 1st and miss 2nd) = (0.48) * (0.62) = 0.2976
p(miss 1st and make 2nd) = (0.52) * (0.38) = 0.1976
Total probability = p(make 1st and miss 2nd) + p(miss 1st and make 2nd) = 0.2976 + 0.1976 = 0.4952
Therefore, the probability that the player makes one of the two free throws is 0.4952, or 49.52%.
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Roger has 4 gallons of juice. He puts the same amount of juice into each of 5 pitchers. How many gallons of juice are in 1 pitcher?
Answer:
0.8 gallons
Step-by-step explanation:
4 gallons of juice divided into 5 pitchers equally, 4/5=0.8 per pitcher.
what is -3 3/4 + 1/2
Answer: -3 1/4 or -13/4
Step-by-step explanation:
Answer:
[tex]\frac{-7}{4}[/tex]
Step-by-step explanation:
-3*3/4-1/2
-9/4+1/2
-9/4+2/4
(-9+2)/4
-7/4