Answer: [tex]SA=117.2\ in^2[/tex]
Step-by-step explanation:
You need to remember the following:
1. The area of a rectangle can be calculated with the following formula:
[tex]A_r=lw[/tex]
Where "l" is the length and "w" is the width.
2. The area of a triangle can be calculated with the following formula:
[tex]A_t=\frac{bh}{2}[/tex]
Where "b" is the base and "h" is the height.
Use those formulas to find the area of each face.
Area of the rectangle
[tex]A_r=(10\ in)(4\ in)=40\ in^2[/tex]
Area of two triangles
There are two equal triangles. Each one has a base of 10 inches and a height of 5 inches. Then, their areas are equal:
[tex]A_{t1}=A_{t2}=\frac{(10\ in)(5\ in)}{2}=25\ in^2[/tex]
The areas of the other two triangles (which are equal) are:
[tex]A_{t3}=A_{t4}=13.6\ in^2[/tex]
Adding the areas of the faces, you get that the surface area of the rectangular pyramid is:
[tex]SA=40\ in^2+25\ in^2+25\ in^2+13.6\ in^2+13.6\ in^2\\\\SA=117.2\ in^2[/tex]
Answer:
117.2 is the answer
(a) Suppose one house from the city will be selected at random. Use the histogram to estimate the probability that the selected house is valued at less than $500,000. Show your work.
(b) Suppose a random sample of 40 houses are selected from the city. Estimate the probability that the mean value of the 40 houses is less than $500,000. Show your work.
Answer:
a. 0.71
b. 0.9863
Step-by-step explanation:
a. The mean of the distribution is given as $403,000 and the standard deviation is $278,000.
-To estimate the probability that a randomly selected house has a value less than $500,000:
[tex]P(X<500,000)=P(X=0)+P(X=500)\\\\=0.34+0.37\\\\=0.71[/tex]
Thus, the probability that a randomly selected house has a value less than $500,000 is 0.71
b. -since 40 is larger than or equal to 30, we assume normal distribution.
-The probability can therefore be calculated as:
[tex]P(\bar X)=P(z<\frac{\bar X-\mu}{\sigma/\sqrt{n}})\\\\=P(z<\frac{500-403}{278/\sqrt{40}})\\\\=P(z<2.2068)\\\\=0.986336\\\\\approx 0.9863[/tex]
Hence, the probability that the mean value of the 40 houses is less than $500,000 is 0.9863
To estimate the probability that a house is valued less than $500,000, we count the bars below that value on the histogram. To estimate the probability that the mean value of 40 houses is less than $500,000, we use the Central Limit Theorem to calculate the z-score.
Explanation:(a) To estimate the probability that the selected house is valued at less than $500,000, we need to find the area under the histogram below the value of $500,000. Looking at the histogram, we see that there are 3 bars below $500,000. Each bar represents a count of houses, so we add up the counts of those 3 bars. The estimated probability is given by:
Estimated Probability = (Count of houses valued less than $500,000) / (Total count of houses)
(b) To estimate the probability that the mean value of the 40 houses is less than $500,000, we can use the Central Limit Theorem. According to the Central Limit Theorem, the distribution of the sample mean approaches a normal distribution 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. We can then calculate the z-score for $500,000 using the formula:
z = (x - mean) / (standard deviation / sqrt(sample size))
Once we have the z-score, we can find the estimated probability using a standard normal distribution table or calculator.
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Factor x^2 +11xy+30y^2
Answer:
(x+5y)(x+6y)
Step-by-step explanation:
Last month, Belinda worked 160 hours at a rate of $10.00 per hour. If her employer retains 9% of her gross salary, is $1,500 a reasonable estimate of her net salary?
We have been given that last month, Belinda worked 160 hours at a rate of $10.00 per hour.
Let us find amount earned by Belinda last month as:
[tex]\text{Amount earned in 160 hours}=\$10\times 160[/tex]
[tex]\text{Amount earned in 160 hours}=\$1600[/tex]
We are also told that Belinda's employer retains 9% of her gross salary. This means that Belinda's net income will be 91% of $1600. [tex](100\%-9\%=91\%)[/tex].
[tex]\text{Belinda's net income would be}=\$1600 \times \frac{91}{100}[/tex]
[tex]\text{Belinda's net income would be}=\$16\times 91[/tex]
[tex]\text{Belinda's net income would be}=\$1456[/tex]
Upon rounding $1456 to nearest hundred, we will get:
[tex]\text{Belinda's net income would be}\approx \$1500[/tex]
Therefore, $1500 is a reasonable estimate of her net salary.
Final answer:
After calculating the gross salary at $1,600 and then determining the tax retained, Belinda's net salary would be $1,456. Hence, $1,500 is not a reasonable estimate for her net salary.
Explanation:
Let's first calculate the gross salary that Belinda earned. She worked for 160 hours at a rate of $10.00 per hour, so her gross salary can be calculated by multiplying the number of work hours by the rate per hour:
Gross Salary = 160 hours * $10.00 per hour = $1,600
The employer retains 9% of her gross salary, so let's find out how much that amounts to:
Tax = 9% of $1,600 = 0.09 * $1,600 = $144
Now, to obtain the net salary, we subtract the tax from the gross salary:
Net Salary = Gross Salary - Tax = $1,600 - $144 = $1,456
Therefore, $1,500 is not a reasonable estimate of her net salary, as the exact calculation shows that her net salary is $1,456.
Seventy-five percent of consumers prefer to purchase electronics online. You randomly select 88 consumers. Find the probability that the number of consumers who prefer to purchase electronics online is (a) exactly five, (b) more than five, and (c) at most five.
Answer:
Step-by-step explanation:
Find attached the solution
Annie spent $70 at a clothing store and $35 at a pet store. What percent of the money did she spend? Check all that apply. 1) 33 1/3% at the pet store 2) 35% at the pet store 3) 50% at the pet store 4) 66 2/3% at the clothing store 5) 70% at the clothing store 6) 100% at the two stores 7) 105% at the two stores
Answer:
1, 4 and 6 are correct
Step-by-step explanation:
In answering this question, we shall be evaluating the validity of the options.
1 is correct
the total amount of money is 70+35 = 105
The percentage spent at pet store = 35/105 * 100 = 33 1/3 %
2. is wrong since 1 is correct
3 is wrong since 1 is correct
4. is correct
since she spent 33 1/3 at pet shop, what is spent at clothing store will be 100 - 33 1/3 = 66 2/3 %
5 is wrong
6 is correct
7 7 is wrong
Answer:
1) [tex]33\frac{1}{3}\%[/tex] at the pet store4)[tex]66\frac{2}{3}\%[/tex] at the clothing store6) 100% at the two storesStep-by-step explanation:
Amount of Money spent by Annie
At clothing store=$70At pet store=$35Total Amount Spent= 70+35=$105
Percentage Spent at each place
Clothing Store
[tex]\frac{70}{105}X100=66\frac{2}{3}\%[/tex]
Pet Store
[tex]\frac{35}{105}X100=33\frac{1}{3}\%[/tex]
Therefore the following applies:
1) 33 1/3% at the pet store4)66 2/3% at the clothing store6) 100% at the two storesWhat is the reasonable estimate of the probability that ragin Cajun score 30 more points in their next football game
Answer:
Step-by-step explanation:
Dali rolled up his painting and placed it in a cylinder 2 inches diameter. If the cylinder is 20 inches long find its volume. Round your answer to the nearest whole number
Answer:
The correct answer is 63 cubic inches.
Step-by-step explanation:
Dali rolled up his painting and placed it in a cylinder 2 inches diameter.
Diameter of the painting is 2 inches. This also implies diameter of the cylinder is 2 inches.
Radius of the cylinder is 1 inch.
Length of the cylinder is 20 inches.
Volume of the cylinder is given by π × [tex]r^{2}[/tex] × h = π × [tex]1^{2}[/tex] × 20 = 20π = 62.85 cubic inches ≈ 63 cubic inches.
Therefore the volume of the cylinder in which Dali placed his painting is given by 63 cubic inches.
What is the value of x in this equation? 4x + 2 – 23(92 + 92x) = 7
Answer:
-707/704
Step-by-step explanation:
4x + 2 - 2116 - 2116x = 7
-2112x = 2121
x = 2121/-2112 = -707/704
Answer:
x= 2121/-2112 = -707/704 = -1.00426136
Step-by-step explanation:
4x + 2 – 23(92 + 92x) = 7
Eliminate the 2 by substracting both side by -24x - 23(92+92x) = 5
2. Discriminate by multiplying -23 with 92 and -23 with 92x
4x - 2116 -2116x = 5
3. Add 2116 both sides to eliminate -2116
4x -2116x = 2121
4. combine 4x-2116x together
-2112x = 2121
5. Divide both sides with -2112
x= 2121/-2112 = -707/704 = -1.00426136
Mark knows that his yard is 214 times as long as it is wide. Which equation shows the length, in feet, of the fence that goes all the way around the yard if Mark measures the width as w feet?
Answer:
Length in feet is equal to [tex]\frac{2P}{6.5}[/tex], where P is the perimeter
Step-by-step explanation:
Let the width (W) of the yard be "X"
[tex]W = w[/tex]
Then the length(L) of the yard will be
[tex]2\frac{1}{4} * w[/tex]
[tex]L = \frac{9}{4} *w[/tex]
The perimeter of the yard will be equal to the sum of twice the length and width of the yard
Thus,
[tex]P = 2 W + 2L\\[/tex]
Substituting the given values in above equation, we get -
[tex]P = 2 w + 2 (\frac{9}{4})w\\P = 2w + 4.5 w\\P = 6.5w[/tex]
Thus, width in terms of perimeter is equal to
[tex]w = \frac{P}{6.5}[/tex]
Length in feet is equal to [tex]\frac{2P}{6.5}[/tex]
An equation was created for the line of best fit from the actual enrollment data. It was used to predict the dance studio enrollment values shown in the table below:
Analyze the data. Determine whether the equation that produced the predicted values represents a good line of best fit.
A. No, the equation is not a good fit because the sum of the residuals is a large number.
B. No, the equation is not a good fit because the residuals are all far from zero.
C. Yes, the equation is a good fit because the residuals are not all far from zero.
D. Yes, the equation is a good fit because the sum of the residuals is a small number.
Answer:
B. No, the equation is not a good fit because the sum of the residuals is far from zero. Should be your answer
Step-by-step explanation:
Have a nice day :)
No, the equation is not a good fit because the sum of the residuals is far from zero.
What is Equation?Two or more expressions with an Equal sign is called as Equation. An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
here, we have,
An equation was created for the line of best fit from the actual enrollment data. which was used to predict the dance studio enrollment values shown in the table.
We need to check whether the equation that produced the predicted values represents a good line of best fit.
No, the equation is not a good fit because the sum of the residuals is far from zero.
A line of best fit is meant to compensate for positive and negative deviation in a matter that balances them. A large residual values' sum shows that they are not balanced.
Hence, No, the equation is not a good fit because the sum of the residuals is far from zero.
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Consider the following data set:
7.8, 0.6, 1.9, 5, 5.7, 0.7, 1.6, 5.9
Work out the IQR.
Answer:
Population size:8
Lower quartile (xL): 0.925
Upper quartile (xU): 5.85
Interquartile range (xU-xL): 4.925
Step-by-step explanation:
Answer:
4.65
Step-by-step explanation:
7.8, 0.6, 1.9, 5, 5.7, 0.7, 1.6, 5.9
Sort the data
0.6, 0.7, 1.6, 1.9, 5, 5.7, 5.9, 7.8
Q1: (0.7+1.6)/2
= 1.15
Q3: (5.7+5.9)/2
= 5.8
IQR = 5.8 - 1.15
= 4.65
-9-(-4) what is the answer to this equation.
Answer:
-5
Step-by-step explanation:
Answer:
The answer is -5
Step-by-step explanation:
Between 0°C and 30°C, the volume V ( in cubic centimeters) of 1 kg of water at a temperature T is given approximately by the formula: V = 999.87 − 0.06426T + 0.0085043T² − 0.0000679T³ Find the temperature at which water has its maximum density.
Answer:
[tex]T \approx 3.967\,^{\textdegree}C[/tex]
Step-by-step explanation:
The density of water is given by the following definition:
[tex]\rho = \frac{m}{V(T)}[/tex]
[tex]\rho = \frac{1000\,g}{999.870.06426\cdot T + 0.0085043\cdot T^{2}-0.0000679\cdot T^{3}}[/tex]
The density is maximum when volume is minimum, which can be found by First and Second Derivative Tests:
First Derivative
[tex]V' = -0.06426 +0.0170086\cdot T -0.0002037\cdot T^{2}[/tex]
Second Derivative
[tex]V'' = 0.0170086 - 0.0004074\cdot T[/tex]
Critical values from the first derivative are:
[tex]T_{1} \approx 79.531\,^{\textdegree}C[/tex] (absolute maximum) and [tex]T_{2} \approx 3.967\,^{\textdegree}C[/tex] (absolute minimum).
The temperature at which water has its maximum density is:
[tex]T \approx 3.967\,^{\textdegree}C[/tex]
PROBLEM 1
Evaluate the expression 9 – z when z = 4.
What’s the answer
Answer:
[tex](9 - 4) \\ ( {3}^{2} - {2}^{2}) \\ (3 - 2)(3 + 2) \\ 1 \times 5 = 5 [/tex]
hope this helps you.
The average of a list of 4 numbers is 90. 0.A new list of 4 numbers has the same first 3 numbers as the original list, but the fourth numberin the list is 80, and the fourth number in the new list is 96. What is the average of this new list of numbers.
Answer:
New Average of New List = 87.5
Step-by-step explanation:
Average is the arithmetic mean (M) of observations.
M = ΣX / N
where ΣX = sum of all observations , N = number of observations
Given : M = 90 ; N = 40
M = ΣX / N
90 = ΣX / 4
ΣX = 90 x 4
ΣX = 360 [ Of Old List of 4 numbers ]
New ΣX of new list of 4th new number = Old ΣX - Old 4th No. + New 4th No.
New ΣX = 360 - 90 + 80
New ΣX = 350
New Average (Mean M) = New ΣX / N
New M = 350 / 4
New M = 87.5
A recipe called for using 2 6/8 cups of flour before baking the another 3 1/2 cups after baking what is the total amount for flour needed in the recipe
Final answer:
To calculate the total flour needed, simplify 2 6/8 cups to 2 3/4 cups and add it to 3 1/2 cups. Convert to a common denominator and sum up to get the total of 6 1/4 cups of flour.
Explanation:
To find the total amount of flour needed in the recipe, we will have to add the two quantities of flour given: 2 6/8 cups and 3 1/2 cups. First, we can simplify 2 6/8 cups to 2 3/4 cups by dividing the numerator by the denominator's GCD (Greatest Common Divisor), which is 2 in this case. Then, we can add the simplified amount to the 3 1/2 cups.
Adding the two amounts together, we have:
2 3/4 cups + 3 1/2 cups
= (2 + 3) + (3/4 + 1/2) cups
= 5 + (3/4 + 1/2) cups
To add fractions, we need a common denominator. Multiply the second fraction by 2/2 to get the same denominator:
5 + (3/4 + 2/4) cups
= 5 + (5/4) cups
= 5 + 1 1/4 cups
= 6 1/4 cups
Therefore, the total amount of flour needed for the recipe is 6 1/4 cups.
If 2^2х = 2^3, what is the value of х?
Answer:
19
Step-by-step explanation:
if x=3
Answer:
x = 2
Evaluate the powers.Divide both sides by 4. Solution should be x = 2(x+4y=5
- 1-2x + 5y = 16
Answer:
x,y( 27/13 ,43/13)
Step-by-step explanation:
x=5-4y
•1-2x+5y=16
1-2(5-4y)+5y=16
y=27/13
x=5-4y
x=5-4×27/13
x=-43/13
Find the value of 1/3 divided by 1/2
When dividing two fractions, it is important to know to multiply the first fraction by the reciprocal of the second fraction.
Reciprocal means basically a flipped fraction. 2/3 as a reciprocal is 3/2, etc.
1/3 / 1/2= 1/3 x 2/1=2/3
4/3 x 3.14 x 13^3
What is the answer
Answer:
(4/3) x 3.14 x (13^3) = 9198.1066666... (repeating decimal)
Step-by-step explanation:
The result of multiplication is: 4/3 x 3.14 x 13³ =9198.11.
Here, we have,
given that,
4/3 x 3.14 x 13³
now, we have to multiply the terms.
so, we get,
4/3 x 3.14 x 13³
=4/3 x 3.14 x 13 x 13 x 13
=4/3 x 3.14 x 2197
=4/3 x 6898.58
=27594.32 /3
=9198.11
Hence, The result of multiplication is: 4/3 x 3.14 x 13³ =9198.11.
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what is the perimeter of DEFG?
A, B, C or D
Given:
Given that the figure DEFG with vertices D(1,2), E(2,6), F(6,7) and G(5,3)
We need to determine the perimeter of DEFG.
The length of the sides can be determined using the formula,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Length of DE:
Substituting the coordinates D(1,2), E(2,6) in the formula, we get;
[tex]DE=\sqrt{(2-1)^2+(6-2)^2}[/tex]
[tex]DE=\sqrt{(1)^2+(4)^2}[/tex]
[tex]DE=\sqrt{17}[/tex]
Length of EF:
Substituting the coordinates E(2,6), F(6,7) in the formula, we get;
[tex]EF=\sqrt{(6-2)^2+(7-6)^2}[/tex]
[tex]EF=\sqrt{(4)^2+(1)^2}[/tex]
[tex]EF=\sqrt{17}[/tex]
Length of FG:
Substituting the coordinates F(6,7), G(5,3) in the formula, we get;
[tex]FG=\sqrt{(5-6)^2+(3-7)^2}[/tex]
[tex]FG=\sqrt{(-1)^2+(-4)^2}[/tex]
[tex]FG=\sqrt{17}[/tex]
Length of DG:
Substituting the coordinates D(1,2), G(5,3) in the formula, we get;
[tex]DG=\sqrt{(5-1)^2+(3-2)^2}[/tex]
[tex]DG=\sqrt{(4)^2+(1)^2}[/tex]
[tex]DG=\sqrt{17}[/tex]
Perimeter of DEFG:
The perimeter of DEFG can be determined by adding the side lengths DE, EF, FG and DG.
Thus, we have;
[tex]Perimeter=DE+EF+FG+DG[/tex]
Substituting the values, we have;
[tex]Perimeter=\sqrt{17}+\sqrt{17}+\sqrt{17}+\sqrt{17}[/tex]
[tex]Perimeter=4\sqrt{17}[/tex]
Thus, the perimeter of DEFG is 4√17
Hence, Option b is the correct answer.
Keith opened an investment account where he is paid 8% annual interest, compounded semi-annually. He wants to have $7,000 in the investment account in 3 years. What is the number of periods for this investment?
Answer:
6 periods
Step-by-step explanation:
The investment is compounded semi-annually which means it is compounded twice in a year. Period of investment is 3 years. So, number of periods compounded is 3 multiplied by 2 that is 6 periods.
Rate would be 8% divided by 2 that is 4%.
Initial investment can be calculated usinf spreadsheet function as =PV(rate,nper, pmt, FV)
Where,
rate is 0.04
nper is 6
pmt is 0
FV is 7,000
So, initial investment is $5,532.20.
It is negative as it is a cash outflow.
Solve for Y
Just checking my answer to see if I’m right,
Thx! :D
A triangle has a perimeter of 10.2 kilometers. Two of the sides measure 3.4 kilometers and 3.4 kilometers. What is the length of the third side?
Answer:
3.4
Step-by-step explanation:
3.4+3.4= 6.8
10.2-6.8=3.4
What percent of 300 is 51
Answer:
17
Step-by-step explanation:
300:51*100 =
(300*100):51 =
30000:51 = 588.24
Now we have: 300 is what percent of 51 = 588.24
Question: 300 is what percent of 51?
Percentage solution with steps:
Step 1: We make the assumption that 51 is 100% since it is our output value.
Step 2: We next represent the value we seek with $x$x.
Step 3: From step 1, it follows that $100\%=51$100%=51.
Step 4: In the same vein, $x\%=300$x%=300.
Step 5: This gives us a pair of simple equations:
$100\%=51(1)$100%=51(1).
$x\%=300(2)$x%=300(2).
Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have
$\frac{100\%}{x\%}=\frac{51}{300}$
100%
x%=
51
300
Step 7: Taking the inverse (or reciprocal) of both sides yields
$\frac{x\%}{100\%}=\frac{300}{51}$
x%
100%=
300
51
$\Rightarrow x=588.24\%$⇒x=588.24%
Therefore, 17% of 300 is 51
Answer:
Answer 17%
Step-by-step explanation:
Solution for 300 is what percent of 51:
300:51*100 =
(300*100):51 =
30000:51 = 588.24
588.24 as a percentage is 17%
I hoped this helped and remember to stay safe!!!Which of the following is NOT true of using the binomial probability distribution to test claims about a proportion? Choose the correct answer below. A. One requirement of this method is that npgreater than>5 and nqgreater than>5. B. In a left-tailed test, the P-value is the probability of getting x or fewer successes among the n trials. C. In a right-tailed test, the P-value is the probability of getting x or more successes among the n trials. D. This method uses the binomial probability distribution with the P-value method and uses the value of p assumed in the null hypothesis.
Answer:
The correct option is;
D. This method uses the binomial probability distribution with the P-value method ans uses the value of p assumed in the null hypothesis
Step-by-step explanation:
Here we have the binomial probability distribution is used to test claims about a proportion then the requirement is np > 5 and nq >5
In a left-tailed test, the P value is the probability of getting x or fewer successes among n trials while in a right tailed test, the P-value is the probability of getting x or more successes among n trials
However, the P-value where a binomial distribution is used to test a claim about a proportion is derived from the z score of the parameters of the statistic and not from the p assumed in the null hypothesis.
The incorrect statement is option B. A left-tailed test in binomial probability distribution does not correspond to the probability of getting x or fewer successes among n trials.
Explanation:The statement among the given options that is NOT true of using the binomial probability distribution for testing claims about a proportion is option B. A left-tailed test does not entail the probability of getting x or fewer successes in the n trials. Instead, it approximates the probability of observing a value as extreme as the test statistic or even more extreme, which leans to the left or lower end of the distribution. Thus, the P-value in a left-tailed test corresponds to the total probability of the shaded region of the curve that falls to the left of observed value or test statistic. The remainder of the options (A, C, and D) are accurate statements.
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Which statement is true about the values of the ones and tenths digit in 346.68? A. The value of the ones digit is 6 more then the value of the tenths digit. B. The value of the ones digit is the same as the value of the tenths digit. C. The value of the ones digit is 6 times as many as the value of the tenths digit. D. The value of the ones digit is 10 times as many as the value of the tenths digit,
Answer:
B. The value of the ones digit is the same as the value of the tenths digit.
Step-by-step explanation:
346.68
From the above digit, the value of one is 6 and the value of tenth is 6.
3 = hundred
4 = ten
6 = unit
6 = tenth
8 = hundredth
The unit is the same for ones.
From the above we can see that unit and tenth have the same value.
So, therefore, the answer is:
B. The value of the ones digit is the same as the value of the tenths digit.
HELP THIS IS DUE IN 5 MINSSSSS! Mr. Viviano would like to report to the principal the smaller measure of center between the mean and the median for the distribution of test scores of his AP Calculus class.
The test scores are as follows: 60, 65, 70, 75, 80, 80, 85, 85, 90, 95, 100.
What is the number that he will report?
Answer:
The median. 80 because the mean is 80.454545
Step-by-step explanation:
Bargain Bikes is having a 50%-off sale. The original price of the bicycle Gillian wants to buy is $72. Find 50% of $72.
50% is equivalent to the unit fraction
To find 50% of $72, divide 72 by
50% of $72 is
Answer:
50% is equivalent to the unit fraction .answer:1/2
To find 50% of $72, divide 72 by . answer: 2
50% of $72 is .answer: $36
Step-by-step explanation:
just answered :) good luck everyone
The sales price of the Bikes are obtained by finding the percent value as $36.
What is percentage?A percentage is a value that indicates 100th part of any quantity. It can be converted into a fraction or a decimal by dividing it by 100. The percent value is useful in representing the large data into a two digit number.
The sales percent is given as 505
And, the original price is $72.
The value of sales price is given as follows,
50% × Original price
⇒ 50/100 × 72
⇒ 1/2 × 72
⇒ 36
Hence, the sales price is obtained as $36.
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A bucket contains five green tennis balls, two yellow tennis balls, six red tennis balls, and eight blue tennis balls. Tony removes for tennis balls, without replacement from the bucket shown. What is the probability that Tony removes one yellow, one green ,one blue,and then one more blue tennis ball?
Answer:
The probability that Tony removes one yellow, one green ,one blue,and then one more blue tennis ball is 0.0039.
Step-by-step explanation:
We are given that a bucket contains five green tennis balls, two yellow tennis balls, six red tennis balls, and eight blue tennis balls.
As we know that, Probability of an event = [tex]\frac{\text{Favorable number of outcomes}}{\text{Total number of outcomes}}[/tex]
Number of green tennis balls = 5
Number of yellow tennis balls = 2
Number of red tennis balls = 6
Number of blue tennis balls = 8
Total number of tennis balls = 5 + 2 + 6 + 8 = 21
{Now it should be notes that Tony removes for tennis balls, without replacement from the bucket means that every time the total number of remaining balls available for selecting will be one less}.
Now, Probability that Tony removes one yellow = [tex]\frac{2}{21}[/tex]
Probability that Tony removes one green = [tex]\frac{5}{20}[/tex]
Probability that Tony removes one blue = [tex]\frac{8}{19}[/tex]
Probability that Tony removes one blue again = [tex]\frac{7}{18}[/tex]
SO, final probability is = [tex]\frac{2}{21} \times \frac{5}{20} \times \frac{8}{19} \times \frac{7}{18}[/tex]
= [tex]\frac{2}{513}[/tex]
= 0.0039