Answer:
Step-by-step explanation:
Hello, just apply the instructions as below.
[tex]3(x-2)^2(x+5)^3[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Suppose that three computer boards in a production run of forty are defective. A sample of five is to be selected to be checked for defects.
a. How many different samples can be chosen?
b. How many samples will contain at least one defective board?
c. What is the probability that a randomly chosen sample of five contains at least one defective board?
Answer:
(a) 658,008 different samples can be chosen.
(b) 222,111 samples will contain at least one defective board.
(c) The probability that a randomly chosen sample of five contains at least one defective board is 0.34.
Step-by-step explanation:
We are given that three computer boards in a production run of forty are defective. A sample of five is to be selected to be checked for defects.
(a) To find how many different samples can be chosen, we will use a combination formula here because the order of selecting a sample of 5 from the production run of 40 doesn't matter.
Here, n = total sample = 40 and r = selected sample = 5
So, the combination formula is; [tex]^{n}C_r= \frac{n!}{r! \times (n-r)!}[/tex]
[tex]^{40}C_5= \frac{40!}{5! \times (40-5)!}[/tex]
[tex]^{40}C_5= \frac{40!}{5! \times 35!}[/tex]
[tex]^{40}C_5[/tex] = 658,008 ways
So, 658,008 different samples can be chosen.
(b) To find how many samples will contain at least one defective board, we will first find how many samples will contain no or 0 defective board.
For this also, we will use a combination where n = 40 - 3 = 37 non-defective computer board and a sample of r = 5 computer boards.
So, [tex]^{n}C_r= \frac{n!}{r! \times (n-r)!}[/tex]
[tex]^{37}C_5= \frac{37!}{5! \times (37-5)!}[/tex]
[tex]^{37}C_5= \frac{37!}{5! \times 32!}[/tex]
[tex]^{37}C_5[/tex] = 435,897 ways
This means that 435,897 of the 658,008 samples will contain no defective board.
Now, the samples that will contain at least one defective board = Total samples - Samples that contain no defective board
= 658,008- 435, 897
= 222,111
(c) The probability that a randomly chosen sample of five contains at least one defective board is given by;
Required Probability = [tex]\frac{222,111}{658,008}[/tex]
= 0.34 or 34%
Find the missing probability. P(A)=7/20,P(A∪B)=191/400,P(A∩B)=49/400 ,P(B)=? A. 7/8 B. 1/4 C. 117/400 D. 19/40
Answer:
B
Step-by-step explanation:
P(AUB)=P(A)+P(B)-P(A∩B)
191/400=7/20+P(B)-49/400
P(B)=191/400+49/400-7/20=240/400-7/20=12/20-7/20=5/20=1/4
The value of P(B) is 1/4.
What is probability?The probability is defined as the possibility of an event is equal to the ratio of the number of favorable outcomes and the total number of outcomes.
For an experiment having q number of outcomes, the number of favorable outcomes can be denoted by p. The formula to calculate the probability of an event is as follows:
Probability(Event) = Favorable Outcomes/Total Outcomes = p/q
Given data as :
P(A) = 7/20,
P(A∪B) = 191/400,
P(A∩B) = 49/400 ,
P(AUB) = P(A) + P(B) - P(A∩B)
Substitute the values of P(A), P(A∪B) and P(A∩B) in formula,
191/400 = 7/20 + P(B) - 49/400
Rearrange the terms in the equation,
P(B) = 191/400 + 49/400 - 7/20
P(B) = 240/400 - 7/20
P(B) = 12/20 - 7/20
P(B) = 5/20
P(B) = 1/4
Hence, the value of P(B) is 1/4.
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You plan to conduct a marketing experiment in which students are to taste one of two different brands of soft drink. Their task is to correctly identify the brand tasted. You select a random sample of 200 students and assume that the students have no ability to distinguish between the two brands. The probability is 90% that the sample percentage is contained within what symmetrical limits of the population percentage
Answer:
the probability is 90% that the sample percentage is contained within 45.5% and 54.5% symmetric limits of the population percentage.
Step-by-step explanation:
From the given information:
Sample size n = 200
The standard deviation for a sampling distribution for two brands are equally likely because the individual has no ability to discriminate between the two soft drinks.
∴
The population proportion [tex]p_o[/tex] = 1/2 = 0.5
NOW;
[tex]\sigma _p = \sqrt{\dfrac{p_o(1-p_o)}{n}}[/tex]
[tex]\sigma _p = \sqrt{\dfrac{0.5(1-0.5)}{200}}[/tex]
[tex]\sigma _p = \sqrt{\dfrac{0.5(0.5)}{200}}[/tex]
[tex]\sigma _p = \sqrt{\dfrac{0.25}{200}}[/tex]
[tex]\sigma _p = \sqrt{0.00125}[/tex]
[tex]\sigma _p = 0.035355[/tex]
However, in order to determine the symmetrical limits of the population percentage given that the z probability is 90%.
we use the Excel function as computed as follows in order to determine the z probability = NORMSINV (0.9)
z value = 1.281552
Now the symmetrical limits of the population percentage can be determined as: ( 1.28, -1.28)
[tex]1.28 = \dfrac{X - 0.5}{0.035355}[/tex]
1.28 × 0.035355 = X - 0.5
0.0452544= X - 0.5
0.0452544 + 0.5 = X
0.5452544 = X
X [tex]\approx[/tex] 0.545
X = 54.5%
[tex]-1.28 = \dfrac{X - 0.5}{0.035355}[/tex]
- 1.28 × 0.035355 = X - 0.5
- 0.0452544= X - 0.5
- 0.0452544 + 0.5 = X
0.4547456 = X
X [tex]\approx[/tex] 0.455
X = 45.5%
Therefore , we can conclude that the probability is 90% that the sample percentage is contained within 45.5% and 54.5% symmetric limits of the population percentage.
what is 90.125 written in expanded from?
Answer:
The answer is 90+0+0.1+0.02+0.005.
Step-by-step explanation:
The reason for my answer is because 90 is in the tens place. 90+0 is equal to 90 so that's why it is a +0 after the 90. Now, we have a decimal. After the decimal, we have 125. It is +0.1 because the 1 in 90.125 is in the tenths place. Next, it is +0.02 because the 2 in 90.125 is in the hundredths place. Last but not least, it is +0.005 because the 5 in 90.125 is in the thousandths place.
Solve for x: 7 > x/4
Answer: x < 28
Step-by-step explanation:
Each cylinder is 12 cm high with a diameter of 8 cm.
Calculate the volume of each cylinder.
Use 3 as a value for π
Give your answer using the correct units.
Answer:
Volume = 576cm^3Step-by-step explanation:
[tex]h = 12 cm\\d = 8cm\\r =d/2 = 8/2 =4\\V = ?\\V =\pi r^2h\\\\V= 3 \times 4^2\times12\\V = 576 cm^3[/tex]
Alex has to pay his car insurance twice a year. Each Payment is 312. How much money should Alex budget for his insurance each month?
Answer:
$52
Step-by-step explanation:
$52. Since Alex pays for car insurance twice a year, divide the cost of each payment by 6, the number of months in half a year. This will tell you how much money Alex needs to set aside each month to cover his insurance costs.
312÷6=52
Jessica just bought a refrigerator for $799. She paid $79.80 in a down payment and will pay the rest in 4 equal installments. How much does she need to pay for each installment?
Answer:
$179.80
Step-by-step explanation:
799-79.80=719. That's the down payment subtracted from the total price of the refrigerator. 719/4, since there's four equal installments, gives you 179.8. Since cents go in 10s, you make it 179.80 and slap a dollar sign in front of that.
For lunch, Kile can eat a sandwich with either ham or a bologna and with or without cheese. Kile also has the choice of drinking water or juice with his sandwich. The total number of lunches Kile can choose is
Answer:
8
Step-by-step explanation:
Ham with or without cheese-2 choices
Bologna with or without cheese-2 choices
Bologna with cheese with water or juice-2 choices
Bologna without cheese with juice or water-2 choices
Ham with cheese with juice or water -2 choices
Ham without cheese with juice or water -2 choices
2+2+2+2=8
Kile has 8 choices for lunch
A researcher is interested in determining whether various stimulant drugs improve maze leaming performance in rats. To find out, the researcher recruits 16 rats and assigns 4 rats to one of 4 research conditions: caffeine, nicotine, cocaine, placebo. Each rat completes the maze once and in only one research condition and is timed; time to complete the maze is the researcher's measure of performance. Answer the following questions considering the data below (alpha)
Caffeine Nicotine Cocaine Placebo
30.00 45.00 30.00 60.00
45.00 75.00 30.00 75.00
45.00 60.00 60,00 60.00
45.00 45.00 30.00
What is the dependent variable in this study?
a. Drug condition
b. Time to complete maze
c. Number of rats
d. Research conditions
16. What analysis should be used to answer the researcher's question?
a. One-way between-subjects (a.ka. independent-samples) ANOVA
b. One-way within-subjects (a.k.a. dependent-samples, repeated-measures) ANOVA
c. Factorial ANOVA
d. T-test 17.
What is the Null hypothesis for this analysis?
a. There will be no difference between any group means
b. Maze performance will get worse with stimulants
c. Maze performance of at least one group will differ from typing of at least one other group
d. Maze performance on placebo will be worse than on all drugs
What are the degrees of freedom for the numerator of the F-ratio?
2
3
8
11
What are the degrees of freedom for the denominator of the F-ratio?
2
3
8
11
What is the critical F value for this analysis?
a. 3.49
b. 4.07
c. 6.04
d. 19.00
What is the SSbetween-groups value?
a. 425.00
b. 1181.25
c. 2517.19
d. 3698.44
What is the SSwithin value?
Answer:
1) The dependent variable is : time to complete the maze
2) The analysis used should be : One -way within-subjects ANOVA ( B )
3) Null hypothesis is ; There will be no difference between any group means
4) Degrees of freedom for the numerator of the F-ratio ; 4 - 1 = 3
5) degree of freedom for the denominator = 11
6) critical F value = 3.49
Step-by-step explanation:
The dependent variable is the time to complete the maze this is because the time depends on the effects of the stimulant drugs on the rats in the maze .
The analysis used should be : One -way within-subjects ANOVA ( B )
Null hypothesis is ; There will be no difference between any group means
Degrees of freedom for the numerator of the F-ratio ; 4 - 1 = 3
degree of freedom for the denominator = N - k = 16 - 4 = 12. the closest answer from the options is 11
The critical value is 3.49 ,because at degree of freedom = 12 , ∝ = 0.05, and Dfn = 3, from the F - table the critical value would be 3.49
Students at the Akademia Podlaka conducted an experiment to determine whether the Belgium-minted Euro coin was equally likely to land heads up or tails up. Coins were spun on a smooth surface, and in 350 spins, 163 landed with the heads side up. Should the students interpret this result as convincing evidence that the proportion of the time the coin would land heads is not 0.5?
Complete question is;
Students at the Akademia Podlaka conducted an experiment to determine whether the Belgium-minted Euro coin was equally likely to land heads up or tails up. Coins were spun on a smooth surface, and in 350 spins, 163 landed with the heads side up. Should the students interpret this result as convincing evidence that the proportion of the time the coin would land heads is not 0.5?
Test the relevant hypotheses using α = 0.01
Answer:
The Test result doesn't support the claim that proportion of the time the coin would land heads is not 0.5. Rather it supports the the probability to be 0.5. So the students shouldn't interpret this result as convincing evidence that the proportion of the time the coin would land heads is not 0.5
Step-by-step explanation:
The hypotheses would be;
Null hypothesis; H0: p = 0.5
Alternative hypothesis; Ha: p ≠ 0.5
We are given, X = 163 and n = 350
Thus; p^ = X/n = 163/350 = 0.4657
Since we are not given standard deviation, we will use test statistic formula;
Z = (p^ - p)/(√(p(1 - p)/n)
Z = (0.4657 - 0.5)/(√(0.5(1 - 0.5)/350)
Z = -1.28
From online P-value from T-score calculator as attached, we have;
p-value = 0.201395.
Since the p-value is > 0.01, it's not significant and so we will fail to reject the null hypothesis H0.
We will conclude that the Test result supports the conclusion that p = 0.5
solve 3/4x+5=-9 please
Answer:
exact form: x=-56/3
mixed number form: -18 2/3
Solve for x by simplifying both sides of the equation, then isolating the variable.
Hi I need help with 800×200= 8 × ______ hundreds=_____ Hundreds = _______ plz help me
Answer:
800×200= 8 × 200 hundreds= 1600 Hundreds = 160000
Which of the following relations is a function? A. (1, 4), (-4, 2), (8, 1), (-8, 2) B. (1, 4), (-4, 6), (1, 3), (-8, 2) C. (1, 0), (-4, 3), (8, 1), (-4, 5) D. (8, 1), (-4, 4), (1, 1), (8, 2)
Answer:
A. (1, 4), (-4, 2), (8, 1), (-8, 2)
Step-by-step explanation:
Each x goes to only 1 y to be a function
A. (1, 4), (-4, 2), (8, 1), (-8, 2)
function
B. (1, 4), (-4, 6), (1, 3), (-8, 2)
1 goes to 4 and 3 so not a function
C. (1, 0), (-4, 3), (8, 1), (-4, 5)
-4 goes to 3 and 5 so not a function
D. (8, 1), (-4, 4), (1, 1), (8, 2)
8 goes to 1 and 2 so not a function
Answer:
[tex]\Large \boxed{\mathrm{A. \ (1, 4), (-4, 2), (8, 1), (-8, 2)}}[/tex]
Step-by-step explanation:
[tex]\sf A \ function \ is \ a \ relation \ if \ each \ x \ value \ is \ for \ each \ y \ value.[/tex]
[tex](1, 4), (-4, 2), (8, 1), (-8, 2) \ \sf represents \ a \ function.[/tex]
[tex](1, 4), (-4, 6), (1, 3), (-8, 2) \ \sf does \ not \ represent \ a \ function.[/tex]
[tex](1, 0), (-4, 3), (8, 1), (-4, 5) \ \sf does \ not \ represent \ a \ function.[/tex]
[tex](8, 1), (-4, 4), (1, 1), (8, 2) \ \sf does \ not \ represent \ a \ function.[/tex]
PICK AN ANSWER!!! BRAINLIEST IF RIGHT
Answer:
Hey there!
This is an obtuse isosceles, because two sides are congruent, and one angle is greater than 90 degrees.
Let me know if this helps :)
Answer:
[tex]\Large \boxed{\mathrm{C. \ obtuse \ isosceles }}[/tex]
Step-by-step explanation:
An isosceles triangle has two equal angles. This triangle has two base angles equal.
An obtuse triangle has an angle measuring greater than 90 degrees. This triangle has an angle measuring 136 degrees.
This triangle is an obtuse isosceles triangle.
Given the exponential growth function f(x)=87(1.02)^x
What is the initial value of the function? _____
What is the growth factor, or growth rate of the function (as a percent)? _____%
Answer:
87; 2%
Step-by-step explanation:
An exponential growth model is defined as :
F(x) = A( 1 + r)^x
Where;
A = Initial amount,
r = rate of increase
x = time
Comparing the exponential growth function with the exponential growth model given;
f(x)=87(1.02)^x
A = 87 = Initial amount
The growth rate of the model expressed as a percentage :
Taking :
(1 + r) = 1.02
1 + r = 1.02
r = 1.02 - 1
r = 0.02
Expressing r as a percentage :
0.02 * 100% = 2%
1 rabbit saw 9 elephants while going to the river. Every elephant saw 3 monkeys going to the river. Each monkey had 1 tortoise in each hand.
How many animals were going to the river?
Answer:
91 animals
Step-by-step explanation:
Because every elephant saw 3 monkeys, there were 9 * 3 = 27 monkeys and because every monkey had 1 tortoise in each hand and we know that monkeys have 2 hands, there were 27 * 2 = 54 tortoises. To find the total number of animals that were going to the river, we can calculate 1 + 9 + 27 + 54 = 91 animals.
Answer:
10
Step-by-step explanation:
Only the rabbit and the 3 monkeys are described as going to the river. The tortoises seem to be going to the river by virtue of being taken there by the monkeys. Those on the path to the river were ...
1 rabbit
3 monkeys
6 tortoises
A total of 10 animals.
Find the next three terms in the sequence 4, 16, 36, 64, 100, ...
Answer:
144 196 256
. .............
Please help answer the following questions!!! :D I will do anything in return!
Joe drove 315 miles on 15 gallons of gas. What is his mileage in miles/gallon?
miles/gallon
Answer:
21 miles/gallon
Step-by-step explanation:
To find his mileage in miles/gallon, divide the number of miles by the number of gallons.
315/15
= 21
= 21 miles/gallon
Answer:
21 miles / gallon
Step-by-step explanation:
Take the miles and divide by the gallons
315 miles / 15 gallons
21 miles / gallon
Which statements are true?
Answer:
Step-by-step explanation:
The first statement is true. We use 4 as the base and 3.33 as the exponent, obtaining 101.
The second statement is true. Using 2 as the base and 6.15 as the exponent, we get 71.01, or approximately 71.
Third statement: 3^4.14 = 94.47, which is NOT equal to 24. False
Fourth statement: Raise the base (5) to the power 2.60, obtaining 65.66, or approximately 66. True
Fifth statement: Raise the base (6) to the power 0.17, obtaining 1.36. This does not match the '11' given. False
You have worked these hours this week: 5 4/5, 6 1/3, 8 2/5, 4 2/3. How many hours did you work
1472 minutes
OR
24 hours and 32 minutes
OR
1 day and 32 minutes
OR
1 day, half an hour, and 2 minutes
Using the addition operator, the total number of hours worked this week would be 26.65 hours
Given the work hours thus :
Converting to improper fraction :
29/4 + 19/3 + 42/5 + 14/3Taking the L. C. M ; = 60
(435 + 380 + 504 + 280) / 60
= 1599 / 60
= 26.65 hours.
Hence, total hours worked would be 26.65 hours.
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3/4=x/20,find the value of 'x'
Answer:
[tex]\boxed{x=15}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4} =\frac{x}{20}[/tex]
[tex]\sf Cross \ multiply.[/tex]
[tex]4 \cdot x = 20 \cdot 3[/tex]
[tex]4x=60[/tex]
[tex]\sf Divide \ both \ sides \ by \ 4.[/tex]
[tex]\frac{4x}{4} =\frac{60}{4}[/tex]
[tex]x=15[/tex]
when graphed on a coordinate plane , point a and point b are reflections across the x-axis. Point a is located at (5, 2). Which ordered pair describes the location of point b
Answer:
Point b has coordinates (5, -2)
Step-by-step explanation:
If point a has coordinates (5, 2) then its reflection across the x axis would have the same value for the x-coordinate, and exactly opposite value for the y-coordinate (that is y-coordinate = -2.
then point's a reflection is: (5, -2)
since its reflection is point b then point b has this coordinates.
The sum of two numbers is 15. One number is 101 less than the other. Find the numbers.
Answer:
The numbers:
-43 and 58
Step-by-step explanation:
a + b = 15
a = b - 101
then:
(b-101) + b = 15
2b = 15+101
2b = 116
b = 116/2
b = 58
a = b - 101
a = 58 - 101
a = -43
Check:
a + b = 15
-43 + 58 = 15
Adrianna has a court to play basketball with her friends.
The it is 600 square feet. It is 30 feet long. How many feet across is
court?
Answer:
Hey there!
The area of a rectangle is the length times width.
Thus, we can write the equation, 600=30w.
Solving for the width, we get that the width is equal to 20 ft.
Let me know if this helps :)
Answer:
20 feet across.
Step-by-step explanation:
You will have to do a simple equation solve.
x is how many feet across the court is.
* could be our multiplying sign
600 = 30*x
Now divide 30 on both sides. 30 will cross out (since 30/30 is 1 and anything times 1 is the same number as it was before) on the right side and 600/30 is 20 so we change the 600 to 20.
That leaves 20 = x.
So it is 20 feet across.
If the sides of a square measure 9.3 units the.find the length of the diagonal
Answer:
Approximately 13.1521 units.
Step-by-step explanation:
To find the diagonal, we can use the Pythagorean Theorem.
Since the figure is a square, all four sides are equivalent. A square also has four right angles. Therefore, we can use the Pythagorean Theorem to find the diagonal d. Therefore:
[tex]a^2+b^2=c^2[/tex]
Substitute 9.3 for a and b, and let c equal d:
[tex](9.3)^2+(9.3)^2=d^2[/tex]
Instead of squaring, add the like-terms:
[tex]2(9.3)^2=d^2[/tex]
Take the square root of both sides:
[tex]d=\sqrt{2(9.3)^2}[/tex]
Expand:
[tex]d=\sqrt{2}\cdot\sqrt{(9.3)^2}[/tex]
The right cancels:
[tex]d=\sqrt2\cdot(9.3)\\d=9.3\sqrt2\\d\approx13.1521\text{ units}[/tex]
Please help me how to do no 5
Answer:
-864
Step-by-step explanation:
The determinant of a matrix product is the product of the determinants. The determinant of a transpose is the same as the determinant of the original. Hence ...
[tex]|AB^5C^T|=(4)(-2)^5(\frac{1}{4})=-32[/tex]
The multiplication of an n×n matrix by a scalar 'a' multiplies its determinant by a^n, so the desired determinant is ...
[tex]|3AB^5C^T|=3^3(-32) = \boxed{-864}[/tex]
Kevin's total payroll deductions are 30% of his earnings. If his deductions add up to $369 for a two week period, how much were his earnings for the period?
Answer:
His earnings for the period= $123
Step-by-step explanation:
Kevin's total payroll deductions are 30% of his earnings. His deductions add up to $369 for a two week period.
If 30% of his earnings = $369
His earnings = x
30/100 * x= 369
X= 369*100/30
X= 123*10
X=$ 1230
His earnings for the period= $123
In the adjoining figure, in ΔABC, D is the midpoint of the side BC.Hence a) AD is ___________ A b) AM is ____________ c) Is BD = DC please help!!!!!!!!!!!!!!
Answer:
a) AD is Median
b) AM is Perpendicular Bisector
Step-by-step explanation:
c) Yes because the Median divides the line into two equal parts