Answer:
The mean is [tex]\mu = 2.1[/tex]
Step-by-step explanation:
The mean number of employees calling sick per day can be mathematically represented as
[tex]\mu = 0* 0.05 + 1 * 0.40 + 2 * 0.3 + 3 * 0.3 + 4*0.05[/tex]
[tex]\mu = 2.1[/tex]
what is the product? (4x)(-3x^8)(-7x^3)
1. -84x^12
2. -84x^24
3. 84x^12
4. 84x^24
Answer:
84 x^12
Step-by-step explanation:
(4x)(-3x^8)(-7x^3)
Multiply the numbers
4*-3 *-7 = 84
x* x^8 * x^3 = Add the exponents = x^(1+8+3) = x^12
84 x^12
Answer:
C. 84x^12
Step-by-step explanation:
edge 2020
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. P(X≤2), n=5, p=0.8
Answer:
0.0579
Step-by-step explanation:
P(X≤2) = P(X=0) + P(X=1) + P(X=2)
P(X≤2) = ₅C₀ (0.8)⁰ (0.2)⁵ + ₅C₁ (0.8)¹ (0.2)⁴ + ₅C₂ (0.8)² (0.2)³
P(X≤2) = 0.00032 + 0.0064 + 0.0512
P(X≤2) = 0.0579
Probability of obtaining a success is 0.0579 .
Here,
Binomial distribution formula:
P(x:n,p) = nCx px (1-p)n-x Or P(x:n,p) = nCx px (q)n-x
Substituting the values of n and p
n = 5
p = 0.8
So,
P(X≤2) = P(X=0) + P(X=1) + P(X=2)
P(X≤2) = ₅C₀ (0.8)⁰ (0.2)⁵ + ₅C₁ (0.8)¹ (0.2)⁴ + ₅C₂ (0.8)² (0.2)³
P(X≤2) = 0.00032 + 0.0064 + 0.0512
P(X≤2) = 0.0579
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An equilateral triangle has an altitude of 4.8in. What are the length of the sides? Round to the nearest tenth.
Answer:
5.5 in
Step-by-step explanation:
The altitude is (√3)/2 times the length of a side, so the side length is the inverse of that times the length of the altitude:
side length = (2/√3)(4.8 in) ≈ 5.5 in
finding angle measures between intersecting lines.
Answer:
56
Step-by-step explanation:
to find x u add 60 and 64 which is 124
the total is 180 so u would subtract 180 by 124
hope this helps
Please answer this correctly
Answer:
1/2 (simplified)
Step-by-step explanation:
6 numbers (that's the total probability) --> 6 denominator
3 are odd (odd numbers in the probability) --> 3 numerator
so => 3/6
--> simplify
1/2
Hope this helps!
Can someone answer this question for me pleas?
Answer:
Step-by-step explanation:
The justification of each given statements in the question are:
11) F. Definition of right angle.
12) D. Definition of supplementary <'s.
13) A. Definition of congruence.
14) C. Definition of complementary <'s.
15) L. Congruent supplementary theorem
16) H. Vertical angle theorem.
17) G. Angle addition postulate.
18) J. Supplementary theorem.
4. Rational, irrational (4 points) (1) (2 points) Prove or disprove that if x y is an irrational number, then x or y is also an irrational number. (2) (2 points) Prove that if x 2 is irrational, then x is irrational. (Hint: try a proof by contrapositive)
Answer:
See explanation below
Step-by-step explanation:
1) Prove or disprove that if [tex] x^y[/tex] is an irrational number, then x or y is also an irrational number.
Let's take the following instances:
i) When x= 2 and y=[tex] \sqrt{2} [/tex] we have: [tex] 2^\sqrt^{^2^} [/tex]
ii) When [tex] x=2\sqrt{2} [/tex] and y=3, we have: [tex] (x=2\sqrt{2})^3 [/tex]
iii) When [tex] x=2\sqrt{2} [/tex] and [tex] y = \sqrt{2}[/tex], we have: [tex] (2\sqrt{2})^\sqrt^{^2^}[/tex]
It is proven because, in scenario
i) x is rational and y is irrational
ii) x is irrational and y is rational
iii) x and y are irrational
2) Prove tha x² is irrational, then x is irrational.
Use contradiction here.
Thus, x² is irrational and x is rational.
[tex] x =\frac{b}{a} [/tex] when x is rational, a & b are integers.
Therefore, [tex] x^2 =\frac{b^2}{a^2} [/tex]. This x² is rational.
This contradicts the statement that x² is irrational.
Therefore, if x² is irrational, x is also irrational.
a circle with radius of 1 cm sits inside a 11 cm x 12 cm rectangle.
Answer:
125.72
Step-by-step explanation:
radius equals pi(r)2
rectangle equals b times h
radius is 6.28
rectangle is 132
you now subtract them
132 minus 6.28 which is 125.72
hope this helps
Answer:
No the other answer is wrong, I just did it, this is the right answer for sure, I will give it right after you subscibe to Iconic Cooking, here is the answer...
Step-by-step explanation:
128.86
The function yp=3x2+4x is a particular solution to the nonhomogeneous equation y′′−6y′+9y=27x2−18 Find the general solution of the nonhomogeneous equation y′′−6y′+9y=27x2−18. (Hint: you need yc.)
Answer:
[tex]y(x)==(c_1+c_2x)e^{3x}+3x^2+4x[/tex]
Step-by-step explanation:
We are given that non-homogeneous equation
[tex]y''-6y'+9y=27x^2-18[/tex]
Particular solution of given equation is given by
[tex]y_p=3x^2+4x[/tex]
We have to find the general solution of the non-homogeneous equation.
Auxillary equation
[tex]m^2-6m+9=0[/tex]
[tex]m^2-3m-3m+9=0[/tex]
[tex]m(m-3)-3(m-3)=0[/tex]
[tex](m-3)(m-3)=0[/tex]
[tex]m=3,3[/tex]
[tex]y_c=(c_1+c_2x)e^{3x}[/tex]
General solution is given by
[tex]y(x)=y_c+y_p[/tex]
[tex]y(x)==(c_1+c_2x)e^{3x}+3x^2+4x[/tex]
Which is equivalent to 3/8*1/4x
Answer:
9 1/2
Step-by-step explanation:
Answer:
[tex]\frac{3x}{32}[/tex]
Step-by-step explanation:
[tex]\frac{3}{8}\times \frac{1}{4}x[/tex]
[tex]\frac{3\times \:1\times \:x}{8\times \:4}[/tex]
[tex]=\frac{3x}{32}[/tex]
The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 228 customers on the number of hours cars are parked and the amount they are charged.
Number of Hours Frequency Amount Charged
1 21 $4
2 36 6
3 53 9
4 40 13
5 22 14
6 11 16
7 9 18
8 36 22
228
A. Convert the information on the number of hours parked to a probability distribution. Is this a discrete or a continuous probability distribution?
B. Find the mean and the standard deviation of the number of hours parked. How would you answer the question: How long is a typical customer parked?
C. Find the mean and the standard deviation of the amount charged.
Answer: A. This is a discrete probability distribution.
hours probability
1 0.09
2 0.16
3 0.23
4 0.17
5 0.09
6 0.05
7 0.04
8 0.16
B. E(X) = 4.12; σ = 2.21
C. μ = 12.75; s = 6.11
Step-by-step explanation: Probability Distribution is an equation or table linking each outcome of an experiment with its probability of ocurrence. For this case, since the experiment is performed a high number of times and in a long run, the relative frequency of the event is its probability. Therefore:
A. To convert to a probability distribution, find the probability through the frequency by doing:
Hour 1
P(X) = [tex]\frac{21}{228}[/tex] = 0.09
Hour 2
P(X) = [tex]\frac{36}{228}[/tex] = 0.16
Hour 3
P(X) = [tex]\frac{53}{228}[/tex] = 0.23
Hour 4
P(X) = [tex]\frac{40}{228}[/tex] = 0.17
Hour 5
P(X) = [tex]\frac{22}{228}[/tex] = 0.09
Hour 6
P(X) = [tex]\frac{11}{228}[/tex] = 0.05
Hour 7
P(X) = [tex]\frac{9}{228}[/tex] = 0.04
Hour 8
P(X) = [tex]\frac{36}{228}[/tex] = 0.16
The table will be:
hours probability
1 0.09
2 0.16
3 0.23
4 0.17
5 0.09
6 0.05
7 0.04
8 0.16
This is a discrete distribution because it lists all the possible values that the discrete variable can be and its associated probabilities.
B. Mean for a probability distribution is calculated as:
E(X) = ∑[[tex]x_{i}[/tex].P([tex]x_{i}[/tex])]
E(X) = 1*0.09 + 2*0.16+3*0.23+4*0.17+5*0.09+6*0.05+7*0.04+8*0.16
E(X) = 4.12
Standard Deviation is:
σ = √∑{[x - E(x)]² . P(x)}
σ = [tex]\sqrt{(1-4.12)^{2}*0.09 + (2-4.12)^{2}*0.16 + ... + (7-4.12)^{2}*0.04 + (8-4.12)^{2}*0.16}[/tex]
σ = [tex]\sqrt{4.87}[/tex]
σ = 2.21
The average number of hours parked is approximately 4h with a standard deviation of approximately 2 hours, which means that a typical costumer parks between 2 to 6 hours.
C. Mean for a sample is given by: μ = ∑[tex]\frac{x_{i}}{n}[/tex] , which is this case is:
μ = [tex]\frac{4+6+9+13+14+16+18+22}{8}[/tex]
μ = 12.75
Standard Deviation of a sample: s = √[tex]\frac{1}{n-1}[/tex]∑([tex]x_{i}[/tex] - μ)²
s = [tex]\sqrt{ \frac{(4-12.75)^{2} + (6-12.74)^{2} + ... + (18-12.75)^{2} + (22-12.75)^{2} }{8-1}}[/tex]
s = 6.11
The average amount charged is 12.75±6.11.
An Undergraduate Study Committee of 6 members at a major university is to be formed from a pool of faculty of 18 men and 6 women. If the committee members are chosen randomly, what is the probability that precisely half of the members will be women?
Answer:
5/33649= approx 0.00015
Step-by-step explanation:
Total number of outcomes are C24 6= 24!/(24-6)!/6!=19*20*21*22*23*24/(2*3*4*5*6)= 19*14*22*23
Half of the Committee =3 persons. That mens that number of the women in Commettee=3. 3 women from 6 can be elected C6 3 ways ( outputs)=
6!/3!/3!=4*5*6*/2/3=20
So the probability that 3 members of the commettee are women is
P(women=3)= 20/(19*14*22*23)=5/(77*19*23)=5/33649=approx 0.00015
The probability that precisely half of the members will be women is;
P(3 women) = 0.1213
This question will be solved by hypergeometric distribution which has the formula;
P(x) = [S_C_s × (N - S)_C_(n - s)]/(NC_n)
where;
S is success from population
s is success from sample
N is population size
n is sample size
We are give;
s = 3 women (which is precisely half of the members selected)
S = 6 women
N = 24 men and women
n = 6 people selected
Thus;
P(3 women) = (⁶C₃ * ⁽¹⁸⁾C₍₃₎)/(²⁴C₆)
P(3 women) = (20 * 816)/134596
P(3 women) = 0.1213
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Owen gets paid $280 per week plus 5% commission on all sales for selling electronic equipment. If he sells d dollar worth of electronic equipment in one week, which algebraic expression represents the amount of money he will earn in weeks?a. (2800 + 5)w b. 280 +0.05dw c. (280+ 0.050d)w d. 280w +0.050d
Answer:
c. (280+ 0.050d)w
Step-by-step explanation:
Owen gets paid $280 per week
=$280 per week
Plus 5% commission on all sales of electronic equipment
=0.05
If he sells the dollar(d) worth of electronic equipment in one week
=(0.05d)w
Total earnings
=280w+0.05(d)w
Factorise
=(280+0.05d)w
Owen=(280+0.05d)w
c. (280+ 0.050d)w
*0.050=0.05
3. Factor the expression.
d2 + 120 + 36
A (d + 6)2
B (d - 36)(0 - 1)
OC (d - 6)2
D (d + 6)(d - 6)
Answer:
The complete factored form of this equation is (d + 6)²
Step-by-step explanation:
The first step in factoring this equation is multiply the first term and the last term together. Out first term is d² and our last term is 36. Since d² does not have a coefficient, then we assume this number to be 1.
1 × 36 = 36
So, now we need to find two factors that multiply to 36 and add together to get 12. Two factors that best represents this is 6 and 6. So, we will plug these numbers into our equation. Replace 12d with 6d + 6d.
d² + 6d + 6d + 36
Group the first two terms together and the last two terms together.
(d² + 6d) + (6d + 36)
Now, find the greatest common factor of each parentheses and factor the terms.
d(d + 6) + 6(d + 6)
From looking at this, we can tell that this equation is a perfect squared equation. So, this means instead of writing both parentheses, we can just write one of the parentheses and square it.
So, the factored form of this equation is (d + 6)²
The function h(t) = –16t2 + 28t + 500 represents the height of a rock t seconds after it is propelled by a slingshot.
What does h(3.2) represent?
the height of the rock 3.2 seconds before it reaches the ground
the time it takes the rock to reach the ground, or 3.2 seconds
the time it takes the rock to reach a height of 3.2 meters
the height of the rock 3.2 seconds after it is propelled
Answer:
h(3.2) represents the height of the rock 3.2 seconds after it is propelled. Remember, h(t) represents the height of a rock t seconds after it is propelled.
Answer:
D
Step-by-step explanation:
the height of the rock 3.2 seconds before it reaches the ground
the time it takes the rock to reach the ground, or 3.2 seconds
the time it takes the rock to reach a height of 3.2 meters
the height of the rock 3.2 seconds after it is propelled
What are the zeros of f(x) = x^2 + x - 20?
A. x= -4 and x = 5
B. x= -2 and x = 10
C. x= -5 and x = 4
O D. x= -10 and x = 2
In Denver, Colorado, they experience a lot of snow in the winter. During the last
snow storm, it snowed for 3 straight days and the snow consistently accumulated at
a rate of inch per hour. How much snow did Denver get over three days?
Your answer
Answer:
Denver got 72 inches of snow over three days.
Step-by-step explanation:
Since it has snowed consistently for 3 days, accumulating an inch of snow per hour, over that number of days at least 72 inches of snow would have accumulated.
This is so because, since each day has 24 hours, in the event of a 3-day snowfall, it would have lasted 72 hours. Thus, while every hour a new inch of snow would accumulate, at the end of the storm the city of Denver would have accumulated 72 inches of snow (1 x 24 x 3 = 72).
A car can travel 45 miles on 2 gallons of gasoline. How far can it travel on 5.6
gallons?
Answer:
It can travel 45 / 2 = 22.5 miles per gallon so the answer is 22.5 * 5.6 = 126 miles.
Please answer this correctly
Answer:
66.7%
Step-by-step explanation:
The numbers less than 7 on the list are 3, 4, 5, and 6.
4 numbers are less than 7 out of total 6 numbers.
4/6 = 2/3 = 0.667 = 66.7%
When $\frac{1}{1111}$ is expressed as a decimal, what is the sum of the first 40 digits after the decimal point?
Answer:
90
Step-by-step explanation:
1/1111= 0. (0009) cycles of 0009 after decimal point (one 9 per 4 digits)
Number of digits 9:
40/4= 1010*9= 90Answer:
90
Step-by-step explanation:
Plz help for 80 points question is attached
Answer:
2 and 256
Step-by-step explanation:
Check the attachment
Answer:
2 and255
Step-by-step explanation:
look atyourquestion
The manager of a coffee shop wants to know if his customers’ drink preferences have changed in the past year. He knows that last year the preferences followed the following proportions – 34% Americano, 21% Cappuccino, 14% Espresso, 11% Latte, 10% Macchiato, 10% Other. In a random sample of 450 customers, he finds that 115 ordered Americanos, 88 ordered Cappuccinos, 69 ordered Espressos, 59 ordered Lattes, 44 ordered Macchiatos, and the rest ordered something in the Other category. Run a Goodness of Fit test to determine whether or not drink preferences have changed at his coffee shop. Use a 0.05 level of significance. Americanos Capp. Espresso Lattes Macchiatos Other Observed Counts 115 88 69 59 44 75 Expected Counts 153 94.5 63 49.5 45 45 Enter the p-value - round to 5 decimal places. Make sure you put a 0 in front of the decimal. P-value =
Answer:
Step-by-step explanation:
[tex]H_0 : \texttt {null hypothesis}\\\\H_1 : \texttt {alternative hypothesis}[/tex]
The null hypothesis is the drink preferences are not changed at coffee shop.
The alternative hypothesis is the drink preferences are changed at coffee shop.
the level of significance = α = 0.05
We get the Test statistic
[tex]\texttt {Chi square}=\frac{\sum (F_o-F_e)}{F_e}[/tex]
Where, [tex]F_o[/tex] is observed frequencies and
[tex]F_e[/tex] is expected frequencies.
N = 6
Degrees of freedom = df = (N – 1)
= 6 – 1
= 5
the level of significance α = 0.05
Critical value = 11.07049775
( using Chi square table or excel)
Tables for test statistic are given below
F_o F_e Chi square
Americanos 115 153 9.4379
Capp. 88 94.5 0.447
Espresso 69 63 0.5714
Lattes 59 49.5 1.823
Macchiatos 44 45 0.022
Other 75 45 20
Total 450 450 32.30
[tex]\texttt {Chi square}=\frac{\sum (F_o-F_e)}{F_e}[/tex] = 32.30
P-value = 0.00000517
( using Chi square table or excel)
P-value < α = 0.05
So, we reject the null hypothesis
This is because their sufficient evidence to conclude that Drink preferences are changed at coffee shop.
which of the following is equivalent to this?
a: b over a divided by d over c
b: a over b divided by d over c
c: b over a divided by d over c
d: b over a divided by c over d
please help me!
Answer:
b: a over b divided by do over c
Step-by-step explanation:
You can solve this by plugging in numbers for each variable.
For example: a=1, b=4, c=1, d=2
1/4 ÷ 1/2 = 0.125
If you plug in the numbers for all the equations listed, only 1/4 ÷ 2/1 = 0.125.
What is the conjugate of 3+3i?
Answer:
3 - 3i
Step-by-step explanation:
The conjugate is the opposite sign i of the original. So you simply switch the sign of 3i to -3i to find your conjugate.
Answer:
3 - 3i
Step-by-step explanation:
Change the sign only of the imaginary part.
The conjugate of 3 + 3i is 3 - 3i.
Determine whether the following statement is true or false.
To construct a confidence interval about the mean, the population from which the sample is drawn must be approximately normal.
a. True
b. False
Answer:
Step-by-step explanation:
In constructing a confidence interval about the mean, the central limit theorem is usually applied. This makes it possible to use the normal distribution. As the number of samples is increasing, the distribution tends to be normal. This would require using the z distribution. In the case where the sample size is small, we assume a normal distribution and use the t distribution. Therefore, the given statement is true.
Need help with this . The picture is enclosed
Answer: (fоg)(24)=5
Step-by-step explanation:
(fоg)(24) is f of g of 24. This means you plug in g(24) into f(x).
[tex]g(24)=\sqrt{24-8}[/tex]
[tex]g(24)=\sqrt{16}[/tex]
[tex]g(24)=4[/tex]
Now that we know g(24), we can plug it into f(x).
f(4)=2(4)-3
f(4)=8-3
f(4)=5
The First National Bank of Wilson has 600 checking account customers. Recent sample of 50 of these customers show 29 have a visa card with the bank. Construct the 90% confidence interval for the proportion of checking account customers who have a visa card with the bank. (Use a Z distribution table0
Answer:
[tex]0.58 - 1.64\sqrt{\frac{0.58(1-0.58)}{50}}=0.466[/tex]
[tex]0.58 + 1.64\sqrt{\frac{0.58(1-0.58)}{50}}=0.694[/tex]
The 90% confidence interval would be given by (0.466;0.694)
Step-by-step explanation:
The estimated proportion of interest would be:
[tex] \hat p=\frac{29}{50}= 0.58[/tex]
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by [tex]\alpha=1-0.90=0.1[/tex] and [tex]\alpha/2 =0.05[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64[/tex]
The confidence interval for the mean is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
If we replace the values obtained we got:
[tex]0.58 - 1.64\sqrt{\frac{0.58(1-0.58)}{50}}=0.466[/tex]
[tex]0.58 + 1.64\sqrt{\frac{0.58(1-0.58)}{50}}=0.694[/tex]
The 90% confidence interval would be given by (0.466;0.694)
Please answer this correctly without making mistakes I want Genius,ace and expert people to answer this correctly
Answer:
It would increase by 1
Step-by-step explanation:
Step 1: Find the mean of the original
(9+6+1+1+3)/5 = 4
Step 2: Find the mean of the new
(9+6+1+1+8)/5 = 5
Step 3: Find the difference
5 - 4 = 1
george cut a cake into 8 equal pieces. what is the unit fraction for the cake
Answer: 1/8
Step-by-step explanation:
Unit Fractions: A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. A unit fraction is therefore the reciprocal of a positive integer, 1/n.
Example of Unit Fractions: 1/1, 1/2, 1/3, 1/4 ,1/5, etc.
Hope this helps! Please mark as brainliest!
The unit fraction of the cake is 1/8
What is a unit fraction?A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer.
A unit fraction is therefore the reciprocal of a positive integer, 1/n.
Examples are 1/1, 1/2, 1/3, 1/4, 1/5, etc.
Given that, George cut a cake into 8 equal pieces, we need to find the unit fraction for the cake
Since, George cut the cake in 8 equal pieces so, 1 part will be shown by 1/8 of the cake, that mean 1/8 is one unit of the cake, we can say that 1/8 is the unit of the whole cake.
Hence, the unit fraction of the cake is 1/8
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Microsoft excel was used on a set of data involving the number of defective items found in a random sample of 46 cases of light bulbs produced during a morning shift at a plant. A manager wants to know if the mean number of defective bulbs per case is greater than 20 during the morning shift. She will make her decision using a test with a level of significance of 0.10. The following information was extracted from the microsoft excel output for the sample of 46 cases:
n=46, Arithmetic mean=28.00, Std Dev =25.92, standard error=3.82, Null hypothesis: H0 : u<=20, alpha =0.10, df=45, t-test statistic=2.09, one tail test upper critical value =1.3006, p-value=0.021
i) what parameter is the manager interested in?
ii) state the alternative hypothesis for this study.
iii) what critical value should the manager use to determine the rejection region.
iv) explain if the, null hypothesis should be rejected and why or why not?
v) explain our risk of committing of a type1 error.
vi) explain if the data evidence proves beyond a doubt that the mean number of defective bulbs per case is greater than 20 during the morning shift
vii) what can the manager conclude about the mean number of defective bulbs per case during the morning shift using a level of significance of 0.10?
viii) what would the p-value be if these data were used to perform a two tail test?
Answer:
Step-by-step explanation:
i. The parameter the manager is interested in is number of defective bulbs in a case.
ii. Null hypothesis: u <= 20
Alternative hypothesis: u > 20
iii. The critical value the manager should use to determine the rejection region is 1.645.
iv. Using the p value which is 0.021 at 0.10 significance level we will reject the null as the p value is less than 0.1. Thus, we will conclude that there is enough statistical evidence to prove that the mean number of defective bulbs per case is greater than 20.
v. Our risk of committing type one error is alpha which is the level of significance set for the hypothesis test. An alpha level of 0.1 shows that we are willing to accept a 10% chance that we are wrong when you reject the null hypothesis.
vi. With a low p value, the data has enough evidence to prove that the mean number of defective bulbs per case is greater than 20 during the morning shift
vii. The manager will conclude that there is sufficient statistical evidence to prove that mean number of defective bulbs per case is greater than 20 during the morning shift.
viii. the p value if this is a two tail test would be 0.03662