Answer:
the answer is 7.2
Step-by-step explanation:
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.
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
A manufacturer has determined that the total cost C of operating a factory is
C = 2.5x2 + 75x + 25000,
where x is the number of units produced. At what level of production will the average cost per unit be minimized? (The average cost per unit is C/x.)
x = _____ units
Answer:
x = 100 units
Step-by-step explanation:
C = 2.5x^2 + 75x + 25000
To find average cost per unit, divide C by x:
C/x or Average cost (AC) per unit = [tex]\frac{2.5x^2 + 75x + 25000}{x}[/tex] = 2.5x + 75 + 25000/x ⇔ 2.5x + 75 + 25000x^-1 (equation 1)
To find cost minimising, we use differentiation (differentiate equation 1 in respect to x and set it equal to 0):
d(AC)/dx = 0
d(AC)/dx ⇔ 2.5 - 25000x^-2 = 0
2.5 = 25000x^-2
2.5 = [tex]\frac{25000}{x^2}[/tex]
2.5x^2 = 25000
x^2 = 10000
x = [tex]\sqrt{10000}[/tex]
x = 100 units
Cost functions are used to model the outputs from inputs.
The average cost per unit will be minimized at 100 units of production level.
The cost function is given as:
[tex]\mathbf{C(x) = 2.5x^2 + 75x + 25000}[/tex]
Calculate the average cost function using
[tex]\mathbf{A(x) = \frac{C(x)}{x}}[/tex]
So, we have:
[tex]\mathbf{A(x) = \frac{2.5x^2 + 75x + 25000}{x}}[/tex]
Simplify
[tex]\mathbf{A(x) = 2.5x + 75 + \frac{25000}{x}}[/tex]
Differentiate
[tex]\mathbf{A'(x) = 2.5 + 0 - \frac{25000}{x^2}}[/tex]
[tex]\mathbf{A'(x) = 2.5 - \frac{25000}{x^2}}[/tex]
Set to 0
[tex]\mathbf{2.5 - \frac{25000}{x^2} = 0}[/tex]
Collect like terms
[tex]\mathbf{-\frac{25000}{x^2} = -2.5}[/tex]
Cross multiply
[tex]\mathbf{-2.5x^2 = -25000 }[/tex]
Make x^2 the subject
[tex]\mathbf{x^2 = 10000 }[/tex]
Take square roots of both sides
[tex]\mathbf{x = 100 }[/tex]
Hence, the average cost per unit will be minimized at 100 units of production level.
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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.
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 12 ft ladder leans against the side of a house. The top of the ladder is 10ft off the ground. Find x, the angle of elevation of the ladder.
1. Remember to address each of the critical elements of the prompt:
Articulate your overall approach to solving this problem before tackling the details. In other words, think about what the question is actually asking, which pieces of information are relevant, and how you can use what you have learned to fill in the missing pieces.
2. Apply the mathematical process to solve the problem:
Interpret the word problem to identify any missing information.
Translate the word problem into an equation.
Appropriately use the order of operations and law of sines and cosines to determine the solution.
Check your work by ensuring that the known properties of triangles are met.
The image is missing, so i have attached it.
Answer:
x = 56.44°
Step-by-step explanation:
From the attached image, we can see that this is a right angle triangle which has opposite, adjacent and hypotenuse as sides. Since we want to find the angle x, thus, we can make use of trigonometric ratios.
From the attached image, the side opposite to angle x is 10ft and the hypotenuse is 12 ft.
From trigonometric ratios, we know that, sin x = opposite/hypotenuse
So, sin x = 10/12
x = sin^(-1) (10/12)
x = sin^(-1) 0.8333
x = 56.44°
I need help for the solution
Answer:
[tex]\boxed{ \ dY_t=(2\theta+2\psi Y_t+\phi^2)dt+2\phi \sqrt{Y_t}dW_t\ }[/tex]
Step-by-step explanation:
it is a long time I have not applied Ito's lemma
I would say the following
for [tex]f(x)=x^2[/tex]
f'(x)=2x
f''(x)=2
so using Ito's lemma we can write that
[tex]dY_t=2V_tdV_t+\phi^2dt[/tex]
[tex]dY_t=2(\theta+\psi V_t^2)dt+2\phi V_tdW_t+\phi^2dt[/tex]
[tex]dY_t=(2\theta+2\psi V_t^2+\phi^2)dt+2\phi V_tdW_t[/tex]
so it comes
[tex]dY_t=(2\theta+2\psi Y_t+\phi^2)dt+2\phi \sqrt{Y_t}dW_t[/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
two sides of a parallelogram meet at an angle of 50 degrees. If the length of one side is 3 meters and the length of the other side is 5 meters, find the length of the longest diagonal and the angles that it forms with each of the given sides.
Answer:
The longer diagonal has a length of 7.3 meters.
The angles are 31.65° and 18.35°
Step-by-step explanation:
If one angle of the parallelogram is 50°, another angle is also 50° and the other two angles are the supplement of this angle. so the other three angles are:
50°, 130° and 130°.
The longer diagonal will be the one opposite to the bigger angle (130°), and this diagonal divides the parallelogram in two triangles.
Using the law of cosines in one of these two triangles, we have:
[tex]diagonal^2 = a^2 + b^2 - 2ab*cos(130\°)[/tex]
[tex]diagonal^2 = 3^2 + 5^2 - 2*3*5*(-0.6428)[/tex]
[tex]diagonal^2 = 53.284[/tex]
[tex]diagonal = 7.3\ meters[/tex]
So the longer diagonal has a length of 7.3 meters.
To find the angles that this diagonal forms with the sides, we can use the law of sines:
[tex]a / sin(A) = b/sin(B)[/tex]
[tex]5 / sin(A) = diagonal / sin(130)[/tex]
[tex]sin(A) = 5 * sin(130) / 7.3[/tex]
[tex]sin(A) = 0.5247[/tex]
[tex]A = 31.65\°[/tex]
The other angle is B = 50 - 31.65 = 18.35°
Please check the image attached for better comprehension.
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!
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
A TV on ebay is described to be 35.7 inches wide and 20.1 inches
high. To the nearest whole number how many inches is it's diagonal?
(Enter your answer without units.)
Answer:
41 in.
Step-by-step explanation:
You have to use the Pythagorean Theorem. You have the values for the two sides (length and width). Now, you need to solve for the hypotenuse (diagonal).
a² + b² = c²
(35.7)² + (20.1)² = c²
1274.49 + 404.01 = c²
1678.5 = c²
√1678.5 = c
c = 40.97
c ≈ 41
The diagonal length is 41 in., to the nearest whole number.
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]
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%
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.
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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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.
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)
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]
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
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.
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
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.
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
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
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
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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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
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