Answer:
Should not be rejected.
Step-by-step explanation:
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.
Factor as the product of two binomials. x^2-8x+16
Answer:
(x-4) (x-4)
Step-by-step explanation:
x^2-8x+16
What 2 numbers multiply to 16 and add to -8
-4*-4 = 16
-4+-4 = -8
(x-4) (x-4)
Answer:
correct ^
Step-by-step explanation:
Five individuals have responded to a request by a blood bank for blood donations. None of them has donated before, so their blood types are unknown. Suppose only type O is desired and only one of the five actually has this type. If the potential donors are selected in random order for typing, what is the probability that at least four individuals must be typed to obtain the desired type
Answer:
The probability that at least four individuals must be typed to obtain the desired type is P=0.2.
Step-by-step explanation:
The donors are randomly selected to be typed.
The probability of selecting a random donor and it does not have type O is 4/5=0.8.
The probability of selecting the second donor and he does not have type O is 3/4, as one of the donors has been already tested and does not have type O.
Then, we can apply the same reasoning for the next two donors and calculate the probability that at least four individuals as:
[tex]P(k=4)=\left(\dfrac{4}{5}\right)\cdot\left(\dfrac{3}{4}\right)\cdot\left(\dfrac{2}{3}\right)\cdot\left(\dfrac{1}{2}\right)=\dfrac{1}{5}=0.2[/tex]
Consider random samples of size 900 from a population with proportion 0.75 . Find the standard error of the distribution of sample proportions. Round your answer for the standard error to three decimal places. standard error
Answer:
[tex] SE =\sqrt{\frac{p(1-p)}{n}}[/tex]
And replacing we got:
[tex] SE=\sqrt{\frac{0.75*(1-0.75)}{900}}= 0.014[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex] n=900[/tex] represent the sample size selected
[tex]p = 0.75[/tex] represent the population proportion
We want to find the standard error and we can use the distribution for the sample proportion and for this case since the sample size is large enough and we satisfy np>10 and n(1-p) >10 we have:
[tex] \hat p \sim N (p,\sqrt{\frac{p(1-p)}{n}})[/tex]
And the standard error is given;
[tex] SE =\sqrt{\frac{p(1-p)}{n}}[/tex]
And replacing we got:
[tex] SE= \sqrt{\frac{0.75* (1-0.75)}{900}}= 0.014[/tex]
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.
Suppose that 40 percent of the drivers stopped at State Police checkpoints in Storrs on Spring Weekend show evidence of driving while intoxicated. Consider a sample of 5 drivers. a. Find the probability that none of the drivers shows evidence of intoxication. b. Find the probability that at least one of the drivers shows evidence of intoxication. c. Find the probability that at most two of the drivers show evidence of intoxication. d. Find the probability that more than two of the drivers show evidence of intoxication. e. What is the expected number of intoxicated drivers
Answer:
a) 0.778
b) 0.9222
c) 0.6826
d) 0.3174
e) 2 drivers
Step-by-step explanation:
Given:
Sample size, n = 5
P = 40% = 0.4
a) Probability that none of the drivers shows evidence of intoxication.
[tex] P(x=0) = ^nC_x P^x (1-P)^n^-^x[/tex]
[tex]P(x=0) = ^5C_0 (0.4)^0 (1-0.4)^5^-^0[/tex]
[tex] P(x=0) = ^5C_0 (0.4)^0 (0.60)^5[/tex]
[tex] P(x=0) = 0.778 [/tex]
b) Probability that at least one of the drivers shows evidence of intoxication would be:
P(X ≥ 1) = 1 - P(X < 1)
[tex] = 1 - P(X = 0) [/tex]
[tex] = 1 - ^5C_0 (0.4)^0 * (0.6)^5[/tex]
[tex] = 1 - 0.0778 [/tex]
[tex] = 0.9222 [/tex]
c) The probability that at most two of the drivers show evidence of intoxication.
P(x≤2) = P(X = 0) + P(X = 1) + P(X = 2)
[tex] ^5C_0 (0.4)^0 (0.6)^5 + ^5C_1 (0.4)^1 (0.6)^4 + ^5C_2 (0.4)^2 (0.6)^3 [/tex]
[tex] = 0.6826 [/tex]
d) Probability that more than two of the drivers show evidence of intoxication.
P(x>2) = 1 - P(X ≤ 2)
[tex] = 1 - [^5C_0 (0.4)^0 (0.6)^5 + ^5C_1 (0.4)^1 (0.6)^4 + ^5C_2 * (0.4)^2 (0.6)^3] [/tex]
[tex] = 1 - 0.6826 [/tex]
[tex] = 0.3174 [/tex]
e) Expected number of intoxicated drivers.
To find this, use:
Sample size multiplied by sample proportion
n * p
= 5 * 0.40
= 2
Expected number of intoxicated drivers would be 2
Given the system:
2x – 4y = -34
-3x - y = 2
Solve for the variables that make up the coefficient
matrix:
[a b]
[c d]
a=
b =
c=
d=
Answer:
X= -3
Y= 7
a= -6
b = -28
C = 9
D= -7
Step-by-step explanation:
2x – 4y = -34
-3x - y = 2
2x – 4y = -34
-12x - 4y = 8
-14x = 42
X= 42/-14
X= -3
-3x - y = 2
-3(-3) -y = 2
9-y = 2
9-2= y
Y= 7
a = 2x
a= 2*-3
a= -6
b = -4y
b = -4*7
b = -28
C= -3x
C= -3*-3
C = 9
D= -y
D= -7
Answer:
A= 2 B=-4
C= -3 D= -1
Step-by-step explanation:
Took it on Edge
An industrial expert claims that the average useful lifetime of a typical car transimssion which comes with ten years warranty is significantly more than 10 years. In order to test this claim, 9 car transmissions are randomly selected and their useful lifetimes are recorded. The sample mean lifetime is 13.5 years and the sample standard deviation is 3.2 years. Assuming that the useful lifetime of a typical car transmission has a normal distribution, based on these sample result, the correct conclusion at 1% significance level for this testing hypotheses problem is: Group of answer choices
Answer:
Step-by-step explanation:
The question is incomplete. The missing information is the group of answer choices. The group of answer choices are
a) none of the above
b) Data provides sufficient evidence, at 1% significance level, to reject the expert's claim. In addition the p-value (or the observed significance level) is equal to P( T < -3.281).
c) Data provides insufficient evidence, at 1% significance level, to support the expert's claim. In addition the p-value (or the observed significance level) is equal to P( Z > 2.896).
d) Data provides sufficient evidence, at 1% significance level, to support the expert's claim. In addition the p-value (or the observed significance level) is equal to P( T >3.355).
e) Data provides insufficient evidence, at 1% significance level, to support the researcher's claim. In addition the p-value (or the observed significance level) is equal to P(Z > 2.896).
Solution:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ ≥ 10
For the alternative hypothesis,
µ < 10
This is a left tailed test.
Since the number of samples is small and the population standard deviation is not given, the distribution is a student's t.
Since n = 9,
Degrees of freedom, df = n - 1 = 9 - 1 = 8
t = (x - µ)/(s/√n)
Where
x = sample mean = 13.5
µ = population mean = 10
s = samples standard deviation = 3.2
t = (13.5 - 10)/(3.2/√9) = 3.28
Since α = 0.01, the critical value is determined from the t distribution table. Recall that this is a left tailed test. Therefore, we would find the critical value corresponding to 1 - α and reject the null hypothesis if the test statistic is less than the negative of the table value.
1 - α = 1 - 0.01 = 0.99
The negative critical value is - 2.896
Since - 3.28 is lesser than - 2.896, then we would reject the null hypothesis.
By using probability value,
We would determine the p value using the t test calculator. It becomes
p = 0.0056
Level of significance = 1%
Since alpha, 0.01 > than the p value, 0.0056, then we would reject the null hypothesis. Therefore, At a 1% level of significance, the sample data showed significant evidence that the average useful lifetime of a typical car transimssion which comes with ten years warranty is significantly less than 10 years
The correct option is
a) none of the above
The weights of a certain brand of candies are normally distributed with a mean weight of .8551 g and a standard deviation of 0.0518 g. A sample of these candies came from a package containing 467 candies, and the package label stated that the net weight is 399 g. (If every package has 467467 candies, the mean weight of the candies must exceed 399.0/467 = .8544 g for the net contents to weigh at least 399 g.)If 1 candy is randomly selected, find the probability that it weighs more than 0.8544 g.
Answer:
50.40% probability that it weighs more than 0.8544 g.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 0.8551, \sigma = 0.0518[/tex]
If 1 candy is randomly selected, find the probability that it weighs more than 0.8544 g.
This is 1 subtracted by the pvalue of Z when X = 0.8544. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.8544 - 0.8551}{0.0518}[/tex]
[tex]Z = -0.01[/tex]
[tex]Z = -0.01[/tex] has a pvalue of 0.4960
1 - 0.4960 = 0.5040
50.40% probability that it weighs more than 0.8544 g.
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.
Given: ABCD is a parallelogram.
Diagonals AC, BD intersect at E.
Prove: AE = CE and BE = DE
B.
С
E
A
D
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Answer:
the gram
Step-by-step explanation:
casegunnell is my gram, follow if your a real g
Following are the calculation to the given points:
When the ABCD is parallelogram:
The properties of parallelogram:
[tex]\to \angle CBD = \angle ADB \\\\[/tex]
[tex]\to \angle BCA = \angle DAC \\\\[/tex]
When the Two-lines are parallel and alternate interior angles are equal:
[tex]\to \Delta BEC \cong \Delta AED \ \ \ \ \ \ \ \{ASA\} \\\\\to \overline {AE} \cong \overline{CE}\\\\ \to \overline{BE} \cong \overline{ED} \\\\[/tex]
When the properties of congruent triangle.
Learn more:
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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
A student sets up the following equation to convert a measurement. Fill in the missing part of the equation
Answer:
We have the equation:
(14 N/mm)*X = Y N/cm
So we want to transform 1/mm to 1/cm.
We know that:
10mm = 1cm
1 = 10mm/1cm (we want to have mm on the numerator, so it cancelates with the mm in the denominator)
then the conversion is from 1/mm to 1/cm is:
X = 10mm/cm
then we have:
(14N/mm)*(10mm/cm) = 140 N/cm
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.
A door of a lecture hall is in a parabolic shape. The door is 56 inches across at the bottom of the door and parallel to the floor and 32 inches high. Sketch and find the equation describing the shape of the door. If you are 22 inches tall, how far must you stand from the edge of the door to keep from hitting your head?
Answer:
The parabolic shape of the door is represented by [tex]y - 32 = -\frac{2}{49}\cdot x^{2}[/tex]. (See attachment included below). Head must 15.652 inches away from the edge of the door.
Step-by-step explanation:
A parabola is represented by the following mathematical expression:
[tex]y - k = C \cdot (x-h)^{2}[/tex]
Where:
[tex]h[/tex] - Horizontal component of the vertix, measured in inches.
[tex]k[/tex] - Vertical component of the vertix, measured in inches.
[tex]C[/tex] - Parabola constant, dimensionless. (Where vertix is an absolute maximum when [tex]C < 0[/tex] or an absolute minimum when [tex]C > 0[/tex])
For the design of the door, the parabola must have an absolute maximum and x-intercepts must exist. The following information is required after considering symmetry:
[tex]V (x,y) = (0, 32)[/tex] (Vertix)
[tex]A (x, y) = (-28, 0)[/tex] (x-Intercept)
[tex]B (x,y) = (28. 0)[/tex] (x-Intercept)
The following equation are constructed from the definition of a parabola:
[tex]0-32 = C \cdot (28 - 0)^{2}[/tex]
[tex]-32 = 784\cdot C[/tex]
[tex]C = -\frac{2}{49}[/tex]
The parabolic shape of the door is represented by [tex]y - 32 = -\frac{2}{49}\cdot x^{2}[/tex]. Now, the representation of the equation is included below as attachment.
At x = 0 inches and y = 22 inches, the distance from the edge of the door that head must observed to avoid being hit is:
[tex]y -32 = -\frac{2}{49} \cdot x^{2}[/tex]
[tex]x^{2} = -\frac{49}{2}\cdot (y-32)[/tex]
[tex]x = \sqrt{-\frac{49}{2}\cdot (y-32) }[/tex]
If y = 22 inches, then x is:
[tex]x = \sqrt{-\frac{49}{2}\cdot (22-32)}[/tex]
[tex]x = \pm 7\sqrt{5}\,in[/tex]
[tex]x \approx \pm 15.652\,in[/tex]
Head must 15.652 inches away from the edge of the door.
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.
Read more about cost functions at:
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can someone help me again please im giving 20 points
Answer:
I answered this one for you already I think.
A laptop computer is purchased for $2300. Each year, its value is 75% of its value the year before. After how many years will the laptop computer be worth $700 or less? (Use the calculator provided if necessary.) Write the smallest possible whole number answer.
Answer:
after the 1st year
Step-by-step explanation:
$2300 × 75% = $1725.00
$2300-$1725= $575
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
Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of seven per hour. If it takes approximately ten minutes to serve each customer, find the mean and variance of the total service time in minutes for customers arriving during a 1-hour period. What is the probability that the total service time will exceed 2.5 hours?
Answer:
Step-by-step explanation:
60 minutes = 1 hour
The statement would be
"Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of seven per 60 minutes
If it takes approximately ten minutes to serve each customer, then the mean service time for in minutes for customers arriving during a 1-hour period is
10/60 × 7 = 1.67
In Poisson distribution, variance = mean
Therefore,
Variance = 1.67
The probability that the total service time will exceed 2.5 hours is expressed as P(x > 2.5)
Converting 2.5 hours to minutes, it becomes 2.5 × 60 = 150 minutes
From the Poisson distribution calculator,
P(x > 150) = 0
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]
Find the value of the expression 8x3 if: x=3
Answer:
48
Step-by-step explanation:
You times 8 by 3 to get 24. Then you multiply 24 by 3 to get 48
Answer:
216
Step-by-step explanation:
8x³
Put x as 3.
8(3)³
Solve for the power first.
8(27)
Multiply both terms.
216
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°
Any help would be great
identify the property being demonstrated
if x/5 = 7, then x=35
a. division
b. multiplication
c. reflexive
d. symmetric
Answer:
[tex] \: \: \: \: \: \: \: \: \: \: \dfrac{x}{5} = 7 \\ \implies \: x = 7 \times 5 \\ \implies \: x = 35[/tex]
So,b. multiplication
Answer:
A. division
Step-by-step explanation:
[tex]x/5=7[/tex]
[tex]x[/tex] is being divided by an integer.
[tex]x=35[/tex]
[tex]35/5=7[/tex]
35 divided by 5 is equal to 7.
A hotel manager believes that 27% of the hotel rooms are booked. If the manager is correct, what is the probability that the proportion of rooms booked in a sample of 423 rooms would differ from the population proportion by less than 6%
Answer:
The probability that the proportion of rooms booked in a sample of 423 rooms would differ from the population proportion by less than 6% is 0.9946.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
[tex]\mu_{\hat p}=p[/tex]
The standard deviation of this sampling distribution of sample proportion is:
[tex]\sigma_{\hat p}=\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The information provided here is:
p = 0.27
n = 423
As n = 423 > 30, the sampling distribution of sample proportion can be approximated by the Normal distribution.
The mean and standard deviation of the sampling distribution of sample proportion are:
[tex]\mu_{\hat p}=p=0.27\\\\\sigma_{\hat p}=\sqrt{\frac{\hat p(1-\hat p)}{n}}=\sqrt{\frac{0.27\times(1-0.27)}{423}}=0.0216[/tex]
Compute the probability that the proportion of rooms booked in a sample of 423 rooms would differ from the population proportion by less than 6% as follows:
[tex]P(|\hat p-p|<0.06)=P(p-0.06<\hat p<p+0.06)[/tex]
[tex]=P(0.27-0.06<\hat p<0.27+0.06)\\\\=P(0.21<\hat p<0.33)\\\\=P(\frac{0.21-0.27}{0.0216}<\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}<\frac{0.33-0.27}{0.0216})\\\\=P(-2.78<Z<2.78)\\\\=P(Z<2.78)-P(Z<-2.78)\\\\=0.99728-0.00272\\\\=0.99456\\\\\approx 0.9946[/tex]
*Use a z-table.
Thus, the probability that the proportion of rooms booked in a sample of 423 rooms would differ from the population proportion by less than 6% is 0.9946.
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.
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
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
Read more at; https://brainly.com/question/5733654
Consider three consecutive positive integers, such that the sum of the
squares of the two larger integers is 5 more than 40 times the smaller
one. Find the smaller integer.
Answer:
17
Step-by-step explanation:
Let x represent the smaller integer. Then we have ...
(x +1)² +(x +2)² = 40x +5
2x² +6x +5 = 40x +5
x² -17x = 0 . . . . . subtract (40x+5), divide by 2
x(x -17) = 0 . . . . . factor
The solution of interest is x = 17.
The smaller integer is 17.