Answers
Answer:
8/17
Step-by-step explanation:
The sine of an angle is defined as the opposite side to the reference angle divided by the hypotenuse.
The side opposite the angle is always the side not connected to the reference angle. In this case the opposite side = ZY
The hypotenuse = XZ
Sin(X) = ZY/XZ
Sin(X) = 1634 = 8 / 17
Related Questions
Find the following integral
Answers
There's nothing preventing us from computing one integral at a time:
[tex]\displaystyle \int_0^{2-x} xyz \,\mathrm dz = \frac12xyz^2\bigg|_{z=0}^{z=2-x} \\\\ = \frac12xy(2-x)^2[/tex]
[tex]\displaystyle \int_0^{1-x}\int_0^{2-x}xyz\,\mathrm dz\,\mathrm dy = \frac12\int_0^{1-x}xy(2-x)^2\,\mathrm dy \\\\ = \frac14xy^2(2-x)^2\bigg|_{y=0}^{y=1-x} \\\\= \frac14x(1-x)^2(2-x)^2[/tex]
[tex]\displaystyle\int_0^1\int_0^{1-x}\int_0^{2-x}xyz\,\mathrm dz\,\mathrm dy\,\mathrm dx = \frac14\int_0^1x(1-x)^2(2-x)^2\,\mathrm dx[/tex]
Expand the integrand completely:
[tex]x(1-x)^2(2-x)^2 = x^5-6x^4+13x^3-12x^2+4x[/tex]
Then
[tex]\displaystyle\frac14\int_0^1x(1-x)^2(2-x)^2\,\mathrm dx = \left(\frac16x^6-\frac65x^5+\frac{13}4x^4-4x^3+2x^2\right)\bigg|_{x=0}^{x=1} \\\\ = \boxed{\frac{13}{240}}[/tex]
Weekly wages at a certain factory are
normally distributed with a mean of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makes between
$350 and $400.
Answers
Answer:
b or a
Step-by-step explanation:
What is the domain of the function?
Answers
Answer: The answer is -2
Step-by-step explanation:
that is where the line starts
hope this helped
Answer:
x > -2
Step-by-step explanation:
The domain is the values that the input can take
x goes from -2( not including -2) to infinity
x > -2
make m the subject of this eequation please help!! asap
Answers
Answer: [tex]M = \pm\sqrt{\frac{3K}{4(5+7NK)}}\\\\[/tex]
======================================
Work Shown:
[tex]\frac{5}{K} = \frac{3}{4M^2} - 7N\\\\\frac{5}{K}+7N = \frac{3}{4M^2}\\\\\frac{5}{K}+7N*\frac{K}{K} = \frac{3}{4M^2}\\\\\frac{5}{K}+\frac{7NK}{K} = \frac{3}{4M^2}\\\\\frac{5+7NK}{K} = \frac{3}{4M^2}\\\\4M^2*(5+7NK) = K*3\\\\M^2 = \frac{3K}{4(5+7NK)}\\\\M = \pm\sqrt{\frac{3K}{4(5+7NK)}}\\\\[/tex]
Other forms are possible, but those forms would be equivalent to what is shown above.
What two numbers add to 13 and multiply to -48?
Answers
Answer:
16 x -3 and 16-3
Step-by-step explanation:
If you multiply 16 and -3 you get -48 and if you subtract 3 from 16 you get 13 (hope this helped) :)
(x+16)²=12 plz help me and show work
Answers
Answer:
The answer is [tex]x=-16[/tex] ±[tex]2\sqrt{3}[/tex] in exact form or [tex]x=-12.535898[/tex], [tex]x=-19.464102[/tex] in decimal form.
Step-by-step explanation:
To solve this problem, start by moving all terms to the left side of the equation and simplify. Simplify the equation by subtracting 12 from both sides of the equation and squaring [tex]x+16[/tex], which will look like [tex]x^{2} +32x+256-12=0[/tex]. Next, simplify the equation again, which will look like [tex]x^{2} +32x+244=0[/tex].
Then, use the quadratic formula to find the solutions. The quadratic formula looks like[tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex].
For this problem, the quadratic variables are as follows:
[tex]a=1[/tex]
[tex]b=32[/tex]
[tex]c=244[/tex]
The next step is to substitute the values [tex]a=1[/tex], [tex]b=32[/tex], and [tex]c=244[/tex] into the quadratic formula and solve. The quadratic formula will look like [tex]\frac{-32(+-)\sqrt{32^2-4(1*244)} }{2*1}[/tex]. To simplify the equation, start by simplifying the numerator, which will look like [tex]x=\frac{-32(+-)4\sqrt{3} }{2*1}[/tex]. Then, multiply 2 by 1 and simplify the equation, which will look like [tex]x=-16(+-)2\sqrt{3}[/tex]. The final answer is [tex]x=-16[/tex] ±[tex]2\sqrt{3}[/tex] in exact form. In decimal form, the final answer is [tex]x=-12.535898[/tex], [tex]x=-19.464102[/tex].
The degree of the polynomial function f(x) is 4. The roots of the equation f(x) =0 are -2,-1,1 and 3. Which graph could be the graph of f(x)?
Answers
Answer:
top right
Step-by-step explanation:
roots of an equation = x-intercepts
Answer:
top right is the answer from my calculatins
Given that 3y = x + 6 and y = kx + 12 are perpendicular, find the value of k
Answers
k = -3
Step-by-step explanation:
Let's rewrite the equations in their slope-intercept forms:
[tex]y = \frac{1}{3}x + 2\:\:\:\:\:\:\:(1)[/tex]
[tex]y = kx + 12\:\:\:\:\:(2)[/tex]
In order for Eqn(2) to be perpendicular to Eqn(1), the slope of Eqn(2) must be the negative reciprocal of that of Eqn(1). Therefore, [tex]k = -3[/tex].
During a test period, an experimental group of 10 vehicles using an 85 percent ethanol-gasoline mixture showed mean CO2 emissions of 667 pounds per 1000 miles, with a standard deviation of 20 pounds. A control group of 14 vehicles using regular gasoline showed mean CO2 emissions of 679 pounds per 1000 miles with a standard deviation of 15 pounds. At α = 0.05, in a left-tailed test (assuming equal variances) the test statistic is:______.
A. 1.321.
B. -2.508.
C. -2.074.
D. -1.717.
Answers
Answer:
-1.683
Step-by-step explanation:
Given :
Group 1 :
x1 = 667 ; n1 = 10 ; s1 = 20
Group 2 :
x2 = 679 ; n2 = 14 ; s2 = 15
The test statistic assuming equal variance :
x1 - x2 / √[Sp² * (1/n1 + 1/n2)]
sp² = [(n1 - 1)*s1² + (n2 - 1)*s2²] ÷ (n1 + n2 - 2)
Sp² = [(10 - 1)*20² + (14 - 1)*15²] = 296.59
Test statistic =
(667 - 679)/ √[296.59 * (1/10 + 1/14)]
-12 / 7.1304978
Test statistic = - 1.682
Here's the result of this question
The point (-2,7) has undergone the following transformations:
1. Translated 1 unit up and 4 units left
Then
2. Reflected about the c-axis
Then
3. Rotated 90° anticlockwise about the origin
A) Its final coordinates are (3,-1)
B) Its final coordinates are (8,-6)
C) Its final coordinates are (-8,6)
D) Its final coordinates are (-3,1)
Answers
Answer:
B) Its final coordinates are (8,-6)
Step-by-step explanation:
1. Translated 1 unit up and 4 units left
(-2,7) becomes (-6, 8)
2. Reflected about the x-axis
(-6,8) becomes (-6, -8)
3. Rotated 90° anticlockwise about the origin
(-6, -8) becomes (8, -6) because when rotating 90 degrees anticlockwise about the origin, point A (x,y) becomes point A' (-y,x). In other words, switch the x and y and make y negative.
Select the correct answer which expression is equivalent to the product 2x+14/x^2-25 • 8x+40/6x+42
Answers
Answer:
A) 8/ 3(x-5)
Step-by-step explanation:
1) 2x+14/x^2-25 • 8x+40/6x+42=2(x+7)/ (x-5)(x+5) * 8(x+5)/ 6(x+7)
2)
after expressing every part of every fraction as product you should reduce the fraction. You can get rid of common divisor (x+5) in the denominator of the first fraction and the numerator of the second one and the common divisor (x+7) for the numerator of the first fraction and denominatorof the second one.
Then you'll get 2*8/ 6(x+5) reduce it again, 2 and 6 have the common divisor 2
Then 8/3(x-5) is the correct answer
Find the missing side lengths leave your answer as a racials simplest form
Answers
Answer:
x = 20
y = 10
it's a 30-60-90 triangle
Researchers studied symptom distress and palliative care designation among a sample of 710 hospitalized patients. Controlling for age, they used a t-test to compare average distress from nausea scores in men and women. Lower scores indicated less distress from nausea. They report men had an average score of 1.02 and woman had an average score of 1.79. Which statement is correct?
(2pts)
Select Men had significantly less distress from nausea. as your answer
Men had significantly less distress from nausea.
Select Men had half as much distress from nausea as woman but we can not determine if this is a significant difference. as your answer
Men had half as much distress from nausea as woman but we can not determine if this is a significant difference.
Select Men had less distress from nausea on average than women but we can not determine if this is a significant difference. as your answer
Men had less distress from nausea on average than women but we can not determine if this is a significant difference.
Select There is a positive correlation between distress from nausea and gender. as your answer
There is a positive correlation between distress from nausea and gender.
Answers
Answer:
A. Men had less distress from nausea on average than women but we can not determine if this is a significant difference.
Step-by-step explanation:
Working based on the information given, the mean values of each group with with men having an average score of 1.02 and women have an average of 1.79 this reveals that distressing nausea on average is higher in women than in men . However, to test if there is a significant difference would be challenging as the information given isn't enough to make proceed with the test as the standard deviations of the two groups aren't given and no accompanying sample data is given.
Suppose that, in the past, 40% of all adults favored capital punishment. Do we have reason to believe that the proportion of adults favoring capital punishment today has increased if, in a random sample of 15 adults, 8 favor capital punishment? Use a 0.05 level of significance.
Answers
Answer:
The p-value of the test is 0.1469 > 0.05, which means that there is no reason to believe that the proportion of adults favoring capital punishment today has increased, using a 0.05 level of significance.
Step-by-step explanation:
Suppose that, in the past, 40% of all adults favored capital punishment. Test if the proportion has increased:
At the null hypothesis, we test if the proportion is still of 40%, that is:
[tex]H_0: p = 0.4[/tex]
At the alternative hypothesis, we test if the proportion has increased, that is, is greater than 40%, so:
[tex]H_1: p > 0.4[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.4 is tested at the null hypothesis:
This means that [tex]\mu = 0.4, \sigma = \sqrt{0.4*0.6}[/tex]
Random sample of 15 adults, 8 favor capital punishment.
This means that [tex]n = 15, X = \frac{8}{15} = 0.5333[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.5333 - 0.4}{\frac{\sqrt{0.4*0.6}}{\sqrt{15}}}[/tex]
[tex]z = 1.05[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion of 0.5333 or more, which is 1 subtracted by the p-value of z = 1.05.
Looking at the z-table, z = 1.05 has a p-value of 0.8531.
1 - 0.8531 = 0.1469.
The p-value of the test is 0.1469 > 0.05, which means that there is no reason to believe that the proportion of adults favoring capital punishment today has increased, using a 0.05 level of significance.
find x on this special right triangle, 45 is not an option!!!!
Answers
let the line between 2 tria be y
sin 60/8√2 = sin 90/y
y=13.06
sin 45/13.06 = sin 90/x
x=18.46
Answer:
First, find the hypotenuse of the right triangle with the 60° & 30°.
Hypotenuse = hsin(x) = opposite side/hypotenuse[tex]sin(60) = \frac{8\sqrt{2}}{h} \\\\sin(60)h=8\sqrt{2}\\\\\frac{\sqrt{3}}{2} h=8\sqrt{2}\\\\h=\frac{8\sqrt{2}}{\frac{\sqrt{3}}{2}}=8\sqrt{2}*\frac{2}{\sqrt{3}} =\frac{16\sqrt{2} }{\sqrt{3}} =\frac{16\sqrt{2}(\sqrt{3}) }{\sqrt{3}(\sqrt{3})} =\frac{16\sqrt{6} }{3}[/tex]
Use that side length to find x.
sin(x) = opposite side/hypotenuse[tex]sin(45)=\frac{\frac{16\sqrt{6}}{3}}{x}\\\\sin(45)x=\frac{16\sqrt{6}}{3} \\\\\frac{\sqrt{2}}{2}x=\frac{16\sqrt{6}}{3} \\\\x=\frac{\frac{16\sqrt{6}}{3}}{\frac{\sqrt{2}}{2}}=\frac{16\sqrt{6}}{3}*\frac{2}{\sqrt{2}}=\frac{16\sqrt{2}\sqrt{3}(2)}{3\sqrt{2} }=\frac{32\sqrt{3} }{3}[/tex]
Which of the relations given by the following sets of ordered pairs is a function?
o {(5,2), ( - 4, 2), (3,6), (0,4), (- 1, 2)}
o {(5, 4), (5, 6), (5,8), (5, 10), (5, 12)}
{(-3, - 2), ( - 2, – 1), (0, - 1), (0, 1), (1, 2)}
{(7,3), ( – 6,8), ( – 3,5), (0, – 3), (7, 11)}
Answers
9514 1404 393
Answer:
(a) {(5, 2), (-4, 2), (3, 6), (0, 4), (-1, 2)}
Step-by-step explanation:
The only relation with no repeated x-values is the first one. The first relation is a function.
Jenny has borrowed K2500from a bank at 9.25% p.a. invested for 185 days. How much will she pay back to the bank?
Answers
Answer:
115.625
PRT/100
Steve thinks he can drive legally 30 minutes after he drinks 5 beers. The legal limit is BAC = 0.08. Give a 90% prediction interval for Steve’s BAC. Can he be confident he won’t be arrested if he drives and is stopped?
Answers
Answer: Hello your question has some missing data attached below is the missing data
How well does the number of beers a student drinks predict his or her blood alcohol content (BAC)? Sixteen student volunteers at Ohio State University drank a randomly assigned number of 12-ounce cans of beer. Thirty minutes later, a police officer measured their BAC. Here are the data. The students were equally divided between men and women and differed in weight and usual drinking habits. Because of this variation, many students don’t believe that number of drinks predicts BAC well.
answer:
prediction interval : (0.040 , 0.114)
Step-by-step explanation:
Given data:
Confidence level = 90%
Legal limit ( BAC ) = 0.08
solution
sample size = 16
Degree of freedom ( df ) = 14
critical t value = 1.761
X = 4.81
Σ(x-x)² (Sx) = 72.44
also standard error of estimates = 0.0204
Y= -0.01270 + 0.01796 * 5 = 0.077
given that ; the predicted value of Y at x = 5
Considering individual response Y
standard error = 0.0211
margin of error = 1.761 * 0.021 = 0.0371
Hence the limits of the prediction interval is :
Lower limit = 0.077 - 0.037 = 0.040.
Upper limit = 0.077 + 0.037 = 0.114
Finally
90% prediction interval = (0.040 , 0.114)
If (-2, y) lies on the graph of y = 3Y, then y =
Answers
y = 1/9
Step-by-step explanation:
(-2, y) = (x, y)
y = 3^x
y = 3^(-2)
y = 1/9
Therefore y = 1/9
Answer:
[tex]\displaystyle \frac{1}{9}[/tex]
Step-by-step explanation:
Hi there!
This question is asking us what the value of y is when x is -2, hence the point (-2,y).
[tex]y=3^x[/tex]
To find y, replace x in the equation with -2 and evaluate:
[tex]y=3^-^2[/tex]
When [tex]a^-^n[/tex] where n>0, [tex]a^-^n=\displaystyle \frac{1}{a^n}[/tex]:
[tex]y=\displaystyle \frac{1}{3^2} \\\\y=\displaystyle \frac{1}{9}[/tex]
I hope this helps!
Solve by elimination.
16x – 8y = 16
8x – 4y = 8
A. infinite number of solutions
B. (-2,-5)
c. (-20, -4)
R. (2,0)
Answers
Answer:
Step-by-step explanation:
16x-8y = 16 ⇒ 8x - 4y = 8, which is identical to the second equation.
The equations are equivalent, so there are an infinite number of solutions.
You are playing a game by drawing a card from a standard deck and replacing it. If the card is a face card, you win $30. If it is not a face card, you pay $2. There are 12 face cards in a deck of 52 cards. What is the expected value of playing the game
Answers
92 cardsㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
a motercycle can travel 60 miles per gallon. approximently how many gallons of fuel will the motercycle need to travel 40 km
[1 mile = 1.6km]
Answers
Answer:
Step-by-step ex0.72
If there is a maximum of 4,000 hours of labor available per month and 300 ping-pong balls (x1) or 125 wiffle balls (x2) can be produced per hour of labor, which of the following constraints reflects this situation?
a. 300x1 + 125x2 > = 4,000
b. 300x1 + 125x2 < = 4,000
c. 425(x1 + x2) < = 4,000
d. 300x1 + 125x2 = 4,000
Answers
Answer:
b. 300x1 + 125x2 < = 4,000
Step-by-step explanation:
Maximum of 4,000 hours
This means that the the total amount of labor has to be of at most 4,000, that is:
[tex]T \leq 4000[/tex]
300 ping-pong balls (x1) or 125 wiffle balls (x2) can be produced per hour of labor
The total amount of labor is:
[tex]T = 300x1 + 125x2[/tex]
Uniting the two equations:
[tex]T \leq 4000[/tex]
[tex]300x1 + 125x2 \leq 4000[/tex]
And thus the correct answer is given by option b.
Pls help I literally am crying I don’t understand ):
Answers
Answer: Passes out in slow
Step-by-step explanation:
Step 1 be Einstein
find the equation of the line
Answers
Megan and Suzanne each have a plant. They track the growth of their plants for four weeks.
Whose plant grew at a faster rate, and what was the rate?
Suzanne’s at 2 inches per week
Suzanne’s at 1.5 inches per week
Megan’s at 3 inches per week
Megan’s at 2.5 inches per week
Answers
Answer:
Megan’s at 2.5 inches per week
Suppose your Unit Quiz grades have been: 85%, 80%, 96%, 72%, 78%, 85% and 92%
a) What is your average/mean score?
b) What is the median score?
c) What is the mode score?
d) Why is the mean lower than the median?
e) What will your mean be if you get a perfect score of 100% on your next quiz?
Answers
Answer:
mean: 84
median: 85
mode: 85
explainations for d and e below.
Step-by-step explanation:
mean:
(85+80+96+72+78+85+92)/7 = 544/7 = 84
median:
sort them in order from least to greatest first
72, 78, 80, 85, 85, 92, 96
find the middle number in that order, that's your median. in this case, it's 85.
mode:
number that appears the most in the order; the frequency. in this case as well, it's also 85.
answer for d:
the reason why the mean is lower than the median is because of the fact we were figuring out the average and had to divide, unlike the median where it's just the middle of the order we have.
answer for e:
(85+80+96+72+78+85+92+100)/8 = 644/8 = 80.5%
p.s: please subscribe to #gauthmath# sub reddit if you can for more help.
Use the drop-down menu to create true statements,
If the graph of an inverse passes the
, you know that the inverse is
a function,
The composition of a function and its inverse is
always
DONE
DOWE
The range values of an inverse are the
values of the original function,
The graph of an inverse is the reflection of the
graph of the function over the line
DONE
DOWE
Answers
Answer:
A) Vertical test
B) y=x
C) x
D) domain
If the graph of an inverse passes the Vertical Line Test, you know that the inverse is a function.
What is Inverse Function?Inverse functions are functions which can be reversed in to another function.
Then the function is said to be the inverse of the second function.
The test which is used to know whether an inverse is a function or not is Vertical line Test.
So, if the graph of an inverse passes the Vertical Line Test, you know that the inverse is a function.
Composition of a function and it's inverse is always x.
Let y = f(x) be a function. Then x = f⁻¹ (y)
(f⁻¹of)(x) = f⁻¹ (f(x)) = f⁻¹ (y) = x
The graph of an inverse is the reflection of the graph of the function over the line y = x.
The range values of the inverse function are the domain values of the original function.
Hence the blank terms are found.
Learn more about Inverse of Functions here :
https://brainly.com/question/30350743
#SPJ7
Name this triangle by its sides and angles. This is a(n) ____________________ triangle.
A.obtuse, isosceles
B.right, scalene
C.obtuse, scalene
D.right, isosceles
Answers
Answer:
right scalene
Step-by-step explanation:
Since all three sides have different lengths , this is a scalene triangle
(isosceles means two sides have the same lengths and equilateral means all three sides have the same length)
We have a right angle indicated by the box in the corner
I conducted a poll and asked 1012 students how many books they read last year. The data indicates x = 12.1 books and s = 16.6 books. Construct a 90% confidence interval for the number of books the students read. Z = 1.645
Answers
Answer:
(11.242 ; 12.958)
Step-by-step explanation:
The confidence interval is obtained using the relation :
C. I = xbar ± Zcritical * s/√n
Given that ::
xbar = 12.1 ;
Standard deviation, s = 16.6
n = 1012
C. I = 12.1 ± 1.645 * (16.6/√1012)
C.I = 12.1 ± 0.8583881
C. I = 11.242 ; 12.958
