Answers
2500=8100+3025-2(90)(55)cos(C)
cos(C)=.8712
C=arccos(.8712)=29.4 degrees
Answer:
29.4 degrees
Step-by-step explanation:
i divided sin by 55 degrees
Related Questions
Solve the formula for the perimeter of a rectangle, with width w and length I,
for the length.
P= 2W + 2/
Answers
Answer:
( P -2w) /2 = l
Step-by-step explanation:
P= 2W + 2l
Subtract 2W from each side
P= 2W -2W + 2l
P -2W = 2l
Divide by 2
( P -2w) /2 = l
Answer:
A. [tex]\frac{P - 2w}{2} = l[/tex]
Step-by-step explanation:
Well in,
P = 2w + 2l
to solve for l we need to single it out.
P = 2w + 2l
-2w
P - 2w = 2l
divide everything by 2
[tex]\frac{P - 2w}{2} = l[/tex]
Thus,
the answer is A.
Hope this helps :)
A psychologist is studying the effects of lack of sleep on the performance of various perceptual-motor tasks. After a given period of sleep deprivation, a measurement of reaction time to an auditory stimulus was taken for each of 36 adult male subjects.The mean and standard deviation of the reaction times (in seconds) for the fifty adult male subjects were 1.82 seconds and 0.28 seconds respectively. Previous psychological studies have shown that the true mean reaction time for non-sleep-deprived male subjects is 1.70 seconds. Does the sample evidence indicate that the mean reaction time for sleep-deprived adult males is longer than that of non-sleep-deprived adult males.
A. H0:μ=1.82;Ha:μ<1.82
B. H0:μ=1.70;Ha:μ<1.70
C. H0:μ=1.82;Ha:μ>1.82
D. H0:μ=1.70;Ha:μ>1.70
E. None of the above
Answers
Answer:
D. [tex]H_{0}[/tex] : μ = 1.70, [tex]H_{a}[/tex] : μ > 1.70
Step-by-step explanation:
The correct order of the steps of a hypothesis test is given following
1. Determine the null and alternative hypothesis.
2. Select a sample and compute the z - score for the sample mean.
3. Determine the probability at which you will conclude that the sample outcome is very unlikely.
4. Make a decision about the unknown population.
These steps are performed in the given sequence to test a hypothesis
The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.
Use an appropriate series to find Taylor series of the given function centered at the indicated value of a. Write your answer in summation notation.
sinx, a= 2π
Answers
Answer:
The Taylor series is [tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]
Step-by-step explanation:
From the question we are told that
The function is [tex]f(x) = sin (x)[/tex]
This is centered at
[tex]a = 2 \pi[/tex]
Now the next step is to represent the function sin (x) in it Maclaurin series form which is
[tex]sin (x) = \frac{x^3}{3! } + \frac{x^5}{5!} - \frac{x^7}{7 !} +***[/tex]
=> [tex]sin (x) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]
Now since the function is centered at [tex]a = 2 \pi[/tex]
We have that
[tex]sin (x - 2 \pi ) = (x-2 \pi ) - \frac{(x - 2 \pi)^3 }{3 \ !} + \frac{(x - 2 \pi)^5 }{5 \ !} - \frac{(x - 2 \pi)^7 }{7 \ !} + ***[/tex]
This above equation is generated because the function is not centered at the origin but at [tex]a = 2 \pi[/tex]
[tex]sin (x-2 \pi ) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x - 2 \pi)^{2n+1}][/tex]
Now due to the fact that [tex]sin (x- 2 \pi) = sin (x)[/tex]
This because [tex]2 \pi[/tex] is a constant
Then it implies that the Taylor series of the function centered at [tex]a = 2 \pi[/tex] is
[tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]
√9m^2n^2 + 2√m^2n^2 - 3mn
Answers
Answer:
I think it is
Step-by-step explanation:
Answer:
5n√2m^ - 3mn
Step-by-step explanation:
Determine the measure of the unknown variables.
Answers
Answer:
75
Step-by-step explanation:
x = 75°
yes x = 75°(OPPOSITE ANGLES ARE EQUAL)
..
A group of 59 randomly selected students have a mean score of 29.5 with a standard deviation of 5.2 on a placement test. What is the 95% confidence interval for the mean score, , of all students taking the test
Answers
Answer:
The 95% confidence interval for the mean score, , of all students taking the test is
[tex]28.37< L\ 30.63[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 59[/tex]
The mean score is [tex]\= x = 29.5[/tex]
The standard deviation [tex]\sigma = 5.2[/tex]
Generally the standard deviation of mean is mathematically represented as
[tex]\sigma _{\= x} = \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]\sigma _{\= x} = \frac{5.2 }{\sqrt{59} }[/tex]
[tex]\sigma _{\= x} = 0.677[/tex]
The degree of freedom is mathematically represented as
[tex]df = n - 1[/tex]
substituting values
[tex]df = 59 -1[/tex]
[tex]df = 58[/tex]
Given that the confidence interval is 95% then the level of significance is mathematically represented as
[tex]\alpha = 100 -95[/tex]
[tex]\alpha =[/tex]5%
[tex]\alpha = 0.05[/tex]
Now the critical value at this significance level and degree of freedom is
[tex]t_{df , \alpha } = t_{58, 0.05 } = 1.672[/tex]
Obtained from the critical value table
So the the 95% confidence interval for the mean score, , of all students taking the test is mathematically represented as
[tex]\= x - t*(\sigma_{\= x}) < L\ \= x + t*(\sigma_{\= x})[/tex]
substituting value
[tex](29.5 - 1.672* 0.677) < L\ (29.5 + 1.672* 0.677)[/tex]
[tex]28.37< L\ 30.63[/tex]
If y>0, which of these values of x is NOT in the domain of this equation? y=x2+7x
Answers
Answer:
[tex]\boxed{\sf \ \ \ [-7,0] \ \ \ }[/tex]
Step-by-step explanation:
Hello
[tex]y=x^2+7x=x(x+7) >0\\<=> x>0 \ and \ x+7 >0 \ \ or \ \ x<0 \ and \ x+7<0\\<=> x>0 \ \ or \ \ x<-7\\[/tex]
So values of x which is not in this domain is
[tex]-7\leq x\leq 0[/tex]
which is [-7,0]
hope this helps
From past records it is known that 10% of items from a production
line are defective. If two items are selected at random, what is the
probability that only one is defective?
Answers
Answer: 0.18
Step-by-step explanation:
P(1 unit is defective)= C2 1* P^1*Q^1
C2 1= 2!/(1!*(2-1)!)=2
P=0.1 - probability that items from a production line are defective
Q=1-0.1=0.9 - probability that items from a production line are functional.
P(1 unit is defective)= 2*0.1*0.9=0.18
144 + h^2 = 225 WHAT THE HECK DOES ^ MEAN!???
Answers
Answer:
h^2 means h²
(h squared)
Step-by-step explanation:
Step 1: Write equation
144 + h² = 225
Step 2: Subtract 144 on both sides
h² = 81
Step 3: Take square root
√h² = √81
h = 9
solve the rational equation 5/x = 4x+1/x^2
Answers
Answer:
x = 1
Step-by-step explanation:
Set up the rational expression with the same denominator over the entire equation.
Since the expression on each side of the equation has the same denominator, the numerators must be equal
5x =4x+1
Move all terms containing x to the left side of the equation.
Hope this can help you
if 5x - 17 = -x +7, then x =
Answers
Answer:
x=4
Step-by-step explanation:
5x - 17 = -x +7
Add x to each side
5x+x - 17 = -x+x +7
6x -17 = 7
Add 17 to each side
6x-17+17 = 7+17
6x =24
Divide each side by 6
6x/6 = 24/6
x = 4
Answer:
4
Step-by-step explanation:
5x - 17 = -x + 7
Add x on both sides.
5x - 17 + x = -x + 7 + x
6x - 17 = 7
Add 17 on both sides.
6x - 17 + 17 = 7 + 17
6x = 24
Divide both sides by 6.
(6x)/6 = 24/6
x = 4
the perimeter of a square flower bed is 100 feet. what is the area of the flower bed in sqaure feet
Answers
Answer:
A =625 ft^2
Step-by-step explanation:
The perimeter of a square is
P = 4s where s is the side length
100 =4s
Divide each side by 4
100/4 = 4s/4
25 = s
A = s^2 for a square
A = 25^2
A =625
Sketch the region that corresponds to the given inequality. HINT [See Example 1.] 2x + y ≤ 10 Say whether the region is bounded or unbounded. The region is bounded. The region is unbounded. Find the coordinates of all corner points (if any). (If an answer does not exist, enter DNE.)
Answers
Answer:
See the attachment for sketch
Thr region is unbounded
DNE
Step-by-step explanation:
y≤ -2x + 10
The inequality is a straight line and region marked by the inequality. It has no boundaries. The boundaries extend to infinity. So the region is unbounded. Unbounded region has no corner points.
What is the next term in the sequence −10,−17,−24,−31,…?
Answers
Answer:
-38
Step-by-step explanation:
it's subtracting 7 everytime, and -31-7=-38
A pyramid shaped building is 311 feet tall and has a square base with sides of 619 ft. The sides of the building are made from reflective glass. what is the surface area of the reflective glass
Answers
Answer:
Surface area of the reflective glass is 543234.4 square feet.
Step-by-step explanation:
Given that: height = 311 feet, sides of square base = 619 feet.
To determine the slant height, we have;
[tex]l^{2}[/tex] = [tex]311^{2}[/tex] + [tex]309.5^{2}[/tex]
= 96721 + 95790.25
= 192511.25
⇒ l = [tex]\sqrt{192511.25}[/tex]
= 438.761
The slant height, l is 438.8 feet.
Considering one reflecting surface of the pyramid, its area = [tex]\frac{1}{2}[/tex] × base × height
area = [tex]\frac{1}{2}[/tex] × 619 × 438.8
= 135808.6
= 135808.6 square feet
Since the pyramid has four reflective surfaces,
surface area of the reflective glass = 4 × 135808.6
= 543234.4 square feet
A submarine is moving parallel to the surface of the ocean at a depth of 626 m. It begins a
constant ascent so that it will reach the surface after travelling a distance of 4420 m.
a) What angle of ascent, to the nearest tenth of a degree, did the submarine make? (3
marks)
b) How far did the submarine travel horizontally, to the nearest metre, during its ascent to
the surface? (3 marks)
Answers
Answer:
a) the angle of ascent is 8.2°
b) the horizontal distance traveled is 4375 m
Step-by-step explanation:
depth of ocean = 626 m
distance traveled in the ascent = 4420 m
This is an angle of elevation problem with
opposite side to the angle = 626 m
hypotenuse side = 4420 m
a) angle of ascent ∅ is gotten from
sin ∅ = opp/hyp = 626/4420
sin ∅ = 0.142
∅ = [tex]sin^{-1}[/tex] 0.142
∅ = 8.2° this is the angle of ascent of the submarine.
b) The horizontal distance traveled will be gotten from Pythagoras theorem
[tex]hyp^{2}[/tex] = [tex]opp^{2}[/tex] + [tex]adj^{2}[/tex]
The horizontal distance traveled will be the adjacent side of the right angle triangle formed by these distances
[tex]4420^{2}[/tex] = [tex]626^{2}[/tex] + [tex]adj^{2}[/tex]
adj = [tex]\sqrt{4420^{2}-626^{2} }[/tex]
adj = 4375 m this is the horizontal distance traveled.
Given f(x) and g(x) = f(x) + k, use the graph to determine the value of k. A) 2 B) 3 C) 4 D) 5 IF YOU ANSWER IN 5 MINUTES I WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!
Answers
Ans k = 4
Step-by-step explanation:
Here g(x) =[tex]\frac{-1}{3}x + 1[/tex] and
f(x) = [tex]\frac{-1}{3} x -3[/tex]
Now, g(x) = f(x) + k
or, [tex]\frac{-1}{3}x + 1[/tex] = [tex]\frac{-1}{3} x -3 + k[/tex]
or, 1 + 3 = k
So, k = 4 Answer.
Write the expression as the sine, cosine, or tangent of an angle. (6 points) cos 94° cos 37° + sin 94° sin 37°
Answers
Answer:
[tex]cos57 = 0.5446[/tex]
[tex]sin57 = 0.8387[/tex]
[tex]tan57 = 1.5399[/tex]
Step-by-step explanation:
Given
[tex]cos 94\° cos 37\° + sin 94\° sin 37\°[/tex]
Required
Determine the
- sin
- cosine
- tangent
of an angle
The given expression can be represented as follows;
[tex]cosAcosB + sinAsinB[/tex]
Where A = 94 and B = 37
In trigonometry:
[tex]cosAcosB + sinAsinB = cos(A - B)[/tex]
Substitute 94 for A and 37 for B
[tex]cos(A - B) = cos(94 - 37)[/tex]
[tex]cos(A - B) = cos(57)[/tex]
Hence, the angle is 57;
Since 57 is not a special angle; I'll solve using a calculator
[tex]cos57 = 0.5446[/tex]
[tex]sin57 = 0.8387[/tex]
[tex]tan57 = 1.5399[/tex]
h(x)=-4+16 find x when h(x)=48 Plz don't say it is incomplete
Answers
Answer:
x = -8
Step-by-step explanation:
When h(x) = 48, you can simply just plug it back into the first equation. Don't let the h(x) confuse you!
Think of it like saying y = -4x + 16, y = 48.
48 = - 4x + 16
32 = - 4x
8 = -x
Divide by -1 both sides.
-8 = x
A car dealership earns a portion of its profit on the accessories sold with a car. The dealer sold a Toyota Camry loaded with accessories for $24,000. The total cost of the car was 8 times as much as the accessories. How much did the accessories cost? Cost of Accessories
Answers
Answer:
y = 2666.67
Step-by-step explanation:
Well to solve this we can make a system of equations.
x = cost of car alone
y = cost of accesories,
[tex]\left \{ {{x+y=24000} \atop {x=8y}} \right.[/tex]
So now we plug in 8y for x in x + y = 24000.
(8y) + y = 24000
9y = 24000
Divide both sides by 9
y = 2666.666666
or 2666.67 rounded to the nearest hundredth.
Now that we have y we can plug that in for y in x=8y.
x = 8(2.666.67)
x = 21,333.33 rounded to the nearest hundredth.
Thus,
accessories "y" cost around 2666.67.
Hope this helps :)
What is the slope of the line
described by -4X + 2Y = 16?
A. -2
B. -4
C. 4
D. 2
E. 16
Answers
Answer: THe slope is 2
SO answer d
Step-by-step explanation:
-4X + 2Y = 16 add 4x to the other side so equation is
2y=16+4x divided by 2
y=8+2x
What is 24-(-6) because in confused
Answers
Answer:
30
Step-by-step explanation:
24 - (-6)
Apply rule : -(-a) = a
Negative (-) times a negative (-) is positive (+).
24 + 6
= 30
Answer:
-6 is in parentheses because it is a negative number. this prevents the equation from looking like a too long subtraction sign (24--6); therefore it is written as 24 - (-6).
this simplifies to 24 + 6 = 30
to negatives = a positive
Can you draw the reflection Across the y-axis of the attached image.
Answers
Answer:
see graph
Step-by-step explanation:
A reflection across the y-axis means the point is equal but opposite distance from the y-axis. This has no change on the y-value of the point, because no matter the y-value, the point will still be the same distance from the y-axis. Long story short, if you're reflecting across the y-axis, change the sign of the x-coordinate. If you're reflecting across the x- axis, change the sign of the y-coordinate.
WHY CAN'T ANYONE HELP ME? PLEASE What one is the standard form of the equation y = – 1/4 x – 2? A. x + 4y = 8 B. x + 4y = – 2 C. x + 4y = – 8 or D. –x + 4y = – 8
Answers
Answer:
C. x+4y=-8
Step-by-step explanation:
The standard form of an equation is Ax+Bx=C
y= -[tex]\frac{1}{4}[/tex]x-2
Multiply 4 by both sides
4y= -x-8
1+4y= -8
The average college lecture hall (auditorium) can seat 60 students with a standard deviation of 21. Assume that a total of 60 lecture halls are selected for a sample. What is the standard deviation for the sample mean?
Answers
Answer:
The standard deviation of the sample mean is [tex]\sigma _ {\= x } = 2.711[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\= x = 60[/tex]
The standard deviation is [tex]\sigma = 21[/tex]
The sample size is [tex]n = 60[/tex]
Generally the standard deviation of the sample mean is mathematically represented as
[tex]\sigma _ {\= x } = \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]\sigma _ {\= x } = \frac{ 21 }{\sqrt{60} }[/tex]
[tex]\sigma _ {\= x } = 2.711[/tex]
67.805 what is the value of the 0 help please asap!
Answers
Answer:
hundreths
Step-by-step explanation:
After the decimal there is tenths, hundreths thousandnths, tens of thousands e.t.c
Answer:
Hello! The answer will be hundredths.
Step-by-step explanation:
The 5 means the thousandths.
The 0 means the hundredths.
The 8 means the tenths.
The 7 means the ones
And the 6 means the tens.
Hope this helps! :)
( below I attached a picture, which might be helpful.)
A distribution has a mean of 90 and a standard deviation of 15. Samples of size 25 are drawn randomly from the population. Find the probability that the sample mean is more than 85 g
Answers
Answer:
The probability is 0.04746
Step-by-step explanation:
Firstly, we calculate the z-score here
Mathematically;
z-score = x-mean/SD/√n
Where from the question;
x = 85, mean = 90 , SD = 15 and n = 25
Plugging these values into the equation, we have;
Z = (85-90)/15/√25 = -5/15/5 = -1.67
So the probability we want to calculate is ;
P(z > -1.67)
We use the standard normal distribution table for this;
P(z > -1.67) = 0.04746
An HR manager would like to test the hypothesis that the proportion of agenda-less meetings is more than 45%. Based on the information below, choose the correct conclusion for this hypothesis test. To test this, he randomly selected minutes from 100 past meeting, and found that 65 of them had no agenda. The following is the setup for this hypothesis test: H0:p=0.45 Ha:p>0.45 The p-value for this hypothesis test is 0.025. At the 5% significance level, should he reject or fail to reject the null hypothesis? Select the correct answer below: Reject the null hypothesis because 0.45>0.05. Fail to reject the null hypothesis because 0.45>0.05. Reject the null hypothesis because the p-value =0.025 is less than the significance level α=0.05. Fail to reject the null hypothesis because the p-value =0.025 is less than the significance level α=0.05.
Answers
Answer: Reject the null hypothesis because the p-value =0.025 is less than the significance level α=0.05.
Step-by-step explanation: Trust me
Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative.)
f ''(x)= 6x +sinx
Answers
Answer:
[tex]f(x) = x^3 -sinx +Cx+D[/tex]
Step-by-step explanation:
Given that:
[tex]f ''(x)= 6x +sinx[/tex]
We are given the 2nd derivative of a function f(x) and we need to find f(x) from that.
We will have to integrate it twice to find the value of f(x).
Let us have a look at the basic formula of integration that we will use in the solution:
[tex]1.\ \int {(a\pm b)} \, dx =\int {a} \, dx + \int {b} \, dx \\2.\ \int {x^n} \, dx = \dfrac{x^{n+1}}{n+1}+C\\3.\ \int {sinx} \, dx = -cosx+C\\4.\ \int {cosx} \, dx = sinx+C[/tex]
[tex]\int\ {f''(x)} \, dx =\int\ {(6x +sinx)} \, dx \\\Rightarrow \int\ {6x} \, dx + \int\ {sinx} \, dx \\\\\Rightarrow 6\dfrac{x^2}{2} -cosx +C\\\Rightarrow 3{x^2} -cosx +C\\\Rightarrow f'(x)=3{x^2} -cosx +C\\[/tex]
Now, integrating it again to find f(x):
[tex]f(x) =\int {f'(x)} \, dx =\int{(3{x^2} -cosx +C)} \, dx \\\Rightarrow \int{3{x^2}} \, dx -\int{cosx} \, dx +\int{C} \, dx\\\Rightarrow 3\times \dfrac{x^3}{3} -sinx +Cx+D\\\Rightarrow x^3 -sinx +Cx+D\\\\\therefore f(x) = x^3 -sinx +Cx+D[/tex]
What is the value of y iin this equation? 4(y-3) =48
Answers
Answer:
y = 15Step-by-step explanation:
Question:
4(y - 3) = 48
1. Distribute
4y - 12 = 48
2. Simplify Like terms
4y - 12 = 48
+ 12 + 12
4y = 60
3. Solve
4y = 60
/4 /4
y = 15
4. Check:
4(y - 3) = 48
4((15) - 3) = 48
4(12) = 48
48 = 48 Correct!
Hope this helped,
Kavitha
Answer:
[tex]y=15\\[/tex]
Step 1:
To find y, we first have to multiply [tex]4(y-3)[/tex]. When we do that (4 * y, 4 * - 3), we get [tex]4y-12[/tex].
Step 2:
Our equation looks like this now:
[tex]4y-12=48[/tex]
To solve this equation, we have to add 12 on both sides so we can cancel out the -12 on the left side of the equation.
[tex]4y-12(+12)=48(+12)[/tex]
[tex]4y=60[/tex]
Now, we can divide 4 on both sides to get y by itself.
[tex]4y/4\\60/4[/tex]
[tex]y=15[/tex]