Answers
Answer:
6. 156.6 cm
7. 687.7’
Step-by-step explanation:
45 cm and 150 cm are the legs of one triangle.
The longest side is the hypotenuse.
Apply Pythagorean theorem, since the two triangles are right triangles.
a² + b² = c²
a and b are the legs, c is the hypotenuse.
45² + 150² = c²
24525 = c²
√24525 = c
c = 156.604597634...
c ≈ 156.6
Brain hang-glided from a 520’ high cliff. He landed 450’ away from the base of the cliff. Create a right triangle and apply Pythagorean theorem. The distance he travelled is the hypotenuse of the triangle. The 520’ and 450’ are the legs.
a² + b² = c²
450² + 520² = c²
c² = 472900
c = √472900
c = 687.677249878...
c ≈ 687.7
Answer: 6) =approx 156.60 cm
7) =approx 687.68'
Step-by-step explanation:
6. Let the shortest side of the triangle is AB=45 cm ( ∡A=90° so ABCD is a rectangle). The middle side AD=150 cm. The longest side is BD
The length of BD can be calculated using Phitagore theorem because triangle BAD ia right angle.
BD=sqrt(AD²+AB²)=sqrt(2025+22500)=approx 156.60 cm
7. So we can create the model of the situation described in this problem.
The model is right-angle triangle ABC with side AB=520' ,side AC=450', right angle is A. So we have to find the length of side BC .
BC is hypotenuse of triangle ABC. We can find it using Phitagore theorem again.
BC=sqrt(AC²+AB²)=sqrt(450²+520²)=sqrt(472900)=approx 687.68'
Related Questions
A circle has a radius of 8ft. Find the length s of the arc intercepted by a central angle of π3 radians. Do not round any intermediate computations, and round your answer to the nearest tenth.
Answers
Answer:
8.4ft
Step-by-step explanation:
Formula for calculating the length of an arc is expressed as [tex]L = \frac{\theta}{360} * 2\pi r\\[/tex]
[tex]\theta[/tex] is the central angle = π/3 rad
r is the radius of the circle = 8ft
Substituting the values into the formula above we have;
[tex]L =[/tex] [tex]\frac{(\frac{\pi}{3} )}{2 \pi} * 2\pi (8)\\\\[/tex]
[tex]L = \frac{\pi}{6 \pi} * 2\pi(8) \\\\L = 1/6 * 16\pi\\\\L = 8\pi/3\\\\L = \frac{8(22/7)}{3} \\\\L = \frac{8*22}{7*3}\\ \\L = 176/21\\\\L = 8.4 ft (to\ the\ nearest\ tenth)[/tex]
Hence, the length of the arc s is approximately 8.4 ft.
Does the data in the table represent a direct variation or an inverse variation write an equation to model the data in the table x 6,8,12,20 y 9,12,18,30
Answers
Answer:
direct variation
Step-by-step explanation:
For direct variation k = [tex]\frac{y}{x}[/tex] ← k is the constant of variation
For inverse variation k = yx
Expressing the data as ordered pairs
(6, 9), (8, 12), (12, 18), (20, 30)
k = [tex]\frac{9}{6}[/tex] = [tex]\frac{12}{8}[/tex] = [tex]\frac{18}{12}[/tex] = [tex]\frac{30}{20}[/tex] = [tex]\frac{3}{2}[/tex] = 1.5 ← indicating direct variation
Equation is
y = kx = 1.5x
I got the 90 and 8.9 for them but it’s wrong. I really confused now. What is the right answer??? Can someone explain to me ASAP?!!!!
Answers
Answer:
[tex] A = 70.6 [/tex] ≈ 71°
[tex] x = 36.5 [/tex]
Step-by-step explanation:
Step 1: Use the Law of sine to find A
[tex] \frac{sin(A)}{38} = \frac{sin(44)}{28} [/tex]
Cross multiply:
[tex] sin(A)*28 = sin(44)*38 [/tex]
[tex] sin(A)*28 = 0.695*38 [/tex]
Divide both sides by 28:
[tex] \frac{sin(A)*28}{28} = \frac{0.695*38}{28} [/tex]
[tex] sin(A) = 0.9432 [/tex]
[tex] A = sin^{-1}(0.9432) [/tex]
[tex] A = 70.6 [/tex]
A ≈ 71°
Step 2: find the measure of the angle opposite side x
Angle opposite side x = 180 - (71+44) (sum of triangle)
= 180 - 115 = 65°
Step 3: find x using the law of sines
[tex] \frac{x}{sin(65)} = \frac{28}{sin(44)} [/tex]
[tex] \frac{x}{0.906} = \frac{28}{0.695} [/tex]
Multiply both sides by 0.906
[tex] x*0.695= 28*0.906 [/tex]
Divide both sides by 0.695
[tex] \frac{x*0.695}{0.695} = \frac{28*0.906}{0.695} [/tex]
[tex] x = \frac{28*0.906}{0.695} [/tex]
[tex] x = 36.5 [/tex]
prove identity trigonometric equation
[tex]2 \tan(x) = \frac{ \cos(x) }{ \csc(x - 1) } + \frac{ \cos(x) }{ \csc(x + 1) } [/tex]
Answers
Explanation:
The given equation is False, so cannot be proven to be true.
__
Perhaps you want to prove ...
[tex]2\tan{x}=\dfrac{\cos{x}}{\csc{(x)}-1}+\dfrac{\cos{x}}{\csc{(x)}+1}[/tex]
This is one way to show it:
[tex]2\tan{x}=\cos{(x)}\dfrac{(\csc{(x)}+1)+(\csc{(x)}-1)}{(\csc{(x)}-1)(\csc{(x)}+1)}\\\\=\cos{(x)}\dfrac{2\csc{(x)}}{\csc{(x)}^2-1}=2\cos{(x)}\dfrac{\csc{x}}{\cot{(x)}^2}=2\dfrac{\cos{(x)}\sin{(x)}^2}{\cos{(x)}^2\sin{(x)}}\\\\=2\dfrac{\sin{x}}{\cos{x}}\\\\2\tan{x}=2\tan{x}\qquad\text{QED}[/tex]
__
We have used the identities ...
csc = 1/sin
cot = cos/sin
csc^2 -1 = cot^2
tan = sin/cos
What are the next three terms in the sequence -27, -19, -11, -3, 5, ...?
Answers
Answer:
13, 21
Step-by-step explanation:
Add 8 to the next number from the left to the right.
Answer:
The next three numbers in the sequence are: 13, 21, 29.
Step-by-step explanation:
Common Pattern: +8
-27 +8 = -19
-19 + 8 = -11
-3 + 8 = 5
5 + 8 = 13
13 + 8 = 21
21 + 8 = 29
In horse race betting, a trifecta bet is one in which you try to pick which horses will finish first, second, and third, in the correct order. If 8 horses are running in a race and you randomly place a trifecta bet, what is the probability of winning the bet
Answers
Answer:
The probability of winning the bet is 1/336
Step-by-step explanation:
We should understand that there is only one possible arrangement of the winning selection
Now, the horse that comes first can be selected in 8 ways given that all the horses have equal chances
The horse that comes second can be selected in 7 ways given that all the horses have equal chances
The horse that comes third can be selected in 6 ways given that all the horses have equal chances
Now the total number of ways of selection would be;
8 * 7 * 6 = 336
Since there is only one of the selections that is correct, the probability of making the correct choice is thus 1/336
The true average diameter of ball bearings of a certain type is supposed to be 0.5 in. A one-sample t test will be carried out to see whether this is the case. What conclusion is appropriate in each of the following situations?
(a) n = 15, t = 1.66, a = 0.05
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(b) n = 15, t = 1.66, a = 0.05
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(c) n = 26, t = 2.55, a = 0.01
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(d) n = 26, t = 3.95
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
You may need to use the appropriate table in the Appendix of Tables to answer this question.
Answers
Answer:
Option C - Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
Step-by-step explanation:
We are given;
n = 15
t-value = 1.66
Significance level;α = 0.05
So, DF = n - 1 = 15 - 1 = 14
From the one-sample t - table attached, we can see that the p - value of 0.06 at a t-value of 1.66 and a DF of 14
Now, since the P-value is 0.06,it is greater than the significance level of 0.05. Thus we do not reject the null hypothesis. We conclude that there is not sufficient evidence that the true diameter differs from 0.5 in.
For f(x) = 4x + 1 and g(x) = x2 – 5, find (f – g)(x).
Answers
Answer:
(f – g)(x) = - x² + 4x + 6Step-by-step explanation:
f(x) = 4x + 1
g(x) = x² – 5
To find (f – g)(x) subtract g(x) from f(x)
That's
(f – g)(x) = 4x + 1 - ( x² - 5)
Remove the bracket
(f – g)(x) = 4x + 1 - x² + 5
Group like terms
(f – g)(x) = - x² + 4x + 1 + 5
We have the final answer as
(f – g)(x) = - x² + 4x + 6Hope this helps you
What is the 13th term of this arithmetic sequence? 132, 135, 138, 141, …
a 168
b 172
c 176
d 179
Answers
Answer:
182
Step-by-step explanation:
The sequence has a common difference of +3.
Answer:
It's none of those. It's supposed to be 171.
Step-by-step explanation:
That's because in an arithmetic sequence it's a list of numbers with a definite pattern, and all you're doing is adding 3 to each number.
Edgar accumulated $5,000 in credit card debt. If the interest rate is 20% per year and he does not make any payments for 2 years, how much will he owe on this debt in 2 years by compounding continuously? Round to the nearest cent.
Answers
Answer:
Loan amount due after 2 years =$7,387.28
Explanation:
The amount due on the loan would be equal to the total accrued interest plus the accumulated amount amount.
Note that, since Edgar did not pay any amount off the loan in the course of the 2 years, the interest due per quarter would be equal to the quarterly interest rate multiplied by the unpaid balance till date.
To determine the amount due, we would compound $5,000 at a quarterly interest rate of for 8 quarters. The formula below would suffice
Loan amount due = loan balance × (1+r)^(n)
Quarterly interest rate -20%/4 =5%, number of quarters - 2× 4 =8, loan balance - 5,000
Loan amount due = 5,000 × (1.05)^(8)
= 7,387.28
Loan amount due after 2 years =$7,387.28
Step-by-step explanation:
Answer:
7434.57
Step-by-step explanation:
Simplify the polynomial, then evaluate for x=3 x^2+2x-3-2x^2+x+4
Answers
Answer:
The answer is
19Step-by-step explanation:
x² + 2x - 3 - 2x² + x + 4
Group like terms
That's
x² - 2x² + 2x + x - 3 + 4
Simplify
- x² + 3x + 1
when x = 3
We have
(-3)² + 3(3) + 1
9 + 9 + 1
18 + 1
19
Hope this helps you
WILL MARK AS BRAINLIEST 4. Suppose there is a card game where you are dealt a hand of three cards. You have already learned that the total number of three-card hands that can be dealt from a deck of 52 cards is: 52C3=52!/49!3! 52C3=22100 Calculate the probability of getting a hand that has exactly two aces in it (A A X). Do this by finding out the number of possible hands that have exactly two aces, and then dividing by the total possible number of three-card hands that is stated above. Part A: Use the multiplication principle to tell the total number of three-card hands (permutations) that can be made with two aces. (2 points) Part B: In the answer from Part I, each two-ace hand got counted twice. For example, A A X got counted as a separate hand from A A X. Since order should not matter in a card hand, these are really the same hand. What is the actual number of two-ace hands (combinations) you can get from a deck of 52 cards?(2 points) Part C: Find the probability of drawing a three-card hand that includes two aces from a deck of 52 cards. Write your answer as a fraction. (2 points)
Answers
Answer:
Part A- 6
Part B- 3
Part C- 3/22100
Step-by-step explanation:
Part A-
Use the permutation formula and plug in 3 for n and 2 for k.
nPr=n!/(n-k)!
3P2=3!/(3-2)!
Simplify.
3P2=3!/1!
3P2=6
Part B-
Use the combination formula and plug in 3 for n and 2 for k.
nCk=n!/k!(n-k)!
3C2=3!/2!(3-2)!
Simplify.
3C2=3!/2!(1!)
3C2=3
Part C-
It is given that the total number of three-card hands that can be dealt from a deck of 52 cards is 22100. Use the fact that the probability of something equals the total successful outcomes over the sample space. In this case the total successful outcomes is 3 and the sample space is 22100.
I believe the answer is 3/22100
I honestly suck at probability but I tried my best.
Factories fully 18x-9
Answers
Answer:
Factor 9 out of 18x.
9(2x)−9
Factor 9 out of −9
9(2x)+9(−1)
Factor 9 out of 9(2x)+9(−1)
9(2x−1)
Answer:
9 ( 2x - 1 )
Step-by-step explanation:
→ Look for the HCF of the whole numbers
HCF of 18 and 9 is 9
→ Put 9 outside the brackets
9 ( ? - ? )
→ Perform the calculation 18x ÷ 9 to determine the first question mark
18x ÷ 9 = 2x ⇔ 9 ( 2x - ? )
→ Perform the calculation 9 ÷ 9 to determine the second question mark
9 ÷ 9 = 1 ⇔ 9 ( 2x - 1 )
Please answer this correctly without making a mistake I need a correct answer
Answers
Answer: 45.5
Step-by-step explanation:
Im in 6th grade and all you had to do was add 18.3 and 27.2 and you’ll get 45.5
Answer:
The garbage dump is 58.3 miles west of the hotel, and the hotel is 57.1 miles west of the hardware store. The hardware store is 44.8 miles west of the library. The hardware store is 57.9 miles north of the office supply store, and the office supply store is 55.5 miles north of the science lab.
Step-by-step explanation:
Emma buys 3 and two-thirds yards of blue fabric and some yellow fabric at a store. She buys a total of 5 and one-third yards of fabric. The equation 5 and one-third = 3 and two-thirds + y can be used to represent this situation, where y is the number of yards of yellow fabric she buys. How much yellow fabric does she buy?
Answers
Answer:
A) 1 2/3 yards
Step-by-step explanation:
Hope this helped
Answer:
The answer is A
Let me finish the quiz then upload a picture to this answer showing you the correct answer is A
Step-by-step explanation:
An urn contains 3 one-dollar bills, 1 five-dollar bill and 1 ten-dollar bill. A player draws bills one at a time without replacement from the urn until a ten-dollar bill is drawn. Then the game stops. All bills are kept by the player. Determine: (A) The probability of winning $12. (B) The probability of winning all bills in the urn. (C) The probability of the game stopping at the second draw.
Answers
Hey there! I'm happy to help!
PART A
There are 3 $1 bills, 1 $5 bill, and 1 $10 bill. This gives us 5 total bills.
First, we want to find the probability of winning $12. Well, to win, you have to draw the $10 bill. You only have room for two dollars beforehand to equal $12 dollars after pulling out the ten. So, this is the probability of drawing two one dollar bills and the the ten. Let's calculate this below.
[tex]\frac{3}{5} *\frac{1}{2} *\frac{1}{3} =\frac{1}{10}[/tex]
Where did I get these numbers from? Well 3 of the 5 bills are $1, so the first probability is 3/5. Then, if we draw one of the $1 bills, there are only 2 of those left and 4 total bills, so the probability is then one half. Finally, there would be only 3 left and you need to pick the $10 bill, which is a probability of 1/3.
The probability of winning $12 is 1/10 or 10%.
PART B
Now, we want to find the probability of picking every single bill before the ten. This means that we pick the three one dollar bills and the five dollar bill before the ten.
To pick the first $1 bill, our probability is 3/5, and then for the second it is 1/2. For the third, there are three total cards and 1 $1 bill, so the probability is 1/3. Then we have a 1/2 chance of picking the $5 bill over the $10 bill, giving us this solution.
[tex]\frac{3}{5} * \frac{1}{2} * \frac {1}{3} * \frac{1}{2}= \frac{1}{20}[/tex]
The probability of winning all bills in the urn is 1/20 or 5%.
PART C
For this event, we want to get any bill that isn't the $10 and then we want the $10 on the second one.
Since there are 4 bills that aren't the $10, our first probability is 4/5. Then, we only have 4 left, with 1 being the $10, so our second probability is 1/4.
[tex]\frac{4}{5}*\frac{1}{4}=\frac{1}{5}[/tex]
The probability of the game stopping at the second draw is 1/5 or 20%.
Have a wonderful day! :D
The probability of winning $12 will be 0.15.
How to calculate probability?The game stops after drawing$10 bill. There can also be 2 draws of $2 and $10 to make $12.
Therefore, the probability of winning $12 will be calculated thus:
= Probability of getting $2 × probability of getting $10
= 3/5 × 1/4
= 0.15
The probability of winning all balls in the urn will be:
= 4/5 × 3/4 × 2/3 × 1/2
= 0.2
Lastly, the probability of the game stopping at the second draw will be:
= First draw × Second draw
= 4/5 × 1/4
= 0.2
Learn more about probability on:
https://brainly.com/question/24756209
Which situation is most likely to have a constant rate of change?
HELP
Answers
Answer:
the answer i would go with is A
Good luck on your Test :)
Step-by-step explanation:
B doesnt really have a constant rate of change as it depends on how many games happen and usually the longer an arena stays open has no correlation on how many people attend the games there
C has no real constant rate of change as it always ends up stopping after a little bit, and the change is usually not a constant one
D this could count, but since its a number that would go down if its not brought back up, its not a real constant rate of change, since it cant go below or above a certain range
so by process of elimination, A is the answer. also seeing as how its saying the distance with the number of times, that means that its an objective thing, as a track is a set distance, and the distance of a run or the track cant be affected by time or anything and could technically never end. so its a constant thing, meaning the longer the distance is, the higher the laps around the track are, and it could theoretically go on forever.
i hope this helped answer your question! :)
6th grade math, help me please.
Answers
Answer:
1:3
Step-by-step explanation:
3/3=1
9/3=6
Answer:
1 : 3Option A is the correct option.
Step-by-step explanation:
Given,
Number of pears = 3
Number of apples = 9
Find : Ratio of the number of pears to the number of apples on the fruit salad
Now,
[tex] \frac{pear}{apples} [/tex]
Plug the values
[tex] = \frac{3}{9} [/tex]
Divide the numerator and denominator by 3
[tex] = \frac{3 \div 3}{9 \div 3} [/tex]
Divide the numbers
[tex] = \frac{1}{3} [/tex]
It can be written as :
1 : 3
Hope this helps..
Best regards!!!
3. The area of a rectangular deck, in square meters, is given by the polynomial 40p2 + 24p.
The deck is 8p meters wide.
a) Find the polynomial that represents the length of the deck.
b) Find the polynomial that represents the perimeter of the deck.
Answers
Answer:
Length = 5p + 3
Perimeter = 26p + 6
Step-by-step explanation:
Given
Area = 40p² + 24p
Width = 8p
Solving for the length of deck
Given that the deck is rectangular in shape.
The area will be calculated as thus;
Area = Length * Width
Substitute 40p² + 24p and 8p for Area and Width respectively
The formula becomes
40p² + 24p = Length * 8p
Factorize both sides
p(40p + 24) = Length * 8 * p
Divide both sides by P
40p + 24 = Length * 8
Factorize both sides, again
8(5p + 3) = Length * 8
Multiply both sides by ⅛
⅛ * 8(5p + 3) = Length * 8 * ⅛
5p + 3 = Length
Length = 5p + 3
Solving for the perimeter of the deck
The perimeter of the deck is calculated as thus
Perimeter = 2(Length + Width)
Substitute 5p + 3 and 8p for Length and Width, respectively.
Perimeter = 2(5p + 3 + 8p)
Perimeter = 2(5p + 8p + 3)
Perimeter = 2(13p + 3)
Open bracket
Perimeter = 2 * 13p + 2 * 3
Perimeter = 26p + 6
You are returning from Mexico and want to convert 5,00 pesos to US dollar . The rate of exchange that day is 1 pesos is 0.55 . How many dollars will you receive for your pesos ?
Answers
Hey there! I'm happy to help!
We see that 1 peso is equal to 0.55 U.S. dollars. So, the amount we will get in U.S dollars is the same as $5000×0.55 because 0.55 US dollars is equal to one peso!
5000×0.55=2750
Therefore, you will receive $2750.
Have a wonderful day!
Write the equation of the line, in point-slope form. Identify (x, y) as the point (-2, 2). Use the box provided or the upload
option to submit all of your calculations and final answers.
Answers
Answer:
y = -x + 0
Step-by-step explanation:
well the equation of a line is y = mx + b
m = the slope , b = the y-intercept
m = y2 - y1 / x2 - x1
m = -1
and b is the y-intercept of the line.
finally:
y = -1x + 0
Find the area of the polygon shown in the figure.
Answers
Answer:
Hey there!
Area for a triangle: 0.5bh, where b is the base, and h is the height.
Plugging in the values: 0.5(4)(8), or simplified to 16.
The area of the polygon is 16 units^2
Hope this helps :)
Answer:
[tex]\boxed{16 \: units^2}[/tex]
Step-by-step explanation:
Apply formula for area of a triangle.
Area of a triangle = [tex]\frac{1}{2} bh[/tex]
[tex]b:base\\h:height[/tex]
The base is 4 units. The height is 8 units.
[tex]\frac{1}{2} (4)(8)[/tex]
[tex]\frac{1}{2} (32)=16[/tex]
find the product 8x(2x^2+8x-5)
Answers
Answer:
16x^3 +64x^2 -40x
Step-by-step explanation:
Use the distributive property. The factor outside parentheses multiplies each term inside parentheses:
8x(2x^2 +8x -5) = (8x)(2x^2) +(8x)(8x) +(8x)(-5)
= 16x^3 +64x^2 -40x
A small fruit basket with 6 apples and 6 oranges costs $7.50. A different fruit basket with 10 apples and 5 oranges costs $8.75. If x is the cost of one apple and y is the cost of one orange, the system of equations below can be used to determine the cost of one apple and one orange. 6x+6y=7.50 10x+5y=8.75
Answers
Answer:
x = $0.50
y= $0.75
Step-by-step explanation:
1. Multiply the equations to have the same coefficients
5(6x + 6y = 7.5) → 30x + 30y = 37.5
3(10x + 5y = 8.75) → 30x + 15y = 26.25
2. Subtract the equations
30x + 30y = 37.5
- 30x + 15y = 26.25
15y = 11.25
3. Solve for y by dividing both sides by 15
y = 0.75
4. Plug in 0.75 for y into one of the equations
6x + 6(0.75) = 7.5
5. Simplify
6x + 4.5 = 7.5
6. Solve for x
6x = 3
x = 0.5
Answer:
The cost of one apple is $0.5
The cost of one orange is $0.75
Step-by-step explanation:
Given information
The cost of an apple = [tex]x[/tex]
The cost of an orange = [tex]y[/tex]
Equation to find the values are:
[tex]6x=6y=7.50\\10x+5y=8.75[/tex]
Now, convert the equations to have same coefficient as:
[tex]5(6x=6y=7.50)\\=30x+30y=37.5\\3(10x+5y=8.75)\\=30x+15y=26.25[/tex]
Now, on solving the above equation by subtracting one from another.
We get,
[tex]15y=11.25\\y=0.75[/tex]
Now , put the value of [tex]y[/tex] in one equation to find the value of [tex]x[/tex].
As,
[tex]6x+4.5=7.5\\x=0.5[/tex]
Hence,
The cost of one apple is $0.5
The cost of one orange is $0.75
For more information visit
https://brainly.com/question/11897796?referrer=searchResults
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.
Find the work done by the force field F(x, y) = xi + (y + 5)j in moving an object along an arch of the cycloid r(t) = (t − sin(t))i + (1 − cos(t))j, 0 ≤ t ≤ 2π.
Answers
Integrate the force field along the given path (call it C):
[tex]W=\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=\int_0^{2\pi}\mathbf F(x(t),y(t))\cdot\frac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^{2\pi}\bigg((t-\sin t)\,\mathbf i+(6-\cos t)\,\mathbf j\bigg)\cdot\bigg((1-\cos t)\,\mathbf i+\sin t\,\mathbf j\bigg)\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^{2\pi}(t-t\cos t+5\sin t)\,\mathrm dt=\boxed{2\pi^2}[/tex]
By direct calculation we will find that the work done is equal to 2π²
The formula to compute the work done is given by:
[tex]W = \int\limits^a_b {F(x(t), y(t))\cdot\frac{dr(t)}{dt} } \, dt[/tex]
Here we have:
[tex]r(t) = (t - sin(t))i + (1 - cos(t))j[/tex]
This means that:
[tex]x(t) = (t - sin(t))\\y(t) = (1 - cos(t))\\\\\frac{dr(t)}{dt} = (1-cos(t))i + sin(t)j = (1-cos(t), sin(t))[/tex]
And we know that 0 ≤ t ≤ 2π, so b = 0 and a = 2π
Replacing that in the work integral we get:
[tex]W = \int\limits^{2\pi}_0 {(t - sin(t), 1 - cos(t) + 5)\cdot(1-cos(t), sin(t))} \, dt \\\\W = \int\limits^{2\pi}_0 {(t - sin(t), 6 - cos(t))\cdot(1-cos(t), sin(t))} \, dt\\\\W = \int\limits^{2\pi}_0 {(-t*cos(t) +t-sin(t)+ cos(t)*sin(t)+ 6*sin(t) - cos(t)*sin(t) )} \, dt\\\\W = \int\limits^{2\pi}_0 {(-cos(t)*t + 5*sin(t) + t)} \, dt \\\\[/tex]
the sin(t) integral can be removed because it is equal to zero, so we get:
[tex]W = \int\limits^{2\pi}_0 {(-cos(t)*t + t)} \, dtW = [(-t*sin(t) - cos(t)) + \frac{t^2}{2} ]^{2\pi}_0\\\\W = -2\pi*sin(2\pi) - cos(2\pi) + 0*sin(0) + cos(0) + \frac{(2\pi)^2}{2} - \frac{(0)^2}{2}\\\\W = 2\pi^2[/tex]
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Please Help!!! Find X for the triangle shown.
Answers
Answer:
[tex] x = 2 [/tex]
Step-by-step explanation:
Given a right-angled triangle as shown above,
Included angle = 60°
Opposite side length = 3
Adjacent side length = x
To find x, we would use the following trigonometric ratio as shown below:
[tex] tan(60) = \frac{3}{x} [/tex]
multiply both sides by x
[tex] x*tan(60) = \frac{3}{x}*x [/tex]
[tex] x*tan(60) = 3 [/tex]
Divide both sides by tan(60)
[tex] \frac{x*tan(60)}{tan(60} = \frac{3}{tan(60} [/tex]
[tex] x = \frac{3}{tan(60} [/tex]
[tex] x = 1.73 [/tex]
[tex] x = 2 [/tex] (approximated to whole number)
Use differentials to estimate the amount of material in a closed cylindrical can that is 20 cm high and 8 cm in diameter if the metal in the top and bottom is 0.1 cm thick, and the metal in the sides is 0.1 cm thick. Note, you are approximating the volume of metal which makes up the can (i.e. melt the can into a blob and measure its volume), not the volume it encloses
Answers
Answer:
The volume is [tex]dV = 19.2 \pi \ cm^3[/tex]
Step-by-step explanation:
From the question we are told that
The height is h = 20 cm
The diameter is d = 8 cm
The thickness of both top and bottom is dh = 2 * 0.1 = 0.2 m
The thickness of one the side is dr = 0.1 cm
The radius is mathematically represented as
[tex]r = \frac{d}{2}[/tex]
substituting values
[tex]r = \frac{8}{2}[/tex]
[tex]r = 4 \ cm[/tex]
Generally the volume of a cylinder is mathematically represented as
[tex]V_c = \pi r^2 h[/tex]
Now the partial differentiation with respect to h is
[tex]\frac{\delta V_v}{\delta h} = \pi r^2[/tex]
Now the partial differentiation with respect to r is
[tex]\frac{\delta V_v}{\delta r} = 2 \pi r h[/tex]
Now the Total differential of [tex]V_c[/tex] is mathematically represented as
[tex]dV = \frac{\delta V_c }{\delta h} * dh + \frac{\delta V_c }{\delta r} * dr[/tex]
[tex]dV = \pi *r^2 * dh + 2\pi r h * dr[/tex]
substituting values
[tex]dV = \pi (4)^2 * (0.2) + (2 * \pi (4) * 20) * 0.1[/tex]
[tex]dV = 19.2 \pi \ cm^3[/tex]
(I deleted my answer because it was incorrect)
Now find the product (2+ sqrt 5)(2- sqrt 5). The product is ...
the answer is -1
Answers
Answer:
-1
Step-by-step explanation:
Thanks
The product of expression (2 + √5) (2 - √5) is,
⇒ (2 + √5) (2 - √5) = - 1
We have to given that,
An expression to simplify,
⇒ (2 + √5) (2 - √5)
Now, We can simplify it by using formula,
⇒ (a - b) (a + b) = a² - b²
Hence, We get;
⇒ (2 + √5) (2 - √5)
⇒ (2² - √5²)
⇒ 4 - 5
⇒ - 1
Therefore, The product of expression (2 + √5) (2 - √5) is,
⇒ (2 + √5) (2 - √5) = - 1
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2. Tomás compró una bicicleta en $199.900. Primero, canceló la mitad y el resto en 7 cuotas de igual valor, con un interés total de $4000. ¿Cuánto es el valor de cada cuota?
Answers
Answer:
Cada cuota tendrá un valor de $14,850.
Step-by-step explanation:
Dado que Tomás canceló la mitad del valor de la bicicleta, la cual costaba $199.900, el valor pagado al inicio fue de $99,950 (199,900 / 2).
Luego, para el valor restante, Tomás suscribió a una financiación con un interés de $4,000, elevando el monto a pagar a $103,950, pagaderos en 7 cuotas. Por lo tanto, dichas cuotas tendrán cada una un valor de $14,850 (103,950 / 7).