A study was conducted to determine whether magnets were effective in treating pain. The values represent measurements of pain using the visual analog scale. Assume that both samples are independent simple random samples from populations having normal distributions. Use a 0.05 significance level to test the claim that those given a sham treatment have pain reductions that vary more than the pain reductions for those treated with magnets.
Sham:Â n=20, xÌ=0.44,s=1.24n=20, xÌ=0.44,s=1.24
Magnet:Â n=20, xÌ=0.49,s=0.95
Required:
a. Identify the test statistic. (Round to two decimal places as needed)
b. Use technology to identify the P-value. (Round to three decimal places as needed)
c. What is the conclusion for this hypothesis test?
Answers
Answer:
Given:
Sham: n= 20, x=0.44, s=1.24,
Magnet:n= 20, x =0.49, s= 0.95
For Sham:
Sample size, n = 20
Sample mean = 0.44
Standard deviation = 1.24
For Magnet:
Sample size = 20
Sample mean = 0.49
Standard deviation = 0.95
The null and alternative hypotheses:
H0: s1²=s2²
H1: s1² ≠ s2²
a) To find the test statistics, use the formula:
\( \frac{s1^2}{s2^2} \)
\( \frac{1.24^2}{0.95^2} = \frac{1.5376}{0.9025} = 1.7037 \)
Test statistics = 1.7037
b) P-value:
Sham: degrees of freedom \(= n - 1 = 20 - 1 = 19\)
Magnet: degrees of freedom \(= n - 1 = 20 - 1 = 19\)
The critical values:
[Za/2, df1, df2)], [(1 - Za/2), df1, df2]
\( f[0.05/2, 19, 19], f[(1 - 0.05/2), 19, 19] \)
\( f[0.025, 19, 19], f[0.975, 19, 19] \)
\( (2.526, 0.3958) \)
The rejection region:
Reject H0, if F < 0.3958 or if F > 2.526
c) Conclusion:
Since the critical values of test statistic is between (0.3958 < 1.7037 < 2.526), we fail to reject null hypothesis H0.
There is insufficient evidence to to support the claim that those given a sham treatment have reductions that vary more than those treated with magnets
Related Questions
A store is having a sale on jelly beans and almonds. For 5 pounds of jelly beans and 3 pounds of almonds, the total cost is $13. For 2 pounds of jelly beans and 6 pounds of almonds, the total cost is $16. Find the cost for each pound of jelly beans and each pound of almonds.
Answers
Answer:
The cost for each pound of jelly beans and each pound of almonds is $1.25 and $2.25 respectively.
Step-by-step explanation:
Let the cost for each pound of jelly beans and each pound of almonds be x and y respectively.
ATQ,
For 5 pounds of jelly beans and 3 pounds of almonds, the total cost is $13.
5x+3y = 13 ...(1)
For 2 pounds of jelly beans and 6 pounds of almonds, the total cost is $16.
2x+6y = 16
x + 3y = 8 ....(2)
Subtract equation (2) from (1)
5x+3y-(x + 3y)= 13-8
4x = 5
x = 5/4
x = $1.25
Put the value of x in equation (2) as follows :
1.25 + 3y = 8
3y = 8-1.25
y =$2.25
Hence, the cost for each pound of jelly beans and each pound of almonds is $1.25 and $2.25 respectively.
The July bank statement sent by the bank to ABC company shows a balance of cash on deposit at July 31 of Br.4,964.47 Assume that on July 31, assume the on July 31, ABCs ledger shows a bank balance of Br. 4 173. 83. 1. A deposit of Br 410. 90 made after banking hours and doesnt appear in the bank statement2. A check drawn for Br. 79 had been erroneously charged by the bank Br.973. For checks issued in July have not yet been paid by the bank (outstanding checks). : Theses checks are;- Check No date amount 801 June 15 ---Br.100,00 888 July 24 ----Br. 10.25 890 July 27--- Br. 294.50 891 July 30 ---Br. 205.004. A check written for birr 210 had been incorrectly charged by the bank as birr 120 5. Proceeds from collection of a interest bearing note receivable from David. ABC Company had left this note with the banks collection department. The face amount of the note was birr 500 6. Br. 24.75 interest earned on average account balance during July7. A check for Br. 10 returned with the statement had been recorded in the check register as Br. 100. The check was for the payment of an obligation to Davis Equipment Company for the purchase of office supplies on account 8. Br. 5,00 fee charged by bank for handling collection of note receivable 9. Br. 50.25 check from customer John deposited by ABC company charged bank as Non sufficient fund (NSF) 10. Br. 12.70 service charged by bank for the month of July. 11. Check number 875 was issued July 20 in the amount of Br 85 but was erroneously recorded in the cash payment Journal as Br 58 for payment of telephone expense
Answers
After making all the necessary adjustments, the reconciled bank balance for ABC Company's ledger at the end of July is Br. 4,164.42.
To reconcile the bank statement balance with the company's ledger balance for ABC Company, we need to go through the provided information step by step and make the necessary adjustments. Let's calculate the adjusted bank balance:
Starting with the bank statement balance: Br. 4,964.47
Add the deposit made after banking hours: + Br. 410.90
New bank balance: Br. 5,375.37
Now let's make adjustments for the outstanding checks and other transactions:
Deduct the erroneously charged check: - Br. 973
New bank balance: Br. 4,402.37
Deduct the outstanding checks:
Check No. 801: Br. 100.00
Check No. 888: Br. 10.25
Check No. 890: Br. 294.50
Check No. 891: Br. 205.00
Total deduction: Br. 609.75
New bank balance: Br. 3,792.62
Correct the incorrectly charged check: + Br. 90
New bank balance: Br. 3,882.62
Add the proceeds from the collection of the interest-bearing note: + Br. 500.00
New bank balance: Br. 4,382.62
Add the interest earned on the average account balance: + Br. 24.75
New bank balance: Br. 4,407.37
Deduct the incorrectly recorded check: - Br. 90
New bank balance: Br. 4,317.37
Deduct the fee charged for handling the collection of the note: - Br. 5.00
New bank balance: Br. 4,312.37
Deduct the check returned due to insufficient funds: - Br. 50.25
New bank balance: Br. 4,262.12
Deduct the service charge for the month of July: - Br. 12.70
New bank balance: Br. 4,249.42
Deduct the erroneously recorded check: - Br. 85.00
New bank balance: Br. 4,164.42
Now, we compare the adjusted bank balance (Br. 4,164.42) with the ledger balance provided (Br. 4,173.83).
Adjusted bank balance: Br. 4,164.42
Ledger balance: Br. 4,173.83
The difference between the adjusted bank balance and the ledger balance is Br. 9.41. This difference is likely due to some unrecorded transactions or errors in recording. To reconcile the balances fully, further investigation is required to identify the specific cause of the discrepancy and make the necessary adjustments in the company's ledger.
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A BICYCLE WHEEL HAS AN INSIDE RADIUS OF 12 CM. WHAT IS THE WIDTH OF THE TYRE IF THE OUTSIDE CIRCUMFERENCE IS 32П СМ?
Answers
Answer:
Your answer is 4cm.
Step-by-step explanation:
simple calculation
x (12+x) π = 32 π
x = 4cm
A particular disease is tested for and the results determine that it occurs in about 1 of every 750 Hispanic females and about 1 of every 138,000 non-Hispanic females 26,000 Hispanic females were to be tested, about how many of them would you expect to have this particular disease?
Answers
Approximately 34.658 Hispanic females out of 26,000 to have this particular disease.
Hispanic female;A woman or girl who identifies as Hispanic or Latino, which usually refers to persons of Spanish-speaking origin or lineage from Latin America or Spain, is referred to as a "Hispanic female."
The proportion of Hispanic females with the disease is 1 in 750, which can be expressed as:
1 / 750 = 0.001333
This means that for every 750 Hispanic females, one is expected to have the disease.
To calculate the expected number of Hispanic females with the disease in a group of 26,000, we can multiply the proportion by the total number of Hispanic females:
0.001333 * 26,000 = 34.658
So we would expect approximately 34.658 Hispanic females out of 26,000 to have this particular disease.
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A company that produces widgets has found its demand function to be q = –1,500p + 90,000.
a. For each dollar increase in the wholesale price, how many fewer widgets are demanded?
b. How many widgets would be demanded at a price of $20?
c. How many widgets would be demanded at a price of $21?
d. What is the difference in quantity demanded caused by the $1 increase in wholesale price?
e. The company sets a price of $22.50. How many widgets will be demanded?
f. How much will all of the widgets cost the store to purchase at a price of $22.50?
g. If the store marks up the widgets that cost $22.50 at a rate of 50%, what is the retail price of each widget?
Answers
The quantity demanded will decrease by 1,500 widgets, all of the widgets will cost the store $1,233,750 to purchase at a price of $22.50. The retail price of each widget will be $33.75.
a. The demand function is q = –1,500p + 90,000. We can take the derivative of the demand function with respect to p:
dq/dp = -1,500
This means that for every one-dollar increase in price, the quantity demanded will decrease by 1,500 widgets.
b. To find the quantity demanded at a price of $20, we can substitute p = 20 into the demand function:
q = -1,500(20) + 90,000 = 57,000
c. Similarly, to find the quantity demanded at a price of $21, we can substitute p = 21 into the demand function:
q = -1,500(21) + 90,000 = 55,500
d. 57,000 - 55,500 = 1,500
Therefore, a one-dollar increase in price causes a decrease in quantity demanded of 1,500 widgets.
e. To find the quantity demanded at a price of $22.50, we can substitute p = 22.50 into the demand function:
q = -1,500(22.50) + 90,000 = 54,750
f. $22.50 x 54,750 = $1,233,750
Therefore, all of the widgets will cost the store $1,233,750 to purchase at a price of $22.50.
g. $22.50 + ($22.50 x 0.50) = $33.75
Therefore, the retail price of each widget will be $33.75.
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2. which formula should be used to find the area of the composite shape? A = 4(1/2Xbh) lw B. A=4bh+lw C. a=4bh+lw d. 2bh+bh Please select all that apply.
Answers
Answer: the answer is B and D I told the test
Step-by-step explanation:
PLS HELP!!! Ill give 20 points!!!
Answers
Answer:
Step-by-step explanation:
22.57 cm inches are the net weight of the slope
solve for x. show your work. 2x^2+8x=-10
Answers
Answer:
120
Step-by-step explanation:
The exponential model A=433.4e^0.032t describes the population, A, of a country in millions, t years after 2003. Use the model to determine when the population of the country will be 796 million.
The population of the country will be 796 million in
(Round to the nearest year as needed.)
Answers
The population of the country will be 796 million approximately in the year 2022.
To find when the population of the country will be 796 million, we can set the equation equal to 796 and solve for t:
\(A = 433.4e^{(0.032t)}\\796 = 433.4e^{(0.032t)}\)
Divide both sides by 433.4:
\(e^{(0.032t)} = 1.836\)
Take the natural logarithm of both sides:
\(ln(e^{(0.032t)}) = ln(1.836)\)
0.032t = 0.605
Divide both sides by 0.032:
t = 18.91
Therefore, the population of the country will be 796 million approximately 19 years after 2003. To find the year, we add 19 to 2003:
2003 + 19 = 2022
Therefore, the population of the country will be 796 million approximately in the year 2022.
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Name ____________________________________________Date_______ Class __ Score_______
Comparing and Scaling
Unit Test: Show All Your Work for Full Credit
1. The table below shows the medal count of four countries at the 2012 Summer Olympics.
Use the data to complete each statement.
Country Gold Medals Total Medals
United States of America 46 104
Russian Federation 24 82
Australia 7 35
Canada 1 18
SOURCE: The London Organizing Committee of the Olympic Games and Paralympic Games Limited
a. The ratio of United States gold medals to Russia gold medals was about _____ to 1. 2pts
b. Canada had about _____ as many total medals as Australia. 1pt
2. Darthania’s family bought a meal for $80. The tax rate on the meal is 7.25%. Her family left a tip of
10%. What was the total amount she had to pay? 3pts
3. There are 64 pretzels in a 16-ounce bag of chocolate-covered pretzels.
a. Write and solve a proportion that you can use to find the number of chocolate covered pretzels in
a 5-ounce bag. 2pts
b. What is the number of chocolate-covered pretzels per ounce?1pt
c. How many ounces does each pretzel weigh? 1pt
4. The local Farm Market sells peppers at five for $2.25.
a. Complete the rate table. 4pts
Number of
Peppers 1 2 3 4 5 10 15 20 100
Cost 2.25
b. How many peppers could you buy for $20? 2pts
c. Write an equation that relates the number of peppers, n, and the cost, C. 2pts
d. What is the constant of proportionality? How do you know? 2pt
5. Many U.S. employees received a 3% raise in 2012. Suppose an employee made $47,500 in
2011 and received a 3% raise.
a. How much was her raise? 2pts
b. What was her total income in 2012? 1pt
6. The train ride at the zoo covers a distance of miles in of an hour.
a. How many miles per hour does the train go? 3pts
b. How far can the train travel in 3.5 hours? Show your work 2pts
7. The table shows some recipes for organic plant foods.
a. Complete the table to show the unit rates for the ingredients in the Green Tea Recipe. 5pts
b. Write an equation relating the number of cups of green tea G and the number of cups of water W in
the Green Tea recipe. 2pts
8. Ms Robinson wants to purchase a microwave that cost $130. She has a coupon for 15% off. If the
sales tax is 8.25%, how much would be her total cost. 3pts
9. Anna saved $20 in a jar each month for 3 ½ years. She spent 75% of her savings on a computer.
How much money did Anna have left in the jar? 3pts
10. A sporting goods store sells new and used boats. The markup on the boats is 75%.
A salesperson who sells a boat earns a 25% commission on the markup amount. 4pts
Complete the table.
Buying
Price Mark Up
75% of buying price Selling
Price Commission
25% of markup
$2500
Bonus: Melissa wants to purchase a digital camera. The listed price of the camera is
$195.99. The camera is on sale for 10% off and Melissa has a coupon for 5% off. Sales
tax is 7%.
a. How much money will Melissa save with the 10% off?
b. The coupon is applied to the sale price of the camera. How much will Melissa save
by using the coupon?
c. Determine the final cost of the camera?
Answers
Answer:
its very long but ill help you with the first answer:18.5753424657534247
Step-by-step explanation:
Calculus 3 chapter 16
Answers
Evaluate \(\vec F\) at \(\vec r\) :
\(\vec F(x,y,z) = x\,\vec\imath + y\,\vec\jmath + xy\,\vec k \\\\ \implies \vec F(\vec r(t)) = \vec F(\cos(t), \sin(t), t) = \cos(t)\,\vec\imath + \sin(t)\,\vec\jmath + \sin(t)\cos(t)\,\vec k\)
Compute the line element \(d\vec r\) :
\(d\vec r = \dfrac{d\vec r}{dt} dt = \left(-\sin(t)\,\vec\imath+\cos(t)\,\vec\jmath+\vec k\bigg) \, dt\)
Simplifying the integrand, we have
\(\vec F\cdot d\vec r = \bigg(-\cos(t)\sin(t) + \sin(t)\cos(t) + \sin(t)\cos(t)\bigg) \, dt \\ ~~~~~~~~= \sin(t)\cos(t) \, dt \\\\ ~~~~~~~~= \dfrac12 \sin(2t) \, dt\)
Then the line integral evaluates to
\(\displaystyle \int_C \vec F\cdot d\vec r = \int_0^\pi \frac12\sin(2t)\,dt \\\\ ~~~~~~~~ = -\frac14\cos(2t) \bigg|_{t=0}^{t=\pi} \\\\ ~~~~~~~~ = -\frac14(\cos(2\pi)-\cos(0)) = \boxed{0}\)
What is the cos A?Will give 15 points.
Answers
Answer:
Step-by-step explanation:
cos A = \(\frac{\sqrt{8} }{3}\)
What is the most specific name for a quadrilateral with one pair of parallel sides?
A. trapezoid
B. rectangle
C. parallelogram
D. quadrilateral
help me pls
Answers
Answer:
C: parallelogram
Step-by-step explanation:
please help ill mark brainliest
Answers
Answer:
it's 11
Step-by-step explanation:
Solve for x...............
Answers
Answer:
x = 12 degrees
Step-by-step explanation:
They all have to add up to 360, so:
\(5x + 4 + 4x+9+7x+4+9x-6+4x+1=360\\29x + 12 = 360\\29x = 348\\x = 12\)
on : to show More... Then click on √x to enter your answers using the Math Equation editor. Question 5 A frog with bionic legs leaps from a stump with an initial velocity of 64 ft/sec. It is determined that the height of the frog as a function of time can by modeled by h (t) = − 16t² +64t + 3. What is the height of the stump? O 3 ft -3 ft O 16 ft O 64 ft ◄ Previous 1 pts M Next ▸
Answers
The height of the stump is 3 ft.
The given equation represents the height of the frog, h(t), as a function of time, t. To find the height of the stump, we need to determine the height when the time, t, is equal to 0.
In the equation h(t) = -16t² + 64t + 3, we substitute t = 0:
h(0) = -16(0)² + 64(0) + 3
Since any term multiplied by zero is zero, we can simplify further:
h(0) = 0 + 0 + 3
Therefore, the height of the stump, at time t = 0, is 3 ft. This means that when the frog initially leaps from the stump, the height of the stump itself is 3 ft.
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the graph of liner function f passes through the point (1,-9) ad has a slope of -3 what is the zero of f
Answers
Answer:
answer is 4 im pretty sure
Step-by-step explanation:
did da math
A person is looking from a car to the top of a building. The angle of elevation to the top of the building from the car
is 32°. The building is 200 feet away. How tall is the building? Round to the nearest foot.
Answers
Answer:124.29ft (approximately 125ft)
Step-by-step explanation:
May 18, 11:05:10 PM When Jace runs the 400 meter dash, his finishing times are normally distributed with a mean of 81 seconds and a standard deviation of 1.5 seconds. Using the empirical rule, what percentage of races will his finishing time be between 79.5 and 82.5 seconds?
Answers
Answer:
68% of races will his finishing time be between 79.5 and 82.5 seconds
Step-by-step explanation:
Mean time = 81 seconds
Standard deviation = 1.5 seconds
According to the empirical rule : 68%, 95%, 99% lies within 1, 2, and 3 standard deviations of the mean respectively.
Hence, for a finishing time between : 79.5 and 82.5
79.5 = 81 - 1.5 (1 standard deviation to the left of the mean)
82.5 = 81 + 1.5 (1 standard deviation to the right of the mean)
Hence,
79.5 and 82.5 lies within 1 standard deviation from the mean and it is Hence has a percentage of 68%
Number of Computers
72
60
48
36
24
12
V
1 2 3 4 5 6 7 8 9 10 11 12
Number of Days
The graph shows a proportional relationship between
the number of computers produced at a factory per day.
In three days, 36 computers are produced; 48
computers are produced in 4 days; and 60 computers
are produced in 5 days.
Find the unit rate of computers per day using the graph.
Unit rate:
computers per day
Answers
The unit rate of computers per day using the graph is that 12 computers are made per day.
What is a unit rate?The unit rate is how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. Unit rates is said to be the amount of something in each unit or per unit.
How to find the unit rate of computers per dayTo obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x
So, it is given by:
\(\text{Slope} = \dfrac{\text{change in y}}{\text{change in x}}\)
\(\text{Slope} = \dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}\)
\(\text{y}_2 = 60 , \ \text{y}_1 = 36 , \ \text{x}_2 = 5, \ \text{x}_1 = 3.\)
\(\text{Slope} = \dfrac{(60 - 36)}{(5 - 3)} = \dfrac{24}{2} = 12\)
\(\bold{Slope = 12}\)
Unit rate = 12 computers per day.
The attachment of the graph is given below.
Therefore, the unit rate of computers per day is 12.
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Calculate the surface area of this right triangular prism.
Answers
Total surface area of right triangular prism is 750cm²
Define the term right triangular prism?A right triangular prism is a three-dimensional geometric shape with three rectangular faces connecting the edges of its two parallel, congruent triangular bases.
Area of the two opposite side triangles (A₁) = 2 × ( \(\frac{1}{2}\) × 12 × 5)
Area of the two opposite side triangles (A₁) = 60 cm²
Area of upper, lower and side rectangles (A₂) = (5×23) + (12×23) + (13×23)
Area of upper, lower and side rectangles (A₂) = 115 + 276 + 299
Area of upper, lower and side rectangles (A₂) = 690 cm²
Total surface area of right triangular prism = A₁ + A₂
Total surface area of right triangular prism = 60 + 690
Total surface area of right triangular prism = 750 cm²
Therefore, the total area of the right triangular prism is 750cm²
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H(p)=p/5 + 15
What is the independent variable in this function
Answers
In the given function H(p) = p/5 + 15, the independent variable is "p" ,
The independent variable in this function is denoted by "p." The independent variable can also be referred to as the input variable, which means that it is the value that is inputted into the function to produce an output. In this specific function, "p" represents the price of a good or service.
It is important to distinguish between the independent and dependent variables in a function. The dependent variable is denoted by "H(p)" in this case, and it is the output of the function. The value of the dependent variable is determined by the independent variable. In this function, "H(p)" represents the total cost of the good or service, which is dependent on the price "p." p is the input variable representing the price of the good or service.
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Determine the interval(s) for which f(x) ≥ 0. f(x) = x − 2
Answers
The interval(s) for which f(x) ≥ 0. is x ≥ 2
How to determine the interval(s)?The function is given as:
f(x) = x - 2
Also, we have:
f(x) ≥ 0
This means that
x − 2 ≥ 0
Add 2 to both sides of the inequality
x ≥ 2
Hence, the interval(s) for which f(x) ≥ 0. is x ≥ 2
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Algebra transformation
f(x) =
f(x) =
f(x) =
f(x) =
Answers
Algebra transformation
for Graph1 f(x)=f(x)+4
for Graph2 f(x)=-f(x-4)
for Graph3 f(x)=f(x-7)
for Graph4 f(x)=f(x-2)-5
Define reflection of graphIn mathematics, the reflection of a graph is a transformation that produces a mirror image of the original graph across a specific line or point. The line or point across which the reflection occurs is called the axis of reflection.
Graph1
Transform the graph by +4 units in y direction.
f(x)=f(x)+4
Graph2
Transform the graph by +4 units in x direction.
f(x)=f(x-4)
Now take the reflection of graph about x axis
f(x)=-f(x-4)
Graph3
Transform the graph by +7 units in x direction.
f(x)=f(x-7)
Graph5
Transform the graph by -5 units in y direction.
f(x)=f(x)-5
Now Transform the graph by -2 units in x direction.
f(x)=f(x-2)-5
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Given triangle MAT is an isosceles triangle and point H is the midpoint if MT. Prove triangle MHA is congruent to triangle THA
Answers
Answer:
There is everything in the image
The Side-Angle-Side postulate is satisfied. Then the triangle ΔMHA and ΔTHA are congruent with each other.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
In an isosceles triangle, the two legs of the triangle are congruent and their opposite angles too.
A triangle MAT is an isosceles triangle and point H is the midpoint of MT.
In triangle ΔMHA and ΔTHA, we have
AH = AH (Common sides)
MH = HT (H is the midpoint of MT)
∠AMH = ∠ATH (Isosceles angles)
The Side-Angle-Side postulate is satisfied. Then the triangle ΔMHA and ΔTHA are congruent with each other.
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pls pls pls help!! 30 points! show work pls!!
Answers
Answer: 5 Miles and 1,241 Yards and 2 Feet
Step-by-step explanation: There are 5,280 ft in a mile. To convert to miles, you can do 30,125/5,280. This will give you 5 miles with a remainder of 3,725 ft.
Next, we convert to yards. There are 3 yards in a foot. For this you can do 3,725/3. This will give you 1,241 yd. with a remainder of 2 feet.
Combine these and it will give you 5 miles and 1,241 yd. and 2 ft.
To check your work, you can do (5*5,280)+(3,725*3)+2=30,125.
Please reply back if you have any question.
-Your Brainly Helper!
This is the architectural plan for a fenced-in garden.
The shaded region represents an area for trees.
How long is the fence around the edge of the garden?
(Do not include the edge around the tree region.)
Answers
The fence around the edge of the garden is 17.86 m long.
The fence around the edge of the garden is the perimeter of the quarter circle. That is the length of the arc plus the two radii.
Since the radius is 5 units long, its length r = 5 m.
The length of the arc L = rθ where r = radius of quarter circle = 5 m and θ = angle subtended by the arc in radians = π/2 (90°)
So, the length of the fence L' = L + r + r
L' = L + 2r
L' = rθ + 2r
L' = r(θ + 2)
Substituting the values of the varaibles into the equation, we have
L' = r(θ + 2)
L' = 5 m(π/2 + 2)
L' = 5 m(1.571 + 2)
L' = 5 m × 3.571
L' = 17.855 m
L' ≅ 17.86 m
So, the fence around the edge of the garden is 17.86 m long.
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Prime factorization of 45
A. 2³×5
B. 3²×5
C. 5²×3
D. 5²×9
Answers
Answer:
Hello, your answer is:
B. 3²×5
Step-by-step explanation:
Prime factorization of 45 is:
45 = 9 x 5
= 3²×5
Hope this helps you.. Good Luck
Answer:
B. 3² × 5
Step-by-step explanation:
45 can be written as a product of its prime factors.
45 = 3 × 3 × 5
45 = 3² × 5
Evaluate the following expression:
\left( \frac{16}{9} \right)^{2/3} \cdot \left( \frac{4}{3} \right)^{4/3} \cdot \left( \frac{9}{16} \right)^{2/3} \cdot \left( \frac{3}{4} \right)^{4/3}
Answers
We raise the fraction to the power of 4/3.
To evaluate the expression:
\left( \frac{16}{9} \right)^{2/3} \cdot \left( \frac{4}{3} \right)^{4/3} \cdot \left( \frac{9}{16} \right)^{2/3} \cdot \left( \frac{3}{4} \right)^{4/3},
we can simplify each term within the parentheses before multiplying them together.
Let's simplify each term step by step:
\left( \frac{16}{9} \right)^{2/3}:
To simplify this term, we raise the fraction to the power of 2/3.
\left( \frac{16}{9} \right)^{2/3} = \left( \left( \frac{2^4}{3^2} \right)^{1/3} \right)^2 = \left( \frac{2^{4 \cdot 1}}{3^{2 \cdot 1}} \right)^2 = \left( \frac{2^4}{3^2} \right)^2 = \left( \frac{16}{9} \right)^2 = \frac{16^2}{9^2} = \frac{256}{81}
\left( \frac{4}{3} \right)^{4/3}:
Similarly, we raise the fraction to the power of 4/3.
\left( \frac{4}{3} \right)^{4/3} = \left( \left( \frac{2^2}{3^1} \right)^{1/3} \right)^4 = \left( \frac{2^{2 \cdot 1}}{3^{1 \cdot 1}} \right)^4 = \left( \frac{2^2}{3^1} \right)^4 = \left( \frac{4}{3} \right)^4 = \frac{4^4}{3^4} = \frac{256}{81}
\left( \frac{9}{16} \right)^{2/3}:
We raise the fraction to the power of 2/3.
\left( \frac{9}{16} \right)^{2/3} = \left( \left( \frac{3^2}{2^4} \right)^{1/3} \right)^2 = \left( \frac{3^{2 \cdot 1}}{2^{4 \cdot 1}} \right)^2 = \left( \frac{3^2}{2^4} \right)^2 = \left( \frac{9}{16} \right)^2 = \frac{9^2}{16^2} = \frac{81}{256}
\left( \frac{3}{4} \right)^{4/3}:
We raise the fraction to the power of 4/3.
\left( \frac{3}{4} \right)^{4/3} = \left( \left( \frac{3^1}{2^2} \right)^{1/3} \right)^4 = \left( \frac{3^{1 \cdot 1}}{2^{2 \cdot 1}} \right)^4 = \left( \frac{3^1}{2^2} \right)^4 = \left( \frac{3}{4} \right)^4 = \frac{3^4}{4^4} = \frac{81}{256
For more questions on fraction
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You can perform 6 push-ups in 16 seconds. Write and
graph an equation that represents the relationship between
time and the number of push-ups. At this rate, how many
pushups can you perform in 2 minutes?
Answers
Answer:
320 pushups
Step-by-step explanation:
16/6= 8/3
8/3*120=32