Answer:
The equation [tex]7\,\sqrt{x} =14[/tex] is a radical equation.
Step-by-step explanation:
If the equations given are (as I can read them from your typing):
a) [tex]x+\sqrt{5} =12[/tex]
b) [tex]x^2=16[/tex]
c) [tex]3+x\,\sqrt{7} =13[/tex]
d) [tex]7\,\sqrt{x} =14[/tex]
The only radical equation is the last one : [tex]7\,\sqrt{x} =14[/tex], because it is the only one where the unknown appears inside the root. The name "radical equations" is associated with the fact that the unknown is contained inside the root and therefore the process involved in solving for the unknown will need to include the elimination of the root via algebraic methods to free the unknown.
Notice that the options a) and c) have roots, but what appears inside them are numbers (5 and 7 respectively), and not an unknown like "x". Equation b) doesn't contain a root, and wouldn't classify as a radical equation.
A radical equation is one which contains roots in it, specially those which has root over variables or things whose values changes.
Thus, by above definition, we will have the fourth option: [tex]7\sqrt{x} = 14[/tex] as a radical equation.
Given the equations: [tex]x + \sqrt{5} = 12\\[/tex] [tex]x^2 = 16[/tex] [tex]3 + x\sqrt{7} = 13\\[/tex] [tex]7\sqrt{x} = 14[/tex]Explanation:A radical equation is one which contains roots in it, specially those which has root over variables or things whose values changes.
Since only in the fourth option we see there's root over x which is a variable here, thus the fourth option: [tex]7\sqrt{x} = 14[/tex] is a radical equation.
Rest of the options, although containing roots, aren't having variables inside the root, thus they aren't classified as radical equations.
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The distance from the centroid of a triangle to its vertices are 16cm, 17cm, and 18cm. What is the length of the shortest median
Answer:
[tex]24[/tex] [tex]\text{cm}[/tex]
Step-by-step explanation:
Given: The distance from the centroid of a triangle to its vertices are [tex]16\text{cm}[/tex], [tex]17\text{cm}[/tex], and [tex]18\text{cm}[/tex].
To Find: Length of shortest median.
Solution:
Consider the figure attached
A centroid is an intersection point of medians of a triangle.
Also,
A centroid divides a median in a ratio of 2:1.
Let G be the centroid, and vertices are A,B and C.
length of [tex]\text{AG}[/tex] [tex]=16\text{cm}[/tex]
length of [tex]\text{BG}[/tex] [tex]=17\text{cm}[/tex]
length of [tex]\text{CG}[/tex] [tex]=18\text{cm}[/tex]
as centrod divides median in ratio of [tex]2:1[/tex]
length of [tex]\text{AD}[/tex] [tex]=\frac{3}{2}\text{AG}[/tex]
[tex]=\frac{3}{2}\times16[/tex]
[tex]=24\text{cm}[/tex]
length of [tex]\text{BE}[/tex] [tex]=\frac{3}{2}\text{BG}[/tex]
[tex]=\frac{3}{2}\times17[/tex]
[tex]=\frac{51}{2}\text{cm}[/tex]
length of [tex]\text{CF}[/tex] [tex]=\frac{3}{2}\text{CG}[/tex]
[tex]=\frac{3}{2}\times18[/tex]
[tex]=27\text{cm}[/tex]
Hence the shortest median is [tex]\text{AD}[/tex] of length [tex]24\text{cm}[/tex]
The Quadratic Formula 7:Solving Quadratic Equations
laro
The Quadratic Formula
Text
Guided Practice
Use the quadratic formula to solve the equation. If necessary, round answers to the nearest hundredth.
8x2-3x - 7=0
A. 1.12, -0.74
B. 1.14,-0.77
C. -1.14,0.77
Answer:
B. 1.14, -0.77
Step-by-step explanation:
As you know the quadratic formula gives you the solution to
ax² + bx + c = 0
as ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Here, we have a=8, b=-3, c=-7, so the formula tells us the solution is ...
[tex]x=\dfrac{-(-3)\pm\sqrt{(-3)^2-4(8)(-7)}}{2(8)}=\dfrac{3\pm\sqrt{233}}{16}\\\\x\approx \{-0.7665,1.1415\} \qquad\text{matches choice B}[/tex]
Answer:
1.14, –0.77
Step-by-step explanation:
I got it right in grandpoint.
The radius of a circle is increased from 8.008.00 to 8.038.03 m. Estimate the resulting change in area, and then express the estimate as a percentage of the circle's original area. The estimated change in area is nothing msquared2.
Answer:
Step-by-step explanation:
The area of a circle is expressed as
Area = πr^2
Where r = radius of the circle
π = constant = 3.14
The radius of a circle is increased from 8.00800 to 8.03803 m. This means that the original radius of the circle is 8.00800 and the new radius of the circle is 8.03803
Area of original circle =
3.14 × 8.00800^2 = 201.36212096
Area of new circle =
3.14 × 8.03803^2 = 202.87516852203
Increase in area = 202.87516852203 - 201.36212096
= 1.51304756203
Expressing the change as a percentage, it becomes
1.51304756203/201.36212096 ×100
Percentage change = 0.75 %
Geoffrey has 30 problems to do for math homework he finished 60 percent of them before play practice how many problems did Geoffrey finish before play practice
Answer:
18 answers
Step-by-step explanation:
1) 30 of 60%
2)30*.6
3)18
check:
18/30=0.6
0.6=60%
Step-by-step explanation:
30=100%
? =60
=18 problems
24 Attitudes toward alcohol At a party there are 30 students over age 21 and 20 students under age 21. You choose at random 3 of those over 21 and separately choose at random 2 of those under 21 to interview about attitudes toward alcohol. You have given every student at the party the same chance to be interviewed.
Answer:
From the solution we come to know that every student in a party contain 10% chance of being chosen . And it is not SRS because student have been grouped into over 21 and under 21
Step-by-step explanation:
This question asks about sampling methods in statistics to determine attitudes toward alcohol at a party.
Explanation:This question is about sampling methods in statistics. The goal is to determine the attitudes toward alcohol of students at a party. To achieve this, the party attendees are divided into two groups: those over 21 and those under 21. Then, a random sample of 3 students over 21 and a random sample of 2 students under 21 are chosen to be interviewed. This method ensures that each student at the party has an equal chance of being interviewed and provides a representative sample of the party's attendees.
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In his suitcase, Jack has 3 shirts, 4 pants, 2 socks (pairs of socks), and 2 shoes (pairs of shoes). How many unique ways can Jack get fully dressed? Show your work and explain.
Answer:
48
Step-by-step explanation:
the number of shirts are 3, number of pants 4, number of socks pairs 2 and 2 pairs of shoes.
first lets start with shirts and pants, number of unique combinations are,
(for each shirt there are 4 different pant combinations) = [tex](3)(4)[/tex]
=12
similiarly for each shirt pant pair there are 2 shoes and 2 socks pairs.
thus, total number of combinations are=
[tex](12)(2)(2)[/tex]
= 48
Tim is looking at two websites that allow customers to print their own designs on T-shirts. One website charges $24 per T-shirt plus $8 shipping. The other website uses the equation C = 22 n + 12 C=22n+12 to find the total cost, C C, of printing on T-shirts. What is the difference in the cost of each website if Tim orders 10 T-shirts?
Answer: The difference is $16
Step-by-step explanation:
n will equal the amount of t-shirts bought
Website 1's Costs: c = 24n + 8
Website 2's cost: c = 22n + 12
Then, we substitute 10 for n
c = 24(10) + 8
c = 240 + 8
c = 248
c = 22(10) + 12
c = 220 + 12
c = 232
248 - 232 = 16
The difference between the total cost of the first website and that of the second based on the given function will be $16.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
A function can be regarded as a computer, which is helpful.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
As per the given,
On the first website,
Cost to buy 10 T-shirts.
C = 24(10) + 8
C = 240 + 8
C = $248
The second website
The total cost to buy 10 T-shirts
C = 22(10) + 12
C= 220 + 12
C= $232
The differnce $248 - $232 = $16
Hence "The difference between the total cost of the first website and that of the second based on the given function will be $16".
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Matthew picks flowers and sells them to tourists. The function s(t) approximates how many flowers Matthew picks per hour. The function W(h) represents how hours per week Matthew spends picking flowers. What are the units of measurement for the composite function s(W(h))?
a. flowers/hour
b. hours/week
c. flowers/week
d. weeks/flower
Answer:
c Flower/ Week
Step-by-step explanation:
think about it like this
hours (flowers)
____. x. _______
Weeks hours
Both of the hours cancel out similar to unit conversions in chemistry and you are left with flowers per week. since the value of flowers you get per hour you work, and x is dependant on the amount of hours you work in a week. These two functions work in conjuction to give flowers per week picked, this crossing off happens diagonally from left down to the right.
The units of measurement for the composite function s(W(h)) is Option(C) flowers/week.
What is the given unit of the composite function ?Given that the function s(t) approximates how many flowers Matthew picks per hour.
Unit of function s(t) is flowers/hours.
Also given that the function W(h) represents how many hours per week Matthew spends picking flowers.
Unit of W(h) = hours/week .
The composite function s(W(h)) will have unit -
= Flowers/hours * hours/week
= Flowers/week
The units of measurement for the composite function s(W(h)) is Option(C) flowers/week.
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A high school drama club is selling tickets to their show. There is a maximum of 400 tickets. The tickets cost $10 (if bought before day of show) and $15 (if bought day of show). Let x represent the number of tickets sold before the day of the show and y represents the number of tickets sold the day of the show. To meet the expenses of the show, the club must sell at least $3500 worth of tickets. The club sells 300 tickets before the day of the show. Is it possible to sell enough additional tickets on the day of the show to meet the expenses of the show? Justify your answer.
Answer:
yes
Step-by-step explanation:
The club can sell 100 more tickets before they reach their maximum. If they sell those at the "day-of" price, they will have additional revenue of ...
100 × $15 = $1500
Then their total revenue would be ...
300 × $10 + $1500 = $4500 . . . . more than enough to meet expenses.
_____
To make up the additional $500 they need, the drama club only needs to sell ...
ceiling($500/$15) = 34 . . . tickets at the "day-of" price.
Based on counting the number of galaxies in a small patch of the sky and multiplying by the number of such patches needed to cover the entire sky, the total number of galaxies in the observable universe is estimated to be approximately
A) 100 million.
B) 100 billion.
C) 1 billion.
D) 1 trillion.
E) 10 billion.
Answer:
100 billion
Step-by-step explanation:
Some astronauts reveals that there are 100 billion galaxies in the universe.
4x^3+26x^2-15x-74x3+26x 2 −15x−7 is divided by x+7x+7? If there is a remainder, express the result in the form q(x)+\frac{r(x)}{b(x)}q(x)+ b(x) r(x) .
Answer:
4x^2 -2x -1
Step-by-step explanation:
Synthetic division works well for dividing by a linear binomial. See the attached for the working and the interpretation of the result.
Please help!!
What is the equation of the line that represents the initial climb?
Answer:
y = (5/2)x
Step-by-step explanation:
The rise is 5 squares and the run is 2 squares between the two marked points. That means the slope is 5/2. The line starts at (0, 0), so the equation is ...
y = (5/2)x
The monthly output P of a light bulb factory is given by the formula P = 450LK, where L is the amount invested in labor and K the amount invested in equipment (in thousands of dollars). If the company needs to produce 4,000 units per month, how should the investment be divided among labor and equipment to minimize the cost of production? The cost of production is L + K. (Round your answers to the nearest cent.)investment in labor _______ $investment in equipment ________$
Answer:
C(p) = 4,96 (in thousands of dollars)
l = 2980 $ invest in labor
k = 2980 $ invest in equipment
Step-by-step explanation:
Information we have:
Monthly output P = 450*l*k ⇒ k = P/450*l
But the production need to be 4000
Then k = 4000/450*l
Cost of production = l * k (in thousands of dollars)
C(l) = l + 4000/450*l
Taking derivatives (both members of the equation)
C´(l) = 1 - 400 /45*l² ⇒ C´(l) = 0 ⇒ 1 - 400/45l² = 0
45*l² - 400 = 0 ⇒ l² = 400/45
l = 2.98 (in thousands of dollars)
l = 2980 $ And
k = 400/45*l ⇒ k 400/45*2.98
k = 2.98 (in thousands of dollars)
C(p) = l + k
C(p) = 2980 + 2980
C(p) = 5960 $
4^1/2 equals 2. Why? Show steps and explain
raising some base to the power of 1/2 is the same as square root
Answer:
Step-by-step explanation:
4 to the first power is 4
then divide by 2
A rectangular parking lot has a perimeter of 384 meters. The length of the parking lot is 36 meters less than the width. Find the length and the width.
Answer:
The length and width of the parking lot is 78 meters and 114 meters respectively.
Step-by-step explanation:
Given;
Perimeter of the parking lot = [tex]384\ m[/tex]
Solution,
Let the width of the parking lot be x.
Then, according to question length = (x-36).
The perimeter of a rectangle is sum of all the sides of rectangle. Which is given by an expression;
[tex]perimeter=2\times(length+width)[/tex]
Now substituting the values, we get;
[tex]384=2\times(x-36+x)\\\frac{384}{2}=(2x-36)\\192=2x-36\\192+36=2x\\2x=228\\x=\frac{228}{2}= 114[/tex]
Width = [tex]114\ m[/tex]
Length = [tex]x-36=114-36=78\ m[/tex]
Hence the length and width of the parking lot is 78 meters and 114 meters respectively.
Is it possible for two numbers to have a difference of 6
Answer:
yes
Step-by-step explanation:
For example, 8 and 2.
8 - 2 = 6.
6 is the difference
The late fee for library books is $2.00 plus 15 cents each day for a book that is late.If Maria's fee for a late book was $3.20,write and solve a linear equation to find many days late the book was.
First we will subtract $2 from $3.2 since that is late fee to get $1.2.
Now we divide $1.2 by $0.15 to get number of cents hence 8 days.
The answer is Maria is 8 days too late to hand over the book.
Hope this helps.
The linear equation is 3.20 = 2.00 + 0.15*x. Hence, Maria's book was 8 days late.
To find out how many days Maria's book was late, we need to set up a linear equation using the given information.
The total late fee equation is given by:
Late Fee = 2.00 + 0.15*x
Where $2.00 is the base fee, and 0.15 dollars is the additional late fee per day. Since Maria's total fee was $3.20, we can set up the equation as follows:
3.20 = 2.00 + 0.15*x
Now, solve for x, which represents the number of days the book was late:
Subtract $2.00 from both sides:
3.20 - 2.00 = 0.15*x
Simplify the equation:
1.20 = 0.15*x
Divide both sides by 0.15 to isolate x:
x = 1.20 / 0.15
Calculate the result:
x = 8
So, Maria's book was 8 days late.
Serious answers only. Do not answer if you dont know please!How does the graph of the circle described by x^2 + (y-7)^2 = 49 change when its equation is changed to (x +5)^2 + (y-4)^2 =64. Select each correct answer. The circles radious increases, The circle moves up, The circle moves left, The circles radious decreases, The circle moves down, The circle movea right.
Answer:
The circles radious increases The circles moves left The circles moves downStep-by-step explanation:
The equation of a circle can be written as [tex](x-a)^2+(y-b)^2=r^2[/tex], where "r" is the radious, and (a,b) are the coordenates in the axis x and b respectively.Then, in the first circle the coordenates are (0,7), which means that the circle will be center there, and the radious is 7 ([tex]\sqrt{49}[/tex]).The second circle have different coordenates: (-5,4), which means that the circle has moved left (from 0 to -7 in the x axis) and down (from 7 to 4 in the y axis). Additionally, its radious has increased from 7 ([tex]\sqrt{49}[/tex], from 8 ([tex]\sqrt{64}[/tex]).See the attached figure please.Then, the correct answers are:The circles radious increases (from r=7 to r=8)The circles moves left (from x=0 to x=-5)The circles moves down (from y=7 to y=4)$12,400 is invested, part at 6% and the rest at 5%. If the interest earned from the amount invested at 6% exceeds the interest earned from the amount invested at 5% by $577.00, how much is invested at each rate? (Round to two decimal places if necessary.) Define variables x and y and set up a system of two linear equations that represents the information given in the problem.
Answer: $10881.81 is invested at 6% and $1518.18 is invested at 5%.
Step-by-step explanation:
Since we have given that
Amount invested = $12400
Rate of interest for first part = 6%
Rate of interest for second part = 5%
Let the amount invested for 6% be 'x'.
Let the amount invested for 5% be 'y'
According to question, we get that
[tex]0.06x-0.05y=577\\\\x+y=12400\\\\\implies x=12400-y[/tex]
So, it becomes,
[tex]0.06(12400-y)-0.05y=577\\\\744-0.06y-0.05y=577\\\\-0.11y=577-744\\\\-0.11y=-167\\\\y=\dfrac{167}{0.11}\\\\y=1518.18[/tex]
x=12400-y=12400-1518.18=$10881.81
Hence, $10881.81 is invested at 6% and $1518.18 is invested at 5%.
3 friends share the cost of a gift. The gift costs $70, but the store manager takes $10 off the market price. What amount should they each pay? What is the answer
Answer:
Amount each friend pays for the gift = $20
Step-by-step explanation:
Market price of a gift = $70
The store manager takes $10 off the market price.
Marked down amount = $10
New cost price = Marked price - Marked down amount [tex]=\$70-\$10=\$60[/tex]
The cost of the gift is divided among three friends.
This means that the cost of gift which is $60 is divided by three to get each one's contribution in the gift.
∴ Amount each friend pays for the gift [tex]=\frac{60}{3}=\$20[/tex]
Consider the following problem: A farmer with 850 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?
Answer:
18,062.5 square feet
Step-by-step explanation:
The largest area will be obtained when half the fence is used in each of the orthogonal directions. That is, the pen will have two parallel sides that total 425 feet, and 5 parallel sides and partitions that total 425 feet.
The long sides are 212.5 feet, and the short sides are 85 feet, so the overall area is ...
(212.5 ft)(85 ft) = 18,062.5 ft²
__
Working Out
Suppose the long side is length x. Then the lengths of the 2 ends and 3 dividers are ...
short side = (850 -2x)/5
Then the overall area is the product of long side and short side:
A = x(850 -2x)/5 = (2/5)(x)(425 -x)
This equation is that of a parabola that opens downward. Its vertex (maximum) is at the value of x halfway between the zeros of 0 and 425. That is, area is a maximum when x=212.5.
That maximum area is ...
A = (2/5)(212.5)(425 -212.5) = 18,062.5 . . . square feet
six-foot person walks from the base of a streetlight directly toward the tip of the shadow cast by the streetlight. When the person is 11 feet from the streetlight and 5 feet from the tip of the streetlight's shadow, the person's shadow starts to appear beyond the streetlight's shadow. (a) Draw a right triangle that gives a visual representation of the problem. Show the known quantities and us
Answer:
Step-by-step explanation: See annex
The figures are in feet
Miguel took a taxi to the beach 23 miles from his hotel. After his day at the beach, he took a bus back for 11 miles. Then a friend pick him up and drove another 12 miles towards the hotel. How many more miles does Magill need to go until he is back at his hotel
Answer:
0 additional miles
Step-by-step explanation:
Miguel travelled from his hotel to the beach by taxi. Total distance travelled by Miguel during the journey is 23 miles.
During the return journey, he travelled by a bus for 11 miles to an intermediate location.
From this point his friend picked him up and drove him towards the hotel for 12 miles.
So the total distance travelled by Miguel during the return journey = 11 + 12 = 23 miles
But this is the same distance as the onward journey. So at the end, Miguel is back at the hotel and there are 0 additional miles that he needs to cover.
Answer: 0 miles
Step-by-step explanation:
Miguel took a taxi to the beach 23 miles from his hotel. After his day at the beach, he took a bus back for 11 miles. This means at this point, his distance from his hotel is 23 - 11 = 12 miles. Then a friend pick him up and drove another 12 miles towards the hotel. This means that they covered the remaining 12 miles from the hotel. Therefore
Miguel needs to go 12 - 12 = 0 miles until he is back at his hotel.
The previous triangular prism had a surface area of 288 square units. What happens to the surface area of your prism when you double all four measurements?
If all four dimensions of triangular prism having surface area as 288 is doubled than new surface area will be four times than the initial prism that is 1152 square unit.
Solution:Given that
Surface area of a triangular prism = 288 square unit
Need to evaluate new surface area if all four measurement of triangular prism is double.
Relation between surface area and the four dimensions of the triangular prism is given by following formula
Surface Area of triangular prism = bh + 2ls + lb
Where h is height of the prism , b is length of base of the prim , l is length of the prism and s is side length of the prism.
Given that Area of triangular prism = 288 square unit
=> bh + 2ls +lb = 288
Doubling the four dimensions means replace b by 2b, l by 2l , s by 2s and h by 2h in formula of Surface area of triangular prism.
[tex]\text { We get Surface area of new triangular prism }=2 b \times 2 h+2 \times 2 l \times 2 s+2 l \times 2 b[/tex]
[tex]\begin{array}{l}{=4 \times b h+4 \times 2 l s+4 \times l b} \\\\ {=4(b h+2 l s+l b)}\end{array}[/tex]
=> Surface area of new triangular prism = 4 (bh + 2ls +lb)
=> Surface area of new triangular prism = 4 x 288 = 1152 square unit.
Hence we can conclude that if all four dimensions of triangular prism having surface area as 288 is doubled than new surface area will be four times than the initial prism that is 1152 square unit.
Answer: C, the surface area increases by 4 times
Step-by-step explanation:
A baseball player strikes out three times for every two hits he gets if the player strikes out 15 times how many hits does he get if the player gets 46 hit how many times does he strike out
The player will get 10 hits for 15 times strikes out.
The player will strike out 69 times for 46 hits.
Step-by-step explanation:
Given,
Ratio of strike out to hits = 3:2
Condition 1: If the player gets 15 strikes out;
Let,
x be the hits for 15 times strikes out.
Using proportion;
Strike out : hit :: strike out : hit
[tex]3:2::15:x[/tex]
Product of mean = Product of extreme
[tex]15*2=3*x\\3x=30[/tex]
Dividing both sides by 3;
[tex]\frac{3x}{3}=\frac{30}{3}\\x=10[/tex]
The player will get 10 hits for 15 times strikes out.
Condition 2: if the player gets 46 hits
Let,
y be the strikes out.
Using proportion,
Strike out : hit :: strike out : hit
[tex]3:2::y:46[/tex]
Product of mean = Product of extreme
[tex]2*y=46*3\\2y=138[/tex]
Dividing both sides by 2;
[tex]\frac{2y}{2}=\frac{138}{2}\\y=69[/tex]
The player will strike out 69 times for 46 hits.
Keywords: Ratio, proportion
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Answer:The player will get 10 hits for 15 times strikes out.
The player will strike out 69 times for 46 hits.
Step-by-step explanation:
Given,
Ratio of strike out to hits = 3:2
Condition 1: If the player gets 15 strikes out;
Let,
x be the hits for 15 times strikes out.
Using proportion;
Strike out : hit :: strike out : hit
Product of mean = Product of extreme
Dividing both sides by 3;
The player will get 10 hits for 15 times strikes out.
Condition 2: if the player gets 46 hits
Let,
y be the strikes out.
Using proportion,
Strike out : hit :: strike out : hit
Product of mean = Product of extreme
Dividing both sides by 2;
The player will strike out 69 times for 46 hits.
Keywords: Ratio, proportion
Step-by-step explanation:
If 40% of a number is 32, what is 25% of that number?
Answer:
I think that the answer is 24
Answer:
The number is 80. 25% of that number is = 20.
Step-by-step explanation:
Julia makes friendship bracelets. She was recently given nine bracelets from different people. At Christmas, she plans to give away ome third of her bracelets. She will be left with 23. With how many did she start?
Answer:
The number of bracelets with she start are 48.
Step-by-step explanation:
Given:
Julia was recently given 9 bracelets. She plans to give 1/3 of her bracelets. She will be left with 23.
Now, we need to find with how many did she start.
Let the bracelets with she start be [tex]x[/tex].
She plans to give [tex]\frac{1}{3}ofx[/tex] = [tex]\frac{x}{3}[/tex].
According to question:
[tex]x-9-\frac{x}{3}=23[/tex]
On solving the equation:
[tex]\frac{3x-27-x}{3} =23[/tex]
Multiplying both sides by 3 we get:
[tex]3x-27-x=69[/tex]
[tex]2x-27=69[/tex]
Adding both sides by 27 and then dividing by 2 we get:
[tex]x=48[/tex]
Therefore, the number of bracelets with she start are 48.
A potato chip manufacturer has found that in the past the standard deviation of bag weight has been 0.2 ounce. They want to test whether the standard deviation has changed. What is the null hypothesis?
Answer:
Null Hypothesis: [tex]\sigma=0.2[/tex]
Alternative hypothesis: [tex]\sigma \neq 0.2[/tex] (Changes on the deviation)
Step-by-step explanation:
s represent the sample standard deviation
[tex]\sigma[/tex] represent the population standard deviation (variable of interest)
[tex]\sigma_o =0.2[/tex] represent the value that we want to test
n represent the sample size
A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".
The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".
The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".
Based on this the system of hypothesis should be:
Null Hypothesis: [tex]\sigma=0.2[/tex]
Alternative hypothesis: [tex]\sigma \neq 0.2[/tex] (Changes on the deviation)
In order to test these system of hypothesis we need to select a significance level [tex]\alpha[/tex], then we need to calculate an statistic given by this formula.
[tex]\chi^2 =\frac{(n-1)s^2}{\sigma^2_o}[/tex]
Then we need to calculate the degrees of freedom for the statistic on this case
[tex]df=n-1[/tex]
And after this we need to calculate the pvalue based on the significance, the alternative hypothesis and the statistic calculated.
If the [tex]p_v <\alpha[/tex] we reject the null hypothesis
If the [tex]p_v >\alpha[/tex] we FAIL reject the null hypothesis
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Answer:
Option D: 2 . cos(90 + x) = -2a
Step-by-step explanation:
Given that:
sin x = a --------- eq1
As we know that trignometry says:
cos(90 + x) = -sinx-------- eq2
In option two we are given that:
cos(90 + x) = -2a ---------- eq3
So by equating both sides of eq2 and eq3:
-2a = -2sinx
By cancelling -2 from both sides we get:
sinx = a
That is given in eq1
hence proved
i hope it will help you!
The bacterial strain Acinetobacter has been tested for its adhesion properties, which is believed to follow a normal distribution. A sample of five measurements gave readings of 2.69, 5.76, 2.67, 1.62 and 4.12 dyne-cm. Assume that the standard deviation is known to be 0.7 dyne-cm_2 and that the scientists are interested in high adhesion (at least 2.66 dyne-cm^2)(a) Should the alternative hypothesis be one-sided or two-sided? Write down the null and alternative hypotheses.(b) Based on your answer to part (a), test the hypothesis to see if the mean adhesion is at least 2.66 dyne-cm_2 (Use the p-value approach) What can be concluded?
Answer:
a) Alternative hypothesis should be one sided. Because Null and Alternative hypotheses are:
[tex]H_{0}[/tex]: μ=2.66 dyne-cm.
[tex]H_{a}[/tex]: μ<2.66 dyne-cm.
b) the hypothesis that mean adhesion is at least 2.66 dyne-cm is true
Step-by-step explanation:
Let μ be the mean adhesion in dyne-cm.
a)
Null and alternative hypotheses are:
[tex]H_{0}[/tex]: μ=2.66 dyne-cm.
[tex]H_{a}[/tex]: μ<2.66 dyne-cm.
b)
First we need to calculate test statistic and then the p-value of it.
test statistic of sample mean can be calculated as follows:
t=[tex]\frac{X-M}{\frac{s}{\sqrt{N} } }[/tex] where
X is the sample mean M is the mean adhesion assumed under null hypothesis (2.66 dyne-cm) s is the standard deviation known (0.7 dyne-cm_2)N is the sample size(5)Sample mean is the average of 2.69, 5.76, 2.67, 1.62 and 4.12 dyne-cm, that is [tex]\frac{2.69+5.76+2.67+1.62+4.12}{5}[/tex] ≈ 3.37
using the numbers we get
t=[tex]\frac{3.37-2.66}{\frac{0.7}{\sqrt{5} } }[/tex] ≈ 2.27
The p-value is ≈ 0.043. Taking significance level as 0.05, we can conlude that sample proportion is significantly higher than 2.66 dyne-cm.
Thus, according to the sample the hypothesis that mean adhesion is at least 2.66 dyne-cm is true