Answer:
[tex]\sigma =\frac{478}{6}=79.667[/tex]
Step-by-step explanation:
The empirical rule, also referred to as "the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)". The empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).
And on this case since we are within 3 deviations (because we have 99.7% of the data between 568 and 1066hours), the result obtained using the z score agrees with the empirical rule.
So on this case we can find the standard deviation on this ways:
[tex]\mu -3\sigma = 568[/tex] (1)
[tex]\mu +3\sigma = 1066[/tex] (2)
If we subtract conditions (2) and (1) we got:
[tex]1066-588 =\mu +3\sigma -\mu +3\sigma[/tex]
[tex]478= 6\sigma[/tex]
[tex]\sigma =\frac{478}{6}=79.667[/tex]
A strawberry farmer needs to water a strawberry patch of 1500 square yards is in the shape of a sector of a circle with a radius of 40 yards. Through what angle should the sprinkler rotate
Answer:
The sprinkler must rotate by an angle of 107.48°.
Step-by-step explanation:
Given:
Area of strawberry patch( in shape of sector) = 1500 square yards
Radius of circle = 40 yards
To find angle through which the sprinkler should rotate.
Solution.
In order to find the angle of rotation of sprinkler, we will apply the area of sector formula.
[tex]Area\ of\ sector\ = \frac{\theta}{360}\times \pi r^2[/tex]
where [tex]\theta[/tex] is the angle of the sector formed and [tex]r[/tex] is radius of the circle.
Thus, we can plugin the given values to find [tex]\theta[/tex] which would be the angle of rotation.
[tex]1500 = \frac{\theta}{360}\times \pi (40)^2[/tex]
Taking [tex]\pi=3.14[/tex]
[tex]1500 = \frac{\theta}{360}\times \ (3.14) (40)^2[/tex]
[tex]1500 = \frac{\theta}{360}\times 5024[/tex]
Dividing both sides by 5024.
[tex]\frac{1500}{5024} = \frac{\theta}{360}\times 5024\div 5024[/tex]
Multiplying both sides by 360.
[tex]\frac{1500\times 360}{5024} =\frac{\theta}{360}\times 360[/tex]
[tex]107.48=\theta[/tex]
∴ [tex]\theta= 107.48\°[/tex]
Angle of rotation of sprinkler = 107.48°
The strawberry farmer needs the sprinkler to rotate approximately 107.46 degrees to cover the 1500 square yard sector of the circle with a 40-yard radius.
To determine the angle through which the sprinkler should rotate, we first need to find the area of the sector of the circle. The formula for the area of a sector is:
A = 0.5 × r² × θ
where A is the area, r is the radius, and θ is the angle in radians. Here, we know the area A is 1500 square yards and the radius r is 40 yards. Rearranging the formula to solve for θ gives:
θ = (2 × A) / r²
Substituting the given values:
θ = (2 × 1500) / 40²
θ = (3000) / 1600
θ = 1.875 radians
To convert this angle in radians to degrees, we use the conversion factor 180/π:
θ = 1.875 × (180 / π) ≈ 107.46 degrees
Therefore, the sprinkler should rotate through an angle of approximately 107.46 degrees.
A football team won 10 matches out of the total number of matches they played if their win percentage was 40 then how many matches did they play in all
Answer:the football team played 25 games in all
Step-by-step explanation:
Let x represent the total number of matches that the football team played.
The football team won 10 matches out of the total number of matches they played. if their win percentage was 40, it means that
10/x × 100 = 40
1000 = 40x
x = 1000/40 = 25
Leiff goes online to buy a new video game. He finds a site that currently has a promotion of 15% off on all orders over $50. Leiff decides to buy his video game, with a price tag of $128, at this site because he knows that he will get the 15% discount when he checks out. Leiff pays 5.3% sales tax on the discounted price and pays a shipping fee of $4.75. What is the total of Leiff’s online purchase?
Answer:
$119.32
Step-by-step explanation:
Leiff decides to buy his video game, with a price tag of $128, at this site
he will get the 15% discount when he checks out.
100-15= 85%
Discounted price=85% of 128 is [tex]0.85 \cdot 128=108.8[/tex]
Leiff pays 5.3% sales tax on the discounted price
5.3% is 0.053
sales tax amount=0.053 times 108.8=5.7664
So we add the sales tax amount and shipping fee
[tex]108.8+5.7664+4.75=119.32[/tex]
So $119.32 is the total amount
The total of Leiff’s online purchase is $119.31.
To calculate the total of Leiff's online purchase, we need to first calculate the discount on the video game.
The discount is calculated by multiplying the original price of the video game by the discount rate.
Discount = $128 * 15%
= $19.20
The discounted price of the video game is the original price minus the discount.
Discounted price = $128 - $19.20
= $108.80
The sales tax is calculated by multiplying the discounted price of the video game by the sales tax rate.
Sales tax = $108.80 * 5.3%
= $5.76
The total cost of the video game, including the discount and sales tax, is:
Total cost = $108.80 + $5.76
= $114.56
The total cost of Leiff's online purchase is the cost of the video game plus the shipping fee.
Total cost = $114.56 + $4.75
= $119.31
Therefore, the answer is $119.31.
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Explain how to graph a quadratic equation to someone who does not
know how. Make sure you explain how to find the vertex-
formula to use. You should also teach them how to tell whether the
graph opens up or down and how to find the maximum or minimum
and zeros/solutions.
The term quadratic comes from the word quadrate meaning square or rectangular. Similarly, one of the definitions of the term quadratic is a square. In an algebraic sense, the definition of something quadratic involves the square and no higher power of an unknown quantity; second degree. So, for our purposes, we will be working with quadratic equations which mean that the highest degree we'll be encountering is a square. Normally, we see the standard quadratic equation written as the sum of three terms set equal to zero. Simply, the three terms include one that has an [tex]x^{2}[/tex], one has an x, and one term is "by itself" with no [tex]x^{2}[/tex] or x.
Question 9 (5 points)
Lines a, b, and care coplanar. Lines a and b intersect. Line c intersects only with line b. Draw and label a figure
for this relationship.
Answer:
Lines 'a' and 'c' are parallel. Line 'b' is non parallel to 'a' and 'c'.
Step-by-step explanation:
Picture is attached with the answer as a solution to it.
In the question it is give that line 'c' only intersect with line 'b' and not with, so the only way that two lines won't intersect here 'a' and 'c' is that lines are parallel. If the lines are not parallel then those lines will definitely meet.
Heathers weekly pay is directly proportional to the number of hours she works at the record store her pay is 174 for 24 hours of work what is the amount of pay for 40 hours of work
Answer:
Heather pay will be 290 for 40 hours of work.
Step-by-step explanation:
Given:
Amount he gets paid weekly =174
Number of hours of work =24
we need to find the amount of pay for 40 hours of work.
Also Given:
weekly pay is directly proportional to the number of hours.
Framing in equation form we get;
Amount Of Pay ∝ Number of hours of work
Hence Amount of Pay = k × Numbers of hours of work.
where k is constant.
Substituting the values we will find the value of k
[tex]174 = k \times 24\\\\k = \frac{174}{24} = 7.25[/tex]
Now using this we will find the amount of pay when hours of work is 40.
Amount Of Pay = [tex]7.25\times 40 = 290[/tex]
Hence Heather pay will be 290 for 40 hours of work.
The surface area, SA, of a square prism is given by SA = 2s2 + 4sh. In the equation, •s is the length of the side of the square base and •h is the height. Which formula could be used to find h if you know the values of SA and s? A. H = SA + 2s2_______4 B. H = SA – 2s2_______4s C. H = SA – 2s2 – 4s D. H = SA___4s– 2s2
Answer:
[tex]h=\frac{SA-2s^2}{4s}[/tex]
Step-by-step explanation:
we know that'
The formula to calculate the surface area of a square prism is
[tex]SA=2s^2+4sh[/tex]
where
s is the length of the side of the square base
h is the height of the prism
Solve for h
That means ----> Isolate the variable h
so
subtract 2s^2 both sides
[tex]SA-2s^2=4sh[/tex]
Divide by 4s both sides
[tex]\frac{SA-2s^2}{4s}=h[/tex]
Rewrite
[tex]h=\frac{SA-2s^2}{4s}[/tex]
To find the height of a square prism when given the surface area and base side length, use the formula B. H = (SA - 2s^2) / (4s).
Explanation:The question asks for a formula that can be used to find the height (h) of a square prism given the surface area (SA) and the side length of the base (s). The surface area of a square prism is calculated using the formula SA = 2s2 + 4sh. To solve for h, we need to re-arrange this equation:
Subtract 2s2 from both sides: SA - 2s2 = 4sh.Divide both sides by 4s to isolate h: h = (SA - 2s2) / (4s).Therefore, the correct formula to find h is B. H = (SA – 2s2) / 4s.
Prove the identity cos x + cos y = 2cos(x+y/2) cos(x-y/2).
a. Show that x+y/2+x-y/2=x
b. Find a similar expression using x+y/2 and x-y/2 that equals y.
C. Use parts (a) and (b) to prove the identity.
Answer:
Step-by-step explanation:
cos(c+d)=cos c cos d-sin c sin d ...(1)
cos(c-d)=cos c cos d+sin c sin d ...(2)
add (1) and (2)
cos (c+d)+cos (c-d) =2 cos c cos d ...(3)
put c+d=x
c-d=y
add
2c=x+y
c=(x+y)/2
subtract
2d=x-y
d=(x-y)/2
substitute in (3)
[tex]cos~ x+cos~ y=2 cos (\frac{x+y}{2}) ~cos (\frac{x-y}{2})[/tex]
To prove the identity cos x + cos y = 2cos((x+y)/2) cos((x-y)/2), we need to show that x+y/2+x-y/2=x and find a similar expression using x+y/2 and x-y/2 that equals y. Once we have these expressions, we can use them to prove the identity.
Explanation:To prove the identity cos x + cos y = 2cos((x+y)/2) cos((x-y)/2), we need to show that x+y/2+x-y/2=x and find a similar expression using x+y/2 and x-y/2 that equals y. Once we have these expressions, we can use them to prove the identity.
To prove x+y/2+x-y/2=x, we can combine like terms by simplifying the expression. Combining x terms, we have x+x=x. Combining y/2 terms, we have y/2-y/2=0. Therefore, the equation is proven.To find a similar expression using x+y/2 and x-y/2 that equals y, we can subtract the two expressions. Subtracting, we have (x+y/2) - (x-y/2) = x - x + y/2 + y/2 = y. Therefore, the expression is x+y/2 - x-y/2 = y.Using parts (a) and (b), we can now prove the identity. Starting with the left-hand side of the identity (cos x + cos y), we can substitute in the expressions we found in parts (a) and (b). The left-hand side becomes 2cos((x+y)/2) cos((x-y)/2), which is equal to the right-hand side of the identity. Therefore, the identity is proven.Learn more about Proving the identity here:https://brainly.com/question/32435277
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Executive Limousine rentals charges an initial fee of $200 and $40 per hour that the limousine is in service. Jet Limousine rentals charges an intial fee of $120 and $50 per hour that the limosine is in service. At how many hours of service do the two limousine rental companies charge the same amount?
At 8 hours of service, the two limousine rental companies charge the same amount.
Step-by-step explanation:
Given,
Initial fee of Executive Limousine rental = $200
Per hour charges of service = $40
Let,
x be the number of hours.
E(x) = 40x+200
Initial fee of Jet Limousine rental = $120
Per hour charges of service = $50
J(x) = 50x + 120
For the charges to be same;
E(x) = J(x)
[tex]40x+200=50x+120\\200-120=50x-40x\\80=10x\\10x=80[/tex]
Dividing both sides by 10
[tex]\frac{10x}{10}=\frac{80}{10}\\x=8[/tex]
At 8 hours of service, the two limousine rental companies charge the same amount.
Keywords: function, addition
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What is the quotient in simplest form? 8/3 ÷ 2/3
what is the value of cos(x) if tan ( x)= -2 and x is in quadrant of IV?
Answer:
[tex]cos(x)=\frac{\sqrt{5}}{5}[/tex]
Step-by-step explanation:
we have that
[tex]tan(x)=-2[/tex]
The angle x is in quadrant IV
That means ---> The value of cos(x) is positive and the value of sin(x) is negative
Remember that
[tex]cos^2(x)+sin^2(x)=1[/tex] ----> equation A
[tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]
so
[tex]-2=\frac{sin(x)}{cos(x)}[/tex]
[tex]sin(x)=-2cos(x)[/tex] ----> equation B
substitute equation B in equation A
[tex]cos^2(x)+(-2cos(x))^2=1[/tex]
solve for cos(x)
[tex]cos^2(x)+4cos^2(x)=1[/tex]
[tex]5cos^2(x)=1[/tex]
[tex]cos^2(x)=\frac{1}{5}[/tex]
square root both sides
[tex]cos(x)=\pm\frac{1}{\sqrt{5}}[/tex]
but remember that the value of cos(x) is positive (IV quadrant)
[tex]cos(x)=\frac{1}{\sqrt{5}}[/tex]
simplify
[tex]cos(x)=\frac{\sqrt{5}}{5}[/tex]
What is the proper time sequence of the following three political movements/parties, from earliest to latest?
Answer:
The proper time sequence of the three political parties/movements, from earliest to latest is as follow:
Greenback party, Populist Party, Progressive movement.Step-by-step explanation:
Greenback party is such an American political party with the ideology of against the monopoly. It was founded in 1874 and dissolved in 1889. They worked for the rights of the farmers and workers of industries. They ran three candidates for the presidential elections in their era of political life. Populist Party is such an American party that is also known as People's Party which was founded in 1892 and dissolved in 1908. They fought for anti-corruption and were supporter of state control of railways. The women played a very active role in this party.Progressive Moment is also known as Progressive Era that was ended in 1920. This era demanded the reforms in the political system and gave rise to the social activism. The issues like corruption, industrialization and many such issues came in limelight.I need help with these questions. Three of them need to be checked and the last one I need help answering.
(If you cannot see the attachments yet please wait because that means I’m still attaching them)
Answer:
∆ABC ~ ∆DEF . . . as markedEF/LM = FG/MN . . . look againSAS congruence . . . as marked30 ftStep-by-step explanation:
1. Correct. Corresponding vertices are (A, D), (B, E), and (C, F). The triangle names must list corresponding vertices in the same order. Thus the answer is the one you have chosen.
__
2. Look again. As in the first problem, corresponding vertices are in the same order. Line segment EF is named by the first two vertices in the triangle name, so the corresponding segment is LM, also named by the first two vertices of that triangle's name.
Segment FG is named by the last two vertices of the triangle's name, so the corresponding segment in the other triangle is also named by the last two vertices of the triangle's name: MN. Corresponding segments are proportional, so EF/LM = FG/MN.
__
3. Correct. Segment DB is congruent to itself. The halves of the bisected angle at D are congruent to each other, and the segments DA and DC are shown as congruent. Hence, SAS is an appropriate choice for showing congruence of the triangles.
__
4. The 1:1 ratio of these similar triangles tells you they are congruent, so ...
AC = EC
4x -3 = 2x +6 . . . . substitute the given expressions
2x = 9 . . . . . . . . . . add 3-2x
EC = 9+6 = 15 . . . substitute for 2x in the expression for EC
The question asks for AE, which is 2 times the length EC, so is ...
AE = 2·EC = 2·15 = 30 . . . . feet
___
The only indication that the units are feet is that the answer choice with the number 30 has feet as its units. (We should be seeing "(4x-3) feet" as the measure of AC, for example.)
Complete the recursive formula of the geometric sequence 16\,,\,3.2\,,\,0.64\,,\,0.128,...16,3.2,0.64,0.128,
Answer:
[tex]a_{n+1}=0.2a_n[/tex] for all n>0, [tex]a_1=16[/tex]
Step-by-step explanation:
Let [tex]\{a_n\}=\{16,3.2,0.64,0.128,\cdots \}[/tex] be the sequence described.
A geometric sequence has the following property: there exists some r (the ratio of the sequence) such that [tex]\frac{a_{n+1}}{a_n}=r[/tex] forr all n>0.
To find r, note that
[tex]\frac{3.2}{16}=\frac{32}{10(16)}=\frac{2}{10}=\frac{1}{5}=0.2[/tex]
Similarly
[tex]\frac{0.64}{3.2}=\frac{64}{10(32)}=\frac{1}{5}=0.2[/tex]
[tex]\frac{0.128}{0.64}=\frac{1}{5}=0.2[/tex]
Thus [tex]a_{n+1}=r a_n=\frac{a_n}{5}=0.2a_n[/tex] for all n>0, and [tex]a_1=16[/tex]
first term = 16
average ratio = 0.2
involving a carnival fishpond. Assume that the pond contains 100 fish: 78 purple, 21 blue, and 1 silver. A contestant pays $0.65 to randomly catch one fish and receives $0.40 if the fish is purple, $0.80 if the fish is blue, and $13.00 if the fish is silver. How much (on average) does the carnival gain on each play?
Answer:
On average the carnival gain on each play
= 0.04 dollars
Step-by-step explanation:
Given that a pond contains 100 fish: 78 purple, 21 blue, and 1 silver.
Fish Purple Blue Silver total
Frequency 78 21 1 100
Prob 0.78 0.21 0.01 1
Revenue 0.4 0.8 13
game fee 0.65 0.65 0.65
Net revenue -0.25 0.15 12.35
Net Rev*Prob -0.195 0.0315 0.1235 -0.04
Thus we get per player expected net revenue is -0.04
This would be gain for Carnival
Hence On average the carnival gain on each play
= 0.04 dollars
Final answer:
To calculate the carnival's average gain per play, determine the expected payoff for each fish type, subtract the cost to play, and sum these amounts. The carnival gains an average of $0.61 per play.
Explanation:
The student's question involves calculating the average gain for a carnival on each play of a carnival fishpond game. To find this, we need to determine what the carnival earns on average based on the probabilities of catching each type of fish (purple, blue, or silver) and the payoff for each.
Let's calculate the expected profit (gain) per play for the carnival. The probability and payoff for each type of fish are:
Purple fish: Probability = 78/100, Payoff = $0.40
Blue fish: Probability = 21/100, Payoff = $0.80
Silver fish: Probability = 1/100, Payoff = $13.00
The expected payoffs for the carnival from catching each type of fish are:
Purple: 78/100 * $0.40
Blue: 21/100 * $0.80
Silver: 1/100 * $13.00
Subtract the contestant's cost ($0.65) from each expected payoff to find the expected gain. Then, sum these expected gains to find the overall average gain for the carnival.
The carnival's expected gain is:
Expected Gain per Play = (78/100 * $0.40) + (21/100 * $0.80) + (1/100 * $13.00) - $0.65
Calculating:
Expected Gain per Play = ($0.3120) + ($0.1680) + ($0.1300) - $0.65
Expected Gain per Play = $0.61
This calculation shows that on average, the carnival gains $0.61 for each play of the fishpond game.
Carly's family is moving out ,so she needs to pack the dishes .Dishes brake easily so she must wrap them up. She cuts a sheet of bubble wrap into two pieces .What is the fraction ?
1/2, or one half. since she cuts it into 2.
Sally is interested in taking a job in a city which she's not familier with the cost of living. She is especially concerned about the cost of housing and is interested in the average cost of a three bedroom home. Which of the following averages will be most influenced by three bedroom homes owned by millionaires?
a.mode
b.median
c.mean
d.none of the above
Answer:
c.Mean
Step-by-step explanation:
We have been given that the Sally is interested in taking a job in a city in which she's not familiar with the cost of living. She is especially concerned about the cost of housing and is interested in the average cost of a three bedroom home.
We know that in a normal distribution all central tendencies (mean, mode, median) are equal.
When a very large or very small valued data point is added to data set, mean is mostly affected by that outlier.
We know that mode of a data set is the point that appears at-most in the data set, so outliers doesn't affect mode.
Median of a data set is less affected by outliers.
The price of the three bedroom homes owned by millionaires will be greater than prices of houses owned by people in the neighborhood.
Therefore, mean will be most influenced by three bedroom homes owned by millionaires.
The first round of the 2010 FIFA World Cup consisted of several groups of four teams each. Within each group, each of the four teams played each other once. How many matches were there in each group?
Answer:There are 6 matches in each group
Step-by-step explanation:
The first round of the 2010 FIFA World Cup consisted of several groups of four teams each. Within each group, each of the four teams played each other once. Assuming the teams are A, B, C and D.. The way the teams in the group play each other would be
AB, CD first group matches.
AC, BD second group matches.
AD, BC. Third group matches
Therefore, the number of matches in each group would be 6
What is the next term of the sequence -3, 6, -12, 24, ...? Que
Answer:
-48
Step-by-step explanation:
Let me know if you need anything
Answer:
-48
Step-by-step explanation:
next in a row is always equal previous one multiple by -2
-3*(-2)=6
6*(-2)=-12
-12*(-2)=24
24*(-2)=-48
In this problem, the ratios are inversely proportional. Find the missing value. If R1 = 6, R2 = 8, and I1 = 12, what is the value of I2?
Answer:
[tex]I_2=9[/tex]
Step-by-step explanation:
We have been told that the ratios are inversely proportional in our given problem. We are asked to find the missing value.
We know that two inversely proportional quantities are in form [tex]y=\frac{k}{x}[/tex], where, y is inversely proportional to x and k is the constant of proportionality.
Let us find constant of proportionality using [tex]R_1 = 6[/tex] and [tex]I_1 = 12[/tex] in above equation.
[tex]6=\frac{k}{12}[/tex]
[tex]6*12=\frac{k}{12}*12[/tex]
[tex]72=k[/tex]
Now, we will use [tex]72=k[/tex] and [tex]R_2 = 8[/tex] in our equation to find [tex]I_2[/tex] as:
[tex]8=\frac{72}{I_2}[/tex]
[tex]I_2=\frac{72}{8}[/tex]
[tex]I_2=9[/tex]
Therefore, the value of [tex]I_2[/tex] is 9.
The question is about the mathematical concept of inverse proportionality. The missing value of [tex]I_2[/tex] is found by applying the property of inversely proportional quantities, yielding the result [tex]I_2 = 9[/tex].
In an inverse proportionality relationship, the product of the values in one set is equal to the product of the corresponding values in the other set. This can be represented as:
[tex]\[R_1 \cdot I_1 = R_2 \cdot I_2\][/tex]
Given that [tex]\(R_1 = 6\)[/tex], [tex]\(R_2 = 8\)[/tex], and [tex]\(I_1 = 12\)[/tex], you can solve for [tex]\(I_2\)[/tex]:
[tex]\[6 \cdot 12 = 8 \cdot I_2\][/tex]
Now, simplify the equation:
[tex]\[72 = 8 \cdot I_2\][/tex]
To isolate [tex]\(I_2\)[/tex], divide both sides by 8:
[tex]\[I_2 = \frac{72}{8}\][/tex]
[tex]\[I_2 = 9\][/tex]
So, the value of [tex]\(I_2\)[/tex] is 9. In this inverse proportionality relationship, when [tex]R_1[/tex] is 6, [tex]\(R_2\)[/tex] is 8, and [tex]\(I_1\)[/tex] is 12, [tex]\(I_2\)[/tex] is 9. This means that as one variable increases, the other variable decreases in such a way that their product remains constant.
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What is Y?
Question 5 options:
72
18
9
4
Y is a bisector of the two sides, so would be half the length of the base.
Y = 36 / 2
y = 18
PLEASE HELP ME!!!! I CANT DO THIS!!! WILL GIVE BRAINLIEST!!!!
Divide 27x^3 − 72x^2 + 36x by 9x.
A. 3x^2 − 8x + 4
B. 3x^2 + 8x − 4
C. 3x^3 − 8x + 4
D. 3x^3 + 8x − 4
Suppose your current electricity meter reading is 25,789 kWh, and the reading on your last bill was 25,350 kWh. If you are charged $0.0983/kWh, compute the amount of you bill.
Answer:
The answer to your question is $43.15
Step-by-step explanation:
Current bill = 25, 789 kWh
Previous bill = 25, 350 kWh
Charge = $ 0.0983/ kWh
Process
1.- Subtract the current meter from the previous one
25, 789 - 25, 350 = 439 kWh
2.- Find the amount of the bill using a rule of three
$0.0983 ----------------- 1 kWh
x ---------------- 439 kWh
x = (439 x 0.0983) / 1
x = $ 43.15
Find the probability of rolling a sum less than 6 or a sum greater than 8 when a pair of dice is rolled?
Answer:
[tex]\frac{5}{9}\approx0.556[/tex]
Step-by-step explanation:
A pair of dice is rolled so the outcome space will be.
[tex]S= \{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)\\(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)\\(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)\\(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)\\(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)\\(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}[/tex]
Total number of elements [tex]=36[/tex]
Possible outcomes in which sum is less than [tex]6[/tex] or greater than [tex]8[/tex]
[tex]S_{1} = \{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(3,1),(3,2),(3,6),\\(4,1),(4,5),(4,6),(5,4),(5,5),(5,6),(6,3),(6,4),(6,5),(6,6)\}[/tex]
Number of element in this space [tex]=20[/tex]
P(sum is less than [tex]6[/tex] or greater than [tex]8[/tex])
[tex]=\frac{Favourable\ outcomes}{total\ outcomes} \\=\frac{20}{36}\\ =\frac{5}{9}[/tex]
The Vega family has a cell phone plan that costs $75 per month including taxes and fees.The plan lets the 5 members of the Vega family share 1,000 of talk time per month and 400 text messages per month.Any minutes over 1,000 cost $1 per minute,and any texts over 400 cost $2 per text Because of a family emergency,the family uses 1,050 minutes and 415 texts in March.Write an expression you could use to find the amount of the Vega's cell phone bill for March.Evaluate the expression.Show your work.
Answer:the Vega's cell phone bill for March is $155
Step-by-step explanation:
Let x represent the number of talk time in minutes that the family uses for a month.
Let y represent the number of text messages that the family sends in a month.
Let z represent the total cost of using x talk time and sending y text messages in a month.
The cell phone plan costs $75 per month including taxes and fees. Any minutes over 1,000 cost $1 per minute,and any texts over 400 cost $2 per text. This means that the total cost of x minutes and y texts would be
z = 75 + 1(x - 1000) + 2(y - 400)
z = 75 + x - 1000 + 2y - 800
z = 75 - 1000 - 800 + x + 2y
z = x + 2y - 1725
Because of a family emergency,the family uses 1,050 minutes and 415 texts in March. The total cost would be
z = 1050 + 2(415) - 1725
z = 1050 + 830 - 1725 = $155
Consider the function f(x)=x3+3x2â51x+91. What is the remainder if f(x) is divided by (x+9)? Do not include (x+9) in your answer.
Answer:
The remainder is 64
Step-by-step explanation:
Consider the function [tex]f(x)=x^3+3x^2-51x+91[/tex]
Use synthetic division to divide by x+9
x+9=0, x=-9
divide the given f(x) by -9 using synthetic division
-9 1 3 -51 91
0 -9 54 -27
--------------------------------------------------
1 -6 3 64
The remainder is 64
If k = (n + 2)(n – 2), where n is an integer greater than 2, what is the value of k ? (1) k is the product of two primes. (2) k < 100
Answer:
The answer is k=77
Step-by-step explanation:
It is given that n is an integer and greater than 2. Let us simplify k = (n + 2)(n – 2) to k=n^2-4.
In (1) it is stated that k is the product of two primes and in (2) it is stated that k<100. To solve the question we need to consider both cases (1) and (2).
Let say n=9 then k=n^2-4 becomes k=81-4=77. Well, 77 is the product of two prime numbers 7 and 11 (77=7*11). The answer is k=77
For model 5, the tip of the blade travels 0.18 mile per revolution. What is the approximate speed, in revolutions per minute, for model 5?
Answer:
19 revolutions per minute, for model 5.
Step-by-step explanation:
Consider the model shown below:
From the table:
The blade length for model 5 is 148 feet
Also the maximum blade tip speed is 200 miles per hour.
It is given that the tip of the blade travels 0.18 mile per revolution.
To find the number of revolution per hour simply divide the maximum speed of the blade with the revolution.
Number of revolutions per hour = [tex]\frac{200}{0.18}=1111.111[/tex]
We need to find the speed, in revolutions per minute, so divide the obtained revolution per hour with 60.
[tex]\frac{1111.11}{60} =18.52\approx19[/tex]
Hence, 19 revolutions per minute, for model 5.
Final answer:
To determine the speed in revolutions per minute for model 5, we need to know how far the blade tip travels in one minute. This would be divided by 0.18 miles, the distance per revolution, to find the RPM. Without the distance traveled in one minute, we cannot complete the calculation.
Explanation:
To calculate the approximate speed in revolutions per minute for model 5, where the tip of the blade travels 0.18 miles per revolution, we need to find how many revolutions it would complete in one minute. Assuming the tip travels at a constant speed, you would divide the distance it covers in one minute by the distance per revolution.
First, determine the distance traveled by the blade tip in one minute. Since no speed is given for one minute in the question, we cannot provide a direct answer; more information would be needed, such as the distance the blade tip travels in a given time frame. However, if we had information like this, we could proceed with a calculation:
Let's say the tip travels X miles in one minute. You would then divide X by 0.18 miles to find the number of revolutions per minute:
Revolutions per minute (RPM) = Distance in miles per minute / Distance per revolution
RPM = X miles / 0.18 mile
For example, if the tip travels 1.8 miles in one minute, then:
RPM = 1.8 miles / 0.18 mile = 10 RPM
How many positive integers can be expressed ad a product of two or more of the prime numbers 5,7,11,and 13 if no one product is to include the same prime factor more than once?
Answer:
11 positive integers can be expressed.
Step-by-step explanation:
Consider the provided information.
The number of possible prime numbers are 5,7,11,and 13.
There are 4 possible prime numbers.
How many positive integers can be expressed as a product of two or more of the prime numbers, that means there can be product of two numbers, three number or four numbers.
The formula to calculate combinations is: [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
The number of ways are:
[tex]^4C_2+^4C_3+^4C_4=\frac{4!}{2!(4-2)!}+\frac{4!}{3!(4-3)!}+\frac{4!}{4!}[/tex]
[tex]^4C_2+^4C_3+^4C_4=\frac{4!}{2!2!}+\frac{4!}{3!}+1[/tex]
[tex]^4C_2+^4C_3+^4C_4=6+4+1[/tex]
[tex]^4C_2+^4C_3+^4C_4=11[/tex]
Hence, 11 positive integers can be expressed.
Consider a collection of envelopes consisting of 3 red envelopes, 1 blue envelope, 3 green envelopes, and 2 yellow envelopes. If three envelopes are selected at random, without replacement, determine the probability that they are all green envelopes.
Total envelopes: 3 + 1 + 3 + 2 = 9 with a total of 3 green ones.
Probability of picking green first: 3 out of 9 = 3/9 = 1/3
There are 8 envelopes left, with 2 green ones.
Probability of picking a green one is 2 out of 8 = 2/8 = 1/4
There are 7 envelopes left and 1 green one.
Probability of picking green is 1 out of 7 = 1/7
Probability of picking all 3 = 1/3 x 1/4 x 1/7 = 1/84