Answer:
[tex] {p}^{2} \times {p}^{( - 7)} = {p}^{(2 - 7)} = {p}^{ - 5}[/tex]
is the right answer.
A fifth grade teacher gives homework every night in both mathematics and language arts. The time to complete the mathematics homework has a mean of 30 minutes and a standard deviation of 3 minutes. The time to complete the language arts homework has a mean of 40 minutes and a standard deviation of 4 minutes. Assuming both distributions of homework time are Normally distributed, what is the probability that the average time it takes to complete both homework assignments is greater than 82 minutes?
Answer:
0.82% probability that the average time it takes to complete both homework assignments is greater than 82 minutes
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Math homework:
[tex]\mu_M = 30, \sigma_M = 3[/tex]
Arts homework:
[tex]\mu_A = 40, \sigma_A = 4[/tex]
What is the probability that the average time it takes to complete both homework assignments is greater than 82 minutes?
Here, we have a sum of normal variables. The mean will be the sum of the means, while the standard deviation is the square root of the sum of the variances. So
[tex]\mu = \mu_M + \mu_A = 30 + 40 = 70[/tex]
[tex]\sigma = \sqrt{\sigma_M^2 + \sigma_A^2} = \sqrt{3^2+4^2} = 5[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 82. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{82 - 70}{5}[/tex]
[tex]Z = 2.4[/tex]
[tex]Z = 2.4[/tex] has a pvalue of 0.9918
1 - 0.9918 = 0.0082
0.82% probability that the average time it takes to complete both homework assignments is greater than 82 minutes
Which is the simplified form of ,-7 +5-12?
구
12
0 - - s12
s12
0 +11
s12
A class fundraiser is earning $7 per car wash w and $4 per cake c sold. The cakes cost $2 to make and the supplies or the car wash cost $1 per car. They will wash less than 50 cars and bake no more than 30 cakes. They want to raise at least $320 to give to a local charity. What system represents this situation
Answer:
w<50
c≤30
6w+2c≥320
Step-by-step explanation:
W stands for the car wash, and C stands for the cakes. Naturally, it would be 7w+4c≥320 but each cake costs $2 to make and each car wash costs $1 per car. This makes the system 6w+2c≥320. They will wash less than(<) 50 cars and bake no more than(≤) 30 cakes. I hope this helped :).
To solve the problem we must know about Expressions.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Given to us
Earning per car wash = $7
Earning per cake = $4
Cost of supplies per car wash = $1
Cost of cake = $2
They will wash less than 50 cars and
Bake no more than 30 cakes
They want to raise at least $320
Assumption
Let the number of cakes they sold be represented by x, and the number of car washes they did be represented by y.
Profit from Car washProfit from Car wash
= Earning per car wash - Cost of supplies per car wash
= $7 - $1
= $6
Profit from CakeProfit from Cake
= Earning per Cake - Cost of a cake
= $4 - $2
= $2
What is Total Profit?The system that represents profit
$320 = ($6)y + ($2)x
320 = 6y + 2x
Number of Cake they will bake,As it is given that they will not make more than 30 cakes, therefore,
x ≤ 30
Number of Carwashes they will do,As it is given that they will wash less than 50 cars.
y < 50
Hence, the following equations can represent the system,
320 = 6y + 2xx ≤ 30y < 50Learn more about Expression:
https://brainly.com/question/13947055
Determine whether m(t)=(4/5)^t represents exponential growth or exponential decay. And Identify the percent rate of change.
Answer:
Step-by-step explanation:
exponential decay
rate of change: 20%
WILL GIVE BRAINLIEST
the answer is 162
(to add more letters)
Factor.
8xy - 54x^2 how to solve this
[tex]\frac{1}{3}x+6=8[/tex]
ASAP PLEASE!!!!!!!!!!!
Alexis borrows money to buy a new phone. She plans to pay back $301 in 7 months by paying the same amount each month. The total amount she needs to pay back is $645.
7 301
x 645
If she pays the same amount each month, how many months will it take Alexis to pay back $645? Let x represent the number of months it will take Alexis to pay back $645 at the given rate.
X= ___ months
Alexis decides that she wants to pay back the $645 three months sooner. She will need to pay back more each month than she originally planned. How much does Alexis need to pay each month to pay back the money 3 months sooner?
$___per month
Simplify the expression 15-24divide3•2+13=
Answer:
[tex] \frac{ - 9}{19} [/tex]
Step-by-step explanation:
[tex] \frac{15 - 24}{3 \times 2 + 13 } = \frac{ - 9}{19} [/tex]
Laura is stuck in aisle six at the supermarket trying to decide which jar of peanut butter to buy she can buy a 16-ounce jar for $2.59 or 24- ounce jar for $3.29. Which jar has a lower unit price per ounce? Show your calculations and reasoning. REAL ANSWERS ONLY
9514 1404 393
Answer:
24-oz jar is lower cost per ounce
Step-by-step explanation:
The 16-ounce jar is almost $2.60. The 24-ounce jar contains half again as much peanut butter (16 +1/2·16 = 24). So, if the 24-ounce jar were the same price, it would cost half-again as much:
$2.60 +(1/2)2.60 = $2.60 +1.30 = $3.90.
The 24-ounce jar is priced considerably below that amount, so the 24-ounce jar has a lower price per ounce.
__
You could also view the 16-ounce jar as 2/3 the quantity of the 24-ounce jar. If it were the same price, that price would be about (2/3)$3.30 = $2.20. The 16-ounce jar is somewhat more than that, so costs more per ounce.
_____
Additional comment
For the estimates we did here, we needed prices that were divisible by 2 or 3. That involved adding a penny to the given price. So, the estimated equivalent price is off by a penny or so--not an issue in this case.
Note that we didn't actually need to find the per-ounce prices. We only needed to find the price for an equivalent number of ounces, which is much easier mental arithmetic.
There are 90 passengers on a commuter flight from SFO to LAX, of whom 27 are traveling on business. In a random sample of five passengers, use the binomial model to find the approximate hypergeometric probability that there is at least one business passenger.
Answer:
0.8401 = 84.01% probability that there is at least one business passenger.
Step-by-step explanation:
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
In this question:
Samples of 5, so [tex]n = 5[/tex]
90 passengers, so [tex]N = 90[/tex]
27 traveling on businnes, so [tex]k = 27[/tex]
Probability that there is at least one business passenger.
Either none are on business, or at least one is. The sum of these probabilities is 100% = 1.
Probability of none on business:
[tex]P(X = 0) = \frac{C_{27,0}*C_{63,5}}{C_{90,5}} = 0.1599[/tex]
Probability of at least one business passenger:
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1599 = 0.8401[/tex]
0.8401 = 84.01% probability that there is at least one business passenger.
Solve the equation.
5/6b = 1 7/8
Step-by-step explanation:
5/6b=17/8
Cross multiple
40=102b
divide through by 102
b=20/51
In the diagram, GH bisects ZFGI.
a. Solve for x and find mZFGH.
b. Find mZHGI.
c. Find mZFGI.
(3x - 1)º
a.
.X
(Simplify your answer.)
Answer:
"bisect" means: angle FGH = angle HGI
(3x-3)=(4x-14)
-3+14=4x-3x
x=11
Angle FGH = (3x-3) = 30
Angle HGI = Angle FGH = 30
Angle FGI = 60
Step-by-step explanation:
i think this is right im not sure
15) A store is having a sale during which all outdoor furniture is 45% off the original price, p. If
the post-sale price of an outdoor furniture set can be calculated using the expression p
0.45p, which expression also represents the price?
Answer and explanation:
Given that there is 45% off original price of outdoor furniture and price is represented by p
Discount on original price of outdoor furniture = 45% of p=0.45×p=0.45p
Therefore post sale price(after discount) of outdoor furniture can be represented by (1-0.45)p=0.55p
25/3 X 4/15 what’s the answer
Answer:
2 2/9
Step-by-step explanation:
Find the indicated probability. In one town, 71% of adults have health insurance. What is the probability that 4 adults selected at random from the town all have health insurance
Answer:
0.254
Step-by-step explanation:
Given that:
Percentage of those having health insurance = 71%
p = 71 / 100 = 0.71
Number of adults selected at random, n = 4
Probability that 4 selected have health insurance :
p^n = 0.71^4 = 0.25411681
= 0.254
The National Household Travel Survey gathers data on the time of day when people begin a trip in their car or other vehicle. Choose a trip at random and record the time at which the trip started. What probability should replace the "?" in the table?
Time of Day 10PM- 12:59AM 1AM- 5:50AM 6AM- 8:59AM 9AM- 12:59PM 1PM- 3:59PM 4PM- 6:59PM 7PM- 9:59PM
Probability 0.004 0.033 0.144 0.234 0.208 ? 0.123
a. 0.964
b. 0.379
c. 0.752
d. 0.218
Answer:
A probability of 0.254 should replace the "?" in the table
Step-by-step explanation:
We have the probabilities for the time of the day when each person begins a trip, during a 24-hour period.
The sum of these probabilities has to be 100% = 1.
The probabilities are of: 0.004, 0.033, 0.144, 0.234, 0.208, ?, 0.123
Since their sum has to be 1, we can find ?. So
0.004 + 0.033 + 0.144 + 0.234 + 0.208 + ? + 0.123 = 1
0.746 + ? = 1
? = 1 - 0.746
? = 0.254
A probability of 0.254 should replace the "?" in the table
A rectangle and a square have equal areas. The length of the square is 9 cm.The rectangle has width 4 cm. What is the perimeter of the rectangular?
Answer:
Perimeter = 26 cm. Area =
Step-by-step explanation:
The rectangle has a width of 4 cm and the square has a length of 9. cm, so to make them have the same area you make the length of the rectangle 9 cm and the square have a width of 4 cm.
then each shape will have two sides that are 9 cm and two sides that are 4 cm.
Perimeter
9 + 9 = 18
4 + 4 = 8
18 + 8 = 26
the perimeter is 26 cm.
Area
9 x 4 = 36
the area is 36 cm.
Answer:
Width is 4cm and length is 20.25, so perimeter is 48.5
Step-by-step explanation:
Square has same length for each side
Area for the Square 9 x 9 = 81
So find another number that adds up to the area of the square
Area for Rectangle 4 x 20.25 = 81
Width for Rectangle is 4cm and length is 20.25, so perimeter is 48.5
Should be pretty easy if you have a calculator, It'll just take a couple more minutes :D
(30 POINTS) Select the correct answer.
Which equation has no solution?
A. 1/2(8x + 6) -2x = -3(2x + 1)
B. -4(1/2x + 2) = -2x - 8 + 4x
C. 7(x + 2) - 3x = 2/3 (6x + 3)
D. -2x + 5 - 3x + 12 = -5(x - 3) + 2
Answer:
C. 7(x + 2) - 3x = 2/3 (6x + 3)
Step-by-step explanation:
ANSWER FROM PLATO
When solving an equation, if the variable terms cancel out leaving different numbers on each side of the equal sign, then the equation has no solution.
Consider the following equation:
7(x + 2) - 3x = 2/3 (6x + 3)
7x + 14 - 3x = 4x + 2
4x + 14 = 4x + 2
14 = 2
Therefore, the equation has no solution.
A learning experiment requires a rat to run a maze (a network of pathways) until it locates one of three possible exits. Exit 1 presents a reward of food, but exits 2 and 3 do not. (If the rat eventually selects exit 1 almost every time, learning may have taken place.) Let Yi denote the number of times exit i is chosen in successive runnings. For the following, assume that the rat chooses an exit at random on each run.
Required:
Find the probability that n = 6 runs result in Y1=3,Y2=1, and Y3=2
Answer:
Find the probability that n = 6 runs result in Y1=3,Y2=1, and Y3=2
=0.823
Step-by-step explanation:
Multinomial distribution
p(y1;y2,y3…..yk) = (n!/y1!,y2!,y3!…y4!) x p1^y1 x p2^y2 x p3^y3 x pk^yk)
The rat chooses of the three exists at random:
p = 1/3
p(3,2,1) = 6! / 3! 1! 2! (1/3)^3 (1/3)^1 (1/3)^2
=20/243
=0.823
132 is what percent of 880
Answer:
Step-by-step explanation:
132 is what percent of 880? = 15.
SOLVE:
24 - 24 : 3 + 1
Answer
17
its a division sign for : so 24-24 divided by 3 + 1
A model of a rectangular stove top with four circular burners is shown. The side lengths of the stove top and the diameters of the burners are labeled.
Which measurement is the best estimate of the area in square inches of the stove top that does not include the area of the burners?
A) 108 in.2
B) 492 in.2
C) 420 in.2
D) 528 in.2
The required estimate of the area in square inches of the stove top that does not include the area of the burners is 415 square inches.
What is surface area?Surface area is defined as the measure of a region or surface is called as surface area.
The best estimate of the area of the stovetop that does not include the area of the burners can be obtained by subtracting the total area of the four burners from the total area of the stovetop.
The total area of the stove top is given by the product of its length and width:
Length = 24 inches
Width = 22 inches
Area = Length × Width = 24 × 22 = 528 square inches
The area of each burner is given by the formula for the area of a circle:
= π × (diameter/2)²,
where π is approximately equal to 3.14
Since the diameter of each burner is 6 inches, the radius of each burner is 6/2 = 3 inches.
Area of one burner = Pi × (3)² = 3.14 × 9 = 28.26 square inches
The total area of the four burners is 4 × 28.26 = 113 square
The area of the stove top = 528 - 113
= 415 square inches.
Thus, the required estimate of the area in square inches of the stove top that does not include the area of the burners is 415 square inches.
Learn more about the surface area here:
https://brainly.com/question/2835293
#SPJ6
Question: What is the the total area of the kitchen floor?
Answer:
56
Step-by-step explanation:
If we split this figure to 2 parts, we figure the area based upon this composite figure.
1 figure is 10x4(rectangle)
the other figure is a 4x4 square (Note we subtract 8 by 4 because we don't want overlapping area)
After that we find the area of those to figures then we add them up
(4x4)+(10x4)
16+40
56
what a ratio of 4 days to 36 hours
Answer:
4:36
24 x 4:36
96:36
8:4
1day = 24 hours
Step-by-step explanation:
The one-to-one functions g and h are defined as follows.
HELP PLEASE
Answer:
2, (x+13)/6, -7
Step-by-step explanation:
The -1 bit means do it backwards, so look the for the output of the function with the value given.
In g, when we put in 2 we get 9 out, so g^-1(9) is 2.
For the second one we need to rearrange it to get x = something.
h(x) + 13 = 6x
x = (h(x) + 13)/6
Then replace the h(x) with x and the x with h^-1(x) to get
h^-1(x) = (x + 13)/6
The last one is a trick. Note that h and h^-1 are opposites. If we do something then do the opposite of it, we haven't done anything at all! So the number stays the same.
Can someone help me with this please
What is the right answer for it?
Hi, can you please help me? 1 Over a period of 3 hours, 190 leaves fell from a tree. At this rate, about how many leaves fell every hour? (Round your answer to the nearest whole number.)
A. 60 leaves per hour
B. 72 leaves per hour
C. 75 leaves per hour
D. 63 leaves per hour
question 2:Mrs. Hill drove a total of 252 miles and used 12 gallons of gasoline. What is the unit rate?
A. 16 miles per gallon
B. 12 miles per gallon
C. 21 miles per gallon
D. 32 miles per gallon
Answer:
D.63 leaves
Step-by-step explanation:
Divide the given number of leaves by the time it took that many to fall
190/3=63.33 which rounds down to 63
Question #2
21 Miles per gallon
Divide the number of gallons by the amount of gas to get miles per gallon.
252/12=21 miles per gallon
Simplify: 6√3 + 2√75 - 4√27
do you know the answer?
Answer:
4√3 or Decimal form 6.928203
Step-by-step explanation:
ofc i know the answer, ima different breed
20 POINTS (Again) Helppp Hurry!!
Answer:
6
Step-by-step explanation:
Answer:
m∠5=34°
Step-by-step explanation:
angle 1 is a corresponding angle to angle 5 therefore they are congruent