3. Given the function f(x) shown graphed below, what is its average rate of change from } x=1 to x=7 ?
(1) -1
(2) -4/3
(3) 8
(4) 3/5
4. A function h(x) has an average rate of change equal to 7 on the interval 5 ≤ x≤ 9. If h(5)=12, then which of the following must be the value of h(9) ?
Answers
3) The rate of change on the interval [1, 7] is -1, so the correct option is A.
4) By using the rate of change formula, we will see that h(9) = 40
How to find the average rate of change?We know that for a function f(x), the average rate of change on the interval [a, b] is:
r = ( f(b) - f(a))/(b - a)
Here the interval is [1, 7]
Using the graph we can see that:
f(1)= 6
f(7) = 0
Then the average rate of change is:
r = ( f(7) - f(1))/(7 - 1)
r = (0 - 6)/6 = -1
The correct option is A.
4) Which will be value of h(9)?
We know that the average rate of change of h(x) is 7 on the interval [5, 9]
Then we can write:
7 = ( h(9) - h(5))/(9 - 5)
We know that h(15) = 12, then we have the equation:
7 = (h(9) - 12)/4
Now we can solve that for h(9), we will get:
7 = (h(9) - 12)/4
7*4 = h(9) - 12
28 = h(9) - 12
28 + 12 = h(9)
40 = h(9)
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Related Questions
The chances of finding a rare card in a pack of trading cards can be represented with the equation y equals one twenty-second times x, where y represents the number of rare trading cards and x represents the number of packs of trading cards. Determine how many rare trading cards you would find if you bought 110 packs of trading cards.
2,420
22
5
one over 22
Answers
You will find 5 rare trading cards if you bought 110 packs of trading cards
How to determine the number of rare trading cards?
Given that:
The chances of finding a rare card in a pack of trading cards can be represented with the equation y equals one twenty-second times x.
Thus, we can the equation as:
y = (1/22)x
To determine the number of rare trading cards if you bought 110 packs of trading cards, substitute x = 110 into the equation:
y = 1/22 × 110
y = 5
Therefore, you will find 5 rare trading cards if you bought 110 packs of trading cards
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Answer:
Step-by-step explanation:
y = the number of rare trading cards found
x = the number of packs of trading cards
1/22 = the probability of finding a rare card per pack
Equation
y = 1/22(x)
y = 1/22(110)
y = 110/22
y = 5
There is a chance of finding 5 rare cards in 110 packs of trading cards.
Which of the following groups of numbers are all prime numbers?
O A. 3, 11, 23, 31
OB. 7, 17, 29, 49X
OC. 2, 3, 5, 9%
O D. 2, 5, 15, 196
Answers
Answer:
O A. 3, 11, 23, 21
OB. 7, 17, 29
OC. 2, 3, 5
OD. 2, 5
Step-by-step explanation:
Debbie has 4,000 in an account the interest rate is 15% compounded annually to the nearest and how much interest will she earn in 2 years
need answers fast please and thank you
Answers
Answer:
Step-by-step explanation:
The formula you want is: fv=p(1+int/c)^(nc)
future value
principal
int
compound
years
fv=4000(1.04/4)^(16)=$4690.31
If 20% of a number is 40, find 2% of that number.
Answers
Answer:
4
Step-by-step explanation:
20% = 40
10% = 20
100% = 200
200 * .02 = 4
The value of 2% of that number is,
⇒ 4
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
20% of a number is 40.
Let the number = x
Hence, We get;
⇒ 20% of x = 40
⇒ 20/100 × x = 40
⇒ 1/5 × x = 40
⇒ x = 200
Thus, The value of 2% of that number is,
⇒ 2% of 200
⇒ 2/100 x 200
⇒ 4
Thus, The value of 2% of that number is,
⇒ 4
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PLEASE HELP!
Research two different movie production companies. For each company, collect data on a categorial variable and a quantitative variable for comparison purposes. For example, you could determine the genre of the last 20 movies produced, the length of the most
recent 30 movies, the amount of money earned by the 50 highest grossing movies of all time, etc.
Display the categorical data that you collected from each of the two individuals in a side-by-side bar graph, segmented bar graph, or mosaic plot.
Answers
Nominal and ordinal categorical variables are the two different types.
What are the 2 types of categorical variables explain and give examples each?Nominal and ordinal categorical variables are the two different types.A nominal variable's categories do not naturally have an inherent order.For instance, gender is a categorical variable that has two categories (male and female), neither of which have any inherent ordering.The ordering of an ordinal variable is obvious.Any variable where the data indicate amounts is referred to be a quantitative variable.Any variable where the data represent groupings is referred to as a categorical variable.This comprises categories (like where people placed in a race), rankings (like cereal brands), and binary results.To learn more about categorical variables refer
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In an assembly of athletes from three sports, six athletes are from the BASKETBALL team labeled 1,2,3,4,5,6, five athletes are from the SWIM team labeled 1,2,3,4,5, and four athletes are from the HOCKEY team labeled 1,2,3,4. If an athlete is randomly chosen, what is the probability that the athlete is SWIM and EVEN?
Answers
The probability that the card is between four and eight (inclusive) or is a club is 4/13.
What is Probability?Probability helps us to know the chances of an event occurring.
The number of cards can be written as,
The number of cards between 4 and 8 is 3 {4,5,6,7,8}.
Number of club cards = 13
Number of cards between 4 and 8 from heart, spades, and diamonds = 15
Now, the probability that the card is between four and eight (inclusive) or is a club is,
Probability = desired outcomes / total number of outcomes possible
= (Number of club cards+ Number of cards between 4 and 8)/(Total number of cards)
= (13+15)/(52)
= 28/52
= 4/13
Hence, the probability that the card is between four and eight (inclusive) or is a club is 4/13.
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Tami rolled a die 20 times. 14 times it landed on an even number; 6 times it landed on an odd number. How does the experimental and theoretical probability compare, for rolling an odd number?
A)
The theoretical probability is higher.
B)
The experimental probability is higher.
C)
The experimental and theoretical probability are equal.
Answers
The answer is the Theoretical probability is higher than the Experimental probability.
Experimental and Theoretical Probabilities:Experimental probability:
The basis for experimental probability is what actually happens. It is dependent on the outcomes of several tests or experiments.
It is calculated by repeatedly recreating the event, recording the outcomes, and then converting the outcomes into a ratio or decimals.
Experimental probability = No of times event occurs/ No of trials
Theoretical Probability:
Theoretical probability is derived from a theory or what is predicted to occur. It is based on information and math.
It is determined by dividing the total number of outcomes by the proportion of favorable results. Either convert it to decimal form or leave it as a ratio or fraction.
Theoretical probability = No of favorable outcomes/ No of outcomes
Here we have
Tami rolled a die 20 times
14 times it landed on an even number;
6 times it landed on an odd number.
The die rolled for an odd number
As we a die will have 6 faces
Number of odd numbers = 3 [i.e 1, 3, 5 ]
Number of even numbers = 3 [ i.e 2, 4, 6 ]
⇒ Theoretical probability = 3/ 6 × 100 = 50%
The die is rolled 20 times, 6 times it landed on an odd number.
⇒ Experimental probability = 6 / 20 = 30%
As we can see,
The theoretical probability is higher than the Experimental probability.
Therefore,
The answer is the Theoretical probability is higher than the Experimental probability.
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Use the unique factorization for the integers' theorem (Section 4.3) and the definition of logarithm to prove that log3 (7) is irrational.
Answers
It is demonstrated that log3 (7) is irrational using unique factorization for integers theorem and the definition of logarithm.
Explain the term unique factorization theorem?Every integer bigger than 1 is either a prime number by itself or the result of a singular combination of prime numbers, based on the fundamental theorem of arithmetic (FTA), Often known as the unique factorization theorem or even the unique-prime-factorization theorem.If a contradiction is rational, then log3(7) = a/b for some a,b∈R .
In which, b≠0 will be true.
As a result, 7 = 3ᵃ/ᵇ according to the definition of logarithms.
7 = 1*7 is unique according to the unique factorization theorem.
Thus, it is demonstrated that log3 (7) is irrational using unique factorization for integers theorem and the definition of logarithm.
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A worker will waterproof 4 commercial roofs if he spends 1 1/4 of waterproofing for each roof.
How many liters does he need to do the job?
If you already had 2 1/4 liters, then how much waterproofing do you need?
is fractions with procedure
Answers
-First question:
To calculate the number of liters, the number of roofs must be multiplied by the amount of waterproofing used for each roof.
To multiply the fractions, transform the mixed fractions to improper:
[tex]\begin{gathered} \sf1 \frac{1}{4} \times 4 = \\ \\ \sf \frac{4 \times 1 + 1}{4} \times \frac{4}{1} = \\ \\ \sf \frac{4 + 1}{4} \times \frac{4}{1} = \\ \\ \sf\frac{5}{4} \times \frac{4}{1} = \\ \\ \sf \frac {5 \times 4}{4 \times 1} = \\ \\ \boxed{ \sf \frac{ \red{20}}{ \red4}} = \sf \blue5\end{gathered}[/tex]
So you need five liters of waterproofing to get the job done.
-Second question:
To calculate the number of liters; It must be subtracted from the number of liters you need in total, which you already had or had:
[tex]\begin{gathered} \sf5 - 2 \frac{1}{4} = \\ \\ \sf \frac{5}{1} - \frac{4 \times 2 + 1}{4} = \\ \\ \sf\frac {5}{1} - \frac{8 + 1}{4} = \\ \\ \sf \frac{5}{1} - \frac{9}{4} = \\ \\ \sf\frac{4 \div 1 \times 5 - 4 \div 4 \times 9}{4} = \\ \\ \sf \frac{20 - 9}{4} = \\ \\ \boxed{ \sf \frac{11}{4}} = \boxed{ \sf \blue2 \: \: \blue{\sf\frac{3 }{4} }}\end{gathered}[/tex]
So, you need two whole and three quarter liters of waterproofing.
PLEASE HELP
ALGEBRA
Answers
The explicit formula for the geometric sequence would be [tex]a_n =10000.87\times (0.95)^{n-1}[/tex].
What is a geometric sequence?
In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Given:
[tex]a_4=8573.75\\\\a_6=7731.81[/tex]
Now by using the formula for the nth term of a GP, we get
[tex]a_n = ar^{n-1}\\\\a_4=ar{4-1}\\\\8573.75=ar^3[/tex]
Now for n = 6, we get
[tex]a_n = ar^{n-1}\\\\a_6=ar{6-1}\\\\7737.81=ar^5[/tex]
Now divide we get
[tex]\frac{ar^5}{ar^3} =\frac{7737.81}{8573.35} \\\\r^2=0.9025\\\\r=0.95[/tex]
Now we can get the value of a,
[tex]8573.75=ar^3\\\\a = \frac{8573.75}{(0.95)^3}\\\\a = \frac{8573}{0.8573}\\\\a = 10000.87[/tex]
So we can prepare the explicit formula as
[tex]a_n =10000.87\times (0.95)^{n-1}[/tex]
Hence, the explicit formula for the geometric sequence would be [tex]a_n =10000.87\times (0.95)^{n-1}[/tex].
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If M is the centroid of triangle ABC, AM = 44, CE =54, and DM
= 23, find each missing measure.
Answers
The missing sides of triangle ABC, If M is the centroid of triangle ABC, AM = 44, CE =54, and DM = 23, are FM = 22, AM = 44.
What is the centroid of the triangle?Three medians of a triangle intersect to produce the centroid of the triangle. It is one of a triangle's four points of concurrency. When the midpoints of the triangle's opposite sides are linked, the triangle's vertices become the triangle's medians.
Given:
The [tex]M[/tex] is centroid of triangle ABC, AM = 44, CE = 54, and DM = 23,
The centroid of a triangle divides the median in the ratio [tex]2 : 1[/tex]
Therefore, [tex]AM : FM = 2 : 1[/tex]
Let AM = 2x and FM = x
Since, AM = 44
Hence, 2x = 44
x = 44 / 2
x = 22
FM = 22
Therefore, the missing sides are FM = 22 and AM = 44.
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The missing figure is attached below.
Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.(The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below.
(a) x=3 hours
(b) x=4.5 hours
(c) x=13 hours
(d) x=1.5 hours
Answers
ŷ= 6.45x + 31.5 is the equation of the regression line for the given data
How to find the equation of the regression line for a given data?Construct the table of the data as follows:
x >>>> y >>>> x² >>>> y² >>>> xy
1 39 1 1521 39
2 45 4 2025 90
3 52 9 2704 156
4 49 16 2401 196
5 61 25 4096 305
5 72 25 5184 360
................................................................................................
20 318 80 17931 1146
.................................................................................................
∑x = 20, ∑y = 318, ∑x²= 80, ∑xy = 1146, n = 6 (number data points)
The linear regression equation is of the form:
ŷ = ax + b
where a and b are the slope and y-intercept respectively
a = ( n∑xy -(∑x)(∑y) ) / ( n∑x² - (∑x)² )
a = (6×1146 - 20×318) / ( 6×80-20² )
a = 6876-6360 / 480-400
a = 516 / 80
a = 6.45
x' = ∑x/n
x' = 20/6 = 10/3
y' = ∑y/n
y' = 318/6 = 53
b = y' - ax'
b = 53 - 6.45×(10/3)
b = 53 - 21.5
b = 31.5
ŷ = ax + b
ŷ= 6.45x + 31.5
Thus, the equation of the regression line for the given data is ŷ= 6.45x + 31.5. (The scatter plot of the data is shown in the attached image)
(a) x=3 hours
ŷ= 6.45(3) + 31.5 = 50.85
(b) x=4.5 hours
ŷ= 6.45(4.5) + 31.5 = 60.525
(c) x=13 hours
ŷ= 6.45(13) + 31.5 = 115.35
(d) x=1.5 hours
ŷ= 6.45(1.5) + 31.5 = 41.175
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Simplify Tan A + Cot A
Answers
Tan A + Cot A = 2 Cosec 2A.
It is a simple TRIGNOMETRY question, which is directly based on their formulas.
In this question we have one side of formula either LHS or RHS and we have to find other,
Tan A + Cot A
we know Tan A = sin A /Cos A and Cot A = cos A / sin A
So by putting this in place of Tan A + Cot A we get,
⇒ (sin A / cos A) + (cos A / sin A)
⇒ (sin∧2 A + cos∧2 A) / cos A sin A
⇒1/ cos A sin A
⇒2/2cos A sin A
⇒ 2/Sin 2A
⇒ 2 Cosec 2A
Hence, the question is simplified.
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A truck enters a highway driving 60 mph. A car enters the highway at the same place 6 minutes later and drives 73 mph in the same direction. From the time the car enters the highway, how long will
it take the car to pass the truck?
Answers
Answer:
27.7 min
Step-by-step explanation:
In 6 minutes the truck will be 6 miles ahead of the car....
the car is going 13 mph faster and will cover this 6 miles in
6 mi / 13 mi/hr = .4615 hr =27.7 min
Seven more than the quotient of a number and 2 equals 9 .
Answers
Answer:
4
Step-by-step explanation:
n/2 + 7 = 9
n/2 + 7 - 7 = 9 - 7
n/2 = 2
n = 4
Solve for x:
4(x-5)
8
= 9y
X =
= [?]y + []
Enter
Answers
4x - 20 = 72y
4x - 72y = 20
4x = 20 + 72y
X = 20/4 + 72/4 y
X = 5 + 18y
What is 2 3/2 equal to?
Answers
Answer:
(a) √8
Step-by-step explanation:
You want to know the radical equivalent to 2^(3/2).
IndicesThe relationship of indices to radicals is ...
[tex]\large{\sqrt[n]{a^m}}={a^{\frac{m}{n}}[/tex]
ApplicationThe given expression can be rewritten as ...
[tex]2^{\frac{3}{2}}=\sqrt[2]{2^3}=\boxed{\sqrt[2]{8}}[/tex]
__
Additional comment
When the index of the radical is 2, it is usually left off. The radical can be simplified by removing the perfect square factor.
[tex]\sqrt[2]{8}=\sqrt{8}=2\sqrt{2}[/tex]
Ride and simplify two division expressions they have a negative quotient used to fractions -2/3 5/6 and negative one show your work
Answers
The simplification of complex fraction -⅔/⅚ is - 4/5
What are complex fractions?A complex fraction is a rational expression that has a fraction in its numerator, denominator or both. In other words, there is at least one small fraction within the overall fraction.
In fraction when the numerator is bigger than the denominator , then it is called improper fraction, when a fraction consist of whole number and proper fraction is called mixed fraction
-2/3 ÷ 5/6
= -2/3×6/5
= -4/5
Therefore -⅔/⅚ can be simplified to -⅘
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Please help me I really need it
Answers
Answer:
a) 4(8019) +3s ≥ 70000
b) yes
Step-by-step explanation:
Diego has walked an average of 8019 steps per day for 4 days and wants to walk 70000 steps in a week. You want an inequality for the average number of steps per day that Diego must walk for the last 3 days of the week, and you want to know if 12642 is a solution.
a) InequalityThe inequality will express the relationship between the steps walked and the goal. Let s represent the average number of steps walked each day for the last 3 days of the week.
The total number of steps walked in the first 4 days is the average per day times the number of days: 4(8019). The total number of steps walked in the last 3 days is the average per day times the number of days: 3s.
The total for the week is the sum of these. We want that to exceed 70000:
4(8019) +3s ≥ 70000 . . . . . . . the desired inequality
b) SolutionSolving for s, we find ...
3s ≥ 7000 -4(8019)
3s ≥ 37924 . . . . . . . . . subtract 32076
s ≥ 12641 1/3 . . . . . . . . divide by 3
The offered number, 12642, is greater than 12641 1/3, so is a solution.
Diego will meet his goal if he averages 12642 steps per day for the last 3 days of the week.
__
Additional comment
If Diego's 3-day average is 12462, he will have walked 70002 steps for the week, a number that is more than 70000.
What is the perimeter of ? Show your work.
Answers
If the length of the side PR is 7 feet. Then the perimeter of the triangle ΔPQR will be 17 feet.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The perimeter of the triangle is determined by adding together all of its sides.
The triangles ΔPQR and ΔSTU are congruent triangles. Then we have
PR = SU
3y - 2 = y + 4
3y - y = 2 + 4
2y = 6
y = 3
Then the value of the side PR is given as,
PR = 3(3) - 2
PR = 9 - 2
PR = 7 feet
Then the perimeter of the triangle ΔPQR is calculated as,
P = 4 + 6 + 7
P = 17 feet
If the length of the side PR is 7 feet. Then the perimeter of the triangle ΔPQR will be 17 feet.
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Simplify the expression by using a double-angle formula.
sinπ/7·cosπ/7
Answers
After using the trigonometry method the answer is sin 2 (pi/7)/2
What principle underlies trigonometry?
The study of the relationship between the sides and angles of the right-angle triangle is essentially the focus of the branch of mathematics known as "trigonometry." Therefore, using trigonometric formulas, functions, or trigonometric identities can be helpful in determining the missing or unknown angles or sides of a right triangle.
What distinguishes geometry from trigonometry?
The study of triangle properties, particularly those of right triangles, is known as trigonometry. But the study of geometry focuses on the characteristics of all geometrical figures.
Given that:
sinπ/7·cosπ/7
if we can divide and multiply 2 so it can be converted to sin 2 theta
sin 2 (pi/7)/2
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Solve the following inequality:
r/2+15>45
Answers
Answer: r > 30
Step-by-step explanation:
Line t passes through points (9, 9) and (2, 5). Line u is perpendicular to t. What is the slope of line u?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
4/7 is the answer
Factor 132w + 55 using the Distributive Property.
Answers
Answer:
11(12w+5)
Step-by-step explanation:
common factors of 132 and 55 is 11
So we can take it out by dividing both terms by 11
11(12w+5)
Hopes this helps
Answer:I hope this is helps
good luck
Step-by-step explanation:
132w+55
Factor out from the expression
11(12w+5) this is the distributive Property
In a survey of 1000 eligible voters selected at random, it was found that 100 had a college degree. Additionally, it was found that 80% of those who had a college degree voted in the last presidential election, whereas 45% of the people who did not have a college degree voted in the last presidential election. Assuming that the poll is representative of all eligible voters, find the probability that an eligible voter selected at random will have the following characteristics. (Round your answers to three decimal places.) (b) The voter did not have a college degree and did not vote in the last presidential election.
Answers
The probability that an eligible voter selected at random did not have a college degree and did not vote in the last presidential election is 49.5%.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
The no. of people who don't have a college degree is (1000 - 100) = 900.
45% of the people who did not have a college degree voted in the last presidential election hence (100 - 45) = 55% of the people who did not have a college and did not vote in the last presidential election.
∴ (55/100)×900.
= 495 people.
∴ The probability that an eligible voter selected at random did not have a college degree and did not vote in the last presidential election is,
= 495/1000.
= 0.495.
= 49.5%.
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How many boards 6 5/6 in wide will cover floor 205 in wide
Answers
By using fraction, it can be calculated that
30 boards are required to cover a floor of width 205 inches wide
What is fraction?
Suppose there is a collection and a part of collection has to be taken.
The part which is taken is called fraction. In other words part of a whole is called fraction.
The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.
This is a word problem on fraction
Width of each board = [tex]6\frac{5}{6}[/tex] inches = [tex]\frac{41}{6}[/tex] inches.
Total width of floor = 205 inches.
Number of boards required = [tex]205 \div \frac{41}{6}[/tex] = [tex]205 \times \frac{6}{41}[/tex] = 30
30 boards are required
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hi!! can someone do 14 and 16 or just one if you’d rather do that?? thank you sm i’m just trying to get some of my assignments done by tomorrow and i don’t understand how to do these things
Answers
16 would be y=-2x-4
2. Table 1 shows the number of pupils attending a motivation camp.
Two pupils from the group are required to take part in a show.
a) If a pupil is chosen at random from school A and another one from school B, calculate the probability that both are girls.
b) If two pupils are chosen at random from the group of boys, calculate the probability that both are from the same school.
Answers
a) The probability that both are girls is of: 21/150.
b) The probability that both are from the same school is of: 0.7333 = 73.33%.
How to obtain the probabilities?The probabilities are obtained as the division of the number of desired outcomes by the number of total outcomes.
For item a, the outcomes are given as follows:
One girl from school A -> 7/15 probability.One girl from school B -> 3/10 probability.Hence the probability that both are girls is of:
p = 7/15 x 3/10 = 21/150.
The probability that the two boys are from the same school can be given by these two cases:
School A: 8/15 x 7/14.School B: 7/10 x 6/9.Then the probability is of:
p = 8/15 x 7/14 + 7/10 x 6/9 = 0.7333 = 73.33%.
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4+2p=10( 5 3 p−2) i really need help ASAP!!
Answers
Answer:
p=24/528
Step-by-step explanation:
4+2p=10(53p-2)
4+2p=530p-20
24+2p=530p
24=528p
24/528=p
PLS answer this i need it asap
Answers
Answer:
b
step by step explanation