Step-by-step explanation:
For finding k we'll have to plug in the x-value of the coordinate (3,k) into the equation, and solve for the y:
5(3) - 2y = 7
15 - 2y = 7
2y = 8
y = 4 => k =4
2) I assume the gradient is the slope of the line. If so, just isolate the y in the original equation and see what's the coefficient of the x:
-2y = -5x + 7
y = (5/2)x + 7/2 => the gradient is 5/2
3) the condition of perpendicularity is expressed by the following relation:
a * a' = -1
Where a is the slope of the first line and a' of the second line. We need to find a' that will be:
-1/a = -1/(5/2) = -2/5
The perpendicular line will be:
y = (-2/5)x + b
We need to find b, and we know that this line passes through A (1,-1):
-1 = (-2/5)*1 + b
b = -1+(2/5) = -3/5
The equation will be:
y = (-2/5)x - 3/5.
4) I don't know what that symbol means (pV2).
what is the domain and range of : {(2,4) (3'6) (4,8) (5,10) (6,12)}
Answer:
2,3,4,5,6 is the domain
4,6,8,10,12 is the range
Step-by-step explanation:
Answer:
The domain is {2,3,4,5,6} and the range is {4,6,8,10,12}.
Step-by-step explanation:
Jarad, the track star, ran the 88 yards in 10 seconds. How fast is this in miles per hour?
Answer:
18mph
Step-by-step explanation:
We convert this to solve! 1 mile equals 1760 yards,1 yard equals 3 feet, 60 seconds equals a minute, and 1 hour equals 60 minutes.
[tex]\frac{88yd}{10sec} times \frac{3ft}{1yd} times\frac{1mi}{5280ft} times\frac{60sec}{1min} times\frac{60}{1hr}[/tex]
When you multiply all that you get 18 mph
a certain pharmaceutical company know that, on average 4% of a certain type of pill has an ingredient that is below the minimum strength and thus unacceptable. what is the probability that fewer that 5 in a sample of 20 pills will be acceptable?
Using the binomial distribution, it is found that there is a 0% probability that fewer that 5 in a sample of 20 pills will be acceptable.
For each pill, there are only two possible outcomes, either it is acceptable, or it is not. The probability of a pill being acceptable is independent of any other pill, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
The sample has 20 pills, hence [tex]n = 20[/tex].100 - 4 = 96% are acceptable, hence [tex]p = 0.96[/tex]The probability that fewer that 5 in a sample of 20 pills will be acceptable is:
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{20,0}.(0.96)^{0}.(0.04)^{20} = 0[/tex]
[tex]P(X = 1) = C_{20,1}.(0.96)^{1}.(0.04)^{19} = 0[/tex]
[tex]P(X = 2) = C_{20,2}.(0.96)^{2}.(0.04)^{18} = 0[/tex]
[tex]P(X = 3) = C_{20,3}.(0.96)^{3}.(0.04)^{17} = 0[/tex]
[tex]P(X = 4) = C_{20,4}.(0.96)^{4}.(0.04)^{16} = 0[/tex]
0% probability that fewer that 5 in a sample of 20 pills will be acceptable.
A similar problem is given at https://brainly.com/question/24863377
What is the answer to the equation?
The diagonal of an isosceles trapezoid with angle to the base is equal to 30. Find the length of the height of the trapezoid if it is known that the midline of this trapezoid is equal to 8 cm.
Answer:
4.62 cm to nearest hundredth.
Step-by-step explanation:
If the parallel sides are x and y then:
x + y = 2*8 = 16
x + y = 16
If we drop a perpendicular line from one of the upper points on the trapezoid we have the height. Let the upper point be C and the point on the base be A. Let the point on right of the base be B.
AC is the height of the trapezoid. AB is the baseline of the triangle CAB.
In triangle CAB the angle B is 30 degrees.
As this is a 30-60-90 degree triangle
AC/AB = 1/√3 so AC = AB/ √3.
As the trapezoid is isosceles:
AB = x + 0.5(y - x)
AB = 0.5x + 0.5y
So AC = 1 /√3 (0.5x + 0.5y)
= 1 /√3 (0.5x + 0.5(16 - x)) (Substituting for x)
= 1 /√3 (0.5x + 8 - 0.5x)
=8 / √3
. = 4.6188 cm
Triangle A'B'C' is a reflection of triangle ABC across line BC. Prove that ray BC is the angle bisector of angle ABA'.
Answer is below in the picture:-
(From the problem, we know (triangle)ABC (round of equal of) (triangle)A'B'C'. So, <A'B'C' = <ABC {the properties of congruent triangles}. So, ray BC is the angle, bisector of angle ABA')
I hope it helps.
It is proved that the ray BC is the angle bisector of angle ABA'.
What are angle bisectors?Angle bisectors are lines who bisect the considered angle. Bisect refers to splitting in two equal parts. Therefore, the bisected parts of the considered angle are half of the original angle.
When a graph is reflected along an axis, say x axis, then that leads the graph to go just in opposite side of the axis as if it in a mirror.
We will find that its symmetric, thus each point is equidistant from the axis of reflection as that of the image of that point.
From the given problem, we know Triangle A'B'C' is a reflection of triangle ABC across line BC.
Therefore, <A'B'C' = <ABC
By the properties of congruent triangles. Means if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
Hence, the ray BC is the angle, bisector of angle ABA'.
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John Marlow's total income last year was $31,300. Of that amount, he spent
$7,900 for food. What percent of Jon's total income did he spend for food? *
25%
40%
50%
85%
Based on the information given the percent of Jon's total income did he spend for food is 25%.
Using this formula
Percent of total income=Amount spent for food/Total income last year
Where:
Amount spent for food=$7,900
Total income last year=$31,300
Let plug in the formula
Percent of total income=$7,900/$31,300
Percent of total income=25%
Inconclusion the percent of Jon's total income did he spend for food is 25%.
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11. The profit Samantha's company makes is
given by the expression 0.1(1000 + 300m)
where m is the total number of sales.
Rewrite the expression using the distributive
property. What is the profit if her company
sells 50 pieces of merchandise?
Answer: 0.1(1000 + 300m)
Use the distributive property: a x (b + c) = a x b + a x c
0.1 x 1000 + 0.1 x 300m
Evaluate both products: 100 + 30m (1)
Note: Multiplying a number by 0.1 is the same as dividing the number by 10.
We need to determine the profit when 50 pieces are sold.
Substitute m with 50 in equation (1).
100+30(50)
Evaluate product: 100 + 1500
Evaluate sum" 1600
Thus the profit is $1600.
Step-by-step explanation: I hope this helps you on any other problem! :)
Good Luck!
Find BC.
А В
С
ош
=
=
AD = 10.5
AB = 2
СЕ = 11.5
AE = 15
BC = [?]
=
Answer:
8,5
Step-by-step explanation:
BC=AD-AB
BC=10,5-2
BC=8,5
Please look for the question in the picture.
it will be c
as
negative with negative erased together
The owner of a small store buys coats for 55.00 each
He sells the coats for 66.00 each
he must buy 24 jackets to get atheist 260 dollars
Suppose in the year 2000 the population of a country is 20 million. In the year 2010 the
population is now 24 million. If the growth of the population is exponential, approximate what the population would be in the year 2021.
Answer:
Grows by 2.4 million each year
Step-by-step explanation:
❗100 POINTS ❗
FOR a correct explanation of why this ain't right
I'm forced to do this 4 sb and I fr dk what HOW THIS ISNT CORRECT?!
pls help
thx
Factors of 36 are the list of integers that we can split evenly into 36. There are overall 9 factors of 36 among which 36 is the biggest factor and its positive factors are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The Pair Factors of 36 are (1, 36), (2, 18), (3, 12), (4, 9) and (6, 6) and its Prime Factors are 1, 2, 3, 4, 6, 9, 12, 18, 36.
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18 and 36
Negative Factors of 36: -1, -2, -3, -4, -6, -9, -12, -18 and -36
Prime Factors of 36: 2, 3
Prime Factorization of 36: 2 × 2 × 3 × 3 = 22 × 32
Sum of Factors of 36: 91
Factors of a number are the numbers that divide the given number exactly without any remainder. According to the definition of factors, factors of 36 are those numbers that exactly divide 36 leaving no remainder. In other words, we can say if two numbers are multiplied and the product is 36, then the numbers are factors of 36.
Let us do a hit and trial method to find factors of 36.
Divide 36 ÷ 2 = 18
Quotient = 18, remainder = 0
Now multiply 18 × 2 = 36
Hence, 18 and 2 are the factors of 18.
36 is a composite number as it has factors other than 1 and itself.
We can use different methods like the divisibility test, prime factorization, and the upside-down division method to calculate the factors of 36.
The most common method we use to find factors is the prime factorization method.
In prime factorization, we express 36 as a product of its prime factors.
In the division method, we see which numbers divide 36 exactly without a remainder.
Let us calculate factors of 36 using the following two methods:
Factors of 36 by prime factorization factor tree method
Factors of 36 by upside-down division method
Prime Factorization of 36 by Upside-Down Division Method
Now as discussed above, in the prime factorization method we show factors of 36 as a product of prime factors of 36. Follow the steps to find the prime factors of 36 by the prime factorization method.
With the help of divisibility rules, find out the smallest factor of the given number. Here, 36 is an even number. So it is clearly divisible by 2. In other words, 2 divides 36 with no remainder. Therefore, 2 is the smallest prime factor of 36.
36 ÷ 2 = 18. Now find the prime factors of the obtained quotient. Repeat Step 1 and Step 2 till we get a prime number as the quotient. Here, 18 is the quotient.
18 ÷ 2 = 9. Here, 9 is the quotient. Now find the prime factors of the 9.
9 ÷ 3 = 3. Here 3 is the prime number. So we can stop the process.
Prime factorization of 36 using upside-down division method is 2 × 2 × 3 × 3 = 2² × 3².
Prime Factorization of 36 by Factor Tree Method
The factor tree method is another visualization method to represent factors of 36. It also helps in determining prime factors of 36. A factor tree is not unique for a given number. Instead of expressing 36 as 2 × 18, we can express 36 as 6 × 6.
Prime factorization of 36 using factor tree method is 2 × 2 × 3 × 3 = 2² × 3².
Explore factors using illustrations and interactive examples
Factors of 33: The factors of 33 are 1, 3, 11, and 33.
Factors of 34: The factors of 34 are 1, 2, 17, and 34.
Factors of 38: The factors of 38 are 1, 2, 19, and 38.
Factors of 30: The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
Factors of 360: The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.
Factors of 35: The factors of 35 are 1, 5, 7, and 35.
Factors of 37: The factors of 37 are 1 and 37.
Factors of 36 in Pairs
Factor pairs are the two numbers that, when multiplied, give the number 36. Find all of the factors of the number 36 using the steps below:
Step I: Start with 1 and the number itself.
Step II: Count up by ones to see if you can multiply two numbers together to get your target number.
Step III: Stop when you can’t get any more numbers in between.
Step IV: Connect the factor pairs.
Factor pairs of 36 are given below:
36 = 1 × 36
36 = 4 × 9
36 = 6 × 6
36 =12 × 3
36 = 18 × 2
Let us club the numbers in pairs.
The factors of 36 in pairs are (1, 36), (4, 9), (6, 6), (12, 3), and (18, 2).
There are a total of 5 pairs of factors of 36.
We can have negative factors also for a given number.
Since the product of two negative numbers is positive [(-) × (-) = +].
The negative pair factors of 36 are (-1, -36), (-4, -9), (-6, -6), (-12, -3), and (-18, -2)
There are a total of 5 negative pairs of factors of 36.
Important Notes:
36 is a composite number as it has factors other than 1 and itself.
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Pair factors of 36 are (1, 36), (4, 9), (6, 6), (12, 3), and (18, 2).
1 is a factor of every number.
Prime factorization of 36 is 2 × 2 × 3 × 3 = 2² × 3².
Challenging Questions:
Find the factors of 3600 with the help of techniques used in finding factors of 36.
Prove that the factor of a number is always less than or equal to the number itself?
How much does Bethany spend in week 4?
Please help me answer
Answer: Second Choice
Step-by-step explanation:
For the following equation, find a solution for the variable. Show all of your work and use complete sentences to explain the solving process that you used to find a solution for the equation. Be sure to include at least two terms from the word bank. 4+ x = 7
Answer:
x=33
Step-by-step explanation:
you move the 4 to the other side
x=7-4
so
x=3
Answer:
x=3
Step-by-step explanation:
This should be easy.
4+x=7
-4 -4
x=7-4
x=3
Word explanation:
Here, we're solving for the variable x, first, we need to isolate x and therefore subtract 4 on both sides, 7 minus 4 is 3, so x is equal to 3.
Please look for the question in the picture.
the answer for this question is a: -9/-8
How do I add mixed numbers?
A plane traveled 960 miles each way to Jakarta and back. The trip there was with the wind. It took 10 hours. The trip back was into the wind. The trip back took 20 hours. What is the speed of the plane in still air? What is the speed of the wind?
Answer:
Wind speed = 40 km/hr
Speed of the plane in still air = 280km/hr
Step-by-step explanation:
Formula to use
Distance = Rate multiplied by Time
D = R × T
Speed of the plane in still air = a
Speed of the wind = b
Plane with the wind (tailwind) is a + b where the time = 3hours
Plane against the wind is a - b, where the time = 4hours
This would give us 2 equations
3 × (a+ b) = 960
3a + 3b = 960 ...... Equation 1
4 × (a- b) = 960
4a - 4b = 960 ........ Equation 2
Solve this like you would with system of equations:
We solve the equation using elimination method.
Mulitply equation 1 by 4 and equation 2 by -3
4 × (3a + 3b = 960)
12a + 12b = 3840 ..... Equation 4
-3 × (4a- 4b = 960)
-12a + 12b= -2880 ........ Equation 5
Therefore we have
12a + 12b = 3840 ..... Equation 4
-12a + 12b= -2880 ........ Equation 5
24b = 960
b = 960÷ 24
b = 40
Wind Speed = 40km/hr
To find the speed of air, we use equation 2
4a - 4b = 960 ........ Equation 2
Substituting 40 which is wind of speed for b in equation 2 we would have
4a - 4(40) = 960
4a - 160 = 960
4a = 960 + 160
4a = 1120
a = 1120 ÷ 4
a = 280
The speed of the small plane in still air is 280 km/hr
URGENT PLS HELP
John is driving around town. When he reaches the gas station, he notes that he has traveled 18 miles. He reaches home 2 hours later and notes that he has traveled 34 miles. If d represents the distance and t represents the time, in hours, John has traveled since the gas station, which of the following equations can be used to model this situation?
1. d = 18t + 52
2. d = 16 + 18t
3. d = 8t + 18
4. d = 8t - 18
A watch band is 8 in long. What is its diameter when you wrap it around your wrist? Round your answer to the nearest
hundredths.
Please be accurate and explain.
Answer:
well, all you need to do is 8 x 3.14 so then you shall get your answer!
Step-by-step explanation:
A child's height increased from 21 to 32 inches. What was the percent increase in the child's height
Answer:
52.4
Step-by-step explanation:
% change = 100 x final initial/initial
write an equivalent expression for 3(2z+4)
Answer:
6z+12
Step-by-step explanation:
you distribute it
LAST ATTEMPT MARKING AS BRAINLIEST!! (Pythagorean theorem )
Factorize the expressions
px2 + qx
Answer:
SOLUTION
HERE,
=X(P.2+Q)
=X(2P+Q)
Answer:
x(px+q) ( I took x as a common and the remaining are some
Find the value of a
I’m decided go between 40 and 6.4
Oceanside Bike Rental Shop charges 13 dollars plus 8 dollars an hour for renting a bike. Tim paid 45 dollars to rent a bike. How many hours did he pay to have the bike checked out?
Step-by-step explanation:
Shop charges =13
Many left for renting bike = 45-13 =$32
If renting for 1hr cost $8
then renting for X Hrs will cost $32
1/X =8/32 cross multiplying
8X= 32
X= 32÷8= 4hrs
Tom and Rosie are designing a game. In each turn, a player rolls five 666-sided dice and adds the numbers showing on each face to determine how many points they get that turn. For example, the lowest number of points in a given turn is 1+1+1+1+1=51+1+1+1+1=51, plus, 1, plus, 1, plus, 1, plus, 1, equals, 5 points, and the highest is 6+6+6+6+6=306+6+6+6+6=306, plus, 6, plus, 6, plus, 6, plus, 6, equals, 30 points. They let XXX represent the sum in a given turn, and they find the expected value of XXX is E(X)=17.5E(X)=17.5E, left parenthesis, X, right parenthesis, equals, 17, point, 5 points. Tom says, "A player will most likely get 17.517.517, point, 5 points in any given roll." Rosie says, "Over 100100100 turns, we can expect a total of about 175175175 points." Whose statement is correct based on the expected value?
Answer: neither statement is correct
Step-by-step explanation:
on Khan Academy
The statement by Tom "A player will most likely get 17.5 " is correct based on expected value .
What is expected value?Expected value (also known as EV, expectation, average, or mean value) is a long-run average value of random variables. It also indicates the probability-weighted average of all possible values. Expected value is a commonly used financial concept.
According to the question
Tom and Rosie are designing a game.
In each turn, a player rolls five 6-sided dice and adds the numbers showing on each face to determine how many points they get that turn.
let X represent the sum in a given turn
the expected value of X is E(X)=17.5
As
expected value is also called mean value
i.e
highest value of sum = 6+6+6+6+6
= 30
Lowest value of sum = 1+1+1+1+1
= 5
Therefore,
Mean = [tex]\frac{30+5}{2}[/tex]
= 17.5
Now,
Tom says, "A player will most likely get 17.5
This statement is correct as per expected value which is mean value and it is 17.5 .
Rosie says, "Over 100 turns, we can expect a total of about 175
This statement is incorrect as per expected value as
expected value = 17.5
when 100 turn will happen it will
17.5 * 100
= 1750
Hence, The statement by Tom "A player will most likely get 17.5 " is correct based on expected value .
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what does the u stand for in these problems? is it the same as r?
I think "u" stands for units. [tex]u^2[/tex] means units squared which is like saying ft^2 if you were looking for the area of something with feet dimensions. So in this case, the circle has a diameter of x units (u) and an area of x units^2 ([tex]u^2\\[/tex]). It is not the same as r. "r" is most always going to be used to represent the radius.
Is the sentence Equivalent or non equivalent 12:24,50:100
Therefore, the sentence is Equivalent.
Hoped this helped.
[tex]BrainiacUser1357[/tex]