Answer:
We can use distributive law for the multiplication
And after multiplication result will be 264
Step-by-step explanation:
Lydia has to multiply 32×8.25
She is using standard algorithm of multiplication
Now we have to find the other way of multiplication of 32×8.25
We can use distributive law for the multiplication of the above number
We can write 8.25 as 8+0.25
So multiplication will become 32 ( 8+0.25 ) = 256 + 8 = 264
So after multiplication result will be 264
To solve 32 x 8.25 without the standard algorithm, Lydia can use the distributive property to separately multiply 32 by 8 and then by 0.25 (1/4), resulting in two simple multiplications: 256 and 8. Adding these together gives the answer, 264.
Explanation:To solve the multiplication problem 32 x 8.25 without the standard algorithm, Lydia can break down the number 8.25 into 8 and 0.25 (which is 1/4) and use the distributive property of multiplication over addition. This allows Lydia to multiply 32 by each part separately and then add the results together.
Multiply the whole number part: 32 x 8 = 256.Multiply the fractional part, recognizing that multiplying by 1/4 is the same as dividing by 4: 32 x 0.25 = 32/4 = 8.Add the results together: 256 + 8 = 264.This strategy simplifies the calculation and can be done with simpler computations or even mental math.
Kyle sold 28 boxes of fruit for a fundraiser.Omar sold 2 times as many boxes of fruit ad Kyle sold.What is the total number of boxes that Kyle and Omar sold?
Answer: 84
Step-by-step explanation:
K=28
O=2K=2*28=56
O+K=56+28=84
The total number of boxes that Kyle and Omar sold is 84.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Division = divide any two numbers or variables called division.
Multiplication = to multiply any two or more numbers or variables called multiplication.
As per the given,
Kyle sold 28 boxes of fruit.
Omar sold 2 times,
28 x 2 = 56 boxes
Total boxes = 56 + 28 = 84 boxes
Hence "The total number of boxes that Kyle and Omar sold is 84".
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When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?
Final answer:
When a positive integer x, which leaves a remainder of 5 when divided by 9, is multiplied by 3, the remainder when 3x is divided by 9 is 6.
Explanation:
When the positive integer x is divided by 9, the remainder is 5. To determine the remainder when 3x is divided by 9, we should remember that when two positive numbers multiply, the result has a positive sign. So multiplying x by 3, we get 3x. The initial information tells us that x = 9n + 5 for some integer n. Thus, 3x equals 3(9n + 5), which simplifies to 27n + 15. This expression can be further broken down as 27n + 9 + 6, which is the same as 9(3n + 1) + 6. Therefore, when 3x is divided by 9, it is the same as dividing this expression by 9, which leaves us with a remainder of 6. Hence, the remainder when 3x is divided by 9 is 6.
A recent article in the Cincinnati Enquirer reported that the mean labor cost to repair a heat pump is $90 with a standard deviation of $22. Monte’s Plumbing and Heating Service completed repairs on two heat pumps this morning. The labor cost for the first was $75 and it was $100 for the second. Assume the distribution of labor costs follows the normal probability distribution. Compute z values for each.
Answer:
Z value for the first pump = -0.68
Z value for the second pump = 0.45
Step-by-step explanation:
Data provided in the question:
Mean labor cost to repair a heat pump = $90
Standard deviation = $22
Labor cost for the first, X₁ = $75
Labor cost for the Second, X₂ = $100
Now,
Z value for the first pump = [X₁ - Mean] ÷ Standard deviation
thus,
Z value for the first pump = [ $75 - $90] ÷ $22
= - 0.68
Z value for the second pump = [X₁ - Mean] ÷ Standard deviation
thus,
Z value for the second pump = [ $100 - $90] ÷ $22
= 0.45
Answer:
z1= -0.6818
z2= 0.45
Step-by-step explanation:
Mean labor cost to repair the heat pump is μ= $90
standard deviation σ= $22
Labor cost for the first heat pump X_1= $75
labor cost for the second heat pump is X_2= $100
z value for the first heat pump
[tex]z_1= \frac{X_1-\mu}{\sigma}[/tex]
⇒ [tex]z_1= \frac{75-90}{22}[/tex]
= -0.6818
z value for the second heat pump
[tex]z_2= \frac{X_2-\mu}{\sigma}[/tex]
⇒[tex]z_2= \frac{100-90}{22}[/tex]
= 0.45
A standard deck of cards has 52 cards, 4 of each type (Ace, King, Queen, Jack, 10,...,2). From a well-shuffled deck, you are dealt a hand of 5 cards (without replacement).
(a) What is the probability that you are dealt at least one face card (that is a king, queen or jack)?
(b) What is the probability that you are dealt with both; at least one ace and at least one face card?
Answer:
a)%85,5
b)%92,2
Step-by-step explanation:
a) To determine the probability of getting a hand with at least one face, we need to calculate the probability of the hand without any face firstly.
[tex](36/52)*(35/51)*(34/50)*(33/49)*(32/48)=0,145[/tex]
Then, we need to deduct this value from the probability 1
[tex]1-0,145=0,855[/tex]
The probability of the hand with at least one face is %85,5.
b)To determine the probability of a hand with at least one ace and face we will track the same road again.
[tex](32/52)*(31/51)*(30/50)*(29/49)*(28/48)=0,0775[/tex]
Then, we need to deduct this value from the probability 1
[tex]1-0,0775=0,922[/tex]
The probability of the hand with at least one ace and one face is %92,2.
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The number of fish caught during a fishing tournament b. The number of textbook authors now sitting at a computer c. The political party affiliation of adults in the United States d. The square footage of a house e. The number of free dash throw attempts before the first shot is made f. The weight of a Upper T dash bone steak
Answer:
a. Discrete
b. Discrete
c. Not a random variable
d. Continuous
e. Discrete
f. Continuous
Step-by-step explanation:
The discrete random variable is countable while continuous random variable is measurable.
a. The number of fish caught is a discrete random variable because these are countable.
b. The number of text book authors are also countable so it is a discrete random variable.
c. The political party affiliation of adults is not a random variable because the political party affiliation depends on person's interest and it cannot be randomly assigned to person. Also random variable is the numerical outcome of random experiment whereas political affiliation is the categorical variable that results in non numerical responses such as Democrat, Republicans etc.
d. The square footage of a house is measurable and so it is a continuous random variable.
e. The number of free dash throw attempts are countable so it is a discrete random variable
f. The weight of Upper T dash bone steak is measurable and so it is a continuous random variable.
The number of fish caught during a fishing tournament is a discrete random variable, while the square footage of a house is a continuous random variable. The other examples are not random variables.
Explanation:a. The number of fish caught during a fishing tournament is a discrete random variable. The values of the variable are obtained by counting the number of fish caught.
b. The number of textbook authors now sitting at a computer is not a random variable. It is a fixed number and does not vary.
c. The political party affiliation of adults in the United States is not a random variable. It can be determined by surveying adults or analyzing existing data.
d. The square footage of a house is a continuous random variable. The values of the variable are obtained by measuring the size of the house.
e. The number of free-throw attempts before the first shot is made is a discrete random variable. The values of the variable are obtained by counting the number of attempts.
f. The weight of an Upper T-bone steak is a continuous random variable. The values of the variable are obtained by measuring the weight of the steak.
The population of locusts in a certain swarm doubles every two hours. If 4 hours ago there were 1,000 locusts in the swarm, in approximately how many hours will the swarm population exceed 250,000 locusts?A. 6B. 8C. 10D. 12E. 14
4 hours ago = 1,000
2 hours ago = 2,000
Now = 4,000
In 2 hours = 8,000
In 4 hours = 16,000
In 6 hours = 32,000
In 8 hours = 64,000
In 10 hours = 128,000
In 12 hours = 256,000
The answer would be D. 12 hours.
-6y-3=3-6y(if there is no solution,type in ''no solution'')y= Answer
Answer:
No solution
Step-by-step explanation:
-6y - 3 = 3 - 6y , add 6y on both sides to cancel them out
-3 = 3 , you're left with -3=3, which is impossible because they're
different numbers, therefore not solution.
-3 ≠ 3
Identify the monomial function described as odd or even, and indicate whether a is positive or negative.
Answer:
Case 1: As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) decreases.
It is an 'odd' function with 'positive' a.
Case 2: As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) decreases.
It is an 'even' function with 'negative' a.
Case 3: As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) increases.
It is an 'even' function with 'positive' a.
Case 4: As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) increases.
It is an 'odd' function with 'negative' a.
Step-by-step explanation:
Let us consider a monomial function:
f(x) = axⁿ
Case 1:
As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) decreases.
This happens only if a is 'positive' and n is 'odd'. So, it is an 'odd' function with 'positive' a.
Case 2:
As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) decreases.
This happens only if a is 'negative' and n is 'even'. So, it is an 'even' function with 'negative' a.
Case 3:
As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) increases.
This happens only if a is 'positive' and n is 'even'. So, it is an 'even' function with 'positive' a.
Case 4:
As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) increases.
This happens only if a is 'negative' and n is 'odd'. So, it is an 'odd' function with 'negative' a.
Keywords: monomial function, odd function, even function
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Identify the monomial function described as odd or even, and indicate whether a is positive or negative.
A 85cm snowman melts and loses 3cm in height for every hour the sun shine and the sun shine only 6.5 hours a day. How many days will it take for the snowman to melt
Answer:
Step-by-step explanation:
The initial height of the snowman is 85 cm. snowman melts and loses 3cm in height for every hour the sun shine and the sun shine only 6.5 hours a day. This means that the height that the snowman loses in a day would be
3 × 6.5 = 19.5 cm
Therefore, in a day, the snowman loses 19.5 cm in height. Therefore,
the number of days that it will take the snowman to melt would be
85/19.5 = 4.36 days
A number consists of two digits whose sum is 12. If 16 is added to the number, then one of the digits is four times the value of the other. What is the number?
Answer: The number is 12.
Step-by-step explanation:
Since we have given that
Sum of two digits = 12
Let the one's digit be 'x'
Let the ten's digit be '12-x'
So, Original number would be
[tex]x+10(12-x)\\\\=x+120-10x\\\\=-9x+120[/tex]
If 16 is added to the number, then one of the digit is four times the value of the other.
According to question, we get that
[tex]-9x+120+16\\\\=-9x+136[/tex]
so, the one's digit be 'x'.
Let the ten's digit be '4x'.
so, New number would be
[tex]10x+4x=14x[/tex]
According to question, it becomes,
[tex]14x=-9x+136\\\\14x+9x=136\\\\23x=136\\\\x=\dfrac{136}{23}=12[/tex]
So, the number would be
[tex]-9x+120=-9\times 12+120=-108+120=12[/tex]
Hence, the number is 12.
Answer:
66
Step-by-step explanation:
Brute force:
2 digit numbers that has sum of 12:
39, 48, 57, 66
Add 16 to the numbers:
55, 64, 73, 82
Find the number that shows a digit is 4 times the value of other:
82 (2x4 =8)
Find the difference.
(5x2 + 2x + 11) - (7 + 4x - 2x2)
A.
9 - 2x - 2x2
B.
3x2 - 2x + 4
C.
3x2 + 6x + 4
D.
7x2 - 2x + 4
[tex]\text{Solve:}\\\\(5x^2 + 2x + 11) - (7 + 4x - 2x^2)\\\\5x^2+2x+11-7-4x+2x^2\\\\7x^2+2x+11-7-4x\\\\7x^2-2x+11-7\\\\\boxed{7x^2-2x+4}[/tex]
Answer:
D. 7x2 - 2x + 4
Step-by-step explanation:
5x2 + 2x + 11 - 7 - 4x +2x2
7x2 + 2x + 11 - 7 - 4x
7x2 - 2x + 11 - 7
7x2 - 2x + 4
On a final exam, 75 percent of a class had scores that were greater than 70, and 60 percent of the class had scores that were less than 85. What percent of the class had scores that were greater than 70 but less than 85 ?
Answer:
The answer is 35.
35% of the class had scores that were greater than 70 but less than 85.
Step-by-step explanation:
Let's assume the number of students in the class =100
If 75% of the class scored greater than 70, then, it means 25% (100-75) of the scores were less than or equal to 70
In other words, 25 scores were less than or equal to 70.
If 60% of the class had scores that were less than 85, then, it means 40%(100-60) of the scores were greater than or equal to 85
Therefore, of the 100 scores, 25 scores were LESS THAN OR EQUAL to 70, and 40 scores were GREATER THAN OR EQUAL to 85.
We've now accounted for 65 (25+40) scores, which means the remaining 35 (100-65) scores must be between 70 and 85.
Answer:
The answer is 35.
35% of the class had scores that were greater than 70 but less than 85.
Step-by-step explanation:
Let's assume the number of students in the class =100
If 75% of the class scored greater than 70, then, it means 25% (100-75) of the scores were less than or equal to 70
In other words, 25 scores were less than or equal to 70.
If 60% of the class had scores that were less than 85, then, it means 40%(100-60) of the scores were greater than or equal to 85
Therefore, of the 100 scores, 25 scores were LESS THAN OR EQUAL to 70, and 40 scores were GREATER THAN OR EQUAL to 85.
We've now accounted for 65 (25+40) scores, which means the remaining 35 (100-65) scores must be between 70
Write down a 3-digit number where digits are in decreasing order. Reverse the digits and subtract it from the first number.
Step-by-step explanation:
987 → 789
987 - 789 = 198
876 → 678
876 - 678 = 198
765 → 567
765 - 567 = 198
654 → 456
654 - 456 = 198
543 → 345
543 - 345 = 198
432 → 234
432 - 234 = 198
321 → 123
321 - 123 = 198
Generally it is always like that:
3 ≤ x ≤ 9
100x + 10(x-1) + (x - 2) → 100(x - 2) + 10(x - 1) + x
(100x + 10(x - 1) + (x - 2)) - (100(x-2) + 10(x-1) + x)
= 100x + 10(x - 1) + (x - 2) - 100(x - 2) - 10(x - 1) - x cancel 10(x - 1)
= 100x + x - 2 - 100x + 200 - x cancel 100x and x
= 100 - 2
= 198
Lynn rents a luxury car at the Edmonton Internacional Airport. She wants a nice
vehicle for her 3 day trip. She figures she will put on about 400 km during the three
days.
a. What would be the cost of the Standard Daily Rate plus Mileage plan?
b. What would be the cost of the Unlimited Mileage plan?
c. Which is the better plan?
Answer:
Step-by-step explanation:
Looking at the table,
a) the standard daily rate for a luxury car is $70. Since Lynn wants to rent the luxury car for 3 days, it means that the standard rate for 3 days would be
3 × 70 = $210
She figures she will put on about 400 km during the three
days. The cost of renting the luxury car per kilometer(mileage) is 30 cents. Therefore, the cost for 400 kilometers would be
400 × 30 = 12000 cents.
Converting 12000 cents to dollars, it becomes
12000/100 = $120
Total cost of renting the luxury car would be
120 + 210 = $330
b) the daily cost of the unlimited mileage daily for the luxury car is $105
Total cost of renting the luxury car for 3 days would be
105 × 3 = $315
c) the standard daily rate is better because it is cheaper
if the sum of the interior angles of a regular n-gon is 900 degrees, then n=what?
Answer:
n=7
Step-by-step explanation:
let n be number of sides.
(n-2)180=900
n-2=900/180=5
n=5+2=7
Rebecca moves to a large city that had two event stadiums. The larger stadium can hold 4.5 times 10^4 people, which is about 15 times as many people as the smaller stadium can hold. Which expression could represent the approximate amount of people the smaller stadium can hold?
Answer:
3,000 people
Step-by-step explanation:
Total number of people larger stadium can hold equals 4.5 times [tex]10^{4}[/tex] people,
which equals 45,000 people.
Now,
it is given that larger stadium can hold 15 times more people than small stadium .
So, smaller stadium will hold 15 times less people than the larger stadium ,
Which equals , [tex]\frac{45000}{15}[/tex] = 3,000 people.
Thus ,
Smaller stadium can hold a total of 3,000 people.
A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average rate of 3 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?
A. 0.5< t < 0.75
B. 1.75< t < 2.0
C. 2.0 < t < 2.5
D. 2.5 < t < 3.0
E. 3 < t < 3.5
Answer:
C. 2.0 < t < 2.5
Step-by-step explanation:
Diameter of track (D) = 2 miles, Average rate (A) = 3 miles per hour
A = distance/ time
time (t) = distance/A
distance around the track (circumference) = πD = 3.142 × 2 miles = 6.284 miles
t = 6.284miles/3miles/hour = 2.1 hour
Therefore, 2.0 < t < 2.5
In triangle $ABC$, $BC = 20 \sqrt{3}$ and $\angle C = 30^\circ$. Let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$, respectively. Find the length of $DE$.
Answer:
DE=10
Step-by-step explanation:
Given that in triangle ABC, $BC = 20 \sqrt{3}$ and $\angle C = 30^\circ$. Let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$,
To find length of DE
Please refer to the attachment for solution
Since perpendicular bisector we have DC = 1/2 BC = 10 sqrt 3
Using right triangle CDE, we get DE = 10
In how many ways can 8 people be seated in a row if there are no restrictions on the seating arrangement?
persons A and B must sit next to each other?
there are 4 men and 4 women and no 2 men or 2 women can sit next to each other?
there are 5 men and they must sit next to one another?
there are 4 married couples and each couple must sit together?
Answer:
a ) P₈ = 40320
b) P = 576
c) P = 1440
d) P = 24
Step-by-step explanation:
a ) 8 people sitting in a row without restrictions
simple Total ways = P₈ = 8!
P₈ = 8*7*6*5*4*3*2*1
P₈ = 40320
b) There are 4 men and 4 women and no two men or 2 women can sit next to each other
Let letters e women and numbers be men we have something like this
1 a 2 b 3 c 4 d
So we have the permutations of the four digits (men)
P₄ = 4!
P₄ = 4*3*2*1 = 24
And the permutations of the 4 women too equal to 24
Then total ways of sitting in a row in this case is
P = 24*24 = 576
c) There are 5 men and they have to sit next to each other
In this case we have 2 groups:
Group 1 5 men Group 2 3 women
We have two groups and the ways are
group men first group of women second 1 way
group of women first group of men second 2 way
Permutations within men group
P₅ = 5! = 5*4*3*2*1
P₅ = 120
Permutations within the women group
P₃ = 3! = 3*2*1
P₃ = 6
Total ways case c) T = 6*120*2 =
P(c) = 1440
d) There are four couples and each couple must be together
P₄ = 4! = 4*3*2*1
P₄ = 24
A student with two summer jobs earns $10 per hour at a café and $8 per hour at a market. The student would like to earn at least $800 per month.
A. Write and graph an inequality to represent the situation. Include clear labels on the graph.
B. The student works at the market for 60 hours per month and can work at most 90 hours per month. Can the student earn at least $800 each month? Explain how you can use your graph to determine this.
Help
Answer:
A.) View Image
B.) Not possible. If you look at the graph,the student must work at the cafe at least 80 hours and at the the market for at least 100 hours to earn the minimum $800 they wanted.
60 hours is below the minimum required time of both place. 90 hours can only satisfy the minimum work hour of one of the place, they need to satisfy the minimum of both places.
In other word, they must work at least 180 hours to earn the $800+ they wanted
Step-by-step explanation:
Set up your equation.
let c be hour worked at cafe and m be hours worked at market.
solve for any of the variable. I solved for c because it looked easier. solving for m will give you the same graph as well.
Graph your equation like usual. Since it's a ≥ sign then you must shade above the line. The shaded part represents the hours that the student can work at both place to earn at least $800
Thomas brings over 1/2 of his marble collection. He divides these marbles equally among 3 friends. What fraction of Thomas's entire marble collection did each friend get?
Answer:
Each of the three friends will get one-sixth of the Thomas's enitre marble collection.
Step-by-step explanation:
Fraction of the total marble collection brought by Thomas = [tex]\frac{1}{2}[/tex]
Now, Thomas divides these marbles equally among his three friends. So, each of the three friends will get one-third of the total marble collection brought by Thomas.
Fraction of total marble collection got by each friend = [tex]\frac{1}{3} \;of\;fraction\;of\;total\;marble\;collection\;brought\;by\;Thomas[/tex]
= [tex]\frac{1}{3}\times\frac{1}{2}=\frac{1}{6}[/tex]
∴ Each of the three friends of Thomas will get one-sixth of his entire collection of marbles.
For one month, Gilda's cell phone bill costs $40 plus an additional 8 cents per text message. Is she can only afford a total bill of $50 for a month, find the maximum number of text messages she can send in one month.
Answer:
Gilda can send 125 messages in one month.
Step-by-step explanation:
Given,
Total bill of 1 month = $50
Fixed charge of 1 month = $40
Charge of 1 message = 8 cents
∵100 cents = $1
∴8 cents = $0.08
Therefore Charge of 1 message = $0.08
We have to find out the number of messages that Gilda can send in 1 month.
Solution,
Let the total number of messages that Gilda can send in 1 month be 'x'.
Total bill of the month is the sum of fixed charge and charge of 1 message multiplied with total number of messages.
So, framing the above sentence in equation form, we get;
Total bill of 1 month =Fixed charge of 1 month+Charge of 1 message× total number of messages
On substituting the given values, we get;
[tex]40+0.08x=50\\\\0.08x=50-40\\\\0.08x=10\\\\x=\frac{10}{0.08}=125[/tex]
Hence Gilda can send 125 messages in one month.
At the used bookstore, Keisha bought 24 novels. If 3/8 of the book the books are mystery novels and the rest are science fiction novels, how many science fiction novels did Keisha buy?
Keisha bought 15 science fiction novels.
Step-by-step explanation:
Given,
Number of novels bought by Keisha = 24
Mystery novels = 3/8 of total novels
Mystery novels = [tex]\frac{3}{8}*24=\frac{72}{8}[/tex]
Mystery novels = 9
Let,
x represent the number of science fiction novels.
Mystery novels + Science fiction novels = Total novels
[tex]9+x=24\\x=24-9\\x=15[/tex]
Keisha bought 15 science fiction novels.
Keywords: fraction, addition
Learn more about fractions at:
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Triangles Q R S and X Y Z are shown. Angles Q S R and X Z Y are right angles. Angles Q R S and X Y Z are congruent. The length of Y Z is 9, the length of X Z is 12, and the length of hypotenuse X Y is 15. Given △QRS ~ △XYZ, what is the value of tan(Q)? Three-fifths Three-fourths Four-fifths Four-thirds
Answer:
Three-fourths
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
∠QSR≅∠XZY ---> given problem
∠QRS≅∠XYZ ---> given problem
so
△QRS ~ △XYZ ----> by AA Similarity theorem
Remember that, if two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
That means
[tex]\frac{QS}{XZ}=\frac{QR}{XY}=\frac{RS}{YZ}[/tex]
∠Q≅∠X
∠R≅∠Y
∠S≅∠Z
In the right triangle XYZ
Find the tangent of angle X
[tex]tan(X)=\frac{YZ}{XZ}[/tex] ---> opposite side angle X divided by adjacent side angle X
substitute the given values
[tex]tan(X)=\frac{9}{12}[/tex]
Simplify
[tex]tan(X)=\frac{3}{4}[/tex]
Remember that
∠Q≅∠X
so
[tex]tan(Q)=tan(X)[/tex]
therefore
[tex]tan(Q)=\frac{3}{4}[/tex] ---->Three-fourths
What is the Median for the following set of numbers? ​21 23 76 47 55 135 45 30 17
Answer:
Median = 45
Step-by-step explanation:
We are given the following data set:
21, 23, 76, 47, 55, 135, 45, 30, 17
Median is the number that divides the data into two equal parts.
Formula:
[tex]Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}[/tex]
Sorted data:
17, 21, 23, 30, 45, 47, 55, 76, 135
Sample size = 9, which is odd
Median =
[tex]\dfrac{9+1}{2}^{th}\text{ term} = \dfrac{10}{2}^{th}\text{ term} = 5^{th}\text{ term}\\\\= 45[/tex]
The median of given set of numbers is 45.
The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the _____.
a. variance
b. standard error
c. residual
d. predicted interval
Answer:
Option C. Residual
Step-by-step explanation:
Residuals are defined as:
Residual is the error that are not explained by the regression line.It is defined as the difference between observed value of dependent variable and the predicted variable.Residual = Observed value - Predicted value[tex]e = y_{\text{observed}}- \hat{y}[/tex], where e is the residual.Residuals are the unexplained differences.Thus,
The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the residuals.
Option C. Residual
The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the residual.
The following information should be considered:
Residual should be the error i.e. not described by the regression line. It shows the difference between the observed value and the predicted value.Therefore we can conclude that option c is correct.
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Yuan and his friends went to the movies. They ate 8 buckets of popcorn, 4 ice cream bars, and 6 boxes of chocolate. How many snacks did they eat in all?
Answer:
18 snacks
Step-by-step explanation:
Here we are considering that popcorn,icecreams,chocolate are snacks and each quantity represents each unit of snack.
Given that they ate 8 buckets of popcorn, 4 ice cream bars, and 6 boxes of chocolate
So the total number of snacks they ate are 8 + 4 + 6 = 18
Of the students who eat in a certain cafeteria, each student either likes or dislikes lima beans and each student either likes or dislikes brussels sprouts. Of these students, \small \frac{2}{3} dislike lima beans; and of those who dislike lima beans, \small \frac{3}{5} also dislike brussels sprouts. How many of the students like brussels sprouts but dislike lima beans?
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How I got that answer:
Create a two-way table showing the breakdown of students who like or dislike either vegetable. This is shown in the attached image below. Anywhere there is a letter indicates we aren't able to determine that value. Luckily we dont need to know those values to answer the question.
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Let's say we had 3000 students. I picked some large number that is a multiple of 3. That way when we multiply by 2/3, we get a whole number.
Take 2/3 of 3000 and you should get 2000. So there are 2000 students who dislike lima beans. Write "2000" at the end of the "dislike lima beans" row which is where the total is. Above that we'll have 1000 people who like lima beans, but we dont need to use this value.
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Of those 2000 students, 3/5 of them also dont like sprouts either. So (3/5)*2000 = 0.6*2000 = 1200 students do not like both veggies. Furthermore, 2000 - 1200 = 800 like sprouts but dont like lima beans.
Alternatively, 2/5 of the 2000 students like sprouts but dont like lima beans, so (2/5)*2000 = 0.4*2000 = 800.
QUESTION 4 of 5: You have insurance premiums of $250 due quarterly. How much will you pay annually?
Answer:
$1000
Step-by-step explanation:
quarterly is 1/4
12/4 is 3
so every 3 months you pay $250
annually is the whole year so 250*4
Answer:
1000
Step-by-step explanation:
The values of m and n are whole numbers greater than 1. Which is true about the quotient m/n÷1/n? The expression will always equal n. The expression will always equal m. The expression will equal n only when m > n. The expression will equal m only when m > n.
Answer:
The value of the quotient is always equal to m
Step-by-step explanation:
The values of m and n are whole numbers greater than 1.
We are given a quotient that is [tex]\frac{\frac{m}{n} }{\frac{1}{n}}[/tex].
In this we have fractions in both numerator and denominator.
The given quotient will be the same if we multiply the numerator with the inverse of the denominator.
So we multiply the numerator [tex]\frac{m}{n}[/tex] with the inverse n.
So the quotient will become = [tex]\frac{m}{n} \times n[/tex] = m
Hence the value of the quotient is always equal to m.