Clearly, |S| = 50.
Count the multiples of 2 between 1 and 50:
⌊50/2⌋ = ⌊25⌋ = 25
(where ⌊x⌋ denotes the "floor of x", or the largest integer that is smaller than or equal to x; in other words, round down to the nearest integer)
Count the multiples of 3 between 1 and 50:
⌊50/3⌋ ≈ ⌊16.667⌋ = 16
Since LCM(2, 3) = 6, the sets of multiples of 2 and multiples of 3 have some overlap. Count the multiples of 6 between 1 and 50:
⌊50/6⌋ ≈ ⌊8.333⌋ = 8
Then by the inclusion/exclusion principle, we remove from S
25 + 16 - 8 = 33
elements, so that the new set S contains 50 - 33 = 17 elements.
If two terms of an arithmetic sequence are a11 = 23 and a15 = −5, what is a28?
The value of a28 given a11 = 23 and a15 = −5 is -96
Given:
a11 = 23
a15 = −5
Where,
a1 = first term
d = common difference
a11 = a + 10d = 23
a15 = a + 14d = -5
a + 10d = 23 (1)
a + 10d = 23 (1)a + 14d = -5 (2)
subtract (1) from (2) to eliminate a
14d - 10d = -5 - 23
4d = -28
d = -28 / 4
d = -7
Substitute d = -7 into (1)
a + 10d = 23 (1)
a + 10(-7) = 23
a - 70 = 23
a = 23 + 70
a = 93
So,
a28 = a + 27d
= 93 + 27(-7)
= 93 + -189
= 93 - 189
= -96
Therefore, the value of a28 given a11 = 23 and a15 = −5 is -96
Learn more about arithmetic sequence:
https://brainly.com/question/6561461
Help Plz
Rewrite in simplest terms: 4(3d+7f)-5f-3(9f+3d)4(3d+7f)−5f−3(9f+3d)
Answer:
its easy
Look at the pictures.
Please mark brainlest
If you cant see the result is 24f+24d
Pat is saving money to buy a bicycle. The amount he has saved is shown in the table below.
Which of the functions below describe the amount A , in dollars, Pat has saved after t weeks?
Select all that apply.
A(t)=15+15(t−1)
A(t)=30+15(t−1)
A(t)=15+15t
A(t)=15+30t
A(t)=15t
Answer:
I think A and C
Step-by-step explanation:
help ASAP please hmmmm
Answer:
I’d go with number 2 and number 4.
What is the GCF of 14mn, 56m^2n^3, 28m^3n^2?
a) 7m^2n^2
b) 7mn
c) 14m^3n^3
d) 14m^2n^2
e) 14mn
Answer:
e) 14mn.
Step-by-step explanation:
The GCF of 14, 56 and 28 is 14,
The GCF of m, m^2 and m^3 is m.
The GCF of n, n^2 and n^3 is n.
The answer is therefore 14mn.
1.0835 rounded to the nearest tenth
Answer:
1.1
Step-by-step explanation:
Answer:
1.1
Step-by-step explanation:
Can someone help me with this please!!
Step-by-step explanation:
part A
all listed features (A - F) are correct and to be selected.
part B
the average rate of change is
(f(x2) - f(x1)) / (x2 - x1)
so,
(f(0) - f(-2)) / (0 - -2) = (2 - 0) / (0 + 2) = 2/2 = 1
please help with hegarty algebraic fractions and quadratic equations
[tex]\huge \bf༆ Answer ༄[/tex]
Let's solve ~
[tex] \sf \dfrac{3}{x} - \dfrac{3}{x + 4} = 1[/tex][tex] \sf \dfrac{3(x + 4) -3x }{x(x + 4)} = 1[/tex][tex] \sf \dfrac{3x + 12-3x }{x(x + 4)} = 1[/tex][tex] \sf 12 = {x(x + 4)} [/tex][tex] \sf {x}^{2} + 4x = 12[/tex][tex] \sf{ {x}^{2} + 4x - 12 = 0 }[/tex][tex] \sf{ {x}^{2} + 6x - 2x - 12 = 0}[/tex][tex] \sf{x(x + 6) - 2(x + 6) = 0}[/tex][tex] \sf(x - 2)(x + 6) = 0[/tex]Hence,
[tex] \sf x = 2 \: \: or \: \: x = - 6[/tex]Cell phone production engineers have noticed that among a group of 138 customers aged 14-23 who send more text messages tend to use a higher percentage of their phone’s memory.What are the explanatory variable and response variable for this relationship?
Explanatory variable: age of customer
Response variable: percentage of phone memory used
Explanatory variable: percentage of phone memory used
Response variable: age of customer
Explanatory variable: number of text messages sent
Response variable: percentage of phone memory used
Explanatory variable: percentage of phone memory used
Response variable: number
Answer:
it is c my guy
Step-by-step explanation:
on edge2020
The explanatory variable is the number of text messages sent, and the response variable is the percentage of phone memory used. The correct answer is (C)
What is the independent and dependent variable?In mathematics, independent and dependent variables are values that vary in relation to one another. The dependent variable is dependent on the independent variable, which means that if the value of the independent variable changes, so will the dependent variable.
In this situation, the explanatory variable is the number of text messages sent, because it is believed to influence or "explain" the variation in the response variable, which is the percentage of phone memory used.
The explanatory variable is also sometimes called the independent variable, because it is the variable that is being manipulated or controlled in an experiment. The response variable is also sometimes called the dependent variable, because it is the variable that is believed to depend on the explanatory variable.
Therefore, in this problem, the explanatory variable is the number of text messages sent, and the response variable is the percentage of phone memory used.
Learn more about the independent and dependent variables here:
https://brainly.com/question/1479694
#SPJ2
if x(square) plus y(square) is 8.and the froduvt is . what are x and y?
Given :-
x² + y² = 8Product of x and y is 4 .( say )To Find :-
The value of x and y .Answer :-
Here we are given that,
[tex]\red{\longrightarrow}[/tex] x² + y² = 8 .
And ,
[tex]\red{\longrightarrow}[/tex] xy = 4
[tex]\red{\longrightarrow}[/tex] y = 4/x
So that ,
[tex]\red{\longrightarrow}[/tex] x² + (4/x)² = 8
[tex]\red{\longrightarrow}[/tex] x² +16/x² = 8
[tex]\red{\longrightarrow}[/tex] x⁴ + 16 = 8x²
[tex]\red{\longrightarrow}[/tex] x⁴ - 8x² + 16 = 0
Assume k² = x⁴ and k = x²
[tex]\red{\longrightarrow}[/tex] k² - 8k + 16 = 0
[tex]\red{\longrightarrow}[/tex] k² -4k -4k +16 = 0
[tex]\red{\longrightarrow}[/tex] k(k-4) -4(k-4) = 0
[tex]\red{\longrightarrow}[/tex] (k-4)² = 0
[tex]\red{\longrightarrow}[/tex] k = 4
So ,
[tex]\red{\longrightarrow}[/tex] k = x²
[tex]\red{\longrightarrow}[/tex] 4 = x²
[tex]\red{\longrightarrow}[/tex] x = √4
[tex]\red{\longrightarrow}[/tex] x = ±2
Hence the required answer is ±2.
The values of x and y of the given function are; x = y = ±2
Roots of a Polynomial
We are given;
x² + y² = 8 -----(1)
Product of x and y = 4;
Thus; xy = 4
Now, making y the subject we have;
y = 4/x
Putting 4/x for y in eq 1 gives us;
x² + (4/x)² = 8
x² + (16/x²) = 8
Multiply through by by x² to get;
x⁴ + 16 = 8x²
⇒ x⁴ - 8x² + 16 = 0
using online polynomial root calculator, we have x = ±2
Thus, y will also be ±2
Complete question is;
If x² + y² = 8 and the product of x and y is 4, what are x and y?
Read more about roots of a polynomial at; https://brainly.com/question/10702726
omg guys pls help me, its due at 5pm
Answer:
1) 3:4
Step-by-step explanation:
Answer:
1. 3 ratio 5
2. 4 ratio 4
3. 2 ratio 5
4. 2 ratio 4
Jovie is maintaining a camp fire. She has kept the fire steadily burning for 101010 hours with 151515 logs. She wants to know how many hours (h)(h)left parenthesis, h, right parenthesis she could have kept the fire going with 9 logs. She assumes all logs are the same.
How many hours can Jovie keep the fire going with 9 logs?
Answer:
Step-by-step explanation:
101010:151515 is the same as 2:3 or 2 logs for 3 hours. Using that you can set up your equation as such:
2:3
x:9
And then multiply across:
2x9 = 3x
18/3 = x
6 = x
Jovie can keep the fire running for 6 hours with 9 logs.
Another way to do this is to divide the log numbers, 9/3 = 3, and then multiply the hours by this number, 2x3 = 6.
Hope that helps
Nikita began with the figure shown.
A.
с
B
She completed the following actions to construct the angle bisector of ABC, but made a mistake in one of the steps. Select the step in which
her mistake was made.
Step 1: She placed the compass on point B and drew an arc which intersects ray BA at point D and ray BC at point E.
Step 2: Next, she placed the compass on point D and drew an arc on the interior of 2ABC.
Step 3: Then, she placed the compass on point and drew an arc on the interior of ZABC, which intersects the previous arc.
Step 4: She labeled the intersection of the two arcs as point F and drew the ray BF, which represents the angle bisector
of ZABC.
Answer:
no
Step-by-step explanation:
Answer:
Step three
Step-by-step explanation:
She placed the point on C when it was supposed to be on E
Will mark brainly!! :)
If f(2) for f(x) = [tex]\frac{2}{x-1}[/tex]+6 is 8. then what is [tex]f^{-1} (8)[/tex]
Answer:
2
Explanation:
we get inverse functions by interchanging places of domain and range of the original fuction so rhe domain becomes a range and the range becomes a domain.
so if 2 belongs to the domain of the original fuction and its corresponding element in the range is 8, we simply interchange between 2 and 8 in order to solve the fuction without any subistitution in the original function.
pls help me pls help me pls help me
Answer:
C. 35
Step-by-step explanation:
First, let's put the first notebook.
1 2 3
1 2 4
1 2 5
1 2 6
1 2 7
We lose 1 step at each time.
1 3 2 is not ok because 1 2 3 is same as 1 3 2
5+4+3+2+1
Next, the other one.
4+3+2+1
3+2+1
2+1
1
5+4+3+2+1+4+3+2+1+3+2+1+2+1+1=35
35 different ways
1
D
Question 1
Adding the complex numbers 7 - 6i and —3 + 8i is equivalent to the operation
(7 – 6) + (-3+8) i.
X=-2y,x-y=6 solve by substitution show all work
Answer:
y=-3
x=3
Step-by-step explanation:
x=-2y
x-y=9
substitute -2y for x in the second equation
you get:
-2y-y=9
combine like terms
-3y=9
divide by -3 on both sides
y=-3
What is the ratio of cosine of C?
A 24/7
B 24/25
C 7/25
D 25/24
Answer:
Cos C = adjecent/hypotenuse
Cos C = 14/50
divide the numerator and the denominator by 2
Cos C = 7/25
The answer is C
Malik jogged 2 miles in 20 minutes.
What was his rate in miles per hour?
10 miles per hour
6 miles per hour
23 mile per hour
110 mile per hour
Answer:
6 miles per hour
Step-by-step explanation:
2 miles in 20 minutes
x miles in 60 minutes
2×60 = 20x
120 = 20x
6 = x
Answer:
6 miles per hour
Step-by-step explanation:
I took the test
Pls Help T^T ASAP FIRT TO ANSWER GETS BRAINLIEST
Answer:
The answer would be the third one shaded circle at -1 arrow goes left.
Solve -(2x + 4) = 18.
7
-11
11
-7
Answer:
x=7
Step-by-step explanation:
Hope this helps!
help ASAP please again and again
Answer:
14
Step-by-step explanation:
Jan took her brother out to dinner. The cost of Jan’s dinner was $18.50. The cost of her brother’s dinner was $19.00. If they want to add a 15% tip for the waitress, what will be the total bill?
The total bill that would be paid by Jan is equal to $43.125.
Given the following data:
Cost of Jan’s dinner = $18.50.Cost of brother’s dinner = $19.00.Tip = 15%To determine the total bill that would be paid by Jan:
First of all, we would calculate the total cost of their dinner as follows:
[tex]Total\;cost = 18.50 + 19.00[/tex]
Total cost = $37.50
Next, we would calculate the tip cost for the total cost of their dinner:
[tex]Tip\;cost = \frac{15}{100} \times 37.5\\\\Tip\;cost =0.15\times 37.5[/tex]
Tip cost = $5.625
For the total bill:
[tex]Total\;bill = Total\;cost + Tip\;cost\\\\Total\;bill = 37.5 + 5.625[/tex]
Total bill = $43.125.
Read more: https://brainly.com/question/11285399
3. You miss a free throw 3/10 of the time
A) likely
B) unlikely
C) certain
D) equally likely
You miss a free throw 3/10 of the time is unlikely event. Therefore, option B is the correct answer.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Given that, miss a free throw 3/10 of the time.
Here, 3/10 =0.3
The total probability is always equal to unity.
If the event is “certain” to happen, the probability will be 1.
If the event is “likely” to happen, the probability will be between 1/2 and 1.
If the event has an “equal chance” to happen or not, the probability will be 1/2.
If the event is “unlikely” to happen, the probability will be between 0 and 1/2.
You miss a free throw 3/10 of the time is unlikely event.
Therefore, option B is the correct answer.
To learn more about the probability visit:
https://brainly.com/question/11234923.
#SPJ6
LaShawn earned $60.00 for working 8 hours this weekend. What is the total amount of money LaShawn would earn for working 34 hours at the same rate of pay
To find this answer we have to do these steps below
1. Find the amount of money that LaShawn earns in an Hour
We have to do 60/8 which is 7.5
LaShawn earns 7.5 dollars in an hour
2. Multiply 7.5 by 35
The answer to that is 262.5 dollars
Therefore the answer is 262.5 dollars
I hope this helped, if it's wrong, blame me
Ps. Brailents would help a LOT
How i can answer this question, NO LINKS, if you answer correctly i will give u brainliest!
Answer:
A Todays soup will be less tomatoey
Step-by-step explanation:
At a basketball game, for every basket team A scored, team B scored 4 baskets. The ratio of the number of baskets scored by team A to the number of baskets for team B is A. 1 to 3
B. 2 to 3
C. 1 to 4
D. 4 to 1
Answer:
C. 1 to 4
Step-by-step explanation:
The ratio is used to describe situations like "for how many x's, there are many y's". In this case, we are trying to find the ratio for A baskets scored to B baskets scored, team A scores one basket, then team B will score 4 baskets. Then we can write the ratio of A to B as 1:4, which is 1 to 4.
Hope I did this correctly since it was long ago that I lastly worked with ratios
Item 2
A baker displays 72 muffins on 8 identical trays.
How many trays does the baker need to display 54 muffins?
Enter your answer in the box.
Answer:
The baker needs six trays to display 54 muffins
Step-by-step explanation:
72/8 = 9
9 x ? =
56
9 x 6 = 56
Answer:
6
Step-by-step explanation:
Muffins displayed in 8 identical trays = 72
Muffins displayed in 1 identical tray = 72/8 = 9
Tray required to display 54 muffins = 54/9 = 6
The area of the triangle below is 8.91 square inches.
What is the length of the base?
Answer:
8.1
Step-by-step explanation:
Area of a triangle = ½ × base × height = Area
Rearranged =
area/1/2xheight
The base is the length.
8.91/1/2x2.2
=8.1 inches
Katherine Johnson is best known for her work on ________.
Answer:
Pretty sure she was best known for calculating flight paths of spacecraft.