The number of users on new social media site increase as 21, 25, 30, 36,
The average rate of change is given by 5.
The function f (t) = 12 (1.2) ^t show how the rate of users increases in weeks.
Average of the values is the ratio of total sum of values to the number of values.
Here, f (t) = 12 (1.2) ^t is defined in the range of (3, 6)
So the value of the function in its range is given by
1) f (3) = 12 (1.2) ^3
= 21
2) f (4) = 12 (1.2) ^4
= 25
3) f (5) = 12 (1.2) ^5
= 30
4) f (6) = 12 (1.2) ^6
= 36
Now the average rate of change = sum of all difference in values at every week / max. Difference in interval of range(3,6)
= f(6)-f(3)/6-3
= 15/3
= 5
Thus required average change of rate is 5.
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7(x + 1) -2 =5 (x + 1) +2
Answer:
x = 1
Step-by-step explanation:
Simplifying
7(x + 1) + -2 = 5(x + 1) + 2
Reorder the terms:
7(1 + x) + -2 = 5(x + 1) + 2
(1 * 7 + x * 7) + -2 = 5(x + 1) + 2
(7 + 7x) + -2 = 5(x + 1) + 2
Reorder the terms:
7 + -2 + 7x = 5(x + 1) + 2
Combine like terms: 7 + -2 = 5
5 + 7x = 5(x + 1) + 2
Reorder the terms:
5 + 7x = 5(1 + x) + 2
5 + 7x = (1 * 5 + x * 5) + 2
5 + 7x = (5 + 5x) + 2
Reorder the terms:
5 + 7x = 5 + 2 + 5x
Combine like terms: 5 + 2 = 7
5 + 7x = 7 + 5x
Solving
5 + 7x = 7 + 5x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-5x' to each side of the equation.
5 + 7x + -5x = 7 + 5x + -5x
Combine like terms: 7x + -5x = 2x
5 + 2x = 7 + 5x + -5x
Combine like terms: 5x + -5x = 0
5 + 2x = 7 + 0
5 + 2x = 7
Add '-5' to each side of the equation.
5 + -5 + 2x = 7 + -5
Combine like terms: 5 + -5 = 0
0 + 2x = 7 + -5
2x = 7 + -5
Combine like terms: 7 + -5 = 2
2x = 2
Divide each side by '2'.
x = 1
Simplifying
x = 1
Answer:
Hello! The answer is x = 1.
Step-by-step explanation:
To solve this equation, we need to find x.
The first step in approaching this problem would be to use the distributive property:
7(x + 1) - 2 = 5(x + 1) + 2 will turn into:
7x + 7 - 2 = 5x + 5 + 2
Now, you can combine like terms on each side of the equation:
7x + 5 = 5x + 7
Now, you want to get the x's on one side and the whole numbers on the other side. In order to do this, we will subtract 5 from both sides and subtract 5x from both sides:
7x + 5 = 5x + 7
-5x -5 -5x -5
This will leave us with:
2x = 2
We will have to now divide both sides by 2 to get x by itself:
2x = 2
-- --
2 2
This leaves us with the result: x = 1
Evaluate functions from their graph f(−3)=
See the Correct answer attached!
Considering the given graph, it is found that f(-3) = 1.
How to verify the value of f(x) from a graph?First we identity x on the horizontal axis, then we look at the value of y on the vertical axis for which the function is marked at this point.
At this graph, when the horizontal axis is of -3, the vertical axis is of 1, hence f(-3) = 1.
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Review the equation used in writing a partial fraction decomposition.
StartFraction negative 15 x + 10 Over (5 x minus 2) squared EndFraction = StartFraction A Over 5 x minus 2 EndFraction + StartFraction B Over (5 x minus 2) squared EndFraction
or, [tex]\frac{-15x+10}{(5x-2)^2} = \frac{A}{5x-2} + \frac{B}{(5x-2)^2}[/tex]
Which system of equations can be used to determine the values of A and B?
(answer choices in attached image)
Applying partial fractions, the system of equations that can be used to find the values of A and B is given as follows:
5A = -15.-2A + B = 10.What is the partial fraction?The partial fraction is given as follows:
[tex]\frac{-15x + 10}{(5x - 2)^2} = \frac{A}{5x - 2} + \frac{B}{(5x - 2)^2}[/tex]
Applying the least common multiple at the right side, we have that:
[tex]\frac{-15x + 10}{(5x - 2)^2} = \frac{A(5x - 2) + B}{(5x - 2)^2}[/tex]
[tex]\frac{-15x + 10}{(5x - 2)^2} = \frac{5Ax - 2A + B}{(5x - 2)^2}[/tex]
Hence, comparing both sides of the equality:
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Answer:
The answer is Be
Step-by-step explanation:
5A=-15
-2A+B=10
Take a rectangular sheet of paper. Fold it in any way and then unfold it. Draw a line on the crease using a ruler and pencil. Repeat this process 7 more times. Mark the points of intersection as A, B, C, D and so on. Identify polygons and identify whether they are convex or concave.
The polygon formed was convex polygon.
What is a Concave and Convex Polygon ?A polygon that has at least one interior angle greater than 180 degree is called concave polygon . It usually has an irregular shape.
A convex polygon has all angles less than 180 degree.
It is given to follow some steps
1. A rectangular sheet of paper is taken .
2. It if folded and unfolded in random directions
3. Lines are drawn on the creases
4. The intersection points are marked A,B,C,D,E,F,G
5. The figure formed is a convex polygon as all the angles measure were less than 180 degree.
Therefore the polygon formed was convex polygon.
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(a) Which department accounts for approximately one-fifth of the annual budget? Select One (b) Approximately what percentage of the annual budget is used for Marketing and Sales combined? Write your answer as a multiple of - that is, 10%, 20%, 30%, ... (c) If of the annual budget is used for Marketing, approximately what percentage is used for Support? 2% 15% 30% 300%
a. The department that accounts for approximately one-fifth of the annual budget, based on the pie chart, is the Research Department.
b. The percentage of the annual budget used by the Marketing and Sales departments combined is 30%.
c. If 18% of the annual budget is used for Research, approximately the percentage used for Marketing is 9%.
What is a pie chart?A pie chart is a graphical representation of data in a circle. In this pie chart, the area or percentage of the whole circle is 100%
Thus, we can obtain the values of the different groups represented in the pie chart by systematically dividing the circle accordingly.
The rule to follow is that vertical angles are always congruent (equal) as they have two lines that intersect to form opposite angles.
Data and Calculations:Research, Sales, and Marketing = 50% of the budget (half of the pie chart)
Research = 18%
Sales and Marketing = 32% (50% - 18%)
Research equals Media and Support and Media and Support are equal.
Therefore, Media is 9% (18%/2) and Support is also 9%.
Since opposite angles are always equal, Engineering (opposite to Sales and Marketing combined) is 32%.
This results in a total of 100% (18% + 32% + 9% + 9% +32%)
Question Completion:The pie chart attached shows how the annual budget for Equipment Producers Incorporated is divided by department. Use this chart to answer the questions below.
c) If 18% of the annual budget is used for Research, approximately what percentage is used for Marketing?
Thus, the department that accounts for approximately one-fifth of the annual budget, based on the pie chart, is the Research Department.
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If ab=1/4 and bc=1/3 and ac=1/3 then find a*b*c
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
Given
ab = [tex]\frac{1}{4}[/tex]
bc = [tex]\frac{1}{3}[/tex]
ac = [tex]\frac{1}{3}[/tex]
We will use the first equation to find b in terms of a.
b = [tex]\frac{1}{4a}[/tex]
Now we will substitute b into 2nd equation to find c in terms of a.
[tex](\frac{1}{4a} )(c)=\frac{1}{3} \\\frac{c}{4a} =\frac{1}{3} \\3c = 4a\\c = \frac{4a}{3}[/tex]
Now we will substitute c into 3rd equation to find value a.
[tex]a(\frac{4a}{3} )=\frac{1}{3} \\\frac{4a^{2} }{3} =\frac{1}{3} \\4a^{2} =1\\a^{2} =\frac{1}{4} \\a=\sqrt{\frac{1}{4} } \\=\frac{1}{2}[/tex]
Now we will substitute a into first equation to find b.
b = [tex]\frac{1}{4(\frac{1}{2}) } \\=\frac{1}{2}[/tex]
Next we will substitute a into the 3rd equation to find c.
c = [tex]\frac{4(\frac{1}{2}) }{3} \\=\frac{2}{3}[/tex]
Now we got all 3 values, when we multiply them together,
a x b x c = [tex]\frac{1}{2} *\frac{1}{2} *\frac{2}{3} \\=\frac{2}{12} \\=\frac{1}{6}[/tex]
Tom changed the rotating speed of his cement mixer from 6 1/3 rpms to 10 rpms . By how many revolutions per minute did the speed of the mixer increase
Answer:
3 2/3
Step-by-step explanation:
10 rpms - 6 1/3 rpms = 3 2/3
These marbles are placed in a bag and two
of them are randomly drawn.
What is the probability of drawing two
yellow marbles if the first one is placed back
in the bag before the second draw?
Give your answer as a ratio, reduced to
simplest terms.
Answer:
1/25
Step-by-step explanation:
The bag has:
2 yellow marbles3 red marbles5 blue marbles10 total marblesThe probability of picking a yellow marble is 2/10=1/5.
So, the answer is (1/5)² = 1/25
State the domain of the function
F(x)= (x+3)/(x-1)
Answer:
x < 1 or x > 1
Step-by-step explanation:
The domain of a function is the range of values of the input is real and defined
In this particular function, x = 1 is the only value at which the function is not defined since the denominator x -1 becomes 0 and the function is undefined since division by zero is undefined
Which of the following expressions is equivalent to 3x2 + 6x – 24?
A. 3(x + 2)(x – 4)
B. 3(x – 2)(x + 4)
C. (x + 6)(x – 12)
D. (x – 6)(x + 12)
3x² + 6x - 24
Simplify 3.
3(x² + 6x - 8)
Think of x² +2x−8. Factor the expression by grouping. First, we need to rewrite the expression as x² + ax + bx - 8. To find a and b, set up a system to be solved.
a + b = 2ab = 1( −8 ) = −8Since ab is negative, a and b have opposite signs. Since a+b is positive, the positive number has a greater absolute value than the negative. Show all pairs of integers whose product is −8.
−1,8−2,4Calculate the sum of each pair.
−1 + 8 = 7−2 + 4 = 2The solution is the pair that gives sum 2
a=−2b=4Rewrite x² + 2x − 8 as (x² − 2x ) + (4x − 8).
(x² − 2x ) + (4x − 8)Simplify x in the first group and 4 in the second.
x ( x − 2) + 4( x − 2 )Simplify the common term x−2 with the distributive property.
( x − 2 )( x + 4 )The entire factored expression is rewritten.
3 ( x − 2 )( x + 4 ) ===> Answer
We conclude that the correct option is "B".
{ Pisces04 }
Write an equation for the nth term of the arithmetic sequence 8, 3, -2, -7,... Find the 9th term of the sequence.
Step-by-step explanation:
1) the difference betwee the terms given is 3-8=-2-3= -5, then
2) for n-th term: aₙ=8-5(n-1);
3) for the 9-th term: a₉=8-5*8=-32.
Sally is using strings to mark parallel rows for a vegetable garden for her house.
House
Step-by-step explanation:
ATTACHED IS THE SOLUTION.
Answer:
m<2=115
m=180-115
=75
your answer is 75 because house is hanged in 180
Simplify the expression. What classification describes the resulting polynomial? (3x^2-11x-4)-(2x^2-x-6)
The expression can be simplified to a polynomial of degree 2.
[tex]x^2 - 10x + 2[/tex]
How to simplify the expression?
Here we have the expression:
[tex](3x^2 -11x - 4) - (2x^2 - x - 6)[/tex]
We can directly simplify this by taking the variable as common factor:
[tex](3 - 2)*x^2 + (-11 + 1)*x + (-4 + 6)\\\\x^2 - 10x + 2[/tex]
This is a polynomial, as you can see, the maximum exponent is 2, so the degree of the polynomial is 2.
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Graph the image using the given transformation
Answer:
Shown in the attachment.
Step-by-step explanation:
Shown in the attachment.
A wall of a building is 30 inches wide. 14 inches is concrete,10 inches is brick, and 6 inches is like stone. What fraction of the wall is concrete
Answer:
46.67 %
Step-by-step explanation:
Total thickness = 30
14 of this is concrete 14/30 x 100% = 46.67 %
Denver, Colorado, is 5,183 feet above sea level. Convert the height to miles. Round to two decimal places.
Answer:
0.98 miles
Step-by-step explanation:
A hotel offers a reward program based on the number of nights stayed. The function f(x) represents the number of free nights earned as a function of x, the number of nights stayed.
f(x) = Left-bracket StartFraction x Over 10 EndFraction right-bracket
Which describes the meaning of f(x)?
f(x) is a linear function that increases with x. represents the number of free nights earned as a function of x, the number of nights that you stay.
Which describes the meaning of f(x)?
We know that f(x) represents the number of free nights earned as a function of x, the number of nights that you stay.
Such that:
f(x) = x/10.
Notice that, if x = 10, then:
[tex]f(10) = 10/10 = 1[/tex]
This means that if you stay for 10 nights, then you get a free night.
If you stay for 20 nights, then you win two free nights, and so on.
f(x) is a linear function that increases with x.
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Answer:
Step-by-step explanation:
The true statement is (A) A customer earns 1 free night per 10 nights stayed.
The function is given as:
From the above function, we can see that the number of nights (x) is divided by 10.
This means that, for every 10 nights stayed, the visitor gets one free night.
Hence, the true statement is (A) A customer earns 1 free night per 10 nights stayed.
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Please help with this pre algebra question
Answer:
(2) / ((x + 5)(x - 1))
&
(3x) / ((x - 6)(x - 1))
Step-by-step explanation:
The question is asking you to factor the denominator. In this case, you cannot simplify either of the numerators. You can factor the denominator by asking yourself the question: which two numbers multiply to equal the final number in the quadratic and add to equal the middle number in the quadratic?
1.) 2 / (x² + 4x - 5)
-----> Which two numbers multiply to -5 and add to 4? These numbers are 5 and -1. This makes the factors (x + 5) and (x - 1). The fully simplified answer: (2) / ((x + 5)(x - 1))
2.) 3x / (x² - 7x + 6)
------> Which two numbers multiply to 6 and add to -7? These numbers are -6 and -1. This makes the factors (x - 6) and (x - 1). The fully simplified answer: (3x) / ((x - 6)(x - 1))
*Please let me know if I misinterpreted the question or you need further clarification <3
PLEASE HELP MEEEE!!!!!
Using proportions, it is found that the meaning of 1 + x is the percent of original price being paid.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, the total cost of the toy is given by:
15.85(1 + x).
In which x is the sales tax.
We have that:
15.85 is the base cost.15.85(1 + x) is the cost considering sales tax.Hence (1 + x) is the percent of original price being paid.More can be learned about proportions at https://brainly.com/question/24372153
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Y is inversely proportional to the square root of x. If Y = 5 when x = 36, find Y, when x is 16. For full credit: 1. Write a proportion. 2. Solve for y. 3. Show work.
Answer: y=7.5
Step-by-step explanation:
Given
y∝(1/√x)
this implies that
y=k/√x eq(*)
when y=5 and x=36 then
5=k/√36
5=k/6
30=k eq(1)
to find y when x is 16
put values in eq(*)
y=30/√16
y=30/4
y=7.5
To determine a monthly budget for gasoline, Rachael determines that she can not spend more
than 12% of her $400 monthly income on gasoline. To create a budget, she estimates that the cost
per gallon of gas will be $3.15. She writes the following inequality to express the situation where x
represents the number of gallons of gasoline she can purchase.
3.15(x) ≤400-12%
Solve the inequality to determine if she used an appropriate estimate for the cost of gasoline to purchase
no more than 15 gallons of gasoline each week. Show and Explain your work.
The solution of the given inequality is:
x ≤ 15.24
How to solve the inequality?
We know that the maximum that she can spend on gasoline is the 12% of $400.
That is:
(12%/100%)*$400 = 0.12*$400 = $48
Now, we know that each gallon of gas costs $3.15, then if x is the number of gallons of gas that she buys, we have the inequality:
x*$3.15 ≤ $48
To solve the inequality, we need to divide both sides by $3.15
x ≤ $48/$3.15
x ≤ 15.24
So the maximum number of gallons of gasoline that she can buy is 15 gallons (actually a little more).
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An insurance company has provided you with a sample of paid claims. The sample includes the following claims: 192, 113, 200, 287, and 225. What are the mean and the variance respectively of this sample rounded to nearest whole number?
Review Later
203, 63
203, 3942
210, 63
210, 3942
The required value of mean and variance is 203 and 3942 respectively.
Hence option B is correct.
The sample includes the following claims: 192, 113, 200, 287, and 225.
What is Statistic?The statistic is the study of mathematics which deal with relations between comprehensive data.
Mean(x) = 192+113+200+287+225/5
x = 203
variance =[tex]\frac{\sum(x-x_i)^2}{n^2-1}[/tex]
=summation of squared value/n^2−1
=15769/25−1
=15769/24
=3942
Thus, the required value of mean and variance is 203 and 3942 respectively.
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(Need help asap!!)
Rearrange the equation below to solve for y.
6x+6y=c
Answer:
D. c/6 - x
Step-by-step explanation:
Rearranging with subject '6y':
6y = c - 6x
Dividing the above equation by 6 to get subject 'y':
y = c/6 - x
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Extract the common factor 6.
[tex]\bf{6(x+y)=c }[/tex]
Divide both sides by 6.
[tex]\bf{x+y=\dfrac{c}{6} }[/tex]
Subtract x from both sides.
[tex]\bf{y=\dfrac{c}{6}-x \ \ \to \ \ \ Answer }[/tex]
Therefore, the correct option is "D".
{ Pisces04 }Which number could be added to
both sides of this quadratic equation
to complete the square?
1=x²-3x
er the value that belongs in both of these green boxes.
[2]+1=x²-3x+
Hint: Use ()²
The number which could be added to both sides of the equation to complete the square is; -2.25.
Which number could be added to both sides of this quadratic equation to complete the square?The quadratic equations give in the task content is; 1=x²-3x. Hence, to express the equation by completing the square method; we have;
1 - 2.25 = (x -3/2)² - 2.25
Hence, the number which should be added to both sides of the equation is; -2.25.
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If $1.00 at 5.5% interest compounded daily has a value of $1.00513 after 34 days, how much interest would Bonnie’s account have earned on $4,000 after 34 days? (8 points)
Answer:
$4020.52
Step-by-step explanation:
The future value is the principal multiplied by the amount $1.00 is worth in the future.
$4,000 × 1.00513 = $4020.52
Your little brother just learned how to flip and catch a coin. He believes that by catching the coin in mid-air, he can influence the probability that it will land heads up. Based on your understanding of theoretical probability, explain to your little brother why his theory of influence is false.
By performing two experiments a lot of times, your brother will see that catching the coin mid-air does not affect the probability.
How to explain that the theory is false?We assume that the probability of each outcome of the coin is equal, so the probability of getting tails is 0.5 and the probability of getting heads is 0.5
Then, you can say to your brother to perform his experiment a lot of times. In two ways.
First, he lets the coin came down to his hand around 100 times.
Then, he catches the coin in mid-air another 100 times.
He will see that the probability of getting heads (or tails) is (almost) the same in both cases, this will mean that his theory is false.
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A person has 100 notes of Rs. 10 and Rs. 20 each. He went to a shop and bought items for Rs. 220. In how many ways can he pay this amount using the notes he has?
Answer:
look below
Step-by-step explanation:
first way ,10 x 22 = 220
second way , 20 x 11 = 220
There are many ways other than this but I cant tell all of them. for example, the person can just give Rs. 1000 to the shopkeeper and receive a change of Rs. 780
There are 12 ways he can pay this amount using the notes he has the answer is 12.
What are permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
Let x be the number of Rs10 notes and y be the Rs20 note
10x + 20y = 220
The whole number of x and y which satisfy the above equation:
x = 0, y =11
x = 2, y =10
x = 4, y =9
x = 6, y =8
x = 8, y =7
x = 10, y =6
x = 12, y =5
x = 14, y =4
x = 16, y =3
x = 18, y =2
x = 20, y =1
x = 22, y =0
Total number of ways = 12
Thus, there are 12 ways he can pay this amount using the notes he has the answer is 12.
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Do the side lengths 4, 8, and 10 form a triangle? Select the correct answer and reasoning. Question 19 options: A) Yes, because the sum of any two side lengths is greater than the third side length. B) No, because the third side length is greater than the sum of the other two side lengths. C) Yes, because the sum of all three side lengths is greater than 20. D) No, because 4 + 8 is greater than 10.
Answer:
A) Yes, because the sum of any two side lengths is greater than the third side length.
Step-by-step explanation:
All triangles have a property that the sum of two side lengths is greater than the remaining side length.
4 + 8 = 12 > 10, making it a triangle
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A radioactive element has a half-life of 55 days. what percentage of the original sample is left after 115 days? round to 4 decimals when necessary.
The percentage of the original sample that is left after 115 days is; 23.4733%
How to calculate the decay percentage?Formula for radioactive decay is;
A = A₀ * (1/2)^(t/t_¹/₂)
where;
A = quantity of the substance remaining
A₀ = initial quantity of the substance
t = time elapsed
t_¹/₂ = half life of the substance
Thus;
A/A₀ = (1/2)^(115/55)
A/A₀ = 0.234733 or 23.4733%
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Kurt has $9,000 in an account. The interest rate is 5% compounded annually. To the nearest cent, how much will he have in 1 year? Kurt has $ 9,000 in an account . The interest rate is 5 % compounded annually . To the nearest cent , how much will he have in 1 year ?
Answer:
$9450
Step-by-step explanation:
Answer:
A = $9,450.00
A = P + I where
P (principal) = $9,000.00
I (interest) = $450.00
Calculation Steps:
First, convert R as a percent to r as a decimal
r = R/100
r = 5/100
r = 0.05 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 9,000.00(1 + 0.05/1)(1)(1)
A = 9,000.00(1 + 0.05)(1)
A = $9,450.00
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $9,000.00 at a rate of 5% per year compounded 1 times per year over 1 years is $9,450.00.