Answer:
there 32 students and 20 have pets so you take 20 over 30 divide by 2 to get 10/16 then divide by 2 to get 5/8and that is the answer
Mr. Inwood does a job in x hours while Mr. Lui can do it in y hours. How much of the job could they do it together if they were to work for k hours?
If they worked for k hours, the amount of work done would be [tex]\mathbf{ \dfrac{k(x+y)}{xy}}[/tex]hours.
How do we determine the job done using algebraic expressions?Algebraic expression involves the use of variables and their arithmetic operations.
Given that:
Mr. Inwood does a job in x hours, whileMr. Lui can do it in y hoursIf we have a function denoted by k (hours) indicating the work they both can do together. Then we can conclude that they can both work for:
[tex]\mathbf{=\dfrac{k}{x}+\dfrac{k}{y}}[/tex]
[tex]\mathbf{ \dfrac{k(x+y)}{xy}}[/tex]
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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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[GIVING BRAINLYEST ANSWER]
(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
Feel free to mark this as brainliest and hope this helps! :)
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 }Will mark brainliest, need help ASAP!
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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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 }(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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Find the indicated function values for the function f(x) = 3x² + 2x - 6.
a. f(0)
b. f(2)
c. f(-4)
d. f(b)
e. f(4a)
a. f(0) =
(Simplify your answer.)
Answer:
a. f(0) = -6
b. f(2) =10
c. f(-4) = 32
d. f(b) = 3b^2+2b-6
e. f(4a) = 48a^2+8a-6
The function values for the function f(x) = 3x² + 2x - 6, for the values are:
a. f(0) = -6
b. f(2) = 10
c. f(-4) = 34
d. f(b) = 3b² + 2b - 6
e. f(4a) = 48a² + 8a - 6
How are function values calculated?To calculate function value f(k) for a function f(x), we substitute variable x = k, in the function f(x).
How to solve the question?In the question, we are asked to find the function value for the function f(x) = 3x² + 2x - 6 for:
a. f(0)
b. f(2)
c. f(-4)
d. f(b)
e. f(4a).
We calculate these in the following ways:-
a. f(0):
We substitute the value of x = 0 in the function f(x).
Therefore f(0) = 3(0)² + 2(0) - 6,
or, f(0) = 0 + 0 - 6 = -6.
Therefore, the function value f(0) for the function f(x) = 3x² + 2x - 6 is -6.
b. f(2):
We substitute the value of x = 2 in the function f(x).
Therefore f(2) = 3(2)² + 2(2) - 6,
or, f(2) = 12 + 4 - 6 = 10.
Therefore, the function value f(2) for the function f(x) = 3x² + 2x - 6 is 10.
c. f(-4):
We substitute the value of x = -4 in the function f(x).
Therefore f(-4) = 3(-4)² + 2(-4) - 6,
or, f(-4) = 48 - 8 - 6 = 34.
Therefore, the function value f(-4) for the function f(x) = 3x² + 2x - 6 is 34.
d. f(b):
We substitute the value of x = b in the function f(x).
Therefore f(b) = 3(b)² + 2(b) - 6,
or, f(b) = 3b² + 2b - 6.
Therefore, the function value f(b) for the function f(x) = 3x² + 2x - 6 is 3b² + 2b - 6.
e. f(4a):
We substitute the value of x = 4a in the function f(x).
Therefore f(4a) = 3(4a)² + 2(4a) - 6,
or, f(0) = 48a² + 8a - 6.
Therefore, the function value f(0) for the function f(x) = 3x² + 2x - 6 is 48a² + 8a - 6.
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18. In the diagram below, PQRS is a square Find the equation of the circle that will pass through the four vertices of the square
R(2, - 2)
S
P(- 2, 2)
Q
An equation of the circle that will pass through the four (4) vertices of the square is (x + 2)² + y² = 2².
How to find the equation of this circle?Mathematically, the general form of the equation of a circle is given by;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center.r is the radius of a circle.Note: The center of a circle lies on the midpoint of the diagonal of a square, which is formed by joining its endpoints (opposite).
Midpoint on x-coordinate is given by:
Midpoint = (-2 - 2)/2
Midpoint = -4/2 = -2.
Midpoint on y-coordinate is given by:
Midpoint = (-2 + 2)/2
Midpoint = 0/2 = 0.
Thus, the center (h, k) = (-2, 0).
For the radius, we have:
r = √(-2)² + 0²
r = √4 = 2.
Substituting the parameters into the general equation, we have;
(x - (-2))² + (y - 0)² = 2²
(x + 2)² + y² = 2²
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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
If your piece of graph paper goes only 20 blocks above the x-axis, then where will the
function below first go off the page?
y = 2²
The function will go somewhere between x = 4 and x = 5
How to determine the location of the function?The function is given as:
y = 2^x
The question implies that:
If the maximum y value on a graph is x = 20; What is the maximum x value on the graph of y = 2^x
To do this, we start by setting y to 20.
So, we have:
2^x = 20
Take the logarithm of both sides
x log(2) = log(20)
Divide by log(2)
x = 4.32
4.32 is between 4 and 5
Hence, the function will go somewhere between x = 4 and x = 5
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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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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
If 25% of a dozen egg were used to make
breakfast. how many eggs were left?
Answer: 9 eggs were left.
Step-by-step explanation:
A dozen eggs usually mean there are 12 eggs. We have two ways to solve the problems.
First way:
The egg used to make breakfast: 12 x 25% = 12 x 0.25 = 3
The eggs were left: 12 - 3 = 9
Second way:
12 x (1 - 0.25)
= 12 x 0.75
= 9
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
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:
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
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
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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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
Graph the image using the given transformation
Answer:
Shown in the attachment.
Step-by-step explanation:
Shown in the attachment.
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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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]
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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HELLPP
Divide. A POLYNOMIAL BYA A MONOMIAL
Answer:
7z^2/y -8z^4y -(9/2)z^2y^4
Step-by-step explanation:
The quotient of division of a polynomial by a monomial is the sum of quotients of each of the terms divided by the monomial. "Simplify" in this context generally means that no common factors remain factored out.
Rules of exponentsThe rules of exponents apply:
(a^b)/(a^c) = a^(b-c)
a^-b = 1/a^b
DivisionThe problem is effectively three (3) division/simplification problems.
[tex]\dfrac{-14z^4y^2+16z^6y^4+9z^4y^7}{-2z^2y^3}=\dfrac{-14z^4y^2}{-2z^2y^3}+\dfrac{16z^6y^4}{-2z^2y^3}+\dfrac{9z^4y^7}{-2z^2y^3}\\\\=7z^{4-2}y^{2-3}-8z^{6-2}y^{4-3}-\dfrac{9}{2}z^{4-2}y^{7-3}=\boxed{\dfrac{7z^2}{y}-8z^4y-\dfrac{9}{2}z^2y^4}[/tex]
__
Additional comment
We have elected to retain the original order of variables (z then y) and the original order of terms. Ordinarily, standard form would have the variables in alphabetical order (y then z) and the terms in order by decreasing degree. This order of terms also makes the leading coefficient positive. (The minus sign for a negative leading coefficient sometimes gets lost.)
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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How much interest will Brian earn on $875 in his savings account after 3 months if the annual interest rate is 5.5%?
Answer:
$12.03
Step-by-step explanation:
I = prt
I = (875)(0.055)(3/12)
I = 12.03
Answer: $12.03
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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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
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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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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