We developed three functions to model student attendance, per-student expenditure, and total food cost. S(t) = 150 * (1 + 0.08)^t models the number of students, A(t) = 10 * (1 - 0.04)^t models the cost per student, and E(t) = S(t) * A(t) models the total cost.
Explanation:We are asked to model the predicted number of students, the amount spent per student and the total expense for food per year over time.
A. The function S(t) = 150 * (1 + 0.08)^t represents the predicted number of students over time.
'S' stands for the number of students.'t' stands for the time in years.B. The function A(t) = 10 * (1 - 0.04)^t represents the predicted amount spent per student over time.
'A' stands for the amount spent per student.C. The function E(t) = S(t) * A(t), represents the total predicted expense for food each year over time.
'E' stands for the total expense.So, 'S(t)' represents the increase of students, 'A(t)' represents the decrease in the amount spent per student, and 'E(t)' the total expenditure of food each year.
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can someone please help me out with this
Answer:
4 = 15
Step-by-step explanation:
Make them equal to each other first
2x+15=x+30
Put like terms together
x=15
Hope this helped
:)
A linear function has a slope of Negative StartFraction 7 Over 9 EndFraction and a y-intercept of 3. How does this function compare to the linear function that is represented by the equation y + 11 = Negative StartFraction 7 Over 9 EndFraction (x minus 18)?
Answer:
They are the same line written in different forms.
Step-by-step explanation:
Given a linear function with a slope of [tex]-\frac{7}{9}[/tex] and a y-intercept of 3.
The equation of the line in the slope-intercept form is given as:
[tex]y=-\frac{7}{9}x+3[/tex]
Given the other line,
[tex]y+11=-\frac{7}{9}(x-18)[/tex]
Simplified:
[tex]y+11=-\frac{7}{9}x+14\\y=-\frac{7}{9}x+14-11\\y=-\frac{7}{9}x+3[/tex]
The two lines are one and the same line.
Answer:
They are the same line written in different forms.
Question 1
Factor the following expression using the GCF. Type your factored expression below.
4xy + 12w + 12Z
Answer:
4(xy + w + z)
Step-by-step explanation:
The expression to be factored is:
4xy + 12w + 12z
Factoring an equation involves taking out common terms from the expression that will then make it more simpler and simplified.
To solve this problem, we need to find the factors of the given terms:
4xy
12w
12z
The numbers given as coefficients of the variables are;
4 12 12
A factor is any integer that divides a number evenly;
Factors of 4 are 1, 2 and 4
12 are 1, 2,3,4,6 and 12
The common factors between 4 and 12 are those numbers that can divide both digits:
These are 1, 2, and 4, they are common to both
Now, the greatest common factor is the highest of this factors which is 4
Therefore, the greatest common factor of 12 and 4 is 4
Also, xy, w and z has no common factors
Factoring
4xy + 12w + 12z = 4(xy + w + z)
wo lengths of a triangle are shown. wo lengths of a triangle are shown. Triangle J K L. Side J K is 5 inches and side J L is 10 inches. Which could be the length of Side K L? 4 in. 9 in. 16 in. 19 in.Triangle J K L. Side J K is 5 inches and side J L is 10 inches. Which could be the length of Side K L? 4 in. 9 in. 16 in. 19 in.
Answer:
B/2: 9 inches
What is the greatest common factor of 4x^3
and 8x^2?
Answer:
the gcf is 4
Step-by-step explanation:
Final answer:
To find the greatest common factor of 4x³ and 8x², we look at the numerical coefficients and the variables separately. The GCF of the coefficients 4 and 8 is 4, and since x² is the lowest power of x common in both terms, the GCF is 4x².
Explanation:
The greatest common factor (GCF) of two expressions, like 4x³ and 8x², involves finding the highest degree of common terms they share. First, let's compare the numerical coefficients; 4 and 8. The GCF of 4 and 8 is 4. Next, we'll look at the variable part. The lowest exponent of x that appears in both terms is 2. Therefore, the GCF is the product of the GCF of the coefficients and the lowest power of x, which is 4x².
pls help thankssssssssssssssssssssssssssssss
Answer: The answer is 525.
Step-by-step explanation:
7*(5)^2*(3)= 525
My nephew was playing with a book and tore out the pages 7, 8, 100, 101, 222 and 223.
How many sheets did he tear out?
Answer:
Step-by-step explanation:
A sheet has 2 pages
6 pages are torn. So 6 ÷ 2 = 3 sheets
Answer:
3 pages
Step-by-step explanation:
7 and 8 are one page
100 and 101 are one page
222 and 223 are one page
He tore out 3 pages
compare the two groups of data. which statement is true?
Answer:
a) both have the same spread
Step-by-step explanation:
Mean of Brand A > Mean of Brand B
Median of A > Median of B
Spread of:
A: 22 - 18 = 4
B: 18 - 14 = 4
The spread of the data which is obtained by calculating the Interquartile range of each distribution since the distributions are skewed is 2 for brand A and brand B. Hence, the spread is the same.
The distribution of BRAND A chips :
18, 19, 19, 19, 19, 19, 19, 20,20,20,20,20,20,21,21,21,21,21,21,22
The Upper quartile, Q3 ;
Q3 = 0.75 × (n + 1)th term
Q3 = 0.75 × 21 = 15.75 th term = 21
The Lower quartile, Q1 ;
Q1 = 0.25 × (n + 1)th term
Q1 = 0.25 × 21 = 5.25 th term = 19
The IQR = Q3 - Q1 = (21 - 19) = 2
The distribution of BRAND B chips :
14,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,18
The Upper quartile, Q3 ;
Q3 = 0.75 × (n + 1)th term
Q3 = 0.75 × 21 = 15.75 th term = 16
The Lower quartile, Q1 ;
Q1 = 0.25 × (n + 1)th term
Q1 = 0.25 × 21 = 5.25 th term = 14
The IQR = Q3 - Q1 = (16 - 14) = 2
Therefore, the spread of distribution of BRAND A and B are the same.
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In the diagram below, point U is on segment $\overline{BY}$ and the measure of angle BUG is 30 degrees greater than the measure of angle GUY:
Answer: 75
Step-by-step explanation:
We have angle BUG angle GUY = angle BUY = 180. If we let angle GUY = x, then
(x+30) + x = 180 Solving this equation gives x=75.
Using the definition of linear pair angles, the measure of angle GUY is: 75°.
What is a Linear Pair?A linear pair are two angles on a straight line whose sum equals 180 degrees.
Thus:
m∠BUG = m∠GUY + 30°
Therefore:
m∠BUG + m∠GUY = 180°
Substitute
m∠GUY + 30 + m∠GUY = 180 (linear pair)
2(m∠GUY) + 30 = 180
2(m∠GUY) = 180 - 30
2(m∠GUY) = 150
m∠GUY = 150/2
m∠GUY = 75°
Therefore, using the definition of linear pair angles, the measure of angle GUY is: 75°.
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Can you explain it and help me out please
Answer:
D. two real solutions
Step-by-step explanation:
p²+5 = 6p
p² - 6p +5 =0
D = b² - 4ac = (-6)² - 4*(1)*5 = 36 - 20 = 16
D > 0, so this equation has 2 real solutions
help meeeeeeeeeeeeeeee
Answer:
2 years
Step-by-step explanation:
Construct a triangle with the given dimensions:
angle measure of 39°
angle measure of 76°
angle measure of 65°
You can create with the given measurements.
Answer:
you can make 3 different triangles by using the protector and setting the given angles.
Steps:-
1. Make a dot on the page.
2.Point the protector's intersecting point at the dot.
3.Now mark the given angle measurements as well as 0°.
Now connect the angle measurement with the dot and then dot with 0°
i neeeeeeeed heeeeeelp
Can you please help me out plz asap
Answer:
1. A
2. B
3. C
you have to judge the fraction based on the other dilations and the answer choices
5
10. George, Sandy, Carlos, and Michelle all ate a piece of a whole
pecan pie. George ate 0.15 of the pie, Michelle ate of the pie,
and Carlos ate of the pie. Sandy ate more than two of her
friends, but less than the other one. What is a possible
percentage of the ple Sandy ate?
Answer:
0.150 < (Proportion of Sandy's pie) < 0.167
15% < (Percentage of Sandy's pie) < 16.7%
Step-by-step explanation:
Total percentage of pie = 100% or 1
George, Sandy, Carlos, and Michelle all ate a piece of the pie.
George ate a fraction of 0.150
Michelle ate a fraction of (1/6) = 0.167
Carlos ate a fraction of (1/7) = 0.143
The amount of pie left = 1 - 0.15 - (1/6) - (1/7) = 0.5405
And Sandy is known to eat more than two of her friends, but less than one of them.
Of the amount of pie eaten by the first 3 friends, (1/6) is the highest proportion.
Hence, it is evident that Sandy ate more than 0.143 and 0.150 (Carlos and George) but less than Michelle (0.167).
So, mathematically, the possible proportion of cake that Sandy ate is
0.150 < (Proportion of Sandy's pie) < 0.167
Hope this Helps!!!
a 3rd grade teacher has 55 students everyday if those 55 students turned into 100 students how many students would it be.
Answer:
45 because you have to subtract 100-55 which would equal 45
Answer:
Yeah it would be 45
Step-by-step explanation:
Because:
100 - 55 = 45
A cylinder and a cone start with the same radius and height. The radius of the cone is then tripled, and the height of the cone is cut in half. The radius of the cylinder stays the same, but the height of the cylinder is doubled. Which change produces a greater increase in volume (i.e., which figure’s volume increases by a larger factor)? Justify your answer. Write “pi” for ''pi symbol'' and “r^2”.
Answer:
The change in the cone produces a greater increase in volume.
Step-by-step explanation:
Let's start with the cone.
[tex]V = \frac{1}{3} \pi r^{2} h[/tex]
[tex]V = \frac{1}{3} \pi 3r^{2} \frac{h}{2}[/tex] (In your case, you would type V = 1/3pi3r^2h/2)
The changes that occurred are [tex]3^{2}[/tex] and [tex]1/2[/tex]. When we add these together we get [tex]9/2[/tex].
Now the cylinder.
[tex]V = \pi r^{2} h[/tex]
[tex]V = \pi r^{2} 2h[/tex] (In your case, you would type V = pir^2 2h)
The change that occurred is [tex]2[/tex].
[tex]9/2[/tex] is greater than [tex]2[/tex] which means that the change in the cone produces a greater increase in volume.
Answer:
Step-by-step explanation:
For the cone V k1= (Pi/3) .R squared .H
V k2= (pi/3) . (3R)squared . (H/2)=(9/2) .(PI/3) . R squared.H
=(3pi/2) R.squared.H
3pi/2
nk= 2/ pi/3
N k= 9/2
For the cylinder
V c1=Pi .R squared.H
V c2= Pi.R squared.(2H)
N c=V c2/V c1=2
Cone has greatest change in volume
Hope this helps!!!!!!!!
the nth term of a number sequence is 2n+5
Answer:
Step-by-step explanation:
hello you idiot
The results of a survey indicate 50% of seventh-graders watch at least one movie
during the weekend. Based on this survey of a group of 50 seventh-graders, how
many will watch at least one movie this weekend?
Answer:
25 students
Step-by-step explanation:
50% of 50 is 25
50/2 = 25
Answer:25
Step-by-step explanation:
The total number of children is 50
So 50%of50children is
50/100×50=2500/100
=25
Please answer this correct:):)
Mathematics VI
Which property is represented by the following equation?
5 x 13 x 2 = 5x 2 x 13
Answer:
commutative
Step-by-step explanation:
-The ability to change the order to terms in a addition or multiplication problem.
Can someone help me out please
Answer:
The slope is one. I cant graph it for you though. Try plotting the points then drawing a straight line down those points.
Step-by-step explanation:
Evaluate 5 × (4.75 + 1.50) - 3 × 1.25
Answer:
The answer is 27.5
Answer:
25.50
Step-by-step explanation:
5(4.75+1.50)-3 x 1.25
23.75+5.50-3x 1.25
29.25-3x1.25
29.25-3.75
25.50
What does b mean, and how do I work out b and c? No need to answer a
find the value of c so that (x+2) is a factor of the polynomial p(x). p(x)=4x^3+cx^2+x+2
Answer:
c = 8
Step-by-step explanation:
Use synthetic division here; it's the fastest approach.
Given that (x + 2) is a factor, take -2 and use this as the divisor in synthetic division:
-2 4 c 1 2
-8 (-2c+ 16) (4c-34)
---------------------------------------------
4 (c - 8) (-2c + 17) 4c - 32
The remainder, 4c - 32, must equal zero if (x + 2) is a factor.
Then 4c - 32 = 0, and c = 8
Answer:
Altavistard is right, the answer is 8
Step-by-step explanation:
go look at altavistard...
Find the exact volume of the cylinder.
A) 14π m3
B) 28π m3
C) 56π m3
D) 112π m3
(the height is 7 and the radius is 2)
Answer:
Option B) [tex]28\pi\text{ m}^3[/tex]
Step-by-step explanation:
We are given the following in the question:
Radius of cylinder, r = 2 m
Height of cylinder, h = 7 m
We have to find the volume of the cylinder.
Volume of cylinder =
[tex]V = \pi r^2 h[/tex]
where r is the radius and h is the height of the cylinder.
Putting values, we get,
[tex]V = \pi (2)^2(7)\\V = 28\pi\text{ cubic meter}[/tex]
Thus, the volume of cylinder is
Option B) [tex]28\pi\text{ m}^3[/tex]
Hi, love!!
The correct answer is listed below:
A) 14π m3
B) 28π m3
C) 56π m3
D) 112π m3
Please help
Which shapes can be cross sections of the figure?
Check all that apply.
A,circle
B,rectangle
C,trapezoid
D,triangle
E,semicircle
Answer:
The answer is B,C, and D
Step-by-step explanation:
I GOT. THE. QUESTION. RIGHT. ON. EDUNUTITY
I would also love an explanation!
Answer:you go up one over three
Step-by-step explanation:
Order the numbers from greatest to least.
2.34, 234, 94
Answer:
234, 94, 2.34
Step-by-step explanation:
Which of the following best describes the algebraic expression x/3-15
O
A. Three divided by a number minus fifteen.
O
B. A number divided by three less than fifteen.
O
C. Three divided by a number less than fifteen.
O
D. A number divided by three minus fifteen.
Answer:
D. A number divided by three minus fifteen.