The question is incomplete. Here is the complete question.
The number of students, S, serviced by the school system in the town of Emor, t years from 2000 can be modeled by the function S(t) = 10000.[tex](1.1)^{t}[/tex]. The number of classrooms, C, in the town of Emor, t years from 2000 can be modeled by the function C(t) = 450 + 40t. Let D be the average number of students per classroom in Emor's school system t years from 2000.
Write a formula for D(t) in terms of S(t) and C(t).
Write a formula in terms of t.
Answer: D(t) = S(t) / C(t)
D(t) = [tex]\frac{10000.(1.1^{t} )}{450+40t}[/tex]
Step-by-step explanation: First, it is asked to write D(t), which is the average number of students per classroom in terms of students, S(t) and classroom, C(t).
Average is the total number of students divided by the total number of classrooms. Therefore:
D(t) = [tex]\frac{S(t)}{C(t)}[/tex]
Second, to write in term of t, which is time in years, for the average number of students per classroom:
D(t) = [tex]\frac{10000.(1.1)^{t} }{450+40t}[/tex]
In this formula it is clear that the average number of students per classroom is dependent of the growth factor of students each year represented by [tex]1.1^{t}[/tex] and the "growth factor" of classroom each year, represented by 40t.
HDTV screens usually have a width-to-heigh ratio of 16:9. Which screen dimensions are in the same proportion?
Answer:
4: 3
Step-by-step explanation:
In this case, we have that there is a relationship between width and height, which is 16: 9, which means that any screen that has the same ratio would be an identical screen.
How would we do this? it must either be raised to a power or rationalized on both sides of the ratio.
If we raise to a power, it would give very large dimensions for an HDTV, therefore, it is best to remove the square root on both sides, since it has more common values for a TV.
[tex]\sqrt{16} :\sqrt{9}[/tex]
4: 3
Therefore, a 4: 3 screen is a good choice for an HDTV with the same ratio.
Answer:
Ideiidididid
Step-by-step explanation:
Cici
Edith wants to make a paperweight at pottery class. She wants the paperweight to have a pyramid-like shape with a base area of 120120120 square centimeters, and she wants it to weigh 400400400 grams. The density of the clay she is using is 1.61.61, point, 6 grams per cubic centimeter.
What should be the height of the paperweight?
Answer:
Step-by-step explanation:
We would determine the volume of the
pyramid-like paperweight. Formula for volume is expressed as
Volume = mass/density
From the information given,
mass = 400g
Density = 1.61g/cm³
Volume = 400/1.61 = 248.45cm³
The formula for determining the volume of a pyramid us expressed as
Volume = 1/3 × base area × height
From the information given,
Base area = 120 cm²
Volume = 248.45cm³
Therefore,
248.45 = 1/3 × 120 × height
248.45 = 40 × height
height = 248.45/40 = 6.2 cm
SOMEBODY HELP MY FINAL GRADE DEPENDS ON IT THIS IS EASY I JUST FORGOT
Answer:
76
Step-by-step explanation:
The sum of the angles of a triangle add to 180
40+ 3x+10 + 2x+20 = 180
Combine like terms
70 + 5x = 180
Subtract 70
70+5x-70 =180-70
5x = 110
Divide by 5
5x/5 = 110/5
x = 22
We want to find BCA
BCA = 3x+10
= 3(22)+10
= 66+10
=76
Answer:
76
Step-by-step explanation:
The sum of the angles of a triangle add to 180
3x+10 + 2x+20 = 140
5x+30=140
-30 -30
5x=110
x=22
3*22=66+10=76
The Trapezoidal rule Tn on the interval [0,5) will be exact for
all polynomial of degree at most
Select one
O A 5
OB. None
C. 3
O 0.9
OE
Answer:
degree 1
Step-by-step explanation:
The trapezoidal rule is exact when the second derivative is zero. This occurs when the polynomial is degree one or less
A home security system is designed to have a 99% reliability rate. Suppose that nine homes equipped with this system experience an attempted burglary. Find the probabilities of these events:_________.
A. At least one alarm is triggered.
B. More than seven alarms are triggered.
C. Eight or fewer alarms are triggered.
Answer:
a) [tex] P(X \geq 1) = 1-P(X<1) = 1-P(X=0)[/tex]
[tex]P(X=0)=(9C0)(0.99)^0 (1-0.99)^{9-0}=1x10^{-18}[/tex]
And replacing we got:
[tex] P(X \geq 1) =1 -1x10^{-18} \approx 1[/tex]
b) [tex]P(X=7)=(9C7)(0.99)^7 (1-0.99)^{9-7}=0.003355[/tex]
[tex]P(X=8)=(9C8)(0.99)^8 (1-0.99)^{9-8}=0.083047[/tex]
[tex]P(X=9)=(9C9)(0.99)^9 (1-0.99)^{9-9}=0.913517[/tex]
And adding we got:
[tex] P(X \geq 7) = 0.003355+0.083047+0.913517 =0.99992[/tex]
c) [tex] P(X \leq 8) =1 -P(X>8) = 1-P(X=9)[/tex]
[tex]P(X=9)=(9C9)(0.99)^9 (1-0.99)^{9-9}=0.913517[/tex]
And replacing we got:
[tex] P(X \leq 8)= 1-0.913517=0.086483[/tex]
Step-by-step explanation:
Let X the random variable of interest "numebr of times that an alarm is triggered", on this case we now that:
[tex]X \sim Binom(n=9, p=0.99)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
Part a
We want to find this probability:
[tex] P(X \geq 1) = 1-P(X<1) = 1-P(X=0)[/tex]
[tex]P(X=0)=(9C0)(0.99)^0 (1-0.99)^{9-0}=1x10^{-18}[/tex]
And replacing we got:
[tex] P(X \geq 1) =1 -1x10^{-18} \approx 1[/tex]
Part b
[tex] P(X \geq 7)= P(X=7) +P(X=8)+ P(X=9) [/tex]
[tex]P(X=7)=(9C7)(0.99)^7 (1-0.99)^{9-7}=0.003355[/tex]
[tex]P(X=8)=(9C8)(0.99)^8 (1-0.99)^{9-8}=0.083047[/tex]
[tex]P(X=9)=(9C9)(0.99)^9 (1-0.99)^{9-9}=0.913517[/tex]
And adding we got:
[tex] P(X \geq 7) = 0.003355+0.083047+0.913517 =0.99992[/tex]
Part c
[tex] P(X \leq 8) =1 -P(X>8) = 1-P(X=9)[/tex]
[tex]P(X=9)=(9C9)(0.99)^9 (1-0.99)^{9-9}=0.913517[/tex]
And replacing we got:
[tex] P(X \leq 8)= 1-0.913517=0.086483[/tex]
helen rolls a dice and flips a coin calculate the probibility that she gets a 4 and tails
Answer:
1/12
Step-by-step explanation:
dice has 6 sides so the prob of getting 4 is 1/6
coin has 2 sides so the prob of getting tails is 1/2
Probability of getting both tails and a four simultaneously is = 1/2×1/6=1/12.
hope this helped!
Please mark as Brainliest!
Answer:
1/12
Step-by-step explanation:
The probability of get a 4 in a die is 1/6 because a die has the following numbers 1,2,3,4,5,6 ; we see each number occurs just once hence; 1/6 is the probability.
The probability of getting a tail is 1/2 because there are one tail and one head in a 2 side face coin.
Hence getting a tail and a four is ;
1/6 × 1/2 = 1/12
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
A. p(x) = 19x - 15
Step-by-step explanation:
→Set it up, like so:
[tex](25x)-(6x+15)[/tex]
[tex]25x - 6x-15[/tex]
→Add like terms (25x and -6x):
[tex]19x - 15[/tex]
Not sure if I got it right...I know it is one of the first 2.
Answer:
Step-by-step explanation:
-6x^2 + x -3 + 2x + 4
________________________
x^2 + 9
-6x^2 + 3x + 1
__________
x^2 + 9
the solution is the first one
Answer:
D.[tex]\frac{-6x^{2}-x-7 }{x^{2}+9}[/tex]
Step-by-step explanation:
since the [tex]x^{2}+9=x^{2} +9[/tex] you just have to add [tex]\frac{-6x^{2}+x-3-2x-4 }{x^{2}+9 }[/tex] so the answer will be: [tex]\frac{-6x^{2}-x-7 }{x^{2}+9 }[/tex]
Bob raked 30 bags of leaves in 3 hours. If he raked the same leaves did he rake per hour
Divide total bags by total hours:
30 bags / 3 hours = 10 bags per hour
If 8-2x<12 is -2 a solution to the inequality
Answer:
no
Step-by-step explanation:
Let's plug in -2 for x.
8 - 2 (-2) <12
8 + 4 < 12
12 < 12
Since this is a false statement, -2 is not a solution to the inequality.
Answer: No
Step-by-step explanation: To determine whether x = -2 is a solution to the inequality, substitute a -2 in for r.
So we have 8 - 2(-2) < 12.
Notice that I used parentheses.
This is a great habit to get into when
substituting numbers in for variables.
So we have 8 - (-4) which can be changed to 8 + (+4) or +12.
Since 12 is not less than 12, -2 is not a solution.
A box-contains 3 blue and 2 red marbles while another box contains 2
blue and 5 red marldes. A marble drawn at random from one of the boxes
turns out to be blue. what is the probability that it came from the first box?
Answer:
3/5
Step-by-step explanation:
(3/5) · (1/2) over (3/5) · (1/2) + (2/5) · (1/2)
= 3/5
A construction company buys a bulldozer for $26,000. The company expects the useful life of the machine to be 12 years, at which time its value will have depreciated to $6000. The company uses the declining balances method for depreciation, so the annual depreciation rate r (in decimal form) is given by the formula r=1−(S/C)^1/n . In the formula, n is the useful life of the item (in years), S is the salvage value (in dollars), and C is the original cost (in dollars). What annual depreciation rate (in percent form) did the company use? Round your answer to the nearest tenth.
Answer:
11.5%
Step-by-step explanation:
Put the given numbers in the formula and do the arithmetic.
r = 1 - (6000/26000)^(1/12) = 1 -(3/13)^(1/12) ≈ 1 -0.88498 ≈ 11.5%
The company used a depreciation rate of 11.5%.
PLSSSS HELP!!! what is the slope from 0 to 1 seconds?
Answer:
Since there is no change in the height value over that time, the slope is 0
Kyle has decided to start doing crunches as part of his daily exercise routine and is using the bar chart below to keep track of how many he has done each day. How many crunches will he do on day 15?
Answer: 59
Step-by-step explanation:
On 15th day Kyle will do 59 crunches.
What is an Equation?An equation is a statement that consists of algebraic expressions equated with other algebraic expressions by an equal sign.
The crunches Kyle did on Day 1 are 3
The rate by which he is increasing per day is 4 crunches/per day
let t represent the number of days
Let the number of crunches on t day be y
Then the equation formed will be
y = 3 + 4(t-1)
On 15th day, he will do
y = 3+ (15-1) *4
y = 3+56
y = 59
Therefore, on 15th day Kyle will do 59 crunches.
To know more about Equation
https://brainly.com/question/10413253
#SPJ2
Esther, Vida, and Clair were asked to consider two different cash flows: GH¢1000 that they could receive today and GH¢3000 that would be received 3 years from today. Esther wanted the GH¢1000 today, Vida chose to collect GH¢3000 in 3 years, and Clair was indifferent between these two options. Which of the three women made the right choice? Explain
Answer:
Esther made the right option which gives her maximum value at the end of 3 years than Vida and Clair.
Step-by-step explanation:
The life is all about making the right choices. Esther has made a decision to collect GH¢1000 now. To calculate future value of Esther choice at the end of 3 year we will use formula below,
FV = PV [tex](1 + r)^{t}[/tex]
discount factor at year 3 t 10% is 0.751
FV = 1000 (0.751) / (1.1)3
FV = GH¢2487.
Vidha choose to collect GH¢3000 at end of 3 year, the present value of GH¢3000 at 10% discount rate will be;
PV = FV [tex](1 + r)^{-t}[/tex]
PV = 3000 (0.751)
PV = GH¢2253.
Clair is indifferent from the choices given but this is also not a smart choice.
Esther has made the right choice among the three women and she gets maximum value of GH¢2487.
Identify which of these designs is most appropriate for the given experiment: completely randomized design, randomized block design, or matched pairs design. A drug is designed to treat insomnia. In a clinical trial of the drug, amounts of sleep each night are measured before and after subjects have been treated with the drug.
Answer:
Matched pairs design
Step-by-step explanation:
A matched pair design can be used in a case where the same people are being measured in before-and-after comparison. The same set of people are measured for the amount of sleep each night before the administration of the drugs and after the drug administration and this is used to test for a difference.
A coffee shop uses two different-sized bins to store coffee beans. The volume of the smaller bin is x cubic inches and the volume of the larger bin is y cubic inches. The store has S smaller bins and L larger bins. Which expressions represents the total volume of all the bins?
Answer:
Total volume of all the bins = xS + yL
Step-by-step explanation:
Given: x cubic inches represent the volume of the smaller bin and y cubic inches represents the volume of the larger bin. The store has S smaller bins and L larger bins.
To find: an expression that represents the total volume of all the bins
Solution:
The volume of the smaller bin = x cubic inches
The volume of the larger bin = y cubic inches
Also, the store has S smaller bins and L larger bins
So,
Total volume of all the bins = xS + yL
Answer:
xS plus yL
Step-by-step explanation:
The polynomial P(x) = 3 – 2x2 + 5x5 – 7x7 has what order?
Answer:
This, polynomial has order 7.
Step-by-step explanation:
Given the polynomial
P(x) = 3 – 2x2 + 5x5 – 7x7
[tex]P(x) = 3 - 2x^2+ 5x^5 - 7x^7[/tex]
Order for any polynomial is highest exponential value for variables . The exponent for polynomial is also called as degree.
Hence in terms of degree, the term in polynomial which has the highest degree . That degree is the order of the polynomial.
For example ,
in [tex]x^5 + x^8 + x^9[/tex]
here we see that variable x has highest power of 9. Thus, order of the given equation is 9.
Similarly for the polynomial given we see that
in the polynomial [tex]P(x) = 3 - 2x^2+ 5x^5 - 7x^7[/tex]
x has three power 2, 5 and 7 .
As 7 is the highest power of P(x) = 3 - 2x^2+ 5x^5 - 7x^7
This, polynomial has order 7.
the answer to this !!!
Answer: A=12, B=2, C=11
Step-by-step explanation:
With the given problem, you would first expand the numerator.
[tex]\frac{x^1^5y^3z^1^2}{x^3yz}[/tex]. Then you can simply from there. You can subtract the exponents. [tex]x^1^2y^2x^1^1[/tex]
A wire with a length of 100 cm is cut into three parts. The length of wire of the first and second parts are the same. The length of the third part of the wire exceeds the sum of the first two parts by 4 cm. Calculate the length of each part.
The first two pieces are the same, let each of those equal x, so you have x + x = 2x
The 3rd piece is the sum of the first two + 4, so this would be 2x + 4
Now you have 2x + 2x + 4 = 100 cm
Combine like terms:
4x +4 = 100
Subtract 4 from both sides
4x = 96
Divide both sides by 4
X = 24
First piece is 24 cm
Second piece is 24 cm
Third piece is 52 cm
There are 2 new seats in each row in a school auditorium. There are 20 rows in the auditorium. Each new seat costs $84 what is the cost for the new seats
Answer:
$3360
Step-by-step explanation:
First you have to do 20 times 2 to find out how many new seats there are.
Then you have to multiple that number by the cost to get the cost of all the new seats.
I hope this helped ;)
You are building a curio cabinet in the form of a rectangular prism that must be 4 feet tall with a volume of 48 cubic feet. The length and with each must be no more than tot. Which of the following dimensions are the possible width and length of the cabinet? a) 15 foot by feet b) 24 feet by 5 foot c) 25 feet by 4.8 feet d) 3 feet by 4 feet e) 4 feet by 12 feet 19
Answer:
d) 3 feet by 4 feet
Step-by-step explanation:
Volume of the prism = 48 feet³
Height if the prism = 4 feet
To determine the possible values of the length and width of the prism let's divide the volume by the height.
So 48/4 = 12
So we'll be looking for a product of two numbers to give us 12
And it's between 12 and 1, 4 and 3 , and 6 and 2.
We have only 4 and 3 in the option.
Please help! Correct answer only, please! I need to finish this assignment this week. Determine the value of the following if it is possible. If it is not possible, explain. Matrix P has a dimensions of 3 X 4 and Matrix Q has the dimensions 4 X 5. Determine the dimensions of the matrix PQ if it is possible. Explain why if it is not. (refer to video part 4) Group of answer choices A. Matrix PQ would have the dimensions 3 X 4 B. Matrix PQ would have the dimensions 4 X 5 C. Matrix PQ would have the dimensions 3 X 5 D. These matrices can not be multiplied because their dimension don't align.
Answer: c) 3 x 5
Step-by-step explanation:
When multiplying matrices of dimension m x n, the "inside" values MUST be the same. The dimension of their product is the "outside" values.
P = 3 x 4
Q = 4 x 5
The "inside" values are both 4 so the product can be found.
The "outside" values are 3 & 5 so the dimension of the product is 3 x 5.
If the problem was flipped to: find QP, we would get the following:
Q = 4 x 5
P = 3 x 4
the "inside" values of 3 & 5 are not the same so the product does not exist.
ill mark you as brainliest if you get this correct
Answer:
a) 72
b) 9
c) 9
d) 54
Step-by-step explanation:
a) 12 * 6 = 72
b) 3 * 6 = 18. 18 ÷ 2 = 9
c) 3 * 6 = 18. 18 ÷ 2 = 9
d) 72 - 18 = 54
Drew writes down a number between 1 and 1000. Mary must determine that number by asking "yes/no" questions of Drew. Mary knows that Drew always tells the truth. If Mary uses an optimal strategy, then she will determine the answer at the end of exactly how many questions in the worst case?
Answer: 10 questions.
Step-by-step explanation:
The optimal aproach would be divide the total range in half, for example, she can ask:
Is the number equal or greater than 500?
if he answers no, now she knows that the numer is in the range 1 to 499
if he says yes, she can know that the number is in the range 500 to 1000.
Now, suppose that the answer is yes.
Now she can ask if the number is equal or greater than 750.
Now we have two possible sets. (500, 749) and (750 , 1000).
Now we can divide those sets again, depending on the answer.
suppose we got the set of (750, 1000)
we can divide it into two sets and so on.
So, we have 999 options and we want to divide it by 2 until we reach to 1., the number of divisions by 2 is the number of times that she asked a question.
999/2^n ≤ 1.
we must find the smaller n that keeps the above inequality true.
999 ≤ 2^n
knowing that 2^10 = 1024.
999/1024 = 1024
So in the worst case, she should ask 10 questions.
A survey of 250 homeless persons showed that 14 were veterans. Find a point estimate for the population proportion of homeless persons who are veterans.
Answer:
[tex] \hat p =\frac{14}{250}= 0.056[/tex]
And for this case that represent the 5.6% of the homeless persons who are veterans
Step-by-step explanation:
We know that in a survey of 250 homeless persons 14 were veterans. We can find the estimated proportion of homeless persons who are veterans with the following formula:
[tex] \hat p =\frac{X}{n}[/tex]
The last one is an unbiased estimator of the true population proportion p
And replacing the info given we got:
[tex] \hat p =\frac{14}{250}= 0.056[/tex]
And for this case that represent the 5.6% of the homeless persons who are veterans
Find the value of x.
Answer:
x = 98
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
x + 24 = 122
Subtract 24 form each side
x+24-24 =122-24
x =98
Answer:
[tex] x = 98 \: \: degrees \\ [/tex]
Step-by-step explanation:
The exterior angle is equal to sum of opposite interior angles in a triangle.
[tex]24 + x = 122 \\ x = 122 - 24 \\ x = 98 \: \: degrees[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
A student earned a grade of 80% on a math test that had 20 problems. How many problems on this test did the student answer correctly?
The student got____problems correct on the test.
Answer:
The student got 16 problem correct
Step-by-step explanation:
Take the number of problems and multiply by the percent correct
20 * 80%
20 *.80
16
The student got 16 problem correct
Answer: The student got 16 problem correct.
Step-by-step explanation: To solve this problem, you first want to take the number of problems that are on the math test and multiply that by the percent the student got correct.
So we have 20 × 80%
Now write 80% as a decimal to get .80.
So we have 20 × .80 which is equal to 16.
So the student got 16 problems correct
and 4 problems incorrect on their test.
Adrian makes $36.50 per day plus tips. His average tip is 17% of the total amount of money customers spend. Which equation could be used to determine x, the total amount of money customers would need to spend for Adrian to earn a daily income of $150? A. 150 = 36.50 + 17x B. 150 = 0.17 + 36.50x C. 150 = x(17 + 36.50) D. 150 = 36.50 + 0.17x
Answer:
For this case we know that the fixed cost is $36.50 and the variable cost is 17% of the total amount of money customers spend, let's asusme that this variable is x. And we can create a model like this one:
[tex] y = mx +b[/tex]
Where y represent the income and x the the total amount of money customers would need to spend. For this case the value for b = 36.50 and the slope m would be 0.17 since if we convert the % into a fraction we got 0.17. So then the best option is:
[tex] 150 = 36.5 +0.17x[/tex]
D. 150 = 36.50 + 0.17x
Step-by-step explanation:
For this case we know that the fixed cost is $36.50 and the variable cost is 17% of the total amount of money customers spend, let's asusme that this variable is x. And we can create a model like this one:
[tex] y = mx +b[/tex]
Where y represent the income and x the the total amount of money customers would need to spend. For this case the value for b = 36.50 and the slope would be 0.17 since if we convert the % into a fraction we got 0.17. So then the best option is:
[tex] 150 = 36.5 +0.17x[/tex]
D. 150 = 36.50 + 0.17x
The cone-shaped container for the echidna treats holds to 218 cubic centimeters of ants and has a radius of 4 cm. rounded to the nearest whole number, what is the height of the container? use 3.14 for pie symbol
Answer:
13 cm
Step-by-step explanation:
To find the answer, you can use the formula to calculate the volume of a cone and isolate the height:
V= πr^2[tex]\frac{h}{3}[/tex]
V= volume= 218 cubic centimeters
π= 3.14
r= radius= 4 cm
h=height
218= 3.14*4^2*[tex]\frac{h}{3}[/tex]
218*3=3.14*16*h
654=50.24*h
h=654/50.24
h=13
According to this, the height of the container is 13 cm.
