a) The type of function for each case is given as follows:
House 1: Exponential.House 2: Linear.b) The functions for each house are given as follows:
House 1: 294580(1.03)^x.House 2: 295000 + 9000x.c) The value of each house after 25 years is given as follows:
House 1: $616,785.10.House 2: $520,000.There is a significant difference in these valuations, as an exponential function increases faster than a linear function.
How to classify the functions?A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.
Hence House 1 is an exponential function, as:
312519.92/303417.40 = 303417.40/294580 = 1.03.
And the definition is given as follows:
294580(1.03)^x.
The value of the house after 25 years is given as follows:
294580(1.03)^25 = $616,785.10.
A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.
Hence House 2 is a linear function, as each year, the value of the house is increased by 9000.
Then the definition is given as follows;
295000 + 9000x.
The value of the house after 25 years is given as follows:
295000 + 9000(25) = $520,000.
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Answer:
One-third of the volume
Step-by-step explanation:
Volume of cylinder = πr²h
Volume of cone = (1/3)πr²h
A ball is thrown directly upward from a height of 5 ft with an initial velocity of 24 ft/sec. The function s(t) = -16t^2+24t+5 gives the height of the ball, in feet, t seconds after it has been thrown. Determine the time at which the ball reaches its maximum height and find the maximum height.
Answer:
The maximum height is 14 feet and it will take 0.75 s to reach there.
Step-by-step explanation:
A ball is thrown directly upward from a height of 5 ft with an initial velocity of 24 ft/sec.
The function is :
[tex]s(t) = -16t^2+24t+5[/tex] ....(1)
It gives the height of the ball, in feet, t seconds after it has been thrown.
For maximum height,
s'(t) = 0
So,
-32t+24 = 0
t = 0.75 s
It will take 0.75 s to reach the maximum height.
Put t = 0.75 s in equation (1). So,
[tex]s(0.75) = -16(0.75)^2+24(0.75)+5\\\\s=14\ feet[/tex]
So, the maximum height is 14 feet and it will take 0.75 s to reach there.
?? Anyone know what the answer to this is
9514 1404 393
Answer:
(d) 7
Step-by-step explanation:
Put the number where x is and do the arithmetic.
f(2) = 2(2²) -2 +1 = 2(4) -2 +1 = 8 -2 +1 = 6 +1
f(2) = 7
Use a calculator to approximate to expression to the nearest thousandth.
log, 3.8
Answer:
#3 1.92599941856
Step-by-step explanation:
Ann took a taxi home from the airport. The taxi fare was $2.10 per mile, and she gave the driver a tip of
$5. Ann paid a total of $49.10.
Answer:
Ann went 21 miles in the taxi
Step-by-step explanation:
quinn is playing in a trivia competition he earns 50 points for each correct response c he loses 25 points for each wrong response w. which expression represents Quinn's total points in the trivia competition
Answer:
50c – 25w
Step-by-step explanation:
Find the measure of angle B.
Step-by-step explanation:
C = 180 - 112 = 68°
A = 180 - 68 - 51 = 61°
B = 180 - 61 = 119°
Another way :
We know that B = C + 51 ==> B = 68 + 51 = 119°
Two chemical companies can supply a raw material. The concentration of a particular element in this material is important. The mean concentration for both suppliers is the same, but you suspect that the variability in concentration may differ for the two companies. The standard deviation of concentration in a random sample of
n1=10
batches produced by company 1 is
s1=4.7
grams per liter, and for company 2, a random sample of
n2=16
batches yields
s2=5.8
grams per liter. Is there sufficient evidence to conclude that the two population variances differ? Use α = 0.05.
Answer:
As the calculated F lies in the acceptance region therefore we conclude that there is not sufficient evidence to support the claim that the variability in concentration may differ for the two companies. Hence Ha is rejected and H0 is accepted.
Step-by-step explanation:
As we suspect the variability of concentration F - test is applied.
n1=10 s1=4.7
n2=16 s2=5.8
And α = 0.05.
The null and alternate hypothesis are
H0: σ₁²=σ₂² Ha: σ₁²≠σ₂²
The null hypothesis is the variability in concentration does not differ for the two companies.
against the claim
the variability in concentration may differ for the two companies
The critical region F∝(υ1,υ2) = F(0.025)9,15= 3.12
and 1/F∝(υ1,υ2) = 1/3.77= 0.26533
where υ1= n1-1= 10-1= 9 and υ2= n2-1= 16-1= 15
Test Statistic
F = s₁²/s₂²
F= 4.7²/5.8²=0.6566
Conclusion :
As the calculated F lies in the acceptance region therefore we conclude that there is not sufficient evidence to support the claim that the variability in concentration may differ for the two companies. Hence Ha is rejected and H0 is accepted.
Hauls Vegetable Market has the folloeing vegetables for sale.
Carrots cost 3.50$ per pound
Cucumbers cost 0.69$ per pound
Squash cost 2$ per pound
What will be the ckst for 2 1/2 pounds of carrots and 3/4 pound of squash cost
Answer:
The cost of 2 1/2 pounds of carrots and 3/4 pound of squash is $ 10.25.
Step-by-step explanation:
Since Hauls Vegetable Market sells carrots that cost $ 3.50 per pound, cucumbers that cost $ 0.69 per pound, and squash that cost $ 2 per pound, to determine what will be the cost for 2 1/2 pounds of carrots and 3/4 pound. of squash the following calculation must be performed:
1/2 = 0.5
3/4 = 0.75
Carrots: 3.50 x 2.5 = 8.75
Squash: 2 x 0.75 = 1.50
8.75 + 1.50 = 10.25
Thus, the cost of 2 1/2 pounds of carrots and 3/4 pound of squash is $ 10.25.
A representative sample of 50 students from a high school is surveyed. Each student is asked what science class he or she
is taking
This table shows the responses.
Science Class
Physics
Chemistry
Blology
Earth Science
Health Science
Number of
Students
6
10
18
4
12
Select all of the statements that are valid based on the survey results..
The statements that are valid based on the survey results are:
About 20% of the students are taking chemistry.
About twice as many students are taking health science than are taking physics.
For every 150 students we could predict that at least 18 of the students are taking physics.
Option A, B, and C are correct answer.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
About 20% of the students are taking chemistry:
To calculate the percentage of students taking chemistry, we divide the number of students taking chemistry by the total number of students surveyed and multiply by 100:
10/50 x 100% = 20%
Therefore, the statement "About 20% of the students are taking chemistry" is valid based on the survey results.
About twice as many students are taking health science than are taking physics:
The number of students taking health science is 12, and the number of students taking physics is 6. To see if twice as many students are taking health science than physics, we can compare the ratios:
Health science : Physics = 12 : 6 = 2 : 1
Since the ratio is 2:1, we can conclude that the statement "About twice as many students are taking health science than are taking physics" is valid based on the survey results.
For every 150 students, we could predict that at least 18 of the students are taking physics:
To make this prediction, we need to calculate the proportion of students taking physics based on the survey results:
6/50 = 0.12
To predict how many students are taking physics in a larger population, we can multiply the proportion by the size of the population:
0.12 x 150 = 18
Therefore, the statement "For every 150 students we could predict that at least 18 of the students are taking physics" is valid based on the survey results.
For every 25 students, we could predict that at least 4 of the students are taking Earth Science:
To make this prediction, we need to calculate the proportion of students taking Earth Science based on the survey results:
4/50 = 0.08
To predict how many students are taking Earth Science in a larger population, we can multiply the proportion by the size of the population:
0.08 x 25 = 2
Therefore, the statement "For every 25 students we could predict that at least 4 of the students are taking Earth Science" is not valid based on the survey results, as we would predict that at least 2 students are taking Earth Science, not 4.
Therefore,
The statements that are valid based on the survey results are:
About 20% of the students are taking chemistry.
About twice as many students are taking health science than are taking physics.
For every 150 students we could predict that at least 18 of the students are taking physics.
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Identify the need coordinates of the line segment M (10,5) and N (5,5) when it is rotated about 270 degrees clockwise
Answer:
280? srry if i wrong
Step-by-step explanation:
5. A bag contains 21 red marbles and 29 blue marbles. A marble is picked at
random from the bag. What is the probability of picking a red marble?
Answer:
i dont know
Step-by-step explanation:
uhhh
Answer:
42% chance
Step-by-step explanation:
Since there are 21 red marbles and 29 blues ones, the total amount of marbles is 50. There are only 21 red marbles out of 50 marbles so there is a 21/50 chance that you will pick a red marble.
Melody buys a pair of jeans that is priced at $14.95 before tax. (Tax rate is 8.95%). Is the final amount cheaper or more expensive than the original price?
Whoever answers correctly will get Brainliest!
Have an amazing day!! :)))
Answer:
More expensive
Step-by-step explanation:
The price will be about 16.29.
Pretty face cosmetics earned $(1.26 x 10^6) in sales last year. write this number in standard form
Answer:
1,260,000
Explanation:
Using the calculator on any Windows computer, first put "1.26" in. After doing so, press the "exp" button that should be there if you're using the calculator on a Windows computer. After pressing that, put in "6", then press equals. After doing it correctly, you should get this answer.
Which list shows the numbers NOT in order from least to greatest?
4.036 < 4.08 < 42<4.201
3.09 < 3.1 < 3.507 < 3.9
6.4 < 6.51 < 6.387 < 6.995
7.315 < 7.38 < 7.406 < 7.5
PAST DUE DATE NEED DONE NOW! NO LINKS! HELP ME FIND THE EQUATION
To write an equation for this line, you first need to understand how to derive it.
Let's utilize slope-intercept form, as it's the easiest to understand compared to any other form for line functions:
y = mx + b
m: The slope of the line
b: The y-intercept (The point where the line is at the y-axis)
Now that we've defined our variables, how do we go about making the actual equation? Let's start off with the slope, m.
The slope is a measure of how high or low the line is. The number is a ratio between the rise and run of a slope. In other words, it is essentially [tex]\frac{rise}{run}[/tex]
Let's look back at the graph. In the time interval from 1 to 2 seconds, we see that the line rises by 22 feet. Because the time interval is only 1 second, the run is 1 second.
Therefore:
m = [tex]\frac{rise}{run}[/tex]
m = [tex]\frac{22}{1}[/tex]
m = 22
We now have the first variable of the equation.
y = 22x + b
What about b? As we established earlier, b is the value of coordinate y at the y-intercept. Essentially, to find b we need to know what the value of y is when the coordinate x is 0.
As you can see from the graph you made, the value of y when x is 0 is also 0. This makes sense, too. How can the cheetah travel distance at 0 seconds when it obviously hasn't started moving? We now know b = 0. Now, we have gotten all of the variables we need to make a full equation:
y = 22x + 0
y = 22x
If you'd like me to explain how I did anything, just ask!
- breezyツ
Answer:
Equation: y=22x + 0 (you can put 0 if you want)
Step-by-step explanation:
Okay, so this is set up as a y=mx+b equation meaning that m=rate of change and b=y-intercept. If a cheetah runs 22 feet per second which is x, that means that m=22. And if 1 second is equal to 22 feet then in 0 seconds they run 0 feet, which is your y-intercept. Another way to find the rate of change (m) is by using the equation y2-y1/x2-x1 or 44-22/1 in this case. This equation is usually written as y=22x. Hope this helps!
The sum of two numbers is -45. The difis -89. Find the numbers larger and smaller
Answer:
22,-89
Step-by-step explanation:
let the numbers be x and y .
x+y=-45
x-y=-89
add
2x=--134
x=-67
-67+y=-45
y=-45+67=22
B= R/E - T, solve for E
mhairi invest 1000 for 5 years at 4% compound interest p.a calculate how much interest she has gained over the 5 years
Answer:
Step-by-step explanation:
$1000×1.04⁵ ≅ $1216.65
interest ≅ $216.65
A scale drawing of an NFL god post uses a
scale of 2 inches = 5 feet. If the actual width
of the goal post is 182 feet, what is the width
of the goal post on the drawing?
Need the answer for x and y
Answer:
How many molecules of water are there in 10 lbs of water?
Step-by-step explanation:
Answer:
x = 15
AC = 95
Step-by-step explanation:
6x + 5 = 8x - 25
combine like terms:
2x = 30
x = 15
AC = 95
PLEASE HELP!!! I GIVE 15 POINTS!
Flaws in a carpet tend to occur randomly and independently at a rate of one every 260 square feet. What is the probability that a carpet that is 7 feet by 14 feet contains no flaws?
Probability =
Enter your answer in terms of e.
Answer:
The probability that a carpet that is 7 feet by 14 feet contains no flaws is 99.996%.
Step-by-step explanation:
Given that flaws in a carpet tend to occur randomly and independently at a rate of one every 260 square feet, to determine what is the probability that a carpet that is 7 feet by 14 feet contains no flaws, the following calculation must be performed:
7 x 14 = 98
1/260 = 0.003
98 = 100
0.003 = X
0.003 x 100/98 = X
0.0039 = X
100 - 0.0039 = 99.996
Thus, the probability that a carpet that is 7 feet by 14 feet contains no flaws is 99.996%.
Please help thank you
Answer:
x = 140
Step-by-step explanation:
Using the exterior angle rule ( an exterior angle of a triangle is equal to the opposite interior angles of a triangle )
x is the interior angle and the given angles ( 50 and 90 ) are the opposite interior angles
So
x = 50 + 90
50 + 90 = 140
x = 140
Note: there is a right angle ( indicated by the little square. A right angle has a measure of 90 degrees so that's where the 90 came from)
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Answer: C) 1/a^12•b^8
Step-by-step explanation:
When the length of each edge of a cube is increased by 1 cm, the volume is increased by 37 cm3.
What is the length (in centimeters) of each edge of the original cube?
original length =3cm
Answer:
solution given;
let length be x
its
volume be x ³
we have when length is increased by 1cm volume increased by 37cm³ so
(x+1)³=x³+37cm³
x³+1³+3x²+3x=x³+37
3x²+3x-36=0
3(x²+x-12)=0
x²+4x-3x-12=0
x(x+4)-3(x+4)=0
(x+4)(x-3)=0
either
x=-4 rejected
or
x=3cm
The length (in centimeters) of each edge of the original cube will be 3.
How do you calculate the volume of a cube?Assume the side length of the cube under consideration is L units. The volume of the cube is then equal to L³ cubic units.
We have when length is increased by 1 cm volume increased by 37 cm³, so from the given condition the equation formed as;
(L+1)³=L³+37 cm³
Open the bracket and apply the necessary identities;
L³+1³+3L²+3L=L³+37
3L²+3L-36=0
3(x²+x-12)=0
Applying the factorization method;
L²+4L-3L-12=0
L(L+4)-3(L+4)=0
(L+4)(L-3)=0
L=-4 cm (Negative length is not possible.)
L=3cm
Hence,the length (in centimeters) of each edge of the original cube will be 3.
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What is 4 1/7 in simplest form ??
Answer:28
Step-by-step explanation:
Answer:
29/7 or in decimal form: 4.1428...
wyoming electric coop owns a steam-turbine power-generating plant. because wyoming is rich in coal deposits, the plant generates its steam from coal. this, however, may result in emission that does not meet the environmental protection agency (epa) standards. epa regulations limit sulfur dioxide discharge to 2000 parts per million per ton of cual burned and smoke discharge from the plant stacks to 20 ib per hour. the coop receives two grades of pulverized coal, c1 and c2, for use in the steam plant. the two grades are usually mixed together before burning. for simplicity, it can be assumed that the amount of sulfur pollutant discharged (in parts per million) is a weighted average of the proportion of each grade used in the mixture. the following data is based on the consumption of 1 ton per hr of each of the two coal grades. sulfur discharge smoke discharge steam generated coal grade in parts per million in ih per hour in ib per hour cl 1800 2.1 12,000 c2 2100 3 9,000 (a) determine the optimal ratio for mixing the two coal grades. (b) determine the effect of relaxing the smoke discharge limit by 1 ib on the amount of generated steam ner hour.
What are a and b when you write √-16 in the form a+bi, when a and b are real number?
A) a=0, b=-4
B) a=0, b=4
C) a=-4, b=0
D) a=4, b=0
On comparing, we get {a} = 0 and {b} = 4.
What is the general form of a complex number?The general form of a complex number is -
z = a + ib
Given is the number as -
√-16
We can write the number √-16 in the form of (a + ib) as follows. We have -
√-16
√(- 1 x 16)
√(i² x 16)
√i² x √16
i√16
0 + i√16
0 + 4i
Therefore, on comparing, we get {a} = 0 and {b} = 4.
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3 by 5 ratio 8 by 9
Answer:
5:24
Step-by-step explanation:
Given data
3 by 5
=3*5
=15
8 by 9
=8*9
=72
Hence the ratio is
15:72
Equivalent to
5:24
PLEASE HELP ACED + +++++++++