Answer:
The answer is: 325 517 424 395 494
Step-by-step explanation:
Domain and range of T
Answer:
Let's list out the points that belong to T. They are T{(-1, -4), (2, 2), (2, -3)}.
The domain is all of the x values. Therefore the domain is {-1, 2}.
The range is all of the y values. Therefore the range is {-4, -3, 2}.
We don't use ( ) or [ ] because T is a discrete relation.
what is the value of -x+ the absolute value of -y
Answer:
[tex]-x+| \: y\: |[/tex]
Step-by-step explanation:
[tex]-x+|-y|[/tex]
[tex]\mathrm{Apply\:absolute\:rule}: \left|-y\right|\:=| \: y\: |[/tex]
[tex]-x+| \: y\: |[/tex]
Nina had 17 marbles in a bag. Her mother put a handful of marbles in the bag. When Nina counts her marbles, she discovers she now has 34 of them. Which of the following equations will help Nina solve for the number of marbles, m, that her mom put in the bag? 17 + 34 = m 17 + m = 34 17m = 34 m − 17 = 34
Answer:
17+m=34
Step-by-step explanation:
Nina had 17 marbles in a bag + the x amount of marbles that her mom gives her.
so 17+x=34
(x is the variable that I chose however it could be any variable, so it would also mean the same thing as 17+m=34)
Hope this helped!
Answer:
17 + m = 34.
Step-by-step explanation:
Nina had 17 marbles;
Mother put a handful of marbles, let's say m.
Now Nina has 34 marbles.
34 marbles is [=] 17 marbles Nina had before + m from her mother.
17 + m = 34 will be the right equation.
17 + 34 = m — wrong;17 + m = 34 — right;17m = 34 — wrong;m - 17 = 34 — wrong.The Demon family owns a large grape vineyard in western New York along Lake Erie. The grapevines must be sprayed at the beginning of the growing season to protect against various insects. Two new insecticides have just been marketed: Pernod 5 and Action. To test their effectiveness, three long rows were selected and sprayed with Pernod 5, and three other were sprayed with Action. When the grape ripened, 400 of the vines treated with Pernod 5 and 400 of the vines treated with Action were checked for infestation. The number of infested vines treated with Pernod 5 and Action are 24 and 40 respectively.
At 0.05 significance level, can we conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action?
Answer:
At a significance level of 0.05, there is enough evidence to support the claim that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.
Then, the null and alternative hypothesis are:
H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0
The significance level is 0.05.
The sample 1 (Pernod 5), of size n1=400 has a proportion of p1=0.06.
[tex]p_1=X_1/n_1=24/400=0.06[/tex]
The sample 2, of size n2=400 has a proportion of p2=0.1.
[tex]p_2=X_2/n_2=40/400=0.1[/tex]
The difference between proportions is (p1-p2)=-0.04.
[tex]p_d=p_1-p_2=0.06-0.1=-0.04[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{24+40}{400+400}=\dfrac{64}{800}=0.08[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.08*0.92}{400}+\dfrac{0.08*0.92}{400}}\\\\\\s_{p1-p2}=\sqrt{0.000184+0.000184}=\sqrt{0.000368}=0.019[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.04-0}{0.019}=\dfrac{-0.04}{0.019}=-2.085[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]\text{P-value}=2\cdot P(z<-2.085)=0.037[/tex]
As the P-value (0.037) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.
An object of height 2.50cm is placed 20.0cm from a converging mirror of focal length 10.0cm. What are the height and the magnification of the image formed?
First find the distance it is reflected:
D = 20.0 x 10.0 /(20-10) = 200/10 = 20cm away.
Now calculate the magnification: -20/ 20 = -1
Now calculate the height:
-1 x 2.50 = -2.50
The negative sign means the image is inverted.
The mirrored image would be inverted, 2.50 cm tall and 20 cm in front of the mirror.
Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. Solve the original equation by solving the new equation
x2y'' + 9xy' - 20y = 0
Answer:
[tex]\boxed{\sf \ \ \ ax^2+bx^{-10} \ \ \ }[/tex]
Step-by-step explanation:
Hello,
let's follow the advise and proceed with the substitution
first estimate y'(x) and y''(x) in function of y'(t), y''(t) and t
[tex]x(t)=e^t\\\dfrac{dx}{dt}=e^t\\y'(t)=\dfrac{dy}{dt}=\dfrac{dy}{dx}\dfrac{dx}{dt}=e^ty'(x)<=>y'(x)=e^{-t}y'(t)\\y''(x)=\dfrac{d^2y}{dx^2}=\dfrac{d}{dx}(e^{-t}\dfrac{dy}{dt})=-e^{-t}\dfrac{dt}{dx}\dfrac{dy}{dt}+e^{-t}\dfrac{d}{dx}(\dfrac{dy}{dt})\\=-e^{-t}e^{-t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}\dfrac{dt}{dx}=-e^{-2t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}e^{-t}\\=e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt})[/tex]
Now we can substitute in the equation
[tex]x^2y''(x)+9xy'(x)-20y(x)=0\\<=> e^{2t}[ \ e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}) \ ] + 9e^t [ \ e^{-t}\dfrac{dy}{dt} \ ] -20y=0\\<=> \dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}+ 9\dfrac{dy}{dt}-20y=0\\<=> \dfrac{d^2y}{dt^2}+ 8\dfrac{dy}{dt}-20y=0\\[/tex]
so the new equation is
[tex]y''(t)+ 8y'(t)-20y(t)=0[/tex]
the auxiliary equation is
[tex]x^2+8x-20=0\\<=> x^2-2x+10x-20=0\\<=>x(x-2)+10(x-2)=0\\<=>(x+10)(x-2)=0\\<=> x=-10\text{ or }x=2[/tex]
so the solutions of the new equation are
[tex]y(t)=ae^{2t}+be^{-10t}[/tex]
with a and b real
as
[tex]x(t)=e^t\\<=> t(x)=ln(x)[/tex]
[tex]y(x)=ae^{2ln(x)}+be^{-10ln(x)}=ax^2+bx^{-10}[/tex]
hope this helps
do not hesitate if you have any questions
Question 1 of 16,
The area of a trapezoid is 189 cm . The height is 14 cm and the length of one of the parallel sides is 8 cm. Find the length of the second parallel side.
Answer:
19cm
Step-by-step explanation:
The area of a trapezoid [tex]=\dfrac12(a+b)h[/tex] (where a and b are the parallel sides).
Given:
Area = 189 Square cm
Height, h=14cm
a=8cm
We want to find the value of the other parallel side, b.
Substitution of the given values gives:
[tex]189=\dfrac12(8+b)14\\189=7(8+b)\\$Divide both sides by 7\\8+b=27\\Subtract 8 from both sides\\b+8-8=27-8\\b=19cm[/tex]
The length of the second parallel side is 19cm.
An appliance dealer sells three different models of upright freezers having 13.5, 15.9, and 19.1 cubic feet of storage. Let X = the amount of storage space purchased by the next customer to buy a freezer. Suppose that X has pmf:
Answer:
a) E(X) = 16.09 ft³
E(X²) = 262.22 ft⁶
Var(X) = 3.27 ft⁶
b) E(22X) = 354 dollars
c) Var(22X) = 1,581 dollars
d) E(X - 0.01X²) = 13.470 ft³
Step-by-step explanation:
The complete Correct Question is presented in the attached image to this solution.
a) Compute E(X), E(X2), and V(X).
The expected value of a probability distribution is given as
E(X) = Σxᵢpᵢ
xᵢ = Each variable in the distribution
pᵢ = Probability of each distribution
Σxᵢpᵢ = (13.5×0.20) + (15.9×0.59) + (19.1×0.21)
= 2.70 + 9.381 + 4.011
= 16.092 = 16.09 ft³
E(X²) = Σxᵢ²pᵢ
Σxᵢ²pᵢ = (13.5²×0.20) + (15.9²×0.59) + (19.1²×0.21)
= 36.45 + 149.1579 + 76.6101
= 262.218 = 262.22 ft⁶
Var(X) = Σxᵢ²pᵢ - μ²
where μ = E(X) = 16.092
Σxᵢ²pᵢ = E(X²) = 262.218
Var(X) = 262.218 - 16.092²
= 3.265536 = 3.27 ft⁶
b) E(22X) = 22E(X) = 22 × 16.092 = 354.024 = 354 dollars to the nearest whole number.
c) Var(22X) = 22² × Var(X) = 22² × 3.265536 = 1,580.519424 = 1,581 dollars
d) E(X - 0.01X²) = E(X) - 0.01E(X²)
= 16.092 - (0.01×262.218)
= 16.0926- 2.62218
= 13.46982 = 13.470 ft³
Hope this helps!!!
The FDA regulates that a fish that is consumed is allowed to contain at most 1 mg/kg of mercury. In Florida, bass fish were collected in 53 different lakes to measure the amount of mercury in the fish from each of the 53 lakes. Do the data provide enough evidence to show that the fish in all Florida lakes have different mercury than the allowable amount?
Required:
State the random variable, population parameter, and hypotheses.
Answer:
Yes. At a significance level of 0.05, there is enough evidence to support the claim that the fish in all Florida lakes have different mercury than the allowable amount.
The random variable is the sample mean amount of mercury in the bass fish from the lakes of Florida.
The population parameter is the mean amount of mercury in the bass fish of Florida lakes.
The alternative hypothesis (Ha) states that the amount of mercury significantly differs from 1 mg/kg.
The null hypothesis (H0) states that the amount of mercury is not significantly different from 1 mg/kg.
[tex]H_0: \mu=1\\\\H_a:\mu\neq 1[/tex]
Step-by-step explanation:
The question is incomplete.
There is no data provided.
We will work with a sample mean of 0.95 mg/kg and sample standard deviation of 0.15 mg/kg to show the procedure.
This is a hypothesis test for the population mean.
The claim is that the fish in all Florida lakes have different mercury than the allowable amount (1 mg of mercury per kg of fish).
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=1\\\\H_a:\mu\neq 1[/tex]
The significance level is assumed to be 0.05.
The sample has a size n=53.
The sample mean is M=0.95.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.15.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.15}{\sqrt{53}}=0.0206[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{0.95-1}{0.0206}=\dfrac{-0.05}{0.0206}=-2.427[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=53-1=52[/tex]
This test is a two-tailed test, with 52 degrees of freedom and t=-2.427, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t<-2.427)=0.019[/tex]
As the P-value (0.019) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to support the claim that the fish in all Florida lakes have different mercury than the allowable amount.
For each ordered pair, determine whether it is a solution to the system of equations. y=6x-7 9x-2y=8
Answer:
x = 2, y = 5
Step-by-step explanation:
Hello,
y=6x-7
9x-2y=8
can be written as
(1) 6x - y = 7
(2) 9x -2y = 8
(2)-2*(1) gives
9x -2y -12x +2y = 8 - 2*7 = 8 - 14 = -6
<=> -3x=-6
<=> x = 6/3=2
and we replace it in (1)
y = 6*2-7=12-7=5
hope this helps
The formula to convert Fahrenheit to Celsius is C - 5 (F - 32). Convert 30°C to
Fahrenheit. Round to the nearest degree.
A. 30°F
B. -1°F
C. 112°F
D. 86°F
Answer:
D. *6F
Step-by-step explanation:
C=(F-32)*5/9
30=(F-32)*5/9
F = (30*9)/5+32
F = 86
5c + 16.5 = 13.5 + 10c
Answer:
Hello!
________________________
5c + 16.5 = 13.5 + 10c
Exact Form: c = 3/5
Decimal Form: c = 0.6
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
Hope this helped you!
Answer:
3000+3d=noods
Step-by-step explanation:
What is the greatest common factor of 36 and 44?
Answer:
GCF - 4
Step-by-step explanation:
36 - 1, 2, 3, 4, 6, 9, 12, 18, 36
44 - 1, 2, 4, 11, 44
Hope this helps! :)
If x=3 then what is y the equation is 2x -y=5 if you have the answer lets d a t e I m f e m a l e. T a n g ie_man 18 snap without spaces.
Answer:
y = 1Step-by-step explanation:
Given the equation, 2x- y = 5, if x = 3, to get y we will simply substitute the value of x into the expression given as shown;
[tex]2x - y = 5\\\\Substituting \ x = 3\ into \ the \ equation\\\\2(3) - y = 5\\\\6 - y = 5\\\\subtracting\ 6\ from\ both\ sides\\\\6-6-y = 5- 6\\\\-y = -1\\\\multiplying\ both\ sides\ by \ -1\\-(-y) = -(-1)\\\\y = 1[/tex]
Hence, the value of y is 1
How do you write 0.0026 in scientific notation? ___× 10^____
Answer:
It's written as
[tex]2.6 \times {10}^{ - 3} [/tex]
Hope this helps you
Answer:
2.6 × 10⁻³
Step-by-step explanation:
To write a number in scientific notation, move the decimal to the right or left until you reach a number that is 1 or higher.
In the decimal 0.0026, the first number that is 1 or higher is 2.
0.0026 ⇒ 2.6
When trying to figure out the exponent, here are some things to keep in mind:
- when you move the decimal to the right, the exponent is negative
- when you move the decimal to the left, the exponent is positive
You moved the decimal to the right three places. So the exponent will be -3.
The result is 2.6 × 10⁻³.
Hope this helps. :)
Express it in slope-Intercept form
Answer:
Y=1/4x-4
Explanation: The y intercept is -4 that is your B. Using the rise over sun method the line rises 1 and goes to the right 4 making the slope 1/4 or .25
help asapppp....thanks
Answer:
a) -8x^3 + x^2 + 6x
b)16x^2 -9
c) 24x^4 + 37x^3 +13x^2 -18x
Step-by-step explanation:
a) distribute -2x to x and 4x^2 then do the same for the other part and then add the ones w the same exponent.
b) do foil ( multiply first outside inside last) which will be 4x times 4x then 4x times 3 then -3 times 4x and 3 times -3. add like exponents
c) do the same as above
The average daily rainfall for the past week in the town of Hope Cove is normally distributed, with a mean rainfall of 2.1 inches and a standard deviation of 0.2 inches. If the distribution is normal, what percent of data lies between 1.9 inches and 2.3 inches of rainfall? a) 95% b) 99.7% c) 34% d) 68%
Answer:
D
Step-by-step explanation:
We calculate the z-score for each
Mathematically;
z-score = (x-mean)/SD
z1 = (1.9-2.1)/0.2 = -1
z2 = (2.3-2.1)/0.2 = 1
So the proportion we want to calculate is;
P(-1<x<1)
We use the standard score table for this ;
P(-1<x<1) = P(x<1) -P(x<-1) = 0.68269 which is approximately 68%
Answer:
68
Step-by-step explanation:
The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1100 miles. What warranty should the company use if they want 96% of the tires to outlast the warranty? Round the answer to the nearest whole number
Answer:
61,925 miles
Step-by-step explanation:
Given :
The p-value of the tires to outlast the were warranty were given in the the question as = 0.96
Checking the normal distribution table, The probability that corresponds to 0.96
from the Normal distribution table is 1.75.
Mean : 'μ'= 60000 miles
Standard deviation : σ=1100
The formula for z-score is given by
: z= (x-μ)/σ
1.75=(x-60000)/1100
1925=x-60000
x=61925
Therefore, the tread life of tire should be 61,925 miles if they want 96% of the tires to outlast the warranty.
Follow the properties of the equality given for the steps to solve the following equation:
-3(x-4)+5=-x-3
(answers and steps in photo)
Answer:
Step-by-step explanation:
-3x+12+5= -x-3 -3x+17 = -x-317 = 2x-320 =2xx=10In her backyard, Mary is planting rows of tomatoes. To plant a row of tomatoes, mary needs 20/13 square feet. There are 40 square feet in Mary's backyard, so how many rows of tomatoes can mary plant??
Answer:
26 rows
Step-by-step explanation:
[tex]number \: of \: rows \\ = \frac{40}{ \frac{20}{13} } \\ \\ = \frac{40 \times 13}{20} \\ \\ = 2 \times 13 \\ \\ = 26 \: [/tex]
A man is twice the age of his son,in 20 years time, the son's age will be 2/3 of that his father. what is the son's present age?
Answer:
20 years old.
Step-by-step explanation:
Let us say that the man's age is represented by x and the son's age is represented by y.
As of now, x = 2y.
In 20 years, both ages will increase by 20. We can have an equation where the son's age increased by 20 equals 2/3 of the man's age plus 20.
(y + 20) = 2/3(x + 20)
Since x = 2y...
y + 20 = 2/3(2y + 20)
3/2y + 30 = 2y + 20
2y + 20 = 3/2y + 30
1/2y = 10
y = 20
To check our work, the man's age is currently double his son's, so the man is 40 and the son is 20. In 20 years, the man will be 60 and the son will be 40. 40 / 60 = 2/3, so the son's age is 2/3 of his father's.
So, the son's present age is 20 years old.
Hope this helps!
Find a solution to the linear equation y=12x−24
Answer:
I didn't know which one you wanted...
Step-by-step explanation:
1. Finding the x an y-intercepts
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s): (2,0)
y-intercept(s): (0,−24)
2. Finding the slope and y-intercept
Use the slope-intercept form to find the slope and y-intercept.
Slope: 12
y-intercept: −24
When graphing any equation what is a great fall back plan if you can't remember the learned procedure? (on all kinds of equations - some with x squared, x cubed etc)
Answer:
GOOGLE :)
equation:
y=mx+b
m= slope (how steep the line is(negative is \ positive is /))
b= y intercept (where it is on the vertical line(up and down line))
step by step
1. locate y intercept and plotthe point
2.from that point use slop to find second point and plot
Find the volume of the region between the planes x plus y plus 2 z equals 2 and 4 x plus 4 y plus z equals 8 in the first octant.
Find the intercepts for both planes.
Plane 1, x + y + 2z = 2:
[tex]y=z=0\implies x=2\implies (2,0,0)[/tex]
[tex]x=z=0\implies y=2\implies(0,2,0)[/tex]
[tex]x=y=0\implies 2z=2\implies z=1\implies(0,0,1)[/tex]
Plane 2, 4x + 4y + z = 8:
[tex]y=z=0\implies4x=8\implies x=2\implies(2,0,0)[/tex]
[tex]x=z=0\implies4y=8\impliesy=2\implies(0,2,0)[/tex]
[tex]x=y=0\implies z=8\implies(0,0,8)[/tex]
Both planes share the same x- and y-intercepts, but the second plane's z-intercept is higher, so Plane 2 acts as the roof of the bounded region.
Meanwhile, in the (x, y)-plane where z = 0, we see the bounded region projects down to the triangle in the first quadrant with legs x = 0, y = 0, and x + y = 2, or y = 2 - x.
So the volume of the region is
[tex]\displaystyle\int_0^2\int_0^{2-x}\int_{\frac{2-x-y}2}^{8-4x-4y}\mathrm dz\,\mathrm dy\,\mathrm dx=\displaystyle\int_0^2\int_0^{2-x}\left(8-4x-4y-\frac{2-x-y}2\right)\,\mathrm dy\,\mathrm dx[/tex]
[tex]=\displaystyle\int_0^2\int_0^{2-x}\left(7-\frac72(x+y)\right)\,\mathrm dy\,\mathrm dx=\int_0^2\left(7(2-x)-\frac72x(2-x)-\frac74(2-x)^2\right)\,\mathrm dx[/tex]
[tex]=\displaystyle\int_0^2\left(7-7x+\frac74 x^2\right)\,\mathrm dx=\boxed{\frac{14}3}[/tex]
Find the length of KC
Answer:
54
give me brainliest please please please and follow my page
Step-by-step explanation:
To find length of KC...we need to find the length of HM and MU first ...
so....HM= 96- 78 = 14
JU = 96 + HM = 96 + 14 = 110
....
KU = 110 - JK = 110 - 82 = 28
....
UN = 105+ 82 -( 96 + 14 )
187 - 110
= 77
UC = 77 - 51 = 26
KC = UC + KU = 26 + 28 = 54
The length of [tex]\overline{KC}[/tex] along line [tex]\overline{JN}[/tex] is given as 54 (Option A) See the computation below.
How do you compute the length of [tex]\overline{KC}[/tex]?To determine the length of [tex]\overline{KC}[/tex], the length of [tex]\overline{HM}[/tex] and [tex]\overline{MU}[/tex]must first be derived.
[tex]\overline{HM}[/tex] = 96 - 78
[tex]\overline{HM}[/tex] = 14
[tex]\overline{JU}[/tex] = 96 + [tex]\overline{HM}[/tex]
= 96 + 14
[tex]\overline{JU}[/tex]= 110
[tex]\overline{KU}[/tex] = 110 - [tex]\overline{JK}[/tex]
= 110 - 82
[tex]\overline{KU}[/tex]= 28
[tex]\overline{UN}[/tex] = 105+ 82 -( 96 + 14 )
=187 - 110
[tex]\overline{UN}[/tex]= 77
[tex]\overline{UC}[/tex] = 77 - 51
[tex]\overline{UC}[/tex]= 26
Thus,
[tex]\overline{KC}[/tex] = [tex]\overline{UC}[/tex] + [tex]\overline{KU}[/tex]
[tex]\overline{KC}[/tex]= 26 + 28
[tex]\overline{KC}[/tex]= 54
Learn more about computing length of lines at:
https://brainly.com/question/1597347
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The graph of y =ex is transformed as shown in the graph below. Which equation represents the transformed function?
Answer:
B. e^x+3
Step-by-step explanation:
Y=e^x
the graph is moving 3 units up
y= y+3
y=e^x+3
answer = y=e^x+3
Answer: B
Step-by-step explanation:
You want to put a 2 inch thick layer of topsoil for a new 14 ft by 26 ft garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order? The store only sells in increments of 1/4 cubic yards.
Answer:
2 1/4
Step-by-step explanation:
The volume of soil needed is ...
(14/3 yd)(26/3 yd)(2/36 yd) = 728/324 yd³ = 2.247 yd³
The nearest higher quarter-yard is 2.250 yd³. That's how much you need to order.
You need to order 2 1/4 cubic yards.
___
There are 3 ft or 36 inches to a yard.
can someone help me with this please?!?
Answer:
The answer is 60cm^2.
hope it helps..
George has opened a new store and he is monitoring its success closely. He has found that this store’s revenue each month can be modeled by r(x)=x2+5x+14 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars. He has also found that his expenses each month can be modeled by c(x)=x2−3x+4 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars. What does (r−c)(3) mean about George's new store?
This is a great question!
When we are given ( r - c )( 3 ), we are being asked to take 3 as x in the functions r( x ) and c( x ), taking the difference of each afterwards -
[tex]r( 3 ) = ( 3 )^2 + 5( 3 ) + 14,\\x( 3 ) = ( 3 )^2 - 3( 3 ) + 4[/tex]
____
Let us calculate the value of each function, determine their difference, and multiply by 100, considering r( x ) and c( x ) are measured in hundreds of dollars,
[tex]r( 3 ) = 9 + 15 + 14 = 38,\\x( 3 ) = 9 - 9 + 4 = 0 + 4 = 4\\----------------\\( r - c )( 3 ) = 38 - 4 = 34,\\34 * 100 = 3,400( dollars )\\\\Solution = 3,400( dollars )[/tex]
Therefore, ( r - c )( 3 ) " means " that George's new store will have a profit of $3,400 after it's third month in business, given the following options,
( 1. The new store will have a profit of $3400 after its third month in business.
( 2. The new store will have a profit of $2400 after its third month in business.
( 3. The new store will sell 2400 items in its third month in business.
( 4. The new store will sell 3400 items in its third month in business.
The required answer is , [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.
Substitution:The substitution method is the algebraic method to solve simultaneous linear equations.
Given function is,
[tex]r(x) = x^2+5x+14[/tex]...(1)
And [tex]c(x) = x^2-4x+5[/tex]...(2)
Now, substituting the value into the equation (1) and (2).
[tex]r(5) = (5)^2+5(5)+14=64[/tex]
[tex]c(5) = (5)^2-4(5)+5=10[/tex]
Therefore,
[tex](r-c)(5)=r(5)-c(5)\\=64-10\\=54[/tex]
Now, [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.
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