Answer:
The domain for this function is [tex]c > 0[/tex] where [tex]c \in Z[/tex].Step-by-step explanation:
The given function is
[tex]f(c)=7c[/tex]
Where [tex]c[/tex] represents cars. This function models the profits they make.
Now, as you can deduct already, we can define to different domains, the mathematical one and the reasonable one.
The reasonable domain is about all the useful values to the problem. For example, as we are talking about car, they can't wash -5 cars, so negative numbers are excluded. Similarly, they can't wash 6.75 cars, because that would imply an incomplete job.
Therefore, the domain for this function is [tex]c > 0[/tex] where [tex]c \in Z[/tex].
(Notice that we specify that the independent valur can only use whole positive numbers only).
According to the National Institute on Alcohol Abuse and Alcoholism (NIAAA), and the National Institutes of Health (NIH), 41% of college students nationwide engage in "binge drinking" behavior, having five or more drinks on one occasion during the past two weeks. A college president wonders if the proportion of students enrolled at her college that binge drink is lower than the national proportion. In a commissioned study, 462 students are selected randomly from a list of all students enrolled at the college. Of these, 162 admitted to having engaged in binge drinking.
Required:
Using the most conservative estimate, what sample size would be required to reduce the margin of error to 2 percentage points?
Answer:
The sample size required is 2188.
Step-by-step explanation:
The (1 - α)% confidence interval for the population proportion is:
[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The margin of error for this interval is:
[tex]MOE= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The information provided is:
X = 162
n = 462
MOE = 0.02
Assume the confidence level as 95%.
Compute the sample proportion as follows:
[tex]\hat p=\frac{X}{n}=\frac{162}{462}=0.351[/tex]
The z-critical value for 95% confidence interval is:
[tex]z_{0.025}=1.96[/tex]
Compute the sample size required as follows:
[tex]MOE= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]n=[\frac{z_{\alpha/2}\times \sqrt{\hat p(1-\hat p)}}{MOE}]^{2}[/tex]
[tex]=[\frac{1.96\times\sqrt{0.351(1-0.351)}}{0.02}]^{2}\\\\=2187.781596\\\\\approx 2188[/tex]
Thus, the sample size required is 2188.
Which statement is true about the Internet connection cost?
It costs $5 per hour to connect to the Internet at the gaming store,
The first half hour is free, and then it costs $5 per minute to connect to the Internet,
It costs $10 for each 90 minutes spent connected to the Internet at the gaming store,
Any amount of time over an hour and a half would cost $10,
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The question is incomplete:
The function f(t) represents the cost to connect to the Internet at an online gaming store. It is a function of t, the time in minutes spent on the Internet. The function f(t) is attached.
Which statement is true about the Internet connection cost?
It costs $5 per hour to connect to the Internet at the gaming store,
The first half hour is free, and then it costs $5 per minute to connect to the Internet,
It costs $10 for each 90 minutes spent connected to the Internet at the gaming store,
Any amount of time over an hour and a half would cost $10,
Answer:
Any amount of time over an hour and a half would cost $10.
Step-by-step explanation:
-It costs $5 per hour to connect to the Internet at the gaming store. False, if you connect between 31 and 90 minutes it costs $5 but it is not a per hour cost.
-The first half hour is free, and then it costs $5 per minute to connect to the Internet. False, the first half hour is free and it costs $5 when you spent connected more than 30 minutes and less or equal 90 minutes.
-It costs $10 for each 90 minutes spent connected to the Internet at the gaming store. False, according to the function 90 minutes cost $5 and if you spend more than 90 minutes, it costs $10.
-Any amount of time over an hour and a half would cost $10. True. An hour and a half is equal to 90 minutes and according to the function, if you spent more than 90 minutes connected, it costs $10.
According to this, the statement that is true about the Internet connection cost is: Any amount of time over an hour and a half would cost $10.
Answer:
C
Step-by-step explanation:
Your swimming pool containing 65,000 gal of water has been contaminated by 7 kg of a nontoxic dye that leaves a swimmer's skin an unattractive green. The pool's filtering system can take water from the pool, remove the dye, and return the water to the pool at a flow rate of 200 gal/min. Assume that the dye is uniformly distributed throughout the pool.
(a) What is the initial value problem for the filtering process?
(b) You have invited several dozen friends to a pool party that is scheduled to begin in 4 h. You have determined that the effect of the dye is imperceptible if its concentration is less than 0.03 g/gal. Is your filtering system capable of reducing the dye
concentration to this level within 4 h?
Answer:
a) [tex]a(t)=7e^{\frac{-t}{325} }[/tex]
b) it is noticeable
Step-by-step explanation:
a) Let a(t) be the amount of die at time t. a is in kg and t is in minutes. Therefore:
[tex]\frac{da}{dt} =\frac{-a(t)}{65000}*\frac{200gal}{1 min}=\frac{-a}{325}\\\frac{da}{a} =\frac{-1}{325} dt\\\int\limits{\frac{1}{a} } \, da =\int\limits{\frac{-1}{325} } \, dt\\ln(a)=\frac{-1}{325} t+c\\a=ce^{\frac{-t}{325} }\\at\ t=0, a=7\\ 7=ce^0\\c=7\\a(t)=7e^{\frac{-t}{325} }[/tex]
b) 4 hrs = (4 * 60) min = 240 min
[tex]a(t)=7e^{\frac{-t}{325} }\\a(240)=7e^\frac{-240}{325} = 3.345kg[/tex]
3.345 kg = (3.345 * 1000 / 60000) g/gal = 0.0557 g/gal
0.0557 g/gal > 0.03 g/gal, therefore it is noticeable
Un equipo de fútbol se conforma de cuatro líneas de jugadores: portero (9%), defensas (37%), medios (27%) y delanteros (27%), donde los goles anotados por el equipo en cada línea son: portero 1 gol, defensas 11 goles, medios 15 goles y delanteros 23. Supongamos que en un partido se gana por un gol. ¿Qué probabilidad hay de que este fuera anotado (a) por la defensa, (b) por los medios y (c) por los delanteros?
Answer:
According to the proble, the total number of goals are 1+11+15+23 = 50: 1 by the goalkeeper, 11 by defense, 15 by midfielders and 23 by strikers.
So, each probability can be found by using standard probabilities
[tex]P=\frac{events}{total outcomes}[/tex]
(a) Defense[tex]P=\frac{11}{50} \approx 0.22[/tex]
Therefore, the defense has a probability of 22% of score that goal.
(b) Midfielders[tex]P=\frac{15}{50} \approx 0.30[/tex]
Therefore, midfielders have a probability of 30% of scoring that goal.
(c) Strikers.[tex]P=\frac{23}{50} \approx 0.46[/tex]
Therefore, strikers have a probability of 46% of scoring that goal.
Para resolver correctamente el ejercicio debemos tener en cuenta el numero de casos favorables sobre el numero total de casos posibles; el numero de casos favorables corresponde a la proporción de goles por cada linea,lo que quiere decir que son el numero de goles por cada linea según los datos que da el ejercicio.
El numero total de casos posibles corresponde al valor total de los goles por todo el equipo (1+11+15+23=50)
Ahora para calcular las probabilidades debemos hacer lo siguiente:
Para hallar la probabilidad de que fuera anotado un gol por la defensa debemos dividir el numero de goles posibles sobre el total de casos posibles;P=[tex]\frac{11}{50}[/tex] =0.22 ×100=22%; ( la probabilidad de que anoten un gol las defensas es del 22%.
Para hallar la probabilidad de que fuera anotado por los medios debemos dividir el numero de goles posibles sobre el total de casos posibles;P=[tex]\frac{15}{50}[/tex]=0.3 ×100=30% (La probabilidad de que anoten un gol los medios es del 30%
Para hallar la probabilidad de que fuera anotado por los delanteros debemos dividir el numero de goles posibles sobre el total de casos posibles;P=[tex]\frac{23}{50}[/tex]=0.46×100=46%; (La probabilidad de que anoten un gol los delanteros es del 46%)
Como conclusión podemos decir que hay una mayor probabilidad de que los delanteros puedan anotar ese único gol que les permita ganar el partido pues el numero de casos posibles es mayor comparado con las otras lineas del equipo.
Si deseas mas información sobre el tema de las probabilidades puedes dirigirte a este enlace;
https://brainly.com/question/18455475
The table represents the number of milkshakes sold by a restaurant since they were added to the menu.
Time (months) Milkshakes sold
1 259
4 380
7 501
10 622
13 744
Which graph best represents the relationship between time and the number of milkshakes sold?
Answer: the answer to this is A
Answer:A
Step-by-step explanation:
Simple. You'll find the function itself as proportional, and not exponential.
Select all that apply
Answer:
The answer to this is both (3,0) and (0,-3). C and B
Step-by-step explanation:
This is because the points in which these two graphs meet is the solution of equations.
Please mark me Brainliest!
6, 12, 18 and 24 are the first four multiples of 6.
What are the next 2 multiples?
Answer:
30 and 36
Step-by-step explanation:
six times two equals 12
6 * 3 = 18
and six times four equals 24.
to get the next two multiples, You need to multiply 6 by 5, and then 6
6 * 5 = 30 and 6 * 6 = 36
PLEASE HELP ME....which is the unit rate
Answer:
i think it is the first one
Step-by-step explanation:
A unit rate is a ratio between two different units with a denominator of one. When we divide a fraction's numerator by its denominator, the result is a value in decimal form. Examples include 8 / 4 = 2 and 3 / 6 = 0.5
Ms. Sheppard cuts 1/2 of a piece of construction paper. She uses 1/6 of the piece to make a flower. What fraction of the sheet of paper does she used to make flower?
Answer:
1/12
Step-by-step explanation:
Eight more than the number of children is 24.
Answer:
c+8 = 24
16 children
Step-by-step explanation:
Let c = number of children
8 more than
c+8
is means equals
c+8 = 24
Subtract 8 from each side
c+8-8 = 24-8
c = 16
Aaron is building a brick wall. The wall will need 1025 bricks.the weight of each brick is 2.89 kg. Aaron will pay a delivery charge if the total weight of bricks is over 2500kg
Answer:
he will pay
Step-by-step explanation:
2962.25 is the total weight of the bricks
The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. They would like the estimate to have a maximum error of 0.130.13 gallons. A previous study found that for an average family the variance is 2.562.56 gallons and the mean is 16.316.3 gallons per day. If they are using a 80%80% level of confidence, how large of a sample is required to estimate the mean usage of water? Round your answer up to the next integer.
Answer:
Therefore, a sample that is required to estimate the mean usage of water must be at least 249.
Step-by-step explanation:
We are given that they would like the estimate to have a maximum error of 0.13 gallons.
A previous study found that for an average family the variance is 2.56 gallons and the mean is 16.3 gallons per day.
As we know that; Margin of error formula is given by;
Margin of error = [tex]Z_(_\frac{\alpha}{2}_) \times \text{Standard of error}[/tex]
where, [tex]\alpha[/tex] = level of significance = 1 - 0.80 = 20% and [tex](\frac{\alpha}{2} )[/tex] = 10%
Standard of error = [tex]\frac{\sigma}{\sqrt{n} }[/tex]
where, [tex]\sigma[/tex] = standard deviation = [tex]\sqrt{2.56}[/tex] = 1.6
n = sample size
Also, the critical value of z at 10% significance level is given in the z table as 1.282.
SO, Margin of error = [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]
0.13 = [tex]1.282 \times \frac{1.6}{\sqrt{n} }[/tex]
[tex]\sqrt{n}[/tex] = [tex]\frac{1.282 \times 1.6}{0.13}[/tex]
n = [tex]15.8^{2}[/tex]
n = 248.95 ≈ 249.
Therefore, a sample that is required to estimate the mean usage of water must be at least 249.
The diameter of a cylindrical construction pipe is 4 ft, and its
length is 18 ft.
Answer the parts below.
Answer:
72π ft³226.19 ft³Step-by-step explanation:
(a) The figure shows the diameter of the pipe is 4 ft, so its radius is 2 ft. The equation for the volume of a cylinder is ...
V = πr^2·h
Filling in r=2 and h=18, we have ...
V = π(2 ft)^2(18 ft) = 72π ft^3
The exact volume is 72π ft³.
__
(b) Using a sufficiently accurate value of pi, the numerical value of the volume is ...
72π ft^3 ≈ 226.19 ft^3
The approximate volume is 226.19 ft³.
What is the domain of the function
f(x) =
1/3x+2
Answer:
x=-6
Step-by-step explanation:
substitute f(x)=0
0=1/3x+2
solve for x
x=-6
Answer:
x >= -6
Step-by-step explanation:
edg 2020
A line intersects the points (-8,-1) and (1,8). What is the slope-intercept equation for this line?
Slope is the change in y over the change in x:
Slope = (8 - (-1) ) / ( 1 - (-8))
Slope = 9/ 9
Slope = 1
17.
Your gross income is
$4,520.00/month. Your deductions are FICA (7.65%), federal tax withholding (11.75%),
and state tax withholding (8.5%). Your fixed expenses are 30% of your realized income.
You saved 5 months' worth in an emergency fund, placing 75% in a 60-day CD at a 5.25%
APR and the rest in a regular savings account at a 3.8% APR. How much is in the savings
account?
$1,777.10
$1,222.10
$1,969.55
Answer:
1,969.55 is the answer
Two shoppers buy the following at a fruit,paying the amounts given.
Shopper 1: 4 apples and 3 bananas for $2.59
Shopper 2: 6 apples and 5 bananas for $4.11
a) Decide on pronumeral names for the unknown quantities.
b).write equations involving these pronunerals.work in terms of dollars.
c). Solve for the unknowns.
Answer:
a) x is the cost of an apple and y is the cost of a banana.
b)
[tex]4x + 3y = 2.59[/tex]
[tex]6x + 5y = 4.11[/tex]
c) An apple costs $0.31 and a banana costs $0.45.
Step-by-step explanation:
We have to find the cost, in dollars, of an apple and of a banana.
We do this solving a system of equations.
a) Decide on pronumeral names for the unknown quantities.
I am going to say that:
x is the cost of an apple.
y is the cost of a banana.
b).write equations involving these pronunerals.work in terms of dollars.
4 apples and 3 bananas for $2.59
This means that [tex]4x + 3y = 2.59[/tex]
6 apples and 5 bananas for $4.11
This means that [tex]6x + 5y = 4.11[/tex]
c). Solve for the unknowns.
I am going to use the addition method, multiplying the first equation by 5 and the second by -3, and then adding them. So
20x + 15y = 12.95
-18x - 15y = -12.33
20x - 18x + 15y - 15y = 12.95 - 12.33
2x = 0.62
x = 0.62/2
x = 0.31
And
4x + 3y = 2.59
3y = 2.59 - 4x
3y = 2.59 - 4*0.31
3y = 1.35
y = 1.35/3
y = 0.45
An apple costs $0.31 and a banana costs $0.45.
Please answer number three I give brainliest thank y’all so much!
Answer:
Step-by-step explanation:
2 and 6
Answer:
2 and 6
Step-by-step explanation:
mode is the most frequent number and 2 and 6 are both shown the most and that is 4 times for both its a tie so it would be both of them
You are dividing a community garden 35 m long by 15 m wide into equal-sized square gardens. Find the greatest possible dimensions of each square.
Answer:
35 divided by 15 multiplied by 4=9
Step-by-step explanation:
Hope this helps
sean b= 5,79; c= 10,4,el angulo A= 54,46°, el angulo C mide ?
Answer:
[tex]C \approx 91.732^{\circ}[/tex]
Step-by-step explanation:
(This exercise is presented in Spanish and for that reason explanation will be held in such language)
El lado restante se determina por la Ley del Coseno:
[tex]a = \sqrt{b^{2}+c^{2}-2\cdot b\cdot c \cdot \cos A}[/tex]
[tex]a = \sqrt{5.79^{2}+10.4^{2}-2\cdot (5.79)\cdot (10.4)\cdot \cos 54.46^{\circ}}[/tex]
[tex]a \approx 8.466[/tex]
Finalmente, el angulo C se halla por medio de la misma ley:
[tex]\cos C = - \frac{c^{2}-a^{2}-b^{2}}{2\cdot a \cdot b}[/tex]
[tex]\cos C = -\frac{10.4^{2}-8.466^{2}-5.79^{2}}{2\cdot (8.466)\cdot (5.79)}[/tex]
[tex]\cos C = -0.030[/tex]
[tex]C \approx 91.732^{\circ}[/tex]
surface area of a cylinder
Answer:
A=2πrh+2πr2
Step-by-step explanation:
Answer:
the surface area of cylinder is T.S.A=
2πrh+2πr2
HOPE IT HELPS YOU
Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.
Conjecture:
Answer: true
Step-by-step explanation:
In circle C, what is mArc F H?
31°
48°
112°
121°
Answer:
B. 48
Step-by-step explanation:
just took the test <3
Answer:
mArc FH = 48
Step-by-step explanation:
Antoine stands on a balcony and throws a ball to his dog, who is at ground level. The balls height (in meters above ground), x seconds after Antoine threw it, is modeled by: h(x) = 2x^2+4x+16
What is the height of the ball at the time it is thrown?
Answer:
16 meters
Step-by-step explanation:
when the ball is thrown, the initial time is 0 seconds. Therefore, x =0.
h(0) = 2(0)^2 +4(0) + 16
h(0) = 16
the height of the ball at the time it is thrown is 16 meters.
Answer:
16 meters
Step-by-step explanation:
Got it right on khan
Is a parallelogram but not a rectangle
Answer:
A square
Step-by-step explanation:
A square meets the requirements of a parallelogram.
7.987 ot the tenths place
Answer:
If your were rounding 7.987 to the tenths place, you would get 8.
To round to the tenths place, you are trying to make the number enda tthe tenths place.
You are rounding the 9 in the tenths place, so look at the hundredths place. Since 8 is larger than 5, round the 9 up to 10.
We can't write 7.10 because that is a different number, so add the 1 to the 7 to get 8.
The final answer would be 8.0 or just 8.
Mercury is 36 million miles
way from the sun. Venus
672 million miles from
the sun what is the
difference in distance
Answer:
636 million miles.
Step-by-step explanation:
672 minus 36 is 636. (Because they're both in the millions, you can just subtract their face values).
Since they have the same term (million) we simply subtract 672 and 36, then add million to the answer. 636 million miles is the difference in distance.
G
If f(x) = 6x – 4, what is f(x) when x = 8?
Answer: f(x)=44
Step-by-step explanation:
Since x is given, we can directly plug it into our function.
[tex]f(8)=6(8)-4[/tex]
[tex]f(8)=48-4[/tex]
[tex]f(8)=44[/tex]
Twenty-seven minus 2 of a number (™) is not more than 36. What is the number?
A. x > 42
B. X2-6
OC. X<3
OD. X5-6
Suppose IQ scores were obtained for 20 randomly selected sets of couples. The 20 pairs of measurements yield x=97.47​, y=97.35​, r=0.892​, ​P=0.000, and y=-9.15+1.09x​, where x represents the IQ score of the wife. Find the best predicted value of y given that the wife has an IQ of 104​? Use a significance level of 0.05.
Question:
Suppose IQ scores were obtained for 20 randomly selected sets of couples. The 20 pairs of measurements yield x' =97.47, y' =97.35, r=0.892, P=0.000, and y^=-9.15+1.09x, where x represents the IQ score of the wife. Find the best predicted value of y given that the wife has an IQ of 104? Use a significance level of 0.05.
Answer:
y^ = 104.21
Step-by-step explanation:
Given:
n = 20
x' = 97.47
y' = 97.35
r = 0.892
P-value = 0.000
y^ = -9.15 + 1.09x
Here, the wife has an IQ of 104.
The regression equation here is given as:
y^ = -9.15 + 1.09x
Let x represent the IQ of the wife.
x = 104
Hence, the best predicted value of y^ will be:
Let's substitute 104 for x in tge regression equation.
y^ = -9.15 + 1.09(104)
y^ = - 9.15 + 113.36
y^ = 104.21
Therefore, the best predicted value of y^ = 104.21