This problem models pollution effects in the Great Lakes. We assume pollutants are flowing into a lake at a constant rate of I kg/year, and that water is flowing out at a constant rate of F km3/year. We also assume that the pollutants are uniformly distributed throughout the lake. If C(t) denotes the concentration (in kg/km3) of pollutants at time t (in years), then C(t) satisfies the differential equationdC dt = −FVC + IVwhere V is the volume of the lake (in km3). We assume that (pollutant-free) rain and streams flowing into the lake keep the volume of water in the lake constant.A) Suppose that the concentration at time t = 0 is C0. Determine the concentration at any time t by solving the differential equation.B) Find lim t→[infinity] C(t) =C) For Lake Erie, V = 458 km3 and F = 175 km3/year. Suppose that one day its pollutant concentration is C0 and that all incoming pollution suddenly stopped (so I = 0). Determine the number of years it would then take for pollution levels to drop to C0/10.D) For Lake Superior, V = 12221 km3 and F = 65.2 km3/year.
Answers
SEE BELOW FOR THE CORRECT FORMAT OF THE QUESTION
Answer:
(a) [tex]\mathbf{C_{(t)} =\dfrac{I}{F} [ 1- e \dfrac{-Ft}{v}+ C_oe \dfrac{-Ft}{v} ]}[/tex]
(b) [tex]\mathbf{\lim_{t \to \infty} C_t = \dfrac{I}{F}[1-0+ 0 ] \ = \dfrac{I}{F}}[/tex]
(c) T = 6.02619 years
(d) T = 431.593 years
Step-by-step explanation:
(a)
[tex]\dfrac{dC}{dt} = -\dfrac{F}{v}C + \dfrac{I}{v} \\ \\ \\ \dfrac{dC}{dt} + \dfrac{F}{v}C = \dfrac{I}{v}[/tex]
By integrating the factor of this linear differential equation ; we have :
[tex]= e \int\limits \dfrac{F}{v}t \\ \\ \\ = e \dfrac{Ft}{v}[/tex]
[tex]C* e \frac{Ft}{v}= \int\limits \dfrac{I}{v}*e \dfrac{Ft}{v} dt[/tex]
[tex]C* e \frac{Ft}{v}= \dfrac{I}{v}* \dfrac{e \frac{Ft}{v} }{F/v}+ K[/tex]
[tex]C* e \frac{Ft}{v}= \dfrac{I}{v}* \dfrac{V}{F} e \dfrac{Ft}{v} + K[/tex]
[tex]Ce \dfrac{Ft}{v} = \dfrac{I}{F} \ * \ e \dfrac{Ft}{v} + k \ \ \ \ (at \ t = 0 \ ; C = C_o)[/tex]
[tex]C_o = \dfrac{I}{F} e^o + K[/tex]
[tex]K = C_o - \dfrac{I}{F}[/tex]
[tex]C_{(t)} = [ \dfrac{I}{F}e \dfrac{Ft}{v}+ C_o - \dfrac{I}{F}] e\dfrac{-Ft}{v}[/tex]
[tex]C_{(t)} =\dfrac{I}{F} [ e \dfrac{Ft}{v} * e \dfrac{-Ft}{v}+ C_oe \dfrac{-Ft}{v} - 1* e \dfrac{-Ft}{v}][/tex]
[tex]\mathbf{C_{(t)} =\dfrac{I}{F} [ 1- e \dfrac{-Ft}{v}+ C_oe \dfrac{-Ft}{v} ]}[/tex]
(b)
[tex]\lim_{t \to \infty} C_t = \dfrac{I}{F}[1-e^{- \infty} + C_o e^{- \infty} ][/tex]
since [tex](e^{- \infty} = 0)[/tex]
[tex]\mathbf{\lim_{t \to \infty} C_t = \dfrac{I}{F}[1-0+ 0 ] \ = \dfrac{I}{F}}[/tex]
(c)
V = 458 km³ and F = 175 km³ , I = 0
[tex]\dfrac{dC}{dt} = - \dfrac{-175}{458}C[/tex]
[tex]= \int\limits \ \dfrac{dC}{C} = - \dfrac{175}{458}\int\limits dt[/tex]
[tex]In (C_{(t)}) = - \dfrac{175}{458} t + K[/tex]
[tex]C_{(t)} = e \dfrac{-175}{458}t + K[/tex]
Let at time t = 0 [tex]C_{(t)}} = C_o \to C_o = e^{0+k} = e^K[/tex]
[tex]C_{(t)} = e \dfrac{-175}{458}t[/tex]
Now at time t = T ; [tex]C_{9t)} = \dfrac{C_o}{10}[/tex]
[tex]\dfrac{C_o}{10} = C_o e \dfrac{-175}{458}T \to \dfrac{1}{10} = e \dfrac{-175}{458}T[/tex]
[tex]In ( \dfrac{1}{10}) = \dfrac{-175}{459}T[/tex]
[tex]- In (10) = \dfrac{175}{458}T[/tex]
[tex]T = \dfrac{458}{175} In (10)[/tex]
T = 6.02619 years
(d) V = 12221 km³
F = 65.2 km³/ year
[tex]\mathbf{T = \dfrac{v}{F}In (10)}[/tex]
[tex]T = \dfrac{12221}{65.2}In (10)[/tex]
T = 431.593 years
Related Questions
If f(x + 2) = 6x2 + 5x − 8. Find f(6).
Answers
Answer:
108
Step-by-step explanation:
We can rewrite f(x+2) to make it easier to evaluate:
f(x+2) = (6x +5)x -8
Since we want f(6), we want x+2 = 6, or x=4.
f(6) = (6·4 +5)·4 -8 = 29·4 -8
f(6) = 108
A rectangle is removed from the middle of a larger rectangular shaped board. What is the area of the remaining board?
Answers
Answer:
The area of the remaining board is [(L × B) - (l × b)].
Step-by-step explanation:
Suppose the bigger rectangle is labelled as ABCD and the smaller rectangle is labelled as PQRS.
Consider that the length and breadth of the bigger rectangle are L and B respectively. And the length and breadth of the bigger rectangle are l and b respectively.
The area of any rectangle is:
Area = Length × Breadth
The area of the bigger rectangle is:
Area of ABCD = L × B
The area of the smaller rectangle is:
Area of PQRS = l × b
Then the area of the remaining board will be:
Area of remaining board = Area of ABCD - Area of PQRS
= (L × B) - (l × b)
Thus, the area of the remaining board is [(L × B) - (l × b)].
Answer:
112
Step-by-step explanation:
dentify the reference angle for each given angle, . degrees. degrees. degrees. degrees.
Answers
Answer:
S, Z, F
Step-by-step explanation:
i know its not the question but its for anyone who found this and needs it for edge lol
2.-Efraín tiene un terreno rectangular cuya área es de 120 m2 + 280 m como se muestra en la Figura:
120 m2 + 280 m
f
De acuerdo con estos datos ¿Cuánto mide el lado f?
a) 12 m2
+ 35
b) 15 m + 35 cm
c) 12 m + 35
d) 15 m + 35
3.- Un niño elaboró cuatro figuras de plastilina: dos prismas cuadrangulares y dos cilindros. ¿En qué figura ocupó
la mayor cantidad de plastilina? JUSTIFICA TU RESPUESTA
a)
b)
c)
e)
8
Answers
Answer:
2) Option D is correct.
f = (15m + 35)
3) Check Explanation
Step-by-step explanation:
The diagram of the question is presented in the attached image to this question
English Translation
Efraín has a rectangular land whose area is (120m² + 280m) as shown in the figure. According to these data, how much does side f measure?
a) 12 m² + 35
b) 15 m + 35 cm
c) 12 m + 35
d) 15 m + 35
3.- A child made four plasticine figures: two quadrangular prisms and two cylinders. In which figure did you occupy the most amount of modeling clay? JUSTIFY YOUR ANSWER
Solution
2) The area of a rectangle is given as
Area = Length × Breadth
Area = (120m² + 280m)
Length = f
Breadth = 8m
(120m² + 280m) = f × 8m
f = (120m² + 280m)/(8m)
f = (15m + 35)
Option D is correct.
f = (15m + 35)
3) For the second question, the images for the question and the dimensions of the figures aren't provided, hence, a very accurate answer can be provided. But without This, we can only speculate.
The figure that would use the most clay is the figure whose volume is the highest if the volumes of each of the figures are calculated.
Volume of a quadrangular prism = (Area of base) × (perpendicular height)
Volume of a cylinder = (Area of base) × (Height) = (πR² × H) = πR²H
So, it is in the evaluation of these volumes that the solution of this question is obtained.
Hope this Helps!!
Eric's average income for the four months of the year 1450 point to $5 what must be his average income for the remaining eight months so that his average for the year is $1780.75
Answers
Answer:
$2668.63
Step-by-step explanation:
If the average of 4 months is $5
Meaning the total sum for 4 months
4×5 =$20
If the average for the year was $1780.75
It means the total sum for a year is;
$1780.75×12 =$21369
This means the money received for the remaining 8 months is;
$21369-$20=$21349
Hence the average income for the remaining 8months is ;
The total amount for 8 months / 8;
$21349/8= $2668.625
$2668.63
I keep gettin this wrong please help!!!
Answers
Answer: 120 members
Step-by-step explanation: So, we know 12 of the members signed up, and 90% of the member did not sign up.
Therefore, 12 members is equal to 10%...
All we have to do now is...
12 * 10 = 120
The club has 120 members in total, I hope this helps!
Step-by-step Explanation:
12 people are signed up.
90% of people are not signed up.
100% - 90% = 10%
10% = 12 people, This means that every 10% there are 12 people, and if we are looking for 100% of the members, and there are 10 tens in one hundred,
12 x 10 = 120
what is the nominal annual interest rate
Answers
Answer:
the nominal interest rate is the periodic interest rate.
it is the periodic interest rate times the number of periods per year.
In 1960, census results indicated that the age at which men in a certain region first married had a mean of 24.5 years. It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age of first marriage has increased since then.
We plan to test our hypothesis by selecting a random sample of 40 men who married for the first time last year.
The men in our sample married at an average age of 25.3 years, with a standard deviation of 5.4 years. That results in a t-statistic of 0.937 What is the P-value for this?
Answers
Answer:
[tex]t=\frac{25.3-24.5}{\frac{5.4}{\sqrt{40}}}=0.937[/tex]
The degrees of freedom are given by:
[tex]df=n-1=40-1=39[/tex]
And the p value would be given by:
[tex]p_v =P(t_{(39)}>0.937)=0.177[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=25.3[/tex] represent the sample mean
[tex]s=5.4[/tex] represent the sample standard deviation
[tex]n=40[/tex] sample size
[tex]\mu_o =24.5[/tex] represent the value to verify
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true mean is higher than 24.5, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 24.5[/tex]
Alternative hypothesis:[tex]\mu > 24.5[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{25.3-24.5}{\frac{5.4}{\sqrt{40}}}=0.937[/tex]
The degrees of freedom are given by:
[tex]df=n-1=40-1=39[/tex]
And the p value would be given by:
[tex]p_v =P(t_{(39)}>0.937)=0.177[/tex]
Awnser in the lowest terms 5 years 6 months + 8 years 9 months
Answers
5 yrs+ 6 yrs =11 yrs
6 months+9 months=15 months
so,the answer is 11 yrs 15 months.
The circle graph shows the different vitamins present in a health drink. Identify the measure of arc AB. Please help!
Answers
Answer:
79.2° (First Option)
Step-by-step explanation:
To find mAB, recognize that the percents given for the pie chart can represent the percent area of the sector of the circle, the percent measure of the central angle that forms the sector, or the percent measure of the length of the arc.
The measure of an arc is equal to the measure of the central angle between the radii that form its endpoints. So, mAB=m∠AOB.
The measure of the central angle AOB that forms AB is 22 percent of the whole circle, or (0.22)360∘. So, mAB=0.22(360∘)=79.2∘
Therefore, the measure of arc AB
is 79.2∘.
The measure of the arc AB of a circle showing the different vitamins present in a health drink is 79.2 degrees.
Calculate the measure of arcThe measure of an arc is always equivalent to the measure of the central angle between the radii that form its endpoints.
How to find the measure of arc AB.As the measure of an arc is always equivalent to the measure of the central angle between the radii that form its endpoints.
Thus [tex]m\angle{AOB}=\widehat{AB}[/tex].
First, find the measure of angle AOB.
Since the measure of angle AOB shows 22% of vitamins of the whole circle.
This means that the measure of angle AOB is 22% of 360 degrees.
Then we will get
[tex]m\angle{AOB}=\dfrac{22}{100}\times 360^{\circ}\\m\angle{AOB}=79.2^{\circ}[/tex]
Here the measure of angle AOB is 79.2 degrees.
And since [tex]m\angle{AOB}=\widehat{AB}[/tex].
Therefore the measure of arc AB is 79.2 degrees.
That means option A [tex]79.2^{\circ}[/tex] is correct option.
Learn more about the measure of arc here- https://brainly.com/question/12555201
#SPJ2
Traffic speed: The mean speed for a sample of cars at a certain intersection was kilometers per hour with a standard deviation of kilometers per hour, and the mean speed for a sample of motorcycles was kilometers per hour with a standard deviation of kilometers per hour. Construct a confidence interval for the difference between the mean speeds of motorcycles and cars at this intersection. Let denote the mean speed of motorcycles and round the answers to at least two decimal places. A confidence interval for the difference between the mean speeds, in kilometers per hour, of motorcycles and cars at this intersection is ________.
Construct the 98% confidence interval for the difference μ 1-y 2 when x 1 475.12, x 2-32134, s 1-43.48, s 2-21.60, n 1-12, and n 2-15. Use tables to find the critical value and round the answers to two decimal places. A 98% confidence interval for the difference in the population means is ________.
Answers
Answer:
Step-by-step explanation:
Hello!
X₁: speed of a motorcycle at a certain intersection.
n₁= 135
X[bar]₁= 33.99 km/h
S₁= 4.02 km/h
X₂: speed of a car at a certain intersection.
n₂= 42 cars
X[bar]₂= 26.56 km/h
S₂= 2.45 km/h
Assuming
X₁~N(μ₁; σ₁²)
X₂~N(μ₂; σ₂²)
and σ₁² = σ₂²
A 90% confidence interval for the difference between the mean speeds, in kilometers per hour, of motorcycles and cars at this intersection is ________.
The parameter of interest is μ₁-μ₂
(X[bar]₁-X[bar]₂)±[tex]t_{n_1+n_2-2}[/tex] * [tex]Sa\sqrt{\frac{1}{n_1} +\frac{1}{n_2} }[/tex]
[tex]t_{n_1+n_2-2;1-\alpha /2}= t_{175; 0.95}= 1.654[/tex]
[tex]Sa= \sqrt{\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} } = \sqrt{\frac{134*16.1604+41*6.0025}{135+42-2} } = 3.71[/tex]
[(33.99-26.56) ± 1.654 *([tex]3.71*\sqrt{\frac{1}{135} +\frac{1}{42} }[/tex])]
[6.345; 8.514]= [6.35; 8.51]km/h
Construct the 98% confidence interval for the difference μ₁-μ₂ when X[bar]₁= 475.12, S₁= 43.48, X[bar]₂= 321.34, S₂= 21.60, n₁= 12, n₂= 15
[tex]t_{n_1+n_2-2;1-\alpha /2}= t_{25; 0.99}= 2.485[/tex]
[tex]Sa= \sqrt{\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} } = \sqrt{\frac{11*(43.48)^2+14*(21.60)^2}{12+15-2} } = 33.06[/tex]
[(475.12-321.34) ± 2.485 *([tex]33.06*\sqrt{\frac{1}{12} +\frac{1}{15} }[/tex])]
[121.96; 185.60]
I hope this helps!
A random sample of 10 college students was drawn from a large university. Their ages are 22, 17, 27, 20, 23, 19, 24, 18, 19, and 24 years. We want to determine if we can infer at the 5% significance level that the population mean is not equal to 20.
Answers
Answer:
[tex]t=\frac{21.3-20}{\frac{3.199}{\sqrt{10}}}=1.29[/tex]
The degrees of freedom are given by:
[tex]df=n-1=10-1=9[/tex]
And the p value would be:
[tex]p_v =2*P(t_{(9)}>1.29)=0.229[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean is different from 20.
Step-by-step explanation:
Information given
22, 17, 27, 20, 23, 19, 24, 18, 19, and 24
The sample mean and deviation for these data are:
[tex]\bar X=21.3[/tex] represent the ample mean
[tex]s=3.199[/tex] represent the sample standard deviation for the sample
[tex]n=10[/tex] sample size
[tex]\mu_o =20[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to verify if the true mean is equal to 20 or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 20[/tex]
Alternative hypothesis:[tex]\mu \neq 20[/tex]
The statistic would be:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing the info given we got:
[tex]t=\frac{21.3-20}{\frac{3.199}{\sqrt{10}}}=1.29[/tex]
The degrees of freedom are given by:
[tex]df=n-1=10-1=9[/tex]
And the p value would be:
[tex]p_v =2*P(t_{(9)}>1.29)=0.229[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean is different from 20.
What is the quotient? Negative StartFraction 3 over 8 EndFraction divided by negative one-fourth
Answers
Answer:
[tex]\dfrac{3}{2}[/tex]
Step-by-step explanation:
We are given 2 fractions.
1st fraction is Negative StartFraction 3 over 8
i.e.
[tex]-\dfrac{3}{8}[/tex]
2nd fraction is negative one-fourth
i.e.
[tex]-\dfrac{1}{4}[/tex]
We have to find the quotient when 1st fraction is divided by 2nd fraction.
Definition of quotient is given as:
Quotient is the result obtained when one number is divided by other number.
[tex]-\dfrac{3}{8} \div -\dfrac{1}{4} \text{ is to be calculated.}[/tex]
[tex]\div[/tex] is converted to [tex]\times[/tex] and the 2nd fraction is reversed i.e.
if the fraction is [tex]\frac{p}{q}[/tex] it becomes [tex]\frac{q}{p}[/tex] and the sign [tex]\div[/tex] is changed to [tex]\times[/tex].
Solving above:
[tex]-\dfrac{3}{8} \times -\dfrac{4}{1}\\ \text {Multiplication/Division of 2 negative number gives a positive number}\\\Rightarrow \dfrac{3}{2}[/tex]
So, the quotient is [tex]\frac{3}{2}[/tex].
A company that packages peanuts states that at a maximum 6% of the peanut shells contain no nuts. At random, 300 peanuts were selected and 21 of them were empty.
1.With a significance level of 1%, can the statement made by the company be accepted?
2.With the same sample percentage of empty nuts and 1 − α = 0.95, what sample size would be needed to estimate the proportion of nuts with an error of less than 1%?
Answers
Answer:
1) [tex]z=\frac{0.07 -0.06}{\sqrt{\frac{0.06(1-0.06)}{300}}}=0.729[/tex]
We can calculate the p value with the following formula:
[tex]p_v =2*P(z>0.729)=0.466[/tex]
The p value for this case is very high and using the significance level of 0.01 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the statment makes sense.
2) [tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.06(1-0.06)}{(\frac{0.01}{1.96})^2}=2166.66[/tex]
And rounded up we have that n=2167
Step-by-step explanation:
Information given
n=300 represent the random sample taken
X=21 represent the number of peanuts empty
[tex]\hat p=\frac{21}{300}=0.07[/tex] estimated proportion of peanust empty
[tex]p_o=0.06[/tex] is the value to test
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
Part 1
We want to test if the true proportion is 6% or no the system of hypothesis are:
Null hypothesis:[tex]p=0.06[/tex]
Alternative hypothesis:[tex]p \neq 0.06[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.07 -0.06}{\sqrt{\frac{0.06(1-0.06)}{300}}}=0.729[/tex]
We can calculate the p value with the following formula:
[tex]p_v =2*P(z>0.729)=0.466[/tex]
The p value for this case is very high and using the significance level of 0.01 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the statment makes sense.
Part 2
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we have that [tex]ME =\pm 0.01[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.06(1-0.06)}{(\frac{0.01}{1.96})^2}=2166.66[/tex]
And rounded up we have that n=2167
Hello, what is all the scale factors of two.?
Answers
Answer:
all even numbers
Step-by-step explanation:
Answer:
Any and all of the Even numbers are scale factors of two!
) How many kilowatt hours would the model predict on a day that has 14 hours of possible daylight?
Answers
Question:
A solar power company is trying to correlate the total possible hours of daylight (simply the time from sunrise to sunset) on a given day to the production from solar panels on a residential unit. They created a scatter plot for one such unit over the span of five months. The scatter plot is shown below. The equation line of best fit for this bivariate data set was: y = 2.26x + 20.01
How many kilowatt hours would the model predict on a day that has 14 hours of possible daylight?
Answer:
51.65 kilowatt hours
Step-by-step explanation:
We are given the equation line of best fit for this data as:
y = 2.26x + 20.01
On a day that has 14 hours of possible daylight, the model prediction will be calculated as follow:
Let x = 14 in the equation.
Therefore,
y = 2.26x + 20.01
y = 2.26(14) + 20.01
y = 31.64 + 20.01
y = 51.65
On a day that has 14 hours of daylight, the model would predict 51.65 kilowatt hours
Could someone please give me the answer to this?
Answers
Answer:
36.87
Step-by-step explanation:
The cosine of an angle in a right triangle is the length of the adjacent side divided by the length of the hypotenuse, which in this case is 4/5. Therefore, the measure of this angle is the arc cosine of 4/5, or about 36.87 degrees. Hope this helps!
Kennedy and Olivia go to the movie theater and purchase refreshments for their friends.
Kennedy spends a total of $77.50 on 12 bags of popcorn and 2 drinks.
Olivia spends a total of $51.00 on 3 bags of popcorn and 6 drinks.
Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink.
Using these equations, determine and state the price of a drink, to the nearest cent.
Answers
Answer:
6x + y = 38.75
x + 2y = 17
price of drink is $5.75
Step-by-step explanation:
Let the price of popcorn be x
Let the price of drink be y.
price of 12 bags of popcorn will be 12x
price of 2 drinks will be 2y
it is given that "Kennedy spends a total of $77.50 on 12 bags of popcorn and 2 drinks."
thus
12x + 2y = 77.50
dividing LHS and RHS by 2 we have
12x/2 + 2y/2 = 77.50/2
=> 6x + y = 38.75 _________(1)
__________________________________________________
price of 3 bags of popcorn will be 3x
price of 6 drinks will be 6y
it is given that "Olivia spends a total of $51.00 on 3 bags of popcorn and 6 drinks."
thus
3x + 6y = 51.00
dividing LHS and RHS by 3 we have
3x/3 + 6y/3 = 51/3
=> x + 2y = 17 _____________(2)
__________________________________________________
Thus we have two equation
6x + y = 38.75 _________(1)
x + 2y = 17
=> x = 17 - 2y
putting this value of x in equation 1 we have
6( 17 - 2y) + y = 38.75
=> 102 - 12y + y = 38.75
=> 102 - 11y = 38.75
=> -11y = 38.75 -102
=> -11y = -63.25
=> y = -63.25/-11 = 5.75
as we have x = 17 - 2y
using 5.75 in place of y
x = 17 - 2(5.75 )
=> x = 17 - 11.5
=> x = 5.5
Thus, system of equations are
6x + y = 38.75
x + 2y = 17
price of drink is $5.75
100 points for brainiest
Please try!!
Use this link in my comment!
Answers
Answer:
I couldn't find the link you wanted me to click.
Anyway the Pyramid Volume Formula is
Volume= (Area of the Base * Height) ÷ 3
It's hard to determine the volume because I can't tell the dimensions from the graphic.
I'd guess the answer to question 4 is "A" means area of the base
Step-by-step explanation:
I need HELP PLEASE HELP MEEE!
Answers
Answer:
$21
Step-by-step explanation:
Take 40 percent of 35:
35(0.4) = 14
$14 has been taken off the original price:
35 - 14 = 21
And we have our final answer.
Answer:
21
Step-by-step explanation:
$35x40%= $14
$35-$14= $21
------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------
If I get this worng I'm sorry
Brainleist will be appreciated, if not that's ok
Sorry that my spelling is relly bad
Anyway, hope this helps :D
Solve the equation, keeping the value for x as an improper fraction. 2/3 x = − 1/2 x + 5
Answers
Answer:
[tex]x= 30/7[/tex]
Step-by-step explanation:
[tex]2/3 x = -1/2 x + 5[/tex]
[tex]2/3x+1/2x = + 5[/tex]
[tex]7/6x=5[/tex]
[tex]x=5 \times 6/7[/tex]
[tex]x= 30/7[/tex]
help please, surface area!
Answers
Answer:
436
Step-by-step explanation:
A rectangular prism is made up of 3 pairs of rectangles. In this case, one pair has dimensions of 4 by 9, another pair has dimensions of 4 by 14, and the last pair has dimensions of 9 by 14. The surface area of this rectangular prism is therefore:
2(4*9)+2(4*14)+2(9*14)=72+112+252=436 square inches
Hope this helps!
Answer:
436 in²
Step-by-step explanation:
A= 2*(4*14+4*9+9*14) in²= 436 in²
What is the meassure of XYZ in the diagram below HELP ASSAP :)
Answers
I don’t know how to explain it
Please answer this question !! WIll give brainliest !! 20 POINTS !
Answers
Answer:
k=4
Step-by-step explanation:
y=3(1)-1
y=2
2=-2x+k
2=-2(1)+k
2=-2+k
4=k
Answer:
k = 4
Step-by-step explanation:
y = 3x -1
y = -2x+k
Set the two equations equal
3x -1 = -2x+k
Combine like terms
Add 2x to each side
3x+2x -1 =-2x+2x +k
5x - 1 = k
We know they are equal when x= 1
Let x=1
5*1 -1= k
5 -1= k
4 = k
A prominent medical school conducted a study that concluded adults with high blood pressure who consistently ate small amounts of low sugar dark chocolate experienced a significant reduction in blood pressure. As the study was being reviewed prior to publication in a medical journal, it was discovered that the Jershey Chocolate Company provided substantial funding for this research.
a) Identify any bias in this study.
b) Is it reasonable to conclude that adults with high blood pressure who consistently eat small amounts of low sugar dark chocolate experience a significant reduction in blood pressure?
Answers
Step-by-step explanation:
In the given question, the study was performed to analyse the effect of eating dark chocolate on the person with hypertension or increased blood pressure.
a) The biasness in the experiment could be that the funding for the study has been provided with a Private Company which mainly aims at selling their product.
b) The research is reasonable as it has been proved that eating a small amount of Dark chocolate can help cardiovascular disease like hypertension or increased blood pressure.
4. (16 points) A company with a fleet of cars found that in a random sample of 65 chosen and tested cars that 30 had emissions systems which failed to meet pollution control guidelines. A statistician is interested in testing if there is enough evidence to conclude that more than 30% of the fleet might be out of compliance regarding pollution control guidelines. Perform a five step hypothesis test using a 0.05 significance level. Write out the hypotheses: Determine critical value(s): Compute the test statistic: Determine the decision: Write the concluding statement:
Answers
Answer:
Null hypothesis:[tex]p\leq 0.3[/tex]
Alternative hypothesis:[tex]p > 0.3[/tex]
Critical value: [tex] z_{\alpha/2}= 1.64[/tex]
Test statistic: [tex]z=\frac{0.462 -0.3}{\sqrt{\frac{0.3(1-0.3)}{65}}}=2.85[/tex]
For this case the calculated value is higher than the critical value so then we can reject the null hypothesis. And we can conclude that the true proportion of cars with emissions systems which failed to meet pollution control guidelines for this case is significantly higher than 0.30 or 30%
Step-by-step explanation:
Information given
n=65 represent the random sample taken
X=30 represent the number of cars with emissions systems which failed to meet pollution control guidelines
[tex]\hat p=\frac{30}{65}=0.462[/tex] estimated proportion of cars with emissions systems which failed to meet pollution control guidelines
[tex]p_o=0.30[/tex] is the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to verify if the true proportion for this case is higher than 0.3 or no, the system of hypothesis are:
Null hypothesis:[tex]p\leq 0.3[/tex]
Alternative hypothesis:[tex]p > 0.3[/tex]
The statistic for this case would be:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info we got:
[tex]z=\frac{0.462 -0.3}{\sqrt{\frac{0.3(1-0.3)}{65}}}=2.85[/tex]
The critical value for this case would be taking in count the significance level in the right tail:
[tex] z_{\alpha/2}= 1.64[/tex]
For this case the calculated value is higher than the critical value so then we can reject the null hypothesis. And we can conclude that the true proportion of cars with emissions systems which failed to meet pollution control guidelines for this case is significantly higher than 0.30 or 30%
Please help I’ll mark you as brainliest if correct!
Answers
Answer:
(x+7)^2+(y-8)^2=1
(x-x value of center)^2+(y-y value of center)^2=radius
Answer:
(x + 7)² + (y - 8)² = 1
Step-by-step explanation:
(x - h)² + (y - k)² = r²
h = - 7, k = 8, r = 1
(x -(-7))² + (y - 8)² = 1²
(x + 7)² + (y - 8)² = 1
What is the y-intercept of the graph that is shown below? On a coordinate plane, a line goes through points (negative 2, 0) and (4, 0).
Answers
Answer:
b = 0
Step-by-step explanation:
Because the line passes through x values when y = 0, it means that the line is y = 0. The slope would be 0, and because we are given 2 coordinates we can determine that the y intercept would be at 0.
Answer:
c
Step-by-step explanation:
hope this helps i just had this question on edge 2020
What’s the value of x?
Answers
Answer:
x =20
Step-by-step explanation:
7x- 99 = 2x+1 ( vertically opposite angles)
7x - 2x = 1 +99
5x = 100
x =100/5
x =20
hope it helps
00:00
Joseph and Molly each have coin collections.
Joseph starts with 15 coins in his collection and adds 25 coins each month.
Molly starts with 25 coins in her collection and adds 25 coins each month.
Drag numbers from the box to complete the table showing the number of coins in their collections after 4 months.
115
75
65
40
100
90
50
125
Coin Collections
Month
Joseph
Molly
-
Start
15
25
1
1
2
3
4
Answers
Answer:
Step-by-step explanation:
Joseph : y = 25x + 15
Molly: y = 25x + 25
Joseph: y = 25(4)+ 15= 100+ 15= 115
Molly: y = 25(4)+ 25= 100+25= 125
Answer:
I hope this helps! <:
Step-by-step explanation:
The start is 15 and 25 so you keep on adding 25 to each of them, let's start with 15, 15+25=40 and 40 plus 25 is 65 and 65+25 is 90 the last one is 90+25= 115, now let's move on to 25. 25+25= 50 and the next one is 50+25=75 and then 75+25=100 and 100+25= 125.
