A stream traverses two lakes flowing downstream, and carrying fresh water as it enters the upper lake. The upper lake contains 4∗109 gallons of water, and the lower lake contains 2 ∗109 gallons of water. The flow rate of the stream is the same at all points and is 4 ∗ 106 gallons per day. A factory situated at the upper lake releases a pollutant at a rate of 200 lbs. per day. Let Q1(t) and Q2(t) be the amount, in pounds, of pollutant in the upper and lower lakes, respectively, where time t is measured in days. Assuming that each lake is well mixed, Q1 and Q2 obey the system(a) Q'1 = 4 ∗ 106 (200 − Q1), Q'2 = 4 ∗ 106 (Q1 − Q2).(b) Q'1 = 200 − Q1/1000, Q'2 = Q1/1000 − Q2/500.(c) Q'1 = 200 − 4 ∗ 106Q1, Q'2 = 4 ∗ 106 (Q1 − Q2).
(d) Q'1 = 200t − 4 ∗ 106Q1, Q'2 = 4 ∗ 106 (Q1 − Q2).

Answer:

Step-by-step explanation:

The number of people in the cabinet is 7.

n = 7.

Fundamental Counting Principle states that if there are m ways of doing a thing and there are n ways of doing other thing then there are total m*n ways of doing both things.

now using fundamental Counting Principle.

since 7 players can sit on chair in

7 , 6, 5 , 4, 3 , 2, 1 ways then together they can be seated in

7 * 6 * 5 * 4 * 3 * 2 * 1 ways = 5,040 ways.

To arrange this seven people in a straight cabinet, the number of way to arrange them is n!

Then,

n! = 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.

There are 5040 ways of arranging them.

Option A is correct.

Answer:125.6 feet

Step-by-step explanation:

diameter=40 feet

π=3.14

Circumference= π x diameter

Circumference=3.14 x 40

Circumference=125.6

There are 4 teaspoons in 20 mils. I just learned this in class.

-Dhruva;)

Answer:

4.05768 or 4

Step-by-step explanation:

There are 0.202884 teaspoon in a millilitre. If you multiply 0.202884 by 20, you 4.05768.

I am 100% sure (:

Can i pls have brainliest?

-ME

Answer:

D. 1000 miles

Step-by-step explanation:

400 x 2.5 = 1000

Answer:

5X + 8Y >= 300;    intersection at  (-20, 50)

Step-by-step explanation:

let t = work hours

0 < t < 30

X = time lawn mowing

Y = time babysitting.

X + Y < 30

5X + 8Y >= 300

We could solve...

X < 30 - Y

5(30 - Y) + 8Y  >=300

150 - 5Y + 8Y >= 300

3Y >=150

Y >=50

then  X < -20  

intersection at  (-20, 50)

Answer:

Step-by-step explanation:

5x+8y > 300

_

Answer:

420

Step-by-step explanation:

She uses 60 beads per bracelet and is making 7 bracelets

7*60 = 420 beads total

Answer:

= 80y - 56 then it will be the answer, it may be incorrect so i apologize if it is.

Answer:

80y - 56

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Because 9cm2 is 9 times 9 which equals 81 cm.

To find the length of one side of a cube with a surface area of 9 cm², set up the equation s² * 6 = 9. Simplify and solve for s to find that the length of one side is √(9/6) cm.

The question is asking about the surface area of a cube. The surface area of a cube can be found by multiplying the length of one side by itself, and then multiplying that result by 6 since a cube has 6 faces. So, if the surface area of a cube is 9 cm², you can set up the equation: 9 = s² * 6. Simplifying, you get s² = 9/6. Taking the square root of both sides, you find that s = √(9/6). Therefore, the length of one side of the cube is √(9/6) cm.

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Answer:

  D.  c+14 ≤ 24

Step-by-step explanation:

The solutions for these inequalities are ...

  A.  c < 10 -- does not include the value 10

  B.  c ≥ 6 -- does not include the value 5

  C.  c > 6 -- does not include the values 5 or 6

  D.  c ≤ 10 -- includes all of the values listed

The set given is part of the solution set of ...

  c +14 ≤ 24

Answer:

[tex]z=\frac{0.537-0.531}{\sqrt{0.534(1-0.534)(\frac{1}{147}+\frac{1}{147})}}=0.103[/tex]    

Now we can calculate the p value with the following probability taking in count the alternative hypothesis:

[tex]p_v =2*P(Z>0.103) =0.918 [/tex]    

For this case since the p value is large enough we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that we have significant differences between the two proportions analyzed.

Step-by-step explanation:

Information provided

[tex]X_{1}=79[/tex] represent the number of New Yorkers familiar with the brand  

[tex]X_{2}=78[/tex] represent the number of Californians familiar with the brand  

[tex]n_{1}=147[/tex] sample of New Yorkers

[tex]n_{2}=147[/tex] sample of Californians

[tex]p_{1}=\frac{79}{147}=0.537[/tex] represent the proportion New Yorkers familiar with the brand  

[tex]p_{2}=\frac{78}{147}=0.531[/tex] represent the proportion of Californians familiar with the brand  

[tex]\hat p[/tex] represent the pooled estimate of p

z would represent the statistic

[tex]p_v[/tex] represent the value

System of hypothesis

We want to verify if the two proportions of interest for this case are equal, the system of hypothesis would be:    

Null hypothesis:[tex]p_{1} = p_{2}[/tex]    

Alternative hypothesis:[tex]p_{1} \neq p_{2}[/tex]    

The statistic would be given by:    

[tex]z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}[/tex]   (1)  

Where [tex]\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{79+78}{147+147}=0.534[/tex]  

Repalcing the info given we got:

[tex]z=\frac{0.537-0.531}{\sqrt{0.534(1-0.534)(\frac{1}{147}+\frac{1}{147})}}=0.103[/tex]    

Now we can calculate the p value with the following probability taking in count the alternative hypothesis:

[tex]p_v =2*P(Z>0.103) =0.918 [/tex]    

For this case since the p value is large enough we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that we have significant differences between the two proportions analyzed.

Answer:

89.44%

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

[tex]\mu = 45, \sigma = 5.6[/tex]

If you score 52 on the test, what percentage of test takers scored lower than you?

This is the pvalue of Z when X = 52.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{52 - 45}{5.6}[/tex]

[tex]Z = 1.25[/tex]

[tex]Z = 1.25[/tex] has a pvalue of 0.8944.

So 89.44% of test takers scored lower than you.

Answer:

  see below

Step-by-step explanation:

The tangent function has been shifted upward by 2 units, but there has been no horizontal scaling. Any horizontal offset must be equal to some number of whole periods.

Choices A and B show tan( )+2, the correct vertical offset. However, choice A has a horizontal scale factor of 2. The correct choice is B, which has no horizontal scaling (the coefficient of x is 1) and a horizontal offset of π, one full period.

_____

Comment on horizontal scaling

Horizontal scaling is different from vertical scaling in that using k·x in place of x compresses the graph horizontally by a factor of k. On the other hand, using k·f(x) in place of f(x) expands the graph vertically by a factor of k.

Answer:

0.3

Step-by-step explanation:

Given: The odds of winning a contest are 3:7

To find: probability of winning the contest

Solution:

Probability refers to chances of occurrence of an event.

Odds are defined as (chances for success) : (chances against success)

Probability of winning = (chances for success) : (chances for success + chances against success)  

As odds of winning a contest are 3:7,

(chances for success) : (chances against success) = 3:7

So,

Probability of winning the contest = [tex]\frac{3}{3+7} =\frac{3}{10}=0.3[/tex]

Final answer:

To find the probability of winning a contest when given odds, add the two parts of the odds together and divide the favorable outcome by the total outcomes. For odds of 3:7, the probability of winning the contest is 3/10.

Explanation:

The odds of winning a contest are 3:7. What is the probability of winning the contest?

To find the probability from odds, you need to add the two numbers together to get the total possible outcomes. In this case, 3 + 7 = 10. Then, divide the favorable outcome by the total outcomes, so 3/10. This gives a probability of winning the contest as 3/10.

Answer:

(D)117 Cubic Inches

Step-by-step explanation:

Dimensions of the box are:

Length[tex]=7\frac{1}{2}\:inch[/tex]

Width[tex]=4\frac{1}{3}\:inch[/tex]

Height[tex]=3\frac{3}{5}\:inch[/tex]

Volume of the Box =Length X Width X Height

[tex]=7\dfrac{1}{2}X4\dfrac{1}{3}X3\dfrac{3}{5}\\\\=\dfrac{15}{2}X\dfrac{13}{3}X\dfrac{18}{5}\\\\=\dfrac{15X13X18}{2X3X5}\\\\=\dfrac{3510}{30}[/tex]

=117 Cubic Inches

The volume of the box is 117 cubic inches.

Answer:

D) 117 cubic inches

Step-by-step explanation:

Have a wonderful day!

Answer:

184

Step-by-step explanation:

Find the common difference first   d = 6 - 4 = 2

first term  a_1  = 4

a_n = (n -1)*d + a_1

a_91 = (91 - 1) * 2 + 4

a_91  is the 91st term:

a_91 = 90*2 + 4

a_91 = 180 + 4 = 184

The 91st term of the arithmetic sequence 4,6,8 is 184.

The question requires us to find the 91st term of the arithmetic sequence 4,6,8. In an arithmetic sequence, each term is equal to the previous term plus a constant difference. In this case, the common difference is 2 (6-4 or 8-6).

To find the 91st term of an arithmetic sequence, we use the formula a + (n-1)d, where a is the first term, n is the term number, and d is the common difference. Plugging in the values, we get: 4 + (91-1) * 2 = 4 + 180 = 184. So, the 91st term in the sequence is 184.

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Answer:

1). 1.25 / 250 = .005M

.005 = 1 liter

2). (20)(.5) = 10M

have a good day, and be safe

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⊕ΘΞΠΤ⊕

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Answer:

6.40

Step-by-step explanation:

Find the number in the tenth place (the first 4) and look one place to the right for the rounding digit (the second 4).

Round up if this number is greater than or equal to 5

and round down if it is less than 5.

4 is less than five, therefore should be rounded down.

Answer:

6.44

Step-by-step explanation:

The nearest cent is the hundredths place (or two decimals)

6.4442 rounds to 6.44

The next number is less than 5 so we leave the hundredths place alone.

Answer:

  b) perpendicular to the plane containing both vectors

Step-by-step explanation:

The cross product is perpendicular to both contributing vectors. Consequently, it is perpendicular to the plane containing them.

The cross product of two vectors results in a vector that is perpendicular to the plane containing both input vectors. This is a key principle in vector physics.

The resultant vector from the cross product of two vectors is perpendicular to the plane containing both vectors involved in the cross product. This is a fundamental principle in vector physics. To further illustrate, if you have two vectors A and B, and you perform a cross product, the resulting vector, often denoted as AxB, will be a vector perpendicular (or orthogonal) to the plane containing vectors A and B. Therefore, the correct option is 'b'.

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Phytagoras Theorem :

c² = a² + b²

c² = 9² + 2²

c² = 81 + 4

c² = 85

c = √85

So, the distance between the following points is √85

Hope it helpful and useful :)

Answer:

a. 37

Step-by-step explanation:

"Jessica brings her friends to a party. There are 40 people attending. Jessica brings 2 friends there. How many people are at the party without Jessica and her friends?

"

40 total minus Jessica and her friends = 37

Hope this helps!

Answer:

C.) 37 I think

Step-by-step explanation:

SoRrY i'M nOt sMaRt. But i think it's 37 and then minus her and her 2 friends means:

[tex]40-3=37:)[/tex]

We have been given a right triangle. We are asked to find the value of x.

We can see that x is opposite side to angle that measures 62 degrees and adjacent side to angle is 4 units.

We know that tangent relates adjacent and opposite side of right triangle.

[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]

[tex]\text{tan}(62^{\circ})=\frac{x}{4}[/tex]

[tex]4\cdot \text{tan}(62^{\circ})=\frac{x}{4}\cdot 4[/tex]

[tex]4\cdot (1.880726465346)=x[/tex]

[tex]7.522905861384=x[/tex]

[tex]x=7.522905861384[/tex]

[tex]x\approx 7.52[/tex]

Therefore, the value of x is approximately 7.52 units and option 'd' is the correct choice.

The solution to the inequality [tex]\( \frac{2}{3}x - \frac{5}{6} \geq \frac{1}{2} \)[/tex] is [tex]\( x \geq 2 \)[/tex].

Given inequality: [tex]\( \frac{2}{3}x - \frac{5}{6} \geq \frac{1}{2} \)[/tex]

Step 1: To simplify the equation, let's find a common denominator for the fractions. The least common multiple (LCM) of 3 and 6 is 6.

Step 2: Rewrite the fractions with the common denominator, which is 6.

So, [tex]\( \frac{2}{3}x - \frac{5}{6} \)[/tex] becomes [tex]\( \frac{4x}{6} - \frac{5}{6} \).[/tex]

Step 3: Now, we have the equation [tex]\( \frac{4x}{6} - \frac{5}{6} \geq \frac{1}{2} \).[/tex]

Step 4: Combine the fractions on the left side of the equation: [tex]\( \frac{4x - 5}{6} \geq \frac{1}{2} \)[/tex].

Step 5: To get rid of the denominator, multiply both sides of the equation by 6 to clear it.

[tex]\( 6 \times \frac{4x - 5}{6} \geq 6 \times \frac{1}{2} \)[/tex]

This simplifies to: [tex]\( 4x - 5 \geq 3 \)[/tex]

Step 6: Now, let's isolate [tex]\(x\)[/tex] by adding 5 to both sides:

[tex]\( 4x - 5 + 5 \geq 3 + 5 \)[/tex]

[tex]\( 4x \geq 8 \)[/tex]

Step 7: Finally, divide both sides by 4:

[tex]\( \frac{4x}{4} \geq \frac{8}{4} \)[/tex]

[tex]\( x \geq 2 \)[/tex]

Complete correct question:

Solve: [tex]\frac{2}{3} x-\frac{5}{6} \geq \frac{1}{2}[/tex]

Answer:

The probability that a player wins the jackpot is [tex]\frac{1}{292201338}[/tex]

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the first five numbers are selected is not important, so we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

First five numbers:

Desired:

5 correct numbers, from a set of 5. So

[tex]D = C_{5,5} = \frac{5!}{5!(5-5)!} = 1[/tex]

Total:

5 numbers from a set of 69. So

[tex]T = C_{69,5} = \frac{69!}{5!(69-5)!} = 11238513[/tex]

Probability:

[tex]P_{5} = \frac{D}{T} = \frac{1}{11238513}[/tex]

-------------

Sixth number:

1 from a set of 26

Then

[tex]P_{6} = \frac{1}{26}[/tex]

-------------

Probability of winning the prize

[tex]P = P_{5} \times P_{6} = \frac{1}{11238513} \times \frac{1}{26} = \frac{1}{292201338}[/tex]

The probability that a player wins the jackpot is [tex]\frac{1}{292201338}[/tex]

To calculate the probability of winning the jackpot in the Powerball lottery, we need to consider the probability of choosing the first five numbers correctly and the probability of choosing the sixth number correctly. Multiply the probabilities from these two steps to find the overall probability.

To calculate the probability of winning the jackpot in the Powerball lottery, we need to consider two parts: the probability of choosing the first five numbers correctly (regardless of order) and the probability of choosing the sixth number correctly.

To find the overall probability, we multiply the probabilities from the two steps:

P(winning jackpot) = P(choosing first five numbers correctly) x P(choosing sixth number correctly) = [P(choosing one number correctly)]^5 x P(choosing one number correctly) = (5/69)^5 x 1/26

Calculating this expression gives us the probability of winning the jackpot in the Powerball lottery.

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Answer:

Step-by-step explanation:

The mean of the set of data given is

Mean = (60 + 120 + 110 + 80 + 70 + 90 + 100 + 130)/8 = 95

Standard deviation = √(summation(x - mean)/n

n = 8

Summation(x - mean) = (60 - 95)^2 + (120 - 95)^2 + (110 - 95)^2 + (80 - 95)^2 + (70 - 95)^2 + (90 - 95)^2 + (100 - 95)^2 + (130 - 95)^2 = 4200

Standard deviation = √(4200/8) = 22.91

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ ≤ 120

For the alternative hypothesis,

µ > 120

This is a right tailed test.

Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.

Since n = 8,

Degrees of freedom, df = n - 1 = 8 - 1 = 7

t = (x - µ)/(s/√n)

Where

x = sample mean = 95

µ = population mean = 120

s = samples standard deviation = 22.91

t = (95 - 120)/(22.91/√8) = - 3.09

We would determine the p value using the t test calculator. It becomes

p = 0.009

Since alpha, 0.05 > than the p value, 0.009, then we would reject the null hypothesis. Therefore, At a 5% level of significance, the sample data showed significant evidence that the average seven-year-old would be able to swim across an Olympic-sized pool in more than 120 seconds after taking lessons from their instructors.

Using the one - sample t test, we can conclude that average 7year old will swim in less than 120 hours

Given the data :

Using calculator :

The degree of freedom :

The hypothesis :

[tex]H_{0} : μ > 120 [/tex]

[tex]H_{1} : μ ≤ 120 [/tex]

From the equality sign in the alternative hypothesis, we have a left-tailed test

Test statistic :

[tex] \frac{x - μ}{\frac{s}{\sqrt{n}}} [/tex]

Inputting the values :

[tex] \frac{95 - 120}{\frac{24.49}{\sqrt{8}}} [/tex]

[tex] \frac{-25}{8.658} = - 2.887 [/tex]

Calculating the P-value :

Pvalue = 0.012

Decison Region :

Since 0.012 < 0.05 ; we reject [tex]H_{0} [/tex] and conclude that average 7year old will swim in less than 120 hours.

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Beth's number, which indicates 60 parts out of 100, can be expressed as 60%, 0.60, 60/100, or in simplest form, 3/5. These representations are commonly used in mathematics to show percentages and their equivalent values.

Beth writes a number that shows 60 parts out of 100. In mathematics, expressing a part out of 100 is essentially describing a percentage. So, Beth's number could be expressed in several ways that all represent 60 out of 100. The simplest form would be 60%, which directly translates to 60 per 100. Another possible representation could be 0.60, which is the decimal form equivalent to 60%. If we were to convert this percentage into a fraction, it would be
60/100, which can also be simplified to
3/5. It cannot be a number such as N(60, 5.477) which suggests a normal distribution with a mean of 60 and a standard deviation of 5.477, nor can it be .9990 which is not equivalent to 60 parts out of 100 in any common mathematical representation.

Final answer:

No, the given probability experiment does not represent a binomial experiment because it does not meet the three conditions required for a binomial experiment.

Explanation:

No, the given probability experiment does not represent a binomial experiment. In order for an experiment to be considered a binomial experiment, it must meet three conditions:

1. There must be a fixed number of trials, denoted by 'n'. However, in the given experiment, the number of stocks that the investor purchases is not fixed.

2. There must be only two possible outcomes, called success and failure, for each trial. However, in the given experiment, the outcomes can have three possibilities: the stock can increase, decrease, or have no change in value.

3. The 'n' trials must be independent and repeated using identical conditions. However, in the given experiment, the success or failure of one stock can potentially influence the success or failure of another stock.

Answer:

Volume = 20

Step-by-step explanation:

To find volume of the shape you split the shape into two shapes: A triangle or pyramid and a rectangle

The volujme of a rectangle is W x L x H

A = 2 x 5 x 8

A = 80

The volume of a pyramid is

A = [tex]\frac{1}{2}[/tex]Bh    The B is the area of the base so B = L x W = 5 x 2 = 10 so B = 10

A = [tex]\frac{1}{2}[/tex] 10 x 4

A = [tex]\frac{1}{2}[/tex] 40

A = 20

Answer:

27

Step-by-step explanation:

PEMDAS

Answer:

[tex]y = (x+4)^{2}+6[/tex]

Step-by-step explanation:

The parabola with vertex at point (h,k) is described by the following model:

[tex]y - k = C\cdot (x-h)^{2}[/tex]

The equation which satisfies the conditions described above:

[tex]y - 6 = (x+4)^{2}[/tex]

[tex]y = (x+4)^{2}+6[/tex]

The two points are evaluated herein:

x = -6

[tex]y =(-6+4)^{2}+6[/tex]

[tex]y = (-2)^{2}+6[/tex]

[tex]y = 4 + 6[/tex]

[tex]y = 10[/tex]

x = -2

[tex]y = (-2+4)^{2}+6[/tex]

[tex]y = 2^{2} + 6[/tex]

[tex]y = 4 + 6[/tex]

[tex]y = 10[/tex]

The equation of the translated function is [tex]y = (x+4)^{2}+6[/tex].

Answer:

4*4*4*4*4

Step-by-step explanation:

Exponents are written as

b^x

where b is the base, and x is the number of times the base is being multiplied

We have

4^5

Therefore, 4 is the base, and it is being multiplied 5 times.

If we are to write it out, we have:

4*4*4*4*4

Therefore, the correct choice is B