A water tank initially contained 57 liters of water. It is being drained at a constant rate of 2.5 liters per minute.
How many minutes have passed m when the tank contains 35 liters? Round go the nearest tenth

The transformations that change the domain of a function are given as follows:

The domain of a function is defined as the set containing all the values assumed by the independent variable x of the function, which are also all the input values assumed by the function.

Hence we must look at transformations that change the values of x of the function, which are given as follows:

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Answer:

Volume of shed = 38 m³

Step-by-step explanation:

Given:

Length = 5 m

Width = 2 m

Height of wall = 3 m

Height of triangular shed = 1.6 m

Find:

Volume of shed

Computation:

Volume of shed = Volume of walls + Volume of triangular shed

Volume of shed = [lbh] + [1/2][Base area]h

Volume of shed = [(5)(2)(3)] + [1/2][(5)(2)]1.6

Volume of shed = [30] + [8]

Volume of shed = 38 m³

The linear function that predicts the number of calculators sold per week (y) at a price of x dollars is, y = -400x + 46,000

To determine a linear function that predicts the number of calculators sold per week at a certain price, we can use the given information. Let's assign "x" as the price of the calculator and "y" as the number of calculators sold per week.
We have two data points:
At a price of $90, 10,000 calculators are sold per week.
At a price of $85, 12,000 calculators are sold per week.
Using these two points, we can find the slope of the linear function:
Slope (m) = (change in y) / (change in x)
= (12,000 - 10,000) / (85 - 90)
= 2,000 / -5
= -400
Now, let's use one of the data points to find the y-intercept (b):
Using the point (x, y) = (90, 10,000):
y = mx + b
10,000 = -400(90) + b
10,000 = -36,000 + b
b = 46,000
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Answer:

6.

Just count the x's on the graph...

The polynomial that represents the area of the shaded region is given as follows:

x² - 3x + 36.

The area of a rectangle is given by the multiplication of the width and the length of the triangle, as follows:

A = lw.

For the entire region, the area is given as follows:

A = (x + 1)(x + 1)

A = x² + 2x + 1.

The area of the white region is given as follows:

Aw = 5(x - 7)

Aw = 5x - 35.

Then the area of the shaded region is given as follows:

As = A - Aw

A = x² + 2x + 1 - (5x - 35)

A = x² + 2x + 1 - 5x + 35

A = x² - 3x + 36.

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Since the calculated F-value of 7.098 is greater than the critical value of 5.79, we reject the null hypothesis and conclude that the population variance of total sales during active price competition is higher than during duopoly and tacit collusion at the 5% level of significance.

For the above issue, the null and alternate hypotheses are as follows:

The population variations of total sales under duopoly, active price competition, and tacit cooperation are all identical.

In contrast to duopoly and implicit collusion, total sales population variance is larger under active price competition.

To test the null  hypothesis, we must use a two-tailed F- test with a 5 % threshold of significance. The ratio of the sample variances is used to determine the F- statistic.

F = s1² / s2²

Where:
s1² - Sample Variance (Active price competition)

s2² -  SAmple variance (Duopoy and Tacit collusion)


Since n1-1 = 3
and n2-1 = 6

F = 114.09 / 16.08
F = 7.098

Having derived same, we know that the critical values of F for a two-tailed test with 3 and 6 degrees of freedom at 5% level of significance are:

Critical Value (3) = 5.14
Critical Value (6) = 5.79

Therefore, since the F-value > Critical Value in both cases, we must reject the null hypothesis.

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Answer:

2*2•5*2•13

Step-by-step explanation:

* = to the power of.

Answer:

Step-by-step explanation:

5200 = 52 * 100

         = 4 * 13 * 10 * 10

        = 2 * 2 * 13 * 2 * 5 * 2 * 5

        = 2⁴ * 5² * 13

Answer:

X=90

..............

The area of the shaded region is 40π/3 square cm if the radius of the small circle r is 3 cm and the radius of the large circle R is 7 cm.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have a circle in which the shaded region is shown.

The radius of the small circle r = 3 cm

The radius of the large circle R = 3+4 = 7 cm

The area of the shaded region:

= area of the large circle sector - an area of the small circle sector

= (120/360)[π7²] - (120/360)[π3²]

= 49π/3 - 3π

= 40π/3 square cm or

= 13.34π square cm

Thus, the area of the shaded region is 40π/3 square cm if the radius of the small circle r is 3 cm and the radius of the large circle R is 7 cm.

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Answer:

see below

Step-by-step explanation:

b = √3

then move t to the end you'll see

m= -0.4√13

============================================

Work Shown:

P(A and B) = P(A)*P(B|A)

P(A and B) = 0.8*0.31

P(A and B) = 0.248

The notation P(B|A) means "Probability of B given A". It's the same as "P(B) given event A has happened". It is conditional probability notation. The symbol between the A and B is a vertical line and not a letter.

There is a Weak positive association between the amount of goals scored and the number of wins a hockey team has. Most of the data points fall between 4 goals scored and 5  number of wins. Causation cannot be established because their relationship was not in a controlled setting.

When if a relationship between two variables is said to be  negative, it is one that does not just necessarily mean that the association is weak. Although though both variables tend to increase in reaction to one another, a weak positive correlation depicts that the relationship is not very strong.

Therefore, even though  the data tells us that there is a weak positive relationship that exist between the two variables, it is vital to know that that correlation does not equal causation.

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Answer:

6 3/8

Step-by-step explanation:

1.5x4.25=6.375=51/8= 6 3/8

Answer:

y = -8

Step-by-step explanation:

2(y-2)- 6y-28 = 0

2y - 4 -6y - 28 = 0

-4y = 32

y = -8

The expansion of the function \((3x - 4)^4\) simplifies to \(81x^4 - 432x^3 + 864x^2 - 768x + 256.\)

To expand the function \(f(x) = (3x - 4)^4\), we can use the binomial theorem. According to the binomial theorem, for any real numbers a and b and a positive integer n, the expansion of \((a + b)^n\) can be written as:

\((a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^{(n-1)} b^1 + C(n, 2)a^{(n-2)} b^2 + ... + C(n, n-1)a^1 b^{(n-1)} + C(n, n)a^0 b^n\)

where C(n, k) represents the binomial coefficient, which is given by C(n, k) = n! / (k!(n-k)!).

Applying this formula to our function \(f(x) = (3x - 4)^4\), we have:

\(f(x) = C(4, 0)(3x)^4 (-4)^0 + C(4, 1)(3x)^3 (-4)^1 + C(4, 2)(3x)^2 (-4)^2 + C(4, 3)(3x)^1 (-4)^3 + C(4, 4)(3x)^0 (-4)^4\)

Simplifying each term, we get:

\(f(x) = 81x^4 + (-432x^3) + 864x^2 + (-768x) + 256\)

Therefore, the expanded form of the function \(f(x) = (3x - 4)^4\) is \(81x^4 - 432x^3 + 864x^2 - 768x + 256\).

Note that the coefficient of \(x^3\) is -432, the coefficient of \(x^2\) is 864, the coefficient of x is -768, and the constant term is 256.

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Note the complete question is

Answer:

  8

Step-by-step explanation:

You want to know the measure of segment XY if ∆XYZ ≅ ∆MNL and MN = 8.

Segment XY is named using the first two vertices listed in the name of ∆XYZ. That means the segment is the same length as the one named by the first two vertices listed in the name of congruent ∆MNL, segment MN.

Segment MN is given as 8 units long. Segment XY is congruent, so is also 8 units long.

  XY = 8 units

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Answer:

0.7$ permile

32.90$ for 47 mile

Step-by-step explanation:

25.20$ for 36 mile

1. Find the cost for a mile

25.20$ ÷ 36 mile = 0.7$ per mile

2. The cost for 47 mile

0.7$ × 47 mile = 32.90$

Please vote if this helps you! Thanks

Answer:

(a) Null Hypothesis, \(H_0\) : \(\mu\) = 3.3 billion years      

Alternate Hypothesis, \(H_A\) : \(\mu\neq\) 3.3 billion years

(b) The conditions necessary to use this test is that the data must follow a normal distribution and we know about the population standard deviation.

(c) The value of z-test statistics is 1.77 and the P-value is 0.0768.

Step-by-step explanation:

The complete question is: A theory predicts that the mean age of stars within a particular type of star cluster is 3.3 billion years, with a standard deviation of 0.4 billion years. (Their ages are approximately normally distributed.) You think the mean age is actually greater, and that this would lend support to an alternative theory about how the clusters were formed. You use a computer to randomly select the coordinates of 50 stars from the catalog of known stars of the type you're studying and you estimate their ages. You find that the mean age of stars in your sample is 3.4 billion years.

Suppose you doubt the assumption that the mean age of the stars is 3.3 billion years, but you don't know whether the true mean age is less or greater than 3.3 billion years.

Let \(\mu\) = population mean age of the stars

(a) Null Hypothesis, \(H_0\) : \(\mu\) = 3.3 billion years      {means that the population mean is 3.3 billion years}

Alternate Hypothesis, \(H_A\) : \(\mu\neq\) 3.3 billion years      {means that the population mean is different from 3.3 billion years, i.e. the true mean age is less or greater than 3.3 billion years}

(b) The test statistics that will be used here is One-sample z-test statistics because we know about the population standard deviation;

                          T.S.  =  \(\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }\)  ~ N(0,1)

where, \(\bar X\) = sample mean age of stars = 3.4 billion years

            \(\sigma\) = population standard deviation = 0.4 billion years

            n = sample of stars = 50

The conditions necessary to use this test is that the data must follow a normal distribution and we know about the population standard deviation. And the conditions are satisfied here.

(c) So, the test statistics =  \(\frac{3.4-3.3}{\frac{0.4}{\sqrt{50} } }\)

                                         =  1.77

The value of z-test statistics is 1.77.

Also, the P-value of the test statistics is given by;

                P-value = P(Z > 1.77) = 1 - P(Z \(\leq\) 1.77)

                              = 1 - 0.9616 = 0.0384

For the two-tailed test, the P-value is calculated as = \(2 \times 0.0384\) = 0.0768.

As per the concept of probability the value of P(W) is P(W) = P(D1) + P(D2) + P(D1) * P(D2)

The probability of an event is a measure of the likelihood that it will occur.

To find P(W), we need to consider all the possible ways a person could experience the weird symptom. There are three possibilities:

They have only the first disease: P(W | D1) = 1 (since anyone with either disease will experience the symptom)

They have only the second disease: P(W | D2) = 1

They have both diseases: P(W | D1 and D2) = 1

Using the law of total probability, we can find P(W) by adding up the probabilities of each of these possibilities:

P(W) = P(W | D1)P(D1) + P(W | D2)P(D2) + P(W | D1 and D2)P(D1 and D2)

Since D1 and D2 are independent events, we have P(D1 and D2) = P(D1)P(D2). Substituting this into the equation:

P(W) = 1 * P(D1) + 1 * P(D2) + 1 * P(D1) * P(D2)

P(W) = P(D1) + P(D2) + P(D1) * P(D2)

We also know that a person with neither of these diseases will have the weird symptom with probability wo, so we need to subtract this from our final answer:

P(W) = P(D1) + P(D2) + P(D1) * P(D2)

Complete Question:

37. Two different diseases cause a certain weird symptom; anyone who has either or both of these diseases will experience the symptom. Let D₁ be the event of having the first disease, D2 be the event of having the second disease, and W be the event of having the weird symptom. Suppose that D1 and D2 are independent with P(Dj) = Pj, and that a person with neither of these diseases will have the weird symptom with probability wo. Let q;= 1-Pj, and assume that 0 < pj < 1.

Find P(W).

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Answer:

t = 6.8 years

Step-by-step explanation:

The formula for compound interest is

\(A(t)=P(1+r/n)^n^t\), where P is the principal/amount invested, r is the interest rate, n is the number of compound periods per year (4 for quarterly), and t in the time in years.

We know that A = $5900, P = $4000, and r = 0.0575 (we must convert the percentage to a decimal).  We must solve for t and round to the nearest tenth:

\(5900=4000(1+0.0575/4)^(^4^t^)\\\\59/40=(1623/1600)^4^t\\\\log(59/40)=log(1623/1600^4^t)\\\\log(59/40)=4t*log(1623/1600)\\\\log(59/40)/log(1623/1600)=4t\\\\1/4(log(59/40)/log(1623/1600))=t\\\\6.80773607=t\\\\6.8=t\)

Answer:

738

Step-by-step explanation:

1188 - 450 = 738

Answer:

210 = 2 * 3 * 5 * 7

Step-by-step explanation:

210/2 = 105

105 / 3 = 35

35 / 5 = 7

7 / 7 = 0

210 = 2 * 3 * 5 * 7

Answer:

55

Step-by-step explanation:

\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)

Make sure to always round up the required sample size to the nearest integer!

Answer:

did u figure it out?

Step-by-step explanation:

37.902

Step-by-step explanation:

3.14x12+12

Answer: 100

Step-by-step explanation:

200*10% or 200 * 0.10= 20

do the same for savings account 200*40%= 80

20 +80 = 100 subtract that from 200 she has 100 left.

Step-by-step explanation:

Let's call the average speed of the tortoise "t" (in meters per hour) and the average speed of the hare "h" (in meters per hour).

From the problem, we know that:

The tortoise leaves 8 minutes before the hare, so they have a 4-minute head start.

The hare crosses the finish line 4 minutes before the tortoise, so they have a 4-minute lead.

Therefore, the total time it takes for the hare to finish the race is 8 minutes less than the time it takes for the tortoise to finish the race. Let's call this time difference "dt".

The distance the hare runs is 21 meters, and the distance the tortoise runs is also 21 meters, so we have:

h * dt = 21 - t * (dt + 4 minutes)

To solve for the average speeds "t" and "h", we need to convert everything to units of hours. Let's convert 4 minutes to hours:

4 minutes = 4/60 hours = 1/15 hours

So, we can now rewrite the equation in terms of hours:

h * dt = 21 - t * (dt + 1/15 hours)

Rearranging and solving for t, we find:

t = (21 + h * dt) / (dt + 1/15)

Now, the hare runs 0.5 meters per hour faster than the tortoise, so:

h = t + 0.5

Substituting h = t + 0.5 into the equation for t, we get:

t = (21 + (t + 0.5) * dt) / (dt + 1/15)

Solving for t, we find:

t = 40/3 meters per hour

Finally, we can find the average speed of the hare by using h = t + 0.5:

h = 40/3 + 0.5 = 40/3 + 30/60 = 40/3 + 30/3 / 60 = 70/3 meters per hour

So the average speed of the tortoise is 40/3 meters per hour, and the average speed of the hare is 70/3 meters per hour

Answer:

150

Step-by-step explanation:

Answer:

D.)150

Step-by-step explanation:

Hope I helped

Answer:

correct choice is the last one

Step-by-step explanation:

let h = cost of 1 hamburger meal

let c = cost of 1 chicken nugget meal

5h + 6c = 39

9h + 2c = 35