Suppose that water is poured into a tank at a rate of 2000t 1000 gallons per minute for t > 0. If the tank started with 5000 gallons of water how much water is in the tank after 4 minutes

Answer:

13/13.3 or 10

Step-by-step explanation:

You said she paid $10 to join, if she spent at least $40, then we subtract 10, then divide 30 by 3 then you would get 10.

If we don't have to subtract and she spent around $40 on only books, it would be 13/13.3

Based on the histogram above, we will use median to describe this variable.

Hence, option (b) is correct choice.

A histogram is a graphical depiction of data distribution in statistics. The histogram is represented by a series of neighbouring rectangles, with each bar representing a different type of data. Statistics is a branch of mathematics that is used in a variety of areas.

The frequency distribution is represented graphically by a histogram.

The histogram may be analysed as a representation of frequencies and classes as linked rectangles.

Option B is the correct answer to this question.

Because the median is unaffected by big observations, we use it as a measure of central tendency while analysing the left skewed distribution.

The required image/ histogram is attached below:

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Evaluating Georgianna's claim using a hypothesis test.The claim is that the average child takes less than 5 years of piano lessons. Therefore, we use a one-tailed hypothesis test with a null hypothesis asH0: µ ≥ 5 versus the alternative hypothesis Ha: µ < 5.

Level of significance is not given, hence we can assume it to be 0.05. Calculating the test statistic as follows:$$t=\frac{\overline{x}-\mu }{s/\sqrt{n}}$$Substituting the given values in the above equation, we get$$t=\frac{4.6-5}{2.2/\sqrt{20}}$$So, t = -1.69, for a one-tailed test (left-tailed) and the degrees of freedom are n-1 = 19. Using the t-distribution table with α = 0.05 and 19 degrees of freedom, the critical value is -1.73, hence, -1.69 falls within the non-rejection region. Therefore, we cannot reject the null hypothesis. There is not enough evidence to support Georgianna's claim.b. Constructing a 95% confidence interval for the number of years students in this city take piano lessons, and interpret it in the context of the data.

The formula for confidence interval for a population mean is Interpretation: We can be 95% confident that the average number of years students in this city take piano lessons falls between 4.01 and 5.19 years.c. Explaining if the results from the hypothesis test and the confidence interval agreeYes, the results from the hypothesis test and the confidence interval agree because we cannot reject the null hypothesis in the hypothesis test. This means that the null hypothesis, H0: µ ≥ 5 is plausible. Further, the 95% confidence interval for the mean number of years students take piano lessons lies completely above the value of 5 years, which is Georgianna's claim. This is in line with the hypothesis test result. Thus, we can conclude that there is no sufficient evidence to support Georgianna's claim.

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Answer:

x=-4, y=-1

Step-by-step explanation:

Given the following system of equations, solve the system using elimination.

\(\left \{ {{-2x-y=9} \atop {2x-9y=1}} \right.\)

(1) - Add the equations together

\(\left\begin{array}{ccc}&-2x-y=9\\+&2x-9y=1\end{array}\right\\\\\Longrightarrow -10y=10\\\\\therefore \boxed{y=-1}\)

Notice how the x term was eliminated, hence the name for this method is "elimination."

(2) - Take the value we just found for y and plug it into either of the two equations and solve for x

\(2x-9y=1\\\\\Longrightarrow 2x-9(-1)=1\\\\\Longrightarrow 2x+9=1\\\\\Longrightarrow 2x=-8\\\\\therefore \boxed{x=-4}\)

(3) - Thus, the system is solved. When x=-4, y=-1.

Answer:

DE = 14

Step-by-step explanation:

Since, DE is a Mid-segment of triangle ABC.

Therefore,

DE = 1/2 * AC

2 DE = AC

2(5x - 1) = 3x + 19

10x - 2 = 3x + 19

10x - 3x = 19 +2

7x = 21

x = 21/7

x = 3

DE = 5x - 1

DE = 5*3 - 1

DE = 15 - 1

DE = 14

Answer:

x² - 2x - 2

By Completing the Square....

x² - 2x + 1² - 2 - 1²

(x - 1)² - 3 .....

Hope it helps.

Answer:

The sum of the exterior angles of a decagon is 360°

The sum of the exterior angles in an any polygon = 360°

Alternate method:

Each exterior angle in a polygon : 360 ÷ number of sides

Here, decagon has 10 sides.

Then, each exterior angle: 360 ÷ 10 = 36°

Then all 10 sides together has : 36° x 10 = 360°

Step-by-step explanation:

The statement "It is rigid because all side lengths and angles are congruent" is true.

In mathematics, a transformation is considered rigid if it preserves distances and angles. For example, a translation, rotation, or reflection is a rigid transformation because it preserves distances and angles. If a transformation preserves side lengths and angles, then it is considered rigid, regardless of whether the side lengths and angles are congruent or not.

Answer: A. it is rigid because all side lengths and angles are congruent.

Step-by-step explanation: RIGHT ON EDGE 2023

Answer:mie is

Step-by-step explanation: hehe

The equation of the best fit is y = 16.89x + 134.95 and projected profit is $2700.07

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

\(\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}\)

\(\rm c = \dfrac{\sum y -m \sum x}{n}\)

The line of best fit;
y = mx + c

m = 16.89

c = 134.95

y = 16.89x + 134.95

Plug x = 2010 - 2002 = 8

y = 16.89(8) + 134.95

y = $2700.07

Thus, the equation of the best fit is y = 16.89x + 134.95 and projected profit is $2700.07

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Answer:

Step-by-step explanation:

the domain of x is (-2,4)

the domain of y is (-4, 2)

A cylindrical tank standing upright has radius 20cm. If the water is being drained at rate  25 cm³/s the tank level drops at rate 0.02 cm/s.

Recall the formula for the volume of a cylinder:

V = πr². h

Where:

r = radius of the base

h = height of the cylinder

Take the derivative with respect to t

dV/dt = πr². dh/dt

Substitute dV/dt = 25 cm³/s and r = 20 cm:

25 = π x 20² x dh/dt

dh/dt = 25 / (400π) = 0.02 cm/s

Therefore, the level of the cylindrical tank drops at rate 0.02 cm/s

Complete question:

A cylindrical tank standing upright has radius 20cm. How fast does the water level in the tank drop when the water is being drained at 25 cm³/s?

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The statement that correctly compares the water bills for the two neighborhood is D. The range of water bills on Pine Road is higher than the range of water bills on Front Street.

The minimum water bill on Pine Road is $100, while the maximum is $250.

The minimum water bill on Front Street is $100, while the maximum is $225.

Therefore, the range of water bills on Pine Road (250 - 100 = 150) is higher than the range of water bills on Front Street (225 - 100 = 125).

The other statements are not correct. The overall water bills on Pine Road and Front Street are about the same. There are more homes on Front Street with water bills above $225, but there are also more homes on Pine Road with water bills below $150.

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Residents in a city are charged for water usage every three months. The water bill is computed from a common fee, along with the amount of water the customers use. The last water bills for 40 residents from two different neighborhoods are displayed in the histograms. 2 histograms. A histogram titled Pine Road Neighbors has monthly water bill (dollars) on the x-axis and frequency on the y-axis. 100 to 125, 1; 125 to 150, 2; 150 to 175, 5; 175 to 200, 10; 200 to 225, 13; 225 to 250, 8. A histogram titled Front Street Neighbors has monthly water bill (dollars) on the x-axis and frequency on the y-axis. 100 to 125, 5; 125 to 150, 7; 150 to 175, 8; 175 to 200, 5; 200 to 225, 8; 225 to 250, 7. Which statement correctly compares the water bills for the two neighborhoods? Overall, water bills on Pine Road are less than those on Front Street. Overall, water bills on Pine Road are higher than those on Front Street. The range of water bills on Pine Road is lower than the range of water bills on Front Street. The range of water bills on Pine Road is higher than the range of water bills on Front Street.

Answer:

23

ewr

Step-by-step explanation:

Since we mix 5 oz of 30% with 20 oz of 15%, then

Let us add 5 x 30% and 20 x 15%

This 4.5 oz has x concentration of the total amount 5 oz and 20 oz, then

we will multiply x by (5 + 20) and equate the answer by 4.5

Divide both sides by 25

Change it to percent by multiplying it by 100%

The percent of concentration is 18%

The lengths of the diagonals are approximately 10.6 cm and 31.8 cm.

To solve this problem, we can use the formula for the area of a rhombus, which is A = (d₁ x d₂)/2, where A is the area, and d₁ and d₂ are the lengths of the diagonals.

We are given that the area of the rhombus is 168 square centimeters, so we can substitute this value into the formula:

=> 168 = (d₁ x d₂)/2.

We are also given that one diagonal is three times as long as the other, so we can express the length of one diagonal in terms of the other: d₁ = 3d₂.

Substituting this expression for d₁ into the formula for the area, we get:

168 = (3d₂xd₂)/2 336 = 3d₂²2 d₂² = 112 d₂ = √(112) = 10.6 (to the nearest tenth of a centimeter)

Using the expression for d₁ in terms of d₂, we can find the length of the other diagonal:

d₁ = 3d₂ = 3(10.6) = 31.8 (to the nearest tenth of a centimeter)

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In shape (i), there are two electron domains around the central atom. This means that the electron-domain geometry is linear. However, there are two bonding pairs and no lone pairs of electrons around the central atom, resulting in the molecular geometry also being linear.

The concept of electron-domain geometry and molecular geometry is essential in understanding the properties of molecules. The electron-domain geometry is determined by the number of electron domains (bonding or lone pairs) around the central atom in a molecule. On the other hand, the molecular geometry is determined by the arrangement of atoms in the molecule, taking into account the presence of lone pairs.

Knowing the electron-domain geometry and molecular geometry of a molecule is crucial in predicting its polarity and reactivity. For instance, polar molecules have an asymmetric distribution of electron density, while nonpolar molecules have a symmetric distribution. This difference in polarity affects the physical and chemical properties of a molecule, such as boiling point, melting point, and solubility.

In summary, in shape (i), both the electron-domain geometry and molecular geometry are linear, which means that the central atom has two bonding pairs and no lone pairs. Understanding the electron-domain and molecular geometry of molecules is essential in predicting their properties and behavior.

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The given expression is (0 – 267 – 3).We need to expand the above-given expression in the form of partial fractions.

Now, we can write the given expression as(0 – 267 – 3) = 0 – (267 + 3)

Now, (267 + 3) = (k)(0 – 267 – 3) + (A)(0) + (B)(-267) + (C)(-3)

Now, substitute x = 0, we get0 – (267 + 3) = k(0 – 267 – 3) + (A)(0) + (B)(-267) + (C)(-3)⟹ -270 = -3k + (-267B – 3C)

Now, substitute x = 267, we get0 – (267 + 3) = k(0 – 267 – 3) + (A)(0) + (B)(0) + (C)(-3)⟹ -270 = -3k – 3C

Now, substitute x = 3, we get0 – (267 + 3) = k(0 – 267 – 3) + (A)(0) + (B)(-267) + (C)(0)⟹ -270 = -3k – 267B.

Now, solving these three equations we get k = 1, B = 1/267, and C = -90.

Substituting these values in equation 1, we get0 – (267 + 3) = (1)(0 – 267 – 3) + (0)(0) + (1/267)(-267) + (-90)(-3)0 – 270 = -3 – 90(3) 0 – 270 = -3 – 2700 + (1/267)(-267) ⟹ (1/267) = 1/(-890)

Hence, the partial fraction expansion and the coefficients are given by -3 - 90/(x - 3) + 1/(-890)(x + 270).

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Answer:

Shape 1 and Shape 3

Step-by-step explanation:

An obtuse angle is an angle that is greater than 90° but less than 180°.

We can see that the first shape has 2 angles that are greater than 90°, making this a correct choice.
The second shape has 4 boxes, meaning the angles are exactly 90°, making this incorrect.

The third shape has 6 angles that are greater than 90°, making this another correct choice.

The last shape has all 3 angles under 90°, making this also incorrect.

So, the 1st and 3rd shapes are correct.

Hope this helps! :)

Step-by-step explanation:

hope it is helpful to you

the probability of passing either test on the first attempt is 14/15.

The probability of passing either test on the first attempt can be determined using the formula: P(A or B) = P(A) + P(B) - P(A and B)Where A and B are two independent events. Therefore, the probability of passing the written test in the first attempt (A) is 9/10, and the probability of passing the road test in the first attempt (B) is 5/6. The probability of passing both tests the first time is 4/5 (P(A and B) = 4/5).Using the formula, the probability of passing either test on the first attempt is:P(A or B) = P(A) + P(B) - P(A and B)= 9/10 + 5/6 - 4/5= 54/60 + 50/60 - 48/60= 56/60 = 28/30 = 14/15Therefore, the probability of passing either test on the first attempt is 14/15.

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Step-by-step explanation:

14+12x=14x-2

14+2= 14x-12x

16=2x

x=8°

Theoretical probability is what might happen, but the experimental probability is definitely happens in trials. The probability in these cases is 0.25.

Theoretical probability is based on the total outcomes vs the desired outcomes; due to this, this is just the expectation of what will hapen. However, as this is mainly based on expectations, it is not completely accurate.

On the other hand, the experimental probability is based on the observation of reality as the probability is tested, which makes it more accurate.

Desired outcomes /total outcomes

Probability of getting red in the spinner:

Probability of getting a 4 in a dice

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The probability of flipping four coins is 0.0625

Total coins = 4

The study of chances, which are determined by the ratio of favourable occurrences to probable cases, is known as probability.

When flipping a coin, there are two possible outcomes (heads or tails), hence the likelihood of flipping a head-up coin is equal to the likelihood of flipping a tail-up coin.

Thus, the probability is = 1/2

Calculating the probability of getting all heads or all tails when flipping 4 coins -

= 1/2 x 1/2 x 1/2 x 1/2

= 1/16

In decimal form, this will be 0.0625

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Answer:

-3

Step-by-step explanation:

Step 1: Solve (-2+(-1))^2/3 3

           1. -2+(-1) = -3

           2. (-3)^2 = 9

           3. 9/3 = 3

Step 2: Solve (-4)^2-17 -1

           1. 3/-1

Step 3: Simplify 3/-1 = -3. I hope this helped and please don't hesitate to reach out with more questions!

The total number of people that die of the disease after the herd immunity threshold is reached can be determined by looking at the value of the R(t) curve after it reaches the herd immunity threshold.

i) The total population of the Portland-metro area, N, can be determined by looking up the population of the city, county, and other areas that make up the metro area.

ii) To determine the values of a and b, we need to look at the basic reproduction number, R0. For an SIR model, the constant a is equal to the basic reproduction number (R0=4.5), and the constant b is equal to (a/N).

iii) To determine the initial values S(0), I(0) and R(0), we can use the equation S(0)=N-5-0.15N, I(0)=5, and R(0)=0.15N.

iv) To solve the SIR model numerically, we need to create a differential equation for each variable (S, I, and R) and use numerical integration to solve the system. Then, a graph can be created to show the values of S, I, and R over time.

v) From the graph, we can see that the total number of people infected is equal to the peak of the I(t) curve.

vi) The total number of people that die from the disease is equal to the peak of the R(t) curve.

vii) The peak of the outbreak is at the time when the I(t) curve has its highest value.

viii) The outbreak is over when the I(t) curve reaches 0.

ix) The herd immunity threshold is reached when the R(t) curve reaches a value equal to the basic reproduction number (R0).

x) The total number of people that die of the disease after the herd immunity threshold is reached can be determined by looking at the value of the R(t) curve after it reaches the herd immunity threshold.

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Answer:

Points shouldn't be connected by straight lines but rather a curve

Step-by-step explanation:

None of the points seem to be incorrect, and the x and y-axis are labeled correctly as well as the points, the only issue I would say there is, is that this is a quadratic equation, so Brogan shouldn't be drawing straight lines between points, but rather a curve.

The discount given on the cost of the meal is $15

When a government imposes an obligational fee or financial charge on an individual or group in order to raise funds for public projects that support the best facilities and infrastructure, the action is referred to as a tax.

step1

According to the question, we are given the following information

The original cost of the meal = $75

Off coupon = 20%

step2

Required

The number of coupons given

coupon amount = 0.2 * 75

coupon amount = $15

Hence the discount given on the cost of the meal is $15

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If the original price was $75 and Fatima used a 20% coupon, then Fatima saved $15.

    0.20 x 75 = 15

This means the cost of the meal that was taxed was a $60 meal.

Now we also know that after tax, the price of the meal came back to a $75 cost.  This means that the amount of tax was also $15, but it's a $15 tax on a $60 meal, so this is a 25% tax.

    $15 tax / $60 meal = 0.25 = 25%

The trick here is that in the beginning, the savings is based on the $75 meal, while the tax is based on a $60 meal, so the percentages are not the same.

The required limit is 8/3.

To find the limit: lim(x→π/2) (sec(x) − tan(x)).

First, we check whether it is in an indeterminate form. Evaluating the limit directly, we have:

lim(x→π/2) (sec(x) − tan(x)) = sec(π/2) - tan(π/2) = 1/cos(π/2) - sin(π/2).

The denominator of the above expression approaches zero, indicating an indeterminate form of 0/0. Therefore, we can use L'Hôpital's Rule.

We differentiate the numerator and denominator separately and apply the limit again. Differentiating, we get:

lim(x→π/2) [d/dx(sec(x)) - d/dx(tan(x))] / [d/dx(x)] ... [Using L'Hôpital's Rule]

= lim(x→π/2) [sec(x)tan(x) + sec²(x)] / [1].

Putting the limit value, we have:

= sec²(π/2) + sec(π/2)tan(π/2).

We know that sec(π/2) = 1/cos(π/2) and tan(π/2) = sin(π/2)/cos(π/2).

Therefore, sec²(π/2) + sec(π/2)tan(π/2) = [1/cos²(π/2)] + [sin(π/2)/cos²(π/2)]

= [1 + sin(π/2)] / [cos²(π/2)].

Putting the value of π/2, we get:

[1 + sin(π/2)] / [cos²(π/2)] = [1 + 1/2] / [3/4]

= [3/2] * [4/3]

= 8/3.

Therefore, the required limit is 8/3.

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