A large container has 6 gallons of acid that needs to be dilluted by adding water. define the formula that models the ratio of the number of gallons of acid in the container compared to the total volume of liquid in the container when x gallons of water is added

\(\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{h}{3}~~,~~\underset{k}{1})} \qquad \stackrel{radius}{\underset{r}{2}} \\\\[-0.35em] ~\dotfill\\\\( ~~ x - 3 ~~ )^2 ~~ + ~~ ( ~~ y-1 ~~ )^2~~ = ~~2^2\implies (x -3)^2 + (y -1)^2 = 4 \\\\\\ (x^2-6x+9)+(y^2-2y+1)=4\implies x^2-6x+y^2-2y+10=4 \\\\\\ ~\hfill~ {\Large \begin{array}{llll} x^2-6x+y^2-2y+6=0 \end{array}} ~\hfill~\)

The probability that Tom is selected as President is 1 in 10, or 0.1.

The probability of Tom being selected as President is 1 in 10, or 0.1. This is because there are 10 members in the club, and each selection is equally likely. Therefore, the chance of Tom being chosen as President is the same as any other member of the club. This means that there is a 1 in 10 chance of Tom being selected as President, or a 0.1 probability. This probability can also be expressed as a fraction: 1/10, which is the same as 0.1. To calculate the probability of any other selection, such as the Vice-President or Treasurer, the same method can be applied. The probability of any one member of the club being selected for any position is 1 in 10, or 0.1.

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Answer:

-17

Step-by-step explanation:

The  probability is the same as in part (d):

(21/43) * (20/42) = 0.227 (rounded to the nearest thousandth)

Let's begin by calculating the total number of ways to select two students from a group of 43. This can be done using the combination formula:

C(43,2) = (43!)/(2!(43-2)!) = 903

a. To calculate the probability that a male is selected first and then a female, we need to consider that there are 22 ways to select a male from the group of 43 students, and then 21 ways to select a female from the remaining 42 students. Therefore, the probability is:

(22/43) * (21/42) = 0.280 (rounded to the nearest thousandth)

b. To calculate the probability that a female is selected first and then a male, we need to consider that there are 21 ways to select a female from the group of 43 students, and then 22 ways to select a male from the remaining 42 students. Therefore, the probability is:

(21/43) * (22/42) = 0.261 (rounded to the nearest thousandth)

c. To calculate the probability that two males are selected, we need to consider that there are 22 ways to select a male from the group of 43 students, and then 21 ways to select another male from the remaining 42 students. Therefore, the probability is:

(22/43) * (21/42) = 0.280 (rounded to the nearest thousandth)

d. To calculate the probability that two females are selected, we need to consider that there are 21 ways to select a female from the group of 43 students, and then 20 ways to select another female from the remaining 42 students. Therefore, the probability is:

(21/43) * (20/42) = 0.227 (rounded to the nearest thousandth)

e. To calculate the probability that no males are selected, we need to consider that there are 21 ways to select a female from the group of 43 students, and then 20 ways to select another female from the remaining 42 students. Therefore, the probability is the same as in part (d):

(21/43) * (20/42) = 0.227 (rounded to the nearest thousandth)

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Answer:

Ann's bakery

Step-by-step explanation:

450/3=150

560/4=140

Answer:

Native Americans relied heavily on bison for their survival and well-being, using every part of the bison for food, clothing, shelter, tools, jewelry and in ceremonies

Answer:

1800 screws per hour

Step-by-step explanation:

The graph of a certain geometric sequence can be described as a curve increasing from left to right. A sequence that would have a similar graph is the geometric sequence whose common ratio is less than 1.

A geometric sequence is defined as a sequence of numbers where each number is the product of the previous number and a fixed constant. The fixed constant is known as the common ratio, and it is denoted by r.The nth term of a geometric sequence is given by the formula an= ar^(n-1) where a is the first term and r is the common ratio of the sequence.

Similar graphIn a similar graph, the shape of the graph is the same, but the size may be different. Thus, the sequence that would have a similar graph to the given sequence is a geometric sequence whose common ratio is less than 1 because in such a sequence, the successive terms will be smaller than the previous term.This means that as we move from left to right, the values will gradually decrease in size, and the graph will look like a curve increasing from left to right.

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We need to find the work required to pump the water out of the spout. We are also given that water weighs 62.5lb/ft^3.Let us assume that the tank is a cone. The formula for finding the volume of a cone is given by V = 1/3 × πr^2h, where r is the radius and h is the height.

Let us assume that the height of the cone is h, and the radius of the cone at the top is R and at the bottom is r. The volume of the cone is given by the formula: V = 1/3 × πh(R^2 + Rr + r^2) Given that the tank is full of water. Let us assume that the height of the tank is H. Now the volume of water in the tank is equal to the volume of the cone. Thus we have: V = 1/3 × πh(R^2 + Rr + r^2)

= πr^2H

Substituting the value of V from the first equation in the second equation, we get:1/3 × πh(R^2 + Rr + r^2) = πr^2H

Therefore h = 3H(R^2 + Rr + r^2) / (R^2 + Rr + r^2)

Using the formula to find the work done, we have: Work = Force × Distance .Let us assume that the distance of the water from the spout is d. Therefore the work done to pump the water out of the spout is given by: Work = Force × d =mass × g × d

Here, g = 32.2 ft/s^2 (acceleration due to gravity)

mass = density × volume

The density of water is given as 62.5 lb/ft^

The volume of water is given by the formula: V = 1/3 × πh(R^2 + Rr + r^2)

Therefore,

mass = density × volume

= 62.5 × 1/3 × πh(R^2 + Rr + r^2)

Substituting the value of h from the equation (1), we have: m = 62.5 × 1/3 × π × [3H(R^2 + Rr + r^2) / (R^2 + Rr + r^2)] × (R^2 + Rr + r^2)

= 62.5 × πHR^2

We know that Work = Force × d

= mass × g × d

Therefore, the required work to pump the water out of the spout is 2019 ft-lb.

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Answer:

x = 91

Step-by-step explanation:

Opposite angles of an inscribed quadrilateral are supplementary.

x + 89 = 180

x = 91

The standard normal distribution  becomes smaller.

What is standard deviation?

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

becomes smaller.

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Answer:

y = -1/2x + 4

Step-by-step explanation:

y=mx+b

3 = m* 2 + b   .. pass (2,3)

y = 0       x = - b/m  .. x intercept

-b/m = 2b .... divide b both side

-1/m = 2           m= -1/2

b = 3 - 2m = 3 - (2*-1/2) = 4

equation:  y = -1/2x + 4

The estimate for the sum of the numbers is 230, and the actual sum of the numbers is 209.

To estimate the sum of the numbers, we can round each number to the nearest ten and then add them together. When rounding off to the nearest tens, we look at the number at the tenth position. If it is five and above, we round it off to the next nearest tens number and if it is below five, we round it off to the previous nearest tens number.

76 rounds to 80   since 6 is above 5
6 rounds to 10 since 6 is above 5
25 rounds to 30 since 5 is located at 5 and above interval
5 rounds to 10 since 5 is located at 5 and above interval
10 rounds to 10 since 0 is below 5
87 rounds to 90 since 7 is above 5

So, the estimate for the sum of the numbers is: 80 + 10 + 30 + 10 + 10 + 90 = 230

To find the actual sum of the numbers, we simply add them together without rounding:

76 + 6 + 25 + 5 + 10 + 87 = 209

The complete question is: 76. 6 25. 5 10. 87 =

What was Sela's estimate and what is the actual sum of the number?

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Answer:

Step-by-step explanation:

??

Answer:

neither, it should be 5, but there is no 5

Step-by-step explanation:

first of all c and d are too much to be the quotient. Also eliminate b and a, its none of the above

The height of the building is approximately 101.2 feet.

To determine the height of the building, we can use the angle of elevation, the distance between the viewer and the building, and the viewer's eye level. We can set up a right triangle, where the angle of elevation is the angle between the horizontal distance and the line of sight to the top of the building.

First, we need to find the vertical distance from the viewer's eye level to the top of the building. We can use the tangent function for this: tan(angle) = opposite/adjacent. In our case, the angle is 50°, and the adjacent side (the distance between the viewer and the building) is 80 ft. So, we have:

tan(50°) = vertical distance/80 ft

Solving for the vertical distance, we get:

vertical distance = 80 ft * tan(50°) ≈ 95.7 ft

Now, we need to add the viewer's eye level (5.5 ft) to the vertical distance to find the total height of the building:

height of the building = vertical distance + viewer's eye level ≈ 95.7 ft + 5.5 ft ≈ 101.2 ft

Therefore, the height of the building is approximately 101.2 feet when rounded to the nearest tenth of a foot.

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Answer:

Constant of proportionality: 1/3

Equation: y=a/3

Step-by-step explanation:

If you look at the table you’ll see that for y=1, a will equal 3.

So a=3y -> a/3=y

There for the constant is 1/3.

Answer:

y = x² - 9x + 26

hope to help!!

Answer:

The sequence is that, for every page 999 stars are drawn.

Step-by-step explanation:

999

999

999

999

3996

--

The evolution of 999 began when artist Juice WRLD decided to turn the evil number 6 into good... making and upside down 6 become a 9. Think of it as, "turn that frown upside down", or "turn evil into good".

Answer:

112in^2

Step-by-step explanation:

area of square = 10*10

                        = 100in

area of triangle = (6*4)/2

                          = 12in

100+12= 112

area of shape = 112in

Answer:

The area of the figure is 112

Step-by-step explanation:

For area, you multiply length x width

For the triangle, you do HALF THE BASE x height

So for the square, it's fairly simple

10 x 10 = 100

For the triangle, it's a bit more complicated

So we know the length of the square is 10 inches

And we see a 6 inch mark at the top of the square, showing where the square ends and the triangle begins

So the base of the triangle is 10 - 6 = 4 inches

Also, the overall height of the figure is 16 inches, and the height of the square is 10 inches

So the height of the triangle is 16 - 10 = 6 inches

So 4 is the base of the triangle

And 6 is the height of the triangle

So we half 4, which gives us 2

2 x 6 = 12

The area of the triangle is 12

And we already determined that the area of the square is 100

100 + 12 = 112

The area of the whole figure is 112

Answer:

I believe it's 1/3

I haven't done these in a while, but basically since there is 6 places and it's asking the probability of it landing on 2 out of the 6, so the answer would be 2/6. Since the answer isn't there, just simpify. 2/6 simplified is 1/3. I'm so sorry if wrong, I haven't done this in a while!

(a) The probability that a randomly selected policyholder lives more than 80 years is approximately 0.3106.  (b) Given that a male policyholder just turned 80, the probability that he will live for at least three more years is approximately 0.6166.

(a) To find the probability that a randomly selected policyholder lives more than 80 years, we need to calculate the cumulative probability of survival beyond 80 for both males and females separately, and then weigh them based on the gender distribution.

For males: Using the normal distribution with mean 75 and standard deviation 8, we find the probability of survival beyond 80 is approximately 0.3446.

For females: Using the normal distribution with mean 78 and standard deviation 6, we find the probability of survival beyond 80 is approximately 0.2847.

The weighted probability for a randomly selected policyholder is (0.60 * 0.3446) + (0.40 * 0.2847) = 0.3106.

(b) Given that a male policyholder just turned 80 years old today, we can use conditional probability to calculate the likelihood of him living for at least three more years.

Using the normal distribution with mean 75 and standard deviation 8, the probability of survival beyond 83 (80 + 3) is approximately 0.8621.

Therefore, the probability that a male policyholder, who just turned 80, will live for at least three more years is 0.8621.

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The missing information for q2 is the mean squares for treatment, which can be calculated by dividing the sum of squares for treatment. The missing information for q3 is the sum of squares for error.The missing information for q4 is the mean squares for error, which can be calculated by dividing the sum of squares for error.To find the p-value for the above ANOVA table, we need to use the F-distribution with degrees of freedom for treatment  and degrees of freedom for error.

Using the given mean squares for treatment (25.25) and mean squares for error (2.95), we can calculate the F-statistic as follows:

F = mean squares for treatment / mean squares for error
F = 25.25 / 2.95
F = 8.5593

The p-value can then be calculated using a one-tailed F-test with alpha level of 0.05:

p-value = pf(F, degrees of freedom for treatment, degrees of freedom for error)
p-value = pf(8.5593, 3, 16)
p-value = 0.0006

Therefore, the answer is A.
Q2: Mean squares (treatment) = Sum of squares (treatment) / Degree of freedom (treatment)
Mean squares (treatment) = 75.75 / 3
Mean squares (treatment) = 25.25
So, the answer for q2 is: a. 25.25

Q3: Mean squares (error) = Sum of squares (error) / Degree of freedom (error)
Mean squares (error) = 47.2 / 16
Mean squares (error) = 2.95
So, the answer for q3 is: b. 2.95

Q4: F-value = Mean squares (treatment) / Mean squares (error)
F-value = 25.25 / 2.95
F-value ≈ 8.5593
So, the answer for q4 is: c. 8.5593

Q5:P-value = 1 - pf(F-value, Degree of freedom (treatment), Degree of freedom (error))
P-value = 1 - pf(8.5593, 3, 16)

So, the answer for question 5 is: c. 1- pf(8.5593, 3, 16)

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Answer:

2x+10=12/2x-2=0 eS

Step-by-step explanation:

-

G

H

R

Congratulations on the new job posting on the LIS website that you have to

The net work done by the gravitational force on the block as it moves from point A to point C is zero. This means that the gravitational force does not perform any work on the block during this motion.

The reason for this is that the gravitational force acts vertically downward, while the displacement of the block is horizontally along the track. Since the gravitational force and the displacement are perpendicular to each other, the dot product of the force and displacement is zero, resulting in zero work done by the gravitational force.

To understand this conceptually, we can break down the motion of the block into its horizontal and vertical components. The gravitational force acts vertically, while the displacement occurs horizontally. Since the force and displacement vectors are perpendicular to each other, their dot product is zero. Mathematically, the work done by a force is given by the formula W = F · d · cos(θ), where θ is the angle between the force and displacement vectors. In this case, cos(θ) = cos(90°) = 0, resulting in zero work done by the gravitational force.

Therefore, the net work done by the gravitational force on the block as it moves from point A to point C is zero.

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Answer:

Bus 18 is more consistent than Bus 47 based on the IQR, which is smaller for Bus 18 (16) compared to Bus 47 (24), indicating less spread of data between the 25th and 75th percentiles.

Step-by-step explanation:

Answer: The correct option regarding which bus has the least spread among the travel times is given as follows:

Bus 14, with an IQR of 6.

How to obtain the measures of spread?

First, we consider the dot plot, which shows the number of times that each observation appears in the data set.

Then we consider the interquartile range, which gives the difference between the third quartile and the first quartile of the data set.

The interquartile range is a better measure of spread compared to the range of a data set, as it does not consider outliers.

For groups of 15 students, we have that:

The first half is composed of the first seven students, hence the first quartile is the fourth dot, which is the median of the first half.

The second half is composed of the last seven students, hence the first quartile is the eleventh dot, which is the median of the first half.

The quartiles for Bus 14 are given as follows:

Q1 = 12.

Q3 = 18.

Hence the IQR is of:

IQR = Q3 - Q1 = 18 - 12 = 6.

The quartiles for Bus 18 are given as follows:

Q1 = 9.

Q3 = 16.

Hence the IQR is of:

IQR = Q3 - Q1 = 16 - 9 = 7.

Step-by-step explanation:

Answer:

C , r = 6 cm

Step-by-step explanation:

Finding the circumference is really easy. You just have to multiply the radius (r) by 2 and pi. Pi is 3.14 so 3.14*2*6=37 which is bigger than the other numbers. For a question like this where it gives you different radii, you can just pick the biggest number :) hope this helps!

Answer:

C , r = 6 cm should be the answer

Step-by-step explanation:

Answer:

5+(-15) is the given equation. We need to find the matching problem.

First, we need to identify each problem's equation.

A: 15+5

B: 5-15

C: 15-5

D: 5+(15)

I believe the answer is D, it happens to be closest to our given equation.

~Hope this helps~