what is the value of y?

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

Volume is a measure of the amount of space that a three-dimensional object occupies or contains. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet.

In the given question,

The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius of the base, h is the height, and π is approximately 3.14.

Substituting the given values, we get:

V = (1/3) × 3.14 × 3² × 3.8

V ≈ 35.63

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

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Work Shown:

Focus on the angles at the bottom right

Those two angles add to 180 since they form a straight line. We consider them supplementary angles.

x+(4x-20) = 180

5x-20 = 180

5x = 180+20

5x = 200

x = 200/5

x = 40

For this, we need to find the LCM of 6 and 9 which equals 18.

What is LCM?

The smallest positive integer that is divisible by both a and b is known as the LCM of two integers, or lcm(a, b), in mathematics and number theory.

For this, we need to find the LCM of 6 and 9 which equals 18.

Hence, they will drip at the same time after 18 seconds.

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Answer:

Explanation:

Generally, the slope-intercept form of the equation of a line is given as;

where m = the slope of the line

b = y-intercept of the line

From the question, we're told that the required line will pass through the origin and (3, 2), so we can find our slope(m) of the line using the given coordinates x1 = 0, y1 = 0, x2 = 3, and y2 = 2;

So the slope(m) of the line is 2/3.

Since we're told that the line will pass through the origin, it means that the y-intercept (b) = 0.

Since the gragh will be shaded above the dashed line, it means that the inequality will have a greater than sign(>).

We're told that the line will be dashed, it means that the function have only the greater than sign(>) without the equal to sign(=).

Combining all the information above, the function for the line can be

The answer is (B) 27.47 ft.  We can use trigonometry to solve this problem. Let's call the height of the building "h" and the length of the ladder "l". We know that the distance from the base of the ladder to the building is 10 feet, and the angle of elevation is 70 degrees.

Using trigonometry, we can set up the equation:

tan(70) = h/10

Solving for h, we get:

h = 10 * tan(70)

Plugging this into a calculator, we get:

h ≈ 27.47 ft

Therefore, the answer is (B) 27.47 ft.

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a ship leaves a harbor. it travels 35 miles due east and then adjusts its course 40 degrees northward. after traveling 45 miles in that direction,The distance from the ship's point of departure is approximately 59.9 miles.

To determine the distance from the ship's point of departure, we must first break down the distance traveled into x and y components. Initially, the ship traveled 35 miles due east, which can be represented as 35 miles on the x-axis. When the ship adjusted its course 40 degrees northward, it traveled 45 miles in that direction. This can be represented as 45 miles in the y direction, forming a triangle with the origin (point of departure). Using the Pythagorean theorem, we can calculate the hypotenuse of the triangle, which is equal to the distance from the point of departure. The hypotenuse of the triangle is equal to the square root of (35^2 + 45^2), which is equal to approximately 59.9 miles. Therefore, the distance from the ship's point of departure is approximately 59.9 miles.

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Using a t-distribution table or calculator, we get the t-score and are 98% positive that the interval (32.126, 53.874) includes the genuine population mean amount the medicine would drop a typical patient's systolic blood pressure to.

We must create a confidence interval for the population mean decrease in systolic blood pressure in order to calculate how much the medicine will reduce a typical patient's systolic blood pressure with a 98% confidence level.

CI = x t /2 * (s / n)

where x is the sample mean, s is the sample standard deviation, n is the sample size, t /2 is the t-score for the desired degree of confidence, and is the significance level (1 - confidence level).

With the supplied variables plugged in, we obtain:

CI = 43 t0.01/2 * (11 / 10)

The t-score at a 98% confidence level and 9 degrees of freedom (n-1) are roughly 2.821, according to a t-distribution table or calculator.

We obtain the following number by substituting it:

CI = 43 2.821 * (11 / 10) = (32.126, 53.874)

As a result, we have a 98% confidence that the interval (32.126, 53.874) contains the actual population mean amount that the medication would reduce the systolic blood pressure of an average patient.

The following requirements must be met for the interval to be valid:

1. The sample is a straightforward random sample taken from the population.

2. For the Central Limit Theorem to be applicable, either the population is normally distributed or the sample size is sufficient (n > 30).

3. A fair estimate of the population standard deviation is the sample standard deviation (which is assumed to be unknown).

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The common ratio of the geometric series produced by the nth-order Maclaurin series for h(x) = 1/(1-x) is x.

The Maclaurin series for h(x) = 1/(1-x) is an infinite geometric series with the general term given by:

h(x) = x⁰ + x¹ + x² + x³ + ...

The nth order Maclaurin series for h(x) = 1/(1-x) is the sum of the first n terms of this infinite series. The common ratio of a geometric series is the ratio of any term to the previous term.

In this case, each term is the previous term multiplied by x, so the common ratio is x.

It's important to note that the Maclaurin series is a type of Taylor series that is used to approximate a function and it's useful when the function is evaluated at zero, in this case, when x is zero, the function becomes 1/(1-0) = 1, the function is equal to 1 when x=0.

In conclusion, the common ratio of the geometric series produced by the nth-order Maclaurin series for h(x) = 1/(1-x) is x. It's the ratio of any term to the previous term, and it's the same for all the terms in the series.

The Maclaurin series is a type of Taylor series that is used to approximate a function and it's useful when the function is evaluated at zero.

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Answer:

The correct answer is A. -10b - 4

Answer:

A. -10b-4

Step-by-step explanation:

-3b + 4 – 7b – 8 ->

-10b-4

All you have to do is add the terms that are alike :) hope this helps

Answer:

1.) Zero ( 0 )

2.) 55.47 feet , 8.6 feet

3.) 17.2 feet

Step-by-step explanation:

The height, in feet, of the ball is given by the equation h(x)=−.25x2+4.3x, where x is the number of feet away from the golf club (along the ground) the ball is.

1.) Since the equation has no intercept,

The ball will start zero feet above the ground.

2.) The distance of the ball at the maximum height will be achieved by using the formula

X = -b/2a

Where b = 4.3, a = -0.25

Substitutes both into the formula

X = -4.3 / 2( - 0.25 )

X = - 4.3 / - 0.5

X = 8.6 feet

Substitute X into the function to get the maximum height

h(x) = −.25(8.6)^2 + 4.3(8.6)

h(x) = 18.49 + 36.98

h(x) = 55.47 feet

3) As the ball returns to the ground, the height will be equal to zero, therefore,

0 = -0.25x^2 + 4.3x

0.25x^2 = 4.3x

X = 4.3/0.25

X = 17.2 feet

The ball returns to the ground at about 17.2 feet away

Answer:

6 miles

Step-by-step explanation:

Flat fee is $4

Per mile is $3

Equation :

4 + 3m = 22

subtract 4 from both sides

3m = 18

divide each side by 3

m = 6

The ride is 6 miles.

If my answer is incorrect, pls correct me!

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-Chetan K

The expression x + 80 represents the number of coins Arthur has now, since he x pennies and an additional 6 dimes and 4 nickels.

We shall convert the pennies, dimes and nickels into same unit before adding to get the expression for the number of coins Arthur will have in total.

A penny = 1 cent, so

x pennies = x cents

A dime = 10 cents so;

6 dimes = 6 × 10cents

6 dimes = 60 cents

A nickel = 5 cents so;

4 nickels = 4 × 5 cents

4 nickels = 20 cents

Arthur's coins in total = (x + 60 + 40) cents

Arthur's coins in total = (x + 80) cents.

Therefore, the expression expression x + 80 represents the number of coins Arthur will have in total, wether in pennies, dimes or nickels.

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The percentage of patients with type-B blood that are 50 years old or younger is calculated as follows:

P = number of patients with type B blood that are 50 years or younger / number of patients with type B blood x 100%

Two parameters are used to calculate a percentage, as follows:

The proportion is given by the number of desired outcomes divided by the number of total outcomes, while the percentage is the proportion multiplied by 100%.

Hence the rule is given as follows:

P = a/b x 100%.

The problem is incomplete and the table could not be found on the internet, hence the general procedure to obtain the percentage is presented.

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Answer:

The answer is 234

Step-by-step explanation:

Answer:

0.0421

Step-by-step explanation:

We solve using the z score formula

z-score is is z = (x-μ)/σ,

where x is the raw score

μ is the population mean = μ = 8.9 pounds

σ is the population standard deviation = σ = 1.1 pounds

For x < 7 pounds

z = 7 - 8.9/1.1

= -1.72727

Probability value from Z-Table:

P(x<7) = 0.042059

Therefore, the proportion of domestic house cats weigh less than 7 pounds is

0.042059

Approximately = 0.0421

Answer:

second table

Step-by-step explanation:

Out of the 8 options on the spinner, 2 of them are 0's, 1 of them is a 1, 2 of them are 2's and 3 of them are 3's so the probability of spinning a 0, 1, 2 or 3 is 2/8, 1/8, 2/8 or 3/8 which becomes 0.25, 0.125, 0.25 or 0.375 respectively. Therefore, the answer is the second table.

Answer:

x = -4

Step-by-step explanation:

Subtract 17 on both sides to get 6x = -24 then divide 6 to both sides to get your answer of x = -4

First, you need to get 6x by itself. So you would subtract 17 from both sides. After that you should have 6x= -24.Then you need to get x by itself. You divide 6 from both sides. The answer is x= -4.

Hope this helps!!

The equation of a parabola with vertex (h,k) is given by:

Starting from the given equation, complete the square to write the function in vertex form:

By comparing that equation with the vertex form of a parabola, we can see that h=1 and k=2.

Therefore, the vertex of the given quadratic polynomial, is:

Answer:

I think its -128x + 6

Step-by-step explanation:

Answer:

because the line has a slope of 0, you know that it is horizontal

therefore, the equation is y=-8

Step-by-step explanation:

a) P(R) = 0.2, P(B) = 0.12, P(G) = 0.16, P(Y) = 0.16, P(P) = 0.2, P(W) =0.16

b) The sum of the probabilities is equal to 1

c) Probability model shows nonuniform probability.

Probability is a branch of mathematics that deals with the study of random events and the likelihood or chance of their occurrence.

Part A: Let R, B, G, Y, P, and W represent the colors red, blue, green, yellow, purple, and white, respectively. Then, the probability of randomly selecting a balloon of each color can be represented by the following probability model:

P(R) = 5/25 = 0.2

P(B) = 3/25 = 0.12

P(G) = 4/25 = 0.16

P(Y) = 4/25 = 0.16

P(P) = 5/25 = 0.2

P(W) = 4/25 = 0.16

Part B: To verify that all possible outcomes are included in the probability model, we need to check that the sum of the probabilities of all possible outcomes is equal to 1.

P(R) + P(B) + P(G) + P(Y) + P(P) + P(W) = 0.2 + 0.12 + 0.16 + 0.16 + 0.2 + 0.16 = 1

Since the sum of the probabilities is equal to 1, we can conclude that all possible outcomes are included in the probability model.

Part C: To determine whether the probability model shows uniform or nonuniform probability, we need to compare the probabilities of the different outcomes.

Since the probabilities of the different outcomes are not equal, the probability model shows nonuniform probability.

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Here we will evaluate and solve some linear equations.

#18:

f(-1)  = 4

f(0) = 1

f(2) = -5

#19: g(x) is equal to 19 when x = -7

Here we start with the linear function:

f(x) = -3x + 1

And we want to evaluate it in x = -1, 0, and 2

To do so, we just need to replace the variable x by the given numbers

f(-1) = -3*(-1) + 1 = 3 + 1 = 4

f(0) = -3*0 + 1 = 0 + 1 = 1

f(2) = -3*2 + 1 = -6 + 1 = -5

Here we have the linear function:

g(x) = -2x + 5

And we want to find the value of x such that:

g(x) = 19

Then we need to solve:

19 = -2x + 5

19 - 5 = -2x

14 = -2x

14/-2 = x

-7 = x

That is the solution.

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c = 50 liters (initial amount of soup)

d = 10 liters (amount of water added)

1: Calculate the initial amount of broth in the soup.

The soup is 50% broth, so 50% of 50 liters is (50/100) * 50 = 25 liters of broth.

2: Calculate the final amount of soup after adding water.

The initial amount of soup is 50 liters, and 10 liters of water are added, so the final amount of soup is 50 + 10 = 60 liters.

3: Calculate the final amount of broth in the soup.

The initial amount of broth is 25 liters, and no broth is added or removed during the process, so the final amount of broth remains the same at 25 liters.

4: Calculate the final percentage of broth in the soup.

To find the percentage of broth in the soup, divide the final amount of broth by the final amount of soup and multiply by 100.

(25/60) * 100 = 41.67%

c = 50 liters

d = 10 liters

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The number of 4-letter words that can be formed without any condition imposed is 8,064.

To determine the number of 4-letter words that can be formed without any conditions, we can use the concept of permutations. Since we have 8 options (a, b, c, d, e, f, g) for each letter position, we can multiply the number of options for each position to find the total number of possibilities.

For the first letter position, we have 8 options to choose from. Similarly, for the second, third, and fourth positions, we also have 8 options each. Therefore, the total number of possibilities is:

8 options for the first position × 8 options for the second position × 8 options for the third position × 8 options for the fourth position = 8 × 8 × 8 × 8 = 8,064.

Hence, there are 8,064 possible 4-letter words that can be formed without any conditions imposed.

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To find the location of E' after the dilation, we need to apply the dilation rule to the coordinates of point E. The dilation rule states that each coordinate (x, y) is transformed to (3/2x, 3/2y).

The coordinates of point E are given as (2, 2/3). Let's apply the dilation rule to these coordinates:

x-coordinate of E' = (3/2) * x-coordinate of E = (3/2) * 2 = 3

y-coordinate of E' = (3/2) * y-coordinate of E = (3/2) * (2/3) = 1

Therefore, the coordinates of point E' are (3, 1).

None of the answer choices matches the coordinates (3, 1), so none of the given options is correct.

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To find the equation of a parabola with a vertex at the origin and axis along one of the coordinate axes, we need to determine the coordinates of the focus and the equation of the directrix.

a) For the focus to be on the line 3x+4y=12, we can substitute y=0 (since the axis is the x-axis) into the equation to find the x-coordinate of the focus:
3x + 4(0) = 12
3x = 12
x = 4

So, the focus is located at (4, 0).

b) Since the directrix is the line y=6, the equation of the directrix is simply y = -6 (which is parallel to the x-axis and 6 units below the x-axis).

Now, we can use the formula for the equation of a parabola in standard form to find the equation of the parabola. The equation is: (x - h)^2 = 4p(y - k), where (h, k) is the vertex and p is the distance from the vertex to the focus or directrix.

a) Using the vertex (0, 0) and the focus (4, 0), the equation is:
(x - 0)^2 = 4(4)(y - 0)
x^2 = 16y

b) Using the vertex (0, 0) and the directrix y = -6, the equation is:
(x - 0)^2 = 4(-6)(y - 0)
x^2 = -24y

a) The equation of the parabola with the focus on the line 3x+4y=12 is x^2 = 16y.
b) The equation of the parabola with the directrix y=6 is x^2 = -24y.

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Answer:

7:42

Step-by-step explanation:

First off you add the ratio together-

6+1=7

Then you divide-

49÷7= 7

7 is equal to 1 in this ratio.

To write out the ratio you need to multiplicate-

7×1=7

and

6×7= 42

Leaving the as-

7:42

Answer:

7:42  

Step-by-step explanation:

First, add up the two numbers in the ratio to get 49.

Next, divide the total amount by 49, i.e. divide £16 by 8 to get £5. £5 is the amount of each 'unit' in the ratio.

Then you need to divide the total amount using that number i.e. 49/16 = 7/42.

To work out how much each person gets, you then multiply their share by the ratios. Therefore, the answer is 7 yd and 42 yds.

Answer:

y=(-1/2)x-1

Step-by-step explanation:

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Equation of line is y = 1/2x + 9 which passes through the point (-4, 7) and has slope 1/2.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

Point on the line = (-4, 7).

And, The slope of the line = 1/2

Since, The equation of line passes through the point (- 4, 7).

and, Slope of the line is,

⇒ m = 1/2

Hence, The equation of line is,

⇒ y - 7 = 1/2 (x - (-4))

⇒ y - 7 = 1/2 (x + 4)

⇒ y - 7 = 1/2x + 2

⇒ y = 1/2x + 2 + 7

⇒ y = 1/2x + 9

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Answer: P(prime): 5/12 (.41667) P(odd and greater than 5): 3/12 (.25)

Step-by-step explanation:

For the first probability, we can first identify the prime numbers on the wheel. Going around the wheel clockwise, the prime numbers here are: 2, 3, 5, 7, 11.

Since there are 12 total spaces on the wheel, the probability for P(prime) can be found by dividing the 5 prime numbers by 12 total spaces. Giving us 5/12.

For P(odd and greater than 5), similar to the first probability, we should first identify the numbers that follow the given rule. The numbers here that are odd and greater than 5 are: 7, 9, 11. Like the first probability, we divide the number of values here by the total spaces, giving us 3/12, or .25.

Hope this helps! If you have any questions please feel free to ask in the comments.