if AD = 85 and BC =31 find the value of x

The value of x is approximately 8.15.

To find the value of x, we need to use the formula for the volume of a cone, which is V = (1/3)πr^2h, where r is the

radius of the base and h is the height of the cone. We know that the volume of the cone below is 392π, so we can set

up the equation:

[tex]392π = (1/3)πx^2h[/tex]

Simplifying, we can divide both sides by π and multiply by 3 to get:

[tex]1176 = x^2h[/tex]

Using the Pythagorean theorem, we can relate the height, radius, and slant height of the cone:

[tex]h^2 + r^2 = x^2[/tex]

Since the cone is a right cone, we know that the radius is half of the diameter, which is equal to x/2. Substituting this in,

we get:

[tex]h^2 + (x/2)^2 = x^2[/tex]

Simplifying:

[tex]h^2 = x^2 - (x/2)^2

h^2 = 3x^2/4[/tex]

Now we can substitute this expression for [tex]h^2[/tex] into our equation for the volume:

[tex]1176 = x^2(3x^2/4)[/tex]

Simplifying again:

[tex]1176 = 3x^4/4[/tex]

[tex]1568 = 3x^4[/tex]

[tex]x^4 = 1568/3[/tex]

Taking the fourth root of both sides:

[tex]x = (1568/3)^(1/4)[/tex]

x ≈ 8.15

for such more question on volume

https://brainly.com/question/6204273

#SPJ11

Answer: 14

Step-by-step explanation:

(a) To find P(0 < Z < 2.74), you'll want to look up the z-score for 2.74 in a standard normal table or use a calculator with a built-in normal distribution function. The probability is the area under the curve between 0 and 2.74.

(b) To find P(0 < Z < 1), you'll look up the z-score for 1 in a standard normal table or use a calculator. The probability is the area under the curve between 0 and 1.

(c) To find P(-2.40 < Z < 0), you'll look up the z-score for -2.40 in a standard normal table or use a calculator. The probability is the area under the curve between -2.40 and 0.

(d) To find P(-2.40 < Z < 2.40), you can first calculate the probability for P(-2.40 < Z < 0) and P(0 < Z < 2.40), and then sum the two probabilities.

(e) To find P(Z > 1.63), look up the z-score for 1.63 in a standard normal table or use a calculator. The probability is the area under the curve to the right of 1.63.

(f) To find P(Z < -1.74), look up the z-score for -1.74 in a standard normal table or use a calculator. The probability is the area under the curve to the left of -1.74.

(g) To find P(-1.4 < Z < 2.00), first look up the z-scores for -1.4 and 2.00 in a standard normal table or use a calculator. Subtract the smaller probability from the larger probability to find the area under the curve between these two values.

(h) To find P(1.63 < Z < 2.50), first look up the z-scores for 1.63 and 2.50 in a standard normal table or use a calculator. Subtract the smaller probability from the larger probability to find the area under the curve between these two values.

LEARN MORE ABOUT PROBABILITY: https://brainly.com/question/13604758

#SPJ11

The  required value of the ∠DPE = 40°.

Angles that are vertically opposite to one another at a particular vertex are formed by two straight lines meeting. Angles that are vertically opposed to one another are identical. These are referred to as perpendicular angles at times.

Using vertically opposite angle, ∠GPE = 35° and ∠KPF are equal

Then,

∠GPE = ∠KPF = 35°

Then Sum of all angles on straight line is 180°

∠KPF + ∠FP + ∠DPE = 180°

35° + 105° + ∠DPE = 180°

∠DPE = 180° - 140°

∠DPE = 40°

Thus, required value of the ∠DPE = 40°.

To know more about Angle visit:

brainly.com/question/28451077

#SPJ1

Answer:

it's b or 4.03

Step-by-step explanation:

your welcome

An effective visual representation of a function or a mapping between two sets is a mapping diagram. It consists of two vertical columns, one of which represents the domain set items and the other of which represents the range set elements. The items in the range set that match to those in the domain set are listed in the right column, and vice versa.

I assume you are given a mapping rule that relates elements in a set to other elements in another set, and you are asked to complete a mapping diagram based on this rule.

If the mapping rule is not specified, we cannot determine the values of a and b. However, assuming that the mapping rule is such that each element (x, y) in the set R is mapped to [tex](x + a, y + b)[/tex], we can complete the mapping diagram as follows:

The given set R is:

R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}

If we apply the mapping rule to each element in R, we get:

(-3, -2) → (-3 + a, -2 + b)

(-3, 0) → (-3 + a, 0 + b)

(-1, 2) → (-1 + a, 2 + b)

(1, 2) → (1 + a, 2 + b)

To complete the mapping diagram, we need to find the values of a and b such that each mapped element is in the set R. That is, we need to find a and b such that:

(-3 + a, -2 + b) ∈ R

(-3 + a, 0 + b) ∈ R

(-1 + a, 2 + b) ∈ R

(1 + a, 2 + b) ∈ R

Substituting the values of R into each of these equations, we get:

(-3 + a, -2 + b) = (-3, -2), which gives a = 0 and b = 0

(-3 + a, 0 + b) = (-3, 0), which gives a = 0 and b = 0

(-1 + a, 2 + b) = (-1, 2), which gives a = 0 and b = 0

(1 + a, 2 + b) = (1, 2), which gives a = 0 and b = 0

Therefore, the values of a and b that complete the mapping diagram are a = 0 and b = 0.

To know about diagram mapping:

https://brainly.com/question/29006330

#SPJ9

Answer: 56 in

Step-by-step explanation:

4x7x2=56

Answer:

56 in

Step-by-step explanation:

4*7*2

Answer:

16.5 units square

Step-by-step explanation:

The area of a triangle is 1/2bh

To find the base and heights

We use the formula above

Using the formula for my x.-axis I got 11

From 14 - 3

And for the y-axis, I got 3

From 8-5

Then using the formula 1/2bh

The area of the triangle is 1/2 ×11×3

=16.5

The slope-intercept form of the inequality is given as follows:

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

Hence the inequality for this problem is simplified as follows:

More can be learned about slope-intercept at https://brainly.com/question/24808124

#SPJ1

Answer:

Y = 6*y

Step-by-step explanation:

We have Y = b * y by a factor of 6.

That is, b = 6.

now, to find what results only in a horizontal compression of y = b * y by a factor of 6.

By transformation rule, the function would be a horizontal compression f (a * x) if a> 1.

Therefore, knowing the above, the answer would be:

Y = 6 * y

Answer:9/2

Step-by-step explanation:

Answer:

To convert mixed number 4 1/2 to improper fraction, you follow these steps: Multiply the whole number by the denominator 4 × 2 = 8 Add the product from Step 1 to the numerator

Step-by-step explanation:

First, note that 4 1/2 is a mixed number, also know as mixed fraction. It has a whole number and a proper fraction. The numbers in the mixed fraction are defined as follow:

4 = whole number

1 = numerator

2 = denominator

To convert mixed number 4 1/2 to improper fraction, you follow these steps:

Multiply the whole number by the denominator

4 × 2 = 8

Add the product from Step 1 to the numerator

8 + 1 = 9

Write answer from Step 2 over the denominator

9/2

The mixed number 4 1/2 converted to improper fraction is therefore :

9/2

If a client who weighs 207 lb (94.1 kg) is to receive 1.5 mg/kg of gentamicin sulfate iv three times each day, the nurse should administer 141 mg of gentamicin sulfate for each dose.

To calculate the dose of gentamicin sulfate that the nurse should administer to the client, we need to know the client's weight and the desired dosage, which in this case is 1.5 mg/kg.

First, we need to convert the client's weight from pounds to kilograms. To do this, we divide the client's weight in pounds by 2.205 to get the weight in kilograms:

207 lb ÷ 2.205 = 94.1 kg

Now that we have the client's weight in kilograms, we can calculate the dose of gentamicin sulfate for each administration:

1.5 mg/kg × 94.1 kg = 141.15 mg

We round 141.15 mg to the nearest whole number, which is 141 mg.

To learn more about medication click on,

https://brainly.com/question/30363415

#SPJ4

Answer:

A. The initial height, h, in feet, of the object.

Answer:

A The initial height, h, in feet, of the object.

Step-by-step explanation:

Let t = 0

h(t) = -16t ² + 110t + 72

h(0) = -16(0)² + 110 × 0 + 72

h(0) = 72

The height at time zero is 72.

72 is the initial height.

Answer: A The initial height, h, in feet, of the object.

The value of the side of the triangles are;

18. 17. 89

19. y = 9. 43, x = 5. 67

Using the Pythagorean theorem stating that the square of the hypotenuse side is equal to the sum of the squares of the other two sides of a triangle.

From the diagram shown, we have;

21² = 11² + x²

find the squares

441 = 121 + x²

collect the like terms

x² = 320

Find the square root

x = 17. 89

To determine the value of y

sin 59 = y/11

y = 11 × 0. 8571

y = 9. 43

To determine the value of x

11² - 9. 43² = x²

x = √32.096

x = 5. 67

Learn about Pythagorean theorem at: https://brainly.com/question/27997683

#SPJ1

To create a figure of three rectangles with a perimeter of 140 yards, you can stack them on top of each other to make a plus sign, and label each side as 11 and 2/3 yards or 11 yards (by subtracting the fractions).

A rectangle is a four-sided geometric shape that has four right angles (90 degree angles) and opposite sides that are parallel and of equal length. The length of a rectangle is its longer side, while the width is its shorter side.

If we draw three rectangles stacked on top of each other like a plus sign, we can divide the perimeter of 140 yards by the number of sides, which is 12. This gives us a length of 11 and 2/3 yards per side.

To use only integers, we can subtract the fractions from each side to another, which gives us a length of 11 yards per side. We can then label each side of the figure with a length of 11 yards.

In the figure, we have three rectangles of equal size, with a length of 11 yards and a width of 35 yards. We can convert the measurements to feet by multiplying by 3, which gives us a length of 33 feet and a width of 105 feet.

Alternatively, if we wanted to use only whole numbers, we could increase the size of each rectangle slightly, so that the total perimeter is a multiple of 12. For example, we could make each rectangle 11.6667 yards by 35 yards, which gives us a total perimeter of 140.0008 yards. We can then divide this by 12 to get a length of 11 and 2/3 yards per side, and label each side with a length of 11 yards.

To know more about rectangle visit:

https://brainly.com/question/2607596

#SPJ9

The probability that at least one of three randomly selected people has been vaccinated in a large population where 64% of people have been vaccinated is 0.784.

The probability that at least one of three randomly selected people has been vaccinated in a large population where 64% of people have been vaccinated can be calculated using the binomial probability formula.

The binomial probability formula is used to calculate the probability of a given number of successes from a given number of trials when the probability of success is constant. In this case, the number of trials is 3 (i.e. the three randomly selected people) and the probability of success is 64% (i.e. the probability that each of the randomly selected people has been vaccinated).

To calculate the probability that at least one of the three randomly selected people has been vaccinated, we first calculate the probability of none of them having been vaccinated:
P(none) = (1 - 0.64)^3 = 0.216

Then, the probability of at least one of them having been vaccinated is 1 - P(none) = 1 - 0.216 = 0.784.

In conclusion, the probability that at least one of three randomly selected people has been vaccinated in a large population where 64% of people have been vaccinated is 0.784.

See more about binomial probability at: https://brainly.com/question/24756209

#SPJ11

There are 27,720 different arrangements of red and yellow roses.

The total number of roses is 8 + 4 = 12. To find the number of different arrangements, we can use the formula for permutations, which is:

n! / (n - r)!

where n is the total number of objects and r is the number of objects we want to arrange.

In this case, we want to arrange all 12 roses, so n = 12. The number of red roses is 8, so r = 8. Therefore, the number of different arrangements of the roses is:

12! / (12 - 8)! = 12! / 4! = 27,720

So there are 27,720 different arrangements of the 8 red roses and 4 yellow roses.

To know more about permutations refer here:

https://brainly.com/question/30649574

#SPJ11

Answer:

About 92.1 °

Step-by-step explanation:

[tex]cos(U)=(58.8^{2} +38.4^{2} -71.4^{2} )/2(58.8)(38.4)\\[/tex]

[tex]cos(U)= (3457.44+1474.56-5097.96)/4515.84[/tex]

[tex]cos(U)= (-165.96)/4515.84[/tex]

[tex]cos(U)= -0.03675063775[/tex]

[tex]U= cos^{-1} (-0.03675)[/tex]

[tex]U=92.1[/tex]

Answer:

cosA=b^2+c^2-a^2/2xbxc

58.8^2+38.4^2-71.4^2/2x58.8x38.4=-461/12544

cos^-1 (because finding angle)

cos^1(-461/12544)=92.10613071

Answer:

If x = 3 and y = 2.3^3, then we can evaluate y using exponents:

y = 2.3^3 = 2.3 × 2.3 × 2.3 = 12.167

So, y = 12.167 when x = 3.

Next, if we want to solve the equation y = 2[?] using order of operations, we need to evaluate what is inside the brackets first. We know that y = 12.167, so we can substitute that value into the equation:

y = 2[?]

12.167 = 2[?]

To solve for the missing value inside the brackets, we need to divide both sides by 2:

12.167 ÷ 2 = ?

6.0835 = ?

Therefore, the solution is y = 2(6.0835), or y = 12.167, which we already found earlier.

Therefore, liquid water is considered to be unstable on Mars due to the cold temperatures, low atmospheric pressure, and the UV radiation. All of these environmental factors make it difficult for liquid water to persist.

Liquid water is unstable on Mars due to its cold, dry environment. Because the atmospheric pressure is too low to hold liquid water, the water on Mars quickly evaporates, sublimates, and/or is broken down by the ultraviolet radiation in the atmosphere.
The average temperature of the surface of Mars is −63 °C, which is well below the freezing point of water. Because of this, liquid water cannot exist on the surface of Mars. When temperatures are slightly higher, water can exist as a liquid, but it cannot stay in this state for very long.
The atmosphere on Mars also does not contain enough pressure to sustain liquid water. Even when water vapor is present, it will quickly evaporate in the low-pressure environment. Additionally, the UV radiation in the Martian atmosphere will break down water molecules quickly.

for such more questions on atmosphere

https://brainly.com/question/28124272

#SPJ11

By definition, direct variation takes the following form:

y=kx

Where k is the proportionality constant.

You can find k given the information in the problem:

7=3k

k=3/7

You can now find y when x=7 as follows:

y=(7*3)

Values can be substituted. Then:

y=(7*7)/3

y=49/3

If y varies directly from x, then the value of y = 49/3 when x = 7.

If y varies directly from x, we can write its relationship in the form of the equation below :

y = m*x

Where m is the slope of the line on the graph.

From the given data:

y=7

x=3,

We can substitute these values in the above equation and find m :

7 = m*3

m = 7/3

So, the equation can also be written as follow:

y = 7/3 x

Finding y when x=7, then substituting the x value in the above equation we get:

y = (7/3)*(7)

y = 49/3

Therefore the value of the y = 49/3.

to learn more about the slope:

https://brainly.com/question/28645794

The probability of a sample of 10 parts containing more than 3 defective ones is approximately 0.026.

We can use the binomial distribution to calculate the probability of getting more than 3 defective parts in a sample of 10 parts. Let X be the number of defective parts in the sample. Then X follows a binomial distribution with parameters n=10 and p=0.1, where n is the sample size and p is the probability of a part being defective.

We can calculate the probability of getting more than 3 defective parts is:

P(X > 3) = 1 - P(X ≤ 3) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]

Next, we can find that:

P(X > 3) = 0.026

Therefore, the probability of a sample of 10 parts containing more than 3 defective ones is approximately 0.026.

To know more about binomial distribution refer here:

https://brainly.com/question/14565246?referrer=searchResults

#SPJ11

The labor force participation rate is 64.4%.

To calculate the labor force participation rate, we need to know the number of people who are either employed or actively seeking employment. We can calculate this as follows:

Labor force = adult working-age population - not in labor force

Labor force = 320 million - 114 million

Subtract the numbers

Labor force = 206 million

So the labor force participation rate is

Labor force participation rate = (labor force / adult working-age population) x 100%

Substitute the values in the equation

Labor force participation rate = (206 million / 320 million) x 100%

Labor force participation rate = 64.4%

Learn more about Labor force participation rate here

brainly.com/question/30825070

#SPJ4

Answer: I believe he could wear 768 outfits

Step-by-step explanation: I had a similar question consisting of the same numbers.

Answer:

Step-by-step explanation:

36 +55

The property of the average of any two odd integers being odd is true for all integers.

This is because the sum of any two odd integers is always an even integer. For example, if we take any two odd integers, say 3 and 7, then the sum of these two is 10, an even integer. Therefore, the average of 3 and 7, which is (3 + 7)/2, is also an even integer, in this case, 5.

Since all even integers are divisible by 2, the average of any two odd integers must be an odd integer.

Therefore, the property is true for all integers.


To know more about integers refer here:

https://brainly.com/question/15276410#

#SPJ11

If 250 is divided in the ratio 3:7, then 75 is the smaller part. To find the smaller part of 250 divided in the ratio 3:7, you need to first find the total number of parts that the ratio represents.

The total number of parts in the ratio of 3:7 is 3+7=10.

Next, you need to find the value of one part.

To do this, divide the total amount by the total number of parts:

250 ÷ 10 = 25

This means that one part of the ratio is equal to 25.

To find the smaller part, you need to multiply the value of one part (25) by the ratio of 3/10 (which represents the smaller part of the total).

So the smaller part is:

3/10 x 250 = 75

Therefore, the smaller part of 250 divided in the ratio of 3:7 is 75.

To learn more about ratio visit;

https://brainly.com/question/13419413

#SPJ4

Correct question:

If 250 is divided in the ratio 3:7, what is the smaller part?

Answer:

the answer is one solution and to graph you'll need to make the second equation like this y=-2x+7