If the radius is 11 mm, what is the height? Round the answer to the nearest tenth of a millimeter. 3.8 mm 3.8 mm3 14.7 mm 14.7 mm3

Answer:

48

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

edge 2023

To apply the Integral Test to the series, we need to first confirm that the function we're working with is positive, continuous, and decreasing. In this case, the series is:

∑(2 / (3^n * 9)) from n=1 to infinity

And the corresponding function is:
f(x) = 2 / (3^x * 9)

The function f(x) is positive, continuous, and decreasing for x ≥ 1. Therefore, we can apply the Integral Test to this series.

Now, let's evaluate the integral:
∫(2 / (3^x * 9)) dx from x=1 to infinity

To solve this integral, we'll perform a substitution:
u = 3^x
du/dx = ln(3) * 3^x
dx = du / (ln(3) * 3^x)

Now, the integral becomes:
(2/9) * ∫(1 / (u * ln(3))) du from u = 3 to infinity

Evaluating the integral, we get:
(2/9) * [(1/ln(3)) * ∫(1/u) du] from u = 3 to infinity

This is a simple natural logarithm integral:
(2/9) * [(1/ln(3)) * (ln(u))] from u=3 to infinity

When we take the limit as the upper bound approaches infinity, the result is:
(2/9) * [(1/ln(3)) * (ln(infinity) - ln(3))]

Since ln(infinity) goes to infinity, the whole expression diverges. Therefore, by the Integral Test, the original series also diverges.

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Answer:

See below.

Step-by-step explanation:

p: Atlanta is the capital of Georgia.

q: There are 4 feet in a yard.

p is true; q is false

11. p V q:

Atlanta is the capital of Georgia, or there are 4 feet in a yard.

Truth value: true since one of the statements is true.

12. p ▲ q:

Atlanta is the capital of Georgia, and there are 4 feet in a yard.

Truth value: false since not both statements are true.

13. p ▲ ~q:

Atlanta is the capital of Georgia, and there are not 4 feet in a yard.

Truth value: true since both of the statements are true.

11. ~p V q:

Atlanta is not the capital of Georgia, or there are 4 feet in a yard.

Truth value: false since both statements are false.

Answer:

Step-by-step explanation:

Answer:

2x

Step-by-step explanation: given (0,0) and (1,2)

y=mx+b

0=(m*0)+b

0=b (remember anything times 0, is 0)

2=(m*1)+0

2=M+0

y=mx+b

y=2x+0

Step-by-step explanation:

a ) 19 + 7 = 26

26 ÷ 2 = 13

13 - 5 = 8 ans

b) (19+7/2)-5

\(( \frac{19 + 7}{2} ) - 5\)

hope this answer helps you dear...

When the process of observing or measuring yields results that consistently deviate in some way from the true value, this is known as observer/measurement bias. Because of the systematic mistake this adds into the data, the conclusions are incorrect or unreliable.

Observer/measurement bias is a sort of systematic error that happens when the technique used for observation or measurement yields results that consistently deviate in some way from the true value. The observer's own preconceived ideas or expectations, the measurement equipment, and the environment in which the observation or measurement is being conducted can all contribute to this form of bias.An observer's bias, for instance, could cause them to see or measure something in a way that favours one particular result or outcome over another. Similar to how external influences like noise, light, or temperature can skew results, the environment in which the observation or measurement is taking place may add a bias. If feasible, results that are inaccurate or unreliable because of observer/measurement bias should be avoided because they can lead to incorrect inferences about the data.

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Answer:

Step-by-step explanation:

Sorry

Answer:

1380

Step-by-step explanation:

Using proportion, then

1 Km² → 60 people , then

23 Km² → 60 × 23 = 1380 people

Answer:

Perpendicular, 1

Step-by-step explanation:

Parallel means the same slope

Perpendicular is the reciprocal and opposite sign

Answer:

-6

Step-by-step explanation:

\(363.9ft^{2}\)

Step-by-step explanation:

\(Area =\pi r^{2} -\frac{1}{3}\pi r^{2} +\frac{1}{2}r^{2}sin\alpha \\\\\\ = \frac{2}{3}\pi 12^{2} +\frac{1}{2}12^{2}sin120 =363.9ft^{2}\)

Answer:

363.9 ft²

Step-by-step explanation:

The required area is the area of the circle - shaded area

area of circle = πr² = π × 12² = 144π ft²

shaded area = area of sector - area of Δ NBW

area of sector = πr² × \(\frac{120}{360}\) = 144π × \(\frac{1}{3}\) = 48π

area of Δ = \(\frac{1}{2}\) × 12 × 12 × sin120° = 72 × sin120° ≈ 62.35 ft²

Then

shaded area = 48π - 62.35 ≈ 88.45 ft²

area not shaded = 144π - 88.45 ≈ 363.9 ft²

Answer:

Marty's function has larger slope as compared to Ethan's slope.

Step-by-step explanation:

Marty function:

y plus 3 equals StartFraction 1 Over 3 EndFraction left-parenthesis x plus 9 right-parenthesis.

Writing in mathematical form: \(y+3=\frac{1}{3}(x+9)\)

Marty has written expression in point-slope form: \(y-y_1=m(x-x_1)\) where m is slope

So, comparing Marty's equation with general point-slope form equation we get slope \(m=\frac{1}{3}\:or\: 0.3\)

Now, Ethan has a table

x        y

-4      9.2

-2      9.6

0       10

2       10.4

We can find slope using formula: \(Slope=\frac{y_2-y_1}{x_2-x_1}\)

Using any two points, we can find slope of Ethan's equation

\(Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{9.6-9.2}{-2-(-4)} \\Slope=\frac{0.4}{-2+4} \\Slope=\frac{0.4}{2} \\Slope=0.2\)

So, we get Marty's slope = 0.3

Ethan's slope = 0.2

So, Marty's function has larger slope as 0.3 is greater than 0.2

Answer:

C

Step-by-step explanation:

The new value of the house will be $453120.

We can write : a% of b as -

a% of b = a/100 x b

a% of b = ab/100

Given is that a house was valued at $384,000. Over several years, the value increased by 18%.

We can write the new value as -

{x} = 384000 + 18% of 384000

{x} = 384000 + 18/100 x 384000

{x} = 384000 + 18 x 3840

{x} = 384000 + 69120

{x} = 453120

Therefore, the new value of the house will be $453120.

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SOLUTION:

Case: Probability (Deck of cards)

A standard 52-card deck comprises 13 ranks in each of the four French suits: clubs (♣), diamonds (♦), hearts (♥) and spades (♠). Each suit includes three court cards (face cards), King, Queen and Jack, with reversible (double-headed) images. Each suit also includes ten numeral cards or pip cards, from one to ten. The card with one pip is known as an Ace. Each pip card displays the number of pips (symbols of the suit) corresponding to its number, as well as the appropriate numeral (but "A" for the Ace) in at least two corners.

Given:

A deck of cards

Required: To find the probability of obtaining a card that is has the number 3 and is black

Method:

Step 1: First, the total number of cards in a deck is 52

Step 2: The total obtainable black number 3 cards are:

3 clubs and 3 spades. This is a total of 2 outcomes

Step 3: The probability of getting a the number 3 and is black is:

Final answer:

The probability is 1/26

Answer:

Step-by-step explanation:

Let's solve each problem one by one:

1. Adam has $2 and is saving $2 each day. Brodie has $8 and is spending $1 each day. After how many days will each person have the same amount of money?

Let's assume the number of days is represented by 'x'.

Adam's money after 'x' days = $2 + $2x

Brodie's money after 'x' days = $8 - $1x

To find the number of days when they have the same amount of money, we set up an equation:

$2 + $2x = $8 - $1x

Simplifying the equation:

$2x + $1x = $8 - $2

$3x = $6

x = $6 / $3

x = 2

Therefore, after 2 days, Adam and Brodie will have the same amount of money.

Answer: A. 5x + 4 = 3x - 2 (incorrect)

2. A number increased by 8 is equal to twice the same number increased by 7.

Let's represent the number by 'x'.

Equation: x + 8 = 2x + 7

Solving the equation:

x - 2x = 7 - 8

-x = -1

x = 1

Therefore, the number is 1.

Answer: D. x + 8 = 2x + 7 (correct)

3. Spot weighs 6 pounds and gains one pound each week. Buddy weighs 2 pounds and gains 2 pounds each week. After how many weeks will the puppies weigh the same?

Let's represent the number of weeks by 'x'.

Spot's weight after 'x' weeks = 6 + 1x

Buddy's weight after 'x' weeks = 2 + 2x

To find the number of weeks when they weigh the same, we set up an equation:

6 + 1x = 2 + 2x

Simplifying the equation:

x - 2x = 2 - 6

-x = -4

x = 4

Therefore, after 4 weeks, Spot and Buddy will weigh the same.

Answer: A. x + 6 = 2x + 2 (incorrect)

4. Five less than two times a number is equal to 4 less than the same number.

Let's represent the number by 'x'.

Equation: 2x - 5 = x - 4

Solving the equation:

2x - x = -4 + 5

x = 1

Therefore, the number is 1.

Answer: B. 2x - 5 = x - 4 (correct)

5. Ann has an empty cup and adds 1 ounce of water per second. Bob has 12 ounces of water and drinks 2 ounces per second. After how many seconds will they have the same amount of water?

Let's represent the number of seconds by 'x'.

Ann's water after 'x' seconds = 1x ounces

Bob's water after 'x' seconds = 12 - 2x ounces

To find the number of seconds when they have the same amount of water, we set up an equation:

1x = 12 - 2x

Simplifying the equation:

1x + 2x = 12

3x = 12

x = 12 / 3

x = 4

Therefore, after 4 seconds, Ann and Bob will have the same amount of water.

Answer: A. -2x + 12 = -x + 6 (incorrect)

6. Tom has

12 candies and eats 2 each minute. Sue has 6 candies and eats 1 every minute. After how many minutes will they have the same number of candies?

Let's represent the number of minutes by 'x'.

Tom's candies after 'x' minutes = 12 - 2x

Sue's candies after 'x' minutes = 6 - 1x

To find the number of minutes when they have the same number of candies, we set up an equation:

12 - 2x = 6 - 1x

Simplifying the equation:

-2x + 1x = 6 - 12

-x = -6

x = 6

Therefore, after 6 minutes, Tom and Sue will have the same number of candies.

Answer: A. -2x + 12 = -x + 6 (correct)

Answer:

x = 70 and the labeled angles are 110 and 70

Step-by-step explanation:

This is a trapezoid, the bases are parallel.

Since the bases are parallel, given two angles are supplementary and their sum is equal to 180:

x + 40 + x = 180 add like terms

2x + 40 = 180 subtract 40 from both sides

2x = 140 divide both sides by 2

x = 70 and the labeled angles are 110 and 70

Answer:

Step-by-step explanation:

Answer:

p= T-g

Step-by-step explanation:

Answer:

p=t-g

Step-by-step explanation:

Answer:

slope: 4/3

Midpoint: (2,-2)

distance : 20

Step-by-step explanation:

you can find the slop by m=y2-y1/x2-x1

m= 6-(-10)/8-(-4)   m=4/3

use the midpoint formula: (x₁ + x₂)/2, (y₁ + y₂)/2 and we get (2,-2)

distance formula- \(\sqrt{(x2-x1)+(y2-y1)\)

the distance is the square root of 400 which is 20

Age will be 40 years old.

R, in beats per minute, can be approximated by the formulas, where a represents the person's age.

where R= 143 - 0.65a for women.... (1)

and R= 165 - 0.75a for men,..... (2)

So by implementing these two equation we get a = 40

If the sum of ages is X and Y, and the ratio of their ages is p:q, then the age of Y can be calculated using the formula shown below: Y's age = Y's ratio/Sum of ratios x sum of ages The age dependency ratio is the ratio of dependents (people under the age of 15 or over the age of 64) to the working-age population (people between the ages of 15 and 64). The proportion of dependents per 100 working-age population is shown in the data.

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To find the least squares solution of the system Ax = b, we first need to find the pseudoinverse of A (denoted as A+). Then, we can use the formula x = A+ b to find the least squares solution.

To find the pseudoinverse of A, we can use the Moore-Penrose inverse formula:

A+ = (A^T A)^-1 A^T

where A^T is the transpose of A.

Using this formula, we get:

A^T A =
1 0 3 0
0 10 1 4
3 1 2 2
0 4 2 2
0 0 0 6
1 -1 0 0

Taking the inverse of A^T A, we get:

(A^T A)^-1 =
0.0447 -0.0206 0.0358 -0.0323 -0.0171 0.0478
-0.0206 0.0111 -0.0115 0.0074 0.0035 -0.0155
0.0358 -0.0115 0.0505 -0.0395 -0.0125 0.0383
-0.0323 0.0074 -0.0395 0.0356 0.0082 -0.0295
-0.0171 0.0035 -0.0125 0.0082 0.0068 -0.0099
0.0478 -0.0155 0.0383 -0.0295 -0.0099 0.0451

Multiplying A^T and b, we get:

A^T b =
1
1
-1
-1
1
-2

Using the formula x = A+ b, we get:

x =
0.2
0.1
-0.6

Therefore, the least squares solution of the system Ax = b is:

x = (0.2, 0.1, -0.6)

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According to the inscribed angle theorem the measure of angle Y is 43 degrees.

As the inscribed angle equals half of the central angle, the inscribed angle theorem is also known as the angle at the centre theorem. The centre angle is always the same since the endpoints are fixed, regardless of where it is on the same arc between the ends. The measure of the central angle is equal to double the measure of the inscribed angle occupied by the same arc, according to this theorem. OR. Half of a central angle that subtends the same arc is an inscribed angle. OR. The angle in a circle's centre is twice as large as any angle at its perimeter that the same arc occupies.

We know that, an inscribed angle is half of a central angle that subtends the same arc.

Here the given arc = 86 degrees.

The inscribed angle is half the arc of the circle thus,

angle Y = 1/2(86)

angle Y = 43 degrees.

Hence, according to the inscribed angle theorem the measure of angle Y is 43 degrees.

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The maximum area of an individual coop to be built adjacent to one another is 450 ft².

Let the length of each chicken coop be l ft and the width of each chicken coop be w ft. Since the coops are built adjacent to each other, hence,

total length = l + l = 2l and the width = w

The perimeter of the coop = 2(length + width) = 2(2l + w) = 4l + 2w

120 = 4l + 2w

w + 2l = 60

w = 60 - 2l     (1)

The area (A) = length x width

= 2l x  w

= 2l(60 - 2l)

Area = 120l - 4l²

At maximum area, dA/dl = 0, therefore:

dA/dl = 120 - 8l

120 - 8l = 0

8l = 120

length = 15 ft

putting l = 21 ft in equation 1 gives:

w = 60 - 2(15)

= 60 - 30

width = 30 ft.

The dimension of the individual coop has width of 30 ft and length of 15 ft.

Therefor, Area = length x width  = 30 x 15 = 450 ft².

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The required length of the other leg is \($\sqrt{5}$\) cm. If we need to round to the nearest tenth, we get: \($b \approx 2.2$\) cm

Let's use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. So we have:

\($c^2 = a^2 + b^2$\)

where c is the length of the hypotenuse, a and b are the lengths of the legs.

We are given that the length of the hypotenuse is 3 cm and the length of one leg is 2 cm. Let's substitute these values into the equation above:

\($3^2 = 2^2 + b^2$\)

\($9 = 4 + b^2$\)

\($b^2 = 5$\)

\($b = \sqrt{5}$\)

So the length of the other leg is \($\sqrt{5}$\) cm. If we need to round to the nearest tenth, we get: \($b \approx 2.2$\) cm (rounded to one decimal place).

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Answer:

X = 12

Step-by-step explanation:

Just add 8 to both sides to set the equation balanced. I hope this helps :)

The solution for the given problem is (a) P(X ≥ 20,000) = 0.4493, P(X ≤ 30,000) = 0.7769, P(20,000 ≤ X ≤ 30,000) = 0.3276. (b) P(X > 75,000) = 0.0821, P(X > 100,000) = 0.0183.

Solution: a) To find the probability that a randomly selected fan will last at least 20,000 hours. P(X ≥ 20,000). Now, Mean time until failure is 25,000 hours which is given and is represented by µ. Hence, µ = 25,000 hrs. The parameter used for the Exponential distribution is λ.λ = 1 / µλ = 1 / 25,000 hrs. λ = 0.00004. Therefore, the probability that a randomly selected fan will last at least 20,000 hours. P(X ≥ 20,000) =  e -λt = e -0.00004 × 20,000 ≈ 0.4493The probability that a randomly selected fan will last at least 20,000 hours is 0.4493.

To find the probability that a randomly selected fan will last at most 30,000 hours. P(X ≤ 30,000) = 1 - e -λt = 1 - e -0.00004 × 30,000 ≈ 0.7769. The probability that a randomly selected fan will last at most 30,000 hours is 0.7769.

To find the probability that a randomly selected fan will last between 20,000 and 30,000 hours. P(20,000 ≤ X ≤ 30,000) = P(X ≤ 30,000) - P(X ≤ 20,000)P(20,000 ≤ X ≤ 30,000) = (1 - e -λt) - (1 - e -λt)P(20,000 ≤ X ≤ 30,000) = e -0.00004 × 20,000 - e -0.00004 × 30,000 ≈ 0.3276. The probability that a randomly selected fan will last between 20,000 and 30,000 hours is 0.3276.

b) To find the probability that the lifetime of a fan exceeds the mean value by more than 2 standard deviations.

z = (X - µ) / σZ = (X - µ) / σ = (X - 25,000) / (25,000)λ = 1 / µλ = 1 / 25,000 hrs. λ = 0.00004

The formula for z is z = (X - µ) / σ => X = z σ + µ

The standard deviation of the Exponential distribution is σ = 1 / λσ = 1 / 0.00004 = 25,000 hrs

Z = (X - µ) / σ = (X - 25,000) / (25,000)Z > 2z > 2 => (X - 25,000) / (25,000) > 2 => X > 75,000 hrs.

Now, the probability that the lifetime of a fan exceeds the mean value by more than 2 standard deviations.

P(X > 75,000) = e -λt = e -0.00004 × 75,000 ≈ 0.0821

The probability that the lifetime of a fan exceeds the mean value by more than 2 standard deviations is 0.0821

To find the probability that the lifetime of a fan exceeds the mean value by more than 3 standard deviations.

Z > 3z > 3 => (X - 25,000) / (25,000) > 3 => X > 100,000 hrs.

Now, the probability that the lifetime of a fan exceeds the mean value by more than 3 standard deviations P(X > 100,000) = e -λt = e -0.00004 × 100,000 ≈ 0.0183

The probability that the lifetime of a fan exceeds the mean value by more than 3 standard deviations is 0.0183.

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Answer:

23 and 24

Step-by-step explanation:

let the 2 consecutive numbers be n and n + 1 , then

n² + (n + 1)² = 1105

n² + n² + 2n + 1 = 1105 ( subtract 1105 from both sides )

2n² + 2n - 1104 = 0 ( divide through by 2 )

n² + n - 552 = 0 ← in standard form

(n + 24)(n - 23) = 0 ← in factored form

equate each factor to zero and solve for n

n + 24 = 0 ⇒ n = - 24

n - 23 = 0 ⇒ n = 23

However, n > 0 , then n = 23 and n+ 1 = 23 + 1 = 24

the numbers are 23 and 24