Marbles in an urn. Imagine you have an urn containing 5 red, 3 blue, and 2 orange marbles in it.
(a) What is the probability that the first marble you draw is blue?
(b) Suppose you drew a blue marble in the first draw. If drawing with replacement, what is the probability of drawing a blue marble in the second draw?
(c) Suppose you instead drew an orange marble in the first draw. If drawing with replacement, what is the probability of drawing a blue marble in the second draw?
(d) If drawing with replacement, what is the probability of drawing two blue marbles in a row?
(e) When drawing with replacement, are the draws independent? Explain.

For the following set of parametric equations y = θ³ - 5θ; x = 2θ², based on the second derivative result, the curve is concave up.

To locate the first derivative of the parametric equations, we're going to differentiate each equation with admire to θ:

Given:

y = θ³ - 5θ

x = 2θ²

dy/dθ = d/dθ (θ³ - 5θ) = 3θ² - 5

dx/dθ = d/dθ (2θ²) = 4θ

d²y/dθ² = d/dθ (3θ² - 5) = 6θ

d²x/dθ² = d/dθ (4θ) = 4

Now, let's talk the concavity of the curve the use of the second derivative.

If the second by-product (d²y/dθ² or d²x/dθ²) is high quality, the curve is concave up. If the second one spinoff is bad, the curve is concave down.

For d²y/dθ² = 6θ, we don't have enough records to decide its sign without knowing the range of values for θ. The concavity will depend upon the values of θ.

For d²x/dθ² = four, the second one spinoff is a regular advantageous price, indicating that the curve described with the aid of the parametric equations is continually concave up.

Thus, based on the second derivative result, the curve is concave up.

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Answer

It would be 1005

Step-by-step explanation:

because it says what is the maximum potential profit for tent sales.

It would take approximately 48.12 days for the radioactive iodide taken up and held by the thyroid to decay to 0.01% of the original amount.

To determine the time it takes for the radioactive iodide taken up by the thyroid to decay to 0.01% of the original amount, we can use the concept of radioactive decay and the half-life of iodine-131.

Half-life of iodine-131: 8.02 days

Fraction of iodide taken up by a normal thyroid: 12%

Fraction remaining after decay: 0.01% (or 0.0001) of the original amount

Let's assume we start with 100 units of radioactive iodide taken up by the thyroid. After the first half-life (8.02 days), half of the iodide will decay, so we'll have 50 units remaining. Since a normal thyroid takes up 12%, we multiply the remaining units by 0.12 to find the amount taken up: 50 units × 0.12 = 6 units.

Now, we have 6 units remaining in the thyroid, and we'll repeat the process for subsequent half-lives until we reach 0.01% of the original amount.

1st half-life: 50 units remaining (0.12 taken up)

2nd half-life: 25 units remaining (0.12 taken up)

3rd half-life: 12.5 units remaining (0.12 taken up)

4th half-life: 6.25 units remaining (0.12 taken up)

5th half-life: 3.125 units remaining (0.12 taken up)

6th half-life: 1.5625 units remaining (0.12 taken up)

After 6 half-lives, the remaining iodide in the thyroid is approximately 1.5625 units, which is 0.015625% of the original amount (100 units).

To calculate the time it takes for the radioactive iodide taken up by the thyroid to decay to 0.01% of the original amount, we need to multiply the half-life by the number of half-lives

Time = Half-life × Number of half-lives

= 8.02 days × 6

= 48.12 days

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-- The given question is incomplete, the complete question is

"Iodine-131 is a convenient radioisotope to monitor thyroid activity in humans. It is a beta emitter with a half-life of 8.02 days. The thyroid is the only gland in the body that uses iodine. A person undergoing a test of thyroid activity drinks a solution of NaI, in which only a small fraction of the iodide is radioactive. (c) A normal thyroid will take up about 12% of the ingested iodide in a few hours. How long will it take for the radioactive iodide taken up and held by the thyroid to decay to 0.01% of the original amount?" --

The recursive and the explicit formulas are f(n) = 3f(n - 1), where f(1) = 250 and f(n) = 250(3)ⁿ‐¹

From the question, we have the following parameters that can be used in our computation:

This means that

Initial, a = 250 bacterial cultures.

Rate = 3

So, the recursive formulas is

f(n) = 3f(n - 1), where f(1) = 250

For the explicit formula, we have

f(n) = 250(3)ⁿ‐¹

Hence, the recursive and the explicit formulas are f(n) = 3f(n - 1), where f(1) = 250 and f(n) = 250(3)ⁿ‐¹

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Your question is not complete so there are two answers:

The measure of one angle is 13 times the measure of the other angle.

Answer:

Step-by-step explanation:

Two angles of a linear pair create a straight angle therefore they add to 180°

x°     - the other angle

(13x)°  - one angle

x + 13x = 180

   14x = 180

  ÷14      ÷14

   x ≈ 12.86

13x = 13•12.86 = 167.14

Checking:  12.96+167.14 = 180

The measure of one angle is 13 more than the measure of the other angle.

Answer:

Step-by-step explanation:

Two angles of a linear pair create a straight angle therefore they add to 180°

x°     - the other angle

(x+13)°  - one angle

x + x + 13 = 180

       -13        -13

    2x  =  167

    ÷14      ÷14

     x ≈ 83.5

x+13 = 83.5 + 13 = 96.5

Checking:  83.5+96.5 = 180

Step-by-step explanation:

The line representing the equation 7x1 + 4x2 = 28 goes through the points (4,0) and (0,7).

Answer: a parallelogram

Answer:

We need to prove that the function f defined on R by f(x) = 0 if x ≤ 0 and f(x) = e^(-1/x^2) if x > 0 is indefinitely differentiable on R and that f(n)(0) = 0 for all n ≥ 1. Additionally, we conclude that f does not have a converging power series expansion near the origin.

Step-by-step explanation:

f is indefinitely differentiable on R, and f(n)(0) = 0 for all n ≥ 1 and f does not have a converging power series expansion Sumn=0to[infinity] anxn for x near the origin.

Consider the function f defined on R by f(x) =0 if x ≤ 0, f(x) = e−1/x2 if x > 0.

We are to prove that f is indefinitely differentiable on R, and that f(n)(0) = 0 for all n ≥ 1. It must be shown that the derivative of f exists at all points.

Consider the right and left-hand limits of f'(0) which would give an indication of the existence of the derivative of f at 0.

Using the limit definition of derivative we have f′(0)=[f(h)−f(0)]/

where h is any number approaching 0 from the right.

That is h → 0+. On the right of 0, the function is e^(-1/x^2).f′(0+) = limh→0+ [f(h)−f(0)]/h=f(0+)=limh→0+ (e^(-1/h^2))/h^2

Using L'Hospital's rule,f′(0+)=limh→0+[-2e^(-1/h^2)]/h^3=0.

Using the same procedure, we can prove that the left-hand limit of the derivative of f at 0 exists and is zero.Therefore, f′(0) = 0.

Now we can use induction to prove that f is indefinitely differentiable on R, and that f(n)(0) = 0 for all n ≥ 1.

By taking the derivative of f'(0), we have:f″(0+) = limh→0+ [f′(h)−f′(0)]/h=f′(0+)=limh→0+ (-4e^(-1/h^2) + 2h*e^(-1/h^2))/h^4At 0, this limit is zero, and we can use induction to show that all the higher order derivatives of f at 0 are also zero.

Therefore, f is indefinitely differentiable on R, and f(n)(0) = 0 for all n ≥ 1.  

Since the power series expansion of f near x = 0 would require all of its derivatives at x = 0 to exist, we can conclude that the function f does not have a converging power series expansion Sumn=0to[infinity] anxn for x near the origin.

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Answer:

b < -1

Step-by-step explanation:

Step 1: Write inequality

-3(6b - 1) > 18 - 3b

Step 2: Solve for b

Distribute -3: -18b + 3 > 18 - 3b

Add 18b to both sides: 3 > 18 + 15b

Subtract 18 on both sides: -15 > 15b

Divide both sides by 15: -1 > b

Rewrite: b < -1

Therefore, the series 4/5 - 4/7 + 4/9 - 4/11 + 4/13 - ... is convergence in nature.

To test the convergence or divergence of the given series: 4/5 - 4/7 + 4/9 - 4/11 + 4/13 - ..., we can use the alternating series test. The alternating series test states that if a series has the form (-1)^n b_n, where b_n is a positive sequence that is decreasing and approaches zero as n approaches infinity, then the series converges.

In the given series, we have b_n = 4/(2n+3), which is a positive sequence that approaches zero as n approaches infinity. To see that b_n is decreasing, we can note that b_{n+1}/b_n = 2(2n+3)/(2n+5) < 1 for all n, since the numerator is always less than the denominator. Therefore, b_n is a positive, decreasing sequence that approaches zero as n approaches infinity.

Furthermore, the series has the form (-1)^n b_n, where the sign alternates between positive and negative. Therefore, we can apply the alternating series test, which tells us that the series converges.

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Answer:

6.6

Step-by-step explanation:

Answer:

l;sqld

Step-by-step explanation:

d;[sldsa

Answer: 15/16

Step-by-step explanation:

5/4 * (3 * 1/4) =

Mutiply 3 * 1/4

5/4 * 3/4 =

Mutiply 5/4 * 3/4

5/4 * 3/4 = 15/16

Answer:

\(\frac{15}{16}\)

Step-by-step explanation:

\(\frac{5}{4}\cdot \:3\cdot \frac{1}{4}\)

\(\mathrm{Convert\:element\:to\:fraction}:\quad \:3=\frac{3}{1}\)

\(=\frac{5}{4}\cdot \frac{3}{1}\cdot \frac{1}{4}\)

\(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}\)

\(=\frac{5\cdot \:3\cdot \:1}{4\cdot \:1\cdot \:4}\)

\(\mathrm{Multiply\:the\:numbers:}\:5\cdot \:3\cdot \:1=15\)

\(=\frac{15}{4\cdot \:1\cdot \:4}\)

\(\mathrm{Multiply\:the\:numbers:}\:4\cdot \:1\cdot \:4=16\)

\(\frac{15}{16}\)

Hence, 15/16 is the correct Answer.

~Learn with Lenvy~

Answer:

\(344 {cm}^{2} \)

Step-by-step explanation:

\(area \: of \: the \: square \\ = 40cm \times 40cm \\ = 1600 {cm}^{3} \\ \)

\(area \: of \: the \: circle \\ = \pi {r}^{2} \\ = 3.14 \times {(20)}^{2} \\ = 3.14 \times 400 \\ = 1256 {cm}^{2} \\ \)

\(area \: of \: shaded \: region \\ = 1600 {cm}^{2} - 1256 {cm}^{2} \\ = 344 {cm}^{2} \\ \)

The value of angle A is 43⁰.

The value of arc CE is 44⁰.

The value of angle C is 43⁰.

The value of angle ABE is 90⁰

The value of angle A is calculated by applying the following formula as shown below;

∠A  = ¹/₂ arc BD (intersecting chord theorem)

∠A  = ¹/₂ x 86⁰

∠A  = 43⁰

arc CE = 2 ∠mCBE

arc CE = 2 x 22

arc CE = 44⁰

∠A = ∠ C (vertical opposite angles are equal)

∠C = 43⁰

∠ABE = 90⁰

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Answer:

\(2^{100}\)

Step-by-step explanation:

Given expression:

\(2^{40} \times 4^{30}\)

Rewrite 4 as 2²:

\(\implies 2^{40} \times (2^2)^{30}\)

\(\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:\)

\(\implies 2^{40} \times 2^{(2\times30)}\)

\(\implies 2^{40} \times 2^{60}\)

\(\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:\)

\(\implies 2^{(40+60)}\)

\(\implies 2^{100}\)

Therefore, n = 100.

Answer:

A. 72

B. 3

C. 135

Step-by-step explanation:

A. 12 x 6 = 72

B. 15 x 3 = 45 so Nina raise 3x more money than Sandra

C. 45 x 3 = 135

Answer:

C. 3 workbooks and 5 dry erase boards

Total is $46. The rest exceed her budget.

Answer:

the last bubble

Step-by-step explanation:

Perpendicular lines have opposite reciprocal slopes

the original line: y = 5/2x + 5

The perpendicular line: y = -2/5x + b

To find b, we have to plug (-10, 5) into x and y for our perpendicular line

5 = -2/5(-10) + b

Simplify the right side

5 = 4 + b

Subtract 4 from both sides

1 = b

The final answer = y = -2/5x + 1

Answer:

The speed of the slower train is 60km/hr or 80km/hr and the speed of the faster train is 70km/hr or 90km/hr.

Answer:

1/4 inches

Step-by-step explanation:

Answer:

1/4 inches is smaller than 1/2 inches

1/4 inches in cm= 0.635

Step-by-step explanation:

Answer:

okay igu

Step-by-step explanation:

x

x*4

x*14

The skip interval should be 40 if the sampling frame has 2000 names and the desired sample size is 50.

Systematic sampling is a type of sampling which uses the probability method where researchers select members of the group or population at a regular interval.

To determine the skip interval, it is necessary to first determine the sample size. Then the skip interval can be determined by dividing the total population by the target/desired sample size. Therefore;

skip interval = population / target sample size

Substituting the given values;

skip interval = 2000 / 50

skip interval = 40

Hence, the skip interval is calculated to be 40 if the frame has 2000 names and the desired sample size is 50.

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Answer:

A teacher made a copy of a map. To make the map easier to see, the teacher enlarged the area of the map by 38%. Let d represent the area of the original map. The expression d + 0.38d is one way to represent the area of the new map. Write two expressions that represent the area of the new map.​

Step-by-step explanation:

The triple integral in spherical coordinates shows that I = 4π.

Consider the iterated integral TT 2√5 √20-r² I = 3r dz dr de 0.

Denote by G the solid of integration of the integral I, which is bounded by a portion of a sphere S₁ and a circular cylinder S₂.

Equation in Spherical Coordinates for S₂

The equation in the cylindrical coordinate system for the cylinder S₂ can be represented as r = 2.

Let's represent the cylinder S₂ in the spherical coordinate system by replacing r with ρsinφ, where ρ represents the distance of a point from the origin and φ represents the angle between the positive z-axis and the line segment connecting the origin to the point.

The equation of cylinder S₂ in the spherical coordinate system is given by ρsinφ = 2. In the spherical coordinate system, the limits of integration are θ ranges from 0 to 2π, ρ ranges from 0 to 2, and φ ranges from 0 to π/2.

c) Use a Triple Integral in Spherical Coordinates to show that I = 4π

The iterated integral for the given problem is represented in cylindrical coordinates.

So, we need to convert it into spherical coordinates.

We have, I = TT 2√5 √20-r² I

= 3r dz dr de 0

Let's convert this integral to spherical coordinates.

The spherical coordinate system can be represented as given below.

x = r sin φ cos θy = r sin φ sin θz = r cos φ

Here, we have I = TT 2√5 √20-r² I

= 3r dz dr de 0

Multiplying and dividing with the Jacobian, we get

I = TT TT TT 2√5 (ρ²sinφ) (ρ sin φ dφ) (3ρ²cosφ dθ) (dρ/ρ²)

Integrating w.r.t ρ, φ, and θ limits from 0 to 2π, 0 to π/2, and 0 to 2, respectively, we get

I = 4π.

Therefore, the triple integral in spherical coordinates shows that I = 4π.

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Answer:

12

Step-by-step explanation:

is because my teacher just taught me to add 16 + 4 or the dominator with the numerator then subtract 8 or the number that wants to get added

Answer:

Step-by-step explanation:

jjjj

Given: AQ ≅ RQ, it should be noted that AQY ≅ RQF based on SAS Congruence. Therefore, AQY ≅ RQF.

Given: AQ ≅ RQ

∠YAF and ∠FRY are right angles.

Prove: AQY ≅ RQF

1. AQ ≅ RQ (Given)

2. ∠YAF and ∠FRY are right angles (Given)

3. ∠AQY = ∠RQF (Vertical angles are congruent)

4. AQ = RQ (Given)

5. AY = RY (Side-Angle-Side Congruence)

6. ∠QYA = ∠RFQ (Angle-Side-Angle Congruence)

7. AQY ≅ RQF (SAS Congruence)

Therefore, AQY ≅ RQF.

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Given: AQ ≅ RQ

∠YAF and ∠FRY are right angles.

Prove: AQY ≅ RQF

Answer:

f(3) = 9

Step-by-step explanation:

To evaluate f(3) substitute x = 3 into f(x), that is

f(3) = 2(3) + 3 = 6 + 3 = 9

Answer:

f(3) = 9

Step-by-step explanation:

f(3) = 2x + 3

input the 3 into all x values since it is f(x) basically it tells you the value of x

f(3) = 2(3) + 3

f(3) = 9