Between which two whole numbers number is the square root of 51

Answer:

Diana will be able to maek 12

Step-by-step explanation:

There are 495 ways to select 4 balls from an urn that has 4 white balls and 8 red balls.

An urn contains 4 white balls and 8 red balls. Four balls are selected. If we have an urn that has n distinct balls, and we want to know how many possible ways there are to select r of them, we use the combination formula:  

C(n, r) = n! / r! * (n - r)!

Where "!" denotes factorial.

Now, we have an urn that has 4 white balls and 8 red balls, for a total of 12 balls.

We want to know how many ways there are to select 4 balls.

Thus, we use the combination formula as follows:

C(12, 4) = 12! / 4! * (12 - 4)!C(12, 4)

            = (12 * 11 * 10 * 9) / (4 * 3 * 2 * 1)C(12, 4)

            = 495

Therefore, there are 495 ways to select 4 balls from an urn that has 4 white balls and 8 red balls.

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Answer:

17 chickens 2 goats

Step-by-step explanation:

17 chickens is 17×2=34 legs

plus the 2 goats is 42 legs, adding up to 19 animals

Answer:

$400

Step-by-step explanation:

300+25x=?

300+(25•4)=?

300+100=400

The power series solution of the differential equation is:

y(x) = a₀ + a₁x + a₂x² + a₃x³ + ...

To solve the differential equation y" - xy' - y = 0 using a power series method, we assume a power series solution of the form:

y(x) = ∑(n=0 to ∞) aₙxⁿ

where aₙ are the coefficients to be determined.

First, we find the derivatives of y(x) with respect to x:

y'(x) = ∑(n=0 to ∞) (n+1)aₙxⁿ

y''(x) = ∑(n=0 to ∞) (n+1)(n+2)aₙxⁿ

Substituting these expressions into the differential equation, we get:

∑(n=0 to ∞) (n+1)(n+2)aₙxⁿ - x * ∑(n=0 to ∞) (n+1)aₙxⁿ - ∑(n=0 to ∞) aₙxⁿ = 0

To simplify the equation, we reindex the summation by letting n = m-2 in the first summation and n = m-1 in the second summation:

∑(m=2 to ∞) (m-1)m aₘ₋₂xᵐ⁻² - x * ∑(m=1 to ∞) maₘ₋₁xᵐ⁻¹ - ∑(n=0 to ∞) aₙxⁿ = 0

Next, we combine the summations into a single expression:

∑(m=2 to ∞) (m-1)m aₘ₋₂xᵐ⁻² - ∑(m=1 to ∞) maₘ₋₁xᵐ⁻¹ - ∑(n=0 to ∞) aₙxⁿ = 0

Now, we reindex the first summation by letting m = n+2:

∑(n=0 to ∞) (n+1)(n+2) aₙxⁿ - ∑(n=1 to ∞) naₙ₋₁xⁿ - ∑(n=0 to ∞) aₙxⁿ = 0

Combining the summations once again, we have:

2a₀ + ∑(n=1 to ∞) [(n+1)(n+2)aₙ - naₙ₋₁ - aₙ]xⁿ = 0

For this equation to hold for all x, each term multiplying xⁿ must be zero. Therefore, we get the recurrence relation:

(n+1)(n+2)aₙ - naₙ₋₁ - aₙ = 0

Simplifying the recurrence relation, we have:

aₙ₊₂ = (n/(n+1)(n+2))aₙ₊₁

Using this recurrence relation, we can determine the coefficients aₙ iteratively.

To find the specific form of the power series solution, we can start with an initial condition. For example, if we assume y(0) = 1 and y'(0) = 0, we can determine the coefficients a₀ and a₁:

a₀ = y(0) = 1

a₁ = y'(0) = 0

Using the recurrence relation, we can compute the remaining coefficients aₙ for n ≥ 2.

Finally, the power series solution of the differential equation is:

y(x) = a₀ + a₁x + a₂x² + a₃x³ + ...

This power series solution provides an approximation of the actual solution of the differential equation. The convergence and validity of the series depend on the behavior of the coefficients and the range of x values considered.

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Answer:

c

Step-by-step explanation:

using the continously compounded formula, let a be unknown, p= 530, r be 0.05 and t be 12.

the equation would then be a=530e to the (0.05*12)th power, so that's why it's c

The amount of money after 12 years is $965.66. Therefore, option C is the correct answer.

Continuously compounded interest means that an account balance is constantly earning interest, as well as refeeding that interest back into the balance so that it, too, earns interest.

The continuous compound interest formula is \(P(t)=P_0e^{rt}\).

Where, P(t)=value at time t, \(P_0\) =original principal sum, r=nominal annual interest rate and t= length of time the interest is applied

Now, \(P(12)=530\times e^{0.05\times12}\)

⇒ \(P(12)=530\times e^{0.6}\)

⇒ P(12)= 530×1.822

⇒ P(12)= $965.66

The amount of money after 12 years is $965.66. Therefore, option C is the correct answer.

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Answer:

52 years.

Step-by-step explanation:

Represent my current age by c.  Then 400 - 2c = 296, or

104 = 2c

Then c must be 104/2, or 52 years.

In the above case, the possible point system will be:

1st choice vote: 4 points

2nd choice vote: 2 points

In arranging for the turtle to win in this point framework, the point values relegated for 1st choice and 2nd choice votes have to be meet the taking after criteria:

Lets say:

1st choice vote: 4 points

2nd choice vote: 2 points

Thus by the use of these point values, the turtle would have the next chance of winning since 1st choice votes would be worth more point (4 point ) compared to 2nd choice votes (3 point ). This would push individuals to select the turtle as their 1st choice, because it would allow the turtle a better add up to point gains and increase its chances of winning.

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The series [infinity]Σ n=1 (4^n * x^(2n))/n converges conditionally when x is in the interval: (c) x = ±1/2

To determine when the series [infinity]Σ n=1 (4^n * x^(2n))/n converges conditionally, we can use the ratio test. Let's apply the ratio test to the series:

lim(n→∞) |(4^(n+1) * x^(2(n+1)) / (n+1)) / (4^n * x^(2n) / n)|

Simplifying this expression:

lim(n→∞) |(4^(n+1) * x^(2(n+1)) * n) / (4^n * x^(2n) * (n+1))|

Simplifying further:

lim(n→∞) |4 * x^2 * n / (n+1)|

Taking the absolute value and applying the limit:

lim(n→∞) |4 * x^2 * n / (n+1)| = |4 * x^2|

Now, for the series to converge conditionally, the ratio |4 * x^2| must be less than 1. Therefore, we have:

|4 * x^2| < 1

Solving this inequality:

-1 < 4 * x^2 < 1

Dividing all terms by 4:

-1/4 < x^2 < 1/4

Taking the square root of all terms:

-1/2 < x < 1/2

Hence, the series [infinity]Σ n=1 (4^n * x^(2n))/n converges conditionally when x is in the interval: (c) x = ±1/2

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Answer:

A) 2¹²

Step-by-step explanation:

Given :

Equate the equation to y :

Substituting in the expression :

Answer:

0.001 fluid oz.

Step-by-step explanation:

100 : 0.1 = 10,000 = 0.001

Answer:

D=36, x1=1, x2=4

Step-by-step explanation:

Find the D:

D = b2 - 4ac = (-10)2 - 4·2·8 = 100 - 64 = 36

Since the discriminant is greater than zero, the quadratic equation has two real roots

\(x1=\frac{10-\sqrt{36} }{2*2} \\x2=\frac{10+\sqrt{36} }{2*2}\)

Discriminant = b^2 - 4ac

= 36

Roots:

Method: Sum and Product

Sum = -10

Product = 16

(2x^2 - 8x) - (2x + 8) = 0

2x(x - 4) - (x - 4) = 0

x = 0 or x = 4

Answer:

15.4 minutes :)

Step-by-step explanation:

We need to turn the percentage into a decimal first :)

27/100 = 0.27

Now we multiply it by 57 to see how much time has gone by!! :)

0.27 x 57 = 15.39

Now to finish, we round!

9> 5

So 3 becomes 4

She has been on the treadmill for 15.4 minutes!

Now you know how to solve this type of problem!!

Have an amazing day!!

Please rate and mark brainliest!!

The largest area that can be enclose in straight wall is 2450 m².

Let 'x' be the length of rectangle.

Let 'y' be the width rectangle.

Perimeter =  140 meters

2x + y = 140      

y = 140 - 2x

Area = xy

Put the value of y in area.

Area = x(-2x + 140)

Area = -2x² + 140x

Differentiating the area with respect to x.

dA/dx = -4x + 140

Put dA/dx = 0 to get the critical point.

-4x + 140 = 0

x = 140/4

x = 35

Largest area at x = 35.

y = 140 - 2x

y = 140 - 2×35

y = 70

Area = xy

Area = 70×35

Area = 2450 m²

Thus, the largest area that can be enclose in straight wall is 2450 m².

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Answer:

153

Step-by-step explanation:

Triange area = 1/2 b*h

= 1/2 (7)*(9)

=31.5 (for 1 triangle)

2(31.5) = 63 (for 2 triangles, left and right)

Rectangle area = b *h

= 10*9

=90

Total = 2 triangles + rectangle

63+90 = 153

Answer: 108

Step-by-step explanation: the formula, 10+7(2)/2 x 9 = 108

Answer:

7.5

Step-by-step explanation:

Answer:

Obtuse because one angle is over 90 degrees

Answer:

(a) Triangles are similar if corresponding angles are congruent and the ratios of the lengths of corresponding sides are equal.

(b) x = 24

(c) y = 17; z = 51

Step-by-step explanation:

(a) Triangles are similar if corresponding angles are congruent and the ratios of the lengths of corresponding sides are equal.

(b)

15/45 = 8/x

1/3 = 8/x

x = 3 * 8

x = 24

(c)

a^2 + b^2 = c^2

x^2 + 45^2 = z^2

24^2 + 45^2 = z^2

576 + 2025 = z^2

z^2 = 2601

z = 51

15/45 = y/z

1/3 = y/51

3y = 51

y = 17

Answer:

options 4 and 6 I believe

The probability that in a given ten-minute interval, 15 cars arrive at the booth, and 10 of these are japanese imports = 0.0002

We know that the conditions for the Poisson distribution.

1) The occurrence of one event does not affect the probability another event will occur. i.e., the events are independent events.

2) The average rate i.e., the ratio events per time period is constant.

3) Two events cannot occur at the same time.

and the formula for the Poisson distribution is:

\(P(X = k)=\frac{e^{-\lambda}\times {\lambda}^k}{k!}\)

Here, the cars arrive at a toll booth according to a Poisson process at a rate of 3 arrivals per minute.

We need to find the probability tthat in a given ten-minute interval, 15 cars arrive at the booth, and 10 of these are japanese imports.

Here, we need to multiply the Binomial probability of 10 out of 15 cars being Japanese with the Poisson probability of 15 cars arriving in a 10 minute period.

The Binomial probability of 10 out of 15 cars would be:

P₁(x = 10) = ¹⁵C₁₀ (0.6)¹⁰ (0.4)¹⁵⁻¹⁰

P₁ = 0.18594

And the Poisson probability of 15 cars arriving in a 10 minute period.

So we use λ = 30.

P₂(X = 15) = \(\frac{e^{-30}\times {30}^{15}}{15!}\)

P₂ = 0.0010

So, the required probability would be:

P = P₁ × P₂

P =  0.18594 ×  0.001

P = 0.00018594

P= 0.0002

Therefore, the required probability is 0.0002

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The complete question is:

Cars arrive at a toll booth according to a Poisson process at a rate of 3 arrivals per minute.

b) Of the cars arriving at the both, it is known that over the long run 60% are Japanese imports. What is the probability that in a given ten-minute interval. 15 cars arrive at the booth, and 10 of these are Japanese imports? State your assumptions clearly.

Answer:

T ≥ 8x

50 ≥ 8x .......1

x ≤ 6

Liam can buy lunch for 6 people.

Step-by-step explanation:

Let x represent the number of people Liam can buy lunch for.

Given;

Lunch cost per person r = $8 per person

The total amount he has T = $50

The cost of buying lunch for c people is;

C = $8 × x

C = 8x

Therefore, to be able to buy lunch for them, the total cost C must be less than the total amount he has.

T ≥ C

Substituting C, we have;

T ≥ 8x

50 ≥ 8x ,.......1

Solving the inequalities;

8x ≤ 50

x ≤ 50/8

x ≤ 6.25

To the nearest whole number;

x ≤ 6

Liam can buy lunch for 6 people.

The Object 4 with a density of 2.3 g/cm³ would sink in honey. The Option D.

It can be defined as the mass of any object or body per unit volume of the particular object or body. Generally, it is expressed as in gram per cm³ or kilogram per meter³.

To determine which object would sink in honey, we will compare the density of each object with the density of honey. If the density of an object is greater than the density of honey (1.4 g/cm³), it will sink; otherwise, it will float.

Object 1: Density (0.9 g/cm³) < Density of honey (1.4 g/cm³)

Object 2: Density (1.2 g/cm³) < Density of honey (1.4 g/cm³)

Object 3: Density (0.2 g/cm³) < Density of honey (1.4 g/cm³)

Object 4: Density (2.3 g/cm³) > Density of honey (1.4 g/cm³).

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Answer:

3/3=1

Step-by-step explanation:

rise over run

Answer:

$5.71

Step-by-step explanation:

20-5.88=14.12

14.12-8.41=5.71

Answer:

$5.71

Step-by-step explanation:

$20 − $5.88 − $8.41 = $5.71

Answer:

$110.2

Step-by-step explanation:

$76 × 45%

$34.2

$76 + $34.2

$110.2

The true speed of the object is 58.524.

The direction of the object is 163°.

Given that,

An object experiences two velocity vectors in its environment.

v1 = −60i + 3j

v2 = 4i + 14j

Resultant vector is,

V = v1 + v2

   = -56i + 17j

Now the true speed is,

True speed = √(=[(-56)² + (17)²] = 58.524

Direction of the object is,

Direction = tan⁻¹ (17 / -56)

               = - tan⁻¹ (17/56)

               = -16.887° ≈ -17°

                                = 180° - 17 = 163°

Hence the correct option is A.

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The mode salary of a major league baseball player being $600,000 means that more major league baseball players earn $600,000 than any other salary. In this context, "mode" represents the most frequently occurring value in a data-set, which, in this case, is the salaries of major league baseball players.

The correct answer to this question is (a) more major league baseball players earn $600,000 than any other salary. The mode is the value that appears most frequently in a dataset, and in this case, it means that $600,000 is the most common salary among major league baseball players. This doesn't necessarily mean that it's the middle salary or the average salary, as those would be the median and mean respectively. It also doesn't mean that no player makes less than $600,000, as there may be some players who earn less than this amount. Therefore, the correct answer is (a), which is the only option that accurately reflects what the mode represents in this context.

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