The numbers 2, 4, 6, and 8 are a set of four consecutive even numbers. Suppose the sum of five consecutive numbers is 320. What is the smallest of the five numbers?

Answer:

total mass of 6 samples = 538.896 g

in terms of X = 5.283 g

Step-by-step explanation:

Given:

Number of crude oil samples = 6

Density of each sample = 0.8240 kg/L

Volume filled by each sample = 1.09 × 10⁻⁴ m³

now,

1 m³ = 1000 L

thus,

1.09 × 10⁻⁴ m³ = 1.09 × 10⁻⁴ m³ × 1000 = 0.109 L

also,

Mass = Density × Volume

or

Mass of each sample = 0.8240 × 0.109 = 0.089816 kg

Thus,

total mass of 6 samples = Mass of each sample × 6

or

total mass of 6 samples = 0.089816 kg × 6 = 0.538896 kg

or

total mass of 6 samples = 538.896 g

or

in X = [tex]\frac{\textup{total mass of 6 samples}}{\textup{102}}[/tex]

= 5.283 g

To determine the number of subsets that can be formed from a set containing eleven elements, we use the formula [tex]2^n,[/tex] yielding [tex]2^11[/tex] = 2048 possible subsets.

The question is about finding the number of subsets that can be formed from a set containing eleven elements. To determine this, we employ the principle that for any set with n elements, the number of possible subsets is 2n. This includes both the empty set and the set itself as subsets.

Therefore, for a set with 11 elements, the number of possible subsets is 211 = 2048. This calculation reveals that one can form 2048 different subsets from a set of eleven elements. This includes all possible combinations of elements within the set, ranging from choosing no elements (the empty set) to choosing all eleven elements (the set itself).

Answer:

The proposition: The sum of two odd numbers is an even number is true.

Step-by-step explanation:

A proof by contradiction is a proof technique that is based on this principle:

To prove a statement P is true, we begin by assuming P false and show that this leads to a contradiction; something that always false.

Facts that we need:

Proposition. The sum of two odd numbers is an even number

Proof. Suppose this proposition is false in this case we assume that the sum of two odd numbers is not even. (That would mean that there are two odd numbers out there in the world somewhere that'll give us an odd number when we add them.)

Let a, b be odd numbers. Then there exist numbers m, n, such that a = 2m + 1, b = 2n + 1 .Thus a + b = (2m + 1) + (2n + 1) = 2(m + n + 1) which is even. This contradicts the assumption that the sum of two odd numbers is not even.

Answer:

time = 28 years

Step-by-step explanation:

Given,

principal amount = $10,000

rate = 4%

total amount = $30,000

According to compound interest formula

[tex]A\ =\ P(1+r)^t[/tex]

where, A = total amount

            P = principal amount

            r = rate

            t = time in years

so, from the question we can write,

[tex]30000\ =\ 10000(1+0.04)^t[/tex]

[tex]=>\ \dfrac{30000}{10000}\ =\ (1+0.04)^t[/tex]

[tex]=>\ 3\ =\ (1.04)^t[/tex]

by taking log on both sides, we will get

=> log3 = t.log(1.04)

[tex]=>\ t\ =\ \dfrac{log3}{log1.04}[/tex]

=> t = 28.01

So, the time taken to get the amount from 10000 to 30000 is 28 years.

Answer: I don't know if you wanted to write sin(4x) or [tex]sin^{4} (x)[/tex] , but here we go:

ok, sin(4x) = sin(2x + 2x), and we know that:

sin (a + b) = sin(a)*cos(b) + sin(b)*cos(a)

then sin (2x + 2x) = sin(2x)*cos(2x) + cos(2x)*sin(2x) = 2cos(2x)*sin(2x)

So 2*cos(2x)*sin(2x) is equivalent of sin(4x)

If you writed [tex]sin^{4} (x)[/tex] then:

[tex]sin^{4} (x) = sin^{2} (x)*sin^{2} (x)[/tex]

and using that: [tex]sins^{2} (x) = \frac{1-cos(2x)}{2}[/tex]

we have: [tex]sin^{2} (x)*sin^{2} (x) = \frac{(1-cos(2x))*(1-cos(2x))}{4} = \frac{1-2cos(2x) + cos^{2}(2x) }{4}[/tex]

and using that: [tex]cos^{2} (x) = \frac{1 + cos(2x)}{2}[/tex]

[tex]\frac{1-2cos(2x) + cos^{2}(2x) }{4} = \frac{1-2cos(2x) + \frac{1+cos(4x)}{2} }{4}[/tex]

You can keep simplifying it, but there is your representation of [tex]sin^{4} (x)[/tex]  that does not contain powers of trigonometric functions greater than 1.

To write an equivalent expression for sin(4x) without powers of trigonometric functions greater than 1, use the trigonometric identity sin(2x) = 2sin(x)cos(x). Apply this identity twice to get 4sin(x)cos(x)(cos^2(x) - sin^2(x)).

To write an equivalent expression for sin(4x) that does not contain powers of trigonometric functions greater than 1, we can use the trigonometric identity sin(2x) = 2sin(x)cos(x). By applying this identity twice, we get:

Therefore, an equivalent expression for sin(4x) that does not contain powers of trigonometric functions greater than 1 is 4sin(x)cos(x)(cos^2(x) - sin^2(x)).

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Answer:

The function is a parabola described by: [tex]y = 1 +\frac{(x-2)^{2}}{8}[/tex]

Step-by-step explanation:

Since a directrix and a focus are given, then we know that they are talking about a parabola.

We know that the distance from any point in a parabola (x, y), to the focus is exactly the same as the distance to the directrix. Therefore, in order to find the required equation, first we will compute the distance from an arbitrary point on the parabola (x, y) to the focus (2, 1):

[tex]d_{pf} = \sqrt{(x-2)^2+(y-1)^2}[/tex]

Next, we will find the distance from an arbitrary point on the parabola (x, y) to the directrix (y= -3). Since we have an horizontal directrix, the distance is easily calculated as:

[tex]d_{pd}=y-(-3)=y+3[/tex]

Finally, we equate the distances in order to find the parabola equation:

[tex]\sqrt{(x-2)^2+(y-1)^2}=y+3[/tex]

[tex](x-2)^2+(y-1)^2=(y+3)^2[/tex]

[tex](x-2)^{2} +y^{2}-2y+1=y^{2}+6y+9[/tex]

[tex](x-2)^{2}-8=8y[/tex]

[tex]y = \frac{(x-2)^{2}}{8}-1[/tex]

Answer:

1) Base - 5

2) Base - 1.2

3) Base - [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

To find : Write the base number for each expression ?

Solution :

Base number is defined as the number written in exponent form [tex]a^n[/tex]

which tells you to multiply a by itself, so a is the base of power n.

1) [tex]5^{12}[/tex]

In number [tex]5^{12}[/tex] the base is 5 as the power is 12.

2) [tex]1.2^{2}[/tex]

In number [tex]1.2^{2}[/tex] the base is 1.2 as the power is 2.

3) [tex](\frac{1}{3})^{2}[/tex]

In number  [tex](\frac{1}{3})^{2}[/tex] the base is [tex]\frac{1}{3}[/tex] as the power is 4.

The base number for 5^12 is 5, for 1.2^2 is 1.095, and for (1/3)^4 is 0.577.

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For this case we propose a rule of three:

110.2 million -------------> 100%

x --------------------------------------> 17.7%

Where the variable "x" represents the number of households (in millions) that watched the finals of a popular reality series.

[tex]x =  \frac {17.7 * 110.2} {100}\\x = \frac {1950.54} {100}\\x = 19.5054[/tex]

Thus, a total of 19.5054 million homes watched the finals of a popular reality series.

Answer:

19.5054 million homes watched the finals of a popular reality series.

Answer:

[tex]26^{39}[/tex] is greater.

Step-by-step explanation:

Given numbers,

[tex]26^{39}\text{ and }39^{26}[/tex]

∵ HCF ( 26, 39 ) = 13,

That is, we need to make both numbers with the exponent 13.

[tex]26^{39}=((13\times 2)^3)^{13}=(13^3\times 2^3)^{13}=(13^3\times 8)^{13}=(13^2\times 104)^{13}[/tex]

[tex](\because (a)^{mn}=(a^m)^n\text{ and }(ab)^m=a^m.a^n)[/tex]

[tex]39^{26}=((13\times 3)^2)^{13}=(13^2\times 3^2)^{13}=(13^2\times 9)^{13}[/tex]

Since,

[tex]13^2\times 104>13^2\times 9[/tex]

[tex]\implies (13^2\times 104)^{13} > (13^2\times 9)^{13}[/tex]

[tex]\implies 26^{39} > 39^{26}[/tex]

Answer:

(a) 65

(b) -26

(c) 54.6

(d) -54.6

Step-by-step explanation:

(a) [tex]f(5)=8(5)+5(5)=40+25=65[/tex]

(b) [tex]f(-2)=8(-2)+5(-2)=-16-10=-26[/tex]

(c) [tex]f(4.2)=8(4.2)+5(4.2)=33.6+21=54.6[/tex]

(d) [tex]f(-4.2)=8(-4.2)+5(-4.2)=-33.6-21=-54.6[/tex]

Answer: [tex](0.0628,\ 0.1186)[/tex]

Step-by-step explanation:

Given : Significance level : [tex]\alpha:1-0.95=0.05[/tex]

Critical value : [tex]z_{\alpha/2}=\pm1.96[/tex]

Sample size : n= 408

Proportion of new websites registered on the Internet were anonymous :

[tex]\hat{p}=\dfrac{37}{408}\approx0.0907[/tex]

The formula to find the confidence interval for population proportion is given by :-

[tex]\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

i.e. [tex]0.0907\pm (1.96)\sqrt{\dfrac{0.0907(1-0.0907)}{408}}[/tex]

[tex]=0.0907\pm0.0278665515649\\\\\approx 0.0907\pm0.0279\\\\=(0.0907-0.0279,\ 0.0907+0.0279)\\\\=(0.0628,\ 0.1186)[/tex]

Hence,  the 95 percent confidence interval for the proportion of all new websites that were anonymous = [tex](0.0628,\ 0.1186)[/tex]

Answer:

This is the reduced row-echelon form

[tex]\left[\begin{array}{cccccc}1&-2&0&0&3&5\\0&0&1&0&2&-3\\0&0&0&1&-4&7\end{array}\right][/tex]

from the augmented matrix

[tex]\left[\begin{array}{cccccc}1&-2&3&2&1&10\\2&-4&8&3&10&7\\3&-6&10&6&5&27\end{array}\right][/tex]

Step-by-step explanation:

To transform an augmented matrix to the reduced row-echelon form we need to follow this steps:

1. Write the system of equations as an augmented matrix.

The augmented matrix for a system of equations is a matrix of numbers in which each row represents the constants from one equation (both the coefficients and the constant on the other side of the equal sign) and each column represents all the coefficients for a single variable.

[tex]\left[\begin{array}{cccccc}1&-2&3&2&1&10\\2&-4&8&3&10&7\\3&-6&10&6&5&27\end{array}\right][/tex]

2. Make zeros in column 1 except the entry at row 1, column 1 (this is the pivot entry). Subtract row 1 multiplied by 2 from row 2 [tex]\left(R_2=R_2-\left(2\right)R_1\right)[/tex]

[tex]\left[\begin{array}{cccccc}1&-2&3&2&1&10\\0&0&2&-1&8&-13\\3&-6&10&6&5&27\end{array}\right][/tex]

3. Subtract row 1 multiplied by 3 from row 3 [tex]\left(R_3=R_3-\left(3\right)R_1\right)[/tex]

[tex]\left[\begin{array}{cccccc}1&-2&3&2&1&10\\0&0&2&-1&8&-13\\0&0&1&0&2&-3\end{array}\right][/tex]

4. Since element at row 2 and column 2 (pivot element) equals 0, we need to swap rows. Find the first non-zero element in the column 2 under the pivot entry. As can be seen, there are no such entries. So, move to the next column. Make zeros in column 3 except the entry at row 2, column 3 (pivot entry). Divide row 2 by 2 [tex]\left(R_2=\frac{R_2}{2}\right)[/tex]

[tex]\left[\begin{array}{cccccc}1&-2&3&2&1&10\\0&0&1&-1/2&4&-13/2\\0&0&1&0&2&-3\end{array}\right][/tex]

5. Subtract row 2 multiplied by 3 from row 1 [tex]\left(R_1=R_1-\left(3\right)R_2\right)[/tex]

[tex]\left[\begin{array}{cccccc}1&-2&0&7/2&-11&59/2\\0&0&1&-1/2&4&-13/2\\0&0&1&0&2&-3\end{array}\right][/tex]

6. Subtract row 2 from row 3 [tex]\left(R_3=R_3-R_2\right)[/tex]

[tex]\left[\begin{array}{cccccc}1&-2&0&7/2&-11&59/2\\0&0&1&-1/2&4&-13/2\\0&0&0&1/2&-2&7/2\end{array}\right][/tex]

7. Make zeros in column 4 except the entry at row 3, column 4 (pivot entry). Subtract row 3 multiplied by 7 from row 1 [tex]\left(R_1=R_1-\left(7\right)R_3\right)[/tex]

[tex]\left[\begin{array}{cccccc}1&-2&0&0&3&5\\0&0&1&-1/2&4&-13/2\\0&0&0&1/2&-2&7/2\end{array}\right][/tex]

8. Add row 3 to row 2 [tex]\left(R_2=R_2+R_3\righ)[/tex]

[tex]\left[\begin{array}{cccccc}1&-2&0&0&3&5\\0&0&1&0&2&-3\\0&0&0&1/2&-2&7/2\end{array}\right][/tex]

9. Multiply row 3 by 2 [tex]\left(R_3=\left(2\right)R_3\right)[/tex]

[tex]\left[\begin{array}{cccccc}1&-2&0&0&3&5\\0&0&1&0&2&-3\\0&0&0&1&-4&7\end{array}\right][/tex]

Answer:

[tex]\frac{\pi}{43082}\text{ radians per second}[/tex]

Step-by-step explanation:

Given,

Time taken in one rotation of earth = 23 hours, 56 minutes and 4 seconds.

Since, 1 minute = 60 seconds and 1 hour = 3600 seconds,

⇒ Time taken in one rotation of earth = (23 × 3600 + 56 × 60 + 4) seconds

= 86164  seconds,

Now,  the number of radians in one rotation = 2π,

That is, 86164 seconds = 2π radians

[tex]\implies 1\text{ second }=\frac{2\pi}{86164}=\frac{\pi}{43082}\text{ radians}[/tex]

Hence, the number of radians in one second is [tex]\frac{\pi}{43082}[/tex]

The Earth completes a 2π radian rotation about its axis in 23 hours, 56 minutes, and 4 seconds. After converting this time to 86,164 seconds, the number of radians the Earth rotates in one second can be calculated by dividing 2π by 86,164, giving a result of approximately 0.00007292115 radians.

The Earth completes one full rotation about its axis in 23 hours, 56 minutes and 4 seconds. This rotation can be converted into radians, using the principle that one complete rotation is equivalent to 2π radians. So first, convert the rotation time into seconds: (23 x 60 x 60) + (56 x 60) + 4 = 86,164 seconds. Therefore, the Earth rotates through 2π radians in this time.

Now, we want to find out how many radians the Earth rotates in one second. To calculate this, divide 2π (which represent a full rotation in radians), by the total number of seconds in one rotation: 2π/86,164. This will give you approximately 0.00007292115 radians, which is the angular velocity or the number of radians the Earth rotates in one second.

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Answer:  We should dispense 60 tablets.

Step-by-step explanation:

Given : A patient is to receive 2 tablets po ACHS for 30 days.

i.e. Dose for each day = 2 tablets

Number of days = 30

If a patient takes 2 tablets each day , then the number of tablets he require for 30 days will be :-

[tex]2\times30=60[/tex]   [Multiply 2 and 30]

Therefore, the number of tablets we should dispense = 60

Answer:

2 500 000 rad.

Step-by-step explanation:

Mega is the metric prefix for [tex]10^{6}[/tex], therefore you just need to multiply by 1 000 000 to find the value in rads.

Answer:

θ = -33.69°

Step-by-step explanation:

For Φ>0 and Φ<0  (in general Φ≠nπ  where n is an integer), sin(Φ) ≠ 0

Dividing both equations:

[tex]\frac{sin(\phi) sin(\theta)}{sin(\phi)cos(\theta)} = tan(\theta) = 0.2/(-0.3)=-2/3\\[/tex]

Therefore:

arctan(θ) = -2/3

  θ = -33.69°

The answer does not depend on the sign of Φ, in fact we just need that the sine does not become zero, which occurs when Φ is equal to an integer times π (radians) or 180 (degrees)

Have a nice day!

To find theta (θ) given that sin phi (φ) sin theta (θ) = 0.2 and sin phi (φ) cos theta (θ) = -0.3 with sin phi (φ) being positive or negative, one must first eliminate sin phi (φ) by manipulating the given equations, then solve for theta (θ) using trigonometric identities and inverse functions based on the signs of sin and cos.

We have two equations involving sin φ and θ (theta): sin φ sin θ = 0.2 and sin φ cos θ = -0.3. Also, it is given that sin φ > 0 or sin φ < 0. To find θ, first, we need to derive an equation involving only θ by eliminating sin φ. We can do this by squaring and adding both equations.

∑: (sin φ sin θ)^2 + (sin φ cos θ)^2 = 0.2^2 + (-0.3)^2 = 0.04 + 0.09 = 0.13

Using the Pythagorean identity sin^2 θ + cos^2 θ = 1, we can rewrite ∑ as sin^2 φ = 0.13. To solve for θ, we can take either of the initial equations, say sin φ sin θ = 0.2, and substitute sin^2 φ from ∑ giving sin θ = (0.2 / √0.13) or cos θ = (-0.3 / √0.13). Both positive and negative values of sin φ lead to the calculation for different θ values. The actual values of θ are determined by using the arc functions (arcsin, arccos) for both positive and negative scenarios of sin φ, taking into account the range of θ based on the signs of sin and cos.

Answer:

1880 milliliter (mL) = 3.97 pints (pts)

Step-by-step explanation:

This problem can be solved as a rule of three problem.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.

Unit conversion problems, like this one, is an example of a direct relationship between measures.

1 milliliter (mL) is equal to 0.002 pints. How many pints are 1880 milliliter (mL)? We have the following rule of three

1 mL - 0.002 pints

1880 mL - x pints

x = 1880*0.002

x = 3.97 pints

There are 3.97 pints in 1880 milliliters.

Answer:

Cost function C(x) == FC + VC*Q

Revenue function R(x) = Px * Q

Profit function P(x) =(Px * Q)-(FC + VC*Q)

P(12000) = -38000 Loss

P(23000) = 28000 profit

Step-by-step explanation:

Total Cost is Fixed cost plus Variable cost multiplied by the produce quantity.  

(a)Cost function

C(x) = FC + vc*Q

Where  

FC=Fixed cost

VC=Variable cost

Q=produce quantity

(b)

Revenue function

R(x) = Px * Q

Where  

Px= Sales Price

Q=produce quantity

(c) Profit function

Profit = Revenue- Total cost

P(x) =(Px * Q)-(FC + vc*Q)

(d) We have to replace in the profit function

at 12,000 units

P(12000) =($20 * 12,000)-($110,000 + $14*12,000)

P(12000) = -38000

at 23,000 units

P(x) =($20 * 23,000)-($110,000 + $14*23,000)

P(23000) = 28000

Answer:

As consequence of the Taylor theorem with integral remainder we have that

[tex]f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \cdots + \frac{f^{(n)}(a)}{n!}(x-a)^n + \int^a_x f^{(n+1)}(t)\frac{(x-t)^n}{n!}dt[/tex]

If we ask that [tex]f[/tex] has continuous [tex](n+1)[/tex]th derivative we can apply the mean value theorem for integrals. Then, there exists [tex]c[/tex] between [tex]a[/tex] and [tex]x[/tex] such that

[tex] \int^a_x f^{(n+1)}(t)\frac{(x-t)^k}{n!}dt = \frac{f^{(n+1)}(c)}{n!} \int^a_x (x-t)^n d t = \frac{f^{(n+1)}(c)}{n!} \frac{(x-t)^{n+1}}{n+1}\Big|_a^x[/tex]

Hence,

[tex] \int^a_x f^{(n+1)}(t)\frac{(x-t)^k}{n!}d t = \frac{f^{(n+1)}(c)}{n!} \frac{(x-t)^{(n+1)}}{n+1} = \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1} .[/tex]

Thus,

[tex] \int^a_x f^{(n+1)}(t)\frac{(x-t)^k}{n!}d t = \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1} [/tex]

and the Taylor theorem with Lagrange remainder is

[tex] f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \cdots + \frac{f^{(n)}(a)}{n!}(x-a)^n + \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1}[/tex].

Step-by-step explanation:

Step-by-step explanation:

Consider the provided information.

If Fury is the director of SHIELD then Hill and Coulson are SHIELD agents"

For the condition statement [tex]p \rightarrow q[/tex] or equivalent "If p then q"

Part (A) Write the contrapositive.

Here p is Fury is the director of SHIELD, and q is Hill and Coulson are SHIELD agents.

Contrapositive: If Hill and Coulson are not SHIELD agents, then Fury is not the director of SHIELD.

Part (b) Write the converse.

Here p is Fury is the director of SHIELD, and q is Hill and Coulson are SHIELD agents.

Converse: If Hill and Coulson are SHIELD agents, then Fury is the director of SHIELD.

Part (c) Write the inverse.

Here p is Fury is the director of SHIELD, and q is Hill and Coulson are SHIELD agents.

Inverse: If Fury is not the director of SHIELD then Hill and Coulson are not SHIELD agents

Part (D) Write the negation.

Here p is Fury is the director of SHIELD, and q is Hill and Coulson are SHIELD agents.

Negation: Fury is the director of SHIELD and Hill and Coulson are not SHIELD agents"

Step-by-step explanation:

Consider the provided information.

If Fury is the director of SHIELD then Hill and Coulson are SHIELD agents." For the condition statement  or equivalent "If p then q"

The rule for Converse is: Interchange the two statements.

The rule for Inverse is: Negative both statements.

The rule for Contrapositive is: Negative both statements and interchange them.

The rule for Negation is: If p then q" the negation will be: p and not q.

- Part (A) Write the contrapositive.

.Here p is Fury is the director of SHIELD, and q is Hill and Coulson are SHIELD agents.

Contrapositive: If Hill and Coulson are not SHIELD agents, then Fury is not the director of SHIELD.

- Part (b) Write the converse.

 .Here p is Fury is the director of SHIELD, and q is Hill and Coulson are SHIELD agents.

 .Converse: If Hill and Coulson are SHIELD agents, then Fury is the director of SHIELD.

- Part (c) Write the inverse.

 .Here p is Fury is the director of SHIELD, and q is Hill and Coulson are SHIELD agents.

 .Inverse: If Fury is not the director of SHIELD then Hill and Coulson are not SHIELD agents

- Part (D) Write the negation.

 .Here p is Fury is the director of SHIELD, and q is Hill and Coulson are SHIELD agents.

 .Negation: Fury is the director of SHIELD and Hill and Coulson are not SHIELD agents"

Answer:

The age of this sample is 13,417 years.

Step-by-step explanation:

The amount of carbon 14 present in a sample after t years is given by the following equation:

[tex]C(t) = C_{0}e^{-0.00012t}[/tex]

Estimate the age of a sample of wood discoverd by a arecheologist if the carbon level in the sampleis only 20% of it orginal carbon 14 level.

The problem asks us to find the value of t when

[tex]C(t) = 0.2C_{0}[/tex]

So:

[tex]C(t) = C_{0}e^{-0.00012t}[/tex]

[tex]0.2C_{0} = C_{0}e^{-0.00012t}[/tex]

[tex]e^{-0.00012t} = \frac{0.2C_{0}}{C_{0}}[/tex]

[tex]e^{-0.00012t} = 0.2[/tex]

[tex]ln e^{-0.00012t} = ln 0.2[/tex]

[tex]-0.00012t = -1.61[/tex]

[tex]0.00012t = 1.61[/tex]

[tex]t = \frac{1.61}{0.00012}[/tex]

[tex]t = 13,416.7[/tex]

The age of this sample is 13,417 years.

Answer: Our required probability is 0.406.

Step-by-step explanation:

Since we have given that

Probability of selecting an adult over 40 years of age with cancer = 0.05

Probability of a doctor correctly diagnosing a person with cancer as having the disease = 0.78

Probability of incorrectly diagnosing a person without cancer as having the disease = 0.06

Let A be the given event i.e. adult over 40 years of age with cancer. P(A) = 0.05.

So, P(A')=1-0.05 = 0.95

Let C be the event that having cancer.

P(C|A)=0.78

P(C|A')=0.06

So, using the Bayes theorem, we get that

[tex]P(A|C)=\dfrac{P(A).P(C|A)}{P(A).P(C|A)+P(A')P(C|A')}\\\\P(A|C)=\dfrac{0.78\times 0.05}{0.78\times 0.05+0.06\times 0.95}\\\\P(A|C)=0.406[/tex]

Hence, our required probability is 0.406.

There are 11,238,513 ways Powerball tickets can be purchased.

There are 292, 201, 338 ways to win Powerball tickets.

Given

Number of white balls = 69

Number of white balls drawn = 5

Number of red balls = 26

Number of red balls drawn = 1

The combination is the way to select the number of objects from a group.

The formula is used to select the number of the object is;

[tex]\rm = \ ^nC_r \\\\\rm = \dfrac{n!}{(n-r)!r!}[/tex]

Where n is the total number of objects and r is the number of selected objects.

1. How many possible different Powerball tickets can be purchased?

The number of ways Powerball tickets can be purchased is;

[tex]\rm = \ ^{69}C_5\\\\= \dfrac{69!}{(69-5)!. 5!}\\\\= \dfrac{69!}{64!.5!}\\\\= 11238513[/tex]

There are 11,238,513 ways Powerball tickets can be purchased.

2.  How many possible different winning Powerball tickets are there?

A number of ways to win Powerball tickets are there is;

[tex]\rm = \ ^{69}C_5 \times ^{26}C_1\\\\= \dfrac{69!}{(69-5)!. 5!} \times \dfrac{26!}{(26-1)!\times 1!}\\\\= \dfrac{69!}{64!.5!} \times \dfrac{26!}{25!.1!}\\\\= 11238513 \times 26\\\\= 292, 201, 338 ways[/tex]

There are 292, 201, 338 ways to win Powerball tickets.

To know more about Combination click the link given below.

https://brainly.com/question/25351212

The total number of possible different Powerball tickets is 292,201,338, calculated by multiplying 11,238,513 combinations of white balls with the 26 possible red balls. There is only one winning combination for the Powerball jackpot, so there is only one possible winning Powerball ticket.

To calculate the total number of possible different Powerball tickets, we must consider the combination of white balls and the selection of the red Powerball. There are 5 white balls drawn from a set of 69, and this is a combination because the order does not matter. Therefore, the number of combinations of white balls is calculated using the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of balls to choose from and k is the number of balls chosen. So, the calculation is C(69, 5) = 69! / (5!(69-5)!) = 11,238,513 combinations of white balls.

For the red Powerball, there is 1 ball drawn from a set of 26, and since there is only one ball, there are 26 possible outcomes. To find the total number of possible Powerball tickets, multiply the number of white ball combinations by the number of possible red balls: 11,238,513 × 26 = 292,201,338 possible Powerball tickets.

For part b, considering that there is only one winning combination, there is just one possible winning Powerball ticket.

Answer:

Step-by-step explanation:

Estimated because there is no number that can go into 5 and 8 evenly

Answer:

i think the answer is 1,000

Step-by-step explanation:

Before the piper increased his volume, there were approximately 2530 rats. The final total (6578 rats), represents a 160 percent increase over this original amount.

The question is asking about the original number of rats before a 160 percent increase. In this scenario, you must remember that 6578 rats is equal to the original number of rats plus an extra 160 percent of the original number. Hence, 6578 rats signifies 260% of the original quantity of rats because inherently 100% represents the original quantity. To find the original number of rats, we'd divide the final quantity by 2.6. So, the original number of rats would be calculated by: 6578 ÷ 2.6 = 2530 rats approximately. Therefore, before the piper increased his volume, there were approximately 2530 rats.

https://brainly.com/question/5449967

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Answer:

P(A)=1/7

P(B)=1/2

P(C)=1/42

P(A|C)=1/10

P(B|C)=1/10

P(A|B)=1/7

A and B are independent

A and C aren't independent

B and C aren't independent

Step-by-step explanation:

A="b falls in the middle"

- b can fall in seven possible places, but only one is the middle. So, P(A)=1/7

B="c falls to the right of b"

X=i means "b falls in the i-th position"

Y=j means "c falls in the j-th position"

if b falls in the first place, c can fall in the 2nd, 3rd, 4th, 5th, 6th or 7th place.

if b falls in the 2nd place, c can fall in the 3rd, 4th, 5th, 6th or 7th place

 ...

If b falls in the 6th place, c can fall in the 7th place

then:

[tex][tex]P(B)=\displaystyle\sum_{i=1}^{6}( P(X=i)\displaystyle\sum_{j=i+1}^{7} P(Y=j))=\displaystyle\sum_{i=1}^{6}( \frac{1}{7}\displaystyle\sum_{j=i+1}^{7} \frac{1}{6})=\frac{1}{42}\displaystyle\sum_{i=1}^{6}(\displaystyle\sum_{j=i+1}^{7}1)=\frac{6+5+4+3+2+1}{42}=\frac{1}{2}[/tex][/tex]

- if d falls in the 1st place, e falls in the 2nd and f in the 3rd place

- if d falls in the 2nd place, e falls in the 3rd and f in the 4th place

- if d falls in the 3rd place, e falls in the 4th and f in the 5th place

- if d falls in the 4th place, e falls in the 5th and f in the 6th place

- if d falls in the 5th place, e falls in the 6th and f in the 7th place

X=i means "d falls in the i-th position"

Y=j means "e falls in the j-th position"

Z=k means "f falls in the k-th position"

[tex]P(C)=\displaystyle\sum_{i=1}^{5}( P(X=i)P(Y=i+1)P(Z=i+2))=\displaystyle\sum_{i=1}^{5}(\frac{1}{7}\times\frac{1}{6}\times\frac{1}{5})=\frac{1}{210}\displaystyle\sum_{i=1}^{5}(1)=\frac{1}{42}[/tex]

P(A|C)=P(A∩C)/P(C)=?

A∩C:

- d falls in the 1st place, e in the 2nd, f in the 3rd and b in the 4th place

- b falls in the 4th place, d in the 5th place, e in the 6th, f in the 7th place

P(A∩C)=2*(1/7*1/6*1/5*1/4)=1/420

P(A|C)=(1/420)/(1/42)=1/10

P(B|C)=P(B∩C)/P(C)=?

X=i means "d falls in the i-th position"

Y=j means "e falls in the j-th position"

Z=k means "f falls in the k-th position"

V=k means "b falls in the k-th position"

W=k means "c falls in the k-th position"

[tex]P(B\cap C)=\displaystyle\sum_{i=1}^{3} P(X=i)P(Y=i+1)P(Z=i+2)\displaystyle\sum_{j=i+3}^{6}P(V=j)P(W=j+1)[/tex]

[tex]P(B\cap C)=\displaystyle\sum_{i=1}^{3} \frac{1}{7}\times\frac{1}{6}\times\frac{1}{5}(\displaystyle\sum_{j=i+3}^{6}\frac{1}{4}\times\frac{1}{3})=\frac{1}{2520}\displaystyle\sum_{i=1}^{3} \displaystyle\sum_{j=i+3}^{6}1=\frac{1}{420}[/tex]

P(B|C)=(1/420)/(1/42)=1/10

P(A|B)=P(B∩A)/P(B)=?

B∩A:

- b falls in the 4th place and c in the 5th

- b falls in the 4th place and c in the 6th

- b falls in the 4th place and c in the 7th

P(B∩A)=3*(1/7*1/6)=1/14

P(A|B)=(1/14)(1/2)=1/7

If one event is independent of another, P(X∩Y)=P(X)P(Y)

So:

P(A∩B)=1/14=(1/7)*(1/2)=P(A)P(B), A and B are independent

P(A∩C)=1/420≠(1/7)*(1/42)=1/294=P(A)P(C), A and C aren't independent

P(B∩C)=1/420≠(1/2)*(1/42)=1/84=P(A)P(C), B and C aren't independent

Step-by-step explanation:

When we need to subtract a number from another number, in that case, we can take the complement of the first number to add it to the second number, the result will be the same. It is because when we take the complement of 9 of that number, it will represent the negative of that number. Hence, by adding the negative of a number we will get the same result as we get after subtraction.

For example:

Subtract 213 from 843

843 - 213 = 630

complement of 9 of 213= 999-213

                                       =786

Now, add 786 and 843

786+843=1629

We got the result in 4 digits so by adding the left-most digit to the right-sided three-digit number of the result, we will get

629+1 = 630

Answer: 433

Step-by-step explanation:

The given sequence : 19​,42​,65​,88​,...

Here we can see that the difference in each of the two consecutive terms is 23.  [88-65=23, 65-42=23, 42-19=23]

i.e. it has a common difference of 23.

Therefore, it is an arithmetic sequence .

In an arithmetic​ sequence, the nth term an is given by the formula[tex]A_n=a_1+(n-1)d[/tex] , where [tex]a_1[/tex] is the first term and d is the common difference.​

For the given sequence , [tex]a_1=19[/tex]  and [tex]d=23[/tex]

Then,  to find the 19th term of  the sequence, we put n= 19 in the above formula:-

[tex]A_{19}=19+(19-1)(23)=19+(18)(23)=19+414+433[/tex]

Hence, the 19th term of  the sequence = 433

Final answer:

To find the 19th term of the arithmetic sequence 19, 42, 65, 88, ..., the common difference (23) is determined from the sequence and applied in the arithmetic sequence formula. Substituting the values into the formula, the 19th term is calculated to be 433.

Explanation:

To find the 19th term, we must first determine the common difference, d, of the sequence. Observing the given sequence, we see that the difference between consecutive terms is 42 - 19 = 23. Therefore, the common difference is 23.

Next, we apply the formula for the nth term of an arithmetic sequence which is An = a1 + (n-1)d. Here, a1 is the first term, n is the term number, and d is the common difference.

Substituting the values for the 19th term, we have: A19 = 19 + (19-1) × 23 = 19 + 18 × 23 = 19 + 414 = 433. Therefore, the 19th term of the sequence is 433.