"Solve the problem of exponential growth. According to the U.S. Census Bureau, the population of the United States in 2010 was 308 million. This is a 9.6% increase over the 2000 count. Assuming this continued what would the population be in 2030?"

Answers

Answer 1

Answer:

370 million

Step-by-step explanation:

In the 10 years from 2000 to 2010, the population was multiplied by the factor ...

100% + 9.6% = 109.6% = 1.096

In the next 20 years from 2010 to 2030, the population will be multiplied by that factor twice, if it grows at the same rate:

2030 population = (308 million)·(1.096²) ≈ 370 million

Answer 2

Answer:

370 million

Step-by-step explanation:

In the 10 years from 2000 to 2010, the population was multiplied by the factor ...

100% + 9.6% = 109.6% = 1.096

In the next 20 years from 2010 to 2030, the population will be multiplied by that factor twice, if it grows at the same rate:

2030 population = (308 million)·(1.096²) ≈ 370 million


Related Questions

what is the sum of the fractions​

Answers

Answer:

[tex]6\frac{7}{9}[/tex]

Step-by-step explanation:

[tex]6\frac{2}{3}+\frac{1}{9} = 6\frac{6}{9}+\frac{1}{9}=6 \frac{7}{9}[/tex]

Answer:

Step-by-step explanation:

its D

(a) What is a sequence? A sequence is an unordered list of numbers. A sequence is the sum of an ordered list of numbers. A sequence is an ordered list of numbers. A sequence is the sum of an unordered list of numbers. A sequence is the product of an ordered list of numbers. (b) What does it mean to say that lim n → ∞ an = 8? The terms an approach 8 as n becomes large. The terms an approach 8 as n becomes small. The terms an approach infinity as n become large. The terms an approach -infinity as 8 approaches n. The terms an approach infinity as 8 approaches n. (c) What does it mean to say that lim n → ∞ an = ∞? The terms an become large as n becomes large. The terms an become large as n becomes small. The terms an approach zero as n becomes large. The terms an become small as n becomes small. The terms an become small as n becomes large.

Answers

Step-by-step explanation:

A sequence is an ordered list of numbers.

lim n → ∞ an = 8 means that as n approaches infinity (becomes large), an approaches 8.

lim n → ∞ an = ∞ means that as n approaches infinity (becomes large), an approaches infinity (becomes large).

Final answer:

A sequence is an ordered list of numbers, and when lim n → ∞ an = 8, it means the sequence's terms approach 8 as n becomes large. Saying lim n → ∞ an = ∞ indicates that the sequence's terms grow without bound as n increases.

Explanation:

Answering your questions on sequences and limits:

(a) What is a sequence?

A sequence is an ordered list of numbers. Unlike a set where the order of elements does not matter, in a sequence, every number has a distinct place. For instance, the sequence of natural numbers is an ordered list starting from 1 and proceeding indefinitely in the order 1, 2, 3, 4, ... etc.

(b) What does it mean to say that lim n → ∞ an = 8?

This statement means that the terms an approach 8 as n becomes large. In other words, as you progress further along in the sequence, the values of the terms get closer and closer to 8, virtually reaching 8 as the sequence goes towards infinity. This is a fundamental concept in understanding sequences' behavior at their extremities.

(c) What does it mean to say that lim n → ∞ an = ∞?

This implies that the terms an become large as n becomes large. As the n value increases, the sequence's terms grow unlimitedly, indicating the sequence's divergence rather than converging to a definite number.

Please help last question

Answers

Answer:

The total is 8.

And the total of not green is 6

so the probability is 6/8 or you can write as

3/4

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Charles factors the expression 4/3xy+1/3x using a factor of 1/3x. He writes the factored expression 1/3x(4y+1). Which best describes the accuracy of Charles solution?

A. His solution is accurate

B. His solution is inaccurate. The factor does not divide evenly into both terms.

C. His solution is inaccurate. The factoring of 4/3xy using the given GCF is incorrect.

D. His solution is inaccurate. The factoring of 1/3x using the given GCF is incorrect.

Answers

A. His solution is accurate

You can verify this by expanding his factored expression: 1/3x(4y+1), which gives you back the original expression 4/3xy+1/3x

Charles' solution is accurate because expression after factorization  is similar to Charles factor's of expression option (A) is correct.

What is an expression?

It is defined as the combination of constants and variables with mathematical operators.

We have an expression:

[tex]\rm = \dfrac{4}{3}xy+\dfrac{1}{3}x[/tex]

Taking common as (1/3)x

[tex]\rm = \dfrac{1}{3}x(4y+1)[/tex]

The above expression is similar to Charles factor's of expression.

Thus, Charles solution is accurate because expression after factorization  is similar to Charles factor's of expression option (A) is correct.

Learn more about the expression here:

brainly.com/question/14083225


#SPJ2

Given: MNOK is a trapezoid, MN=OK, m∠M=60°, NK⊥MN, MK=16cm
Find: The midsegment of MNOK

Answers

Answer:

  the length of the midsegment is 12 cm

Step-by-step explanation:

ΔMNK is a 30°-60°-90° triangle, so side MK is twice the length of side MN. That makes MN = (16 cm)/2 = 8 cm.

Dropping an altitude from N to intersect MK at X, we have ΔMXN is also a 30°-60°-90° triangle with side MN twice the length of side MX. That makes MX = (8 cm)/2 = 4 cm.

The length of the midsegment of this isosceles trapezoid is the same as the length XK, so is (16 -4) cm = 12 cm.

Answer:

12 cm.

Step-by-step explanation:

1. Consider right triangle MNK. In this triangle, angle N is right and m∠M=60°, then m∠K=30°. Thus, this triangle is a special 30°-60°-90° right triangle with legs MN and NK and hypotenuse MK=16 cm. The leg MN is opposite to the angle with a measure of 30°. This means that this leg is half of the hypotenuse, MN=8 cm.

2. Consider right triangle MNH, where NH is the height of trapezoid drawn from the point N. In this triangle m∠M=60°, angle H is right, then m∠N=30°. Similarly, the leg MH is half of the hypotenuse MN, MH=4 cm.

3. Trapezoid MNOK is isosceles because of MN=OK=8 cm. This means that NO=MK-2MH=16-8=8 cm.

4. The midsegment of the trapezoid is:

[tex]\frac{MK+NO}{2}=\frac{16+8}{2}=12cm[/tex]

rx+2x=4r+3
Solving for X

Answers

Answer:

  x = (4r +3)/(r +2)

Step-by-step explanation:

Collect x terms, then divide by the coefficient of x.

  x(r +2) = 4r +3

  x = (4r +3)/(r +2)

sin C =

Whats the answer ?!?

Answers

The answer would b "C" 15/17 because Sin is Opposite over Hypotenuse

Step-by-step explanation:

The measure of the sin∠C is 15/17 because sin is the ratio of side opposite to the angle to hypotenuse option third is correct.

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

We have a right angle triangle with dimensions shown in the picture:

From the sin ratio in the right angle triangle:

sin∠C = 15/17

Thus, the measure of the sin∠C is 15/17 because sin is the ratio of side opposite to the angle to hypotenuse.

Learn more about the right angle triangle here:

brainly.com/question/3770177

#SPJ2

please help

must show work

number 6
and
number8​

Answers

Answer:

6 is -3        

8 is -5

Step-by-step explanation:

This problem has been solved!See the answerVerify that the line intergral and the surface integral of Stokes Theorem are equal for the following vector field, surface S and closed curve C. Assume that C has counterclockwise orientation and S has a consistent orientation.F= < x,y,z>; S is the paraboloid z = 13 - x^2 - y^2, for 0 less than or equal z less than or equal 13 and C is the circle x^2 + y^2 = 13 in the xy plane.

Answers

Line integral: Parameterize [tex]C[/tex] by

[tex]\vec r(t)=\langle\sqrt{13}\cos t,\sqrt{13}\sin t,0\rangle[/tex]

with [tex]0\le t\le2\pi[/tex]. Then

[tex]\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\int_0^{2\pi}\langle\sqrt{13}\cos t,\sqrt{13}\sin t,0\rangle\cdot\langle-\sqrt{13}\sin t,\sqrt{13}\cos t,0\rangle\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^{2\pi}0\,\mathrm dt=\boxed 0[/tex]

Surface integral: By Stokes' theorem, the line integral of [tex]\vec F[/tex] over [tex]C[/tex] is equivalent to the surface integral of the curl of [tex]\vec F[/tex] over [tex]S[/tex]:

[tex]\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S[/tex]

The curl of [tex]\langle x,y,z\rangle[/tex] is 0, so the value of the surface integral is 0, as expected.

Angle θ is in standard position. If (8, -15) is on the terminal ray of angle θ, find the values of the trigonometric functions.

Answers

ANSWER

[tex]\sin( \theta) = - \frac{15}{17} [/tex]

[tex]\csc( \theta) = - \frac{17}{15} [/tex]

[tex]\cos( \theta) = \frac{8}{17} [/tex]

[tex]\sec( \theta) = \frac{17}{8} [/tex]

[tex]\tan( \theta) = - \frac{15}{8} [/tex]

[tex]\cot( \theta) = - \frac{8}{15} [/tex]

EXPLANATION

From the Pythagoras Theorem, the hypotenuse can be found.

[tex] {h}^{2} = 1 {5}^{2} + {8}^{2} [/tex]

[tex] {h}^{2} = 289[/tex]

[tex]h = \sqrt{289} [/tex]

[tex]h = 17[/tex]

The sine ratio is negative in the fourth quadrant.

[tex] \sin( \theta) = - \frac{opposite}{hypotenuse} [/tex]

[tex]\sin( \theta) = - \frac{15}{17} [/tex]

The cosecant ratio is the reciprocal of the sine ratio.

[tex]\csc( \theta) = - \frac{17}{15} [/tex]

The cosine ratio is positive in the fourth quadrant.

[tex]\cos( \theta) = \frac{adjacent}{hypotenuse} [/tex]

[tex]\cos( \theta) = \frac{8}{17} [/tex]

The secant ratio is the reciprocal of the cosine ratio.

[tex]\sec( \theta) = \frac{17}{8} [/tex]

The tangent ratio is negative in the fourth quadrant.

[tex]\tan( \theta) = - \frac{opposite}{adjacent} [/tex]

[tex]\tan( \theta) = - \frac{15}{8} [/tex]

The reciprocal of the tangent ratio is the cotangent ratio

[tex]\cot( \theta) = - \frac{8}{15} [/tex]

Answer:

sin=-15/17

cos=8/7

tan=-15/8

csc=-17/15

sec=17/8

cot=-8/15

A cylindrical container has a radius of 0.2 meter and a height of 1 meter. The container is filled with honey. The density of honey is 1417 kg/m³. What is the mass of the honey in the container? Enter your answer in the box. Use 3.14 for π . Round your final answer to the nearest whole number.

Answers

Answer:178

Step-by-step explanation: I took the test :)

Answer:

The mass of the container is 178 kg.

Step-by-step explanation:

Since, the volume of a cylinder is,

[tex]V=\pi (r)^2 h[/tex]

Where r is the radius of the cylinder

And, h is its height

Here, r = 0.2 meters,

h = 1 meter,

So, the volume of the cylindrical container is,

[tex]V=\pi (0.2)^2(1)[/tex]

[tex]=3.14\times 0.04=0.1256\text{ cubic meters}[/tex]

Now,

[tex]Density = \frac{Mass}{Volume}[/tex]

[tex]\implies Mass = Density\times Volume[/tex]

Given, Density of the container = 1417 kg/m³,

By substituting the values in the above formula,

[tex]\text{Mass of the container}=1417\times 0.1256=177.9752\text{ kg}\approx 178\text{ kg}[/tex]

what is the solution in this equation -8x+4=36

Answers

Answer:

X=-4

Step-by-step explanation:

Answer:

x = -4

Step-by-step explanation:

-8x+4=36

          -4

-8x     =32

/-8       /-8

  x      = -4

Miriam reduced a square photo by cutting 3 inches away from the length and the width so it will fit in her photo album. The area of the reduced photo is 64 square inches. In the equation (x – 3)2 = 64, x represents the side measure of the original photo.

What were the dimensions of the original photo?

11 inches by 11 inches
5 inches by 5 inches
3 + inches by 3 + inches
3 inches by 3 inches

Answers

Answer:

11 inches by 11 inches

Step-by-step explanation:

The dimensions of the original photo were 11 inches by 11 inches.

We are informed that the area of the reduced photo is 64 square inches and that In the equation (x – 3)^2 = 64, x represents the side measure of the original photo.

In order to solve for x, we shall first take square roots on both sides of the equation;

The square root of (x – 3)^2 is simply (x - 3).

The square root of 64 is ±8 but we ignore -8 since the dimensions of any figure must be positive.

Therefore, we have the following equation;

x - 3 = 8

x = 8 + 3

x = 11

Answer:

Option 1: 11 inches by 11 inches

Step-by-step explanation:

Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) ? 0.]f(x) = 10/x , a= -2f(x) = \sum_{n=0}^{\infty } ______Find the associated radius of convergence R.R = ______

Answers

Rewrite [tex]f[/tex] as

[tex]f(x)=\dfrac{10}x=-\dfrac5{1-\frac{x+2}2}[/tex]

and recall that for [tex]|x|<1[/tex], we have

[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]

so that for [tex]\left|\dfrac{x+2}2\right|<1[/tex], or [tex]|x+2|<2[/tex],

[tex]f(x)=-5\displaystyle\sum_{n=0}^\infty\left(\frac{x+2}2\right)^n[/tex]

Then the radius of convergence is 2.

Final answer:

The Taylor series for the function f(x) = 10/x, centered at a = -2, is given by the formula  ∑(10(-1)^n*n!(x + 2)^n)/n! from n=0 to ∞. The radius of convergence (R) for the series is ∞, which means the series converges for all real numbers x.

Explanation:

Given the function f(x) = 10/x, we're asked to find the Taylor series centered at a = -2. A Taylor series of a function is a series representation which can be found using the formula f(a) + f'(a)(x-a)/1! + f''(a)(x-a)^2/2! + .... For f(x) = 10/x, the Taylor series centered at a = -2 will be ∑(10(-1)^n*n!(x + 2)^n)/n! from n=0 to ∞. The radius of convergence R is determined by the limit as n approaches infinity of the absolute value of the ratio of the nth term and the (n+1)th term. This results in R = ∞, indicating the series converges for all real numbers x.

Learn more about Taylor series here:

https://brainly.com/question/36772829

#SPJ3

A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t)=72t-16t^2. What is the maximum height that the ball will reach?
Do not round your answer

Answers

Answer:

The maximum height that the ball will reach is 81 ft

Step-by-step explanation:

Note that the tray of the ball is given by the equation of a parabola of negative main coefficient. Then, the maximum value for a parabola is at its vertex.

For an equation of the form

[tex]at ^ 2 + bt + c[/tex]

So

the t coordinate of the vertice is:

[tex]t =-\frac{b}{2a}[/tex]

In this case the equation is:

[tex]h(t)=72t-16t^2[/tex]

So

[tex]a=-16\\b=72\\c=0[/tex]

Therefore

[tex]t =-\frac{72}{2(-16)}[/tex]

[tex]t=2.25\ s[/tex]

Finally the maximum height that the ball will reach is

[tex]h(2.25)=72(2.25)-16(2.25)^2[/tex]

[tex]h=81\ ft[/tex]

Final answer:

The ball thrown vertically upwards will reach the maximum height of 81 feet after 2.25 seconds.

Explanation:

To find the maximum height the ball will reach, first, we need to recognize that the equation 'h(t)=72t-16t^2' is a quadratic function in the form of 'f(t)=at^2+bt+c'. The maximum point of a quadratic function, also known as the vertex, happens at 't=-b/2a'. In this case, 'a' is -16 and 'b' is 72.

So the maximum height is achieved at 't=-72/(2*-16)' or 't=72/32 = 2.25' seconds.

To find out the maximum height, we just need to substitute this value of t into the equation for h(t):

h(2.25)=72*2.25-16*2.25^2

The above calculation gives a maximum height of 81 feet.

Learn more about Maximum height here:

https://brainly.com/question/29081143

#SPJ3

This Venn diagram shows sports played by 10 students

Let event A - The student plays basketball.
Let event B - The student plays soccer.
What is P(AB)?

Answers

Answer:

B. 1/10 or 0.10

Step-by-step explanation:

The question asks what's the probability that a student picked randomly will be playing both basketball and soccer.

The answer is right in the diagram.

We have only one student who plays both basketball and soccer: Ella

Since we have 10 students in the selected group, the probably you'll pick Ella is:

1 / 10 = 0.10 = 10%

So, the answer is B.

The value of P(A/B) is 0.33.

Given that, the Venn diagram shows sports played by 10 students.

What is P(A/B)?

P(A/B) is known as conditional probability and it means the probability of event A that depends on another event B. It is also known as "the probability of A given B". The formula for P(A/B)=P(A∩B) / P(B).

Now, P(A/B)=1/3≈0.33

Therefore, the value of P(A/B) is 0.33.

To learn more about the Venn diagram visit:

https://brainly.com/question/1605100.

#SPJ5

Jake is eating dinner at a restaurant. The cost of his meal, including sales tax, is m dollars. After leaving an 18% tip, the amount Jake pays at the restaurant is represented by the following expression. In this expression, what does the term 0.18m represent?

Answers

For this case we have that variable "m" represents the cost of Jake's food. They tell us that he left an 18% tip. That is to say:

m -------------> 100%

tip ------------> 18%

Where "tip" is the cost of the tip based on the cost of the meal.

[tex]tip = \frac {18 * m} {100}\\tip = 0.18m[/tex]

The amount Jake pays is represented by:

[tex]m + 0.18m[/tex]

Where 0.18m is the tip

ANswer:

Tip

Answer:

the tip amount jake pays

Step-by-step explanation:

What transformation has changed the parent function f(x) = log3x to its new appearance shown in the graph below?

logarithmic graph passing through point 1, negative 2.

f(x − 2)
f(x + 2)
f(x) − 2
f(x) + 2

Answers

Answer: Third option

[tex]f(x) - 2[/tex]

Step-by-step explanation:

The function [tex]y=log_3 (x)[/tex] passes through the point (1,0) since the function [tex]y=log_a (x)[/tex] always cuts the x-axis at [tex]x = 1[/tex].

Then, if the transformed function passes through point (1,-2) then this means that the graph of [tex]y=log_3(x)[/tex] was moved vertically 2 units down.

The transformation that displaces the graphically of a function k units downwards is:

[tex]y = f (x) + k[/tex]

Where k is a negative number. In this case [tex]k = -2[/tex]

Then the transformation is:

[tex]f(x) -2[/tex]

and the transformed function is:

[tex]y = log_3 (x) -2[/tex]

f(x)=e^2x-4
Determine inverse of given function

Answers

Answer:

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

Step-by-step explanation:

Start by changing the f(x) into a y.  Then switch the x and the y.  Then solve for the new y.  Like this:

[tex]y=e^{2x-4}[/tex] becomes

[tex]x=e^{2y-4}[/tex]

To solve for the new y, we need to get it out of its current exponential position which requires us to take the natural log of both sides.  Since a natural log has a base of e, natural logs and e's "undo" each other, just like taking the square root of a squared number.  

[tex]ln(x)=ln(e)^{2y-4}[/tex]

When the ln and the e cancel out we are left with

ln(x) = 2y - 4.  Add 4 to both sides to get

ln(x) + 4 = 2y.  Divide both sides by 2 to get

[tex]\frac{1}{2}ln(x) + 4 = y[/tex].

Since that is the inverse of y, we can change the y into inverse function notation:

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

Final answer:

To find the inverse function of f(x) = e²ˣ - 4, you switch x and y, solve for the new y, and arrive at the inverse function f^-1(x) = (1/2) * ln(x + 4).

Explanation:

To find the inverse function of f(x) = e²ˣ - 4, we first need to switch the roles of x and f(x), and then solve for the new x. Here are the steps:

Replace f(x) with y to get y = e²ˣ - 4.Switch x and y to get x = [tex]e^{(2y)} - 4[/tex].Add 4 to both sides to isolate the exponential on one side: x + 4 = [tex]e^{(2y)[/tex].Take the natural logarithm of both sides to get ln(x + 4) = 2y.Divide both sides by 2 to solve for y: y = (1/2) * ln(x + 4).

So, the inverse function of f(x) = e²ˣ - 4 is f-1(x) = (1/2) * ln(x + 4).

3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi. The Radius is 7 inches and the Height is 12.

Answers

The formula for volume of a cone is V = PI x r^2 x h/3 where r is the radius and h is the height.

Volume of cone = 3.14 x 7^2 x 12/3

Volume of cone = 3.14 x 49 x 4

Volume of cone = 615.44 cubic inches.

The formula for volume of half a sphere is : 1/2 x (4/3 x PI x r^3)

Volume for half sphere = 1/2 x (4/3 x 3.14 x 7^3)

= 1/2 x 4/3 x 3.14 x 343

= 718.01 cubic inches.

Total volume = 615.44 + 718.01 = 1333.45 cubic inches.

Rounded to the nearest tenth = 1,333.5 cubic inches.

Given the function f(x)= -5+4x^2 calculate the following value:
f(a+h)
Please help ASAP!!! :(

Answers

Evaluating a function in a specific point means to substitute all occurrences of x with the specific value.

In your case, we have to substitute "x" with "a+h":

[tex]f(x)= -5+4x^2 \implies f(a+h) = -5+4(a+h)^2\\ = -5+4(a^2+2ah+h^2)=-5+4a^2+8ah+h^2[/tex]

Please respond quickly!!

Answers

Answer:

Area of triangle = 6 in^2

Step-by-step explanation:

We need to find the area of triangle. The formula used is:

Area of triangle = 1/2 * b*h

where b=base and h= height

In the given question, b =2 and h= 6

Putting values in the formula:

Area of triangle = 1/2 *2*6

                          = 12/2

                          =  6 in^2

Answer:

The area is 6 in^2

Step-by-step explanation:

Please help ASAP and help me find what the value of x is

Answers

Answer:

x=44

Step-by-step explanation:

33+103+x=180

136+x=180

x=44

The sum of all the angles of a triangle is 180 degrees.  

Add all the angles together and set it equal to 180, then solve for x

33 + 103 + x = 180

(136 - 136) + x = 180 - 136

x = 44

Hope this helped!

Show that if X ∼ Geom(p) then P(X = n + k|X > n) = P(X = k), for every n, k ≥ 1. This one of the ways to define the memoryless property of the geometric distribution. It states the following: given that there are no successes in the first n trials, the probability that the first success comes at trial n + k is the same as the probability that a freshly started sequence of trials yields the first success at trial k.

Answers

Since [tex]X\sim\mathrm{Geom}(p)[/tex], [tex]X[/tex] has PMF

[tex]P(X=x)=\begin{cases}(1-p)^{x-1}p&\text{for }x\in\{1,2,3,\ldots\}\\0&\text{otherwise}\end{cases}[/tex]

By definition of conditional probability,

[tex]P(X=n+k\mid X>n)=\dfrac{P(X=n+k\text{ and }X>n)}{P(X>n)}[/tex]

[tex]X[/tex] has CDF

[tex]P(X\le x)=\begin{cases}0&\text{for }x<1\\1-(1-p)^x&\text{for }x\ge1\end{cases}[/tex]

which is useful for immediately computing the probability in the denominator:

[tex]P(X>n)=1-P(X\le n)=(1-p)^n[/tex]

Meanwhile, if [tex]X=n+k[/tex] and [tex]k\ge1[/tex], then it's always true that [tex]X>n[/tex], so

[tex]P(X=n+k\text{ and }X>n)=P(X=n+k)=(1-p)^{n+k-1}p[/tex]

Then

[tex]P(X=n+k\mid X>n)=\dfrac{(1-p)^{n+k-1}p}{(1-p)^n}=(1-p)^{k-1}p[/tex]

which is exactly [tex]P(X=k)[/tex] according to the PMF.

Final answer:

The memoryless property states that given there are no successes in the first n trials, the probability that the first success comes at trial n + k is the same as the probability that a freshly started sequence of trials yields the first success at trial k.

Explanation:

To show that if X ∼ Geom(p) then P(X = n + k|X > n) = P(X = k), for every n, k ≥ 1, we use the memoryless property of the geometric distribution. The memoryless property states that given that there are no successes in the first n trials, the probability that the first success comes at trial n + k is the same as the probability that a freshly started sequence of trials yields the first success at trial k. So, we have P(X = n + k|X > n) = P(X = k).

Learn more about the memoryless property here:

https://brainly.com/question/34736696

#SPJ2

Write the equation 8y = x – 0.8 in standard form. Identify A, B, and C.
480x + 5y = –48 where A = 480, B = 5, and C = 96

480x – 1y = –48 where A = 480, B = –5, and C = 96

5x – 480y = 48 where A = 5, B = –480, and C = 96

1x + 96y = 9.6 where A = 1, B = –96, and C = 0.8

Answers

Answer:

[tex]5x-40y=4[/tex]

Step-by-step explanation:

we know that

The standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers

In this problem we have

[tex]8y=x-0.8[/tex]

Multiply by 5 both sides

[tex]40y=5x-4[/tex]

Adds both sides 4

[tex]40y+4=5x[/tex]

Subtract 40y both sides    

[tex]4=5x-40y[/tex]

Rewrite

[tex]5x-40y=4[/tex] ----> equation of the line into standard form

A=5

B=-40

C=4

Four research teams each used a different method to collect data on how fast a new iron skillet rusts. Assume that they all agree on the sample size and the sample mean (in days). Use the (confidence level; confidence interval) pairs below to select the team that has the smallest sample standard deviation.

A. Confidence Level: 99.7%; Confidence Interval: 40 to 40
B. Confidence Level: 95%; Confidence Interval: 40 to 50
C. Confidence Level: 68%; Confidence Interval: 43 to 47
D. Confidence Level: 95%; Confidence Interval: 42 to 48

Answers

Answer:

D. Confidence Level: 95%; Confidence Interval: 42 to 48

Step-by-step explanation:

48-42=6

6/2=3

3 is smallest

I tested A and got it incorrect so D is the awnser

Confidence Level: 95%; Confidence Interval: 42 to 48. Then the correct option is D.

How to interpret the confidence interval?

Suppose the confidence interval at P% for some parameter's values is given by x ± y.

That means that the parameter's estimated value is P% probable to lie in the interval

[x - y, x + y]

Four research teams each used a different method to collect data on how fast a new iron skillet rusts.

Assume that they all agree on the sample size and the sample mean (in days).

Use the (confidence level; confidence interval) pairs below to select the team that has the smallest sample standard deviation.

Then we have

48 - 42 = 6

Then we have

6/2=3

3 is smallest

Then the correct option is D.

Learn more about confidence intervals here:

https://brainly.com/question/16148560

#SPJ2

Which statement about the solution of the inequality k<-3 1/4 is true?


The number 7.1 is not a solution to the inequality because -3 1/4 is located to the right of 7.1 on the number line.


The number 0.9 is not a solution to the inequality because -3 1/4 is located to the right of 0.9 on the number line.

The number –3 is a solution to the inequality because –3 is located to the left of -3 1/4 on the number line.

The number -8.4 is a solution to the inequality because -3/14 is located to the left of -3 1/4 on the number line.

Answers

Answer: Last option

The number -8.4 is a solution to the inequality because -8.4 is located to the left of [tex]-3\frac{1}{4}[/tex] on the number line.

Step-by-step explanation:

Note that: [tex]-3\frac{1}{4} =-3-\frac{1}{4} =-3.25[/tex]

The inequality is:

[tex]k<-3 \frac{1}{4}[/tex]

The inequality is:

This means that the inequality includes all values of the number line that are less than -3.25 or that are to the left of -3.25

__-8.4_________-3.25_-3____0___0.9____________7.1__

Note that the number -8.4 is less than -3.25, because it is to its left on the number line.

Then the correct statement is:

The number -8.4 is a solution to the inequality because -8.4 is located to the left of [tex]-3\frac{1}{4}[/tex] on the number line.

Answer:

the last option!!!

Step-by-step explanation:

i took the unit test

Using the distributive property to find the product (y — 4)(y2 + 4y + 16) results in a polynomial of the form y3 + 4y2 + ay – 4y2 – ay – 64. What is the value of a in the polynomial?

Answers

Answer:

a=16

Step-by-step explanation:

Given

(y-4)(y^2+4y+16)

To find the value of a in the resulting polynomial we have to solve the given expression

=y(y^2+4y+16)-4(y^2+4y+16)

= y^3+4y^2+16y-4y^2-16y-64

To find the value of a, both the polynomials will be compared

y^3+4y^2+16y-4y^2-16y-64  

y^3+4y^2+ay-4y^2-ay-64

Comparing the coefficients of both polynomials gives us that

a=16

So, the value of a is 16 ..  

A certain game consists of rolling a single fair die. If a four or five comes​ up, you win 8 ​dollars; otherwise, you lose 4 dollars. Find the expected winnings for this game

Answers

Answer:

3/1

Step-by-step explanation:

Well there's 6 sides on a dice and only 2 winning numbers. 6/2=3/1. You have a good chance of losing lol. Is this what you're looking for?

~Keaura/Cendall.

Follow below steps:

To find the expected winnings for the game described, we need to calculate the expected value of one roll of the die based on the outcomes and their corresponding probabilities and payoffs. This is a classic example of a discrete probability distribution problem where the random variable X represents the winnings from one roll of the die.

There are two winning outcomes, rolling a four and rolling a five, each of which has a probability of 1/6 and a payoff of 8 dollars. There are four losing outcomes, rolling a one, two, three, or six, each with the same probability of 1/6 and a loss of 4 dollars.

Therefore, the expected value E(X) is calculated as follows:

P(rolling a 4 or 5) = 1/6 for each, so 2/6 combined since the die is fair.P(rolling any other number) = 4/6 combined, since there are four other possibilities.

E(X) = (2/6) * 8 + (4/6) * (-4) = (16/6) - (16/6) = 0

So the expected winnings for this game are 0 dollars, which means that, on average, a player neither wins nor loses money in the long term.

"Find four numbers proportional to the numbers 2, 4, 5, and 6 if the difference between the sum of the two last numbers and the sum of the first two numbers is equal to 4.8."

Answers

Answer:

  1.92, 3.84, 4.8, 5.76

Step-by-step explanation:

In the given set, the sum of the last two numbers is 5+6 = 11; the sum of the first two numbers is 2+4 = 6. The difference between these sums is 11-6 = 5.

You want to scale all the numbers by a factor of 4.8/5 = 0.96 so that the difference computed the same way is 4.8 instead of 5.

Then the numbers are ...

  0.96{2, 4, 5, 6} = {1.92, 3.84, 4.8, 5.76}

Answer:

[tex]\boxed{\text{1.92, 3.84, 4.80, and 5.76}}[/tex]

Step-by-step explanation:

The numbers  must be in the ratio 2:4:5:6.

Let's call them 2x, 4x, 5x, and 6x. Then

5x + 6x =  11x = sum of last two numbers

2x + 4x =    6x = sum of first two numbers

According to the condition,

11x – 6x = 4.8

        5x = 4.8

          x = 0.96

2x = 1.92; 4x = 3.84; 5x = 4.80; 6x = 5.76

The numbers are [tex]\boxed{\textbf{1.92, 3.84, 4.80, and 5.76}}[/tex]

Check:

(4.80 + 5.76) – (1.92 + 3.84) = 4.8

     10.56       –       5.76       = 4.8

                              4.8         = 4.8

OK.

Other Questions
Which of the following did the Confederation Congress accomplish?1. It managed to wage a successful war for independence against Britain. 2. It established an orderly process to create new states. 3. It negotiated a good treaty with Britain at the end of the Revolution.4. All of the above Anyone know how to do this? central air conditioner uses 4.5 kilowatts. It runs for 5 hours over the course of a day. How much energy does the air conditioner use during that day? 9.5 kilowatt-hours 0.5 kilowatt-hours 0.9 kilowatt-hours 22.5 kilowatt-hours is my french correct?Je voudrais nager, dessiner et faire ski nautique plus souvent.>>i would swim, draw, and water ski more ofteni would like to add "to get better/in order to get better" at the end or even at the beginning of the sentence, but i dont know how. any suggestions? i wanted to use "deviennent meilleurs">to become better, but meilleur modifies nouns not verbs... Which of the following statements about basic emotions is true? Infants come into the world with the ability to clearly express basic emotions. Newborns emotional expressions closely resemble those of adults. Babies earliest emotional life consists of attraction to pleasant stimulation and withdrawal from unpleasant stimulation. Babies are born with well-organized and specific emotional expressions for happiness and fear. In a nonpolar covalent bond,protons are shared equally by two atoms.electrons are shared equally by two atoms.electrons are shared unequally by two atoms.protons are transferred from one atom to another.Which molecule below has a triple covalent bond? Diatomic FluorineDiatomic NitrogenDiatomic OxygenDiatomic Hydrogen A firm determines its profit by subtracting from . Plss help quick its from algebra nation!!!!which of the following are solutions to the inequality -7x+14>-3x-6?select all that applyA)-10B)10C)-5D)5E)-3F)3G)0 if there are 125 people and only 57 of them have pets, what percent has pets? ___ est tu casa? - Est en la Calle sol. A. Por que B. Cual C. Quien D. Donde what is the slope of the line y= -2/7x Check all choices below that are correct. Increasing the frequency increases the current. Changing the frequency does not affect the current. Voltage leads current. Current and voltage are in phase. Changing Vmax does not affect the current. Changing the resistance does not affect the current. Increasing Vmax decreases the current. Increasing the resistance increases the current. Increasing the resistance decreases the current. Increasing Vmax increases the current. Current leads voltage. Increasing the frequency decreases the current. What is the annual income earned by U.S.-owned firms and U.S. citizens referred to as? Answer this please ! Describe briefly one case in which the Supreme Court upheld a restriction on symbolic speech and one case where it struck down a restriction? what did abraham lincoln say in his inaugural address The indian subcontinent was partitioned into _____. _____ is the most important job a member of Congress does.Running for officeVoting on a billDebating a billServing on committees PLEASE HELP RIGHT AWAY Can someone please help me Steam Workshop Downloader