given the series 1+2+3+4+5+6+...+5000. Write the series in sigma notation if all the powers of 4 are removed from the series.​

Complete Question

Four spinners are spun. Spinner 1 has outcomes {1,2,3,4,5,6,7,8} Spinner 2 has outcomes {1,2,3,4,5,6} Spinner 3 has outcomes {1,2,3,4,5,6} Spinner 4 has outcomes {1,2,3,4,5} The outcomes for each spinner are equally likely. S is the sum of the numbers that come up on the spinners. What is the expected value of S?

Answer:

[tex]E(s)=14.5[/tex]

Step-by-step explanation:

From the question we are told that:

Spinner 1 ={1,2,3,4,5,6,7,8}

Spinner 2=  {1,2,3,4,5,6}

Spinner 3 = {1,2,3,4,5,6}

Spinner 4  {1,2,3,4,5}

Generally the equation for expected outcome is mathematically given by

[tex]E(s)=\sum P(x).x[/tex]

Where

[tex]x=\frac{n(n+1)}{2}[/tex]

For Spinner 1

[tex]E(s_1)=\sum \frac{1}{8}*\frac{8(8+1)}{2}[/tex]

[tex]E(s_1)=4.5[/tex]

For Spinner 2

[tex]E(s_2)=\sum \frac{1}{6}*\frac{6(6+1)}{2}[/tex]

[tex]E(s_2)=3.5[/tex]

For Spinner 3

[tex]E(s_2)=E(s_3)[/tex]

For Spinner 3

[tex]E(s_4)=\sum \frac{1}{6}*\frac{6(6+1)}{2}[/tex]

[tex]E(s_4)=3[/tex]

Therefore The Expected Value

[tex]E(s)=\sum E(s 1..4)[/tex]

[tex]E(s)=4.5+2(3.5)+3[/tex]

[tex]E(s)=14.5[/tex]

Answer:

(1). A = 18 cm² ; (2). TR = 18 units

Step-by-step explanation:

Answer:

y = 3x - 5

Step-by-step explanation:

Slope = 3

x-intercept (what the value of y is when its 0) = -5 so y = 3x - 5

Answer:

y = 3x - 5

Step-by-step explanation:

Find the slope of the line between (0,−5)(0,-5) and (3,4)(3,4) using m=y2−y1x2−x1m=y2-y1x2-x1, which is the change of yy over the change of xx.

m=3m=3

Use the slope 33 and a given point (0,−5)(0,-5) to substitute for x1x1 and y1y1 in the point-slope form y−y1=m(x−x1)y-y1=m(x-x1), which is derived from the slope equation m=y2−y1x2−x1m=y2-y1x2-x1.

y−(−5)=3⋅(x−(0))y-(-5)=3⋅(x-(0))

Simplify the equation and keep it in point-slope form.

y+5=3⋅(x+0)

Add xx and 00.

y+5=3xy+5=3x

Subtract 55 from both sides of the equation.

y=3x−5

9514 1404 393

Answer:

  x² -22 = 0

Step-by-step explanation:

The roots are opposites, so the equation is pretty simple.

  x = ±√22

  x² = 22 . . . . . square both sides

  x² -22 = 0 . . . . your quadratic equation in standard form

Answer:

-3x² - 2x - 54

Step-by-step explanation:

(-7²-x-5)-(3x²+x)

-7² - x - 5 - 3x² - x

-49 - x - 5 - 3x² - x

-3x² - x - x - 49 - 5

-3x² - 2x - 54

Answer:

Sin A = 15 / 17

Step-by-step explanation:

Given a right angled triangle, we are to obtain the Sin of the angle A ;

Using trigonometry, the sin of the angle A, Sin A is the ratio of the angle opposite A to the hypotenus of the right angle triangle.

Hence. Sin A = opposite / hypotenus

Opposite = 15 ; hypotenus = 17

Sin A = 15 / 17

Answer:

0.9099 = 90.99% probability that their mean length is less than 21.9 inches.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 18.2 inches, and standard deviation of 3.9 inches.

This means that [tex]\mu = 18.2, \sigma = 3.9[/tex]

2 itens:

This means that [tex]n = 2, s = \frac{3.9}{\sqrt{2}}[/tex]

What is the probability that their mean length is less than 21.9 inches?

This is the p-value of Z when X = 21.9. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{21.9 - 18.2}{\frac{3.9}{\sqrt{2}}}[/tex]

[tex]Z = 1.34[/tex]

[tex]Z = 1.34[/tex] has a p-value of 0.9099.

0.9099 = 90.99% probability that their mean length is less than 21.9 inches.

Answer: so there are 666 multiples of 3 between 2 and 2000.

Step-by-step explanation:

the smallest number = 3 which is 3*1. The largest number is = 1998 = 3*666

multiples of 3 between {2,2000} = 666-1+1 = 666

Answer:

It's 0

Edge said it's 0

The value of the ratio of the cos(x) and the sin(x) is 0.

Trigonometric ratios are mathematical functions that relate the angles of a right triangle to the ratios of the lengths of its sides. These ratios are fundamental in trigonometry and have applications in various fields, such as physics, engineering, and navigation.

Trigonometry is a branch of mathematics that deals with the relationships and properties of angles and triangles. It explores the ratios between the sides of a triangle and the angles within that triangle. The word "trigonometry" is derived from two Greek words: "trigonal," meaning "triangle," and "metron," meaning "measure."

The value of the sin(x) is 1. The value of cos(x) is 0.

The formula for the cot(x) is written below:

cot(x) = cos(x) / sin(x)

cot(x) = 0 / 1

cot(x) = 0

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Answer:

B

Step-by-step explanation:

5³.5^×

simply means

5³×5^×

using indices rule,

multiplication is addition

5 is common

so 5(³+×)

hence 5^3+×

9514 1404 393

Answer:

  (-5, 4)

Step-by-step explanation:

The inside corner moves from (2, -2) to (-3, 2). That is 5 is subtracted from the x-coordinate, and 4 is added to the y-coordinate. (x, y) ⇒ (x -5, y +4)

The translation vector can be written horizontally as (-5, 4), or vertically as ...

  [tex]\displaystyle\binom{-5}{4}[/tex]

Answer:

(4) 644,000

Step-by-step explanation:

643,581

The 3 is in the thousands place

We look at the hundreds place

5

It is 5 or greater so we round the thousands place up 1

644000

9514 1404 393

Answer:

Step-by-step explanation:

The attached shows the predicted mileage for cars built in 2025 to be 46.3 mpg, 76.2 mpg for cars built in 2050.

__

No doubt, the function is valid over the time period used to derive it. It may or may not be valid for predicting MPG beyond that period.

Virtually any function that predicts future increases without bound will turn out to be unreliable at some point. In this universe, there are always limits to growth.

Answer:

Step-by-step explanation:

Our friend asking what the actual function is has a point. I completed this under the assumption that what we have is:

[tex]f(x)=\frac{e^{3x}}{5x-2}[/tex] and used the quotient rule to find the derivative, as follows:

[tex]f'(x)=\frac{e^{3x}(5)-[(5x-2)(3e^{3x})]}{(5x-2)^2}[/tex] and simplifying a bit:

[tex]f'(x)=\frac{5e^{3x}-[15xe^{3x}-6e^{3x}]}{(5x-2)^2}[/tex]and a bit more to:

[tex]f'(x)=\frac{5e^{3x}-15xe^{3x}+6e^{3x}}{(5x-2)^2}[/tex] and combining like terms:

[tex]f'(x)=\frac{11e^{3x}-15xe^{3x}}{(5x-2)^2}[/tex] and factor out the GFC in the numerator to get:

[tex]f'(x)=\frac{e^{3x}(11-15x)}{(5x-2)^2}[/tex]  That's the derivative simplified. If we want f'(0), we sub in 0's for the x's in there and get the value of the derivative at x = 0:

[tex]f'(0)=\frac{e^0(11-15(0))}{(5(0)-2)^2}[/tex] which simplifies to

[tex]f'(0)=\frac{11}{4}[/tex] which translates to

The slope of the function is 11/4 at the point (0, -1/2)

Answer:

Since [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the normal distribution can be used to approximate the binomial distribution.

The mean is 13.3 and the standard deviation is 3.28.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex], if [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex].

The probability than an adult never had the flu is 19%.

This means that [tex]p = 0.19[/tex]

You randomly select 70 adults and ask if he or she ever had the flu.

This means that [tex]n = 70[/tex]

Decide whether you can use the normal distribution to approximate the binomial distribution

[tex]np = 70*0.19 = 13.3 \geq 10[/tex]

[tex]n(1-p) = 70*0.81 = 56.7 \geq 10[/tex]

Since [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the normal distribution can be used to approximate the binomial distribution.

Mean:

[tex]\mu = E(X) = np = 70*0.19 = 13.3[/tex]

Standard deviation:

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{70*0.19*0.81} = 3.28[/tex]

The mean is 13.3 and the standard deviation is 3.28.

Answer:

AB

Step-by-step explanation:

For the multiplication of two matrices to be defined then the number of columns of the first matrix must be equal to the number of rows of the second matrix. For example, 2*3 and 3*2 matrices can be multiplied since the number of columns of the first matrix must be equal to the number of rows of the second matrix.

Matrix A = 2*2

Matrix B = 2*3

Matrix C = 3*3

Matrix D = 1 * 3

From the matrices given, we can see that the matrices that can be multiplied together are AB and BC since the number of columns of the first matrix must be equal to the number of rows of the second matrix. Hence the correct option is AB

Answer:

(a) 218.6 N

(b) 97.14 N

Step-by-step explanation:

When the system is in equilibrium, the net torque on the system is zero.

AC = 1.5 m, CD = 2.3 m, DB = 5 - 1.5 - 2.3 = 1.2 m

Let the centre of gravity of plank is at G.

AG = 2.5 m, CG = 2.5 - 1.5 = 1 m, GB = 2.5 m

(a) Let the reaction at C is R and at D is R'.

R + R' = 29 x 9.8 = 284.2 N ... (1)

Take the torque about C.

29 x 9.8 x CG = R' x GD

29 x 9.8 x 1 = R' x 1.3

R' = 218.6 N

(b) Take the torque about D.

6 x 9.8 x AD = R x CD

6 x 9.8 x (1.5 + 2.3) = R x 2.3

R = 97.14 N

Answer:

[tex]3-5\left(a-4\right)[/tex]

[tex]-5(a-4)=-5a+20[/tex]

[tex]=3-5a+20[/tex]

[tex]=-5a+23[/tex]

OAmalOHopeO

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\text{3 - 5(a - 4)}\\\\\huge\text{\underline{\underline{DISTRUBUTE -5 within the parentheses}}}\\\\\large\text{3 - 5(a) - 5(-4)}\\\large\text{= 3 - 5a + 20}\\\\\huge\text{\underline{\underline{COMBINE the LIKE TERMS}}}\\\large\text{-5a + (3 + 20)}\\\large\text{= \bf -5a + 23}\\\\\\\boxed{\boxed{\huge\text{Therefore, your answer is: \bf -5a + 23}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!} \\\\\\\frak{Amphitrite1040:)}[/tex]

Answer: [tex](\frac{2}{5},0) ; (0,2)[/tex]

Step-by-step explanation:

(to find the x-intercept, plug in 0 for y)

(to find the y-intercept, plug in 0 for x)

[tex]0=-5x+2\\5x=2\\x=\frac{2}{5}\\(\frac{2}{5},0)\\y=-5(0)+2\\y=2 \\(0,2)[/tex]

Answer:

Look in Step by Step Explanation

Step-by-step explanation:

3)SOHCAHTOA

tan=opposite/adjacent

tan(20)=x/83

83tan(20)=x

x=30.209

2) SOHCAHTOA

Tangent=opposite/adjacent

Tan(62)=x/8

8tan(62)=x

x=15.04

3)SOHCAHTOA

Sin=opposite/hypotonouse

sin(25)=30/x

x=30/sin(25)

x=70.986

this is a special triangle so v = 17

u = 17√2

Answer:

v = 17

u = 17[tex]\sqrt{2}[/tex]

Step-by-step explanation:

If v = 17 (it is because it is a right triangle, so the pythagorean theorum works, and triangles are 180 degrees, so 180 - 90 = 90, so the other two angles are 45 degrees, meaning that v is the same length as 17.) then

17 ^ 2 = u ^2

289 = u^2

17 root to 2

Answer:

B, D, F

Step-by-step explanation:

In a rational exponent, the numerator is an exponent, and the denominator becomes the index of the root.

[tex]a^{\frac{m}{n}} = \sqrt[n] {a^m}[/tex]

Answer: B, D, F

Answer:

[tex]\frac{135}{15} =\frac{15(x+2)}{15}[/tex]

[tex]9=x+2[/tex]

[tex]x=7[/tex]

OAmalOHopeO

Answer:

Step-by-step explanation:

(x-2)(x+4)=x^2+4x-2x-8=0=> x =2, x=0

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

The remainder when f(x) is divided by x + 3 would be 76.

If there is a polynomial p(x), and a constant number 'a', then

[tex]\dfrac{p(x)}{(x-a)} = g(x) + p(a)[/tex]

where g(x) is a factor of p(x).

We have been given a function;

[tex]f(x) = -2x^3 + x^2 - 4x + 1[/tex]

We need to find the remainder when f(x) is divided by x + 3.

So, Let p(x) = x + 3

p(x) = 0

x + 3 = 0

x = -3

Substitute in the given function f(x);

[tex]f(x) = -2x^3 + x^2 - 4x + 1\\\\f(-3) = -2(-3)^3 + (-3)^2 - 4(-3) + 1\\\\f(-3) = 54 + 9 + 12 + 1\\\\f(-3) = 76[/tex]

Thus, the remainder when f(x) is divided by x + 3 would be 76.

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Answer:

The answer is "Specific treatment levels".

Step-by-step explanation:

When we experimenting with 'level' which is related to the quantity or magnitude of treatment. For this part of an experiment or study, a group or individual is exposed to a specified set of circumstances. For example: If four categories are exposed to different doses of a given drug, then each dose reflects a level of a treatment factor in the model.

Answer:

520 feets

Step-by-step explanation:

The height of the building, h can be obtuined using trigonometry ;

From the attached diagram, opposite side = 300 feets ; height, h = adjacent side

Hence,

Tan θ = opposite / Adjacent

Tan 30° = 300 / height

0.5773502 = 300 / height

Height = 300 / 0.5773502

Height = 519.615

Height = 520 feets