YOUR ASSIGNMENT: Difference of 10 Erik and Nita are playing a game with numbers. In the game, they each think of a random number from 0 to 20. If the difference between their two numbers is less than 10, then Erik wins. If the difference between their two numbers is greater than 10, then Nita wins. Use the information in the interactive and what you know about absolute value inequalities to better understand the game. Your Player 1. Choose your player, and record the number chosen by the other player. (2 points: 1 point for each answer) a. Which player did you select

Answer:

a) 0.4772 = 47.72% probability that the average is between 1,142 and 1,150.

b) 0.0228 = 2.28% probability that the average is greater than 1,158.

c) 0 = 0% probability that the average is less than 950.

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 estabilishes 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.

A certain type of automobile battery is known to last an average of 1,150 days with a standard deviation of 40 days.

This means that [tex]\mu = 1150, \sigma = 40[/tex]

Sample of 100:

This means that [tex]n = 100, s = \frac{40}{\sqrt{100}} = 4[/tex]

(a) The average is between 1,142 and 1,150.

This is the pvalue of Z when X = 1150 subtracted by the pvalue of Z when X = 1142. So

X = 1150

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

By the Central Limit Theorem

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

[tex]Z = \frac{1150 - 1150}{4}[/tex]

[tex]Z = 0[/tex]

[tex]Z = 0[/tex] has a pvalue of 0.5

X = 1142

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

[tex]Z = \frac{1142 - 1150}{4}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228

0.5 - 0.0228 = 0.4772

0.4772 = 47.72% probability that the average is between 1,142 and 1,150.

(b) The average is greater than 1,158.

This is 1 subtracted by the pvalue of Z when X = 1158. So

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

[tex]Z = \frac{1158 - 1150}{4}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772

1 - 0.9772 = 0.0228

0.0228 = 2.28% probability that the average is greater than 1,158.

(c) The average is less than 950.

This is the pvalue of Z when X = 950. So

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

[tex]Z = \frac{950 - 1150}{4}[/tex]

[tex]Z = -50[/tex]

[tex]Z = -50[/tex] has a pvalue of 0

0 = 0% probability that the average is less than 950.

Answer:

$7.50

Step-by-step explanation:

you add 40.50 + 4.50 which then equals 45 and you divide that by 6 and you get 7.50

One ticket costs $7.50 without the coupon this we obtained by dividing total cost before discount  by Number of tickets

Let us find the total cost of the tickets before the coupon is applied. We can do this by adding the discount amount ($4.50) to the final cost ($40.50):

Total cost before discount = Final cost + Discount amount

Total cost before discount = $40.50 + $4.50

Total cost before discount = $45.00

Now we can divide the total cost before discount by the number of tickets

(6) to find the cost of one ticket:

Cost of one ticket = Total cost before discount / Number of tickets

Cost of one ticket = $45.00 / 6

Cost of one ticket = $7.50

Therefore, one ticket costs $7.50 without the coupon.

To learn more on Discount click:

https://brainly.com/question/3541148

#SPJ2

Answer:

520=20x+234

15 packages

Step-by-step explanation:

520-234

286

286/20

14.3, so she needs 15 packages

Given:

The polynomial is:

[tex]P(x)=ax+b[/tex]

To find:

Whether [tex]x=-\dfrac{b}{a}[/tex] is a zero of the given polynomial or not.

Solution:

We have,

[tex]P(x)=ax+b[/tex]

Putting [tex]x=-\dfrac{b}{a}[/tex], we get

[tex]P(-\dfrac{b}{a})=a(-\dfrac{b}{a})+b[/tex]

[tex]P(-\dfrac{b}{a})=-b+b[/tex]

[tex]P(-\dfrac{b}{a})=0[/tex]

Since the value of the given polynomial is 0 at [tex]x=-\dfrac{b}{a}[/tex], therefore [tex]x=-\dfrac{b}{a}[/tex] is a zero of the given polynomial.

Answer: C

Step-by-step explanation: 5pi converts to 15.70796

Answer:

slightly less than 15 of b.

Answer:

Outside, as the distance between the point and the center of the circle is more than the radius.

Step-by-step explanation:

Equation of a circle:

The equation of a circle has the following format:

[tex](x-x_0)^2 + (y-y_0)^2 = r^2[/tex]

In which [tex](x_0,y_0)[/tex] is the center and r is the radius.

Testing if a point is inside the circle:

Point (x,y), we replace in the equation. If it is less than the radius squared(in this case, 62), it is in.

In this question:

Point (-3,-5). So

[tex](-3+7)^2 + (-5-2)^2 = 4^2 + (-7)^2 = 16 + 49 = 65[/tex]

The square distance of the point to the center is of 65, which is more than the square of the radius, meaning that the point is outside the circle.

Answer:

Outside

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

the graph is completely proportional so the answer would be 1

Answer:

48

Step-by-step explanation:

Substitute c=6 and d=3 in your formulas

[tex]5*6 + 2*3^{2}\\ 30 + 18\\48[/tex]

Answer:

(-1,10)

Step-by-step explanation:

At the point when the paths cross, the respective x and y values of each equation will be equal.

Your path is y=2x+12, and your friends path is 4x+y=6. Sub 2x+12 in for y (from your path's equation) into your friends equation to find the value of x:

4x+2x+12=6

6x=-6

x=-1

y=2x+12

y=2(-1)+12=10

So you will cross paths at (-1,10)

Answer: The answer is 1:2, i hope it helps.

Answer:

216 cm²

Step-by-step explanation:

Area of ∆ACD = ½*CD*CA

CD = 24 cm

CA = ?

Use pythagorean theorem to find CA.

Thus:

CA² = AB² + BC²

Substitute

CA² = 10.8² + 14.4² = 324

CA = √324

CA = 18 cm

Area of ∆ACD = ½*CD*CA

Substitute

Area = ½*24*18

= 216 cm²

Answer:

i would think it would be the same as angle bcd so 90

Step-by-step explanation:

Answer:

1/3x3 3/4  /2.5 = 0.3

Respuesta:

30

Explicación paso a paso:

Número total de preguntas = 100%

Número de preguntas correctas = 27

Porcentaje de aciertos = 90%

Por eso,

Si 90% = 27

Luego ; 100% = x

Multiplicar en cruz:

0,9 veces = 27

x = 27 / 0,9

x = 30

Número de preguntas = 30

Answer:

6n + 12

Step-by-step explanation:

Given an integer n, the 3 consecutive even integers greater than 2n are 2n+2, 2n+4 and 2n+6

Taking their sum;

Sum = (2n+2)+(2n+4)+(2n+6)

Sum = 2n+2n+2n+2+4+6

Sum = 6n + 12

Hence the sum of the 3 consecutive even integers greater than 2n is 6n+12

Answer:

[tex]P(3\ or\ c) = 0.45[/tex]

Step-by-step explanation:

Given

See attachment for spinner

Required

[tex]P(3\ or\ c)[/tex]

From the first spinner, we have:

[tex]S = \{1,2,3,4,5\}[/tex] --- Sample Space

[tex]n(S)=5[/tex]

So, P(3) is:

[tex]P(3) = \frac{n(3)}{n(S)}[/tex]

[tex]P(3) = \frac{1}{5}[/tex]

[tex]P(3) = 0.20[/tex]

From the second spinner, we have:

[tex]S = \{a,b,c,d\}[/tex]

[tex]n(S) = 4[/tex]

So, P(c) is:

[tex]P(c) = \frac{n(c)}{n(S)}[/tex]

[tex]P(c) = \frac{1}{4}[/tex]

[tex]P(c) = 0.25[/tex]

The required probability is then calculated as:

[tex]P(3\ or\ c) = P(3) + P(c)[/tex]

[tex]P(3\ or\ c) = 0.20 + 0.25[/tex]

[tex]P(3\ or\ c) = 0.45[/tex]

Answer:rf JAMES CHARLE's?!?

Step-by-step explanation:

Answer:

Missing number = 3

Step-by-step explanation:

Let [tex]x[/tex] be the missing number. We have the following:

[tex]7\cdot (6+x)=63,\\6+x=9,\\x=\boxed{3}[/tex]

Answer:

5/9??? I think thats the answer

Answer:

(4000 in^2) * (1 ft/12 in)^2 = 27 7/9 ft^2

Step-by-step explanation:

4,000 Square Inches =

27.777778 Square Feet

Answer:

O.75

Step-by-step explanation:

The value of x in the equation 1.5(4)^2x is equal to 12 is 3/4 after equation the power of same base.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

We have an equation:

[tex]\rm 1.5(4)^2^x=12[/tex]

[tex]\rm (4)^2^x=8[/tex]

[tex]\rm (2^2)^{2x}= 2^3[/tex]

[tex]\rm 2^{4x}=2^3[/tex]

4x = 3  (equating powers of same base)

x = 3/4

Thus, the value of x in the equation 1.5(4)^2x is equal to 12 is 3/4 after equation the power of same base.

Learn more about the integer exponent here:

brainly.com/question/4533599

#SPJ2

Answer:

90-degree clockwise rotation: (x,y)⇒(y,-x)

Step-by-step explanation:

For D⇒D', (0,-3)⇒(-3,0)

For E⇒E', (2,-1)⇒(-1,-2)

For F⇒F', (5,-3)⇒(-3,5)

We can see that the pattern here is (x,y)⇒(y,-x), which is the rule for a 90-degree clockwise rotation.

Answer:

3*1/2= 3/2

Step-by-step explanation:

[tex]\frac{3}{1}[/tex]*[tex]\frac{1}{2}[/tex] = 3/2

3*1/2= 3/2

3 is equal to 3/1

we then directly multiply

equation: (3/1)(1/2)

(3/1)(1/2)

3*1 = 3

1*2= 2

3/2 or 1 1/2.

Decimals can be written in fraction form. To convert a decimal to a fraction, place the decimal number over its place value. For example, in 0.6, the six is in the tenth place, so we place 6 over 10 to create the equivalent fraction, 6/10.

Learn more about fraction form at

https://brainly.com/question/46210

#SPJ2

Answer:for the permieter dont you just add both sides?

Step-by-step explanation:

f(x) times g(x) = 8x^2+8x-6

(2x-1) times (4x+6) = 8x^2+8x-6

====================================================

Explanation:

The functions f(x) and g(x) are linear functions. The result of f(x) ___ g(x) is some quadratic function.

It's very likely that the answer is a multiplication sign because of the general template of

(linear)*(linear) = (quadratic)

For example, x*3x = 3x^2.

Let's see if the two functions multiply out to 8x^2+8x-6 or not.

-----------------------

f(x) * g(x) = ( f(x) ) * ( g(x) )

f(x) * g(x) = ( 2x-1 ) * ( 4x+6 )

f(x) * g(x) = y * ( 4x+6 ) ......... let y = 2x-1

f(x) * g(x) = 4xy + 6y   ......... distribute

f(x) * g(x) = 4x( y ) + 6( y )

f(x) * g(x) = 4x( 2x-1 ) + 6( 2x-1 ) .... replace y with 2x-1

f(x) * g(x) = 8x^2-4x  + 12x-6  .... distribute twice more

f(x) * g(x) = 8x^2+8x-6

We end up getting the correct result. So this confirms that a multiplication sign is needed to fill in the blank.

Answer:

After harvesting, she weighs each pumpkin on a scale and records its height