what condition or conditions must hold true for the sampling distribution of the sample mean to be normal when the sample size is less than 30?

The probability that a young adult chosen at random will achieve an IQ between 85 and 160 is 0.8185.

The problem states that;

A typical IQ test result for individuals between the ages of 20 and 34 has a mean of 110 and a standard deviation of 25, and the values are regularly distributed.

To get the probability that a randomly selected young adult will score between 85 and 160 on this IQ test.

Let,

P(85 < x < 160) = P[ (85 - 110)/ 25) < (x - μ) / σ < (160 - 110) / 25) ]

                        = P(-1 < z < 2)

                        = P(z < 2) - P(z < -1)

                        = 0.9772 - 0.1587

                        = 0.8185

Therefore, the probability that a randomly selected young adult will score between 85 and 160 on this IQ test is 0.8185.

To learn more about probability click here:

brainly.com/question/11234923

#SPJ4

The expected value of the bet if the odds that the horse will win are 3 to 12 is $18.8

What is expected value?

Expected value is the predictive value of all the possibilities that occur by multiplying the value by the probability.

Winning probability = odds / total outcomes

= 3 / (3 + 12)

= 3 / 15

= 0.2

Now, we need to calculate expected value.

= winning probability x amount won - losing probability x amount lost

= 0.2 x 110 - (1 - 0.2) x 4

= 22 - 3.2

= 18.8

Thus, the expected value of the bet if the odds that the horse will win are 3 to 12 is $18.8

Learn more about expected value here:

brainly.com/question/16726343

#SPJ4

Magnitude of an earthquake releasing 3.4*10^14 joules of energy is M ≈ 6.754.

Given:

The magnitude, M, of an earthquake is represented by the equation M=2/3log(E/E0) where E is the amount of energy released by the earthquake in joules and E0=10^4.4 .

E = 3.4*10^14

M = 2/3*log(3.4*10^14 / 10^4.4)

= 2/3*log(13535643798.8)

= 2/3*10.1314

= 20.2628 / 3

M = 6.754

Therefore Magnitude of an earthquake releasing 3.4⋅1014 joules of energy is M ≈ 6.754.

Learn more about the equation here:

https://brainly.com/question/10413253

#SPJ1

The x-intercepts of the quadratic function g(x) = x² - 10x + 24 are given as follows:

(4, 0) and (6, 0).

A function crosses the x-axis when the numeric value of the function is of y = 0, hence these points are called the x-intercepts of the function.

In this problem, the definition of the function is given as follows:

g(x) = x² - 10x + 24.

This function can be simplified as follows:

g(x) = (x - 6)(x - 4).

Applying the inverse of the Factor Theorem, the x-intercepts are given as follows:

Hence the x-intercepts of the function are given by the third option, which is of (4, 0) and (6, 0).

More can be learned about quadratic functions at https://brainly.com/question/24737967

#SPJ1

Answer: C

Step-by-step explanation: trust me

The probability that exactly one insect will die is 142.611.

The subject of a random event is covered in the mathematical field of probability. For instance, if a coin is flung into the air, it could land on its Head or Tail. Probability is equal to the number of favorable outcomes (Total number of outcomes) P = n (E) / n (S) (S) E is the event, P is the probability, and S is the sample area.

Given,

P( an insect will die) = 0.60

q = 1 - p

q = 1 - 0.60

q = 0.40

Sample size,

n = 9

Binomial distribution:

P(X) = ⁿCₓ pˣ qⁿ⁻ˣ

Probability that exactly one insect will die = P(X = 1)

= ⁹C₁ × 0.6¹ × 0.4⁸

= 362880 × 0.6 × 0.000655

= 142.611

The probability that exactly one insect will die is 142.611.

To learn more about probability, visit:

https://brainly.com/question/11234923

#SPJ4

The function (g∘f)(x) expressed as a polynomial in standard form is  9x² - 36x + 40

A function can be defined as an equation, a rule or a law that shows or rather explain the relationship between two variables in an equation.

The variables are known as;

We have the function given;

To determine the composite function (g ∘f)(x), we have to substitute the value of x as fx) in the function g(x), we have;

(g∘f)(x) = (- 3x + 5)² + 2( -3x + 5) + 5

expand the bracket

(g∘f)(x) = 9x² - 15x - 15x + 25 - 6x + 10 + 5

Now, collect like terms, we get;

(g∘f)(x) = 9x² - 15x - 15x - 6x + 25 + 10 + 5

Add or subtract the like terms, we get;

(g∘f)(x) = 9x² - 36x + 40

The polynomial is written as;  9x² - 36x + 40

Hence, the value is  9x² - 36x + 40

Learn more about functions here:

https://brainly.com/question/25638609

#SPJ1

Answer:

t=0

Step-by-step explanation:

Your equation would be 324=-16t^2+324 since 370-46 is 324. subtract each side by 324 and you get 0=-16t^2. t=0

Answer:

X would be 135 degrees

Step-by-step explanation:

35 is a vertical angle

180-(100+35) = 45

By supplements, 180-45 = 135 which would be your answer

hope this helps

the value o f x is 135, it mean x=135°

An inequality to find the number of batches of rolls Liz can make is 13n/4 ≤ 26 and she cannot make more than 8 batches of rolls.

In order to solve this word problem, we would assign a variable to the number of batches, and then translate the word problem into an algebraic inequality as follows:

Let the variable n represent the number of batches.

Since Liz has 26 tablespoons of yeast left in the jar and each batch of biscuits takes 3 1/4 -tablespoons, we have:

3 1/4 (n) ≤ 26

13n/4 ≤ 26

Cross-multiplying, we have:

13n ≤ 26 × 4

13n ≤ 104

n ≤ 104/13

n ≤ 8.

Read more on inequality here: brainly.com/question/12996324

#SPJ1

Complete Question:

Liz wants to make several batches of biscuits. She has 26 tablespoons of yeast left in the jar and each batch of biscuits takes 3 1/4 -tablespoons. Write and solve an inequality to find the number of batches of rolls Liz can make.

The absolute value function y = |x - 3| + 5 generates the representation set on Cartesian plane.

In this question we need to determine the equation behind a representation set on a Cartesian plane. After a quick inspection, we find that the representation shows an absolute value function of the form:

y = |x - a| + b

Where:

Based on all the given facts, the primitive absolute value function (f'(x) = |x|) is translated horizontally 3 units in the +x direction and vertically 5 units in the +y direction. If we know that a = 3 and b = 5, then we find the absolute value function y = |x - 3| + 5, whose representation is shown below.

In a nutshell, the representation comes from the absolute value function y = |x - 3| + 5.

To learn more on absolute value functions: https://brainly.com/question/14364803

#SPJ1

Answer: 4.5m

Step-by-step explanation:

because 12.5 can - by 2.5

then 9.0=9 -5.5=4.5

When the numerical data (number) 0.000007328 is rounded to the nearest millionth, the number is about 0.000007.

A place value can be defined as a numerical value which denotes a digit based on its position in a given number and it includes the following:

Based on the numerical data (number) provided above, the place value of seven (7) is millionth and it would be rounded up as seven (7) because the next number on its right (3) is less than five (5) and as such, it can seven (7) rounded up to eight (8).

In this context, we can reasonably infer and logically deduce that 0.000007 is a numerical data (number) that represents millionth based on the place value of seven (7).

Read more on place value here: brainly.com/question/569339

#SPJ1

The equation of the line in slope intercept form is y = (-4/3)x   .

In the question ,

a line graph is given ,

we need to find the equation of that line .

the two points that are given on the line graph are (-3 , 4) and (0 , 0) ,

the equation of the line passing from the points (x₁ , y₁) with slope m  in the slope intercept form is given by

(y - y₁) = m(x - x₁) .

we first need to find the slope .

So , m = (0 - 4)/(0 + 3)

m = -4/3

The equation of the line passing from the points (-3 , 4) with slope -4/3 , in the slope intercept form is

(y - 4) = (-4/3)(x -(-3))

y - 4 = (-4/3)(x + 3)

y - 4 = (-4/3)x - 4

y = (-4/3)x - 4 + 4

y = (-4/3)x

Therefore , The equation of the line in slope intercept form is  y = (-4/3)x  .

Learn more about Equation Of Line here

https://brainly.com/question/21298390

#SPJ1

Using the simplification of power, [tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=-64w^{-3}z^{6}[/tex] and [tex]\frac{g^{-6}h^8}{h^2}=g^{-6}h^{6}[/tex].

In the given question,

We have to simplify the given expression.

Before simplifying the expression we first learn that the negative power can be positive after changing their position from numerator to denominator.

We use the method of adding the power of expression to solve the expression.

(1) The given expression is [tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}[/tex].

We firstly simplifying the power after the bracket by multiplying the power to each variable.

[tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=(-\frac{1}{4})^{-3}(w^{-1})^{-3}(z^{-2})^{-3}[/tex]

Simplifying the expression.

[tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=(-1)^{-3}(\frac{1}{4})^{-3}(w^{-3})(z^{6})[/tex]

Now we make the power positive by changing their position

[tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=(-1){4}^{3}(w^{-3})(z^{6})[/tex]

Simplifying

[tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=-64w^{-3}z^{6}[/tex]

(2) The given expression is [tex]\frac{g^{-6}h^8}{h^2}[/tex].

Simplifying the expression.

As we know that the power with same base get subtracted when they are in division.

So [tex]\frac{g^{-6}h^8}{h^2}=g^{-6}h^{8-2}[/tex]

[tex]\frac{g^{-6}h^8}{h^2}=g^{-6}h^{6}[/tex]

To learn more about simplification of power link is here

brainly.com/question/4031335

#SPJ1

Answer:

8

Step-by-step explanation:

4*8=32

6*8=48

9*8=72

They are all multiples of 8

Answer: 8

Step-by-step explanation: You can factor out 32, 48, and 72 by using prime factorization which is listing all of the PRIME factors for each number

32: 2 x 2 x 2 x 2 x 2

48: 3 x 2 x 2 x 2 x 2

72: 3 x 3 x 2 x 2 x 2

If you look at all the prime factors, 2 appears in every number 3 times, so you do 2x2x2 to get the final answer, which is 8.

Answer:

x=17

It just is. I don't know how to explain it.

This is an example of Cluster random sampling.

Cluster sampling refers to probability sampling when the population is divided into multiple smaller groups, also called clusters, and then further sampling is performed to check the data.

Here we can see that the principal had selected 222 boxes randomly over here. This implies that she had taken a group of boxes randomly. Then she proceeded to check every t-shirt in this box.

Therefore here we see that the population i.e the boxes were divided into smaller groups. The 222 boxes are the clusters here. Therefore we can conclude that the principal uses the cluster random sampling method.

To know more about Sampling visit

https://brainly.com/question/13669285

#SPJ4

The tuition does not appear to have an association with graduation rate.

A scatter plot is a particular kind of plot or mathematical diagram that displays values for generally two variables for a collection of data. It uses Cartesian coordinates. A dot is used to symbolize each point on the scatter plot. It is used to demonstrate the link between the dots by illustrating how many of them would fall within the path of a straight line.

It is clear that there is no relation between tuition and graduation rate. Some selective colleges may have higher tuition and higher graduation rates but there may be some selective colleges with higher tuition but lower graduation rates.

Hence, the tuition does not appear to have an association with graduation rate. Option 2 is correct.

To learn more about the Scatter plot visit here:

https://brainly.com/question/28605735

#SPJ1

Answer:

I think it's A- Higher tuition causes students to graduate at higher rates.

Step-by-step explanation:

tell me if I'm wrong...  forgive me if i am

The probability that their score is at least  P(X> 555.3) = 0.8275

What is a normal distribution?

A continuous probability distribution for a real-valued random variable is called a normal distribution or a Gaussian distribution.

Here, we have

Let x denotes the score of a man.

standard deviation (σ) = 104

mean (μ) = 507

If 1 of the men is randomly selected, find the probability that his score is at least 553.5 will be :-

P(X > 553.5) = 1 - P(X ≤ x)

= 1 - P{((x - μ)/σ) ≤ (553.5 - 507/104)}

= 1 - P(z ≤ 0.447)

= 1 - 0.1725

= 0.8275

Hence, the probability that their score is at least  P(X> 555.3) = 0.8275

To learn more about the normal distribution from the given link

https://brainly.com/question/4079902

#SPJ1

Answer:

1) t = -2

2) t = 8

3) t = -2
4) t = 1

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

Step-by-step explanation:

1)-22t+6 = 11t + 72

 -33t = 66

      t = -2

2) 3t + 4t - 20 = t + 28

 6t = 48

   t = 8

3) -8 -10t - 6t = 3t + 30

   -19t = 38

       t = -2

4) 12t - 6t + 24 = 12t + 12 +6

   -6t = -6

       t = 1

5) -12-21t-3t=48t-36

    -24t - 48t = 12 - 36

    -72t = -24

     t = [tex]\frac{1}{3}[/tex]

Answer:

x=[tex]log_{2} 7/9[/tex]

Step-by-step explanation:

4-9×2^x+2+1=0

4-9×2^x+3=0

4+3-9×2^x=0

7-9×2^x=0

7-7-9×2^x=0-7

-9×2^x=-7

9×2^x=7

9×2^x/9=7/9

2^x=7/9

[tex]log_{2} 2^x[/tex]=[tex]log_{2} 7/9[/tex]

x=[tex]log_{2} 7/9[/tex]

Answer: -22/5 or -4.4

Step-by-step explanation:

Simplify so 2(22/7*10)(10+h)=352

Distribute so (2*22/7*10)(10) + (2*22/7*10)(h) = 352

Which would equal 4400/7 +440/7h=352

Subtract 4400/7 to both sides

That equals 440/7h=-1396/7

Multiply both sides by 7/440

h=-22/5

Answer:

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

Step-by-step explanation:

So you travel 800 feet in 10 seconds. If you divide that by 2, then you travel 400 feet in 5 seconds, or 100 feet in 5/4 seconds. Multiply by 3 to get 300 feet in 15/4 seconds, or 15 feet in [tex]3\frac{3}{4}[/tex] seconds.

The relationship in the scatterplot is positive and nonlinear.

We utilize correlation to assess the strength of a linear relationship between two numerical variables. The strength of a linear relationship is gauged by correlation.

To learn more about scatterplot refer to:

https://brainly.com/question/6592115

#SPJ13

The option that is a a linear equation is B. 4x - 2 = 20.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign

This is illustrated as 4x - 2 = 20

4x = 20 + 2

4x = 22

x = 22/4 = 5.5

This illustrates an equation.

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

Answer:

-18 + -5

Step-by-step explanation:

Because -18 - 5 is an inverse equation, that means that we are doing one equation that looks like something it usually doesn't. When subtracting a negative and a positive in that order, the result will be the sign of the greater value(-18), so the result will be negative. Subtracting a big number that's a negative by a smaller number that's a positive is the same as adding the same numbers together as if they are both negatives. E.g, -4 - 2 = -4 + -2.

Hope this helps!

Answer:

7

Step-by-step explanation: -13(-1) + 36 + 42(-1)

Step 1: -13(-1)= 13

Step 2: 13 + 36= 49

Step 3: 49 + 42(-1)= 49 + (-42)= 7

Solution: 7