when looking at the results of a 99% confidence interval, we can predict what the results of the two-sided significance test will be:

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

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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.

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Answer:

Last option: 31

Step-by-step explanation:

No. of catalogs that can be arranged

= (longest side of shelf ÷ longest side of catalog) × (shortest side of shelf ÷ shortest side of catalog)

= (56 ÷ 5) × (5 ÷ 4)

= 31

The required numerical expression is evaluated as 67.2. Option A is correct.

Given that,
An expression is given 7.5 × 6.6 ÷ 0.6 − 15.3, we have to evaluate the given expression.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
= 7.5 × 6.6 ÷ 0.6 − 15.3
Simplify,
= 7.5 × 11 - 15.3
= 82.2 - 15.3
= 67.2

Thus, the required numerical expression is evaluated as 67.2. Option A is correct.

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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.

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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 line with no slope will be a horizontal line the correct option is line b.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.

Given that on a coordinate plane, line A has a negative slope, line b is horizontal, line c is vertical, and line d has a positive slope.

The line with no slope will be line b because the line is a horizontal line.

Therefore, the line with no slope will be a horizontal line the correct option is line b.

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Answer:

C. Line C

Step-by-step explanation:

Edge 2023

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]

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).

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Answer: C

Step-by-step explanation: trust me

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

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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  .

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a) 90° counterclockwise about the origin

How can a rectangle be rotated?

A shape with rotational symmetry is a rectangle, for instance. When a rectangle is rotated around its center, the shape and placement remain unchanged. The placement of the specified points is the only distinction. Rectangles are of order 2 because they have half-turn symmetry.

When rectangle ABCD is rotated 90° counterclockwise about the origin , the vertex of 'A' in rectangle ABCD is (2,1) becomes (-1,2) in rectangle A'B'C'D'.

Therefore when rectangle ABCD is rotated we get rectangle A'B'C'D'.

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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

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.

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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°

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:

6.4 packs (7 as integer)

Step-by-step explanation:

Area of the square: 8^2 = 64 m^2

64 : 10 = 6.4

The length of the shortest ladder that will reach from the ground over the fence to the wall of the building is 11.31 feet

Let L stand for the ladder's overall length.

Right angled triangle ΔAGB contains the following:

L² = h² +(x+4)²

( Since by using Pythagorean Theorem)

Triangles AGB and CDB also have similarities.

As a result, the corresponding sides' ratio is equal.

Hence, we have:

h/4 = (x+4)/x

h = 4(x+4)/x

As a result, when we enter the value of h in equation (1), we obtain:

L² = h² +(x+4)²

L² = (4(x+4)/x)² +(x+4)²

L² = (16(x+4)²/x²)+(x+4)²

L² = (x+4)²(16/x² + 1)

We now have to reduce L.

Therefore, we employ the differentiation method.

We distinguish in relation to x as follows:

L² = (x+4)²(16/x² + 1)

2L dL/dx =2(x+4)(16/x² + 1) + (x+4)² (-32/x³)

2L dL/dx =2(x+4){ (16/x² + 1) + (x+4) (-16/x³)

2L dL/dx =2(x+4){ (16/x² + 1 -16/x²-64/x³)

2L dL/dx =2(x+4){ (1-64/x³)

when the derivative is zero we have:

2(x+4){ (1-64/x³) = 0

x= -4 and x³ = 64 and x =∛64 = 4

But x can't be negative.

Hence, we have:

x = 4

After solving equation (2) with this value of x, we get the following result:

L² = (x+4)²(16/x² + 1)

L² = 128

L = 11.313 feet

Hence,

L = 11.313 feet

which on rounding to two decimal places is: 11.31 feet

As a result, the shortest ladder's length, measured from the ground to the building's wall over the fence, is 11.31 feet.

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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]

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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.

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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.

Answer:

6

Step-by-step explanation:

slope = m = [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

put values and find answer:

[tex]=\frac{14+4}{-1+4}[/tex]

=  [tex]\frac{18}{3}[/tex]

=  [tex]6[/tex]

No, to construct a confidence interval, the population should be is approximately normal.

The information about distribution of population is important in order to find out the sampling distribution. When we want to construct confidence interval, the accuracy of results depend on three conditions.

1. The data needs to be randomly selected.

2. The sampling distribution needs to be normally distributed

3. The observations must be independent.

So one of the conditions is to ensure that the population is normally distributed.

We know from the central limit theorem, the sampling distribution is approximately normal as long as the expected number of successes and failures are equal or greater than 10

np ≥ 10

n(1 - p) ≥ 10

When the population follows normal distribution then a small number of samples will be adequate, on the other hand, if the population is skewed then we need a greater sample size to ensure normal sampling distribution.  

Therefore, the population is approximately normal before constructing a confidence interval.

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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

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!

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.

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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.

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