Suppose we are testing the null hypothesis H0: = 16 against the alternative Ha: > 16 from a normal population with known standard deviation =4. A sample of size 324 is taken. We use the usual z statistic as our test statistic. Using the sample, a z value of 2.34 is calculated. (Remember z has a standard normal distribution.)

a) What is the p value for this test?
b) Would the null value have been rejected if this was a 2% level test?

There are six possible ways a person can choose two balls at random from an urn containing five balls numbered 1, 2, 2, 6, and 6.

To understand how to calculate the number of combinations, let's break it down into two parts: selecting the first ball, and then selecting the second ball. Since there are five balls in the urn, the first ball can be chosen in five possible ways. Then, when selecting the second ball, the number of possible selections is reduced to four because one ball has already been selected. This can be expressed mathematically as: n(A)=5x4.

To calculate the total number of combinations, we then multiply the two numbers: 5x4=20. This result is then divided by two because the order of selection does not matter. As a result, 20/2=10, which means that there are ten possible combinations when choosing two balls at random from the urn. In conclusion, if an urn contains five balls numbered 1, 2, 2, 6, and 6, there are six possible ways a person can choose two balls at random. This can be expressed mathematically as n(A)=6 or n(A)=5x4/2.

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a. Using Cramer's rule, we find the values of x, y, and z for the system of equations.
b. The matrix A is invertible if its determinant is nonzero.

a. To solve the system of equations using Cramer's rule, we need to find the determinants of the coefficient matrix and the matrices obtained by replacing each column with the constants.

For the system of equations:
4x + 5y + 2z = 2
11x + y + 2z = 3
x + 5y + 2z = 1

The determinant of the coefficient matrix is:
D = |4 5 2|
|11 1 2|
|1 5 2|

The determinant of the matrix obtained by replacing the first column with the constants is:
Dx = |2 5 2|
|3 1 2|
|1 5 2|

The determinant of the matrix obtained by replacing the second column with the constants is:
Dy = |4 2 2|
|11 3 2|
|1 1 2|

The determinant of the matrix obtained by replacing the third column with the constants is:
Dz = |4 5 2|
|11 1 3|
|1 5 1|

Now we can calculate the values of x, y, and z using Cramer's rule:
x = Dx / D
y = Dy / D
z = Dz / D

b. To determine whether a matrix is invertible, we need to check if its determinant is nonzero.

For the matrix A:
A = |2 5 5|
|-1 -1 2|
|4 3 -3|

The determinant of matrix A is given by:
det(A) = 2(-1)(-3) + 5(2)(4) + 5(-1)(3) - 5(-1)(-3) - 2(2)(5) - 5(4)(3)

If det(A) is nonzero, then the matrix A is invertible. If det(A) is zero, then the matrix A is not invertible.

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Answer:

my x = ⅓

Step-by-step explanation:

\(6 + 3x = 7 \\ 3x = 7 - 6 \\ 3x = 1 \\ x = \frac{1}{3} \)

The solution to the equation 3e^(2x) + 5 = 27 is x = 1.36.

To solve the equation 3e^(2x) + 5 = 27 using natural logarithms, we can follow these steps:

Step 1: Subtract 5 from both sides of the equation:
3e^(2x) = 22

Step 2: Divide both sides of the equation by 3:
e^(2x) = 22/3

Step 3: Take the natural logarithm (ln) of both sides of the equation:
ln(e^(2x)) = ln(22/3)

Step 4: Apply the property of logarithms that states ln(e^a) = a:
2x = ln(22/3)

Step 5: Divide both sides of the equation by 2:
x = ln(22/3)/2

Using a calculator, we can evaluate ln(22/3) to be approximately 2.72.

Therefore, x = 2.72/2 = 1.36.

So, the solution to the equation 3e^(2x) + 5 = 27 is x = 1.36.

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Answer:

yes

Step-by-step explanation:

because although some of the other are missing to be a function, it has to have an element of x and of y, it does not matter that some do not have it with one of y and one of x is enough

And if you are talking about relation it is also because they comply with the rules

The absolute value inequality or equation can be either always true or never true, depending on the value inside the absolute value symbol. The equation |x| = -6 is never true  there is no value of x that would make |x| = -6 true.

In the case of the equation |x| = -6, it is never true.

This is because the absolute value of any number is always non-negative (greater than or equal to zero).

The absolute value of a number represents its distance from zero on the number line.

Since distance cannot be negative, the absolute value cannot equal a negative number.

Therefore, there is no value of x that would make |x| = -6 true.
In summary, the equation |x| = -6 is never true.

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( x - 12 ) ( x + 6 ) = 0

x - 12 = 0 and x + 6 = 0

x = 12 and x = -6

Answer:

\(x=12,\:x=-6\) are your x intercepts

Step-by-step explanation:

\(\left(x-12\right)\left(x+6\right)=0\\\mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)\\\mathrm{Solve\:}\:x-12=0:\quad x=12\\x-12=0\\\mathrm{Add\:}12\mathrm{\:to\:both\:sides}\\x-12+12=0+12\\Simplify\\x=12\\\mathrm{Solve\:}\:x+6=0:\quad x=-6\\x+6=0\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\x+6-6=0-6\\Simplify\\x=-6\\The\:solutions\:to\:the\:quadratic\:equation\:are:\\x=12,\:x=-6\)

Answer:

Slope: -5 Y-intercept: 3

Step-by-step explanation:

the slope intercept of a linear equation is:

y=mx+b

were m is slope. and b is the y intercept

therfore the problem is:

y=-5x+3

m=-5 so the slope is -5

b=3 so the y-intrercept is 3

Answer:

-5

Step-by-step explanation:

The slope is always in front of the x

Answer:

A

Step-by-step explanation:

i think

Answer:

2.15

Step-by-step explanation:

I will assume that "−1/4(−8.6)" is telling us to multiply (-8.6) times -(1/4):

(-1/4)*(-8.6)

= (8.6/4)

= 2.15

The ratios of (a) square kens to square meters (1 ken² / 1 m²) is 3.88

For given question,

We have been given the unit conversion.

A traditional unit of length in Japan is the ken

and 1 ken = 1.97 m

We need to find the the ratios of (a) square kens to square meters.

First we find the square of 1 ken.

⇒ 1 square kens = (1.97 m)²

⇒ 1 square kens = 1.97 × 1.97 m²

⇒ 1 square kens = 3.88 m²                  ..................(1)

And 1 square meters = 1 m²                 ................. (2)

Now we take the ratio of square kens to square meters.

From (1) and (2),

⇒ 1 ken² / 1 m² = 3.88 / 1

⇒ 1 ken² / 1 m² = 3.88

Therefore, the ratios of (a) square kens to square meters (1 ken² / 1 m²) is 3.88

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The speed of the object is 12121 m per week.

What does it mean to do speed?

The object is moving at a speed of 2 centimeters every 7 seconds.

We need to find the speed in m per week.

2 cm = 0.02 m

1 week = 604800 s

7 s =  \(1.65 * 10^{-6} week\)

Speed = distance/time

So,

\(v = \frac{0.02 m}{1.65 * 10^{-6 } week}\)

\(v = 12121.21 m/ week\)

or v = 12121 m/ week

So, the speed of the object is 12121 m per week.

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Answer:

SHould be 11.6 degrees

Answer:

The correct option is;

Horizontal stretch followed by a translation 1 unit left  so g(x) = (3·x + 2)

Step-by-step explanation:

In geometric transformation, a dilation involves the increase in the dimension of the distances between points by a given scale factor.

Therefore, with regards to the question, a dilation can be represented by the product of the initial dimension, x, by a variable, such as an integer

A translation right is represented by an addition to the x value, while a translation left is represented by subtraction from the x value

Therefore, whereby f(x) = x + 1

An horizontal stretch of 3 will be 3 × (x + 1) = 3·x + 3

Followed by an a translation 1 unit left will be;

3·x + 3 - 1 = 3·x + 2;

Therefore;

g(x) = (3·x + 2).

Answer:

The answer is D on e2020

Step-by-step explanation:

Answer:

white: 1/3, blue: 1/4, red: 5/12

Step-by-step explanation:

Take the amount of balls each color has and divide by 12.

White:

4/12 = 1/3

Blue:

3/12 = 1/4

Red:

5/12 (can't simplify)

Answer:

3/44 or 0.068

Step-by-step explanation:

(3/12 × 2/11 × 1/10)+(5/12 × 4/11 × 3/10)+(4/12 × 3/11 × 2/10)

=3/44

Answer: Materials sink in water depending on how  heavy they are. It is about how heavy something is compared to the same amount (volume) of water. This ratio of an object’s mass to its volume is known as density. Density is what really determines whether something will sink or float.

The salesperson needs to make weekly sales of $9,500 to earn the same amount with each option.

The amount he earns by option A can be calculated as follows;

As he works 40 hours per week and the hourly wage is $19; therefore the amount he will earn can be determined by multiplication as follows;

Option A earning: 40 × 19 = $760

Thus, the salesperson earns $760 through option A.

Consider x to be the amount of weekly sales;

As the commission rate is 8% of sales therefore 8% of x should be equal to $760 for the salesman to earn the same amount with both options.

(8/100)x = 760

0.08x = 760

x = 760 / 0.08

x = 9,500

Hence the salesman needs to make weekly sales of $9,500 to earn the same amount with both options.

Although there is a mistake in your question, you might be referring to this question;

A salesperson works 40 hours per week at a job where he has two options for being paid option a is an hourly wage of $19 option B is a commission rate of 8% sales how much does he need to sell in a given week to earn the same amount with each option

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To find an equation of a plane through a given point and perpendicular to a given line, you can follow these steps:

1. Find the direction vector of the given line. This can be done by subtracting the coordinates of any two points on the line. Let's denote this vector as "d".

2. Find the normal vector of the plane. Since the plane is perpendicular to the line, its normal vector will be the same as the direction vector of the line. So, the normal vector of the plane is "d".

3. Use the coordinates of the given point on the plane to find the equation of the plane. Let's denote the coordinates of the point as (x₀, y₀, z₀).

The equation of the plane can be written as:

Ax + By + Cz = D,

where A, B, C are the components of the normal vector "d", and x, y, z are the variables representing any point on the plane.

To find the values of A, B, C, and D, substitute the coordinates of the given point into the equation:

A(x₀) + B(y₀) + C(z₀) = D.

Therefore, the equation of the plane through the given point and perpendicular to the line is:

d₁(x - x₀) + d₂(y - y₀) + d₃(z - z₀) = 0,

where (d₁, d₂, d₃) are the components of the direction vector "d" of the line, and (x₀, y₀, z₀) are the coordinates of the given point.

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Find the equation of the plane passing through the point (−1,3,2) and perpendicular to each of the planes x+2y+3z=5 and 3x+3y+z=0.

The first 20 multiples of 27 are as follows:

27, 54, 81, 108, 135, 162, 189, 216, 243, 270, 297, 324, 351, 378, 405, 432, 459, 486, 513, and 540.

A multiple in mathematics is created by multiplying any number by an integer.

In other words, if b = na for some integer n, known as the multiplier, it can be said that b is a multiple of a given two numbers, a and b.

This is equivalent to stating that b/a is an integer if an is not zero.

A is known as a divisor of b when a and b are both integers and b is a multiple of a.

First 20 multiples of 27:

27, 54, 81, 108, 135, 162, 189, 216, 243, 270, 297, 324, 351, 378, 405, 432, 459, 486, 513, and 540.

Therefore, the first 20 multiples of 27 are as follows:

27, 54, 81, 108, 135, 162, 189, 216, 243, 270, 297, 324, 351, 378, 405, 432, 459, 486, 513, and 540.

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Correct question:

What are the first 20 multiples of 27?

Answer:

38°

Step-by-step explanation:

hope this helps :)

Answer:

40

Step-by-step explanation:

30 minutes times 2 is 60 minutes which is 1 hour.

20 miles times 2 is 40 miles

She went 40 miles in 1 hour.

Please give brainliest if I helped! :)

Answer:

12 different vacation caombinations

Step-by-step explanation:

has 3 options of Theme Park and 4 options of length of trip

\(C=(3)(4)=12\)

Hope this helps

Answer:

x = 14, y = 37

Step-by-step explanation:

The angle vertical to (9x + 12 )° and 3x are same- side interior angles and are supplementary, sum to 180°, then

9x + 12 + 3x = 180

12x + 12 = 180 ( subtract 12 from both sides )

12x = 168 ( divide both sides by 12 )

x = 14, so

3x = 3 × 14 = 42

3x and 4y - 10 are adjacent angles and supplementary, then

3x + 4y - 10 = 180

42 + 4y - 10 = 180

4y + 32 = 180 ( subtract 32 from both sides )

4y = 148 ( divide both sides by 4 )

y = 37

Answer:

a10 = 16

Explanation:

The arithmetic sequence is defined by the equation:

To find the 10th term in the sequence, substitute 10 for i:

Then simplify:

The tenth term in the sequence is 16.

The formula for the nth partial sum of the series is equal to Sn = ln √(n+1), and the series diverges.

Get a formula for the nth partial sum of the series, by writing out the first few terms,

S₁ = (ln √2 - ln √1)

   = ln √2

S₂ = (ln √3 - ln √2) + (ln √2 - ln √1)

   = ln √3 - ln √1

S₃= (ln √4 - ln √3) + (ln √3 - ln √2) + (ln √2 - ln √1)

   = ln √4 - ln √1

Pattern here expressed the nth partial sum is equal to

ln √(n+1) - ln √1.

Simplify this to,

ln (√(n+1)/√1)

= ln √(n+1).

nth partial sum is equal to,

Sn = ln √(n+1)

Series converges or diverges,

Take the limit of the nth partial sum as n approaches infinity we have,

\(\lim_{n \to \infty}\) ln √(n+1)

= ln ∞

= ∞

Here, the limit of the nth partial sum diverges to infinity, the series itself diverges.

⇒the series does not have a sum.

Therefore, the nth partial sum of the series is Sn = ln √(n+1), and the series diverges.

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Answer:

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

Apply geometric mean theorem to find the value of x:

Find the value of y using Pythagorean:

Answer:

\(x = \sqrt{6}\)

\(y=\sqrt{15}\)

Step-by-step explanation:

To find the value of x, apply the Geometric Mean Theorem (Altitude Rule).

The Geometric Mean Theorem (Altitude Rule) states that the altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the altitude to one segment is equal to the ratio of the other segment to the altitude.

From inspection of the given right triangle:

\(\implies \sf \dfrac{altitude}{segment\:1}=\dfrac{segment\:2}{altitude}\)

\(\implies \dfrac{x}{3}=\dfrac{2}{x}\)

\(\implies x^2=6\)

\(\implies x=\sqrt{6}\)

Therefore, the value of x is √6.

To find the value of y, apply the Geometric Mean Theorem (Leg Rule).

The Geometric Mean Theorem (Leg Rule) states that the altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the hypotenuse to one leg is equal to the ratio of the same leg and the segment segment directly opposite the leg.

From inspection of the given right triangle:

\(\implies \sf \dfrac{hypotenuse}{leg\:1}=\dfrac{leg\:1}{segment\;1}\)

\(\implies \dfrac{5}{y}=\dfrac{y}{3}\)

\(\implies y^2=15\)

\(\implies y=\sqrt{15}\)

Therefore, the value of y is √(15).

The probability of both coins landing on tails is 1/4. (option d).

To find the probability of an event, we divide the number of favorable outcomes by the total number of possible outcomes. In this problem, there are two coins, and each coin has two possible outcomes: heads or tails. Therefore, the total number of possible outcomes is:

Total number of possible outcomes = 2 x 2 = 4

Now, we need to determine the number of favorable outcomes, i.e., the number of ways in which both coins land on tails. Since each coin has two possible outcomes, there are four possible outcomes when two coins are flipped:

Heads on the penny, heads on the nickel

Heads on the penny, tails on the nickel

Tails on the penny, heads on the nickel

Tails on the penny, tails on the nickel

Out of these four outcomes, only one outcome is favorable - the fourth outcome, where both coins land on tails. Therefore, the number of favorable outcomes is:

Number of favorable outcomes = 1

Now, we can use the formula for probability to find the probability of both coins landing on tails:

Probability = Number of favorable outcomes / Total number of possible outcomes

Substituting the values, we get:

Probability = 1/4

Therefore, the answer is D. 1/4.

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Answer:

15

Step-by-step explanation:

15= 3*5, so not prime

Answer:

Scalene Triangle

Step-by-step explanation:

Measure the side and if the none of the sides are equal then it will be a scalene triangle