PLEASE HELP! INVERSE QUESTION!

Answer:

H0 : μ = 220

H0 : μ < 220

Rejecting the null when it is actually true

We incorrectly drop a better method.

Step-by-step explanation:

The null hypothesis, H0

H0 : μ = 220

H0 : μ < 220

A type 1 error is committed when a true null hypothesis is incorrectly rejected. This means that we conclude that new method reduces the mean operating cost per hour when in fact it hasn't.

The impact of this on business is that the new method is adopted in place of the old method thinking it works better Than the old method.

Answer:  33) b      34) a        35) none

Step-by-step explanation:

33)

Filling in the Venn Diagram (from Left to right, including outside of circles):

T only           = 13

(T ∩ F)only   =  6

F only           = 21

(T ∩ D) only  =  3

T ∩ F ∩ D     =  5

(F ∩ D) only  =  8

D only           = 15

(T ∪ F ∪ D)'    = 11  

   TOTAL      = 82

\(P(D'\cap F) = \dfrac{6+21}{13+6+21+3+5+8+15+11}\quad =\large\boxed{\dfrac{27}{82}}\)

34)

Red  = 26

Face  = 12

Red ∩ Face = 6

Total cards = 52

R ∪ F = R + F - (R ∩ F)

        = 26 + 12 - 6

        = 32

\(P(R\cup F)=\dfrac{R\cup F}{Total}\quad =\dfrac{32}{52}\quad \rightarrow \quad \large\boxed{\dfrac{8}{13}}\)

35) Note that the total is 34 + 17 + 8 + 3 + 9 + 4 + 5 = 80

I think the teacher made an error, if so, then the answer is "d".

\(P(C) = \dfrac{34+17+3+9}{Total} =\dfrac{53}{80}\quad \bigg(not\ \dfrac{34}{75}\bigg)\qquad \text{This is False.}\\\\\\P(S\cap T)=\dfrac{9+0}{Total}=\dfrac{9}{80}\quad \bigg(not\ \dfrac{12}{75}\bigg)\qquad \text{This is False.}\\\\\\\\P(C\cup T)\cup S = \dfrac{17+9+3+4}{Total}= \dfrac{33}{80}\quad \bigg(not\ \dfrac{38}{75}\bigg)\qquad \text{This is False.}\\\\\\P(C\cup T)\cap S'=\dfrac{34+17+8}{Total}=\dfrac{59}{80}\quad \bigg(not\ \dfrac{59}{75}\bigg)\quad \text{This is False.}\)

The first equation is incorrect.

The second equation is correct.

The third equation is correct.

Let's go through each equation and determine whether it is correct or incorrect:

(b²+7b-9)+(4b-6b²) = -8b² + 14b-9

To determine if this equation is correct, we need to simplify both sides and check if they are equal.

On the left side:

(b²+7b-9)+(4b-6b²) = b² - 6b² + 7b + 4b - 9 = -5b² + 11b - 9

On the right side:

-8b² + 14b - 9

Comparing both sides, we can see that -5b² + 11b - 9 is not equal to -8b² + 14b - 9. Therefore, the equation is incorrect.

(4a+6)-(3a²-9a+1)=-3a²+ 13a +5

Again, we need to simplify both sides of the equation and check if they are equal.

On the left side:

(4a+6)-(3a²-9a+1) = 4a + 6 - 3a² + 9a - 1 = -3a² + 13a + 5

On the right side:

-3a² + 13a + 5

Comparing both sides, we can see that -3a² + 13a + 5 is equal to -3a² + 13a + 5. Therefore, the equation is correct.

(12c-8c²)+(5c²- 10c) = -3c²+2c

Again, let's simplify both sides and compare them.

On the left side:

(12c-8c²)+(5c²- 10c) = 12c - 8c² + 5c² - 10c = -3c² + 2c

On the right side:

-3c² + 2c

Comparing both sides, we can see that -3c² + 2c is equal to -3c² + 2c. Therefore, the equation is correct.

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Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation:

The variance of the data-set in this problem is given as follows:

σ² = 366.3.

The variance of a data-set is calculated as the sum of the differences squared between each observation and the mean, divided by the number of values.

The mean for this problem is given as follows:

205.

Hence the sum of the differences squared is given as follows:

SS = (198 - 205)² + (190 - 205)² + (245 - 205)² + (211 - 205)² + (193 - 205)² + (193 - 205)²

SS = 2198.

There are six values, hence the variance is given as follows:

σ² = 2198/6

σ² = 366.3

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Answer:

V=1/3*pi*radius(to the power of two)*height

Answer: 14 in squared

\((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

We can use the rules of exponents and simplify the terms with the same base.

Dividing the coefficients: 21 / 7 = 3.

For the variables, you subtract the exponents: \(a^6 / a^3 = a^(^6^-^3^) = a^3.\)

Similarly,\(b^5 / b = b^(5-1) = b^4\).

Putting it all together, the simplified expression is:

\(3a^3b^4.\)

Therefore, \((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

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I'll do the first three problems to get you started.

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

Problem 1

y = -2

4x+6 = -2 ... replace or substitute y with 4x+6

4x = -2-6

4x = -8

x = -8/4

x = -2

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

Problem 2

y = -5x-8

3x = -5x-8 .... substitute y with 3x

3x+5x = -8

8x = -8

x = -8/8

x = -1

Use this to find y

y = 3x = 3(-1) = -3

or

y = -5x-8 = -5(-1)-8 = 5-8 = -3

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

Problem 3

y = -4x+5

2x-7 = -4x+5

2x+4x = 5+7

6x = 12

x = 12/6

x = 2

Use this to find y

y = -4x+5 = -4(2)+5 = -8+5 = -3

or

y = 2x-7 = 2(2)-7 = 4-7 = -3

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

Side note:

To check the answers, we plug the coordinates back into the original equations.

For instance, here's what it would look like to check the answer to problem 3.

y = -4x+5

-3 = -4(2)+5 ... plug in (x,y) = (2,-3)

-3 = -8+5

-3 = -3 ... first equation works

y = 2x-7

-3 = 2(2)-7

-3 = 4-7

-3 = -3 ... second equation works

Both equations are true for (x,y) = (2,-3). This verifies the answer to problem 3. The other problems will follow similar steps.

Each letter should be matched to its correct term as follows;

1. A ⇔ Efficiency.

2. B ⇔ Impossible.

3. C ⇔ Inefficiency.

In Economics and Mathematics, a production possibilities curve (PPC) can be defined as a type of graph that is typically used for illustrating the maximum and best combinations of two (2) products that can be produced by a producer (manufacturer) in an economy, if they both depend on the following two (2) factors;

Based on the production possibilities curve shown in the image attached above, we can reasonably infer and logically deduce that each of the letters represent the following terminologies;

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Answer:

Gradient of parallel line= 7

Gradient of perpendicular line \( = - \frac{1}{7} \)

Step-by-step explanation:

The equation of the line is already in slope-intercept form (y= mx +c). This means that the coefficient of x is the gradient and the constant -3 is the y-intercept of the line.

y= 7x -3

Gradient= 7

Parallel lines have the same gradient.

Thus, the slope of the line parallel to this line is also 7.

The product of the gradients of 2 perpendicular lines is -1.

(Gradient of perpendicular line)(7)= -1

Gradient of perpendicular line

= -1 ÷7

\( = - \frac{1}{7} \)

Hello! :)

Parallel lines have the same slope.

If one line has a slope of 7, then the line parallel to it has a slope of 7 as well.

Now, perpendicular lines have slopes that are opposite reciprocals. It means we take the slope of one line, make it negative, and flop it over:

\(7\\-7\\-\frac{1}{7}\)

Hope it helps. Feel free to ask me if you have any questions.

~A determined teen

\(MagicalNature\)

Answer:

26) 70

27) 12.86 sec

28) 350 feet

Step-by-step explanation:

26) Given points A(0, 0) and B(16, 1120)

slope m = \(\frac{y_2-y_1}{x_2-x_1}\)

\(=\frac{1120-0}{16-0}\\ \\=\frac{1120}{16}\\ \\=70\)

slope = 70

27) eq of a line is :

y = mx + c

y = 70x + c

Since the line passes through A(0,0) substituting the points in the equation,

0 = 70(0) + c

⇒ c = 0

eq of line: y = 70x

given distance is 900 ft

y = distance and x = time

⇒ y = 900

sun in eq,

900 = 70x

⇒ x = 900/70

⇒ x = 12.86

28) time is 5 sec

⇒ x = 5

sub in eq

y = 70(5)

⇒ y = 350

Answer: -4x²-11x-7

Step-by-step explanation:

\(-3x^2-3x-7-(x^2+8x)=\\-3x^2-3x-7-x^2-8x=\\-4x^2-11x-7\)

1.  For collecting balls by both Robot A and B the direction will be N->E->E

2. For collecting hat and ball by Robot A and box and hat by Robot B, the direction will be N->N->S->E->E

3. For collecting both the balls by Robot A and a hat and ball by Robot B, the direction will be E->E->N

The direction that both Robot A and Robot B can take are N, E, S and W

For Part 1:

Robot A and Robot B need to collect the ball which is in the 2nd row 5th column for Robot A and 4th row 3rd column for Robot B, therefore the direction will be:

=N->E->E

For Part 2:

Robot A needs to collect a hat and ball which are in the 1st-row third column and 2nd row 5th column respectively. Robot B needs to collect a box and a hat which are in the 3rd row 1st column and 4th row 3rd column respectively. Therefore, the direction will be:

= N->N->S->E->E

For Part 3:

Robot A needs to collect both the balls which are in the 3rd-row 4th column and 2nd row 5th column respectively. Robot B needs to collect a hat and a ball which are in the 5th row and 2nd column & 4th row 3rd column respectively. Therefore, the directions will be:

= E->E->N

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The function f(x) is the linear and the function g(x) is the exponential. Then the equations are f(x) = 6x and g(x) = 3(2)ˣ.

A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.

The functions f(x) and g(x).

The table is shown below.

Let the function f(x) be the linear function and the function g(x) be the exponential. Then we have

Then the function f(x) will be

f(x) = mx + c

Then we have

12 = 2m + c

6 = m + c

Then we have

m = 6 and c = 0

Then the equation will be

f(x) = 6x

Then the function g(x) will be

g(x) = abˣ

Then we have

48 = ab⁴

24 = ab³

We have

a = 3 and b = 2

Then the function g(x) will be

g(x) = 3(2)ˣ

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The inequality could be used to find the greatest number of people, p, that can attend is  3.5p + 5p ≤ 300.

Here the inequality is that the sum of the cost of rentals and food which is represented by 3.5p and 5p, respectively, must be less than or equal to $300. By solving the inequality we can determine the maximum number of people that can attend the party while staying within Xian's budget.

To solve the inequality, we first subtract 5p from both sides to isolate the 3.5p term. This results in 3.5p≤300-5p. Then we divide both sides by 3.5 to isolate p, which yields p≤85.71. Since we can't have a fractional number of people, we can determine the maximum number of 85  people that can attend the party.

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Step-by-step explanation:

Okay so, let's turn these into decimals first (rounded to nearest 2 thousandths).

2/3 = 0.66666 (repeating), to the nearest 2 thousandths would be 0.66.

-2 1/4 = -9/4 = -2.25

-1 1/2 = -3/2 = -1.5

then we set up the problem

0.66 × -2.25 × -1.5 = 2.2275 rounded 2.22 as an improper fraction 111/50 and that cannot be simplified any smaller.

Answer:

13 units

Step-by-step explanation:

absolute value helps but

itd just be 7-(-6) = 13

The distance between the point (5,12) and the line y = 5x + 12 is 4.90 units

If a point P with the coordinates (x₁, y₁), and we need to know its distance from the line represented by ax + by + c = 0

Then the distance of a point from the line is given by the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

Given: the point (5,12) and the line y = 5x + 12. The line can be written as

5x-y+12 = 0. Thus:

x₁ = 5, y₁ = 12, a = 5, b = -1, c = 12. Substitute these into the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

d = (5×5 + (-1×12) + 12) / √(5² + (-1)²)

d = 25/√26 = 4.90 units

Therefore, the distance between the point and the line is 4.90 units. Option D is the answer

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The length of the flat-screen television is approximately 40.01 inches.

Let's assume that the height of the flat-screen television is "h" inches.

From the problem statement, we know that the length of the screen is 175% of its height.

Mathematically, we can write:

Length = 1.75 x Height

We can substitute the value of "h" in this equation to find the length of the screen:

Length = 1.75 x h

Now, we also know that the diagonal length of the screen is 40 inches. Using the Pythagorean, we can write:

(Length)² + (Height)² = (Diagonal)²

Substituting the values we have, we get:

(1.75h)² + h² = (40)²

Expanding and simplifying:

3.0625h² = 1600

Dividing both sides by 3.0625:

h² = 522.24

Taking the square root of both sides (and ignoring the negative root since we're dealing with lengths):

h = 22.86 inches

Now we can use the equation we derived earlier to find the length:

Length = 1.75 x h

Length = 1.75 x 22.86

Length = 40.01 inches (rounded to two decimal places)

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Answer:

\( \boxed{ \tt{0}}\)

Step-by-step explanation:

\(if \: mº - {n}^{2} \: for \: m = 2 \: and \: n = -1. \\ {2}^{0} - ( { - 1)}^{2} = 1 - (1) = 0\)

The slope of line e is -8/7, which represents a proper fraction

The slope of line e, which is perpendicular to line d, can be determined using the concept that the slopes of perpendicular lines are negative reciprocals of each other.

First, let's find the slope of line d using the given points (10, 8) and (2, 1). The slope (m) is calculated using the formula:

m = (y2 - y1) / (x2 - x1)

Plugging in the values, we have:

m = (1 - 8) / (2 - 10)

= (-7) / (-8)

= 7/8

Since line e is perpendicular to line d, its slope will be the negative reciprocal of 7/8. The negative reciprocal is obtained by flipping the fraction and changing its sign. Therefore, the slope of line e is -8/7.

Hence, the slope of line e is -8/7, which represents a proper fraction.

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Answer:

-5x-12

Step-by-step explanation:

Given f(x) = -5x+3, to get f(x+3), we are going to replace x in f(x) with x+3 as shown;

f(x) = -5x+3

f(x+3) = -5(x+3)+3

f(x+3) = -5x-15+3

f(x+3) = -5x-12

Hence the function f(x+3) is -5x-12

Answer:

f(x) = 3 cos  (2Pi / period value ; x  )+ 2

or see answer using 2 as the period see answer in bold below.

Step-by-step explanation:

cosine function amplitude of 3 is  A = 3

The period is used to find B

You need to show period value as the denominator and work out from there with 2PI as a function numerator to show as 2pi / period can be a data angle

C is the adding value.

Acos (Bx) + C

A = 3

Bx =  2 pi / period

C = + 2

However f 2 is also the period found

then we just plug in 2 to above formula

f(x) = 3 cos  (2Pi / 2 ; x  )+ 2

f(x) = 3cos (x pi) + 2

Answer:

300

Step-by-step explanation:

120 ÷ 2/5 = 300

Answer:

(a) To find the mean of the data set, sum up all the values and divide by the total number of values.

44 + 44 + 54 + 54 + 65 + 39 + 54 + 44 = 398

Mean = 398 / 8 = 49.75

Rounded to one decimal place, the mean of this data set is 49.8.

(b) To find the median of the data set, i need to arrange the values in ascending order first:

39, 44, 44, 44, 54, 54, 54, 65

The median is the middle value in the sorted data set. In this case, we have 8 values, so the median is the average of the two middle values:

(44 + 54) / 2 = 98 / 2 = 49

Rounded to one decimal place, the median of this data set is 49.0.

(c) To determine the modes of the data set, identify the values that appear most frequently.

In this case, the mode refers to the value(s) that occur(s) with the highest frequency.

From the data set, i see that the value 44 appears three times, while the value 54 also appears three times. Therefore, there are two modes: 44 and 54.