solve the following for each N, and appropriate p:a. In a group of 10 exactly 3 are fail the class.b. In a group of 8 at least 7 can pass the class.

Answer for 1:

19

Answer for 2:

vertical

Answer for 3:

supplementary

Answer for 4:

96°

Answer for 5:

24°

Answer for 6:

120°

Explanation for All Questions:

I'm an Ace, 80% to Genius. Trust me

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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Given:

a.) He has 12 1/2 cups of milk.

b.) The chef has 3 1/2 more cups of broth than milk.

Step 1: Since it is said that the chef has 3 1/2 more cups of broth than milk, and he has 12 1/2 cups of milk, we will be adding 3 1/2 and 12 1/2 to get the actual number of cups of broth.

We get,

In adding mixed numbers, we add separately the whole numbers and fractions and add them together later on.

Therefore, the chef has 16 cups of broth.

Step 2: Let's now determine the remaining cups of broth after using 14 1/2 cups to make soup. We will be subtracting the current 16 cups of broth by 14 1/2 cups for the soup.

We get,

Let's first convert them into similar fractions before subtracting.

Let's now proceed in subtracting them,

Therefore, the chef will have a remaining 1 1/2 cups of broths after using 14 1/2 cups for the soup.

Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.

2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.

3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.

4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.

5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.

6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.

Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

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3. If triangle ABC was reflected over the x-axis, what would be the coordinate of B'?

When you reflect over the x-axis, you will flip the sign for the y-coordinate. If you reflect over the y-axis, you will flip the sign for the x-coordinate.

In this case, you are reflecting point B (4 , 3) over the x-axis, which will flip the x-coordinate sign to B' (-4 , 3)

D) (-4 , 3)

2. Rotate this figure 270 degrees clockwise

Clock-wise mean you are rotating turning right. 180° is half way, and so it will be D), as 180° is the 3rd option, and then a extra 90° will become D).

Answer:

(4, -3)

last option

Step-by-step explanation:

If a point is reflected over the x-axis then (x, y) → (x, -y)

B = (4, 3)

Therefore, B' = (4, -3)

The original arrowhead is pointing south (down).

If the arrowhead is rotated 270° clockwise, then it will point to the east (right).  So the solution is the last option.

Step-by-step explanation:

p = 2(L+W)

98 < 2(x-2cm + 3x+5cm)

98 < 2x - 4 + 6x + 10

98 < 2x + 6x -4 +10

98 < 8x + 6........the inequality

98 - 6 < 8x

92 < 8x

11.5 < x.......the value of x

Answer:

\(5^{-8}\)

Step-by-step explanation:

\(\sf \boxed{\dfrac{a^{m}}{a^n}=a^{m-n}}\)

  \(\sf \dfrac{5^{-4}}{5^{4}}=5^{-4-4}\)

         \(= 5^{-8}\)

Answer:

3/40

Step-by-step explanation:

Can't simplify

Answer: 3/40

Step-by-step explanation:

Answer:

1/52

Step-by-step explanation:

The probability that the card is a 4 in a pack of cards is 1 /13.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given, A card is selected from a pack of 52 cards. A favorable outcome is getting 4 since there are four 4 in a pack of cards. Thus,

When a card is selected from a pack of 52 cards the number of possible outcomes is 52 i.e., the sample space contains 52 elements

Therefore there are 52 points in the sample space.

Let E be the event in which the card drawn is an ace.

Since there are 4 aces in a pack of 52 cards n(E)=4

∴P(E)=  \(\frac{Totalnumberofpossibleoutcomes}{Numberofoutcomesfavourableto}\)

E = \(\frac{n(S)}{n(E)}\)

E = 4/52 = 1/13

​Therefore, In a deck of cards, there is a 1 in 13 chance that the card is a 4.

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​

Answer:

1. C

2. A

Step-by-step explanation:

Step 1: Write equation

3x - 1 = 7

3x = 8

Step 2: Use 1st equation and solve

3x = 8

x = 8/3

Step 3: Use 2nd equation and solve

3x = 8

x = 8/3

Both equations have equivalent solutions and the 2nd equation is the simplified version of the 1st.

Answer:

27

Step-by-step explanation:

Hi there!

We are given this set of data:

22, 15, 31, 40, 27

And we want to find the average (or the mean) of the set

To find the mean, we add up all of the values of the data set and then divide it by how many pieces of data we have

So first, add 22, 15, 31, 40 and 27 together

22+15+31+40+27=135

We have 5 pieces of data, so divide 135 by 5

135/5=27

The mean is 27

Hope this helps!

\(\boxed{\large{\mathbf{\blue{ANSWER~:) }}}}\)

we know that,

\(\boxed{\sf{mean=\dfrac{sum ~of~ data}{no~ of~ data } }}\)

According to the question,

Therefore,

the average (mean) of the given set of data.(22,15,31,40,27) is 27.

Answer:

D. 63

Step-by-step explanation:

First, add 6 to both sides:

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

\(\frac{x}{7}\) = 9

Multiply each side by 7

x = 63

So, the correct answer is D. 63

Simplify 6⋅ (x+3)

Apply the distributive property.

6x+6⋅3=x⋅76x+6⋅3=x⋅7

Multiply 66 by 33.

6x+18=x⋅76x+18=x⋅7

Move 77 to the left of xx.

6x+18=7x

Move all terms containing x to the left side of the equation.

subtract 7x7x from both sides of the equation.

6x+18−7x=06x+18-7x=0

Subtract 7x7x from 6x6x.

−x+18=0-x+18=0

Subtract 1818 from both sides of the equation.

−x=−18-x=-18

Multiply each term in −x=−18-x=-18 by −1

Multiply −1-1 by −1-1.

1x=(−18)⋅−11x=(-18)⋅-1

Multiply xx by 11.

x=(−18)⋅−1x=(-18)⋅-1

Multiply−18-18 by −1-1.

x=18

Answer:

Step-by-step explanation:

Exponential function is:

If we consider the time difference in years as x and the initial population as a, then we get:

Find the value of b:

The equation we got is:

Here we have y- population after x years since 2010, x - the number of years since 2010 and 1.009 is the population growth rate.

General equation

Total years(x)=2020-2010=10

Now

So.our equation

The required difference will be;

⇒ 6

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The difference between a two-digit number and the number obtained by interchanging the digits is 54.

And, The ratio between the digits of the number is 1 : 3.

Now,

Since, The number is greater than the number obtained in reversing the digits and the ten's digit is greater than the unit digit.

Let the unit and ten's place are x and 3x.

Hence, We get;

⇒ (10 × 3x + x) - (10x + 3x) = 54

⇒ 31x - 13x = 54

⇒ 18x = 54

⇒ x = 3

Thus, The required difference,

⇒ (3x + x) - (3x - x)

⇒ 4x - 2x

⇒ 2x

⇒ 2 × 3

⇒ 6

Therefore, The required difference will be;

⇒ 6

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The original amount is $92.202.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is primarily used to compare and determine ratios and is represented by the symbol %.

Given:

Total amount = 83.82

rate of increase = 10%

So, the original amount

= 83.82 + 83.82 x 0.1

= 83.82 + 8.382

= $92.202

Hence, the original amount is $92.202.

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Answer: 14 feet

Step-by-step explanation:

Answer: 12 feet

Step-by-step explanation: The longest flagpole that could be shipped in a box is approximately 12 ft .

Answer:

(-1, 7)

Step-by-step explanation:

2 unites left would movie from 1 to -1.

1 unit down would move from 8 to 7.

Answer:

The answer is -1, 7

Step-by-step explanation:

I did this type of math last year

The main idea behind statistical inference is that through the use of sample data, we are able to draw conclusions about the population from which the data was drawn (option c).

Statistical inference allows us to make inferences and draw conclusions about a larger population based on the analysis of a smaller representative sample.

By collecting data from a sample, we can use statistical methods to analyze and summarize the information. These methods include estimating population parameters, testing hypotheses, and making predictions.

The key assumption underlying statistical inference is that the sample is representative of the larger population, allowing us to generalize the findings to the population as a whole.

Statistical inference provides a way to make reliable and informed decisions, identify patterns and relationships, and make predictions about future observations based on the available data. It allows researchers, scientists, and decision-makers to make evidence-based conclusions and draw meaningful insights from limited observations.

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Answer:

1 unit

Step-by-step explanation:

- 1 1/2 - (- 2 1/2)

= 1 unit

The equation 3x₁ + 5x₂ = 30 intersects the x₁-axis at point D (10, 0) and the x₂-axis at point C (0, 6). Option B (0, 8) is not an intercept on the x₂-axis. Option C (6, 10) is not an intercept on the x₁-axis. The correct answer is option D (10, 0) as the x₁-axis intercept.

The equation given is 3x₁ + 5x₂ = 30. To find the axis intercept, we need to determine the points at which the line intersects the x₁ and x₂ axes. To find the x₁-axis intercept, we set x₂ = 0 and solve for x₁ 3x₁ + 5(0) = 30 3x₁ = 30
x₁ = 10

So, the x₁-axis intercept is (10, 0) which corresponds to point D in the given options. To find the x₂-axis intercept, we set x₁ = 0 and solve for x₂: 3(0) + 5x₂ = 30 5x₂ = 30 x₂ = 6 Therefore, the x₂-axis intercept is (0, 6) which corresponds to point C in the given options. To summarize, the equation 3x₁ + 5x₂ = 30 intersects the x₁-axis at point D (10, 0) and the x₂-axis at point C (0, 6).

In the given options, option A (10, 6) is not an intercept on either axis. Option B (0, 8) is not an intercept on the x₂-axis. Option C (6, 10) is not an intercept on the x₁-axis. The correct answer is option D (10, 0) as the x₁-axis intercept.

Remember, the x₁-axis intercept is found by setting x₂ = 0, and the x₂-axis intercept is found by setting x₁ = 0 in the equation.The correct answer is option D

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The statement is false. The existence of a scalar α such that αv is an eigenvector of a does not imply that v itself is an eigenvector of a.

A group of numbers built up in a rectangular array with rows and columns. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.

The statement is false. An eigenvector is a non-zero vector that, when multiplied by a matrix, produces a scalar multiple of itself. In other words, if v is an eigenvector of a matrix A, then Av = λv, where λ is the corresponding eigenvalue.

The statement suggests that if a is an nn matrix (presumably an n x n matrix), and a scalar α exists such that αv is an eigenvector of a, then v must also be an eigenvector of a. However, this is not necessarily true.

Let's consider a counterexample to demonstrate this. Suppose we have the 2x2 identity matrix I:

I = [[1, 0],

    [0, 1]]

In this case, any non-zero vector v will satisfy the condition αv = v for α = 1. However, not all non-zero vectors v are eigenvectors of I. In fact, the only eigenvectors of I are [1, 0] and [0, 1] with corresponding eigenvalues of 1.

Therefore, the statement is false. The existence of a scalar α such that αv is an eigenvector of a does not imply that v itself is an eigenvector of a.

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Answer:

\(\frac{14}{9}, \sqrt{7}, \sqrt{13}, \sqrt{40}, 4^3\)

Step-by-step explanation:

Given

\(4^3, \sqrt{40}, \sqrt{13}, \frac{14}{9}, \sqrt 7\)

Required

Order from least to greatest

First, we solve for each expression

\(4^3 = 64\)

\(\sqrt{40} = 6.32\)

\(\sqrt{13} = 3.61\)

\(\frac{14}{9} = 1.56\)

\(\sqrt{7} = 2.66\)

From least to greatest, we have:

\(1.56, 2.66. 3.61, 6.32, 64\)

Hence, the list is:

\(\frac{14}{9}, \sqrt{7}, \sqrt{13}, \sqrt{40}, 4^3\)

Answer:

$0.99

Step-by-step explanation:

A thin blue marker = $0.80

A bright yellow highlighter = $0.74

First, find the total cost of these two products. Add the costs together:

0.80 + 0.74 = 1.54

Anna has $2.53 in all. Subtract 1.54 from 2.53:

2.53 - 1.54 = $0.99

Anna will have $0.99 left.

~

Answer:  the answer i actually A  $44,840.00

Step-by-step explanation:  because its asking u to subtract police/detective and an EMT so 76,820-31980= 44,840.00

sorry if im wrong (:

Answer:

The missing frequencies are x = 8 and y = 43.

Step-by-step explanation:

Median Value =70

Then the median Class =60-80

Let the missing frequencies be x and y.

Given: Total Frequncy = 200 , Median = 46

\(\left|\begin{array}{c|ccccccc}Value&0-20&20-40&40-60&60-80&80-100&100-120&120-140\\Frequency&12&30&x&66&y&27&14\\$Cumu.Freq&12&42&42+x&108+x&108+x+y&135+x+y&149+x+y\end{array}\right|\)

From the table

\(\sum f_i =149+x+y\)  

Here, n = 200

n/2 = 100

Lower Class Boundary of the median class, l=60

Frequency of the median class(f) =66

Cumulative Frequency before the median class, f=42+x

Class Width, h=10

\(Median = l + \dfrac{\dfrac{n}{2} - c.f }{f} \times h\)

\(70 = 60+ \dfrac{100- 42+x }{66}\times 10\\70 = 60+ \dfrac{58+x }{66}\times 10\\70-60=\dfrac{58+x }{66}\times 10\\10*66=10(58+x)\\58+x=66\\x=66-58\\x=8\)

200=149+x+y

200=149+8+y

y=200-(149+8)

y=43

Hence, the missing frequencies are x = 8 and y = 43.

By finding out the HCF, we can infer that the maximum number of groups that can be formed will be 32.

The number that divides two or more numbers exactly is said to be the highest common factor (HCF) of those numbers.

Given data:

Number of girls = 128.

Number of boys = 96.

In order to find the maximum number of groups that can be formed, we need to find highest common factor of 96 and 128.

To find HCF, we have to divide each number into it's prime factors.

Prime factors of 128 are 2×2×2×2×2×2×2

Prime factors of 96 are 2×2×2×2×2×3

Out of those two groups (2×2×2×2×2×2×2) and ( 2×2×2×2×2×3), the only thing in common is 2⁵. So, 2⁵ is the highest common factor.

Hence, the maximum number of groups that can be formed is 32.

Now, to find out the number of pupil in each group, we divide the total by 2⁵, so:

128/32 = 4

96/32 = 3

So, there will be 4 girls and 3 boys in each group.

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