The x-intercept of this line are -1 and 3. What do you notice?

Answer:

The file contains the solution to the question

Answer:

Graph 2

Step-by-step explanation:

We are given the inequality x≤2

First off, with the inequality sign being ≤ rather than <, we know that 2 is also included. This means that x can be equal to 2 or less than 2.

Since 2 is included, we know we are looking for a solid line.

That said, we can eliminate the 1st and 4th graphs because there is a dotted line at 2, meaning that 2 is not included.

Next, based on the inequality sign, we know that values less than 2 satisfy it. So judging by the shaded region on each graph, we see that Graph 2 is the one that satisfies it.

For clarity's sake, one trick you can use is thinking of the inequality sign as an arrow. If it points left, values toward the left should be shaded and vice versa.

Lastly, I'll give you the inequality for each graph.

Graph 1: x<2

Graph 2: x≤2

Graph 3: x≥2

Graph 4: x>2

Hope that helps, let me know if you have any questions!

Answer: 6

Step-by-step explanation:

85-79=6

Answer:

6

Step-by-step explanation:

85-79=6

Answer:

12 + \(4\sqrt{5}\) approximates to 20.944

Step-by-step explanation:

VU - 8 units

UW - 4 units

VW - \(\sqrt{64+16} = \sqrt{80} =4\sqrt{5}\)

12 + 4sqrt(5)

Answer:

6 (2 + √5) units

Step-by-step explanation:

Finding the length of the 3rd side :

*Applying Pythagorean Theorem*

The perimeter :

Answer:

150

Step-by-step explanation:

Increase = New Number - Original Number.

divide the increase by the original number and multiply the answer by 100.

The total number of different signals consisting of flags is 216

Given data ,

The number of different signals consisting of 9 flags that can be made using 3 white flags, 3 red flags, and 3 blue flags can be calculated using combinatorial principles.

There are 3 choices for the top flag (white, red, or blue), 2 choices for the second flag (since we've already used one color for the top flag), and 1 choice for the third flag.

Similarly, there are 3 choices for the fourth flag, 2 choices for the fifth flag, and 1 choice for the sixth flag. Finally, there are 3 choices for the seventh flag, 2 choices for the eighth flag, and 1 choice for the ninth flag.

Using the multiplication principle, we can multiply the number of choices at each step to get the total number of different signals:

3 × 2 × 1 × 3 × 2 × 1 × 3 × 2 × 1 = 3! × 3! × 3!

where "!" represents the factorial operation, which is the product of all positive integers up to a given number.

So, the total number of different signals consisting of 9 flags that can be made using 3 white flags, 3 red flags, and 3 blue flags is:

3! × 3! × 3! = 6 × 6 × 6 = 216

Hence , the number of signals is 216

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Answer:b

Step-by-step explanation:

Step-by-step explanation:

For problems 1 through 15, evaluate the function at the given x value.

1. f(5) = 2(5) − 1 = 9

2. f(3) = 3² − 3(3) − 1 = -1

3. f(0) = 2(0) + 5 = 5

So on and so forth.

Then, match each answer with the corresponding letter.

The answer to #1 was 9.  9 corresponds to the letter A.

The answer to #2 was -1.  -1 corresponds to the letter C.

The answer to #3 was 5.  5 corresponds to the letter P.

Finally, write each letter with its corresponding problem number.

So everywhere you see a 1, write A.

Everywhere you see a 2, write C.

Everywhere you see a 3, write P.

Continue until every blank has a letter and the problem is solved.

Answer:

For problems 1 through 15, evaluate the function at the given x value.

1. f(5) = 2(5) − 1 = 9

2. f(3) = 3² − 3(3) − 1 = -1

3. f(0) = 2(0) + 5 = 5

So on and so forth.

Step-by-step explanation:

Answer:

17 is the answer

Step-by-step explanation

Answer:

17

Step-by-step explanation:

This is order of operation so you use bidmas (brackets, indicies,  division /multiplacation, subtraction/addition). You go from left to right so if there is both a multiplication factor in your equation you go from left to right.

37 - 6 * 4 + 32 / 8

= 37 - 24 + 32/8

= 37 - 24 + 32/8

= 37 - 24 + 4

= 13+4

= 17

Answer:

(48, 3), (80, 5), (160, 10)

SOLUTION

The given data set is

The mean of the data is

The standard deviation is calculated using

Substituting the data gives

Therefore the standard deviation is 8.333

Answer:

\(d = 9.2\)

Step-by-step explanation:

Given

Points: (-2,-2) and (0,7)

Required

Determine the distance between them.

Distance is calculated as thus:

\(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

Where:

\((x_1,y_1) = (-2,-2)\)

\((x_2,y_2) = (0,7)\)

So, we have:

\(d = \sqrt{(0 - (-2))^2 + (7 - (-2))^2}\)

\(d = \sqrt{(0 +2)^2 + (7 +2)^2}\)

\(d = \sqrt{2^2 + 9^2}\)

\(d = \sqrt{4 + 81}\)

\(d = \sqrt{85}\)

\(d = 9.2\) --- Approximated

The function g(x) is a discrete function. It is continuous between -7 to -2, -2 to 3, and 3 to 8. And the open circle at -7, -2, 3, and 8. And the jump of the g(x) is 4 units after every interval.

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

\(g(x) = \left\{\begin{matrix} \ \ \ \ 6, -7 < x < -2\\\ \ \ 2, -2 < x < 3\\-2, 3 < x < 8\\\end{matrix}\right.\)

The function g(x) is a discrete function. It is continuous between -7 to -2, -2 to 3, and 3 to 8. And the open circle at -7, -2, 3, and 8.

And the jump of the g(x) is 4 units after every interval.

The graph is shown below.

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Answer:

Step-by-step explanation:

I got 100% on this test

The margin of error for a survey with a sample size of 6400 and a 95% confidence level is approximately 1.6%.

Confidence level is a statistical concept that measures the degree of certainty or reliability associated with an estimate, such as the mean, proportion, or regression coefficient, derived from a sample of data.

The margin of error (ME) for a survey depends on several factors, including the size of the sample, the level of confidence desired, and the population size (if applicable). Assuming a 95% confidence level, a sample size of 6400, and no information about the population size, the formula for calculating the margin of error is:

ME = 1.96 × √[(p × q) / n]

where:

1.96 is the z-score associated with a 95% confidence level

p is the estimated proportion of the population that has the characteristic of interest (this is usually unknown and is typically replaced with 0.5 to get the maximum possible margin of error)

q is 1 - p

n is the sample size

Assuming a conservative estimate of p = 0.5, we have:

ME = 1.96 × √[(0.5 × 0.5) / 6400]

≈ 0.016 or 1.6%

Therefore, the margin of error for a survey with a sample size of 6400 and a 95% confidence level is approximately 1.6%. This means that if the survey were conducted multiple times using the same sample size and methodology, the results would likely differ by no more than 1.6% in either direction (plus or minus) from the true population value.

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

\( \large \sf \underline{Problem:}\)

Its volume V. If r varies directly as s and inversly as t, r=27, when s=18 and t=2 find:

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

\( \large \sf \underline{Answers:}\)

\( \qquad \quad \huge \sf{1. r= 27} \\ \\ \qquad \huge \sf{2. s= 2 } \\ \\ \qquad \quad \huge \sf{3. t = 18} \\ \\ \qquad \huge \sf{4. r = 6 } \\ \\ \qquad \quad \huge \sf{5. s = 10}\)

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

\( \large \sf \underline{Solution:}\)

\( \large\bold{r=\frac{ks}{t}}\:\:,\:\:\sf s=\frac{rt}{k}\:\:,\:\:\sf t=\frac{ks}{r}\:\:,\:\:\sf k=\frac{rt}{s}\)

Given:

\( \begin{gathered}\begin{aligned}&\sf k=\frac{rt}{s}\\&\sf k=\frac{27(2)}{18}\\&\sf k=\frac{54}{18}\\&\sf k=3\end{aligned}\end{gathered} \)

Use k = 3 to solve the following

Number 1:

\(\begin{gathered}\begin{aligned}&\sf r=\frac{ks}{t}\\&\sf r=\frac{\cancel3\times 27}{\cancel3}\\&\underline{\bold{\pmb{r=27}}}\end{aligned}\end{gathered} \)

Number 2:

\(\begin{gathered}\begin{aligned}&\sf s=\frac{rt}{k}\\&\sf s=\frac{\cancel3\times 2}{\cancel3}\\&\underline{\bold{\pmb{s=2}}}\end{aligned}\end{gathered} \)

Number 3:

\(\begin{gathered}\begin{aligned}&\sf t=\frac{ks}{r}\\&\sf t=\frac{3\times 6}{1}\\&\underline{\bold{\pmb{t=18}}}\end{aligned}\end{gathered} \)

Number 4:

\(\begin{gathered}\begin{aligned}&\sf r=\frac{ks}{t}\\&\sf r=\frac{3\times \cancel4}{\cancel2}\\&\sf r=3\times 2\\&\underline{\bold{\pmb{r=6}}}\end{aligned}\end{gathered} \)

Number 5:

\(\begin{gathered}\begin{aligned}&\sf s=\frac{rt}{k}\\&\sf s=\frac{\cancel6 \times 5}{\cancel3}\\&\sf s=2\times 5\\&\underline{\bold{\pmb{s=10}}}\end{aligned}\end{gathered} \)

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

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\(\qquad\qquad\huge\underline{{\sf Answer}}\)

According to the question :

\(\qquad \sf  \dashrightarrow \:r \propto s\)

and

\(\qquad \sf  \dashrightarrow \:r \propto \dfrac{1}{t} \)

Now, by both equations we can infer that ~

\(\qquad \sf  \dashrightarrow \:r \propto \dfrac{s}{t} \)

now, assume k to be a proportionality constant

\(\qquad \sf  \dashrightarrow \:r = k \cdot \dfrac{s}{t} \)

Now, plug in the value of given values, to find value of k ~

\(\qquad \sf  \dashrightarrow \:27 = \dfrac{18}{2} \cdot k\)

\(\qquad \sf  \dashrightarrow \:27 = 9{} k\)

\(\qquad \sf  \dashrightarrow \:k = 27 \div 9\)

\(\qquad \sf  \dashrightarrow \:k = 3\)

Now, let's evaluate the required values ~

\(\qquad \sf  \dashrightarrow \:r = 3 \cdot \dfrac{s}{t} \)

\(\qquad \sf  \dashrightarrow \:r = 3 \cdot \dfrac{27}{ 3} \)

\(\qquad \sf  \dashrightarrow \:r = 27\)

\(\qquad \sf  \dashrightarrow \:r= 3 \cdot \dfrac{s}{t} \)

\(\qquad \sf  \dashrightarrow \:3= 3 \cdot \dfrac{s}{2} \)

\(\qquad \sf  \dashrightarrow \:{s}{} = \dfrac{3 \times 2}{3} \)

\(\qquad \sf  \dashrightarrow \:s = 2\)

\(\qquad \sf  \dashrightarrow \:r= 3 \cdot \dfrac{s}{t} \)

\(\qquad \sf  \dashrightarrow \:1= 3 \cdot \dfrac{6}{t} \)

\(\qquad \sf  \dashrightarrow \:t = 6\cdot3\)

\(\qquad \sf  \dashrightarrow \:t = 18\)

\(\qquad \sf  \dashrightarrow \:r = 3 \cdot \dfrac{s}{t} \)

\(\qquad \sf  \dashrightarrow \:r = 3 \cdot \dfrac{4}{2} \)

\(\qquad \sf  \dashrightarrow \:r = \dfrac{12}{2} \)

\(\qquad \sf  \dashrightarrow \:r =6\)

\(\qquad \sf  \dashrightarrow \:r = 3 \cdot \dfrac{s}{t} \)

\(\qquad \sf  \dashrightarrow \:6= 3 \cdot \dfrac{s}{5} \)

\(\qquad \sf  \dashrightarrow \:s = \dfrac{6 \times 5}{3} \)

\(\qquad \sf  \dashrightarrow \:s = 10\)

The function that would have the greatest value at x = 16 include the following: B. y = x² - 17x + 182.

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

In this exercise, we would determine the corresponding output value for this function of y based on the x-value (x = 16) in simplified form as follows;

\(y = 10^{16}\)

y = 10,000,000,000,000,000.

y = x² - 17x + 182

y = 16² - 17(16) + 182

y = 256 - 272 + 182

y = 166.

\(y = 1.17^x\\\\y = 1.17^{16}\)

y = 12.330304108137675851908392069373.

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Answer:

Dilacey took a loan of $2800

Step-by-step explanation:

P=(Simple Interest×100)/R×T

P=$420×100/10×1½

P=$42000/15

P=$2800

Answer:

(A)

Step-by-step explanation:

The survey follows of women's height a normal distribution.

The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.

The new height requirements would be 57.7 to 68.6 inches

The given parameters are:

\mathbf{\mu = 63.5}μ=63.5 --- mean

\mathbf{\sigma = 2.5}σ=2.5 --- standard deviation

(a) Percentage of women between 58 and 80 inches

This means that: x = 58 and x = 80

When x = 58, the z-score is:

\mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

This gives

\mathbf{z_1= \frac{58 - 63.5}{2.5}}z

1

=

2.5

58−63.5

\mathbf{z_1= \frac{-5.5}{2.5}}z

1

=

2.5

−5.5

\mathbf{z_1= -2.2}z

1

=−2.2

When x = 80, the z-score is:

\mathbf{z_2= \frac{80 - 63.5}{2.5}}z

2

=

2.5

80−63.5

\mathbf{z_2= \frac{16.5}{2.5}}z

2

=

2.5

16.5

\mathbf{z_2= 6.6}z

2

=6.6

So, the percentage of women is:

\mathbf{p = P(z < z_2) - P(z < z_1)}p=P(z<z

2

)−P(z<z

1

)

Substitute known values

\mathbf{p = P(z < 6.6) - P(z < -2.2)}p=P(z<6.6)−P(z<−2.2)

Using the p-value table, we have:

\mathbf{p = 0.9999982 - 0.0139034}p=0.9999982−0.0139034

\mathbf{p = 0.9860948}p=0.9860948

Express as percentage

\mathbf{p = 0.9860948 \times 100\%}p=0.9860948×100%

\mathbf{p = 98.60948\%}p=98.60948%

Approximate

\mathbf{p = 98.61\%}p=98.61%

This means that:

The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.

So, many women (outside this range) would be denied the opportunity, because they are either too short or too tall.

(b) Change of requirement

Shortest = 1%

Tallest = 2%

If the tallest is 2%, then the upper end of the shortest range is 98% (i.e. 100% - 2%).

So, we have:

Shortest = 1% to 98%

This means that:

The p values are: 1% to 98%

Using the z-score table

When p = 1%, z = -2.32635

When p = 98%, z = 2.05375

Next, we calculate the x values from \mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

Substitute \mathbf{z = -2.32635}z=−2.32635

\mathbf{-2.32635 = \frac{x - 63.5}{2.5}}−2.32635=

2.5

x−63.5

Multiply through by 2.5

\mathbf{-2.32635 \times 2.5= x - 63.5}−2.32635×2.5=x−63.5

Make x the subject

\mathbf{x = -2.32635 \times 2.5 + 63.5}x=−2.32635×2.5+63.5

\mathbf{x = 57.684125}x=57.684125

Approximate

\mathbf{x = 57.7}x=57.7

Similarly, substitute \mathbf{z = 2.05375}z=2.05375 in \mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

\mathbf{2.05375= \frac{x - 63.5}{2.5}}2.05375=

2.5

x−63.5

Multiply through by 2.5

\mathbf{2.05375\times 2.5= x - 63.5}2.05375×2.5=x−63.5

Make x the subject

\mathbf{x= 2.05375\times 2.5 + 63.5}x=2.05375×2.5+63.5

\mathbf{x= 68.634375}x=68.634375

Approximate

\mathbf{x= 68.6}x=68.6

Hence, the new height requirements would be 57.7 to 68.6 inches

Answer:

the event is odds against an event of the 19 to 12 is probability is the 19

The probability of occurring the event is 12/31.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

We know if the odds against an event is a : b then the probability of occurring the event is b/(a + b).

Given, The odds against an event are 19 to 12.

∴ The probability of occurring the event is 12/(19 + 12) = 12/31.

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The standard error represents the average deviation of the sample means from the true population mean. Rounding this value to four decimal places, the standard error of X¯¯¯ is approximtely 0.6500 mpg.

A smaller standard error indicates that the sample means are more likely to be close to the population mean.To calculate the standard error of X¯¯¯, the mean from a random sample of 25 fill-ups by one driver, we can use the formula:

Standard Error (SE) = σ / sqrt(n),

where σ is the standard deviation and n is the sample size.

In this case, the standard deviation (σ) is given as 3.25 mpg, and the sample size (n) is 25.

Plugging in these values into the formula, we have:

SE = 3.25 / sqrt(25).

Calculating the square root of 25, we get:

SE = 3.25 / 5.

Performing the division, we find:

SE ≈ 0.65.

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Answer:

60°

Step-by-step explanation:

they are equal.....

The significance of the quoted text is to illustrate the less privileged in an overwhelmingly crowded and disordered chronological reality.

Quote means to cite something as a form of proof. It has several other senses as a verb and a noun. It should be noted that to quote something or someone is to repeat the exact words they said or to recite the exact words written in a book.

Great speakers often quote other inspiring people when making speeches. When you quote, you include the words and ideas of others in your text exactly as they have expressed them.

You signal this inclusion by placing quotation marks (“ ”) around the source author's words and providing an in-text citation after the quotation.

In this case, the significance of the quoted text is to illustrate the less privileged in an overwhelmingly crowded and disordered chronological reality. A quotation is the repetition of a sentence, phrase, or passage from speech or text that someone has said or written.

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Given the frequency and number of possible outcomes, the number of days that must pass before it becomes probable that Janice will have had to pick up lunch at least once is 8.

Note that the probability of any of the staff at the office picking the food is 1/8.

Even if She does not pick up lunch on her first day or second, the number of days that must pass to make sure that Janice picks up lunch AT LEAST once is 1 in 8 days.

The formula to compute the probability of an event is equivalent to the ratio of favorable outputs to the total number of outputs. It is to be noted that probabilities always range between 0 and 1.

The expression is given as:

P (E) = f/O; where

P(E) is the Probability of an event E happening;

f =  The number of possible outcomes for an event (frequency)

n = Total number of outputs that are likely

Hence,

P(E) = 1/8

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Answer: To find the absolute value of the expression 1 1/2 - 2/31, we first need to convert the mixed number 1 1/2 into an improper fraction.

1 1/2 can be written as (2 * 1 + 1) / 2, which is equal to 3/2.

Now we can subtract 2/31 from 3/2:

3/2 - 2/31 = (3 * 31 - 2 * 2) / (2 * 31) = (93 - 4) / 62 = 89/62.

The absolute value of a fraction is the positive value without considering its sign. So, the absolute value of 89/62 is 89/62.

Therefore, the absolute value of 1 1/2 - 2/31 is 89/62.

Answer:

Irrational

Step-by-step explanation:

Prime numbers are numbers that only have the factors of one and itself. Rational numbers include all numbers except for non terminating, non repeating decimals. An imaginary number is a number that is expressed in terms of the square root of a negative number (usually the square root of −1, represented by i or j).

The length of the side P is 15 cm. And the right option is C.

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides.

To calculate the length of side P we use Pythagoras theorem's formula

Pythagoras formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the right option is C 15 cm.

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Answer:

The answer toy our problem is, The maximum number of days by which the completion of work can be delayed is 15.

Step-by-step explanation:

We are given that the penalty amount paid by the construction company from the first day as sequence, 4000, 5000, 6000, ‘ and so on ‘. The company can pay 165000 as penalty for this delay at maximum that is

 \(S_{n}\)​ = 165000.

Let us find the amount as arithmetic series as follows:

4000 + 5000 + 6000

The arithmetic series being, first term is \(a_{1}\) = 4000, second term is \(a_{2}\) = 5000.

We would have to find our common difference ‘ d ‘ by subtracting the first term from the second term as shown below:

\(d = a_{2} - a_{1} = 5000 - 4000 = 1000\)

The sum of the arithmetic series with our first term ‘ a ‘ which the common difference being, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) ( ‘ d ‘ being the difference. )

Next we can substitute a = 4000, d = 1000 and \(S_{n}\) = 165000 in “ \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) “ which can be represented as:

Determining, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\)

⇒ 165000 = \(\frac{n}{2}\) [( 2 x 4000 ) + ( n - 1 ) 1000 ]

⇒ 2 x 165000 = n(8000 + 1000n - 1000 )

⇒ 330000 = n(7000 + 1000n)

⇒ 330000 = 7000n + \(1000n^2\)

⇒ \(1000n^2\) + 7000n - 330000 = 0

⇒ \(1000n^2\) ( \(n^2\) + 7n - 330 ) = 0

⇒  \(n^2\) + 7n - 330 = 0

⇒ \(n^2\) + 22n - 15n - 330 = 0

⇒ n( n + 22 ) - 15 ( n + 22 ) = 0

⇒ ( n + 22 )( n - 15 ) = 0

⇒ n = -22, n = 15

We need to ‘ forget ‘ the negative value of ‘ n ‘ which will represent number of days delayed, therefore, we get n=15.

Thus the answer to your problem is, The maximum number of days by which the completion of work can be delayed is 15.