A machine in a factory makes 2 1/4 pounds of nails in 1 1/2 hours. At what rate, in
pounds per hour, does the machine make nails? Show your work.

From the given table that represents the population in a small coastal communityfor the period 1997 to 2006, let's answer the following questions.

(a) Average rate of change of the population between 1999 and 2002.

To find the average rate of change, apply the formula below:

Where:

x1 = 1999

x2 = 2002

y1 = the population in 1999 = 1,336

y2 = the population in 2002 = 1,483

Thus, we have:

Therefore, the average rate of change of the population between 1999 and 2002 is

49

(b) What was the average rate of change of the population between 2001 and 2005.

To find the average rate of change, apply the formula:

Where:

x1 = 2001

x2 = 2005

y1 = population in 2001 = 1591

y2 = population in 2005 = 801

Thus, we have:

Therefore, the average rate of change in the population between 2001 and 2005 was -197.5

(c) For what period of time was the population increasing.

From the given table, we can see the table was increasing from 1997 to 2001

The population was increasing from 1997 to 2001

(d) For what period was the population decreasing.

From the table, the population was decreasing from 2002 to 2006

The population was decreasing from 2001 to 2006

ANSWER:

• (a) 49

• (b) -197.5

• (c) 1997 to 2001

• (d) 2001 to 2006

Answer:

See the picture below

Step-by-step explanation:

Answer:

3.456e+12
or

3,456,000,000,000

Step-by-step explanation:

400 x 600 = 240,000

240,000 x 800 = 192,000,000

192,000,000 x 150 = 28,800,000,000

28,800,000,000 x 120 = 3,456,000,000,000

hope this helps you :D

The graph that is hardest to write the transformation using algebraic notation is the second top graph counting from left to right

A graph is a pictorial representation of data

A transformation is a movement that can be represented in a cartesian plane.

There several types of movement involved in transformation, some of them are:

The first top graph counting from the left is a translation to the left.

The first graph at the bottom counting from the left is a translation downwards

The next bottom graph is reflection along x axis and translation downwards

The most difficult which is the second at the top counting from left involves dilation.

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Answer:

0

Step-by-step explanation:

Whole numbers are 0.1.2.3...  Follows that pattern forever.

Answer:

Inline range: 2 ≤ n < 8

Interval range: [ - 2, 8 )

Loop: n = - 2; n < 8;

Step-by-step explanation:

The filled circle means inclusive while outlined circle means exclusive.

Answer:

-2 ≤ x > 8

Step-by-step explanation:

x = a possible number based on the diagram

the black-filled-in dot on the line above the number line indicated that it can either be '≤' or '≥'

the empty-not-filled-in dot means that it can be either '<' or '>'

the '≤' means x can be equal or greater to -2

and the '>' means that x must be less than 8

hope this helps!

Answer:

So the probability of this happening is exactly 1 - it must be true

Step-by-step explanation:

If we calculate modulo(5) for each of the six numbers (the integer remainder after dividing by 5), we will get six values from 0 to 4.

By the pigeonhole principle, since there are 6 numbers and only 5 possible values, at least two must share the same value modulo 5. Pick two of those, say x and y, in which case x mod 5 = y mod 5, therefore (x - y) mod 5 = 0. In other words, their difference is a multiple of 5.

So the probability of this happening is exactly 1 - it must be true

Step-by-step explanation:

I assume, based on what I see, that the solid line is just cos(x), right ?

and we need to find the equation that draws the dotted line, correct ?

the notation is strange, as it seems we need to find a multiplication factor for x in the cos function.

but there is no multiplication factor that moves the cosine wave by pi to the left or to the right (so that the max. happens, where originally the minimum happens, and vice versa).

so, we need to add (or subtract) pi in the cosine function.

the rest is clear :

the normal distance between min. and max. of the cosine function is 2 (between +1 and -1). the target is 4. so we need to multiply by 2.

and since the values of that function have to be between -4 and 0 (instead of -2 and +2), we have to subtract overall 2.

giving us the function :

y = 2×cos(pi + x) + -2

Answer:

32.5

Step-by-step explanation:

What is 25% of 130?

0.25 * 130 = 32.5

Answer: [tex]x=15[/tex]

Step-by-step explanation:

By the consecutive interior angles theorem,

[tex]150+3x-15=180\\\\3x-15=30\\\\3x=45\\\\x=15[/tex]

Answer: [tex]\frac{21}{2}+\frac{\sqrt{41}}{2}, \frac{21}{2}-\frac{\sqrt{41}}{2}[/tex]

Step-by-step explanation:

Let the two numbers be x and y.

[tex]x+y=21 \implies y=21-x\\\\xy=100\\\\\therefore x(21-x)=100\\\\21x-x^2 =100\\\\x^2 -21x+100=0\\\\x=\frac{21 \pm \sqrt{21^2 -400}}{2}=\frac{21}{2} \pm \frac{\sqrt{41}}{2}[/tex]

Answer:

A. y - 2 = 2/3 (x - 0)

Step-by-step explanation:

We can infer that we have sufficient evidence to reject the null hypothesis and that the true mean is significantly lower than 6.7 at 10% of significance if we compare the p value and the significance level given =0.05 and observe that p'.

Hypothesis test: A statistical hypothesis test is a technique for determining if the available data are sufficient to support a specific hypothesis. We can make probabilistic claims regarding population parameters thanks to hypothesis testing.

Data are provided and noted.

X=6.8 display the sample mean

σ= 0.9 show the population's standard deviation.

n= 280 samples taken

μο=6.7 the value that we wish to test should be represented

α=0.1 signify the hypothesis test's level of significance.

The stat would be represented as z. (variable of interest)

p' indicate the test's p value (variable of interest)

Name the prevailing and competing hypothesis

The system of hypothesis must be tested to see if the true mean is below the criteria.

Null hypothesis:  μ ≥ 6.7

Alternative hypothesis: μ < 6.7

Applying a z test to compare the actual mean to the reference value is preferable if the sample size is greater than 30 and we are aware of the population variation. The statistic is given by:

z=(X-μο)/σ[tex]\sqrt{n}[/tex]  ......(1)

z-test: "enables the comparison of group means. One of the most widely used tests, it is used to determine whether the mean is (higher, lower, or not equal) to a given value ".

Calculate the statistic

We can replace in formula (1) the info given like this:

z=(6.8-6.7)/0.9[tex]\sqrt{280}[/tex]

P-value

Since is a one sided test the p value would be:

p'=p(z<0.0066)

We can infer that we have sufficient evidence to reject the null hypothesis and that the true mean is considerably lower than 6.7 at 10% of significance if we compare the p value and the significance level given =0.1 and observe that p'.

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The image of the function after it is vertically stretched is f'(x) = 4|x + 3|

The function is given as

f(x) = |x + 3|

The transformation is given as

Vertical stretch by a factor of 4

This implies that we stretch the function f(x) by a factor of 4

This transformation is represented mathematically as

(x, y) = (x, 4y)

So, we have

f'(x) = 4 * f(x)

So, we have the following equation

f'(x) = 4 * (|x + 3|)

Remove the bracket

So, we have

f'(x) = 4 * |x + 3|

Evaluate the products

So, we have

f'(x) = 4|x + 3|

Hence, the equation of f'(x) is f'(x) = 4|x + 3|

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The correct statement about the function is the y-intercept is (0.71), and 71 represents the starting temperature.

A graph can be described as a pictorial representation of data. A graph has a y-axis and a x-axis. The x-axis in this question represents time and the y-axis is the temperature.

The function shown in the graph is a linear function. This is because the curve is a straight line.  The y-intercept is the point where the line crosses the y-axis. The y-intercept is the value of the data set when x is zero. The y-intercept represents the initial temperature or the starting temperature.

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Answer:

-3

Step-by-step explanation:

We know that,

( + ) × ( + ) = ( + )

( - ) × ( - ) = ( + )

( + ) × ( - ) = ( - )

Accordingly, let us solve the given fraction.

-7 - ( - 4 )

-7 + 4

-3

I will ask my question here

is p(x)

bye :)

For the length to be sides of a triangle, the sum of any two sides triangle must be greater than third side.

Condition is true.

Condition is true.

Condition is true.

The triangle inequality satisfied for the triangle. So length belongs to a side of triangle.

Answer: yes

Since we are measuring bank preference, we want to see the data in order of importance, then, the pareto chart is the most useful graph in this situation

The simplified form of the given expression is option c 1 1/2x - 1 3/4

Given,

The expression; 1/4 (3x - 7) + 3/4x

We have to simplify this expression;

Simplification of expressions;

To simplify a phrase, create an equivalent expression without any terms that are identical. The expression will then be rewritten using the fewest terms feasible.

Then,

1/4 (3x - 7) + 3/4x

= 1/4 × 3x - 1/4 × 7 + 3/4x

= 3/4x - 7/4x + 3/4x

= 6x/4 - 7/4

= 3x/2 - 7/4

= 1 1/2x - 1 3/4

Therefore,

The simplified form of the given expression is option c 1 1/2x - 1 3/4

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According to the combination method, there are 6 ways for the selection to be made if one worker is to be a receptionist, one a secretary, and one a technical typist.

Combinations:

A combination is all about grouping. The number of different groups which can be formed from the available things can be calculated using combinations.

The standard form for calculating the combinations is,

[tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex]

where,

0 ≤ r ≤ n.

This formula is sometimes also called as ncr formula.

Given,

An executive hires 3 office workers from 8 applicants.

Here we need to find how many ways can the selection be made if one worker is to be a receptionist, one a secretary, and one a technical typist.

Here we have to split the problem like the following,

We know that the total number of office workers is 3.

Like, if one worker is to be a receptionist, the the combination is like,

So, the value of n = 3 and r = 1.

Then, according to the ncr formula,

=> ³C₁ = [tex]\frac{3!}{1!(3-1)!}[/tex]

=> 3!/1!2!

=> (3 x 2 x 1) / 1 x 2 x 1

=> 3

Similarly,  if one worker is to be a secretary,

Here the value of n = 2 (Because we have already select one person as receptionist) and r = 1

So,

=> ²C₁ = (2!)/1!(2-1)!

=> (2x1)/ 1 x 1

=> 2

Similarly,  if one worker is to be a technical typist,

Here the value of n = 1 (Because we have already select one person as receptionist) and r = 1

So,

=> ¹C₁ = 1

Therefore, the total number of possible ways are,

=> 3 x 2 x 1

=> 6

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Answer:

3rd option

Step-by-step explanation:

the factors of 48 are

1 , 2, 3, 4, 6, 8, 12, 16 , 24 , 48

the factor pairs are

1 × 48 , 2 × 24 , 3 × 16 , 4 × 12 , 6 × 8

The way in which the graph of 2y − x = 1 compare with the graph of 3y − x = 1 is that: A. the graph of 2y − x = 1 has a steeper slope than the graph of 3y − x = 1.

In Mathematics, a steeper slope simply means that the slope of a line is bigger than the slope of another line. This ultimately implies that, a graph with a steeper slope has a greater (faster) rate of change in comparison with another graph.

Mathematically, the standard form of the equation of a straight line is given by;

y = mx + c

Where:

For the graph of 2y − x = 1, the slope is given by:

2y − x = 1

2y = x + 1

y = x/2 + 1/2  

Slope, m₁ = 1/2 or 0.5.

For the graph of 3y − x = 1, the slope is given by:

3y − x = 1

3y = x + 1

y = x/3 + 1/3

Slope, m₂ = 1/3 or 0.3.

Therefore, m₁ > m₂ (steeper slope).

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The area of a circle can be calculated as follows:

Using the area given in the problem and solving for the radius r:

Finally, the diameter is twice the radius:

Then the answer is the first option 3.27 in

The mean and standard deviation are given as 6 and 0.48 respectively.

According to the question The Population Mean number of strikes per square kilometer (μ) = 6 and the Population standard deviation of strikes per square kilometer (σ) = 2.4. The Sample size is equal to (n) = 16. We know that the sample mean number of strikes per square kilometer (m) = mean Number of strikes per square kilometer in the population. From this observation it is clear that the mean will be equal to

μ = m = 6

So, the Sample mean = 5

Now, the Standard deviation = standard error = σ/√n. Now we get

Standard Error = 2.4 / √25

Standard Error = 2.4 / 5

Standard Error = 0.48

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Considering the Graph and reading the distance blocks from the store to the bank we see a progression of 3blocks

This is further explained below.

Generally, There is a concept referred to as distance that may be used to quantify, either quantitatively or qualitatively, the distance that separates two items or sites.

When speaking about physics or using the phrase in everyday language, "distance" may either refer to a literal measurement or an estimate based on a number of other parameters.

Both meanings are appropriate when discussing or using the term.

The progression of existence and events that occur in what seems to be an unstoppable order beginning in the past, continuing through the present, and moving into the future is what we refer to as time.

Time may be broken down into three distinct parts: the past, the present, and the future.

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We were told that Ben earned 625.5 points out of 700 on an essay. Expressing his score in the essay in terms of percentage, it becomes

625.5/700 x 100 = 89.29%

Also, he scored 65 out of 70 on an assignment. Expressing his score in the assignment in terms of percentage, it becomes

65/70 x 100 = 92.86%

We would find the average between the two percentages

Average = sum of percentages/number of percentages

Average = (89.29 + 92.86)/2

Average = 91.075

Average is approximately 91%

Since in order to earn an A in the class, he needed to average a 91 on these two

assignments and he got an average of 91%, then we can conclude that he got an A

The most appropriate choice for exponent will be given by-

Fourth option is correct

What are exponent?

Exponent tells us how many times a number is multiplied by itself.

For example : In [tex]2^4 = 2\times 2\times 2 \times 2[/tex], here, 2 is multiplied by itself 4 times.

If  [tex]a^m = a\times a\times a \times.....\times a[/tex] (m times), a is the base and m is the index.

The laws of index are

[tex]a^m \times a^n = a^{m + n}\\\\\frac{a^m}{a^n} = a^{m-n}\\\\a^0 = 1\\\\(a^m)^n = a^{mn}\\\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\\\a^mb^m = (ab)^m[/tex]

Here,

For first option

[tex]\frac{4^{11}}{4^{14}}\\\frac{1}{4^{14 - 11}}\\\frac{1}{4^3}\\\frac{1}{64} < 1[/tex]

For second option

[tex](5^4)^2 \times 5^{-11}\\5^8 \times 5^{-11}\\5^{8-11}\\5^{-3}\\(\frac{1}{5})^3\\\frac{1}{125} < 1[/tex]

For the third option,

[tex](2^3)^{-2}\\2^{-6}\\(\frac{1}{2})^6\\\frac{1}{64} < 1[/tex]

For the fourth option
[tex]\frac{(3^5)^2}{3^4}[/tex]

[tex]\frac{3^{10}}{3^4}\\3^{10 - 4}\\3^6\\ 729 > 1[/tex]

Fourth option does not have an expression greater than 1

Fourth option is correct.

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Answer:

The equation is an example of the associative property of addition.

Step-by-step explanation:

Associative property of addition: changing the grouping of addends does not change the sum.

For example: A+(B+C) = (A+B)+C.

The factors of the quadratic equation are found as the 7 and -3/2

For the given question, the quadratic equation is give as;

2x² - 11x - 21 = 0

Find the factors of -21×2 = 42 such that on subtraction it gives -11.

2x² - 14x + 3x - 21 = 0

Take 2x common from the first two terms and 3 from the last two terms.

2x(x - 7) + 3(x - 7) = 0

Take (x - 7) common from the terms.

(x - 7)(2x + 3) = 0

Then,

x - 7 = 0

x = 7

and, 2x + 3 = 0

x = -3/2

Thus, the factors of the quadratic equation are found as the 7 and -3/2.

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