2x – 1 < 11
What is the solution to this equation?

Evaluate f(3)

f(3) = 4(3)-2 = 12 - 2 = 10

f(3) = 10

f(x) = 6 = 4x- 2

4x=8

x = 2

Answer:

This proves that f is continous at x=5.

Step-by-step explanation:

Taking f(x) = 3x-1 and \(\varepsilon>0\), we want to find a \(\delta \) such that \(|f(x)-14|<\varepsilon\)

At first, we will assume that this delta exists and we will try to figure out its value.

Suppose that \(|x-5|<\delta\). Then

\(|f(x)-14| = |3x-1-14| = |3x-15|=|3(x-5)| = 3|x-5|< 3\delta\).

Then, if \(|x-5|<\delta\), then \(|f(x)-14|<3\delta\). So, in this case, if \(3\delta \leq \varepsilon\) we get that \(|f(x)-14|<\varepsilon\). The maximum value of delta is \(\frac{\varepsilon}{3}\).

By definition, this procedure proves that \(\lim_{x\to 5}f(x) = 14\). Note that f(5)=14, so this proves that f is continous at x=5.

Answer:

Find the volume of a concrete block that is 2.5 metres long,. 12 centimetres wide and. 10 centimetres high. Two of the dimensions, the width and height,

Answer:

480,000 cm3

Step-by-step explanation:

give crown please ( brainliest )

Answer:

the slope is -3  and the y intercept is -3 because in this type of equation, the equation y=mx+b, the slope is m and the y-intercept is b

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(\pmb {sin(22)^o=\cfrac{x}{35} }\)

\(\pmb {35sin(22)=w}\)

\(\pmb {w=13.11}\)

_________________

Hope this helps!

Have a great day! :)

The dealers included in the sample are dealers 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, and 98.

To use systematic random sampling, we need to choose a starting point and a sampling interval. In this case, we are starting with the third dealer in the list, so we need to skip the first two dealers.

Let's assume that the dealers are numbered 1 to 100 in the list. Since we are starting with the third dealer, our starting point is dealer 3. We also need to choose a sampling interval of 5, since we want to select every fifth dealer.

To find out which dealers are included in the sample, we can use the following formula:

Sampled Dealers = Starting Point + (Sampling Interval * Number of Samples)

Using the formula, we can calculate the dealers that are included in the sample as follows:

Sampled Dealers = 3 + (5 * n)

where n is the number of samples.

If we want to select a sample of 20 dealers, we can substitute n = 1 to 20 into the formula to get the following list of dealers:

3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, 98

Therefore, the dealers included in the sample are dealers 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, and 98.

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1) A translation of 3 units down, option D.

2) The vertex moves 3 units down.

3) The new range is y ≥ -3, correct option is C.

For a function f(x) a vertical shift of N units is written as:

g(x) = f(x) + N

In this case, we have:

f(x) = |x|

h(x) = |x| - 3

Then h(x) = f(x) - 3

This is a shift of 3 units down, the correct option is D.

How is the vertex affected?

The vertex is translated 3 units down, like the whole graph of the function.

How is the range affected?

The vertex defines the minimum of the range, so if the vertex goes 3 units down, then the range also does, the new range will be:

y ≥ -3.

So the correct option is C.

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Answer:

Using a standard normal distribution table, we can find that the percentage of homes that have a monthly utility bill of more than $83 is approximately 13.6%.

Step-by-step explanation:

If the distribution of the monthly utility bill for gas or electric energy can be considered mound-shaped and symmetric, we can use the standard normal distribution table to find the percentage of homes that have a monthly utility bill of more than $83.

To use the standard normal distribution table, we need to standardize the variable by subtracting the mean and dividing by the standard deviation:

(83 - 91) / 8 = -0.875

This means that a monthly utility bill of $83 is 0.875 standard deviations below the mean.

Using a standard normal distribution table, we can find that the percentage of homes that have a monthly utility bill of more than $83 is approximately 13.6%.

The inverse of the functions are f⁻¹(x) = 2/[3(x + 4)], f⁻¹(x) = √[(x + 1)/2] and f⁻¹(x) = 1/x + 1

Function (a)

This function is given as

f(x)=2/(3x) - 4

The function needs to be represented as an equation

So, we have

y = 2/(3x) - 4

Swap the positions of x and y

x = 2/(3y) - 4

So, we have

2/(3y) = x + 4

Take the reciprocal of both sides

3y/2 = 1/(x + 4)

Multiply both sides by 2/3

y = 2/[3(x + 4)]

So, the inverse function is

f⁻¹(x) = 2/[3(x + 4)]

The inverse is a function with the domain x ≠ -4 and range of f(x) ≠ 0

See attachment 1 for the graphs

Function (b)

This function is given as

f(x) = 2x² - 1

The function needs to be represented as an equation

So, we have

y = 2x²- 1

Swap the positions of x and y

x = 2y² - 1

So, we have

2y²= x + 1

Divide both sides by 2

y²= 1/2(x + 1)

Take the square roots

y= √[(x + 1)/2]

So, the inverse function is

f⁻¹(x) = √[(x + 1)/2]

The inverse is a function with the domain x ≥ -1 and range of f(x) ≥ 0

See attachment 2 for the graphs

Function (c)

This function is given as

f(x) = 1/(x - 1)

The function needs to be represented as an equation

So, we have

y = 1/(x - 1)

Swap the positions of r and y

x = 1/(y - 1)

So, we have

y - 1 = 1/x

Add 1 to both sides

y = 1/x + 1

So, the inverse function is

f⁻¹(x) = 1/x + 1

The inverse is a function with the domain x ≠ 0 and range of f(x) ≠ 1

See attachment for the graphs

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Your answer: {1, 2, 3, 4, 5, 6} in roster notation

To list the elements of the set in, follow these steps:

1. Identify the distinct digits in the number 654,323.
2. Arrange them in roster notation, which means listing them within curly brackets.

The distinct digits in the number 654,323 are 2, 3, 4, 5, and 6.

So, the elements of the set in roster notation are {2, 3, 4, 5, 6}.

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The correct options are -

For the stated function.

The graph for the function g(x) is given in the question.

As the slope of function g(x) is most steep for the interval [1,2].

Thus, g(x) increases at a faster rate over the interval [1,2].

The graph for the function f(x) is attached,

f(x) = 3x+ 2

From the graph, it is shown that the slope of the function g(x) is most steep for the interval [0,1].

Thus, f(x) increases at a faster rate over the interval [0,1].

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Answer:

The answer to your problem is, in the graph ↓

Step-by-step explanation:

I 400

I 350

I 300————2009(275).2010(290).2011(315).2012(280)

I 250 - 2008(250)

I 100

I 50

I 0

           2008      2009    2010     2011   2012

——-——-——-——-——-——-——-——-——-——-——-——-——-——-——-————

Easier:

2008 : 250 ( 250 )

2009: 300 ( 250 )

2010: 300 ( 290 )

2011: 300 ( 315 )

2012: 300 ( 280 )

Parenthesis = Number

Number after “ : “ = Graph on SIDE

First number = Year

Thus the answer is, above!

(i) Yes, it is even and divisible by 3 as 1 + 0 + 2 = 3

(ii) No, it does not end in 5 or 0

What are Divisibility Rules?

Divisibility criteria can be used to determine whether or not to diminish a fraction. The rules are based on patterns seen while listing the multiples of any integer.

Solution:

(i) 102 is divisible by 6 - TRUE

It is because 102 is even number thus, it is divisible by 2 and since the sum of digits 1 + 0 + 2 is 3 therefore, it is divisible by 3

- Yes, it is even and divisible by 3 as 1 + 0 + 2 = 3

(ii) 102 is divisible by 5 - FALSE

It is because any number to be divisible by 5 it should always end with 5 or 0 at ones place.

- No, it does not end in 5 or 0

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The required equation of the line is y = x + 1

One of the common ways to describe the equation of a line is in the slope-intercept form of the line. You may use this formula to determine a line's equation given its slope and y-intercept.

The Slope intercept form of a line is y = mx + c,

where m is slope and c is the y-intercept

Here we have

Points (1, 2) and (2, 3)

The Slope intercept form of a line is y = mx + c,

As we know, Slope (m) = (y₂ - y₁)/(x₂ - x₁)  

=> Slope of required line = (3 - 2)/(2 - 1) = 1/1 = 1

=> Slope, m = 1

The equation of the line will be: y = (1)x + c,

=> y = x + c

Since (1, 2) passes through the line

=> 2 = 1 + c

=> c = 1

then the equation will be y = x + 1  

Therefore,

The required equation of the line is y = x + 1  

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The towers ZQ and ZR are the closest together.

Triangle is a three-sided polygon which has three vertices.

Solution

If the measure of ZP is x,

Then the measure of ZQ is x-10 and the measure of ZR is x-5.

To find the two towers that are closest together, we need to find the minimum value of the difference between any two angles.

ZP and ZQ: x - (x-10) = 10

ZQ and ZR: (x-5) - (x-10) = 5

So, the towers ZQ and ZR are the closest together, with an angle difference of 5°.

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The required answer is the annual cost saved by shifting from the 500-bag lot size to the EOQ is $1,059.92.

Explanation:-

a. Economic order quantity (EOQ) is defined as the optimal quantity of inventory to be ordered each time to reduce the total annual inventory costs.

It is calculated as follows: EOQ = sqrt(2DS/H)

Where, D = Annual demand = 100 x 52 = 5200S = Order cost = $57 per order H = Annual holding cost = 0.30 x 10.75 = $3.23 per bag per year .Therefore, EOQ = sqrt(2 x 5200 x 57 / 3.23) = 234 bags. The average time between orders (TBO) can be calculated using the formula: TBO = EOQ / D = 234 / 100 = 2.34 weeks ≈ 2 weeks (rounded to nearest whole number).

Hence, the EOQ is 234 bags and the average time between orders is 2 weeks (approx).b. R is the reorder point, which is the inventory level at which an order should be placed to avoid a stockout.

It can be calculated using the formula:R = dL + zσL

Where,d = Demand per day = 100 / 5 = 20L = Lead time = 1 week (5 working days) = 5 day

z = z-value for 92% cycle-service level = 1.75 (from standard normal table)σL = Standard deviation of lead time demand = σ / sqrt(L) = 16 / sqrt(5) = 7.14 (approx)

Therefore,R = 20 x 5 + 1.75 x 7.14 = 119.2 ≈ 120 bags

Hence, the reorder point R should be 120 bags.c. An inventory withdraw of 10 bags was just made. Is it time to reorder?The current inventory level is 310 bags, which is greater than the reorder point of 120 bags. Since there are no open orders or backorders, it is not time to reorder.d. The store currently uses a lot size of 500 bags (i.e., Q = 500).What is the annual holding cost of this policy.

Annual ordering cost. Without calculating the EOQ, how can you conclude the lot size is too large?Annual ordering cost = (D / Q) x S = (5200 / 500) x 57 = $592.80 per year.

Annual holding cost = Q / 2 x H = 500 / 2 x 0.30 x 10.75 = $806.25 per year. Total annual inventory cost = Annual ordering cost + Annual holding cost= $592.80 + $806.25 = $1,399.05Without calculating the EOQ, we can conclude that the lot size is too large if the annual holding cost exceeds the annual ordering cost.

In this case, the annual holding cost of $806.25 is greater than the annual ordering cost of $592.80, indicating that the lot size of 500 bags is too large.e.

The annual cost saved by shifting from the 500-bag lot size to the EOQ can be calculated as follows:Total cost at Q = 500 bags = $1,399.05Total cost at Q = EOQ = Annual ordering cost + Annual holding cost= (D / EOQ) x S + EOQ / 2 x H= (5200 / 234) x 57 + 234 / 2 x 0.30 x 10.75= $245.45 + $93.68= $339.13

Annual cost saved = Total cost at Q = 500 bags - Total cost at Q = EOQ= $1,399.05 - $339.13= $1,059.92

Hence, the annual cost saved by shifting from the 500-bag lot size to the EOQ is $1,059.92.

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The measure of the length of the dotted line is 3.75 inches. Then the correct option is B.

The hexagon is a 2D geometry that has a 6 number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

The perimeter of the hexagon is 7.5 inches.

Then the length of the hexagon will be

\(\rm 7.5 = 6x\\\\x \ \ = 1.25\)

The length of the hexagon is 1.25 inches.

Then the diagonal length of the hexagon will be

y = 2 × 1.25

y = 2.5

The diagonal length of the hexagon is 2.5 inches.

Then the length of the dotted line is 3.75 inches.

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Answer:

m = -1/2

Step-by-step explanation:

let me know if it helped

(too lazy to write a explanation)

Hence, the deal of  $\(479\) is best unit price per blender.

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

Oliver is buying equipment for his restaurant. He can buy two blenders for $\(396\) or three blenders for $\(479\).

So,

Oliver buying two blenders at  $\(396\) so the cost of one blender is

i.e., \(\frac{396}{2}=198\)$

Oliver buying two blenders at  $\(479\)  so the cost of three blenders is

i.e., \(\frac{479}{3}=159\)$

Hence, the deal of  $\(479\) is best unit price per blender.

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Answer:

120°

Step-by-step explanation:

\(m\angle S = 180\degree - 2\times 30\degree \\\\

m\angle S = 180\degree - 60\degree \\\\

\huge\purple {\boxed{m\angle S = 120\degree}} \)

The following diagram shows the number of people who know the riddle per day.

The values of x would be from day 1 to 6 while the values of y will be 5, 20, 60, 240, 960, 3840. Thus, we may write the following in the table as follows:

Notice that 5 is always multiplied by a power of 4.

Thus, on day 1, we have

On day 2, we have

On day 3, we have

On day 4, we have

On day 5, we have

And on day 6, we have

Therefore, we may say that the formula to obtain the number of people who know the riddle on x days will be

where y is the number of people and x is the number of days.

Therefore, on the 15th day, we substitute 15 to x in the obtained equation.

Therefore, there will be 1,342,177,280 people who will know the answer on the 15th day.

\((\stackrel{x_1}{-19}~,~\stackrel{y_1}{17})\hspace{10em} \stackrel{slope}{m} ~=~ - 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{17}=\stackrel{m}{- 1}(x-\stackrel{x_1}{(-19)}) \implies y -17 = - 1 ( x +19) \\\\\\ y-17=-x-19\implies {\Large \begin{array}{llll} y=-x-2 \end{array}}\)

Answer:

y = -x - 2

Step-by-step explanation:

We are given that a line has a slope (m) of -1 and passes through (-19,17).

We want to write the equation of this line in slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y intercept, hence the name

As we are already given the slope of the line, we can plug it into the equation.

Replace m with -1.

y = -1x + b

This can be rewritten to:

y = -x + b

Now, we need to find b.

As the equation passes through (-19,17), we can use its values to help solve for b.

Substitute -19 as x and 17 as y.

17 = -(-19) + b

17 = 19 + b

Subtract 19 from both sides.

-2 = b

Substitute -2 as b into the equation.

y = -x - 2

All the numbers are equal in decimal form, they are equivalent.

To determine if the numbers in Exercise 8 are equivalent, you must compare them using a standard form or convert them to a common form, such as fractions, decimals, or percentages.

Follow these steps to decide whether the numbers are equivalent:

1. Identify the form of the numbers (fractions, decimals, or percentages).
2. If necessary, convert the numbers to a common form for comparison.
3. Compare the converted numbers.

Let's assume the numbers in Exercise 8 are a fraction, a decimal, and a percentage (e.g., 1/2, 0.5, and 50%). To determine if they are equivalent, first, convert them all to the same form:

1. Convert the fraction (1/2) to a decimal by dividing the numerator by the denominator: 1 ÷ 2 = 0.5
2. Convert the percentage (50%) to a decimal by dividing it by 100: 50 ÷ 100 = 0.5

Now that all the numbers are in decimal form, compare them:

1. Compare 0.5 (fraction) to 0.5 (decimal) - they are equal.
2. Compare 0.5 (fraction) to 0.5 (percentage) - they are equal.
3. Compare 0.5 (decimal) to 0.5 (percentage) - they are equal.

Since all the numbers are equal in decimal form, they are equivalent.

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The 95% confidence interval for the true proportion of people who favor candidate is (0.419,0.481).

A random sample of 1000 people was condidered for testing.

Number of people in sample favoured candidate

= 450

So, sample proportion, p = 450/1000 = 0.45

Confidence level= 95% i.e, alpha = 1 - 0.95=0.05, From standard normal Z- table, the value of Z( 0.025) is equals to 1.96..

Confidence interval formula,

CL = p ± Z× √(p×(1-p)/n)

Lower bound of interval is ,

=0.45 - 1.96× √(0.45× (1-0.45)/1000)

= 0.45 - 1.96× √(0.45× 0.55/1000)

= 0.45 - 1.96× √(0.0002475)

=0.419165~ 0.419

So the Upper bound is

= p + Z×√(p×(1-p)/n)

= 0.45 + 1.96× √(0.45× (1-0.45)/1000)

= 0.45 + 1.96× √(0.0002475)

= 0.480835 ~0.481

Hence, the required confidence interval is (0.419,0.481).

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Answer:

D. (-3;-3)

Step-by-step explanation:

2x-3y<9

A. 2×6-3×(-4)=24 FALSE, because 24>9

B. 2×(-1)-3×(-9)=25 FALSE, because 25>9

C. 2×2-3×(-5)=11 FALSE, because 11>9

D. 2×(-3)-3×(-3)=9 TRUE, because 3<9

The value of the exponent is  80000000000.

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Answer:

3

Step-by-step explanation:

I think why but i think

number but