What is the difference between -4 and 6?
O -10
0 -2
2
10

Answer:

Step-by-step explanation:

Because of the word "or", this is a disjunction, or a union of all the solutions to the inequality as they present on a number line.

For the first inequality:

4(x + 1) > -4 we distribute through the parenthesis to get

4x + 4 > -4 and subtract 4 from both sides to get

4x > -8 and then divide both sides by 4 to get

x > -2.  That will be graphed on a number line with an open hole over the -2 and the arrow will go to the right where the numbers are bigger than -2. This arrow continues into positive infinity.

For the other inequality:

2x - 4 ≤ -10 we add 4 to both sides to get

2x ≤ -6 and then divide by 2 to get

x ≤ -3. That is a closed hole over -3 and the arrow goes to negative infinity (to the left). Since one arrow goes off to the right forever, and the other arrow goes off to the left forever, and the arrows do not intersect at any point, the interval notation answer is

(-∞, -3] or (-2, ∞).  The parenthesis mean that the number following it is not included (you can't include infinity, either negative or positive, because it's not actually a number) and the brackets mean that the number following it IS included. The hole is closed over the -3 so -3 is included in the solution, where the hole over the -2 is open and is not included.

We can simplify \((16x^4)^(-1/2) to 1/(4x^2)\) using the properties of rational exponents.

Certainly! Here's an example:

Simplify the expression: \((16x^4)^(-1/2)\)

We can apply the property of rational exponents which states that \((a^m)^n = a^(m*n)\). Using this property, we get:

\((16x^4)^(-1/2) = 16^(-1/2) * (x^4)^(-1/2)\)

Next, we can simplify \(16^(-1/2)\) using the rule that \(a^(-n) = 1/a^n\):

\(16^(-1/2) = 1/16^(1/2) = 1/4\)

Similarly, we can simplify \((x^4)^(-1/2)\) using the rule that \((a^m)^n = a^(m*n)\):

\((x^4)^(-1/2) = x^(4*(-1/2)) = x^(-2)\)

Substituting these simplifications back into the original expression, we get:

\((16x^4)^(-1/2) = 1/4 * x^(-2) = 1/(4x^2)\)

Therefore, the simplified expression is \(1/(4x^2).\)

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To find the selling price that will yield the maximum profit, we need to find the vertex of the quadratic function given by the profit equation y = -5x² + 286x - 2275.The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -5 and b = 286.

x = -b/2a

x = -286/(2(-5))

x = 28.6

So, the selling price that will yield the maximum profit is $28.60 (rounded to the nearest cent).

Therefore, the widgets should be sold for $28.60 to maximize the company's profit.

Hope I helped ya...

Answer:

29 cents

Step-by-step explanation:

The amount of profit, y, made by the company selling widgets, is related to the selling price of each widget, x, by the given equation:

\(y=-5x^2+286x-2275\)

The maximum profit is the y-value of the vertex of the given quadratic equation. Therefore, to find the price of the widgets that maximises profit, we need to find the x-value of the vertex.

The formula to find the x-value of the vertex of a quadratic equation in the form y = ax² + bx + c is:

\(\boxed{x_{\sf vertex}=\dfrac{-b}{2a}}\)

For the given equation, a = -5 and b = 286.

Substitute these into the formula:

\(\implies x_{\sf vertex}=\dfrac{-286}{2(-5)}\)

\(\implies x_{\sf vertex}=\dfrac{-286}{-10}\)

\(\implies x_{\sf vertex}=\dfrac{286}{10}\)

\(\implies x_{\sf vertex}=28.6\)

Assuming the value of x is in cents, the widget should be sold for 29 cents (to the nearest cent) to maximise profit.

Note: The question does not stipulate if the value of x is in cents or dollars. If the value of x is in dollars, the price of the widget should be $28.60 to the nearest cent.

If you want to round a number within an arithmetic expression, you should use the ROUND function.

The ROUND function allows you to specify the number of decimal places to which you want to round a given number. It is commonly used in programming languages and spreadsheet software.

The syntax for the ROUND function typically involves specifying the number or expression you want to round and the number of decimal places to round to. For example, if you want to round a number, let's say 3.14159, to two decimal places, you would use the ROUND function like this: ROUND(3.14159, 2), which would result in 3.14.

Using the ROUND function ensures that the rounded number is calculated within the arithmetic expression, providing the desired level of precision in the calculation.

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Answer:

Z= 4

Step-by-step explanation:

SOLVE FOR Z by cross multiplying

To show that H, the set of all even numbers, is a cyclic group, we need to find a generator that can create all even numbers using addition. The additive group H1 is cyclic, and its generator is 15.

For the first part, to show that the additive group H (the set of all even numbers) is cyclic, we need to find an element that generates the entire group. One such element is 2, as every even number can be written as a multiple of 2. Therefore, the generator of H is 2.

For the second part, to show that the additive group H1 = {30n + 45m | n, m € Z} is cyclic, we need to find an element that generates the entire group. We can simplify the expression as H1 = {15(2n + 3m) | n, m € Z}. Since every integer can be written as a linear combination of 2 and 3, we can choose 15 as the generator of H1. This is because every element in H1 can be written as a multiple of 15, i.e., H1 = {15k | k € Z}, and 15 generates the entire group. Therefore, the generator of H1 is 15.

1. To show that H, the set of all even numbers, is a cyclic group, we need to find a generator that can create all even numbers using addition.

Let's consider the number 2 as a potential generator. Since any even number can be expressed as 2 times an integer (2n, where n is an integer), it's clear that adding 2 to itself repeatedly will generate all even numbers. Therefore, the additive group H is cyclic, and its generator is 2.

2. For H1 = {30n + 45m | n, m ∈ Z}, we need to show that this additive group is cyclic and find its generator.

First, let's find the greatest common divisor (GCD) of 30 and 45, as it will help us determine if there's a single generator for this group. The GCD(30, 45) = 15.

Now, let's consider the number 15 as a potential generator. Since any element in H1 can be expressed as a linear combination of 30n and 45m with integer coefficients n and m, and the GCD(30, 45) = 15, we can generate any element in H1 by repeatedly adding 15 to itself.

Therefore, the additive group H1 is cyclic, and its generator is 15.

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Answer:

$150

Step-by-step explanation:

50+25=75

since he spent another half 75 is the other half

so 75+75

150

The values in b are compared with the true volume. And we conclude that b is precise and accurate.

Accuracy determines how closely measured values match the actual value. The degree to which two measured values are inside a certain range, or how closely they agree, is called precision.

First calculate the mean of a, b, and c. We get, the mean of a is 87.63, the mean of b is 87.06, and the mean of c is 87.77.

From the values in "a", we can tell there is no good agreement between the given values, and just one (87.1) value is near to the true value. So a is neither precise nor accurate.

From the values in "b", we can tell these given values are reasonably close to the true value and exhibit good agreement. So b is precise and accurate.

From the values in "c", we can tell there is a considerable agreement between the given values but they are not very close to the true value. So c is precise but not accurate.

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The angle measure of minor arc KM is 41 degrees

From the given diagram, we have the following parameters

mKLM = 82 degrees

Required

arcKM

Since the angle at the vertex is twice that of the intercepted arc, then:

<KLM = 2(arcKM)
arcKM = <KLM/2

arcKM = 82/2

arcKM = 41 degrees

Hence the angle measure of minor arc KM is 41 degrees

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Answer:

f(-2) = 3.

Step-by-step explanation:

Reading off the graph, f(-2) = 3.

Answer:

$0.05

Step-by-step explanation:

All you have to do us divide the cost by the amount of ounces

3.45 ÷ 64 is about 0.05

The full answer is 0.05390625

Since we are talking about money, it should be $0.05

All numbers with an absolute value greater than 3 but less than 7 is {4, 5, 6}.

The absolute value of a number is defined as its magnitude irrespective of the sign of the number. To find the absolute value of a real number, we consider only the number and remove the sign. It can only be a non-negative value.

We need to write all numbers with an absolute value greater than 3 but less than 7.

Absolute value greater than 3, that is

|x|>3

Absolute value less than 7, that is

|x|<7

Now, 3<|x|<7

3<x<7

Solution set ={4, 5, 6}

Therefore, all numbers with an absolute value greater than 3 but less than 7 is {4, 5, 6}.

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Answer:

m = 2k/v²

Step-by-step explanation:

I think you mean solve for m, not k

Multiply both sides of the equation by 2

2 * 1/2 *(mv²) = 2 * k

Rewrite the expression.

1*(mv²) = 2*k

Multiply mv² by 1

mv² = 2*k

Divide each term by v² and simplify

mv²/v² = 2k/v²

mv²/v² cancel out and you get

m = 2k/v²

Answer:

10 pages

Step-by-step explanation:

To find 20% of 50, multiply .20 x 50

.2 × 50 = 10

Answer:

10 pages

Step-by-step explanation:

20% of 50 pages

One way is converting 20% to a decimal 0.2

0.2 x 50 = 10 pages.

Answer:

x=-5

Step-by-step explanation:

(5)(3x)+(5)(12)=−15

15x+60=−15

Subtract 60 from both sides.

15x=−75

Divide both sides by 15

x=-5

Answer:

525

Step-by-step explanation:

So its 25 a day and hes doing it for 21 days because 7*3=21.

so 25*21= 525

Answer:

a) 7x-2

b) 28x-8

c) length of a side: 26 in, perimeter: 104 in, area: 676 square inches

i’m not quite sure abt c but i hope this helps :)

360÷20 = 18sides

U divide 360 by 20 because angles at the center add up to 360°

The given polygon will have 18 sides in total.

Given information:

The diagram shows part of a regular polygon.

The sides of this polygon subtend angles of 20° at the center of the polygon.

Let the polygon has n number of sides.

Now, the polygon is regular. So, its each side will be equal and it will make equal angle with the center.

The sum of angles made by all the sides will be equal to 360 degrees.

So, the number of sides n can be calculated as,

\(20\times n=360\\n=\dfrac{360}{20}\\n=18\)

Therefore, the given polygon will have 18 sides in total.

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The mean of the data values is 17. The median of the data values is 18.

To find the mean of a set of data values, we sum up all the values and divide by the total number of values. In this case, the sum of the data values is 10 + 20 + 21 + 14 + 18 + 19 = 102. Since there are 6 data values, the mean is 102/6 = 17.

The median is the middle value of a set of data when it is arranged in ascending or descending order. In this case, the data values arranged in ascending order are 10, 14, 18, 19, 20, 21. Since there are 6 values, the middle two values are 18 and 19. Therefore, the median is 18.

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An equation that represent the graph is: C. y = −2x − 2.

A graph that represent the linear equation y equals one fourth times x plus 1 on the coordinate plane is: D. graph of a line passing through the points 0 comma 1 and negative 4 comma 0.

A graph which shows the solution to the system of linear equations is: B. coordinate plane with one line that passes through the points 0 comma 2 and negative 3 comma 3 and another line that passes through the points 0 comma 0 and negative 3 comma negative 1.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At data point (0, 2), a linear equation of this line can be calculated in point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-2) = (2 - (-2))/(-2 - 0)(x - 0)

y + 2 = -4/2(x - 0)

y + 2 = -2x

y = -2x - 2.

In this exercise, we would use an online graphing calculator to plot the the given system of linear equations in order to determine its solution as shown in the graph attached below.

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Answer:

£990

Step-by-step explanation:

£11000 * 2.25% * 4 = £990

Answer:

6.6

Step-by-step explanation:

Answer:

6.6

Step-by-step explanation:

The sampling technique used in this scenario is Random sampling

The correct answer is an option (a)

We know that the random sampling is nothing but a method of choosing a sample of observations from a population to make assumptions about the population. It is also called as a porbability sampling.

It  allows for the randomization of sample selection.

There are four random sampling methods –

simple random sampling,

systematic sampling,

stratified sampling,

and cluster sampling.

In random sampling, the randomized selection of a small segment of individuals or members from a whole population.

Here, the soda bottle company  have equipment that can pull every tenth bottle from the assembly line without causing a backup on the line.

Therefore,  the sampling technique used: Random

The correct answer is an option (a)

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The complete question is:

Select the sampling technique used:

A soda bottling company needs to test the quality of the bottles they produce. They have equipment that can pull every tenth bottle from the assembly line without causing a backup on the line.

a) Random

b) Stratified

c) Cluster

d) Systematic

e) Convenience

Answer:

$169.96 dollars

Step-by-step explanation:

Given the following questions:

8.25% of 22.55 and 134.45

In order to find the answer, we will have to add the initial costs of the items together, then we will calculate using the formula for percentages to find the tax rate.

\(22.55+134.45=157\)
\(157\)

Calculate the percentage:
\(\frac{p\times c}{100}\)
\(\frac{8.25\times157}{100} =8.25\times157=1295.25\div100=12.9525\)
\(=12.9525\)
\(12.9525\)
\(2 < 5\)
\(=12.96\)

Add the sales tax:
\(157+12.96=169.96\)
\(=169.96\)

Which means the two items along with an 8.25% sales tax costs "$169.96 dollars."

Hope this helps.

The definition of the domain of the function f: {4, 6, 8} ⇒{2, 3} over  {(4, 2), (6, 2), (8, 2)} is given as {4,6,8}, while the range is given as 2.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Four main categories can be used to classify different sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element. A relation between a domain and range is called a function when each value in the domain only has one value in the range.

Here,

function f : {4, 6, 8} → {2, 3} is defined as {(4, 2), (6, 2), (8, 2)},

domain={4,6,8}

range={2}

The domain of function f : {4, 6, 8} → {2, 3} is defined as {(4, 2), (6, 2), (8, 2)} will be {4,6,8} and range will be {2}.

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Answer:

A

I took a picture of your mom and my phone ran out of storage.

A metric is a single, quantifiable type of data that can be utilized for various tasks in different domains. Metrics serve as essential tools for measuring progress, assessing performance, and making informed decisions.

By converting complex information into manageable and comparable units, metrics enable individuals and organizations to monitor their objectives and drive improvement.
In business, metrics are often employed to evaluate the success of marketing campaigns, employee performance, or financial growth. They assist in identifying trends, pinpointing areas that need attention, and guiding strategic planning. Key performance indicators (KPIs) are a common type of metric used to measure the effectiveness of business processes and track progress toward organizational goals.
In scientific research, metrics provide valuable insight into the progress and impact of studies. For example, citation metrics measure the influence of a published work within a given field. Metrics also facilitate the assessment of experimental results and the development of new theories, ultimately advancing scientific knowledge.
In education, metrics serve as essential tools for gauging student performance and the quality of educational programs. They provide data on student learning outcomes, helping educators refine their teaching methods and tailor instruction to the needs of individual learners.
Overall, a metric is a versatile, quantifiable data type that plays a vital role in assessing and improving various aspects of performance across multiple domains. By offering concrete, measurable information, metrics empower decision-makers to make informed choices and drive progress.

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Answer:

27

Step-by-step explanation:

f(x) = 5x - 8

f(7) = 5(7) - 8 = 27

Answer:

27

Step-by-step explanation:

f(x)=5x-8

Let x=7

f(7) = 5*7 -8

       =35-8

         27