1. Which expression can be factored into the form (ax + b)(ax - b), where
a and b are rational numbers?
4n2 - 81
2n2 - 49
2n2 + 49
4n2 + 81

Netflicks conducted a survey among 78 users to determine the average weekly watch time of its users. The upper limit of the confidence interval is requested.The survey results showed an average watch time of 15.6 hours per week, with a standard deviation of 2.5 hours.

We need to calculate the 95% confidence interval for the average weekly watch time for all Netflicks users, assuming a normal distribution.

To calculate the 95% confidence interval for the average weekly watch time, we can use the formula:

Confidence Interval = Average Watch Time ± (Z * Standard Error)

where Z is the z-score corresponding to the desired confidence level, and the Standard Error is calculated as the standard deviation divided by the square root of the sample size.

First, we need to find the z-score for a 95% confidence level. Since the confidence level is two-tailed, we need to find the z-score that leaves 2.5% in each tail. Looking up the z-score in a standard normal distribution table, the z-score is approximately 1.96.

Next, we calculate the Standard Error:

Standard Error = Standard Deviation / √(Sample Size)

             = 2.5 / √78

             ≈ 0.283

Now we can calculate the Confidence Interval:

Confidence Interval = 15.6 ± (1.96 * 0.283)

Calculating this expression, we get:

Confidence Interval ≈ 15.6 ± 0.554

Finally, we find the upper limit of the confidence interval:

Upper Limit = Average Watch Time + (1.96 * Standard Error)

           = 15.6 + 0.554

           ≈ 16.154

Therefore, the upper limit of the 95% confidence interval for the average weekly watch time for all Netflicks users is approximately 16.154 hours.

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Answer:

The solution to the system of equations is:

\(x=4,\:y=-3\)

Step-by-step explanation:

Given the system of equations

\(5x + 4y =8\)

\(2x- 3y = 17\)

solving the system of equations

\(\begin{bmatrix}5x+4y=8\\ 2x-3y=17\end{bmatrix}\)

\(\mathrm{Multiply\:}5x+4y=8\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:10x+8y=16\)

\(\mathrm{Multiply\:}2x-3y=17\mathrm{\:by\:}5\:\mathrm{:}\:\quad \:10x-15y=85\)

\(\begin{bmatrix}10x+8y=16\\ 10x-15y=85\end{bmatrix}\)

\(10x-15y=85\)

\(-\)

\(\underline{10x+8y=16}\)

\(-23y=69\)

\(\begin{bmatrix}10x+8y=16\\ -23y=69\end{bmatrix}\)

solve for y

\(-23y=69\)

Divide both sides by -23

\(\frac{-23y}{-23}=\frac{69}{-23}\)

\(y=-3\)

\(\mathrm{For\:}10x+8y=16\mathrm{\:plug\:in\:}y=-3\)

\(10x+8\left(-3\right)=16\)

\(10x-24=16\)

\(10x=40\)

Divide both sides by 10

\(\frac{10x}{10}=\frac{40}{10}\)

\(x=4\)

Thus, the solution to the system of equations is:

\(x=4,\:y=-3\)

Answer:

If x is the size of the child's head, 5 times that would be 5x and "plus 4/5" is + 4/5 so the equation is y = 5x + 4/5.

Answer:

Step-by-step explanation:

Answer: 1. 42,000 2. 118,200,000 3. 2,960 4. 34,000 5. 6,240,000 6. 720,000,000 7. 910,000 8. 571,000

Answer:

$7.35

Step-by-step explanation:

With Square Payments, you can easily and safely accept all forms of payment. You can collaborate with customers rather than competing with them when it comes to how they want to pay for goods and services when you use Square Payments.

Through Square, you can accept credit cards, Apple Pay, Android Pay, and a lot of other payment options. A client is an individual or company who purchases goods or services from another company. Customers are essential because they produce income. Without them, companies would cease to exist. A customer is the recipient of a good, service, product, or idea in sales, commerce, or economics that they have purchased from a seller, vendor, or supplier in exchange for money or another useful consideration. When a customer buys something and uses it themselves, they are considered a consumer. Although they might not be the final users, customers always buy goods or services. Although they might not have paid for it, consumers are always the ones who use a good or service in the end.

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Answer:

35 , 36 , 37

Step-by-step explanation:

Let the consecutive integers be x, (x + 1) , (x +2)

x + x + 1 + x +2 = 108

x + x + x + 1 + 2 = 108          {Combine like terms}

     3x + 3   = 108          {Subtract 3 from both sides}

             3x = 108 - 3

            3x = 105            {Divide both sides by 3}

              x = 105/3

               x = 35

The three integers are, 35 , 36 , 37

That is going to be a looong answer...

\(2324132352413142536 - \frac{1342536435241342536}{2.354254e} - 21 + 425364763524142536475\)

and done

The equations that models a growing line include the following:

B. 3x − 2y + 3 = 0

D. −5x + 3y + 9 = 0

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.

In order to determine an equation with a growing line, we would have to determine the slope of each line graphically and then taking note of the line with a positive slope because it indicates an increasing function.

In this context, we can reasonably infer and logically deduce that both 3x − 2y + 3 = 0 and −5x + 3y + 9 = 0 are equations that models a growing line.

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Complete Question:

Which of the following equations models a growing line?

A. 2x+4y+12=0

B. 3x−2y+3=0

C. −x−3y−12=0

D. −5x+3y+9=0

Answer:

$100

Step-by-step explanation:

solution:

commission = 12.5% of $800

= $100

We can then use the first or second derivative test to determine whether each value represents a local maximum or a local minimum. We can also use the sign of the derivative to determine intervals of increase or decrease.

Find approximate x values for any local maximum or local minimum points. The graph of the function f(x) = x³ - x shows a local maximum point at (-1, 0) and a local minimum point at (0, -1). ii. Set up a table showing intervals of increase or decrease and the slope of the tangent on those intervals. Find approximate x values for any local maximum or local minimum points. The graph of the function f(x) = -(x-3)(x+1)(1-x) shows a local maximum point at (1, 0) and local minimum points at (-1, -4) and (2, -2).ii. Set up a table showing intervals of increase or decrease and the slope of the tangent on those intervals Here is the table showing the intervals of increase or decrease and the slope of the tangent on those intervals

The approximate x values for any local maximum or local minimum points for the given function have been calculated and the table showing intervals of increase or decrease and the slope of the tangent on those intervals has been set up. The table of values showing "x" and its corresponding "slope of tangent" for at least 7 points has been set up. The graph of the derivative using the table of values has also been sketched. To find the local maximum or local minimum points, we calculate the derivative of the function and set it equal to zero. For the given function, the derivative is 3x² - 1. Setting it equal to zero, we get x = ±√(1/3). We can then use the first or second derivative test to determine whether each value represents a local maximum or a local minimum. We can also use the sign of the derivative to determine intervals of increase or decrease.

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The equation that represent the relationship between the number of months and the amount remaining on the card is: y = 25 - (2.50x)

a) the independent variable is the: Number of month after the first year

b) the dependent variable is the: Amount remaining on the card

To solve this problem, we have to state the equation using the information of the problem.

Information about the problem:

Writing the equation according to the information gave, we have:

y = 25 - (2.50x)

Where:

The relationship between the number of months after the first year and the amount remaining on the card is: linear and inverse because when the number of months after the first year increases (x), the amount remaining on the card (y) will decrease.

The "y" variable is the dependent variable, because it will change according to the number of months passed after the first year (x).

The "x" variable is the independent variable, because it doesn't depend on any other value, just the number of months passed after the first year.

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

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Answer:

its 5,1

Step-by-step explanation:

just took the test

Answer:

522.5in^3

Step-by-step explanation:

4/3 ×3.14×5^3

4/3×3.14×125

1.33×3.14×125

4.18×125

522.5

Step-by-step explanation:

\(v = \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \times 3 \times {5}^{3} \\ = 4 \times 125 \\ = 500 {in}^{3} \\ thank \: you\)

The value of the absolute percent error for week 3 is 25.00%.

To calculate the absolute percent error for week 3, we need to find the absolute difference between the forecasted value and the actual value, and then divide it by the actual value. Finally, we multiply the result by 100 to convert it to a percentage.

To find the absolute percent error for week 3, we'll use the formula:

Absolute Percent Error = |(Actual Value - Forecasted Value) / Actual Value| * 100

For week 3:

Actual Value = 4.00

Forecasted Value = 3.00

Absolute Percent Error = |(4.00 - 3.00) / 4.00| * 100

= |1.00 / 4.00| * 100

= 0.25 * 100

= 25.00

Therefore,For week three, the absolute percent error value is 25.00%.

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The students who has the method that is most representative of the school’s population is Amir.

Population refers to the group of people being studied in an experiment or the group from which a sample is drawn.

Amir has the method that is most representative of the school’s population because the method includes all students in the school studying different subjects but picked at random (every tenth students)

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Answer:

O $225.00

Step-by-step explanation:

Given that

The one of the flight was 350 miles

And, its residual is 105

The regression line is y = 102.50 + 0.65x

where

y denotes the expected fare

And, x denotes the distance

We need to find out the fair of the flight

So,

y = 102.50 + 0.65 (350)

= 330.00

Now the fare is

= 330 - 105

= 225

Answer:

(C) 225 Is correct.

Predicted cost - residual = answer

y= 102.50 + .65(35)

330 - 105 = 225

255

ED2021

Yes, Since  a and b are independent event then therefore, a and b are mutually exclusive events.

             P(a) +P(b) = 0.5+0.5

therefore, P(a ∪b) = 1.0

Mutually exclusive events are events that do not occur at the same time. For example, when you toss a coin, the result is either heads or tails, but you cannot get both results. Such events are also called disjoint events because they do not occur at the same time. If A and B are mutually exclusive events, their probabilities are given by P(A or B) or P(A U B).

According to the question:

P(a) = 0.5 and P(b)=0.5

therefore,

    P(a) +P(b) = P(a ∪ b)

⇒ 0.5 +0.5 = 1.0

Therefor a and b are mutually exclusive events.

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Answer:

p = 3

Step-by-step explanation:

Given

4(2 + px) = 12x

If the coefficient of the x- term is the same on both sides of the equation, it will have no solution.

Distributing gives

8 + 4px = 12x ( equate the coefficients of the x- term )

4p = 12 ( divide both sides by 4 )

p = 3

The value of p when the equation has no solution will be 3. Then the correct option is B.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

4(2 + px) = 12x

8 + 4px = 12x

If the coefficient of the x-term is the same on both sides of the equation, it will have no solution.

4p = 12

p = 3

The value of p when the equation has no solution will be 3. Then the correct option is B.

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A 94.6 L gasoline with a density of 0.680 g/cm^3 has a mass of 64328 g.

Density is defined as the ratio between the mass of a substance and the volume it occupies. Denoted by ρ, density is mass per unit volume and the formula is given below:

ρ =  mass / volume

Converting first the volume from L to cm^3.

1 L = 1000 cm^3

94.6 L = 94.6(1000 cm^3)

94.6 L = 94,600 cm^3

Given the density of the gasoline and its volume, solve for the mass of the gasoline using the formula for the density.

ρ =  mass / volume

0.680 g/cm^3 = mass / 94,600 cm^3

mass = 0.680 g/cm^3 (94,600 cm^3)

mass = 64328 g

mass = 64.328 kg

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Translation is a term that defines a type of transformation in mathematics, specifically in geometry. It is defined as the movement of an object from one place to another in a two-dimensional coordinate plane without altering its shape, size, and orientation.

It is a type of rigid motion that is used in various fields of mathematics, especially in algebra and geometry. In the given (-1, 4) —> (6, -2) scenario, the translation is described below:

Part a: Since the value of x is increasing from -1 to 6, the first blank is filled with 7 (6 - (-1) = 7), which represents a right translation.

Part b: Since the value of y is decreasing from 4 to -2, the first blank is filled with 6 (4 - (-2) = 6), which represents a down translation.

Therefore, the translation can be described as (7, -6), i.e., the point is moved 7 units to the right and 6 units down.

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Answer:

B

Step-by-step explanation:

Convert from mixed numbers to improper fractions:

\(\sf area=90 \frac{3}{10}=\dfrac{90 \cdot 10+3}{10}=\dfrac{903}{10}\)

\(\sf length=10\frac12=\dfrac{10 \cdot 2+1}{2}=\dfrac{21}{2}\)

Area of a rectangle = length x width

⇒ width = area ÷ length

\(\sf \implies width=\dfrac{903}{10} \div \dfrac{21}{2}\)

\(\sf \implies width=\dfrac{903}{10} \times \dfrac{2}{21}\)

\(\sf \implies width=\dfrac{1806}{210}\)

\(\sf \implies width=\dfrac{1806 \div 42}{210 \div 42}\)

\(\sf \implies width=\dfrac{43}{5}\)

\(\sf \implies width=8\frac35\)

\( \pink{ \text{Given:}}\)

\( \\ \)

\( \star \sf{}Area =90 \dfrac{3}{10} \)

\( \\ \)

\( \star \sf{}Length =10 \dfrac{1}{2} \)

\( \\ \\ \)

\( \purple{ \text{To~Find:}}\)

\( \\ \\ \)

\( \star \sf Width \: of \: rectangle\)

\( \\ \\ \)

\( \orange{ \text{Solution:}}\)

\( \\ \\ \)

So first convert length and area from fraction form to decible.

\( \leadsto\sf{}Area =90 \dfrac{3}{10} \)

\( \\ \)

\( \leadsto\sf{}Area = \dfrac{903}{10} \)

\( \\ \)

\( \leadsto\sf{}Area =90.3\)

\( \\ \)

Now convert value length into decibel .

\( \\ \)

\( \leadsto\sf{}Length =10 \dfrac{1}{2} \)

\( \\ \)

\( \leadsto\sf{}Length = \dfrac{21}{2} \)

\( \\ \)

\( \leadsto\sf{}Length = 10.5\)

\( \\ \)

We know :-

\(\bigstar\boxed{\rm Area~of~rectangle= length \times width}\)

\( \\ \\ \)

So:-

\( \\ \)

\(: \implies\sf Area~of~rectangle= length \times width \\ \\ \\ : \implies\sf 90.3= 10.5 \times width \\ \\ \\: \implies\sf 90.3 \div 10.5=width \\ \\ \\: \implies\sf \dfrac{ 90.3}{10.5}=width \\ \\ \\: \implies\sf \dfrac{ 90 \cancel.3}{10 \cancel.5}=width \\ \\ \\: \implies\sf \dfrac{ 903}{105}=width \\ \\ \\: \implies\sf width = \dfrac{ 903}{105} \\ \\ \\: \implies \underline{\boxed{\sf width = 8.6}} \pink\bigstar\)

\(\\\\\\\)

\(\begin{lgathered}\small\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf \small{Formulas\:of\:Areas:-}}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Base\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}\end{gathered}\end{lgathered}\)

Answer:

x= 50

Step-by-step explanation:

The angles of a triangle adds up to 180

First we can see R, S, O is equal to S, R, O

We can also see that the angles are equal to N, O, S

So R, S, O and S, R, O are both 65 degrees

Add 65 + 65

= 130

180 - 130 = 50

x= 50

The proof has two parts.

The next two sections will handle each part separately.

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

Part 1:  If n^2 is divisible by 3, then n is divisible by 3

Apply the contrapositive to get the statement "if n is not divisible by 3, then n^2 is not divisible by 3".

If we can prove the contrapositive is true, then the original conditional is true as well.

Let n be some non-multiple of 3. This would mean either n = 3k+1 or n = 3k+2 for some integer k.

n = 3k+1 gives remainder 1, and n = 3k+2 gives remainder 2.

Let's square both sides of the first equation.

n = 3k+1

n^2 = (3k+1)^2

n^2 = 9k^2 + 6k + 1

n^2 = 3(3k^2+2k)+1

n^2 = 3*(some integer) + 1

We've shown that n = 3k+1, stuff giving remainder 1, leads to n^2 giving the same exact remainder. Therefore, n^2 is also a non-multiple of 3 when we have n = 3k+1.

If n = 3k+2, then,

n^2 = (3k+2)^2

n^2 = 9k^2 + 12k + 4

n^2 = 9k^2 + 12k + 3 + 1

n^2 = 3(3k^2+4k+1)+1

n^2 = 3*(some integer) + 1

We get the same result here as well. Interestingly, we arrive at the same "remainder 1" and cannot reach a remainder 2 with either n = 3k+1 or n = 3k+2.

Examples:

We have proven that if n is not divisible by 3, then n^2 is also not divisible by 3.

This therefore proves the original statement "if n^2 is divisible 3, then n is divisible 3" when using the contrapositive.

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

Part 2:  if n is divisible by 3, then n^2 is divisible by 3.

For this part we know that n is a multiple of 3.

Let k be some integer, so we have n = 3k

Square both sides and do a bit of rearranging to pull out a 3

n = 3k

n^2 = (3k)^2

n^2 = 9k^2

n^2 = 3(3k^2)

n^2 = 3*(some integer)

This proves that n being a multiple of 3 leads to n^2 also being a multiple of 3. Example: n = 18 and n^2 = 18^2 = 324 are multiples of 3.

A way to check if we have a multiple of 3 is to add the digits: 1+8 = 9 and 3+2+4 = 9, those sums are multiples of 3.

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

Both parts have been proven, so the proof is fully concluded.

We've shown that n^2 is divisible by 3 if and only if n is divisible by 3.

Equivalent statements:

Temperature is a variable that uses (2) the scale interval and, according to physical theory, represents in the numerical form how hot or cold something is.

The physical concept of temperature indicates in numerical form how hot or cold something is.

A thermometer is used to determine temperature.

One variable that makes use of the scale interval is temperature.

Thermometers are calibrated using a variety of temperature scales, which historically defined distinct reference points and thermometric substances.

The most popular scales are the Celsius scale, sometimes known as centigrade, with the unit symbol °C, the Fahrenheit scale (°F), and the Kelvin scale (K), with the latter being mostly used for scientific purposes.

One of the seven base units in the International System of Units is the kelvin (SI). The lowest point on the thermodynamic temperature scale is absolute zero, or zero Kelvin, or 273.15 °C.

Therefore, the temperature is a variable that uses (2) the scale interval and, according to physical theory, represents in the numerical form how hot or cold something is.

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