The sum of 8 times a number and 2 equals 6.

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

\( \sf x=\dfrac{\sqrt3-\sqrt2}{\sqrt3+\sqrt2}\)

On rationalising,

\(\sf\longmapsto x=\dfrac{\sqrt3-\sqrt2}{\sqrt3+\sqrt2}\times\dfrac{\sqrt3-\sqrt2}{\sqrt3-\sqrt2}\)

So,

\(\sf\longmapsto x=\dfrac{(\sqrt3-\sqrt2)^2}{(\sqrt3+\sqrt2)(\sqrt3-\sqrt2)}\)

We know that,

And,

So,

\(\sf\longmapsto x=\dfrac{(\sqrt3)^2-2(\sqrt3)(\sqrt2)+(\sqrt2)^2}{(\sqrt3)^2-(\sqrt2)^2}\)

\(\sf\longmapsto x=\dfrac{3-2\sqrt6+2}{3-2}\)

\(\sf\longmapsto x=\dfrac{5-2\sqrt6}{1}\)

Hence,

\(\sf\longmapsto x=5-2\sqrt6\)

\(\sf y=\dfrac{\sqrt3+\sqrt2}{\sqrt3-\sqrt2}\)

On rationalising,

\(\sf\longmapsto y=\dfrac{\sqrt3+\sqrt2}{\sqrt3-\sqrt2}\times\dfrac{\sqrt3+\sqrt2}{\sqrt3+\sqrt2}\)

So,

\(\sf\longmapsto y=\dfrac{(\sqrt3+\sqrt2)^2}{(\sqrt3+\sqrt2)(\sqrt3-\sqrt2)}\)

We know that,

And,

So,

\(\sf\longmapsto y=\dfrac{(\sqrt3)^2+2(\sqrt3)(\sqrt2)+(\sqrt2)^2}{(\sqrt3)^2-(\sqrt2)^2}\)

\(\sf\longmapsto y=\dfrac{3+2\sqrt6+2}{3-2}\)

\(\sf\longmapsto y=\dfrac{5+2\sqrt6}{1}\)

Hence,

\(\sf\longmapsto y=5+2\sqrt6\)

Now, finding the value of,↓↓

\(\sf x^2+y^2+xy\)

Now, substituting the values of x and y in equation,

\(\sf\longmapsto (5-2\sqrt6)^2+(5+2\sqrt6)^2+(5-2\sqrt6)(5+2\sqrt6)\)

So,

\(\sf\longmapsto [(5)^2-2(5)(2\sqrt6)+(2\sqrt6)^2]+[(5)^2+2(5)(2\sqrt6)+(2\sqrt6)^2]+[(5)^2-(2\sqrt6)^2]\)

\(\sf\longmapsto 25-20\sqrt6+24+25+20\sqrt6+24+(25-24)\)

Cancelling 20√6,

\(\sf\longmapsto 25+24+25+24+(25-24)\)

\(\sf\longmapsto 98+1\)

\(\longmapsto\bf 99\)

\(\textsf{Therefore, the value of x²+y²+xy is 99.}\\\)

Answer: It is option 2 or B

Step-by-step explanation: Simple and easy, the test said it was right too.

\(2x+10 =28\\\\\implies 2(x+5) = 2 \cdot 14\\\\\implies x+5 =14\\\\\implies x = 14 -5 = 9\)

Answer:

2000

Step-by-step explanation:

100/25=4

500*4=2000

Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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Answer:

The answer is (x+3)(x-10)

Step-by-step explanation:

x²-7x-30

x²-10x+3x-30

x(x-10)+3(x-10)

(x+3)(x-10)

The point is [-13,-7] when the actual numbers are all at least two units away from 4.

Given that,

To specify the interval (or pair of intervals) on the real number line, use absolute value notation. (Utilize the x variable.) actual numbers are all at least two units away from 4.

We know that,

We get,

|-4-x| = 3

-3 = -4-x = 3

7 = -x = 13

-13 = x = -7

Therefore, The point is [-13,-7] when the actual numbers are all at least two units away from 4.

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Answer:  12.5%

Explanation:

Rewrite the 1.125 as 1+0.125

So we have the equation y = 254000(1+0.125)^t

Compare that to y = a(1+r)^t and you'll find that r = 0.125

In other words, solving 1+r = 1.125 leads to r = 0.125

That corresponds to a 12.5% growth rate. If r was negative, then you'd have exponential decay.

Answer:

if ur asking whether or not the equality is true or false it’s false

Step-by-step explanation:

The cutoff score for determining higher reading proficiency would be 76 (national mean score) as the cutoff point. Any score above 76 can be considered higher than the national norm.

To determine whether the reading proficiency of high school seniors in your city is higher than the national norm, we can conduct a hypothesis test using the given information. Here are the steps to follow:

State the hypotheses:

The null hypothesis (H0) assumes that the reading proficiency of high school seniors in your city is not higher than the national norm.

The alternative hypothesis (H1) assumes that the reading proficiency of high school seniors in your city is higher than the national norm.

H0: μ ≤ 76 (population mean reading score is less than or equal to the national mean)

H1: μ > 76 (population mean reading score is greater than the national mean)

Determine the significance level:

The significance level (α) is given as 5%, which means we can reject the null hypothesis if the probability of observing the given data is less than 5%.

Calculate the z-score:

To compare the sample reading score of 78 with the national norm, we need to calculate the z-score using the formula:

z = (x - μ) / σ

Where:

x = Sample mean (78)

μ = Population mean (76)

σ = Population standard deviation (1.2)

Substituting the values into the formula:

z = (78 - 76) / 1.2

z = 2 / 1.2

z = 1.67

Find the critical value:

Since our alternative hypothesis is one-tailed (μ > 76), we need to find the critical value from the z-table corresponding to a 5% significance level in the right tail.

Looking up the z-table, we find that the critical z-value for a 5% significance level is approximately 1.645.

Compare the z-score with the critical value:

If the calculated z-score is greater than the critical value, we can reject the null hypothesis; otherwise, we fail to reject it.

In this case, the calculated z-score is 1.67, which is greater than the critical value of 1.645.

Make a decision:

Since the calculated z-score is greater than the critical value, we can reject the null hypothesis.

Conclusion:

Based on the sample reading score of 78 and the given information, there is sufficient evidence to conclude that the reading proficiency of high school seniors in your city is higher than the national norm at a 5% significance level.

In summary, the cutoff score for determining higher reading proficiency would be 76 (national mean score) as the cutoff point. Any score above 76 can be considered higher than the national norm.

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The possible value for the width is 10.

What is the length of a rectangle?

Since its sides are coupled, it essentially only has two distinct dimensions. The length of the rectangle is traditionally thought of as being the longer of these two dimensions, however, when the rectangle is depicted standing on the ground, the vertical side is typically referred to as the length.

Here, we have

The length of a rectangle is 5 times the width

L = 5w

120 < Perimeter = 2L + 2w

= 2(5w) + 2w

= 10w+2w = 12w

10 > w

w < 10

Hence, the possible value for the width is 10.

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Answer:

I'm gonna say false

GDP or Gross Domestic Profit is the money that is being spent/made inside the country. So it stands to reason that if people are spending more, the GDP would go up.

Hope this helps!

The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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Answer:

c) ab/14

Step-by-step explanation:

\(\frac{a}{7} * \frac{b}{2} =\frac{ab}{14}\)

multipling fractions rule is to multiply nominators and denominators separately

The area under the curve over [2,5] is 24.

Given function is f(x) = 2xIntervals [2, 5] is given and it is to be divided into subintervals.

Let us consider n subintervals. Therefore, width of each subinterval would be:

$$
\Delta x=\frac{b-a}{n}=\frac{5-2}{n}=\frac{3}{n}
$$Here, we are using right-hand end point. Therefore, the right-hand end points would be:$${ c }_{ k }=a+k\Delta x=2+k\cdot\frac{3}{n}=2+\frac{3k}{n}$$$$
\begin{aligned}
\therefore R &= \sum _{ k=1 }^{ n }{ f\left( { c }_{ k } \right) \Delta x } \\&=\sum _{ k=1 }^{ n }{ f\left( 2+\frac{3k}{n} \right) \cdot \frac{3}{n} }\\&=\sum _{ k=1 }^{ n }{ 2\cdot\left( 2+\frac{3k}{n} \right) \cdot \frac{3}{n} }\\&=\sum _{ k=1 }^{ n }{ \frac{12}{n}\cdot\left( 2+\frac{3k}{n} \right) }\\&=\sum _{ k=1 }^{ n }{ \frac{24}{n}+\frac{36k}{n^{ 2 }} }\\&=\frac{24}{n}\sum _{ k=1 }^{ n }{ 1 } +\frac{36}{n^{ 2 }}\sum _{ k=1 }^{ n }{ k } \\&= \frac{24n}{n}+\frac{36}{n^{ 2 }}\cdot\frac{n\left( n+1 \right)}{2}\\&= 24 + \frac{18\left( n+1 \right)}{n}
\end{aligned}
$$Take limit as n → ∞, so that $$
\begin{aligned}
A&=\lim _{ n\rightarrow \infty  }{ R } \\&= \lim _{ n\rightarrow \infty  }{ 24 + \frac{18\left( n+1 \right)}{n} } \\&= \boxed{24}
\end{aligned}
$$

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Given function f(x) = 2x. The interval is [2,5]. The number of subintervals, n is 3.

Therefore, the area under the curve over [2,5] is 21.

From the given data, we can see that the width of the interval is:

Δx = (5 - 2) / n

= 3/n

The endpoints of the subintervals are:

[2, 2 + Δx], [2 + Δx, 2 + 2Δx], [2 + 2Δx, 5]

Thus, the right endpoints of the subintervals are: 2 + Δx, 2 + 2Δx, 5

The formula for the Riemann sum is:

S = f(c1)Δx + f(c2)Δx + ... + f(cn)Δx

Here, we have to find a formula for the Riemann sum obtained by dividing the interval [2.5] subintervals and using the right hand endpoint for each ck. The width of each subinterval is:

Δx = (5 - 2) / n

= 3/n

Therefore,

Δx = 3/3

= 1

So, the subintervals are: [2, 3], [3, 4], [4, 5]

The right endpoints are:3, 4, 5. The formula for the Riemann sum is:

S = f(c1)Δx + f(c2)Δx + ... + f(cn)Δx

Here, Δx is 1, f(x) is 2x

∴ f(c1) = 2(3)

= 6,

f(c2) = 2(4)

= 8, and

f(c3) = 2(5)

= 10

∴ S = f(c1)Δx + f(c2)Δx + f(c3)Δx

= 6(1) + 8(1) + 10(1)

= 6 + 8 + 10

= 24

Therefore, the Riemann sum is 24.

To calculate the area under the curve over [2, 5], we take the limit of the Riemann sum as n → ∞.

∴ Area = ∫2^5f(x)dx

= ∫2^52xdx

= [x^2]2^5

= 25 - 4

= 21

Therefore, the area under the curve over [2,5] is 21.

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Answer:

18.682

Step-by-step explanation:

Given that :

E = (-7, - 2) ; x1 = - 7 ; y1 = - 2

F = (11, 3) ; x2 = 11 ; y2 = 3

EF = √((x2 - x1)² + (y2 - y1)²)

EF = √((11 - -7)² + (3 - -2)²)

EF = √((11 + 7)² + (3 + 2)²)

EF = √(18² + 5²)

EF = √324 + 25

EF = √349

EF = 18.6815

EF = 18.682 units (3 decimal places )

The relative cumulative frequency of students who earned a score of 20 or lower on the quiz is: B. 68%.

In Mathematics and Statistics, a frequency table can be used to graphically represent the frequencies or relative frequencies that are associated with a categorical variable.

In Mathematics and Statistics, the cumulative frequency of a data set can be calculated by adding each frequency from a frequency distribution table to the sum of the preceding frequency. Thus, the relative cumulative frequency would be calculated as follows;

Cumulative frequency of students = 4 + 8 + 15 + 7 = 34.

Cumulative frequency of students = 34.

Total frequency = 4 + 8 + 15 + 7 + 7 + 3 + 4 + 2

Total frequency = 50.

Therefore, the relative cumulative frequency can now be determined;

Relative cumulative frequency = 34/50

Relative cumulative frequency = 0.68 or 68%

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Answer:

68%

Step-by-step explanation:

Got it right.

Answer:

Prizefight Irish Whiskey

Step-by-step explanation:

The least positive number n that satisfies all of the conditions is n = 60.

To find the least positive number n that satisfies all of these conditions, we need to find the least common multiple (LCM) of the numbers 1, 2, 3, 4, and 5. The LCM is the smallest positive number that is divisible by all of these numbers.

To find the LCM, we can list the prime factors of each number and then take the highest power of each prime factor that appears in any of the numbers. The prime factorization of each number is:

1: 1

2: 2

3: 3

4: 2 x 2

5: 5

The highest power of each prime factor that appears in any of the numbers is:

2: 2 x 2

3: 3

5: 5

So the LCM is:

\(2 \times 2 \times 3 \times 5$ = 60\)

Therefore, the least positive number n that satisfies all of the conditions is n = 60.

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Answer:

umm???????????? let me try doin it

Knowledge extraction, pattern analysis, data archaeology, information harvesting, pattern searching, and data dredging are all alternative names for Data mining.

Data mining refers to the process of discovering patterns, extracting useful information, and uncovering hidden insights from large datasets. It involves applying various computational techniques, statistical algorithms, and machine learning methods to analyze vast amounts of data.

Knowledge extraction, pattern analysis, data archaeology, information harvesting, pattern searching, and data dredging are all alternative names for data mining because they all encompass the fundamental goal of extracting valuable knowledge and insights from data. These terms emphasize different aspects of the data mining process.

Knowledge extraction highlights the extraction of meaningful information, while pattern analysis focuses on identifying recurring patterns. Data archaeology suggests uncovering hidden information from historical or legacy data sources. Information harvesting and data dredging both emphasize the systematic exploration of data to uncover valuable insights.

Pattern searching highlights the process of searching for specific patterns or relationships within the data. These terms all revolve around the core concept of extracting meaningful knowledge from large datasets.

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Gareth has a capital gain of $34,894, which he will need to include in his assessable income.

To determine the amount Gareth has to include in his assessable income, we need to calculate the capital gain or loss on the sale of the rental house. Here's a breakdown of the calculations based on the given information:

Cost Base:

The cost base is the initial purchase price of the house plus any additional costs incurred to acquire or improve the property. In this case:

Cost Base = Purchase Price + Stamp Duty + Initial Repairs + Rates and Taxes + Interest on Loan

Cost Base = $175,000 + $8,425 + $3,100 + $15,300 + $56,000

Cost Base = $257,825

Adjusted Cost Base:

The adjusted cost base takes into account the depreciation deductions claimed (Division 43 deductions in this case).

Adjusted Cost Base = Cost Base - Division 43 Deductions

Adjusted Cost Base = $257,825 - $42,719

Adjusted Cost Base = $215,106

Capital Gain or Loss:

Capital Gain or Loss = Sale Price - Adjusted Cost Base

Capital Gain or Loss = $250,000 - $215,106

Capital Gain or Loss = $34,894

Gareth's assessable income from the sale of the rental house is $34,894. This is calculated by subtracting the adjusted cost base from the sale price, resulting in the capital gain. It's important to note that tax rules and regulations may vary depending on the jurisdiction, so it's advisable to consult a tax professional or accountant for accurate and personalized advice.

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Answer: a

Step-by-step explanation:

Answer:

the answer is d. it is written in scientific notation.

Step-by-step explanation:

have a nice day!

Answer:

Preetyy sure its D

Step-by-step explanation:

Its not a hollow cylinder

The resulting object will be a solid cylinder. Then the correct option is A.

When a figure is revolved around some fixed axis, the whole three-dimensional solid formed from the area that it swaps out is called a solid of revolution.

A rectangle and a vertical line are shown. If the rectangle is revolved around the vertical line.

Then the resulting object will be

If the rectangle is rotated about the vertical axis then the resulting shape will be a solid cylinder.

The diagram is shown below.

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A bar chart or a histogram are visual representations of data that can be used to explore a single column of data.

A bar chart is used to compare different categories of data, and a histogram is used to measure the frequency of data within a given range. Bar charts allow a user to compare the differences between the categories of data, while histograms provide a better indication of how the data is distributed within the range.

Both bar charts and histograms are useful for identifying patterns, outliers, and trends in the data. By using a bar chart or a histogram, a user can quickly and easily identify where the data is concentrated, as well as identify any outliers or trends in the data.

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The y-intercept of line m₂ is 7.

To determine the y-intercept of line m₂, we need to use the information given and apply the concept of parallel lines. We know that line m₁ can be described by the equation y = +7.

This equation represents a horizontal line that is parallel to the x-axis, and its y-coordinate is always 7, regardless of the value of x.

Since line m₂ is parallel to line m₁, it will also be a horizontal line with a constant y-coordinate. Additionally, we are told that line m₂ contains the point (6, ?), where the x-coordinate is 6.

Since line m₂ is horizontal, its slope is 0. This means that for any value of x, the change in y is 0. Therefore, the y-coordinate of the point (6, ?) must also be 7, just like line m₁.

Hence, the y-intercept of line m₂ is 7, as it passes through the point (0, 7) and is parallel to line m₁.

In conclusion, the y-intercept of line m₂ is 7.

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Answer:

99

Step-by-step explanation:

4x³-2x²+3x​

4×3³-2×3²+3×3

4(27)-2(9)+9

108-18+9

99

99

=(4)(27)−2(32)+(3)(3)

=108−2(32)+(3)(3)

=108−(2)(9)+(3)(3)

=108−18+(3)(3)

=90+(3)(3)

=90+9

=99

Answer:

both are equal

Step-by-step explanation: