The coordinate 2 has a weight of 2,

the coordinate 3 has a weight of 2,

and the coordinate 10 has a weight of 1.

Find the weighted average.

I believe the answer is 3

They are tryng to compare the ladder to Mark

If Mark is 6 ft. Long he would have a shadow with the length of 3

The ladders shdw is half of its actual size!

So Marks wouldbe too

1. 5/6

2. 7/8

3. 1/2

4. 5/4

5. 4/5

6. 5/4

7. 11/12

8. 5/4

9. 11/12

10. 2/3

11. 13/20

12. 1/12

13. 7/22

14. 7/18

15. 2/3

16. 5/12

17. 5/12

18. 3/8

The value of Lucas number L(4) is 4.

To find L(4) using the recursive definition of Lucas numbers, we'll follow these steps:

1. L(n) = 1 if n = 1
2. L(n) = 3 if n = 2
3. L(n) = L(n-1) + L(n-2) if n > 2

Since we want to find L(4), we need to first find L(3) using the recursive formula:

L(3) = L(2) + L(1)
L(3) = 3 (from step 2) + 1 (from step 1)
L(3) = 4

Now we can find L(4):

L(4) = L(3) + L(2)
L(4) = 4 (from L(3) calculation) + 3 (from step 2)
L(4) = 7

So, the value of L(4) in the Lucas numbers is 7.

Explanation;-

STEP 1:-  First we the recursive relation of the Lucas number, In order to find the value of the L(4) we must know the value of the L(3) and L(2)

STEP 2:- Value of the L(2) is given in question, and we find the value of L(3) by the recursion formula.

STEP 3:-when we get the value of L(3) and L(2) substitute this value in L(4) = L(3) + L(2) to get the value of L(4).

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Answer:

I want to say False.

Step-by-step explanation:

I would think that the opposite of 4 would be -4.

Good luck! :)

Answer:

True

Step-by-step explanation:

4 = 4/1 1/4 is the reciprocal or the opposite of 4

Answer:

Step-by-step explanation:

¹/₂y + 4 = 2             {subtract 4 from both sides}

¹/₂y = -2                  {multiply both sides by 2}

   y = -4

Answer:

\( \frac{m}{k} = x \\ \\ kx = m \\ \\ k = \frac{m}{x} \)

I hope I helped you^_^

Answer:

\( \frac{m}{k} = x \\ \\ \frac{1}{k} = \frac{x}{m} \\ \\ k = \frac{m}{x} \)

Hope it helps

Answer:

13.9%

Explanation:

Rolling for 2 : (1, 1)

Rolling for 5 : (1, 4), (4, 1), (2, 3), (3, 2)

So, there are (4 + 1) = 5 possible outcomes out of 36 outcomes

Note: There are 36 outcomes when rolling a two fair cubes.

\(\sf Probability = \dfrac{possible \ outcomes}{Total \ outcomes}\)

\(\rightarrow \sf \dfrac{5}{36} \ x \ 100\)

\(\rightarrow \sf \dfrac{125}9} \%\)

\(\rightarrow \sf 13.9 \%\)

Answer:

20

Step-by-step explanation:

Basically, Yout take 60 and divide it by the number 3 and you get 20. Doing the inverse operation (opposite).

There are four levels of measurements in statistics, namely nominal, ordinal, interval, ratio. These levels are important when it comes to analyzing data, since it helps us determine the technique that we can use to support or refute our study.

In the nominal level, we can categorize data but they cannot be ranked. An example would be hair color. In an ordinal data, the data can be both categorize and ranked, but doing mathematical calculation may not make sense. Also, the intervals between rankings doesn't necessarily dictate how close or far apart the data are.

A good example is level of education. In an interval level, the data can be categorized, ranked, and measured but they do not have a true zero. An example could be a range of values that does not include zero. Lastly, in the Ratio level the data can be categorized, rank, and measured, and it has a true zero.

So ratio level is most appropriate for ages of children. Note that ages can be categorized, rank, and measured .Moreover, an age equal to zero means that there is no age or the absence of age.  

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As per the given confidence interval, the value of P is lees than significant.

Confidence interval:

In statistics, a range around a measurement that conveys how precise the measurement is referred as confidence interval.

Given,

A precision instrument is guaranteed to read accurately to within 2 units. a sample of four instrument readings on the same object yielded the measurements 353, 351, 351, and 355. find a 90% confidence interval for the population variance.

Here we need to find the assumptions of the given situation,

From the given question we have identified the following,

Reading of instruments = 353, 351, 351, and 355.

Confidence interval = 90% = 0.09

Number of units = 2.

Based on these details, the standard deviation of this temple is 0.7.

So, the Z score is the same as the sample mean minus the population mean divided by the standard error, which is 2.857.

Therefore, P value was less than significant.

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For starters,

\(\cos(6t+\pi) = \cos(6t) \cos(\pi) - \sin(6t) \sin(\pi) = -\cos(6t)\)

Now by the fundamental theorem of calculus, integrating both sides gives

\(\displaystyle \frac{ds}{dt} = s'(0) + \int_0^t 36 \cos(6u) \, du = 100 + 6 \sin(6t)\)

Integrating again, we get

\(\displaystyle s(t) = s(0) + \int_0^t (100 + 6\sin(6u)) \, du = \boxed{100t - \cos(6t) + 1}\)

Alternatively, you can work with antiderivatives, then find the particular constants of integration later using the initial values.

\(\displaystyle \int \frac{d^2s}{dt^2} \, dt = \int 36\cos(6t) \, dt \implies \frac{ds}{dt} = 6\sin(6t) + C_1\)

\(\displaystyle \int \frac{ds}{dt} \, dt = \int (6\sin(6t) + C_1) \, dt \implies s(t) = -\cos(6t) + C_1t + C_2\)

Now,

\(s(0) = 0 \implies 0 = -1 + C_2 \implies C_2 = 1\)

and

\(s'(0) = 100 \implies 100 = 0 + C_1 \implies C_1 = 100\)

Then the particular solution to the IVP is

\(s(t) = -\cos(6t) + 100t + 1\)

just as before.

Answer:

The answer is image 3.

Step-by-step explanation:

The equation for the line will be y = (-1/2)x + 3 so the gradient is negative and you will have to find the x-intercept and y-intercept.

x-intercept :

\(let \: y = 0\)

\(0 = - \frac{1}{2} x + 3\)

\( \frac{1}{2} x = 3\)

\(x = 3 \div \frac{1}{2} \)

\(x = 6\)

y-intercept :

\(let \: x = 0\)

\(y = - \frac{1}{2} (0) + 3\)

\(y = 3\)

Answerc

Step-by-step explanation:

Therefore, the relative accuracy of features plotted on the map is 500 meters.

To calculate the relative accuracy of features plotted on the map in meters, we need to convert the given accuracy from millimeters to meters.

Given:

Relative accuracy = 90%

Accuracy within 5 mm

To convert millimeters to meters, we divide by 1000:

5 mm = 5/1000 = 0.005 meters

Relative accuracy can be defined as the ratio of the actual accuracy to the map scale. In this case, the map scale is given as 1:100,000, which means that one unit on the map represents 100,000 units in reality.

To calculate the relative accuracy in meters, we multiply the actual accuracy (0.005 meters) by the map scale (100,000):

Relative accuracy = 0.005 meters * 100,000 = 500 meters

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Answer:

Step-by-step explanation:

Both of the points have same y- coordinate of 50.

It means the slope is zero and the line is parallel to the x- axis.

The line has equation:

Correct choice is D

Slope

Points are parallel

Equation

Answer:

Step-by-step explanation:

It's a cube. The volume formula is V = s * s * s

s = 14 meters

V = 14 * 14 * 14

V = 2744 m^3

Answer:

He promised her a new and better life out in Arizona

Underneath the blue neverending sky, swore that he was gonna

Get things in order he'd send for her

When he left her behind, it never crossed her mind

There is no Arizona

No painted desert, no Sedona

If there was a Grand Canyon

She could fill it up with the lies he's told her

But they don't exist, those dreams he sold her

She'll wake up and find

There is no Arizona

Step-by-step explanation:

Market classes and grades are used to describe the quality and characteristics of agricultural products, including meat, poultry, fruits, and vegetables.  True

They provide a common language for buyers and sellers to communicate about the characteristics, such as the age, sex, fat content, and muscling, of the product. Market classes and grades help ensure that buyers receive products that meet their quality standards and help sellers receive a fair price for their products. For example, beef is graded based on marbling, maturity, and lean color, with the highest grade being USDA Prime, followed by USDA Choice and USDA Select.

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Full Question: market classes and grades encompass descriptive terminology of carcasses and products for the understanding of different groups or buyers. T/F

This standardized system of classification allows for easier communication and understanding between buyers and sellers, and ensures consistency and fairness in the marketplace.

Market classes and grades refer to the categorization and labeling of carcasses and products based on their quality and characteristics. These classifications use descriptive terminology that is understood by different groups of buyers, such as meat packers, wholesalers, retailers, and consumers. Market classes typically group animals based on their intended use, such as beef cattle for slaughter, while grades are assigned based on factors such as maturity, marbling, and fat content. This standardized system of classification allows for easier communication and understanding between buyers and sellers, and ensures consistency and fairness in the marketplace.

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The value of the expression according to the order of operations is -11. Thus option D is correct.

According to the statement

We have to find that the value of the given expression.

So, For this purpose, we know that the

The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression.

From the given information:

The expression are :

(-2)-3-6

Now solve it with the order then

(-2)-3-6 = (-2)-3-6

(-2)-3-6 = -2-3-6

Now add the first two terms

then

(-2)-3-6 = -5-6

Now, Add next two terms

Then

(-2)-3-6 = -11.

The value becomes -11.

So, The value of the expression according to the order of operations is -11. Thus option D is correct.

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Answer:

the answer is the first one

Step-by-step explanation:

if you see good the line is going up, so there is you just have to count 1 up and 2 to the right I hope it help

We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

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U.S. currency, cargo shipping weights, and project completion times are continuous data, while the number of defects in production runs is a discrete data. So, option A, B, C are continuous and option D is not continuous.

In the given options, U.S. currency and cargo shipping weights are continuous data. Currency can take any value in the range of denominations, and shipping weights can be measured to any level of precision. Project completion times can also be treated as continuous data, as they can be measured in hours, minutes, or seconds.

On the other hand, the number of defects in production runs is a discrete data, as it represents a count of distinct events. The number of defects cannot take any value within a range, but only specific integer values.

Therefore, options A, B, C are continuous and option D is not continuous.

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We will solve this in steps to understand better! :)

We have \(\begin{gathered}\sf a {x}^{2} + bx + c = 0 \end{gathered}\) here a ≠ 0

Step 1 : Subtract 'c' from both sides of this equation

\(\begin{gathered} \implies \sf a {x}^{2} + bx + c - c = - c \end{gathered}\)

\(\begin{gathered} \implies \sf a {x}^{2} + bx= - c \end{gathered}\)

Step 2 : Dividing both side by coefficient of x² i.e 'a' [why? because we want the coefficient of x² as 1]

\(\begin{gathered} \implies \sf \frac{ a {x}^{2}}{a} + \frac{bx}{a} = - \frac{c}{a} \end{gathered}\)

\(\begin{gathered} \implies \sf {x}^{2} + \frac{bx}{a} = - \frac{c}{a} \end{gathered}\)

Step 3 : Adding \(\begin{gathered} { \bigg(\frac{1}{2} \times {\sf{coefficient}} \: x \bigg)}^{2} \end{gathered}\) i.e,

\( \begin{gathered}{ \bigg(\frac{1}{2} \times \frac{b}{a} \bigg)}^{2} \end{gathered}\)

\(\begin{gathered}{ \bigg( \frac{b}{2a} \bigg)}^{2} \end{gathered}\) to both sides

\(\begin{gathered} \implies \sf {x}^{2} + \frac{bx}{a} +{ \bigg( \frac{b}{2a} \bigg)}^{2} = - \frac{c}{a} +{ \bigg( \frac{b}{2a} \bigg)}^{2} \end{gathered}\)

Step 4 : From the left side of equation an identity is formed i.e (a + b)² which is equal to a² + 2ab + b²

\(\begin{gathered} \implies \sf { \bigg( x + \frac{b}{2a} \bigg)}^{2} = - \frac{c}{a} +{ \bigg( \frac{b}{2a} \bigg)}^{2} \end{gathered}\)

Note : If we expand \({ ( x + \frac{b}{2a} )}^{2} \) it will again form \( {x}^{2} + \dfrac{bx}{a} +{ \bigg( \dfrac{b}{2a} \bigg)}^{2}\)

Step 5 : Solving!

\(\begin{gathered} \implies \sf { \bigg( x + \frac{b}{2a} \bigg)}^{2} = - \frac{c}{a} + \frac{ {b}^{2} }{4 {a}^{2} } \end{gathered}\)

\(\begin{gathered} \implies \sf { \bigg( x + \frac{b}{2a} \bigg)}^{2} = \frac{ {b}^{2} }{4 {a}^{2} } - \frac{c}{a} \end{gathered}\)

Here, [On right side of equation for LCM]

4a² = 4×a×a

a = a

Hence LCM = 4a²

\(\begin{gathered} \implies \sf { \bigg( x + \frac{b}{2a} \bigg)}^{2} = \frac{ {b }^{2} - 4ac }{ 4{a}^{2} } \end{gathered}\)

\(\begin{gathered} \implies \sf { \bigg( x + \frac{b}{2a} \bigg)}^{2} = \frac{ {b }^{2} - 4ac }{ {(2a)}^{2} } \end{gathered}\)

\(\begin{gathered} \implies \sf x + \frac{b}{2a} = \pm \sqrt{\frac{ {b }^{2} - 4ac }{ {(2a)}^{2} }} \end{gathered}\)

\(\begin{gathered} \implies \sf x = - \frac{b}{2a} \pm \sqrt{\frac{ {b }^{2} - 4ac }{ {(2a)}^{2} }} \end{gathered}\)

\(\begin{gathered} \implies \sf x = - \frac{b}{2a} \pm {\frac{\sqrt{ {b }^{2} - 4ac }}{ 2a }} \end{gathered}\)

\(\begin{gathered} \implies \boxed{ \sf x = {\frac{ - b \pm \sqrt{ {b }^{2} - 4ac }}{ 2a }}} \end{gathered}\)

Our quadratic formula is formed!

Therefore,

The roots of general quadratic equation are

\(\begin{gathered} \sf \alpha = {\frac{ - b + \sqrt{ {b }^{2} - 4ac }}{ 2a }} \end{gathered}\)

\(\begin{gathered} \sf \beta = {\frac{ - b - \sqrt{ {b }^{2} - 4ac }}{ 2a }} \end{gathered}\)

Sum of roots \( \alpha + \beta \)

\(\begin{gathered} \implies \sf {\frac{ - b + \sqrt{ {b }^{2} - 4ac }}{ 2a }} + {\frac{ - b - \sqrt{ {b }^{2} - 4ac }}{ 2a }} \end{gathered}\)

\(\begin{gathered} \implies \sf {\frac{- b \: \cancel{+ \sqrt{ {b }^{2} - 4ac }} - b \: \cancel{- \sqrt{ {b }^{2} - 4ac }}}{ 2a }} \end{gathered}\)

\(\begin{gathered} \implies \sf {\frac{- b - b }{ 2a }} \end{gathered}\)

\(\begin{gathered} \implies \sf {\frac{ - 2b }{ 2a }} \end{gathered}\)

\(\begin{gathered} \implies \boxed{ \sf {\frac{ - b }{ a }} }\end{gathered}\)

So, the sum of roots = -b/a

Now,

Product of roots = \( \alpha \beta \)

\(\begin{gathered} \implies \sf \bigg( {\frac{ - b + \sqrt{ {b }^{2} - 4ac }}{ 2a }} \bigg) \bigg({\frac{ - b - \sqrt{ {b }^{2} - 4ac }}{ 2a }} \bigg) \end{gathered}\)

\(\begin{gathered} \implies \sf \bigg( \frac{ \sf{\overbrace{{ (- b)}}^{{a}}\: + \: \overbrace{{\sqrt{ {b }^{2} - 4ac}}}^{{b}} }}{ 2a } \bigg) \bigg({\frac{ { \overbrace{{ (- b)}}^{{a}}\: - \: \overbrace{{\sqrt{ {b }^{2} - 4ac}}}^{{b}}}}{ 2a }} \bigg) \end{gathered}\)

Using (a + b) (a - b) = a² - b²

\(\begin{gathered} \implies \sf {\frac{ { (- b)}^{2} - {( \sqrt{ {b }^{2} - 4ac })}^{2} }{ 4 {a}^{2} }} \end{gathered}\)

\(\begin{gathered} \implies \sf {\frac{ { b}^{2} - ( {b}^{2} - 4ac) }{ 4 {a}^{2} }} \end{gathered}\)

\(\begin{gathered} \implies \sf {\frac{ { b}^{2} - {b}^{2} + 4ac }{ 4 {a}^{2} }} \end{gathered}\)

\(\begin{gathered} \implies \sf {\frac{ 4ac }{ 4 {a}^{2} }} \end{gathered}\)

\(\begin{gathered} \implies \boxed{ \sf {\frac{ c }{ a}}} \end{gathered}\)

So, Product of roots = c/a

We are done with our solution! :D

Move from left to right to see the full answer.

Answer:

(-3, 1)

Step-by-step explanation:

hope this helps if you need explication just told me

Answer:

-1/10

Step-by-step explanation:

-7/24 by the reciprocal of 35/12

The reciproical of 35/12 is 12/35

-7/24 * 12/35

Rewriting

-7/35 * 12/24

-1/5 * 1/2

-1/10

a) f(x) = sin(x) about a = 3:

sin(x) = x - x^3/3! + x^5/5! - ...

b) f(x) = 7x^3 + 5x^2 - 2x + 4 about a = 3:

f(x) = 7x^3 + 5x^2 - 2x + 4 + (x-3)^2(14x^2 + 10x - 2)/2! + ...

c) f(x) = cos(x) about a = 7π/6:

cos(x) = -1/2 + (x-7π/6)^2/2! + ...

The Taylor series of a function is a power series that approximates the function near a given point. The Taylor series for sin(x) about a = 3 is given by:

sin(x) = x - x^3/3! + x^5/5! - ...

This series can be obtained by using the power series for e^x and the trigonometric identity sin(x) = (e^ix - e^-ix)/2.

The Taylor series for f(x) = 7x^3 + 5x^2 - 2x + 4 about a = 3 is given by:

f(x) = 7x^3 + 5x^2 - 2x + 4 + (x-3)^2(14x^2 + 10x - 2)/2! + ...

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This series can be obtained by using the Taylor series for a polynomial function.

The Taylor series for cos(x) about a = 7π/6 is given by:

cos(x) = -1/2 + (x-7π/6)^2/2! + ...

This series can be obtained by using the power series for e^ix and the trigonometric identity cos(x) = (e^ix + e^-ix)/2.

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Instead of developing the geometry, some examples of creating the workpart geometry during machining include:

Contour turning:

Profile milling:

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Answer:

The area of a rectangle is:

\sf A=lw

Plug in what we know:

\sf x^2-7x+10=l(x-5)

Factor the left side:

\sf (x-2)(x-5)=l(x-5)

Divide (x - 5) to both sides:

\sf l=\boxed{\sf x-2}

So the length is x - 2 meters.

Step-by-step explanation: