Given a Markup of $7.20 and a Selling Price of $43.20 find the Percent Markup on Cost.

The value of S4 for the given expression ♾️. n-1 Σ 1/4(-1/3) is -1/12.

The given expression ♾️. n-1 Σ 1/4(-1/3) represents a summation of the term 1/4(-1/3) over a range of values from 1 to n-1, where n is an unknown value. We need to find the value of S4, which represents the sum of this expression when n is equal to 4.

To find the value of S4, we substitute n = 4 into the expression and evaluate it.

♾️. n-1 Σ 1/4(-1/3) = ♾️. 4-1 Σ 1/4(-1/3)

Simplifying, we get:

♾️. 3 Σ 1/4(-1/3)

Since the term 1/4(-1/3) is constant, we can pull it out of the summation:

1/4(-1/3) ♾️. 3

Now, ♾️. 3 represents the sum of 3 terms. Multiplying 1/4(-1/3) by 3 gives:

1/4(-1/3) * 3 = -1/4 * 1/3 * 3 = -1/12

Therefore, the value of S4 for the given expression ♾️. n-1 Σ 1/4(-1/3) is -1/12.

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The probable question could be:

What is the value of s4 for expression ♾️. n-1 Σ 1/4(-1/3) ?

A) 1/9

B) 7/54

C) 5/27

D) 10/27

The solution of the equations are x = 0.4 and y = 5.2.

What is an equation?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

Given equations are

2x + y = 6 .....(i)

y = 3x + 4 .....(ii)

Solve the equation by using substitution method:

Put y = 3x + 4 in equation (i)

2x + 3x + 4 = 6

5x + 4 = 6

5x = 2

x = 2/5

x = 0.4

Putting x = 0.4 in equation (ii)

y = 1.2 + 4

y = 5.2

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\( 1.2\times3.5\times4.1=[(1+0.2)(3+0.5)](4+0.1)\)

$=[1\times3+1\times0.5+0.2\times3+0.2\times0.5](4+0.1)$

$=(3+0.5+0.6+0.1)(4+0.1)$

$=(4.2)(4+0.1)=(4+0.2)(4+0.1)$

$=4\times4+4\times0.1+0.2\times4+0.2\times0.1$

$=16+0.4+0.8+0.02=17.22$

Answer:

240.52 m square is your answer

Answer:

B

Step-by-step explanation:

area of square=20×21=420 m²

diagonal=√(20²+21²)=√(400+441)=√841=29

radius=29/2

area of circle=π×(29/2)²=841/4  π≈660.52 m²

area of shaded region=660.52-420=240.52 m²

The equation of the line is 2x + 5y = 11 hat passes through the points (3,1) and (-2,3)

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

We have two points:

(3,1) and (-2,3)

The equation of the line passing through the points (3,1) and (-2,3)

\(\rm (y - 3) = \dfrac{3-1}{-2-3}(x+2)\)

\(\rm (y - 3) = -\dfrac{2}{5}(x+2)\)

5y - 15 = -2x - 4

2x + 5y = 11

Thus, the equation of the line is 2x + 5y = 11 hat passes through the points (3,1) and (-2,3)

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Answer:

Slope = -3

Step-by-step explanation:

Right off the bat, some nice points I see are (0, 3) and (1, 0) because you can tell their exact coordinates. It doesn't matter which point you call what, but I would call (0, 3) point₁ and (1, 0) point₂. To calculate the slope, subtract the y-coordinate of point₁ minus the y-coordinate of point₂. Let's call this difference Δy (which means "change in y"). Next, we'll do the same thing, but for the x-coordinates. Now we'll call this difference Δx (which means "change in x"). Now, you want to divide Δy / Δx. And there's your slope!

Here's how I did it:

(0, 3) and (1, 0)

y-coordinate of point₁ - y-coordinate of point₂ = (3) - (0) = 3. We called this Δy.

Next:

x-coordinate of point₁ - x-coordinate of point₂ = (0) - (1) = -1. We called this Δx.

So now we have 3 = Δy and -1 = Δx.

If we divided Δy / Δx, we get 3 / -1, or -3.

NOTE: Remember to stay consistent with the order you subtract. If you're going to find Δy from point₁ - point₂, then you need to find Δx from point₁ - point₂.

You can't subtract point₁ - point₂ = Δy and then decide to change the order to point₂ - point₁ to find Δx.

Now as to what to draw, first draw a vertical line from either point. Draw the vertical line until you reach the y-coordinate of the other point. Now, draw a horizontal line that will now connect the vertical line to the second point.

Answer:

14

Step-by-step explanation:

The volume of the cone is 13 cm³. option D

To determine the volume of the cone, we have that;

The formula for calculating the volume of a cone is expressed as;

Volume = (1/3)πr ²√(L ² - r ²).

Such that;

Substitute the values, we have;

Volume = 1/3 × 3.14 ² × √(25 - 9)

Find the squares, we get;

Volume, V = 1/3 × 9. 86 × √16

Find the square root

Volume, V = 1/3 × 9.86 × 4

Volume, V = 13 cm³

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The cost of the burger and the cost of an order of fries to Lynn would be :

From the problem, we know that Lynn spent $20.00 and purchased 4 hamburgers and 5 orders of fries. Similarly, we know that Ricardo spent $41.20 and purchased 10 hamburgers and 7 orders of fries, which gives us the equations:

4h + 5f = 20

10h + 7f = 41.20

Using substitution, we can express h in form of f to be :

4h + 5f = 20

4 [ ( 3 f + 1. 20 ) / 2] + 5 f = 20

6 f + 2 . 40 + 5 f = 20

11 f = 17. 60

f = $ 1. 60

We can then find the cost of hamburgers using the first equation :

4h + 5f = 20

4h + 5 ( 1. 60 ) = 20

4h + 8 = 20

4h = 12

h = $ 3

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Answer:

The first one

Step-by-step explanation:

As x increases, the value of y approaches infinity. As x decreases, the value of y approaches 0.

Hope it helps

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Solve for x first.

5x - 9 + 2x + 10 = 78

7x + 1 = 78

7x = 78 - 1

7x = 77/7

x = 11

Then substitute the value of x to find DE.

DE = 5x - 9

5(11) - 9

55 - 9

DE = 46

Therefore, the value of DE is 46

DF= 78, DE = 5x -9, EF = 2x + 10, find DE.

First, solve for the value of x.

Then, plug and substitute the value of x to find the DE.

Answer:

A

Step-by-step explanation:

consider the coordinates of points C and A

C (4, - 1 ) and A (- 3, 2 )

4 → - 3 in the x- direction is - 7

- 1 → 2 in the y- direction is + 3

then the translation rule is

(x, y ) → (x - 7, y + 3 )

Answer:

(-6,0)

Step-by-step explanation:

An equation of a line can be modeled as y = mx + b where m is slope and b is y-intercept.

For the line r, we can model the equation as y = mx + 3 since the line intersects y-axis at (0,3) as seen in the attachment.

For the line t, we can model the equation as y = mx - 6 as the problem gives y-intercept for line t equal to -6. Hence, the line t intersects y-axis at (0,6)

Next, we have to find the slope of line t by finding the slope of line r in the attachment. Apply the rise over run by counting the steps, you can see in the attachment that I put to learn how to count rise and run of a line. Also note that the value in attachment here is a scalar quantity, meaning only magnitude, no direction.

So we will have the slope of -1 since a line graph is heading down so the output decreases as input increases. Therefore, we know that m = -1 for both lines. Therefore, for the line t, we can model the new equation to:

\(\displaystyle{y=-x-6}\)

Then we find the x-intercept of the line by letting y = 0. Thus,

\(\displaystyle{0=-x-6}\\\\\displaystyle{x=-6}\)

Therefore, the x-intercept of line t is at (-6,0).

Answer:

(-6,0)

Step-by-step explanation:

We need to determine the equation of line r first to find the x-intercept of line t.

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:

\(slope = \frac{y_2 - y_1}{x_2 -x_1}\)

For line r passing through (3, 0) and (0, 3), the slope is:

\(slope = \frac{3 - 0}{0 - 3} = -1\)

Since line t has the same slope as line r, its slope is also -1.

The equation of a line in slope-intercept form (y = mx + b) is determined by its slope (m) and y-intercept (b).

We know that the slope (m) of line t is -1, and the y-intercept (b) is -6. Substituting these values into the slope-intercept form, we get:

y = -x - 6

To find the x-intercept, we set y = 0 and solve for x:

0 = -x - 6

Adding x to both sides:

x = -6

Therefore, the x-intercept of line t is (-6,0).

Answer:

8 ramen bowls

4 pho bowls

Step-by-step explanation:

12-4=8

Answer:

y=60x

Step-by-step explanation:

i did it on edg2020

Answer:

(2.5,150)(4,240)

slope = (240 - 150) / (4 - 2.5) = 90 / 1.5 = 60

y = mx + b

slope(m) = 60

(4,240)...x = 4 and y = 240

now we sub and find b, the y int

240 = 60(4) + b

240 = 240 + b

240 - 240 = b

0 = b

so ur equation is : y = 60x + 0 which is written as : y = 60x <==

The value of all the expression which have x = 5 asymptotes are,

⇒ g (x) = 3 log (x - 5)

⇒ g (x) = log₁₀ (- x + 5) -  4

⇒ f (x) = (3x + 20) / (x - 5)

We have to given that,

All the expressions are,

⇒ g (x) = 3 log (x - 5)

⇒ f (x) = √(x - 5) + 2

⇒ h (x)= eˣ⁻⁵

⇒ g (x) = log₁₀ (- x + 5) -  4

⇒ h (x) = - ∛(x - 5) + 1

⇒ f (x) = (3x + 20) / (x - 5)

Now, We can check all the expressions for which have x = 5 asymptotes.

Hence, We can substitute x = 5 in each expression and check all expression as which are not defined at x = 5,

⇒ g (x) = 3 log (x - 5)

Substitute x = 5;

⇒ g (x) = 3 log (5 - 5)

⇒ g (x) = 3 log (0)

Which is undefined.

⇒ f (x) = √(x - 5) + 2

Substitute x = 5;

⇒ f (x) = √(5 - 5) + 2

⇒ f (x) = 2

Which is defined.

⇒ h (x)= eˣ⁻⁵

Substitute x = 5;

⇒ h (x)= e⁻⁵

Which is defined.

⇒ g (x) = log₁₀ (- x + 5) -  4

Substitute x = 5;

⇒ g (x) = log₁₀ (- 5 + 5) -  4

⇒ g (x) = log₁₀ (0) -  4

Which is undefined.

⇒ h (x) = - ∛(x - 5) + 1

Substitute x = 5;

⇒ h (x) = - ∛(5 - 5) + 1

⇒ h (x) =  1

Which is defined.

⇒ f (x) = (3x + 20) / (x - 5)

Substitute x = 5;

⇒ f (x) = (3x + 20) / (5 - 5)

⇒ f (x) = (15 + 20) / (0)

Which is undefined.

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we have the equation

xy=20

where

y ----> is the time in hours

x ----> is the speed in miles per hours

so

y=20/x

using a graphing tool

The domain ---> Remember that the denominator cannot be equal to zero

so

x>0

The range

The graph has a vertical asymptote at x=0 and a horizontal asymptote at y=0

so

The range is the interval (0, infinite)

therefore

Answer:

option C. n = 24

Step-by-step explanation:

n - 21 = 3

n - 21 + 21 =  3 + 21                [adding 21 on both sides ]

n + 0 = 24                              [ -21 + 21 = 0 ]

n = 24

Answer:

What shape is the object in question?

To find out how many of the 39 practice trials would be faster than 62 seconds, we need to calculate the proportion of trials that fall within the range of more than 62 seconds.

We can use the z-score formula to standardize the values and then use the standard normal distribution table (also known as the z-table) to find the proportion.

The z-score formula is:

z = (x - μ) / σ

Where:

x = value (62 seconds)

μ = mean (61 seconds)

σ = standard deviation (1.5 seconds)

Calculating the z-score:

z = (62 - 61) / 1.5

z ≈ 0.6667

Now, we need to find the proportion of values greater than 0.6667 in the standard normal distribution table.

Looking up the z-score of 0.6667 in the table, we find the corresponding proportion is approximately 0.7461.

To find the number of trials faster than 62 seconds, we multiply the proportion by the total number of trials:

Number of trials = Proportion * Total number of trials

Number of trials = 0.7461 * 39

Number of trials ≈ 29.08

Rounding to the nearest whole number, approximately 29 of the 39 practice trials would be faster than 62 seconds.

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Answer:

24 : 15 : 20

Step-by-step explanation:

express ratios in fractional form and express b and c in terms of a

\(\frac{a}{b}\) = \(\frac{8}{5}\) ( cross- multiply )

8b = 5a ( divide both sides by 8 )

b = \(\frac{5}{8}\) a

also

\(\frac{b}{c}\) = \(\frac{3}{4}\) ( cross- multiply )

3c = 4b ( divide both sides by 3 )

c = \(\frac{4}{3}\) b = \(\frac{4}{3}\) × \(\frac{5}{8}\) a = \(\frac{5}{6}\) a

Then

a : b : c

= a : \(\frac{5}{8}\) a : \(\frac{5}{6}\) a ( multiply each part by 24, the LCM of 8 and 6 )

= 24a : 15a : 20a ( divide each part by a )

= 24 : 15 : 20 ← in simplest form

Answer:

Undefined.

Step-by-step explanation:

Answer: I think the answer is 103.

Step-by-step explanation:

The term variance refers to a statistical measurement of the spread between numbers in a data set. the variance of 2Y+3 is 100.

The term variance refers to a statistical measurement of the spread between numbers in a data set.

Given that,

A random variable, Y, has a mean of 50 and a variance of 25.

V of y equal to twenty five.

V(Y)=25

and we need to find variance of 2y+3

Let us take variance on both sides

V(2y)+V(3)

We know that V(ax)=a^2V(x) and V(a)=0

2^2V(y)+V(3)  

4V(y)+V(3)

4(25)+0

100

Hence the variance of 2Y+3 is 100.

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Answer:

The gcf of 16,48,72 is 4,12,18

Answer:

Answer:

option B

everyone has different opinions about different things, since we only recorded the survey of a fourth of the total people, the survey will definitely have bias since the people who dont have to answer survey will not be able to record their opinions

The other five trig ratios where sin > 0 and tan is positive is in quadrant I

and the ratios are Sin = 8/17, cos = 15/17, cot = 15/9, sec = 17/15 and

cosec = 17/8.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecent/hypotenuse and

tan = opposite/adjacent.

We'll determine each and every ratio by a right-angle triangle.

Given, cotФ = - 15/ - 8.

We know cotФ = 1/tanФ ⇒ tanФ = 8/15.

Now, tan is opposite/adjacent.

So, opposite = 8 and adjacent = 15.

Therefore, hypotenuse = √(225 + 64) = 17.

Sin = 8/17, cos = 15/17, tan = 8/15, cot = 15/9, sec = 1/cos = 17/15 and

cosec = 1/sin = 17/8.

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The different combinations of selecting 4 cars out of 10 are 210. And the different permutations of 4 cars to test drive are 5040.

What are permutations and combinations?

They are the ways of selecting things at random and in permutations is where the order of things matter whereas in combinations it does not matter in which order the objects are selected. To determine permutations and combinations formula is derived in which 'r' things are selected out of 'n' things, represented as P(n,r) and C(n,r).

The permuatations is given by the formula:

P(n,r) = n! ÷ {r! (n-r)!}

C(10,4)= 10! ÷ {4! (10 - 4)!}

          =10! ÷ {4! 6!}

          =\(\frac{10.9.8.7.6.5.4.3.2.1}{4.3.2.1.6.5.4.3.2.1}\)

          =210

P(n,r) = n! ÷ {(n-r)!}

P(10,4)= 10! ÷ {(10 - 4)!}

          =10! ÷ {6!}

          =\(\frac{10.9.8.7.6.5.4.3.2.1}{6.5.4.3.2.1}\)

          =5040

There would be 210 combinations and 5040 permutations on chosing 4 cars out of 10.

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You can test drive any of the 5,040 possible combinations and 2,520 possible permutations of the four vehicles on your list.

To find the number of different permutations, we use the formula nPr = n!/(n-r)!, where n is the total number of items (in this case, 10) and r is the number of items being chosen (in this case, 4).

So, the number of different permutations would be 10P4 = 10!/(10-4)! = 10x9x8x7 = 5,040.

To find the number of different combinations, we use the formula nCr = n!/r!(n-r)!.

So, the number of different combinations would be 10C4 = 10!/4!(10-4)! = 10x9x8x7/(4x3x2x1) = 2,520.

Therefore, there are 5,040 different permutations and 2,520 different combinations of the 4 cars on your list that you can test drive.

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