The equation of line, L is given by r=3i+3j-k+t 2i-j+3k Find an Cartesian equation for the plane pi which contains L and the origin.​

The percentage of refrigerators that have lives between 11 years and 18 years is approximately 83.01%.

The values of 11 years and 18 years using the given mean and standard deviation, and then find the area under the standard normal curve between those two standardized values.

First, we standardize the value of 11 years:

z1 = (11 - 14) / 2.5 = -1.2

Next, we standardize the value of 18 years:

z2 = (18 - 14) / 2.5 = 1.6

Now we need to find the area under the standard normal curve between these two standardized values.

We can use a standard normal table or calculator to find this area.

Using a standard normal table, we can find the area between z = -1.2 and z = 1.6 by finding the area to the left of z = 1.6 and subtracting the area to the left of z = -1.2:

Area = P(-1.2 < z < 1.6) = P(z < 1.6) - P(z < -1.2)

Looking up these values in the standard normal table, we find:

P(z < 1.6) = 0.9452

P(z < -1.2) = 0.1151

Substituting these values, we get:

Area = 0.9452 - 0.1151 = 0.8301

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Diego is correct as the number of groups result to 6/5 or 1 1/5.

We have to find the number of groups of 5/6 in 1.

So, we need to perform the division as

= 1/ (5/6)

= 1 x 6/5

= 6/5

= 1 1/5

Thus, Diego is correct as the number of groups result to 6/5 or 1 1/5.

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The inverse variation is y = 9/x, using that equation we can see that n = 9.

An inverse variation between two variables x and y can be written as:

y = k/x

Where k is a constant.

We know that this inverse variation contains the point (3, 3), replacing these values we have:

3 = k/3

3*3 = k

9 = k

Then the inverse variation is:

y = 9/x

Now we want to find n such that (1, n) is on the relation above, then we will get:

n = 9/1

n = 9

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Answer:

  y = -10·sin(πt/5) +12

Step-by-step explanation:

You want the equation of the height of a rider of a Ferris wheel that has a radius of 10 and is 2 off the ground, with a period of 10 seconds, moving downward, starting from even with the center.

The general form of the equation will be ...

  y = A·sin(2πt/T) + B

where A is a scale factor that is based on the radius and initial direction, and B is the height of the center of the wheel above the ground.

We assume that 2 [units] off the ground means the low point of the travel is at that height. Then the middle of the wheel is those 2 [units] plus the radius of the wheel:

  B = 2 + 10 = 12

The scale factor A will be the radius of the wheel, made negative because the initial direction is downward from the initial height. That is, ...

  A = 10

The period (T) is given as 10 seconds.

Putting these parameters together gives ...

  y = -10·sin(2πt/10) +12

  y = -10·sin(πt/5) +12

__

Additional comment

We wonder if this wheel is really only 20 inches (20 in) in diameter, as that dimension seems suitable only for a model. We suspect it is probably 20 meters (20 m) in diameter.

Sometimes "m" is confused with "in" when it is written in Roman font and reproduced with poor resolution.

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For positive acute angles A and B, if it is known that SinA= 11/61 and tan B=4/3, cos(A-B) = 224/305.

We can use the trigonometric identity cos(A-B) = cosA cosB + sinA sinB to find the value of cos(A-B).

First, we need to find the value of cosA and sinB:

Since sinA = opposite/hypotenuse, we can draw a right triangle with opposite side 11 and hypotenuse 61, and use the Pythagorean theorem to find the adjacent side:

cosA = adjacent/hypotenuse = √(61² - 11²)/61 = 60/61

Since tanB = opposite/adjacent, we can draw another right triangle with opposite side 4 and adjacent side 3, and use the Pythagorean theorem to find the hypotenuse:

hypotenuse = √(4² + 3²) = 5

sinB = opposite/hypotenuse = 4/5

Now we can substitute these values into the formula:

cos(A-B) = cosA cosB + sinA sinB

= (60/61)(3/5) + (11/61)(4/5)

= 180/305 + 44/305

= 224/305

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Using the cosine ratio, the value of the marked side in the image given below is approximately: y = 167.7.

The cosine ratio is defined as the ratio of the length of the hypotenuse of the right triangle over the length of the side that is adjacent to the reference angle. It is given as:

cos ∅ = length of hypotenuse/length of adjacent side.

From the image attached below, we have the following:

Reference angle (∅) = 37°

length of hypotenuse = 210

length of adjacent side = y

Plug in the values:

cos 37 = y/210

210 * cos 37 = y

y = 167.7

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Answer:

6 1/243

Step-by-step explanation:

6 goes into 1459, 243 times

243*6=1458

1459-1458=1

So there is a remainder of 1

So the answer would be 6 1/243

The volume of cylinder which is having radius as 5 units and height as 11 units, is 863.5 cubic units.

A "Cylinder" is a 3-dimensional geometric shape that consists of a circular base and a curved surface which extends up from base to fixed height.

The volume(V) of a cylinder is the amount of space enclosed by the cylinder, and it is given by the formula : V = πr²h;, where π is = 3.14, "r" denotes radius of base; "h" denotes the height;

Given that the radius is 5 units and the height is 11 units,

Substituting the values,

We get,

V = π × (5)² × (11);

V = 275π cubic units;

V = 275×3.14 = 863.5 cubic units;

Therefore, the required volume is = 863.5 cubic units.

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The given question is incomplete, the complete question is

If radius is 5 units, and height is 11 units, Find the Volume of the Cylinder.

The equation of the Damari's investment is B(x) = 30000 * 1.03ˣ

Damari's investment

Given that

Initial value, a = 30000

B(3) = 32306.72

The function is calculated as

B(x) = a * bˣ

Using B(3), we have

30000 * b³ = 32306.72

So, we have

b³ = 1.077

Take the cube root of both sides

b = 1.03

So, we have

B(x) = 30000 * 1.03ˣ

So, the function is B(x) = 30000 * 1.03ˣ

The boat of Sky's family

Here, we have

Initial value = 6000

Rate of depreciation = 6%

So, the function is

f(x) = 6000 * (1 - 6%)ˣ

So, we have

f(x) = 6000 * (0.94)ˣ

In 2024, we have

x = 2024 - 2021

x = 3

So, we have

f(3) = 6000 * (0.94)³

Evaluate

f(3) = 4983.50

This value is less than the offered value of $5000

This means that Sky's family should take the offer

The rule of the function

Here, we have the graph

From the graph, we have

Initial value, a = 8

Rate, b = 4.8/8

So, we have

Rate, b = 0.6

So, the function is

f(x) = 8 * 0.6ˣ

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The values of the constants m and c include the following:

m = -1.3

c = 7.1

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Since the point P(-7, 2) is mapped onto P' (3, -11) by the reflection y = mx + c, we can write the following system of equations;

2 = -7m + c    ...equation 1.

-11 = 3m + c    ...equation 2.

By solving the system of equations simultaneously, we have:

2 = -7m - 3m - 11

11 + 2 = -10m

13 = -10m

m = -1.3

c = 7m + 2

c = 7(-1.3) + 2

c = -7.1

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The total amount in the account when turning 60 years is A = $ 11,13,706.08

Given data ,

A savings account with an interest rate of 6% per year and you aren't adding any additional funds in the future

Now , you make $80,000 within the year you turn 60

So , the number of years = 60 - 16 = 44 years

And , from the compound interest , we get

A = P ( 1 + r/n )ⁿᵇ

On simplifying , we get

Where A is the final amount, P is the initial amount (which is 0 in this case), r is the annual interest rate (6% or 0.06), n is the number of times the interest is compounded per year (let's assume it is compounded monthly, so n=12), t is the time in years (44 years from age 16 to age 60).

A = 80,000 ( 1 + 0.06/12 )¹²ˣ⁴⁴

A = $ 11,13,706.08

Hence , the amount in account is A = $ 11,13,706.08

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Answer:

1)

7+9-15 = add 7 and 9, then subtract 15

2)

15-(7+9) = The sum of 7 and 9 subtracted from 15

3)

15-(7+9) =  subtract 7 from 15, then add 9

Step-by-step explanation:

Learn BODMAS. The order of how to do equations. A simple tutorial on yt should be sufficient

Answer:

xs7

Step-by-step explanation:

The calculated number of plants the flower bed can contain is 120

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

Dimensions = 16 m by 9 m

So, the area of the flower bed is

Area = 16 * 9

Evaluate

Area =  144

Also, we have

Each plant requires a space of 1.2m x 1m?

This means that

Plant area = 1.2 * 1

Plant area = 1.2

So, we have

Plants = 144/1.2

Evaluate

Plants = 120

Hence, the number of plants is 120

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Answer:

Step-by-step explanation:

To calculate the number of plants that can be planted in the rectangular flower bed, we need to calculate the area of the flower bed and divide it by the space required for each plant.

The area of the flower bed is calculated by multiplying its length and breadth.

So, the area of the flower bed is 16m x 9m = 144 sq.m.

Each plant requires a space of 1.2m x 1m = 1.2 sq.m.

Therefore, the number of plants that can be planted in the flower bed is:

144 sq.m. ÷ 1.2 sq.m./plant = 120 plants.

So, you can plant 120 plants in the rectangular flower bed.

The x-intercepts, in order from least to greatest, are (2.46, 0) and (5.54, 0).

Use the vertex form of a quadratic function, which is [tex]y = a(x-h)^2 + k,[/tex] where (h, k) is the vertex and "a" is the coefficient of the[tex]x^2[/tex]term. Since the vertex is at (4, 8 1/3), the quadratic function's equation is y = a(x-[tex]4)^2 + 8 1/3.[/tex]

Use the y-intercept to find the value of "a".

The y-intercept is (0,3), so when x=0, y=3.

Plugging these values into the equation above, we get: [tex]3 = a(0-4)^2 + 8 1/3[/tex].

Simplifying, we get 3 = 16a + 25/3, or 9/3 = 16a. Therefore, a = 9/48 or a = 3/16.

To obtain the complete equation, enter the value of "a" into the vertex form equation: [tex]y = (3/16)(x-4)^2 + 8 1/3.[/tex]

To find the x-intercepts, set y = 0 and solve for x.

The equation becomes: [tex]0 = (3/16)(x-4)^2 + 8 1/3[/tex].

Subtracting 8 1/3 from both sides, we get: [tex]-8 1/3 = (3/16)(x-4)^2[/tex]. Multiplying both sides by -1, we get: [tex]8 1/3 = (3/16)(x-4)^2.[/tex]

Take the square root of both sides to isolate[tex]x-4: \sqrt{(8 1/3) } = \sqrt{((3/16)(x-4)^2)}[/tex] Simplifying,

we get: [tex]\sqrt{(25/3)} = (3/4)(x-4).[/tex]

Solving for x, we get two solutions: [tex]x = 4 + 4\sqrt{(3)/3 } or x = 4 - 4\sqrt{(3)/3 }[/tex]

Sort the answers in order of best to worst. The x-intercepts are (2.46, 0) and (5.54, 0) because the first answer is around 5.54 and the second solution is roughly 2.46.

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The ratios for the rectangles and the ovals is 4 : 3

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

Rectangle = 4

Oval = 3

The ratio can be represented as

Ratio = Rectangle : Oval

When the given values are substituted in the above equation, we have the following equation

Rectangle : Oval = 4 : 3

The above ratio cannot be further simplified

This means that the ratio expression would remain as 4 : 3

Hence, the solution is 4 : 3

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Answer:

im an expert

Step-by-step explanation:

About 88.49% of cellphone plans have charges that are less than $83.60.

To determine the percentage of plans that have charges less than $83.60, we need to find the z-score (z) using the given mean and standard deviation, and then look up the corresponding area under the normal distribution curve.

z = (x – μ) / σ

where x = 83.60, mean, μ =  62 and standard deviation, σ = 18

Thus, the z-score of $83.60 is:

z = (83.60 - 62) / 18 = 1.2

Using a standard normal distribution table, we can find that the area to the left of z = 1.20 is 0.8849 or 88.49% (check image attached).

Therefore, about 88.49% of cellphone plans have charges that are less than $83.60.

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Total water bill for the month is $62.37.

It seems that you may have accidentally left out the total amount of your water bill.

The total amount by simply adding the amounts of the individual bills together:

Total water bill =[tex]$36.34 + $26.03[/tex]

= [tex]$62.37[/tex]

You have not provided enough information to determine your total water bill.

You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.

To find your total water bill, you simply need to add the two bills together.

So, the total amount you owe for water this month would be:

Total water bill = [tex]$36.34 + $26.03[/tex]

= [tex]$62.37[/tex]

It appears that you may have forgotten to include the full amount of your water bill by accident.

Simple addition of the separate bill amounts yields the following sum:

Water bill total = [tex]$36.34 + $26.03[/tex]

= [tex]$62.37[/tex]

Your total water bill cannot be calculated because not enough information has been given.

Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.

You just need to combine the two invoices together to get your total water bill.

As a result, this month's total water bill for you would be:

Water bill total =  [tex]$36.34 + $26.03[/tex]

= [tex]$62.37[/tex]

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Answer:91.26ft squared

The difference in temperature between Rome and Munich is given as follows:

6ºC.

The difference in temperature between Rome and Munich is given by the subtraction of Rome's temperature by Munich's temperature.

The bar graph in the context of this problem gives the temperature for each town.

From the bar graph given by the image presented at the end of the answer, the temperatures for Rome and Munich are given as follows:

Hence the difference in temperature between Rome and Munich is given as follows:

11 - 5 = 6ºC.

The graph is given by the image presented at the end of the answer.

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Answer:

he should have subtracted 17 from both sides of the equation

Step-by-step explanation:

x+ 17 = 22

subtract 17 from both sides

X + 17 = 22

-17 -17

x = 5

Answer:

To convert square millimeters to square centimeters, we need to divide the area in square millimeters by 100 (since there are 100 square millimeters in a square centimeter).

So, the area of the top of Katrina's laptop in square centimeters would be:

57,000 mm² ÷ 100 = 570 cm²

Therefore, the area of the top of Katrina's laptop in square centimeters is 570 cm².

The correct step to prove that [tex]BC^2 = AB^2 + AC^2[/tex] is:

By the cross product property, [tex]AC^2 = BC \cdot AD[/tex].

To prove that [tex]BC^2 = AB^2 + AC^2[/tex], we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:

Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.

By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).

Using the proportionality of similar triangles, we can write the following ratio:

[tex]$\frac{AB}{BC} = \frac{AD}{AB}$[/tex]

Cross-multiplying, we get:

[tex]$AB^2 = BC \cdot AD$[/tex]

Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:

[tex]$\frac{AC}{BC} = \frac{AD}{AC}$[/tex]

Cross-multiplying, we have:

[tex]$AC^2 = BC \cdot AD$[/tex]

Now, we can substitute the derived expressions into the original equation:

[tex]$BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$[/tex]

It was made possible by cross-product property.

Therefore, the correct step to prove that [tex]BC^2 = AB^2 + AC^2[/tex] is:

By the cross product property, [tex]AC^2 = BC \cdot AD[/tex].

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Step-by-step explanation:

40 :100        yellow to purple,  divide both sides by 20

2:5

Answer:

the ratio of yellow to purple is 40:100 that is 2:5 in the simplest form.

Step-by-step explanation:

Hope it helps.

The function that represents the number of comic book as a function of the number of years, t is expressed as y = 30x or f(t) = 30t.

We can use the given data to create a linear equation of the form y = mx + b, where y represents the number of comic books and x represents the number of years.

To find the equation, we can use any two pairs of (x, y) values. Let's use the first and fourth years:

First year: (1, 30)

Fourth year: (4, 120)

The slope, m, of the line can be calculated using the formula:

m = change in y / change in x = (120 - 30) / (4 - 1)

m = 90 / 3

m = 30

The y-intercept, b, can be found by substituting one of the (x, y) values and the slope into the linear equation, y = mx + b:

30 = 30(1) + b

b = 0

Therefore, the equation that represents the number of comic books, y, as a function of the number of years, x, is:

y = 30x

or

f(t) = 30t [where t represents the number of years.]

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Answer:

45 degrees

Step-by-step explanation:

The 4 angles of a quadrilateral will add to 360.

We know 1 of them (angle B) is 90 degrees.

We can set up an equation to solve the others.

2x+3x+x+90 = 360

Now solve for x.

Start by combining the x terms together.

6x+90 = 360

6x = 360-90

6x = 270

(6x/6) = 270/6

x = 45 degrees

Check back to see if that makes sense and if the equation equals 360 when x is 45:

2x+3x+x+90 = 360

2(45)+3(45)+45+90=360.

The range of possible values for the population parameter can be estimated using the margin of error, which is calculated as the critical value times the standard error.

Assuming a 95% confidence level, the critical value is approximately 1.96. The standard error for a sample proportion can be calculated as:

SE = sqrt[(p * (1 - p)) / n]

Where p is the sample proportion and n is the sample size. Substituting the values given in the question, we get:

SE = sqrt[(0.65 * 0.35) / n]

We do not know the sample size, so we cannot calculate the standard error exactly. However, we can use a rule of thumb that states that if the sample size is at least 30, we can use the normal distribution to estimate the margin of error.

With a sample proportion of 0.65, the margin of error can be estimated as:

ME = 1.96 * sqrt[(0.65 * 0.35) / n]

We do not know the sample size, so we cannot calculate the margin of error exactly. However, we can use the rule of thumb that a margin of error of about ±5% is typical for a 95% confidence level.

Using this margin of error, we can construct the following range of possible values for the population parameter:

0.65 ± 0.05

This range can be expressed as (0.6, 0.7), which corresponds to option A.

Therefore, the correct answer is option A) (0.6, 0.69).

a. The first term of the arithmetic sequence is 12.

b. The value of n for which the nth term is -33 is 16.

c. The common difference of the arithmetic sequence is -3.

a. The first term, u1, can be found by substituting n=1 into the given formula for the nth term:

u1 = 15 - 3(1) = 12

b. To find the value of n for which the nth term is -33, we set the formula for the nth term equal to -33 and solve for n:

un = 15 - 3n = -33

Adding 3n to both sides, we get:

15 = -33 + 3n

Adding 33 to both sides, we get:

48 = 3n

Dividing both sides by 3, we get:

n = 16

c. The common difference, d, is the difference between any two consecutive terms of the sequence. To find d, we can subtract any two consecutive terms, such as u2 and u1:

u2 = 15 - 3(2) = 9

u1 = 15 - 3(1) = 12

d = u2 - u1 = 9 - 12 = -3

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The length of the ladder that is leaning on the building would be = 24ft. That is option B.

To determine the length of the ladder, the sine rule needs to be obeyed. That is

= a/sinA = b/sinB

Where;

a = 8.2 ft

A = 180-( 70+90

= 180- 160

= 20°

b = X

B = 90°

That is;

8.2/sin20° = b/sin90°

Make b the subject of formula;

b = 8.2×1/0.342020

= 23.9

= 24 ft

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