Sarun is thrice as old as his sister Anita. If five years is subtracted (5) from Anita’s age and seven years added to Sarun’s age , then
Sarun will be five times Anita’s age. How old were they three years ago?

To check whether the given lines are parallel, perpendicular, skew or neither, we will find their direction vectors. If the direction vectors are parallel, then the lines are parallel. If the direction vectors are perpendicular, then the lines are perpendicular. If the direction vectors are neither parallel nor perpendicular, then the lines are skew. If the direction vectors of one line is parallel to the vector joining two points of the other line, then the lines are neither parallel nor perpendicular.

Line 1:x=t−3, y=3t+8, z=5−2tThis line can be written as(r_1): r= a_1+ t u_1where r_1 is the position vector of any point on the line. a_1 = i(-3) + j(8) + k(5) = -3i + 8j + 5k is the point of intersection of the line with the coordinate axis. And u_1 is the direction vector of the line.u_1 = i + 3j - 2k

Line 2: x=2s−1, y=s−1, z=s−4This line can be written as(r_2): r= a_2+ s u_2where r_2 is the position vector of any point on the line. a_2 = i(-1) + j(-1) + k(-4) = -i - j - 4k is the point of intersection of the line with the coordinate axis. And u_2 is the direction vector of the line.u_2 = 2i + j + k Now we will find the direction vectors of the two lines and then check their properties. The direction vectors of the lines areu_1 = i + 3j - 2ku_2 = 2i + j + kSince the direction vectors are not parallel, we need to check whether they are perpendicular or not.u_1.u_2 = (i + 3j - 2k).(2i + j + k) = 2 + 3 - 2 = 3Since u_1.u_2 is not equal to zero, the two lines are neither parallel nor perpendicular to each other. Therefore, the lines are skew lines.

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Answer:

148.5 π

Step-by-step explanation:

Cone = 1/3 * base * height

1/3 * 22 * (9/2)^2 π = 148.5 π

Answer:

75% correct

Step-by-step explanation:

The probabilities for the given event is Pr(exactly 2) = 0.0283. Pr(exactly 1) = 0.2901, and Pr(exactly 3) = 0.001331.

The possibility of an event occurring can be expressed in terms of probability and odds, but they are not the same thing. The ratio of positive events to all conceivable outcomes, represented as a fraction or decimal, is known as probability. On the other hand, odds represent the proportion of good outcomes to those that are unfavourable. Odds can be stated as a ratio, fraction, or by dividing the favourable outcomes by the total number of outcomes to get their equivalent in probability.

The binomial probability is given as:

[tex]P(x) = (nCx) * p^x * (1-p)^{(n-x)}[/tex]

Here, n = 3, p = 0.11, and q = 1 - p = 0.89.

Thus,

[tex]Pr(exactly 2) = P(2) = (3C2) * 0.11^2 * 0.89^{(3-2)} = 0.0283\\Pr(exactly 1) = P(1) = (3C1) * 0.11^1 * 0.89^{(3-1)} = 0.2901\\Pr(exactly 3) = P(3) = (3C3) * 0.11^3 * 0.89^{(3-3)} = 0.001331[/tex]

Hence, the probabilities for the given event is Pr(exactly 2) = 0.0283. Pr(exactly 1) = 0.2901, and Pr(exactly 3) = 0.001331.

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Answer:

6 29 25

Step-by-step explanation:

those are the prime numbers on the 2023 feb calendar

The experimental probability of the arrow stopping over section 1 is 7/13, or 0.538.

To calculate this, you need to take the number of times the arrow stopped on section 1 (45) and divide it by the total number of times the arrow was spun (80). This can be expressed as a fraction (45/80), which can be simplified to 7/13. To convert this fraction to a decimal, divide the numerator by the denominator (7/13 = 0.538).

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the sale price of the cell phone after the 35% discount is $315.25.

How to solve and what is sale?

To find the sale price of the cell phone, we need to apply the discount of 35% to the regular price of $485. We can do this by multiplying the regular price by 0.35 and then subtracting the result from the regular price:

Sale price = Regular price - Discount amount

Sale price = $485 - (0.35 x $485)

Sale price = $485 - $169.75

Sale price = $315.25

Therefore, the sale price of the cell phone after the 35% discount is $315.25.

A sale is a temporary reduction in the price of a product or service. Sales are often used by businesses to attract customers and increase sales volume. Sales can be offered for many reasons, such as to clear out inventory, promote a new product, or attract customers during a slow period.

In a sale, the price of a product or service is discounted, either by a fixed amount or by a percentage of the regular price. For example, a store might offer a 20% discount on all clothing items, or a car dealership might offer a $5,000 discount on a particular model of car.

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Therefore, the slope of the line passing through the points (0,5) and (2,0) is -5/2.

In mathematics, slope refers to the measure of steepness of a line. It is the ratio of the change in y (vertical change) over the change in x (horizontal change) between any two points on the line. The slope of a line is represented by the letter "m" and can be calculated using the slope formula: m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

Here,

To find the slope of a line, we use the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are any two points on the line.

Using the given coordinates, we have:

x1 = 0, y1 = 5

x2 = 2, y2 = 0

slope = (0 - 5) / (2 - 0)

slope = -5/2

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The example of 2×3 matrix A and a 3×2 matrix B such that, letting T(x)=Ax and U(x)=Bx is reflection Ab.

Matrices, the plural form of matrix, are the groupings of numbers, variables, symbols, or phrases in a rectangular table with varying rows and columns. These are rectangular arrays with specified operations such as addition, multiplication, and transposition. The elements of the matrix are the numbers or entries in it. The horizontal entries of matrices are referred to as rows, whereas the vertical elements are referred to as columns.

Let,

[tex]B = \left[\begin{array}{cc}0&1\\1&0&0&0\end{array}\right] , A = \left[\begin{array}{ccc}1&0&0\\0&1&0\\\end{array}\right][/tex]

Then,

[tex]AB =\left[\begin{array}{ccc}1&0&0\\0&1&0\\\end{array}\right] \left[\begin{array}{cc}0&1&1&0&0&0\\\end{array}\right] \\\\AB = \left[\begin{array}{cc}0&1&1&0\\\end{array}\right][/tex]

Therefore, Ab is reflection about y = x .

As U = Bx and T∘U    

A matrix is a rectangular array of integers, variables, symbols, or expressions that are defined for subtraction, addition, and multiplication operations. The number of rows and columns in a matrix determines its size (also known as the order of the matrix).          

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Making r the subject of formula in this equation A = V²/r gives r = V²/A.

In Mathematics and Science, the centripetal acceleration of a physical object (body) can be calculated by using the following mathematical expression:

A = V²/r

Where:

In this exercise, you are required to make radius (r) the subject of formula. Therefore, by making radius (r) the subject of formula, we have the following:

Radius, r = V²/A

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In the following question, the Total cost to production 50 barstools: $1,200 Total cost to produce 51 barstools: $1,228.91 "Total cost to produce 52 barstools: $1,258.44" Total cost to produce 53 barstools: $1,288.59 Therefore, the approximate total cost of producing 53 barstools is $559.15.

The cost function for producing $x$ items of a certain brand of barstool is given by C(x)=0.01x3-0.6x2+13x+200.

(a) C(x)=0.03x3- 0.12x2+13

(b) MC(50)=-82 dollars per barstool.

It approximately represents the cost of producing the 50th barstool.

(c) The exact cost of producing the 51st barstool is C51=C50+MC(50)=$28.91 dollars.

(d) Using C(50) and MC (50), the total cost of producing 53 barstools is approximately C50+(53-50) MC(50)=$229.82.

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Answer:

[tex] \frac{3}{2} {x}^{8} [/tex]

Step-by-step explanation:

[tex] \frac{9 {x}^{16} }{6 {( {x}^{2} )}^{3}{x}^{2} } = \frac{9 {x}^{16} }{6 {x}^{6} {x}^{2} } = \frac{9 {x}^{16} }{6 {x}^{8} } = \frac{3}{2} {x}^{8} [/tex]

There will be a population of 2,097,152 rabbits after 5 years.

A form of growth known as exponential growth occurs when a quantity's rate of expansion is proportionate to its present value. In other words, a quantity expands more quickly the greater it is. A prime example of exponential expansion is the rabbit population, which doubles in size every three months.

Given that, population of rabbits is doubling every 3 months.

That is,

5 years = 5 x 12 = 60 months

Number of doublings = 60 / 3 = 20

For every doubling, the population will be twice as large.

Thus,

P = 2 x 2²⁰ = 2 x 1,048,576 = 2,097,152 rabbits

Therefore, there will be approximately 2,097,152 rabbits after 5 years.

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Angela's score is in the 87th percentile, which means that 87% of the scores were at or below her score.

To calculate the percentage of scores above her score, we subtract 87% from 100%. Therefore, the percentage of scores above Angela's score is 13%.

In summary, Angela's score is at or below 87% of the scores, and 13% of the scores are above her score. The percentile score indicates the percentage of scores that fall below a particular score. Therefore, Angela performed better than 87% of the test takers who took the aptitude test in accounting.

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Answer: 500 cm

Step-by-step explanation:

multiply by 0.5 by 10000

The number of claims filed by the policyholders has a poisson distribution. Therefore, the variance of the number of claims filed will be about 2.5.

We need to use the Poisson Distribution for solving the question, which is as follows:

P(x) = (λˣ/x!) × [tex]e^(-lambda)[/tex]

where is the mean value of distribution and x is the number of events we want to calculate.

If a random variable follows a Poisson distribution, its variance is equal to its mean.

So, the mean will be λ.

Let the probability of filing four claims be p1.

Then, probability of filing two claims will be ⁵p₁

We know the sum of probabilities of different events of Poisson distribution will always be equal to 1.

So,

p₁ + ⁵p₁ = 1

p₁ = 1/6

The mean number of claims is λ, which is given by:

Now, the variance of the Poisson distribution is also λ.

So, the variance of the number of claims filed is 2.5.

Hence, the answer is variance of the number of claims filed is 2.5.

The mean number of claims is λ, which is given by:

λ = ⁴p₁ + 2⁵p₁ = 2.5

Now, the variance of the Poisson distribution is also λ.

So, the variance of the number of claims filed is 2.5.

Hence, the answer is variance of the number of claims filed is 2.5.

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Answer:

a = 3

Step-by-step explanation:

since the parabola passes through (7, 27 ) then te coordinates of the point make the equation true.

substitute x = 7 and y = 27 into the equation and solve for a

27 = a(7 + 2)(7 - 6) = a(9)(1) = 9a ( divide both sides by 9 )

3 = a

New width w'$ is 75% of the original width w. Therefore, the width of the land is reduced by 25%, just like the area.

The area of the tennis court is given by:

A = lw

where l is the length of the court and w is the width of the court.

Substituting the given values, we have:

[tex]$$260.7569 = l \cdot 10.97$$[/tex]

Solving for l, we get:

[tex]$l = \frac{260.7569}{10.97} \approx 23.76 \text{ m}$$[/tex]

To find the area of the court without the white bands, we need to subtract the areas of the two white bands from the total area. Since the white bands are on the top and bottom, we need to subtract twice the product of the width of the court and the width of the white band. The width of the white band is not given, but we know that the width of the court will be reduced by 25%, so the new width of the court will be:

w' = w - 0.25w = 0.75w

Substituting the given values, we have:

[tex]$$\begin{aligned}A' &= lw' - 2(0.75w)(l) \ &= l(0.75w) - 1.5wl \ &= 0.5625lw\end{aligned}$$[/tex]

where A' is the new area of the court without the white bands. Substituting the values of l and w that we found earlier, we have:

[tex]$$A' = 0.5625 \cdot 23.76 \cdot 10.97 \approx 146.17 \text{ m}^2$$[/tex]

Therefore, the new area of the court is reduced by 25%.

To find out if the width of the land is also reduced by 25%, we need to compare the original width w with the new width w'. We have:

[tex]$w' = 0.75w$$[/tex]

Dividing both sides by w, we get:

[tex]$\frac{w'}{w} = 0.75$$[/tex]

This means that the new width w'$ is 75% of the original width w. Therefore, the width of the land is reduced by 25%, just like the area.

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The shopper must spend at least $444.44 to get the 10% discount.

If a shopper gets a 10% discount, it means they pay only 90% of the original price. Let's say the original spending is represented by x. Then the spending after the 10% discount would be:

d = 0.9x

Now, we know that the shopper must spend at least $400 to get the discount, so we can set up an inequality:

d ≥ 400

Substituting the expression we found for d, we get:

0.9x ≥ 400

Dividing both sides by 0.9, we get:

x ≥ 444.44

So the shopper must spend at least $444.44 to get the 10% discount.

Answer:

83.6%

Step-by-step explanation:

Let's say the original price is x

x decreased by 12% means 88% of x is left.

0.88x decreased by 5% means 95% of 0.88x is left.

This means the answer is: 0.88x * 0.95 = 0.836

The percent of the total decrease is 83.6%

Hope this helps :)

Have a great day!

Answer:

[tex]\frac{xa}{28}[/tex]

Step-by-step explanation:

   [tex]\frac{4x^2}{y7a^3} * \frac{a^4}{16+8x}[/tex]

= [tex]\frac{2x(2+x)}{7a^3} * \frac{a^4}{8(2+x)}[/tex]

= [tex]\frac{xa}{28}[/tex]

[tex]\frac{x^{2}a }{28}[/tex]

Explination:

Factor the numerator and the denominator and cancel the common factors

The width of the automobile parking space is 52.8 meters.

First, we want to convert the duration of the second one base from centimeters to meters

3760 cm = 37.6 m

Subsequent, we're suitable to use the system for the vicinity of a trapezoid

A = ( b1 b2) h/ 2

In which b1 and b2 are the lengths of the two bases, h is the height( or range) of the trapezoid, and A is the area.

Substituting the given values, we have

= (73.437.6) h/ 2

= 111h/ 2

Multiplying both angles through 2 and dividing by 111, we get

h = 52.8

Hence, the width of the automobile parking space is 52.8 meters.

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Therefore, the net result of the transaction is a loss of $21.36. The answer is A) $21.36.

Selling price refers to the price at which a product or service is sold to customers or clients. It is the amount of money that a buyer pays to the seller in exchange for the product or service. The selling price is usually higher than the cost of producing or acquiring the product or service, and the difference between the selling price and the cost is the profit earned by the seller. In some cases, the selling price may also include additional charges such as taxes, shipping fees, or handling fees.

by the question.

To calculate the net result of the transaction, we need to determine how many shares were purchased with the $3,200 investment.

$3,200 divided by $11.95/sh = approximately 267.36 shares (rounded to the nearest hundredth)

Therefore, the total cost of purchasing 267 shares at $11.95/sh is:

267 shares x $11.95/sh = $3,195.65

The total revenue from selling 267 shares at $11.87/sh is:

267 shares x $11.87/sh = $3,174.29

To determine the net result of the transaction, we subtract the total revenue from the total cost:

$3,174.29 - $3,195.65 = -$21.36

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The sugar concentration would be approximately 62.5%.

To find the concentration of sugar in the solution, we need to use the formula:

In this case, the solute is sugar and the solvent is water. We are given that the mass of sugar is 50 grams and the mass of water is 30 grams. However, we need to convert the mass of water to volume since we need the volume of the entire solution to calculate the concentration.

We can assume that the density of water is 1 g/mL, so the volume of water is 30 mL. The total volume of the solution is therefore 50 mL + 30 mL = 80 mL.

Now we can use the formula to find the concentration of sugar:

So the concentration of sugar in the solution is approximately 0.625 grams per milliliter.

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Answer:

$12

Step-by-step explanation:

Cans : Dollars

6 cans : 9 dollars

DIVIDE BY 3

2 cans : 3 dollars

MULTIPLY BY 4

8 cans : 12 dollars

Hope this helps :)

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The probability of drawing either a queen or a diamond is 15/52

To determine the probability of drawing either a queen or a diamond, we have to find the sum of the probabilities of drawing a queen and drawing a diamond, then subtract the probability of drawing both a queen and a diamond. This is because the probability of drawing both a queen and a diamond has been added twice when we added the individual probabilities.

Thus, we have:P(queen or diamond) = P(queen) + P(diamond) - P(queen and diamond)

The probability of drawing a queen is 4/52, since there are four queens in a deck of 52 cards. The probability of drawing a diamond is 13/52, since there are 13 diamonds in a deck of 52 cards.

There are two ways to draw a card that is both a queen and a diamond, namely the queen of diamonds and the diamond queen. Thus, the probability of drawing both a queen and a diamond is 2/52. Therefore, P(queen or diamond) = 4/52 + 13/52 - 2/52 = 15/52 = 15/4 = 3.75 As a reduced fraction, this is 15/52.

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a. The probability of guessing a wrong answer is 4/5

Since there are three guesses, the probability of the first 2 guesses being wrong and the 3rd being correct can be calculated using the multiplication rule as follows: P(2 wrong and 1 correct) = (4/5)^2 * 1/5 = 0.128.

b. The complete list of possibilities for 2 wrong and 1 correct is: WWC, WCW, CWW.

The probability of each can be calculated using the multiplication rule as follows: P(WWC) = (4/5)^2 * 1/5 = 0.128, P(WCW) = (4/5) * (1/5) * (4/5) = 0.128, and P(CWW) = 1/5 * (4/5)^2 = 0.128.

c. The probability of getting exactly one correct answer when 3 guesses are made is the sum of the probabilities of the three possible outcomes of 2 wrong and 1 correct, which is 0.128 + 0.128 + 0.128 = 0.384.

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