solve the following pair of simultaneous equation graphically
X+2y=3,2x-y=7

The probability that the department store will get at most 3 calls in a 55 minute period is 0.066

The Poisson distribution is a discrete probability function that means the variable can only take specific values in a given list of numbers, probably infinite. A Poisson distribution measures how many times an event is likely to occur within “x” period of time.

It is given that a department store gets an average of 16 calls in a 2 hour or 161055 = 223 calls per minute

Find the probability by Poisson distribution with parameter

λ = 223

P(X = x) = λˣе - λx!

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

   = (223)⁰е - 223(0!) +(223)¹е - 223(1!) +(223)²е - 223(2!) +(223)³е - 223(3!)

  = 0.0006 + 0.004 + 0.018 + 0.043

P(X ≤ 3) ≈ 0.066

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Answer:

The length of one lap around the path is 2π x 350 m, which is equal to 2200 m.

Jimmy jogs 2200 m x 3 laps x 5 days, which is equal to 33000 m or 33 km.

Step-by-step explanation:

The number of people who become aware of the product at time t is [tex]p(t) = 5(1 - 0.9^{\frac{t}{10} })[/tex]

The advertising company wants to introduce a new product to a population of 5 million people. They assume that no one was aware of the product at the beginning of the campaign. They also know that after 10 days of advertising, 10% of the people became aware of the product. To find out how many people become aware of the product at time t, they use a function called p(t).

The function p(t) represents the number of people (in millions) who become aware of the product by time t. The company assumes that the rate at which p increases is proportional to the number of people still unaware of the product. This means that the more people who are unaware of the product, the faster the number of people who become aware of it will increase.

To express the proportionality mathematically, we can use the equation:

p'(t) = k [5 - p(t)]

Where p'(t) is the rate of change of p with respect to time t, and k is the proportionality constant that determines the speed of the increase. The quantity (5 - p(t)) represents the number of people who are still unaware of the product at time t. This means that as p(t) gets closer to 5 million, the rate of increase of p(t) will slow down.

To solve this equation, we need to use calculus. Integrating both sides of the equation, we get:

ln|5 - p(t)| = kt + C

Where C is the constant of integration. To determine the value of C, we use the initial condition that p(0) = 0. This means that at the beginning of the campaign, no one was aware of the product. Substituting this into the equation, we get:

ln|5 - 0| = k(0) + C

Simplifying, we get:

C = ln(5)

Substituting this value into the equation, we get:

ln|5 - p(t)| = kt + ln(5)

To find the value of p(t) at a specific time t, we can solve for p(t) by taking the exponential of both sides of the equation:

[tex]|5 - p(t)| = e^{kt+ln(5)}[/tex]

Simplifying, we get:

[tex]5 - p(t) = 5e^{kt}[/tex]

Or:

[tex]p(t) = 5(1 - e^{kt})[/tex]

To find the value of k, we can use the fact that 10% of the people were aware of the product after 10 days of advertising. This means that:

p(10) = 0.1(5) = 0.5

Substituting this into the equation, we get:

[tex]0.5 = 5(1 - e^{10k})[/tex]

Solving for k, we get:

k = -0.1 ln(0.9)

Substituting this value into the equation for p(t), we get:

[tex]p(t) = 5(1 - e^{-0.1ln(0.9)t})[/tex]

Simplifying, we get:

[tex]p(t) = 5(1 - 0.9^{\frac{t}{10} })[/tex]

This is the formula that tells us how many people will become aware of the product at time t.

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The expression for the number of different samples is: C(3, 2) x C(47, 4) = 3 x C(47, 4) = 3 x

(47! / (4! x 43!)).

The number of different samples of size 6 that contain exactly 2 defective parts can be calculated using the binomial coefficient formula:

C(3, 2) x C(47, 4)

where C(n, k) represents the number of ways to choose k objects from a set of n objects.

In this case, we first choose 2 defective parts from the 3 defective parts in the bin, which can be done in C(3, 2) ways. Then we choose 4 nondefective parts from the 47 nondefective parts in

the bin, which can be done in C(47, 4) ways. We multiply these two quantities together to obtain the total number of different samples of size 6 that contain exactly 2 defective parts.

Therefore, the expression for the number of different samples of size 6 that contain exactly 2 defective parts is:

C(3, 2) x C(47, 4) = 3 x C(47, 4) = 3 x (47! / (4! x 43!))

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The probability that, if the car selected is older than two years old,  it is not a foreign car is 57/118, so the correct option is A.

We want to find the probability that if the car selected is older than two years old,  it is not a foreign car.

Looking at the table, we can see that there are 200 - 82= 118 cars older than two years.

And of these 118 cars, 25 + 10 + 26 = 61 are foreign cars.

Then the number of non-foreign cars is:

118 - 61 = 57

And the probability will be equal to the quotient between the number of non-foreigner cars and the total number:

P = 57/118

So the correct option is A.

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Answer:

y – 7 = 3(x – 5)

Step-by-step explanation:

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ 3}(x-\stackrel{x_1}{5}) \\\\\\ y-7=3x-15\implies {\Large \begin{array}{llll} y=3x-8 \end{array}}[/tex]

The mentioned  scenario can be calculated using the distance equation, the number of seconds in which explosion would occur is 1.125 seconds.

The distance covered by the object is equal to the  product of the speed of object and the time required for it.

Distance = Time x speed

Firework A :

D = 360xt - - - (1)

Firework B:

D = 280x(0.25) + 280xt

D= 70 + 280xt - - - (2)

Equate equation (1) and (2) :

360t = 280t + 70

Collect like terms

360t - 280t = 70

80t = 70

t = 70/80

t = 0.875 seconds

0.875 + 0.25 = 1.125 seconds

Hence, the fireworks will explode after 1.125 seconds of launching Firework B.

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Daniella and her friends collected a total of 44 shells.

What is linear equation ?

Linear equation can be defined as equation in which highest degree is one.

Given ,

Daniella and her 10 friends are collecting shells on the beach to make crafts.

After they have collected the shells and put them in a pile, they split them evenly among the group. Each person gets 4 shells.

The correct equation for this problem is:

s = 11 x 4

where s is the total number of shells collected.

Simplifying this equation, we have:

s = 44

Therefore, they collected a total of 44 shells.

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Answer: approx 13.54 (full decimal : 13.416666667)

Step-by-step explanation:

Area = Base Area x Height   OR    Length x Width x Height

5/3 x 13/4 x 5/2

5 x 13 x 5 = 325

3 x 4 x 2 = 24

325/24 = approx 13.54

In total they knocked down 104 pins.

I got this by multiplying 26 by 3, which equals 78, then adding 26 to 78 to get the final answer, 104.

Hope this helps!

Answer:

A(t) = 9000(1 + 0.036/12)^12t

[Function formula for the compound interest]

A = 9000(1 + 0.036/12)^12t

[General formula for the compound interest]

A(1) ≈ 9329.40 $

[Compound interest over 1 year]

Step-by-step explanation:

Compound interest formula:

A = P(1 + r/n)^nt.

P is the principal or starting amount.

r is the interest rate.

n is the number of times compounded per year.

t is the period of time.

Given P is 9000, r is 3.6% or 0.036, n is 12 or monthly, and t is variable.

The following function represents the relationship over time:

A(t) = 9000(1 + 0.036/12)^12t

The number of ways to choose 2 toppings from a menu of 18 toppings is a classic example of a combinatorial problem.

We have a set of 18 items (toppings), and we want to know how many ways there are to choose 2 of these items. The answer is given by the binomial coefficient C(18, 2), which is the number of ways to choose 2 items from a set of 18 items, where order does not matter and repetition is not allowed.

The formula for a binomial coefficient is:

C(n, k) = n! / (k! * (n - k)!)

where n! means n factorial, which is the product of all positive integers from 1 to n. So, for example, 5! = 5 * 4 * 3 * 2 * 1 = 120.

Using this formula, we can calculate the number of ways to choose 2 toppings from a menu of 18 toppings:

C(18, 2) = 18! / (2! * (18 - 2)!) = 18 * 17 / (2 * 1) = 153 ways

So there are 153 different ways to choose 2 toppings from a menu of 18 toppings.

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If 18% of middle school student voted in a school election and number of students who voted is 213 , then the total students in the middle school is approximately 1184 students .

Let "x" be = total number of middle school students.

We know that 18 percent  of the students voted = 0.18x, and is equal to 213  ;

that means , ⇒ 0.18x = 213 ;

Now we need to solve for x,

We divide both sides by 0.18 ;

⇒ x = 213/0.18  ;

Simplifying, we get:

⇒ x = 1183.33

Since the number of students cannot be in decimal ,

So ,  the actual number of students must be greater than or equal to 1183.33.

Therefore, the middle school has approximately 1184 students.

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3 minutes is the cost of the call that is same for both plans

Two or more expressions with an Equal sign is called as Equation.

Let's assume the call duration in minutes is represented by x.

For David, the cost of the call can be represented by the equation: C(d) = 4 + x

For Alec, the cost of the call can be represented by the equation: C(a) = 1 + 2x

Since the cost of the call is the same for both plans, we can set the two equations equal to each other and solve for x:

4 + x = 1 + 2x

Solve for x.

3 = x

Hence, the call duration that costs the same on both plans is 3 minutes.

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We can simplify the expression to get:

[tex]\sqrt[4]{x^3}[/tex]

Here we want to simplify the following expression:

[tex]\sqrt[]{x} *\sqrt[4]{x}[/tex]

Remember that a square root is equivalent to a power of 1/2, and the fourth root is equivalent to a power of 1/4.

Then we can write:

[tex]\sqrt[]{x} *\sqrt[4]{x} = x^{1/2}*x^{1/4}[/tex]

Now in the product we just add the exponents:

[tex]\sqrt[]{x} *\sqrt[4]{x} = x^{1/2}*x^{1/4} = x^{1/2 + 1/4} = x^{3/4} = \sqrt[4]{x^3}[/tex]

That is the expression si,plified.

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The equation of the line that cuts the x-axis at x = 1 and has a slope of -1 is y = -x + 1.

The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.

Since the line has a slope of -1 and cuts the x-axis at x = 1, we can find the y-intercept by using the point-slope form of the line equation:

y - y₁ = m(x - x₁)

y - 0 = -1(x - 1)

y = -x + 1

So the equation of the line that cuts the x-axis at x = 1 and has a slope of -1 is y = -x + 1.

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An estimated Rs. 1863.40 will be needed to cement the route.

Diameter of park [tex]$=7 \mathrm{~m}$[/tex]

so, radius of park [tex]$=\mathrm{r}_1=3.5 \mathrm{~m}$[/tex]

Width of park [tex]$=0.7 \mathrm{~m}$[/tex]

Bigger radius of park [tex]$=\mathrm{r}_2=0.7+3.4=4.2 \mathrm{~m}$[/tex]

Now, Area of path = area of bigger circle -area of smaller circle

[tex]$=\pi r_2^2-\pi r_1^2=$ $\pi\left(r_2^2-\mathrm{r}_1^2\right)=\frac{22}{7}\left(4.2^2-3.5^2\right)=\frac{22}{7}(17.64-12.25)=16.94 \mathrm{~m}^2$[/tex]

Also, Cost of expenditure = rate [tex]$\times$[/tex] area [tex]$=110 \times 16.94=1863.40$[/tex]

Cost of Expenditure of cementing the path is Rs. 1863.40.

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The measure of the length of the shortest side will be 15 units.

If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio. How frequently one value contains or is contained within another is shown by the numerical connection between the two values.

Given that the perimeter of the triangle is 100 and the ratio of the sides of the triangle is 3:5:12.

The length of the shortest side will be calculated as:-

3x + 5x + 12x = 100

20x = 100

x = 20

Length = 3x

Length = 3 x 5 = 15 units

Hence, the shortest side will be 15 units.

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A polygon with a sum of interior angles of 3960 has 22 sides.

The sum of the interior angles of a polygon can be calculated using the formula:

(n-2) * 180

where n is the number of sides of the polygon. This formula is derived from the fact that the total degree measure of a polygon is equal to the sum of the degree measures of its interior angles. In a polygon with n sides, there are n angles, each measuring 180 degrees. So the total degree measure of a polygon with n sides is n * 180.

Now, if we subtract the degree measures of two angles, we are left with the sum of the degree measures of the remaining n-2 angles. This is why the formula for the sum of the interior angles of a polygon is given as (n-2) * 180.

To find the number of sides of a polygon given its sum of interior angles, we can rearrange the formula as follows:

n = (Sum of interior angles / 180) + 2

So, if the sum of the interior angles is given as 3960, we can plug that into the formula:

n = (3960 / 180) + 2

n = 22

Therefore, a polygon with a sum of interior angles of 3960 has 22 sides.

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How many sides does a polygon have if the sum of the interior angles is 3960?

The solutions of the given absolute value equation |4/3 x + 2| - 6 = 0 are x = 3 and x = -6.

Absolute value equations are kind of equations which includes the absolute value symbol in the expression.

For example : |x - 5| = 4 is an absolute value equation.

The given absolute value equation is,

four thirds times x plus 2 end quantity minus 6 equals 0.

|4/3 x + 2| - 6 = 0

Isolating the absolute value quantity on one side,

|4/3 x + 2| - 6 + 6 = 0 + 6

|4/3 x + 2| = 6

This can be written as,

4/3 x + 2 = 6 and 4/3 x + 2 = -6

Solving each of these,

4/3 x + 2 = 6

4/3 x = 4

x = 3

4/3 x + 2 = -6

4/3 x = -8

x = -6

Hence the value of x are 3 and -6.

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Answer:

b.  53.1°

c.  126.9⁰

Step-by-step explanation:

These are SSA triangles;  use Law of Sines to find the unknown angle:

b)  sin30/15 = sinA/24

sinA(15) = sin30(24)

sinA = sin30(24)/15 = 0.80

m∠A = sin⁻1(0.80) = 53.1°

c)  m∠A = 180 - 53.1 = 126.9⁰

Answer:

∠ BAC = 53.13° , ∠ BAC = 126.87°

Step-by-step explanation:

using the Sine rule in Δ ABC

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex]

where a is the side opposite ∠ A and c is the side opposite ∠ C

here a = BC = 24 and c = AB = 15 , then

[tex]\frac{24}{sinA}[/tex] = [tex]\frac{15}{sin30}[/tex] ( cross- multiply )

15 sinA = 24 sin30° ( divide both sides by 15 )

sin A = [tex]\frac{24sin30}{15}[/tex] , then

A = [tex]sin^{-1}[/tex] ( [tex]\frac{24sin30}{15}[/tex] ) = 53.13°

(b)

acute angle BAC = 53.13°

(c)

the sine of an angle is positive in both the first and second quadrant , so

obtuse angle BAC = 180° - 53.13° = 126.87°

If $4400 is placed in account at 8.25% for 22 years , then the final amount received after 22 years will be $26480.08  .  

We use the formula for compound interest to find the final amount  :

that is ⇒  A = P(1 + r)ˣ  ;

where:  A = the amount of money in the account after "x years"  ;

P(initial amount) = $4400 ;   r (interest rate) = 0.0825  ;

⇒ x(time) = 22 years

we get ;

⇒ A = 4400×(1 + 0.0825)²²  ;

⇒ A =  4400×(1.0825)²²  ;

⇒ A =  4400×6.018028  ;

⇒ A = 26480.08  ;

Therefore , the amount in the account after 22 years is $26480.08  .

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The best description of the transformation for the image being projected on the retina is A. A dilation with a scale factor between 0 and - 1 and center at the nodal point.

An mage is inverted and reversed as it passes through the lens of the eye, and is then projected upside down and reversed onto the retina. The process of transforming the image is called "rectification."

In mathematical terms, a dilation would have taken place because the object was shrunken by the eyes at the nodal point. When an object shrinks , then the scale factor is between 0 and 1 but because this image is inverted, the scale factor is between 0 and - 1.

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The total cost of the item would be [tex]$115[/tex].The original price of oranges purchased by Mr. S Ralph can be calculated by subtracting the sales tax from the total cost.

Sales tax is calculated as a percentage of the original price. In this case, the sales tax is 15%, meaning that the original price can be found by dividing the total cost (which includes the sales tax) by 1.15.To calculate the original price of the oranges, divide the total cost of $165.31 by 1.15. This gives us a total of $143.87. Thus, the original price of the oranges purchased by Mr. S Ralph is $143.87 without the sales tax included.Sales tax is a form of taxation imposed by governments on goods and services. Generally, for the majority of goods and services, the sales tax is calculated as a percentage of the original price. This means that the total cost of the goods or services can be calculated by adding the percentage of sales tax to the original price.For example, if an item costs $100, and the sales tax rate is 15%, the total cost of the item would be calculated by multiplying the original price by 1.15 (100% + 15% = 115%). The total cost of the item would be [tex]$115[/tex].

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Mae Ling make $590 in a work week if she sold $4,500 worth of merchandise.

The given is:

We need to find how much she would earns in a work week

Mae Ling earns a weekly salary of $320

She earns a 6.0% commission on sales

She sold by $4,500 in that week

Add $320 to the product of 6.0% and $4,500

She made = 320 + (6.0% × 4,500)

6.0% = 6.0 ÷ 100 = 0.06

She made = 320 + (0.06 × 4,500)

She made = 320 + 270

She made = 590

She would make $590 in a work if she sold $4,500 worth of merchandise.

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Answer:

Rs 3520 is divided in the ratio 11:12:17 as rs 968, rs 1056, and rs 1469

Step-by-step explanation:

According to the question, we have to divide rs 3520 in the ratio 11:12:17

let the common ratio be x

so, total share= (11+12+17)x = 40 x

for the first person, share would be (11x/40x)*(Rs 3520)

=Rs 968

for the second person, share would be (12x/40x)*(Rs 3520)

=Rs 1056

for the third person, share would be (17x/40x)*(Rs 3520)

=Rs 1496

The shares are Rs 968, Rs 1056, and Rs 1469

hope this helps :)

Answer: x=8

Step-by-step explanation: since we know 2 sides of both quadrilaterals and they are similar,

just put 32/40 = 24/3x+6 ,

cross multiply ( 32 x 3x+6   and 40 x 24),

they become 96x +192 = 960.

move 192 to the other side and divide both sides by 96

The amount of time that Nora practices flips is; t = 1 ¹/₄

How to Solve Algebra problems?

The BODMAS rule would be used to simplify the expression, BODMAS is an abbreviation for bracket, of, division, multiplication, addition and subtraction. It dictates the order in which a mathematical expression should be solved.

We are told that;

Nora spends time practicing flips on the trampolines. Let this be t.

Then, she spends 1/2 of an hour eating birthday cake with her friends.

Thus, total amount of time spent on flips and eating with her friends is;

t + ¹/₂ = 1 ³/₄

t = 1 ³/₄ - ¹/₂

t = 1 ¹/₄

Thus , the amount of time that Nora practices flips is; t = 1 ¹/₄

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Given question is incomplete , Complete Question is;

After arguing for two weeks, Nora convinced her parents to have her birthday party at FlyZone trampoline park. As soon as she gets there, Nora spends time practicing flips on the trampolines. Then, she spends 1/2 of an hour eating birthday cake with her friends. In all, Nora spends 1 3/4 hours at FlyZone. Which equation can you use to find the amount of time Nora practices flips?

Solve this equation for (t) to find the amount of time Nora practices flips