The angles of a triangle are in the ratio of 2 : 3 : 7. Find the measure of the two greatest angles of the triangle.

a) The bearing of B from C is; 45° South-East.

b) The bearing of D from B is; 58.39° South Of West

a) Distance Between B  and C is;

BC = √( 40² + 40²)

= 40√2

= 56.57  km

Angle of  B from C =  Tan⁻¹( 40/40)  =   45°

Bearing of B  From C   =  45° South Of East

Or 90 - 45°  = 45°    

45°  East of South

Thus, that is the bearing of B from C

b) Distance Between B and  D is;

BD = √(40² + 65²)

= 76.32  km

Angle of  D from B =  Tan⁻¹( 65/40)  

= 58.39 °

Bearing of D  From B   =  58.39° South Of West

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If a rectangular room is 2 meters longer than it is wide, and its perimeter is 24 meters then the  dimensions of the room: 7 meter x 5 meter

Perimeter is a mathematical term, it indicates total outer boundary of a figure, we define it only for two dimensional figures.

Perimeter = Sum of length of the all the sides

Let x be the width of the room in meters.

Then the length of the room is 2 meters longer, which means it is x+2 meters.

In this case, we know that the perimeter is 24 meters.

So we can set up an equation:

Perimeter = 2Length + 2Width

Substituting the values we know:

24 = 2(x+2) + 2x

Simplifying the equation:

24 = 2x + 4 + 2x

24 = 4x + 4

20 = 4x

x = 5

So the width of the room is 5 meters, and the length is x+2 = 7 meters.

Therefore, the dimensions of the room are 7 meters by 5 meters.

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The probability that none of them will default 0.0066

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

(a) If 1,000 student loans are made, what is the probability of fewer than 50 defaults?

It's a binomial problem but the large n requires using a normal approximation.

mean = np = 1000*0.07 = 70

std = sqrt(npq) = sqrt(70*0.93) = 8.0685

z(50) = (50-70)/[8.0685] = -2.4788

P(# of defaults < 50) = P(z<-2.4788) = 0.0066

(b) More than 100?

z(100) = (100-70)/8.0685 = 3.7182

P(defaults > 100) = P(z>3.7182) = 0.00010035

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Correct question

The default rate on government-guaranteed student loans at a certaing public 4-year institution is 7% (a) If 1,000 student loans are made, what is the probability of fewer than 50 defaults? (b) More than 100? Show your work carefully.

a) The probability that on a random minute, at least 3 people show up is 0.080.

b) The probability that he will have to wait at least 3 minutes for the next person to show up is 1 - (5/2e) .

c) The probability that he will have to wait at least 3 more minutes for the next person to show up is 2/e.

A probability distribution called the Poisson distribution is used to indicate how frequently an event is likely to happen over a given timeframe.

Given:

a)  Let X be the number of people who show up during a random minute.

Then X follows a Poisson distribution with parameter λ = 1.

The probability of at least 3 people showing up in a random minute is:

P(X ≥ 3) = 1 - P(X < 3)

= 1 - (P(X = 0) + P(X = 1) + P(X = 2))

We can use the Poisson probability mass function to find P(X = k) for k = 0, 1, 2:

P(X = k) = ([tex]e^{-\lambda[/tex]) x ([tex]\lambda^k[/tex]) / k!

Plugging in λ = 1, we get:

P(X = 0) = [tex]e^{-1[/tex] / 0! = 1/e

P(X = 1) = [tex]e^{-1[/tex] x 1 / 1! = 1/e

P(X = 2) = [tex]e^{-1[/tex] x 1 / 2! = 1/2e

So, the probability of at least 3 people showing up in a random minute is:

= 1 - (P(X = 0) + P(X = 1) + P(X = 2))

= 1 - (1/e + 1/e + 1/2e)

= 1 - (2/e + 1/2e)

= 1 - (5/2e)

= 0.080

b) The probability of having to wait at least 3 minutes for the next person to show up

= 1 - P(X <= 2)

= 1 - (5/2e)

c) Now,

P(X ≤ 1)

= P(X = 0) + P(X = 1)

= (1/e) + (1/e)

= 2/e

So, the probability of having to wait at least 3 more minutes for the next person to show up

= 1 - (2/e)

= 1 - P(X <= 1).

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Answer:

x <-1.5

or

x <9.6

Step-by-step explanation:

12x + 7 < - 11

12x < -11 - 7

12x < - 18

12x/12 < -18/12

x = -1.5

OR.

5x - 8 > 40

5x > 40 + 8

5x > 48

5x/5 > 48/5

x > 9.6.

The distance at which Allison should stand to catch the ball will be 8.32 m.

What is speed?

Speed of an object is defined as the ratio of distance covered by the object to the time taken by the object to cover that distance. In other words its tell how much times an object takes to cover a particular distance.

Now for the given question:

Emily throw the ball at 30° below the horizontal towards Allison at a speed of 12m/s. So here we will calculate the Horizontal and Vertical components of the speed.

[tex]v_{x}[/tex]=12cos30°=10.4 m/s

[tex]v_{y}[/tex]=12sin30°=6 m/s

Vertical distance between Alice and Emily according the question is 8 m.

s= 8 m.

Now by applying Second equation of motion to calculate time take by ball to move from Emily to Allison.

s=[tex]v_{y}[/tex]×t+[tex]\frac{1}{2}[/tex]×a×[tex]t^{2}[/tex]

4= 6×t+[tex]\frac{1}{2}[/tex]×9.8×[tex]t^{2}[/tex]           (a=9.8 m/[tex]s^{2}[/tex] acc. due to gravity a constant)

By solving above quadratic equation we get

t= 0.8 s

To find horizontal distance

d= [tex]v_{x}[/tex]×t

d=10.4×0.8

d= 8.32 m

Hence Allison should stand at a distance of 8.32 m to catch the ball.

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C

The answer to the question is C

Answer:

D is the answer cuz 2x-1=5

2x=5-1

2x=4

X=2

We divide both side by two

Answer:domain is (2, ∞), range is (-∞,∞)

Step-by-step explanation:

domain is (2, ∞) as it aproaches 2 but never reaches and range is (-∞,∞)

The quotient is -3x²/2 + 7x/4 + 7/8 and the remainder is 23x/8 - 1. The solution has been obtained by using polynomial long division method.

What is polynomial long division?

A formula for multiplying one polynomial by another of the same degree or lower is known as a long division polynomial. Like with long division of numbers, the components of long division of polynomials include the divisor, quotient, dividend, and remainder.

We are given dividend as -3x⁴+5x³+0x²+2x-1 and divisor as 2x²-x.

Using Polynomial Long Division,

Dividing : -3x⁴+5x³+0x²+2x-1 ("Dividend")

By : 2x²-x ("Divisor")

Dividend                   -3x⁴ + 5x³ + 0x² + 2x - 1

- divisor * -3x²/2       -3x⁴ + 3x³/2

Remainder                       + 7x³/2 + 0x² + 2x - 1

- divisor * 7x/4                  + 7x³/2 - 7x²/4

Remainder                                      7x²/4 + 2x - 1

- divisor * 7/8                                   7x²/4 - 7x/8

Remainder                                                  23x/8 - 1

Quotient : -3x²/2 + 7x/4 + 7/8

Remainder: 23x/8 - 1

Hence, the solution has been obtained.

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The perimeter of the triangle is 23x + 17.

Perimeter is simply the sum of all sides of a polygon.

Given the sides of the triangle;

Side one = 10x + 19

Side two = 12x - 2

Side three = x

To find the perimeter, we add the sides

Perimeter = Side one + Side two + side three

Perimeter = 10x + 19 + 12x - 2 + x

Collect and add like terms

Perimeter = 10x + 12x + x - 2 + 19

Perimeter = 23x - 2 + 19

Perimeter = 23x + 17

Therefore, the perimeter is 23x + 17.

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The absolute humidity is 500g/m³, specific humidity = 16.67% and mixing ratio = 20%.

Absolute humidity is a measure of the amount of water vapor in a given volume of air, regardless of the total mass of the air. It is expressed as the mass of water vapor per unit volume of air, typically in units of grams per cubic meter (g/m³).

First, we need to find the mass of dry air in the package. Since the total volume of air is 1m³ and the volume of dry air is 2.5m³, the volume of water vapor is 1 -2.5 = -1.5 m³. This means that the water vapor must have condensed and become liquid water, which we can ignore for the purposes of this problem. So the mass of dry air is:

mass of dry air = density of air * volume of dry air

mass of dry air = 1000g/m³ × 2.5m³

mass of dry air = 2500 g

Now we can use this value, along with the given mass of water vapor, to calculate the three measures of humidity:

       absolute humidity = 500g/ 1m³

       absolute humidity =  500g/m³

       specific humidity = 500g/(2500g + 500g)

       specific humidity = 0.1667 (or 16.67% as a percentage)

       mixing ratio = 500g/2500g

       mixing ratio = 0.2 (or 20% as a percentage)

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Answer:

Step-by-step explanation:

In the compound interest formula: A = P(1 + r)^t

A represents the amount of money in the account at the end of the term t, including interest.

P represents the initial principal, or the amount of money invested.

r represents the interest rate, usually expressed as a decimal.

t represents the number of time periods over which the interest is compounded.

In the continuously compounded interest formula: A = Pe^(rt)

A represents the amount of money in the account at the end of the term t, including interest.

P represents the initial principal, or the amount of money invested.

r represents the interest rate, usually expressed as a decimal.

t represents the number of time periods over which the interest is compounded.

So the variables in the formulas and their descriptions are:

A: the amount of money in the account at the end of the term t, including interest

P: the initial principal, or the amount of money invested

r: the interest rate, usually expressed as a decimal

t: the number of time periods over which the interest is compounded.

The measure of <1 is 36 degree.

Complementary angles are those whose combined angle is exactly 90 degrees.

For example, 30 degrees and 60 degrees are complementary angles.

As, the complementary angle have sum of angles are 90 degree.

So, 2x+ 3x= 90

5x = 90

x= 18

Then, the measure of <CBD is 3x = 3(18)= 54 degree.

As, <1 is Complementary angle of <CBD.

So, the measure of <1 = 90- 54 = 36 degree

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On solving the provided question we can say that The average rate of change between x₁ and x₂ and a function f(x), is 10.

The subject of mathematics includes quantities and their variatiοns, equations and related structures, shapes and their locations, and places where they can be fοund. The term "functiοn" refers to the relationship between a set of inputs, each of which has an assοciated output.

A connectiοn between inputs and οutputs in which each input leads tο a single, distinct result is known as a function. Each functiοn is given a domain and a codοmain, or scope. Usually, f is used to denοte functions (x). input is an x. There are fοur main types of functiοns accessible. based οn the following factors: on functiοns, one-to-one functiοns, many-to-one functions, inside functiοns, and on functions.

The average rate of change between x=x and a function f(x)

F(x₂) - F(x₁)/(x₂) - x₁

so,

f(x) = x²

average rate = f(6) - f(4) / 6-4 = 36-16 / 2 = 20/2 = 10

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Answer:

Step-by-step explanation:

There are several ways to approach this problem, but one common method is to use the complementary counting principle, which states that the number of favorable outcomes can be obtained by subtracting the number of unfavorable outcomes from the total number of outcomes. In this case, the favorable outcome is that the sample contains at least one defective phone, and the unfavorable outcome is that the sample contains no defective phones.

The number of possible samples of 4 phones out of 15 can be calculated as the number of combinations of 4 items from a set of 15, which can be written as:

C(15, 4) = 15! / (4! * (15 - 4)!) = 1365

The number of samples containing no defective phones can be calculated as the number of combinations of 4 phones out of the remaining 12 non-defective phones, which can be written as:

C(12, 4) = 12! / (4! * (12 - 4)!) = 495

So, the number of samples containing at least one defective phone can be calculated as:

1365 - 495 = 870

Therefore, out of the 1365 possible samples of 4 phones, 870 of them contain at least one defective phone.

Answer: To calculate the total cost of the units in beginning inventory for each year, we need to multiply the number of units by the per-unit cost:

Year 1: Cost of units in beginning inventory = 0 units * $13 + $5 + $5 = $0

Year 2: Cost of units in beginning inventory = 1,000 units * ($13 + $5 + $5) = 1,000 * $23 = $23,000

To calculate the total cost of the units produced during each year, we need to multiply the number of units by the per-unit cost:

Year 1: Cost of units produced = 10,000 units * ($13 + $5 + $5) = 10,000 * $23 = $230,000

Year 2: Cost of units produced = 9,000 units * ($13 + $5 + $5) = 9,000 * $23 = $207,000

To calculate the total cost of the units sold during each year, we need to multiply the number of units sold by the per-unit cost:

Year 1: Cost of units sold = 9,000 units * ($13 + $5 + $5 + $6) = 9,000 * $29 = $261,000

Year 2: Cost of units sold = 8,000 units * ($13 + $5 + $5 + $6) = 8,000 * $29 = $232,000

To calculate the total variable manufacturing costs for each year, we need to sum the costs of the units in beginning inventory, units produced, and units sold:

Year 1: Total variable manufacturing costs = $0 + $230,000 + $261,000 = $491,000

Year 2: Total variable manufacturing costs = $23,000 + $207,000 + $232,000 = $462,000

To calculate the total fixed manufacturing overhead costs for each year, we need to add the fixed manufacturing overhead per year to the total variable manufacturing costs:

Year 1: Total manufacturing costs = $491,000 + $90,000 = $581,000

Year 2: Total manufacturing costs = $462,000 + $90,000 = $552,000

To calculate the total variable selling and administrative expenses for each year, we need to multiply the number of units sold by the variable selling and administrative expense per unit:

Year 1: Total variable selling and administrative expenses = 9,000 units * $6 = $54,000

Year 2: Total variable selling and administrative expenses = 8,000 units * $6 = $48,000

To calculate the total selling and administrative expenses for each year, we need to add the fixed selling and administrative expenses per year to the total variable selling and administrative expenses:

Year 1: Total selling and administrative expenses = $54,000 + $61,000 = $115,000

Year 2: Total selling and administrative expenses = $48,000 + $61,000 = $109,000

Step-by-step explanation:

The probability of getting two twos is 0.003

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

probability = sample space/total outcome

probability of getting two = 1/6

probability of getting two twos = 1/36

getting two two can only 10times = 1/36 ÷ 10

= 10/36 = 0.003 (nearest thousandth)

therefore the probability of getting two twos in 20 rolls is 0.003( nearest thousandth)

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The equation which is in the quadratic form is 6x⁴ + 7x² - 3 = 0. So Option B is correct.

An equation is quadratic in form if it can be written in the form of ax + bx + c = 0, where a, b, and c are constants and x is the variable.

Among the given equations, we can see that the first, third, and fourth equations are not quadratic in form, since they contain x raised to powers other than 2.

The second equation, 6x⁴ + 7x² - 3 = 0, can be written in quadratic form by making a substitution.

If we let y = x², then we can write the equation as 6y² + 7y - 3 = 0,

which is a quadratic equation in y. Substituting back x² for y,

we get:

6x⁴ + 7x² - 3 = 0

So the second equation is quadratic in form.

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Answer:

Step-by-step explanation:

answer b, trust

Answer:

2 . of(0)=2/1/2 this is answer number 2

The solution is, option 2 neither linear nor exponential.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

The given function is

x    : -5       -3      -1       1      3

f(x) :8192   512   32      2    18

when we plot this function in the excel we get to know that it a regression as shown in the figure attached  

because value of  lies between (0,1)

which shows regression

therefore it is neither linear nor exponential.

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The equation of the plane containing the line x = 2 + t, y = 4 − t, z = 3 − 3t and is parallel to the plane 5x + 2y + z = 3 is 5x + 2y + z = 21

What is a plane?

Any flat, three-dimensional, infinitely long surface is considered to be a plane. It can alternatively be thought of as the two-dimensional equivalent of a point with zero dimensions, a line with one dimension, and a space with three dimensions.

Given that, a plane is containing the line x = 2 + t, y = 4 − t, z = 3 − 3t and is parallel to the plane 5x + 2y + z = 3

Any  plan e parallel to the plane 5x + 2y + z = 3 , should be in the form of 5x + 2y + z = k

Now, this plane should contain the line mentioned above

On substituting the terms,

5(2 + t) + 2(4 - t) + (3 - 3t) = k

10 + 5t + 8 - 2t + 3 -3t = k

21 = k

Therefore, The equation of the required plane is 5x + 2y + z = 21

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The discounted price of the ticket is $198.

The total cost of the ticket with the discount and service fee is $214.33.

A percentage is a ratio or number that may be expressed as a fraction of 100. Moreover, it is denoted by the sign "%."

Given:

The cost of a ticket on an airline is $220.

And Jameson receives a discount of 10%.

To find the discounted price:

The discounted price = 220 - 220 x 10 / 100

The discounted price = $198.

And the service charge is 8.25%.

So, the amount of service charge,

= 198 x 8.25/100

= 16.33

The total cost of a ticket = $198 + $16.33 = $214.33

Therefore, the cost is $214.33.

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The required modulus is 41 .

A real and imaginary number combo with the formula a + bi , where

a and b are real numbers, and

i is the "unit imaginary number" √(−1)

a and b may also have zero values.

We are aware that complex numbers are made up of both actual and fictitious numbers.

The imaginary part, y, is multiplied by I the square root of -1, and the real part, x.

Modulus of x+iy = [tex]\sqrt{x^2 +y^2}[/tex]

Here, 9 and 40 are substituted for x and y.

i.e. 9+40i

We square the coefficients, add them, and then find the square root to obtain the modulus.

|9+40i| =[tex]\sqrt{9^2 +40^2} =\sqrt{81+1600} =\sqrt{1681}[/tex][tex]=41[/tex]

By long division method we find that

|9+40i| =41

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The number of ways to arrange all the letters if the arrangement must end in a vowel is; 25,200.

The number of arrangement using only five letters is; 6720.

Since there are 5 options for the last letter, and there a 7 letters left to make an arrangement of 7.

Hence, The number of ways can you arrange all of the letters if the arrangement must end in a vowel is; 5 × 7!

= 5 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 25,200.

b). The number of arrangements if one can only use five letters is; ⁸P₅

= 6720.

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Answer: If the lady sells each brouse for 1500 KSH and makes a profit of 150 KSH for each brouse, then the cost price of the brouse is 1500 KSH - 150 KSH = 1350 KSH.

So, the lady pays 1350 KSH for each brouse.

Step-by-step explanation:

Based on the given data, the distance from center to center of two consecutive holes is approximately 25.83 inches.

To solve this problem, we need to divide the length of the metal strip (excluding the 2 inches on each end) by the number of holes to be drilled, and that will give us the distance from center to center of two consecutive holes.

So the length of the metal strip available for the 12 holes is:

3414 - 2 - 2 = 3410 inches

Dividing this length by the number of holes gives us:

3410 ÷ 12 = 284.166666... inches

To find the distance from center to center of two consecutive holes, we need to divide this value by the number of spaces between the holes, which is 11 (since there are 12 holes, but only 11 spaces between them). So:

284.166666... ÷ 11 = 25.833333...

Rounding this to the nearest hundredth of an inch, we get:

25.83 inches (to the nearest hundredth)

Therefore, the distance from center to center of two consecutive holes is approximately 25.83 inches.

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Answer:

Length = 26 feet; Width = 8 feet

Step-by-step explanation:

Let:

x = Length of rectangle

y = Width of rectangle

4 times the width = 4y

∴ 6 less than 4 times the width = 4y - 6

Perimeter of a rectangle = 2 × [Length + Width]
                                     68 = 2 × [(4y - 6) + y]

Expand the brackets or parenthesis by applying the Distributive Law and bring the like terms together:

                                    68 = 2 × [4y - 6 + y]
                                    68 = 2 × [5y - 6]

                                    68 = 10y - 12

                             68 + 12 = 10y

Isolate y by making it the subject of the equation:

                                  80 = 10y

                                    y = [tex]\frac{80}{10}[/tex]

                            y = Width of rectangle: 8 feet

Substitute y into the equation to calculate x:

       x = 4(8) - 6

         x = Length of rectangle = [tex](32 - 6)[/tex] feet

                                               x = 26 feet

The amount after 13 years with a compound interest of 6.9 % is given by the equation A = $ 5,149.69

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

Let the amount after compound interest be represented as A

Now , the equation will be

The principal amount P = $ 2,100

The rate of interest r = 6.9 %

The number of years b = 13 years

when compounded continuously ,

The compound interest amount A = Pe^rt

Substituting the values in the equation , we get

A = 2,100.00 ( 2.71828 ) ^ ( 0.069 ) ( 13 )

A = 2,100 ( 2.71828 )^( 0.897 )

On further simplification , we get

A = $ 5,149.69

Hence , the amount after 13 years is $ 5,149.69

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The amount of money which would be in the account after 14 years is; $18,123.77.

The number of years it'd take for the money to double is; 13.86 years.

Since the given model of the account is;

A (t) = 9000e^0.05t

After 14 years, it follows that; t = 14.

Therefore;

A (14) = 9000e^0.05(14)

A (14) = 9000 × 2.013752707

A (14) = $18,123.77.

Also, the doubling time implies that; A (t) = 18,000

Therefore, 18000 = 9000e^0.05t

2 = e^0.05t

0.05t = ln (2)

t = ln (2) / 0.05

t = 13.86 years.

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