Read the following description of a relationship:
Victoria signed up for a gym membership 21 weeks after Monica.
Let a represent the number of weeks Victoria has been a member and b
represent the number of weeks Monica has been a member.
Find the value of b when a = 9.
b= _

The magnitude of the sum of these two vectors is 2.9486m

In trigonometry, the law of cosines (also known as the cosine formula, cosine rule, or al-Kashi's theorem) relates the lengths of the sides of a triangle to the cosine of one of its angles.

The parameters that will help us to find the magnitude are

/OB/ = 3.14m

/OA/ = 2.71 m

Let /AB/= x

Sum of the angles is (-60+30)⁰ = 30⁰

Using cosine rule

x²= 3.14² +2.71² - 2*3.14*2.71 *cos30⁰

x² = 9.8596+7.3441 -8.5094

x²= 17.2037 -8.5094

x²= 8.6943

x = √8.6943

x = 2.9486

Therefore, the magnitude of the sum

of these two vectors is 2.9486m or 2.9m approximately

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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: If the ratio of first-class, second-class, and third-class passengers who survived the shipwreck is 101:59:89, then for every 101 first-class passengers who survived, there were 59 second-class and 89 third-class passengers who survived.

If the total number of first-class passengers was 202, then there were 202 * 59/101 = 118 second-class passengers who survived, and 202 * 89/101 = 180 third-class passengers who survived.

Therefore, the total number of passengers who survived the shipwreck is 202 + 118 + 180 = 500 passengers.

Step-by-step explanation:

Answer:

Step-by-step explanation:

S+8=D

S+D equals 94.

94/2= 45+2=47

47-8=39

Sydney is 39

Answer:

43

Step-by-step explanation:

94-8= 86

86/2= 43

43+8= 51

a:43

prove it :

51+43= 94

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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A.) f(x-2)+f(2x)

To find this expression, we can substitute the definition of f(x) into the expression and simplify:

f(x-2)+f(2x) = [10(x-2)-4] + [10(2x)-4]

= 10x - 20 - 4 + 20x - 4

= 30x - 28

Therefore, f(x-2)+f(2x) = 30x - 28.

Given f(x) = 10x - 4, we need to find f(2a) - f(a).

f(2a) = 10(2a) - 4 = 20a - 4

f(a) = 10a - 4

Therefore,

f(2a) - f(a) = (20a - 4) - (10a - 4)

= 10a

Answer: f(2a) - f(a) = 10a. This means that the difference between the function evaluated at 2a and a is simply 10 times a.

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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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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:

The simplified expression of  K-7 ft-X-8 ft-K-20 ft is -35ft-X

An expression is combination of variables, numbers and operators.

The given expression is K-7 ft-X-8 ft-K-20 ft

We need to simplify the given expression.

Add the like terms

-7 ft-X-8 ft-20 ft

-27ft-X-8 ft

-35ft-X

Hence, -35ft-X is the simplified expression of  K-7 ft-X-8 ft-K-20 ft

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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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Answer: OD. 13

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

using the rules of logarithms

• log a - log b = log ([tex]\frac{a}{b}[/tex] )

• log [tex]x^{n}[/tex] = nlog x

then

[tex]log_{4}[/tex] [tex]\frac{7}{x^3}[/tex]

= [tex]log_{4}[/tex] 7 - [tex]log_{4}[/tex] x³

= [tex]log_{4}[/tex] 7 - 3[tex]log_{4}[/tex] x

The total area of the figure with points A(-5,4), B(4,4), C(4,1),  D(1,1), E(4,-3) F(4,-6), G(-5, -6) is 51 square units.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Divide the figure is into two rectangles and a triangle.

The points B, C, E, and F form a rectangle with base BC and height 7 units.

The points A, D, and G form a rectangle with base AG and height 5 units. The points C, D, and E form a triangle with base CE and height 4 units.

The length of BC is 4 - 4 = 0, so the area of the rectangle with base BC is 0.

The area of the rectangle with base AG is (4 - (-5)) x 5 = 45 square units. The area of the triangle with base CE is (4 - 1) x 4 / 2 = 6 square units.

Therefore, the total area of the figure with points A(-5,4), B(4,4), C(4,1),  D(1,1), E(4,-3) F(4,-6), G(-5, -6)  is 45 + 6 = 51 square units.

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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.

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 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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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 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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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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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

After 1 day, each woman would have made 8 scarves.

The expression that represents the number of scarves that Greta can make each day is:

Number of scarves she can make = number of scarves already made + (number of scarves she can make per day x number of days)

= 7 + d

The expression that represents the number of scarves that Evelyn can make each day is:

Number of days x number of scarves she can make per day

d x 8 = 8d

When both of them make the same number of scarves, the two expressions above would be equal.

7 + d = 8d

7 = 8d - d

7 = 7d

d = 7/7

d = 1 day

Number of scarves that would be made in 1 day = 8 x 1 = 8 scarves

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The graph that represents the function f(x) = sqrt(x - 1) is given by the following option:

C. Graph Y.

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

For this problem, the function is defined as f(x) = sqrt(x - 1), meaning that the parent square root function was moved one unit right, and thus the correct graph is given by graph Y.

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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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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.

Answer:

2/35

Step-by-step explanation:

[tex](-\frac{1}{5})(-\frac{2}{7}) = \frac{2}{35}[/tex]

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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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:

[tex]x = -64\\\\y = -63\\\\z = -57[/tex]

Step-by-step explanation:

Diagonally opposite angles of a parallelogram are equal

Therefore

-y - 3 = 60

Add 3 to both sides; -3 terms on left side cancel out

- y = 60 + 3

- y = 63

Multiply both sides by -1

-1(-y) = -1(63)

y = - 63

Another property of a parallelogram is that the angles formed on either end by a side must equal 180°.

Rephrased,

The consecutive or adjacent angles are supplementary which means they add up to 180°

We see that -2z + 6 and 60° are adjacent angles
So

- 2z + 6 + 60 = 180

-2z + 66 = 180

-2z = 180 - 66

-2z = 114

z = 114/-2

z = -57

Similarly

-2x - 8 + 60 = 180

-2x + 52 = 180

-2x = 180 - 52

-2x = 128

x = 128/-2

x = -64

Answer:

Step-by-step explanation:

6x4=24

another way of writing it is using addition

add 4, six times

so

4+4+4+4+4+4

6 boxes each has four cakes