Find the sum of the geometric sequence if the first term is -8, the common ratio is -3 and there are 10 terms

To show that var(aX + bY + c) = a^2 var X + b^2 varY + 2ab cov(X, Y), we can start by using the definition of variance, which is var(X) = E[(X - E[X])^2], and the definition of covariance, which is cov(X, Y) = E[(X - E[X])(Y - E[Y])].

Variance is a measure of the spread of a random variable's possible values. It is defined as the expected value of the squared deviation of a random variable from its mean. For a random variable X, the variance is denoted as Var(X) or σ^2(X) and is calculated as:

Var(X) = E[(X - E[X])^2]

Using these definitions, we can write:

var(aX + bY + c) = E[(aX + bY + c - E[aX + bY + c])^2]

Using the properties of expectations and bilinearity, we can simplify this to:

var(aX + bY + c) = E[(a(X - E[X]) + b(Y - E[Y]))^2]

Expanding the square and using bilinearity again, we get:

var(aX + bY + c) = a^2 E[(X - E[X])^2] + b^2 E[(Y - E[Y])^2] + 2ab E[(X - E[X])(Y - E[Y])]

Since the expectations of (X - E[X])^2 and (Y - E[Y])^2 are equal to var(X) and var(Y) respectively, we can substitute these values into the above equation to get:

var(aX + bY + c) = a^2 var X + b^2 varY + 2ab cov(X,Y)

Therefore, we have shown that var(aX + bY + c) = a^2 var X + b^2 varY + 2ab cov(X,Y)

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Answer: Undefined

Step-by-step explanation:[tex]\sqrt{x}[/tex]

This seems to be undefined.

Let's make a chart:

x #s | y #s

1

2

0

-1

-2

-------------------------------------

Let's take a number out of the chart to act as x:

f(x)=[tex]\sqrt{-2^4 -16}[/tex] -> f(x)=[tex]\sqrt{-16-16}[/tex] -> [tex]\sqrt{-32}[/tex]

Since the answer is negative, the answer should be the one that says undefined.

---- SORRY IGNORE WHAT I TYPED I JUST REALIZED IT IS WRONG PLS DELETE THIS

Answer:

24

Step-by-step explanation:

There are 4 sides to a box. Meaning you will have to divide 96 by 4. Giving you 24. Since perimeter means to add, add 24 4 times and you will be given the result of 96.

Ms. Young should use the data to decide on her next steps.

Data in math is any information that is used to make decisions and/or can be used to analyze patterns. It can be numerical, such as statistics, or qualitative, such as observational data. Data can be collected in various ways, including surveys, experiments, and observations. Data can also be represented graphically, such as in charts or diagrams, to help better illustrate the patterns or trends it may contain. Data is often used in the context of problem solving and decision making and is a key element in the scientific method.

She should identify the areas of difficulty for Kim, where she is having trouble identifying coins. She should then design lessons that focus on these areas, providing more practice on identifying coins. Using a variety of instructional strategies, such as hands-on activities, games, and visual aids, can help Kim to better understand the differences between the coins and increase her accuracy. Additionally, Ms. Young should provide more frequent feedback to Kim on her performance to ensure that she is making progress. Finally, Ms. Young should consider decreasing the number of coins presented to Kim each day, to give her more time to practice and increase her accuracy.

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Answer: 8 shirts for 128 shekels

Step-by-step explanation:

First, we can set up fractions and simplify to find the cost of one shirt.

5shirts/100shekels = 1shirt/20 shekels

8 shirts/128 shekels = 1shirt/16 shekels

Ultimately, whichever cost per shirt is lower is going to be the better buy. Since 16shekels/shirt is less than 20shekels/shirt, you are ultimately buying more shirts for a lower cost. Hope this helps

The expression [tex](4^{(2/5)})^{(1/4)}[/tex] can be rewritten as the radical expression [tex]4^{(1/1280)}.[/tex]

What is the rational exponent?

A rational exponent is an exponent that is a fraction. In mathematics, a number raised to a fractional power represents a root of the number. For example, the expression[tex]x^{(1/3)}[/tex] represents the cube root of x. Similarly, the expression [tex]x^{(2/5)}[/tex] represents the fifth root of x².

The given expression can be rewritten as a radical expression as follows:

[tex](4^{(2/5)})^{(1/4)} = 4^{(2/5) * (1/4)}[/tex]

Using the property of exponents that (a^b)^c = a^(b*c), we simplify the right side of the equation:

[tex]4^{((2/5) * (1/4))} = 4^{(2/5 * 1/256)} = 4^{(1/1280)}[/tex]

So, the expression [tex](4^{(2/5)})^{(1/4)}[/tex] can be rewritten as the radical expression [tex]4^{(1/1280)}.[/tex]

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The final answers are as follows gross profit $321,600, cost of goods sold of $528,000 and balance due $782,980.

(a) The terms of the sale are 3/10, n/30 which means that if Cullumber Company pays the invoice within 10 days, they will receive a 3% discount on the total invoice amount. However, if they pay within 30 days, they will not receive a discount.

To calculate the amount due if Cullumber Company takes the discount:

$914,000 x 3/100 = $27,420

$914,000 - $27,420 = $886,580

To calculate the gross profit:

$914,000 - $592,400 = $321,600

(b) The return of merchandise means that Cullumber Company is returning $104,600 worth of merchandise and thus the amount due to Marin will be:

$886,580 - $104,600 = $782,980

And the cost of goods sold will be:

$592,400 - $64,400 = $528,000

(c) On March 12, Marin Company received the balance due from Cullumber Company which is $782,980.

This means that the net amount received by Marin Company after the discount and return of merchandise is $782,980.

Therefore, The final answers are as follows gross profit $321,600, cost of goods sold of $528,000 and balance due $782,980.

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Kasey is trying to run 60 miles by the end of the month.

Let us assume that Kasey tries to run 't' miles by the end of the month.

Kasey is 60% close to reaching her goal.

This means, she has already completed 40% of her goal.

Foven that she has already run 24 miles.

This means 40 percent of total distance is 24 miles.

i.e., 40 percent of 't' miles = 24 miles

We calculate 40 percent of t.

(40/100) × t = 24

(2/5) × t = 24

2 × t = 24 × 5

2 × t = 120

t = 120/2

t = 60 miles

i.e., she tries to run a 60 miles by the end of the month.

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The probability of getting one defective component per customer is very low, less than 1/14,254. The probability of getting five defective components to a single customer is also low, 1/14,254. And the probability of getting two defective components to two different customers and the rest of the customers getting none is 10/14,254.

(a) The probability that each customer will receive one defective component is the probability that the five defective components will be drawn in a specific order, divided by the total number of ways the 50 components can be drawn. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a specific order. So the probability is (5!)/(5049484746) = 1/14,254.

(b) The probability that one customer will have drawn five defective components is the probability that all five defective components will be drawn in a row, divided by the total number of ways the 50 components can be drawn. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a row. So the probability is (1!)/(5049484746) = 1/14,254,

(c) The probability that two customers will receive two defective components each, two none, and the other one, is the probability that the five defective components will be drawn in a specific order and then divided among the five customers in a specific way, divided by the total number of ways the 50 components can be drawn. The number of ways to divide the defective components among the customers is 5!/(2!2!1!) = 10. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a specific order, so the probability is (105!)/(50494847*46) = 10/14,254.

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Answer:

Step-by-step explanation:

Total Number of balls = 3+5+2=10

a)Probability both are red:  3/10 * 2/9 = 1/15

b)First ball blue, other green : 5/10 * 2/9 = 1/9

c) Both are different color : (3/10*7/9)+(5/10*5/9)+(2/10*8/9)

=21/90+25/90+16/90=62/90=31/45

d)Both are same color: (3/10*2/9)+(5/10*4/9)+(2/10*1/9)

=6/90+20/90+2/90 = 28/90 = 14/45

Answer:

yes dont listen to anything isay because i just wants the points its to harda for me

Step-by-step explanation:

Answer:

To solve the equation cos (2x) = √2 - cos (2x), we can first isolate the variable on one side of the equation.

cos (2x) = √2 - cos (2x)

add cos(2x) to both sides

2*cos(2x) = √2

divide both sides by 2

cos(2x) = √2/2

Now we can use the identity cos 2x = 2cos^2 x - 1, so

2cos^2 x - 1 = √2/2

Square both sides

4cos^2 x - 2 = 2 - 1

4cos^2 x = 1

Divide both sides by 4

cos^2 x = 1/4

Since cos^2 x = 1/4, then cos x = +/- √(1/4) = +/- 1/2

So x = pi/3 + 2npi or x = 5pi/3 + 2n*pi

As per the unitary method, the original price of the watch is 217.11

The term unitary method is defined as a basic concept to find the value of a single unit and then using that value to find the value of multiple units.

Here we have given that the price of a watch was decreased by 35% and sold for $75. 99.

Let us consider that x be the original price of watch.

Here we have given that the amount of discount is calculated as,

=> 35% of x = 75.99

=> 35/100 of x = 75.99

When we simplify this then we get,

=> 0.35 of x = 75.99

Then the value of x is calculated as,

=> x = 75.99/0.35

=> x = 217.11

Therefore, the correct option is (D).

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The area of the shaded circular region is given as follows:

18π cm².

The shaded region is part of a circle, hence the area of the circle has to be obtained.

The area of a circle of radius r is given by the multiplication of π and the square of the radius, as follows:
A = πr².

The radius of the circle in this problem is given as follows:

r = 9 cm.

Hence the area of the entire circle for this problem is given as follows:

A = π x (9)² = 81π cm².

The shaded region corresponds to an angle of 80º, while the entire circumference corresponds to an angle of 360º, hence the area of the shaded region is obtained as follows:

A = 80/360 x 81π = 18π cm².

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

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Answer:

Step-by-step explanation:

nai dunga

Answer:

  $18.97

Step-by-step explanation:

You want to know Ai Mi's bill if her $16 lunch had 6% tax added, and she tipped 14% on the amount with tax.

Adding tax multiplies the bill by (1 +6%) = 1.06.

Adding the tip on the amount with tax multiplies that amount by (1 +14%) = 1.14.

The total cost of Ai Mi's lunch is ...

  ($16(1.04))(1.14) ≈ $18.97

The total cost with tax and tip was $18.97.

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Therefore , the solution of the given problem of surface area comes out to be Concave hexagonal area equals 24.

Its surface area serves as a proxy for how much overall space it occupies. The whole environment of a three-dimensional shape is taken into account when calculating its surface area. The overall size of something is its surface area. The volume of water in a cuboid can be determined by summing the faces on all of its six rectangular sides. To determine the box's measurements, apply the following formula: For 2lh, 2lw, but also 2hw, the surface is the identical (SA). The region is represented by the surface area of the muti form.

Here,

Given :

The Pythagorean theorem can be used to calculate the distance between it circle centers and the difference in the radii of two circles (4-2=2) to determine the lengths of the rectangle's sides. 

We can calculate the area of rectangular as well as the two triangles using that. The regions of the these three forms are added to create the hexagon's surface area.

Let d be the distance between both the circle centers in the scenario described.

d² = (4+2)^2

d = √((4+2)^2) = √(36) = 6

Rectangle area = 26 divided by 12

Each triangle's area is equal to (1/2)(2d)/(1/2)(2*6), or 6

Hexagonal area equals 12 + 2 * 6 = 24.

Concave hexagonal area equals 24.

Therefore , the solution of the given problem of surface area comes out to be Concave hexagonal area equals 24.

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No these ratios 1/2 is not equal to 2/3 because 2/3 is not the multiple of 1/2

What is an equivalent ratios?

A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.

Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.

Given ratios are 2:1 and 3:1

we can write it as 2/1 and 3/1.

The lcm of 2 and 3 is 6.

Multiply denominator of both ratio with 6, we get

2/6 and 3/6 And we can see both the ratios are not equal.

Hence, there are not equivalent ratios.

4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2

11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)

3:1 and 9:3 are equivalent ratios ------> is true

because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3

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D. The retail price of the phone is given as follows: 42.

E. The percent reduction in the price to $31.50 is given as follows: 25%.

The prices and the percentages are obtained applying the proportions in the context of this problem.

The purchase price is given as follows:

$12.

The markup rate is given as follows:

250%.

Meaning that the retail price is of 100% + 250% = 350% of the purchase price, hence it's value is obtained as follows:

3.5 x 12 = $42.

The percentage reduction is given by the reduction in the price divided by the initial price and then multiplied by 100%.

The reduction from $42 to $31.50 is given as follows:

42 - 31.50 = $10.50.

Hence the percent reduction is given as follows:

10.5/42 x 100% = 25%.

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Answer:

The vertex of a parabolic function like V(x) = 325x² - 4600x + 145000 can be found by using the vertex form of the equation, which is y = a(x-h)² + k. In this form, (h,k) is the vertex of the parabola. To convert the equation V(x) = 325x² - 4600x + 145000 into vertex form, we can complete the square to get the following:

V(x) = 325(x² - 14x) + 145000

To complete the square we will add and subtract (14/2)² = 49

V(x) = 325(x-7)² + 145000 - 49*325 = 325(x-7)² + 138375

So the vertex of the parabola is (h,k) = (7, 138375).

The vertex of a parabolic function represents the minimum or maximum point of the parabola, depending on whether the parabola opens upwards or downwards. In this case, the vertex represents the maximum value of the home. It means that the value of the home reaches its highest point at 7 years after 2020, and this highest point is 138375.

So in terms of the value of the home, the vertex of the function represents the point at which the housing market reaches its peak, after which the value of the home begins to decrease.

Answer:

it is 28 cm^2 ig

you got to solve it in the same way as the first question ( divide the shape into rectangles and find the area of each then add them )

Answer:

18, 16, 22, 14, 17, 19, 15, 19, 22 add and divide by 9 = 17 feet

Step-by-step explanation:

Answer:

The equation csc^5 (theta) - 4 csc (theta) + 1 = 0 can be solved by factoring the left-hand side of the equation.

csc^5 (theta) - 4 csc (theta) + 1 = 0

csc (theta) (csc^4 (theta) - 4) + 1 = 0

csc (theta) (csc^2 (theta) - 2)(csc^2 (theta) + 2) + 1 = 0

We can see that the last expression is a polynomial equation of the form (ax+1)(bx^2+c*x+d)=0 where x= csc(theta) , a=1, b=1, c= -2, d=2

Solving for x = 0, we get x=0 which is not a valid solution because csc(theta) is defined only for theta != k*pi where k is an integer.

Solving for x= -1/2 and x= 1/2, we get csc(theta) = -1/2 and csc(theta) = 1/2

To find theta, we can use the reciprocal cosecant function (csc) which is defined as 1/sin(theta)

csc(theta) = -1/2 => sin(theta) = -2

csc(theta) = 1/2 => sin(theta) = 2

Answer: 0 is cos^4(theta) = (4 - 1/sin(theta))(1-sin^2(theta))^2.

Step-by-step explanation: To solve the equation csc^5(theta) - 4csc(theta) + 1 = 0, we can use the identity csc^n(theta) = 1/sin^n(theta).

First, we can apply the identity:

1/sin^5(theta) - 4/sin(theta) + 1 = 0

Next, we can factor out sin(theta) from the first two terms:

sin(theta)(1/sin^4(theta) - 4) + 1 = 0

We can then use the identity sin^2(theta) = 1 - cos^2(theta) to rewrite the first term:

sin(theta)(1 - cos^4(theta)/(1-cos^2(theta))^2 - 4) + 1 = 0

We can then divide both sides of the equation by sin(theta), and we get:

1 - cos^4(theta)/(1-cos^2(theta))^2 - 4 + 1/sin(theta) = 0

We can then simplify this equation to get:

cos^4(theta)/(1-cos^2(theta))^2 = 4 - 1/sin(theta)

By using the identity cos^2(theta) = 1-sin^2(theta) we can simplify the equation further:

cos^4(theta) = (4 - 1/sin(theta))(1-sin^2(theta))^2

So to find the solution we can use double angle identities to simplify the right side of the equation.

Therefore, the solution to the equation csc^5(theta) - 4csc(theta) + 1 = 0 is cos^4(theta) = (4 - 1/sin(theta))(1-sin^2(theta))^2.

The diameter of the DVD in centimeters found by adding together the ridges and valleys across the diameter is about 11.998 centimeters.

The diameter of a circle is the measured distance between the outer rim of the circumference of the circle, passing through the center of the circle.

The number and dimensions of the ridges (bumps) and valleys (without bumps) on the DVD disc are as follows;

The number of bumps across the diameter = 73,000

The thickness of a bump = 0.00032 cm

The number of valleys across the diameter = 73,000

The thickness of valley = 0.000074 cm

The diameter of the circle left blank at the middle of the DVD disc = 4.26 cm

The diameter of the DVD, D, is therefore obtained by multiplying thickness of the bumps and valleys then adding the result to the diameter of the circle in the middle as follows;

D = 73,000 × 0.000032 cm + 73,000 × 0.000074 cm + 4.26 cm = 11.998 cm

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Answer:

  (c)  a reflection across the y-axis followed by a translation 2 units up

Step-by-step explanation:

You want to know transformations that will give the red figure from the blue one.

The red figure is reversed left-to-right with respect to the blue figure, so a reflection across a vertical line is required. The only answer choice that has such a reflection is ...

C. a reflection across the y axis followed by a translation of 2 units up

With a mean of 1.5 and a standard deviation of 0.35. if 5 rats are selected, the probability that their total completion time in the maze for all rats is between 6 and 8 minutes is 0.4455.

First, we need to convert the given mean and standard deviation from "one rat" to "five rats". The mean for five rats would be 5 x 1.5 = 7.5, and the standard deviation for five rats would be sqrt(5) x 0.35 = 0.87.  Next, we need to convert the given time range of 6-8 minutes to the standard normal distribution, using the z-score formula: z = (x - mean) / standard deviation.  

For 6 minutes, z = (6 - 7.5) / 0.87 = -1.72 ,For 8 minutes, z = (8 - 7.5) / 0.87 = 0.58  Finally, we can use a standard normal distribution table to find the probability that the rats will complete the maze in between 6 and 8 minutes. This is the area under the standard normal curve between -1.72 and 0.58. The probability is 0.4455.

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The maximum number of zeros that the polynomial function f(x) = 4x^9 + 5x^8 + 4x^6 + 9x + 1 may have is 9

A polynomial function is a function in an equation, such as the quadratic equation, cubic equation, etc., that only uses non-negative integer powers or only positive integer exponents of a variable.

A polynomial with an exponent of 1 is, for instance, 2x + 5.

The degree of a polynomial is the highest exponent in the polynomial, the polynomial in the problem is f(x) = 4x^9 + 5x^8 + 4x^6 + 9x + 1. The degrees of the polynomial is 9

The zeros of the polynomial will never be more than the degree of the polynomial

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The measure of the missing angles are a = 65°, b = 115°, c = 115°, d = 65° and e = 65°

Angle geometry is a branch of mathematics that deals with angles and the properties of angles in geometric shapes such as measuring angles, classifying angles, and solving problems involving angles.

The measure of the missing angles are as follow:

a = 65° (corresponding angles are equal)

a + b = 180° (sum of angles of straight line is 180°)

65° + b = 180°

b = 180-65 = 115°

c = b  (corresponding angles are equal)

c = 115°

d = 180 - c (sum of angles of straight line is 180°)

d = 180 - 115 = 65°

e = d (corresponding angles are equal)

e = 65°

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Answer: 4/10 of those people have cats because 3/5 multiplied by 2/3 is 4/10.