You've probably heard of Albert Einstein's formula regarding the speed of light: E = mc2. While this is an important formula that you will use throughout your academic career, it is not a formula you apply in your daily life. Describe some common or unique formulas that you use in your life. I DIDNT GET THE FULL ANSWER ON some unique formlas

Answer:

  see below

Step-by-step explanation:

The double angle formulas for trig functions are generally based on the sum of angle formulas, where the two angles are equal.

  cos(a+b) = cos(a)cos(b) -sin(a)sin(b)

When a=b=x, then ...

  cos(2x) = cos(x)² -sin(x)²

The Pythagorean identity can be used to substitute for either of the squares:

  cos(2x) = (1 -sin(x)²) -sin(x)²

  cos(2x) = 1 - 2sin(x)²

or

  cos(2x) = cos(x)² -(1 -cos(x)²)

  cos(2x) = 2cos(x)² - 1

The correct representations of the identity cos2x from the provided options are A (1 - 2sin²x), B (2sin²x - 1), and D (cos²x - sin²x). The Option C (sin²x - cos²x) is not correct. Therefore, option A,B and D are correct

The question is asking for various forms of the identity cos2x, where x is an angle.

From the given options, A, B, and D are correct.

We know that cos2x can be represented in three possible ways: 1 - 2sin²x (Option A), 2cos²x - 1 (not provided in the options), and 2sin²x - 1 (Option B).

Thus, the correct options are A (1-2sin²x) and B (2sin²x - 1). Option D (cos²x - sin²x) is another equivalent form of cos2x based on the identity cos²x + sin²x = 1 (provided as Reference 7). Option C (sin²x - cos²x) is not a formula for cos2x so it's incorrect.

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The correct statement is written below:

cos2x=____. Check all that apply.

A. 1-2sin^2 x.

B. 2sin^2 x-1.

C. sin^2 x-cos^2 x.

D. cos^2 x-sin^2 x

Answer:

2-sqrt14/2, 2+sqrt13/2.

Step-by-step explanation:

What you do is you have to do the quadratic equation like it says in the problem.

x=  −b± sqrtb^2 −4ac /2a .

a=-2, b=4, c=5.

x=-4±sqrt(4)^2-4(-2)(5)/2(-2).

x=-4±sqrt16+40/-4.

x=-4±2sqrt14/-2.

2-sqrt14/2, 2+sqrt13/2. is your answer once you have done everything.

​  

​

Answer:

5 seconds

Step-by-step explanation:

:0

➷ Angles in a triangle total to 108 degrees

180 - (45 + 15) = 120

Angle B is 120 degrees.

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

The correct option is D.

Step-by-step explanation:

From the given figure it is clear that the measure of angle A is 45° and the measure of angle C is 15°.

According to the angle sum property of triangles, the sum of interior angles of a triangle is 180°. It means in triangle ABC,

[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]

[tex]45^{\circ}+\angle B+15^{\circ}=180^{\circ}[/tex]

[tex]\angle B+60^{\circ}=180^{\circ}[/tex]

[tex]\angle B=180^{\circ}-60^{\circ}[/tex]

[tex]\angle B=120^{\circ}[/tex]

The measure of angle B is 120°. Therefore the correct option is D.

Answer:

a) a continuous random variable; b) a discrete random variable; c) not a random variable; d) a discrete random variable; e) a discrete random variable; f) a discrete random variable

Step-by-step explanation:

A continuous random variable is one that can take multiple values between whole number values; for instance, fractions and decimals.  Snowfall is a continuous random variable.

A discrete random variable is one that can only take whole number values.  The number of bald eagles, the number of students reading a book, the number of people with blood type A, and the number of points scored in a  basketball game are discrete random variables.

Gender of students is not a numerical value; this is not a random variable.

Here, we are required to determine whether the value a list of data sets are, discrete random variable, continuous random variable, or not a random variable.

First, it is important to know the characteristics of each type of value as follows;

2. A continuous random variable is one which has an infinite number of possible values. This means that the value of a continuous variable is usually associated with fractions of whole numbers, i.e continuous random variables are used majorly for measurements such as length, height and so on. An example from the question above is;

3. A non-random variable is one whose values are definite. An example from above is;

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The graph of the equation y − 2 = 2⁄3(x + 4) is a blue line that passes through the points (0, 2) and (3, 4).

To graph the equation `y − 2 = 2⁄3(x + 4)` using the Line Tool and selecting two points, we can use the following steps:

1. Find the slope and y-intercept of the line.

The equation is already in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 2⁄3 and the y-intercept is 2.

2. Find a point on the line.

The y-intercept is always a point on the line, so we can use the point (0, 2) as our first point.

3. Use the slope to find another point on the line.

The slope tells us how much to move up or down and how much to move to the right to find another point on the line. In this case, the slope is 2⁄3, so we need to move up 2 units and to the right 3 units from our first point. This gives us the point (3, 4).

4. Select the two points in the Line Tool and draw the line.

Once we have selected the two points, we can draw the line by clicking and dragging the mouse.

Step 1: Find the slope and y-intercept of the line.

The equation `y − 2 = 2⁄3(x + 4)` is already in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 2⁄3 and the y-intercept is 2.

Step 2: Find a point on the line.

The y-intercept is always a point on the line, so we can use the point (0, 2) as our first point.

Step 3: Use the slope to find another point on the line.

The slope tells us how much to move up or down and how much to move to the right to find another point on the line. In this case, the slope is 2⁄3, so we need to move up 2 units and to the right 3 units from our first point. This gives us the point (3, 4).

Step 4: Select the two points in the Line Tool and draw the line.

Once we have selected the two points, we can draw the line by clicking and dragging the mouse.

Here is a diagram of the graph:

[Image of a graph of the equation y − 2 = 2⁄3(x + 4)]

The blue line is the graph of the equation. The red point is the point (0, 2) and the green point is the point (3, 4).

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Answer:

32 units²

Step-by-step explanation:

From point 1 to point 2, the y values change by 8 units while the x values stay the same.  This side of the rectangle has a length of 8

From point 1 to point 3, the x values change by 4 units while the y values stay the same.  This side of the polygon has a length of 4

The area of the rectangle is 8x4 = 32 units²

Answer:

32 square units

Step-by-step explanation:

A rectangle has vertices at (-1, 6), (-1, -2), (3, 6), and (3,-2)

Area of a rectangle = length times width

LEts find the distance between  (-1, 6) and  (3, 6)

Apply distance formula

[tex]D= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]D= \sqrt{(3+1)^2+(6-6)^2}=\sqrt(16)= 4[/tex]

LEts find the distance between   (-1, 6), (-1, -2)

[tex]D= \sqrt{(-1+1)^2+(-2-6)^2}=\sqrt(64)= 8[/tex]

Area of the rectangle = 4 times 8= 32 square units

a) There are 6 sides, one of them having 6 on it. Therefore, the chances is 1/6.

b) Rolling a six or not rolling a six is guaranteed, because there is no other option. The probability is 1.

c) There are 6 sides, five of them not having a 6. So, the probability is 5/6.

Where are the statements ?

Answer: The data is skewed right.

Answer:

A) 0.2253, 0.0153; B) 0.4925, 0.0017

Step-by-step explanation:

This is a binomial distribution.  This is because there are only two outcomes; each trial is independent of each other; and the outcomes are independent.

This means we use the formula

[tex]_nC_r\times p^r\times (1-p)^{n-r}[/tex]

For part A,

There are 12 wolves selected; this means n = 12.  We want the probability that 9 or more are male; this makes r = 9, 10, 11 or 12.  We will find each probability and add them together.

p, the probability of success, is 0.6 for the first question (males).  This makes 1-p = 1-0.6 = 0.4.  Together this gives us

[tex]_{12}C_9(0.6)^9(0.4)^3+_{12}C_{10}(0.6)^{10}(0.4)^2+_{12}C_{11}(0.6)^{11}(0.4)^1+_{12}C_{12}(0.6)^{12}(0.4)^0\\\\=220(0.6)^9(0.4)^3+66(0.6)^{10}(0.4)^2+12(0.6)^{11}(0.4)+1(0.6)^{12}(1)\\\\\\= 0.2253[/tex]

We now want the probability that 9 or more are female; this makes r = 9, 10, 11 or 12.  p is now 0.4; this makes 1-p = 1-0.4 = 0.6.  This gives us

[tex]_{12}C_9(0.4)^9(0.6)^3+_{12}C_{10}(0.4)^{10}(0.6)^2+_{12}C_{11}(0.4)^{11}(0.6)^1+_{12}C_{12}(0.4)^{12}(0.6)^0\\\\=220(0.4)^9(0.6)^3+66(0.4)^{10}(0.6)^2+12(0.4)^{11}(0.6)^1+1(0.4)^{12}(1)\\\\=0.0153[/tex]

For part B,

There are again 12 wolves selected, so n = 12.  We want the probability in the first question that 9 or more are male; this makes r = 9, 10, 11 or 12.  The probability of success is now 0.7, so 1-p = 1-0.7 = 0.3[tex]_{12}C_9(0.7)^9(0.3)^3+_{12}C_{10}(0.7)^{10}(0.3)^2+_{12}C_{11}(0.7)^{11}(0.3)^1+_{12}C_{12}(0.7)^{12}(0.3)^0\\\\=220(0.7)^9(0.3)^3+66(0.7)^{10}(0.3)^2+12(0.7)^{11}(0.3)^1+1(0.7)^{12}(0.3)^0\\\\= 0.4925[/tex]

For the second question, the probability of success is now 0.3 and 1-p = 1-0.3 = 0.7:

[tex]220(0.3)^9(0.7)^3+66(0.3)^{10}(0.7)^2+12(0.3)^{11}(0.7)^1+1(0.3)^{12}(0.7)^0\\\\=0.0017[/tex]

Probabilities are used to determine the outcomes of events.

Before 1918,

Since 1918,

The question is an illustration of binomial probability, where:

[tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex]

(a i) Probability of selecting 9 or more wolves out of 12, before 1918

The given parameters are:

[tex]\mathbf{p = 0.60}[/tex] --- the probability of selecting a male wolf

So, we have:

[tex]\mathbf{P(x \ge 9) = P(9) + P(10) + P(11) + P(12)}[/tex]

Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:

[tex]\mathbf{P(x \ge 9) = ^{12}C_9 \times 0.6^9 \times (1 - 0.6)^{12-9} +..............+^{12}C_{12} \times 0.6^{12} \times (1 - 0.6)^{12-12} }[/tex]

[tex]\mathbf{P(x \ge 9) = 220 \times 0.00064497254 +..........+1 \times 0.00217678233}[/tex]

[tex]\mathbf{P(x \ge 9) =0.225 }[/tex]

(a ii) Probability of selecting 9 or more female wolves

The given parameters are:

[tex]\mathbf{p = 0.40}[/tex] --- the probability of selecting a female wolf

So, we have:

[tex]\mathbf{P(x \ge 9) = P(9) + P(10) + P(11) + P(12)}[/tex]

Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:

[tex]\mathbf{P(x \ge 9) = ^{12}C_9 \times 0.4^9 \times (1 - 0.4)^{12-9} +..............+^{12}C_{12} \times 0.4^{12} \times (1 - 0.4)^{12-12} }[/tex]

[tex]\mathbf{P(x \ge 9) = 220 \times 0.0000566231+..........+1 \times 0.00001677721}[/tex]

[tex]\mathbf{P(x \ge 9) =0.015 }[/tex]

(a ii) Probability of selecting fewer than 6 female wolves

The given parameters are:

[tex]\mathbf{p = 0.40}[/tex] --- the probability of selecting a female wolf

Using the complement rule, we have:

[tex]\mathbf{P(x < 6) = 1 - P(x \ge 6)}[/tex]

So, we have:

[tex]\mathbf{P(x < 6) = 1 - [P(6) + P(7) + P(8) + P(x \ge 9)]}[/tex]

Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:

[tex]\mathbf{P(x < 6) = 1 - [^{12}C_6 \times 0.4^6 \times 0.6^6 + ^{12}C_7 \times 0.4^7 \times 0.6^5 + ^{12}C_8 \times 0.4^8 \times 0.6^4 + P(x \ge 9)}[/tex][tex]\mathbf{P(x < 6) = 1 - [924 \times 0.00019110297 +........ + 0.0153]}[/tex]

[tex]\mathbf{P(x < 6) = 1 - [0.335]}[/tex]

[tex]\mathbf{P(x < 6) = 0.665}[/tex]

(b i) Probability of selecting 9 or more wolves out of 12, since 1918

The given parameters are:

[tex]\mathbf{p = 0.70}[/tex] --- the probability of selecting a male wolf

So, we have:

[tex]\mathbf{P(x \ge 9) = P(9) + P(10) + P(11) + P(12)}[/tex]

Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:

[tex]\mathbf{P(x \ge 9) = ^{12}C_9 \times 0.7^9 \times (1 - 0.7)^{12-9} +..............+^{12}C_{12} \times 0.7^{12} \times (1 - 0.7)^{12-12} }[/tex]

[tex]\mathbf{P(x \ge 9) = 220 \times 0.00108954738+..........+1 \times 0.0138412872}[/tex]

[tex]\mathbf{P(x \ge 9) =0.493 }[/tex]

(b ii) Probability of selecting 9 or more female wolves

The given parameters are:

[tex]\mathbf{p = 0.30}[/tex] --- the probability of selecting a female wolf

So, we have:

[tex]\mathbf{P(x \ge 9) = P(9) + P(10) + P(11) + P(12)}[/tex]

Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:

[tex]\mathbf{P(x \ge 9) = ^{12}C_9 \times 0.3^9 \times (1 - 0.3)^{12-9} +..............+^{12}C_{12} \times 0.3^{12} \times (1 - 0.3)^{12-12} }[/tex]

[tex]\mathbf{P(x \ge 9) = 220 \times 0.00000675126+..........+1 \times 5.31441e-7}[/tex]

[tex]\mathbf{P(x \ge 9) =0.002 }[/tex]

(b iii) Probability of selecting fewer than 6 female wolves

The given parameters are:

[tex]\mathbf{p = 0.40}[/tex] --- the probability of selecting a female wolf

Using the complement rule, we have:

[tex]\mathbf{P(x < 6) = 1 - P(x \ge 6)}[/tex]

So, we have:

[tex]\mathbf{P(x < 6) = 1 - [P(6) + P(7) + P(8) + P(x \ge 9)]}[/tex]

Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:

[tex]\mathbf{P(x < 6) = 1 - [^{12}C_6 \times 0.3^6 \times 0.7^6 + ^{12}C_7 \times 0.3^7 \times 0.7^5 + ^{12}C_8 \times 0.3^8 \times 0.7^4 + P(x \ge 9)}[/tex]

[tex]\mathbf{P(x < 6) = 1 - [924 \times 0.4^6 \times 0.7^6 + 792 \times 0.3^7 \times 0.7^5 + 495 \times 0.3^8 \times 0.7^4 + 0.002}[/tex]

[tex]\mathbf{P(x < 6) = 1 - [0.484]}[/tex]

[tex]\mathbf{P(x < 6) = 0.516}[/tex]

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Answer:

[tex]x = 150 * 3^{y}[/tex]

Step-by-step explanation:

Let's start by creating the beginning of the data sample, knowing the population of bees triples each year.

Year 0 = 150

Year 1 = 450

Year 2 = 1350

Year 3 = 4050

Year 4 = 12150

If we look at the numbers, we see they are all divided by 150:

Year 0 = 150 / 150 = 1

Year 1 = 450 / 150 = 3

Year 2 = 1350 / 150 = 9

Year 3 = 4050 / 150 = 27

Year 4 = 12150 / 150 = 81

We then see the result of the division by 150 is in fact the table of multiplication by 3.

So, by inverting the operation, we can see the number of bees (x) for any given year starting from now is 150 times 3 at the power of the year (y).

Answer:

y=150(3)^x

Step-by-step explanation:

I had to do an assignment with the same question, this is the answer :)

Answer:

30

Step-by-step explanation:

A = x = 110 degrees

B = 117 degrees

C = y = 63 degrees

D = 70 degrees

In a trapezoid, the two angles on the same side of the parallel lines are supplementary, meaning their measures add up to 180 degrees.

So, for angle A and angle D:

A + D = 180

x + 70 = 180

x = 180 - 70

x = 110

For angle B and angle C:

B + C = 180

117 + y = 180

y = 180 - 117

y = 63

Therefore, in the trapezoid ABCD:

A = x = 110 degrees

B = 117 degrees

C = y = 63 degrees

D = 70 degrees

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Step-by-step explanation:

x^2 - 8x = 20

1. Subtract 20 from both sides

x^2 - 8x - 20 = 20 - 20

2. Simplify

x^2 - 8x - 20 = 0

3. Factor the equation out by grouping

(x - 10)(x + 2) = 0

4. Change signs:

x = 10, x = -2

Hope This Helped!!

~Shane

Answer:{-2,10}

Step-by-step explanation:

trust

The answer has to be A) r(n) = 15n +55, as when n=0, r(n)=55 so the equation must end with +55.

Answer:

A. [tex]r(n)=15*n+55[/tex]

Step-by-step explanation

Since the value of n is given in the table as 0,5,15,30 and 35.So we will put the value of n in the given option starting from A.

Now putting the value of n as 0 in option A

we get [tex]r(n)=15*n+55[/tex]

[tex]r(0)=15*0+55\\r(0)=55[/tex]

Now putting the value of n as 5 in option A

we get [tex]r(n)=15*n+55[/tex]

[tex]r(5)=15*5+55\\r(0)=130[/tex]

Now putting the value of n as 15 in option A

we get [tex]r(n)=15*n+55[/tex]

[tex]r(15)=15*15+55\\r(0)=280[/tex]

Now putting the value of n as 30 in option A

we get [tex]r(n)=15*n+55[/tex]

[tex]r(30)=15*30+55\\r(0)=505[/tex]

Now putting the value of n as 35 in option A

we get [tex]r(n)=15*n+55[/tex]

[tex]r(35)=15*35+55\\r(0)=580[/tex]

After seeing the results of each value we see that option A is matching with all the given values. So the correct answer is A.

The answer should be B: $1,785.25

Answer:

$1785.245

Step-by-step explanation:

Cost of truck = $32,459

We are given that Bobby gets 5.5% commission on the cost of each vehicle he sells.

So, Commission = [tex]\frac{5.5}{100} \times 32459[/tex]

Commission = [tex]1785.245[/tex]

Hence his commission if he sells a truck for $32,459 is $1785.245

Answer:

The surface area of the cube is [tex]288\ units^{2}[/tex]

Step-by-step explanation:

we know that

The length of a diagonal of a cube is equal to

[tex]D=b\sqrt{3}[/tex]

where

b is the length side of a cube

In this problem we have

[tex]D=12\ units[/tex]

so

[tex]12=b\sqrt{3}[/tex]

solve for b

[tex]b=\frac{12}{\sqrt{3}}\ units[/tex]

Simplify

[tex]b=4\sqrt{3}\ units[/tex]

Find the surface area of the cube

The surface area of the cube is equal to

[tex]SA=6b^{2}[/tex]

substitute the value of b

[tex]SA=6(4\sqrt{3})^{2}=288\ units^{2}[/tex]

Answer:

The selling price is $21

Step-by-step explanation:

What is the markup

Take the original price and multiply by the markup percent

markup = 15*40%

             = 15*.4

              = 6

The new price is the original price plus the markup

new price = 15+6

new price = 21

The selling price is $21

Answer:

The area of rectangle is [tex]72\ units^{2}[/tex]

Step-by-step explanation:

see the attached figure with letters to better understand the problem

Let

[tex]A(3.10),B(12,1),C(16,5),D(7,14)[/tex]

we know that

The area of rectangle is equal to

[tex]A=(AB)(BC)[/tex]

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Find the distance AB

we have

[tex]A(3.10),B(12,1)[/tex]

substitute in the formula

[tex]AB=\sqrt{(1-10)^{2}+(12-3)^{2}}[/tex]

[tex]AB=\sqrt{(-9)^{2}+(9)^{2}}[/tex]

[tex]AB=\sqrt{162}\ units[/tex]

Find the distance BC

we have

[tex]B(12,1),C(16,5[/tex]

substitute in the formula

[tex]BC=\sqrt{(5-1)^{2}+(16-12)^{2}}[/tex]

[tex]BC=\sqrt{(4)^{2}+(4)^{2}}[/tex]

[tex]BC=\sqrt{32}\ units[/tex]

Find the area of rectangle

[tex]A=(\sqrt{162})*(\sqrt{32})=72\ units^{2}[/tex]

Answer:

d is the answer

Step-by-step explanation:

The answer to your question is a. TRUE

Final answer:

The statement that the probability of a Type II error is represented by the Greek symbol β is true. The β symbol denotes the likelihood of failing to reject a false null hypothesis, while the power of a test (1-β) indicates the probability of accurately detecting a false null hypothesis.

Explanation:

The question is asking whether the statement 'The probability of a type ii error is represented by the greek symbol, β' is true or false. The correct answer is a. True. In statistics, a Type II error, which occurs when a false null hypothesis is not rejected, is indeed represented by the Greek letter β (beta). Therefore, the probability of committing a Type II error is denoted as β (beta). Conversely, a Type I error, symbolized by α (alpha), happens when the null hypothesis is incorrectly rejected. It is important to minimize both α and β as they represent the probabilities of these two types of errors. While α is often set by the researcher (commonly at 0.05), β is affected by factors such as effect size, sample size, and the chosen significance level α.

The power of a statistical test, defined as 1 - β, is the probability of correctly rejecting a false null hypothesis. A high statistical power is desirable as it indicates a lower chance of committing a Type II error. Estimating or calculating β directly can be complex, but understanding its role is crucial for interpreting the results of hypothesis testing.

Answer:

The answer is -6.

Step-by-step explanation:

To find the value of y in (3, y), plug in 3 for x in y = -(2x) and solve for y.

y = -(2(3))

y = -6

y = -6, so the answer is -6.

Answer:

-8

Step-by-step explanation:

I think the equation you want is y=-(2^x) because if you meant what you put originally the first guy is right.

What you do is take 2^3 which equals 8 and then you have the negative left which gets you to -8. I probably explained this terribly and I am sorry.

Answer:

See below.

Step-by-step explanation:

Temperature at 5 pm = 1.5 + 0.7 - 2.6 - 0.9

(= -1.3 degrees C).

Answer:=1.5 + 0.7 - 2.6 - 0.9

Step-by-step explanation:

Answer:

The series is convergent answer ⇒ (a)

Step-by-step explanation:

* The series is -8/5 + 32/25 + -128/125 + ........

- It is a geometric series with:

- first term a = -8/5 and common ratio r = 32/25 ÷ -8/5 = -4/5

* The difference between the convergent and divergent

  in the geometric series is :

- If the geometric series is given by  sum  = a + a r + a r² + a r³ + ...

* Where a is the first term and r is the common ratio

* If |r| < 1 then the following geometric series converges to a / (1 - r).  

- Where a/1 - r is the sum to infinity

* The proof is:

∵ S = a(1 - r^n)/(1 - r) ⇒ when IrI < 1 and n very large number

∴ r^n approach to zero

∴ S = a(1 - 0)/(1 - r) = a/(1 - r)

∴ S∞ = a/1 - r

* If |r| ≥ 1 then the above geometric series diverges

∵ r = -4/5

∴ IrI = 4/5

∴ IrI < 1

∴ The series is convergent

The ratio of successive terms leads to a limit of 4/5, which is less than 1. Hence, the series is convergent.

Convergence or Divergence of a Series

To determine whether the series -8/5+32/25-128/125+... is convergent or divergent, we observe the series' structure and apply the ratio test. For a series ∑a_n, the ratio test considers the limit L = lim (n→∞) |a_(n+1) / a_n|.

Let's compute this for our series:

[tex]a_n = (-1)^{(n+1)} * 8 * (4/5)^{(n-1)}[/tex]

Compute [tex]a_(n+1): a_(n+1) = (-1)^{(n+2)} * 8 * (4/5)^n[/tex]

Calculate |a_(n+1) / a_n| = [tex]|(-1)^{(n+2)} * 8 * (4/5)^n / (-1)^{(n+1)} * 8 * (4/5)^{(n-1)}| = |(4/5)|[/tex]

The limit L = |(4/5)| = 4/5 which is less than 1.

Since L < 1, by the ratio test, the series -8/5+32/25-128/125+... is convergent.

Capacity of the fish tank is 40 gallons

Answer:

Your answer is 2/1. 2 donuts every minute.

Step-by-step explanation: The rate you are given is 30 donuts every 30 minutes. This equals 30/15.

To make a unit rate, you must make the fraction have a ratio of x/1. You can simply do this by dividing and/or simplifying the equation 30/15.

The unit rate at which the bakery makes donuts is 2 donuts per minute. This is determined by dividing the total number of donuts (30) by the total time in minutes (15).

The question is asking for the unit rate at which the bakery makes donuts. A unit rate is a ratio that compares the quantity of one thing to 1 of something else. In this case, we want to find how many donuts the bakery makes in 1 minute. Given that the bakery can make 30 donuts every 15 minutes, we divide 30 (donuts) by 15 (minutes) to find the unit rate. So, 30 donuts ÷ 15 minutes = 2 donuts per minute. Therefore, the unit rate at which the bakery makes donuts is 2 donuts per minute.

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Answer:

C(1,99) and E(5,8)

Step-by-step explanation:

Discrete data are numerical values that are distinct and outstanding mostly assigned from surveys by counting e.t.c

Thus, these numerical values cannot be negative as we can not count negative  values.

the data can only take known exact values so it is not continuous. From the given sets of data the sets that satisfy the given guidelines are C(1,99) and E(5,8)

Answer:

B. triangular pyramid.

Step-by-step explanation:

-Octahedron has eight faces that are equilateral  triangles, six vertices and twelve edges.

-Triangular pyramid has four triangular faces that have congruent isosceles triangles in which one of them is considered the base.

-Right triangular pyramid has a triangle base, three faces and six edges and the line that is located between the centre of the base and the vertex is perpendicular to the base.

-Regular rectangular prism has twelve sides, 8 vertices and six rectangular faces.

According to this, the answer is triangular pyramid.

Answer:

42,000 dollars was the value of the plot last year

Step-by-step explanation:

[tex]x*\frac{110}{100}=46200\\110x=4620000\\x=\frac{4620000}{110} \\x=42000[/tex]

Answer:

The answer is $6

Step-by-step explanation:

20 divided by 30% is 6! So it’s therefore 6$

Answer:

3^-3

Step-by-step explanation:

So first 81^-3/4 is cubing 81, finding the forth root, and then putting it on the denominator. Doing this you get 1/27.

Now you think, how do I get 3 to equal 27?

3^1 = 3

3^2 = 9

3^3 = 27

From here you just put a negative in front of the power, 3^-3, which puts the 27 on the bottom of the fraction, leaving you with 1/27, which is what we were trying to get.

Answer:

x=6

Step-by-step explanation:

2(x+4)+2x=32

2x+8+2x=32

4x+8=32

4x=24

x=6

The dimensions of the room are 6 meters in width and 10 meters in length.

The student's question pertains to finding the dimensions of a rectangular room based on given conditions: the room is 4 meters longer than it is wide and the perimeter is 32 meters. Let's denote the width of the room as w meters. Therefore, the length will be w + 4 meters. The perimeter of a rectangle is calculated by the formula

P = 2(length + width), which in this case is:

2(w + w + 4) = 32

4w + 8 = 32

4w = 32 - 8

4w = 24

w = 24 / 4

w = 6 meters

Now, since the length is 4 meters longer, it will be:

length = w + 4

length = 6 + 4 = 10 meters

Therefore, the dimensions of the room are 6 meters in width and 10 meters in length.