Which of the following statements is not true? a) The standard deviation of the sampling distribution of sample mean = σ/√n b) The larger the sample size, the better will be the normal approximation to the sampling distribution of sample mean. c) The sampling distribution of the sample mean is always reasonably like the distribution of X, the distribution from which the sample is taken. d) The sampling distribution of sample mean is approximately normal, mound-shaped, and symmetric for n > 30 or n = 30. e) The mean of the sampling distribution of sample mean is always the same as that of X, the distribution from which the sample is taken. f) None of the above

Where are the statements ?

Answer: The data is skewed right.

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 answer is Ф = 1.82 or 4.46 ⇒ answer (c)

Step-by-step explanation:

* The domain of the function is 0 ≤ Ф ≤ 2π

- Lets revise the ASTC rule to solve the problem

# In the 1st quadrant all trigonometry functions are +ve

# In the 2nd quadrant sinФ and cscФ only are +ve

# In the 3nd quadrant tanФ and cotФ only are +ve

# In the 4th quadrant cosФ and secФ only are +ve

* Lets solve the problem

∵ secФ = -4.0545 ⇒ negative value

∴ Angle Ф is in the 2nd or 3rd quadrant

- In the 2nd quadrant Ф = π - α ⇒ (1)

- In the 3rd quadrant Ф = π + α ⇒ (2)

where α is an acute angle

* Now use the calculator to find α with radiant mode

- Let secα = 4.0545

∴ cosα = 1/4.0545

∴ α = cos^-1(1/4.0545) = 1.321585

* Substitute the value of α in (1) and (2)

∴ Ф = π - 1.321585 = 1.82

∴ Ф = π + 1.321585 = 4.46

* The answer is Ф = 1.82 or 4.46

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:

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:

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.

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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➷ 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.

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

Answer:

The length of the container is [tex]14\ in[/tex]

Step-by-step explanation:

we know that

The surface area of a triangular prism (a mailing container) is equal to

[tex]SA=2B+PL[/tex]

where

B is the area of the triangular base

P is the perimeter of the triangular base

L is the length of the container

step 1

Find the area of the base B

[tex]B=\frac{1}{2}(2)(1.7)=1.7\ in^{2}[/tex]

step 2

Find the perimeter of the base P

[tex]P=3(2)=6\ in[/tex]

step 3

Find the length L of the container

we have

[tex]SA=87.4\ in^{2}[/tex]

[tex]B=1.7\ in^{2}[/tex]

[tex]P=6\ in[/tex]

substitute and solve for L

[tex]87.4=2(1.7)+(6)L[/tex]

[tex]L=[87.4-2(1.7)]/(6)[/tex]

[tex]L=14\ in[/tex]

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

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:

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

Answer:

  5/9

Step-by-step explanation:

The scale factor by which T was dilated is ...

   (side of T')/(corresponding side of T)

   = 20/36 = 10/18 = 5/9 . . . (reduced form)

Answer:

C) the answer is 5/9 or C

Step-by-step explanation:

i got it roght on the edgen quiz.

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:

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]

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.

Answer:

[tex]\$20[/tex]

Step-by-step explanation:

Let

x-----> the cost of his lunch

y----> the cost of his dinner

we know that

[tex]x+y=872-136-210-500[/tex]

[tex]x+y=26[/tex] -----> equation A

[tex]x=0.3y[/tex] ---> equation B

substitute equation B in equation A

[tex]0.3y+y=26[/tex]

[tex]1.3y=26[/tex]

[tex]y=\$20[/tex] -----> the cost of the dinner

[tex] \cot(x) \sin(x) = \frac{ \cos(x) }{ \sin(x) } \sin(x) = \cos(x) \\ \Rightarrow b. \cot(x) = \frac{ \cos(x) }{ \sin(x) } [/tex]

Answer:

B

Step-by-step explanation:

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

Capacity of the fish tank is 40 gallons

X=1/2

Explanation

Multiple both sides times 5

Then the 5 just cancels out on the left side and you’re left with 1/2

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:

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:

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.

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:

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]

Step-by-step explanation:

We transform the system of equations to the form:

[tex]\left\{\begin{array}{ccc}ax+by=c\\dx+ey=f\end{array}\right[/tex]

Where a & b and d & e are relatively prime number.

If a ≠ d or b ≠ e then the system of equations has one solution.

Example:

[tex]\left\{\begin{array}{ccc}2x-3y=-4\\3x+3y=9\end{array}\right[/tex]

Add both sides of equations:

[tex]5x=5[/tex]     divide both sides by 5

[tex]x=1[/tex]

Substitute it to the second equation:

[tex]3(1)+3y=9[/tex]

[tex]3+3y=9[/tex]           subtract 3 from both sides

[tex]3y=6[/tex]       divide both sides by 3

[tex]y=2[/tex]

[tex]\boxed{x=1,\ y=2\to(1,\ 2)}[/tex]

If a = d and b = e and c = f then the system of equations has infinitely many solutions.

Example:

[tex]\left\{\begin{array}{ccc}2x+3y=5\\2x+3y=5\end{array}\right[/tex]

Change the signs in the second equation. Next add both sides of equations:

[tex]\underline{+\left\{\begin{array}{ccc}2x+3y=5\\-2x-3y=-5\end{array}\right}\\.\qquad0=0\qquad\bold{TRUE}[/tex]

[tex]\boxed{x\in\mathbb{R},\ y=\dfrac{5-2x}{3}}[/tex]

If  a = d and b = e and c ≠ f then the system of equations has no solution.

Example:

[tex]\left\{\begin{array}{ccc}3x+2y=6\\3x+2y=1\end{array}\right[/tex]

Change the signs in the second equation. Next add both sides of equations:

[tex]\underline{+\left\{\begin{array}{ccc}3x+2y=6\\-3x-2y=-1\end{array}\right}\\.\qquad0=5\qquad\bold{FALSE}[/tex]

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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