There are 45 members on the board of directors for a certain​ non-profit institution. if they must elect a​ chairperson, first vice​ chairperson, second vice​ chairperson, and​ secretary, how many different slates of candidates are​ possible?

Answer:

1. The Pythagoras theorem

Hypotenuse^2 = base^2 + perpendicular^2

2. Formula for calculating speed

Speed = Distance  Time

3. Areas

Rectangle = length * width

Square = side^2

4. Profit and loss formulas

Step-by-step explanation:

Final answer:

Einstein's second postulate on the constant speed of light in a vacuum led to the famous equation [tex]E = mc^2,[/tex] demonstrating mass-energy equivalence. Although not commonly used in everyday life, other practical formulas impact daily activities such as finance, medicine, and cooking.

Explanation:

The second postulate upon which Albert Einstein based his theory of special relativity is related to the speed of light. This principle states that light travels at a constant speed of [tex]c = 3.00 imes 10^8 m/s[/tex] in a vacuum and does not depend on the frame of reference from which it is observed. This postulate led to one of the most renowned equations in physics, [tex]E = mc^2[/tex], which describes the relationship between energy (E), mass (m), and the speed of light (c). In this equation, E represents the energy equivalent of a certain mass (m) when it is converted into energy, revealing the profound concept that mass and energy are interchangeable.

While [tex]E = mc^2[/tex] is a groundbreaking equation in theoretical physics, it is not commonly applied in everyday situations. However, there are many other formulas that are routinely used in daily life. Examples include calculations for simple interest in finance, dose calculations in medicine, and recipes in cooking that require proportional adjustments. These formulas help us to navigate various practical aspects of our day-to-day activities.

Answer:

A) 0.123; B) 0.8078; C) Because the population is normally distributed.

Step-by-step explanation:

For part A,

We first calculate the z-score, which tells us how many standard deviations from the mean our score is.

Since we are finding the z-score of an individual score and not a sample, we use the formula

[tex]z=\frac{X-\mu}{\sigma}[/tex]

Our score, X, is 209.3; our mean, μ, is 200; and our standard deviation, σ, is σ.  This gives us

[tex]z=\frac{209.3-200}{8}=\frac{9.3}{8}=1.1625[/tex]

We look this value up in a z-table.  However, we must round it to the nearest hundredth first; this is 1.16.  From a z-table, we get that the area under the curve to the left of, or less than or equal to, this score is 0.8770.

However we want the probability that the value is greater than this; this means we subtract our found probability from 1:

1-0.8770 = 0.123

For part B,

Again we first calculate the z-score.  However this time we are finding the probability of a mean of a sample rather than an individual score; this means we use the formula

[tex]z=\frac{\bar{X}-\mu}{\sigma\div \sqrt{n}}[/tex]

Our X is 198.20; our μ is still 200, and our σ is still 8; our value of n is our sample size, 15:

[tex]z=\frac{198.20-200}{8\div \sqrt{15}}=\frac{-1.8}{2.0656}=-0.87[/tex]

Looking up this value in a z-table, we get 0.1922.

However, we want the probability that the area, or probability, is greater than this; so we subtract from 1:

1-0.1922 = 0.8078

For part C,

When a population is normally distributed, this means that a sample taken from this population will also be normal; this means we can use the normal distribution.

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

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:

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;

Read more:

https://brainly.com/question/17751843

25. Step-by-step explanation:

[tex]\text{The general form of an ellipse is:}\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1\\\\\bullet \text{(h, k) is the Center}\\\bullet \text{a is the radius of x}\\\bullet \text{b is the radius of y}\\\bullet \text{the largest value between a and b is the major}\\\bullet \text{the smallest value between a and b is the minor}\\\bullet \text{the vertices are the (h, k) value plus the major (a or b) value}\\\bullet \text{the co-vertices are the (h, k) value plus the minor (a or b) value}\\\bullet \text{Length is the diameter}=2r\\[/tex]

[tex]\dfrac{x^2}{16}+\dfrac{y^2}{25}=1\quad \text{can be rewritten as}\ \dfrac{(x-0)^2}{4^2}+\dfrac{(y-0)^2}{5^2}=1\\\\\bullet (h, k)=(0,0)\\\bullet a=4\\\bullet b=5\\\bullet \text{b is the largest value so: b is the major and a is the minor}\\\bullet \text{Vertices are }(0, 0+5)\ and\ (0, 0-5)\implies (0, 5)\ and\ (0, -5)\\\bullet \text{Co-vertices are }(0+4, 0)\ and\ (0-4, 0)\implies (4,0)\ and\ (-4,0)\\\bullet \text{Length of major is }2b:2(5)=10\\\bullet \text{Length of minor is }2a:2(4)=8[/tex]

To find the foci, first we must find the length of the foci using the formula:

[tex](r_{major})^2-(r_{minor})^2=c^2[/tex]

Then add the c-value to the h (or k)-value that represents the major.

b² - a² = c²

25 - 16 = c²

        9 = c²

       ±3 = c

The center is (0, 0) and the major is the y-value so the foci is:

(0, 0+3) and (0, 0-3) ⇒ (0, 3) and (0, -3)

26. Answers

Follow the same steps as #25:

Center: (0, 0)

Vertices (7, 0) and (-7, 0)

Co-vertices: (0, 3) and (0, -3)

foci: (2√10, 0) and (-2√10, 0)

length of major: 14

length of minor: 6

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.

https://brainly.com/question/24377281

#SPJ3

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:

200 smaller lots

Step-by-step explanation:

10 ÷ 1/20 = 200

The number of smaller lots should be 200

Ms.Beard bought 10 acres of land she plans to divide the land into smaller slots that are each 1/20 of an acre

= 10 ÷ 1/20

= 200

Learn more about land here: https://brainly.com/question/136360

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.

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:

79.5688 < µ < 83.1646

Step-by-step explanation:

Sample mean is the sum of all scores, divided the the total number of test takers.  In this case, the sample mean is:

(87.4 + 86.9 + 89.9 + 78.3 + 75.1 + 70.6)/6 =  488.2/2 = 81.3667

The sample standard deviation is the square root of the sample variance.  See attached photo 1 for calculation of these values...

The sample standard deviation is 3.1856

We need to make a 90% confidence interval for this data.  Since n < 30, we will use a t-value.  The degrees of freedom is always one less than the sample size so on the t-distribution chart, look under the column for Area under the curve = 0.10, and the row for 5.  The t-value you should see is t = 2.015

See attached photo 2 for the construction of the confidence interval

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:

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

sides of right angle triangle follows Pythagoras theroem

which states

a^2 +b^2 = c^2

where a , b and c are sides of right angle triangle.

here none of options do not follow this.

so answer is option D

Answer:

D

Step-by-step explanation:

Which of the following are measurements of the sides of a right triangle?

Check c^2 = a^2 + b^2 where c is the largest of the 3 sides.

If c^2 = a^2+b^2 you have a right triangle. If it doesn't, you don't.

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 :)

12,500-11,625=875

1%=125

10%=1250

5%=625

625+125=750=6%

750+125=875=7%

so the percentage is 7%

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]

Read more about probabilities at:

https://brainly.com/question/11234923

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.

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).

For such more questions on graph

https://brainly.com/question/19040584

#SPJ6

Answer:

Multiply both sides of the equation by -2

Distribute -1/2 over (x+4)

Step-by-step explanation:

we have

[tex]-\frac{1}{2}(x+4)=6[/tex]

Method 1

Multiply both sides of the equation by -2 ------> Step 1

[tex](x+4)=6*(-2)[/tex]

[tex](x+4)=-12[/tex]

Subtract 4 from both sides of the equation

[tex]x=-12-4=-16[/tex]

Method 2

Distribute -1/2 over (x+4)-------> Step 1

[tex]-\frac{1}{2}x-2=6[/tex]

Multiply both sides of the equation by -2

[tex]x+4=6(-2)[/tex]

[tex]x+4=-12[/tex]

Subtract 4 from both sides of the equation

[tex]x=-12-4=-16[/tex]

Answer:

⇒ Multiply both sides of the equation by -2

⇒ Distribute -1/2 over (x+4)

Those are the 2 answers.

Answer:

2 2/3 lbs

Step-by-step explanation:

Convert Alya's mixed number to an improper fraction

   3*1+1 = 4/3

multiply 4/3 times 2/1

    4*2 = 8

    3*1 = 3

8/3 - convert back to mixed number

    8/3 = 2 2/3

Where are the statements ?

Answer: The data is skewed right.

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:

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:

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:

Step-by-step explanation:

Area = 7.6 × 3.7

Area = 28.12 cm²

I hope I helped you.

Answer:

[tex]28.12cm^2[/tex]

Step-by-step explanation:

The figure shown in the diagram  is  a parallelogram.

The area of a parallelogram is [tex]base \times height.[/tex].

The base of the parallelogram is 3.7cm

The height of the parallelogram is 7.6cm.

The area of the parallelogram

[tex]3.7\times 7.6=28.12cm^2[/tex]

The first choice is the correct answer

a.

3x = 30

x = 30/3

x = 10

b.

12x = 12

x = 12/12

x = 1

c.

1 = x-3

x = 1+3

x = 4

d.

-24 = 4x

x = -24/4

x = -6

HOPE THIS WILL HELP YOU

Answer:

30

Step-by-step explanation:

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.

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]