A population of 430,000 toads is expected to shrink at a rate of 5.5% per year. Which is the best prediction for the toad population in 14 years?


A. 236,500

B. 194,766

C. 59,125

D. 13,821

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

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:

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:

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

I. If the linear correlation coefficient for two variables is zero, then there is no relationship between the variables.

True.

II. If the slope of the regression line is negative, then the linear correlation coefficient is negative.

False.

III. The value of the linear correlation coefficient always lies between -1 and 1.

True.

IV. A linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of -0.82.

False.

So, the correct statements are I and III.

Therefore, the correct answer is:

OB. I and II

Let's evaluate each statement:

I. If the linear correlation coefficient for two variables is zero, then there is no relationship between the variables.

True. A correlation coefficient of zero indicates no linear relationship between the variables. However, it's important to note that there could still be a nonlinear relationship.

II. If the slope of the regression line is negative, then the linear correlation coefficient is negative.

False. The linear correlation coefficient (Pearson correlation coefficient) measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1. The sign of the correlation coefficient indicates the direction of the relationship (positive or negative), not the slope of the regression line. So, this statement is not necessarily true.

III. The value of the linear correlation coefficient always lies between -1 and 1.

True. The linear correlation coefficient, also known as Pearson's correlation coefficient, ranges from -1 to 1. A correlation coefficient of -1 indicates a perfect negative linear relationship, 0 indicates no linear relationship, and 1 indicates a perfect positive linear relationship.

IV. A linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of -0.82.

False. The magnitude (absolute value) of the correlation coefficient indicates the strength of the linear relationship, regardless of the sign. Therefore, a correlation coefficient of -0.82 suggests a stronger linear relationship compared to a correlation coefficient of 0.62.

So, the correct statements are I and III.

Therefore, the correct answer is:

OB. I and IV

The complete question is here:

Which of the following statements concerning the linear correlation coefficient are true? 1: If the linear correlation coefficient for two variables is zero, then there is no relationship between the variables. II: If the slope of the regression line is negative, then the linear correlation coefficient is negative. III: The value of the linear correlation coefficient always lies between - 1 and 1. IV: A linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of -0.82. A. III and IV

B. I and IV

C. I and II

D. II and III

The true statements for the given information are:

I: If the linear correlation coefficient for two variables is zero, then there is no relationship between the variables.

III: The value of the linear correlation coefficient always lies betweenminus1 and 1.

The correct options are I and III.

I: If the linear correlation coefficient for two variables is zero, then there is no relationship between the variables. This statement is true. The linear correlation coefficient, also known as Pearson's correlation coefficient (r), measures the strength and direction of the linear relationship between two variables. When r = 0, it indicates that there is no linear relationship between the variables.

II: If the slope of the regression line is negative, then the linear correlation coefficient is negative. This statement is not necessarily true. The slope of the regression line indicates the direction and steepness of the relationship between the variables, while the correlation coefficient indicates the strength and direction of the linear relationship. The correlation coefficient can be negative even if the slope of the regression line is positive, and vice versa.

III: The value of the linear correlation coefficient always lies between -1 and 1. This statement is true. The correlation coefficient ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 0 indicates no linear relationship, and 1 indicates a perfect positive linear relationship. Therefore, the correlation coefficient always falls within this range.

IV: A linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of -0.82. This statement is false. The magnitude of the correlation coefficient indicates the strength of the linear relationship, regardless of whether it is positive or negative. Therefore, in this case, the correlation coefficient of -0.82 suggests a stronger linear relationship compared to 0.62 because the magnitude of -0.82 is larger than that of 0.62.

In summary, statements I and III are true, while statements II and IV are false.

Complete question

Which of the following statements concerning the linear correlation coefficient are true?

I: If the linear correlation coefficient for two variables is zero, then there is no relationship between the variables.

II: If the slope of the regression line is negative, then the linear correlation coefficient is negative. III: The value of the linear correlation coefficient always lies betweenminus1 and 1.

IV: A linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of minus 0.82.

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:

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

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:

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.

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:

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:

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:

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)

10

6/3 =n/5

times n by 2 basically

answer is 10

it’s basically ratios

I think the answer is 5

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:

30

Step-by-step explanation:

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:

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.

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:

  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

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.

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:

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.

There are no compound periods given, so use the simple interest formula:

A = P(1+rt) where P is the principal, r is the rate and t is the time.

A = 5000(1+0.0975(6))

A = 5000(1+0.585)

A = 5000(1.585)

A = $7,925

Interest = 7925 - 5000 = $2,925

Total paid back = $7,925

Answer:

The Interest is 2,925.00 and now you owe 7,925.00. I hope this helps

Step-by-step explanation:

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:

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

Answer:   a) 36x + 3

                b) 36x + 27

                c) 16x + 15

                d) 81x

Step-by-step explanation:

f(x) = 4x + 3         g(x) = 9x

a) f(g(x)) = 4(9x) + 3       replaced x in f(x) equation with 9x

             = 36x + 3

b) g(f(x)) = 9(4x + 3)      replaced x in g(x) with 4x + 3

             = 36x + 27

c) f(f(x)) = 4(4x + 3) + 3     replaced x in f(x) with 4x + 3

           = 16x + 12   + 3

           = 16x + 15

d) g(g(x)) = 9(9x)            replaced x in g(x) with 9x

              = 81x

Answer:

solution given:

f(x) = 4x + 3

g(x) = 9x

answer:

a.fog(x)=f(9x)=4×9x+3=36x+3

domain=real number

b.gof (x)=g(4x+3)=9(4x+3)=36x+26

domain=real number

c.fof(x)=f(4x+3)=4(4x+3)+3=16x+12+3

=16x+15

domain: real number

d.

gog(x)=g(9x)=9×9x=81x

domain: real number.

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.

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Answer:

5 seconds

Step-by-step explanation:

:0

Answer:

[tex]\large\boxed{Q1.\ A_{\triangle PQR}=90\ cm^2}\\\\\boxed{Q2.\ V\approx321\ m^3}[/tex]

Step-by-step explanation:

[tex]Q1.\\\\\text{If}\ \triangle ABC\sim\triangle PQR\ \text{then the quotient of the areas is equal}\\\text{the square of the similarity scale}\ k.\\\\\text{The sides}\ AB\ \text{and}\ QP\ \text{are corresponding}.\ \text{Calculate the scale:}\\\\k=\dfrac{4}{6}=\dfrac{4:2}{6:2}=\dfrac{2}{3}\\\\\text{The area of }\ \triangle ABC=40\ cm^2.\\\\\text{Let the area of}\ \triangle PQR=x,\ \text{then}\\\\\dfrac{40}{x}=\left(\dfrac{2}{3}\right)^2\\\\\dfrac{40}{x}=\dfrac{4}{9}\qquad\text{cross multiply}\\\\4x=(9)(40)\qquad\text{divide both sides by 4}\\\\x=(9)(10)\\\\x=90\ cm^2[/tex]

[tex]Q2.\\\\\text{The formula of a volume of a sphere:}\\\\V=\dfrac{4}{3}\pi R^3\\\\R-radius\\\\\text{We have the diameter}\ 2R=8.5\ m\to R=\dfrac{8.5}{2}\ m=4.25\ m.\\\\\text{Substitute:}\\\\V=\dfrac{4}{3}\pi(4.25)^3=\dfrac{4}{3}\pi(76.765625)=(4)(25.588541)\pi=102.354164\pi\\\\\pi\approx3.14\\\\V=(102.354164)(3.14)\approx321\ m^3[/tex]

Answer: The answers are

(1) 90 cm²   and (2) 321 m³.

Step-by-step explanation:  The calculations are as follows:

(1) The triangles ABC and PQR are similar. And the area of ΔABC is 40 cm².

Also, AB = 4 cm  and PQ = 6 cm.

We are to find the area of triangle PQR.

Similarity ratio of two similar triangles is equal to the ratio of any two corresponding sides of the triangles.

So, the similarity ratio of ΔABC and ΔPQR is given by

[tex]\dfrac{AB}{PQ}=\dfrac{4}{6}=\dfrac{2}{3} =2:3\\\\\\\Rightarrow AB:PQ=2:3.[/tex]

Now, let the area of ΔPQR be denoted by [tex]A_{PQR}.[/tex]

We know that the ratios of the area of two similar triangles is equal to the ratios of the squares of any two corresponding sides of the triangles.

Therefore, we must have

[tex]\dfrac{\textup{area of triangle ABC}}{\textup{area of triangle PQR}}=\dfrac{AB^2}{PQ^2}\\\\\\\Rightarrow \dfrac{40}{A_{PQR}}=\left(\dfrac{AB}{PQ}\right)^2\\\\\\\Rightarrow \dfrac{40}{A_{PQR}}=\left(\dfrac{2}{3}\right)^2\\\\\\\Rightarrow \dfrac{40}{A_{PQR}}=\dfrac{4}{9}\\\\\\\Rightarrow 4\times A_{PQR}=40\times 9\\\\\\\Rightarrow A_{PQR}=90~\textup{cm}^2.[/tex]

Thus, the area of triangle PQR is 90 cm².

(2) Given that a science museum has a spherical model of the earth with a diameter of 8.5 m.

We are to find the volume of the model.

Since the model is spherical in shape, so will be using the following formula:

the volume of a sphere with radius 'r' units is given by

[tex]V=\dfrac{4}{3}\pi r^3.[/tex]

The diameter of the model is 8.5 cm, so the radius of the model will be

[tex]r=\dfrac{8.5}{2}=4.25~\textup{m}.[/tex]

Therefore, the volume of the model is given by

[tex]V\\\\\\=\dfrac{4}{3}\pi r^3\\\\\\=\dfrac{4}{3}\times3.14\times(4.25)^3\\\\\\=\dfrac{964.17625}{3}\\\\\\=321.39\sim 321~\textup{m}^3.[/tex]

Thus, the volume of the model is 321 m³.

Hence, the answers are

(1) 90 cm²   and (2) 321 m³.