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The required approximate value of the relative frequency of students with green eyes is 0.27. Option A is correct.

Statistics is the study of mathematics that deals with relations between comprehensive data.

Here,
The population of the student having blond hair = 78
Total number of students with blond hair and green eyes = 21
Now,
Approximate value of the relative frequency of students with green eyes,
= 21 / 78
= 0.27

Thus, the required approximate value of the relative frequency of students with green eyes is 0.27. Option A is correct.

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Step-by-step explanation:

w = width

2w + 2 =  Length

Area = W x L  = 84 = w (2w+2)

                          84 = 2w^2 + 2w

                            0 = 2w^2 + 2w - 84        Use Quadratic Formula

                                                                 a = 2    b=2    c = -84

to find  

W = 6      then     L =  14 inches

The equation of a line parallel to the given line and passing through the point (0, 8) is 5y - 3x = 40

The equation of a line in point-slope form is expressed as;

y - y0 = m(x -x0)

where

m is the slope

(x0, y0) is the point on the line

Given the following parameters

Point (0,8)

Slope from the equation = 3/5

Substitute

y - 8 = 3/5(x - 0)
5(y -8) =3x

5y - 40 = 3x

5y - 3x = 40

Hence the equation of a line parallel to the given line and passing through the point (0, 8) is 5y - 3x = 40

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The sum of the decimal values given is 0.93

Simplifying the decimal values can be done thus :

Both values are in two decimal places, hence we can multiply by 100 to obtain a whole number .

0.36*100 = 36

0.57*100 = 57

Adding the whole numbers :

__36

+_57

_____

__93

Dividing the sum by 100 to convert to an equivalent decimal value,

Therefore, the required value is 0.93

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The value of x, considering the Pythagorean Theorem, is given as follows:

x = 9.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

The sides for the problem are given as follows:

15 and 8 (segment of 8 is the radius, which is the distance from the center to a point on the circumference of the circle).

Hence the hypotenuse is obtained as follows:

h² = 15² + 8²

h² = 289

h = 17.

Hence the value of x is obtained as follows:

x = 17 - 8

x = 9.

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Answer:

9(9 + x) = -25

x = 6.22222 repeating

Step-by-step explanation:

First, we have to distribute. 9 times 9 = 81 and 9 times x = 9x. The equation now becomes 81 + 9x = -25.

Second, we have to get the coefficient alone. Since the opposite of positive 81 is negative 81, we subtract it to get 0. Since we did that to one side we have to do it to the other. -25 - (-81) = 56. Now we have 9x = 56.

Third, we have to get the variable by itself. To do that we divide 9 by 9 to get 0 and that gets the variable alone. Since we did that to one side we have to do it to the other. 56 divided by 9 = 6.222 with the 2 repeating over 8 times.

       A) -  Event  "A  or  B"  Consists  of  the Outcomes:

               {2, 3, 4, 5, 6, 8}

      B) - Event  "A  or  "B"  Consists  of the Outcomes:

             {4,  6}

      C) -  The "COMPLEMENT  of EVENT  "A"  Consists of the Outcomes:

             {1, 3, 5, 7}

MAKE A PLAN:

List The OUTCOMES for EACH EVENT and their COMBINATIONS:

        a) -  EVENT  "A":  {2, 4, 6, 8}

               EVENT "B":   {3, 4, 5, 6}

               EVENT "A" or "B": {2, 3, 4, 5, 6, 8}

        b) - EVENT "A"  or "B":  {4, 6}

        c) -  The COMPLEMENT of the EVENT "A":  {1, 3, 5, 7}

       A) -  Event  "A  or  B"  Consists  of  the Outcomes:

               {2, 3, 4, 5, 6, 8}

      B) - Event  "A  or  "B"  Consists  of the Outcomes:

            {4,  6}

      C) - The "COMPLEMENT  of EVENT  "A"  Consists of the Outcomes:

             {1, 3, 5, 7}

I hope this helps!

The interest rate which will save the most money if the balance on a loan from one month to the next is carried is the compound interest rate.

What is compound interest?

Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.

The formula for the final amount with the compound interest formula can be given as,

A = P x (1+ \(\frac{r}{n . 100}\)\()^{nt}\)

Here, A is the final amount (principal plus interest amount) on the principal amount P of with the rate r of in the time period of t.

While carrying the balance on a loan from one month to the next month, the compound interest rate is better, as it allows the funds to grow faster than the other rate mentioned.

Thus, the interest rate which will save the most money if the balance on a loan from one month to the next is carried is the compound interest rate.

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Answer:

Step-by-step explanation:

It's not compound its simple

The value of m that satisfies the equation -3 + m = 9 is m = 12.

To solve the equation -3 + m = 9, we can isolate the variable m by moving the constant term -3 to the other side of the equation.

-3 + m = 9

To move -3 to the other side, we can add 3 to both sides of the equation:

-3 + 3 + m = 9 + 3

Simplifying, we have:

m = 12

Therefore, the value of m that satisfies the equation -3 + m = 9 is m = 12.

None of the provided answer options (A, B, C, D) match the correct solution.

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Answer:

B

3(x^2−3)(x^2+4)

Step-by-step explanation:

i pinky promise

Answer:

Step-by-step explanation:

208

Answer: 5/7 of the kids chose New York or L.A.

Step-by-step explanation:

All you need to do in this problem is add the fraction of people that chose New York and the fraction of people that chose L.A:

4/7 + 1/7 = 5/7

\(57=\cfrac{5}{8}z+7\implies 57=\cfrac{5z}{8}+7\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{8}}{8(57)=8\left( \cfrac{5z}{8}+7 \right)} \\\\\\ 456=5z+56\implies 400=5z\implies \cfrac{400}{5}=z\implies 80=z\)

Answer:

(10, 5π/3)

Step-by-step explanation:

To convert rectangular coordinates (5, -5√3) to polar form, we can use the following formulas:

r = √(x^2 + y^2)

θ = arctan(y/x)

Substituting the given values, we get:

r = √(5^2 + (-5√3)^2) = √(25 + 75) = √100 = 10

θ = arctan((-5√3)/5) = arctan(-√3) = -π/3

Note that the value of θ is in the fourth quadrant, which corresponds to a negative angle. However, we need to express the angle θ in the range 0 ≤ θ < 2π. To do this, we can add 2π to the angle if it is negative:

θ = -π/3 + 2π = (5π/3)

Therefore, the rectangular coordinates (5, -5√3) in polar form are (10, 5π/3).

Some of the 20th century's biggest market shifts were sparked by technological breakthroughs that impacted market supply curves.

The supply curve illustrates the relationship between the price of an item or service and the volume delivered over a specific time period.

In a typical scenario, the amount supplied will be shown on the horizontal axis and the price will be shown on the left vertical axis.

It should be noted that some of the 20th century's biggest market shifts were sparked by technological breakthroughs that impacted market supply curves.

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To convert  Celsius to Fahrenheit, Josh needs to use the formula; F = (9/5)C + 32

Let C represent the degrees Celsius and F represent the degrees Fahrenheit.

The relationship between C and F is given as:

C = (F-32) × 5/9

Hence to convert Celsius to Fahrenheit, we make F the subject of formula:

C = (F-32) × 5/9

9C/5 = (F-32)

F = (9/5)C + 32

To convert  Celsius to Fahrenheit, Josh needs to use the formula; F = (9/5)C + 32

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Answer:

Step-by-step explanation: This is one of the most common examples given in math textbooks, and it's useful to know if you ever travel outside the U.S., or if you are from outside the U.S. and travel here.

C = 5/9 (F - 32)

9C = 5(F - 32)

9/5 C = F - 32

9/5 C + 32 = F

F = 9/5 C + 32

Answer:

The area of a rectangle is a natural number, an integer and a rational number.

Step-by-step explanation:

The area of a rectangle is a member of the following three subsets of real numbers:

(i) Natural numbers (\(\mathbb{N}\)) - The area of the rectangle has no decimal parts and is positive.

(ii) Integer (\(\mathbb{Z}\)) - The area of the rectangle has no decimal parts.

(iii) Rational numbers (\(\mathbb{Q}\)) - The area of the rectangle can be obtained by dividing a natural number by other natural number. For instance:

\(\frac{36}{2} = 18\)

In a nutshell, the area of a rectangle is a natural number, an integer and a rational number.

Answer:

The right answer is letter D. (2,3,4)

The equation of the line in fully simplified slope-intercept form is y = x + 7.

We have,

From the graph,

The coordinates of the line are:

(0, 7), (-7, 0), and (-2, 5).

We can use any coordinates the line touches on the graph.

We will use,

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

The equation can be written in the form y = mx + c

m = (0 - 7) / (-7 - 0)

m = -7/-7

m = 1 ______(1)

And,

(0, 7) = (x, y)

So,

y = mx + c ______(2)

7 = 1 x 0 + c

7 = c

c = 7 ______(3)

Now,

From (1), (2), and (3).

y = x + 7

Thus,

The equation of the line in fully simplified slope-intercept form is y = x + 7.

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Answer:

\(\textsf{A.} \quad (2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)

Step-by-step explanation:

Replace f(x) with y in the given function:

\(y=(x+2)^x\)

Take natural logs of both sides of the equation:

\(\ln y=\ln (x+2)^x\)

\(\textsf{Apply the log power law to the right side of the equation:} \quad \ln a^n=n \ln a\)

\(\ln y=x\ln (x+2)\)

Differentiate using implicit differentiation.

Place d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}\ln y=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)

First, use the chain rule to differentiate terms in y only.

In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)

Now use the product rule to differentiate the terms in x (the right side of the equation).

\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let}\; u=x \implies \dfrac{\text{d}u}{\text{d}x}=1\)

\(\textsf{Let}\; v=\ln(x+2) \implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{1}{x+2}\)

Therefore:

\(\begin{aligned}\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&=x\cdot \dfrac{1}{x+2}+\ln(x+2) \cdot 1\\\\\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&= \dfrac{x}{x+2}+\ln(x+2)\end{aligned}\)

Multiply both sides of the equation by y:

\(\dfrac{\text{d}y}{\text{d}x}&=y\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)

Substitute back in the expression for y:

\(\dfrac{\text{d}y}{\text{d}x}&=(x+2)^x\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)

Therefore, the differentiated function is:

\(f'(x)=(x+2)^x\left[\dfrac{x}{x+2}+\ln(x+2)\right]\)

\(f'(x)=(2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)

Answer:

25

Step-by-step explanation:

Count all the squares on the edge.

Answer:

29cm

Step-by-step explanation:

Answer:

Yes, the triangles are congruent.

Step-by-step explanation:

The triangles are the same size and shape. Even though they are flipped they are a mirror image of eachother, meaning they are congruent.

By using trigonometric relations we will see that the area is:

\(A = h*tan(60\°)*/2 = tan(60\°)*h^2/2\)

Remember that the area of a right triangle is equal to the product between the cathetus divided by 2.

Sadly, here we don't have the measures of any sides of the triangle, so getting the actual area is impossible, but if we assume that some dimension is given (like the height, let's say that is h).

h is the cathetus adjacent to the 60° angle, then the other cathetus (the bottom one) is given by:

tan(60°) = x/h

x = tan(60°)*h

Then our two catheti are h and tan(60°)*h.

This means that the area will be:

\(A = h*tan(60\°)*/2 = tan(60\°)*h^2/2\)

Here we only used trigonometric properties, so this area will work for any height given (always that the value of h is the cathetus adjacent to the 60° angle).

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Answer:

the guy on top is correct

Step-by-step explanation:

The equation system is appropriately described by the formula 4x - y=6.A mathematical formula known as an equation combines two assertions .

A mathematical formula known as an equation combines two assertions using the equal sign (=) to denote equivalence. The terms 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14, for example. Mathematical equations are used to express the relationship between two phrases on either side of a letter. In most cases, the symbol serves as the sole variable. a good example is 2x - 4 = 2.

given

Graphing, substitution, and elimination are the three techniques used to solve systems of equations.

By graphing the given equations, you can easily solve a system by finding the point(s) where they all cross.

The values of the variables you are solving for will be provided by the coordinate of this point.

The equation system is appropriately described by the formula 4x - y=6.

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Answer:

0.090909

Step-by-step explanation:

I used a calculator

Answer: A.

Step-by-step explanation:

I just took the exam

can i get brainlyiest?

Divide the 8-digit student ID by the leftmost 3 digits to find q and r using the Quotient Remainder Theorem. If your 8-digit student ID is 12345678, then d = 123, n = 45,678, q = 371, and r = 45.

Suppose your 8-digit understudy ID is 12345678. Then, at that point, we can take the furthest left three digits to get d = 123. Also, we can take the excess 5 digits to get n = 45,678.

To find q and r, we can utilize the condition n = dq + r and address for q and r.

To begin with, we really want to see as the biggest various of d that is not exactly or equivalent to n. We can do this by separating n by d and taking the floor of the outcome:

q = ⌊n/d⌋ = ⌊45,678/123⌋ = 371

Then, we can track down the rest of taking away the result of d and q from n:

r = n - dq = 45,678 - 123 × 371 = 45,678 - 45,633 = 45

Along these lines, in the event that your 8-digit understudy ID is 12345678, d = 123, n = 45,678, q = 371, and r = 45.

The Remainder Leftover portion Hypothesis expresses that for any whole number n and positive whole number d, there exist whole numbers q and r with the end goal that n=dq+r, where q is the remainder and r is the rest of. We can track down q and r by separating n by d and taking the floor of the outcome for q, and deducting the result of d and q from n for r.

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Answer: Yes, they are mutually exclusive. You cannot have 2+ heads and 0 heads at the same time. They are not independent. The result of 2+ heads nullifies the chance that 0 heads are flipped!