simplify: (8 2/3^4)​

Explanation:

Rewrite the left side in terms of sine and cosine, then rearrange.

[tex](1+\tan^2{A})+(1+\dfrac{1}{\tan^2{A}})=\dfrac{1}{\sin^2{A}-\sin^4{A}}\\\\(1+\dfrac{\sin^2{A}}{\cos^2{A}})+(1+\dfrac{\cos^2{A}}{\sin^2{A}})=\\\\\dfrac{\sin^2{A}+\cos^2{A}}{\cos^2{A}}+\dfrac{\sin^2{A}+\cos^2{A}}{\sin^2{A}}=\\\\\dfrac{1}{\cos^2{A}}+\dfrac{1}{\sin^2{A}}=\\\\\dfrac{\sin^2{A}+\cos^2{A}}{(\sin^2{A})(\cos^2{A})}=\\\\\dfrac{1}{(\sin^2{A})(1-\sin^2{A})}=\dfrac{1}{\sin^2{A}-\sin^4{A}} \qquad\text{Q.E.D.}[/tex]

Answer:

[tex]P(A\cap B)=0.12[/tex]

Step-by-step explanation:

If two events, A and B are independent, then [tex]P(A\cap B)=P(A)\times P(B)[/tex], otherwise the two events are dependent.

If P(A)=0.60 and P(B) =0.20, then A and B are independent events, if

[tex]P(A\cap B)=0.60\times 0.20[/tex]

[tex]\implies P(A\cap B)=0.12[/tex]

Therefore the best complete is:

If P(A) = 0.60 and P(B) = 0.20, then A and B are independent events if [tex]P(A\cap B)=0.12[/tex]

Answer:

Step-by-step explanation:

p(a and b) = 0.12

Answer:

A.   y = 9(x +1/2)^2 - 13/4.

Step-by-step explanation:

y = 9x^2 + 9x - 1

y = 9(x^2 + x) - 1

y = 9 [ (x + 1/2)^2 - 1/4] - 1

y = 9 (x + 1/2)^2  - 9/4 - 1

y = 9(x +1/2)^2 - 13/4.

Answer: First Option

[tex]y = (x+\frac{1}{2}) ^ 2 -\frac{13}{4}[[/tex]

Step-by-step explanation:

For a quadratic function of the form:

[tex]y = ax ^ 2 + bx + c[/tex]

The vertex form of the equation is:

[tex]y = (x-h) ^ 2 + k[/tex]

Where the vertex is the point (h, k) and [tex]h =-\frac{b}{2a}[/tex]

In this case the equation is: [tex]y=9x^2+9x-1[/tex]

So:

[tex]a=9\\b=9\\c=-1[/tex]

Therefore:

[tex]h =-\frac{9}{2*(9)}[/tex]

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

[tex]k=9(-\frac{1}{2})^2+9(-\frac{1}{2})-1\\\\k=-\frac{13}{4}[/tex]

Finally the equation in vertex form is:

[tex]y = (x+\frac{1}{2}) ^ 2 -\frac{13}{4}[[/tex]

Answer:

640 miles per hour.

Step-by-step explanation:

I calculated this by 3200/5

Is this appropriate?

Answer: (AoPS)

125

Step-by-step explanation:

A distance of 1 meter is 50 times 2 cm, so the actual distance between the two cities is 50 times 2.5 km, which is 125 km.

To find the actual distance between two cities on a map given a scale, convert the map distance to real-world distance using the scale ratio.

The actual distance between two cities on the map can be calculated as follows:

So, the actual distance between the two cities is 1.25 kilometers.

Answer:

y = 1/3x -8

Step-by-step explanation:

3x+y=−5

First we need to get the equation in slope intercept form to find the slope

Subtract 3x from each side

3x-3x+y=-3x−5

y = -3x-5

The slope is -3

We want a line perpendicular.  Perpendicualr lines have slopes that are the negative reciprocal.  Take the negative reciprocal

m new = - (1/-3) = 1/3

The slope of the new line is 1/3

We have the slope (1/3) and a point (3,-7)

We can use the point slope form for the equation of a line

y-y1 = m(x-x1)

y--7 = 1/3 (x-3)

y+7 = 1/3 (x-3)

or if we want the slope intercept form

Distribute

y+7 = 1/3x -1

Subtract 7 from each side

y+7-7 = 1/3x -1-7

y = 1/3x -8

Answer:

27.5 m/s

275 m

Step-by-step explanation:

99 km/hr × (1000 m / km) × (1 hr / 3600 s) = 27.5 m/s

Distance = rate × time

d = 27.5 m/s × 10 s

d = 275 m

Answer:

He needs to get 1 right

Step-by-step explanation:

1/40 is equal to .025. This means the other 39/40 incorrect ones are worth .975(97.5%). If we multiply the .975 by the 15 percent of his overall grade, we get 14.625. When you subtract this from the overall grade, you get 70.075, which is just above a 70%.

For this case we have that the general qualification is 70, of it Evan has accumulated 84.7%. Making a rule of three:

70 ----------> 100%

x -------------> 84.7%

Where "x" represents the rating that Evan has accumulated:

[tex]x = \frac {84.7 * 70} {100}\\x = 59.29\\70-59.29 = 10.71[/tex]

Evan is missing 10.71 to get 70.

In percentage, we have to:

100% -84.7% = 15.3%

Now we have that the exam represents 15% of the grade, this is divided into 40 questions.

It is observed that Evan must correctly answer the 40 questions of the exam, so he would get 15%. Even so, it would lack a 0.3% note to reach 70.

Answer:

He must answer the 40 questions correctly.

[tex]\bf x^2-x-6\div x^2-4\implies \cfrac{x^2-x-6}{x^2-4}\implies \cfrac{(x-3)(x+2)}{\underset{\textit{difference of squares}}{x^2-2^2}} \\\\\\ \cfrac{(x-3)~~\begin{matrix} (x+2) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{(x-2)~~\begin{matrix} (x+2) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{x-3}{x-2}[/tex]

Answer:

The person on top is wrong the answer is 14,400 in.² or D

Step-by-step explanation:

The correct option is B. 720in squared. The area of the rectangle, when enlarged by a factor of 6, scales by the square of 6, resulting in an enlarged area of 720 square inches.

To determine the area of a rectangle after it has been enlarged by a factor, we need to understand how area scales with respect to the linear dimensions. When a shape is enlarged by a factor, the area scales by the square of that factor.

Given:

→ Original area = 20 square inches

→ Enlargement factor = 6

Steps to Find the Enlarged Area:

→ Calculate the scaling factor for the area:

= 6²

= 36.

→ Multiply the original area by this scaling factor:

= 20 in² * 36

= 720 in².

Therefore, the area of the enlarged rectangle is 720 square inches, which corresponds to answer choice B.

Answer:

$394.5

Step-by-step explanation:

40 x 6 = 240

6.5 x 9 = 58.5

(6 x 2) x 8 = 96

240 + 58.5 + 96

Answer: 13

Step-by-step explanation:

2x-27=-1

2x=26

X=13

The expression of the given mathematical phrase Twenty-seven less than twice a number is -1 is 2x - 27 = -1 and that number will be 13.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

As per the given,

Twenty-seven less than twice a number is -1

Let's say that number is x.

Twice of x = 2x

27 less will be 2x - 27

It is equal to -1.

2x - 27 = -1

2x = -1 + 27

2x = 26

x = 13

Hence "The expression of the given mathematical phrase Twenty-seven less than twice a number is -1 is 2x - 27 = -1 and that number will be 13".

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Answer:

9.13 cm^2.

Step-by-step explanation:

The diagonal of the square = the diameter of the circle.

The length of the diagonal = 4√2 cm (because we have a 45-45-90 triangle), so the radius of the circle is half of this = 2√2 cm.

The area of the shaded part = area of the circle - area of the square

= π (2√2)^2 - 4^2

=  25.13 - 16

= 9.13 cm^2.

Answer:

C(x) =24+6(z-1) where z is the total of units sold.

Therefore if z=10 units, the answer is: C(x)=24+6(10-1)

Or 24+6(9)

Or $78

Step-by-step explanation:

Answer:

10 Units would cost $78

Step-by-step explanation:

We will be using the following equation to solve this problem

[tex]C(x) = 24+6(x-1)[/tex]

Where x will be the amount of units of coverage that are sold. The equation subtracts 1 from the amount of units sold (since the first unit costs $24) and multiplies that by $6 which is the cost per unit. Then it adds $24 to that, which gives us the total cost.

Since we sold 10 units of coverage we plug that into the equation

[tex]C(10) = 24+6(10-1)[/tex]

[tex]C(10) = 24+6(9)[/tex]

[tex]C(10) = 24+54[/tex]

[tex]C(10) = 78[/tex]

So 10 units of coverage sold would cost $78

Answer:

-4 is the mimumum of y=-3+cos(x+4)

Step-by-step explanation:

The minimum value of y=cos(x) is -1.

The minimum value of y=cos(x+4) is still -1; the +4 inside the cosine function only affected the horizontal shift.

The minimum value of y=-3+cos(x+4) is -3-1 which is -4.  This brought the graph down 3 units so if the minimum was previously -1 and it got brought down 3 units then it's new minimum is -4.

The domain of the function can be written as [-1,2]-{2}, therefore the function is defined from -1 to 2 except 2.

• Domain is the set of values for which the given function is defined.

• Range is the set of all values which the given function can output.

Since the dark point of the function show that is the beginning of the function therefore the function will be defined from that point to all values of x but will not be defined at the point where there is a blank dot, also, the function is defined till the line is drawn.

Thus, the domain of the function will be,

Domain: [-1,2]-{2}

Hence, the domain of the function can be written as [-1,2]-{2}, therefore the function is defined from -1 to 2 except 2.

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Answer:

W'(-3,3) V'(-4,3) U'(-4,5)

Step-by-step explanation:

The mapping for 90 degrees counterclockwise rotation is;

[tex](x,y)\to (-y,x)[/tex]

The given points have coordinates: W(3,3) V(3,4) U(5,4)

[tex](x,y)\to (-y,x)[/tex]

This implies that:

[tex]W(3,3)\to W'(-3,3)[/tex]

[tex]V(3,4)\to V'(-4,3)[/tex]

[tex]U(5,4)\to U'(-4,5)[/tex]

The required points of the image are:

W'(-3,3) V'(-4,3) U'(-4,5)

Answer: 1 1/6 cups of sugar

Step-by-step explanation:

First let’s convert 3 1/2 into an improper fraction: 7/2

Then we multiply 7/2 by 1/3: 7/2*1/3=7/6

Then finally we convert 7/6 into a mixed number, so your answer will be 1 1/6

Answer:

8

Step-by-step explanation

First you have to plug in 3 for x:

5(3-1)-2

Then using PEMDAS you would simplify that:

5(2)-2

10-2

8

Answer:

C. x + 9 = 11

Step-by-step explanation:

We are trying to identify which of the equations does not match with the others. In this case, solve for x in each equation:

Option A):

6 + x = 9

Subtract 6 from both sides:

6 (-6) + x = 9 (-6)

x = 9 - 6

x = 3

Option B):

15 = x + 12

Subtract 12 from both sides:

15 (-12) = x + 12 (-12)

15 - 12 =  x

x = 3

Option C):

x + 9 = 11

Subtract 9 from both sides:

x + 9 (-9) = 11 (-9)

x = 11 - 9

x = 2

Option D):

7 + x = 10

Subtract 7 from both sides:

x + 7 (-7) = 10 (-7)

x = 10 - 7

x = 3

---------------------------------------------------------------------------------------------------------

As you can tell, all the equations end with x = 3 as there answers except C. x+9=11, making (C) your answer.

~

1 and 3 I believe are the correct answers

Answer:

Option 1 , Option 3 and Option 4 are correct.

Step-by-step explanation:

Number of customers using landlines decreases 10% per year.

Let x be the umber of customers using landlines in 2002.

⇒ Number of customer using landlines in 2003 = [tex]x-\frac{10}{100}\times x[/tex]

                                                                               = [tex]x-0.1x[/tex]

                                                                               = 0.9x

Number of customers using landlines in 2004 =  [tex]0.9x-\frac{10}{100}\times 0.9x[/tex]

                                                                              = [tex]0.9x-0.1\times0.9x[/tex]

                                                                              = [tex]0.9x-0.09x[/tex]

                                                                              = [tex]0.81x[/tex]

Therefore, from this Option 1 , Option 3 and Option 4 are correct.

Answer:

The answer is 12a^3+2a²+23a+18 ....

Step-by-step explanation:

The given terms are:

(3a + 2)(4a² - 2a + 9)

Now multiply each value of second bracket with the first bracket:

=4a²(3a+2) -2a(3a+2)+9(3a+2)

=12a^3+8a²-6a²-4a+27a+18

Solve the like terms:

=12a^3+2a²+23a+18

Therefore the answer is 12a^3+2a²+23a+18 ....

Answer:

We know that the formula to mix chemical solutions is: C1V1 = C2V2

where C represents the concentration of the solute, and V represents volume in milliliters or ml.

In this case, we have:

0.06V1 = 0.15×350

Solving for 'V1' we have:

V1 = (0.15×350)/0.06 = 52.5/0.06 = 875

Therefre I can make 875 mL of a 6% solution by diluting 350 mL of a 15% solution.

See the attached picture for the solution.

Answer:

Option: C is the correct answer.

                   C. 80

Step-by-step explanation:

PG=9 in. The radius of the circle is 41 inches.

We know that the side CT is given by:

CT=CS+ST

The side CS is calculated by using the Pythagorean Theorem in ΔCSP

i.e.

[tex]CP^2=CS^2+SP^2\\\\i.e.\\\\[/tex]

as CP is the radius of the circle

and SP=PG=9 in.

i.e.

[tex]41^2=9^2+CS^2\\\\i.e.\\\\1681=81+CS^2\\\\i.e.\\\\CS^2=1681-81\\\\i.e.\\\\CS^2=1600\\\\i.e.\\\\CS=40\ units[/tex]

and

similarly in right angled triangle ΔPST

we have:

[tex]TP^2=ST^2+PS^2\\\\i.e.\\\\41^2=9^2+ST^2\\\\i.e.\\\\ST=40\ units[/tex]

Hence,

[tex]CT=CS+ST\\\\i.e.\\\\CT=40+40\\\\i.e.\\\\CT=80\ in.[/tex]

Answer:

$895.09

Step-by-step explanation:

Applying the given formula:

A = $600e^(0.04*10), or

   = $895.09

We find that the answer is  $895.09.

Compound interest is interest calculated on the initial principal, which also includes all of the accumulated interest from the previous.

How to find how much would $600 be worth after 10 years, if it were invested at 4% interest compounded continuously?

Hint: Use the formula below and round your answer to the nearest cent.)

A(t)=P•e^rt.

Applying the given formula:

A = $600e^(0.04*10),

or

= $895.09.

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Answer:

Incorrectly distributing the 3 and (x-3).

Step-by-step explanation:

A common mistake when solving 3(x-3) <3 would be incorrectly distributing the 3 and (x-3).

Answer:

[tex]\large\boxed{(f+g)(x)=x^2+2x-6}[/tex]

Step-by-step explanation:

[tex](f+g)(x)+f(x)+g(x)\\\\f(x)=2x+1,\ g(x)=x^2-7\\\\(f+g)(x)=(2x+1)+(x^2-7)=2x+1+x^2-7=x^2+2x-6[/tex]

Answer:

2/9

Step-by-step explanation:

We have [tex]f(x)=2 \cdot 3^x[/tex] and are asked to find [tex]f(-2)[/tex].

[tex]f(-2)[/tex] means to replace x with -2 and evaluate the expression named f.

Let's do that:

[tex]f(x)=2 \cdot 3^x[/tex]

[tex]f(-2)=2 \cdot 3^{-2}[/tex]

[tex]f(-2)=2 \cdot \frac{1}{3^2}[/tex]

[tex]f(-2)=2 \cdot \frac{1}{9}[/tex]

[tex]f(-2)=\frac{2}{9}[/tex]

Answer:

2/9

Step-by-step explanation:

Given:

We'd substitute x with -2:

[tex]2 *3^{-2}[/tex]

Using order of operations, we'd solve the exponent first:

[tex]3^{-2}=.111[/tex](repeating)

Multiply by 2:

.111(repeating) * 2 = 2/9

Our answer is 2/9

On a plotted graph, 'm' commonly represents the slope indicating how much the line rises or falls for each step across. On the other hand, 'n' usually demonstrates the y-intercept - the point where the line crosses the y-axis.

The relationship between the values of m and n plotted on a number line depends on the mathematic law or concept being applied. But in many cases, such as on a graph, 'm' typically represents the slope while the 'n' value shows the y-intercept.

Slope (m) shows how much a line moves up or down along the y-axis for each step across the x-axis ('run'). The equation for this is ∆y/∆x meaning the change in y over the change in x. For example, if the slope (m) is three, each time the x value increases by one, the y value will rise by three.

The y-intercept (n) is the point where the line crosses the y-axis. This is the value of y when x = 0.

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Answer:

5.9

Step-by-step explanation:

The mean means arithmetic average (some people just say average here).

The average of 4 numbers is the sum of those 4 numbers divided by the number of numbers which is 4 in this case.

So we have this formula:

[tex]\frac{3.8+4.2+5.3+x}{4}=4.8[/tex]

Multiply both sides by 4:

[tex]3.8+4.2+5.3+x=4(4.8)[/tex]

Simplify:

[tex]13.3+x=19.2[/tex]

Subtract 13.3 on both sides:

[tex]x=19.2-13.3[/tex]

Simplify:

[tex]x=5.9[/tex]