select an expression that is equivalent to 4√x2/3
A x14x14
B x94x94
C x16x16
D x83x83

Answer:

Step-by-step explanation:

343: = 7 * 7 * 7

x^9: = x^3 * x^3 * x * x * x = x^3 * x * √x

y^12: = y^6 * y^6

z^6: = z^3 * z^3

So the square root  is

√343 = 7 √7

√x^9 = x^4√x

√y^12 = y^6

√z^6 = x^3

The rule is for every pair of equal factors, you take one outside the root sign and throw the other one away.

So z^6 for example is z^3 * z^3 Take one of the pair outside the root sign and throw the other one away.

x^9 is rather tricky. You take x^4 out and there is still one x left over. You leave it under the root sign.

So the answer is

7  * x^4 * y^6 * z^3 * √7x

Given:

x-intercepts of the hyperbola are ±4.

The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].

Center of the hyperbola is at origin.

To find:

The equation of the hyperbola.

Solution:

The general equation of a hyperbola:

[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex]            ...(i)

Where, (h,k) is the center of the hyperbola, ±a are x-intercepts, [tex](\pm c,0)[/tex] are foci.

Center of the hyperbola is at origin. So, h=0 and k=0.

x-intercepts of the hyperbola are ±4. So,

[tex]\pm a=\pm 4[/tex]

[tex]a=4[/tex]

The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].

[tex]\pm c=\pm 2\sqrt{5}[/tex]

[tex]c=2\sqrt{5}[/tex]

We know that,

[tex]a^2+b^2=c^2[/tex]

[tex](4)^2+b^2=(2\sqrt{5})^2[/tex]

[tex]16+b^2=20[/tex]

[tex]b^2=20-16[/tex]

[tex]b^2=4[/tex]

Taking square root on both sides, we get

[tex]b=\sqrt{4}[/tex]                    [b>0]

[tex]b=2[/tex]

Substituting [tex]h=0,k=0,a=4,b=2[/tex] in (i), we get

[tex]\dfrac{(x-0)^2}{4^2}-\dfrac{(y-0)^2}{2^2}=1[/tex]

[tex]\dfrac{x^2}{4^2}-\dfrac{y^2}{2^2}=1[/tex]

Therefore, the correct option is (d).

Answer:

The answer is "Option 5"

Step-by-step explanation:

Please find the complete question in the attached file.

Throughout the above output the regression equation is:

Delivery cost [tex]=0.469\times weight +9.617[/tex]

(i) 3 csc²(x) - 4 = 0

3 csc²(x) = 4

csc²(x) = 4/3

sin²(x) = 3/4

sin(x) = ± √3/2

x = arcsin(√3/2) + 2nπ  or   x = arcsin(-√3/2) + 2nπ

x = π/3 + 2nπ   or   x = -π/3 + 2nπ

where n is any integer. The general result follows from the fact that sin(x) is 2π-periodic.

In the interval 0 ≤ x ≤ 2π, the first family of solutions gives x = π/3 and x = 4π/3 for n = 0 and n = 1, respectively; the second family gives x = 2π/3 and x = 5π/3 for n = 1 and n = 2.

(ii) 4 cos²(x) + 2 cos(x) - 2 = 0

2 cos²(x) + cos(x) - 1 = 0

(2 cos(x) - 1) (cos(x) + 1) = 0

2 cos(x) - 1 = 0   or   cos(x) + 1 = 0

2 cos(x) = 1   or   cos(x) = -1

cos(x) = 1/2   or   cos(x) = -1

[x = arccos(1/2) + 2nπ   or   x = 2π - arccos(1/2) + 2nπ]   or   x = arccos(-1) + 2nπ

[x = π/3 + 2nπ   or   x = 5π/3 + 2nπ]   or   x = π + 2nπ

For 0 ≤ x ≤ 2π, the solutions are x = π/3, x = 5π/3, and x = π.

Answer:

f(x) = x^2 ( x -4i) (x+4i)

Step-by-step explanation:

f(x) = x^4 + 16x^2

Factor out x^2

f(x) = x^2 ( x^2 +16)

f(x) = x^2 ( x^2 - -16)

The square root of -16 is 4i and -4i

Using the difference of square (a^2 - b^2) = (a-b)(a+b)

f(x) = x^2 ( x -4i) (x+4i)

===============================================

Explanation:

Let x be the net winnings the customer gets

Saying something like x = 24 means you've walked away with $24. This occurs when you pay $1, and get $25 back in prizes, so 25-1 = 24 dollars overall.

The probability of this event occurring is 1/100 since there's only one ticket with the $25 prize

Make a table as shown below. It represents all the possible x values which are all the possible net winnings. Note how 1/100 = 0.01, 3/100 = 0.03 and 95/100 = 0.95

The third column is x*p(x) which is the product of the first two columns. Adding everything in the third column (that isn't highlighted in yellow) gets us the value -0.45 which is the expected value for the customer.

This represents a loss of $0.45, aka a loss of 45 cents. This is from the perspective of the customer.

Flipping things around, the pizza company will see this is as a gain of $0.45 or a gain of 45 cents.

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

Here's another way to see why this works:

The pizza company earns $100 in revenue since 100 tickets are sold for a dollar each. The company pays out 25+15+3*5 = 55 dollars in prizes overall. That means the company will make a profit of 100-55 = 45 dollars. So the average profit per ticket is 45/100 = $0.45 aka 45 cents and this is from the viewpoint of the pizza company (not the customer). The positive average profit represents a gain.

Answer:

Step-by-step explanation:

The element decay percentage rate of change 2.22% per minute.

Radioisotope, radionuclide, or radioactive nuclide, any of several species of the same chemical element with different masses whose nuclei are unstable and dissipate excess energy by spontaneously emitting radiation in the form of alpha, beta, and gamma rays.

Here, mass decreases by 73% every hour.

Weight of element X is 680 grams.

According to question,

f(t) = 680 (1 - 73%)ⁿ

f(t) = 680 (1 - 0.73)ⁿ

f(t) = 680 X 0.27ⁿ

f(t) = 680 X 0.9778ⁿ

f(t) = 680 X (1 - 0.02322)ⁿ

Thus, the element decay percentage rate of change 2.22% per minute.

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Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

120 free throws

Step-by-step explanation:

If she misses 15% of her free throws, that means she makes 85% of them.

Find how many she attempted by dividing 102 by 0.85:

102/0.85

= 120

So, she attempted 120 free throws

The number of free throws that were attempted is 120 free throws.

Since the basketball player missed 15% of her free throws, This means that the percentage scored will be:

= 100% - 15% = 85%

Therefore, 85% of x = 102

0.85x = 102

x = 102/0.85.

x = 120

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See the graph in the attached image.

Answer:

There are more females dropping than males each year and that there are more females than males

Answer:

14 (B)

Step-by-step explanation:

Area = L * h

L = 7 in^2

h = 2

Area = 7 * 2

Area = 14 in^2

Answer:

14

Step-by-step explanation:

Did lesson

Answer:

Maybe Plants products...

Answer:

60

[tex]2^{2} * 3 * 5[/tex]

Step-by-step explanation:

Answer:

4th option is correct

Step-by-step explanation:

[tex]8 x - 4 = 6 - 3 x[/tex]

[tex]8x−4+3x=6[/tex]

[tex]11x−4=6[/tex]

[tex]11x=6+4[/tex]

[tex]11x=10[/tex]

Answer:

option 4 ,

x=10/11

is the answer of your question

explanation is attached below .

hope it is helpful to you

Answer:

[tex]\% = 11.96\%[/tex]

Step-by-step explanation:

Given

See attachment for box plot

Required

Percentage greater than or equal to 233

From the box plot, the maximum is:

[tex]Max = 244[/tex]

The minimum is:

[tex]Min = 152[/tex]

Percentage greater than 233 is calculated as:

[tex]\% = \frac{Max - 233}{Max - Min}[/tex]

[tex]\% = \frac{244 - 233}{244-152}[/tex]

[tex]\% = \frac{11}{92}[/tex]

Express as percentage

[tex]\% = \frac{11}{92}*100\%[/tex]

[tex]\% = \frac{1100}{92}\%[/tex]

[tex]\% = 11.96\%[/tex]

Answer:

38

Step-by-step explanation:

Have a nice day :)

Answer:

28/16=14/8 true

3/5=9/15 true

4/32=10/78 false

3/4=12/16 true

Step-by-step explanation:

DID IT ON BRIDGE

Answer: You didnt mention how much Dan mows in 1 hour, but just do that divided by 60

Step-by-step explanation:

Answer:

592 Votes

Step-by-step explanation:

According to the Question,

                                 A        B       С

Candidates Votes     67      57     54

And, There are 1571 students in the school.

⇒(1571/178)×67

⇒591.33 ≈ 592 Votes(Approximately)

Answer:

She must buy more than 5 lbs

Step-by-step explanation:

First write the inequality

cost per pound * number of pounds >  total cost

8 * lbs > 40

Divide each side by 8

8 lbs /8 > 40/8

lbs > 5

She must buy more than 5 lbs

Answer:

good question

Step-by-step explanation:

Answer:

3.141

Step-by-step explanation:

3 decimals is .xxx, and you round the last digit up, so it becomes 3.141

Answer:

3.141

Step-by-step explanation:

since the forth number behind the decimal place is bigger than 5 we round up the third number.

I hope this helps in anyway.

Answer:

A

Step-by-step explanation:

The table represents a proportional function which has a rate of proportionality equal to 5

In fact

5:1 = 5

15 : 3 = 5

25 : 5 = 5

35 : 7 = 5

If we make 90 : 18, the result is 5, so this dates can be part of the table

Answer:

S>1

Step-by-step explanation:

5s + 2 > 7

Subtract 2 from both sides

5s>5

Divide 5 from both sides

S>1

Solution of the inequality is s>1.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to one another.

Adding the same amount to each side, taking the same amount away from each side, multiplying or dividing each side by the same positive integer, and other operations can be used to solve the inequality.

The inequality sign must be reversed if either side is multiplied or divided by a negative number.

5s+2 > 7

Subtracting 2 on both side,

5s > 5

s>1

Therefore, the solution set of inequality is s>1.

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Answer:

A) 3 ways

B) sorry don't know.

Step-by-step explanation:

2 P and 2 N

3P and 1 N

4P

So 3 ways.

Answer:

1/36

Step-by-step explanation:

P(2 then 1) = 1/6 x 1/6 = 1/36

Answer: Graph B

=====================================================

Explanation:

Point A appears to be at (2.5, -1)

If we shift 6 units to the left, then we subtract 6 from the x coordinate. So the new x coordinate is now 2.5-6 = -3.5

If we shift 4 units up, then we add 4 to the y coordinate to go from -1 to -1+4 = 3

Overall, the point A(2.5, -1) moves to A'(-3.5, 3)

Graph B is the answer because of this. The other points B and C will follow the same pattern as point A does.