I'd be happy if you could help!​

Answer:C

Step-by-step explanation:

Answer:

Its A

Step-by-step explanation:

The expression of ⁴√(81x³y⁴z⁸) with rational exponents is: 3x(¾)yz²

The 8 laws of exponents can be listed as follows:

Zero Exponent Law: a^(0) = 1.

Identity Exponent Law: a^(1) = a.

Product Law: a^m × a^n = a^(m+n)

Quotient Law: a^m/a^n = a^(m - n)

Negative Exponents Law: a^(-m) = 1/a^(m)

Power of a Power: (a^m)^n = a^(mn)

Power of a Product: (ab)^m = a^m*b^m

Power of a Quotient: (a/b)^m = a^m/b^m

We are given the algebra expression as:

⁴√81x³y⁴z⁸

This gives us:

81^(1/4) * x^(3/4) * y^(4/4) * z^(8/4)

= 3x^(3/4)yz²

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Answer:

substitution

Step-by-step explanation:

y = - 2x + 9 → (1)

- 8x + 7y = - 3 → (2)

substitute y = - 2x + 9 into (2)

- 8x + 7(- 2x + 9) = - 3

- 8x - 14x + 63 = - 3

- 22x + 63 = - 3 ( subtract 63 from both sides )

- 22x = - 66 ( divide both sides by - 22 )

x = 3

substitute x = 3 into (1)

y = - 2(3) + 9 = - 6 + 9 = 3

solution is (3, 3 )

Answer:

4

Step-by-step explanation:

78

Answer:

(a−5)(a−7)

Step-by-step explanation:

factor a2−12a+35

a2−12a+35

The middle number is -12 and the last number is 35.

Factoring means we want something like

(a+_)(a+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get -12

Multiply together to get 35

Can you think of the two numbers?

Try -5 and -7:

-5+-7 = -12

-5*-7 = 35

Fill in the blanks in

(a+_)(a+_)

with -5 and -7 to get...

(a-5)(a-7)

Answer:

Quadrant IV

Step-by-step explanation:

If x is greater than 0, then it will remain on the right side, on quadrants I and IV. If y is less than 0, then it will be on the bottom, so we are left with quadrant IV:

x is greater than 0, so all possible values are positive

y is less than 0, so all possible values are negative

(x,-y)

Following are the description of the wrong choice:

That's why the "Quadrant IV" is the correct answer.

Learn more:

Answer:

x = 6

Step-by-step explanation:

9+3 = (4x+2x)/3

12 = 6x/3

(12)(3) = 6x

36 = 6x

36/6 = x

6 = x

Answer:

thanks for the points

Step-by-step explanation:

thanks for the points

Answer: 821 yds^3

Step-by-step explanation:

Answer:

Step-by-step explanation:

(x-4) (x+10)  ⇒ (x+a)(x+b)=x²+(a+b)x+ab

a=-4 , b=10

x²+(-4+10)x+-4(10)

x²+6x-40

(3x+4) (3x +5)

3(x+4/3) *3(x+5/3)  ⇒ identity : (x+a)(x+b)=x²+(a+b)x+ab  

a=4/3    b=5/3

3*3=9

9[x²+(4/3 +5/3)x+4/3(5/3)]

9[x²+9/3 x+20/9]

9x²+27x+20

(-3a +5b +4c)^2  ⇒  

suitable identity is (a+b+c)²= a² + b² + c² + 2ab + 2bc + 2ca

a=-3a , b=5b , c=4c

9a²+25b²+16c²- 30ab +40bc - 24ca

Step-by-step explanation:

B=tan⁻¹(9÷22)

B=22.2

C=180-(97+22.2)

C= 180- 119.2

C= 60.8

Carl Friedrich Gauss, the "Prince of Mathematicians," made groundbreaking contributions to number theory, geometry, physics, and statistics, leaving a lasting impact on the field of mathematics.

We have,

Carl Friedrich Gauss, known as the "Prince of Mathematicians," made significant contributions to number theory, geometry, physics, and statistics.

He formulated the fundamental theorem of arithmetic, developed concepts in differential geometry such as intrinsic curvature and Gaussian curvature, and formulated Gauss's law for electric fields.

Gauss's work laid the foundation for modern mathematics and his emphasis on rigor and precision influenced subsequent generations of mathematicians.

His legacy as one of the greatest mathematicians of all time is based on his profound theorems, laws, and concepts that continue to shape the field.

Thus,

Carl Friedrich Gauss, the "Prince of Mathematicians," made groundbreaking contributions to number theory, geometry, physics, and statistics, leaving a lasting impact on the field of mathematics.

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A particular concentration of a chemical found in polluted water has been found to be lethal to 20% of the fish that are exposed to the concentration for 24 hours. Twenty fish are placed in a tank containing this concentration of chemical in water. Therefore

a) Probability that exactly 14 fish survive, Let x be the number of fish that survive. Using Binomial distribution, we have:\(P(X = x) = C(n,x) * p^x * (1-p)^{(n-x)}\) where n is the total number of fish, p is the probability of survival and C(n,x) is the binomial coefficient. We have n = 20, p = 0.8 (since 20% die) and x = 14. \(C(20,14) * (0.8)^14 * (0.2)^6 = 38760 * 0.000016777216 * 0.0264241152 = 0.263\) Therefore, the probability that exactly 14 fish survive is 0.263

b) Probability that at least 10 fish survive To find this probability, we can find the probability that 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 fish die, and subtract this probability from 1. Using the same formula as in (a), we have: \(P(X <= 9) = \sum  C(n,x) * p^x * (1-p)^{(n-x)}\) where n = 20, p = 0.8 and x varies from 0 to 9. Using a calculator or software, we find:P(X <= 9) = 0.0169Therefore,P(X >= 10) = 1 - P(X <= 9) = 1 - 0.0169 = 0.983 Therefore, the probability that at least 10 fish survive is 0.983.

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Answer:

D.

Step-by-step explanation:

x ={-1, 0, 2, 4, 7}

We see every x value only one time, so given pairs (x,y) is a function.

Answer is D.

The smallest possible volume of the cake, rounded to the nearest cubic centimeter, is approximately 408 cm³.

The smallest possible volume of the cake to the nearest cubic centimeter can be calculated by finding the lower bound of each dimension and multiplying them together.

For the given cake dimensions:

Length (L) = 10 cm

Width (W) = 10 cm

Height (H) = 5 cm

Since the measurements are accurate to the nearest 1 cm, we consider the lower bound for each dimension by subtracting 0.5 cm from each side.

Lower bound length = L - 0.5 cm = 10 cm - 0.5 cm = 9.5 cm

Lower bound width = W - 0.5 cm = 10 cm - 0.5 cm = 9.5 cm

Lower bound height = H - 0.5 cm = 5 cm - 0.5 cm = 4.5 cm

To find the smallest possible volume, we multiply these lower bounds together:

Smallest possible volume = Lower bound length * Lower bound width * Lower bound height

= 9.5 cm * 9.5 cm * 4.5 cm

= 407.625 cm³

Rounded to the nearest cubic centimeter, the smallest possible volume of the cake is approximately 408 cm³.

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Answer:

see explanation

Step-by-step explanation:

Using the rule of radicals

\(\sqrt{a}\) × \(\sqrt{b}\) ⇔ \(\sqrt{ab}\)

Given

(2 - 5\(\sqrt{8}\) )(4 - 6\(\sqrt{3}\) )

Each term in the second factor is multiplied by each term in the first factor, that is

2(4 - 6\(\sqrt{3}\) ) - 5\(\sqrt{8}\)(4 - 6\(\sqrt{3}\) ) ← distribute both parenthesis

= 8 - 12\(\sqrt{3}\) - 20\(\sqrt{8}\) + 30\(\sqrt{24}\) → *

Simplify \(\sqrt{8}\) and \(\sqrt{24}\)

\(\sqrt{8}\) = \(\sqrt{4(2)}\) = \(\sqrt{4}\) × \(\sqrt{2}\) = 2\(\sqrt{2}\)

\(\sqrt{24}\) = \(\sqrt{4(6)}\) = \(\sqrt{4}\) × \(\sqrt{6}\) = 2\(\sqrt{6}\)

Back to *

= 8 - 12\(\sqrt{3}\) - 20(2\(\sqrt{2}\) ) + 30(2\(\sqrt{6}\) )

= 8 - 12\(\sqrt{3}\) - 40\(\sqrt{2}\) + 60\(\sqrt{6}\)

Answer:

y+5

Step-by-step explanation:

Answer: y+5

Step-by-step explanation:hope this help

The area of the shaded part is 33.04 \(cm^2\)

In the given figure the radius of the circle is not given so seeing the figure we are assuming the radius of the circle to be 6 cm.

We need to find the area of the circle and then subtract the area of the non-shaded part to get the area of the shaded part.

To find the area of the circle we know the formula:

Area of the circle = \(\pi r^2\)

here we know that the radius is 6 cm and pi holds the value of 3.14.

Substituting the values in the formula we get

area = 3.14 * 6 * 6

area= 113.04 \(cm^2\).

Now we need to find the area covered by the non-shaded structure we can see the structure consists of a rectangle of length 4 cm and width 12cm and two squares with sides 4cm. We can add the area of all of them to get the area of the non-shaded part.

Area of the rectangle = 4*12= 48

Area of one the squares = 4*4 = 16

Area of both the squares = 2*16= 32

The total area covered by non-shaded part = 48+32=80 \(cm^2\)

Now the area of the shaded part = 113.04 - 80 = 33.04 \(cm^2\).

Therefore, the area of the shaded part is 33.04 \(cm^2\)

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Answer:

A

Step-by-step explanation:

To find the length of the curve r(t) = sqrt(2)ti, we need to use the arc length formula:L = ∫[a,b] ||r'(t)|| dt,where ||r'(t)|| is the magnitude of the derivative of the curve.

First, we need to find r'(t):

r'(t) = (d/dt) [sqrt(2)ti] = sqrt(2)i

The magnitude of r'(t) is ||r'(t)|| = sqrt(2).

So, the length of the curve is:

L = ∫[0,1] sqrt(2) dt = sqrt(2) * [t] [0,1] = sqrt(2)

Therefore, the length of the curve r(t) = sqrt(2)ti is sqrt(2).

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Answer:

101/8 or 12.625 or 12 5/8

Step-by-step explanation:

These are all the same you can just write it however you'd like.

Hope this helps.

Answer:

Trent drank more Water than Nicholas because 3/5 is bigger than 2/3

Answer:

x + 7

Step-by-step explanation:

Step 1: Translate

x = x

more than = addition (+)

7 = 7

Step 2: Combine

x + 7

Answer:

y = 7 + x

Step-by-step explanation:

If we have the number 7 and what x more we can represent that with 7 + x. The total can be repesented as y. So your answer is 7 + x or y = 7 + x.

Hope that helps!

The derivative of the function is

A) dw/dz=z^5 (7z-18)

B) dh/dx=192x^11+36x^5-6x^2+19

C) dy/dx=24x^2-38x-15

In mathematics, the derivative of a function measures the sensitivity to change of the function value with respect to a change in its argument. It is the rate of change of a function with respect to a variable.

A) w = z^7 – 3z^6 + 14

dw/dz=7z^6-18z^5

dw/dz=z^5 (7z-18)

B) h(x) = 16x^12 + 6x^6 – 2x^3 + 19x – 7

dh/dx=192x^11+36x^5-6x^2+19

C) y = (8x + 5)(x^2 – 3x)

dy/dx=  d/dx  [8x+5]*〖(x〗^2-3x)+(8x+5)*d/dx[x^2-3x]

dy/dx=(8*  d/dx  [x}+d/dx[5])*〖(x〗^2-3x)+(8x+5)*(d/dx[x^2]-3 d/dx[x])

dy/dx=(8*1+0)(x^2-3x)+(8x+5)(2x-3*1)

dy/dx=8(x^2-3x)+(2x-3)(8x+5)

dy/dx=24x^2-38x-15

Note: The question is incomplete. The complete question probably is: Find the derivative of the following function: A) w = z^7 – 3z^6 + 14 B) h(x) = 16x^12 + 6x^6 – 2x^3 + 19x – 7 C) y = (8x + 5)(x^2 – 3x).

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Answer:

24/64

Step-by-step explanation:

Answer:

A) -20

Step-by-step explanation:

AS it passes through the origin (0,0) and the point (3,5) we can find the slope
(y2-y1) / (x2-x1) =
(5 -0 ) / (3-0)   =

 5/3

Becasue is passes through the origin the equation is :
5/3x = y

For the other point (-12,b)  -12 is "x" and  "b" represent "y" in the equation

  -12 * 5/3 = -60/3 = -20

b = -20

The Answer A) -20 is the one

Answer:

1/6

Step-by-step explanation:

1/2 + 1/3 + x =1

5/6 + x = 1

x = 1 - 5/6

x = 1/6

Answer:

Step-by-step explanation:

We have been given that,

Level of significance,

α

=

0.05

Standard deviation,

σ

=

160

Margin of error, {eq}ME =...

See full answer below.

Answer: 17.9%

Step-by-step explanation:

Answer:

The answer is C

Explain:

Solve for x in the first equation.

Add 4y to both sides of the equation

3x=12+4y

12y-9x=36

Divide each term by 3 and simplify

X=4+4y/3

12y-9x=36

Replace all occurrences of x with 4+4y/3 in each equation.

-36=36

X=4+4y/3

Since -36=36 is not true, there is no solution