What is the exact area of a circle with a diameter of 20 cm?

400πcm^2

10πcm^2

100πcm^2

20πcm^2

Answer:

Step-by-step explanation:

How do do a 3/4 as a fraction, decimal, and percent?

1) 3/4 is just a fraction

2) 3:4 = 0.75 (0.75 = 75%)

3) 75%

We have been given a system of nonlinear equations.

[tex]\\y=40x^{2},y=19x+3[/tex]

In order to solve this system we can first equate the two equations in order to get a quadratic in x.

[tex]\\40x^{2}=19x+3[/tex]

Our next step is to bring all the terms on one side.

[tex]\\40x^{2}-19x-3=0[/tex]

Now we have to solve this equation. We can solve it by factoring using the splitting middle term method.

[tex]\\40x^{2}-24x+5x-3=0[/tex]

[tex]\\8x(5x-3)+(5x-3)=0[/tex]

[tex]\\(8x+1)(5x-3)=0[/tex]

Upon setting each of these factors equal to zero using zero product property we get

[tex]\\8x+1=0 \text{ or } 5x-3 = 0[/tex]

Upon solving both these equations we get

[tex]\\x=-\frac{1}{8} \text{ or } x=\frac{3}{5}[/tex]

Now we can substitute these values of x in the equation

[tex]y=19x+3[/tex]

We get

[tex]\text{For }x=- \frac{1}{8} \Rightarrow y=19(- \frac{1}{8})+3= \frac{5}{8}\\[/tex]

[tex]\text{For }x= \frac{3}{5}\Rightarrow y=19( \frac{3}{5})+3= \frac{72}{5}\\[/tex]

Therefore, our final set of solutions are

[tex](x,y)=(- \frac{1}{8},\frac{5}{8}) \text{ and } ( \frac{3}{5}, \frac{72}{5})[/tex]

Answer with explanation:

We know that a polynomial is classified based on the degree as follows:

Constant-

If it has a degree zero.

and the equation of such a polynomial is:

   p(x)=a

Linear--

It has degree 1.

and the equation of such a polynomial is:   p(x)=ax+b

Quadratic--

If it has degree two and the equation of the polynomial is given by:

     [tex]p(x)=ax^2+bx+c[/tex]

Based on number of Terms--

Monomial--

If it has just one term.

Binomial--

If it has two terms.

Trinomial--

If it has three terms.

Answer:

Step-by-step explanation:

Given is a rational algebraic expression in x as

[tex]\frac{5x+2}{x^4-4x^2}[/tex]

First let us factorize the denominator.

[tex]x^2(x^2-4)\\=x^2(x+2)(x-2)[/tex]

Let the given term be

[tex]\frac{A}{x} +\frac{B}{x^2} +\frac{C}{x-2} +\frac{c}{x+2} \\\\=\frac{Ax(x^2-4)+B(x^2-4)+cx^2(x+2)+Dx^2(x-2)}{x^4-4x^2}[/tex]

Equate the numerator to get

[tex]Ax(x^2-4)+B(x^2-4)+cx^2(x+2)+Dx^2(x-2)[/tex]=[tex]5x+2[/tex]

Substitute x =-2

[tex]4D (-4) = -8\\D=\frac{1}{2}[/tex]

Now substitute x =2

We get

[tex]16C=12\\C=\frac{3}{4}[/tex]

Put x=0

[tex]-4B=2\\B=\frac{-1}{2}[/tex]

Next equate X cube terms to 0 on right side

[tex]A+C+D=0\\A=\frac{-5}{4}[/tex]

Hence partial fraction is

[tex]\frac{-1}{2x^2} -\frac{5}{4x} +\frac{1}{2(x+2)} +\frac{3}{4(x-2)}[/tex]

To decompose the rational expression startfraction 5x + 2 over x4 - 4x2 endfraction into partial fractions, we need to factor the denominator. The partial fraction decomposition of the given rational expression is startfraction A over x + B over x2 + C over (x - 2)2, where A, B, and C are the determined coefficients.

To decompose the rational expression startfraction 5x + 2 over x4 - 4x2 endfraction into partial fractions, we need to factor the denominator. The denominator can be factored as x2(x2 - 4) which gives us two distinct linear factors x and x + 2, and a repeated linear factor x - 2. Therefore, we can express the rational expression as follows: startfraction A over x + B over x2 + C over (x - 2)2.

To find the values of A, B, and C, we can use the method of equating coefficients. By multiplying both sides of the equation by the common denominator, we can eliminate the fractions and solve for the unknowns. Finally, we substitute the values of A, B, and C back into the partial fraction decomposition expression.

Therefore, the partial fraction decomposition of the given rational expression is startfraction A over x + B over x2 + C over (x - 2)2, where A, B, and C are the determined coefficients.

Answer:

The answer is A. The events are independent because P(red) • P(green) = P(red and green).

Answer:

A. The events are independent because P(red) • P(green) = P(red and green).

Step-by-step explanation:

EDGE 2021 AQR

The volume of the coffee in the can if the can has a radius of 4 inches and height of 9 inches is 452.16 inches³.

The can must be in the shape of a cylinder.

The formula to find the volume of the cylinder is,

Volume of cylinder = π r² h

Here r is the radius of the base of the cylinder and h is the height of the cylinder.

Given, Radius, r = 4 inches and Height, h = 9 inches

Volume of the coffee = π (4)² (9)

                                    = 144 π

                                    = 144 × 3.14

                                    = 452.16 inches³

Thus, the volume of the coffee in the can is 452.16 inches³.

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Answer:

8 times

Step-by-step explanation:

I found the volume of the sphere. Then increased it how many times he blew. That was the ratio.

Also, Khan :)

The ratio of the current volume of the balloon to the original volume of the balloon is 8.

The volume of a sphere is given by (4\3)πr³ where r is the radius of the sphere.

The initial volume of the balloon = [tex]\frac{4}{3} \pi 2^{3}[/tex]

The initial volume of the balloon =[tex]\frac{32}{3} \pi[/tex]

Radius of the balloon after first breath = 2+1 =3cm

The Radius of the balloon after the second breath = 2+2=4cm

So, the new volume of the balloon = [tex]\frac{4}{3} \pi 4^{3}[/tex]

The new volume of the balloon = [tex]\frac{256}{3} \pi[/tex]

The ratio of new volume to the initial volume = [tex]\frac{\frac{256}{3 } \pi }{\frac{32}{3}\pi }[/tex]

The ratio of new volume to the initial volume =8

Hence, the ratio of the current volume of the balloon to the original volume of the balloon is 8.

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By calculating the probability of choosing a counter at random, we find that we are least likely to choose a white counter as it has the least probability.

Probability is simply how likely something is to happen.

Probability of choosing a red counter  = 6/25 = 0.24

Probability of choosing a white counter  = 4/25 = 0.16

Probability of choosing a blue counter  = 7/25 = 0.28

Probability of choosing a yellow counter  = 8/25 = 0.32

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Answer:

Option C. 140

Step-by-step explanation:

Base of a pyramid which has four triangular sides is four sided.

If pyramid contains seven layers of oranges then the layer at the bottom will have 7 oranges.

Since base is a square then other side of the square base will have the same number of oranges = 7.

Therefore number of oranges at the first layer will be = 7×7

Similarly other layers above this layer will have the same sequence

6×6, 5×5, 4×4, 3×3, 2×2, 1×1

Therefore total number of oranges = 7×7 + 6×6 + 5×5 + 4×4 + 3×3 + 2×2 + 1×1 = 49 + 36 + 25 + 16 + 9 + 4 + 1 = 140

Option C. 140 is the answer.

A grocer stacks oranges in a four-sided pyramid that is 7 layers high. Many oranges are in the pile are C.140

The orange is the fruit of the citrus species Citrus and sinensis in the family Rutaceae, native to China. Orange is also called sweet orange, to distinguish it from the related Citrus and aurantium, referred to as bitter orange.

The proper name of four-sided pyramid is a "tetrahedron". The tetrahedron has the extra interesting property of having all four triangular sides congruent

1st Layer: The 1st layer contains only 1 orange so it has only 1 orange

2nd layer: The 2nd layer has total 4 oranges. Calculation:   [tex]2*2=4[/tex]

3rd layer: The 3rd layer has total 9 oranges. Calculation: [tex]3 * 3 = 9[/tex]

4th Layer: The 4th layer has total 16 oranges. Calculation: [tex]4 * 4 = 16[/tex].

5th layer: The 5th layer has total 25 oranges. Calculation:  [tex]5 * 5 = 25[/tex]

6th layer: The 6th layer has total 36 oranges. Calculation: [tex]6 * 6 = 36[/tex]

7th layer: The 7th layer has total 49 oranges. Calculation: [tex]7 * 7 = 49[/tex].

Sum of all layers:

[tex]1+4+9+16+25+36+49 = 140[/tex]

Grade:  9

Subject:  mathematics

Chapter:  pyramid

Keywords:  oranges, pyramid, four-sided, layers, pile

Answer:

y-axis... just look at the graph on desmos.com

Answer:

c 42 degrees

Step-by-step explanation:

Answer:

the answer is 675

Step-by-step explanation:

1. there is a tank with 1000 gallons, and we have 65 cans with a capacity of 5 gallons, so if we multiply the 65 cans with the capacity we would have as result

  65 x 5 = 325

2-  already having the value of gallons used (325) we can subtract this difference to the 1000 gallons that were in the tank at first.

 1000 - 325 = 675

Firstly, simplife the function [tex] -x^3-x^2+4x+4 [/tex] in the following way:

[tex] -x^3-x^2+4x+4=-(x^3+x^2)+4(x+1)=-x^2(x+1)+4(x+1)=(x+1)(4-x^2)=(x+1)(2-x)(2+x)=-(x+2)(x+1)(x-2) [/tex].

There are three x-intercepts: x=-1; x=2 and x=-2 (therefore, options A and D are incorrect).

Since before brackets is sign "-", you should state that graph starts down on the left (you can check this substituting smaller negative number than -2 into function expression. For example, if x=-10, then f(-10)=-(-10+2)(-10+1)(-10-2)=-(-8)(-9)(-12)>0) and goes up on the right (you can check this substituting greater positive number than 2 into function expression. For example, if x=10, then f(-10)=-(10+2)(10+1)(10-2)=-(12)(11)(8)<0).

Answer: correct choice is B.

Solution: The test statistic under the null hypothesis is:

[tex]t=\frac{\bar{x_{1}}-\bar{x_{2}}}{s_{p}\sqrt{(\frac{1}{n_{1}})+(\frac{1}{n_{2}})}}[/tex]

Where:

[tex]s_{p} = \sqrt{\frac{(n_{1}-1)s^{2}_{1}+(n_{2}-1)s^{2}_{2}}{n_{1}+n_{2}-2} }[/tex]

[tex]s_{p} = \sqrt{\frac{(16-1)14.8^{2}+(18-1)16^{2}}{16+18-2} }[/tex]

               [tex]=15.45[/tex]

[tex]\therefore t=\frac{85.4-74.9}{15.45\sqrt{(\frac{1}{16})+(\frac{1}{18})}}[/tex]

                   [tex]=\frac{10.5}{5.31}[/tex]

                   [tex]=1.98[/tex]

Now, to find the critical values, we need to use the t distribution table at 0.01 significance level for [tex]df=n_{1} + n_{2} -2 = 16+18-2=32[/tex] and is given below:

[tex]t_{critical}=-2.738,2.738[/tex]

Since the t statistic is less than the  t critical value, we therefore fail to reject the null hypothesis and conclude that the two population means are equal.