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adell [148]
3 years ago
12

What is the area of a circle with a radius of 8 inches? Use 3.14 for .

Mathematics
1 answer:
OleMash [197]3 years ago
8 0
Use pi•r^2 for the formula of a circle. filling it in, you get 3.14•64 which is 200.96
You might be interested in
Explain how to use Pascal's Triangle to expand the binomial (3x-4y)^11
Mars2501 [29]

The solution to the binomial expression by using Pascal's triangle is:

\mathbf{=177147x^{11}-2598156x^{10}y +17321040x^9y^2-69284160x^8y^3+184757760x^7y^4}

\mathbf{-344881152x^6y^5+459841536x^5y^6-437944320x^4y^7+291962880x^3y^8}

\mathbf{-129761280x2y^9+34603008xy^{10}-4194304y^{11}}

<h3>How can we use Pascal's triangle to expand a binomial expression?</h3>

Pascal's triangle can be used to calculate the coefficients of the expansion of (a+b)ⁿ by taking the exponent (n) and adding the value of 1 to it. The coefficients will correspond with the line (n+1) of the triangle.

We can have the Pascal tree triangle expressed as follows:

                          1

               1                   1

        1                2                 1

    1          3              3               1

1      4            6                4            1

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

From the given information:

The expansion of (3x-4y)^11 will correspond to line 11.

Using the general formula for the Pascal triangle:

\mathbf{(a+b)^n = c_oa^nb^0 + c_1 a^{n-1}b^1+c_{n-1}a^1b^{n-1}+c_na^0b^n}

The solution to the expansion of the binomial (3x-4y)^11 can be computed as:

\mathbf{=177147x^{11}-2598156x^{10}y +17321040x^9y^2-69284160x^8y^3+184757760x^7y^4}

\mathbf{-344881152x^6y^5+459841536x^5y^6-437944320x^4y^7+291962880x^3y^8}

\mathbf{-129761280x2y^9+34603008xy^{10}-4194304y^{11}}

Learn more about Pascal's triangle here:

brainly.com/question/16978014

#SPJ1

5 0
2 years ago
A quarterback throws a football to a teammate. The football is 6.5ft above the ground when it leaves the quarterback's hand. His
sergejj [24]

Answer:

y = - 16t² + 55.6t + 6

Step-by-step explanation:

Using y - y₀ = vt - 1/2gt² where g = 32 ft/s², and v the velocity of the football

So y = y₀ + vt - 1/2 × (32 ft/s²)t²

y = y₀ + vt - 16t² where y₀ = 6.5 ft

y = 6 + vt - 16t²

Now, when t = 3.5 s, that is the time the teammate catches the ball after the quarterback throws it, y = 5 ft. Substituting these into the equation, we have

5 = 6.5 + v(3.5 s) - 16(3.5 s)²

5 = 6.5 + 3.5v - 196

collecting like terms, we have

5 - 6.5 + 196 = 3.5v

194.5 = 3.5v

v = 194.5/3.5 = 55.57 ft/s ≅ 55.6 ft/s

So, substituting v into y, our quadratic model is

y = 6 + 55.6t - 16t²

re-arranging, we have

y = - 16t² + 55.6t + 6

6 0
3 years ago
In a survey, the planning value for the population proportion is p* = 0.35. How large a sample should be taken to provide a 95%
lions [1.4K]

Answer:

n=\frac{0.35(1-0.35)}{(\frac{0.05}{1.96})^2}=349.59  

And rounded up we have that n=350  

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

p represent the real population proportion of interest

\aht p represent the estimated proportion for the sample

n is the sample size required (variable of interest)

z represent the critical value for the margin of error

Solution to the problem

The population proportion have the following distribution  

p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})  

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:  

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96  

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}} (a)  

And on this case we have that ME =\pm 0.05 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2} (b)

And replacing into equation (b) the values from part a we got:  

n=\frac{0.35(1-0.35)}{(\frac{0.05}{1.96})^2}=349.59  

And rounded up we have that n=350  

6 0
3 years ago
the height of a triangle is 4x inches and the base is (5x+1) inches. the area of a triangle is 500 square inches. what are the d
marin [14]
You mean what x is? Please add more detail.
8 0
3 years ago
Evan is going to the country fair this weekend. The admission to the fair is $10
ankoles [38]
I need more information.
6 0
3 years ago
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