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Pavlova-9 [17]
3 years ago
10

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Mathematics
1 answer:
goblinko [34]3 years ago
3 0

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Liam wants to estimate the percentage of people who lease a car. He surveys 240 individuals and finds that 54 lease a car. Find
scoundrel [369]

Answer:

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

The confidence interval is 95% and the significance level is \alpha=1-0.95=0.05 and \alpha/2 =0.025 and the critical value would be:

z_{\alpha/2}= 1.96

And the margin of error would be:

ME = 1.96 \sqrt{\frac{0.225 (1-0.225)}{240}}= 0.0528

Step-by-step explanation:

We have the following info given:

n =240 the sample size selected

X=54 the number of people who lease a car

\hat p =\frac{54}{240}= 0.225 the estimated proportion of people who lease a car

The margin of error is given by:

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

The confidence interval is 95% and the significance level is \alpha=1-0.95=0.05 and \alpha/2 =0.025 and the critical value would be:

z_{\alpha/2}= 1.96

And the margin of error would be:

ME = 1.96 \sqrt{\frac{0.225 (1-0.225)}{240}}= 0.0528

6 0
3 years ago
HELP!!!! I think its C but I'm not sure!
MA_775_DIABLO [31]

Answer:

The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are x=1\pm i\sqrt{7}.

Step-by-step explanation:

Consider the provided information.

Algebra's fundamental theorem states that: Every polynomial equation of degree n with complex coefficients has n roots in the complex numbers.

Now consider the provided equation.

2x^2-4x+16=0

The degree of the polynomial equation is 2, therefore according to Algebra's fundamental theorem the equation have two complex roots.

Now find the root of the equation.

For the quadratic equation of the form ax^2+bx+c=0 the solutions are: x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

Substitute a=2,\:b=-4,\:\ and \ c=16 in above formula.

x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:2\cdot \:16}}{2\cdot \:2}

x_{1,\:2}=\frac{4\pm \sqrt{16-128}}{4}

x_{1,\:2}=\frac{4\pm \sqrt{-112}}{4}

x_{1,\:2}=\frac{4\pm 4i\sqrt{7}}{4}

x_{1,\:2}=1\pm i\sqrt{7}

Hence, the fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are x=1\pm i\sqrt{7}.

4 0
3 years ago
The sum of three consecutive even numbers is-138. What is the smallest of the 3 numbers?
Vlada [557]

Answer:

the smallest of the three consecutive even numbers is 44

Step-by-step explanation:

44+46+48=138

5 0
3 years ago
The sum of two numbers is 36 . The larger number is 22 more than the smaller number. What are the numbers?
Setler [38]
X + y = 36
x = y + 22

y + 22 + y = 36
2y + 22 = 36
2y = 36 - 22
2y = 14
y = 14/2
y = 7

x + y = 36
x + 7 = 36
x = 36 - 7
x = 29

so ur 2 numbers are : 7 and 29
4 0
3 years ago
What is the answer to 2<0.75v<4.5
Vlad [161]
I hope this helps you

3 0
3 years ago
Read 2 more answers
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