How to solve the proportion

Find the approximate value of the circumference of a circle with the given radius. Use pi = 3.14. Round your results to one more

svetlana [45]

C = 2πr
C = 2 * 3.14 * 5.1
C = 32.028

You can round that to A. 32.03, because if the decimal after 2 is greater than it, then you round it to the number which is higher than it, which is 3.

4 0

3 years ago

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COMPLETE THE SQUARE TO REWRITE Y=X>2+8X+3 IN VERTEX FORM , AND THEN IDENTIFY THE MINIMUN Y-VALUE OF THE FUNCTION

kicyunya [14]

Answer:

The vertex form is y = (x + 4)² - 13

The minimum value of the function is -13

Step-by-step explanation:

∵ y = x² + 8x + 3

∵ 8x ÷ 2 = 4x ⇒ (x) × (4)

∴ We need ⇒ x² + 8x + 16 to be completed square

∴ y = (x² + 8x + 16) - 16 + 3 ⇒ we add 16 and subtract 16

∴ y = (x + 4)² - 13 ⇒ vertex form

∵ The vertex form is (x - a)² + b

Where a is the x-coordinate of the minimum point and b is y-coordinate of the minimum point (b is the minimum value of the function)

∴ The minimum value is -13

6 0

3 years ago

Solve using long division Please

madreJ [45]

1. $Solution,\frac{2x^3+4x^2-5}{x+3}:\quad 2x^2-2x+6-\frac{23}{x+3}$

$Steps:$

$\mathrm{Divide}\:\frac{2x^3+4x^2-5}{x+3}:\quad \frac{2x^3+4x^2-5}{x+3}=2x^2+\frac{-2x^2-5}{x+3}$

$\mathrm{Divide}\:\frac{-2x^2-5}{x+3}:\quad \frac{-2x^2-5}{x+3}=-2x+\frac{6x-5}{x+3}$

$\mathrm{Divide}\:\frac{6x-5}{x+3}:\quad \frac{6x-5}{x+3}=6+\frac{-23}{x+3}$

$\mathrm{Simplify}, =2x^2-2x+6-\frac{23}{x+3}$

$\mathrm{The\:Correct\:Answer\:is\:2x^2-2x+6-\frac{23}{x+3}}$

2. $Solution, \frac{4x^3-2x^2-3}{2x^2-1}:\quad 2x-1+\frac{2x-4}{2x^2-1}$

$Steps:$

$\mathrm{Divide}\:\frac{4x^3-2x^2-3}{2x^2-1}:\quad \frac{4x^3-2x^2-3}{2x^2-1}=2x+\frac{-2x^2+2x-3}{2x^2-1}$

$\mathrm{Divide}\:\frac{-2x^2+2x-3}{2x^2-1}:\quad \frac{-2x^2+2x-3}{2x^2-1}=-1+\frac{2x-4}{2x^2-1}$

$\mathrm{The\:Correct\:Answer\:is\:2x-1+\frac{2x-4}{2x^2-1}}$

$\mathrm{Hope\:This\:Helps!!!}$

$\mathrm{-Austint1414}$

4 0

3 years ago

The sum of three consecutive integers is 114. what are the three integers?

RSB [31]

Answer: 37, 38, and 39

Step-by-step explanation: This problem states that the sum of 3 consecutive integers is 114 and it asks us to find the integers.

3 consecutive integers can be represented as followed.

X ⇒ first integer

X + 1 ⇒ second integer

X + 2 ⇒ third integer

Since the sum of our 3 consecutive integers is 114, we can set up an equation to represent this.

X + X + 1 + X + 2 = 114

We can simplify on the left side by combining the X's and the numbers.

3x + 3 = 114

-3 -3 ← subtract 3 from both sides of the equation

3x = 111

÷3 ÷3 ← divide both sides of the equation by 3

X = 37

X ⇒ first integer = 37

X + 1 ⇒ second integer = 38

X + 2 ⇒ third integer = 39

Therefore, our 3 consecutive integers are 37, 38, and 39.

5 0

3 years ago

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The Damon family owns a large grape vineyard in western New York along Lake Erie. The grapevines must be sprayed at the beginnin

vazorg [7]

Answer:

$z=\frac{0.0955-0.0611}{\sqrt{0.08(1-0.08)(\frac{1}{440}+\frac{1}{360})}}=1.784$

$p_v =2*P(Z>1.784) =0.074$

Comparing the p value with the significance level given $\alpha=0.1$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that the two proportions differes at 10% of significance.

Step-by-step explanation:

Data given and notation

$X_{1}=42$ represent the number of infested vines for Pernod5

$X_{2}=22$ represent the number of infested vines for Action

$n_{1}=440$ sample of Pernod5

$n_{2}=360$ sample of Action

$\hat p_{1}=\frac{42}{440}=0.0955$ represent the proportion of residents of infested vines for Pernod5

$\hat p_{2}=\frac{22}{360}=0.0611$ represent the proportion of infested vines for Action

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha=0.1$ significance level given

Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference between thw two population proportions, the system of hypothesis would be:

Null hypothesis: $p_{1} - p_{2}=0$

Alternative hypothesis: $p_{1} - p_{2} \neq 0$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{1}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{42+22}{440+360}=0.08$

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.0955-0.0611}{\sqrt{0.08(1-0.08)(\frac{1}{440}+\frac{1}{360})}}=1.784$

Statistical decision

Since is a two sided test the p value would be:

$p_v =2*P(Z>1.784) =0.074$

Comparing the p value with the significance level given $\alpha=0.1$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that the two proportions differes at 10% of significance.

4 0

3 years ago