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4 years ago

Solve each equation by completing the square 6) m² + 16m – 8 = 0

Mathematics

1 answer:

Natali5045456 [20]4 years ago

3 0

Answer:

m = - 8 ± 6 $\sqrt{2}$

Step-by-step explanation:

Given

m² + 16m - 8 = 0 ( add 8 to both sides )

m² + 16m = 8

To complete the square

add ( half the coefficient of the m- term )² to both sides

m² + 2(8)m + 64 = 8 + 64

(m + 8)² = 72 ( take the square root of both sides )

m + 8 = ± $\sqrt{72}$ = ± $\sqrt{36(2)}$ = ± 6 $\sqrt{2}$

Subtract 8 from both sides

m = - 8 ± 6 $\sqrt{2}$

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Anas wants to build a one-sample z interval with 85% confidence to estimate what proportion of users will click an advertisement

klasskru [66]

Answer:

See below

Step-by-step explanation:

Check One Sample Z-Interval Conditions

Simple Random Sample? √

np≥10? √

n(1-p)≥10? √

One-Sample Z-Interval Information

Formula --> $CI=\hat{p}\pm z^*\biggr(\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\biggr)$
Sample Proportion --> $\hat{p}=\frac{54}{250}=0.216$
Critical Value --> $z^*=1.4395$ (for a 85% confidence level)
Sample Size --> $n=250$
Margin of Error (MOE) --> $\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$

Problem 1

As stated previously, Anas should use the critical value $z^*=1.4395$ to construct the 85% confidence interval

Problem 2

Given our formula for the margin of error (MOE), the value is $MOE=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=\sqrt{\frac{0.216(1-0.216)}{250}}\approx0.026$

Problem 3

The 85% confidence interval would be $CI=\hat{p}\pm z^*\biggr(\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\biggr)=CI=0.216\pm 1.4395(0.026)\appro=\{0.1786,0.2534\}$ , which means that we are 85% confident that the true proportion of people that clicked on the advertisement is between 0.1786 (~45 people) and 0.2534 (~63 people)

Problem 4

Increasing the sample size to $n=500$ is going to decrease the margin of error because it is a closer representation of the population, but, alas, requires more time, energy, and resources to observe.

8 0

2 years ago

Is the equation linear or nonlinear? a+2/b=8

amid [387]

nonlinear
hope this helps.

5 0

3 years ago

Estimate 3 2/5 to the nearest integer

pickupchik [31]

4 is the nearest integer

as a decimal this number would be 3.5, which would round up to 4.

8 0

3 years ago

Which of the following graphs could be the graph of the function f(x)=-0.08x(x^2-11x+18)?

MariettaO [177]

Answer:

option C

Step-by-step explanation:

f(x)=-0.08x(x^2-11x+18)

Factor the parenthesis and find out the x intercepts

(x^2-11x+18)

We find out two factors whose product is 18 and sum is -11

-9 and -2 gives us product 18

-9 -2 gives us sum -11

(x^2-11x+18) =(x-9)(x-2)

f(x)=-0.08x(x^2-11x+18)

f(x)= -0.08x(x-9)(x-2)

set f(x) =0 and solve for x

-0.08x(x-9)(x-2) =0

-0.08x =0, so x=0

x-9 = 0 , so x=9

x-2 =0 , so x=2

x intercepts are (0,0) (2,0) and (9,0)

x intercepts are not repeating

so the graph crosses x -axis at x=0, 2,9

option C is correct

The graph is attached below4

5 0

3 years ago

Read 2 more answers

What is the solution to the system of equations

Gnesinka [82]

Answer: x=-4, y=-7

Problem:
4x-6y = 26
5x-4y=8

You can use substitution or elimination to solve the problem. I’m going to use elimination.

Multiply by -2 => -8x+12y = -52
Multiply by 3 => 15x- 12y = 24

Add those equations together:
7x=-28
x=-4
Plug that into one of the original equations to get y.

4(-4)-6y=26
-16 - 6y=26
-6y=42
y=-7

Check for the other equation to see if this is true. Which in this case it is. So that’s your answer. x=-4, y=-7

5 0

3 years ago

Read 2 more answers