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2 years ago

An angle bisector always creates two acute angles. find a counterexample to show that the conjecture is false.

1 answer:

5 0

An acute angle is an angle that is less than 90°. An angle bisector is a ray drawn along an angle that bisects it into two equal and adjacent parts. Now, if the total angle is, say 270°, which is more than a half circle, it would result to two 135-degree angles. In this case, the angle is no longer acute, but obtuse.

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Kathy has $50,000 to invest today and would like to determine whether it is realistic for her to achieve her goal of buying a ho

olga_2 [115]

Answer:

a) About 12%

Step-by-step explanation:

We need to find the interest rate required to achieve her goal, so we will need to use the interest-compound formula:

$FV=PV(1+i)^{n}$

Where:

PV= Present Value

i= interest rate

FV= Future Value

n= number of periods

replacing the data provided:

$150.000=50.000(1+i)^{10}$

solving for i:

first, divide both sides by 50.000 to simplify the equation:

$3=(1+i)^{10}$

Take $10^{th}$ roots of both sides:

$1+i=$ ± $\sqrt[10]{3}$

solve for i:

$i=$ ± $\sqrt[10]{3} -1$

We get two answers, but we look for a coherent value. So we take the positive one:

$i=11.6123174$ ≈12

6 0

2 years ago

According to the Rational Root Theorem, the following are potential fox) 2x2 +2x 24.roots of -4, -3, 2, 3, 4Which are actual roo

aksik [14]

Correct Answer: First Option

Explanation:

There are two ways to find the actual roots:

a) Either solve the given quadratic equation to find the actual roots

b) Or substitute the value of Possible Rational Roots one by one to find out which satisfies the given equation.

Method a is more convenient and less time consuming, so I'll be solving the given equation by factorization to find its actual roots. To find the actual roots set the given equation equal to zero and solve for x as given below:

$2x^{2} +2x-24=0\\ \\ 2(x^{2} +x-12)=0\\ \\ x^{2} +x-12=0\\ \\ x^{2} +4x-3x-12=0\\ \\ x(x+4)-3(x+4)=0\\ \\ (x-3)(x+4)=0\\ \\ x-3=0, x=3\\ \\ or\\\\x+4=0, x=-4$

This means the actual roots of the given equation are 3 and -4. So first option gives the correct answer.

7 0

2 years ago

Read 2 more answers

Two processes are used to produce forgings used in an aircraft wing assembly. Of 200 forgings selected from process 1, 10 do not

tangare [24]

Answer:

$\bar p_1=0.05\\\bar p_2=0.067$

b-Check illustration below

c.(-0.0517,0.0177

Step-by-step explanation:

a.let $p_1 \& p_2$ denote processes 1 & 2.

For $p_1$ : T1=10,n1=200

For $p_2$ :T2=20,n2=300

Therefore

$\bar p_1=\frac{t_1}{N_1}=\frac{10}{200}=0.05\\\bar p_2=\frac{t_2}{N_2}=\frac{20}{300}=0.067$

b. To test for hypothesis:-

$H_0:p_1=p_2\\H_A=p_1\neq p_2\\\alpha=0.05$

ii.For a two sample Proportion test

$Z=\frac{\bar p_1-\bar p_2}{\sqrt(\bar p(1-\bar p)(\frac{1}{n_1}+\frac{1}{n_2})}\\$

iii. for $\frac{\alpha}{2}=(-1.96,+1.96)$ (0.5 alpha IS 0.025),

reject $H_o$ if $|Z|>1.96$

iv. Do not reject $H_o$ . The noncomforting proportions are not significantly different as calculated below:

$z=\frac{0.050-0.067}{\sqrt {(0.06\times0.94)\times \frac{1}{500}}}$

z=-0.78

c. $(1-\alpha).100\%$ for the p1-p2 is given as:

$(\bar p_1-\bar p_2)\pm Z_0_._5_\alpha \times \sqrt \frac{ \bar p_1(1-\bar p_1)}{n_1}+\frac{\bar p_2(1-\bar p_2)}{n_2}\\\\=(0.05-0.067)\pm 1.645 \times \sqrt \ \frac{0.05+0.95}{200}+\frac{0.067+0.933}{300}\\$

=(-0.0517,+0.0177)

*CI contains o, which implies that proportions are NOT significantly different.

4 0

2 years ago

You pull out the plug from the bathtub. After 40 seconds, there are 13 gallons of water left in the tub. One minute after you pu

SCORPION-xisa [38]

Answer:

g = -3/20s + 19

Step-by-step explanation:

Let's assume this is a function

The points are

(40, 13) and (60, 10)

Since it is linear relation, we'll get the slope intercept form

g = ms + b, where g- number of gallons, s- time in seconds, b- y intercept

Using the points, let's calculate the formula

m = (10 - 13)/(60 - 40) = -3/20
10 = -3/20*60 + b
10 = - 9 + b
b = 19

So the formula is:

g = -3/20s + 19

7 0

2 years ago

Find the length of 2004-04-02-01-00_files/i0230000.jpg. Round the answer to the nearest hundredth.

notsponge [240]

The answer should be b

8 0

2 years ago

Read 2 more answers