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3 years ago

A conjecture and the paragraph proof used to prove the conjecture are shown.

Mathematics

2 answers:

Neko [114]3 years ago

8 0

Answer:

I did the quiz here is what I got:

Brilliant_brown [7]3 years ago

7 0

Answer:

∠2; vertical angle theorem; ∠3; transitive property of congruence

Step-by-step explanation:

∠2 and ∠1 are opposite angles that share only a vertex. This is the definition of vertical angles, and by the vertical angle theorem they are congruent.

Substituting ∠2 for ∠1 in our "given" statement, we now know that ∠2≅∠4.

∠4 and ∠3 are opposite angles that share a vertex. This makes them vertical angles, and the vertical angle theorem states that they are congruent.

The transitive property, algebraically, states "if a=b and b=c, then a=c." Applied to this proof, it states "if ∠2≅∠4, and ∠4≅∠3, then ∠2≅∠3."

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A survey of 73 students found that 37% were in favor of raising tuition to pave new parking lots. The standard deviation of the

KatRina [158]

Answer:

The value is $n_2 = 317$

Step-by-step explanation:

From the question we are told that

The sample size is n = 73

The proportion that in favor of raising the tuition is $\^{p} = 0.37$

The standard deviation is $s_1 = 0.098$

The required standard deviation $s_2 = 0.047$

Generally the requires standard deviation is mathematically represented as

$s_2 = s_1 * \sqrt{\frac{n_1}{n_2} }$

=> $\frac{s_2}{s_1} = \sqrt{\frac{n_1}{n_2} }$

=> $\frac{n_1}{n_2} =[\frac{s_2}{s_1} ]^2$

=> $\frac{73}{n_2} =[\frac{0.047}{0.098} ]^2$

=> $\frac{73}{n_2} =0.2300$

=> $n_2 = \frac{73}{0.2300}$

=> $n_2 = 317$

3 0

3 years ago

Find the number of possible ways one can choose marbles from a bag containing three marbles: a) if the order is important b) if

vladimir1956 [14]

Answer:

There are 3 marbles, that we assume are different.

Let's define them as marble 1, marble 2, and marble 3.

a) If the order is important, and we select the 3 marbles, then:

for the first marble, we have 3 options.

For the second marble, we have 2 options (because one is already taken)

for the third marble is only one option.

The total number of combinations is equal to the product between the numbers of options, so in this case, we have:

C = 3*2*1 = 6 combinations.

Now, if we only select 2 marbles from the bag, we have:

for the first marble, we have 3 options.

For the second marble, we have 2 options

Here the number of different combinations is:

C = 3*2 = 6 combinations.

And if we select only one marble from the bag, we have:

for the first marble, we have 3 options.

Then here are only 3 combinations.

the total number of combinations is:

C' = 6 + 6 + 3 = 15 different combinations.

b) If the order is not important, then there is only one combination when we draw the 3 marbles.

When we draw one marble there are 3 combinations (one for each marble)

When we draw two marbles, again there are 3 combinations (one for each marble that we do not draw)

then the total number of combinations in this case is:

C = 1 + 3 + 3 = 7

3 0

3 years ago

Which expression is equivalent to the expression below

musickatia [10]

9.2 + (-8) = 1.2

-(-7/6)= 1.16

3 0

3 years ago

Add 77 -10 with its additive inverse.

Ganezh [65]

Answer: 77 - 10 = 67, and the additive inverse of 77 - 10 is 77 + 10. 77 + 10 = 87.

Hope this helps! This question was kind of confusing for me, because I didn’t understand why you said to add 77 - 10… is this is the incorrect answer sorry your question was worded weird

4 0

2 years ago

if a quadratic equation with real coefficients has a discriminant of -36 then what type of roots does it have

Aleks04 [339]

Step-by-step explanation:

We have,

If a quadratic equation with real coefficients has a discriminant of -36.

The general form of quadratic equation is :

$ax^2+bx+c=0$

The discriminant of this equation is : $D=b^2-4ac$

If D=0, it will have 1 real roots

If D>0, it will have 2 real roots

If D<0, it will have no real roots

We have,

D = -36 < 0, so, the quadratic equation will have no real roots.

5 0

3 years ago