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Vikentia [17]
3 years ago
12

Determine which equations have the same solution set as StartFraction 2 Over 3 EndFraction minus x plus StartFraction 1 Over 6 E

ndFraction equals 6 x. – x + = 6x by recognizing properties, rather than solving. Check all that apply.
Mathematics
1 answer:
Lina20 [59]3 years ago
4 0

Answer:

A, B, F

Step-by-step explanation:

2/3 - x + 1/6 = 6x

Collect like terms

2/3 + 1/6 = 6x + x

(4+1) / 6 = 7x

5/6 = 7x

x = 5/6 ÷ 7

= 5/6 × 1/7

x = 5/42

a) 4 - 6x + 1 = 36x

4 + 1 = 36x + 6x

5 = 42x

x = 5/42

Equivalent to the last step of the simplification above

b) 5/6 - x = 6x

5/6 = 6x + x

5/6 = 7x

This is equivalent to the third step of the simplification

c) 4 - x + 1 = 6x

4 + 1 = 6x + x

5 = 7x

x = 5/7

Not equivalent to any of the steps in the simplification above

d) 5/6 + x = 6x

5/6 = 6x - x

5/6 = 5x

x = 5/6 ÷ 5

= 5/6 × 1/5

x = 5/30

Not equivalent to any of the steps in the simplification above

e) 5 = 30x

x = 5/30

Not equivalent to any of the steps in the simplification above

f) 5 = 42x

x = 5/42

Equivalent to the last step of the simplification above

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This last one I need help on too
ExtremeBDS [4]

Answer:

x=\frac{3}{4}+i\frac{\sqrt{7}}{4},\:x=\frac{3}{4}-i\frac{\sqrt{7}}{4}

Step-by-step explanation:

simplify \frac{-3}{x-2} by putting the negative sign on the outside. \frac{2x}{x-1}-\frac{2x-5}{x^2-3x+2}=-\frac{3}{x-2}

find the LCM of the denominators. It is (x-1)(x-2). Multiply by the LCM:

\frac{2x}{x-1}\left(x-1\right)\left(x-2\right)-\frac{2x-5}{x^2-3x+2}\left(x-1\right)\left(x-2\right)=-\frac{3}{x-2}\left(x-1\right)\left(x-2\right)

Simplify:

2x\left(x-2\right)-\left(2x-5\right)=-3\left(x-1\right)

solve: x=\frac{3}{4}+i\frac{\sqrt{7}}{4},\:x=\frac{3}{4}-i\frac{\sqrt{7}}{4}

3 0
3 years ago
What is the experamental probability that the coin lands on heads?
sammy [17]

Answer:

The experamental probability that the coin lands on head is 50 %

Step-by-step explanation:

Given:

Experiment:

A coin is Toss

Let the Sample Space be 'S' that is total number of outcomes for a coin has been tossed = { Head, Tail }

∴ n ( S ) =  2

Let A be the event of getting a Head on tossing a coin i.e  { Head }

∴ n( A ) = 1

Now,

\textrm{Probability} =\frac{\textrm{outcomes for the experiment}}{\textrm{total number of outcomes}}

Substituting the values we get

P(A) = \frac{n(A)}{n(S)} \\\\P(A) = \frac{1}{2} \\\\P(A) = 0.5\\\\P(A) = 50\%

The experamental probability that the coin lands on head is 50 %

5 0
3 years ago
If you drive 9hours and 465 kilometers how long would it take you to drive 768 kilometers
romanna [79]
 I think it would be 13 hours possibly
8 0
3 years ago
The differfence between the product of seven and a number and two times the number
olga2289 [7]

Answer:

7(x-10)

Step-by-step explanation:

7×(x-10)

you ×7by whatever x-10 is

4 0
2 years ago
Refer to the following scenario:You want to see if there is a difference between the exercise habits of Science majors and Math
bekas [8.4K]

Answer:

1. H0: P1 = P2

2. Ha: P1 ≠ P2

3. pooled proportion p = 0.542

4. P-value = 0.0171

5. The null hypothesis failed to be rejected.

At a signficance level of 0.01, there is not enough evidence to support the claim that there is significant difference between the exercise habits of Science majors and Math majors .

6. The 99% confidence interval for the difference between proportions is (-0.012, 0.335).

Step-by-step explanation:

We should perform a hypothesis test on the difference of proportions.

As we want to test if there is significant difference, the hypothesis are:

Null hypothesis: there is no significant difference between the proportions (p1-p2 = 0).

Alternative hypothesis: there is significant difference between the proportions (p1-p2 ≠ 0).

The sample 1 (science), of size n1=135 has a proportion of p1=0.607.

p_1=X_1/n_1=82/135=0.607

The sample 2 (math), of size n2=92 has a proportion of p2=0.446.

p_2=X_2/n_2=41/92=0.446

The difference between proportions is (p1-p2)=0.162.

p_d=p_1-p_2=0.607-0.446=0.162

The pooled proportion, needed to calculate the standard error, is:

p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{82+41}{135+92}=\dfrac{123}{227}=0.542

The estimated standard error of the difference between means is computed using the formula:

s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.542*0.458}{135}+\dfrac{0.542*0.458}{92}}\\\\\\s_{p1-p2}=\sqrt{0.001839+0.002698}=\sqrt{0.004537}=0.067

Then, we can calculate the z-statistic as:

z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.162-0}{0.067}=\dfrac{0.162}{0.067}=2.4014

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

\text{P-value}=2\cdot P(z>2.4014)=0.0171

As the P-value (0.0171) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

At a signficance level of 0.01, there is not enough evidence to support the claim that there is significant difference between the exercise habits of Science majors and Math majors .

We want to calculate the bounds of a 99% confidence interval of the difference between proportions.

For a 99% CI, the critical value for z is z=2.576.

The margin of error is:

MOE=z \cdot s_{p1-p2}=2.576\cdot 0.067=0.1735

Then, the lower and upper bounds of the confidence interval are:

LL=(p_1-p_2)-z\cdot s_{p1-p2} = 0.162-0.1735=-0.012\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= 0.162+0.1735=0.335

The 99% confidence interval for the difference between proportions is (-0.012, 0.335).

6 0
3 years ago
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