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3 years ago

Rewrite the following as like fractions (having the same denominator) and place them in order from least to greatest.

1 answer:

3 0

2/3, 5/6, 4/7....common denominator is 42
2/3 = 28/42
5/6 = 35/42
4/7 = 24/42
least to greatest : 2/3, 5/6, 4/7

3/4, 7/12, 4/5....common denominator is 60
3/4 = 45/60
7/12 = 35/60
4/5 = 48/60
least to greatest : 7/12, 3/4, 4/5

7/10, 8/15, 11/20.....common denominator is 60
7/10 = 42/60
8/15 = 32/60
11/20 = 33/60
least to greatest : 8/15, 11/20, 7/10

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A line with a slope of 4 passes through the point (2, 1). What is the equation of this line?

mariarad [96]

Answer:

y = 4x - 7

Step-by-step explanation:

Slope = 4 ; x1 = 2 , y1 = 1

Slope point form: y -y1 = m(x -x1)

y - 1 = 4(x - 2)

y - 1 = 4x - 2*4

y -1 = 4x - 8

y = 4x - 8 +1

y = 4x - 7

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3 years ago

Which of the following characteristics best describes the given function of f(x) = 3x - 6?

Trava [24]

Answer:

Step-by-step explanation:

degree 1 ( linear function

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2 years ago

A coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that

mafiozo [28]

Answer:

(a) The significance level of the test is 0.002.

(b) The power of the test is 0.3487.

Step-by-step explanation:

We are given that a coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that the probability is not 0.5.

The test rejects the null hypothesis if either 0 or 10 heads are observed.

Let p = probability of obtaining head.

So, Null Hypothesis, $H_0$ : p = 0.5

Alternate Hypothesis, $H_A$ : p $\neq$ 0.5

(a) The significance level of the test which is represented by $\alpha$ is the probability of Type I error.

Type I error states the probability of rejecting the null hypothesis given the fact that the null hypothesis is true.

Here, the probability of rejecting the null hypothesis means we obtain the probability of observing either 0 or 10 heads, that is;

P(Type I error) = $\alpha$

P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true) = $\alpha$

Also, the event of obtaining heads when a coin is thrown 10 times can be considered as a binomial experiment.

So, X ~ Binom(n = 10, p = 0.5)

P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true) = $\alpha$

$\binom{10}{0}\times 0.5^{0} \times (1-0.5)^{10-0} +\binom{10}{10}\times 0.5^{10} \times (1-0.5)^{10-10}$ = $\alpha$

$(1\times 1\times 0.5^{10}) +(1 \times 0.5^{10} \times 0.5^{0})$ = $\alpha$

$\alpha$ = 0.0019

So, the significance level of the test is 0.002.

(b) It is stated that the probability of heads is 0.1, and we have to find the power of the test.

Here the Type II error is used which states the probability of accepting the null hypothesis given the fact that the null hypothesis is false.

Also, the power of the test is represented by (1 - $\beta$ ).

So, here, X ~ Binom(n = 10, p = 0.1)

$1-\beta$ = P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true)

$1-\beta$ = $\binom{10}{0}\times 0.1^{0} \times (1-0.1)^{10-0} +\binom{10}{10}\times 0.1^{10} \times (1-0.1)^{10-10}$

$1-\beta$ = $(1\times 1\times 0.9^{10}) +(1 \times 0.1^{10} \times 0.9^{0})$

$1-\beta$ = 0.3487

Hence, the power of the test is 0.3487.

3 0

3 years ago

HELP ME PLZZZ!!! Solve for x. Show each step of the solution. 4.5(4 − x) + 36 = 202 − 2.5(3 + 28)

Veronika [31]

4.5{4_x}+36=202-2.5{3+28}
you first multiply 4.5 and the numbers in the bracket.
4.5*4=18
4.5*x=4.5x
you will obtain 18-4.5x=202_2.5{3+28}
2.5*3=7.5 2.5*28=70
18_4.5x=202_7.5_70
18_4.5x=124.5_18
-4.5x=106.5
x=23.67

5 0

2 years ago

Evaluate t-u/v, when t=-1,u=-3 and v=1/2

mars1129 [50]

Answer:

Step-by-step explanation:

t-u/v

substitute (-1) - (-3)/(1/2)

divide (-1) - (-6)

simplify (-1) + 6

add 5

3 0

2 years ago