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3 years ago

10

Mathematics

1 answer:

motikmotik3 years ago

5 0

Answer:

9) x = 89°

10) x = 118°

11) x = 145°

12) x = 40°

Step-by-step explanation:

9) 180-91 = 89

10) x = 118° because it is alternate interior to 118

11) x-30 = 115, x = 145

12) 4x-15 = 145, 4x = 160, x = 40

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There are 3 bags each containing 100 marbles. Bag 1 has 75 red and 25 blue marbles. Bag 2 has 60 red and 40 blue marbles. Bag 3

jekas [21]

Answer:

0.4 ; 0.6125

Step-by-step explanation:

Given the following :

Bag 1 : 75 red ; 25 blue

Bag 2: 60 red ; 40 blue

Bag 3: 45 red ; 55 blue

Probability = (required outcome / Total possible outcomes)

A) since the probability of choosing each bag is equal :

BAG A:

P(choosing bag A) = 1 / total number of bags = 1/3 ; P(choosing blue marble) = number of blue marbles / total number of marbles = 25/100

HENCE, choosing a blue marble from bag A : = (1/3 × 75/100) = 25/300

BAG B:

P(choosing bag B) = 1/3 ;

P(choosing blue marble) = number of blue marbles / total number of marbles = 40/100

HENCE, choosing a blue marble from bag A : = (1/3 × 40/100) = 40/300

BAG C:

P(choosing bag C) = 1/3

P(choosing blue marble) = number of blue marbles / total number of marbles = 55/100

HENCE, choosing a blue marble from bag A : = (1/3 × 55/100) = 55/300

= (25/300) × (40/300) × (55/300) = (25 + 40 + 55)/300 = 120/300 = 0.4

2) What is the probability that the marble is blue when the first bag is chosen with probability 0.5 and other bags with equal probability each?

BAG A:

P(choosing bag A) = 0.5 ; P(choosing blue marble) = number of blue marbles / total number of marbles = 25/100

HENCE, choosing a blue marble from bag A : = (0.5 × 75/100) = (0.5 * 0.75) = 0.375

BAG B:

P(choosing bag B) = (1-0.5) / 2 = 0.25 ;

P(choosing blue marble) = number of blue marbles / total number of marbles = 40/100

HENCE, choosing a blue marble from bag A : = (0.25 × 40/100) = (0.25 × 0.4) = 0.1

BAG C:

P(choosing bag C) = (1 - (0.5+0.25)) = 0.25

P(choosing blue marble) = number of blue marbles / total number of marbles = 55/100

HENCE, choosing a blue marble from bag A : = (0.25 × 55/100) = 0.25 × 0.55 = 0.1375

= 0.1375 + 0.1 + 0.375 = 0.6125

7 0

3 years ago

A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. Of interest is whether the liquid diet

brilliants [131]

Answer:

There is not enough evidence to support the claim that the liquid diet yields a higher mean weight loss than the powder diet (P-value = 0.15).

Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that the liquid diet yields a higher mean weight loss than the powder diet.

Then, the null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2< 0$

The significance level is 0.05.

The sample 1 (powder diet group), of size n1=49 has a mean of 42 and a standard deviation of 12.

The sample 2 (liquid diet group), of size n2=36 has a mean of 45 and a standard deviation of 14.

The difference between sample means is Md=-3.

$M_d=M_1-M_2=42-45=-3$

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

$s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{12^2}{49}+\dfrac{14^2}{36}}\\\\\\s_{M_d}=\sqrt{2.939+5.444}=\sqrt{8.383}=2.895$

Then, we can calculate the t-statistic as:

$t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-3-0}{2.895}=\dfrac{-3}{2.895}=-1.04$

The degrees of freedom for this test are:

$df=n_1+n_2-1=49+36-2=83$

This test is a left-tailed test, with 83 degrees of freedom and t=-1.04, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=P(t$

As the P-value (0.15) is greater than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the liquid diet yields a higher mean weight loss than the powder diet.

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3 years ago

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Wes measures the floor area of rectangular living room to replace the carpet with tiles. The room is 12.4 feet long and 9.8 feet

olasank [31]

12.4*2+9.8*2=44.4
Wes needs 44.4 tiles

5 0

3 years ago

What is the value of x in the equation 9/10 (x + 2/3)=4 1/2

garri49 [273]

Get the x variable on one side and the numbers another side.

9/10(x + 2/3) = 4 1/2

Distribute the 9/10 across the x and 2/3.

(9/10)x + 18/30 = 4 1/2

Simplify 18/30 to make our life easier.

(9/10)x + 3/5 = 4 1/2

Subtract 3/5 from each side of the equation.

(9/10)x = 3 9/10

Divide both sides by 9/10.

x = 4 1/3

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3 years ago

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What is the product of (x+9)(x-9)

Verdich [7]

Answer:

x^2 - 81

Step-by-step explanation:

There is a formula called the difference of squares, which is

(a+b)(a-b) = a^2 - b^2

8 0

3 years ago

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