Simplify 4/96 in fractions?

Find the sum. then use commutative property of addition to write the related sentence

adelina 88 [10]

Addition is defined as one of the main basic operation of mathematics. Addition is also defined as the process of adding one of more numbers. For the addition operation, there are many number of properties used. In that, one of the property is known as the commutative property of addition. It states that the change of order does not change the value of addition. Commutative property of addition is true for all types of numbers including imaginary numbers. So you can pretty much use any numbers ex.2 + 3 = 3 + 2

4 0

4 years ago

Is this a complementary ,linear pair,vertical or adjacent?

Simora [160]

Step-by-step explanation:

Adjacent angles.

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3 0

3 years ago

Read 2 more answers

2.What is the value of x? Enter your answer, as a decimal, in the box.

Maurinko [17]

I am going to assign the first image to problem 2, the second image to problem 3, and the third image to problem 4 and solve for x in each image. Basically, all of these problems can be solved used the law of sines which is as follows:

a/sinA = b/sinB = c/sinC

This states that the length of a side, divided by the sine of the opposite angle, is the same for every side in a triangle.

2.) We must solve for side x in the smaller triangle. We know two sides of the large triangle, and one side of the smaller triangle. The two parallel lines tell us that angle A = angle N and angle B = angle P. The side of the smaller triangle that we do know is, 67.2 - 32 = 35.2 m. Now we can plug values into the law of sines.

35.2/sinB = x/sinA
sinA = (x/35.2)sinB

81.9/sinB = 67.2/sinA
sinA = (67.2/81.9)sinB

We can now equate both sinA equations and solve for x.

(x/35.2)sinB = (67.2/81.9)sinB
x/35.2 = 67.2/81.9
x = (35.2)(67.2/81.9)
x = 42.9 m

3.) We will make the assumption that the angle divided by the line inside the triangle is split in equal halves, therefore, both angles are the same. The angles at point D are angle D and and 180-D. It turns out that sinD = sin(180-D). If you do not believe this principle, test it out in a calculator. This will simplify our problems. We can simply use the law of sines once more.

(x+4)/sinE = 44.8/sinD
sinE = ((x+4)/44.8)sinD

35/sinE = 56/sinD
sinE = (35/56)sinD

((x+4)/44.8)sinD = (35/56)sinD
(x+4)/44.8 = 35/56
x+4 = (35/56)(44.8)
x = (35/56)(44.8) - 4
x = 24 m

4.) This problem is very similar to problem two, containing a parallel line that results in angles on the same side of the parallel line being equivalent.

45/sinθ = (13+2x)/sinθₓ
sinθ = (45/(13+2x))sinθₓ

5/sinθ = 3/sinθₓ
sinθ = (5/3)sinθₓ

(5/3)sinθₓ = ((45/(13+2x))sinθₓ
5/3 = 45/(13+2x)
13+2x = 27
2x = 14
x = 7m

5.) The area of a triangle is found using the formula, A = (1/2)b·h. We are already given the area of the triangle and the height of the triangle. The base of this triangle IS the hypotenuse, so solving for the base will answer this question.

A = (1/2)(b)(15) = 270
b = (270)(2/15)
b = 36 m

4 0

3 years ago

Use the normal distribution to find a confidence interval for a difference in proportions p1-p2 given the relevant sample result

9966 [12]

Answer:

a) $\hat p_1 -\hat p_2= 0.2-0.35= -0.15$

b) $ME= 2.58 \sqrt{\frac{0.2(1-0.2)}{60} +\frac{0.8(1-0.8)}{100}} =0.169$

c) $(0.2-0.35) - 2.58 \sqrt{\frac{0.2(1-0.2)}{60} +\frac{0.8(1-0.8)}{100}} =-0.319$

$(0.2-0.35) + 2.58 \sqrt{\frac{0.2(1-0.2)}{60} +\frac{0.8(1-0.8)}{100}} =0.0185$

And the 99% confidence interval would be given (-0.319;0.0185).

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p_1$ represent the real population proportion 1

$\hat p_1=0.2$ represent the estimated proportion 1

$n_1=60$ is the sample size required 1

$p_2$ represent the real population proportion for 2

$\hat p_2 =0.35$ represent the estimated proportion 2

$n_2=100$ is the sample size required for Brand B

$z$ represent the critical value for the margin of error

Solution to the problem

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_1 -\hat p_2) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1(1-\hat p_2)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}$

Part a

The best estimate is given by:

$\hat p_1 -\hat p_2= 0.2-0.35= -0.15$

Part b

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.