All categories

3 years ago

Is 12/42=10/35 a true proportion

1 answer:

3 0

Yes, they both are 2/7

Proof: Left-hand side

Simplify the following:
12/42

The gcd of 12 and 42 is 6, so 12/42 = (6×2)/(6×7) = 6/6×2/7 = 2/7:
Answer: 2/7
Right-hand side:

Simplify the following:
10/35
The gcd of 10 and 35 is 5, so 10/35 = (5×2)/(5×7) = 5/5×2/7 = 2/7:
Answer: 2/7

You might be interested in

If a = {6 6 4 7 -4 4 -6 9 -3} and B= {1 5 -8 9 -5 -8 9 -5 2}, find 3a +9B Matrix operations

V125BC [204]

Answer:

$3A+9B=\begin{bmatrix} 27 & 63 & -60 \\\\ 102 & -57 & -60\\\\ 63 & -18 & 9 \end{bmatrix}$

Step-by-step explanation

$A=\begin{bmatrix} 6 & 6 & 4\\\\7 & -4 & 4\\\\ -6 & 9 & -3\end{bmatrix}\: and \: B=\begin{bmatrix}1 & 5 & -8\\\\ 9 & -5 & -8\\\\ 9 & -5 & 2\end{bmatrix}$

$\rightarrow 3A=3\begin{bmatrix} 6 & 6 & 4\\\\7 & -4 & 4\\\\ -6 & 9 & -3\end{bmatrix},\: \: 9B =9\begin{bmatrix}1 & 5 & -8\\\\ 9 & -5 & -8\\\\ 9 & -5 & 2\end{bmatrix}$

$\rightarrow 3A=\begin{bmatrix} 3*6 & 3*6 & 3*4\\\\3*7 & 3(-4) & 3*4\\\\ 3(-6) & 3*9 & 3(-3)\end{bmatrix},\:\: 9B =\begin{bmatrix}9*1 &9* 5 &9( -8)\\\\ 9*9 & 9(-5) & 9(-8)\\\\ 9*9 & 9(-5) & 9*2\end{bmatrix}$

$\rightarrow 3A=\begin{bmatrix} 18 & 18 & 12 \\\\ 21 & -12 & 12\\\\ -18 & 27 & -9\end{bmatrix},\:\: 9B =\begin{bmatrix} 9 & 45 & -72 \\\\ 81 & -45 & -72\\\\ 81 & -45 & 18\end{bmatrix}$

$\rightarrow 3A+9B=\begin{bmatrix}18+9 & 18+45 & 12+(-72) \\\\ 21+81 & -12 +(-45) & 12+(-72)\\\\ -18+81 & 27+(-45) & -9+18 \end{bmatrix}$

$\rightarrow 3A+9B=\begin{bmatrix} 18+9 & 18+45 & 12-72 \\\\ 21+81 & -12 -45 & 12-72\\\\ -18+81 & 27-45 & -9+18 \end{bmatrix}$

$\rightarrow \purple{\bold{3A+9B=\begin{bmatrix} 27 & 63 & -60 \\\\ 102 & -57 & -60\\\\ 63 & -18 & 9 \end{bmatrix}}}$

6 0

2 years ago

An insurance company states that it settles 85% of all life insurance claims within 30 days. A consumer group asks the state ins

BlackZzzverrR [31]

Using the z-distribution, it is found that since the p-value of the test is less than 0.05, we reject the null hypothesis and find that there is enough evidence to conclude that the true proportion of all life insurance claims made to this company that are settled within 30 days is less than 85%.

<h3>What are the hypothesis tested?</h3>

At the null hypothesis, it is tested if there is not enough evidence that the proportion is below 85%, that is:

$H_0: p \geq 0.85$

At the alternative hypothesis, it is tested if there is enough evidence that the proportion is below 85%, that is:

$H_0: p < 0.85$

<h3>What is the test statistic?</h3>

The test statistic is given by:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}$

In which:

$\overline{p}$ is the sample proportion.

p is the proportion tested at the null hypothesis.

n is the sample size.

For this problem, the parameters are:

$p = 0.85, n = 250, \overline{p} = \frac{203}{250} = 0.812$

Hence the test statistic is:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}$

$z = \frac{0.812 - 0.85}{\sqrt{\frac{0.85(0.15)}{250}}}$

z = -1.68

<h3>What is the p-value and the conclusion</h3>

Using a z-distribution calculator, with a left-tailed test, as we are testing if the proportion is less than a value, and z = -1.68, the p-value is of 0.0465.

Since the p-value of the test is less than 0.05, we reject the null hypothesis and find that there is enough evidence to conclude that the true proportion of all life insurance claims made to this company that are settled within 30 days is less than 85%.

More can be learned about the z-distribution at brainly.com/question/16313918

#SPJ1

4 0

1 year ago

Negate the conditional statement.<br><br> c⇒(a∧∼b)

gulaghasi [49]

The negate of this conditional statement as : a∨(∼b).

<h3>What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?</h3>

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.

A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.

We have the the following conditional statement -

c ⇒ (a∧∼b)

We can write the negate of this conditional statement as -

a∨(∼b)

Therefore, the negate of this conditional statement as : a∨(∼b).

To solve more questions on Equations, Equation Modelling and Expressions visit the link below -

brainly.com/question/14441381

#SPJ1

7 0

7 months ago

Graph the line by plotting y=x+8

Zarrin [17]

The equation y = x + 8 uses the slope intercept form

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

In this case

y = 1x + 8

m = 1

y = x + 8

b = 8 OR y-intercept of this line is (0, 8)

You can plot the point (0, 8) on a graph. Then to find the next point you will rise up 1 and over right 1 (this is the slope). You can find another point after that by going down one and left one from the point (0, 8)

The graph should look like the one in the image below

Hope this helped! Let me know if you have any further questions

~Just a girl in love with Shawn Mendes

6 0

3 years ago

A high school has 44 players on the football team. The summary of the players' weights is given in the box plot. What is the int

lutik1710 [3]

Answer:

Where’s the plot box???

Step-by-step explanation:

???

3 0

2 years ago