All categories

3 years ago

Can someone please solve this problem for me?

Mathematics

1 answer:

statuscvo [17]3 years ago

5 0

Answer:

5 and 7.

Step-by-step explanation:

Hey! So to start you need to create an algebraic expression. You can express this problem through the following equation:

*Note: if x is an odd integer, x + 2 is the next consecutive odd integer.

$x *(x+2)=35$

Expanding, you get:

$x^{2}+2x = 35.$

And moving the 35 to the other side, you get a simple quadratic.

$x^{2}+2x -35 =0.$

Solving by factoring:

$(x+7)(x-5)$

This means two possible solutions for the smaller consecutive number are -7 and 5. However the question asks for two positive odd integers, so one of the numbers must be 5. The next will be 7(as its x + 2).

You might be interested in

There are two games involving flipping a coin. In the first game you win a prize if you can throw between 45% and 55% heads. In

Nina [5.8K]

Answer:

d) 300 times for the first game and 30 times for the second

Step-by-step explanation:

We start by noting that the coin is fair and the flip of a coin has a probability of 0.5 of getting heads.

As the coin is flipped more than one time and calculated the proportion, we have to use the sampling distribution of the sampling proportions.

The mean and standard deviation of this sampling distribution is:

$\mu_p=p\\\\ \sigma_p=\sqrt{\dfrac{p(1-p)}{N}}$

We will perform an analyisis for the first game, where we win the game if the proportion is between 45% and 55%.

The probability of getting a proportion within this interval can be calculated as:

$P(0.45$

referring the z values to the z-score of the standard normal distirbution.

We can calculate this values of z as:

$z_H=\dfrac{p_H-\mu_p}{\sigma_p}=\dfrac{(p_H-p)}{\sqrt{\dfrac{p(1-p)}{N}}}=\sqrt{\dfrac{N}{p(1-p)}}*(p_H-p)>0\\\\\\z_L=\dfrac{p_L-\mu_p}{\sigma_p}=\dfrac{p_L-p}{\sqrt{\dfrac{p(1-p)}{N}}}=\sqrt{\dfrac{N}{p(1-p)}}*(p_L-p)$

If we take into account the z values, we notice that the interval increases with the number of trials, and so does the probability of getting a value within this interval.

With this information, our chances of winning increase with the number of trials. We prefer for this game the option of 300 games.

For the second game, we win if we get a proportion over 80%.

The probability of winning is:

$P(p>0.8)=P(z>z^*)$

The z value is calculated as before:

$z^*=\dfrac{p^*-\mu_p}{\sigma_p}=\dfrac{p^*-p}{\sqrt{\dfrac{p(1-p)}{N}}}=\sqrt{\dfrac{N}{p(1-p)}}*(p^*-p)>0$

As (p*-p)=0.8-0.5=0.3>0, the value z* increase with the number of trials (N).

If our chances of winnings depend on P(z>z*), they become lower as z* increases.

Then, we can conclude that our chances of winning decrease with the increase of the number of trials.

We prefer the option of 30 trials for this game.

8 0

3 years ago

Is 50.2 a rational or an irrational number, why?

Greeley [361]

Answer:

Rational.

Step-by-step explanation:

$\textbf{A rational number is a real number that can be expressed as}~ \dfrac{p}{q},\\\\\textbf{where}~ p~ \textbf{and}~ q~ \textbf{are integers.}\\\\ \boxed{50.2 = \dfrac{502}{10}}\\\\ \textbf{50.2 can be expressed as a ratio of two integers,}~ \textbf{so it is a rational number.}$

4 0

2 years ago

A circle is inscribed in a square. A point in the figure is selected at random. Find the probability that the point will be in t

hram777 [196]

P of selecting point on the shaded region = shaded area/whole area
P( selecting point on the shaded ) = ( the four shaded circles ) / the whole square 
P of selecting point on the shaded = ( 4 * ( π * r^2 ) )/ x^2 
P of selecting point on the shaded = ( 4 * ( π * (x/4)^2 ) )/ x^2 
P of selecting point on the shaded = ( 4 * ( π * x^2/16 ) )/ x^2 
P of selecting point on the shaded = ( π * x^2/4 )/ x^2 
P of selecting point on the shaded = x^2( π/4 )/ x^2 
P( selecting point on the shaded ) = π/4 ≈ 0.7854 ≈ 79%
=80%
D is right option hope this helps

4 0

4 years ago

Find the volume of the prism height 3 in 5 and 12

Keith_Richards [23]

Step-by-step explanation:

To find the volume of a rectangular prism V=whl so w=3 x 5 x 12. Multiply all those numbers together to get 180 inches cubed.

4 0

3 years ago

Read 2 more answers

PLEASE HELP!!! WILL MARK BRAINLIEST!! Use the diagram to solve for x

bearhunter [10]

Answer: 3

Step-by-step explanation:

Set them equal because they are the same so 15x+5=16x+2 so x+2=5 so x=3

3 0

3 years ago