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Arianys wants to ride her bicycle 55.5 miles this week. She has already ridden 19 miles. If she rides for 5 more days, which equ

Sergeu [11.5K]

The equation that could be used to determine, m, is 5m = 55.5 - 19. The correct option is C. m = (55.5 - 19)/5

<h3>Writing equation</h3>

From the question, we are to determine the equation that could be used to determine, m, the average number of miles she would have to ride to meet her goal

From the given information,

"<em>Arianys wants to ride her bicycle 55.5 miles</em>"

and

"<em>She has already ridden 19 miles</em>"

Thus,

The number of miles she needs to ride more is

55.5 miles - 19 miles

= 36.5 miles

If m is the average number of miles she would have to ride for 5 more days to complete her goal,

Then, we can write that

m = 36.5/5

OR

m = (55.5 - 19)/5

Hence, the equation that could be used to determine, m, is 5m = 55.5 - 19. The correct option is C. m = (55.5 - 19)/5

Learn more on Writing equation here: brainly.com/question/28351087

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4 0

1 year ago

Read 2 more answers

Formula for the area of a circle in terms of its circumference

Usimov [2.4K]

$\bf \textit{circumference of a circle}\\\\
C=2\pi r\qquad \qquad \implies \cfrac{C}{2\pi }=\boxed{r}\\\\
-------------------------------\\\\
\textit{area of a circle}\\\\
A=\pi r^2\qquad \qquad \implies A=\pi \left( \boxed{\cfrac{C}{2\pi }} \right)^2\implies A=\pi \left( \cfrac{C^2}{(2\pi )^2} \right)
\\\\\\
A=\cfrac{\pi C^2}{2^2\pi^2}\implies A=\cfrac{C^2}{4\pi }$

5 0

2 years ago

The National Institute of Standards and Technology (NIST) supplies "standard materials" whose physical properties are supposed t

Lady bird [3.3K]

Answer:

$10.08-1.64\frac{0.1}{\sqrt{6}}=10.013$

$10.08+1.64\frac{0.1}{\sqrt{6}}=10.147$

So on this case the 90% confidence interval would be given by (10.013;10.147)

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma =0.1$ represent the population standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=10.08$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$

Now we have everything in order to replace into formula (1):

$10.08-1.64\frac{0.1}{\sqrt{6}}=10.013$

$10.08+1.64\frac{0.1}{\sqrt{6}}=10.147$

So on this case the 90% confidence interval would be given by (10.013;10.147)

5 0

2 years ago

For the expansion of (x-y)^7 find the indicated term. sixth term

RoseWind [281]

What do you mean by this question?

8 0

3 years ago

Y=x^2-6x-16 in vertex form

satela [25.4K]

Answer:

$y=(x-3)^{2} -25$

Step-by-step explanation:

The standard form of a quadratic equation is $y=ax^{2} +bx+c$

The vertex form of a quadratic equation is $y=a(x-h)^{2} +k$

The vertex of a quadratic is (h,k) which is the maximum or minimum of a quadratic equation. To find the vertex of a quadratic, you can either graph the function and find the vertex, or you can find it algebraically.

To find the h-value of the vertex, you use the following equation:

$h=\frac{-b}{2a}$

In this case, our quadratic equation is $y=x^{2} -6x-16$ . Our a-value is 1, our b-value is -6, and our c-value is -16. We will only be using the a and b values. To find the h-value, we will plug in these values into the equation shown below.

$h=\frac{-b}{2a}$ ⇒ $h=\frac{-(-6)}{2(1)}=\frac{6}{2} =3$

Now, that we found our h-value, we need to find our k-value. To find the k-value, you plug in the h-value we found into the given quadratic equation which in this case is $y=x^{2} -6x-16$

$y=x^{2} -6x-16$ ⇒ $y=(3)^{2} -6(3)-16$ ⇒ $y=9-18-16$ ⇒ $y=-25$

This y-value that we just found is our k-value.

Next, we are going to set up our equation in vertex form. As a reminder, vertex form is: $y=a(x-h)^{2} +k$

a: 1

h: 3

k: -25

$y=(x-3)^{2} -25$

Hope this helps!

3 0

3 years ago