The formula = 21+ 2m is used when calculating:

Which conic's equation has 2 squares with the same signs and different leading coefficients?

Romashka [77]

We want to see which is the conic equation that has 2 squares with the same sign and different leading coefficients.

We will see that it is the equation of the ellipse.

Now let's see why that is the correct answer.

The general conic equation is of the form:

$A*(x - a)^2 + B*(x - b)^2 = R^2$

Where A and B are the leading coefficients, (a, b) is the center of the figure, and R is the average radius of the figure.

For example, if A = B, this would be the equation of a circle, but we must have two different leading coefficients.

If we write:

A = 1/C

B = 1/K

(both are positive, because "it has two squares with the same signs").

Then we get the equation:

$\frac{ (x - a)^2}{C} + \frac{(x - b)^2}{K} = R^2$

We get the equation we wanted.

The same sign in both square parts and different leading coefficients.

The above equation is the general equation of an ellipse.

If you want to learn more, you can read:

brainly.com/question/10311514

7 0

2 years ago

Mindy, a local artist, sells a piece of art at the pizza shop for $15, and the shop takes 15 percent commission. Instead of rece

Yuliya22 [10]

In this question the first thing that needs to be determined is the commission taken by the pizza shop and the amount of money that falls in the part of Mindy.
We already know that Mindy sells the piece of art for $15 and the pizza shop takes 15% commission on it.
Then
Commission taken by the pizza shop = (15/100) * 15
   = 225/100
   = 2.25 dollars
So the pizza shop takes a commission of $2.25 from the sales of each art piece from Mindy.
Then amount that falls in Mindy's part = (15 - 2.25) dollars
   = 12.75 dollars
Now Mindy is not taking the money but taking a pizza worth rupees $12 including 5% sales tax.
Initially it looks like Mindy is making a profit of $0.75 plus the pizza worth $12. So it is a fair deal for Mindy. Now coming to the part of the pizza shop owner, we find that he also gains extra $2.25 from this deal. So it is a fair deal for both the shop keeper and Mindy.

4 0

3 years ago

Read 2 more answers

2h − 3 = 3 Need some help

QveST [7]

Answer: Let's solve your equation step-by-step.

2h−3=3

Step 1: Add 3 to both sides.

2h−3+3=3+3

2h=6

Step 2: Divide both sides by 2.

2h/2 = 6/2

h = 3.

8 0

3 years ago

The amount of coffee that a filling machine puts into an 8-ounce jar is normally distributed with a mean of 8.2 ounces and a sta

nordsb [41]

Answer:

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 8.2, \sigma = 0.18, n = 100, s = \frac{0.18}{\sqrt{100}} = 0.018$

What is the probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce?

This is the pvalue of Z when X = 8.2 + 0.02 = 8.22 subtracted by the pvalue of Z when X = 8.2 - 0.02 = 8.18. So

X = 8.22

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{8.22 - 8.2}{0.018}$

$Z = 1.11$

$Z = 1.11$ has a pvalue of 0.8665

X = 8.18

$Z = \frac{X - \mu}{s}$

$Z = \frac{8.18 - 8.2}{0.018}$

$Z = -1.11$

$Z = -1.11$ has a pvalue of 0.1335

0.8665 - 0.1335 = 0.7330

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce

8 0

3 years ago

Replace ∗ with a monomial so that the derived expression may be represented as a square of a binomial: * +14b+49

anyanavicka [17]

Answer:

* = b²

Step-by-step explanation:

You know that the square of a binomial is of the form ...

(x + y)² = x² + 2xy + y²

Matching given terms, we have ...

49 = y²

2xy = 14b

Solving the first of these relations for y, we have

y = √49 = 7

Putting that in the second relation and solving for x, we find ...

2x·7 = 14b

14x = 14b

x = b

Then the first term of the expansion, x², will be b².

The missing term is b².

7 0

3 years ago