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3 years ago

Elijah and Jonathan play on the same soccer team. They have played 3 of their 15,

Mathematics

1 answer:

Lynna [10]3 years ago

5 0

Answer:

Only Elijah's model is correct

Step-by-step explanation:

The data given in the question tells us they have 12 games left on their soccer team. Each one of them tried to simulate the fact by creating some model which look like a balance between quantities.

Elijah placed 3 cubes of value 1 and a cube of value x on one side of a balance. On the other side, he placed 15 cubes of value 1. He was obviously modeling the fact that 15 cubes (games due to play in our case) should be equal to 3 cubes (games already played) plus the x numbers left to play

This model if perfect, since the only way to equilibrate the balance is setting x to 12, the games left to play

Jonathan used a table with 3 x's in a row and a 15 in the second row, trying to model the same situation. To our interpretation, this table doesn't show the number of games left to play. If we equate 3x = 15, we get x=5 which has nothing to do with the situation explained in the question, so this model is not correct.

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Which of the following statements are true about a reflection? Select all that apply.

krok68 [10]

Answer: *An image created by a reflection will always be congruent to its pre-image.

*Corresponding angles and segments are always congruent in a reflection of a figure.

*An image and its pre-image are always the same distance from the line of reflection.

Step-by-step explanation:

Since, reflection is a rigid transformation therefore, it preserves the shape of the figure and create congruent images.

And we know that if if two figures are congruent then their corresponding angles and sides are congruent.

Reflection maps a figure to create its mirror image, and the distance of object and image is always equal from the mirror, therefore "An image and its pre-image are always the same distance from the line of reflection."

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4 years ago

Read 2 more answers

Th sum of the cost of dinner d a $12 tip divided equally between 3 people

Bond [772]

12 / 3 so the answer would be 4

5 0

3 years ago

Which one would the equation be?

aleksley [76]

Answer:

a. $y = \frac{2}{5}x - 6$

Step-by-step explanation:

The slope-intercept form of equation of a line is given as $y = mx + b$ . Where,

m = slope

b = y-intercept.

Rewrite the equations, $2x - 5y = 12$ and $4y + 24 = 5x$ , in the slope-intercept form by making y the subject of the formula. Then, derive our new equation that has the same slope as the first equation, and the same y-intercept as the second equation.

$2x - 5y = 12$

$2x - 12 = 5y$

Divide both sides by 5

$\frac{2x - 12}{5} = \frac{5y}{5}$

$\frac{2x}{5} - \frac{12}{5} = y$

Rewrite

$y = \frac{2x}{5} - \frac{12}{5}$

The slope of $2x - 5y = 12$ is ⅖.

$4y + 24 = 5x$

$4y = 5x - 24$ (subtraction property of equality)

Divide both sides by 4

$\frac{4y}{4} = \frac{5x - 24}{4}$

$y = \frac{5x}{4} - \frac{24}{4}$

$y = \frac{5x}{4} - 6$

The y-intercet of $4y + 24 = 5x$ is -6

Therefore, the equation that has the same slope as the first equation and the same y-intercept as the second equation would be:

$y = mx + b$

Plug in the values of m and b

$y = \frac{2}{5}x + (-6)$

$y = \frac{2}{5}x - 6$

5 0

4 years ago

A researcher takes a simple random sample of 83 homes in a city and finds that the mean square footage is 1628 with a standard d

Anna [14]

Answer: (1583.63, 1672.37)

Step-by-step explanation:

Given : Sample size : n= 83

Sample mean : $\overline{x}=1628$

Sample standard deviation : $\sigma=243$

The population standard deviation $(\sigma)$ is unknown .

The confidence interval for population mean :

$\overline{x}\pm t_{\alpha/2}\dfrac{s}{\sqrt{n}}$

For 90% confidence , significance level = $\alpha=1-0.90=0.10$

Using t-distribution table , Critical t-value = $t_{(\alpha/2, n-1)}=t_{0.05,82}=1.6636$

, where n-1 is the degree of freedom.

Now , 90% confidence interval for the mean square footage of all the homes in that city will be :-

$1628\pm (1.6636)\dfrac{243}{\sqrt{83}}\\\\ 1628\pm (1.6636)(26.672715)\\\\\\\\\approx1628\pm 44.37\\\\=(1628- 44.37,\ 1628+ 44.37)\\\\=(1583.63,\ 1672.37)$

Hence, the 90% confidence interval for the mean square footage of all the homes in that city = (1583.63, 1672.37)

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3 years ago