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3 years ago

The greater of two numbers is six more

Mathematics

1 answer:

pickupchik [31]3 years ago

5 0

Answer:

Let's begin by writing the mathematical equations given by the sentences.

Let X = smaller number

Let Y = larger number

The first sentence tells us

X + Y = 38

The second sentence tells us

X = Y/3 + 6

Since you weren't given a specific method to use, you can use either the substitution method or the elimination(addition) method, whichever works best for you.

Since the 2nd equation has the X isolated, I'm going to isolate the X in the first equation,

X = 38 - Y

Since both equations are equal to X, I can set them equal to one another and solve for Y.

Y/3 + 6 = 38 - Y

Y + 18 = 114 - 3Y

4Y = 96

Y = 24

Then use either of the two original equations to solve for X

X + Y = 38

X + 24 = 38

X = 14

Step-by-step explanation:

PLS MAKE ME AS BRAINLIST

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One person wants to get a 95% z-confidence interval with a margin of error of at most 15 based on a population standard deviatio

Bess [88]

Answer:

$n=(\frac{1.96(60)}{15})^2 =61.46 \approx 62$

So the answer for this case would be n=62 rounded up to the nearest integer

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

$\sigma=60$ represent the population standard deviation

n represent the sample size (variable of interest)

Confidence =95% or 0.95

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

And on this case we have that ME =15, and we are interested in order to find the value of n, if we solve n from equation (1) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (2)

The critical value for 95% of confidence interval is provided, $z_{\alpha/2}=1.96$ , replacing into formula (2) we got:

$n=(\frac{1.96(60)}{15})^2 =61.46 \approx 62$

So the answer for this case would be n=62 rounded up to the nearest integer

6 0

3 years ago

Factor 3x2 - 15x - 42.

11Alexandr11 [23.1K]

3 x^{2} - 15x - 42
(x-7)(x+2)
x-7=0 x+2=0
x=7,-2

8 0

3 years ago

write an equation of the line containing the specified point and perpendicular to indicated line. (-5,6) 4x-y=3

Radda [10]

<h2>Greetings!</h2>

Answer:

y = $\frac{1}{2}x + \frac{29}{4}$

Step-by-step explanation:

First, we need to rearrange the equation to make it y = mx + c

4x - y = 3

y + 3 = 4x

y = 4x -3

So the slope of the line is 4.

The slope of a line perpendicular to an equation is:

$\frac{-1}{gradient}$

So the slope of the perpendicular line is:

$\frac{-1}{4}$ = -0.25

Now to find the equation of a line you can use the following equation:

y - y₁ = m(x - x₁)

Where y₁ is the y-coordinate, x₁ is the x-coordinate and m is the gradient. Plug the values in:

y₁ = 6

x₁ = -5

m = $\frac{-1}{4}$

y - 6 = $\frac{-1}{4}$ (x - - 5)

To get rid of the fraction we need to multiply the whole equation by 4:

4y - 24 = -1(x - - 5)

The two negatives cancel out:

4y - 24 = -1(x + 5)

Multiply the brackets out:

4y - 24 = -x + 5

Now, to rearrange the formula back into y = mx + c

Move the -24 over to the other side making it a +24:

4y = 2x + 5 + 24

4y = 2x + 29

Divide everything by 4:

y = $\frac{2}{4}x + \frac{29}{4}$

y = $\frac{1}{2}x + \frac{29}{4}$

<h2>Hope this helps!</h2>

8 0

3 years ago

Ramon earns $1,735 each month and pays $53.10 on electricity. To the nearest tenth of a percent, what perfect of ramons earnings

Alenkinab [10]

Answer:

$\boxed{3.1 \, \%}$

Step-by-step explanation:

The formula for calculating percentage is

$\text{Percentage} = \dfrac{\text{Part}}{\text{Whole}} \times 100 \, \%$

The "part" is the electricity payment.

The "whole" is Ramon's earnings.

$\begin{array}{rcl}\text{\% of earnings} & = & \dfrac{53.10}{1735} \times 100 \, \% \\\\& = & \mathbf{3.1 \, \%}\\\end{array}\\\boxed{\mathbf{3.1 \, \%}} \text{ of Ramon's earnings are on electricity}$

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3 years ago

a survey was conducted with s students. 30% of those surveyed said that they have traveled out of the country. Of the students w

Ivenika [448]

40÷30s? I think that is the answer, but I'm not completely sure...

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3 years ago