Which graph correctly represents x + 2y ≤ 4?

Anna bought 8 goldfish and 2 rainbow fish for her aquarium. The rainbow fish cost 6 dollars more than the goldfish. She paid a t

Anton [14]

Let the price of the goldfish be x
Let the price of the rainbow fish be y

Anna bought 8 fish, therefore, Anna paid 8x for the gold fish
Anna bought 2 rainbow fish, therefore, Anna paid 2y for the rainbow fish

We know that the total amount that Anna paid is 37$.
Therefore:
8x + 2y = 37 ..................> equation I

Now, we know that the rainbow fish cost 6$ more than the goldfish (since the verb "cost" is plural, therefore the total payment of rainbow fish is 6$ more than the total payment of gold fish).
Based on this,
2y + 6 = 8x
2y = 8x - 6 ...................> equation II

Substitute by equation II in equation I, we can get the following equation:
8x + 8x - 6 = 37
16x = 43 ................> The desired equation (equation III)

Solving equation III, we can calculate the price of one gold fish as follows:
16x = 43
x = 2.6875$

If we substitute by the value of x in equation I, we can calculate the price of one rainbow fish as follows:
8(2.6875) + 2y = 37
y = 7.75$

5 0

3 years ago

Vf²=vi²+ 2ad A) solve for vi B) solve for d Using the same equation

diamong [38]

A)
Vf² = vi² + 2ad Subtract 2ad from both sides
Vf² - 2ad = vi² Find the square roots of both sides
√(Vf² - 2ad) = √(vi²) Cancel out the squares with the square roots
Vf - √(2ad) = vi Switch the sides to make it easier to read
vi = Vf - √(2ad)

B) Vf² = vi² + 2ad Subtract vi² from both sides
Vf² - vi² = 2ad Divide both sides by 2a
(Vf² - vi²) / 2a = d Switch the sdies to make it easier to read
d = (Vf² - vi²) / 2a

7 0

3 years ago

Equation:

jekas [21]

Answer:

x = 41; B = 41°; A = 77°

Step-by-step explanation:

All of the angles add up to 180 so to solve for X you do (x) + (2x-5) + (62) = 180. Solve for X and you get 41. Lastly plut the answer back into the equation.

4 0

3 years ago

a cup was filled at a constant rate. it started empty. after 2 seconds, it held 70 cm cubes of water. the radius is 4 and te hei

Viktor [21]

Answer:

89.51%

Step-by-step explanation:

Assuming given units are in cm

Tge rate of filling the cup is 70/2= 35 cm3/s

Volume of the cup is $\pi r^{2}\frac {h}{3}$ and replacing r with 4 cm and h with 7 cm then the volume is equivalent to

$\pi*4^{2}*\frac {7}{3}= 117.3 cm^{3}$

Volume filled after 3 seconds will be 3*35=105 cm3

Percentage filled is $\frac {105}{117.3}\times 100\approx 89.51$

8 0

3 years ago

Scores on the SAT Mathematics test are believed to be normally distributed. The scores of a simple random sample of five student

AysviL [449]

Answer:

The mean calculated for this case is $\bar X=584$

And the 95% confidence interval is given by:

$584-2.776\frac{86.776}{\sqrt{5}}=476.271$

$584+2.776\frac{86.776}{\sqrt{5}}=691.729$

So on this case the 95% confidence interval would be given by (476.271;691.729)

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)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

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

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (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 $\bar X=584$

The sample deviation calculated $s=86.776$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=5-1=4$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,4)".And we see that $t_{\alpha/2}=2.776$

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

$584-2.776\frac{86.776}{\sqrt{5}}=476.271$

$584+2.776\frac{86.776}{\sqrt{5}}=691.729$

So on this case the 95% confidence interval would be given by (476.271;691.729)

3 0

2 years ago