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Snezhnost [94]
2 years ago
11

Which graph correctly represents x + 2y ≤ 4?

Mathematics
1 answer:
Artyom0805 [142]2 years ago
8 0
The answer is y < -x/2 + 2 hope this helped you
                         -
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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 <br><br> A) solve for vi<br><br> B) solve for d <br><br> 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
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