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3 years ago

8. Find an equation in standard form for the ellipse with the vertical major axis of length 16 and minor axis of length 4

Mathematics

1 answer:

MA_775_DIABLO [31]3 years ago

3 0

Hello,

If center is (0,0)

x²/a²+y²/b²=1 for a half horizontal axis of a, and a half vertical axis of b

Here

a=2 ==> a²=4

b=8 ==> b²=64

$\boxed{\dfrac{x^2}{4}+ \dfrac{y^2}{64}=1}\\$

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A scientist used 2 gallons of liquid for every 3 hours he works. He uses __ of a gallon each hour he works.

tiny-mole [99]

He uses 2/3 of a gallon each hour he works.

8 0

2 years ago

Here is an addition sentence.

kiruha [24]

Answer: B. $3+(1+11)=15$

Step-by-step explanation:

1. By definition, the associative property of addition is:

$(a+b)+c=a+(b+c)$

2. Therefore, if you have the following expression:

$(3+1)+11=15$

You apply the Asociative property of addition by regrouping the numbers as following:

$3+(1+11)=15$

3. Then, you can conclude that the correct option is B.

4 0

3 years ago

NO LINKS!!!!!

8090 [49]

9514 1404 393

Answer:

5x^2 +10x = -5

Step-by-step explanation:

The equation will have one solution when the discriminant is zero.

In standard form, the equation is ...

ax^2 +10x -c = 0

The discriminant of the equation ax^2+bx+c=0 is ...

b^2 -4ac

so the discriminant of your equation is ...

10^2 -4a(-c) = 100 +4ac

We want that to be zero, so we require ...

100 +4ac = 0

25 +ac = 0

ac = -25

Any pair of values of 'a' and 'c' that have a product of -25 will satisfy the requirement. As you state, one possible pair is a = 5 and c = -5. Putting these values into the given equation makes it ...

5x^2 +10x = -5 . . . . . the equation with a=5, c=-5

_____

Additional comment

Your problem statement does not require that 'a' be non-zero. If a=0, then the equation will have one real solution for any value of c.

If you restrict the solutions to integers, then possibilities include ...

(a, c) = (1, -25), (5, -5), (25, -1), (-25, 1), (-5, 5), (-1, 25)

6 0

2 years ago

PLEASE HELP ME ANSWER! im so desperate bro !!

sergey [27]

a)13

b) skewed

c) IQR

d)Sam's observation is correct

e)6.17

Step-by-step explanation:

Step 1 :

From the histogram we can infer that

0 to 2 texts has been sent by 1 student

2 to 4 texts has been sent by 3 student

4 to 6 texts has been sent by 4 student

6 to 8 texts has been sent by 4 student

8 to 10 texts has been sent by 5 student

Step 2:

From step 1 , we can see that there are total of 17 students represented by the histogram

Step 3:

This is a skewed histogram because we have all large values of students on the right of the histogram and smaller values on the left of the histogram.

In symmetrical histogram, there would be large values on the center and the smaller values on both sides.

Step 4:

IQR would be better recommendation for this as this is a skewed histogram

Standard deviation would be recommended for a symmetrical histogram

Step 5:

Total number of students is 17

Number of students who text between 8 to 10 messages is 5

Hence the students who text between 8 and 10 messages is 5/17

which is nearly 1/3 rd of the total students.

Hence Sam's observation is correct

Step 6:

Mean amount of the texts = (1 * 3 + 3* 3 + 5*4 +7*4 + 9* 5) /17 = 6.17

6 0

3 years ago

ACT scores have a mean of 20.8 and 9 percent of the scores are above 28. The scores have a distribution that is approximately no

dimaraw [331]

Answer: 5.37

Step-by-step explanation:

Let x = ACT scores.

Given: ACT scores have a mean of 20.8 and 9 percent of the scores are above 28. The scores have a distribution that is approximately normal.

i.e. P(X>28)=0.09 (i)

Now,

$P(X>28)=P(\dfrac{X-\mu}{\sigma}>\dfrac{28-20.8}{\sigma})\\\\= P(z>\dfrac{7.2}{\sigma})\ \ \ \ [z=\dfrac{X-\mu}{\sigma}]$ (ii)

One -tailed z value for p-value of 0.09 =1.3408 [By z-table]

From (i) and (ii)

$\dfrac{7.2}{\sigma}=1.3408\\\\\Rightarrow\ \sigma=\dfrac{7.2}{1.3408}\\\\\Rightarrow\ \sigma=5.37$

Hence, the standard deviation = 5.37

5 0

3 years ago