Consider the following parametric equation. x equals (t plus 5 )squared​; y equals t plus 8​; negative 10 less than or equals t less than or equals 10 ​(a) Eliminate the parameter to obtain an equation in x and y. ​(b) Describe the curve and indicate the positive orientation. ​(a) Eliminate the parameter to obtain an equation in x and y. Choose the correct equation below. A. y equals StartRoot x plus 3 EndRoot B. y equals (x plus 3 )squared C. y equals x squared plus 3 D. y equals 3 plus or minus StartRoot x EndRoot ​(b) Describe the curve and indicate the positive orientation. A. -15 15 -5 15 x y

Answers

Answer 1

Answer:

  a)  D. y = 3 ±√x

  b)  parabola opening to the right

Step-by-step explanation:

(a) Solving for t in the equation for y:

  y = t+8

  t = y -8 . . . . subtract 8

Substituting into the equation for x, we have ...

  x = ((y -8) +5)^2 = (y -3)^2

Solving for y, we get

  ±√x = y -3 . . . . . take the square root

  y = 3 ±√x

__

(b) The equation describes a parabola that opens to the right.

Consider The Following Parametric Equation. X Equals (t Plus 5 )squared; Y Equals T Plus 8; Negative

Related Questions

a circle with circumference 18 had an arc with 120 central angle. what is the length of the arc

Answers

Answer:

A circle with circumference 18 had an arc with 120 central angle.

=> Radius of that circle: R = 18/(2 x pi) = 2.86

=> Length of that arc: L = R x 120 x pi/180 = 2.86 x (2/3) x pi = 5.99

Hope this helps!

:)

Answer:

6

Step-by-step explanation:

Angle: arc length

360 : 18

120 : X

X/120 = 18/360

X = 120 × 18/360

X = 6

Stacy uses a spinner with six equal sections numbered 2, 2, 3, 4, 5, and 6 to play a game. Stacy spins the pointer 120 times and records the results. The pointer lands 30 times on a section numbered 2, 19 times on 3, 25 times on 4, 29 times on 5, and 17 times on 6.



Write a probability model for this experiment, and use the probability model to predict how many times Stacy would spin a 6 if she spun 50 times. Give the probabilities as decimals, rounded to 2 decimal places

Answers

Answer:

Hence, Stacy will spin 6,  8.33 times out of her n = 50 attempts.

Step-by-step explanation:

Let us consider a success to get a 6. In this case, note that the probability of having a 6 in one spin is 1/6. We can consider the number of 6's in 50 spins to be a binomial random variable. Then, let X to be the number of trials we get a 6 out of 50 trials. Then, we have the following model.

We will estimate the number of times that she spins a 6 as the expected value of this random variable.

Recall that if we have X as a binomial random variable of n trials with a probability of success of p, then it's expected value is np.

Then , in this case, with n=50 and p=1/6 we expect to have  number of times of having a 6, which is 8.33.

Help ! I don’t know if I have it correct. Can somebody check it out. I got 81/65536 which I know has to be incorrect.

Answers

Answer:  9

Work Shown:

In the numerator, we have 2^2*x^2, which is really just 4x^2. Replace x with 3 and we get 4*x^2 = 4*3^2 = 36.

For the denominator, xy^2, we get

x*y^2 = 3*2^2 = 12

So far we have,

[tex]\frac{2^2x^2}{xy^2} = \frac{4x^2}{xy^2} = \frac{36}{12} = 3\\\\\text{ or simply} \\\\\frac{2^2x^2}{xy^2} = 3[/tex]

when x = 3 and y = 2.

Square both sides to end up with...

[tex]\frac{2^2x^2}{xy^2} = 3\\\\\left(\frac{2^2x^2}{xy^2}\right)^2 = 3^2\\\\\left(\frac{2^2x^2}{xy^2}\right)^2 = 9[/tex]

What is the period of the sinusoidal function?

Answers

Answer:

4

Explanation:

If one period is just how far it takes for one wave to go up and come back down, then we can see one of the waves of the graph starts at 2.5 and ends at 6.5, making the period 4. Of course, there's a more proper formula to it, but this is the easier way my teacher taught me.
Happy studying!

The initial number of bacteria in the dish was 1,150. The amount of bacteria doubles at the end of each hour. Write a function b(t) that would represent this relationship after t hours. Use this function to determine how many bacteria would be in the dish after 10 hours and write it only as a number without units.

Answers

Answer:

[tex]B(t) = 1150*(2)^{t}[/tex]

After 10 hours: 1,177,600

Step-by-step explanation:

The number of bacteria after b hours is given by the following equation:

[tex]B(t) = B(0)(1+r)^{t}[/tex]

In which B(0) is the initial number of bacteria and r is the rate that it increases.

The initial number of bacteria in the dish was 1,150. The amount of bacteria doubles at the end of each hour.

This means that [tex]B(0) = 1150, B(1) = 2*1150[/tex]

So

[tex]B(t) = B(0)(1+r)^{t}[/tex]

[tex]2*1150 = 1150(1+r)^{1}[/tex]

[tex]1 + r = 2[/tex]

[tex]r = 1[/tex]

So

[tex]B(t) = 1150*(2)^{t}[/tex]

After 10 hours:

[tex]B(10) = 1150*(2)^{10} = 1177600[/tex]

1,177,600 bacteria after 10 hours.

please ASAP , giving BRAINLIEST if correct.

Answers

Answer:

B. -3(4x + 1) (x - 4)

Step-by-step explanation:

Out of the other answer choices, "B," is the only that factorizes correctly and ends up with the correct factorization (It already gives you the break-down of the trinomial).

However, if you're unsure about the answer, you can always take the end result: -3(4x + 1) (x - 4), and multiply it together to see if you can end up with the original trinomial: [tex]-12x^2 + 45x + 12[/tex]

The average temperature of the atmosphere in the world is approximated as a function of altitude by the relation Tatm=288.15−6.5z where Tatm is the temperature of the atmosphere in K, and z is the altitude in km with z = 0 at sea level. Determine the average temperature of the atmosphere outside an airplane that is cruising at an altitude of 12600 m. The average temperature of the atmosphere outside an airplane is

Answers

Answer:

The average temperature of the atmosphere outside the airplane is [tex]206.25\,K[/tex].

Step-by-step explanation:

The average temperature of the atmosphere outside an airplane flying at an altitude of 12600 meters is computed by evaluating the linear function:

[tex]T (12.6\,km) = 288.15 - 6.5\cdot (12.6\,km)[/tex]

[tex]T (12.6\,km) = 206.25\,K[/tex]

The average temperature of the atmosphere outside the airplane is [tex]206.25\,K[/tex].

What’s the volume of the pic

Answers

Answer:

100[tex]\pi[/tex] cubic cm

Step-by-step explanation:

The volume of a cone can be represented by the formula [tex]\frac{1}{3} \pi r^{2} h[/tex]. Since we know the radius is 5, all we need to find id the height. To do that, we can use the Pythagorean theorem, and see that the height is equal to 12. Plugging the numbers into the formula gives us:

[tex]V =\frac{1}{3} \pi (5^{2}) (12)[/tex]

[tex]V = 100\pi[/tex]

HOPE THIS HELPED! :)

A recent survey showed 3 out of 65 Happy Meals contained a “special” prize. How many “special” prizes should a person expect to win if 130 Happy Meals were purchased?

Answers

Answer:

6

Step-by-step explanation:

The ratio would be 3:65, so to get it to ?:130 you would multiply by 2 (65•2=130). So all you have to do is do 3•2=6 to get the correct ratio which is 6:130. So that answer would be 6.

A national survey of companies included a question that asked whether the customers like the new flavor of a cola from company A. The sample results of 1000 customers, and 850 of them indicated that they liked the new flavor. The 98% confidence interval on the population proportion of people who like the new flavor is _______________.

Answers

Answer:

The 98% confidence interval on the population proportion of people who like the new flavor is (0.8237, 0.8763).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 1000, \pi = \frac{850}{1000} = 0.85[/tex]

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.85 - 2.327\sqrt{\frac{0.85*0.15}{1000}} = 0.8237[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.85 + 2.327\sqrt{\frac{0.85*0.15}{1000}} = 0.8763[/tex]

The 98% confidence interval on the population proportion of people who like the new flavor is (0.8237, 0.8763).

In ΔXYZ, the measure of ∠Z=90°, the measure of ∠X=57°, and XY = 8 feet. Find the length of YZ to the nearest tenth of a foot.

Answers

Answer:

21

Step-by-step explanation:

Answer:

6.7

Step-by-step explanation:

If the base-ten blocks shown are to be divided into 5 equal groups, what should be done first?

Answers

Answer:

2 divided

Step-by-step explanation:

What’s the correct answer for this?

Answers

Answer:

A number, such as 10 is a composite number because it is even.

The ten because it’s even

Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing! CHECK ALL THAT APPLY

Answers

Answer:

E 39

Step-by-step explanation:

x+6 = 45

Subtract 6 from each side

x+6-6 = 45-6

x = 39

what is the sum of this arithmetic series? 586+564+542+...+212

Answers

Answer:

Basically it's asking for the sum of 212 + 216 + 220 + ..... 586

Each number is 22 more than the previous one.

Therefore the sum will be 212 + (212+22) + (212+22*2) + (212+22*3)

the amount of numbers from 212 through 586 is 18.

Therefore we will need 212 plus 212 * 17 = 3,816 *******************

We will also need all those 22's.

We must add 22 *1 plus 22*2 plus 22*3 ..... plus 22*17

Which equals 22 + 44 + 66 + 88 ... 374

Which totals 3,366 *****************

So, we total 3,816 + 3,366 which equals 7,182

Step-by-step explanation:

 

[tex]\displaystyle\bf\\Sum=586+564+542+...+212\\\\Sum=212+234+256+...+586\\\\\textbf{We calculate the number of terms (n):}\\\\n=\frac{586-212}{22}+1=\frac{374}{22}+1=17+1=18\\\\\boxed{\bf~n=18~terms}\\\\Sum=\frac{n(586+212)}{2}\\\\Sum=\frac{18\times 798}{2}\\\\Sum=9\times798\\\\\boxed{\bf~Sum=7182}[/tex]

 

A mirror frame in the shape of an oval is shown below. The ends of the frame form semicircles: (5 points)

An oval is formed by a rectangle with semicircles at each end. The length of the rectangle is 62 inches. The width of the rectangle is 27 inches.
Which of the following is the perimeter of the inner edge of the frame?

Answers

Answer:

696.265 inches

Step-by-step explanation:

Radius = 27/2 = 13.5

2 semicircles + 2 lengths

(3.14 × 13.5²) + 2(62)

696.265 inches

Answer:

696

Step-by-step explanation:

Find the arc length of a partial circle with a radius of 5
Will mark brainlist! pleaseeee

Answers

Answer:23.55

Step-by-step explanation:

radius=r=5

Φ=360-90

Φ=270

π=3.14

Length of arc=Φ/360 x 2 x π x r

length of arc=270/360 x 2 x 3.14 x 5

Length of arc=0.75 x 2 x 3.14 x 5

Length of arc=23.55

Answer:

23.55 units

Step-by-step explanation:

Hope this helps!


An ice chest contains 4 cans of apple juice, 5 cans of grape juice, 8 cans of orange juice, and 6 cans of mango juice. Suppose that you reach into the container and
randomly select three cans in succession. Find the probability of selecting three cans of apple juice.







Please help I’m stressing and it’s my last question ‼️‼️

Answers

Answer:

(19/23)(18/22)(17/21) or 969/1771

Step-by-step explanation:

You add up the total number of cans, giving you 6+4+5+8 = 23 cans total. From there, you only have 4 cans of grape juice. That means 19 of these cans aren't grape, meaning you are checking the probability of choosing these three times in a row.

The probability of selecting the first can and it not being grape is 19/23. Then, when you select another can in succession, without replacing the cans, you now only have 22 cans left, meaning 18 also will not be grape, so it will be a 18/22 chance. Then, selecting your third can, 21 cans are left, and 17 of them are not grape since you have not yet chosen one, giving you 17/21. You multiply them together.

Hopefully I reduced the fraction properly (or even did this question properly)

What type of triangle is shown in the image?


Acute triangle
Right triangle
Equilateral triangle
Obtuse triangle

Answers

The triangle is an Obtuse triangle

The type of triangle shown in the image is the Obtuse triangle.

What is an obtuse triangle?

A triangle is said to be an obtuse triangle if one of its angles measures more than 90 degrees.

In the given diagram, one of the angles measures more than 90 degrees.

So, the given triangle is an obtuse triangle.

Hence, the type of triangle shown in the image is the Obtuse triangle.

To get more about obtuse triangles visit:

https://brainly.com/question/5023725

the stained glass below shows bilateral symmetry. The two overlapping squares are congruent. What is the area of the window?

Answers

Answer:

  116.82 square inches

Step-by-step explanation:

The overall shape is that of a 10-inch square with four triangles attached. Each of those is an isosceles right triangle with leg lengths of 2.9 inches.

The area of the four triangles is ...

  total triangle area = 4(1/2)(2.9 in)(2.9 in) = 16.82 in²

The area of the 10-inch square is ...

  square area = (10 in)² = 100 in²

Then the total window area is ...

  window area = 16.82 in² +100 in²

  window area = 116.82 in²

The median and mode of this set of data (23,13,17,11,11)

Answers

Answer:

Mode: 11

Median: 13

Answer:

(23, 13, 17, 11, 11):

Median: 13

Arithmetic mean: 15

Geometric mean: 14.380735416546

Harmonic mean: 13.848764056076

Mode: 11

Standard deviation: 4.5607017003966

Variance: 20.8

Mean Absolute Deviation: 4

Range: 12

Interquartile range: 9

Lower quartile: 11

Upper quartile: 20

Quartile deviation: 4.5

Population size:5

Which line is parallel to y = 1/2x -5

Answers

Answer:

Any line with a slope of 1/2 would be parallel to that line.

Step-by-step explanation:

A line is parallel when the slopes are the same, causing the situation where the lines will never intercept. The line in the question has a slope of 1/2, so a parallel line must have that same slope.

A box below needs to be painted. ​

​How many square inches of paint will be needed to cover the entire surface?



A
80/12 in2
B
61/9 in2
C
49/5 in2
D
77/55 in2

Answers

Answer: c

Step-by-step explanation:

Answer:B

Step-by-step explanation:

Sally wants to fill ten 8-inch tea glasses. How much tea does she need?
A) 80 ounces
B) 40 ounces
C) 80 cubic inches
D) Not enough information to answer

Answers

Answer

I believe C considering cubic mass

Answer:

D

Step-by-step explanation:

A boat sailed 560 km in 8 hours. It took three hours to travel
the first 150 km. What was its average speed for the
remaining journey?
km/h​

Answers

Step-by-step explanation:

150 km in 3 hours

= 150 ÷ 3 = 50km/h

Remaining distance = 560 - 150 = 410

Remaining hours = 8 - 3 = 5

Then average speed = 410 ÷ 5 = 82 km / h

at the dade county fair, the williams family bought 6 burgers and 4 gatorades for $14.10. the jackson family bought 3 burgers and 4 gatorades for $9.15.find the price of a burger and the price of a gatorade sn: i need help like really fast

Answers

Answer:

The cost of a burger is $1.65 and the cost of a gatorade is $1.05.

Step-by-step explanation:

We can solve this question using a system of equations.

I am going to say that:

x is the price of a burger.

y is the price of a gatorade.

6 burgers and 4 gatorades for $14.10

This means that [tex]6x + 4y = 14.10[/tex]

3 burgers and 4 gatorades for $9.15.

This means that [tex]3x + 4y = 9.15[/tex]

Will write 4y as a function of x.

[tex]4y = 9.15 - 3x[/tex]

Replacing in the first equation:

[tex]6x + 4y = 14.10[/tex]

[tex]6x + 9.15 - 3x = 14.10[/tex]

[tex]3x = 4.95[/tex]

[tex]x = \frac{4.95}{3}[/tex]

[tex]x = 1.65[/tex]

And

[tex]4y = 9.15 - 3x[/tex]

[tex]4y = 9.15 - 3*1.65[/tex]

[tex]4y = 4.2[/tex]

[tex]y = \frac{4.2}{4}[/tex]

[tex]y = 1.05[/tex]

The cost of a burger is $1.65 and the cost of a gatorade is $1.05.




Aiden wanted to model -15 + 15 = 0 on the number line. He first drew an arrow 15 units long starting from zero that pointed to the left. He then draws another arrow 15 units long starting from zero that points to the right. What error did Aiden make?
A. The first arrow he drew should have pointed to the right to represent -15.
B. The second arrow he drew should have pointed to the left to represent 15.
C. The first arrow he drew should have started at -15 instead of 0.
D. The second arrow he drew should have started at -15 instead of 0.

Answers

Answer:

I think it's D

Step-by-step explanation:

The number never goes over 0 so there is no need to put anything above 0

Answer:

the answer is D. The second arrow he drew should have started at -15 instead of 0.

Step-by-step explanation:

was on a test I took and got 100

How many factors does 12 have

Answers

Answer:

6 if you count 1 and 12

Step-by-step explanation:

1*12

6*2

3*4

(1,12,3,4,6,2)

(12,1) (1,12) (3,4) (4,3) (6,2) (2,6)
2 negatives make a positive**
(-12,-1) (-1,-12) (-3,-4) (-4,-3) (-6,-2) (-2,6)

please help me with this question

Answers

Answer:  yes

Step-by-step explanation:

Answer:

Step-by-step explanation:

A = 3

B = 5.5

C = 11

A company makes car batteries and claims 80% of its ABC batteries are good for 70 months or longer. Assume that this claim is true. Let p ˆ be the proportion in a sample of 100 such ABC batteries. What is the probability that this sample proportion is within 0.05 of the population proportion.

Answers

Answer:

78.88% probability that this sample proportion is within 0.05 of the population proportion

Step-by-step explanation:

We need to understand the normal probability distribution and the central limit theorem to solve this question.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For proportion p in a sample of size n, we have that [tex]\mu = p, s = \sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In this question:

[tex]p = 0.8, n = 100[/tex]

So

[tex]\mu = 0.8, s = \sqrt{\frac{0.8*0.2}{100}} = 0.04[/tex]

What is the probability that this sample proportion is within 0.05 of the population proportion.

This is the pvalue of Z when X = 0.8 + 0.05 = 0.85 subtracted by the pvalue of Z when X = 0.8 - 0.05 = 0.75.

X = 0.85

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.85 - 0.8}{0.04}[/tex]

[tex]Z = 1.25[/tex]

[tex]Z = 1.25[/tex] has a pvalue of 0.8944.

X = 0.75

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.75 - 0.8}{0.04}[/tex]

[tex]Z = -1.25[/tex]

[tex]Z = -1.25[/tex] has a pvalue of 0.1056.

0.8944 - 0.1056 = 0.7888

78.88% probability that this sample proportion is within 0.05 of the population proportion

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