PLWASE HELP GEOMETRY
A hot-air balloon is tied to the ground with two taut ropes. One rope is directly under the balloon and makes a right
angle with the ground. The other rope forms an angle of 60° with the ground. Which statements are correct?

Hey there!

I hope you have a great one too :)

Answer:

[tex]a) x = k \times \frac{1}{y^2} \ , \ where \ k \ is \ a \ constant\\\\b) x = 3, \ when\ y\ =\ 10\\\\c) y = 10, \ when \ x = 3[/tex]

Step-by-step explanation:

a)

[tex]x \ \alpha \ \frac{1}{y^2}\\\\x = k \times \frac{1}{y^2}\\\\[/tex]                [tex][ \ where \ k \ is \ a \ constant \ ][/tex]

Find k.

Given x = 12, y = 5,

[tex]12 = k \times \frac{1}{5^2}\\\\k = 12 \times 25 = 300[/tex]

b)

Find x.

Given y = 10

We have k = 300

[tex]x = k \times \frac{1}{y^2}\\x = 300 \times \frac{1}{10^2} \\\\x= \frac{300}{100} = 3[/tex]

c)

Find y

Given x = 3

We have k = 300

[tex]x = k \times \frac{1}{y^2}\\\\3 = 300 \times \frac{1}{y^2}\\\\\frac{1}{y^2} = \frac{3}{300}\\\\\frac{1}{y^2} = \frac{1}{100}\\\\y^2 = 100\\\\y = \sqrt{100} = 10[/tex]

Answer:

a) = 7/10

b)= 9/10

c)= 1  1/10

Step-by-step explanation:

a) green and a 2 = 1/2 + 1/5 = 0.7 = 7/10

b) red and an even number = 1/2 + 2/5 = 0.9 = 9/10

c) green and a prime number = 1/2 + 3/5 = 1.1 = 1  1/10

Answer: C is the correct option.

Step-by-step explanation:

Confidence interval for population mean:

[tex]\overline{x}\pm E[/tex]

, where [tex]\overline{x}[/tex] = Sample mean

E = Margin of error

Given confidence interval : 150 ± 3.29

Here , [tex]\overline{x}=150, E=3.29[/tex]

Since the sample mean is the best estimate for the population mean.

Thus, the correct notation is [tex]\overline{x}=150[/tex]

i.e. C is the correct option.

Answer:

Answer is A

Step-by-step explanation:

Answer:

y = 27

Step-by-step explanation:

The sum of the two angles is a right angle, which is 90 degrees

y+63 = 90

y = 90-63

y =27

Answer:

The measures of angle y is 30 °.

Step-by-step explanation:

We know that, the sum of two side of right angle is 90 °.

60 ° + y = 90 °

subtract 60 ° from each side

y = 90 ° - 60

y = 30 °

Therefore, the measures of angle y is 30°.

Answer:

IIII..I.I.I.I.I.I.I.I.I.I.I.I.I.I.I.I.I.I.I.I..II..II.I.

Step-by-step explanation:

EAS1

Answer:

112 bags are contained in

Step-by-step explanation:

a bag which is 70 kg

Answer:

28

Step-by-step explanation:

28/2=14

28/4=7

28/7=4

28 is an even number

Step-by-step explanation:

28 is the answer

28 is a number between 20 and 30

and divisible by

28/2=14

28/4=7

28/7=4

Answer:

1/3 x 70

= $ 23 / 1/3

= 70 - 23 / 1/3

= $ 46 /2/3

Answer:

[tex]\displaystyle y = 2sin\:1\frac{1}{3}\pi{x} + 3[/tex]

Step-by-step explanation:

[tex]\displaystyle \boxed{y = 2cos\:(1\frac{1}{3}\pi{x} - \frac{\pi}{2}) + 3} \\ \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 3 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{3}{8}} \hookrightarrow \frac{\frac{\pi}{2}}{1\frac{1}{3}\pi} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{1\frac{1}{2}} \hookrightarrow \frac{2}{1\frac{1}{3}\pi}\pi \\ Amplitude \hookrightarrow 2[/tex]

OR

[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 3 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{1\frac{1}{2}} \hookrightarrow \frac{2}{1\frac{1}{3}\pi}\pi \\ Amplitude \hookrightarrow 2[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although the exercise told you to write the sine equation based on the speculations it gave you, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 2cos\:1\frac{1}{3}\pi{x} + 3,[/tex]in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph on the right] is shifted [tex]\displaystyle \frac{3}{8}\:unit[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle \frac{3}{8}\:unit,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\frac{3}{8}} = \frac{\frac{\pi}{2}}{1\frac{1}{3}\pi}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 2cos\:(1\frac{1}{3}\pi{x} - \frac{\pi}{2}) + 3.[/tex]Now, with all that being said, in this case, sinse you ONLY have the exercise to wourk with, take a look at the above information next to [tex]\displaystyle Wavelength\:[Period].[/tex]It displays the formula on how to define each wavelength of the graph. You just need to remember that the B-term has [tex]\displaystyle \pi[/tex]in it as well, meaning both of them strike each other out, leaving you with just a fraction. Now, the amplitude is obvious to figure out because it is the A-term, so this is self-explanatory. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 3,[/tex]in which each crest is extended three units beyond the midline, hence, your amplitude. So, no matter what the vertical shift is, that will ALWAYS be the equation of the midline, and if viewed from a graph, no matter how far it shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Answer:

[tex]P(x > 0.28) = 1[/tex]

Step-by-step explanation:

Given

[tex]p = 33\%[/tex] --- orders from first time customer

[tex]n =163[/tex] --- samples

Required

[tex]P(x >0.28)[/tex]

First, calculate the mean

[tex]\bar x = np[/tex]

[tex]\bar x = 163 * 33\%[/tex]

[tex]\bar x = 53.79[/tex]

Next, the standard deviation

[tex]\sigma = \sqrt{\bar x * (1 - p)[/tex]

[tex]\sigma = \sqrt{53.79* (1 - 33\%)[/tex]

[tex]\sigma = \sqrt{53.79* (1 - 0.33)[/tex]

[tex]\sigma = \sqrt{53.79* 0.67[/tex]

[tex]\sigma = 6.00[/tex]

For [tex]P(x >0.28)[/tex],

The z score is:

[tex]z = \frac{x - \bar x}{\sigma}[/tex]

[tex]z = \frac{0.28 - 53.79}{6}[/tex]

[tex]z = \frac{-53.51}{6}[/tex]

[tex]z = -8.92[/tex]

So:

[tex]P(x > 0.28) = P(z > -8.92)[/tex]

From z probability:

[tex]P(z > -8.92) =1[/tex]

Hence:

[tex]P(x > 0.28) = 1[/tex]

Answer:

B.10

Step-by-step explanation:

15=1/2b(3)

30=3b

10= base

Answer:

0.02x^2=6.28

0.02x^2/0.02 = 6.28/0.02

x^2 = 314

Exact form: x = [tex]\sqrt{314}, -\sqrt{314},[/tex]

Hope this helps!

Answer:

The first one.

Step-by-step explanation:

The correct scientific notation for the first option would make it a decimal (1.1), so it is not in the correct scientific notation.

Answer:

the percent above the cost price is 10%

Answer:

2022 students

Step-by-step explanation:

15:1

? :179

?=179×15

=2685

2685-663=2022

Answer:

2022 students

Step-by-step explanation:

15:1

?:179

?=179×15

=2685

2685-663

=2022

the total number of second-, third-, and fourth-year students are 2022 students.

Answer:

A 91.

Step-by-step explanation:

[tex]\frac{75+87+90+88+79+x}{6}=85\\\\\frac{419+x}{6}=85\\\\(\frac{419+x}{6})6=85*6\\\\419 + x = 510\\\\419-419+x=510-419\\\\\boxed{x = 91}[/tex]

9514 1404 393

Answer:

Step-by-step explanation:

The amortization formula can be used to find the payment value.

  A = P(r/2)/(1 -(1 +r/2)^(2n))

where P is the principal amount at the beginning of the loan period, r is the annual interest rate, n is the number of years remaining on the loan

The value of A in this scenario is the semi-annual payment.

Initially, the interest rate is 0.055 and the number of years remaining is 25.

After the first 5-year period, the interest rate goes up by 12%, so is multiplied by a factor of 1.12 to become 6.16% per year. The same growth factor is applied to the interest rate at the beginning of each 5-year period.

Of course, the number of years remaining is decreased by 5 years at the beginning of the next 5-year period.

__

The Principal remaining at the end of each 5-year period is the starting principal for the next period. It is calculated from ...

  FV = P(1 +r/2)^10 -A((1 +r/2)^10 -1)/(r/2)

Where P is the starting principal, A is the loan payment as calculated above, and r is the annual interest rate.

__

These formulas are built into spreadsheet functions, so the desired set of loan payments can be calculated easily by that technology. The result is attached. In the "# pmts" column is the value used to amortize the loan for the 5-year period. The semiannual payment is calculated as though the loan would be completely paid off in that number of payments, keeping the same interest rate for the duration. Of course, that payment series is interrupted and the loan recalculated at the beginning of the next 5 years.

The half-yearly payments for each 5-year interval are ...

  $33,336.83

  $35,176.68

  $36,869.23

  $38,266.75

  $39,158.08

_____

Additional comment

The values displayed in the spreadsheet are rounded to the values shown. The values used in calculation have 14 or more significant digits. This means the numbers here may vary from those provided by a lending institution. In the real world, the principal and interest values are rounded to cents with each payment, so actual results may vary by a few cents either way.

Answer:

B

Step-by-step explanation:

1) initial circumference

radius * 2 * pi = 24 * pi = 75,398224

2) final circumference

diameter * pi = 48 * pi = 150,796447

150,796447 - 75,398224 = 75.36 m

Answer:

$78.12

Step-by-step explanation:

10÷62×100%

=16.12

Therefore price of gold necklace ($62) + 10% tax ($16.12) will be equal to total cost which is $78.12

Answer:

-7

Step-by-step explanation:

3 v + 2 x

3 ( - 1) + 2 ( -2)

-3 - 4

-7

Answer:

1/6

Step-by-step explanation:

For Omar to drive, he has to get a six when a die is rolled ;

The probability that Omar will get to drive his car is :

Required outcome = (6) = 1

Total possible outcomes = (1,2,3,4,5,6)

P(rolling a 6) = required outcome / Total possible outcomes

P(rolling a 6) = 1/6

Probability of Omar driving his car is 1/6

Answer:

It would be the letter B :)