Verizon charges a $40 sign-up fee and the $60 a month for their new hotspot. T-Mobile
charges $100 sign-up fee and then $45 per month for their new hotspot. After how many
months of service will the two company's fees be the same?

Answers

Answer 1

Step-by-step explanation:

Start Unlimited: 

$70 for one line

$60 for two lines

$45 for three lines

$35 for four lines

Play More Unlimited: 

$80 for one line

$70 for two lines

$55 for three lines

$45 for four lines

Do More Unlimited: 

$80 for one line

$70 for two lines

$55 for three lines

$45 for four lines

Get More Unlimited: 

$90 for one line

$80 for two lines

$65 for three lines

$55 for four lines

Answer 2

Answer:

4 months

As we show that ;

40 + (60x * 4)  = 280

100 + (45x * 4) = 280

but in simultaneous equations Verizon must be set equal to 240 being 80 x 3

and T mobile must be equal to 45 x 4 = 180

so that 240+ 180 = 420 to find 4

This would be a method on distribution as "60 sign up is 1/3 more than 1st equation.

Step-by-step explanation:

This is a simultaneous equation but trial and error is below to prove all is true.

step 1 make all equations same

40s + (60x)      * 3 = 180x  LCM   = 80 x 3   =  1   1/3 of 60

100s + (45x)     * 4 = 180x LCM   = 45  x 4   =  1 of 45 as verizon charges 1/3 more sign up.

100s- 40s + 180x = (180x) =  240 + 180

60s + 180x = 420

s = 60

so our equations must each end with 420

when we get 60s + 180x = 420  then

420 - 180 = 240

240/60 =  4

x = 4 months

Verizon = 1st and T mobile = 2nd

40 + (60x * 5)  = 340

100 + 45x * 5 = 325

with $15 out after 5 months so we try 6 months

40 + (60x * 6)  = 400

100 + 45x * 6 = 370

and see this is increasing in difference, so try a smaller value of months..

We try 4 months;

40 + (60x * 4)  = 280

100 + (45x * 4) = 280


Related Questions

Which figure always has exactly one line of symmetry?
A. rectangle
B. trapezoid
C. isosceles right triangle
D. circle

Answers

Trapezoid only has one because sides are slanted

A shape of a trapezoid has exactly one line of symmetry. The correct option is B.

What is a trapezoid?

An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.

A balanced and proportionate likeness between an object's two halves is referred to as symmetry in geometry. It implies that one half is the other's mirror image.

A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.

Therefore, the shape of a trapezoid has exactly one line of symmetry. The correct option is B.

To know more about Trapezoids follow

https://brainly.com/question/1410008

#SPJ5

Given the central angle, name the arc formed.
Major arc for ∠EQD

A. EQDˆ
B. GDFˆ
C. EGDˆ
D. EDˆ

Answers

9514 1404 393

Answer:

  C. EGD

Step-by-step explanation:

A major arc is typically named using the end points and a point on the arc. Here, the end points are E and D, and points on the major arc include C, G, and F. The major arc ED could be named any of

arc ECDarc EGD . . . . choice Carc EFD

Of course, the reverse of any of these names could also be used: DCE, DGE, DFE.

Given f(x) = 4x - 3 and g(x) = 9x + 2, solve for (f + g)(x).

Answers

f(x)=4x-3g(x)=9x+2

[tex]\\ \sf\longmapsto (f+g)(x)[/tex]

[tex]\\ \sf\longmapsto f(x)+g(x)[/tex]

[tex]\\ \sf\longmapsto 4x-3+9x+2[/tex]

[tex]\\ \sf\longmapsto 4x+9x-3+2[/tex]

[tex]\\ \sf\longmapsto 13x-1[/tex]

Answer:

13x - 1

Step-by-step explanation:

f(x) + g(x) = 4x - 3 + 9x + 2

f(x) + g(x) = 4x+9x + 2 - 3

f(x) + g(x) = 13x - 1

on the same graph draw line 2y-x=10 and y=3x​

Answers

Answer:

Step-by-step explanation:

Suppose that 22 inches of wire costs 66 cents.
At the same rate, how much (in cents) will 17 inches of wire cost?
cents
Х
?

Answers

Answer:

51 cents for 17 inches of wire

Step-by-step explanation:

22 = 66

17 = x

22x = 66 * 17

22x = 1122

x = 51 cents

or

22 inches costs 66 cents

1 inch costs 3  cents (66 / 22 = 3  cents)

17 inches costs 51  cents (17 * 3 = 51 cents)

The weekly amount of money spent on maintenance and repairs by a company was observed, over a long period of time, to be approximately normally distributed with mean $440 and standard deviation $20. How much should be budgeted for weekly repairs and maintenance so that the probability the budgeted amount will be exceeded in a given week is only 0.1

Answers

Answer:

$465.6 should be budgeted.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with mean $440 and standard deviation $20.

This means that [tex]\mu = 440, \sigma = 20[/tex]

How much should be budgeted for weekly repairs and maintenance so that the probability the budgeted amount will be exceeded in a given week is only 0.1?

The 100 - 10 = 90th percentile should be budgeted, which is X when Z has a p-value of 0.9, so X when Z = 1.28. Then

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

[tex]1.28 = \frac{X - 440}{20}[/tex]

[tex]X - 440 = 1.28*20[/tex]

[tex]X = 465.6[/tex]

$465.6 should be budgeted.

In an assembly-line production of industrial robots, gearbox assemblies can be installed in one minute each if holes have been properly drilled in the boxes and in ten minutes if the holes must be redrilled. Twenty-four gearboxes are in stock, 6 with improperly drilled holes. Five gearboxes must be selected from the 24 that are available for installation in the next five robots. (Round your answers to four decimal places.) (a) Find the probability that all 5 gearboxes will fit properly. (b) Find the mean, variance, and standard deviation of the time it takes to install these 5 gearboxes.

Answers

Answer:

The right answer is:

(a) 0.1456

(b) 18.125, 69.1202, 8.3139

Step-by-step explanation:

Given:

N = 24

n = 5

r = 7

The improperly drilled gearboxes "X".

then,

⇒ [tex]P(X) = \frac{\binom{7}{x} \binom {17}{5-x}}{\binom{24}{5}}[/tex]

(a)

P (all gearboxes fit properly) = [tex]P(x=0)[/tex]

                                               = [tex]\frac{\binom{7}{0} \binom{17}{5}}{\binom{24}{5}}[/tex]

                                               = [tex]0.1456[/tex]

(b)

According to the question,

[tex]X = 91+5[/tex]

Mean will be:

⇒ [tex]\mu = E(x)[/tex]

       [tex]=E(91+5)[/tex]

       [tex]=9E(1)+5[/tex]

       [tex]=9.\frac{nr}{N}+5[/tex]

       [tex]=9.\frac{5.7}{24} +5[/tex]

       [tex]=18.125[/tex]

Variance will be:

⇒ [tex]\sigma^2=Var(X)[/tex]

         [tex]=V(9Y+5)[/tex]

         [tex]=81.V(Y)[/tex]

         [tex]=81.n.\frac{r}{N}.\frac{N-r}{N}.\frac{N-n}{N-1}[/tex]

         [tex]=81.5.\frac{7}{24}.\frac{24-7}{24}.\frac{24-5}{24-1}[/tex]

         [tex]=69.1202[/tex]

Standard deviation will be:

⇒ [tex]\sigma = \sqrt{69.1202}[/tex]

       [tex]=8.3139[/tex]      

what is the volume of a cube with a length of a 10cm,
a width of 8cm and a height of 8cm​

Answers

Answer:

640

Step-by-step explanation:

Volume = Length • Width • Height

Volume = 10 • 8 • 8

Volume = 640

Answer:

640

Step-by-step explanation:

muntiply all the number length width height

Team A scored 30 points less than four times the number of points that Team B scored. Team C scored 61 points more than half of the number of points that Team B scored. If Team A and Team C shared in the victory, having earned the same number of points, how many more points did each team have than Team B?

Answers

Answer:

team a and team c scored 74 points which is 48 points more than team b, scoring 26 points.

Step-by-step explanation:

Which of the following inequalities matches the graph?
10
6
-10
Oxs-1
Ox>-1
Oys-1
Oy 2-1

Answers

Answer:

y > -1

Step-by-step explanation:

the line is going across the y axis and is everything above -1

Each course at college X is worth either 2 or 3 credits. The members of the men's swim team are taking a total of 48 courses that are worth a total of 107 credits. How many 2-credit courses and how many 3-credit courses are being taken?

Answers

Answer:

Let the number of courses that are worth 3 credits each be x and those worth 4 credits be y. With the given information, you can write the following equations:  

x + y = 48

3x + 4y = 155

 

You can solve the above equations by method of elimination/substitution

x + y = 48 ⇒ x = 48 - y (Now, substitution this equation into 3x + 4y = 155)

3(48 - y) + 4y = 155

144 -3y + 4y = 155

y + 144 = 155

y = 11

 

Now plug this solution back into x = 48 - y  

x = 48 - 11 = 37  

 

Check work (by plugging the solutions back into the 3x + 4y and see if it's equal to 155):

3(37) + 4(11) = 155

Answer: There are 37 of the 3-credit course and 11 of the 4-credit course

find the measure of d

Answers

You’re looking at an 90 degree angle. So you would just subtract 14 degrees from 90 degrees. Your answer is 76 degrees

After leaving an airport, a plane flies for 2 hours on a course of 60 degrees at a speed of 200 kilometers per hour. The plane then flies for 3 hours on a course of 210 degrees at a speed of 100 kilometers per hour What is the distance of the airport from the plane in kilometers? Round to the nearest tenth​

Answers

Answer: 205.3

I suppose all measures of angles are done from the same axis (for example x-axis)

Step-by-step explanation:

You just have to use the theorem of Al'Kashi:

[tex]d^2=400^2+300^2-2*300*400*cos(30^o)\\\\d\approx{205.3(km)}[/tex]

f=((-1,1),(1,-2),(3,-4)) g=((5,0),(-3,4),(1,1),(-4,1)) find (fg)(1)

Answers

Answer:

f(g(1)) = - 2

Step-by-step explanation:

Find g(1) then use the value obtained to find f(x)

g(1) = 1 ← value of y when x = 1 (1, 1 ) , then

f(1) = - 2 ← value of y when x = 1 (1, - 2 )

Assume the random variable X is normally distributed with mean μ = 50 and standard deviation σ = 7. Compute the probability

P(35 < X < 58)= ________

Answers

Answer:

Probability-Between    .8574 = 85.74%

Step-by-step explanation:

Z1=-2.14 Z2=1.14

*x-1 35

*x-2  58

*µ 50

*σ 7

Which of the following theorems verifies that AABC - ASTU?
A. AA
B. HL
C. HA
D. LL

Answers

Answer:

AA

Step-by-step explanation:

See In Triangle ABC and Triangle STU

[tex]\because\begin{cases}\sf \angle A=\angle S=90° \\ \sf \angle B=\angle T=31°\end{cases}[/tex]

Hence

[tex]\sf \Delta ABC~\Delta STU(Angle-Angle)[/tex]

By AA similarity  triangle ABC is similar to triangle SUT. Therefore, option A is the correct answer.

What are similar triangles?

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

In the given triangle ABC, ∠C=180°-90°-31°

∠C=59°

In the given triangle SUT, ∠U=180°-90°-31°

∠U=59°

Here, ∠B=∠T (Given)

∠C=∠U (Obtained using angle sum property of a triangle)

So, by AA similarity ΔABC is similar to ΔSUT.

Therefore, option A is the correct answer.

To learn more about the similar triangles visit:

https://brainly.com/question/25882965.

#SPJ7

If it takes 5 years for an animal population to double, how many years will it take until the population
triples?

Answers

9514 1404 393

Answer:

  7.92 years

Step-by-step explanation:

We want to find t such that ...

  3 = 2^(t/5)

where 2^(t/5) is the annual multiplier when doubling time is 5 years.

Taking logs, we have ...

  log(3) = (t/5)log(2)

  t = 5·log(3)/log(2) ≈ 7.92 . . . years

It will take about 7.92 years for the population to triple.

Question
(X-5y/y3)-1=

Answers

Answer:

[tex]x = y^3+5y[/tex]

Step-by-step explanation:

Complete question

[tex]\frac{x - 5y}{y^3} - 1=0\\[/tex]

Required

Solve for x

We have:

[tex]\frac{x - 5y}{y^3} - 1=0[/tex]

Collect like terms

[tex]\frac{x - 5y}{y^3} = 1[/tex]

Multiply through by [tex]y^3[/tex]

[tex]x - 5y = y^3[/tex]

Make x the subject

[tex]x = y^3+5y[/tex]

HELP ASAP!!
The equation (blank) has no solution​

Answers

Answer:

Just to recap, an equation has no solution when it results in an incorrect "equation".

For  example:

Equation: x+3 = x+4

Subtract x: 3 = 4???

But clearly, 3 is not equal to 4, so this equation has NO SOLUTION.

Now onto our problem:

13y+2-2y = 10y+3-y

11y+2 = 9y+3

2y=1

y=1/2

9(3y+7)-2 = 3(-9y+9)

27y+61 = -27y+27

54y = -34

y = -34/54

32.1y+3.1+2.4y-8.2=34.5y-5.1

34.5-5.1=34.5y-5.1

5.1=5.1

infinite solutions

5(2.2y+3.4) = 5(y-2)+6y

11y+17 = 11y-10

17 = -10??

That's not true, so the option "5(2.2y+3.4) = 5(y-2)+6y" has no solution.

Let me know if this helps

a) __m=10km 25m =___km

b) __m=__km__m=1.5 km

Example :
a) 7250m= 7km 250m = 7.250km


Please help me

Answers

Answer:

a) 10,025 m = 10km 25m = 10.025 km

b) 1,500 m = 1 km 500 m = 1.5 km

Answer:

a) 10025m = 10km 25m = 10.025km

b) 1500m = 1km 500m = 1.5km

Step-by-step explanation:

Concept:

Here, we need to know the idea of unit conversion.

Unit conversion is the conversion between different units of measurement for the same quantity.

1 km = 1000 m

Solve:

a)

10km 25m = 10×1000 + 25 = 10025 m10km 25m = 10 + 25/1000 = 10.025 km

b)

1.5km = 1 + 0.5 × 1000 = 1km 500m1.5km = 1.5 × 1000 = 1500m

Hope this helps!! :)

Please let me know if you have any questions

It is estimated that 75% of all young adults between the ages of 18-35 do not have a landline in their homes and only use a cell phone at home.
(a) On average, how many young adults do not own a landline in a random sample of 100?
(b) What is the standard deviation of probability of young adults who do not own a landline in a simple random sample of 100?
(c) What is the proportion of young adults who do not own a landline?
(d) What is the probability that no one in a simple random sample of 100 young adults owns a landline?
(e) What is the probability that everyone in a simple random sample of 100 young adults owns a landline?
(f) What is the distribution of the number of young adults in a sample of 100 who do not own a landline?
(g) What is the probability that exactly half the young adults in a simple random sample of 100 do not own a landline?

Answers

Answer:

a) 75

b) 4.33

c) 0.75

d) [tex]3.2 \times 10^{-13}[/tex] probability that no one in a simple random sample of 100 young adults owns a landline

e) [tex]6.2 \times 10^{-61}[/tex] probability that everyone in a simple random sample of 100 young adults owns a landline.

f) Binomial, with [tex]n = 100, p = 0.75[/tex]

g) [tex]4.5 \times 10^{-8}[/tex] probability that exactly half the young adults in a simple random sample of 100 do not own a landline.

Step-by-step explanation:

For each young adult, there are only two possible outcomes. Either they do not own a landline, or they do. The probability of an young adult not having a landline is independent of any other adult, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

75% of all young adults between the ages of 18-35 do not have a landline in their homes and only use a cell phone at home.

This means that [tex]p = 0.75[/tex]

(a) On average, how many young adults do not own a landline in a random sample of 100?

Sample of 100, so [tex]n = 100[/tex]

[tex]E(X) = np = 100(0.75) = 75[/tex]

(b) What is the standard deviation of probability of young adults who do not own a landline in a simple random sample of 100?

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100(0.75)(0.25)} = 4.33[/tex]

(c) What is the proportion of young adults who do not own a landline?

The estimation, of 75% = 0.75.

(d) What is the probability that no one in a simple random sample of 100 young adults owns a landline?

This is P(X = 100), that is, all do not own. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 100) = C_{100,100}.(0.75)^{100}.(0.25)^{0} = 3.2 \times 10^{-13}[/tex]

[tex]3.2 \times 10^{-13}[/tex] probability that no one in a simple random sample of 100 young adults owns a landline.

(e) What is the probability that everyone in a simple random sample of 100 young adults owns a landline?

This is P(X = 0), that is, all own. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{100,0}.(0.75)^{0}.(0.25)^{100} = 6.2 \times 10^{-61}[/tex]

[tex]6.2 \times 10^{-61}[/tex] probability that everyone in a simple random sample of 100 young adults owns a landline.

(f) What is the distribution of the number of young adults in a sample of 100 who do not own a landline?

Binomial, with [tex]n = 100, p = 0.75[/tex]

(g) What is the probability that exactly half the young adults in a simple random sample of 100 do not own a landline?

This is P(X = 50). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 50) = C_{100,50}.(0.75)^{50}.(0.25)^{50} = 4.5 \times 10^{-8}[/tex]

[tex]4.5 \times 10^{-8}[/tex] probability that exactly half the young adults in a simple random sample of 100 do not own a landline.


[tex] \frac{3x - 2}{7} - \frac{5x - 8}{4} = \frac{1}{14} [/tex]

Answers

Answer:

[tex]x=2[/tex]

Step-by-step explanation:

[tex]\frac{3x-2}{7}-\frac{5x-8}{4}=\frac{1}{14}[/tex]

In order to factor an integer, we need to divide it by the ascending sequence of primes 2, 3, 5.

The number of times that each prime divides the original integer becomes its exponent in the final result.

In here,  Prime number 2 to the power of 2 equals 4.

[tex]\frac{3x-2}{7}-\frac{5x-8}{2^{2} }=\frac{1}{14}[/tex]

First, We need to add fractions-

Rule:-

[tex]\frac{A}{B} +\frac{C}{D} =\frac{\frac{LCD}{B}+\frac{LCD}{D}C }{LCD}[/tex]

LCD = [tex]7 \cdot 2^{2}[/tex]

[tex]\frac{4(3x-2)+7(-(5x-8))}{7*2^{2} } =\frac{1}{14}[/tex]

[tex]x=2[/tex]

OAmalOHopeO

Consider an x distribution with standard deviation o = 34.
(a) If specifications for a research project require the standard error of the corresponding distribution to be 2, how
large does the sample size need to be?
B) If specifications for a research project require the standard error of the corresponding x distribution to be 1, how large does the sample size need to be?

Answers

Part (a)

The standard error (SE) formula is

[tex]\text{SE} = \frac{\sigma}{\sqrt{n}}\\\\[/tex]

where n is the sample size. We're given SE = 2 and sigma = 34, so,

[tex]\text{SE} = \frac{\sigma}{\sqrt{n}}\\\\2 = \frac{34}{\sqrt{n}}\\\\2\sqrt{n} = 34\\\\\sqrt{n} = \frac{34}{2}\\\\\sqrt{n} = 17\\\\n = 17^2\\\\n = 289\\\\[/tex]

So we need a sample size of n = 289 to have an SE value of 2.

Answer: 289

========================================================

Part (b)

We'll use SE = 1 this time

[tex]\text{SE} = \frac{\sigma}{\sqrt{n}}\\\\1 = \frac{34}{\sqrt{n}}\\\\1*\sqrt{n} = 34\\\\\sqrt{n} = 34\\\\n = 34^2\\\\n = 1156\\\\[/tex]

Because we require greater precision (i.e. a smaller SE value), the sample size must be larger to account for this. In other words, as SE goes down, then n must go up, and vice versa.

Answer:  1156

The sum of the 3rd and 7th terms of an A.P. is 38, and the 9th term is 37. Find the A.P.

Answers

Answer:

The AP is 1, 11/2, 10, 29/2, 19, ....

Step-by-step explanation:

Let the first term be a and d be the common difference of the arithmetic progression.

ATQ, a+2d+a+6d=38, 2a+8d=38 and a+8d=37. Solving this, we will get a=1 and d=9/2. The AP is 1, 11/2, 10, 29/2, 19, ....

Plz help a beggar I don’t get it

Answers

Answer: 3

happy learning

Answer:

B.

Step-by-step explanation:

From the point (-1,0) the next point on the graph is up 3, right 1, making the slope a positive 3.

help pls! I need the answer quickly and pls explain. thank you!

Answers

Answer:

h = 6[tex]\sqrt{3}[/tex]

Step-by-step explanation:

The given is the special right triangle with angle measures : 90-60-30

and the side lengths for the given angles are represented by :

2a-a[tex]\sqrt{3}[/tex]-a

the side length that sees 60 degrees is represented by a[tex]\sqrt{3}[/tex] (h in this case)

the area of a triangle is calculated by multiplying height and base and that is divided by 2

a[tex]\sqrt{3}[/tex]*a/2 = 18[tex]\sqrt{3}[/tex] multiply both sides by 2

a^2[tex]\sqrt{3}[/tex] = 36[tex]\sqrt{3}[/tex] divide both sides by [tex]\sqrt{3}[/tex]

a^2 = 36 find the roots for both sides

a = 6

since h sees angle measure 60 and is represented by a[tex]\sqrt{3}[/tex]

h = 6[tex]\sqrt{3}[/tex]

The legend on a map states that 1 inch is 20 miles. If you measure 5 inches on the map, how many miles would the actual distance be? Actual distance = [ ? ] miles​

Answers

Answer:

1 inch= 20 miles. 5*20=100 miles. The answer is 100 miles.

Step-by-step explanation:

On these types of questions just do that every time, then you don't need to ask, for example:

1 foot = 50 miles

If it measures 3 feet.

3*50=150 miles.

If you have any questions regarding my answer, tell me in the comments, and I will answer them.

The sum of three numbers is 124
The first number is 10 more than the third.
The second number is 4 times the third. What are the numbers?

Answers

Answer:

182/3,3 8/3, 152/3

Step-by-step explanation:

a+b+c=124

a trừ c=  10

4b=c

Answer:

a=29,b=79,c=19

Step-by-step explanation:

a=c+10

b=4c

=> a+b+c=c+10+4c+c=124

=> c=19

=> a= 29, b=79

If Bobby drinks 5 waters in 10 hours how many does he drink in 1 hour ?

Answers

Water drunk by Bobby in 10 hours = 5 units

So, water drink by Bobby in 1 hour

= 5/10 units

= 1/2 units

= 0.5 units

Answer:

1/2 water

Step-by-step explanation:

We can use a ratio to solve

5 waters        x waters

-----------   = ------------

10 hours             1 hours

Using cross products

5*1 = 10 *x

5 = 10x

Divide by 10

5/10 = x

1/2 waters =x

A telescope contains both a parabolic mirror and a hyperbolic mirror. They share focus ​, which is 46feet above the vertex of the parabola. The​ hyperbola's second focus is 6 ft above the​ parabola's vertex. The vertex of the hyperbolic mirror is 3 ft below . Find the equation of the hyperbola if the center is at the origin of a coordinate system and the foci are on the​ y-axis. Complete the equation.

Answers

the center is at the origin of a coordinate system and the foci are on the y-axis, then the foci are symmetric about the origin.

The hyperbola focus F1 is 46 feet above the vertex of the parabola and the hyperbola focus F2 is 6 ft above the parabola's vertex. Then the distance F1F2 is 46-6=40 ft.

In terms of hyperbola, F1F2=2c, c=20.

The vertex of the hyperba is 2 ft below focus F1, then in terms of hyperbola c-a=2 and a=c-2=18 ft.

Use formula c^2=a^2+b^2c

2

=a

2

+b

2

to find b:

\begin{gathered} (20)^2=(18)^2+b^2,\\ b^2=400-324=76 \end{gathered}

(20)

2

=(18)

2

+b

2

,

b

2

=400−324=76

.

The branches of hyperbola go in y-direction, so the equation of hyperbola is

\dfrac{y^2}{b^2}- \dfrac{x^2}{a^2}=1

b

2

y

2

a

2

x

2

=1 .

Substitute a and b:

\dfrac{y^2}{76}- \dfrac{x^2}{324}=1

76

y

2

324

x

2

=1 .

Other Questions
Which of the following fractions converts to a repeating decimals Why is the title of the story: The Good Samaritan? Explain. Aaron, Blaine, and Cruz are solving the equation 4 7 (7 n) = 1. Aaron started his solution by multiplying both sides of the equation by 7 4 . Blaine started by using the distributive property to multiply 4 7 by both 7 and n. Cruz started by dividing both sides of the equation by 4 7 . Why did the Native American's observe the stars? What is the mean of the following list of extra credit points earned on a statistics test?10,8,18,17,7 List 4 Black American theatre makers (discussed in lecture) and briefly describe some of their significant contributions to contemporary theatre find the missing side length in the image below using trig to solve for the missing angle which primitive organic molecule was essential to form lipid bilayer? Researchers studied symptom distress and palliative care designation among a sample of 710 hospitalized patients. Controlling for age, they used a t-test to compare average distress from nausea scores in men and women. Lower scores indicated less distress from nausea. They report men had an average score of 1.02 and woman had an average score of 1.79. Which statement is correct?(2pts)Select Men had significantly less distress from nausea. as your answerMen had significantly less distress from nausea.Select Men had half as much distress from nausea as woman but we can not determine if this is a significant difference. as your answerMen had half as much distress from nausea as woman but we can not determine if this is a significant difference.Select Men had less distress from nausea on average than women but we can not determine if this is a significant difference. as your answerMen had less distress from nausea on average than women but we can not determine if this is a significant difference.Select There is a positive correlation between distress from nausea and gender. as your answerThere is a positive correlation between distress from nausea and gender. 1. alveoli, tiny air sacs within the lungs muscle below the lungs used for, 2. bronchi, breathing the two tubes into which the, 3. diaphragm, trachea divides before entering the lung What is the recursive rule for this geometric sequence? 7, 21, 63, 189,1. a1 = 7;an = 3 an - 12. a1 = 7;an = 1/3 an - 13. a1 = 3;an = 7 an - 14. a1 = 21;an = 7 an - 1 HELP!!!!!!!!!!!!!!!!!!!!!!!!!! What is the median of 12, 9 , 16, 1, 6 , 5, 84 -3x^5y^7/6xy^8PLEASE HELP laws of thermodynamics Cho bit tan ca NH4Cl trong nc 20oC v 70oC ln lt l 37,2 g/100 gam nc v 60,2 gam/100 g nc. Ha tan 166,8 gam NH4Cl vo 400 gam nc 70oC thu c dung dch X. Sau , h nhit dung dch X xung 20oC. Tnh khi lng (gam) NH4Cl kt tinh li trong X? Please help with the Volume one Which of the following functions best describes this graph? y=(x+2)(x+7) There are two main methods of child study used todaythe ______________ and the __________ methods.