Express 8.5454545454... as a rational number, in the form p/q where p and q are positive integers with no common factors.

Answers

Answer 1

[tex]x=8.\overline{54}\\ 100=854.\overline{54}\\ 100x-x=854.\overline{54}-8.\overline{54}\\ 99x=846\\ x=\dfrac{846}{99}=\dfrac{94}{11} [/tex]

Related Questions

Solve 2 cos theta + 2 = 3 in the interval from 0 to 2pi. Round to the nearest hundredth.

Answers

2cos theta = 1 -> cos theta = 1/2

Then theta = pi/3 + 2npi or -pi/3 + 2npi, where n is random interger

And the domain is restricted in [0,2pi]

So answer will be pi/3 or 5pi/3

Final answer:

The solutions to the equation 2 cos θ + 2 = 3 in the interval from 0 to 2π are θ = π/3 and θ = 5π/3, which approximate to 60 degrees and 300 degrees.

Explanation:

The equation given is 2 cos θ + 2 = 3. To solve this equation, first subtract 2 from both sides to get 2 cos θ = 1. Then, divide both sides of the equation by 2 to isolate cos θ, yielding cos θ = 0.5.

In the interval from 0 to 2π (0 to 360 degrees), cos θ = 0.5 occurs at θ = π/3 and θ = 5π/3 (60 degrees and 300 degrees), as these are the angles in the first and fourth quadrants where the cosine value is positive and equal to 0.5.

Therefore, the solutions to the equation are θ = π/3 (θ ≈ 1.05 radians) and θ = 5π/3 (θ ≈ 5.24 radians), or θ ≈ 60 degrees (θ ≈ 1.05) and θ ≈ 300 degrees (θ ≈ 5.24) when rounded to the nearest hundredth of a radian.

What is the exponential function modeled by the following table? x f(x) 2 10 3 28 4 82 f(x) = 2x f(x) = 2x + 1 f(x) = 3x f(x) = 3x + 1

A f(x) = 2x
B f(x) = 2x + 1
Cf(x) = 3x
D f(x) = 3x + 1

Answers

The given table is
x 2 3 4;
f(x): 10 28 82

Note:
The equations were mistyped. They should read as follows:
A) [tex]f(x) = 2^{x}[/tex]
B) [tex]f(x)=2^{x}+1[/tex]
C) [tex]f(x)=3^{x}[/tex]
D) [tex]f(x)=3^{x}+1[/tex]

Answer:
The correct answer is D.

Verify the answer.
When x=2, [tex]3^{2}+1 =9+1=10[/tex] CORRECT
When x=3, [tex]3^{3}+1=27+1=28[/tex] CORRECT
When x=4, [tex]3^{4}+1=81+1=82[/tex] CORRECT

Answer:

D f(x) = 3x + 1

Step-by-step explanation:

In standard notation, 2.34 x 102 is 23,400. true or false

Answers

In standard notation, 10² equals to 10×10 = 100

2.34 × 10² equals to 2.34 × 100 which gives the result of 234

Hence, the statement given is false

I spent 25 Points, PLEASE HELP! In a graph, x represents the number of months since a business opened, and y represents the total amount of money the business has earned. The following three points are from the graph:
(2, 1990) (5, 4225) (9, 7205)

Find the slope and y-intercept. Explain what each represents.

Answers

First find the slope. m=(y2-y1)/(x2-x1)

m=(4225-1990)/(5-2)=745,

m is the slope, this represents the amount of money earned each month that the business operates.

so far we have:

y=745x+b, using any point we can solve for b, I'll use (2,1990)

1990=745(2)+b

1990=1490+b

500=b

b is the y-intercept which is $500, it represents the amount of moeny that the business started with.

The slope of this scenario is 745. The slope represents the profit made each month.

p=2L+2w solve for w helppppp

Answers

l=-w+p/2 i found it on auto calculator

P=2l+2w

Subtract 2l from both sides
P-2l=2w

Divide all terms by 2
(1/2)P-l= w

Final answer: w= (1/2)P-l

simplify the expression.
cos^2(pi/2-x)/sqrt1-sin^2(x)

a. tan(x)
b. cos(x)tan(x)
c. cos(x)cot(x)
d. sin(x)tan(x)

Answers

[tex]\bf \textit{Cofunction Identities} \\ \quad \\ sin\left(\frac{\pi}{2}-{{ \theta}}\right)=cos({{ \theta}})\qquad \boxed{cos\left(\frac{\pi}{2}-{{ \theta}}\right)=sin({{ \theta}})} \\ \quad \\ \quad \\ tan\left(\frac{\pi}{2}-{{ \theta}}\right)=cot({{ \theta}})\qquad cot\left(\frac{\pi}{2}-{{ \theta}}\right)=tan({{ \theta}}) \\ \quad \\ \quad \\ sec\left(\frac{\pi}{2}-{{ \theta}}\right)=csc({{ \theta}})\qquad csc\left(\frac{\pi}{2}-{{ \theta}}\right)=sec({{ \theta}})[/tex]

[tex]\bf \\\\ -------------------------------\\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta ) \\\\\\ \boxed{cos(\theta )=\sqrt{1-sin^2(\theta )}}[/tex]

[tex]\bf \\\\ -------------------------------\\\\ \cfrac{cos^2\left(\frac{\pi }{2}-x \right)}{\sqrt{1-sin^2(x)}}\implies \cfrac{\left[ cos\left(\frac{\pi }{2}-x \right)\right]^2}{cos(x)}\implies \cfrac{[sin(x)]^2}{cos(x)}\implies \cfrac{sin(x)sin(x)}{cos(x)} \\\\\\ sin(x)\cdot \cfrac{sin(x)}{cos(x)}\implies sin(x)tan(x)[/tex]

Which represents the number 7,776 in exponential form? 68 36 28 65

Answers

6^5 = 6 x 6 x 6 x 6 x 6 = 7776

Marla is looking for a new car. She has test-driven two cars but can only purchase one. The probability that she will purchase car A is 0.52, and the probability that she will purchase car B is 0.38. What is the probability that she will not purchase either car A or car B?

Answers

The probability that she won't buy either car is .10. You add the two probabilities that were previously stated and then subtract them from 1.00.

.52 + .38 = .90

1.00 - .90 = .10

Answer: The required probability is 0.10.

Step-by-step explanation: Given that Marla is looking for a new car. She has test-driven two cars A and B but can only purchase one.

We are to find the probability that she will not purchase either car A or car B.

Let, 'C' denotes the event that Marla will purchase car A and 'D' denotes the event that Marla will purchase car 'B'.

Then, according to the given information, we have

[tex]P(A)=0.52,~~~P(B)=0.38.[/tex]

Since Marla cannot purchase both the cars, so the events A and B are disjoint.

That is,

[tex]A\cap B=\phi~~~~~\Rightarrow P(A\cap B)=0.[/tex]

Therefore, the probability that Marla will purchase either car A or car B is given by

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)=0.52+0.38-0=0.90.[/tex]

Hence, the probability that she will not purchase either car A or car B will be

[tex]P^\prime(A\cup B)=1-P(A\cup B)=0-0.90=0.10.[/tex]

Thus, the required probability is 0.10.

when do we say that a real number, say r, is a root of a given polynomial equation in x?

Answers

check picture below.

A long distance runner can run 9 miles per hour. how many hours will it take the runner to run 27 miles

Answers

You divide 27 miles by 9 miles per hour, getting 27/9 (miles/(miles))*hour. The units cancel out to make hours, and your final answer is 27/9 = 3 hours.

The long-distance runner will take 3 hours to run 27 miles.

What is a unitary method example?

In simple terms, the unitary method is used to find the price of a single unit from a given multiple.

Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

You divide 27 miles by 9 miles per hour, getting 27/9 (miles/(miles))hour.

The units cancel out to make hours

This runner takes 1 hr to run 9 miles.

So, to run 27 miles the runner will take

= 27/9

= 3 hours.

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Find the equation of the parabola whose vertex is the origin and whose directrix is x=-4

Answers

Answer:

Step-by-step explanation:

2020 2021

Equation of the parabola whose vertex is the origin and whose directrix is x=-4 is x=0.

What is Parabola?

A parabola is a curve where any point is at an equal distance from: a fixed point (the focus ), and; a fixed straight line (the directrix )

As we have vertex at the origin i.e. (0,0) and directrix is x=-4 and a line parallel to y-axis,

it must have a focus at (4,0)

Equation of the parabola represents locus of a point (x, y), which moves so that its distance from x=-4 to (4,0) are equal.

Hence, equation of parabola is

(x-4)²+(y-0)²=(x+4)²

(x-4)²+y²=(x+4)²

x²+16-8x=x²+16+8x

-16x=0

x=0

Hence, equation of the parabola whose vertex is the origin and whose directrix is x=-4 is x=0.

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PLEASE HELP IMAGE ATTACHED!! can u explain how to do it

Answers

Answer: x = 10

------------------------------------------

The two blue chords are equally distant from the center. This is shown by the segments with single tick marks. These segments are 3.5 units long.

The bottom blue chord is 10 units long because half of it is 5 units.

Since the chords are the same distance away from the center, this means that the blue chords are equal in length. Both blue chords are 10 units long.

Abcd is a quadrilateral. three of the angles of abcd measure 100°, 87°, and 106°, respectively. find the measure of the missing angle.
a. 67°
b. 74°
c. 80°
d. 87°

Answers

A quadrilateral in total is 360 degrees.
(x = the missing length)

100 + 87 + 106 + x = 360
293 + x = 360
-293 -293
x = 67 degrees.

The answer to your question is option A, 67 degrees.

MN = 2AB, so 3MN = 6AB. This is an illustration of which property?

Answers

In general:

For any 3 numbers a, b, and c≠0,

If a=b then a.c=b.c (a times c = b times c)

This is called the "multiplication property"

In or case, a=|MN|, b=|2AB|, c=3

MN=2AB so 3.MN=3.2ab, so 3MN=6AB

Answer: Multiplication property.

What expression represents the area of the triangle?

Answers

A=bh/2, that is area is equal to half of the product of the base and height, so in this case:

A=(1/2)*10*24

Answer:

Option first is the answer.

Step-by-step explanation:

For finding the are of a right angle triangle, we use the base and the height of the triangle. The height is the right angle leg of the triangle. Hypotenuse is not considered here.

In the given diagram, the base or 'b' is = 10 units

And the height or 'h' is = 24 units

Area of a right triangle is given as :

[tex]A=\frac{bh}{2}[/tex]

So, in the given options the correct option is : Option first.

[tex]A= \frac{10*24}{2 }[/tex] or [tex]\frac{1}{2}(10*24)[/tex]

If wx = XZ, then WX = YZ

Answers

False, because there is not enough information to prove that it is true

hope this helps

False, because there is not enough information to provide that it true

Grace is planning a move to a different city. She contacts two local rental companies and obtains the following information for the one-day cost of renting a truck: Company A: $40.95 per day plus $0.19 per mile Company B: $19.95 per day plus $0.49 per mile Let n represent the total number of miles driven in one day. Write an inequality that can be used to determine for what number of miles it is less expensive to rent the truck from Company B.

Answers

You would write a linear inequality.

40.95 + 0.19n > 19.95 + 0.49n

A system of equations is shown below: x + 3y = 5 (equation 1) 7x − 8y = 6 (equation 2) A student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. If equation 2 is multiplied by 1, which of the following steps should the student use for the proof?

Answers

(1) x + 3y = 5

(2) 7x - 8y = 6

Condition: equation (2) is multiplied by 1

If you multiply equation (1) by 1 and add the equation (2), you get

x + 3y = 5
7x - 8y = 6
----------------
8x - 5y = 11

So, if the student proves that the system formed by the new equation and the second equation is the same, he/she will have the proof:

So, the answer is "show that the solution to the system of equations 8x − 5y = 11 and 7x − 8y = 6 is the same as the solution to the given system of equations"

Answer:

The correct answer is B. Show that the solution to the system of equations 8x − 5y = 11 and 7x − 8y = 6 is the same as the solution to the given system of equations"

Step-by-step explanation:

The graph shows the distance, y, in miles, of a moving motorboat from an island for a certain amount of time, x, in hours:

A graph titled Distance Vs Time is shown with Time in hours labeled on x axis and Distance from Island in miles labeled on y axis. The scale on the x axis shows the numbers 1, 2, 3, 4, 5, 6, 7, and the scale on the y axis shows the numbers 0, 25, 50, 75, 100, 125, 150, 175, 200, 225. The graph shows a straight line joining the ordered pairs 0, 25, and 1, 75, and 2, 125, and 3, 175, and 4,225.

What is the speed of the motorboat?
225 miles per hour
25 miles per hour
75 miles per hour
50 miles per hour

Answers

the graph is showing for every 1 hour the boat is 50 miles further away

so the speed of the boat is 50 miles per hour

The speed of the boat is 50 miles per hour.

We have given that,

The graph shows the distance, y, in miles, of a moving motorboat from an island for a certain amount of time, x, in hours

A graph titled Distance Vs Time is shown with Time in hours labeled on the x-axis and Distance from Island in miles labeled on the y-axis. The scale on the x-axis shows the numbers 1, 2, 3, 4, 5, 6, 7, and the scale on the y-axis shows the numbers 0, 25, 50, 75, 100, 125, 150, 175, 200, 225. The graph shows a straight line joining the ordered pairs 0, 25, and 1, 75, and 2, 125, and 3, 175, and 4,225.

We have to determine the speed of the motorboat.

What is the speed?

The speed of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time it is thus a scalar quantity.

The graph is showing for every 1 hour the boat is 50 miles further away

1hour=50 miles from the graph

So the speed of the boat is 50 miles per hour.

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in an isosceles trapezoid, how do you prove the base angles are congruent?

Answers

If two sides are congruent then those opposite of it are congruent

PLEASE HURRY!!! 30 POINTS

A rectangle has an area of 102 cm2. The length of the rectangle is 17 cm.

What is the perimeter of the rectangle?

Answers

102/17 = 6

(6*2)+(17*2) = 46

Hope this helps! :)

Answer:

(Really really really sorry if this incorrect)... ok so it's 17 cm tall in length. That would be 17 blocks high, for example. The area is 102, so 102 cm2 divided in half equals 51, so the width would be 51 cm. So the perimeter is 17 + 17 + 51 + 51 = 136 cm.

Arby's age is 6 years less than 7 times Anna's age. If Anna's age is x years, which expression best shows Arby's age?

x
7x âˆ’ 6
x âˆ’ 1
6x âˆ’ 7

Answers

Answer:

A = 7x - 6

Step-by-step explanation:

The options aren't very clear, but the answer would be (assume that A is Arby's age):

A = 7x - 6

Answer:

Step-by-step explanation:

The level of detail that infants can see at 20 feet is equivalent to the level of detail that adults can see at _____ feet.

Answers

The level of detail that infants can see at 20 feet is equivalent to the level of detail that adults can see at 600 feet.

600

Hope this helps : )

Help me with this please

Answers

The fraction is written as 3/4.
If you divide 3 by 4 you will get the decimal.

How many numbers between 1 and 101 are evenly divisible by 4 but not by 8?

Answers

101/4 = 25.25

so 25 numbers are divisible by 4

101/8 = 12.625

so 12 numbers are divisible by 8

25-12 =13

so 13 numbers are divisible by 4 but not by 8

Determine the sample size required to estimate the mean score on a standardized test within 5 points of the true mean with 99% confidence. assume that s=17 based on earlier studies.

Answers

Given:
Accuracy = 5
99% confidence interval
s = 17, sample standard deviation.

Because the population standard deviation is unknown, we should use the Student's t distribution.
The accuracy at the 99% confidence level for estimating the true mean is
[tex]t*( \frac{s}{ \sqrt{n} )} [/tex]
where
n = the sample size.
t* is provided by the t-table.

That is,
(17t*)/√n = 5
√n = (17t*)/5 = 3.4t*
n = 11.56(t*)²

A table of t* values versus df (degrees of freedom) is as follows.
Note that df = n-1.

n df t*
------ -------- -------
1001 1000 2.581
101 100 2.626
81 80 2.639
61 60 2.660

We should evaluate iteratively until the guessed value, n, agrees with the computed value, N.

Try n = 1001 => df = 1000.
t* = 2.581
N = 11.56*(2.581²) = 77
No agreement.

Try n = 81 => df = 80
t* = 2.639
N = 11.56*(2.639²) = 80.5
Good agreement

We conclude that n = 81.

Answer: The sample size is 81.

Based on the mean score and the confidence interval, the sample size required to estimate the mean score is 77.

What is the sample size required?

This can be found as:

= (Z score for 99% interval² x Sample size²) / Points off the true mean ²

Solving gives:

= (2.576² x 17²) / 5²

= 76.7

= 77

Find out more on the Z score at https://brainly.com/question/25638875.

A 50 foot ramp makes an angle of 4.9° with the horizontal. to meet new accessibility guidelines, a new ramp must be built so it makes an angle of 2.7° with the horizontal as shown below. what is the length of the new ramp?

Answers

This is the concept of trigonometry, for us to calculate the new length we will need to calculate the adjacent length, this will be given by:
cos theta=[adjacent]/[hypotenuse]
theta=4.9°
hypotenuse=50 ft
adjacent=a
thus;
cos 4.9=a/50
a=50cos4.9
a=49.82ft
thus the new length will be given by:
cos 2.7=49.82/h
h=49.82/cos 2.7
h=49.97
the new length will be 49.97 ft

To solve the system of linear equations 3x+5y=2 and 6x+10y=8 by using the linear combination method, Laura correctly multiplied the first equation by –2 to get -6x-10y=-4 and then correctly added the equations -6x-10y=-4 and and then correctly added the equations -6x-10y=-4 and 6x+10y=8 to get 0 = 4. How many solutions are there to the system of equations?

A. 0
B. 1
C. 2
D. 4

Answers

The answer is A, those linear lines will never intersect

Answer:

The two linear equation are

1. 3 x + 5 y =2

2. 6 x + 10 y = 8

If you will multiply equation (1), by number ,2 you will get

6 x + 10 y=4

or, if you will divide equation 2,by 2 you will get ,line

2 × (3 x + 5 y)=2 × 4

3 x + 5 y=4

→Slope of line 1

[tex]=\frac{-3}{5}[/tex]

→Slope of line 2

[tex]=\frac{-6}{10}=\frac{-3}{5}[/tex]

→→Slope of two lines are equal , so they are parallel.

Parallel lines never intersect. So,there is no solution.

Option A: 0

Simplify the expression.

a. square root 6

b. square root 12

c. 9 square root 12

d. 9 square root 6

Answers

Work: 4√6 + 5√6
All you need to do is add both terms together since the square root in each is 6, and 6 has no perfect squares:
4√6 + 5√6 = 9√6
Answer: 9√6

I hope this helps!

The expression is d) [tex]9 \sqrt{6}[/tex]

To simplify the given expressions involving square roots, follow these steps:

a. Square root 6

Since 6 is not a perfect square and has no perfect square factors, [tex]\sqrt{6} i[/tex]s already in its simplest form.

b. Square root 12

Break down 12 into its prime factors: 12 = [tex]2 \times 2 \times 3[/tex]. Therefore,[tex]\sqrt{12}[/tex]can be simplified as follows:

[tex]\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}[/tex]

c. 9 square root 12

We already know that [tex]\sqrt{12} = 2\sqrt{3},[/tex] so we substitute it into the expression:

[tex]9 \sqrt{12} = 9 \times 2\sqrt{3} = 18\sqrt{3}[/tex]

d. 9 square root 6

Since [tex]\sqrt{6[/tex]} is already in its simplest form, the expression remains:

[tex]9 \sqrt{6}[/tex]

Use a table of function values to approximate an x-value in which the exponential function exceeds the polynomial function. f(x) = 5x + 4 h(x) = x2 + 8x + 24

x = -3
x = 3
x = 4
x = 5

Answers

The exponential function is [tex]f(x)= 5^{x} +4[/tex]
The polynomial function is [tex]h(x)= x^{2} +8x+24[/tex]

We want a value of x as such that [tex]f(x)\ \textgreater \ h(x)[/tex], so

[tex] 5^{x}+4 [/tex] > [tex] x^{2} +8x+24[/tex]

We are provided with four possible value of x. By process of trial and error, we will narrow down two values of x when the statement is changing from false to true

first, we try [tex]x=-3[/tex] by substituting into [tex]f(x)[/tex] and [tex]h(x)[/tex]

[tex] f(-3)=5^{-3}+4 = 4.008 [/tex] and [tex]h(-3)= (-3)^{2}+8(-3)+24=9 [/tex]
so [tex]f(x)[/tex]>[tex]h(x)[/tex] which is not the inequality wanted

We try [tex]x=3[/tex] by substituting into [tex]f(x)[/tex] and [tex]h(x)[/tex]
[tex]f(3)= 5^{3}+4=129 [/tex] and [tex]h(3)= (3)^{2}+8(3)+24=57 [/tex],
so [tex]f(x)[/tex] > [tex]h(x)[/tex] as wanted

We know that any values of [tex]x[/tex] greater than three will give [tex]f(x)[/tex] greater than [tex]h(x)[/tex], so we narrow down to two values that make the statement changes from false to true.

There is one value between -3 and three that makes [tex]f(x)[/tex] greater than [tex]h(x)[/tex]. From here we use the method of trial and error.

We can start with the mid value between -3 and three which is 0
[tex]f(0)= 5^{0}+4=5 [/tex]
[tex]h(0)= 0^{2}+8(0)+24=24 [/tex]
[tex]f(x)[/tex] is less than [tex]h(x)[/tex] which isn't the inequality we want so here we narrow down the value of x must be between 0 and 3

We can try mid-value between 0 and three which is 1.5
[tex]f(1.5)= 5^{1.5}+4=15.18 [/tex]
[tex]h(1.5)= (1.5)^{2}+8(1.5)+24=38.25 [/tex]
[tex]f(x)[/tex] is still less than [tex]h(x)[/tex], so we now narrow down the value of x between 1.5 and 3

We try again using the mid-value between 1.5 and three which is 2.25
[tex]f(2.25)= 5^{2.25}+4=41.38 [/tex]
[tex]h(2.25)= 2.25^{2}+8(2.25)+24=47.0625 [/tex]
We still have [tex]f(x)[/tex] less than [tex]h(x)[/tex] so we can narrow down further the value of x between 2.25 and 3 (which is quite a short interval already)

We can keep trying by choosing a value of x says x=2.6
[tex]f(2.6)= 5^{2.6}+4=69.66 [/tex]
[tex]h(2.6)= 2.6^{2}+8(2.6)+24=51.56 [/tex]
We have [tex]f(x)[/tex] greater then [tex]h(x)[/tex]

The narrowing down process continues where we now have the interval of x between 2.25 and 2.6. Keeping to one decimal place we can find the
value of x=2.4 is the approximate value where [tex]f(x)[/tex] is greater than [tex]h(x)[/tex].

Answer: x=2.4

The correct answer is x = 5.

Trust me, I just did the quiz.

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