Convert (87.1352) 10 to base 8
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Hypotenuse = 17cm

From the question we have that,

Since this is a right-angled triangle, we can apply the Pythagoras formula:

[tex]H^{2} = C_{1}^{2} + C_{2}^{2}[/tex]

This says that the square of the hypotenuse is the sum of the square of the other sides.

From this, we can replace the variables with the actual values:

[tex](2x + 1)^{2} = (2x - 1)^{2} + x^{2}[/tex]

We can then expand the exponents to have:

[tex]4x^{2} + 4x + 1 = 4x^{2} - 4x + 1 + x^{2}[/tex]

We can proceed to isolate x:

[tex]4x^{2} + 4x + 1 = 4x^{2} - 4x + 1 + x^{2}\\\\4x^{2} + 4x + 1 = 5x^{2} - 4x + 1\\\\4x^{2} + 4x + 1 - 5x^{2} = - 4x + 1\\\\- x^{2} + 4x + 1 = - 4x + 1\\\\- x^{2} + 4x + 1 + 4x = 1\\\\- x^{2} + 8x + 1 = 1\\\\- x^{2} + 8x = 1 - 1\\\\- x^{2} + 8x = 0\\\\[/tex]

We can now multiply the whole equation by -1 just to have a positive [tex]x^{2}[/tex]:

[tex]x^{2} - 8x = 0[/tex]

And we can now solve it using Bhaskara:

[tex]x = \frac{-b\ \pm \sqrt{b^{2} - 4ac }}{2a}[/tex]

Replacing out values, we've got:

[tex]a = 1\\b = -8\\c = 0\\x = \frac{8\ \pm \sqrt{(-8)^{2} - 4*1*0 }}{2*1}\\x = \frac{8\ \pm \sqrt{(-8)^{2} - 0 }}{2}\\x = \frac{8\ \pm \ 8}{2}\\x = 0\ or\ x = 8[/tex]

Since x can't be 0 because we're talking about a drawn triangle, x can only be 8.

We can then calculate the hypotenuse based on this value:

[tex]Hypotenuse = 2x + 1\\Hypotenuse = 2*8 + 1\\Hypotenuse = 17[/tex]

160 students ordered a yearbook.

Step-by-step explanation:

Batman, cross multiply 400×40 then divide by 100 and you get your answer.

Answer:

Hope the picture will help you.............

Answer:

ok the owner is 2..a under score 4

Step-by-step explanation:

or 5,244

A number that is divided by another, like 1 divided by 2 is one half, it is a fraction of a number.

Answer:

To find the surface area of this pyramid, we must find the area of one triangle flap which we then multiply by 4 because there are 4 of those equal triangle flaps surrounding the base(square). Once we find the area of those triangles, we then find the base(square)'s area. Next, we add all those areas together to get the result of the surface area.

Formula for area of triangle;

A = BH x 1/2

Where 'B' represents the base, 'H' represents the height, and 1/2 is just dividing the product of those two lengths by 2.

Plug in what you know, given that the base of one triangle is 4, and the height is 6.

A = 4(6) x 1/2

A = 24 x 1/2

A = 24/2

A = 12, the area of one triangle is 12 inches.

Now, we find the area of all the triangles by multiplying the area of one triangle by 4.

12 = Area of triangle

4 triangles in total, so:

12(4)

= 48 inches is the area of all the triangles.

Now we find the area of the base(square) using the formula;

(vol of square formula)
A = [tex]s^{2}[/tex]

Where 's' represents one side of the square which is being squared.

or

A = l · w

Where 'l' represents the length and 'w' represents the width.

Plug in what you know, given that one side of the square is 4 inches (as well as the length and width).

(I'll be using the formula [tex]s^{2}[/tex])

A = [tex]s^{2}[/tex]

A = 4^2 ← (The symbol ' ^ ' means raised to the power of.)

A = 16, the area of the base(square) is 16 inches.

Now we add both areas together:-

48 + 16

= 64 inches^2 is the surface area, your answer is A.

Answer:

Hope this helped and brainliest please

Step-by-step explanation:

Scientific notation is standard form.

To write a number in standard form, we use the format:

a×10^b

where 1 ≤ a < 10

a would be 2.11 in this question.

As we can see the decimal point has move 5 places to be after 2 so our b value will be 5

Our answer will be :

2.11×10^5

Hope this helped and brainliest please

Some 679 admissions were appropriate, some 260 were inappropriate, and some 193 were unnecessary.

Given that a New England Journal of Medicine study found that a substantial portion of acute hospital care is reported to be unnecessary, and the physicians who conducted the study reviewed the medical records of 1,132 patients hospitalized at six different locations across the country, and overall, 60% of admissions in the sample were judged to be appropriate, 23% were deemed inappropriate, whereas 17% could have been avoided by the use of ambulatory surgery, to determine the number of patients in each group, the following calculation should be made:

Thus, some 679 admissions were appropriate, some 260 were inappropriate, and some 193 were unnecessary.

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Answer:Some 679 admissions were appropriate, some 260 were inappropriate, and some 193 were unnecessary.

Step-by-step explanation:

Answer:

set 1 and 2

Step-by-step explanation:

Set 1 has 10

Set 2 has 13

Answer:

15800

Step-by-step explanation:

17600/10 =

1760

17600

-1760

15800

The mean of the discrete probability distribution is of 1.28.

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

Then, considering the given distribution, the mean is given by:

E(X) = 0(0.13) + 1(0.61) + 2(0.15) + 3(0.07) + 4(0.04) = 1.28.

More can be learned about the mean of a discrete probability distribution at https://brainly.com/question/24855677

Using confidence interval concepts, it is found that:

Given a confidence interval with two bounds a and b, the margin of error is half the difference of the two bounds.

So, for an interval that is (8%, 12%), the margin of error is given by:

M = (12 - 8)/2 = 2%.

Which means that for the first question, option B is correct.

Additionally, an increase in the sample size results in a decrease of the margin of error, which means that for the second question, option B is also correct.

More can be learned about confidence interval concepts at https://brainly.com/question/25890103

Answer:The tax revenue Australia would generate each year is $96,054,697,991.

What is the percentage?

The percentage is the value per hundred.

Working population of Australia =  11,565,470 people

Annual average salary = $26,450

Income tax rate = 31.4%

Tax revenue generated by each resident = 26450*(31.4/100)

Tax revenue generated by each resident =$8305.3

So, Tax revenue generated by 11,565,470 residents =  11,565,470*8305.3

Tax revenue generated by 11,565,470 residents = $96,054,697,991

Therefore, the tax revenue Australia would generate each year is $96,054,697,991.

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Step-by-step explanation:

Answer:

I think that it is C

Step-by-step explanation:

If the accident causes $6,750 of damage to his own car. The amount that the insurance company will pay to fix both cars is $14,750.

Using this formula

Insurance coverage=Total cost of damages-Deductible

Where:

Total cost of damages=($8,500+$6,750)

Deductible=$500

Let plug in the formula

Insurance coverage=($8,500+$6,750)-$500

Insurance coverage=$15,250-$500

Insurance coverage=$14,750

Therefore the amount that the insurance company will pay to fix both cars is $14,750.

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Answer:

20 minutes

Step-by-step explanation:

60÷3=20

Step 1 you divide 60 minutes by 1/3 which is gonna give you 20 mins

20 min

Hope it helps.

Do comment if you have any query.

The relation is given by the equation (z/21) = 42, then the value of the z will be 882.

The quotient means the separation of something into different parts, sharing of something among different people, places, etc.

The quotient of a number, z, and 21 is 42.

The relation can be given as

[tex]\rm \dfrac{z}{21} = 42[/tex]

Then the value of z will be

[tex]\rm z = 21 \times 42\\\\z = 882[/tex]

More about the quotient link is given below.

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Answer:

keep adding four until u reach day twelve

Answer:

Option D. all real numbers.

Step-by-step explanation:

The given function is a logarithmic function represented as

f(x) = log0.6x

In this logarithmic function for any value of x > 0 will be the domain and range of the function will be a set all real numbers.

As for any value of x>0 we get a real number if we rewrite a function in the form of an equation

y = log0.6x

Therefore Range will be (-∞ ∞) {y | y ∈ R}

Answer:

ST = 63

HI = 28

IJ = 21

Step-by-step explanation:

Given:  RSTUV ~ JFGHI

From inspection of the diagram, the corresponding sides are:

RS~JF

ST~FG

TU~GH

UV~HI

VR~IJ

The only pair of sides that both have side lengths are TU and GH. Therefore, we can use these to figure out the scale factor of dilation.

TU = 72   and   GH = 56

⇒ TU/GH = 72/56 = 9/7

Therefore, RSTUV is an enlargement of JFGHI by a scale factor of 9/7

If FG = 49

⇒ ST = 49 × 9/7 = 63

If UV = 36

⇒ HI = 36 ÷ 9/7 = 28

If VR = 27

⇒ IJ = 27 ÷ 9/7 = 21

Answer:

ST = 63, HI = 28, IJ = 21

Step-by-step explanation:

Step 1:  Determine the scale

UT = 72 and HG = 56

[tex]72 / 56 = 9/7[/tex]

Step 2:  Determine ST

We can determine ST by multipliying GF by 9/7 which will give us the upscaled ratio which will produce ST.

[tex]ST = GF * 9/7[/tex]

[tex]ST = 49 * 9/7[/tex]

[tex]ST = 63[/tex]

Step 3:  Determine HI

We can determine ST by dividng VU by 9/7 which will give us the upscaled ratio which will produce ST.

[tex]HI = VU / (9/7)[/tex]

[tex]HI = 36 / (9/7)[/tex]

[tex]HI = 28[/tex]

Step 4:  Determine IJ

We can determine IJ by dividng RV by 9/7 which will give us the upscaled ratio which will produce IJ.

[tex]IJ = RV / (9/7)[/tex]

[tex]IJ = 27 / (9/7)[/tex]

[tex]IJ = 21[/tex]

Answer: ST = 63, HI = 28, IJ = 21

The area that the considered search plane searches with the given figures is 16957.42 miles² approximately.

Suppose the circle has radius of 'r' units, then, its area is given as:

[tex]A = \pi \times r^2[/tex] sq. units

Since radius of a circle is half of its diameter, so if diameter is of 'd' length, then r= d/2, thus, area can be rewritten as:

[tex]\pi \times (\dfrac{d}{2})^2[/tex] sq. units

Suppose that a considered circle has:

Then, we get:

[tex]C = 2\pi r \: \rm units[/tex]

So, the radar scans the surface of ocean in a circular area with radius of 15.5 miles.

That circular area is itself moved in a circular path (due to circular motion of the plane with 471 miles circumference of the circular path).

The graph given describes the region of scan.

The blue region's area = Outer circle's area - Internal circle's area

The Internal circle has circumference 471 miles, let its radius be 'r' miles, then:

[tex]471 = 2\pi r\\\\r = \dfrac{471}{2\pi} \: \rm miles[/tex]

The outer circle has the radius = internal circle's radius + diameter of the radar circle =  [tex]\dfrac{471}{2\pi} + 2(15.5) =\dfrac{471}{2\pi} + 30 \: \rm miles[/tex]

Thus, we get:

Net area which is searched by the search plane ≈ 34610.98 - 17653.56 miles²

Net area which is searched by the search plane ≈ 16957.42 miles²

Thus, the area that the considered search plane searches with the given figures is 16957.42 miles² approximately.

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Answer: The larger angle (Angle 2) is 120 degrees

Step-by-step explanation:

Let's call Angle 1 x and call Angle 2 y.

Two angles being supplementary means that they add to 180.

This means x+y=180

Angle 2 is twice the measurement of angle 1.

This means 2x=y and that we can sub 2x in for y

x+2x=180

3x=180

Now solve for x

[tex]3x=180\\\frac{3x}{3} =\frac{180}{3} \\x=60[/tex]

We know the value of x, so now let's sub in to find the value of y

[tex]2x=y\\2(60)=y\\120=y[/tex]

The answer is 0.06

Step-by-step explanation:

Finding Volume

25 x 12 = 300

300 x 10 = 3,000

Into Cubic yards

3,000 / 46,656 = 0.06430041152

Nearest hundredth

0.06

Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Also remember to rate answers to help other students, While leaving thanks to answers that help you. Have a great day!

Step-by-step explanation:

I’m assuming that you’re asking about quadratic equations, but suffice it to say that the method may even work for polynomials of higher degrees.

Let’s take an example. You have x^2+6x+8.

First, multiply the term in x^2 with the constant; in this case we get 8x^2.Next, break the value in x into two numbers, such that when you add them, the value becomes that of the middle term and when you multiply them, the value becomes that which you have just calculated.

Step 1:

x^2 * 8= 8x^2

Step 2:

(break the middle term)

x^2+4x+2x+8 (notice how 4x when added to 2x gives 6x but when multiplied, gives 8x^2)

Step 3:

(separate the common terms)

x(x+4)+2(x+4)

(x+2)(x+4)

Answer:

[tex]area = \pi {d}^{2} \\ area = \pi {24}^{2} \\ area = 1808.64[/tex]m^2

Question no.1:

Debbie bought 8 oranges and 7 apples for $10.20. Katrina bought 5 oranges and 14 apples for $12.15. How much did one apple and one orange cost?

Solution:

Let the cost of one apple be "y" and the cost of one orange be "x".

Here,

According to question,

8x + 7y = $10.20 5x + 14y = $12.15

=> 5(8x + 7y) = 10.20 × 5 => 8(5x + 14y) = 12.15*8

=> 40x + 35y = 51 -->(i) => 40x + 112y = 97.2-->(ii)

By Elimination method,

Equation (i) - (ii)

(40x + 35y) - (40x + 112y) = 51 - 97.2

=> 40x + 35y - 40x - 112y = - 46.2

=> - 77y = - 46.2

=> y = 46.2/77

=> y = 0.6

Putting the value of "y" in equation (i) we get,

40x + 35y = 51

=> 40x + 35 × 0.6 = 51

=> 40x + 21 = 51

=> 40x = 51 - 21

=> 40x = 30

=> x = 0.75

Question no.2:

Joel and Janie are selling fruit. Joel sold 2 small boxes of fruit and 5 large boxes for $31. Janie sold 4 small boxes of fruit and 7 large boxes for $47. How much does one small box of fruit and one large box of fruit cost?

Solution:

Let the cost of a small box be "x" and the cost of a large box be "y".

Here,

According to question,

2x + 5y = $31 4x + 7y = $47

4(2x + 5y) = 31 × 4 2(4x + 7y) = 47 × 2

=> 8x + 20y = 124 ->(i) => 8x + 14y = 94 ->(ii)

By Elimination method,

Equation (i) - (ii)

(8x + 20y) - (8x + 14y) = 124 - 94

=> 8x + 20y - 8x - 14y = 30

=> 6y = 30

=> y = 30/6

=> y = 5

Putting the value of "y" in Equation (ii) we get,

8x + 14y = 94

=> 8x + 14 × 5 = 94

=> 8x + 70 = 94

=> 8x = 94 - 70

=> 8x = 24

=> x = 24/8

=> x = 3

Answer:

A. 64.98

Step-by-step explanation:

See the attachment .

_________

Hope it helps ⚜