Suppose the population of a town is 8,200 and is growing 4% each year, what is the population expected to be in 10 years

Answer:

[tex]12-[20-2(6^2\div3\times2^2)]=88[/tex]

Step-by-step explanation:

So we have the expression:

[tex]12-[20-2(6^2\div3\times2^2)][/tex]

Recall the order of operations or PEMDAS:

P: Operations within parentheses must be done first. On a side note, do parentheses before brackets.

E: Within the parentheses, if exponents are present, do them before all other operations.

M/D: Multiplication and division next, whichever comes first.

A/S: Addition and subtraction next, whichever comes first.

(Note: This is how the order of operations is traditionally taught and how it was to me. If this is different for you, I do apologize. However, the answer should be the same.)

Thus, we should do the operations inside the parentheses first. Therefore:

[tex]12-[20-2(6^2\div3\times2^2)][/tex]

The parentheses is:

[tex](6^2\div3\times2^2)[/tex]

Square the 6 and the 4:

[tex](36\div3\times4)[/tex]

Do the operations from left to right. 36 divided by 3 is 12. 12 times 4 is 48:

[tex](36\div3\times4)\\=(12\times4)\\=48[/tex]

Therefore, the original equation is now:

[tex]12-[20-2(6^2\div3\times2^2)]\\=12- [20-2(48)][/tex]

Multiply with the brackets:

[tex]=12-[20-96][/tex]

Subtract with the brackets:

[tex]=12-[-76][/tex]

Two negatives make a positive. Add:

[tex]=12+76=88[/tex]

Therefore:

[tex]12-[20-2(6^2\div3\times2^2)]=88[/tex]

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

Explanation:

The arc measures of 60 and x average to the angle 70, which is the the angle formed between the intersecting chords

70 = (60+x)/2

70*2 = 60+x

140 = x+60

x+60 = 140

x = 140-60

x = 80

The full 360 degree circle has the arc measures of 60, 79, x = 80, and w, where we don't know w yet. But we can add the four pieces of the circle to get 360

60+79+x+w = 360

60+79+80+w = 360

w+219 = 360

w = 360-219

w = 141

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

Or you could find angle z first

z+70 = 180

z = 180-70

z = 110

Then use the averaging technique done at the start of this problem

z = (79+w)/2

110 = (79+w)/2

2*110 = w+79

220 = w+79

w+79 = 220

w = 220-79

w = 141

The geometric figures are drawn on the diagram are option A,B,D, and F.

One of the theorems of a circle states that the angles in the same segments or on the same chord are equal.

we know that

case a) ∠ABC

The geometric figure is not drawn in the diagram case is b) ∠BCE

The geometric figure is drawn in the diagram case is c) line segment CA

The geometric figure is drawn in the diagram case is d) Ray CA

The geometric figure is drawn in the diagram case is e) Circle C

The geometric figure is drawn in the diagram  case is f) Ray BE

The geometric figure is not drawn in the diagram case is g) LIne segment AE

Hence, The geometric figures are drawn on the diagram are option A,B,D, and F.

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Answer:

Moshe made $1875 and Jamal made $5625

Step-by-step explanation:

divide it in half, then divde Moshe's half in half because he only made half as much,

hope this helps and remember to mark brainliest

Moshe furnishes $5000 and Jamal furnishes $2500 of the capital. Computed by solving the linear equation x + x/2 = 7500, where x is the capital furnished by Moshe.

Linear equations are an equation involving constants and variables, where variables are raised to a power of not greater than 1.

We are informed that Jamal and Moshe starts a business with a capital of $7500. Also, we are informed that Jamal furnishes half as much capital as Moshe does.

We will try to make a linear equation and solve for it to find the capital furnished by each of them.

Let the capital furnished by Moshe be $x.

Jamal furnishes half as much capital as Moshe does.

∴ Capital furnished by Jamal = 1/2 of Moshe's capital = 1/2 of $x.

∴ Jamal's capital + Moshe's capital = Total capital furnished

We know the total capital is $7500.

∴ Our linear equation is: 1/2 of $x + $x = $7500.

Now we solve this equation in the following ways:

or, (1/2)*x + x = 7500

or, x/2 + x = 7500

or, (x + 2x)/2 = 7500

or, 3x/2 = 7500

or, x = (7500*2)/3 = 15000/3 = 5000.

∴ x = 5000.

∴ Moshe's share = $x = $5000

Jamal's share = 1/2 of $x = 1/2 of $5000 = $2500.

∴ Moshe furnishes $5000 and Jamal furnishes $2500 of the capital. Computed by solving the linear equation x + x/2 = 7500, where x is the capital furnished by Moshe.

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Answer:

p=50

Step-by-step explanation:

Subtract 30 from both sides and you have your answer

Answer: 50

Step-by-step explanation:

p + 30 = 80

subtract 30 from both sides to isolate the value of "p". subtracting 30 from positive 30 cancels that out. 80 minus 30 is 50. you are left with p = 50, so the value of p is 50.

Step-by-step explanation:

43. P, U

44. 7

53. Airplanes can be traveling on different planes, one plane above the other. Cars on the same intersection are on the same plane.

55

a. You can choose (4 * 3 * 2)/(3 * 2) = 4 groups of 3 points in which order does not matter.

One of those combinations does not have K, so 3 combinations of the 4 have K.

p = 3/4

b. p = 1 since any three points are always coplanar.

Answer:

Step-by-step explanation:

Length ( L ) = 8 cm

Perimeter of square = 4 L

( where L is the side of the square )

Plug the value of length

⇒[tex] \sf{4 \times 8}[/tex]

Multiply the numbers

⇒[tex] \sf{32 }[/tex] cm

Hope I helped!

Best regards!

Answer:

[tex]\huge \boxed{\mathrm{32 \ cm}}[/tex]

Step-by-step explanation:

The formula to calculate the perimeter of a square is given as:

[tex]\sf Perimeter = 4 \times side \ length[/tex]

The side length of the square is 8 centimeters.

[tex]P=4 \times 8[/tex]

Solve for the perimeter.

[tex]P=32[/tex]

The perimeter of the square is 32 centimeters.

Answer:

(-infinity, 20)

Step-by-step explanation:

the lower bound is negative infinity because no lower bound was given. The higher bound is 20, and it has a parentathesis because it is less than.

Answer:

a) 22:53

b)213 min

Step-by-step explanation:

c) 10 17 + 4 = 14 17

she has 2 minutes to spare

Answer:

she has 2 minutes to spare

Step-by-step explanation:

Answer:

x  = 7.45 inch for the maximum volume.

The area of the square = x² = 7.45² = 55.5025  inch²

Step-by-step explanation:

From the given information:

An open-top box is to be made from a 42-inch by 48-inch piece of plastic by removing a square from each corner of the plastic and folding up the flaps on each side.

The objective is to determine the length of the side x of the square cut out of each corner to get a box with the maximum volume

The volume of the box = l×b×h

The volume of the box = [tex](42 - 2x) \times (48-2x) \times (x)[/tex]

The volume of the box = [tex](2016 - 84x - 96x +4x^2)x[/tex]

The volume of the box = [tex](2016 -180x+4x^2)x[/tex]

The volume of the box = [tex](2016x -180x^2+4x^3)[/tex]

The volume of the box = [tex]4x^3 - 180x^2 +2016x[/tex]

For the maximum volume V' = 0

V' = [tex]12x^2 - 360x + 2016[/tex]

Using the quadratic formula; we have:

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

where;

a = 12 , b = -360 c = 2016

[tex]= \dfrac{-(-360) \pm \sqrt{(-360)^2 -4(12)(2016)}}{2(12)}[/tex]

[tex]= \dfrac{360 \pm \sqrt{129600 -96768}}{24}[/tex]

[tex]= \dfrac{360 \pm \sqrt{32832}}{24}[/tex]

[tex]= \dfrac{360 \pm 181.196}{24}[/tex]

[tex]= \dfrac{360 + 181.196}{24} \ \ \ OR \ \ \ \dfrac{360 - 181.196}{24}[/tex]

[tex]= \dfrac{541.196}{24} \ \ \ OR \ \ \ \dfrac{178.804}{24}[/tex]

[tex]= 22.55 \ \ \ OR \ \ \ 7.45[/tex]

For the maximum value , we check the points in the second derivative term

V'' = 24x - 360

V'' ( 22.55) = 24(22.55) - 360

V'' ( 22.55) = 541.2 - 360  

V'' ( 22.55) = 181.2   (minimum)

V'' ( 7.45) = 24(7.45) - 360

V'' ( 7.45) = 178.8 - 360  

V'' ( 7.45) = -181.2  < 0  (maximum)

Therefore, x  = 7.45 inch for the maximum volume.

The area of the square = x² = 7.45² = 55.5025  inch²

The maximum volume of a box is the highest volume the box can take.

The side length that ensures maximum volume is 22.55 inches or 7.45 inches.

The dimension of the plastic is:

[tex]\mathbf{Length = 42}[/tex]

[tex]\mathbf{Width = 48}[/tex]

Assume the side length cut-out is x

So, the dimension of the box is:

[tex]\mathbf{Length = 42 - 2x}[/tex]

[tex]\mathbf{Width = 48 - 2x}[/tex]

[tex]\mathbf{Height = x}[/tex]

So, the volume of the box is:

[tex]\mathbf{Volume = Length \times Width \times Height}[/tex]

This gives;

[tex]\mathbf{Volume = (42 - 2x) \times (48 - 2x) \times x}[/tex]

Expand

[tex]\mathbf{Volume = (42 - 2x) \times (48x - 2x^2)}[/tex]

Expand

[tex]\mathbf{Volume = 2016x - 96x^2 - 84x^2 + 4x^3}[/tex]

Differentiate

[tex]\mathbf{V' = 2016 - 192x - 168x + 12x^2}[/tex]

[tex]\mathbf{V' = 2016 -360x + 12x^2}[/tex]

Rewrite as:

[tex]\mathbf{V' = 12x^2 -360x + 2016}[/tex]

Set to 0

[tex]\mathbf{12x^2 -360x + 2016 = 0}[/tex]

Divide through by 12

[tex]\mathbf{x^2 -30x + 168 = 0}[/tex]

Using a calculator, the values of x are:

[tex]\mathbf{x = 22.55\ or\ x = 7.45}[/tex] ------ approximated to 2 decimal places

Hence, the side length that ensures maximum volume is 22.55 inches or 7.45 inches.

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Answer:

Distance = 17.5 miles

Step-by-step explanation:

Note.

Given question is not complete

Given:

Speed upstream = x

Time taken in upstream = 3.5 hour

Speed in return trip = (x+2)

Time taken in return trip = 2.5 hour

Computation:

Distance = speed × time

Distance = x (3.5)

Distance = 2.5 (x+2)

Distance = 2.5x + 5

So,

2.5x + 5 = 3.5 x

1.5 x = 5

x = 5 miles/hour

Distance = x (3.5)

Distance = 5 (3.5)

Distance = 17.5 miles

Answer:

(1, 6).

Step-by-step explanation:

The reflection of  the x coordinate of (1, 2) creates a point with y -coordinate

-1 - 3 = -4 while the x-coordinate  remains 1.

The point (1, -4) is now reflected about  y = 1, so  -4 translates to 1 + 5 = 6. and x stays at 1.

Answer is (1, 6).

Answer:

3/8 or a a decimal 0.375

Answer:

Step-by-step explanation:

hello :

2x²+x-1=2  means : 2x²+x-3=0

a=2  b= 1  c= -3

the solutios are :   x1 and x2 when the product is : x1×x2 = c/a  

let x1 = -3/2  you have : (-3/2)×x2 = -3/2   so x2 = (-3/2)/(-3/2) = 1  

The solutions to the equation 2x²+x-1=2 are x=-3/2 or x= 1

Answer:

The correct option is x = 5

Please find the attached graph of the function

Step-by-step explanation:

The given functions are;

1) f(x) = -x² + 4·x + 12

2) g(x) = x + 2

The table of values are therefore;

x,        f(x),      g(x)

-7,       -65,     -5

-6,       -48,     -4

-5,       -33,     -3

-4,       -20,     -2

-3,        -9,      -1

-2,        0,        0

-1,         7,         1

0,        12,        2

1,        15,         3

2,       16,         4

3,       15,         5

4,       12,         6

5,        7,          7

6,       0,           8

Therefore the solution to the equation f(x) = g(x), occurs at x = -2 and x = 5, where  f(x) = g(x) = 0 and 7 respectively

To verify, we have;

Equating the two functions gives;

f(x) = g(x)

-x² + 4·x + 12 = x + 2

-x² + 4·x + 12 - (x + 2) = 0

-x² + 3·x + 10  = 0

(x + 2)(x - 5) = 0

x = 5 or -2

The correct option is x = 5.

Answer:

C. x=5

Step-by-step explanation:

Please see attachments. You'll see that at the x=5 y will equal 7.

Hope this helps!

Answer:

21.37 days.

Step-by-step explanation:

Step 1

Find the total amount Nancy is paying for her iPhone

Cost of the phone = $899

Tax = 8.50%

Amount paid for tax = 8.5% × 899

= 8.5/100 × 899

= $76.415

Total amount Nancy is paying = Tax + Cost of the phone

= $76.415 + $899

= $975.415

Step 2

We are told in the question that Nancy had already saved $78

Hence, Totally amount left for Nancy to buy her iPhone = $975.415 - $78

= $897.415

Step 3

Nancy works at a car wash and earns $42 every day.

The number of days left for her to work in the car wash in order to buy her phone is calculated as:

$42 = 1 day

$897.415 = x days

Cross Multiply

= $42 × x = $897.415 × 1 day

x = $897.415/$42

x = 21.36702381 days.

Approximately, x = 21.37 days

Therefore, Nancy has to work for 21.37 days at the car wash to have enough money for her iphone

Answer:

Steve got 32 points

Step-by-step explanation:

Take the total score and multiply by the percentage received

40 * 80%

Change to decimal form

40 * .80

32

Steve got 32 points

Answer:

  each of the 12 turns is 150°

Step-by-step explanation:

If we number the points of the star 1–12, in order for the star to be symmetrical, each point must connect to two points symmetrically located around the centerline.

That is, point 1 may connect to points {2, 12} or {3, 11} or {4, 10}, or {5, 9} or {6, 8} or {7, 7}. For each of these connections, the angle made at the point of the "star" is, respectively, 150°, 120°, 90°, 60°, 30° or 0°. For these angles, the figure obtained will be ...

  150° - dodecagon, a 12-sided figure

  120° - hexagon

  90° - square

  60° - equilateral triangle

  30° - 12-pointed star

  0° - straight line

The two 12-pointed figures are shown in the attachment.

__

We suspect the star you're interested in is the one with points that are 30°. In order to have that point angle, the spider must make a turn of 180° -30° = 150°.

The spider will make 12 turns of 150°, for a total of 1800°, for a total of 5 full turns of 360°.

Answer:

Move the spide by 100 units and then turn the spider by 150 degrees. Repeat until you complete the star.

Step-by-step explanation:

people above are correct! I'm just making the steps as clear as possible for those who need it :)

Answer:

Binomial Distribution

Step-by-step explanation:

Unlike the normal or Gaussian probability distribution, the binomial distribution gives a curve representing the coefficient of the outcomes of every item in a sample or population.

the formula is ;

             mean ( υ ) = n x p

where p is the probability and n is the population.

The probability density function which generates the probability curve;

           Binomial Distribution function= f( k, n, p ) = [tex]\frac{n!}{k!(n-k)}[/tex] [tex]P^{k}[/tex][tex](1- P)^{(n -k)}[/tex]

Answer:

See below.

Step-by-step explanation:

The domain of a function is simply the span of x-values the graph will encompass.

And the range of a function is simply the span of y-values the graph will encompass.

Since the function is a quadratic, the domain is all real numbers. From the graph, the graph will continue to expand left and right. Therefore, the domain is all real numbers.

In interval notation, this is:

[tex](-\infty,\infty)[/tex]

And in set notation, this is:

[tex]\{x|x\in\mathbb{R}\}[/tex]

For the range, notice that the graph is going downwards. In other words, the graph has a maximum value. From the graph, we can see that this maximum value is at y=-4. The graph never reaches any value above -4. Therefore, our range is all numbers equal to or less than -4.

In interval notation, this is:

[tex](-\infty,-4][/tex]

We use brackets because we include the -4 in the solution set.

Also, note that we write the infinity first because the smallest number should be on the left. [-4, -∞) would not be correct.

And in set notation, this is:

[tex]\{y|y\in\mathbb{R},y\leq 4}\}[/tex]

Answer:

r=1

Step-by-step explanation:

-5r+2r=-3r

-3r=-3

Divide by -3 on both sides

r=1

Answer:

I have not J.H.S 3 , because the questions look like some J.H.S 3 ,so please I am very sorry that I can't help u in this questions . Thanks

Answer:

The number is -30.

Step-by-step explanation:

Given that,

Eight plus the quotient of a number and 3 is −2 . We need to find the number.

So, putting given condition into mathematical expression. Let the number is x. So,

[tex]8+\dfrac{x}{3}=-2[/tex]

Subtracting  on both sides,

[tex]8+\dfrac{x}{3}-8=-2-8\\\\\dfrac{x}{3}=-10[/tex]

Now cross multiplying, we get

x = -30

So, the number is -30.

Answer:

aa

Step-by-step explanation:

Answer:

200 meters per minute

Step-by-step explanation:

12/60 since hr into minutes

0.2 x 1000 since km and meters

Answer

the answer is 254 cm 2

Step-by-step explanation:

The area of the circle will be 254 square cm. Then the correct option is C.

Let r be the diameter of the circle. Then the area of the circle will be

A = (π / 4)d² square units

The radius of the circle is 18 cm.

Then the area of the circle will be

A = (π / 4) x (18)²

A = 254.46 ≈ 254 square cm

Then the correct option is C.

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Answer:

a) Area=9 units²

Perimeter=18 units

b) Area=28ft²

Perimeter=24ft

c) Area=120cm²

Perimeter=46cm

Step-by-step explanation:

a) Area=9 units²

Perimeter=18 units

b) Area=28ft² (7x4)

Perimeter=24ft (7+5+7+5)

c) Area=120cm² (15x8)

Perimeter=46cm (15+8+15+8)

Answer:

done same as before put value and do process like simplify

Answer:

[tex]\huge \boxed{\mathrm{500 \ miles}}[/tex]

Step-by-step explanation:

A right triangle is formed.

300 miles and 400 miles are the legs of the triangle.

We can apply Pythagorean theorem.

[tex]c=\sqrt{300^2 +400^2 }[/tex]

[tex]c=\sqrt{90000 +160000}[/tex]

[tex]c=\sqrt{250000}[/tex]

[tex]c=500[/tex]