Ann is 4 years older than julie. 4 years ago ann was twice as old as julie find their present ages

Answer:

The number is 15.

Step-by-step explanation:

Let n be the number.

[tex] \frac{1}{5} n + 21 = 2(n - 3)[/tex]

[tex]n + 105 = 10(n - 3)[/tex]

[tex]n + 105 = 10n - 30[/tex]

[tex]9n = 135[/tex]

[tex]n = 15[/tex]

Rich has to pay an interest of $1525.10  during the 4.5 year non payment period.

In the question

it is given that the Amount of loan taken by Rich = $7900

non payment time period = 4.5years

Interest charged during the non payment time = 4.29%

Interest charge for the first year = 4.29% of 7900

= 0.0429 * 7900                       ...(as 4.29% = 0.0429)

= 338.91

So , the interest charge for first non payment year = $338.91

to find the interest for 4.5 years , multiply the first year interest by 4.5.

So the interest charge for 4.5 years = 4.5*338.91

=1525.095

≅1525.10

Therefore , Rich has to pay an interest of $1525.10  during the 4.5 year non payment period.

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According to given triangle the value of cos A = 3/5

We know that cos theta = Adjacent Side / Hypotenuse Side

According to the question given that Adjacent side = 3

And Hypotenuse Side  = 5

Then cos A = 3/5

Hence, option 3 is correct

Each geometrical shape has unique side and angle characteristics that enable us to recognize it. The following is a list of a triangle's key characteristics.

Three vertices, three internal angles, and three sides make up a triangle.

According to the triangle's "angle sum property," a triangle's three inner angles can never add up to more than 180 degrees. Take note of the triangle PQR shown above, where the angles P, Q, and R all add up to 180 degrees.

A closed triangle has three vertices, three sides, and three angles. The symbol for a triangle with the three vertices P, Q, and R is PQR. Sandwiches and signboards in the shape of triangles are the most prevalent triangle-shaped objects.

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In the picture there is a triangle with ABC angles. Sides AB=5, BC=3, CA=4. The ratio of CosA=4/5.

Given that,

In the picture there is a triangle with ABC angles.

Sides AB=5, BC=3, CA=4

Trigonometric ratios, which contain the values of all trigonometric functions, are based on the ratio of sides of a right-angled triangle. The ratios of a right-angled triangle's sides with regard to a certain acute angle are known as its trigonometric ratios.

The right triangle's three sides are as follows:

Hypotenuse (the longest side)

Perpendicular (opposite side to the angle)

Base (Adjacent side to the angle)

According to the cos theta formula, the cos of an angle in a right-angled triangle is equal to the ratio of the Adjacent side to the hypotenuse.

Cos A = Adjacent side / hypotenuse

CosA=4/5

Therefore, CosA=4/5.

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Yes, I would play the game, because the probability of winning is 13/18.

Probability:

Probability refer the possible occurrence of any particular event.

Given,

A game where two players each throw two dice each. if any one die matches the other, you win a dollar. if there is no match, you lose a dollar.

Here we need to find whether we able to play this one or not.

To find that one, first, we have to identify the winning scenarios,

Let us consider five winning scenarios. Lets represent the dice outcomes as A, B, C, and D, where your dice are A and B and the other player's are C and D. The five scenarios are:

1) A = B

2) A = C

3) A = D

4) B = C

5) B = D

We know that the total possible outcomes is 6^4. We can go through each scenario and count the possible outcomes. We must be careful to avoid overcounting.

Based on this,

The probability that none match is

=> 6*5*4*3/6^4

=> 360 / 1296

=> 5 / 18

So, probability of winning is,

=> 1 - 5/18

=> 13/18.

So, based on the probability the chance of winning is high. So, we can play it.

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Answer:

Step-by-step explanation:

The last option

This is because we are going to multiply in order. The -6 is only in parenthesis because its a negative number. this means we are multiplying 2 x 4 , then multiplying that answer by -6.

Hope this helps! ^^

Answer:

Step-by-step explanation:

Answer:

if (23)n=(1111)2find the base n

The submarine can descend to a maximum depth of 780 feet.

Let x be the maximum depth.

It is now 650 feet below sea level after descending the depths above.

Thus;

Therefore, the submarine can descend to a maximum depth of 780 feet.

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The correct answer is 28.8.

Everything is stated as though it were a fraction of a hundred in terms of quantity. The ratio can be expressed as a quarter of one hundred. The word "percent" denotes a percentage of 100. It is represented by the '%' symbol.

120 cupcakes were sold by a bakery in a single day, with 45% of them having a chocolate flavour.

The total quantity of chocolate-flavoured cupcakes served on that particular day will then be

Let x represent how many chocolate-flavoured cupcakes were sold on that particular day.

x = 24% of 120

x = 0.24 × 120

x = 28.8

Consequently, the quantity of chocolate-flavoured cupcakes sold that day will be 28.8.

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Thus coordiante of point H is(4,6)

The Midpoint Formula: The midpoint of two points,

(x1,y1) and (x2,y2) is the point

M=(x1+x2)/2 and (y1+y2)/2

(2+x2)/2=3

(6+y2)/2=6

solving above equation

x2=4

y2=6

Thus coordiante of point H is(4,6)

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Answer:

b

Step-by-step explanation:

To find the percent of Cara's gross pay, divide what was deducted for Medicare tax by what her bi-weekly gross pay is.

So,

13.97 ÷ 735.18 = 0.019

Which means 1.9%

Answer: 13.5

Step-by-step explanation:

First arrange the scores in order:

5, 5, 9, 12, 15, 23, 26, 27

**remove 1st and last number in the set of scores every time**

Median of 5, 5, 9, 12, 15, 23, 26, 27=

Median of 5, 9, 12, 15, 23, 26=

Median of 9, 12, 15, 23=

Median of 12, 15 =

**Take mean of remaining two numbers**

(12+15)/2=

27/2=13.5

Answer: 250/43

Step-by-step explanation

Answer:

he would need seven weeks, i believe.

Given hats are forming a conical shape and the volume of the cone will be 27.28 inches³.

Volume is the scalar quantity of any object that specified occupied space in 3D.

For example, the space in our room is referred to as volume.

Given that,

4 inches in diameter, 6.5 inches tall, slant height of 6.8 inches

So,

D = 4 inches

Now radius r = D/2

r = 4/2 = 2 inches.

Height h = 6.5 inches.

The volume of the conical bar is given as ;

(1/3)πr²h

So,

Volume = (1/3)π(2)²6.5

Volume = 27.28 inches³

Hence "The volume of the given conical-shaped hat will be 27.28 inches³".

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Answer:

0.72 or 18/25

Step-by-step explanation:

Multiply -(-31/50)

0.1 + 31/50

To write 0.1 as a fraction with a common denominator, multiply by 50/50.

0.1*50/50+31/50

Combine 0.1 and 50/50.

0.1+50/50 + 31/50

Combine the numerators over the common denominator.

0.1*50+30/50

Simplify the numerator.

36/50

Cancel the common factor of 36 and 50.

Results are 18/25 and 0.72.

Hope this helps.

The area of the sheet of paper in correct metric units is 602.6c[tex]m^{2}[/tex].

A region's size on a plane or curved surface is expressed by the term "area," which is a mathematical concept. As opposed to surface area, which refers to the area of an open surface or the boundary of a three-dimensional object, plane region or plane area refers to the area of a form or planar lamina. Area can be thought of as the volume of material, at a particular thickness, required to create a model of the shape, or as the volume of paint required to paint the surface in a single coat. It is equivalent to the volume of a solid or the length of a curve in two dimensions (a three-dimensional concept).

Calculations:

The length of a 8 X 11 paper in metric unit is 27.9 cm and width of 8 X 11 paper in metric unit is 21.6 cm.

Area of sheet of paper=length*width

               =27.9*21.6

               =602.6 c[tex]m^{2}[/tex]

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​

The actual height of the library is 36 feet.

Given a scale of 1/3 inch = 1 foot

therefore, 1 inch = 3 feet

then, 12 inches = 12 × 3

36 inches.

therefore the actual height of the library is:

12 × 36

= 432 inches

= 36 feet.

It is obvious which dimension is intended when a rectangle is drawn with both horizontal and vertical sides when the term height is used; height designates how high (or how tall) the rectangle is. As a result, using the word width to describe the other dimension—the width of the rectangle from side to side—is simple. As long as there is no ambiguity, it is also appropriate to refer to the side-to-side measurement as the rectangle's length if it is bigger than its height.

hence we get the height of the library as 36 feet.

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Answer:

x = -6

Step-by-step explanation:

3x + 8 = -10

3x = -10-8

3x=-18

divide both sides by the coefficient of x which is 3

3x/3 = -18/3

x = -6.

The MATHCOUNTS International airport had the mean number of seconds between departure time of 43 seconds in 2001.

For given question,

In 2001 there were 738,114 departures.

As we can see, 2001 was not a leap year.

So, the number of days in 2001 = 365

We find the number of departures per day in 2001.

738,114 / 365 = 2,022.23

So, approximately 2,022 departures per day.

Now we find the number of departures in an hour.

2,022 / 24 = 84.25

This means, approximately 84 departures per hour

We know that, 1 hour = 3,600 seconds

Now we find the mean number of seconds between departure time.

3,600 / 84 = 42.8

                  ≈ 43 seconds

Therefore, the MATHCOUNTS International airport had the mean number of seconds between departure time of 43 seconds in 2001.

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The true statements are,

⇒ If the price is marked up 25%, the selling price will be $50.

⇒ If the selling price is $70, the price is marked up 75%.

What is the Cost price?

Cost price is the total amount of money that it costs a manufacturer to produce a given product or provide a service.

Given that:-

A Store bought jeans at a cost of $40 a pair.

If the price is marked up 25%, the selling price will be $50

⇒ 40 x 25 / 100 = 10

Selling Price = $50

Hence, This is true statement.

And, If the selling price is $70, the price is marked up 75%.

P = 70 - 40 = $30

40 x 75  / 100 = $30

Hence, This statement is true.

Therefore, the true statements are;

⇒ If the price is marked up 25%, the selling price will be $50.

⇒ If the selling price is $70, the price is marked up 75%.

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The complete question is this,

A store bought jeans at a cost of $40 a pair. Select all the statements that are true.

A. If the price is marked up 20%, the selling price will be $60.

B. If the price is marked up 25%, the selling price will be $50.

C. If the selling price is $65, the price is marked up 50%.

D. If the selling price is $70, the price is marked up 75%.

Answer:

S / 2πh

Explanation:

2πrh are all multiplied together to make S, so in order to isolate the r, we need to divide (the opposite operation of multiplication) 2πh from both sides.

Answer:

A=10. D=_3

Step-by-step explanation:

Start from 10 and make minus 3 every time

Answer:

  16

Step-by-step explanation:

You want the middle of three consecutive even integers that have a sum of 48.

We can let x represent the middle of the three integers. Then the other two are (x -2) and (x +2), and their sum is ...

  (x -2) +x +(x +2) = 48

  3x = 48  . . . . . simplify

  x = 16 . . . . . . divide by 3

The middle integer of the three is 16.

__

Additional comment

As we see here, the average of the three integers is their sum divided by their number: 48/3 = 16. The middle of an odd number of consecutive integers will be equal to their average value. Hence, the middle integer must be 16.

Since a negative number's exponent is always positive, [(-4)⁴]⁵ will always be greater than -[(4¹²)³].

What is number system?

The Number System covers any of the several sets of symbols and usage guidelines for indicating numbers, which are used to indicate how many items are present in a particular group. Thus, the Roman numeral I, the Greek letter alpha, the first letter used as a numeral, the Hebrew letter aleph, or the modern number 1, which is nothing more than Hindu-Arabic in origin, can all be used to express the idea of "oneness."

A mathematical representation of the numbers in a given set is called a number system.

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The given statement is a descriptive statistic.

So, the statement "Robin expects to serve 12% fewer meals this year than last year" is a descriptive statistic.

Therefore, the given statement is a descriptive statistic.

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The dimensions of the carpet are 73 x 43. = 3139.

In mathematics, a dimension is a way to quantify the size or separation of an area, an object, or a space inside one direction. In simpler terms, It is just the measurements of an object's length, width, and height.

Geometric figures can be created using any configuration of points, lines, or planes. Depending on their dimensions, geometric figures can be categorized as either a space figure, a surface figure, a line, another line segment, a ray, or a point.

The perimeter of the carpets = is 232.

The length of the carpet = 30 in.

In a rectangle, the edge is P = 2W + 2L

In this case 232 = 2W + 2L

Also, the 2nd sentence says L = W + 30

This length variable can be changed in the perimeter formula:

232 = 2W + 2(W+30)

232 = 2W + 2W + 60

232 = 4W + 60

172 = 4W

43 = W

Then, since L = W+30

L = 43+30 = 73

So the dimensions of the carpet are 73 x 43. = 3139.

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We are to calculate the value of 4p. The value of 4p will be π / 4.

Let's give the numbers we get from the calculator the names x and y. Independent random variables with a uniform[0,1] distribution are x and y.

Let's take notice that since x and y are both between 0 and 1, 1 is the triangle's longest side.

Let's start by interpreting geometry. If the triangle were a rectangle, the side with length 1 would be the hypotenuse, and x and y would then need to meet the following criteria:

x²+y² = 1

Keep in mind that we are supposing the triangle to be a rectangle in this instance. However, the task requires us to create an acute triangle.

To do that, we must widen the angle formed by the sides of length x and y. We can do that by 'growing' the triangle, but if we do so while maintaining the x and y values, the length of side 1 should rise, which is not what we want.

Therefore, if we enlarge the triangle, we should likewise decrease the value of x and/or y so that the length of the first side may be maintained. This insight allowed us to conclude that

x²+y² < 1

Let's now employ a more mathematical strategy. The Cosine Theorem states that a triangle with three sides of length a, b, and c is satisfying.

A2 is equal to b2+c2 - 2bc* cos(), where is the angle formed by the lengths of b and c's sides.

The result of applying this formula to our triangle is that

[tex]1+x^{2} +y^{2} - 2bc * cos\alpha[/tex] , where aplha is the angle between x and y.

Let's call the figures we obtain from the calculator x and y. X and Y are independent random variables with uniform[0,1] distribution.

Consequently, we must ascertain P(x2+y2 1). This likelihood may be calculated using integration. You need polar coordinates.

(X, Y) = (r*cos, r*sen), where r is an integer between 0 and 1, and (that way, the numbers are positive).

Because the Jacobian matrix has determinant r, X2 + Y2 = 1.

On integrating, we get out answer as π / 4

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Answer:

y = 5/2 √6x

Solution.

Rewrite

y = 5/2a√6x

y = 5a√6x

----------

2

Cross multiply

2y = 5a√6x

Swap both sides

√6x = 2y

-----

5a

Take the square of both sides

6x = 2y²

------

5a²

Divide both sides by 6

x = 2y² 6

----- ÷ -----

5a². 1

x = 2y² 1

---- × ----

5a². 6

x = 2y²

-----

75a²