the frequency of the letter e in written English is about 13%. On a page of a novel that has bout 2000 letters per page, about how many occurrences of the letter e can we expect to find?

Answer:

  57 cm²

Step-by-step explanation:

You have a composite figure and you want to find its area.

There are several ways you can decompose the given figure. Three of them are shown in the attachments. The missing dimensions are found by realizing that the sum of the right-side dimensions is equal to the left-side dimension, and the sum of the bottom-side dimensions is equal to the top dimension.

Extending the vertical boundary line divides the figure into a left rectangle that is 7 cm high and 7 cm wide, and a right rectangle that is 2 cm high and 4 cm wide. This is shown in the first attachment.

The area of each rectangle is the product of its height and width, and the total area is the sum of these:

  Area = (height)×(width) . . . . . area formula for one rectangle

  Area = (7 cm)(7 cm) +(2 cm)(4 cm) = 49 cm² +8 cm² = 57 cm²

Extending the horizontal boundary line divides the figure into a top rectangle 2 cm high and 11 cm wide, and a bottom rectangle 5 cm high and 7 cm wide. This is shown in the second attachment. The total area is ...

  Area = (2 cm)(11 cm) +(5 cm)(7 cm) = 22 cm² +35 cm² = 57 cm²

A line can be drawn corner-to-corner to divide the figure into two trapezoids. This is shown in the third attachment.

The upper right trapezoid has bases 11 cm and 4 cm, and height 2 cm.

The lower left trapezoid has bases 7 cm and 5 cm, and height 7 cm.

The area of a trapezoid is given by the formula ...

  A = 1/2(b1 +b2)h

Then the total area is ...

  Area = 1/2(11 cm +4 cm)(2 cm) +1/2(7 cm +5 cm)(7 cm) = 15 cm² +42 cm²

  Area = 57 cm²

The rectangle that encloses the entire figure is 7 cm high and 11 cm wide, so has an area of ...

  A = HW = (7 cm)(11 cm) = 77 cm²

From that area, the lower right corner space is cut out. It has dimensions 5 cm high by 4 cm wide, so an area of (5 cm)(4 cm) = 20 cm².

The area of the figure itself is the difference between the area of the bounding rectangle and the area of the cut-out space at lower right:

  Area = 77 cm² -20 cm² = 57 cm²

The area of the figure in the picture is 57 cm².

Answer:

8.  x = 9

9.  x = 9

10. x = 36

11.  x = 8

Step-by-step explanation:

Question 8

As the base of the triangle has been bisected, set the expressions either side of the perpendicular bisector equal to each other and solve for x:

[tex]\implies 5x-15=2x+12[/tex]

[tex]\implies 5x-15-2x=2x+12-2x[/tex]

[tex]\implies 3x-15=12[/tex]

[tex]\implies 3x-15+15=12+15[/tex]

[tex]\implies 3x=27[/tex]

[tex]\implies \dfrac{3x}{3}=\dfrac{27}{3}[/tex]

[tex]\implies x=9[/tex]

Question 9

As the base of the triangle has been bisected, set the expressions either side of the perpendicular bisector equal to each other and solve for x:

[tex]\implies 8x-63=4x-27[/tex]

[tex]\implies 8x-63-4x=4x-27-4x[/tex]

[tex]\implies 4x-63=-27[/tex]

[tex]\implies 4x-63+63=-27+63[/tex]

[tex]\implies 4x=36[/tex]

[tex]\implies \dfrac{4x}{4}=\dfrac{36}{4}[/tex]

[tex]\implies x=9[/tex]

Question 10

Angles on a straight line sum to 180°.  Therefore, as the other angle on the line is a right angle, equate the given expression to 90° and solve for x:

[tex]\implies (3x-18)^{\circ}=90^{\circ}[/tex]

[tex]\implies 3x-18=90[/tex]

[tex]\implies 3x-18+18=90+18[/tex]

[tex]\implies 3x=108[/tex]

[tex]\implies \dfrac{3x}{3}=\dfrac{108}{3}[/tex]

[tex]\implies x=36[/tex]

Question 11

Interior angles of a triangle sum to 180°.  Therefore, equate the sum of the given angles to 180° and solve for x:

[tex]\implies 90^{\circ}+(3x)^{\circ}+(8x+2)^{\circ}=180^{\circ}[/tex]

[tex]\implies 90+3x+8x+2=180[/tex]

[tex]\implies 11x+92=180[/tex]

[tex]\implies 11x+92-92=180-92[/tex]

[tex]\implies 11x=88[/tex]

[tex]\implies \dfrac{11x}{11}=\dfrac{88}{11}[/tex]

[tex]\implies x=8[/tex]

Answer:

Step-by-step explanation:

we cant see it so this is not able to answer

Answer:

Take a look at the attachments...

Hope this helps! :)

Answer:  64.95/5= C, C= 12.99

Step-by-step explanation:

If you want to figure out what the cost of 1 book you must divide the total cost of the books ($64.95) by how many books Jamal bought (5).

So the equation should look like this 64.95/5=C. Each book is $12.99.

Hope this helped!

3)The first angle in the triangle is three times that of the second angle. The second angle is two times that of the third angle. The ratio of angles in the triangle is 6:2:1.

4)The scale of a map measures 1 inch : 1250 miles. If the distance between two cities measures 3 inches on the map. The actual distance between the two cities on the ground is 3750 miles.

5)A sum of 2700 dollars is shared among Eric, Jo and Richard. Jo's share is two times that of Richard's share. Eric's share is three times that of Jo's share. Eric's share is 1800 dollars.

3) Let A,B,C are the angles of a triangle.

Given that, A =3B, B=2C

A = 3B =3(2C) = 6C

B=2C

Thus, A:B:C = 6C: 2C: C = 6:2:1

4) Given, scale of the map is 1 inch : 1250 miles

The distance between two cities is given as 3 inches.

The actual distance between two cities is 3*1250 = 3750 miles.

5) J is Jo's share, E is Eric's share, R is Richard's share

Given that, J=2R, E=3J

E=3J = 3*2R = 6R

E+J+R = 2700

6R + 2R + R = 2700

9R = 2700

R = 300 dollars

Eric's share = 6R = 6(300) = 1800 dollars

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The derivative of the function is  [tex]\frac{dy}{dx}=\frac{9x^2(x^3-4)^2}{1+(x^3-4)^6}[/tex].

The chain rule is a method for calculating the derivative of composite functions, which are created by joining one or more functions.

The given function is y = tan⁻¹(x³ -4)³.

The derivative of tan⁻¹(x) is 1/(1+x²).

Use the above fact and the chain rule to differentiate the function as follows:

[tex]y = \tan^{-1}(x^3-4)^3\\\\\frac{dy}{dx} = \frac{1}{1+((x^3-4)^3)^2}\cdot\frac{d}{dx}(x^3-4)^3\\\\=\frac{1}{1+(x^3-4)^6}\cdot3(x^3-4)^2\cdot3x^2\\\\=\frac{9x^2(x^3-4)^2}{1+(x^3-4)^6}[/tex]

Hence, the derivative of the function is  [tex]\frac{dy}{dx}=\frac{9x^2(x^3-4)^2}{1+(x^3-4)^6}[/tex].

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In 2014, the predicted population of Boca Raton will be 100000.

Given that the population function of Boca Raton is,

p(n) = 74760+1940n

So when the population of Boca Raton is 100000, then

p(n) = 100000

So,

100000 = 74760+1940n

1940n = 100000-74760

1940n = 25240

n = 25240/1940 = 14 (approximately)

So, the year in which the predicted population of Boca Raton reach 100000 is = 2000+14 = 2014

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Answer:

D)

Can you please mark me as "Brainliest"

x>1

below is the graph.

any questions in the comments:

The translation rule is T<5, 2> and the image of U' is (0,3)

Translation.

The transformation of a shape in a plane that preserves length, which means that the object is transformed without getting its dimensions affected. i.e., it may just be shifted to left/right/up/down is referred as translation.

Given,

The vertices of a rectangle are R(-5, -5), S(-1,-5), T(-1, 1), and U(-5, 1). A translation maps R to the point (0, -3).

Here we need to find the translation rule and the image of U

Here we know the given the vertices of rectangle which are  R(–5, –5), S(–1, –5), T(–1, 1), and  U(–5, 1).

And it is also given that the translation maps R(-5,-5) to the point (0, -3). we have to find the translation rule and the image of U.

In order to find the translation rule,

First we have to identify the Horizontal shift for the given point

That is calculated as,

=> 0 - (-5) = 5 unit

Which means R is shifted to 5 units horizontally.

Now, the Vertical shift is calculated as,

=> -3 - (-5) = 2 units

Which means R is shifted to 2 units vertically.

Therefore, the translation rule is < 5, 2 >  

So, the image of U(-5, 1) is calculated as,

=> -5 + 5 = 0

=> 1 + 2 = 3

Therefore, the point of the image U' is (0, 3)

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Answer:

x = 9

Step-by-step explanation:

7x + 18 = 81

     -18     -18

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

7x = 63

÷7    ÷7

-----------

x = 9

I hope this helps!

The total surface area of the cylinder is 175.84 squared inches

The surface area of a cylinder can be defined as the amount of space covered by the flat surface of the bases of the cylinder and the curved surface of the cylinder. The total surface area of the cylinder includes the area of the 2 bases of the cylinder which are in the shape of a circle and the area of the curved surface.

The formula is given as

A = 2πrh + 2πr²

We can substitute the values into the equation and solve

A = 2(3.14 * 4 * 3) + 2(3.14 * 4²)

A = 175.84 in²

The cylinder has a surface area of 175.84 in²

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Answer: 175.84

Step-by-step explanation:

Answer: 6/10

Step-by-step explanation: Six parts are shaded and even though the shaded parts are not touching each other, they will still count as shaded. 4 parts are not shaded and there is a total of 10 parts so the answer would be 6/10.

Hoped This Helped!

Answer:

If it is asking for the fraction of shaded parts the answer is A

If it is asking for the fraction of non-shaded parts the answer is B

Step-by-step explanation:

I would most likely go with A, because I have very rarely gotten a question asking for the non-shaded parts.

Answer:

Decimal: 0.08

Fraction: 2/25

Step-by-step explanation:

To convert a percentage to a decimal, we divide the percentage by 100, or move the decimal point to the left 2 times:

8/100 = 0.08

To convert a percentage to a fraction, we need to understand what a percentage is first. A percentage is a "number or ratio expressed as a fraction of 100". This means that percentages are numbers out of 100 (x% = x/100). Therefore, to convert 8% to a fraction, we divide 8 by 100:

8% = 8/100

Next, simplify the fraction

8/100 = 2/25

The value of x is x = -3.

What is solving an equation?

Finding an equation's solutions, or the values that satisfy the condition given by the equation, is known as solving an equation in mathematics. Solutions often consist of two expressions connected by an equals sign. One or more variables are marked as unknowns in order to find a solution.

Consider the given equation,

27 = (1/3)^x

This equation can be written as,

[tex]27 = \frac{1^x}{3^x}[/tex]

Here 1^x

1[tex]27 = \frac{1}{3^x}[/tex]

Take 3^x on numerator.

[tex]27 = 3^-^x[/tex]

Now 27 can be written as,  [tex]27 = (3)(3)(3) = 3^3[/tex]

⇒ [tex]3^3 = 3^-^x[/tex]

Applying the exponent rule: [tex]a^b=a^c[/tex] ⇒ b = c

So we get,

3 = -x

Multiply both sides by -1.

-3 = x

x = -3

Hence the value of x is x = 3.

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Answer:

x=([tex]\sqrt{41}[/tex]+7)/4, (-[tex]\sqrt{41}[/tex]+7)/4

Step-by-step explanation:

2x²+1=7x

2x²-7x+1=7x-7x

2x²-7x+1=0

2(x²-7x/2+1/2)=0

x²-7x/2+1/2=0

x²-7x/2+8/16=0

x²-7x/2+49/16-41/16=0

(x-7/4)^2-41/16=0

(x-7/4)^2-41/16+41/16=0+41/16

(x-7/4)^2=41/16

x-7/4=[tex]\sqrt{41}[/tex]/4    x-7/4=-[tex]\sqrt{41}[/tex]/4

x=[tex]\sqrt{41}[/tex]/4+7/4    x=-[tex]\sqrt{41}[/tex]/4+7/4

x=([tex]\sqrt{41}[/tex]+7)/4, (-[tex]\sqrt{41}[/tex]+7)/4

The equation of the parabola as described in the task content is; f (x) = -3 (x - 5)² + 9.

It follows from the task content that the equation of the parabola which has the same shape as f(x)=-3 x² but with vertex (5,9) in the form f (x) = a (x-h)² + k be determined.

Recall that the vertex of a quadratic equations of the given form is defined by the coordinates (h, k).

On this note, the required equation of the parabola by substitution of h and k is;

f (x) = -3 (x - 5)² + 9.

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The solution of the system of equations using substitution is, (2500, 5).

What is substitution method?

In the "by substitution" method, one of the equations is solved for one of the variables (you choose which one), which is then plugged back into the other equation where the chosen variable is "substituted" for and the second equation is then solved for. The first variable is then back-solved.

The equations are,

d = 200m + 1500             ..(1)

d = 500m                         ..(2)

Substitute d = 500m in equation (1),

500m = 200m + 1500

300m = 1500

      m = 5

Plug m = 5 in equation (2),

d = 500(5) = 2500

Hence, the solution of the system of equations using substitution is, (2500, 5).

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Answer: 16720yd

Step-by-step explanation:

Henry biked 9.5 miles to the park. How far is this in yards?

5280 ÷ 3 x 9.5 = 16720yd

Answer: 33 1/3 percent

Step-by-step explanation:

First, we need to find the volume of the tennis ball can, which is a cylinder.

The formula for the volume of a cylinder is pi r^2 h.

The radius of a tennis ball is 3.2 cm, so the radius of the cylinder would be 3.2 cm as well.

The height is equivalent to the height of three tennis balls, which is the diameter of 3 tennis balls. The diameter of one tennis ball is 6.4 cm, and we can multiply this by 6 to get 38.4 as our height.

We can plug in these values to our equation for the volume of the cylinder.

pi * 3.2^2 * 38.4

The volume of the cylinder is 393.216 pi.

Now, we need to find the volume of one tennis ball and multiply that by six.

The volume of a sphere is 4/3 pi r^3

We know our radius, 3.2, so we just have to substitute that into the equation.

4/3 pi 3.2^3 = 4/3 * pi * 32.768 = 43.69 and 2/3 pi for the volume of one tennis ball. If we multiply this by six, we get the volume of all the tennis balls, which is 43.6 and 2/3 *3 = 262.144 pi.

Now we have to find the percentage of the cylinder not occupied, so we can find one percent of the container and divide that by 262.144 pi.

1% of 393.216 = 3.93216

262.144 divided by this = 66 and 2/3, so 33 and 1/3 percent of the can is not occupied. The answer depends on how many places to round to, or whether or not to keep the answer as a fraction.

Answer:

u= 3

Step-by-step explanation:

Isolate a square root on the left hand side

Original equation

    √5u-10-√2u-1 = 0

    Isolate

    √5u-10 = √2u-1+0

Eliminate the radical on the left hand side

Raise both sides to the second power(√5u-10)2 = (√2u-1)2 After squaring

5u-10 = 2u-1

Solve the linear equation

Rearranged equation

     3u  -9 = 0

    Add  9  to both sides

     3u  = 9

    Divide both sides by 3

    A possible solution is :

    u = 3

Answer:

1. [tex]\frac{4}{27}[/tex]

2. D

Step-by-step explanation:

1. [tex]3^{-2} * 1 * 4^3 * 3^{-1}*4^{-2[/tex]

= [tex]3^{-3} * 4^1[/tex]

= [tex]\frac{4^1}{3^3}[/tex]

= [tex]\frac{4}{27}[/tex]

2. Remember the rule that 1/a^b is equal a^-b, in this case, [tex]\frac{1}{2^3}[/tex] is the same as [tex]2^{-3}[/tex], now 6 + (-3) = 3 -- which will be the exponent. [tex]2^3[/tex] is correct.

Answer:

C

Step-by-step explanation:

the directrix and focus are equidistant from the vertex

vertex = (0, 1 ) and focus = (0, - 2 ) then directrix is a horizontal line above the vertex with equation

y = 4

the focus and directrix are equidistant from any point (x, y ) on the curve.

using the distance formula

[tex]\sqrt{x-0)^2+(y-(-2))^2}[/tex] = | y - 4 |

[tex]\sqrt{x^2+(y+2)^2}[/tex] = | y - 4 | ( squaring both sides )

x² + (y + 2)² = (y - 4)²

x² + y² + 4y + 4 = y² - 8y + 16 ( subtract y² from both sides )

x² + 4y + 4 = - 8y + 16 ( add 8y to both sides )

x² + 12y + 4 = 16 ( subtract x² + 4 from both sides )

12y = - x² + 12 ( divide through by 12 )

y = - [tex]\frac{1}{12}[/tex] x² + 1

Answer: Y = -[tex]\frac{1}{12}[/tex][tex]x^{2}[/tex] + 1

Step-by-step explanation: Correct on Edmentum

Answer:

(x +5)/-16=-1 this is the answer

Answer:

shsjsjsjsjshsh#6#7#7##+-##6#3

The value of expression when r = 0.1 , n = 12 and t = 2 is,

⇒ 24.192

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ (1 + r/n) nt

Now, We can put r = 0.1 , n = 12 and t = 2 in above equation as;

⇒ (1 + r/n) nt

⇒ (1 + 0.1/12) 12 x 2

⇒ (1 + 0.008) 24

⇒ 1.008 x 24

⇒ 24.192

Thus, The value of expression when r = 0.1 , n = 12 and t = 2 is,

⇒ 24.192

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