The graph below represents the result of a survey in which a number of students
reported how many letters were in their last names.


How many students have a name that's longer than 8
letters?

The image of the triangle is missing, so i have attached it.

Also, the options are;

A) The apothem can be found using the Pythagorean theorem.

B) The apothem can be found using the tangent ratio.

C) The perimeter of the equilateral triangle is 15 cm.

D) The length of the apothem is approximately 2.5 cm.

E) The area of the equilateral triangle is approximately 65 cm².

Answer:

Options A, B & D are true

Step-by-step explanation:

A) We are told that the triangle is an equilateral triangle.

Thus, the 3 sides equal 8.7 cm.

Now from the image, b is half of one of the sides.

Thus, b = 8.7/2 = 4.35 cm

Now, we want to find the apothem "a".

Using Pythagoras theorem, we have;

a² + 4.35² = 5²

a² = 25 - 18.9225

a² = 6.0775

a = √6.0775

a ≈ 2.5 cm.

Thus, option A is true as Pythagoras theorem was able to calculate the apothem "a"

B) since the main triangle is equilateral, it means each angle is 60°.

Now, the radius line from one corner point to the center will divide the 60° angle into 2 equal parts.

Thus, the angle made by the radius line with the base of the triangle is 60/2 = 30°

Now, from tangent ratios, we know that;

Opposite/Adjacent = tan θ

In the small triangle, opposite is apothem "a" while adjacent is b = 4.35 cm

Thus;

a/4.35 = tan 30

a = 4.35 tan 30

a ≈ 2.5 cm.

Thus, option B is correct as Tangent ratio can be used to find the apothem

C) The perimeter of equilateral triangle = 3x

Where x is length of one side.

One side is 8.7 cm

Thus, perimeter = 3 × 8.7 = 26.1 cm

Thus option C is not correct.

D) From calculations above, we saw that in both options A & B, the apothem is approximately 2.5 cm.

Thus, option D is true.

E) Area of triangle is;

A = ½ × base × height

Base = 8.7 cm

To get height, we will use trigonometric ratio. Thus;

h/8.7 = sin 60°

h = 8.7 sin 60°

Thus;

A = ½ × 8.7 × 8.7 sin 60°

A = 32.77 cm²

Thus is not equal to 65 cm². Thus, option E is not correct.

The statements that are true for the considered equilateral triangle are:

For a regular polygon, the apothem is the line segment from the center of the polygon to the mid of one of the sides of the considered polygon.

For this case, referring to the figure attached below, we have:

Since the triangle is equilateral, there can be 6 congruent triangles like BOD.

Thus, Area of triangle ABC = 6 × Area of triangle BOD

Area of BOD = [tex]\dfrac{1}{2} \times x \times 4.35 = 2.175x \: \rm cm^2[/tex]

Area of ABC = [tex]6 \times 2.175x = 13.05x \: \rm cm^2[/tex]

The length of the apothem is x cm, and can be obtained by using Pythagoras theorem.

We can also use the tangent ratio as the line segment BO is bisecting the internal angle B (each internal angle is of 60 degrees in an equilateral triangle), so angle OBD is of 60/2 = 30 degrees. So using angle and the fact that tangent ratio is ratio of side opposite to angle and the remaining adjacent side(not hypotenuse).

[tex]tan(30^\circ) = x/4.35 \implies x = 4.35 \times \tan(30^\circ) \approx 2.5 \: \rm cm[/tex]

Using Pythagoras theorem too, we can get the value of x as:

[tex]5^2 = 4.35^2 + x^2\\x = \sqrt{25 - 18.9225} \approx 2.465 \: \rm cm \approx 2.5 cm[/tex]

Thus, area of the equilateral triangle ≈ [tex]13.05 \times x \approx 13.05 \times 2.5 = 32.575 \: \rm cm^2[/tex]

This isn't 65 sq. cm.

Thus, the statements that are true for the considered equilateral triangle are:

Learn more about tangent ratio here:

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Answer:

a. There is a phase shift to the left

Step-by-step explanation:

The correct statement for the graph of y = cos (x + pi/6) compared to the graph of y = cos(x) is given by: Option A: There is a phase shift to the left.

The transformation of a function may involve any change.

Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:

Horizontal shift (also called phase shift):

Vertical shift:

Stretching:

For this case, the parent function y = cos(x) is transformed to make the function y = cos (x + pi/6)

Thus, there is left shift of the graph of the function y =cos(x).

The graphs of both functions (parent function in red color and transformed function in blue color) is given below.

Thus, the correct statement for the graph of y = cos (x + pi/6) compared to the graph of y = cos(x) is given by: Option A: There is a phase shift to the left.

Learn more about transforming functions here:

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Answer:

y = 1/2x - 1

Step-by-step explanation:

The x value is divided by 2 and then has 1 subtracted from it.

also for future posts, put the question in the title that way people know what you need and can click if they know the answer.

Answer: C and B

Step-by-step explanation: because its rational.

-LearnWithBrainly

Answer:

The one on the very top left corner is the right one.

Step-by-step explanation:

It shows the exact data that you were looking for: ten small apples were green and 3 out of the 12 large apples were red.

Answer:

Can you please give us figure of following ?

Answer:

its the last one 212°

212°

212°

212°

212°

212°

Step-by-step explanation:

212°

Answer:

Q = mCpΔT where Q is the energy in heat (joules), m is the mass (grams), Cp is the specific heat capacity (J/g/°C), and ΔT is the change in temperature (T2 - T1) in °C.

Step-by-step explanation:

So, since Q = mCpΔT then m = Q/(CpΔT) or (45.0)/(0.780•2.00) = 45/1.56 = 28.846 grams. Since there are 3 sig figs, we round to:

m = 28.8 g

Using the relation between velocity, distance and time, it is found that:

Velocity is distance divided by time, that is:

[tex]v = \frac{d}{t}[/tex]

A plane traveling with the wind travels 900 miles in 5 hours, hence:

[tex]v_a + v_w = \frac{900}{5}[/tex]

[tex]v_a + v_w = 180[/tex]

The return trip is against the wind and takes 9 hours, hence:

[tex]v_a - v_w = \frac{900}{9}[/tex]

[tex]v_a - v_w = 100[/tex]

From the first equation, we have that:

[tex]v_w = 180 - v_a{/tex]

Replacing on the second:

[tex]v_a - v_w = 100[/tex]

[tex]v_a - 180 + v_a = 100[/tex]

[tex]2v_a = 280[/tex]

[tex]v_a = 140[/tex]

[tex]v_w = 180 - 140 = 40{/tex]

Hence:

More can be learned about the relation between velocity, distance and time at https://brainly.com/question/24316569

The minimum possible area of each square cardboard piece which is used to produce circular drink coasters is 72.25 in².

The equation of the circle is the equation which is used to represent the circle in the algebraic equation form with the value of center point in the coordinate plane and measure of radius.

The standard form of the equation of the circle can be given as,

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Here (h,k) is the center of the circle and (r) is the radius of the circle.

A company produces circular drink coasters. the equation which represents the size of a coaster is,

[tex]x^2+ y^2 = 18.0625[/tex]

The units are in the inches. This equation can be written as,

[tex]x^2+ y^2 = \dfrac{289}{16}\\x^2+ y^2 =\left( \dfrac{17}{4}\right)^2[/tex]

Compare it with the equation of the circle, we get,

[tex]h=0\\k=0\\r=\dfrac{17}{4}\rm\; in[/tex]

The radius of the circular coaster is 17/4. The diameter of it is,

[tex]d=2\times\dfrac{17}{4}\\d=\dfrac{17}{2}\rm \; in[/tex]

Now, each coaster is cut from a square piece of cardboard. The diameter of the circular coaster will be equal to the side of the square piece of cardboard.

[tex]a=d=\dfrac{17}{2}\rm\; in[/tex]

The area of the square is the square of its side. Thus, the area of a square piece of cardboard is,

[tex]A=a^2\\A=\left(\dfrac{17}{2}\right)^2\\A=72.25\rm\; in^2[/tex]

Thus, the minimum possible area of each square cardboard piece which is used to produce circular drink coasters is 72.25 in².

Learn more about the equation of circle here;

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Answer:

20

Step-by-step explanation:

Given:

Lisa is checking out at the bookstore.

Each book (b) costs $1.50 and she has a $5 off coupon she can use.

She wants to spend $25 or less in the bookstore.

Solve:

Since there is a $5 off coupon..

$1.5b - $5.00<=$25.00

$1.5b<= $30.00

$1.5b/1.5 = $30.00/1.5

b=20

Lisa can buy 20 book.

~lenvy~

Answer:

we should take common first

3n+12

taking 3 common

3(n+4)

Answer:

1. 155 yd², 2. 379.54 ft², 5. x = 65.82π

Step-by-step explanation:

1. A = (1/2) · (3 + 13) · 8

A = (1/2)(16)(8)
A = 64
A = bh
A = 13*7
A = 91
64 + 91 = 155
155 yd²

2. A = bh
A = 25x25
A = 625
A = πr²
A = 3.14*12.5²
A = 3.14*156.25
A = 490.625
490.925/2 = 245.4625
625 - 245.4625 = 379.5375
379.54 ft²

3. and 4. Sorry, I don't know how to solve these

5. A = πr²
A = 3.14*7²
A = 3.14*49
A = 153.86
x/154 = 153.86π/360
360x = 154*153.86π
360x = 23694.44π
x = 65.8178889π
x = 65.82π

Hope this helps :)

Answer:

I believe the answer is 760 ft²

Step-by-step explanation:

16×39/2=312

(17+39)(16)/2=448

448+312=760ft²

let me know if it was right. good luck!

The value of the hypotenuse y will be equal to y = 2.8 inches.

The volume of the prism is equal to the product of the area of its base and the height of the prism.

[tex]\rm V=Area \ of\ triangular \ base\times Height \ of \ prism[/tex]

The volume oif the prism is =4 cubic inches

Height of the prism = x inches

Base of the right angle isosceles triangle will be =x inches

The hypotenuse is given = y

Now

[tex]\rm V=\dfrac{1}{2}\times Base\times Height \times height \ of \ prism[/tex]

[tex]V=\dfrac{1}{2} \times x \times x \times x[/tex]

[tex]x^3=8[/tex]

[tex]x=2[/tex]

Now by pythagorus theorem

[tex]y^2=h^2+b^2[/tex]

[tex]y^2=x^2+x^2[/tex]

[tex]y^2=2x^2=2\times 2^2[/tex]

[tex]y=2\sqrt{2}=2.82[/tex]

Thus the value of the hypotenuse y will be equal to y = 2.8 inches.

To know more about Volume of prism follow

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Answer:

2.8 INCHES

Step-by-step explanation:

Answer:

(b1+b2)h divided by 2 is the formula for a trapezoid

Step-by-step explanation:

ANSWER: 468 ft (squared?)

Answer:   If you sketch this out, you should be able to convince yourself that if you drew a line parallel to the bases and halfway between them, and a vertical at the end of that line, there would be an extra triangle on the longer base that would just fit into the space at the end of the shorter base, if you cut and pasted it.

You should also be able to convince yourself by what you know about similarity that the length of that parallel halfway line is just halfway between the lengths of the bases (you can add them and divide by two).

So your trapezoid (trapezium, we call ’em this side of the pond) has the same area as a rectangle with an altitude equal to the trapezoid’s and a width equal to the sum of those bases divided by two. And since you know about rectangles, you’re home and dry. I suggest you do the sketch, fill in the numbers, and then you’ve completed a model piece of homework that should earn full marks and the teacher’s approval.

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

-9=9

9+12=21

Answer:

144

Step-by-step explanation:

Because if you multiply 9*12=108 and 12*12=144

Answer: 144 Cubic Feet

Explanation: Multiply all of your numbers together to get your volume.

Numbers : Length(12) x Width(3) x Height(4) = 144 cubic feet.

I hope this helps you! :)

try to understand the example.

I used 20/100 since 20% is obviously 20/100 and I used ×1000 cus for 1000, you want 20%

hope it helps...!!!

Answer:

3x + 5y = 15

Find gradient:

coordinates taken: (5, 0), (0, 3)

[tex]\rightarrow \sf \dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\rightarrow \sf \dfrac{3-0}{0-5}[/tex]

[tex]\rightarrow \sf -\dfrac{3}{5}[/tex]

equation:

[tex]\sf \bold{ y = m(x) + b}[/tex]

[tex]\rightarrow \sf y = -\dfrac{3}{5} x + 3[/tex]

[tex]\rightarrow \sf y = -\dfrac{3}{5} x + \dfrac{15}{5}[/tex]

[tex]\rightarrow \sf 5y =-3x+15[/tex]

[tex]\rightarrow \sf 3x+5y =15[/tex]

Take two points

So

equation of line in intercept form

[tex]\\ \rm\rightarrowtail \dfrac{x}{a}+\dfrac{y}{b}=1[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{x}{5}+\dfrac{y}{3}=1[/tex]

[tex]\\ \rm\rightarrowtail 3x+5y=15[/tex]

Answer:

8.16, 8.2, 8.245, 8.25

Step-by-step explanation:

8 1/6 = 8.16

41/5 = 8.2

The exact numbers listed in this problem are given by:

Exact numbers are numbers that are not rounded. Volumes and lengths, for example, are usually rounded, hence they cannot be called exact.

Thus, the exact numbers listed in this problem are given by:

More can be learned about exact numbers at https://brainly.com/question/14089554

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The random selection of a blue marble is an illustration of probability

You should expected to pull a blue marble 10 times

The given parameters are:

Blue = 16

Red = 12

Green = 12

The total number of marbles is:

Total = 16 + 12 + 12

So we have:

Total = 40

The probability of selecting a blue marble is:

[tex]P(Blue) = \frac{16}{40}[/tex]

When 25 marbles are selected, the expected number of blue is:

[tex]Blue = n * P(Blue)[/tex]

So, we have:

[tex]Blue = 25 * 16/40[/tex]

[tex]Blue = 10[/tex]

Hence, the expected number of blue marbles is 10

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Answer: look at the image

Step-by-step explanation:

Answer:

approximately 14

Step-by-step explanation:

first find out how many sets of 60 there are

200/60=3.3

3.3 sets of 4 apples

but you can't have 2/3 of a rotten apple

so 3.5 sets of 4 rotten apples

4x3.5=14

Answer:

its 4 i think tell me if i am wrong

Step-by-step explanation:

The geometric sequence can increase or decrease exponentially

The correct sum of the 4th and the 5th terms is 432

The given parameters are:

Initial value (a) = 4

Growth factor (r) = 3

The nth term of a geometric sequence is calculated as:

[tex]T_n = ar^{n-1}[/tex]

This gives

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

For the 4th term; we have:

[tex]T_4 = 4 * 3^{4-1}[/tex]

[tex]T_4 = 108[/tex]

For the 5th term, we have:

[tex]T_5 = 4 * 3^{5-1}[/tex]

[tex]T_5 = 324[/tex]

Add the 4th and the 5th terms

Sum = 108 + 324

Sum = 432

Hence, the correct sum of the 4th and the 5th terms is 432

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