Toula has just baked a cake in the shape of a rectangle. She
wants to divide the cake into two right-angled triangles by
cutting along a diagonal of the cake. Toula is then going to place
a cake ribbon around the outside of each of the two triangular
pieces of cake. If the length of the cake is 32 cm and its width is
24 cm, how much cake ribbon will she need to buy, giving your
answer to an appropriate accuracy.

Answer:

9.9 inches

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh  where b is the length of the base and h is the length of the height

49 = 1/2 x*x

Multiply each side by 2

2*49 = x^2

98 = x^2

Take the square root of each side

sqrt(98) = sqrt(x^2)

9.899494937 =x

Rounding to the nearest tenth

9.9 =x

Experimental probability of the name Alex being drawn is 4/10

This is because out of the ten times a name was drawn, Alex was drawn four times.

If the experiment was repeated 1,000 times, Ella's name could be expected to be drawn 200 times.

This is because of the ten names drawn, Ella's name was drawn twice which is 20% and 20% of 1,000 is 200.

Answer:

diverging

Step-by-step explanation:

A regular way to know if a series is converging or diverging, is to check is as the number of terms increase, the value of such terms also increase.

So, if for example, we have:

[tex]A_n > A_{n-1}[/tex]

We know that the series will not converge, because eventually the terms will be very large, and the series will diverge.

In this case we have the series:

1/4, 1/2, 1, 2

So each term is two times the previous one, thus, the n-th term will be larger than the n-th minus one term, so we can conclude that this series diverges.

Answer:

D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

XYZ is congruent to DEF so:

X = D

Y = E

Z = F

Answer:

R (3,-2) S(5,2) T(6,0)

Step-by-step explanation:

Answer:

[tex] {x}^{2} - 9[/tex]

Step-by-step explanation:

[tex](x−3)(x+3)[/tex]

[tex]x(x+3)−3(x+3)[/tex]

[tex]x \times x+x \times 3−3x−3 \times 3[/tex]

[tex]x \times x−3 \times 3[/tex]

[tex] {x}^{2} - 9[/tex]

Respuesta:

Media = 6

Mediana = 6

Modo = 6

Desviación media = 1

Desviación estándar = 1.317

Explicación paso a paso:

Dados los datos:

5, 5, 8, 4, 6, 6, 7, 5, 6, 7, 4, 8, 6, 5, 6, 8

Datos reorganizados: 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8

La media: Σx / n = 96/16 = 6

El modo, = 6 (valor más alto que ocurre en los datos, valor de datos con la frecuencia más alta)

La mediana = 1/2 (n + 1) ésimo término

Mediana = 1/2 (17) término = 8.5 th término = (6 + 6) / 2 = 6

La desviación media = Σ (x - media) / n

Usando la calculadora, la desviación media = 1

La desviación estándar = √ (Σ (x - media) ² / n-1)

Desviación estándar = 1.317

Answer:

A

Step-by-step explanation:

2x + x = 3x

y - 3y = 2y

Answer:

[tex]x= 23.775.[/tex]

Step-by-step explanation:

[tex]\text{We have} \\\cos(18\textdegree) = \frac{x}{25} \\\Rightarrow x= 25\cos(18\textdegree)\\\Rightarrow x= 25 \times 0.951\\\Rightarrow x= 23.775.[/tex]

Step-by-step explanation:

b= 140 ( alternate angle)

k = 130 ( veetically opposite angles)

may it help ub

Answer:

(-1, 8)

the value of a is 8

Answer:

(c) 84

hope this helps!!!!

Answer:

31793 cm^3

Step-by-step explanation:

Equation

Volume = [tex]\pi[/tex] * r^2 * h

Givens

d = 2*r

d  = 30

r = 15

h = 45

[tex]\pi[/tex] = 3.14

Solution

V = 3.14 * 15^2 * 45

V = 31793 rounded.

Answer:

y < 4 or y > 9

Step-by-step explanation:

The symbol < means less than, while the symbol > means greater than. So, the inequality y < 4 means that y is less than 4, and the inequality y > 9 means that y is greater than 9. When put together you have all real numbers y that are less than 4 or greater than 9.

Answers:

[tex]\csc(\theta) = \frac{7\sqrt{33}}{33}\\\\\sin(\theta) = \frac{\sqrt{33}}{7}\\\\\cot(\theta) = \frac{4\sqrt{33}}{33}\\\\[/tex]

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

Explanation:

Before we can find the trig ratios, we need to determine the length of the missing side. Apply the pythagorean theorem

[tex]a^2+b^2 = c^2\\\\4^2+b^2 = 7^2\\\\16+b^2 = 49\\\\b^2 = 49-16\\\\b^2 = 33\\\\b = \sqrt{33}[/tex]

The vertical side is [tex]\sqrt{33}[/tex] units long.

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

The side we just found is the opposite side to angle [tex]\theta[/tex] (greek letter theta)

The hypotenuse is 7 units long. The hypotenuse is always opposite the right angle.

Divide the hypotenuse over opposite to get the cosecant.

[tex]\csc(\theta) = \frac{\text{hypotenuse}}{\text{opposite}}\\\\\csc(\theta) = \frac{7}{\sqrt{33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33}*\sqrt{33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33*33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33^2}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{33}\\\\[/tex]

Note: In the third step, I multiplied top and bottom by sqrt(33) to rationalize the denominator.

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

Recall that sine is the reciprocal of cosecant, and vice versa.

So we'll use the same idea as before, but flip the original fraction.

[tex]\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\theta) = \frac{\sqrt{33}}{7}\\\\[/tex]

The denominator is already a rational number, so there's not much else to do here.

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

Cotangent is the ratio of adjacent over opposite

[tex]\cot(\theta) = \frac{\text{adjacent}}{\text{opposite}}\\\\\cot(\theta) = \frac{4}{\sqrt{33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33}*\sqrt{33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33*33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33^2}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{33}\\\\[/tex]

The steps are pretty much nearly identical as the section involving csc, except we're using the adjacent in place of the hypotenuse (so that means we use 4 in place of 7).

Answer:

Answer:

It is y = -4/5x - 2 because you go left 4 and down 5 which makes both negative. And of course it is minus two.

Answer:

11-

3 / 8 * 5 / 5 = 15 / 40

2 / 5 * 8 / 8 = 16 / 40

16 / 45 + 15 / 45 =

31 / 40

12-

5 / 6 * 9 /9 = 45 / 54

4 / 9 * 6 / 6 = 24 / 54

24 / 54 + 45 + 54 = 69 / 54

69 / 54 =

1   15 / 54

Answer:

85.7 ounces.

Step-by-step explanation:

428.5/5 = 85.7

Therefore, Ms. Emily put 85.7 ounces of pretzels into each bowl.

Answer:

85.7 ounces

Step-by-step explanation:

428.5 ounces ÷ 5=85.7 ounces

Answer:

x = 80

Step-by-step explanation:

Both angles together form 180, therefore x is 80

Answer:

x = 80

Step-by-step explanation:

100 and x form a straight line so they add to 180

x+100 =180

Subtract 100 from each side

x = 180-100

x = 80

Answer:

the missing side is 6

Step-by-step explanation:

Using the Pythagorean theorem, ([tex]a^{2} + b^{2} = c^{2}[/tex]), for right triangles, you get [tex]4^{2} + (2\sqrt{5}) ^{2} = c^{2}[/tex].  Since the square cancels the square root for side b you get [tex](2^{2})*(5)[/tex] which equals 20. This makes your equation go to 16+20 = [tex]c^{2}[/tex]. Then add the numbers to make [tex]36=c^{2}[/tex]  solve for c by taking the square root of both sides to get c = 6.

Answer:

Step-by-step explanation:

here,

base=28 ft

height=24 ft

are of parallelogram=base*height

=28*24

=672 ft^2

Answer:

672 ft²

Step-by-step explanation:

Area of parallelogram is the same as the area of a rectangle.

28 × 24 = 672 ft²

Answer:

Daylilies- $11, Ornamental grass- $7

Step-by-step explanation:

For this one, you want to convert this into simultaneous equations.

If we let d be cost of one daylily and o be cost of one bunch of ornamental grass, we can write the equations as 2d+3o=43 and 6d+3o=87.

From there, we can see they share a like term (3o), so we subtract one equation from the other (since they both are preceded by a +). This gives 4d=44.

Dividing both sides by 4 isolates d, leaving d=$11.

We can substitute this value into either equation to work out o (I'm using the first one as it is easier). This makes it 2×11+3o=43, or 22+3o=43.

From there, we subtract 22 from both sides, giving 3o=21, and dividing by 3 gives a final result of o=$7.

**This content involves writing and solving simultaneous equations, which you may wish to revise. I'm always happy to help!

All working out:

d- cost of one daylily o- cost of one bunch of ornamental grass

2d+3o=43 6d+3o=87

6d+3o=87

 -     -     -

2d+3o=43

=     =    =

4d      =44

÷4        ÷4

d        =11

2d+3o=43

2×11+3o=43

22+3o=43

3o=21

o=7

Answer:33

Step-by-step explanation:

trust

Answer:

hope this helps

Step-by-step explanation:

-they do not have the same slope

-their lines are not parallel

there's probably more but i cant quite think of it as of now

Answer:

5x2+20x−15

Step-by-step explanation:

Answer:

B. -√13/4

Step-by-step explanation:

cos 0 = -√3/4 => x=-√3 , h=4

tan 0 > 0

y should be on quadrant III

y= √4²-3= √16-3=√13 => -√13

so, sin 0 = y/h = -√13/4

Answer:

B. -√13/4

Step-by-step explanation:

:)

Answer:

Sum of the four numbers in terms of x would be 4x+4

Step-by-step explanation:

x-2 + x + x+2 + x+4 = sum

4x+4 = sum

Answer:

43347

Step-by-step explanation:

just move decimal to the right 4 times.

Answer:

please give me brainliest for quest

Step-by-step explanation: