The dual bar chart shows the hair colour of boys and girls in a year group.
20
18
16
14
12
10
8
6
4
Black
Brown
Blonde
What fraction of the students are girls?
Give your answer in its simplest form
Frequency
20
Hair colour
Red
Boys
Girls

Answer:

[tex]A=41\pi\: \text{units}^2\approxA\approx128.8053\:\text{units}^2[/tex]

Step-by-step explanation:

I assume you mean [tex]r=3+8\sin\theta[/tex]:

Use the formula [tex]\displaystyle A=\int\limits^a_b \frac{1}{2} {r(\theta)^2} \, d\theta[/tex] where [tex]a[/tex] and [tex]b[/tex] are the lower and upper bounds and [tex]r(\theta)[/tex] is the equation of the polar curve.

Since the graph is symmetrical about the line [tex]\displaystyle \theta=\frac{\pi}{2}[/tex], let the bounds of integration be [tex]\displaystyle \biggr(-\frac{\pi}{2},\frac{\pi}{2}\biggr)[/tex] to find half the area of the curve, and then find twice of that area:

[tex]\displaystyle A=\int\limits^a_b \frac{1}{2} {r(\theta)^2} \, d\theta\\\\A=2\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \frac{1}{2} {(3+8\sin\theta)^2} \, d\theta\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} 9+48\sin\theta+64\sin^2\theta \, d\theta\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} 9+48\sin\theta+64\biggr(\frac{1-\cos2\theta}{2} \biggr) \, d\theta\\\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} (9+48\sin\theta+32-32\cos2\theta) \, d\theta[/tex]

[tex]\displaystyle A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} (41+48\sin\theta-32\cos2\theta) \, d\theta\\\\A=41\theta-48\cos\theta-16\sin2\theta\biggr|^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\[/tex]

[tex]A=\biggr[41\biggr(\frac{\pi}{2}\biggr)-48\cos\biggr(\frac{\pi}{2}\biggr)-16\sin2\biggr(\frac{\pi}{2}\biggr)\biggr]-\biggr[41\biggr(-\frac{\pi}{2}\biggr)-48\cos\biggr(-\frac{\pi}{2}\biggr)-16\sin2\biggr(-\frac{\pi}{2}\biggr)\biggr]\\\\A=\biggr[\frac{41\pi}{2}-24\sqrt{2}\biggr]-\biggr[-\frac{41\pi}{2}+24\sqrt{2}\biggr]\\ \\A=41\pi\\\\A\approx128.8053[/tex]

Thus, the area of the curve is 41π square units. See below for a graph of the curve and its shaded area.

Answer:

8 cm

Step-by-step explanation:

because when it's reduced we multiply the side length by 1/3 * 6 = 2cm and the volume will equal v = a^3 = 2^3 = 8cm

Answer:

8cm

Step-by-step explanation:

step1: 6/3=2

volume of a cube =x*x*

v

:=8cm

v=2×2×2

vvv v

Answer:

x=7

Step-by-step explanation:

x(x-2) (x+4) =385

distribute the x and solve

The value of x is 8 in.

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

Length = x + 4

Width = x

Height = x - 2

The volume of the rectangular prism = 385 in³

The volume of the rectangular prism = length x width x height

Now,

length x width x height = 385

(x + 4) x (x - 2) = 385

(x + 4) (x² - 2x) = 385

x³ - 2x² + 4x² - 8x = 385

x³ + 2x² - 8x = 385

This is a cubic polynomial.

f(x) = x³ + 2x² - 8x - 385

f(x) = a³ + bx² + cx + d = 0

Using the calculator we get,

Roots:

x = -3.20181 + 5.96339 i (rejected)

x = -3.20181 - 5.96339 i (rejected)

x = 8.40362 = 8

Thus,

The value of x is 8 in.

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Answer:

hope this will help you........

Answer:

25

Step-by-step explanation:

Please refer to the picture;

By using partial products to multiply, 52 × 6 is 312

From the question, we are to use partial products to multiply 52 × 6

The partial multiplication is shown below

5 2

× 6

300       6 × 5 tens (That is, 6 × 5 × 10 = 300)

+ 12       6 × 2 ones (That is, 6 × 2 × 1 = 12)

312  

Hence, by using partial products to multiply, 52 × 6 is 312

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Answer:

x = 31.

Step-by-step explanation:

93 = x + 62  (External Angle Theorem).

x = 93 - 62

= 31

Answer:

Number of terms = 4 (there are four terms)

coefficients = the coefficient of ab = 4

✓✓✓ ✓✓✓ ✓ b = -5

✓✓✓ ✓✓✓ ✓ m = 1

constant terms = 3

Hope it helped!!

Number of terms, Coefficients, Constant terms are 4,2 and 1

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

3 + 4ab - 5b + m

Number of terms here are

=4

Coefficients we have

=2

Constant terms

=1

Therefore, the answer to this algebra will be 4,2 and 1

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After the reflection over the line x = 0, the coordinates will be:

J' = (2, 1)

K' = (0, 4) = K

For any point (x, y), if we apply a reflection across the line x = 0, the image after the reflection will be (-x, y).

So it only changes the sign of the x-component.

In the graph, we can see that J = (-2, 1). So after the reflection, we will have:

J' = (2, 1).

And we also can see that K = (0, 4), then after the reflection, we have:

K' = (-0, 4) = (0, 4) = K

So point K does not change under that reflection.

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Answer:

e.  0.308.

Step-by-step explanation:

I can't draw the tree diagram but the answer is

P(red first) = 7/14 = 1/2

P( then black)  = 4/13

P(red then black) = 1/2 * 4/13 = 2/13

P(black first) = 4/14 =  2/7

P( then red)  = 7/13

P(black then red) =2/7 * 7/13 = 2/13

So Probability of red and black in any order

= 2/13 + 2/13  = 4/13

= 0.308.

Assuming that the all the cards have the same probability of being drawn we get:

We have a deck of 52 cards.

A) The probability of drawing an even-numbered card is given by the quotient between the number of even-numbered cards and the total number of cards.

On the 52 card deck, there are 16 even cards (2, 4, 6, 8 for each type), so the probability is:

p = 16/52

Then the probability of drawing a face card is given in the same way, notice that now there are 51 cards in the deck and 12 face cards, so we get:

q = 12/51

The joint probability is the product of these two:

P = (16/52)*(12/51)  = 0.07

b) Both cards are 4 or larger.

There are 6 cards equal or larger than 4 for each type, so the probability for the first card is:

p = 24/52

For the second card, there is one card less in the deck (and one card less that is equal or larger than 4) so the probability is:

q = 23/51

The joint probability is:

P = (24/52)*(23/51) = 0.21

C) There are 6 black face cards, so the probability first is:

p = 6/52

Then there are 2 black cards with the number 5, so the probability is:

q = 2/51

The joint probability is:

P = (6/52)*(2/51) = 0.001

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The probability that a student who plays a sport does not play an instrument is 13 / 30.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that a student who plays a sport does not play an instrument = 13 / total number of students

13 / (12 + 13 + 2 + 3) = 13 / 30

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Answer:

2.96 cm to the nearest hundredth.

Step-by-step explanation:

V = 3.14 r^2 h

226 = 3.14 * r^2 * 8.2

r^2 = 226 / (3.14*8.2)

r^2 = 8.7774

r =  2.96 cm to the nearest hundredth.

Answer:

60 degrees

Step-by-step explanation:

since its a vertically opposite angle so angle 1 will equal angle 3

Answer:

60

Step-by-step explanation:

Answer:

32 1/3

Step-by-step explanation:

Answer:

The answer is [tex]31\frac{9}{10}[/tex].

Step-by-step explanation:

Make sure to follow this formula

[tex]2(lw)+(lh)+(wh)[/tex]

[tex]2(1.3x1.5)+(1.3x5)+(1.5x5) \\= 2(1.95+6.5+7.5)\\=31.9=31\frac{9}{10}[/tex]

Answer:

y = -5x + 4.

Step-by-step explanation:

y = mx + c  is the general form

- where m = the slope of the line and c is the y-value where the graph cuts the y-axis.

The graph passes through the points (0, 4) and (1, -1) so the slope

= (Y2 - y1) / (x2 - x1)

= (-1-4) / (1-0)

= -5 = m.

and c = 4.

Answer:

84 ft

Step-by-step explanation:

16 + 16 + 26 +26 = 84

Answer:

I do believe its 5 units, if I am incorrect I apologize

Step-by-step explanation:

Answer:

13 x 3 ft

Step-by-step explanation:

RECTANGULAR deck

L x W = 39 ft^2

(w+10)  x w = 39

w^2 + 10w - 39 = 0

(w-3)(w+13) = 0        w = 3    or  -13 (throw out)

w = 3    then l = 10 +3 = 13

Answer: height of a building

Step-by-step explanation:

a^2 + b^2 = c^2

used for finding missing side angle of a triangle

The integer representing the change in the number of DVDs sold is -10000.

Given, The number of DVDs shipped to an online retailer was 10,000 less than the previous year.  

We have to Use an integer to describe the change in the number of DVDs sold.

Now, let the number of DVDs shipped to an online retailer in the previous year be x.

Then, according to the given information, DVDs shipped to the online retailer this year will become x – 10000

So, now, the change in the number of DVDs sold = DVDs sold this year – DVDs sold last year

= x – 10000 – x

= 0 – 10000

= - 10000

Hence, the integer representing the change in the number of DVDs sold is -10000.

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The resulting ordered pair if the value of the independent variable is –2 will be B. (-2, -4).

From the information given, it was stated that we should calculate the resulting ordered pair if the value of the independent variable is –2.

Therefore, in this case, x = -2. Therefore, we will play it into the equation. This will be:

f(x)=2x³ +3x²

= 2(-2)³ + 3(-2)²

= -16 + 12

= -4

Therefore, the ordered pair will be (-2, -4).

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The probability that the director chooses 3 boy kittens and 2 girl kittens is 0.32.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have total number of kitten = 4+5 = 9

Total number of outcomes if the director is going to choose 5 of these kittens at random to be in the commercial:

= C(9, 5) = 126

The director chooses 3 boy kittens number of ways:

= C(4, 3) = 4

The director chooses 2 girl kittens number of ways:

=C(5, 2) = 10

Total favourable outcomes = 10×4 = 40

The probability = 40/126

= 0.317 ≈ 0.32

Thus, the probability that the director chooses 3 boy kittens and 2 girl kittens is 0.32.

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12 students are wearing sneakers.

Answer:

12

Step-by-step explanation:

So, the ratio is 3:4. That means this is for every 7 students. We have 28 students, so we need to know how many times 7 was multiplied to get to 28. 28 divided by 7 gives you 4. Now, we have to multiply both numbers in the ratio by 4. 3 times 4 is 12, and 4 times 4 is 16. The new ratio is 12:16. The students wearing sneakers were originally the 3 that got multiplied into 12, so the answer is 12.

Hope this helps!

The value of x in the right angle triangle is approximately 45 degrees.

The angle of the right angle triangle can be found as follows:

Therefore, let's find the hypotenuse side using Pythagoras theorem,

6² + 6² = c²

c² = 72

c = √72

c = 8.48528137424

c = 8.5 cm

Hence,

sin x = opposite / hypotenuse

sin x = 6 / 8.5

sin x = 0.70588235294

x = sin⁻¹ 0.70588235294

x = 44.9006818301

x = 45°

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Answer: 60

Step-by-step explanation:

See

Hence

m<COB=60°