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3 years ago

Describe how you labled the bar model and wrote a number sentence to solve exercise 2

Mathematics

2 answers:

mafiozo [28]3 years ago

6 0

Answer:

Step-by-step explanation:

In the above problem it is given that

No of Bees in the hive = 14

Number of bees in the garden = 17

In order to solve it

First of all I wrote 14 in the first box which represents the number of bees in the hive.

Secondly, I wrote 17 in the second box which represents the number of bees in the garden.

Now, in order to calculate the total number of bees i added the number in both boxes

Total Number of bees = 14 + 17

Total Number of bees = 31

So our total number of bees are 31

suter [353]3 years ago

4 0

I knew there were 14 bees in one and 17 in the garden there and together that equals 31. I wrote it out to show that I added the two to get 31 bees in all

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A box contains 5 red balls, 6 white balls and 9 black balls. Two balls are drawn at

valina [46]

Answer:

$P(Same)=\frac{61}{190}$

Step-by-step explanation:

Given

$Red = 5$

$White = 6$

$Black = 9$

Required

The probability of selecting 2 same colors when the first is not replaced

The total number of ball is:

$Total = 5 + 6 + 9$

$Total = 20$

This is calculated as:

$P(Same)=P(Red\ and\ Red) + P(White\ and\ White) + P(Black\ and\ Black)$

So, we have:

$P(Same)=\frac{n(Red)}{Total} * \frac{n(Red) - 1}{Total - 1} + \frac{n(White)}{Total} * \frac{n(White) - 1}{Total - 1} + \frac{n(Black)}{Total} * \frac{n(Black) - 1}{Total - 1}$

<em>Note that: 1 is subtracted because it is a probability without replacement</em>

$P(Same)=\frac{5}{20} * \frac{5 - 1}{20- 1} + \frac{6}{20} * \frac{6 - 1}{20- 1} + \frac{9}{20} * \frac{9- 1}{20- 1}$

$P(Same)=\frac{5}{20} * \frac{4}{19} + \frac{6}{20} * \frac{5}{19} + \frac{9}{20} * \frac{8}{19}$

$P(Same)=\frac{20}{380} + \frac{30}{380} + \frac{72}{380}$

$P(Same)=\frac{20+30+72}{380}$

$P(Same)=\frac{122}{380}$

$P(Same)=\frac{61}{190}$

4 0

3 years ago

The area of the regular hexagon is 10.4 in.2. a regular hexagon has side lengths of 2 inches and an area of 10.4 inches squared.

VARVARA [1.3K]

Answer:

(b) 1.7 in

Step-by-step explanation:

The area of a regular polygon in terms of perimeter and apothem is given by the formula ...

A = 1/2Pa

For a hexagon, the perimeter is 6 times the side length, so this becomes ...

A = 1/2(6s)a = 3sa . . . . . for side length 's' and apothem 'a'

Solving for the apothem, we find ...

a = A/(3s)

For the given values of area and side length the apothem is ...

a = 10.4/(3·2) = 1.733... ≈ 1.7 . . . inches

The apothem, rounded to tenths, is 1.7 inches.

5 0

3 years ago

Marsha wants to determine the vertex of the quadratic function f(x) = x2 – x + 2. What is the function’s vertex?

BaLLatris [955]

Answer:

$Vertex = (\frac{1}{2},\frac{7}{4})$

Step-by-step explanation:

Given

$f(x) = x^2 - x +2$

Required

The vertex

We have:

$f(x) = x^2 - x +2$

First, we express the equation as:

$f(x) = a(x - h)^2 +k$

Where

$Vertex = (h,k)$

So, we have:

$f(x) = x^2 - x +2$

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

Take the coefficient of x: -1

Divide by 2: (-1/2)

Square: (-1/2)^2

Add and subtract this to the equation

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

$f(x) = x^2 - x +2$

$f(x) = x^2 - x + (-\frac{1}{2})^2+2 -(-\frac{1}{2})^2$

$f(x) = x^2 - x + \frac{1}{4}+2 -\frac{1}{4}$

Expand

$f(x) = x^2 - \frac{1}{2}x- \frac{1}{2}x + \frac{1}{4}+2 -\frac{1}{4}$

Factorize

$f(x) = x(x - \frac{1}{2})- \frac{1}{2}(x - \frac{1}{2})+2 -\frac{1}{4}$

Factor out x - 1/2

$f(x) = (x - \frac{1}{2})(x - \frac{1}{2})+2 -\frac{1}{4}$

$f(x) = (x - \frac{1}{2})^2+2 -\frac{1}{4}$

$f(x) = (x - \frac{1}{2})^2+ \frac{8 -1 }{4}$

$f(x) = (x - \frac{1}{2})^2+ \frac{7}{4}$

Compare to: $f(x) = a(x - h)^2 +k$

$h = \frac{1}{2}$

$k = \frac{7}{4}$

Hence:

$Vertex = (\frac{1}{2},\frac{7}{4})$

8 0

3 years ago

Read 2 more answers

Writing a Linear Equation Given Two Points

sveticcg [70]

Answer:

y=-3x+5

Step-by-step explanation: y=mx+b

to find slope (m) use the equation $\frac{y2-y1}{x2-x1} \\$

$\frac{-10-(-1)}{5-2}$ = -3

to find b

use y=mx+b

-1=-3(2)+b

-1=-6+b

5=b

Hope this helps :)

5 0

2 years ago

. The slope of the line is 4/9, and it contains the point (-6,8). Enter an equation in point-slope form

Serga [27]

Answer:

Step-by-step explanation:

m =4(-6, 8)/9

4 0

3 years ago