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3 years ago

5. The area of the greatest square that is cut from a rectangle of sides

Mathematics

1 answer:

den301095 [7]3 years ago

3 0

Answer:

16 cm²

Step-by-step explanation:

The dimension of rectangle = 7cm by 4 cm

The Area of the greatest square that can be cut from the rectangle :

The dimension has to be the Same to form a square :

Hence, the greatest width = 4cm

Therefore, taking the length also as 4cm

Area of square = side length²

Greatest area of square that can be cut = 4² = 16cm²

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In a group of a hundred and fifty students attending a youth workshop in mombasa, 125 of them are fluent in kiswahili, 135 in en

jek_recluse [69]

Answer:

The probability that a student chosen at random is fluent in English or Swahili.

P(S∪E) = 1.1

Step-by-step explanation:

Step(i):-

Given total number of students n(T) = 150

Given 125 of them are fluent in Swahili

Let 'S' be the event of fluent in Swahili language

n(S) = 125

The probability that the fluent in Swahili language

$P(S) = \frac{n(S)}{n(T)} = \frac{125}{150} = 0.8333$

Let 'E' be the event of fluent in English language

n(E) = 135

The probability that the fluent in English language

$P(E) = \frac{n(E)}{n(T)} = \frac{135}{150} = 0.9$

n(E∩S) = 95

The probability that the fluent in English and Swahili

$P(SnE) = \frac{n(SnE)}{n(T)} = \frac{95}{150} = 0.633$

Step(ii):-

The probability that a student chosen at random is fluent in English or Swahili.

P(S∪E) = P(S) + P(E) - P(S∩E)

= 0.833+0.9-0.633

= 1.1

Final answer:-

The probability that a student chosen at random is fluent in English or Swahili.

P(S∪E) = 1.1

8 0

3 years ago

8(x) = x^3 - 3 What is the value of x when g(x) = 24? Enter the answer in the box.

IRINA_888 [86]

Answer:

x=3

Step-by-step explanation:

x³ - 3 =24

x³ = 27

x = 3

6 0

3 years ago

Alicia is making headbands using ribbon she would like to make to make 12headbands each one requires 15.5 inches of ribbon she e

Umnica [9.8K]

Do 15.5×12
then you will know how much ribbon you need. Hope that helps!

6 0

3 years ago

Desperately need help and an explanation so I can do it on my own later.

Mashutka [201]

Step-by-step explanation:

since the sumation of f(x) of a probability is 1

thw probability to win is o.5 and to lose is o.5 so expected value is xf(x

your expected value will b 0.5 multiply by 5 thats is 2.5 thats your expected gain

4 0

2 years ago

* Let S = Span {(2,-1, 1), (3, 1, 1), (1, 2, 0)}. (i) Calculate the dimension of S.

Sholpan [36]

The span of 3 vectors can have dimension at most 3, so 9 is certainly not correct.

Check whether the 3 vectors are linearly independent. If they are not, then there is some choice of scalars $c_1,c_2,c_3$ (not all zero) such that

$c_1 (2,-1,1) + c_2 (3,1,1) + c_3 (1,2,0) = (0,0,0)$

which leads to the system of linear equations,

$\begin{cases} 2c_1 + 3c_2 + c_3 = 0 \\ -c_1 + c_2 + 2c_3 = 0 \\ c_1 + c_2 = 0 \end{cases}$

From the third equation, we have $c_1=-c_2$ , and substituting this into the second equation gives

$-c_1 + c_2 + 2c_3 = 2c_2 + 2c_3 = 0 \implies c_2 + c_3 = 0 \implies c_2 = -c_3$

and in turn, $c_1=c_3$ . Substituting these into the first equation gives

$2c_1 + 3c_2 + c_3 = 2c_3 - 3c_3 + c_3 = 0 \implies 0=0$

which tells us that any value of $c_3$ will work. If $c_3 = t$ , then $c_1=t$ and $c_2 = -t$ . Therefore the 3 vectors are not linearly independent, so their span cannot have dimension 3.

Repeating the calculations above while taking only 2 of the given vectors at a time, we see that they are pairwise linearly independent, so the span of each pair has dimension 2. This means the span of all 3 vectors taken at once must be 2.

3 0

2 years ago