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2 years ago

A group of students were given a spelling test.

Mathematics

2 answers:

VLD [36.1K]2 years ago

5 0

Answer:

4
30 students
8.1

Step-by-step explanation:

Range of data :

Maximum value - Minimum value
10 - 6
4

Students in the group :

Sum of frequencies
5 + 4 + 7 + 10 + 4
9 + 7 + 10 + 4
16 + 10 + 4
26 + 4
30 students

Mean mark :

6(5) + 7(4) + 8(7) + 9(10) + 10(4) / 30
30 + 28 + 56 + 90 + 40
160 + 84 / 30
244/30
8.1

skad [1K]2 years ago

5 0

Answer:

a) 4

b) 30

c) 8

Step-by-step explanation:

The range is the difference between the biggest and the smallest number. The biggest mark is 10, and the smallest mark is 6.

⇒ Range = 10 - 6 = 4

To calculate how many students are in the group, add the values in the frequency column:

⇒ Total number of students = 5 + 4 + 7 + 10 + 4 = 30

To calculate the mean mark of the group, multiply each mark by its frequency, add these up, then divide by the total number of students:

⇒ Mean Mark = [ (6 × 5) + (7 × 4) + (8 × 7) + (9 × 10) + (10 × 4) ] ÷ 30

= [ 30 + 28 + 56 + 90 + 40 ] ÷ 30

= 244 ÷ 30

= 8.1333333333...

= 8 (nearest whole number)

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At what point does the curve have maximum curvature? Y = 4ex (x, y) = what happens to the curvature as x → ∞? Κ(x) approaches as

MAXImum [283]

Answer-

At $x= \frac{1}{2304e^4-16e^2}$ the curve has maximum curvature.

Solution-

The formula for curvature =

$K(x)=\frac{{y}''}{(1+({y}')^2)^{\frac{3}{2}}}$

Here,

$y=4e^{x}$

Then,

${y}' = 4e^{x} \ and \ {y}''=4e^{x}$

Putting the values,

$K(x)=\frac{{4e^{x}}}{(1+(4e^{x})^2)^{\frac{3}{2}}} = \frac{{4e^{x}}}{(1+16e^{2x})^{\frac{3}{2}}}$

Now, in order to get the max curvature value, we have to calculate the first derivative of this function and then to get where its value is max, we have to equate it to 0.

${k}'(x) = \frac{(1+16e^{2x})^{\frac{3}{2} } (4e^{x})-(4e^{x})(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})}{(1+16e^{2x} )^{2}}$

Now, equating this to 0

$(1+16e^{2x})^{\frac{3}{2} } (4e^{x})-(4e^{x})(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x}) =0$

$\Rightarrow (1+16e^{2x})^{\frac{3}{2}}-(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})$

$\Rightarrow (1+16e^{2x})^{\frac{3}{2}}=(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})$

$\Rightarrow (1+16e^{2x})^{\frac{1}{2}}=48e^{2x}$

$\Rightarrow (1+16e^{2x})}=48^2e^{2x}=2304e^{2x}$

$\Rightarrow 2304e^{2x}-16e^{2x}-1=0$

Solving this eq,

we get $x= \frac{1}{2304e^4-16e^2}$

∴ At $x= \frac{1}{2304e^4-16e^2}$ the curvature is maximum.

6 0

3 years ago

GIVING BRAINLIEST FOR CORRECT ANSWER WITH EXPLANATION HELP NOW

Serjik [45]

Answer:

x = 250°

Step-by-step explanation:

"Angle formed between a chord and tangent intersecting on a circle measure the half of the intercepted arc"

From the figure attached,

Angle between the chord and the tangent = 55°

Measure of intercepted arc (minor arc AB) = h°

Therefore, 55° = $\frac{1}{2}(h)$

$h=110^0$

And m(minor arc AB) + m(major arc AB) = 360°

h° + x° = 360°

110° + x° = 360°

x° = 360° - 110°°

x = 250°

Therefore, measure of the intercepted arc is 250°.

3 0

3 years ago

HELP!

PSYCHO15rus [73]

Answer:

74676.

Step-by-step explanation:

Lets try multiplying 127 by 294 ( 127 is a prime number):

127 * 294 = 37338.

37338 / 196 = 190.5

37338 * 2 = 74676 which will now be divisible by 196.

74676 will be divisible by 98, 49 and 7 (because they are factors of 196).

It is also divisible by 84 ( to give 889) and therefore by 42, 28, 21, 14, 12, 6, 4, 3 , 2 and 1 which are all factors of 84.

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fomenos

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