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3 years ago

Q#1:The volume of a cube is 46656 cubic metres.Find the length of each side?

Mathematics

1 answer:

Lady_Fox [76]3 years ago

3 0

Answer:

Step-by-step explanation:

1) To find the cube root of a number prime factorize

46656 = 2*2*2*2*2*2 * 3 * 3 * 3 * 3 * 3 * 3

$\sqrt[3]{46656}=\sqrt[3]{2*2*2*2*2*2*3*3*3*3*3*3} =2*2*3*3 = 36$

Length of each side = 36 m

Q) i) -512 = (-8) * (-8)*(-8)

-512 is a cube number

v) -17576 = (-26) * (-26)*(-26)

-17576 is cube number

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) It has been estimated that 53% of all college students change their major at least once during the course of their college car

Ymorist [56]

Answer:

116 students

Step-by-step explanation:

The standard deviation for a proportion is:

$s=\sqrt{\frac{(1-p)*p}{n}}$

For any measured sample proportion x, the z score is given by:

$z = \frac{x-p}{s}$

The population proportion is 0.53

At the 14th percentile, the corresponding z-score is z =-1.08.

Since 0.48 is at the 14th percentile, the standard deviation is:

$-1.08=\frac{0.48-0.53}{s}\\ s=0.46296$

Therefore, the sample size 'n' is given by:

$0.046296=\sqrt{\frac{(1-0.53)*0.53}{n}}\\n=\frac{0.47*0.53}{0.046296^2}\\n= 116\ students$

The sample size must have been of 116 students.

6 0

3 years ago

The cost to manufacture a product is proportional to the quantity produced, with a cost of $35000 dollars per day when 700 items

ollegr [7]

Solution :

$T_1$ = k.n (cost proportional to quantity)

35000 = k . 700

k = $\frac{35000}{700}$

= 50

So $T_1$ = 50 n

Now $T_2=Pn^2$ (cost proportional to square of n)

$3430= P(700)^2$

3430 = 490000 P

$P = \frac{3430}{490000}$

$P = \frac{7}{1000}$

$T_2=\frac{7}{1000}n^2$

Now, $T_3= 7000$ (fixed)

Therefore,

Total, $T=T_1+T_2+T_3$

$T=50n+\frac{7}{1000}n^2+7000$

$T=0.007n^2+50n+7000$

7 0

3 years ago

Given that x is an integer, what is the solution of <br>|x-1|<img src="https://tex.z-dn.net/?f=%20%5Cleqslant%201" id="TexFormul

Varvara68 [4.7K]

Answer:

see explanation

Step-by-step explanation:

Inequalities of the type | x | ≤ a always have solutions of the form

- a ≤ x ≤ a

Given

| x - 1 | ≤ 1 then

- 1 ≤ x - 1 ≤ 1 ( add 1 to each of the 3 intervals )

0 ≤ x ≤ 2

Since we require an integer solution then x = 0, 1, 2

5 0

3 years ago

HELP ASAP ~ WILL GIVE BRAINLIEST ASAP

dimaraw [331]

Answer:

Domain [-5,∞)

Range [0,∞)

Step-by-step explanation:

Part 1) Find the domain

we have

$f(x)=\frac{1}{2}\sqrt{x+5}$

we know that

The radicand must be greater than or equal to zero

$x+5\geq 0$

solve for x

subtract 5 both sides

$x\geq -5$

The solution for x is the interval [-5,∞)

All real numbers greater than or equal to -5

Remember that

The domain of a function is the set of all possible values of x

therefore

The domain of the function f(x) is the interval [-5,∞)

Part 2) Find the range

we have

$f(x)=\frac{1}{2}\sqrt{x+5}$

Find the value of f(x) for the minimum value of x

For x=-5

$f(x)=\frac{1}{2}\sqrt{-5+5}$

$f(x)=0$

The minimum value of f(x) is equal to zero

The solution for f(x) is the interval [0,∞)

All real numbers greater than or equal to 0

Remember that

The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.

therefore

The range of the function is the interval [0,∞)

8 0

3 years ago

100 points Hannah factored the expression 24xy + 15y. Her work is shown below.

sleet_krkn [62]

1. She divided by 3 instead of the GCF.

4. She didn’t complete step 4 and use the distributive property to be sure the expressions are equivalent.

5. She didn’t undistribute the GCF from the original expression.

8 0

3 years ago

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