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3 years ago

Factors of 38 and 48

Mathematics

2 answers:

dsp733 years ago

4 0

38 is 48
24x2
12x2
4x3 The answer is 3
19x2
9x2
3x3

Nikolay [14]3 years ago

3 0

1, 2, 16

These are the factors of 38 and 48

Hope this helps!

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6 of 10 equal pieces is the same as 60 of 100 equal pieces and ___ of 5 equal pieces?

gizmo_the_mogwai [7]

3 of 5 because you can halve each number for example 6 can be halved to make 3 and 10 can be halved to make 5

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3 years ago

How do i draw 4 angles forming 4 linear pairs?

ser-zykov [4K]

Just do a line crossing another in a angle of 90°

1 is linear pair with 2, 2 is linear pair with 3, 3 is linear pair with 4 and 4 is linear pair with 1.

8 0

3 years ago

2. The quality assurance department inspects its production line. The product either fails or passes the inspection. Past experi

Oksana_A [137]

Answer:

(a) $E(X) = 950$

(b) $COV = 0.007255$

Step-by-step explanation:

The given problem can be solved using binomial distribution since the product either fails or passes, the probability of failure or success is fixed and there are n repeated trials.

probability of failure = q = 0.05

probability of success = p = 1 - 0.05 = 0.95

number of trials = n = 1000

(a) What is the expected number of non-defective units?

The expected number of non-defective units is given by

$E(X) = n \times p \\\\E(X) = 1000 \times 0.95 \\\\E(X) = 950$

(b) what is the COV of the number of non-defective units?

The coefficient of variance is given by

$COV = \frac{\sigma}{E(X)}$

Where the standard deviation is given by

$\sigma = \sqrt{n \times p\times q} \\\\\sigma = \sqrt{1000 \times 0.95\times 0.05} \\\\\sigma = 6.892$

So the coefficient of variance is

$COV = \frac{6.892}{950}$

$COV = 0.007255$

(c) What is the probability of having more than 980 non-defective units?

We can use the Normal distribution as an approximation to the Binomial distribution since n is quite large and so is p.

$P(X > 980) = 1 - P(X < 980)\\\\P(X > 980) = 1 - P(Z < \frac{x - \mu}{\sigma} )\\\\$

We need to consider the continuity correction factor whenever we use continuous probability distribution (Normal distribution) to approximate discrete probability distribution (Binomial distribution).

$P(X > 980) = 1 - P(Z < \frac{979.5 - 950}{6.892} )\\\\P(X > 980) = 1 - P(Z < \frac{29.5}{6.892} )\\\\P(X > 980) = 1 - P(Z < 4.28)\\\\$

The z-score corresponding to 4.28 is 0.99999

$P(X > 980) = 1 - 0.99999\\\\P(X > 980) = 0.00001\\\\$

So it means that it is very unlikely that there will be more than 980 non-defective units.

8 0

3 years ago

Log_{7 }(5 - 3x) Find the derivative

V125BC [204]

Let y be the expression you want to differentiate:

$y=\log_7(5-3x) \implies 7^y=5-3x$

Now,

$7^y=e^{\ln(7^y)}=e^{y\ln(7)}$

Use the chain rule to differentiate both sides with respect to x :

$\ln(7)e^{y\ln(7)}\dfrac{\mathrm dy}{\mathrm dx}=-3$

Solve for dy/dx :

$\ln(7)7^y\dfrac{\mathrm dy}{\mathrm dx}=-3$

$\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac3{\ln(7)7^y}$

$\dfrac{\mathrm dy}{\mathrm dx}=\boxed{-\dfrac3{\ln(7)(5-3x)}}$

6 0

2 years ago

Checking account A charged a monthly fee of $5 and a per-check fee of $0.25, and checking account B charged a monthly fee of $6

Genrish500 [490]

First we need to know both the formula of A and B.

The formula of A is
C = 5 + 0.25p
with C representing total cost and p representing the amount of checks.

The formula of B is
C = 6 + 0.15p
with C representing total cost and p representing the amount of checks.

To find the point where A and B cost the same, we solve the following equation:
5 + 0.25p = 6 + 0.15p

Collecting terms gives us
-1 = -0.1p

Now we have to divide by -0.1 and we get.
10 = p
p = 10

So our answer: after 10 checks both accounts cost the same amount of money. Answer A.

7 0

3 years ago