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3 years ago

Make t the subject of the formula: S = at + bt

2 answers:

riadik2000 [5.3K]3 years ago

8 0

To make t the subject is basically isolating t

S = at + bt
We see on the right side that t is common, so we factor it out.

S = t(a + b)
Divide by (a+b) to isolate t

$\frac{S}{a + b} = \frac{t(a+b)}{(a+b)}$
a + b and a + b cancels out
We are left with the answer:
t = $\frac{S}{a+b}$

goldfiish [28.3K]3 years ago

6 0

$S = at + bt \\
t(a+b)=S\\
t=\dfrac{S}{a+b}$

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aliina [53]

Answer:

a. X~N(2,885, 651)

b. 0.086291

c. 0.00058

d. 3213.10 calories

Step-by-step explanation:

a. -A normal distribution is expressed in the form X~N(mean, standard deviation).

-Let X a random variable denoting the number of calories consumed.

-X is a is a normally distributed random variable with mean 2885 and standard deviation 651.

-This distribution is expressed as X~N(2,885, 651)

b. The probability that less than 2000 calories are consumed is calculated using the formula:

$P(X$

#substitute the given values in the formula to solve for P:

$P(X$

Hence, the probability of consuming less than 2000 calories is 0.08691

c. The proportion of customers consuming more than 5000 calories is calculated as:

$P(X>x)=P(z>\frac{\bar X-\mu}{\sigma})\\\\=P(Z>\frac{5000-2885}{651})\\\\=P(z>3.2488)\\\\=1-0.99942\\\\=0.00058$

Hence, the proportion of customers consuming over 5000 calories is 0.00058

d. The least amount of calories to get the award is calculated as:

1% is equivalent to a z value of 0.50399.

-We equate this to the formula to solve for the mean consumption:

$0.01=P(z>\frac{\bar X-\mu}{\sigma})\\\\=P(z>\frac{\bar X-2885}{651})\\\\\1\%=0.50399 \\\\\frac{\bar X-2885}{651}=0.50399 \\\\\bar X=0.50399\times 651+2885\\\\=3213.09$

Hence, the least amount of calories consumed to qualify for the award is 3213.10 calories.

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4 years ago

What is the sales price of a $18.95 football with a 15% discount?

skelet666 [1.2K]

$18.95 x 15/100 is equal to 2.84

18.95 - 2.84 is equal to $16.11

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3 years ago

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4 years ago

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