Find the length of DF or state what additional information you would need to find it.

Brody is purchasing some tools for his workshop. He has a budget of $120 and needs to buy at least 14 tools. Each hammer costs $

STatiana [176]

Answer:

For this case, the first thing we must do is define variables:

x: number of hammers

y: number of wrenches

We write the system of inequations:

10x + 6y <= 120

x + y> = 14

Step-by-step explanation:

5 0

1 year ago

A financial advisor tells you that you can make your child a millionaire if you just start saving early. You decide to put an eq

Blababa [14]

Answer:

$12159 per year.

Step-by-step explanation:

If I invest $x each year at the simple interest of 7.5%, then the first $x will grow for 35 years, the second $x will grow for 34 years and so on.

So, the total amount that will grow after 35 years by investing $x at the start of each year at the rate of 7.5% simple interest will be given by

$x( 1 + \frac{35 \times 7.5}{100}) + x( 1 + \frac{34 \times 7.5}{100}) + x( 1 + \frac{33 \times 7.5}{100}) + ......... + x( 1 + \frac{1 \times 7.5}{100})$

= $35x + \frac{x \times 7.5}{100} [35 + 34 + 33 + ......... + 1]$

= $35x + \frac{x \times 7.5}{100} [\frac{1}{2} (35) (35 + 1)]$

{Since sum of n natural numbers is given by $\frac{1}{2} (n)(n + 1)$ }

= 35x + 47.25x

= 82.25x

Now, given that the final amount will be i million dollars = $1000000

So, 82.25x = 1000000

⇒ x = $12,158. 05 ≈ $12159

Therefore. I have to invest $12159 per year. (Answer)

5 0

1 year ago

If 2.5 mol of dust particles were laid end to end along the equator, how many times would they encircle the planet? The circumfe

Natalka [10]

Answer:

They encircle the planet $3.76\times 10^{11}$ times.

Step-by-step explanation:

Consider the provided information.

We have 2.5 mole of dust particles and the Avogadro's number is $6.022\times 10^{23}$

Thus, the number of dust particles is:

$2.5\times 6.022\times 10^{23}=15.055\times 10^{23}$

Diameter of a dust particles is 10μm and the circumference of earth is 40,076 km.

Convert the measurement in meters.

Diameter: $10\mu m\times \frac{10^{-6}m}{\mu m} =10^{-5}m$

If we line up the particles the distance they could cover is:

$15.055\times 10^{23}\times 10^{-5}=15.055\times 10^{18}=1.5055\times 10^{19}$

Circumference in meters:

$40,076km\times \frac{1000m}{1km}=40,076,000 m$

Therefore,

$\frac{1.5055\times 10^{19}}{40,076,000} = 3.76\times 10^{11}$

Hence, they encircle the planet $3.76\times 10^{11}$ times.

8 0

1 year ago

The distribution of the amount of a customer’s purchase at a convenience store is approximately normal, with mean $15.50 and sta

viktelen [127]

Answer:

0.42 is closest to the proportion of customer purchase amounts between $14.00 and $16.00

Step-by-step explanation:

Mean = $\mu = 15.50$

Standard deviation = $\sigma = 1.72$

We are supposed to find the proportion of customer purchase amounts between $14.00 and $16.00

P(14<x<16)

Formula : $z=\frac{x-\mu}{\sigma}$

At x = 14

$z=\frac{14-15.50}{1.72}$

$z=-0.8720$

Refer the z table for p value

P(x<14)=0.1922

At x = 16

$z=\frac{16-15.50}{1.72}$

$z=0.290$

Refer the z table for p value

P(x<16)=0.6141

P(14<x<16)=P(x<16)-P(x<14)=0.6141-0.1922=0.42

So, Option C is true

Hence 0.42 is closest to the proportion of customer purchase amounts between $14.00 and $16.00

4 0

1 year ago

At a gas station, suppose that 45% of the customers purchase premium grade gas. Assume that these customers decide independently

valkas [14]

Answer:

The answer to the question is

The probability that at least one of the next three customers purchases premium gas is the complement of the probability that none of the next three customers purchase premium gas = 1 - (1-P(A))³ = 0.834

Step-by-step explanation:

The probability that a customer would purchase premium grade = 45 %

That is P(A) = 0.45 and

The probability that the customer would purchase another grade = P(B) = 0.55

Therefore the probability of at least one of the next three customers purchase premium gas is

P(k=0) = (1 - P)ⁿ and the probability of at least one customer purchases premium gas is the compliment of the probability that the next three customers purchase another gas brand

that is (1 - P(A))×(1 - P(A))×(1 - P(A)) = P(B)×P(B)×P(B) = 0.55³ and the complement is 1 - 0.55³ = 0.834

8 0

1 year ago

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