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bezimeni [28]
3 years ago
10

At the beginning of the year, Adrian's savings account balance was $28. Each week, he deposits another $15 into that account, an

d he doesn't spend any of his savings. Is his savings account balance proportional to the number of weeks since the start of the year?
Yes
No
Mathematics
1 answer:
Dovator [93]3 years ago
8 0

Answer:

Yes

Step-by-step explanation:

Let's consider what Adrian does for a few weeks, that is, we will make a table where we can see the behavior of the savings with respect to the weeks that pass:

time (week)   savings ($)

       0               28

       1                43

       2               58

       3               73

       4               88

       5              103

and if we continue doing we see that it has a similar behavior, and the equation would be:

s = 15 * m + 28

where s are the savings and m the number of months, which means that 15 is that constant of proportionality and therefore they are proportional.

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Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the popu
tia_tia [17]

Answer:

The minimum head breadth that will fit the clientele is 4.4 inches.

The maximum head breadth that will fit the clientele is 7.8 inches.

Step-by-step explanation:

Let <em>X</em> = head breadths of men that is considered for the helmets.

The random variable <em>X</em> is normally distributed with mean, <em>μ</em> = 6.1 and standard deviation, <em>σ</em> = 1.

To compute the probability of a normal distribution we first need to convert the raw scores to <em>z</em>-scores using the formula:

z=\frac{x-\mu}{\sigma}

It is provided that the helmets will be designed to fit all men except those with head breadths that are in the smallest 4.3% or largest 4.3%.

Compute the minimum head breadth that will fit the clientele as follows:

P (X < x) = 0.043

⇒ P (Z < z) = 0.043

The value of <em>z</em> for this probability is:

<em>z</em> = -1.717

*Use a <em>z</em>-table.

Compute the value of <em>x</em> as follows:

z=\frac{x-\mu}{\sigma}\\-1.717=\frac{x-6.1}{1}\\x=6.1-(1.717\times 1)\\x=4.383\\x\approx4.4

Thus, the minimum head breadth that will fit the clientele is 4.4 inches.

Compute the maximum head breadth that will fit the clientele as follows:

P (X > x) = 0.043

⇒ P (Z > z) = 0.043

⇒ P (Z < z) = 1 - 0.043

⇒ P (Z < z) = 0.957

The value of <em>z</em> for this probability is:

<em>z</em> = 1.717

*Use a <em>z</em>-table.

Compute the value of <em>x</em> as follows:

z=\frac{x-\mu}{\sigma}\\1.717=\frac{x-6.1}{1}\\x=6.1+(1.717\times 1)\\x=7.817\\x\approx7.8

Thus, the maximum head breadth that will fit the clientele is 7.8 inches.

5 0
3 years ago
HELP DUE IN 5 MINS!!!
UkoKoshka [18]

What are the units? Tell me the units so I can solve this please.

3 0
2 years ago
Read 2 more answers
5p-3r=1
Brilliant_brown [7]
If you would like to solve the system of equations, you can do this using the following steps:

5p - 3r = 1     /*2
8p + 6r = 4
__________
10p - 6r = 2
<span>8p + 6r = 4
</span>__________
10p - 6r + 8p + 6r = 2 + 4
18p = 6
p = 6/18
p = 1/3

<span>5p - 3r = 1
</span>5 * 1/3 - 3r = 1
5/3 - 3r = 1
5/3 - 1 = 3r
5/3 - 3/3 = 3r
2/3 = 3r
r = 2/9

(p, r) = (1/3, 2/9)

The correct result would be <span>(1/3, 2/9)</span>.
4 0
3 years ago
Read 2 more answers
if the diameter of a cone is 16cm and the height is 15cm what is the volume? I've tried the formula v=1/3*3.14*r^2*h but the ans
Alisiya [41]

Answer:

V= volume of cone A=Ah A= πr2

A= area of base 3

H= height

V= (3.1416)(16)(15) 3.1416x16x15= 753.9

3

V= 753.9 753.9÷3= 251.3 cu. in

3

Volume of the cone is 251.3 cu. in

I hope this helps you. Good luck!

5 0
2 years ago
What is 2 meters and 10 cm together
Alika [10]
10cm=10 * 10^-2 = 10^-1 meters

so its 2 meters + 0.1 meters = 2.1 meters

4 0
4 years ago
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