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Thepotemich [5.8K]

3 years ago

11

1. Yousaf deposits $5000 in a savings account at his local bank. The account pays 5.5 % interest compounded annually. At the end

of 6 years, how much will he have in his account?

1 answer:

irina [24]3 years ago

4 0

Answer:

I think its $6894.21

Step-by-step explanation:

compound interest formula: A= P(1+ r/n)^nt

A= 5000(1+ 0.055/1)^1(6)

A= 6894.21403

A= $6894.21

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Suppose a research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. A samp

shutvik [7]

Answer:

0.9910 = 99.10% probability that a sample of 170 steady smokers spend between $19 and $21

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 20, standard deviation of 5:

This means that $\mu = 20, \sigma = 5$

Sample of 170:

This means that $n = 170, s = \frac{5}{\sqrt{170}}$

What is the probability that a sample of 170 steady smokers spend between $19 and $21?

This is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 19.

X = 21

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{21 - 20}{\frac{5}{\sqrt{170}}}$

$Z = 2.61$

$Z = 2.61$ has a p-value of 0.9955

X = 19

$Z = \frac{X - \mu}{s}$

$Z = \frac{19 - 20}{\frac{5}{\sqrt{170}}}$

$Z = -2.61$

$Z = -2.61$ has a p-value of 0.0045

0.9955 - 0.0045 = 0.9910

0.9910 = 99.10% probability that a sample of 170 steady smokers spend between $19 and $21

3 0

3 years ago

IgorLugansk [536]

Answer:

45 cubic units

Step-by-step explanation:

See attached.

3 0

3 years ago

How many times does a dragonfly's wing beat per minute

marshall27 [118]

<span>A dragonfly beats its wings about 30 times a second. This is necessary to allow the insect to keep itself airborne, due to the relative weight of its body. Luckily, dragonflies have two sets of wings, or they would have to work even harder to stay up in the air.</span>

5 0

3 years ago

A rectangle has one of its sides on the x-axis and corners of the opposite side on the piece of the parabola y = 12 − x 2 above

saw5 [17]

Answer:

$A(x) = 24x - 2x^3$

Step-by-step explanation:

first we need to visualize what the question is trying to represent

A rectangle with one of its sides on the x-axis
The corners of the opposite two sides of the rectangle intersect with a parabola

the equation of the parabola is $y = 12 - x^2$

the equation of the parabola can also be written as

$y = -x^2 + 12$ this shows that the parabola has a $\cap$ shape and the turning point (peak) lies at the y-axis at y = 12. The parabola is symmetric along the y-axis!

right corner of the lower side of the rectangle has the coordinates (x,0)

we can also say that the coordinates of the lower left side are (-x,0). This is because the parabola is symmetric along the y-axis.

Solution:

We have enough information to express the sides lengths of the rectangle:

1) Lower side, (L)

We'll name the lower side 'L' and since this is a rectangle, this side length is the same as the upper side.

The lower side coordinates are (-x,0) and (x,0). Hence the side length is the difference of the two coordinates.

$L = x-(-x)$

$L = 2x$

2) The Left and Right side have the same height (H)

since the the lower side is on the x-axis (y=0), the only side moving is the upper one, i.e the coordinates of the upper corners are (0,y) where $y = 12- x^2$ . The side length of either the left or right sides is $y$

$H = y$

$H = 12 - x^2$

The Area of the rectangle is:

$Area\,\,= L \times H$

$Area\,\,= 2x(12 - x^2)$

$Area\,\,= 24x-2x^3$

3 0

3 years ago

a farmer has horses and cows if the radio of horses to cows is 3 to 5 and there are 15 horses how many animals are there

Paha777 [63]

Answer:

Step-by-step explanation:

h/c=3/5=15/c

c=25, 25+15=40 animals

7 0

3 years ago