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3 years ago

The population P = P(t) of Helm, can be modeled by

Mathematics

1 answer:

MariettaO [177]3 years ago

7 0

Answer:

A.) 0.0129 = k

B.) 2024

Step-by-step explanation:

A.)

267,000 = 250,300e^k5

267,000/250,300 = e^k5

1.0667 = e^k5

ln(1.0667) = lne^k5

ln(1.0667) = 5k

ln(1.0667)/5 = k

0.0129 = k

B.)

300,000 = 250,300^0.0129t

300,000/250,300 = e^0.0129t

1.1986 = e^0.0129t

ln(1.1986) = lne^0.0129t

ln(1.1986) = 0.0129t

ln(1.1986)/0.0129 = t

14.03 = t

so the year would be: 2024

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The probability distribution of the amount of memory X (GB) in a purchased flash drive is given below. x 1 2 4 8 16 p(x) .05 .10

Rama09 [41]

Answer:

a) $E(X) = 6.45$

b) $E(X^{2} )= 57.25$

c) $V(X) = 15.648$

d) E(3X + 2) = 21.35

e) $E(3X^{2} +2) = 173.75$

f) V(3X+2) = 140.832

g) E(X+1) = 7.45

h) V(X+1) = 15.648

Step-by-step explanation:

a) $E(X) = \sum xP(x)$

$E(X) = (1*0.05) + (2*0.10) + (4*0.35) + (8*0.40) + (16*0.10)\\E(X) = 6.45$

$E(X^{2} ) = (1^{2} *0.05) + (2^{2} *0.10) + (4^{2} *0.35) + (8^{2} *0.40) + (16^{2} *0.10)\\ E(X^{2} )= 57.25$

$V(X) = E(X^{2} ) - (E(X))^{2} \\V(X) = 57.25 - 6.45^{2} \\V(X) = 15.648$

$E(3X+2) = 3E(X) + 2\\E(3X+2) = (3*6.45) + 2 \\E(3X+2) = 21.35$

$E(3X^{2} +2) = 3E(X^{2} ) + 2\\E(3X^{2} +2) = (3*57.25) + 2 \\E(3X^{2} +2) = 173.75$

$V(3X+2) = 3^{2} V(X)\\V(3X+2) = 9*15.648\\V(3X+2) = 140.832$

$E(X+1) = E(X) + 1\\E(X+1) = 6.45 + 1\\E(X+1) =7.45$

$V(X+1) = 1^{2} V(X)\\V(X+1) = 15.648$

6 0

3 years ago

What is the equation of the function that is graphed as line a?

Andrei [34K]

Answer:

Step-by-step explanation:

We see that the line intersects the y-axis at -1. As a result, we need to choose an equation with -1, either B or C. We see that the different is the slope. For choice B, the slope is $\frac{1}{3}$ , meaning that every unit up equates to 3 blocks to the right. Counting along the line, we see that this is correct.

4 0

2 years ago

In an ellipse, the ratio of the distance between the foci and the length of the major axis is called:

Anni [7]

The ratio of the distance between the foci and the length of the <em>major</em> axis is called eccentricity.

<h3>Definitions of dimensions in ellipses</h3>

Dimensionally speaking, an ellipse is characterized by three variables:

Length of the <em>major</em> semiaxis ( $a$ ).
Length of the <em>minor</em> semiaxis ( $b$ ).
Distance between the foci and the center of the ellipse ( $c$ ).

And there is the following relationship:

$c = \sqrt{a^{2}-b^{2}}$ (1)

Another variable that measure how "similar" is an ellipse to a circle is the eccentricity ( $e$ ), which is defined by the following formula:

$e = \frac{c}{a}$ , $0 \ge c \ge 1$ (2)

The greater the eccentricity, the more similar the ellipse to a circle.

Therefore, the ratio of the distance between the foci and the length of the <em>major</em> axis is called eccentricity. $\blacksquare$

To learn more on ellipses, we kindly invite to check this verified question: brainly.com/question/19507943

3 0

2 years ago

Lourdes plans to jog at least 1.5 miles. Write an inequality and solve an inequality to find x, the number of hours Lourdes will

Paraphin [41]

Answer:

1.5 ≤ 3.75x

Step-by-step explanation:

Given that:

Distance, D to jog is atleast 1.5 miles

D ≥ 1.5 miles

x = number of hours to jog

Jog rate = 3.75 mph

Actual distance covered if jog last for X hours

Actual Distance = speed * time

Actual Distance = 3.75 * x = 3.75x

Hence,

D ≤ Actual distance

1.5 ≤ 3.75x

4 0

2 years ago

The mean value of 500 homes in a county is $225,000 and the standard deviation is $25,000. approximately how many of the homes i

dusya [7]

240 homes in the county are between $175,000 and $225,000.

The image attached is associated with this question and m in it refers to the mean value which is $225000 here and d refers to the standard deviation which is $25000 here.

Now since m= $225000

and $175000= $225000-$50000= $225000-(2* $25000)= m-2d

Thus, as per the image area covered between m and m-2d= $225000

and $175000 is (34%+14%)of 500 homes= 68% of 500= 240 homes, is the answer.

A random variable X is said to follow a normal distribution if its parameters are mean and standard deviation. Every other distribution can be reduced to a normal distribution.

Learn to know more about normal distributions on brainly.com/question/4079902

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3 0

1 year ago