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2 years ago

The exponentia growth model A=30e^.198026t describes the population by what % is the population of the city increasing each year

Mathematics

1 answer:

Artyom0805 [142]2 years ago

8 0

A=30e^.198026t
= 30(e^.198026)^t
= 30(1.218994087)^t

approximately 21.90% every year

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During a sale at a bookstore, Joseph buys a book at full price. He is given a 50 percent discount on a second book of equal or l

NARA [144]

Total cost of books was 15 + 10 or 25. With the 50 % discount on the $10 book, the total is now $20. The total cost was reduced by (B) 20%.
$5 off the $25 price is a 20% discount.

5 0

3 years ago

Suppose you received a score of 95 out of 100 on exam 1 . The mean was 79 and the standard deviation was 8 . If your score on ex

Schach [20]

Answer:

You did the same on both exams.

Step-by-step explanation:

To compare both the scores, we need to compute the z scores of both the exams and then compare the values. The formula for z-score is:

Z = (X - μ)/σ

Where X = score obtained

μ = mean score

σ = standard deviation

For Exam 1:

Z = (95 - 79)/8

= 16/8

Z = 2

For Exam 2:

Z = (90 - 60)/15

= 30/15

Z = 2

The z-scores for both the tests are same hence the third option is correct i.e. you did the same on both exams.

8 0

3 years ago

PLEASE ANSWER FAST WILL GIVE BRAINLIEST

Yuliya22 [10]

you will save $84***

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3 years ago

If y = x - 6 were changed to y = x + 8, how would the graph of the new function

Paraphin [41]

It would be shifted up

5 0

2 years ago

Can someone answer these as well worth lots of points. Only Appropriate Answers Pls :).

Rashid [163]

1. To solve this we are going to find the distance of the three sides of each triangle, and then, we are going to use Heron's formula.
- For triangle RTS:
S (2,1), T (1,3) and R (5,5). Using a graphic tool or the distance formula $d= \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$ we realize that ST=2.2, SR=5, and TR=4.5. Now we are going to find the semi-perimeter of our triangle:
$s= \frac{ST+SR+TR}{2}$
$s= \frac{2.2+5+4.5}{2}$
$s= \frac{11.7}{2}$
$s=5.85$
Now we can use Heron's formula:
$A= \sqrt{s(s-ST)(s-SR)(s-TR)}$
$A= \sqrt{5.85(5.85-2.2)(5.85-5)(5.85-4.5)}$
$A=4.9$ square units
We can conclude that the area of triangle RTS is 4.9 square units.

- For triangle MNL:
M (2,-4), N (-2,-3), and L (0,-1). Once again, using a graphic tool or the distance formula we get that MN=4.1, ML=3.6, and NL=2.8.
Lets find the semi-perimeter of our triangle to use Heron's formula:
$s= \frac{4.1+3.6+2.8}{2}$
$s=5.25$
$A= \sqrt{5.25(5.25-4.1)(5.25-3.6)(5.25-2.8)}$
$A=4.9$ square units
We can conclude that the area of triangle MNL is 4.9 square units.

2. To find the volume of our pyramid, we are going to use the formula for the volume of a rectangular pyramid: $V= \frac{lwh}{3}$
where
$l$ is the length of the rectangular base
$w$ is the width of the rectangular base
$h$ is the height of the pyramid
From our picture we can infer that $l=15$ , $w=10$ , and $h=12$ , so lets replace the values in our formula:
$V= \frac{lwh}{3}$
$V= \frac{(15)(10)(12)}{3}$
$V=600$ cubic units

To find the volume of the cone, we are going to use the formula: $V= \pi r^2 \frac{h}{3}$
where
$r$ is the radius
$h$ is the height
From our picture we can infer that the diameter of the cone is 9; since radius is half the diameter, $r= \frac{9}{2} =4.5$ . We also know that $h=12$ , so lets replace the values:
$V= \pi r^2 \frac{h}{3}$
$V= \pi (4.5)^2 \frac{12}{3}$
$V=254.5$ cubic units
We can conclude that the volume of the pyramid is 600 cubic units and the volume of the cone is 254.5 cubic units

3. To find $y$ , we are going to use the tangent trigonometric function:
$tan( \alpha )= \frac{opposite.side}{adjacent.side}$
$tan(53)= \frac{4cm}{y}$
$y= \frac{4cm}{tan(53)}$
$y=3.01cm$
and to the nearest whole number:
$y=3cm$
We can conclude that $y=3cm$

4. To solve this, we are going to find the volume of the cube first; to do it we are going to use the formula for the volume of a cube: $V=a^3$
where
$a$ is the edge of the cube
Since the sphere fits exactly in the cube, the edge of the cube is equal to the diameter of the sphere; therefore, $a=12$ . Lets replace the value in our formula:
$V=(12)^3$
$V=1728$ cubic units
Next, we are going to use the formula for the volume of a sphere: $V= \frac{4}{3} \pi r^3$
where
$r$ is the radius of the sphere
We know form our problem that the diameter of the sphere is 12 units, since radius is half the diameter, $r= \frac{12}{2} =6$ . Lest replace the value in our formula:
$V= \frac{4}{3} \pi r^3$
$V= \frac{4}{3} \pi (6)^3$
$V=904.8$ cubic units
Now, to find the volume of the empty space in the cube, we just need to subtract the volume of the sphere form the volume of the cube:
$V_{empty}=1728-904.8=823.2$ cubic units
We can conclude that the volume of the empty space in the cube is 823.2 cubic units

4. To solve this, we are going to use the arc length formula: $s= \frac{ \alpha}{360} 2 \pi r$
where
$s$ =mBC
$s$ is the length of the arc
$r$ is the radius of the circle
Lets, find $x$ first. From the picture we can infer that:
$x+2x+x=180$
$4x=180$
$x= \frac{180}{4}$
$x=45$
Since BE is the diameter of the circle, AB is its radius; therefore $r=AB$ . Lets replace the values in our formula:
$s= \frac{ \alpha}{360} 2 \pi r$
$s= \frac{45}{360} 2 \pi AB$
$s= \frac{ \pi }{4} AB$
$mBC= \frac{ \pi }{4} AB$
We can conclude that $mBC= \frac{ \pi }{4} AB$

3 0

3 years ago