3. Elizabeth opened a library with 19,000 books in the year 1998. The number of books increases at a rate of 6.49% each year. Use a graph to predict the number of books in 2020.
A) ≈ 71,160
B) ≈ 75,779
C) ≈ 80,697
D) ≈ 66,824
Answers
V (t)=V0 (1+r)^t
V (t) number of books in 2020 ?
V0 books in the year 1998 19000
R rate of growth 0.0649
T time 2,020−1,998=22 years
V (22)=19,000×(1+0.0649)^(22)
V (22)=75,778.81 Round your answer to get 75779
Answer: ≈ 75,779
Step-by-step explanation:
Related Questions
Find the arc length of a central angle of pi/4 in a circle whose radius is 8 inches
A) pi/32 in
B) 2pi in
C) 360 in
D) 60 in
Answers
Arc Length = 2πR.(C°/360°), where R is the radius, C°(in degrees) is the central angle of the arc:
We are given:
R = 8 in
Central angle = π/4 ≈ (180°/4) = 45°
Length of the arc= 2π x 8 x (45°/360°) →16π(1/8) :
Length of the arc = 2π in (answer B)
The arc length of a central angle of π/4 in a circle whose radius is 8 inches is 2π inches. Therefore, option B is the correct answer.
What is arc length of a circle?The arc length is defined as the interspace between the two points along a section of a curve. An arc of a circle is any part of the circumference. The angle subtended by an arc at any point is the angle formed between the two line segments joining the center to the end-points of the arc.
The formula to find the arc length of a circle is θ/360° ×2πr.
Given that, θ=π/4 =180/4 = 45° and radius = 8 inches.
Now, arc length = 45°/360° ×2×3.14×8
= 1/8×2×3.14×8
= 6.28 inches or 2π inches
Therefore, option B is the correct answer.
Learn more about the arc length of a circle here:
https://brainly.com/question/1577784.
#SPJ3
Ariel has a plastic ice cream cone in her food playset. The ice cream cone is a half-sphere sitting on top of a cone. What is the approximate volume of the toy ice cream cone? Use 3.14 for ππ .
Answers
the approximate volume of the toy ice cream cone is around [tex]\( \frac{32}{3}π \)[/tex]cubic inches, considering the half-sphere as[tex]\( \frac{16}{3}π \)[/tex] and the cone as [tex]\( \frac{16}{3}π \).[/tex]
let's calculate the approximate volume of the toy ice cream cone step by step.
First, we need to determine the volume of the half-sphere, which is the ice cream part.
The formula for the volume of a sphere is:
[tex]\[ V_{\text{sphere}} = \frac{4}{3}πr^3 \][/tex]
But since we only have a half-sphere, we'll divide the result by 2.
Now, we need to find the radius ((r)) of the half-sphere. We can do this by measuring the radius of the ice cream cone's base.
Let's say the radius of the ice cream cone's base is (r = 2) inches.
Substituting the value of (r) into the formula:
[tex]\[ V_{\text{half-sphere}} = \frac{1}{2} \times \frac{4}{3}π(2)^3 \][/tex]
[tex]\[ V_{\text{half-sphere}} = \frac{1}{2} \times \frac{4}{3}π(8) \][/tex]
[tex]\[ V_{\text{half-sphere}} = \frac{1}{2} \times \frac{32}{3}π \][/tex]
[tex]\[ V_{\text{half-sphere}} = \frac{16}{3}π \][/tex]
Now, let's find the volume of the cone part.
The formula for the volume of a cone is:
[tex]\[ V_{\text{cone}} = \frac{1}{3}πr^2h \][/tex]
Where (h) is the height of the cone.
Let's say the height of the cone is (h = 4) inches.
Substituting the values into the formula:
[tex]\[ V_{\text{cone}} = \frac{1}{3}π(2)^2(4) \][/tex]
[tex]\[ V_{\text{cone}} = \frac{1}{3}π(16) \][/tex]
[tex]\[ V_{\text{cone}} = \frac{16}{3}π \][/tex]
Now, to find the total volume of the ice cream cone, we'll add the volumes of the half-sphere and the cone together:
[tex]\[ V_{\text{total}} = V_{\text{half-sphere}} + V_{\text{cone}} \][/tex]
[tex]\[ V_{\text{total}} = \frac{16}{3}π + \frac{16}{3}π \][/tex]
[tex]\[ V_{\text{total}} = \frac{32}{3}π \][/tex]
So, the approximate volume of the toy ice cream cone is [tex]\( \frac{32}{3}π \)[/tex]cubic inches.
Use Gauss-Jordan elimination to solve the following linear system. –4x + 4y + 5z = 9 –2x + 2y + z = 3 –4x + 5y = 4
Answers
- 4 x + 4 y + 5 z = 9
- 2 x + 2 y + z = 3
- 4 x + 5 y = 4
-------------------------
Let`s take the 1st and the 2nd equation:
- 4 x + 4 y + 5 z = 8
- 2 x + 2 y + z = 3 / * ( - 2 ) / multiply both sides of equation by - 2 . /
------------------------------------
- 4 x + 4 y + 5 z = 9
+
4 x - 4 y - 2 z = - 6
------------------------------
3 z = 3 = > z = 1
Then the 2nd and the 3rd equation:
- 2 x + 2 y = 3 - 1 / * ( - 2 )
- 4 x + 5 y = 4
--------------------------------------
4 x - 4 y = - 4
+
- 4 x + 5 y = 4
----------------------------
y = 0
- 4 x + 5 * 0 = 4
- 4 x = 4
x = - 1
Answer: x = - 1, y = 0, z = 1.
what is 345,000 in expanded form
Answers
To put something in expanded form, start with the first digit, and turn the rest of the numbers to 0s, add it to the second digit, also turning the numbers to the right to 0s, and si on and so on.
300,000 + 40,000 + 5,000 (the rest are just zeroes so..)
The answer is 300,000 + 40,000 + 5,000
Hopefully this makes sense, and good luck! :)
(01.01) Evaluate −6 − (−3). Answers:18 −9 3 −3
Answers
-6 - (-3) = -6 + 3
-6 + 3
So, -3 is the answer.
so here since we have -6 - -3 we switch 3 signs 3 becomes positive -6 + 3=-3
and there's your answer
what is the slope of the line that passes through (1,4) and (1,-3)?
A. 7
B. -7
C. undefined
D. 0
Answers
M = y2 - y1 / x2 - x1
= -3 - 4 / 1 - 1
= -7 / 0
= undefined.
Therefore the answer is C.
x1 = 1
y1 = 4
The second point is (1,-3) meaning that (x2,y2) = (1,-3). So,
x2 = 1
y2 = -3
Now use the slope formula. Plug in those four values mentioned above
m = (y2 - y1)/(x2 - x1)
m = (-3 - 4)/(1 - 1)
m = -7/0
This is where we run into issues. The denominator is 0. We CANNOT divide by zero. So the result is undefined.
Your calculator may say "UND" for "Undefined", it might say "NaN" for "Not a Number", or it might produce some other type of error.
Answer: Choice C) undefined
Note: if you draw a line through the two given points, the line is completely vertical
solve the inequality 9x-11 > 4x +12
Answers
What is the simplified form of 30 times x to the sixth power over 14 times y to the fifth power times the fraction 7 times y-squared over 6 times x to the fourth power ?
Answers
(30x⁶/14y⁵)(7y²/6x⁴)
It can be observed that the numerator of the first and the denominator of the second have a common factor of 6x⁴. Also, the denominator of the first and the numerator of the second expression have a common factor of 7y².
((6x⁴)(5x²)/(7y²)(2y³))(7y²/6x⁴)
Cancellation of the common terms will give us an answer of,
5x²/2y³
Therefore, the simplified version of the involved operation is 5x²/2y³.
Is the relationship between the variables in the table a direct variation, an inverse variation, or neither? If it is a direct or inverse variation, write a function to model it.
Answers
k = y/x
test some of the values in table :-
y/x = -17/9 and -1/11 - not equal so not direct
For indirect yx will be a constant :=
yx = 9*-17 , 11*-1 - s it not indirect variation.
Answer is neither
The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $2510 to rent trucks plus an additional fee of $125.25 for each ton of sugar. The second company does not charge to rent trucks but charges $250.75 for each ton of sugar.
For what amount of sugar do the two companies charge the same?
What is the cost when the two companies charge the same?
Answers
2510 = 250.75s - 125.25s
2510 = 125.50s
2510 / 125.50 = 20 = s.......they charge the same at 20 tons of sugar
they will both cost : 250.75(20) = $ 5015
The two companies charge the same when transporting 20 tons of sugar, for $5015 for transporting that amount.
To determine what amount of sugar the two companies charge the same, we should set up an equation where both companies' cost functions are equal. For the first company, the cost function is C1 = 2510 + 125.25x, where x is the number of tons of sugar. For the second company, the cost function is C2 = 250.75x. To find the point at which C1 equals C2, we solve for x:
2510 + 125.25x = 250.75x
Subtract 125.25x from both sides:
2510 = (250.75 - 125.25)x
2510 = 125.5x
Divide both sides by 125.5:
x = 2510 / 125.5
x = 20 tons
Therefore, the two companies charge the same for transporting 20 tons of sugar. To find the cost when they charge the same, substitute x into one of the cost functions:
C1 = 2510 + 125.25(20) = 2510 + 2505 = $5015
Thus, the cost when the two companies charge the same is $5015 for 20 tons of sugar.
A square is inscribed in the circle. A point in the figure is selected at random. Find the probability that the point will be in the part that is NOT shaded.
Answers
Probability (the point will be on unshaded part) = area of unshaded part / area of the circle.
= pi r^2 - s^2
-------------- where r = radius of circle and s = length of the side of the square.
pi r^2
To find the probability of selecting an unshaded area within a circle where a square is inscribed, one must calculate the areas of the shaded and unshaded regions and use these areas to determine the ratio representing the probability.
The question seeks to determine the probability that a randomly selected point within a figure that includes both a circle and a square will be in the unshaded area. To solve this problem, we would typically need to calculate the area of the shaded and unshaded regions and then use these areas to determine the probability. When calculating probability in a geometric context, the ratio of the area of the desired region to the area of the entire space (in this case, the circle) gives the probability of randomly selecting a point in that region.
Similarly, if the question pertained to the probability of selecting a chord shorter than the side of an inscribed equilateral triangle, we would consider the probability distribution of chord lengths within the circle. This problem involves understanding that selecting a chord at random equates to selecting its midpoint at random. If the midpoint lies within a certain area, the chord will be shorter than the triangle's side.
When dealing with probability questions like the one about Times Square visitors, the random variable would typically represent the characteristic we're interested in, such as being a visitor versus a resident. In evaluating probabilities, graphical methods, such as shading areas on a graph, can be useful to visually represent and calculate the likelihood of a specific range of outcomes.
Kim's softball team is playing in the championship game. they are losing by a score of 171717 to 666. there are 444 innings to go. kim wants to know how many runs her team needs per inning to win the game if the other team does not score. (each run is worth 111 point.)
Answers
answer is : 4 runs per inning to win
#12 with work please
Answers
[tex]\bf \pm\sqrt{3^2-2^2}=b\implies \pm\sqrt{9-4}=b\implies\boxed{ \pm\sqrt{5}=b}\\\\ -------------------------------\\\\ cos^{-1}\left( \frac{2}{3} \right)=\theta \implies sin\left[ cos^{-1}\left( \frac{2}{3} \right) \right]\implies sin(\theta ) \\\\\\ sin(\theta )=\cfrac{\pm\sqrt{5}}{3}\cfrac{\leftarrow opposite}{\leftarrow hypotenuse}[/tex]
it doesn't say the angle is in a certain quadrant, thus the +/- versions of it are both valid.
Order of operation:3[10-(27 divided by 9)] sorry I don't have the division sign
Answers
first you do parthesis (27/9) = 3
then you subtract from 10 [10-3] = 7
then multiply 3 (this is last because it is outside the parenthesis and [ ].
7 x 3 = 21
21 is your answer
hope this helps
#23 please!!! Thanks
Answers
45|3
15|3
5|5
1
[tex]xy^2=3^2\cdot5[/tex]
Since x and y are both positive integers, then there's only one possible solution to the above - [tex]x=5,y=3[/tex]
So E.
what is another name for the set of all x-values from its graph
Answers
The graph of f(x)=x^2 has been shifted into the form f(x)=(x-h)^2+k
What is the value of h?:
A. 1
B. -1
C. -3
D. 3
Answers
Answer:
D. 3
Step-by-step explanation:
Here h represents the horizontal shift. In the given graph, the graph shifted 3 units to the right from the origin.
Therefore, h = 3.
Answer: D. 3
Hope this will helpful.
Thank you.
how do i solve this??
Answers
area for the hexagon = 1/2*p*a
p = perimeter = 18*6=108
a = apothem = 15.59
108*15.59 = 1683.72/2 = 841.86 sq units
Area of rectangle = 18 x 21 = 378
841.86-378 = 463.86 rounded to 464 square units
A computer company makes a rectangular screen with a diagonal of 20 inches. The width of the screen is 4 inches less than its length. The dimensions of the computer screen are modeled by the equation x2 + (x – 4)2 = 202. What is the value of x, the length of the screen?
A.) x = –16
B.) x = –12
C.) x = 12
D.) x = 16
*The answer is D, x=16. If anyone wants to answer with an explanation of how this is the answer, I will reward them with brainliest.*
Answers
x^2 +(x-4)^2 =20^2
x^2 +(x-4)^2 =400
x^2 +(x-4)^2 -400=0
factor:
2x^2-8x-384=0
Factor the 2 out of 2X^2
2(x-16) (x+12) =0
Divide both sides by 2
(x-16) (x+12) =0
X=16 , x=-12
Number cannot be negative so x=16
Answer: D.) x = 16
Step-by-step explanation:
Given: The dimensions of the computer screen are modeled by the equation :
[tex]x^2+(x-4)^2=20^2[/tex]
To find the value of x , we need to solve the equation.
Now, the above equation can be written as :
[tex]x^2+x^2+16-8x=400\\\\\Rightarrow\ 2x^2-8x+16=400\\\\\Rightarrow2x^2-8x+384=0\\\\\Rightarrow\ 2(x^2-4x+192)=0\\\\\Rightarrow\ x^2-4x+192=0\\\\\Rightarrow(x-16)(x+12)=0\\\\\Rightarrow\ x=16\ or\ x=-12[/tex]
Since side cannot be negative therefore, x= 16
The length of a rectangle is 9 feet longer than the width. if the perimeter is 78 feet, find the length and width of the rectangle.
Answers
Width - w
Given,
Perimeter = 78 ft
2(l + w) = 78
l + w = 39
l = 39 - w
Given,
l = 9 + w
39 - w = 9 + w
2w = 30
--- w = 15
--- l = 39 -w = 39 - 15 = 24
Therefore, the length of the rectangle is 24 ft and width is 15 ft.
If the circumference of a circle is 24, and the angle measure of an arc is 120o, which is the length of the arc?
Answers
The arc length is 8.
Which number line represents the solutions to |x – 2| = 6?
Answers
x-2=6 add two to both sides
x=8
and
x-2=-6 add two to both sides
x=-4
So x=-4 and 8
So the solution on the number line is solid dots as x=-4 and x=8
Answer: D IS THE ANSWER
What is the slope of the line that contains the points (-4,2) and (6,-3)
Answers
slope = (-3 - 2) / (6 - (-4) = -5/10 = 1/2 <=
Find the volume of each figure to the nearest tenth. Show your work. please
Answers
[tex] \frac{4}{3} \pi 6^3 [/tex]
[tex] \frac{4}{3}*216 \pi [/tex]
[tex]288 \pi [/tex]
V = 288π = 288*3,14 = 904,3 m³
Cone volume: [tex] \frac{ \pi r^2h}{3} [/tex]
We don't have the height, so we should find it firstly.
Watch the triangle "inside" the cone. It is a right triangle. The apothem is the hypothenuse and the radius is the shortest leg.
Apply Pitagora.
h (longest leg) = √13²-5² = √169-25 = √144 = 12 m
V = [tex] \frac{ 5^2*12 \pi}{3} [/tex]
[tex] \frac{25*12* \pi }{3} [/tex]
[tex] \frac{300 \pi }{3} [/tex]
(300*3,14)/3 = 942/3 = 314 m³
Parallelepiped volume: a*b*h
a = 11, b = 5, h = 6
V = 11*5*6 = 330 cm³
A rectangle is 13 centimeters longer than it is wide. Its perimeter is 226 centimeters. What are the length and width?
Answers
let length be x+13
perimeter=2*(L+W)
226=2*(x+x+13)
226=2*(2x+13)
226=4x+26
subtract 26 from each sides
200=4x
x=50, which is the width
length=63
The figure below is a square pyramid. Which of the following could not be a cross section in the figure?
Square
Rectangle that is not a square
Trapezoid
Isosceles triangle
Answers
Answer:
A rectangle that is not a square is the actual answer.
The Empire State Building is just over 1,450 feet tall. In anticipation of visiting this landmark on your vacation, you create a model of it using blocks.
a. Suppose you are making a model where one block represents 2 feet. About how many blocks tall is your model of the Empire State Building? What is the scale factor?
Answers
Number of blocks=1,450 feet * (1 block/2 feet)
Number of blocks = 725 blocks
Therefore, you would use a model requiring 725 blocks. The scale factor for the model is 1 block per two feet.
Answer:
725, 1 per every 2 ft.
Step-by-step explanation:
It gives the actual height for the building, 1,450, and it says one block is two feet. Divide 1,450 by 2 and you'd get 725. And we already know dat one block is two feet so it's 1:2
(why did I start singing ``You Reposted in the Wrong Hero Academia?`` UwUz)
How do I find the coordinates of angels lab.
Answers
thus
[tex]\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 4}}\quad ,&{{ 6}})\quad % (c,d) &({{ x}}\quad ,&{{ y}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)[/tex]
[tex]\bf \left(\cfrac{{{ x}} + {{ 4}}}{2}\quad ,\quad \cfrac{{{ y}} + {{ 6}}}{2} \right)=(\underline{7,2})\implies \begin{cases} \cfrac{x+4}{2}=\underline{7}\\\\ x+4=14\\ x=14-4\\ \boxed{x=10}\\ ----------\\ \cfrac{y+6}{2}=\underline{2}\\\\ y+6=4\\ y=4-6\\ \boxed{y=-2} \end{cases}[/tex]
The graph of F(x) can be compressrd vertically and shifted to the right to produce the graph of G(x). If F(x) = x^3, which of the following could be the equation of g(x)?
A.) G(x) = 1/2(x-6)^3
B.) G(x) = 2(x-6)^3
C.) G(x) = 2(x+6)^3
D.) G(x) = 1/2(x+6)^3
Answers
It is option A. A vertical compression means that
the function is only a "fraction" of its original height, hence the
fractional coefficient.
REMEMBER, movement along the x-axis is always the OPPOSITE of
what you think. So left = + and right = -
So (x-6) actually means a shift 6 units to the right. (NOT
left like you would naturally think)
Two horses are ready to return to their barn after a long workout session at the track. the horses are at coordinates H(1,10) and Z(10,1). Their barns are located in the same building, which is at coordinates B(-3,-9). Each unit/grid on the coordinate plane represents 100 meters. Which horse is closer to the barn? Justify your answer?
Answers
d = √(x₂ - x₁)² + (y₂ - y₁)²
Use the coordinates of the two points to know their linear distances. These are represented by the red and green lines for each of the horses.
Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = 19.4165
Since the scale is 1 unit = 100 meters, the actual distance between horse H and barn B is 19.416*100 = 1,941.65 meters
Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = 16.4012
Since the scale is 1 unit = 100 meters, the actual distance between horse Z and barn B is 16.4012*100 = 1,640.12 meters
Comparing the distances: 1,941.65 meters > 1,640.12 meters. Therefore, it justifies that horse Z is nearer to the barn.