Answer:
The growth rate is 35%
Step-by-step explanation:
We are given that the amount of people in a population can be determined by using the model :
[tex]y=1000(1.35)^x[/tex]
Formula of exponential growth : [tex]y=a(1+r)^t ----1[/tex]
Where y is the population in t years
a = Initial population
r = growth rate
The given equation can be written as [tex]y=1000(1+0.35)^x[/tex]
Om comparing it with 1
r = 0.35
So, Growth rate = 35%
Hence The growth rate is 35%
John recorded the weight of his dog Spot at different ages as shown in the scatter plot below.
Part A:
Write an equation that would describe the line of best fit.
Part B:
Using the line of best fit, make a prediction of Spot's weight after 18 months.
Answer:
A) y = 1.875x + 1.25
B) 35 pounds
Step-by-step explanation:
A) We need two points to define a line. To find an equation that would describe the line of best fit, we can use one of the first points and one of the last points. Let's use (2, 5) and (10, 20).
General equation of a line:
y = mx + b
Slope of the line:
m = (20 - 5)/(10 - 2) = 1.875
y-intercept is found replacing a known point and the slope into the general equation:
5 = 1.875*2 + b
b = 5 - 1.875*2 = 1.25
The final equation is:
y = 1.875x + 1.25
where y represents weight (in pounds) and x represents age (in months)
B) At x = 18:
y = 1.875*18 + 1.25 = 35
Find the solutions for a triangle with a = 16, c =12, and B = 63º.
a. A = 71.6°; C = 52.89; b =12.0
C. A = 68.6° C = 45.40; b=12.0
b. A = 71.6°; C = 45.40; b =15.0
d. A = 68.6°; C = 52.89; b=15.0
Answer:
b. A = 71.6°; C = 45.40°; b =15.0
Step-by-step explanation:
The missing values can be found with the help of the Law of Cosine and properties of triangles:
Side b (Law of Cosine)
[tex]b = \sqrt{a^{2}+c^{2}-2\cdot a \cdot c \cdot \cos B}[/tex]
[tex]b = \sqrt{16^{2}+12^{2}-2\cdot (16)\cdot (12) \cdot \cos 63^{\circ}}[/tex]
[tex]b \approx 15.022[/tex]
Angle A (Law of Cosine)
[tex]\cos A = -\frac{a^{2} - b^{2}-c^{2}}{2\cdot b \cdot c}[/tex]
[tex]\cos A = - \frac{16^{2}-15.022^{2}-12^{2}}{2\cdot (15.022)\cdot (12)}[/tex]
[tex]\cos A = 0.315[/tex]
[tex]A= \cos^{-1} 0.315[/tex]
[tex]A \approx 71.639^{\circ}[/tex]
Angle C (Sum of internal angles in triangles)
[tex]C = 180^{\circ} - 63^{\circ} - 71.639^{\circ}[/tex]
[tex]C = 45.361^{\circ}[/tex]
Hence, the right answer is B.
It's quadratic, linear or exponential?
what is the equation of the line passing through ( -5, -3 ) and perpendicular
to the line representing the equation y = - 5/7x + 2?
Answer:
y = 7/5x + 4
Step-by-step explanation:
use the slope from the equation -5/7 and take the negative reciprocal to get the perpendicular slope = 7/5. Then use the equation y=mx+b. Plug in x and y from the point given and the new slope and solve for b.
(-3) = (7/5)(-5) + b, (-3) = -7 + b, add 7 to both sides. b = 4. Rewrite the equation now to be y = 7/5x + 4
For this Prism to be a right prism, all the lateral faces must be rectangles. Is enough infromation given to prove the lateral faces are rectangles? Why or why not?
Answer:
No, there isn't enough information to prove that the lateral faces are rectangles
Step-by-step explanation:
If the probability of a chance event is 0.67, it is less likely to happen
than which of the following probabilities of another chance event?
Select one:
0.76
0.61
0.65
0
Answer:
.76
Step-by-step explanation:
QUICK ILL GIVE YOU 20 POINTS
Paul weighs 36 kg. Felix weighs half as much as Paul, and Frank weighs 4 kg more than Felix.
Answer:
Idk what you need but here is everything possible
Step-by-step explanation:
Paul = 36kg
Felix = 18kg
Frank = 22kg
36+18+22=76
Their weight all together is 76kg.
Answer:
Paul is 36 kg
Felix is 18 kg
Frank is 22 kg
Step-by-step explanation:
Pauls answer is in the question (36kg)
Felix is half of paul 36/2=18
Frank is 4 kg more than Felix 36/2=18 18+4=22
Math question down below
Answer: E. 2/3
Step-by-step explanation:
Division is the same thing as fractions. So 2 divided by 3 is the same thing as 2/3
Answer:
E.
Step-by-step explanation:
A) 3(1/2)= 3/2= 1 1/2 X
B) 3/1(2/3)= 6/3= 2 X
C) 2(3)= 6 X
D) 3/2= 1 1/2 X
E) 2/3= 2/3 lol
This would make it E
This graph shows a proportional relationship. (2/3, 3/4)
What is the constant of proportionality?
Answer: Hi! I'd love to help you but I'd need to see the graph.
Step-by-step explanation: Can you add a picture?
Find the area. Will mark brainliest.
Answer:
a = 70
Step-by-step explanation:
a = h * b / 2
a = 10 * 14 / 2
a = 140/2
a = 70
Simplify: 327
A)
3
B)
4
0)
7
D)
8
Your drawer contains seven red socks and five green socks. It's too dark to see which are which. What is the
probability that the two socks that you pick are both red if you don't replace the first sock after you draw it?
7/24
7/12
7/15
14/35
Answer:
7/22
Step-by-step explanation:
Probability of picking a red sock the first time: 7/12
Probability of picking a red sock the second time: 6/11 (Since you already took out one sock, thus decreasing both the number of red and total socks in the drawer.)
7/12 * 6/11 = 42/132
42/132 = 7/22
Which number is equal to 10 Superscript 4?
40
1,000
10,000
40,000
Answer: The answer is 10,000
Step-by-step explanation:
10^4 is equal to 10,000
10^4 to the second power means that you have too add 4 zeros to the end of the number.
Since 10 already has a 0, you would add 3 more.
Therefore, the answer would be 10,000.
(Your Welcome)
Answer:
10^4 is equal to 10,000
10^4 to the second power means that you have too add 4 zeros to the end of the number.
Since 10 already has a 0, you would add 3 more.
Therefore, the answer would be 10,000.
What equation is represented in this graph.
15 Points need ASAP.
Thanks!
Answer:
y = [tex]e^{x}[/tex]
The ordered pair below is a solution to which equation?
(5,40)
Answer:
y = 8x
Step-by-step explanation:
a y = 8x
40 = 8*5
40 = 40
This is a solution
A person standing on level ground is 2000 feet away from the foot of a 420-foot-tall building, as shown in the accompanying diagram. To the nearest degree, what is the value of X?
Answer:
12
Step-by-step explanation:
The formula for the tangent of an angle is the length of the opposite side divided by the length of the adjacent side. Therefore, the tangent of angle x is 420/2000=0.21. Taking the arctangent of that to get the angle, you get about 12 degrees. Hope this helps!
HELP ME QUICK PLZ WITH THIS MATH PROBLEM!!!!!!!!!!!!!!
Answer:
I believe it’s 1/2
Step-by-step explanation:
Take a point on the graph and use rise over run method
Answer:
D. 5/8 poundsStep-by-step explanation:
You can find the slope by picking a point such as (8,5).
Slope = rise over run.
(8,5) is 8 units right and 5 units up, thus the slope is 5/8
Hope this helps.
The slope intercept equation
Answer:
y=mx+b
Step-by-step explanation:
Hope this helps.
Drag the tiles to the correct boxes to complete the pairs.
Match each quadratic equation with its roots.
Answer:
Step-by-step explanation:
top side is 6 just couldn’t fit in picture
Answer: [tex]6<z<18[/tex]
Step-by-step explanation:
Use the pythagorean theorem to find z first.
[tex]c^2=a^2+b^2\\c=\sqrt{a^2+b^2}[/tex]
a = 12
b = 6
c = z
[tex]c=\sqrt{(12)^2+(6)^2}\\ c=\sqrt{144+36}\\ c=\sqrt{180} \\c=13.4[/tex]
z is greater than a and b
The length of two sides of a right triangle are leg 12 M and hypotenuse 15 M find find the length of the third side
Answer:
9 M
Step-by-step explanation:
a^2+b^2=c^2
12^2+b^2=15^2
144+b^2=225
-144 -144
b^2=81
b=sqrt of 81
b=9
What is the probability of rolling a die 6 times and getting the numbers 1, 2, 3, 4, 5, 6 in that order? Select the best answer from the choices provided.
A. 0.001389
B. 0.000129
C. 0.000021
D. 0.0000038
Answer:
C. 0.000021
Step-by-step explanation:
Each roll of the die is an independent event.
The probability of rolling a 1, then a 2, then a 3, then a 4, then a 5, then a 6 is the product of the 6 individual probabilities.
Probability of rolling a 1:
There are 6 possible outcomes, rolling 1, 2, 3, 4, 5, or 6.
There is one desired outcome, rolling a 1.
p(1) = 1/6
Probability of rolling a 2:
Similar to rolling a 1, there is 1 desired outcome,rolling a 2, out of 6 possible outcomes.
p(2) = 1/6
The same is true for rolling a 3, 4, 5, or 6. Each one has a probability of 1/6.
p(1, 2, 3, 4, 5, 6, in that order) = p(1) * p(2) * p(3) * p(4) * p(5) * p(6)
= (1/6)^6
= 1/6 * 1/6 * 1/6 * 1/6 * 1/6 * 1/6
= 1/46,656
= 0.000021433
Answer: C. 0.000021
Evaluate: 4+8= 2 x (6 - 3)
16
33
25
Answer:
I'm not so sure because there is no solution to that equation
Step-by-step explanation:
Always start by solving the parenthesis equation and multiply, divide, subtract, or add before you get into adding. Next you add those 2 numbers together and when you look at the answer on the left and on the right.. when they are different numbers, you know there is no solution. I'm not sure if this helped and if it didn't I'm sorry.. I tried.
What is a reasonable estimate for the volume of a number cube:
8 cm3, 27 in?, or 1 ft??
Answer:
I think the 8 cm one :D
At the end of the school year a school system has a table with the total absences and tardies in its 10 schools what is the best way to display these data?
A. Bar Graph
B.Circle Graph
C. Stem and leaf plot
D.Ogive graph
Answer:
A
Step-by-step explanation:
Which of these are NOT expressions?
Check all that are true.
123
9 + 3 = 12
3(4x + 5)
6 − 5 − 4 = z
3z + 2x
HELP
Answer:
6-5-4=z
9+3=12
Step-by-step explanation:
Expressions has no equal sign
hi what is the answer to c
Can someone please help me with these problems?
Answer:
number 1 is 5 inches
Step-by-step explanation:
it fits in the 15 inches 3 times.
5*3=15
Mariana picked x apples at an orchard. She and her friends ate 6 of them, leaving 36 apples.
The number of apples can be represented by the equation 2 – 6 = 36. Plot a point on the
number line to represent x, the number of apples Mariana picked.
39
40
43
41
42.
44
36
37
38
32
31
33
35
30
34
A snack mix recipe calls for 2 1/2 cups of pretzels, 4 1/2 cups of dry cereal, 2 1/4 or peanuts, and 3/4 cups of raisins.If you want to make servings of 3/4 cup each, how many can you have with those ingredients?
Answer:
13 1/3 cups
Step-by-step explanation:
find common denominator then add all of the fractions then divide by 3/4
