Answer:
197
Step-by-step explanation:
Initial population of rabbit is 139
after 2 years , rabbit population is 556
For exponential growth use y=ab^x
where a is the initial population
x is the time period
b is the growth rate, y is the final population
a= 139 is already given
when x=2, the value of y = 557
plug in all the values in the formula and find out 'b'
[tex]y=ab^x[/tex]
[tex]557=139(b)^2[/tex]
Divide both sides by 139
[tex]\frac{557}{139} =b^2[/tex]
take square root on both sides
b=2.00180 and b=-2.00180
growth factor cannot be negative
So b= 2.0018
The equation y=ab^x becomes
[tex]y=139(2.0018)^x[/tex]
To find population after 6 months
1 year = 12 months
so 6 months = 0.5 years
we plug in 0.5 for x
[tex]y=139(2.0018)^{0.5}[/tex]
y= 196.66
so population after 6 months = 197
Give the equation of the line in slope-intercept form that has the slope of 5 and goes through the point (0, -3).
Answer:
y=-3x+5
-3 is y ntercept
(4b) A rocking horse has a weight limit of 60 pounds. What percentage of the weight limit is 114 pounds? *
Answer:
190 percentage of the weight limit is 114 pounds.
Step-by-step explanation:
Given: A rocking horse has a weight limit of 60 pounds.
We have to find what percentage of the weight limit is 114 pounds.
x percentage of the weight limit is 114 pounds.
⇒ x% of 60 = 114
[tex]\frac{x}{100} \times 60 = 114[/tex]
Solve for x;
[tex]\frac{6x}{10} = 114[/tex]
Multiply both sides by 10 we get;
[tex]\frac{6x}{10} \times 10 = 114 \times 10[/tex]
[tex]6x = 1140[/tex]
Divide both sides by 6 we get;
[tex]x = \frac{1140}{6}[/tex]
Simplify:
x = 190%
Therefore, 190 percentage of the weight limit is 114 pounds.
To find the percentage, divide the given weight by the weight limit and multiply by 100. 114 pounds is 190% of the weight limit of 60 pounds.
To find the percentage of the weight limit, we need to divide the given weight (114 pounds) by the weight limit (60 pounds) and then multiply the result by 100. So, the calculation would be:
Percentage = (114 pounds / 60 pounds) * 100
Simplifying this equation, we get:
Percentage = 190%
Therefore, 114 pounds is 190% of the weight limit of 60 pounds.
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The graph of the function f(x) is shown below. When f(x) = 0, determine x
Answer:
When f(x) is 0, then x is -1.8.
Step-by-step explanation:
To find this, you simply have to look for the place where the line crosses the x axis. This is where y (or f(x)) is equal to 0. Since this graph only crosses that axis at x = -1.8, that is the number we are looking for.
Jenna has some chocolate tat she wants to give to her friends. She wants to give 1/5 of a pound of chocolate to each friend. If jenna has 7pounds of chocolate, to how many friends can she give chocolate
25 friends because 7*5=35
The commission Gary earns is proportional to the cost of the shoes he sellis. Gary earns $15 in commission for every S150 worth of shoes that he sells. Which equation gives the total commission, C Gary will earn based on the cost, s, of the shoes he sels?
Answer:
15x + 150
Step-by-step explanation:
Given the position function s(t)=(t^3/3)-(12t^2/2)+36t between t=0 and t=15, where s is given in feet and t is measured in seconds, find the interval in seconds where the particle is moving to the right.
Answer: [0, 6) ∪ (6, 15]
Step-by-step explanation:
The particle is moving to the right when the velocity is positive.
[tex]s(t)=\dfrac{t^3}{3} -\dfrac{12t^2}{2}+36t[/tex]
v(t) = s'(t)
= t² - 12t + 36
First, find the zeros of v(t): ⇒ v(t) = 0
0 = t² - 12t + 36
= (t - 6)²
0 = t - 6
6 = t
The zero occurs when t = 6
Next, find when v(t) > 0
Choose a test point between 0 and 6:
v(5) = (5 - 6)²
= (-²)
= (+)
Since velocity is positive between 0 and 6, the particle is moving to the right during that interval.
Choose a test point between 6 and 15:
v(7) = (7 - 6)²
= (+)²
= (+)
Since velocity is positive when t > 6, the particle is moving to the right.
Joel has 7 pounds of clay. He splits the clay into groups of 1/3 pound. How many groups does he have
Jon is looking into a $4250 vacation package that is offered for 25% off. There is a 9% resort fee added on to the total. How much will the vacation cost Jon?
Answer:
3187.59
Step-by-step explanation:
Add 4250 - 25% + 9% and u should have this exact answer
- The one guy who has a F in math
What is m∠C?
Enter your answer in the box.
Answer:
angle C is 60 degrees
Step-by-step explanation:
First you would solve for X
once you have that plug it in angle C
2(30)=60
Answer:
60°
Step-by-step explanation:
∠B is a right angle and all right angles are 90°, so if ∠B = 3*x then to find x you divid 3 by 90 to get x because 3*x = 90 once you do that you get 30 so x=30 then to find ∠C you just multiply 2 by 30 which gives you 60 which means the measure of ∠C = 60°
hope this helps :D
What is the length of cloth needed to make 18 shirts if each shirt is made from 0.8 yards of material?
Answer:
14.4 yards
Step-by-step explanation:
Each shirt needs 0.8 yards so 18 shirts needs 18 * 0.8 = 14.4 yards of material.
14.4 yards of material will be needed to make 18 shirts.
What is multiplication?Multiplication is when you take one number and add it together a number of times.
Given that, one shirt is of 0.8 yards of material,
18*0.8 = 14.4
Hence, 14.4 yards of material will be needed to make 18 shirts.
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Use the Distance Formula and the Pythagorean Theorem to find the distance between each pair of points. M (5, −3) and N (4, −8)
well, we don't have to use the pythagorean theorem per se, only the distance formula, since the distance formula is really the pythagorean theorem in disguise.
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ M(\stackrel{x_1}{5}~,~\stackrel{y_1}{-3})\qquad N(\stackrel{x_2}{4}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ MN=\sqrt{[4-5]^2+[-8-(-3)]^2}\implies MN=\sqrt{(4-5)^2+(-8+3)^2} \\\\\\ MN=\sqrt{(-1)^2+(-5)^2}\implies MN=\sqrt{26}[/tex]
What is the value of [tex]\alpha[/tex] in this function?
Answer:
hello :
the graph passes by ( -4; 7/128) : f(-4) = 7/128
a/ (-4)^4 = 7/128
a / 256 = 7/128
a/2 = 7
a = 14
We have the point:
[tex]\left(-4,\ \dfrac{7}{128}\right)[/tex]
Put the coordinates of the point to the equation of the function f:
[tex]f(x)=\dfrac{a}{x^4}\to y=\dfrac{a}{x^4}\\\\\left(-4,\ \dfrac{7}{128}\right)\to x=-4,\ y=\dfrac{7}{128}\\\\\dfrac{a}{(-4)^4}=\dfrac{7}{128}\\\\\dfrac{a}{256}=\dfrac{7}{128}\qquad\text{multiply both sides by 256}\\\\a=\dfrac{7}{128}\cdot256\\\\\boxed{a=14}[/tex]
Results from choosing a counter 20 times, green 10, yellow 3, blue 7. What is the experimental probability of geting blue?
How many soccer players that are getting paid around the world are there???
Answer for 15 points! PLZ be correct info!!!
Help me with these math questions........ WITH SCREENIES
Answer: 6.3093
Step-by-step explanation:
[tex]3^{\frac{x}{5}} = 4[/tex]
[tex]ln3^{\frac{x}{5}} = ln4[/tex]
[tex]\frac{x}{5} ln3 = ln4[/tex]
xln3 = 5ln4
[tex]x = \frac{5ln4}{ln3}[/tex]
x = 6.3093
************************************************************
Answer: 5, 3, [tex]\frac{1}{5}[/tex], D
Step-by-step explanation:
a) x ≤ 0 so, f(-5) = | -5 | = 5
x ≤ 0 so, f(-3) = | -3 | = 3
x > 0 so, f(5) = [tex]\frac{1}{5}[/tex]
b) graph D
************************************************************
Answer: [tex]\frac{\pi}{12}[/tex]
Step-by-step explanation:
[tex]\frac{25\pi}{12} - \frac{2\pi}{}[/tex]
= [tex]\frac{25\pi}{12} - \frac{24\pi}{12}[/tex]
= [tex]\frac{\pi}{12}[/tex]
In the figure below, if BE is the perpendicular bisector of AD , what is the value of x?
Answer:
x = 10Step-by-step explanation:
Since BE is perpendicular bisector AE=EDSubstituting we have:3x + 5 = x + 25 solving for x x = 10How many ways can the letters be arranged?
TJKL
A) 10 ways
B) 16 ways
C) 18 ways
D) 24 ways
TJKL - different letters
for the first place you have 4 letters to choose from
for the second place you have 3 letters to choose from
for the third place you have 2 letters to choose from
for the last place you have only one letter
Therefore your answer is:
[tex]\boxed{4}\cdot\boxed{3}\cdot\boxed{2}\cdot\boxed{1}=24\to\boxed{D)}[/tex]
Write 4/9, 5/9, and 6/9 as decimals. What pattern do you see? Use the pattern to predict the decimal form of 7/9 and 8/9
Find the value of x to the nearest tenth.
a. 11.3
b. 12.5
c. 12.9
d. 13.1
Answer:
B
Step-by-step explanation:
We have perpendicular bisector through a chord of the circle. We know the length, so either side of the chord is 11 due to the bisector cutting it directly in half. Since the radius is a fixed distance from the center to any point on the edge of the circle, we can draw the radius x from the circle to the end of the chord to form a right triangle.
We can use Pythagorean Theorem [tex]a^{2} +b^{2} =c^{2}[/tex] to find the missing side length x. a=6, b=11 and c=x.
[tex](6)^{2} +(11)^{2} =x^{2}[/tex]
[tex]36+121=x^2\\157=x^2\\\sqrt{157}=x\\ 12.5=x[/tex]
Can someone help me with these 2 problems plz
can someone help me please and thank you
Find the ratio of the two similar sides that both dimensions are given.
The smaller triangle aide that is 4 units is the similar side of the larger triangle given as 8 units.
8 / 4 =2, this means the larger triangle is 2 times the size of the smaller triangle, which also means the smaller triangle is 1/2 the size of the larger triangle.
X on the smaller triangle is 1/2 11 units which equals 5.5 units.
Y is 2 times 3, which equals 6 units.
x = 5.5
y = 6
As a part of a contest, a store is giving a special prize if a contestant can roll 3 standard six-sided number cubes, and get the same number on each. What is the probability a contestant will be successful?
Answer: [tex]\bold{\dfrac{1}{36}}[/tex]
Step-by-step explanation:
The first die can be any number: [tex]P = (\dfrac{6}{6}) = 1[/tex]
The second die must match the first die: [tex]P = \dfrac{1}{6}[/tex]
The third die must also match the first die: [tex]P = \dfrac{1}{6}[/tex]
1st die and 2nd die and 3rd die = Probability of success
1 x [tex]\dfrac{1}{6}[/tex] x [tex]\dfrac{1}{6}[/tex] = [tex]\dfrac{1}{36}[/tex]
So the correct answer Is A, but can you explain how you get that answer?
The first thing to notice is that the smaller triangle on the left is equilateral, because of the same single tickmarks on each of the three sides. For any equilateral triangle, each interior angle is 60 degrees as you have marked it on the drawing.
Once you determine that, you would solve for the 120 degree angle (60+120 = 180). Afterward, solve the equation 120+x+x = 180 to find that x = 30. The equation 120+x+x = 180 refers to adding up the three angles of the smaller triangle on the right side (with angles 120, x, x). The two missing angles are both x due to the fact that this triangle is isosceles.
Answer:
Step-by-step explanation:
Since ∆ABC is equilateral, all of its angles would be the same (60°). Since a line is 180°, the other part of ∠C is 120°. Since we also know that △BCD is isosceles, we know that angles ∠B and ∠D are equal. If a triangle is 180°, and we already know that ∠C is 120°, we can do 180-120, which is 60°. If angles ∠B and ∠D are equal, we can do 60/2=30. Therefore, ∠D is 30°.
Function g is transformed to obtain function h as shown.
(x)=4g(x+5)
A.
The graph of h is the graph of g vertically stretched by a factor of 4 and shifted 5 units to the left.
B.
The graph of h is the graph of g vertically shrunk by a factor of 4 and shifted 5 units to the right.
C.
The graph of h is the graph of g vertically stretched by a factor of 4 and shifted 5 units to the right.
D.
The graph of h is the graph of g vertically shrunk by a factor of 4 and shifted 5 units to the left.
Answer:
A
Step-by-step explanation:
The transformation is [tex]h(x)=4*g(x+5)[/tex].
4*g(x+5) means g(x) is vertically shifted by a factor if 4 by multiplying the entire function by 4. The values increase and are stretched (not shrunk to smaller).g(x+5) means the input x is increased by 5 each time. This results in a horizontal shift left on the graphThe answer is A. The graph of h is the graph of g vertically stretched by a factor of 4 and shifted 5 units to the left.
Answer: A for plato users
Triangle STU is dilated to form new triangle VWX. If angle S is congruent to angle V, what other information will prove that the two triangles are similar? Side ST is congruent to side VW. Angle T is congruent to angle V. Side US is congruent to side XV. Angle U is congruent to angle X.
Answer:
(D)
Step-by-step explanation:
Two triangles are similar if it satisfies the following properties:
1) Corresponding angles are congruent.
2) Corresponding sides are all in same proportion.
Here, ΔSTU and ΔVWX are given, where ∠S is congruent to ∠V.
To prove these two triangles similar, we need one more corresponding angle to be congruent.
And from all the options, (d) Angle U is congruent to angle X. will help in proving ΔSTU and ΔVWX similar triangles.
Therefore, (d) is correct.
Answer:
d)Angle U is congruent to angle X.
Step-by-step explanation:
Which equation represents this problem?
Carol's age is three more than two times Lindsay's age. Carol is 39 years old. How old is Lindsay?
Let l = Lindsay's age in years.
3l + 2 = 39
2l–3=39
3l–2=39
2l + 3 = 39
Answer:
2l + 3 = 39
Step-by-step explanation:
the equation is 3 + 2L = C, where L is Lindsay's age and C is Carol's age
3 + 2L = 39
Could someone help I can’t get this one
Statement Reason
1. AB = CD, AD = CB 1. Given
2. AC = AC 2. Reflexive Property
3. ΔADC ≅ ΔCBA 3. SSS
4. ∠1 = ∠4 4. CPCTC
5. DC || AB 5. Alternate Interior Angles Converse Thm
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
If the table is that of f(x), find a point that lies on the graph of f-^1(x).
Answer: D
Step-by-step explanation:
Inverse is when the x's and y's are swapped
x | y Inverse
-3 | 5 (5, -3)
-2 | -3 (-3, -2)
0 | 3 (3, 0)
1 | -5 (-5, 1) ← this matches choice D
2 | 6 (6, 2)
3 | 10 (10, 3)
A student bought a truck with a down payment of 4000 and monthly payments of $250 for four years. What was the total cost of the truck
Use the table below to answer this question:
x y
−3 −3
0 3
1 5
Find the average rate of change for the given function from x = −3 to x = 1.
2
−3
−1
−2
Answer:
2
Step-by-step explanation:
We can find the average rate of change by using the formula
rate of change = (y2-y1) /(x2-x1)
= (5-3)/(1-0)
= 2/1
=2
Answer:
A. 2
Step-by-step explanation:
average rate of change from x1 to x2 is
[f(x2) - f(x1)]/(x2 - x1)
Here we have x1 = -3; f(x1) = -3; x2 = 1; f(x2) = 5
average rate of change from x1 to x2 =
= [f(x2) - f(x1)]/(x2 - x1)
= [5 - (-3)]/(1 - (-3))
= 8/4
= 2