Using an exponential function, it is found that it will take 24 years for the current population of 4800 deer to reduce to 600.
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex]
In which:
a is the initial value.b is the rate of change, as a decimal.In this problem, considering the initial value of 4800, and that the population halves every 8 years, the equation is given by:
[tex]A(t) = 4800\left(\frac{1}{2}\right)^{\frac{t}{8}}[/tex]
The population will be of 600 when A(t) = 600, hence:
[tex]A(t) = 4800\left(\frac{1}{2}\right)^{\frac{t}{8}}[/tex]
[tex]600 = 4800\left(\frac{1}{2}\right)^{\frac{t}{8}}[/tex]
[tex]\left(\frac{1}{2}\right)^{\frac{t}{8}} = \frac{600}{4800}[/tex]
[tex]\left(\frac{1}{2}\right)^{\frac{t}{8}} = \frac{1}{8}[/tex]
[tex]\left(\frac{1}{2}\right)^{\frac{t}{8}} = \left(\frac{1}{2}\right)^3[/tex]
Hence:
t/8 = 3.
t = 24.
It will take 24 years for the current population of 4800 deer to reduce to 600.
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PLS HELP! If Cyrus knows that △ABC∼△EDC and AB¯¯¯¯¯¯¯¯∥ED¯¯¯¯¯¯¯¯, how can he prove that line m passing through AB¯¯¯¯¯¯¯¯ has the same slope as line l passing through ED¯¯¯¯¯¯¯¯?
Answer:
AB and DE are parallel because they have the same slope.
Step-by-step explanation:
Slope of the line AB :
[tex]=\frac{\text{rise} }{\text{run} } =\frac{CA}{-BC} =\frac{12}{-8} =-\frac{3}{2}[/tex]
Slope of the line DE :
[tex]=\frac{\text{rise} }{\text{run} } =\frac{CE}{-DC} =\frac{9}{-6} =-\frac{3}{2}[/tex]
Suppose that $b$ is a positive integer greater than or equal to $2.$ When $197$ is converted to base $b$, the resulting representation has $4$ digits. What is the number of possible values for $b$
Suppose that b is a positive integer greater than or equal to 2. When 197 is converted to base b, the resulting representation has 4 digits. What is the number of possible values for b?
The possible values of b are 4 and 5
How to determine the possible numbers of b?The conditions are given as:
b is at least 2When 197 in base b has 4 digits.So, we start by converting 197 to base 2 and above.
This is done as follows:
197 to base 2
2 | 197
98 R 1
49 R 0
24 R 1
12 R 0
6 R 0
3 R 0
1 R 1
0 R 1
So, we have:
197 = 11000101 in base 2
11000101 has more than 4 digits.
This means that b cannot be 2
Using the above method of conversion, we have:
197 = 21022 in base 3197 = 3011 in base 4197 = 1242 in base 5197 = 525 in base 6197 = 401 in base 7See that as the base increases, the number of digits decreases.
The numbers in base 4 and 5 have 4 digits.
Hence, the possible values of b are 4 and 5
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what are the solutions to to the equation x^2+4x+4=12
Answer:
[tex]x = -2 +2\sqrt 3\\\\x = -2 -2\sqrt 3[/tex]
Step by step explanation:
[tex]~~~~~~x^2 +4x +4 = 12\\\\\implies x^2 +2\cdot 2x + 2^2 = 12\\ \\\implies (x+2)^2 = 12\\\\\implies x +2 = \pm\sqrt{12}\\\\\implies x = -2 \pm\sqrt{12}\\\\\implies x = -2\pm\sqrt{4 \times 3}\\\\\implies x = -2 \pm2\sqrt 3[/tex]
The graph of a quadratic function passes through the points (0,-4) and (-2,0). what is a zero of the function
Answer:
-2
Step-by-step explanation:
the zero of the function is -2 because it's the root of the equation when y= 0
As seen in the diagram below, Shandra is building a walkway with a width of xx feet to go around a swimming pool that measures 8 feet by 6 feet. If the total area of the pool and the walkway will be 168 square feet, how wide should the walkway be?
The total surface area of the building is the sum of the total faces an object contains. The walkway should be about 2.57feet
How to calculate the total surface area the building?The total surface area of the building is the sum of the total faces an object contains. The formula is expressed as:
TSA = 2(lw + wh + lh)
where
l is the lengthw is the widthh is the heightGiven the following parameters
TSA = 168 square feet
length = 8feet
Height = 6 feet
Required
Width of the walkway
Substitute
168 = 2(lw + wh + lh)
84 = (8(6) + 6w + 8w)
84 = 48 + 14w
14w = 84 - 48
14w = 36
w = 2.57feet
Hence the walkway should be about 2.57feet
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1
2
X
-5
-4
-3
2
1
0
1
2
3
6
f(x)
-6
-2
0
4
4
0
-2
-6
-10
Based on the table, which best predicts the end
behavior of the graph of f(x)?
O As x, f(x)→∞, and as x→→∞, f(x)→∞.
O As x→∞, f(x)→∞, and as x→∞, f(x)→→∞
O As x, f(x)→∞, and as x→→∞, f(x)→∞
O As x→∞, f(x)→∞, and as x→∞, f(x)→
818
The statement that best describes the end behavior of the graph is given as follows:
As [tex]x \rightarrow -\infty, f(x) \rightarrow -\infty[/tex], and as [tex]x \rightarrow -\infty, f(x) \rightarrow \infty[/tex].
What is the end behavior of a function?It is given by it's limits as x goes to negative and positive infinity.
From the given table, it is found that f(x) starts with negative values, increases until it's maximum value then decays again, hence the correct statement is:
As [tex]x \rightarrow -\infty, f(x) \rightarrow -\infty[/tex], and as [tex]x \rightarrow -\infty, f(x) \rightarrow \infty[/tex].
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Question 9 of 10
Which pairs of angles in the figure below are vertical angles?
Check all that apply.
Answer:
B and C
Step-by-step explanation:
vertical angles are angles that are opposite of each other when two lines cross. Vertical angles are congruent = they are equally large.
the angles listed in B and C are mirrored across either an imaginary or a directly visible line. and that makes them vertical angles.
How many solutions are in 17x-8=3x+16
Consider the original triangle and the scale drawing enlargement.
A triangle with a side measurement of 2 centimeters. 2 triangles have corresponding side lengths of 2 centimeters and 8 centimeters.
Figures not drawn to scale.
What is the scale factor?
Answer:
scale factor = 4
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, image to original
scale factor = [tex]\frac{8}{2}[/tex] = 4
What is the center of the circle described by the equation (x-6)² + (y + 5)² = 25?
Reason:
Rewrite the given equation into [tex](x-6)^2 + (y-(-5))^2 = 5^2[/tex]
I changed the y+5 into y-(-5), and also replaced 25 with [tex]5^2[/tex]
Then compare that to the circle template of [tex](x-h)^2 + (y-k)^2 = r^2[/tex]
We see that h = 6 and k = -5 to give a center of (h,k) = (6, -5)
Side note: the radius is r = 5 units
100 points plus brainliest
Answer:
45 degrees
Step-by-step explanation:
so we know there is one 90 degree angle
and the other two angles are congruent
so the math would go like this
180-90=90
90/2= 45
(the 2 represents the two angles)
Answer:
x = 22.62° (nearest hundredth)
Step-by-step explanation:
As this is a right triangle, we can use the cosine trigonometric ratio to find x.
[tex]\sf \cos(\theta)=\dfrac{A}{H}[/tex]
where:
[tex]\theta[/tex] is the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)Given:
[tex]\theta=x[/tex]A = 12H = 13Substitute the given values into the formula and solve for x:
[tex]\implies \cos(x)=\dfrac{12}{13}[/tex]
[tex]\implies x=\cos^{-1}\left(\dfrac{12}{13}\right)[/tex]
[tex]\implies x=22.61986495...^{\circ}[/tex]
[tex]\implies x=22.62^{\circ}\:\: \sf(nearest\:hundredth)[/tex]
13 = m/4 + 7 can you show work too
The correct value of this equation is m = 24
Resolution methodThis equation contains a fractional term. We note that the denominator of this equation is the term 4. Therefore, we will multiply the sides by 4:
13 = m/4 + 7
13 . 4 = 4(m/4) + 7 . 4
52 = m + 28
Now, let's isolate the variable "as negative" and after the equality - we'll be subtracting the terms:
52 = m + 28
-m = 28 - 58
-m = -24
m = 24
Therefore, the correct value of this equation will be m = 24
A 2-ft vertical post casts a 20-in shadow at the same time a nearby cell phone tower casts a 115-ft shadow. how tall is the cell phone tower?
the cell phone tower is _ ft
The height of the cell phone tower will be 138 feet.
What are ratio and proportion?A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.
A 2-ft vertical post casts a 20-in shadow at the same time a nearby cell phone tower casts a 115-ft shadow.
Then the height of the cell phone tower will be
Let x be the height of the cell phone tower.
x / 2 = 115 x 12 / 20
x = 69 x 2
x = 138 feet
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U.S. Birth Rate, 1950-2000
Year
Birth Rate
(per 1000 population)
1950
24.1
1960
23.7
1970
18.4
1980
15.9
1990
15.7
2000
14.7
Source: World Almanac 2003
Is the relation (year, birth rate) a function? Explain.
a.
No, there is a year with two birth rates paired with it.
b.
Yes, each year is paired with only one value for the birth rate.
c.
No, two years have a birth rate of over 20.
d.
No, there are no negative birth rate values.
Using it's concept, it is found that the correct option regarding whether the relation is a function is given by:
b. Yes, each year is paired with only one value for the birth rate.
When a relation represents a function?It represents a function if each value of the input is mapped to only one value of the output.
In this problem, the inputs are the decades(1950 to 2000), and each has only one rate, hence it is a function and option b is correct.
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can someone help me out?
The factor if the root is 2 is x - 2 and the factor if the root is -3 is c + 3
Factors of a polynomialAccording to the question, we are to find the factors of the polynomial expression
Given the polynomial expression
y = x² + x - 6
Factorize
y = x² + 3x - 2x - 6
y = x(x+3)-2(x+3)
y = (x-2)(x+3)
Hence the factor if the root is 2 is x - 2 and the factor if the root is -3 is c + 3
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Courtney was making curtains from some fabric she had in her closet. She measured 7 3/4 yards of fabric and needed to make 4 curtains that were the same size. How much fabric does she need for each curtain? Estimate:
Answer:
About 32
Step-by-step explanation:
It says 7 3/4 and she makes 4 curtains ESTIMATE!! So you round the 7 3/4 to 8 and do 8 x 4 since she made 4 curtains. Hope this helped!
A bakery sold a total of 400 cupcakes in a day, and 43% of them were vanilla flavored. how many of the cupcakes sold that day were vanilla flavored?
The number of the cupcakes sold that day that were vanilla flavored is 172.
How do we calculate a number from a percentage?The number of the cupcakes sold that day that were vanilla flavored can be calculated using the following formula:
Number of vanilla flavored cupcakes sold = Total number of cupcakes sold * Percentage that were vanilla flavored .............. (1)
Substituting the relevant values into equation (1), we have:
Number of vanilla flavored cupcakes sold = 400 * 43% = 172
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Shelby mixes a 25% bleach solution with 5 cups of a 10% bleach solution, resulting in a 20% bleach solution. The table shows the amount of each solution used.
A table titled Bleach Solution showing Cups, Bleach concentration, and Total. The first row shows 10 percent Bleach with 5, 0.10, and 0.5. The second row shows, 25 percent bleach, with x, 0.25, and 0.25 x. The third row shows Mixture, with 5 plus x, 0.20, and 3.
What is the value of x?
Answer: is C
Step-by-step explanation: like i said making it easier .
Explain how the expression 32 relates to the diver's depth
Answer:
See below
Step-by-step explanation:
Each 32 feet of depth is 1 more atmosphere of pressure on the diver
Find the volume of the sphere. Round your answer to the nearest tenth.
A sphere is shown with a radius of 7 feet.
The volume is about
cubic feet.
So we all know the FORMULA for a sphere is v=4/3 x π x r^3
So, now we SUBSTITUTE ,V=4/3 x π x 7^
This leaves us with the answer of 1436.76 ft ^2 maybe?
(hope this is correct!)
A factory made 424 items in 4 hours at a
constant rate. Plot the points on the graph
to represent the total number of items
made each hour.
ty
400
300
200
100
X
Items
0
1
2 3
Hours
4
A graph is a way to represent a lot of data in a visual format. The graph can be drawn as using the equation y=100x+24.
What is a graph?A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.
Given a factory-made 424 items in 4 hours at a constant rate. Also, the table is given, therefore, the slope of the line can be written as,
m = (400-300)/(4-3) = 100
Therefore, the equation can be written as y=100x+C
now, substituting the point we will get,
424 = 100(4) + C
424 - 400 = C
C = 24
Therefore, the graph can be drawn as using the equation y=100x+24.
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Find CE.
Show your work!
The length of the chord CE is 24.46 in
To find the length of the chord CE, we solve the question using pythagoras' theorem
What is a chord?A chord is a line segment touching two points in a circle.
What is pythagoras' theorem?Pythagoras' theorem states that in any right angled triangle with sides a, b and c where c is the hypotenuse side, we have that
c² = a² + b²
The required triangle
Now form the diagram the radius of the circle BE forms a right angled triangle with the perpendicular to the chord, BO and the midway between the chord, OE.
BO = BD - OD
= 20 in - 5 in
= 15 in
From pythagoras,
BE² = DE² + BO²
making DE subject of the formula, we have
DE = √(BE² - BO²)
DE = √((20 in)² - (15 in)²)
DE = √(400 in² - 225 in²)
DE = √(175 in²)
DE = 13.23 cm
The length of the chord
Since the chord CE = 2DE,
So, CE = 2 × 13.23 in
= 26.46 in
So, the length of the chord CE is 24.46 in
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Amelie wants to decorate the outside of the box but not the bottom. It is a 5 in. by 3 in. by 2 rectangular prism. If the beads that she is using cost $0.25 per square inch, how much will she pay for the beads? Her work is shown. surface area = 15 + 15 + 6 + 6 + 10 + 10 = 62 in. 2 cost = 0.25(62) = $15.50 Did she make an error? Yes, she should have only added the area of five of the six faces. Yes, she did not use the correct area formula for a rectangle. Yes, she calculated the cost incorrectly. No, she didn’t make any errors.
Answer:
Yes, she should have only added the area of five of the six faces.
Step-by-step explanation:
The formula for determining the surface area of a cuboid or box is expressed as
Surface area = 2lw + 2lh + 2wh
Where l, w and h represents length, width and height of the box respectively.
2lw represents the area of the top and the bottom of the box. Since she doesn't want to cover the bottom, it becomes lw. Therefore,
Surface area = 15 + 6 + 6 + 10 + 10 = 47 in².
The cost would be
0.25 × 47 = $11.75
Therefore,
Yes, she should have only added the area of five of the six faces.
Factor 4x² - 121 a) (2x + 11) (2x + 11) b) (2x - 11) (2x - 11) (2x + 11) (2x - 11) d) (4x + 11) (4x - 11)
Answer:
(2x-11)(2x+11)
Step-by-step explanation:
2x-11 × 2x+11 yields
4x^2 + 22x -22x +121
22x subtracts itself and final result is
4x^2 -121
A trellis consists of overlapping wooden slats.
1.What is the position of the indicated angles?
2.What should the value of x be in order for the two slats to be parallel?
3. Which theorem or postulate will you use to prove the parallel slats?
4. Find the measure of the indicated angle
The position of the angles are corresponding angles.
The value of x should be 6 for the slats to be parallel.
The theorem use to prove the parallel slat is the corresponding angle theorem.
The measure of the indicated angles are 42 degrees.
How to know a corresponding angles?Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal.
Therefore, the position of the angles are corresponding angles
Since the angles are corresponding angles, they are congruent.
Therefore,
3x + 24 = 7x
24 = 7x - 3x
24 = 4x
x = 6
The theorem use to prove the postulate is the corresponding angle theorem.
The measure of the indicated angle can be calculated as follows:
7(6) = 42 degrees.
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x⁶y⁴/xy²
how would I simplify?
Answer choices:
A: x⁵y²
B:x⁶y²
C:x²y⁵
D:(xy)⁷
Step-by-step explanation:
please mark me as brainlest
Solve for d given -4d+6>10
Answer:
Scientific notation: 4 ⋅ 10 -4
expanded form: 0.0004
Simon easily defeats the kidnapper in
hand-to-hand combat outside the water tower,
but to get inside the tower he must figure out the
last digit to the combination lock on the door.
A riddle was left for Simon to solve, giving him the
number he needs... if he can solve it in time!
The riddle reads:
2
"A rectangle has an area given by x² + 2x - 24.
The number you seek is the sum of its length
and width when x = 5."
9) Find the last digit to the password by solving
the riddle! (A /4) hint factor to get the dimensions of the rectangle
The dimensions of the rectangle will be 4 and 6.
How to solve the value?From the information given, we are told that the area is given by x² + 2x - 24. We will expand this as follows:
x² + 2x - 24
x² + 6x - 4x - 24
x(x + 6) + 6(x - 4)
x - 4 = 0
x = 0 + 4
Therefore, the other dimension will be:
= 24/4
= 6
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can you solve the question but tell me how to do it I'm trying to study but don't know how to solve it?
Answer:
8x+19=9x+9
Step-by-step explanation:
Simplifying
(8x + 19) = (9x + 9)
Reorder the terms:
(19 + 8x) = (9x + 9)
Remove parenthesis around (19 + 8x)
19 + 8x = (9x + 9)
Reorder the terms:
19 + 8x = (9 + 9x)
Remove parenthesis around (9 + 9x)
19 + 8x = 9 + 9x
Solving
19 + 8x = 9 + 9x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-9x' to each side of the equation.
19 + 8x + -9x = 9 + 9x + -9x
Combine like terms: 8x + -9x = -1x
19 + -1x = 9 + 9x + -9x
Combine like terms: 9x + -9x = 0
19 + -1x = 9 + 0
19 + -1x = 9
Add '-19' to each side of the equation.
19 + -19 + -1x = 9 + -19
Combine like terms: 19 + -19 = 0
0 + -1x = 9 + -19
-1x = 9 + -19
Combine like terms: 9 + -19 = -10
-1x = -10
Divide each side by '-1'.
x = 10
Simplifying
x = 10
Answer:
x = 10Step-by-step explanation:
they are opposite angles, therefore congruentwe solve with an equation8x + 19 = 9x +9
19 - 9 = 9x - 8x
10 = 1x
x = 10
check
-------------------
8 * 10 + 19 = 9 * 10 + 9
80 + 19 = 90 + 9
99 = 99
the answer is good
Carmen used a random number generator to simulate a survey of how many children live in the households in her town. There are 1,346 unique addresses in her town with numbers ranging from zero to five children. The results of 50 randomly generated households are shown below.
Children in 50 Households
Number of Children
Number of Households
0
5
1
11
2
13
3
10
4
9
5
2
Using a proportion, what can you infer about the number of households in her town that have more than three children?
About 242 households have more than three children.
About 269 households have more than three children.
About 296 households have more than three children.
About 565 households have more than three children.
About 296 households have more than three children. Then the correct option is C.
How to find that a given condition can be modeled by binomial distribution?Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as
The expected value will be
E(X) = np
Carmen used a random number generator to simulate a survey of how many children live in the households in her town.
There are 1,346 unique addresses in her town with numbers ranging from zero to five children.
The results of 50 randomly generated households are shown below.
Children in 50 Households
Number of Children Number of Households
0 5
1 11
2 13
3 10
4 9
5 2
Then the value of p and n will be
p = 11/50
n = 1346
Then the expected value will be
E(x) = (11/50) x 1346
E(x) = 296.12 ≈ 296
Then the correct option is C.
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