Using a decaying exponential function, it is found that the maximum height reached after the 10th bounce is of 20.62 cm.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem, the parameters are:
A(0) = 192, r = 0.2.
Hence the maximum height after the nth bounce is:
[tex]A[n] = 192(0.8)^n[/tex]
After the 10th bounce, the maximum height in cm is of:
[tex]A[10] = 192(0.8)^10 = 20.62[/tex]
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Pls help me I’m so stuck :(
Answer:
B
Step-by-step explanation:
using Pythagoras' identity in the right triangle
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , then
(x + 1)² + (x + 3)² = (x + 5)² ← expand all factors using FOIL
x² + 2x + 1 + x² + 6x + 9 = x² + 10x + 25 , that is
2x² + 8x + 10 = x² + 10x + 25 ← subtract x² + 10x + 25 from both sides
x² - 2x - 15 = 0 ← in standard form
(x - 5)(x + 3) = 0 ← in factored form
equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 3 = 0 ⇒ x = - 3
however, x > 0 , then x = 5
Answer:
B. 5
Step-by-step explanation:
[tex] \sf{C = \sqrt{ A {}^{2} + B {}^{2} }}[/tex]
[tex]\sf{x + 5 = \sqrt{ {(x + 3)}^{2} + {(x + 1)}^{2} }}[/tex]
[tex]\sf{x + 5 = \sqrt{ {(x {}^{2} + 6x + 9)} + {(x {}^{2} + 2x + 1)}}}[/tex]
[tex]\sf{x + 5 = \sqrt{ {(2x {}^{2} + 8x + 10)}}}[/tex]
[tex]\sf{(x + 5) {}^{2} = { {2x {}^{2} + 8x + 10}}}[/tex]
[tex]\sf{ {x}^{2} + 10x + 25= { {2x {}^{2} + 8x + 10}}}[/tex]
[tex]\sf{0= { {2x {}^{2} \red{ { - x}^{2} } + 8x \red{ - 10x} + 10 \red{ - 25}}}}[/tex]
[tex]\sf{0= x^{2} } - 2x { - 15}[/tex]
[tex]\sf{0= x^{2} } - 2x { - 15}[/tex]
[tex]\sf{0= (x - 5)(x + 3)}[/tex]
[tex] \sf{x_{1} - 5 = 0 }[/tex]
[tex] \sf{x_{1} = 0 + 5 }[/tex]
[tex] \sf{x_{1} = \boxed{5 }}[/tex]
[tex] \sf{x_{2} + 3 = 0 }[/tex]
[tex] \sf{x_{2} = 0 - 3 }[/tex]
[tex] \sf{x_{2} = \boxed{- 3 }}[/tex]
Option B. 5
Suppose 44% of the students in a university are baseball players. If a sample of 736 students is selected, what is the probability that the sample proportion of baseball players will differ from the population proportion by less than 3%
Required probability is 0.8990
Given that,
p = 0.44
1 - p = 0.56
n = 736
[tex]\mu_\hat{p}} = p = 0.44\\\sigma_\hat{p}} = \frac{p*(1-p)}{n} = \sqrt(\frac{0.44*0.56)}{736} ) =[/tex]0.01830
Converting Normal distribution to standard normal because A normal distribution is determined by two parameters the mean and the variance. A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution. Hence it's easy to work with standard normal distribution.
P(0.14<[tex]\hat{p}[/tex]<0.47) = P((0.41-0.44)/0.01830) < [tex]\frac{\hat{p} - \mu _{\hat{p}} }{\sigma _{\hat{p}} }[/tex]<(0.47-0.44)/0.01830
Using normal algebra we get:
= P(-1.64 < z < 1.64)
= P(z < 1.64) - P(z < -1.64)
= 0.9495 - 0.0505
= 0.8990
Thus, required probability is 0.8990
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Can someone do this whole page please? I REALLY NEED IT!
Answer:
1. A(-8,3) B(-8,-2) C(-4,-2)
2. A'(8,3) B'(8,-2) C'(4,-2)
3. A"(-12,1.5) B"(-12,-3) C"(-6,-3)
4. they give you the coordinates, haha. Just graph and connect the dots.
5. Coordinates of ABC: A(-8,3) B(-8,-2) C(-4,-2)
Coordinates of A'''B'''C''': A'''(-3,10) B'''(-3,5) C'''(1,5)
The correct coordinates for a 90 degree rotation is: A''''(3,8) B''''(-2,8) C''''(-2,4)
Most of these are formulas so I hope you have this memorized in preparation for tests! Good luck!
Having trouble question is in attachment
Answer:
[tex]x=\frac{35}{9} .[/tex]
Step-by-step explanation:
[tex](3\sqrt{3})^{-x+1} =\frac{1}{3}*27^{x-5}\\( \sqrt{3^2*3}) ^{1-x}=\frac{1}{3} *((3)^3)^{x-5}\\(\sqrt{27} )^{1-x}=\frac{1}{3}*3^{3*(x-5)}\\ (\sqrt{3^3})^{1-x} =\frac{1}{3}*3^{3x-15}\\ 3^{\frac{3 }{2}*(1-x)}=\frac{1}{3}*3^{3x-15}\ |*3\\ 3*3^{\frac{3}{2}-\frac{3}{2}x}=3^{3x-15}\\ 3^{1+1,5-1,5}=3^{3x-15}\\ 3^{2,5-1,5x}=3^{3x-15}\ \ \ \ \Rightarrow\\2,5-1,5x=3x-15\\4,5x =17,5\ |*2\\9x=35\ |:9\\x=\frac{35}{9}.[/tex]
Graph the equation y=−x 2 −8x−7 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.
The graph of the given quadratic function is shown below
Graph of Quadratic equationsFrom the question, we are to graph the given quadratic function.
The given quadratic equation is
y = −x² −8x −7
The graph of the given quadratic function is shown below
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Select the correct texts in the table.
Consider function f.
f(x) =
=
(-x² + 6x + 36, x < -2
4x - 15,
35-4,
-2 ≤ x ≤ 4
> 4
Are the statements about the graph of function true or false?
The graph crosses the y-axis at (0,-15). True/false
The graph has a point of discontinuity at x = -2. True/false
The graph is increasing over the interval (4, ∞o). True/false
The graph is decreasing over the interval (-12, -2). True/false
The domain of the function is all real numbers. True/false
Based on the given texts in the table about the graph of the function, the true statements are:
The graph crosses the y-axis at (0,-15).The graph has a point of discontinuity at x = -2.The graph is increasing over the interval (4, ∞o).The domain of the function is all real numbers.Which statements are true of the graph of the function?The function, 4x - 15 shows that 15 is the y-intercept which means that the graph will cross the y-axis at (0,15).
The point of discontinuity is x = - 2 and we see this with the gap created at x < -2 and -2 ≤ x ≤ 4.
The graph is indeed increasing over the interval (4, ∞o) because any value of x that is greater than 4 will increase f(x) = [tex]3^x^-^4[/tex].
The domain of the function is also all real numbers as it begins at negative infinity and ends at infinity, (-∞, ∞).
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Which graph represents an even function? A coordinate plane has 5 points. The points are (negative 6, negative 4), (negative 4, 2), (2, 4), (4, negative 2), (6, 2). A coordinate plane has 7 points. The points are (negative 3, negative 6), (negative 2, negative 4), (negative 1, negative 2), (0, 0), (1, 2), (2, 4), (3, 6). A coordinate plane has 7 points. The points are (negative 5, 2), (negative 4, 1), (negative 3, 3), (negative 2, 5), (2, negative 2), (3, negative 5), (4, negative 6). A coordinate plane has 7 points. The points are (negative 4, negative 3), (negative 3, negative 5), (negative 2, 1), (0, 0), (2, 1), (3, negative 5), (4, negative 3).
A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position. The correct option is D.
What are coordinates?A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
For a function to be even, the graph of the function should be such that it should be symmetrical about the x-axis. Therefore, the points of the graph will be the opposite.
The 7 points of option D can be plotted as shown below, which is symmetrical about the X-axis. Hence, the correct option is D.
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9. Find all function values f(x) such that the distance
from f(x) to the value 8 is less than 0.03 units.
Express this using absolute value notation.
Answer: [tex]|f(x)-8| < 0.03[/tex]
In the first quadrant, you start at (6,7) and move 5units down
Answer:
(6,2)
Step-by-step explanation:
If you are looking for the coordinates then that is the correct answer.
Answer:
(6,2)
Step-by-step explanation:
Because the Y axis is vertical so you would move down and subtract 5 from the 7. Your X would stay the same. So the answer will be (6,2)
A recent forest fire near Littleville destroyed four-fifths of the trees in Bigtree National Forest. The
forest covers 4920 km2. There is now about 30 tons of salvageable wood per km2 in the burned area. The
part of the forest that was not destroyed by fire will not be open to the salvagers. Assuming the trees are
evenly distributed throughout the park, about how long will it take to remove all the salvageable wood at
a rate of 53 1/2 tons per day? Round your answer to the nearest whole number.
Step-by-step explanation:
the whole forest is 4920 km².
4/5 if that was destroyed with salvageable wood :
4/5 × 4920 = 3,936 km²
there is 30 tons of salvageable wood per km², so in total :
3936 × 30 = 118,080 tons.
the wood can be removed at av rate of 53.5 tons per day.
how many days until cleaned up ?
as many days as 53.5 fits into the total amount of 118,080 :
118080 / 53.5 = 2,207.102804... days.
so, it will take about 2,207 days to remove all the salvageable wood.
in the year 2000 February 26 was a Friday, what day was 8 April the same year??
Someone help me please
(a) The gradient is [tex]\frac{40}{5}=\boxed{8}[/tex], and represents the cost of buying one book in dollars.
(b) Draw the line through (0,0) and (20, 130).
(c) Since the gradient of the line representing company B is less (6.5 vs 8), it is better to buy books from company B because they are cheaper.
The population of a town was 25,00 people then 3,200 people moved away.What was the percent of decrease
Answer:
-12.8 %
Step-by-step explanation:
-3200 / 25 000 x 100% = - 12.8 %
Answer:
Your answer is -12.8%
Step-by-step explanation:
To calculate the percent decrease, we:
Find the difference between the new value and the original
Divide the number by the original
Multiply by 100 and the % symbol.
The population of the town originally had 25,000. 3,200 people moved away. This means that the new population is 21,800.
21,800-25,000=-3,200
-3,200/25,000=-0.128
-0.128(100)=-12.8%
The towns population decreased by 12.8%.
Hope its helpful!
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A cat gave birth to 11 calico kittens and 16 non-calico kittens. What is the ratio of calico kittens to non-calico kittens?
Answer:
11:16
Step-by-step explanation:
A box has dimensions of 2.5 cm by 3.0 cm by 4.0 cm. The volume of the box in milliliters and liters is:
Answer:
30000 milliliters
0.03 liters
Step-by-step explanation:
The volume of the box is 2.5 x 3.0 x 4.0 = 30 cc
There are 1000 ml in 1 cc so 30cc = 30 x 1000 = 30000 ml
There are 1000 cc in 1 liter so 30 cc = 30/1000 = 0.03 liters
The volume of the box is 30 mL or 0.03 L.
What is volume?Volume is a metric magnitude that is defined as the extension in three dimensions of a region of space. Volume is defined as the amount of space occupied by the object or figure in three-dimensional space. Volume is measured in cubic units.
The volume of this prism depends on its three dimensions and is calculated as the multiplication of these dimensions,
Volume= Dimension 1× Dimension 2× Dimension 3
The volume of the box = 2.5 x 3.0 x 4.0 = 30 cc
There are 1000 ml in 1 cc so 30cc = 30 x 1000 = 30000 ml
There are 1000 cc in 1 liter so 30 cc = 30/1000 = 0.03 liters
Hence, the volume of the box is 30 mL or 0.03 L.
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What is the additive inverse of the polynomial? –6x3 4x2 – 4x 6x3 4x2 4x 6x3 – 4x2 4x –6x3 – 4x2 – 4x 6x3 4x2 – 4x
The additive inverse of the polynomial is 6x³-4x²+4x.
Given The polynomial is -6x³+4x²-4x.
A polynomial is an expression that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. It consists of indeterminates and coefficients.
The number that results in zero when a number is added to it is said to be a number's additive inverse. The opposite, a shift in the sign, and negation are other names for this number.
The given polynomial is -6x³+4x²-4x.
To find the additive inverse of the polynomial, multiply the polynomial with minus sign, we get
-(-6x³+4x²-4x)=6x³-4x²+4x.
Hence, the additive inverse of the polynomial -6x³+4x²-4x is 6x³-4x²+4x.
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Paul needs to find 310% of 72. Which expression should he use?
Step-by-step explanation:
310/100 × 72
= 223.2
using fraction × total
hope you understand.
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a group of 31 friends gets together to play a sport. first person must be more be divided into teams . each team has to have exactly 3 players , and no one can be on more than one team .how many teams can make ?
The number of teams that can be made is 10.
How many teams can he make?
In order to determine the number of teams he can make, divide the number of friends by the total number of people that must be in the team. Division is the process of grouping a number into equal parts using another number.
31 / 3 = 10 remainder 1
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Type the equation for the graph below
Answer:
y = sin3x
Step-by-step explanation:
the equation is of the form y = sinbx
the period of the sine wave is
period = [tex]\frac{2\pi }{b}[/tex] ( b is the coefficient of x )
here period = [tex]\frac{\pi }{3}[/tex] × 2 = [tex]\frac{2\pi }{3}[/tex] , then
[tex]\frac{2\pi }{3}[/tex] = [tex]\frac{2\pi }{b}[/tex] ⇒ b = 3
y = sin3x ← equation of graph
The function g(x) is graphed.
On a coordinate plane, a curved line enters the plane at point (negative 2.3, 5), crosses the x- and y-axis at (0, 0), and leaves the plane at point (2.3, 5).
Which statements about the function are true? Choose three options.
The statements about the function that are true include:
g(0) = 0
g(1) = -1
g(-1) = 1
How to depict the function?From the information, the points include:
(x1, y1) = (-2, 2, 5).
(x2, y2) = (0, 0)
(x3, y3) = (2, 3, 5).
It should be noted that (x2, y2) implies that g(0) = 0. In this case, the statements about the function that are true include g(0) = 0, g(1) = -1, and g(-1) = 1. This is illustrated in ten graph.
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Answer: the answer is b, d, and e.
g(0) = 0
g(1) = 1
g(-1) = 1
Step-by-step explanation:
its timed help me please
AREA UNDER A CURVE - GEOMETRY
Recall that the area of a trapezoid is equal to the average of its bases times its height.
For the trapezoids shown here, each base corresponds to the value of [tex]y=2x^2[/tex] when [tex]x[/tex] is one of the endpoints of some interval, while the height is the length of that interval.
On the interval [-2, -1], the trapezoids has bases 2(-2)² = 8 and 2(-1)² = 2, and "height" -1 - (-2) = 1. Then its area is (8 + 2)/2 × 1 = 5.
On the interval [-1, 0], one of the bases is 2(-1)² = 2 and the other is 2(0)² = 0, and the height is again 0 - (-1) = 1. Then the trapezoid's/triangle's area is (2 + 0)/2 × 1 = 1.
Then the total area under the curve [tex]y=2x^2[/tex] on the interval [-2, 0] is approximately 5 + 1 = 6.
Compare this to the actual value of the area given by the definite integral,
[tex]\displaystyle \int_{-2}^0 2x^2 \, dx = \frac{16}3 \approx 5.333\ldots[/tex]
ii) Verify whether the point (1,5) lies on the locus a point which moves so that its distance from x-axis exceeds three times the distance from y-axis by 2.
The locus of the point represented by the equation y = 3•x + 2, indicates that the point (1, 5) is on the locus of the point.
How can the location of the point in relation to the point be found?The distance from the x-axis is the y-value
The distance from the y-axis is the x-value
Therefore;
The equation of the locus of the point is presented as follows;
y = 3•x + 2When x = 1, y = 3 × 1 + 2 = 5
When x = 1, y= 5
Therefore;
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Which of the following is the correct factorization of the polynomial below x3 - 12
a x+3 x-4
b x-3 x+4
c x+3 x^2-4x+4
d the polynomial is irreducible
Answer:this is all I could find
Step-by-step explanation:
a number b times 18 is greater than -10
The number b is b > -5/9
How to determine the number?The statement is given as:
a number b times 18 is greater than -10
This can be represented as:
b * 18 > -10
Divide both sides by 18
b > -10/18
Simplify
b > -5/9
Hence, the number b is b > -5/9
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Penny attended a four year state college. She took out a student loan to pay for her tuition and room & board for the four years she was attending the college. Her tuition fees were $6,970 per year, and the cost of her room and board was $11,320 per year. Now that she has graduated, she will have to start paying back her loan. Fortunately, Penny has a grace period of one year before she has to start paying back the loan. Her loan details are as follows: there is a fixed-rate interest of 4.5% and the interest compounds each month. During her one year grace period, interest will accrue on the loan, so that when she has to start paying the loan back she will owe more than what she owes now. Her goal is to be able to payoff the loan in 10 years.
What is the new loan amount after the one-year grace period (remember that interest will accrue on the loan during this initial 12-month period that she is not paying anything back on the loan)? This is the amount that she will be responsible for paying back. (Round your answer to the nearest whole dollar)
Given that she can pay back the loan in full after 10 years of payments, what is the total amount she will end up paying back (both principal and interest that has accrued over the 10 years)? And how much will her monthly payments on the loan be for those 10 years? (Round your answers to the nearest whole dollar)
The loan amount is given as $76521
We first have to calculate the total amount of tuition
6970 x 4 + 11320 x 4
= 73160
a. How to solve for the new loan amount[tex]73160 (1+\frac{\frac{4.5}{100} }{12} )^1^2[/tex]
= 73160 x (1 + 0.00375)¹²
= 76520.95
Hence the new loan amount after agrace period of 1 year = $76521
b. PV = $76521
i = [tex]\frac{4.5/100}{12}[/tex]
= 0.00375
t = 10 years
[tex]PMT[\frac{1-(1+0.00375)^-^1^2^0}{0.0375} ]= 76521[/tex]
pmt = 793. 05
The monthly payment is $793. 05.
In ten years the total payment is 793.05 x 10 x 12
= 95166
Difference = 95166 - 76521
= $18645
In ten years her ,monthly payment on the loan would be $18645.
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Side A B is parallel to Side D E in the map below. Triangle A B C. Side A B is 15 feet and side B C is 9 feet. Triangle C D E. Side C D is 6 feet and side D E is x feet. Which proportion solves for the distance between D and E? Start Fraction 9 Over 6 End Fraction = Start Fraction x Over 15 End Fraction Start Fraction 6 Over x End Fraction = Start Fraction 15 Over 9 End Fraction Start Fraction 9 Over 6 End Fraction = Start Fraction 15 Over x End Fraction Start Fraction 6 Over 15 End Fraction = Start Fraction 9 Over x End Fraction
The proportion that solves for the distance between D and E is x/15 = 6/9
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Triangle ABC and CDE are similar triangles, hence the ratio of their corresponding sides are in the same proportion.
Hence:
x/15 = 6/9
The proportion that solves for the distance between D and E is x/15 = 6/9
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What is the volume of the carton?
Answer:
c.) 6 1/2
Step-by-step explanation:
Volume = length × width × height
2 1/6 × 1 1/5 × 2 1/2
13/6 × 6/5 × 5/2
13/5 × 5/2
13/2 = 6 1/2
Two side lengths of a triangle are $11$ and $17$. What is the longest possible integer length of the third side of the triangle
The longest possible integer length of the third side of the triangle is 6 < x < 28
The sum of any two sides must be greater than the third side for a triangle to exist
let the third side be x
x + 11 > 17 and x + 17 > 11 and 11 + 17 > x
x > 6 and x > - 6 and x < 28
The longest possible integer length of the third side of the triangle is 6 < x < 28
The length of the 3 sides of a triangle needs to always be among (however no longer the same) the sum and the difference of the opposite two sides. As an example, take the instance of two, 6, and seven. and. consequently, the third side period should be extra than 4 and less than 8.
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Answer:
27
Step-by-step explanation:
Let the third side length be s. Then, by the Triangle Inequality, we know that s satisfies the inequalities
[tex]s + 11 & > 17, \\ s + 17 & > 11, \\ 11 + 17 & > s.[/tex]
[tex]\begin{align*} s + 11 & > 17, \\ s + 17 & > 11, \\ 11 + 17 & > s.\end{align*}[/tex]
The first two inequalities hold as long as s > 6 and the third holds if s < 28. The largest possible integer s that satisfies all of these is 27.
Fill in the blank. Someone who works 40 hours per week for 50 weeks per year, with two weeks off, would work around __________________hours per year.
Answer:
about 1920
step by step explanation:
40×50weeks=2000hours per year.
40×2weeks(the weeks off) = 80
2000-80= 1920hours per year