After solving, the height in feet of the sixth bounce is 1.892 feet.
In the given question, we ave to find the height, in feet, of the sixth bounce.
From the given question,
Height on the first bounce = 6.7
Subsequent bounce reaches a height of the previous bounce = 81%
Suppose the height is h.
So according to the question:
h(6) = height on the first bounce*(subsequent bounce reaches a height of the previous bounce)^6
h(6) = 6.7*(81%)^6
h(6) = 1.892 feet
So the height of sixth bounce is 1.892 feet.
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Nelson wants to buy gifts for Thanksgiving. Hs bought three roses for $1.99 each, three bows for $0.99 each, and three vases for $7.99 each. Write an equation for his total cost for the gifts. Someone help please
The equation can be written using the arithmetic operation and the cost is
$32.91.
What are arithmetic operations?The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.
The cost for each roses, bows and vases are given as $1.99, $0.99 and $7.99 respectively.
Then, the equation for the total cost is as below,
⇒ 3 × 1.99 + 3 × 0.99 + 3 × 7.99 = 32.91
Hence, the equation for the cost is given in the answer part and the cost is $32.91.
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12. Sarah uses long division to convert
a rational number 2 to a decimal.
P
Which of the following statements
cannot be true?
A. The decimal form of P
q
terminates with a zero in the
tenths place.
B. The decimal form of P
eventually repeats.
C. The decimal form of never
terminates or repeats.
D. The decimal form ofis 0.
Select the correct answer.A wooden board that is 108 inches long is cut into two equal parts. What is the length of each part in feet
4.5 is the length of each part in feet. This can be solved by using the concept of feet.
What is feet?foot, plural feet, any of a wide range of ancient, medieval, and modern linear measurements (often 25 to 34 cm) based on the length of the human foot and used only in English-speaking nations, where it typically consists of 12 inches or one-third yard.
The foot measured [tex]11^{\frac{1}{42}[/tex] inches in antiquity. The typical man's foot measures 12 inches in length nowadays.
Given that:
The length of the wooden board is given as = 108 inches.
As it is cut in 2 equal parts, it becomes: 108/2 = 54 inches in each
We have to calculate the length of each part in feet, so divide 54 by 12.
As we know,
12 inches = 1 feet
Thus, 54 inches = 54/12 feet = 4.5 feet
So, the length of each part is 4.5 feet.
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How do you find the missing side of a right triangle without a calculator?
The missing side of a right triangle without using a calculator can be found by using the Pythagoras theorem .
What is Pythagoras Theorem ?
The Pythagoras Theorem states that the square of the hypotnuse (longest side) is equal to the sum of the square of the perpendicular and base .
that means : [tex]Hypotnuse^{2} = Perpendicular^{2} + Base^{2}[/tex] ;
let the missing side of the right triangle be the hypotnuse ;
So , missing side can written as : [tex]Hypotnuse = \sqrt{Perpendicular^{2} + Base^{2}}[/tex] .
For Example : Let the right triangle has sides lengths as perpendicular = 6 and hypotnuse = 10
The length of side "base" is unknown.
So , to find length of side b, we put the known values into theorem:
[tex]10^{2} = 6^{2} + Base^{2}[/tex] ;
[tex]base^{2} = 100 - 36[/tex] ;
So , the missing side "base" = 8 ;
Therefore , the missing side without using calculator can be found by the Pythagoras Theorem .
The given question is incomplete , the complete question is
How do you find the missing side of a right triangle without a calculator when the other two sides are given ?
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What is a parent function example?
An example of a parent function is [tex]f(x) = x^{2}[/tex], which is the parent function to any quadratic equation.
The most basic form of a function is a parent function. Its essential shape is not changed in any manner. In mathematics, some graphs are frequently seen. Because of this, the graphs of quadratic functions, square roots, absolute values, cubics, and cube roots are among the original, widespread functions that are referred to as parent graphs.
For instance, you should still be able to identify the parabola that has undergone various transformations when you view a u-shaped graph that has been inverted and stretched vertically.
Here are a few examples to understand this concept further.
For a quadratic equation, the parent graph is [tex]f(x) = x^{2}[/tex], which is a parabola.For a cubic equation, the parent graph is [tex]f(x) = x^{3}[/tex].Let us take [tex]f(x) = x^{2}[/tex], which is the parent equation of any quadratic equation. The graph of this parent function is a parabola, which is shown below.
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Exponential from Two Points (Level 1)
Write an exponential function in the form y = ab* that goes through points (0, 13)
and (2, 325).
a = 13. b^0 = 1, y=a(1), 13 = a 325 = 13(b)^2 b^2 = 325/13 = 25
b = sqr25 = 5 y=13(5)^x is the exponential equation going through the two given points
What is Exponential function?An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.The graphs of all exponential functions have these characteristics. They all contain the point (0, 1), because a0 = 1. The x-axis is always an asymptote. They are decreasing if 0 < a < 1, and increasing if 1 < a. If your function can be written in the form y = a b x , where and are constants, a ≠ 0 , b > 0 , and b ≠ 1 , then it must be exponential. In quadratic equations, your functions were always to the 2nd power. In exponential functions, the exponent is a variableTo learn more about Exponential function refers to:
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2. Ask one of your teachers how tall they are in feet/in. Write it here:
Now, covert their height into centimeters (cm).
feet
in.
1 ft = 12 in
1 in = 2.54 cm
My teacher:
- 5'3
- 5.25 ft
- 63 in
- 160 cm
at the same time that a 60 foot tall buidling casts s shadow hat is 21.5 feet long a nearby tree casts a shadow that is 18 feet long, Which measure is closest to the height of the tree
The height of the tree is closest to 40 feet.
We can use the proportion of similar triangles to determine the height of the tree.
Let h be the height of the tree and s be the length of the shadow cast by the tree.
We know that the height of the building is 60 feet and the length of its shadow is 21.5 feet. So:
(h/s) = (60/21.5)
We also know that the length of the shadow cast by the tree is 18 feet.
So we can substitute that into the proportion and solve for h:
h = (60/21.5) * 18
h = (60*18)/21.5
h ≈ 40
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The sequence one-sixth, negative two-sevenths, three eighths, negative four ninths, and so on is given.
Part A: Assuming the pattern continues, list the next four terms in the sequence. Show all necessary math work. (4 points)
Part B: Write the explicit equation for f (n) to represent the sequence. Show all necessary math work. (4 points)
Part C: Is the sign of f (53) positive or negative? Justify your reasoning mathematically without determining the value of f (53). (2 points)
A. 5/10, -6/11, 7/12, -8/13
B. f(n) = n/(n+5)
C. Positive
What is a sequence?A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members, just like a set does. The length of the sequence is determined by the number of items.
Here, we have
A. From inspection of the sequence, the pattern is:
Add 1 to the numerator of the previous term.
Add 1 to the denominator of the previous term.
Make every other term negative.
Hence, assuming the pattern continues, the next four terms in the sequence will be:
5/10, -6/11, 7/12, -8/13
B. An explicit formula for an arithmetic sequence allows you to find the [tex]n^{th}[/tex] term of the sequence.
f(1) = 1/6
f(2) = -2/7
We can see that the numerator is the position of the term (n) in the sequence. So when n = 1 the numerator is 1, when n = 2 the numerator is 2, etc.
The denominator is 5 more than the position of the term in the sequence. So when n = 1 the denominator is 1 + 5 = 6, and when n = 2 the denominator is 2 + 5 = 7.
We observe that if the numerator (the value of n) is odd then the term is positive, and if the numerator (the value of n) is even then the term is negative.
Hence, the rule for the nth term is:
f(n) = n/(n+5)
If n is odd then f(n) is positive.
If n is even then f(n) is negative.
C. 53 is an odd number.
As the function f(n) is positive when n is odd, the sign of f(53) is positive.
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Speedometer readings for a motorcycle at 12-second intervals are given in the table.
t (s) 0 12 24 36 48 60
v (ft/s) 30 28 25 21 25 27
(a) Estimate the distance traveled by the motorcycle during this time period using the velocities at the beginning of the time intervals.
ft
(b) Give another estimate using the velocities at the end of the time periods.
ft
(c) Are your estimates in parts (a) and (b) upper and lower estimates? Explain.
O (b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t.
O (a) and (b) are neither lower nor upper estimates since v is neither an increasing nor decreasing function of t.
O (a) is a lower estimate and (b) is an upper estimate since v is an increasing function of t.
(a) The distance traveled by motorcycle is 1548 ft.
(b) The distance traveled by motorcycle is 1512 ft.
(c) (b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t.
What is velocity?
The primary indicator of an object's position and speed is its velocity. It is the distance that an object travels in one unit of time. The displacement of the item in one unit of time is the definition of velocity.
Given table is:
t (s) 0 12 24 36 48 60
v (ft/s) 30 28 25 21 25 27
The distance traveled by motorcycle during this time period using the velocities at the beginning of the time intervals is:
12(30 + 28 + 25 + 21 + 25)
=12 × 129
= 1548 ft
The distance traveled by motorcycle during this time period using the velocities at the end of the time intervals is:
12(28 + 25 + 21 + 25 + 27)
=12 × 126
= 1512 ft
The distance traveled by motorcycle at the end of the time intervals is greater than the distance traveled by motorcycle at the beginning of the time intervals.
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Graph the image of square KLMN after a translation 6 units left and 4 units up.
The coordinates of the image of the square KLMN are:
K = (0, -1)
L = (2, -1)
M = (2, 1)
N = (0, 1)
The graph of the image is given below.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
The coordinates of the square KLMN are:
K = (6, -5)
L = (8, -5)
M = (8, -3)
N = (6, -3)
Now,
Translation of 6 units left and 4 units up.
This means,
K = (6 - 6, -5 + 4) = (0, -1)
L = (8 - 6, -5 + 4) = (2, -1)
M = (8 - 6, -3 + 4) = (2, 1)
N = (6 - 6, -3 + 4) = (0, 1)
Thus,
The image of the square KLMN will be on the following coordinates.
K = (0, -1)
L = (2, -1)
M = (2, 1)
N = (0, 1)
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Name three pairs of parallel segments below.
Answer:
hypotenuse,adjacent and opposite
h(a) = a^2 + 4 when a = -3
Answer:
[tex] \sf \: h(-3) = 13[/tex]
Step-by-step explanation:
Given information,
→ h(a) = a² + 4
The value of h(a) when a is -3,
→ h(a) = a² + 4
→ h(-3) = (-3)² + 4
→ h(-3) = 9 + 4
→ [ h(-3) = 13 ]
Hence, required answer is 13.
How to find coordinates of the center of dilation?
We label points A=(x1,y1)=(1,1) A = (x1, y1) = (1,1) and A′=(x2,y2)=(3,3) A ′ = (x 2, y 2) = (3,3) to identify the centre of dilation. The centre of dilation's coordinates are then determined using the formula. (xo,yo) ( xo,yo) ( xo,yo )
What is the location of a dilation's centre?When the scale factor exceeds 1, the dilation becomes an enlargement. If it falls within the range of 0 and 1, the dilation is a contraction. The point from which the image is dilated is known as the centre of dilation (or point of dilation).
The centre point formula is what?The equation for the circle must be converted into standard form, (x h), in order to be able to determine the centre and radius.[tex](x-h)^2+(y-k)^2=r^2[/tex], where r is the radius and h and k are the coordinates for the centre.
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If a coin is tossed 4 times, the odds of it coming up either heads every time or tails every time are 1:7. What is the probability the coin comes up all heads or all tails after 4 tosses?
The probability the coin comes up all heads or all tails after 4 tosses is 1/8
How to determine the probability from the odds?The value of the odds is given as
Odds = 1 : 7
Represent the odds as a fraction
So, we have the following representation
Odds = 1/7
To convert the odds to probability, we make use of the following equation
Probability = Odds/(1 + Odds)
Substitute the known values in the above equation, so, we have the following representation
Probability = (1/7)/(1/7 + 1)
Evaluate the sum
Probability = (1/7)/(8/7)
Evaluate the quotient
Probability = 1/8
Hence, the probability is 1/8
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What is the measure or a
The measures of the angles of the parallelogram are
The measure of ∠A = 72°
The measure of ∠B = 108°
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
Let the parallelogram be represented as ABCD
Now , the measure of ∠A = ( 5y - 3 )°
The measure of ∠C = ( 3y + 27 )°
For a parallelogram , opposite angles are congruent
So , measure of ∠A = measure of ∠C
Substituting the values in the equation , we get
( 5y - 3 )° = ( 3y + 27 )°
On simplifying the equation , we get
( 5y - 3 ) = ( 3y + 27 )
Subtracting 3y on both sides of the equation , we get
2y - 3 = 27
Adding 3 on both sides of the equation , we get
2y = 30
Divide by 2 on both sides of the equation , we get
y = 15
So , the measure of ∠A = ( 5y - 3 )°
The measure of ∠A = ( 5 ( 15 ) - 3 ) )°
The measure of ∠A = ( 75 - 3 )°
The measure of ∠A = 72°
Now , for a parallelogram , same-side interior angles (consecutive angles) are supplementary
So , the measure of ∠A + the measure of ∠B = 180°
Substituting the values in the equation , we get
72° + the measure of ∠B = 180°
Subtracting 72° on both sides of the equation , we get
The measure of ∠B = 108°
Hence , the measures of angles of the parallelogram are 72° and 108° respectively
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A woman looking out from the window of a height 30m, observed that the angle of depression of the top of a flagpole was 44°. if the foot of the pole is 25m from the foot of the building and on the same horizontal ground, find, correct to the nearest whole number, the angle of depression of the foot of the pole from the woman
Answer:
here is your answer = 56.7m
Is there a triangle whose sides have length 10.2 cm 5.8 cm and 4.5 cm justify the answer?
Yes, a triangle whose sides have lengths 10.2 cm, 5.8 cm and 4.5 cm is possible.
As we know if these sides form a triangle, then
the sum of two sides > the third side
Now, the sum of 10.2 cm and 5.8 cm = 16 cm > 4.5 cm
The sum of 5.8 cm and 4.5 cm = 10.3 cm > 10.2 cm
The sum of 10.2 cm and 4.5 cm = 14.7 cm > 5.8 cm
Here the sum of the two sides is greater than the third side in all three cases.
Therefore a triangle whose sides are 10.2 cm, 5.8 cm and 4.5 cm is possible.
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What is value of tan 90?
Answer:
Step-by-step explanation: infinity or undefined.
-2/3 + y = -2 1/6
....................
Answer:
y = -3/2 or -1.5
Step-by-step explanation:
-2/3 + y = -2 1/6
-2 1/6 = -13/6
So, our equation is
-2/3 + y = -13/6
Add 2/3 to both sides
y = -3/2
So, the answer is
y = -3/2 or -1.5
Answer:
Y= -3/2
in decimal form it is -1.5
in mixed number form it is -1 1/2
Step-by-step explanation:
A baker places 4 muffins in each box. Which is the total number of muffins in 8 boxes?
Answer: 32
Step-by-step explanation: 4 x 8 = 32 . I am concerned how simple this is ;-;
Answer:
32
Step-by-step explanation:
each boxes have 4 muffins
so,in 8 boxes
by question
8×4=32
2 of 10
x
Colin buys a car for £27900.
It depreciates at a rate of 3% per year.
How much will it be worth in 2 years?
Give your answer to the nearest penny where appropriate.
Answer:
Below
Step-by-step explanation:
3% loss means 97% (.97 in decimal ) remains
after 2 years :
27 900 ( .97)^2 = £ 26251 .11
please help!!! write the equation of the line in fully simplified slope intercept form
Answer:
y=[tex]-\frac{1}{4}[/tex] x -6
Step-by-step explanation:
y=mx+b is the slope-intercept formula, m representing the slope and the b representing the y-intercept. Pick two points shown in the graph,
such as (4,-7) and (8,-8) and use what is called rise over run. This means you count the distance between these two points by subtracting the y values (rise) and placing the difference in a fraction over the difference between the x values (run). This is where you get the fraction [tex]\frac{1}{4}[/tex]. Because the slope is going down from left to right, it means that the slope is negative, hence the [tex]-\frac{1}{4}[/tex]. The y-intercept is the point where the line intercepts the y-axis, which in this case is -6, so if you replace the representative letters with the corresponding numbers in the slope-intercept formula, the answer is y=[tex]-\frac{1}{4}[/tex] x -6.
What is line segment class 7?
In geometry, a line segment is bordered by two distinct points on a line. Or we can say a line segment is a portion of the line that connects two points.
The length of the line segment does not differ and the distance between them does not change. The units in which a line can be estimated are centimetres, millimetres, meters, inches, or feet.
A closed-line segment has both endpoints, whereas an open-line segment has two endpoints. A line segment that has only one endpoint is known as a half-open line segment.
A line segment with two endpoints P and Q and is denoted by the bar symbol (—).
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If you could take one sample from the mystery bag in order to make a prediction, would you rather draw a sample of 10 marbles or a sample of 20 marbles. Explain your choice by referring to the representations of the two distributions.
I would choose to draw a sample of 20 marbles in order to make a more accurate prediction.
How to illustrate the sample?In general, it is generally better to draw a larger sample if you are trying to make a prediction. This is because a larger sample will provide more information and will therefore lead to a more accurate prediction.
For example, imagine that you are trying to predict the proportion of red marbles in a bag based on the samples that you draw. If you draw a sample of 10 marbles, there is a good chance that the proportion of red marbles in your sample will be different from the true proportion of red marbles in the bag.
However, if you draw a sample of 20 marbles, the proportion of red marbles in your sample will be more likely to be closer to the true proportion of red marbles in the bag.
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where h is the height of the car in metres, t is the time that has elapsed in minutes and a, b and c are constants.
Find values for a, b and c that will effectively model your motion on the big wheel.
The graph of the variation of the height of a person on the Ferris wheel with time, created with MS Excel is attached
The values of the constants in the sinusoidal function, h = a + b·(c·t) are;
a = 30
b = -20
c = π/1.5
What is a sinusoidal function?A sinusoidal function is a periodic, oscillatory function, that is based on the sine (or cosine) trigonometric ratios.
The diameter of the Ferris wheel = 40 m
The location of the axle above the ground = 30 m
The time it takes to make a complete a rotation = 3 minutes
The formula for modelling the elevation or height, h, of a person above the ground is presented as follows;
h = a + b·cos(c·t)
The details in the question is that at time, t = 0, the person enters the wheel at the lowest point.
Therefore;
At t = 0, h = 30 - 40/2 = 10
h = 10 = a + b·cos(c × 0) = a + b·cos(0) = a + b
a + b = 10
Whereby the height of the axis of the wheel above the ground is a constant, for visibility in the analysis, let the constant a represent the constant height of the axis from the ground, we get;
a = 30
a + b = 10, therefore;
b = 10 - a
b = 10 - 30 = -20
b = -20
At t = 1.5 minutes, the location on the wheel the person enters is at the maximum height on the wheel = 30 + 20 = 50
50 = a + b·cos(1.5·c)
50 = 30 - 20 × cos(1.5·c)
20 × cos(1.5·c) = 30 - 50 = -20
cos(1.5·c) = -1
cos(π) = -1
Therefore; 1.5·c = π
c = π/1.5
The equation is therefore;
h = 30 - 20·cos((π/1.5)·t)
a = 30, b = -20, c = π/1.5
Please find attached a graph showing the variation of height with time of the motion on a Ferris created with MS Excel
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What is represented by P ∨ Q?
The statement [tex]P\land Q[/tex] in Tautology is represented as P and Q , and the symbol "[tex]\land[/tex]" is called as AND operator .
What is Tautology ?
Tautology can be defined as a compound statement which always results in Truth value. It does not matter what individual part consists of, the result in tautology is always true.
AND Operator : The AND is represented by the symbol "[tex]\land[/tex]". When the 2 simple statements are used in forming the compound statement by using AND operator , then it is called as a conjunction of two statements .
The AND operator returns TRUE value only when both the statements P and Q are TRUE , if any one of the statement is FALSE , then it returns FALSE value .
The given question is incomplete , the complete question is
What is represented by [tex]P\land Q[/tex] in Tautology ?
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mrs blackwell put 4 2/3 grams on the scale during a lab in science class. then, she added 2 5/6 grams to the scale. how many grams are on the scale in all
There are [tex]7\frac{1}2}[/tex] grams on the scale in all once she added 2 5/6 grams to the scale.
What is the International System of Units (SI)?The International System of Units (SI) is the modern form of the metric system and is the most widely used measurement system in the world. It consists of seven basic units of seven basic quantities.
Length is the meter, mass is the kilogram, time is the second, electric current is the ampere, temperature is the kelvin, amount of matter is the mole, and luminosity is the cand. SI also includes derived units such as Newton (force) and Pascal (pressure), which are combinations of base units. SI is the standard measurement system in most countries around the world and is used in scientific, engineering, and commercial applications.
Given,
initial weight = [tex]4\frac{2}{3} = \frac{14}{3}[/tex]
Final weight = [tex]2\frac{5}{6} = \frac{17}{6}[/tex]
Final weight = [tex]\frac{14}{3} + \frac{17}{6} = \frac{45}{6} = \frac{15}{2} = 7\frac{1}{2}[/tex]
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For what value of a the system of linear equations Ax 3y a 3 12x ay A has no solutions?
The system of linear equations Ax + 3y = a, 3x + ay = A has no solutions for any value of a.
To determine if the system of linear equations Ax + 3y = a, 3x + ay = A has no solutions for any value of a, we can use the elimination method.
We want to eliminate one of the variables, so let's start by multiplying the first equation by 3 and the second equation by -1.
This gives us:
3Ax + 9y = 3a, -3x - ay = -A.
Now we add the equations together to get:
2Ax + 8y = 3a - A.
Now we can see that the equation is not solvable as there is no value of a that will make the equation true. Therefore, the system of linear equations Ax + 3y = a, 3x + ay = A has no solutions for any value of a.
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What is the difference between a reasonable and unreasonable time algorithm?
Reasonable algorithms expand at polynomial rates or less quickly. Unreasonable algorithms expand exponentially. Even for relatively small problem sizes, the time to solve an unreasonable algorithm increases very quickly.
What is Unreasonable time algorithms?When the algorithm takes an excessively long time, we say that the number of steps is an exponential function of the size of the input (or some other function that is larger than any polynomial). Simply increasing the input size (n) by 1 doubles the number of steps for an algorithm that runs in 2n time.
Depending on the polynomial, polynomial time can be further decomposed. Algorithms with a runtime of approximately n2 operate in quadratic time. (If the input size is doubled, the number of steps is quadrupled.) In practise, polynomial time algorithms that take longer than cubic (n³) time are uncommon.
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