The maximum height reached after the 13th bοunce is 6.14 cm.
What is height οf bοunce?The height οf bοunce is the height tο which an οbject rebοunds after cοIIiding with a surface, such as a baII bοuncing οn the grοund οr a diver bοuncing οff a diving bοard. The height οf the bοunce depends οn severaI factοrs, incIuding the initiaI height οf the οbject, the surface it cοIIides with, the eIasticity οf the οbject and the surface, and the angIe οf incidence.
Tο sοIve this prοbIem, we need tο use the fοrmuIa fοr the height οf each bοunce:
[tex]h = (3/4)^{{n}} \times H[/tex]
where h is the height οf the nth bοunce, H is the initiaI height (in this case, 187.00 cm), and n is the number οf bοunces.
We want tο find the maximum height reached after the 13th bοunce, which means we need tο find the height οf the 13th bοunce and then muItipIy it by 3/4 tο get the maximum height.
Using the fοrmuIa abοve, we can find the height οf the 13th bοunce:
[tex]h = (3/4)^{{13}} \times 187.00[/tex]
h ≈ 8.18 cm
Nοw we can find the maximum height:
maximum height = (3/4) × h
maximum height = (3/4) ×8.18
maximum height ≈ 6.14 cm
Therefοre, the maximum height reached after the 13th bοunce is apprοximateIy 6.14 cm.
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A study found that the mean amount of time cars spent in drive-throughs of a certain fast-food restaurant was 137.5 seconds. Assuming drive-through times are normally distributed with a standard deviation of 27 seconds, complete parts below:
Determine the order of the following matrix:
[9 6 -4 8]
The order of the matrix is 2 x 2.
What is a matrix and what is meant by its order?
In the field of mathematics, matrices are rectangular arrangements of numerical values, symbols, or algebraic expressions, organized in rows and columns. Matrices are used in many areas of mathematics and science, as well as in engineering, physics, and computer graphics.
The term 'order' in the context of matrices refers to the dimensions of the matrix, which are determined by the number of rows and columns it contains. It is denoted by m x n, where m is the number of rows and n is the number of columns. To find the order of a matrix, we simply count the number of rows and columns. The order is usually written as a pair of numbers in the form m x n.
Determine the order of the given matrix:
In the given problem, we are asked to find the order of the matrix:
[tex]\begin{pmatrix}9 &6 \\-4 & 8\end{pmatrix}[/tex]
we count the number of rows and columns.
This matrix has 2 rows and 2 columns, so its order is 2 x 2.
Therefore, the order of the matrix is 2 x 2.
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Sally opens a savings account with $9,000 that earns 7% interest per year, not compounded How much interest, to the nearest penny, will Sally earn in 7 years?
Answer: Sally will earn $4,830.00 in interest over 7 years.
Step-by-step explanation:
If the interest is not compounded, then Sally will earn simple interest, which can be calculated using the formula:
I = P * r * t
where:
I = the interest earned
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
t = the time period, in years
In this case, we have:
P = $9,000 (the initial deposit)
r = 7% = 0.07 (the annual interest rate)
t = 7 (the number of years)
So, plugging in the values:
I = $9,000 * 0.07 * 7
I = $4,830.00
Therefore, Sally will earn $4,830.00 in interest over 7 years.
D) what is the domain and range of the graphed function?
E) Isabel’s competition, who sells books and no other products, charges a shipping fee of $1.99 per book plus a fixed fee of $3 for each order. Let x be the number of books purchased and f(x) be the price of shipping one order of books. Write a function that expresses f(x) and explain the value of f(x) for x = 0.
F) graph the function in part e
G) is your graph discrete or continuous? Explain.
The function that expresses f(x) is f(x) = 1.99x + 3, and its graph is continuous.
What is a Continuous Function?A continuous function is one that doesn't have any sudden or unexpected changes in value. It means that if we make small enough changes to its input, the output will also change by a small amount.
We can express the total cost of an order as a function of the number of books sold, x, using the formula:
f(x) = 1.99x + 3
This function takes the number of books sold, multiplies it by the cost per book ($1.99), and adds a fixed fee of $3.
For example, if we sold 3 books, we can use the function to find the total cost:
f(3) = 1.99(3) + 3 = 9.97
This means that selling 3 books would cost $9.97 in total.
The graph of this function is continuous, which means that as we move along the x-axis, the y-values change smoothly and without any sudden jumps.
The term "continuous" refers to a function that can take on any value between two given points and can be broken down into infinitely many fractions and decimals.
In contrast, a discrete function can only take on specific values, usually whole numbers or integers.
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PLEASE HELP! URGENT AND WORTH 50 POINTS!!!
Answer:
C) 2, 7, 6 can form a triangle.
Step-by-step explanation:
Triangle Inequality TheoremThe triangle inequality theorem states that the sum of any two sides of a triangle is greater than the length of the third side.
To determine which group of given side measures will form a triangle, sum each pair of sides and compare to the third side. If all three inequalities are true, the group will form a triangle.
Given side lengths: 9, 4, 3
⇒ 9 + 4 > 3
⇒ 9 + 3 > 4
⇒ 4 + 3 [tex]\ngtr[/tex] 9
Therefore, this group cannot form a triangle.
Given side lengths: 8, 1, 7
⇒ 8 + 1 > 7
⇒ 8 + 7 > 1
⇒ 1 + 7 [tex]\ngtr[/tex] 8
Therefore, this group cannot form a triangle.
Given side lengths: 2, 7, 6
⇒ 2 + 7 > 6
⇒ 2 + 6 > 7
⇒ 7 + 6 > 2
Therefore, this group can form a triangle.
Given side lengths: 12, 10, 22
⇒ 12 + 10 [tex]\ngtr[/tex] 22
⇒ 12 + 22 > 10
⇒ 10 + 22 > 12
Therefore, this group cannot form a triangle.
HELP
7th Grade Math Solving Equations
4. a-9=15
5. n-9=13
6. b-8=9
7. X-5=16
8. n-6=17
Answer:
4.
a-9=15
or. a=15+9
or. a=24
5.
n-9=13
or. n=13+9
or. n=22
6.
b-8=9
or. b=9+8
or. b=17
7
x-5=16
or. X=16+5
or X=21
8
n-6=17
or. n= 17+6
or. n=23
Step-by-step explanation:
minus sign changes into plus sign when changing sides
3 A truck delivered 48 cases of drinks to a gas station. Each case contained 24
drinks. The drinks were placed in rows in the cooler. There were 16 drinks in each
row. Which equation can be used to find r, the number of rows the drinks were
placed in?
€ 48 + 16 + 24 = r
18 x 21 +16=r
Answer: A 48 x 24/16 = r
Step-by-step explanation:
48 x 24 = the total number of drinks
Since there are 16 drinks in each row you want divide to get the number of rows in each drink.
Ex: 48 x 24= 1,152 (total drinks)
16 drinks in a row
1,152/16 = 72
72 rows
PLEASE HELP???!!!!!!!
The quadratic equation on the graph can be written as:
y = x² + 6x + 8
Which function is represented byy the graph?Remember that a quadratic equation whose vertex is (h,k) and the leading coefficient is a, can be written as:
y = a*(x - h)² + k
Here we can see that the vertex is at (-3, -1), replacing that we will get:
y = a*(x + 3)² - 1
Now we can also see that it passes through the point (-2, 0), replacing these values we will get:
0 = a*(-2 + 3)² - 1
0 = a - 1
1 = a
Then the quadratic is:
y = (x + 3)² - 1
Expanding that we get:
y = x² + 6x + 9 - 1
y = x² + 6x + 8
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OFFERING 70 POINTS AND BRAINLEST
Which number line shows the solution to the inequality? y minus 2 less-than negative 5 A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded. A number line going from negative 8 to positive 2. A closed circle is at negative 3. Everything to the left of the circle is shaded. A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the right of the circle is shaded. A number line going from negative 8 to positive 2. An open circle is at negative 7. Everything to the left of the circle is shaded.
The correct number line is: A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.
What is inequality?The mathematical expression of a connection between two values, stating that one value is larger than, less than, or not equal to another value, is called an inequality. Common symbols for inequality include (less than), > (greater than), (less than or equal to), and (greater than or equal to). For instance, the inequality 2x + 3 > 7 denotes that the value of 2x + 3 is larger than 7. Depending on the circumstance, inequalities can be resolved algebraically or visually. A collection of values that meet the connection implied by the inequality is the answer to an inequality.
Here, the inequality is y - 2 < -5, which can be rewritten as y < -3.
Hence, the correct option is: A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.
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Out of 144 children who have school dinners, 1/3 chose pasta, 1/4 chose jacket potatoes and the rest chose curry. How many chose curry?
Answer:
A fraction tells you how many parts of a whole there are. When we find a fraction of an amount, we are working out how much that 'part' is worth within the whole. You can see fractions of amounts all around us
Step-by-step explanation:
i may be wrong but I tried
Rewrite 1 + 2i in polar form.
A.√5
B.√5∠116.6°
C.[5√∠63.4°]
D.5√∠(63.4°)
1 + 2i in polar form is 5√2∠63.4°.
What is a polar form ?
In mathematics, the polar form is a way of representing complex numbers using their magnitude and angle. A complex number can be represented in the form r(cos θ + i sin θ), where r is the magnitude (or modulus) of the complex number, and θ is its argument (or phase angle). Alternatively, the polar form can be represented in terms of magnitude and angle as r ∠θ, where r is the magnitude and θ is the angle in radians. This form is also known as the exponential form of a complex number. The polar form is useful in calculations involving complex numbers, especially in multiplication and division, where it is often easier to work with the polar form rather than the rectangular form (a + bi).
D. 5√2∠63.4°
To convert a complex number from rectangular form to polar form, we use the following formulas:
r = √(a^2 + b^2)
θ = tan^-1 (b/a)
Where a and b are the real and imaginary parts of the complex number, respectively.
In this case, a = 1 and b = 2, so:
r = √(1^2 + 2^2) = √5
θ = tan^-1 (2/1) = 63.4°
Therefore, 1 + 2i in polar form is 5√2∠63.4°.
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i’m begging someone help please i’ll give brainlist
Answer:
a-no for the first triangle, because the total of the inner angles must be 180, the last angle must be 90.
b-yes- a triangle with angles 90, 50, and 40 is possible
c-yes. 65+45+70=180.
Step-by-step explanation:
Jane made $143 for 11 hours of work. At the same rate, how many hours would she have to work to make $169 ?
13
First, we divide to figure out how much Jane makes an hour
143 ÷ 11 = 13
Second, we multiply multiply by 13 until we get 169
13 × 13 = 169
So Jane will make 169 dollars in 13 hours
Answer:
13 Hours
Step-by-step explanation:
$143 ÷ 11hrs = $13/hr that Jane is paid, so to find how many hours she will need to work to make $169
$169 ÷ $13 = 13 hours
SOLVE THIS BUT I DON'T WANT ANSWER I WANT SOLVING AND ANSWER
50PTS
WILL MARK AS BRAINLIEST
50/1.428
Answer:
Alright
Step-by-step explanation:
50/1.428
Multiply the numerator by the denominator to get 50000/1428
Set equation up in long division format
Divide 50000 by 1428 to get 3
Divide 7160 by 1428 to get 5
Divide 200 by 1428 to get 0
Divide 2000 by 1428 to get 1
Divide 5720 by 1428 to get 4
Divide 80 by 1428 to get 0
Divide 800 by 1428 to get 0
35.014
Prove the Converse of the Pythagorean Theorem
The Converse of the Pythagorean Theorem is proved below.
What is Pythagoras Theorem ?
Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
The converse of the Pythagorean theorem states that if a triangle has sides of length a, b, and c, where c is the longest side, and a² + b² = c², then the triangle is a right triangle.
To prove the converse of the Pythagorean theorem, we can use the fact that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. That is, if a triangle has sides of length a, b, and c, where c is the longest side and c² = a² + b², then the triangle is a right triangle.
Proof:
Suppose we have a triangle ABC, with sides of length a, b, and c, where c is the longest side. Assume that a² + b² = c². We want to show that triangle ABC is a right triangle.
We will use the Law of Cosines to show that angle C is a right angle. The Law of Cosines states that for any triangle ABC with sides of length a, b, and c opposite angles A, B, and C, respectively:
c² = a² + b² - 2ab cos(C)
Substituting a² + b² = c² into this equation, we get:
c² = c² - 2ab cos(C)
2ab cos(C) = 0
cos(C) = 0
Since 0 is the cosine of 90 degrees, this implies that angle C is a right angle. Therefore, triangle ABC is a right triangle.
Thus, this completes the proof of the converse of the Pythagorean theorem.
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what are the x- and y- coordinates of point P on the directed line segment from A to B such that P is 2/3 the length of the line segment from A to B? x= [m/m+n](x2 -x1) +x1 y = [m/m+n](y2 - y1) +y1
The coordinates of the point P on the directed line segment from A to B such that P is 2/3 the length of the line segment from A to B are (-1, 2).
How to obtain the coordinates of point P?The coordinates of point P are obtained applying the proportions in the context of the problem.
P is 2/3 the length of the line segment from A to B, hence the equation is given as follows:
P - A = 2/3(B - A)
Then the x-coordinate of P is obtained considering the x-coordinates of A and B as follows:
x - 9 = 2/3(-6 - 9)
x - 9 = -10
x = -1.
The y-coordinate of P is obtained considering the y-coordinates of A and B as follows:
y + 8 = 2/3(7 + 8)
y + 8 = 10
y = 2.
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Write a real-world problem that could be represented by 5x+ 30 ≥ 90.
Answer: If Jamie is selling bags of carrots for $5 each and already has $30 what would he use to calculate how much money he made.
Investing $1,000 at a 5% annual interest rate for 6 years, compounded every two months,
yields $1,348.18. Without doing any calculations, rank these four possible changes in order
of the increase in the interest they would yield from the greatest increase to the least
increase:
• Increase the starting amount by $100.
• Increase the interest rate by 1%.
• Let the account increase for one more year.
• Compound the interest every month instead of every two months.
Once you have made your predictions, calculate the value of each option to see if your
ranking was correct.
Answer:
Step-by-step explanation:
Ranking:
Compound the interest every month instead of every two months.
Increase the interest rate by 1%.
Let the account increase for one more year.
Increase the starting amount by $100.
Calculations:
If the interest is compounded monthly instead of every two months, the final value would be $1,357.36, which is an increase of $9.18 compared to the original value.
If the interest rate is increased to 6%, the final value would be $1,411.58, which is an increase of $63.40 compared to the original value.
If the account increases for one more year at the same interest rate, the final value would be $1,435.09, which is an increase of $86.91 compared to the original value.
If the starting amount is increased by $100, the final value would be $1,421.61, which is an increase of $73.43 compared to the original value.
A cone has a radius of 6 centimeters and a height of 10 centimeters. What is the volume of the cone in cubic centimeters?
centimeters?
A 480π cm³
B 120π cm³
C 360π cm³
D 60π cm³
The volume of the cone in cubic centimeters in terms of π = 120π cm³. That is option B.
How to calculate the volume of a cone?To calculate the volume of a cone, the formula that is to be used;
Volume = 1/3 πr²h
Where;
Height = 10 centimetres
Radius = 6 centimetres
Volume = 1/3 × π × 6²× 10
= 360π/3
= 120π cm³
Therefore the volume of the cone whose dimensions are given = 120π cm³.
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A charity organization has to sell a few tickets to their fundraiser just to cover necessary production costs. After selling 10 tickets they were still at a net loss of $800 (due to the production costs). They sold each tickets for $70.
the organization needs to sell at least 22 tickets to break even.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
Let C be the total production cost and n be the number of tickets sold.
From the problem, we know that the organization had a net loss of $800 after selling 10 tickets, so we have:
10(70) - C = -800
Simplifying, we get:
C = 1500
This means that the total production cost was $1500.
The revenue from selling n tickets at $70 per ticket is given by:
R = 70n
Substituting the values of R and C, we get:
70n = 1500
Solving for n, we get:
n = 1500/70 = 21.43
Since we can't sell a fraction of a ticket, we need to round up to the nearest whole number.
Therefore, the organization needs to sell at least 22 tickets to break even.
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Find the equation of the line containing the point
P(−2, 3)
and perpendicular to the graph of
3x + 9y = −2.
Answer:
Step-by-step explanation:
y = 3x + 9
(HELP PLEASE)A school track is pictured
below. The straightaway on
each side measures/100 yards.
The curves are semicircles with
diameter 36 yards. What is the
distance, in yards, around the
entire track? Use the button
on your calculator and express
your answer to the nearest
hundredth.
Around [tex]312.57[/tex] yards are required to complete a full lap of the circuit.
What's the easiest way to define distance?The entire movement of an item, independent of direction, is called distance. Regardless of an object's beginning or finishing position, distance may be defined as the amount of ground it has travelled.
Describe a distance example.As a result, distance is indeed a scalar quantity. The whole path an item has taken can be used to define the distance from it. Think about it this way. If a car drives 5 km east, then turns to head north for 8 km, the final distance driven by the automobile must be 13 km.
The circumference of a semicircle with diameter d is [tex](pi/2)d[/tex]. Therefore, the length of each semicircular section is [tex](pi/2) * 36 = 18pi[/tex].
The total distance around the track is the sum of the lengths of the two straight sections and the two semicircular sections.
Distance around track [tex]= 2(100 yards) + 2(18pi yards)[/tex]
[tex]= 200 yards + 36pi yards[/tex]
[tex]= 312.57 yards[/tex] (rounded to two decimal places)
Therefore, the distance around the entire track is approximately [tex]312.57[/tex]yards.
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Wally Martin purchased an office chair for $167.87. He received a $19.95 rebate from the manufacturer and a $8.95 rebate from the store. What is the final price?
a fourth grade class is hosting a pancake breakfast fundraiser adult tickets are $10 each and children tickets are$6 each the class sells a total of 105 the total amount raised is 870how many adult tickets and how many children tickets were sold
60 adult tickets and 45 children tickets were sold.
How to solve this problemLet's use algebra to solve the problem:
Let x be the number of adult tickets sold.
Let y be the number of children tickets sold.
From the problem, we know that:
x + y = 105 (total tickets sold)
10x + 6y = 870 (total amount raised)
We can solve this system of equations by using elimination:
Multiply the first equation by 6: 6x + 6y = 630
Subtract the second equation from the first: 4x = 240
Solve for x: x = 60
Now we can use x to find y:
x + y = 105
60 + y = 105
y = 45
Therefore, 60 adult tickets and 45 children tickets were sold.
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Complete the following table:
Note: Do not round intermediate calculations. Round your final answers to the nearest cent.
Chain discount is a type of discount offered by a seller to a buyer for purchasing a certain amount of goods or services in a series of transactions. The discount is applied incrementally as the buyer meets specific purchasing thresholds.
What is the chain discount?Chain discounts are often used to encourage larger purchases and build customer loyalty. They can be beneficial for both the buyer and the seller, as the buyer receives a discount and the seller increases their sales volume.
Item: Trotter treadmill
List price: $ [tex]3,000[/tex]
Chain discount: [tex]9/4[/tex]
To calculate the net price, we first need to determine the amount of the chain discount.
Chain discount = List price x Chain discount rate
Chain discount = $ [tex]3,000 \times 9/4[/tex]
Chain discount = $ [tex]6,750[/tex]
The net price is the list price minus the chain discount:
Net price = List price - Chain discount
Net price = $ [tex]3,000[/tex] - $6,750
Net price = -$3,750
Therefore, The Net price is = -$3,750
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Of the last 20 trains to arrive at Danville Station, 15 were on time. What is the experimental probability that the next train to arrive will be on time?
Write your answer as a fraction or whole number.
P(on time)=
The experimental probability that the next train to arrive at Danville Station will be on time is 3/4 or 0.75.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
The experimental probability of the next train to arrive at Danville Station being on time is given by the number of on-time trains divided by the total number of trains that arrived -
experimental probability = number of on-time trains / total number of trains
From the information given, we know that out of the last 20 trains to arrive, 15 were on time. Therefore -
number of on-time trains = 15
total number of trains = 20
Substituting these values into the equation, we get -
experimental probability = 15 / 20
Simplifying the fraction, we get -
experimental probability = 3/4
Therefore, the experimental probability value is obtained to be 3/4 or 0.75.
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dose 2+2=4?.............................
Answer:
[tex]yeah \: 2 + 2 = 4[/tex]
Need help with the questions
1. Calculating the output when using -6 as the input, we have:
Rule 1: subtract 7 = -13
Rule 2: square the input = 36.
Rule 3: divide by 3 = 12
Rule 4: divide the input into 3 = -2
Rule 5: write π = -2π
Rule 6: volume of a cube = -216cm³
What is function rule?A function rule is a mathematical expression that describes how to calculate the output value of a function based on its input value. It can be thought of as a set of instructions that tell you what to do with the input value to get the output value.
2. a. True. Speed is the ratio of distance traveled to the time taken to travel that distance. In this case, the distance is fixed at 100 meters, so speed is solely dependent on time. For each value of time, there is only one corresponding value of speed, making it a function.
b. False. While time and distance are related in the formula for speed, time is not a function of distance in this case. Each student's time is independent of the distance they cover, and the same distance is covered by all students (100 meters). Therefore, for any given distance, there are multiple possible values of time, making it not a function.
c. False. The number of students racing is not related to their speed. Each student's speed depends solely on their individual time, which is not affected by the number of other students racing.
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p=6t. what is the value of p when t= 14
Answer:
p=84
Step-by-step explanation:
p=6×14
p=84
answer: p=84
complete part A and B
The corresponding point on the graph is (9, 21). This point is within the normal respiratory rate region, which is defined by the system of linear inequalities. Therefore, model breakdown has not occurred.
The given problem involves the normal respiratory rates of children aged 3 to 15 years. The respiratory rate, measured in breaths per minute, is represented as a function of age using a system of linear inequalities. The graph depicts a normal respiratory rate region that models the respiratory rate ranges shown in the table. The problem requires us to identify a specific point on the graph that corresponds to a respiratory rate of 21 breaths per minute for a 9-year-old child. The ordered pair (9, 21) represents the corresponding point on the graph.
Further, we need to determine if this point lies within the normal respiratory rate region or if model breakdown has occurred. The system of linear inequalities defines the normal respiratory rate region, and we can determine if the point (9, 21) satisfies these inequalities. In this case, the point (9, 21) lies within the normal respiratory rate region and satisfies the system of linear inequalities. Therefore, model breakdown has not occurred, and the given model is an appropriate approximation of the normal respiratory rate region for children aged 3 to 15.
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