Answers
Step-by-step explanation:
3.
remember the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c are the sides. A, B, C are the corresponding opposite angles.
and again, the sum of all angles in a triangle is always 180°.
so, the angle opposite of W = 180 - 90 - 60 = 30°.
and we get
6×sqrt(3)/sin(60) = W/sin(30) = W / 1/2 = 2W
W = 6/2 × sqrt(3)/sin(60) = 3×sqrt(3)/sin(60) =
= 3×sqrt(3) / sqrt(3)/2 = 6
X we get via Pythagoras
X² = (6×sqrt(3))² + W² = 36×3 + 6² = 108+36 = 144
X = sqrt(144) = 12
in the lower triangle the angle opposite of X = 180 - 90 - 45 = 45°
so, it is an isoceles triangle (both legs are equal).
therefore,
Y = X = 12
Z² = 12² + 12² = 144 + 144 = 288
Z = sqrt(288) = sqrt(16×18) = sqrt(16×9×2) =
= 4×3×sqrt(2) = 12×sqrt(2)
4.
x² + 2x - 1 = 2
x² + 2x + 1 = 4
(x + 1)² = 4
x + 1 = ±2
x = ±2 - 1
x1 = 2 - 1 = 1
x2 = -2 - 1 = -3
5.
in a rhombus all 4 sides are equal, and the opposite sides are parallel.
a.
so, PQ = QR
3x + 7 = -x + 17
4x = 10
x = 10/4 = 2.5
b.
the diagonals are perpendicular to each other (90°), intersect each other at their midpoints and cut their corner angles in half.
the angle RSM = angle PSM = 40°.
c.
the sum of all angles in any quadrilateral is always 360°.
in a rhombus the opposing angles are equal.
so,
the angle SPQ = angle SRQ
360 = SPQ + SRQ + PSR + PQR = 2×SPQ + 2×40 + 2×40 =
= 2×SPQ + 160
2×SPQ = 360 - 160 = 200
the angle SPQ = 200/2 = 100°.
Related Questions
A parallelogram has an area of 14.4 square feet. The base is 4.5 centimeters. What is the height?
Answers
We know that the area of a parallelogram is given by the formula A = bh, where A is the area, b is the base, and h is the height. In this case, we are given the area and the base, and we need to find the height.
We can rearrange the formula to solve for h: h = A/b
Plugging in the given values, we get:
h = 14.4 sq ft / 4.5 cm
Note that the units are different for area and base, so we need to convert them to the same units. Let's convert the base to feet, since the area is given in square feet:
h = 14.4 sq ft / (4.5 cm / 30.48 cm/ft) [converting cm to ft]
h = 14.4 sq ft / 0.148 ft
h ≈ 97.3 cm
Therefore, the height of the parallelogram is approximately 97.3 cm.
Please help me i need the answers pleasee
Starting with the graph of f(x)=9^x , write the equation of the graph that results when:
(a) f(x) is shifted 2 units upward. y=-----------
(b) f(x) is shifted 4 units to the right. y=----------
(c) f(x) is reflected about the x-axis and the y-axis. y=------------
Answers
Answer: (a) To shift the graph of f(x)=9^x 2 units upward, we can add 2 to the function. Therefore, the new equation is:
y = 9^x + 2
(b) To shift the graph of f(x)=9^x 4 units to the right, we can replace x with (x - 4). Therefore, the new equation is:
y = 9^(x - 4)
(c) To reflect the graph of f(x)=9^x about the x-axis and the y-axis, we can replace x with (-x) and take the negative of the function. Therefore, the new equation is:
y = -9^(-x)
Step-by-step explanation:
Jean drew a blueprint of her family's home for a school project. She used the following scale of 0.25 inch =1 foot to make the scale drawing. The width of Jean's bedroom is 75% of the room's length. If the room is 9 feet wide , how long is it on both the blueprint and in real life?
Answers
The length of the room on the blueprint is 12 inches.
what is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
To solve this problem, we first need to find the length of Jean's bedroom in real life.
Let L be the length of Jean's bedroom in real life. According to the problem, the width of the room is 9 feet, so we can write:
9 = 0.25x, where x is the width of the room on the blueprint.
Solving for x, we get:
x = 9/0.25 = 36
So the width of the room on the blueprint is 36 inches.
Since the width of the room on the blueprint is 75% of its length, we can write:
36 = 0.75L
Solving for L, we get:
L = 36/0.75 = 48
So the length of Jean's bedroom in real life is 48 feet.
To find the length of the room on the blueprint, we use the same scale of 0.25 inch = 1 foot. Therefore:
1 foot = 0.25 inch on the blueprint
48 feet = 48 x 0.25 = 12 inches on the blueprint
Therefore, the length of the room on the blueprint is 12 inches.
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Calculator What is the value of y in the triangle? Enter your answer in the box. Round your final answer to the nearest hundredth.
Answers
Answer:
Step-by-step explanation:
Value of y can be found using the tan ratio of the angle.
tan 26.5 = opposite/adjacent
.49858161 = y/24
mulitply each side by 24
11.97 = y
Answer: The value of y=116.28ft
Step-by-step explanation:
tan x = opposite side/adjacent side
let x=26.5 degree
opposite side= y
adjacent side=24ft
Therefore,
tan(26.5) = y/24
y = tan(26.5) * 24
tan(26.5) = 4.8450
y = 4.8450*24
y = 116.28ft
please send the correct answer
Answers
The values that complete the missing segments are shown below
Completing the missing segmentsFrom the question, we have the following parameters that can be used in our computation:
Blue segment = length of the rectangle
Where
length of the rectangle = radius of circle
So, we have
Blue segment = 12 units
Similarly, we have
Violet segment = width of rectangle
So, we have
Violet segment = 18 units
The green segment is the base circumference
So, we have
Green segment = 2 * 22/7 * 12
Green segment = 75.4 units
The orange segment is the diameter
So, we have
Orange segment = 2 * 12
Orange segment = 24
The area of one base is
Area of one base = 22/7 * 12^2
Area of one base = 452.4
The area of one rectangle is
Area of rectangle = 12 * 18
Area of rectangle = 216
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At this year's State Fair, there was a dice rolling gamne. If you rolled two dice and got a sum of 2 or 12, you won $12. If you rolled a 7, you won $5. Any other roll was a loss. It cost $1 to play one game with one roll of the dice. What is the expectation of the game? Round your answer to the nearest cent.
The expectation of this game is approximately dollars.
Answers
the expectation of the game is $0.22 per game. This means that on average, for every game played, the player can expect to win $0.22. However, this does not guarantee that the player will actually win $0.22 every time they play the game. It simply means that over many plays of the game, the player's winnings will average out to $0.22 per game.
How to solve the probability?
To find the expectation of the game, we need to calculate the probability of winning and losing and multiply them by their corresponding payoffs.
First, let's calculate the probability of rolling a sum of 2 or 12. There is only one way to roll a sum of 2 or 12, which is by rolling a pair of ones or a pair of sixes, respectively. So, the probability of rolling a sum of 2 or 12 is:
P(2 or 12) = P(1,1) + P(6,6) = (1/6) * (1/6) + (1/6) * (1/6) = 1/18
Next, let's calculate the probability of rolling a 7. There are six ways to roll a sum of 7, which are: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). So, the probability of rolling a 7 is:
P(7) = P(1,6) + P(2,5) + P(3,4) + P(4,3) + P(5,2) + P(6,1) = 6 * (1/6) * (1/6) = 1/6
Finally, the probability of losing is:
P(loss) = 1 - P(2 or 12) - P(7) = 1 - 1/18 - 1/6 = 11/18
Now, we can calculate the expectation of the game as follows:
E(X) = (12 * P(2 or 12)) + (5 * P(7)) - (1 * P(loss))
= (12 * 1/18) + (5 * 1/6) - (1 * 11/18)
= 2/9 + 5/6 - 11/18
= 0.22
So, the expectation of the game is $0.22 per game. This means that on average, for every game played, the player can expect to win $0.22. However, this does not guarantee that the player will actually win $0.22 every time they play the game. It simply means that over many plays of the game, the player's winnings will average out to $0.22 per game.
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Match each sum or difference with the correct simplified expression.
(x-5)-(x + 1)
(x-5)+ (x + 1)
(x-5)+ (x-1)
(x-5)-(x-1)
Intro
-4
2x-6
-6
2x-4
Answers
Answer:
Step-by-step explanation:
[tex](x-5)-(x + 1)=x-5-x-1=-6[/tex]
[tex](x-5)+ (x + 1)=x-5+x+1=2x-4[/tex]
[tex](x-5)+ (x-1)=x-5+x-1=2x-6[/tex]
[tex](x-5)-(x-1)=x-5-x+1=-4[/tex]
Use substitution to determine whether the given number is a zero of the given
polynomial.
3; f(x) = -x^4 -8x²-x-5
also
Answers
As f(3) is not equal to zero, 3 is not a zero of the polynomial f(x) = -x⁴ -8x²-x-5.
How to determine whether a given number is a zero of the a polynomial?Given the polynomial in the question;
f(x) = -x⁴ -8x²-x-5
Given number: 3
To check if 3 is a zero of the polynomial f(x) = -x⁴ -8x²-x-5, we need to substitute x = 3 into the polynomial and see if the result will give zero.
f(x) = -x⁴ -8x²-x-5
plug i x = 3
f(3) = -3⁴ - 8(3)² - 3 - 5
= -81 - 72 - 3 - 5
= -161
Therefore, 3 is not a zero of the polynomial f(x) = -x⁴ -8x²-x-5.
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how many degrees is a obtuce angel
Answers
Angels between 90 and 180 degrees are obtuse angels.
What would be the total amount of money she made in the month if she babysat 10
days?
The total would be ____ dollars
Answers
The total earnings for the month if she babysat 10 days would be $360.
How are the total earnings determined?Using the mathematical operation of multiplication, the total earnings can be determined as follows:
Multiplication operation involves the multiplicand, the multiplier, and the product.
Hourly pay rate = $4.50
Daily working hours = 8 hours
The number of days worked in the month = 10 days
Total working hours for the month = 80 hours (10 x 8)
Total earnings for the month = $360 ($4.50 x 80)
Thus, we can conclude that she earned $360 gross for the month.
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Question Completion:Assuming that the Hourly pay rate is $4.50 and she worked for 8 hours daily.
You spin the spinner once. 123 What is P(odd or divisor of 54)? Simplify your answer and write it as a fraction or whole number.
Answers
After answering the given question, we can conclude that As a result, the probability of receiving an odd or a divisor of 54 is one, or 100% confidence.
What is probability?Probability is a gauge of how likely an occurrence is to occur. It is represented by a figure between 0 and 1, with 0 representing an unlikely occurrence and 1 representing an inevitable event. Switching a fair coin and coin turns has a chance of 0.5 or 50% because there are two equally likely results. (Heads or tails). Probability theory is a branch of mathematics that studies random occurrences rather than their characteristics. It is applied in many areas, including statistics, economics, science, and engineering.
There are three equally probable results from the spinner: 1, 2, and 3. To determine the likelihood of receiving an odd or divisor of 54, we must tally the number of events that meet this requirement.
54 has divisors of 1, 2, 3, 6, 9, 18, 27, and 54. Only one, three, and nine are unusual. As a result, the potential results that are either odd or divisors of 54 are 1, 3, and 2.
P(odd or divisor of 54) = P(1) + P(2) + P(3) + P(9) = 1/3 + 1/3 + 1/3 + 0 (because 9 is not a spinning choice) = 1
As a result, the chance of receiving an odd or a divisor of 54 is one, or 100% confidence.
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The average retail price of gasoline (all types) for the first half of 2005 was 212.2 cents. What would the standard deviation have to be in order for a 11% probability that a gallon of gas costs less than $1.80? Round z-value calculations to two decimal places and final answer to the nearest cent.
Answers
Average retail price of gasoline (all types) for the first half of 2005 = 212.2 cents
Probability that a gallon of gas costs less than $1.80 = 11%
We need to find the standard deviation required for this probability
First, we need to convert the price of $1.80 to cents:
$1.80 = 180 cents
Next, we need to find the z-score corresponding to the 11th percentile (since we want the probability of a price less than $1.80):
Using a standard normal distribution table or calculator, we find that the z-score for the 11th percentile is approximately -1.22.
Now, we can use the formula for z-score to find the standard deviation:
z = (x - μ) / σ
where:
z = -1.22
x = 180 cents (price of gas)
μ = 212.2 cents (average price of gas)
σ = standard deviation
Rearranging the formula and substituting the values, we get:
σ = (x - μ) / z
σ = (180 - 212.2) / (-1.22)
σ = 26.2 / 1.22
σ ≈ 21.48
Therefore, the standard deviation required for an 11% probability that a gallon of gas costs less than $1.80 is approximately 21.48 cents.
Solve the right
triangle.
...
$
Find the measure of ZB.
A
35°
19
B
C
mZB= (Round to one decimal place as needed.)
C
Answers
Answer:
∠ B = 55°
Step-by-step explanation:
the sum of the 3 angles in triangle = 180° , that is
∠ B + 35° + 90° = 180°
∠ B + 125° = 180° ( subtract 125° from both sides )
∠ B = 55°
1. Solve the following system of equations graphically. Make sure to check the solution.
y = 1/2x - 3
y = 3/4x + 2
Answers
Answer:
Step-by-step explanation:
Solve using the substitution method
2x -y = 7 and -6x + 3y = 21
Answers
There is no solution to the given system of equations. Therefore, the system is inconsistent.
How to solve the equation using substitution method?
To solve this system of equations using the substitution method, we need to solve one of the equations for one of the variables, and then substitute that expression into the other equation. Let's solve the first equation for y:
2x - y = 7
-y = -2x + 7
y = 2x - 7
Now we substitute this expression for y into the second equation:
-6x + 3y = 21
-6x + 3(2x - 7) = 21
-6x + 6x - 21 = 21
-21 = 21
This is a contradiction, and there is no solution to the system of equations. Therefore, the system is inconsistent.
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A rectangular basket has a height of 6 inches, a width of 4 inches, and a length of 12 inches. What is the volume of the basket? Show how you found your answer.
V= l x w x h
V= B x h
Answers
The volume of a rectangular box or basket can be calculated using the formula:
V = l x w x h
where l is the length, w is the width, and h is the height of the box or basket.
In this case, the height of the basket is 6 inches, the width is 4 inches, and the length is 12 inches. Therefore, we can substitute these values into the formula and calculate the volume:
V = l x w x h
V = 12 x 4 x 6
V = 288 cubic inches
Therefore, the volume of the rectangular basket is 288 cubic inches.
The volume of the basket is 288 cubic inches.
What is Volume?The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
The volume of a rectangular prism can be calculated
= length x width x height.
Given that the height is 6 inches, the width is 4 inches, and the length is 12 inches, the volume of the basket can be calculated as:
Volume = Length x Width x Height
Volume = 12 inches x 4 inches x 6 inches
Volume = 288 cubic inches
Therefore, the volume of the basket is 288 cubic inches.
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pls help lol it’s due tomorrow
Answers
(If you need an explanation, just comment)
(Also if you can please give me brainliest)
4) Two Truths and a Lie. Use what you know about the patterns in area models to determine which two area models correctly represent a factorable polynomial in the form of ax^2 + bx + c where c = 40. The middle “b” term is unknown
Answers
The correct area models are 4e and none of the given models for 4d and 4c.
What is the quadratic equation?
The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
The area model of 4c is incorrect because the last term of the polynomial, which is 40, is represented by the bottom right box of the area model. However, in the given area model, the box representing 40 is in the upper row.
The area model of 4e is correct because it represents the polynomial as the product of two binomials, where the factors are (x-5) and (x-8).
When multiplied using the distributive property, the resulting polynomial is x² - 13x + 40, which matches the given polynomial form.
The area model of 4d is incorrect because it does not properly represent a factorable polynomial.
It only includes three boxes, representing the three terms of the polynomial, but it does not show how the terms can be factored into binomials.
Therefore, the correct area models are 4e and none of the given models for 4d and 4c.
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I NEED HELP ON THIS
Answers
The expression that correctly name the angle below is ∠K, So correct option is C.
Describe Angles?In geometry, an angle is a figure formed by two rays, or half-lines, that originate from a common endpoint, which is called the vertex. The rays can be thought of as emanating from the vertex and extending infinitely in opposite directions.
The measure of an angle is typically given in degrees, where a full circle is 360 degrees. Angles can be classified according to their size:
An acute angle is less than 90 degrees.
A right angle measures exactly 90 degrees.
An obtuse angle is greater than 90 degrees but less than 180 degrees.
A straight angle measures exactly 180 degrees.
A reflex angle is greater than 180 degrees but less than 360 degrees.
A full angle measures exactly 360 degrees.
Angles can also be classified based on their position relative to other angles or lines:
Adjacent angles share a common vertex and one common side.
Complementary angles add up to 90 degrees.
Supplementary angles add up to 180 degrees.
Vertical angles are formed by two intersecting lines and are opposite each other.
The expression that correctly name the angle below is ∠K.
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The answer C is accurate since the formula that correctly identifies the angle below is ∠K.
Describe Angles?An angle is a figure in geometry made up of two rays, or half-lines, that start from a single endpoint known as the vertex. You can imagine the rays coming from the vertex and continuing in opposing directions indefinitely.
A whole circle has 360 degrees, hence an angle is commonly measured in degrees. Angles can be grouped based on their size:
Any angle that is below ninety degrees is considered acute.
Obtuse angles are those that are greater than 90 degrees but below 180 degrees.
The length of a straight angle is 180 degrees.
A reflex angle is one that is above 180 degrees and less than 360 degrees.
Angles can also be categorised according on where they are situated in relation to other angles or lines:
Adjacent angles have one shared side as well as a common vertex.
Complementary angles add up to 90 degrees.
The sum of all supplementary angles is 180 degrees.
Two intersecting lines that are opposite one another form vertical angles.
The formula K accurately identifies the angle below.
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A DVD rotates through an angle of 20pi radians in 1 second. At this speed, the DVD will make ____ revolutions in 1 minute!
Answers
In 1 second, the DVD rotates through an angle of 20π radians. To find the number of revolutions, we can divide this angle by 2π:
20π radians ÷ 2π radians/revolution = 10 revolutions
Therefore, in 1 second, the DVD makes 10 revolutions. To find the number of revolutions in 1 minute, we can multiply by 60:
10 revolutions/second × 60 seconds/minute = 600 revolutions/minute
So the DVD will make 600 revolutions in 1 minute.
Please help with this
Answers
The probability that a passenger is traveling for business is 67.1%.
The probability of a passenger bringing a laptop on a flight if the passenger is traveling for business is 0.352 or approximately 35.2%.
How to calculate the probabilityThe probability that a passenger is traveling for business can be calculated by adding the number of passengers traveling for business and dividing by the total number of passengers:
P(traveling for business) = (274 + 397) / 1000 = 0.671
Therefore, the probability that a passenger is traveling for business is 0.671 or approximately 67.1%.
b. The probability of a passenger bringing a laptop on a flight if the passenger is traveling for business can be calculated as follows:
P(laptop | traveling for business) = number of passengers with a laptop and traveling for business / number of passengers traveling for business
P(laptop | traveling for business) = 236 / 671 = 0.352
Therefore, the probability of a passenger bringing a laptop on a flight if the passenger is traveling for business is 0.352 or approximately 35.2%.
c. It should be noted that to determine if there is an association between bringing a laptop on a flight and traveling for business, we can compare the proportion of passengers who bring a laptop when traveling for business versus when not traveling for business. If the proportions are different, it suggests an association.
P(laptop | traveling for business) = 0.352
P(laptop | not traveling for business) = 0.093
The proportions are different, which suggests an association between bringing a laptop on a flight and traveling for business.
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Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number.
the product of 6 less than a number and 2 more than the number
The complete verbal phrase translates to
(Do not perform the calculation.)
Answers
The expression represents the product of two terms = (x - 6) × (x + 2)
What do you mean by Linear Equation ?An equation in mathematics that is linear has a variable whose maximum power is 1. Alternatively said, it is an algebraic equation of the following form:
ax+ b = 0
where an is a constant that cannot equal zero, b is a constant, and x is a variable. Another way to express a linear equation in its general form is as follows:
y = mx + b
where the y variable is the dependent variable, the independent variable is x, the slope is m, and the y-intercept is b.
The product of 6 less than a number and 2 more than the number can be translated into the mathematical expression:
(x - 6) × (x + 2)
Here, x represents the unknown number, and the expression represents the product of two terms: "6 less than a number" (x - 6) and "2 more than the number" (x + 2).
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How many different committees can be formed from 12 teachers and 43 students if the committee consists of 2 teachers and 2 students
Answers
Answer: 59598
Step-by-step explanation:
It would be 12C2 for the teachers
and 43C2 for the students
12C2=66
43C2=903
66*903=59598
Can anybody help please? 8/10 + ___ = 95/100, Please help I really need to get this correct for my DBA (Discussion Based Assignment)
Answers
Answer:
15/100
Step-by-step explanation:
8/10 is equal to 80/100
95/100 - 80/100 = 15/100
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answers
Answer:
1. m∠5 + m∠6 = 180°
2. ∠ 2+ ∠ 3 = ∠ 6
3. m∠2 + m∠3 + m∠5 = 180°
Step-by-step explanation:
IF ITS WRONG CONTACT ME AND I WILL FIX IT
evaluate the expression -5+7-(-3)
Answers
Answer:
the answer is 5........
Answer: I rechecked and confirmed the answer. The answer is 5.
What was the age distribution of prehistoric Native Americans? Suppose an extensive anthropological studies in the southwestern United States gave the following information about a prehistoric extended family group of 84 members on what is now a Native American reservation.
Age range (years) 1-10 11-20 21-30 31 and over
Number of individuals 35 22 20 7
For this community, estimate the mean age expressed in years, the sample variance, and the sample standard deviation. For the class 31 and over, use 35.5 as the class midpoint. (Round your answers to one decimal place.)
x =
years
s2 =
s =
years
Answers
Mean age: 16.1 years, Sample variance: 50.47 square years and Sample standard deviation: 7.10 years for the given problem.
To estimate the mean age, we need to find the midpoint of each age range and multiply it by the number of individuals in that range. Then we add up these products and divide by the total number of individuals:
Mean age = [(1+10)/2 x 35 + (11+20)/2 x 22 + (21+30)/2 x 20 + 35.5 x 7] / 84
= (5.5 x 35 + 15.5 x 22 + 25.5 x 20 + 35.5 x 7) / 84
= 16.1
Therefore, the estimated mean age of this extended family group is 16.1 years.
To calculate the sample variance, we need to find the deviation of each age from the mean, square each deviation, and add up these squared deviations. Then we divide this sum by the total number of individuals minus one:
s2 = [(1-16.1)2 x 35 + (11-16.1)2 x 22 + (21-16.1)2 x 20 + (35.5-16.1)2 x 7] / (84-1)
= (2254.05 + 537.08 + 220.89 + 253.68) / 83
= 50.47
Therefore, the estimated sample variance is 50.47 square years.
We simply take the square root of the sample variance to calculate the sample standard deviation:
s = [tex]\sqrt{s2}[/tex]
= s[tex]\sqrt{50.47}[/tex]
= 7.10
Therefore, the estimated sample standard deviation is 7.10 years.
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1) A bowl is a hemisphere with radius 6 cm Water fills two-fifths of the volume of the bowl.?
2) The water is poured into a hollow cone. The depth of the water in the cone is 12 cm
Answers
1. First, we need to find the volume of the hemisphere bowl:
V_bowl = (2/3)πr^3
V_bowl = (2/3)π(6 cm)^3
V_bowl = 288π cm^3
Since water fills two-fifths of the volume, we can find the volume of water:
V_water = (2/5)V_bowl
V_water = (2/5)(288π cm^3)
V_water = 115.2π cm^3
2. Now, we need to find the radius and height of the cone to which the water is poured. Let's call the radius of the cone r and the height h. We know that the volume of the cone is equal to the volume of the water in the bowl:
V_cone = V_water
(1/3)πr^2h = 115.2π
r^2h = 345.6
We also know that the depth of the water in the cone is 12 cm, so h = 12 cm. Substituting this value into the equation above, we get:
r^2(12 cm) = 345.6
r^2 = 28.8
r ≈ 5.36 cm
So, the radius of the cone is approximately 5.36 cm, and the height is 12 cm.
Lynne read 2.5 chapters of her book on Tuesday, 4.25 chapters on Wednesday, and 5 chapters on Thursday. How many chapters did she read in total during those three days? I think you have to add them
Answers
Answer:
11.75
Step-by-step explanation:
2.5 + 4.25 + 5
Answer:
11.75 chapters in total
Step-by-step explanation:
Given:
2.5, 4.25, 5
The question ask for total
2.5 + 4.25 + 5 = 11.75
Pls help, Micheal tracked the value of his boat each year after he purchased it. Determine whether the data are linear, quadratic, or exponential. Use regression to the function that models the data.
Answers
This means that after two years since the purchase, the boat was worth $24.57.
What is worth?In general, worth refers to the value or monetary equivalent of something. It can be used to describe the financial value of assets such as property, stocks, or commodities, or to describe the value of something in terms of its usefulness, importance, or significance.
Michael tracked the value of his boat each year after he purchased it. Determine whether the data are linear, quadratic, or exponential. Use regression to find the function that models the data.
16.75
19.5
4
3
22.9
27.25
2
1
32
0
Years Since Purchase
To better understand the exponential function that models the data, let's break it down:
y = 10.92 * 1.50ˣ
The constant "10.92" represents the initial value of the boat when it was purchased. This means that the boat was worth $10.92 when Michael first bought it.
The constant "1.50" represents the growth factor of the boat's value. This means that each year, the value of the boat increases by a factor of 1.50.
The variable "x" represents the number of years since the boat was purchased. The function takes this input and returns the value of the boat at that time.
For example, if we plug in x=1 into the function, we get:
y = 10.92 * 1.50¹
y = 16.38
This means that after one year since the purchase, the boat was worth $16.38. Similarly, if we plug in x=2 into the function, we get:
y = 10.92 * 1.50²
y = 24.57
This means that after two years since the purchase, the boat was worth $24.57.
It's important to note that the exponential function assumes that the growth rate remains constant over time. In reality, the value of the boat may be affected by other factors such as wear and tear, maintenance, and market fluctuations. Nevertheless, the exponential function provides a useful model for understanding the trend in the data and making predictions about the future value of the boat.
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