Answer: To find the time it takes for the toy boat to bob down from its peak to a height of -35 cm, we need to find the value of t when H(t) = -35.
So, we can substitute -35 for H(t) in the given equation:
5 cos (2π/3t) - 35.5 = -35
Now we can solve for t by isolating it on one side of the equation:
5 cos (2π/3t) = 0.5
cos (2π/3t) = 0.1
2π/3t = cos^-1(0.1)
3t = 2π * cos^-1(0.1)/π
t = 2 * cos^-1(0.1)
The time it takes for the toy boat to bob down from its peak to a height of -35 cm is approximately 2 * cos^-1(0.1) seconds.
Step-by-step explanation:
DATA COLLECTION Rafaella collected data to determine the number of
books her schoolmates were bringing home each evening. Her data is
shown in the mapping. She let x be the number of textbooks brought
home after school and y be the number of students with x textbooks.
a. Express the relation as a set of ordered pairs.
b. What is the domain of the relation?
c. What is the range of the relation?
The relation as a set of ordered pairs is expressed below.
The domain of the relation is {0, 1, 2, 3, 4, 5}.
The range of the relation is {8, 11, 12, 23, 28}.
What is an ordered pair?In Mathematics, an ordered pair can be defined as a pair of two (2) elements that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph such as the following:
Mathematically, the set of ordered pairs which represents the relation include the following:
Ordered pair = (0, 12)Ordered pair = (1, 8).Ordered pair = (2, 23).Ordered pair = (3, 38).Ordered pair = (4, 11).Ordered pair = (5, 11).Based on the mapping diagram (see attachment), the domain and range of the relation is given by:
Domain = {0, 1, 2, 3, 4, 5}.
Range = {8, 11, 12, 23, 28}.
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The density of titanium is 4. 5 g/cm3. A titanium object is accelerating at a rate of 800 cm/s2. The mass of the object can be modeled by the function m(v) = 4. 5v, where v is the volume in cubic centimeters. Additionally, the force of the object can be found using the function F(m) = 800m. Which composite function can be used to find the force of the object based on its volume?
Which composite function can be used to find the force of the object based on its volume?
F(m(v)) = 177. 8v
F(m(v)) = 795. 5v
F(m(v)) = 804. 5v
F(m(v)) = 3,600v
F(m(v)) = 3,600 v composite function can be used to find the force of the object based on its volume. So the option d is correct.
We have to determine which composite function can be used to find the force of the object based on its volume.
The density of titanium is 4. 5 g/cm^3.
A titanium object is accelerating at a rate of 800 cm/s^2.
The mass of the object can be modeled by the function m(v) = 4.5v, where v is the volume in cubic centimeters.
The force of the object can be found using the function F(m) = 800m.
F(m(v)) = 800 × 4.5 v
F(m(v)) = 3600 v
As a result, the function that can be utilized to simulate the force depending on volume is 3600 v.
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Joel needs to make 200 milliliters of a solution that is 35% sulfuric
acid for science class.
In the cabinet there is a 15% sulfuric acid solution and a 55% sulfuric
acid solution.
How much of the 15% solution and how much of the 55% solution
does Joel need?
Round to the nearest milliliter if necessary.
The amounts of each solution are given as follows:
15% solution: 100 milliliters.55% solution: 100 milliliters.How to obtain the amounts?The amounts are obtained solving a system of equations, for which the variables are given as follows:
Variable x: amount of the 15% solution.Variable y: amount of the 55% solution.Joel needs to make 200 milliliters, hence:
x + y = 200.
x = 200 - y.
The rate is of 35%, hence:
0.15x + 0.55y = 0.35 x 200
0.15x + 0.55y = 70.
The solution for y is given as follows:
0.15(200 - y) + 0.55y = 70
0.4y = 40
y = 40/0.4
y = 100.
The solution for x is given as follows:
x = 200 - y
x = 100.
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I'LL WRITE A GOOD REVIEW AND 5 STARS!
The original length is 250 meters and the scale drawing width is 0.67 cm
The original length of the landFrom the question (see attachment), we have the following parameters that can be used in our computation:
Scale length = 0.5 meters
So, we have
Original length = 0.5/(1/500)
Evaluate
Original length = 250
This means that the original length is 250 meters
The scale drawing widthHere, we have
Scale drawing width = 335 cm * 1/500
Scale drawing width = 0.67 cm
Hence, the scale drawing width is 0.67 cm
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Total consumption of fruit juice in a particular country in 2006 was about 1.78 billion gallons. The population of that country in 2006 was 500 million. What was the average number of gallons of fruit juice consumed per person in the country in 2006? Use pencil and paper. Using the per person amount from this problem, about how many gallons would your class consume?
The average number of gallons of fruit juice consumed per person in the country in 2006 is 3.56 gallons per person
What is average number?The average value in a set of numbers is the middle value calculated by dividing the total of all the values by the number of values.
Given:
Total consumption of fruit = 1.78 billion gallons
= 1,780,000,000
Total population = 500 million
= 500,000,000
Average number of gallons of fruit juice consumed per person = 1,780,000,000 ÷ 500,000,000
= 3.56 gallons per person
About how many gallons would your class consume?
Assume, there are 7 students in your class
Average number of gallons of fruit juice consumed per person = 3.56 gallons / 7
= 0.50 gallons per student
Therefore, the average number of gallons of fruit juice consumed per person in the country in 2006 is 3.56 gallons per person
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consider the random variable that assigns the number 0 to red and white, the number 1 to green and blue, and the number 2 to yellow and violet. what is the distribution of this random variable?
A variable whose value is decided by a random process or experiment is known as a random variable.
Depending on how the experiment or random process turns out, it may have a range of distinct numerical values. Random variables come in two varieties: discrete and continuous. A continuous random variable can take on any value within a specific range, such as real numbers, but a discrete random variable can only take on a countable number of values, such as integers.
This random variable has the following distribution and is discrete in nature:
P(X=0) = probability of red or white = P(red) + P(white)
P(X=1) = probability of green or blue = P(green) + P(blue)
P(X=2) = probability of yellow or violet = P(yellow) + P(violet)
P(X=x) must have a sum of all possible values of 1, which indicates that
P(red) + P(white) + P(green) + P(blue) + P(yellow) + P(violet) = 1
Therefore ,with a probability of 1/3 for each value, this random variable has a discontinuous uniform distribution over the set of values 0, 1, and 2.
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11 (4 - 6) + 5 (13 + 1) = 9
Answer: False because 20 doesn't equal to 9. Have a nice day ;)
Answer: the answer is false
Step-by-step explanation:
Pls answers this I need help on homework
The equation of the trend line, can be found to be y = - 25 + 250
How to find the equation of the trend line ?To find the equation of the trend line, you first need to find the slope. To do this, pick two points on the trend line. ( 4, 150) and ( 8, 50 ).
The slope is:
= ( Y2 - Y1 )/ ( X 2 - X 1 )
= ( 50 - 150 ) / ( 8 - 4 )
= - 100 / 4
= - 25
The equation of the trend line takes the form:
y = mx + b
m = slope
b = y - intercept
The slope allows you to find the y - intercept :
y = mx + b
50 = - 25 ( 8 ) + b
b = 250
The equation is:
y = - 25 + 250
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what’s the answer??? please
The rational inequality is not provided, so it is not possible to determine the next smallest critical value, b. To determine the critical values, or the values of x that make the denominator of the rational inequality equal to zero, you would need to set the denominator equal to zero and solve for x.
What is rational inequality?Once you have the critical values, you would then need to determine the sign of the numerator and denominator around each critical value to determine which side of the critical value the solution is on. The next smallest critical value, b, would then be the next lowest value of x that is a solution to the inequality.To solve the inequality, you can follow these steps:Set the denominator of the inequality equal to zero and solve for xFactor the numerator and denominatorDetermine the critical values by finding the zeros of the denominatorTest each critical value by plugging it back into the inequalityExamine the signs of the numerator and denominator around each critical value to determine which side of the critical value the solution is on.The next smallest critical value, b, would then be the next lowest value of x that is a solution to the inequality.Graph the inequality on a number line and shade the solution setIdentify the solution set in interval notation.To learn more about rational inequality refer:
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I need help with this proof
The proof that shows that triangles ABC and EDC are similar is explained in the table below.
How to Write a Proof?A proof is a logical argument that demonstrates the truth of a statement. So, each step must be justified and flow logically from the previous step.
The proof that shows that the triangles are similar is explained as shown below.
Statement Reason
1. AB || DE 1. Given
2. <A ≅ <E 2. Alternate interior <s theorem
3. <B ≅ <D 3. Alternate interior <s theorem
4. ∆ABC ~ ∆EDC 4. AA Similarity theorem
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Some fireworks are fired vertically into the air from the ground at an initial speed of 80 feet per second. The equation for this object's height h at time t seconds after launch is h(t) = -16(t)^2 +80t. Find the domain of the function.
The domain of the function h(t) = -16(t)² + 80t is,
⇒ (- ∞, ∞)
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
The equation for this object's height h at time t seconds after launch is,
⇒ h(t) = -16(t)² + 80t
Now, The function is shown a Quadratic equation.
Hence, The domain of the function h(t) = -16(t)² + 80t is,
⇒ (- ∞, ∞)
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The electronics department is having a no sales tax scale in addition all of the items in the department are on sale for 24% off Wyatt is looking at a music player that normally costs $120 he has $ 95 to spend and he is wondering if he has enough money to but it. A. Find 25% of $120 is this the price he will pay? B. Does Wyatt have enough
25 percent of $120 is $30 and yes, he has enough money to buy the music player.
A) Find 25% of $120:
To find 25% of $120, we divide $120 by 100 and then multiply by 25:
$120 / 100 * 25 = $30
So, 25% of $120 is $30.
B) Does Wyatt have enough:
To find the sale price of the music player, we need to apply the 24% discount:
$120 - $120 * 24% = $120 - $120 * 0.24 = $120 - $28.80 = $91.20
So, the music player will be sold for $91.20.
Wyatt has $95, so he has enough money to buy the music player.
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adding and subtracting fractions with whole numbers
The steps for adding and subtracting fractions with whole numbers:
- Write the whole number in the form of a fraction.
- Convert the fractions to like fractions.
- Add/Subtract the numerators while the denominator remains the same.
We know that the fraction is used to represent the portion or part of the whole thing.
The fraction has two parts: numerator and denominator.
The top part of fraction is numerator and the bottom part of fraction is denominator.
consider a fraction 1/8.
Here, numerator is 1, denominator is 8
When certain thing is divided into 8 equal parts then each part of is represented by fraction1/8
In case of adding and subtracting fractions with whole numbers:
Let us assume that 'a' represents the whole number and [tex]\frac{x}{y}[/tex] be fraction
First we write the whole number in the form of a fraction.
So, a = [tex]a = \frac{a}{1}[/tex]
Now we find the LCM of the denominators of fractions [tex]\frac{a}{1} ,\frac{x}{y}[/tex] and then convert the given fractions to like fractions.
Let m be the LCM of the denominators of fractions [tex]\frac{a}{1} ,\frac{x}{y}[/tex]
So, the fractions becomes [tex]\frac{a}{m} ,\frac{x}{m}[/tex]
Last we Add/Subtract the numerators while the denominator remains the same.
i.e., [tex]\frac{a\pm x}{m}[/tex]
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The complete question is:
How to add /subtract fractions with whole numbers?
One of the tables shows a proportional relationship.
Graph the line representing the proportional relationship from this table.
Keyboard Instructions
Initial graph state
The horizontal axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).
The vertical axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).
x 1 2 3 5
y 2 3 4 6
x 2 4 6 8
y 0 2 3 4
x 0 2 4 6
y 1 3 5 7
x −2 1 2 3
y −6 3 6 9
Two variables are primarily linked when there is a proportionate relationship, which means that as 1 variable rises or falls, the other rises or falls at the same rate.
What factors determine if one relationship is proportional?The ratios between both the two variables should be considered in order to determine whether a relationship is proportional. The relation is proportional if the ratio remains constant. The relationship is indeed not proportional if the ratio shifts.
What are the two proportional relationships principles?When two or more items are directly proportionate or change in size according to equivalent ratios, the relationship is said to be proportional. This proportional relationship can be expressed using the formula y = kx.
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Answer:
Two variables are primarily linked when there is a proportionate relationship, which means that as 1 variable rises or falls, the other rises or falls at the same rate.
What factors determine if one relationship is proportional?
The ratios between both the two variables should be considered in order to determine whether a relationship is proportional. The relation is proportional if the ratio remains constant. The relationship is indeed not proportional if the ratio shifts.
What are the two proportional relationships principles?
When two or more items are directly proportionate or change in size according to equivalent ratios, the relationship is said to be proportional. This proportional relationship can be expressed using the formula y = kx.
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Step-by-step explanation:
15/4 + 7/2 = ????????
Answer:
29/4 or as a mixed fraction 7 1/4
Step-by-step explanation:
Andy buys x cakes
Betty buys 4 times as many cakes as andy
colin buys 3 more cakes than andy
each cake costs 65p
the total cost of the cakes is £52.65
How many cakes did each person buy?
Andy:
Betty:
Colin:
Each person buys a number of cakes
Andy: 13Betty: 52Colin:16What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, Andy buys x cakes, Betty buys 4 times as many cakes as andy, and colin buys 3 more cakes than andy
So,
Andy has = x Cakes
Betty have = 4x Cakes
Clin has = x +3 Cakes
Since each cake costs 65p and the total cost of the cakes is £52.65
thus,
0.65( x + 4x + x +3) = 52.62
x + 4x + x +3 = 81
6x = 78
x = 13
Therefore,
Andy has = 13 cakes
Betty has = 4x = 4*13 = 52 cakes
Colin has = x + 3 = 16 cakes
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X
Joe is buying 4 tires for his truck The table shows the prices and the advertised sales for the same type of tire at 4 tire stores.
Based on the advertised sales, at which store will Jimmy get the lowest price on 4 tires?
es ))
A)
B)
9)
D)
Store A: Buy 3 tires and get the 4th tire free
Store B: Buy 4 tires and receive $60 off the price of each tire
Store C: Buy 4 tires and receive $200 off the total price
Store D: Buy 4 tires and receive 20% off the total price
Answer:
C
Step-by-step explanation:
not D because B is better than D. not A, still expencive. C is the most reasonable for getting $200 off. unless total is over $600.
Answer:A Store A: Buy 3 tires and get the 4th tire free
Step-by-step explanation:its A
(n^4-14n^3+51n^2-19n-30)/(n-8) Synthetic Division
The solution of (n⁴ - 14n³ + 51n² - 19n - 30) / (n - 8) using synthetic division is n³ - 6n² + 3n + 5 + 10/n - 8.
What is the solution of (x³ - 5x² -24x) / (x + 8) using synthetic division?The solution of (n⁴ - 14n³ + 51n² - 19n - 30) / (n - 8) using synthetic division is given below:
(n⁴ - 14n³ + 51n² - 19n - 30) / (n - 8)
The divisor is 8
The coefficients are:
1 -14 51 -19 -30
Using synthetic division:
the first coefficient is 1
the second coefficient = 1 * (8) + (-14)
the second coefficient = -6
the third coefficient = -6 * (8) + (51)
the third coefficient = 3
the fourth coefficient = 3 * (8) + (-19)
the third coefficient = 5
the remainder = 5 * (8) + (-30)
the remainder = 10
Therefore, the solution = 1(n⁴/n) -6(n³/n) + 3(n²/n) + 5(n/n) + 10/n - 8
The solution = n³ - 6n² + 3n + 5 + 10/n - 8
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A square painting has a diagonal of 44 in. Lorraine wants to frame the picture. The framing material is sold by the inch.
What is the minimum amount of framing she needs?
The minimum amount of framing Lorraine needs for the square painting is 31 inches.
We can use the Pythagorean theorem to calculate the length of the side of the square given the length of its diagonal. The Pythagorean theorem states that in a right-angled 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 other two sides.
We know that the diagonal of the square painting is 44 inches, and since the diagonal of a square bisects its angles, the square can be divided into two congruent right-angled triangles. Therefore, the length of one side of the square can be calculated using the Pythagorean theorem:
44 inches^2 = x^2 + x^2
x^2 = 11*11
x = 11 inches
Since the square painting has a side length of 11 inches, and the framing material is sold by the inch, Lorraine will need a minimum of 11 inches of framing on each side, for a total of 44 inches.
I need help with question 7 part (ii)
Answer:
18 years old
Step-by-step explanation:
H=17- A/
H=8hours
8=17- A/
-9=- A/
A=18years
Which is a correct solution for the following system of Inequalities
A correct solution for the following system of Inequalities is; (-2, 6)
What is the solution to the inequality graph?From the graph, it represents two inequalities and we can say that the solution of the two inequalities is the coordinate of the point where both lines of the inequalities intersect each other.
In the given graph, the coordinate of the point where both lines intersect each other is expressed as;
(-0.5, 4.2)
Now, that coordinate is not among the options but then the solution to the inequality graph will be the region shaded purple which in this case the only correct one is the coordinate (-2, 6)
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v = 14.2(12.5 - s) The velocity, , in meters per second, of an airplane seconds after landing is given by the equation above. What is the best interpretation of 14.2 as shown in the equation above? HURRYYYY TIMEDDD TESTTT
The best interpretation of 14.2 as shown in the equation above is the constant acceleration of the airplane.
What is the constant acceleration?A particle's acceleration is the rate at which its velocity changes over time. The term "constant acceleration" refers to the rate at which a particle's velocity changes. When acceleration is constant, the rate of change in velocity is also constant. In the absence of any acceleration, velocity remains constant.
When acceleration is positive, velocity becomes more significant. Acceleration causes a decrease in velocity. The value 14.2 in the equation above represents the constant acceleration of the airplane in meters per second squared (m/s^2). It is the rate at which the velocity of the airplane is changing with respect to time.
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what is 30 x 8/12+18
Need HELP ASAP PLEASE HELP ME
MARKING BEST ANSWER BRAINLIST.
The path of a fast moving particle traces a circle with equation (x-3)² + (y-4)² = 25. It starts at point (3,-1), moves counter clockwise, and passes the point (8,4) for the first time after traveling 7 microseconds. Where is the particle after traveling for 20 microseconds.
The particle is at the point (-1.112,3.909) after traveling for 20 microseconds.
We have been given a circle,
(x-3)²+(y-4)²=25
whose center is (3,4)
and with a radius of 5 units.
The particle starts at (3,-1) which is the 6 o'clock position in the circle, and ends at (8,4) after 7 microseconds which are at the 3 o'clock position in the circle.
So, the particle traveled 1/4 of the circumference of the circle in 7 microseconds
therefore according to the unitary method it will travel 5/7 of the circumference of the given circle.
so it will subtend 2π×5/7 of the circle from (3,-1)
from the polar form of the circle and the shifting of center of the circle we can conclude
that it's location will be
(5 × cos (10π/7) - 3 , 5 × sin (10π/7) - 4)
= (-1.112,3.909)
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Which function represents the reflection over the x-axis of f(x)=x
The reflected function is the one below:
g(x) = -√x
This function is represented by the last table.
Which one represents the reflected fucntion?For a general function y = f(x), we define a reflection over the x-axis as:
g(x) = -f(x)
In this case f(x)= √x, then the reflected function will be:
g(x) = -f(x) = -√x
Now we can evaluate this function to get some pairs of values.
Then when x = 1
g(1) = -√1 = -1
g(2) = -√2 = -1.41
And so on.
Then the correct option is the last table.
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Amanda and Marvin are going to a movie this evening. Marvin wants to have at least $60 in his wallet.
He currently has $15. Write and solve an inequality to find how much more cash Marvin should put in his wallet.
Marvin should put at least $45 more cash in his wallet in order to have at least $60.
Solving inequality questionsLet x be the amount of cash that Marvin needs to put in his wallet. We know that he wants to have at least $60, and he currently has $15, so we can write the inequality as:
x + 15 ≥ 60
To solve for x, we need to subtract 15 from both sides of the inequality:
x ≥ 60 - 15
x ≥ 45
Marvin should put at least $45 more cash in his wallet in order to have at least $60.
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Please help!!
Seven friends accept the invitation to the twins' birthday party. At the last minute, Tomas and Emilio learn that their neighbor also wants to attend. The twins realize that they can stay within their budget by buying different amounts of popcorn.
Small popcorn that serves 1 = $4. 50,
Medium popcorn that serves 2 = $5. 75,
Large popcorn that serves 2-3 = $6. 50.
Describe a different popcorn scenario that will allow the twins to bring 8 friends, including their neighbor, and still stay within their budget.
Your description must be able to be proven mathematically and make sense
The equation for Tomas and Emilio birthday party's celebration is 200 = 45.99 + 17p
In math the term called equation is defined as a mathematical statement that shows that two mathematical expressions are equal.
Here we have know that seven friends accept the invitation to the twins' birthday party.
Where the possible equation that can be set up will have the total budget equal to total expenses.
So it can be written as the Total Cost of party is 200,
Then the amount can be divided as
=> Cost of Party Room + Cost of Movie Tickets + Cost of popcorns
Let us consider that if p people attend the party, then the cost of movie tickets will be $12.50p and cost of popcorns will be $4.50p, assuming that each person get a small popcorn bag.
Hence the equation will be written as
=> 200 = 45.99 + 12.50p + 4.50p
=> 200 = 45.99 + 17p
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5.
Find the coordinates of B, C, and D given that AB = 5 and BC
= 10.
The coordinates of B, C, and D are (3,-5), (3,5), and (-7,5) respectively.
Given point A (-2,-5) and the lengths of the sides AB = 5 and BC = 10, we can use this information to determine the coordinates of B, C, and D.
Using the information provided, we know that B is 5 units away from A in the positive x-direction. Therefore, the x-coordinate of B is (-2) + 5 = 3 and the y-coordinate of B is the same as that of A, which is -5. So point B is (3,-5).
Next, we know that C is 10 units away from B in the positive y-direction. Therefore, the x-coordinate of C is the same as that of B, which is 3, and the y-coordinate of C is (-5) + 10 = 5. So point C is (3,5).
Finally, we know that D is 10 units away from C in the negative x-direction. Therefore, the x-coordinate of D is 3 - 10 = -7 and the y-coordinate of D is the same as that of C, which is 5. So point D is (-7,5).
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The question is -
Find the coordinates of B, C, and D given that AB = 5 and BC = 10 where A = (-2,-5).
g the radius of a sphere is increasing at a rate of 4 mm/s. how fast is the volume increasing when the diameter is 100 mm?
Answer:
125,664 mm³/s
Step-by-step explanation:
V = (4/3)πr³
dV/dt = (4π/3) × 3r² × dr/dt
dV/dt = 4πr² × dr/dt
dr/dt = 4 mm/s
d = 100 mm; r = 50 mm
dV/dt = 4π(50 mm)² × 4 mm/s
dV/dt = 125,664 mm³/s
are the responses to the survey question quantitative or categorical? quantitative b. how many of the respondents said that they expect driverless cars to be common in the next years? round your answer to nearest whole number. 79659 c. how many respondents answered in the range years? round your answer to nearest whole number. 15030
The responses to the survey question are quantitative, as the respondents were asked to provide a numerical answer.
Out of the 79,659 respondents, 79,659 said that they expect driverless cars to be common in the next years.
Out of the 79,659 respondents, 15,030 answered in the range of years. This means that 15,030 respondents provided a numerical answer that was within the range of years.
It is important to note that the survey question was quantitative, so the responses provided by the respondents were numerical. This means that the responses were not categorical, as categorical responses would have been in the form of words or phrases.
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