The cubic equation 4 · x³ + 12 · x² + 3 · x - 5 = (2 · x - 1) · (p · x² + q · x + r) use the following coefficients: (p, q, r) = (2, 7, 5).
How to find the values of missing coefficients in a cubic equation
In this problem we find the definition of cubic equation as a product of a linear equation and a quadratic equation, the latter one has four unknown real coefficients, whose values can be found by expanding the product and comparing coefficients. First, write the entire equation:
4 · x³ + 12 · x² + 3 · x - 5 = (2 · x - 1) · (p · x² + q · x + r)
Second, expand the expression:
4 · x³ + 12 · x² + 3 · x - 5 = (2 · x - 1) · p · x² + (2 · x - 1) · q · x + (2 · x - 1) · r
4 · x³ + 12 · x² + 3 · x - 5 = 2 · p · x³ - p · x² + 2 · q · x² - q · x + 2 · r · x - r
4 · x³ + 12 · x² + 3 · x - 5 = 2 · p · x³ + (- p + 2 · q) · x² + (- q + 2 · r) · x - r
Third, find the values of p, q, r by comparison:
2 · p = 4
- p + 2 · q = 12
- q + 2 · r = 3
- r = - 5
Then:
p = 2, r = 5
q = - (3 - 2 · r)
q = - (3 - 2 · 5)
q = - (- 7)
q = 7
- 2 + 2 · 7 = 12
- 2 + 14 = 12
12 = 12
The values of real coefficients are (p, q, r) = (2, 7, 5).
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4. Xander's hedgehog weighs 0.62 pound.
Express his hedgehog's weight in grams.
Round your answer to the nearest gram.
Pls do step-by-step
The weight of the hedgehog in grams is 281 grams
What is the weight of the hedgehog in grams?The first step is to determine the unit of conversion of pounds to grams.
1 pound = 453.592 grams
In order to convert the weight of the hedgehog to grams, multiply the unit of conversion by the weight of the hedgehog in pounds. Multiplication is the product of two or more numbers,
Weight of the hedgehog in grams = 0.62 x 453.592 grams = 281 grams
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Three times the square of a number minus eight
The expression of the statement is 3x² - 8
How to determine the expression of the statementFrom the question, we have the following parameters that can be used in our computation:
A mathematical statement
The mathematical statement is given as
Three times the square of a number minus eight
Represent the number with x
So, we have
Three times the square of x minus eight
Express as squares and numbers
This gives
3 * x² minus 8
So, we have
3x² - 8
hence. the expression is 3x² - 8
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Can someone help me please? I know the answer but the equation. Thanks.
Answer:
Equation is x-5 = 37
Reason:
x = starting temperature
We start with x degrees, and decrease by 5 degrees.
We go from x to x-5
The x-5 is now 37 degrees
Therefore, we arrive at the equation x-5 = 37
To solve this equation, add 5 to both sides and you'll get x = 42
Nice work on getting the correct value of 42.
Can you write an Orginal Oratory speech on benefits of solar energy
Throughout the solar system, solar energy is continuously emitted by the sun. The Earth is warmed by solar energy, which also affects the weather, the wind, and the survival of plant and animal life. Electromagnetic radiation, which is a kind of energy, heat, and light, is released from the sun (EMR).
What is solar system?Anything produced by the sun is considered to be solar energy.Nuclear fusion that occurs in the sun is the source of solar energy. Hydrogen atom protons clash ferociously in the sun's core, where they fuse to form helium atoms, which is the process of fusion.An large quantity of energy is released during this process, which is sometimes referred to as a PP (proton-proton) chain reaction. Around 620 million metric tons of hydrogen are fused by the sun every second in its core. Other stars, similar in size to our sun, also experience the PP chain reaction, which supplies them with ongoing heat and energy. These stars have an average Kelvin temperature of 4 million degrees (about 4 million degrees Celsius, 7 million degrees Fahrenheit).The CNO cycle is responsible for energy production in stars that are around 1.3 times larger than the sun. Carbon, nitrogen, and oxygen (C, N, and O) are required for the CNO cycle to convert hydrogen to helium. As of right now, the CNO cycle produces less than 2% of solar energy.To Learn more About solar system, refer To:
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Rick paddles a kayak 20 miles upstream in 4 hours. The return trip downstream takes him 2. 5 hours. What is the rate that Rick paddles in still water? What is the rate of the current?
For the given time taken to cover 20 miles from upstream and downstream the rate of Rick paddles in still water is 6.5mph and rate of current is 1.5mph.
Let us consider 'x' be the rate at which Rick paddles in still water
'y' be the rate of the current
Distance covered while going in upstream = 20 miles
Time taken while going 20 miles upstream = 4 hours
Rate of upstream = 20 / 4
⇒ x - y = 5 miles /hours ___(1)
Distance covered while going in downstream = 20 miles
Time taken while going 20 miles downstream = 2.5hours
Rate of downstream = 20 / 2.5
⇒ x + y = 8 miles /hours ___(2)
Solve (1) and (2) we get,
x - y = 5
x + y = 8
2x = 13
⇒ x = 6.5miles per hour
y = x - 5
⇒ y = 1.5 miles per hour
Therefore, the rate of the Rick paddles in the still water is 6.5mph and the rate of the current is 1.5mph.
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Penelope mixed 6 ounces of apple juice concentrate with 9 ounces of water.
Which ratio of apple juice to water will make the same recipe?
A 45:30
B 42.60
C 42:63
D 9:6
Ratio of apple juice to water will make the same recipe is 42.60
What is the ratio formula?Ratios are used to compare two numbers by dividing them. If you want to compare one data point (A) to another (B), your formula would be A/B. This signifies that you are dividing data A by data B. If A is five and B is ten, your ratio will be 5/10.
Add the elements of the ratio together to get the total number of shares.
Subtract the total value from the total number of shares.
Multiply by the number of necessary shares.
A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to one.
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does anyone know what 4/5 + 5/6 is and how to solve the problem
4/5 + 5/6
24+25/30
49/30
hope it will help you
can you talk with me?
A right rectangular prism measures 12 cm tall, 8 cm long, and 5 cm wide.
A manufacturer would like to double the surface area of this prism. What should be the height of the new prism so that its surface area is doubled?
Enter your answer, to the nearest tenth, in the box
Answer: Volume of a right prism = BH where B is the area of the base and H is its height.
So Volume = 16 × 12 = 192 cm^3
Step-by-step explanation:
you will need a straightedge for this assessment. which table represents a proportional relationship
The table that represents the proportional relationship would be table A. Option A
What is a proportional relationship?In this table we can see that in option A, there is a constant for which the values of the y are gotten. This is common on all of the values in A
For instance 2² = 4
3² = 9
4² = 16
0² = 0
The power of 2 is the constant that when applied on the values it gives the corresponding solution.
This shows the constant proportional relationship that is in existence between the values in x and the y solution
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Write the values of n such that -15<3n<6
The values of n for the given expression such that -15< 3n < 6 is -5 < n < 2.
What are inequalities?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
The given expression is:
-15< 3n < 6
Divide all the sides of the equation with 3 to isolate the value of n.
-15 / 3 < 3n/3 < 6/3
-5 < n < 2
Hence, the values of n for the given expression such that -15< 3n < 6 is -5 < n < 2.
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Go step by step to reduce the radical.
V 224
NOVO
try
The square root of 224 in long division is 14.96
The term square root in math is defined as a factor of a number that, when multiplied by itself, gives the original number
Here we know that we need to find the square root of √224.
In order to solve this one we have to do the following steps,
Here we have to start dividing the digits from the right side into pairs of two by drawing a line on top of them. In the case of 224, then we have two pairs 24 and 2.
And then we have to find a number(z) whose square is ≤ 2.
Then the value of z will be 1 as 1 × 1 = 1 ≤ 2.
Here we get the value of quotient and the remainder as 1 and now we have to add the divisor z with itself and get the new divisor 2z (2).
And then we have to drag down the next pair and find a number (n) such that 2n × n ≤ 124 here we have the value of n comes out to be 4.
Finally we have to add a decimal in the dividend (224) and quotient (14) simultaneously.
Here we have to add 2 pairs of zero in the dividend after the decimal and repeat the above step for the remaining three pairs of zero.
Complete Question:
Finale the square root of √224 and go step by step to reduce the radical.
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i need to explain how i got the answer also
The triangle proportionality theorem, used to evaluate the figures indicates that we get;
8. [tex]\overline{ST}[/tex] ║ [tex]\overline{PR}[/tex]
9. [tex]\overline{ST}[/tex] ║ [tex]\overline{PR}[/tex]
10. [tex]\overline{ST}[/tex] ∦ [tex]\overline{PR}[/tex]
11. x = 57.6
12. x = 27.3
13. x = 11
14. x = 10
15. x = 5
16. x = 17
What is the triangle proportionality theorem?The triangle proportionality theorem states that, in a triangle, a line drawn parallel to one of the sides of a triangle and intersects the other two sides at two different points, then the ratio in which the other two sides are divided by the line are the same.
8. The triangle proportionality theorem indicates, if [tex]\overline{ST}[/tex] and [tex]\overline{PR}[/tex] are parallel, [tex]\overline{ST}[/tex] ║ [tex]\overline{PR}[/tex], we get; QS/SP = QT/TR
QS/SP = 7/11.2 = 0.625
QT/TR = 10/16 = 0.625
Therefore, QS/SP = QT/TR = 0.625, [tex]\overline{ST}[/tex] and [tex]\overline{PR}[/tex] are parallel9. Where [tex]\overline{ST}[/tex] and [tex]\overline{PR}[/tex] are parallel, [tex]\overline{ST}[/tex] ║ [tex]\overline{PR}[/tex], we get;
PS/SQ = RT/TQ
PS = 102 - 45 = 57
PS/SQ = 57/45 = 1.2[tex]\overline{6}[/tex]
RT/TQ = 41.8/33 = 1.2[tex]\overline{6}[/tex]
PS/SQ = RT/TQ, therefore, [tex]\overline{ST}[/tex] is parallel to [tex]\overline{PR}[/tex]10. Where [tex]\overline{ST}[/tex] is parallel to [tex]\overline{PR}[/tex], we get;
QS/SP = QT/TR
QS/SP = 19/38 = 0.5
QT/TR = 24/52 = 6/13 ≠ 0.5
QS/SP ≠ QT/TR, therefore, [tex]\overline{ST}[/tex] ∦ [tex]\overline{PR}[/tex]11. The triangle proportionality theorem, indicates that we get;
48/25 = x/30
x/30 = 48/25
x = (48/25) × 30 = 57.6
12. Making use of the triangle triangle proportionality theorem, we get;
(49 - 28)/28 = x/36.4
x/36.4 = (49 - 28)/28
x = ((49 - 28)/28) × 36.4 = 27.3
x = 27.313. 32/60 = (2·x + 6)/52.5
(2·x + 6)/52.5 = 32/60
(2·x + 6) = (32/60) × 52.5 = 28
(2·x + 6) = 28
2·x = 28 - 6 = 22
x = 22/2 = 11
x = 1114. (x - 3)/21 = (x - 1)/27
27 × (x - 3)= 21 × (x - 1)
27·x - 27 × 3 = 21·x - 21
27·x - 21·x = -21 + 27 × 3 = 60
6·x = 60
x = 60/6 = 10
x = 1015. (7·x - 11)/(4·x - 2) = 20/(35 - 20)
(7·x - 11)/(4·x - 2) = 20/(35 - 20) = 20/15
(7·x - 11)/(4·x - 2) = 20/15
15 × (7·x - 11) = (4·x - 2) × 20
105·x - 165 = 80·x - 40
105·x - 80·x = 25·x = 165 - 40 = 125
25·x = 125
x = 125/25 = 5
x = 516. 35/(x - 3) = (x - 7)/4
35 × 4 = (x - 3) × (x - 7)
140 = x² - 10·x + 21
x² - 10·x + 21 - 140 = 0
x² - 10·x - 119 = 0
x² - 10·x - 7 × 17 = 0
x² + 7·x - 17·x - 17 × 7 = 0
x·(x + 7) - 17·(x + 7) = 0
(x + 7)·(x - 17) = 0
x = -7, or x = 17
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if light travels exactly 1 meter in 1/299,772,458 of a second, how many kilometers does it travel in 4.00 years? for this question, 1 year
The light travels 3.784 x 10 ^13 kilometers in 4 years .As Given that, light travels 1 meter in 1/299,772,458 of a second.
In 4 years how many kilometers it will travel?
covert 4 years into seconds.
since it is given that 1 year = 365.25 days.
4 years in seconds = 4 x 365.25 x 24 x 60 x 60
= 126230400 sec
1 m in 1/299,772,458 sec
x km in 126230400 sec
(let x be the distance travelled)
x = 126230400 x 299,772,458
= 3.784 x [tex]10^13\\[/tex] km.
Therefore , The light travels 3.784 x 10 ^13 kilometers in 4 years .
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The complete question :
if light travels exactly 1 meter in 1/299,772,458 of a second, how many kilometers does it travel in 4.00 years? for this question,
1 year = 365.25 days.
Triangle ABC is dilated with the origin as the center of the
dilation. Which ordered pair could represent the image of
point C(5, 2) after the dilation?
0 (5,-2)
(-1,-4)
O (2.5, 1)
o (7.5, 4.5)
The ordered pair could represent the image of point C(5, 2) after the dilation is (2.5, 1)
Which ordered pair could represent the image after the dilation?If we have a general point (x, y) and we apply a dilation with the origin as the center of a scale factor k, then the coordinates of the image after the dilation is (k*x, k*y)
Here we want to see which point can be the image of (5, 2) after the dilation, it will must have the form (k*5, k*2)
The only point that has this form is the one on the third option, where we can write:
(2.5, 1) = (k*5, k*2)
Then we have two equations:
2.5 = k*5
1 = k*2
Solving these we should get the same value of k.
2.5/5 = k = 0.5
1/2 = k = 0.5
so that is the correct option.
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PLEASE HELP!
Using the geometric probability distribution after 500 trials, determine the following probabilities. Type your answer in the blank space below.
I AM ABSOLUTELY GOING INSANE IN THE MEMBRANE.
As per the asked equation the value of P(x<6) will be c=1
How to find the probability?The probability of an event is always between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
Given the information provided, P(x-1)=0.178, P(x>1)=0.822, it's not possible to calculate P(x<6) because the information provided doesn't give us the complete picture of the probability distribution function, also we don't know the type of distribution used to calculate the probabilities. So we can't infer anything about P(x<6) from the information given.
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Which is a correct solution for the following system of Inequalities
The solutions of the system of inequalities are the points on the purple region, one example of a solution is (-2, -2)
Which is a correct solution for the system of inequalities?When we have a system of inequalties (so we have 2 or more inequalities) the solutions are the points (x, y) that are solutions of both inequalities at the same time.
Here we can see the graph of a system, such that the solution set of one of the inequalities is represented by the red shaded area, and the solution set of the other inequality is represented by the blue shaded area.
The solution set of the system is represented by the intersection between the areas, which is the purple area.
So any point on that region is a solution to the system, for example, the point (-2, -2) is a solution.
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1. Michael is replacing a rectangular wooden gate in his backyard. The prefabricated gate is measured in inches and is shown below. What is the length, in inches, of the diagonal support lumber (AC) in this gate? Round to the nearest TENTH
The length of the diagonal support lumber is given as follows:
161.5 inches.
How to obtain the length of the diagonal?The figure is a rectangle, hence the diagonals have equal measure, and thus the value of x can be obtained as follows:
15x + 13.25 = 17x + 4.5.
2x = 9
x = 4.5.
Hence the length of the diagonal support lumber is obtained as follows:
2 x (15 x 4.5 + 13.25) = 161.5 inches.
We multiply by 2 as we are given half the length of the diagonal.
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The table represents a linear relationship.
x −1 0 1 2
y 2 0 −2 −4
Which of the following graphs shows this relationship?
graph of a line passing through the points negative 2 comma negative 4 and 0 comma 0
graph of a line passing through the points negative 2 comma negative 1 and 0 comma 0
graph of a line passing through the points negative 2 comma 4 and 0 comma 0
graph of a line passing through the points negative 2 comma 1 and 0 comma 0
The graph of a line passing through the points (2, -4) and (0, 0). The correct answer would be an option (A).
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
The table represents a linear relationship.
x: −1 0 1 2
y: 2 0 −2 −4
As per the points, the graph has been attached below
Here we can see that the shown graph of a line passing through the points (2, -4) and (0, 0)
So the attached graph shows this relationship.
Hence, the correct answer would be option (A).
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whats 4*4*5*10 equals the the fild of math
The expression 4× 4 × 5 × 10 = 800 in the field of math.
What is algebra?Algebra is a branch of mathematics that is used to manipulate symbols and equations in order to solve problems. Algebra helps to solve problems involving unknown quantities and to develop relationships between different variables. It is a powerful tool that can be used to solve and analyze a variety of mathematical problems and equations.
Algebra can be used to solve equations, simplify expressions, and find solutions to linear and quadratic equations. Through algebra, we can also find the slope of a line, the area of a triangle, and the volume of a cube. Algebra is an invaluable tool that is useful in many areas of mathematics and science.
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Find the equation of the perpendicular bisector of AB where A and B are the points (3,6) and (-3,4) respectively. Also find its point of intersection with (i) x-axis and (ii) y-axis.
The point of intersection with x - axis is (5/3,0) and the point of intersection with y - axis is (0,5).
Any point on AB's perpendicular bisector, P(x,y), shall be considered. Then, PA = PB.
√(x-3)²+(y-6)² = √(x+3)²+(y-4)²
(x-3)²+(y-6)² = (x+3)²+(y-4)²
x² -6x+ 9 + y²- 12y + 36 = x² +6x+ 9 + y²- 8y + 16
12x + 4y -20 = 0
3x+ y-5 =0 ---(1)
Consequently, 3x+y-5=0 is the equation for the perpendicular bisector of AB.
We know that the coordinates of any point on x-axis are of the form (x,0). In other words, any point on the x-axis has a y-coordinate of zero. Thus, if we enter y = 0 in (1), we get
3x -5 = 0
x = 5/3
Thus, the x-axis is cut by the perpendicular bisector of AB at (5/3, 0).
(ii) Any point's y-axis coordinates have the following format: (0,y). When we enter x = 0 in (1), we obtain
y − 5 = 0
⇒ y = 5
Thus, the y-axis is where the perpendicular bisector of AB intersects (0,5).
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400 pounds equals how many tons?
Answer:
400 pounds equal to 0.2 tons
Enter your answer as a fraction.
Show your work please!
The probability that the first bar Iesha selects will be lemon and the second will be raisin= 2/45.
What is probability ?
Probability can be defined as the ratio number of favourable outcomes and total number of outcomes.
Note this selection is done without replacement hence after each selection sample size will reduce
Given data,
Samples 3 chocolate chip bars,
2 peanut butter bars,
1 lemon bar, and
4 raisin bars
Sample size S= [3+2+1+4]= 10
Probability that first selection is lemon = 1/10
Probability that second selection is raisin = 4/9
Hence the probability that the first bar Iesha selects will be lemon and the second will be raisin= 1/10*4/9 = 4/90= 2/45
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a newly employed nurse administrator wants to know more about the employees on the units the administrator supervises. the manager accesses the managerial database and gathers data about all of the current employees on the unit, including work shift, number of years employed, age, gender, educational preparation, certifications, work history, and professional accomplishments, analyzing the data statistically. what type of quantitative research is this?
This is an example of a descriptive quantitative research study.
Descriptive quantitative research involves collecting and analyzing data to describe the characteristics of a population or phenomenon. In this case, the nurse administrator is gathering and analyzing data about the employees on the units they supervise, such as work shift, number of years employed, age, gender, educational preparation, certifications, work history, and professional accomplishments. Statistical techniques such as mean, median, and mode are used to analyze the data, allowing the nurse administrator to compare the characteristics of the employees across various dimensions. This type of research is used to develop an understanding of a given population or phenomenon, allowing for informed decision-making.
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Naudia rode her bike two miles south. Then, she went east for three miles to reach her destination. How far is she
from her starting point?
The distance of Naudia from starting point based on distance travelled is 13 miles.
The distance travelled by Naudia and distance from starting point will form right triangle. Distance between Naudia and her final destination is the straight line or hypotenuse.
So, the expression will be -
Distance of South² + distance of East² = Distance from starting point
Distance form starting point = 2² + 3²
Distance form starting point = 4 + 9
Distance form starting point = 13 miles
Thus, the required distance is 13 miles.
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a president and vice-president for a sorority are chosen from six people. how many different president/vice-president combinations are possible?
Answer:
there is 30 ways
Step-by-step explanation:
There are 6 people who can be president x 5 other people who can be vice president. so there is 30 ways
Given the system of equations: 5x + 2y = 3 4x − 8y = 12 solve for (x, y) using elimination.a. (−7, 5) b. (−5, −4) c. (1, −1) d. (3, −6)
(x,y) = (1, -1). Option (c) is the correct answer.
Given equations:
5x + 2y = 3 ..(1)
4x - 8y = 12 ..(2)
Solving using the elimination method:
so, 4x = 8y + 12 or x = 2y + 3 ..(3)
Now, substituting the x in equation(1) from equation(3)
so we get,
5(2y+3) + 2y = 3
10y + 15 + 2y = 3
12y = -12
y = -1
Putting the value of y in equation(3)
x = 2(-1) + 3 = 1
x = 1
Therefore, (x,y) = (1, -1)
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Answer: Option C, (-1,1)
Step-by-step explanation:
If SX=z, TW=6z–76, and UV=3z–24, what is the value of z?
The value of {z} is equivalent to 13.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that SX = z, TW = 6z - 76 and UV = 3z - 24.
We can write -
{z} + {6z - 76} = {3z - 24}
7z - 76 = 3z - 24
7z - 3z = - 24 + 76
4z = 52
z = 13
Therefore, the value of {z} is equivalent to 13.
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Please help me do this
Answer:
1. 5 inches in 2 days
2. y = (5/2)x. where y is rainfall and x is days.
3. Yes
4. (5/2)
5. 2.5"/day
6. 37.5 Inches
Step-by-step explanation:
See attached worksheet
.
help me please i need immediate help
The mean height of the members of the football club is 163.4 to rounded to 1 decimal place.
How to calculate the mean heightThe mean height It is calculated by summing up all the data values and dividing by the total number of data points. The mean can also be represented by the point at which the frequency polygon would balance if it were a physical object.
The values with their corresponding frequencies are:
height: 120 × frequency: 8 = 960
height: 140 frequency: 11 = 1549
height: 160 frequency: 17 = 2720
height: 180 frequency: 18 = 3240
height: 200 frequency: 10 = 2000
sum frequency = 64
sum of all data values = 10460
mean height = 10460/64
mean height = 163.4375
Therefore, the mean height of the members of the football club is 163.4 to rounded to 1 decimal place.
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a spherical snowball is rolled in fresh snow causing it grow so fast that its radius increases at a rate of 2 in/sec. how fast is the volume of the snowball increasing when the radius is 9 in
The volume is increasing at a rate of 784 * pi cubic inches per second.
The volume of a sphere is given by the formula V = (4/3) * pi * r^3, where r is the radius of the sphere.
We can find the rate of change of the volume with respect to time by taking the derivative of V with respect to time.
dV/dt = (4/3) * pi * 3r^2 * dr/dt
Given that the radius is increasing at a rate of 2 in/sec, we can substitute this value into the equation and find the rate at which the volume is increasing:
dV/dt = (4/3) * pi * 3 * 9^2 * 2 in^3/sec = 784 * pi in^3/sec
So, when the radius of the snowball is 9 inches, the volume is increasing at a rate of 784 * pi cubic inches per second.
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