Answer:
1935
Step-by-step explanation:
Step 1: If 4% of a number is 77, then what is 100% of that number? Setup the equation.
77
4% = Y
100%
Step 2: Solve for Y
Using cross multiplication of two fractions, we get
4Y = 77 x 100
4Y = 7700
Y = 7700
100 = 1,925
Rewrite the exponential model as a logarithmic model that calculates the number of years, g(x), for the number of infected tree to reach the value of x
The logarithmic model that calculates the number of years, g(x), for the number of infected tree to reach the value of x is-
[tex]g(x)[/tex] = ㏑[tex](x) / 0.4[/tex]
For the number of infected trees f(x) after x years, we are given an exponential function.We find the inverse function by using the natural logarithm to calculate the number of years required for the number of infected trees to reach x.The equation can be written as-
[tex]y = f(x) = e x^{0.4x}[/tex]
The natural logarithm is now applied to both sides of the equality after we have isolated y.
[tex]0.4y = ln x[/tex][tex]y = ln x / 0.4[/tex]
This is how the exponential model as a logarithmic model that calculates the number of years, g(x) can be explained as.
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Eric spent $21.88, including sales tax, on 2 jerseys and 3 pairs of socks. The jerseys cost $6.75 each and the total sales tax was $1.03. Fill in the table with the correct prices.
Answer:
Step-by-step explanation:
Select all ratios equivalent to 3:1
a)12:24
b)26:28
c)1:2
Answer:
a)12:4
Step-by-step explanation:
We know
The ratio is 3:1; we time 4 and get a ratio is 12:4
So, the answer is A
The sequence a0, a1, a2,. Is defined by letting a0 = 1, and for integers n > 0, an = a b n 2c + a b 2n 3 c + n. (A) Find a1, a2, a3, a4, a5, a6, a7 and a8. (B) Use part (a) to find the least integer a so that an > 4n for all integers n ≥ a. (C) Prove by strong induction that an > 4n for all integers n ≥ a where a is the integer you chose in part (b). (D) Use part (a) to find the least integer b so that an > 45 for all integers n ≥ b. (E) Prove by strong induction that an > 5n for all integers n ≥ b where b is the integer you chose in part (d)
The first 8 terms of the sequence are 12, 16, 22, 30, 40, 52, 66, 82 respectively.
(a) The first 8 terms of the sequence are as follows:
a1 = 1 + (1^2) + (2^3) + 2 = 12
a2 = 1 + (2^2) + (2^3) + 3 = 16
a3 = 1 + (3^2) + (2^3) + 4 = 22
a4 = 1 + (4^2) + (2^3) + 5 = 30
a5 = 1 + (5^2) + (2^3) + 6 = 40
a6 = 1 + (6^2) + (2^3) + 7 = 52
a7 = 1 + (7^2) + (2^3) + 8 = 66
a8 = 1 + (8^2) + (2^3) + 9 = 82
(b) Observing the values of a1, a2, a3, a4, and so on, we can see that an > 4n for all n ≥ 3. Hence, a = 3.
(c) We will prove the statement "an > 4n for all integers n ≥ a" using strong induction.
Base case (n=3): a3 = 28 and 28 > 4 * 3 = 12, which is true.
Inductive step: Suppose an > 4n for all integers n = k (k ≥ 3). We need to show that a(k+1) > 4(k+1).
a(k+1) = 1 + (k+1)^2 + (2^3) + (k+1) = 1 + (k^2 + 2k + 1) + (2^3) + (k+1) = an + 2k + 3 > 4k + 3 = 4(k+1)
(d) Observing the values of a1, a2, a3, a4, and so on, we can see that an > 45 for all n ≥ 7. Hence, b = 7.
(e) We will prove the statement "an > 5n for all integers n ≥ b" using strong induction.
Base case (n=7): a7 = 120 and 120 > 7 * 5 = 35, which is true.
Inductive step: Suppose an > 5n for all integers n = k (k ≥ 7). We need to show that a(k+1) > 5(k+1).
a(k+1) = 1 + (k+1)^2 + (2^3) + (k+1) = 1 + (k^2 + 2k + 1) + (2^3) + (k+1) = an + 2k + 3 > 5k + 3 = 5(k+1)
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suppose a university has only one women's softball scholarship remaining for the coming year. the final two players that the university is considering are allison fraley and emily janson. the coaching staff has concluded that the speed and defensive skills are virtually identical for the two players, and that the final decision will be based on which player has the best batting average. cross tabulations of each player's batting performance in their junior and senior years of high school are as follows. outcome allison feeley junior senior hit 15 76 no hit 25 175 total at-bats 40 251 outcome emily janson junior senior hit 71 35 no hit 130 85 total at-bats 201 120 a player's batting average is computed by dividing the number of hits a player has by the total number of at-bats. batting averages are represented as a decimal number with three places after the decimal. (round your answers to three decimal places.) (a) calculate the batting average for each player in her junior year. allison feeley emily janson calculate the batting average of each player in her senior year. allison fealey emily janson using this analysis, which player should be awarded the scholarship? explain. because ---select--- had the higher batting average in both her junior year and senior year, ---select--- should receive the scholarship offer. (b) combine or aggregate the data for the junior and senior years into one crosstabulation. outcome player fealey janson hit no hit total at-bats calculate each player's batting average for the combined two years. (round your answers to three decimal places.) allison fealey emily janson using this analysis, which player should be awarded the scholarship? explain. because ---select--- has the higher batting average over the combined junior and senior years, ---select--- should receive the scholarship offer. (c) are the recommendations you made in parts (a) and (b) consistent? explain any apparent inconsistencies. the recommendations in parts (a) and (b) ---select--- consistent. this is an example of ---select--- . it shows that in interpreting the results based upon separate or un-aggregated crosstabulations, the conclusion can be ---select--- when the crosstabulations are grouped or aggregated.
The recommendations in parts (a) and (b) are not consistent. This is the best example of Simpson’s Paradox.
(a) Allison Feeley's junior year batting average: 15/40 = 0.375 Emily Janson's junior year batting average: 71/201 = 0.353 Allison Feeley's senior year batting average: 76/251 = 0.302 Emily Janson's senior year batting average: 35/120 = 0.292
Using this analysis, Allison Feeley should be awarded the scholarship, as she has the higher batting average in both her junior and senior years.
(b) Outcome: Player | Hit | No Hit | Total At-Bats Fealey | 91 | 200 | 291 Janson | 106 | 215 | 321
Allison Fealey's combined two years batting average: 91/291 = 0.313 Emily Janson's combined two years batting average: 106/321 = 0.331
Using this analysis, Emily Janson should be awarded the scholarship, as she has the higher batting average over the combined junior and senior years.
(c) The recommendations in parts (a) and (b) are not consistent. This is an example of Simpson's Paradox, it shows that in interpreting the results based upon separate or un-aggregated crosstabulations, the conclusion can be different when the crosstabulations are grouped or aggregated.
Therefore, [a] and [b] are not consistent according to Simpson’s Paradox.
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The recommendations in parts (a) and (b) are not consistent. This is the best example of Simpson’s Paradox.
a) Allison Feeley's junior year batting average: 15/40 = 0.375 Emily Janson's junior year batting average: 71/201 = 0.353 Allison Feeley's senior year batting average: 76/251 = 0.302 Emily Janson's senior year batting average: 35/120 = 0.292
Using this analysis, Allison Feeley should be awarded the scholarship, as she has the higher batting average in both her junior and senior years.
(b) Outcome: Player | Hit | No Hit | Total At-Bats Fealey | 91 | 200 | 291 Janson | 106 | 215 | 321
Allison Fealey's combined two years batting average: 91/291 = 0.313 Emily Janson's combined two years batting average: 106/321 = 0.331
Using this analysis, Emily Janson should be awarded the scholarship, as she has the higher batting average over the combined junior and senior years.
(c) The recommendations in parts (a) and (b) are not consistent. This is an example of Simpson's Paradox, it shows that in interpreting the results based upon separate or un-aggregated crosstabulations, the conclusion can be different when the crosstabulations are grouped or aggregated.
Therefore, [a] and [b] are not consistent according to Simpson’s Paradox.
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4. The isosceles triangle shown has congruent side lengths of 12 cm and a base of 10 cm.
What is the height of the triangle?
The height of the triangle which is also called the altitude is; 6.63 cm
How to use Pythagoras Theorem?The triangle is an Isosceles Triangle that has two congruent sides and we have the parameters as;
Length of congruent sides = 12 cm.
Base length = 10 cm
Half of the base will be 5 cm and as such, we can use the Pythagorean Theorem to find the altitude as;
Altitude² = Hypotenuse² - Base length²
Thus;
A² = 12² - 10²
A = √44
A ≈ 6.63 cm
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These base-10 blocks model 68.
Which answer shows how to correctly rearrange the blocks to find the quotient 68 ÷ 7?
There will be 9 columns which each has 9 blocks and the 10th column will be 5 blocks. Then the correct option is D.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ 68 ÷ 7
Simplify the expression, then we have
⇒ 68 ÷ 7
⇒ (63 + 5) / 7
⇒ 63 / 7 + 5 / 7
⇒ 9 + 5/7
There will be 9 columns which each has 9 blocks and the 10th column will be 5 blocks. Then the correct option is D.
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The last D option is missing. The option D is given as,
D. 9 columns which each has 9 blocks and the 10th column will be 5 blocks.
Write an inequality involving absolute value for the graph. Find the point that is the same distance from 2 as it is from 4.
The inequality involving absolute value is 2 < x < 4 and the graph is attached below.
The term called inequality in math is defined as when two real numbers or two algebraic expressions are represented with symbols like <, > or ≤, ≥.
Here we need to find the inequality involving absolute value for the graph. And here we also need to find the point that is the same distance from 2 as it is from 4.
Here we have consider that x be the number that the inequality is formed than it can be written as
=> 2 < x < 4
And the graph of the inequality is plotted and attached below.
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A rectangle has a length of 9 centimeters. The width of the rectangle is 4 centimeters. What is the area of the rectangle?
Answer:
36 cm²
Step-by-step explanation:
Area=Length*Width
so... 9*4 = 36
36 cm²
The width of a rectangular garden is 4 meters less than 2 times the length. The area of the garden is 6 square meters. Which is the function to find the dimensions of the the garden?
a) 2l^2−4l−6=0
b) 2w^2+4w+6=0
c) 2w^2+4w−6=0
d) 2l^2−4l+6=0
The dimensions of the the garden are 8 x 12
What is Quadratic Equation?
The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" is for the absolute term of f. (x).
A = l x w
l = 2w-4
A = w (2w-4)
A = 2w² -4w
96m² = 2w² - 4w
0 = 2w² - 4w - 96 divide both sides by 2
0 = w² - 2w -48
(w-8) ( w +6) = 0
w = 8 since it can't equal -6
length therefore = 2w-4 = 16-4 = 12
Hence, the dimensions of the garden are 8 x 12
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Full question:
A rectangular garden has a length that is 4 meters less than twice its width. Can you set up a quadratic equation to find the dimensions of the garden if its area is 96m^2?
Mrs. Everett, the P.E. teacher, is pairing off students to race against each other. Antonio can run 8 meters per second, and Devin can run 9 meters per second. Mrs. Everett decides to give Antonio a head start of 50 meters since he runs more slowly. Once the students start running, Devin will quickly catch up to Antonio. How long will that take?
Write a system of equations, graph them, and type the solution.
The time it took for Devin to catch Antonio is given as follows:
50 seconds.
How to model the situation?The position functions for each of Antonio and Devin can be modeled by linear functions in slope-intercept format, as follows:
y = mx + b.
In which:
The slope m represents the velocity.The intercept b represents the initial position.Antonio starts 50 meters in front of Devin, hence the functions, considering their velocities, are given as follows:
A(x) = 50 + 8x.D(x) = 9x.(these two equations compose the system of equations).
Devin will catch up to Antonio when:
D(x) = A(x).
Hence:
9x = 50 + 8x
x = 50 seconds.
(which is shown by the point of intersection of the graph).
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A software company in Morristown used to bill clients $160 per hour for work done by its consultants.
The company recently adjusted its rates and now charges 5% less. What is the new billing rate?
Answer:
$152
Step-by-step explanation:
160*.95 = 152
Tyee was driving down a road and after 2 hours he had traveled 54 miles. At this speed, how many miles could Tyee travel in 8 hours?
The number of miles that Tyee will travel in 8 hours, given the speed is 216 miles
How to find the miles driven ?To find the number of miles that Tyree would drive in 8 hours, given the speed he is going, you first need to find the speed Tyree is going which is:
= Number of miles travelled / Number of hours
= 54 / 2
= 27 miles per hour
The number of miles that Tyree would travel in 8 hours is:
= Number of hours of travelling x Speed travelled
= 8 x 27
= 216 miles
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Someone i having a wedding, and they need champagne bottle. The bottle are 25.4 oz, the glae are 6 oz a peron, and there are going to be 80 guet. How many champagne bottle are going to be needed to erve all the guet?
The total number of ounces needed to serve all guests (6 oz/guest * 80 guests) and then divide that number by the size of the bottle (25.4 oz) to get the total number of bottles needed.
In order to calculate the number of champagne bottles needed to serve all 80 guests, we need to use the formula for calculating the total number of ounces needed. The formula is: Number of bottles * size of bottle + total ounces of glasses * number of guests. In this case, the number of bottles needed is: (6 oz/guest * 80 guests)/25.4 oz bottle = 18.9 bottles. Therefore, 19 champagne bottles will be needed to serve all 80 guests. This is because each bottle holds 25.4 ounces and each guest needs 6 ounces of champagne, so we need to calculate the total number of ounces needed to serve all guests (6 oz/guest * 80 guests) and then divide that number by the size of the bottle (25.4 oz) to get the total number of bottles needed.
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Match the name of the number property used to get to each step from the previous step.
[-5 + (1/2 + 5)] · 2
commutative property
associative property
inverse property of multiplication
identity property of addition
inverse property of addition
NEED ASAP!
The name of the number property matched below with each step from the previous step.
What is the commutative property of addition?The commutative property of addition:
Let a and b are numbers.
a + b = b + a
The change in the position of two numbers in an addition operation does not change the sum.
Given:
We have an expression,
[-5 + (1/2 + 5)] × 2
Applying commutative property of addition,
= [-5 + (5 + 1/2)] × 2
= [ (-5 + 5) + 1/2] × 2
Applying inverse property of addition,
= [0 + 1/2] × 2
Applying identity property of addition,
= 1/2 x 2
Applying inverse property of multiplication,
= 1
Therefore, the solution is 1.
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9/3 x + 4 + 2x ?????
Answer:
5x + 4
Step-by-step explanation:
Base on the given:
[tex]\mathrm{\frac{9}{3}x+4+2x}[/tex] → Divide 9 by 3. 9 ÷ 3 = 3
[tex]\mathrm{3x+4+2x}[/tex] → Combine similar term {2x + 3x = 5x}
No farther can be simplify. Hence, 5x + 4 is the answer.
RevyBreeze
For the function f(x)= 3x-5 find f(3)+10
Answer:
14
Step-by-step explanation:
f(3) = 3(3) - 5 + 10
f(3) = 9 - 5 + 10
f(3) = 4 + 10
f(3) = 14
Answer:
14
Step-by-step explanation:
Start by finding f(3), which would include plugging in a 3 everywhere you see an x
f(3) = 3(3)-5
f(3) = 9-5
f(3) = 4
Now we can use f(3)+10 because we know what f(3) is, it's 4. So replacing it
f(3) + 10 is now 4+10, which equals 14
[tex]x^{2} +22x[/tex]
The solution for the expression when x= 3 is 75
How to determine the solution for the expressionFrom the question, we have the following expression that can be used in our computation:
x² + 22x
Also from the question, we have
x = 3
This means that the value of x is 3, and we calculate the value of the expression
Substitute the known values in the above equation, so, we have the following representation
x² + 22x = 3² + 22 * 3
Evaluate
x² + 22x = 75
Hence, the solution is 75
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Possible question
Given x² + 22x, calculate the value when x = 3
RIGHT ANSWER GETS 10 POINTS
In the figure below, angle y and angle x form vertical angles. Angle y forms a straight line with the 60° angle and the 70° angle.
A straight line is shown and is marked with three angles. The first angle measures 60 degrees. The second angle measures 60 degrees. The third angle is labeled y. The line between the 70 degree angle and angle y extends below the straight line. The angle formed is labeled angle x.
Write and solve an equation to determine the measure of angle x. (5 points)
Your answer:
The equation x + (60 + 70)° = 180° is used to solve for the measure of the vertical angle x = 50°
What are vertically opposite anglesVertical angles also called vertically opposite angles are formed when two lines intersect each other, the opposite angles formed by these lines are vertically opposite angles and are equal to each other.
The angle y and x form vertical angles, so x = y
Angle y form a straight line with 60° and 70° so we have the equation to solve for x as:
x + 60° + 70° = 180° {sum of angles on a straight line}
x + 130° = 180°
x = 180° - 130° {subtract 139° from both sides}
x = 50°
Therefore, the measure of the vertical angle x is equal to 50° derived with the equation x + (60° + 70°) = 180°.
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questions, You must show work to
Which correctly explains the number of solutions of the following system of linear
equations?
-3x + 3y = 12
y=x+4
A
The graphs of the equations are parallel lines because they have the same slope
but different y-intercepts. The system has no solution.
B
The graphs of the equations are lines that intersect at one point because
equations have the same slope but different y-intercepts. The system has
exactly one solution.
C The graphs of the equations are lines that intersect at one point because the
equations have the same slope and same y-intercept. The system has exactiy
one solution.
D The graphs of the equations are the same line because the equations have
same slope and same y-intercept. The system has infinitely many solutions.
Answer:
Step-by-step explanation:
from the first ... 3y = 3x + 12 or
y = x + 4
This is the same as the second, so D
What percent of 102 is 17
Answer:
16.6666666666667%
Step-by-step explanation:
17/102 = x/100
17*100/102 = x
x = 16.66666667
Answer:
The percent is:
16.667%
Step-by-step explanation:
17 / 102 = 0.16667
0.16667 * 100 = 16.667%
Graph the function for the given domain.
Answer: x=2
Step-by-step explanation:
One quarter of this pie chart is blue.
15% is orange.
Yellow
Grey
Blue
are some number cards.
Orange
What percentage is blue or orange?
The other two sections are equal in size.
What percentage of the whole chart is yellow?
I
As per the given equation, the percentage of the whole chart that is yellow is 15%.
How to find the percentage of whole chart yellowed?One quarter of the pie chart is blue, which is 25%.
15% of the pie chart is orange.
When we add the percentages of blue and orange sections, we get 25% + 15% = 40%. So, 40% of the pie chart is blue or orange.
As the other two sections, Yellow and Grey, are equal in size, we can assume that they make up half of the remaining 60% of the pie chart. So each of the Yellow and Grey sections make up 30%/2 = 15% of the pie chart.
Therefore, the percentage of the whole chart that is yellow is 15%.
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on an architects blueprint, 1 inch corresponds to 2 feet. Find the length of a wall represented by a line 4 and 1/2 inches long on the blueprint
The graph shown here is the graph of which of the following rational
functions?
-10
10
FOO
10
O A. F(X) = (2+1)(²-3)
B. F(x) = (z+1)(x-2)(z-3)
D-2
O C. F(x) = (2-1)(x+3)
According to the graph the rational function represented in the graph is [tex]F(x) = \frac{x-2}{(x+1 )(x-3)}[/tex], and option A is correct answer.
What is vertical asymptote?At the margins of the coordinate plane, the curve approaches lines known as asymptotes. When the denominator of such a rational function gets close to zero, vertical asymptotes happen. Since it would divide by zero, a rational function never traverse a vertical asymptote. A graph's vertical asymptote is a vertical line with the equation x=a, where the graph tends to positive or negative infinity as the inputs go closer to a.
For the given graph we can see that the vertical asymptotes are -1 and 3, and there is no horizontal asymptote.
In option A:
[tex]F(x) = \frac{x-2}{(x+1 )(x-3)}[/tex]
The horizontal asymptote is none.
The vertical asymptote is -1 and 3.
Hence, this is the correct option.
Option B:
[tex]F(x) = \frac{1}{(x-2)(x+1 )(x-3)}[/tex]
The horizontal asymptote is 0.
The vertical asymptote is 2, -1 , and 3.
Hence, option B is incorrect.
Option C:
[tex]F(x) = \frac{x-2}{(x-1 )(x+3)}[/tex]
The horizontal asymptote is none.
The vertical asymptote is 1 and -3.
Hence, option C is incorrect.
Hence, according to the graph the rational function represented in the graph is [tex]F(x) = \frac{x-2}{(x+1 )(x-3)}[/tex], and option A is correct answer.
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Chapter 8 review tesyremember a builder has an 8acre plot divided into 1/4 acre home sites. How many 1/4 acre home sites are there? this is in your test
There are 32 home sites on the 8-acre plot.
An acre, a standard unit of measurement used by land sellers, is roughly the same size as a typical football field. An acre is a product of any rectangular land plot with a total area of 4,046 square Metre, or 43,560 square feet. Six plots of 6 x 120 feet each make up an acre.
To find out how many 1/4 acre home sites are on the 8-acre plot, you can divide the total number of acres by the number of acres per home site.
8 acres / 0.25 acres/home site = 32 home sites.
So, there are 32 home sites on the 8-acre plot.
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8th grade math the function f=18g describes the distance d that rick can drive his truck on g gallons of gasolie. Grph this function in the upper right quadrant only
The distance travelled by rick on 2.5 gallons of gasoline is calculated to be 45 mi.
The given function can be written as d = 18 g , where, d is the distance and g is gasoline.
It is also said that, gasoline g = 2.5 gallons
So, to calculate the distance travelled by rick, we should place the value of g in the equation above.
d = 18 g = 18(2.5) = 45 mi
From the graph, the maximum possible gasoline is 10. So, when we place in the above equation, we have,
d = 18 g = 18(10) = 180 gallons
As, the both quantities on the x-axis and y-axis are positive, the graph is possible in first quadrant only.
The given question is incomplete. The complete question is 'How far can rick drive on 2.5 gallons of gasoline?' The picture of graph is attached in the attachment below.
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- What do you think would happen to the area of a figure if one of its dimensions is quadrupled?
- What do you think would happen to the area of a figure if one of its dimensions is multiplied by 5?
answer:
1.the total area is quadrupled.
2.(I'm not sure, so sorry!!!!!)
Step-by-step explanation:
somsome else can do number 2 because questions on brainly have a max of 2 answers.... again, so sorry.
Step-by-step explanation:
If one dimension of a figure is quadrupled, its area would increase by a factor of 16 (2 to the power of 4). If one dimension is multiplied by 5, the area would increase by a factor of 25 (5 to the power of 2).
The function h = 3d models the height, in centimeters, of a corn plant as a function of days after sprouting, for 0 < d <7.
The slope of the function represents
The slope of the Function represents the change in height per day.
A line's slope in mathematics is defined as the ratio of the change in the y coordinates to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.
Consequently, the formula for the change in the y-coordinate with respect to the change in the x-coordinate is
[tex]m=\frac{dy}{dx}[/tex] = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line can be shown as
tan θ = Δy/Δx
So, the slope of a line is tanΘ.
So as slope represents a change in y per change in x, in the given question as y is height and x is days, slope changes in height per day.
The slope of the Function represents the change in height per day.
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A cylinder has a height of 6 in. and a radius of 8 in.
How does the cylinder's lateral area compare to the sum of the areas of the two bases?
Use π≈3.14.
Enter your answer rounded to the nearest tenth in the box to correctly complete the statement.
The lateral area of the cylinder is approximately
square inches less than the sum of the areas of the two bases.
Answer:
see below
Step-by-step explanation:
h = 6
r = 8 ==> area = πr² = 3.14*8² = 3.14 *64 =201.0
top & bottom = 2*200.96 = 401.9
r=8 ==> perimeter = 2πr = 2*3.14 *8 = 16* 3.14 =50.2
lateral area = h*perimeter = 6*50.24 = 301.44
so it's about 100 sq inch less