a.The velocity function is: v = ds/dt = (2/5)t^(5/2) - 6t^(1/2) + 16.
b. The position function is: s = (4/35)t^(7/2) - 8t^(3/2) + 16t - 12.
a. To find the velocity, we need to integrate the acceleration function. We get:
v = ds/dt = ∫a dt = ∫(15√t - 3/t^(1/2)) dt
Integrating the first term, we get (2/5)t^(5/2), and integrating the second term, we get -6t^(1/2) + C. Thus, the velocity function is:
v = ds/dt = (2/5)t^(5/2) - 6t^(1/2) + C
We can find the constant C using the initial condition that ds/dt = 4 when t = 1. Substituting these values into the equation, we get:
4 = (2/5)(1)^(5/2) - 6(1)^(1/2) + C
C = 4 + 12 = 16
Therefore, the velocity function is:
v = ds/dt = (2/5)t^(5/2) - 6t^(1/2) + 16
b. To find the position function, we need to integrate the velocity function. We get:
s = ∫v dt = ∫((2/5)t^(5/2) - 6t^(1/2) + 16) dt
Integrating the first term, we get (4/35)t^(7/2), integrating the second term, we get -8t^(3/2), and integrating the third term, we get 16t. Thus, the position function is:
s = ∫v dt = (4/35)t^(7/2) - 8t^(3/2) + 16t + C2
We can find the constant C2 using the initial condition that s = 0 when t = 1. Substituting these values into the equation, we get:
0 = (4/35)(1)^(7/2) - 8(1)^(3/2) + 16(1) + C2
C2 = -12
Therefore, the position function is:
s = (4/35)t^(7/2) - 8t^(3/2) + 16t - 12
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Which of the following groups listed below is a subset of the whole numbers?
Rational Numbers
Real Numbers
Natural Numbers
Irrational Numbers
Integers
The group of natural numbers is a subset of the whole numbers.
What is Whole number ?
Whole numbers are a set of numbers that includes all positive integers (1, 2, 3, ...) and zero (0). They do not include negative numbers or fractions. Whole numbers are often used to count objects or represent quantities that cannot be divided into smaller parts.
Out of the given options, the group of natural numbers is the only one that is a subset of whole numbers. The other options - Rational numbers, Real numbers, Irrational numbers, and Integers - are not subsets of the whole numbers.
Rational numbers include fractions and decimal numbers, which can be expressed as a ratio of two integers, including non-whole numbers.
Real numbers include all rational and irrational numbers, including non-whole numbers. Irrational numbers are non-repeating, non-terminating decimals that cannot be expressed as a fraction. Integers include both positive and negative whole numbers, as well as zero.
The subset of whole numbers is called natural numbers.
Therefore, the group of natural numbers is a subset of the whole numbers.
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Arturo has completed 27 math problems, which is 75% of the assignment. How many problems total did he have to complete?
I need help!
The total number of problems he solved is 36 if after completion of 27 problems he has completed 75% of the assignments.
Percentage of completion = 75 % of the work
The percentage can be converted to decimal by dividing the percentage by 100.
Thus, the part that has been completed = 75% = 0.75 of the work
The number of questions done = 27
Let the total number of questions be x
Thus, 75% of x is given as 27
75% of x = 27
0.75 * x = 27
0.75x = 27
x = 27/0.75
x = 36
Thus, the total number of questions is 36.
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this table shows incidence rates (per 100,000) of groups exposed to neither risk factors or to one or two risk factors for lung cancer. what is the expected value of incidence rate x on asbestos exposure group among smokers in multiplicative scale?
The correct response is 12, as finding the predicted smoking and asbestos exposure group requires finding x, and in that case, the ratios in the rows and columns are equal.
4/2 = x/6 Or 6/2= x/4
This suggests that x = 12.
Smoking refers to the act of inhaling and exhaling the smoke produced by burning tobacco or other substances such as marijuana or hookah. It is a highly addictive habit that poses significant health risks to both smokers and those exposed to secondhand smoke. Smoking can lead to a variety of illnesses and diseases, including lung cancer, heart disease, stroke, chronic obstructive pulmonary disease (COPD), and various other cancers. It is estimated that smoking is responsible for nearly 8 million deaths globally each year.
The chemicals in tobacco smoke can also harm the environment, contributing to air pollution and litter. Despite the well-known risks associated with smoking, many people continue to smoke due to addiction, peer pressure, or a lack of understanding about the long-term consequences.
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Polygon JKLM is drawn with vertices J(−2, −5), K(−4, 0), L(−1, 2), M (0, −1). Determine the image coordinates of K′ if the preimage is translated 6 units up.
A. K′(−10, 0)
B. K′(−4, −6)
C. K′(−4, 6)
D. K′(2, 0)
The coordinates of the images after the translation are K' (-4, 6).
Finding the coordinates of the image of points K'To find the image coordinates of K', we need to translate the coordinates of K 6 units up.
This can be done by adding 6 to the y-coordinate of K.
So, the y-coordinate of K' will be:
y-coordinate of K' = y-coordinate of K + 6
= 0 + 6
= 6
To find the x-coordinate of K', we just need to keep the x-coordinate of K the same, since the translation is only in the vertical direction.
Therefore, the image coordinates of K' are (-4, 6).
So, the correct answer is C. K′(−4, 6).
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For the differential equation
s′′+bs′+6s=0,
find the values of b that make the general solution overdamped, underdamped, or critically damped.
(For each, give an interval or intervals for b for which the equation is as indicated. Thus if the the equation is overdamped for all b in the range −1
If the equation is overdamped, b∈
If the equation is underdamped, b∈
If the equation is critically damped, b∈
- If the equation is overdamped, b ∈ (-∞, -2√6) ∪ (2√6, ∞).
- If the equation is underdamped, b ∈ (-2√6, 2√6).
- If the equation is critically damped, b ∈ {-2√6, 2√6}.
To determine the behavior of the solution for the given differential equation s′′ + bs′ + 6s = 0, we need to analyze the roots of the characteristic equation:
r^2 + br + 6 = 0
For this quadratic equation, the discriminant Δ is given by:
Δ = b^2 - 4(1)(6) = b^2 - 24
The behavior of the solution depends on the value of Δ:
1. Overdamped: If Δ > 0, the solution will be overdamped.
2. Underdamped: If Δ < 0, the solution will be underdamped.
3. Critically damped: If Δ = 0, the solution will be critically damped.
Now, we find the intervals of b for each case:
1. Overdamped (Δ > 0):
b^2 - 24 > 0
This inequality holds for b ∈ (-∞, -2√6) ∪ (2√6, ∞).
2. Underdamped (Δ < 0):
b^2 - 24 < 0
This inequality holds for b ∈ (-2√6, 2√6).
3. Critically damped (Δ = 0):
b^2 - 24 = 0
This equation holds for b = -2√6 and b = 2√6.
In conclusion:
- If the equation is overdamped, b ∈ (-∞, -2√6) ∪ (2√6, ∞).
- If the equation is underdamped, b ∈ (-2√6, 2√6).
- If the equation is critically damped, b ∈ {-2√6, 2√6}.
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If a cone with a volume of 6 cm3 is enlarged by a scale factor of 2, what is the volume, in cubic centimeters, of the similar, larger cone?
The volume of the larger cone will be 48 cm³.
This is because when a shape is enlarged by a scale factor of 2, the volume is increased by a factor of 2³ (or 8). So, 6 x 8 = 48.
When we enlarge a shape by a scale factor, we are multiplying all of its dimensions by that factor. In the case of a cone, this means that we are increasing the radius and the height of the cone by a factor of 2.
We can use the formula for the volume of a cone to find out how the volume changes when we enlarge it. The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius and h is the height.
If we multiply the radius and the height of the cone by 2, we get a new cone with a radius of 2r and a height of 2h. Plugging these new values into the formula for the volume of a cone, we get:
V' = (1/3)π(2r)²(2h) = (1/3)π(4r²)(2h) = (8/3)πr²h
We can simplify this expression by multiplying the original volume by 8/3:
V' = (8/3) x 6 = 48
So the volume of the larger cone is 48 cubic centimeters.
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Point A is located at (−2, 2), and point M is located at (1, 0). If point M is the midpoint of segment AB, find the location of point B.
(−0. 5, 1)
(4, −2)
(−5, 4)
(−1, 1)
The location of point B is (4, −2). So the answer is (4, −2).
How to find the location of the point B?To find the location of point B, we can use the midpoint formula, which states that the coordinates of the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) are:
((x1 + x2)/2, (y1 + y2)/2)
In this case, we know that point M is the midpoint of segment AB, and we know the coordinates of point M. We also know the coordinates of point A. So we can use the midpoint formula to solve for the coordinates of point B.
Let's call the coordinates of point B (x, y). We know that point M is the midpoint of segment AB, so we can set up the following equation:
((−2 + x)/2, (2 + y)/2) = (1, 0)
Simplifying this equation, we get:
(−2 + x)/2 = 1 and (2 + y)/2 = 0
Solving for x and y, we get:
x = 4 and y = −2
Therefore, the location of point B is (4, −2). So the answer is (4, −2).
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A model rocket is show from ground level. The height h(t) in meters of the rocket t seconds
after lift-off is given by the equation h(t) - 160t - 16t?| What is the height of the rocket
after 2. 5 seconds?
To find the height of the rocket after 2.5 seconds,
you'll need to plug in t = 2.5 into the given equation h(t) = 160t - 16t².
h(2.5) = 160(2.5) - 16(2.5)²
h(2.5) = 400 - 100
h(2.5) = 300 meters
The height of the rocket after 2.5 seconds is 300 meters.
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Y’all pls help this is due tmrwww
Step-by-step explanation:
1kL = 100 dal
x = 470 dal .... you will criss cross it
1 kl × 470 dal = x ×100dal
470 dal kl = 100dal x ... then you will divide 100 dal from both side
4.7 kl = x
x = 4.7 kl
so our result is 4.7kl which is equal to 470 dal
Step-by-step explanation:
470 dal = 4.7 kl
because 1 kl = 100 dal
[tex] \frac{1}{x} = \frac{100}{470} \\ \\ 100x = 470 \\ x = \frac{470}{100} \\ x = 4.7[/tex]
#CMIIWLuis tiene una mochila de ruedas
que mide 3.5 pies de alto cuando se extiende el mango.Al hacer rodar
su mochila, la mano de Luis se
encuentra a 3 pies del suelo. ?Que ángulo forma su mochila con el suelo? Aproxima al grado más cercano
As a result, the angle formed by Luis's backpack and the ground is roughly 53 degrees (rounded to the nearest degree).
what is function ?A function in mathematics is a relationship between a set of potential outputs and a number of potential inputs, with the feature that each input is associated to only one possible output. It is a principle or set of guidelines that allots a different output value towards each input value. Equations, graphs, and tables are frequently used to depict functions in order to explain how the output changes as the input does. They are employed to express relationships between various quantities, such as the length of time it takes for an automobile to drive a certain distance or the height of an object in relation to its weight. The concept of a function is crucial to many departments of science and math, and it is widely applied in areas like engineering,
given
We can use trigonometry to determine the angle that Luis's backpack creates with the ground.
Consider the backpack's handle to represent the hypotenuse of a right triangle, with the vertical leg being Luis's hand's distance from the ground (3 feet) and the horizontal leg being the backpack's height (3.5 feet).
The angle can be determined using the inverse tangent function (tan-1):
53.13 degrees at tan-1(3.5/3)
As a result, the angle formed by Luis's backpack and the ground is roughly 53 degrees (rounded to the nearest degree).
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Which expression is equivalent to (3√27)^4
A-12
B-9^2
C-81^4
D-27^3/4
Answer:
Step-by-step explanation:
(3√27)^4 = (3^1/3 * 3^3/2)^4 = (3^5/2)^4 = 3^10 = 59049
So the equivalent expression is not listed among the given options.
A study is designed to test the hypotheses h0: m $ 26 versus ha: m , 26. a random sample of 50 units was selected from a specified population, and the measurements were summarized to y 5 25.9 and s 5 7.6. a. with a 5 .05, is there substantial evidence that the population mean is less than 26
The p-value for a t-score of -0.92 is approximately 0.18 and since it is greater than the significant level, the null hypothesis is rejected.
The first step in testing this hypothesis is to calculate the test statistic, which in this case is a t-score. The formula for the t-score is (y - mu) / (s / sqrt(n)), where y is the sample mean, mu is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
In this case, the sample mean is 25.9, the hypothesized population mean is 26, the sample standard deviation is 7.6, and the sample size is 50. Plugging these values into the formula, we get a t-score of -0.92.
Next, we need to find the p-value associated with this t-score. We can use a t-table or a calculator to do this. Using a t-table with 49 degrees of freedom (since we have a sample size of 50 and one parameter estimated from the sample), we find that the p-value for a t-score of -0.92 is approximately 0.18.
Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. In other words, we do not have substantial evidence to conclude that the population mean is less than 26. However, it is important to note that the sample mean is slightly below the hypothesized population mean, and the p-value is relatively close to the significance level. Therefore, it may be worthwhile to conduct additional studies with larger sample sizes or different populations to further investigate this question.
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In milling operations, the spindle speed S (in revolutions per minute) is directly related to the cutting speed C (in feet per minute) and inversely related to the tool diameter D (in inches). A milling cut taken with a 3-inch high-speed drill and a cutting speed of 70 feet per minute has a spindle speed of 88.2 revolutions per minute. What is the spindle speed for a cut taken with a 4-inch high-speed drill and a cutting speed of 30 feet per minute?
The spindle speed for a cut taken with a 4-inch high-speed drill and a cutting speed of 30 feet per minute is approximately 35.1 revolutions per minute.
Speed is a measure of how fast an object is moving. It is usually measured in units of distance per unit time, such as miles per hour or meters per second. Speed is an important concept in physics, engineering, and everyday life
We can use the formula for spindle speed that relates spindle speed to cutting speed and tool diameter:
S = (C × 12) / (π × D)
where S is spindle speed, C is cutting speed in feet per minute, D is tool diameter in inches, and π is the mathematical constant pi.
We know that for a 3-inch high-speed drill with a cutting speed of 70 feet per minute, the spindle speed is 88.2 revolutions per minute. We can use this information to solve for the constant of proportionality k:
88.2 = (70 × 12) / (π × 3)
k = 88.2 × (π × 3) / (70 × 12)
k ≈ 0.0039
Now we can use the value of k to find the spindle speed for a 4-inch high-speed drill with a cutting speed of 30 feet per minute:
S = k × C × 12 / D
S = 0.0039 × 30 × 12 / 4
S = 35.1
Therefore, the spindle speed for a cut taken with a 4-inch high-speed drill and a cutting speed of 30 feet per minute is approximately 35.1 revolutions per minute.
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Josh lit a 14-inch candle. She noticed that it was getting an inch shorter every 30 minutes. Let x be the number of hours and y be the total height of the candle
The height of the candle after x hours is given by the equation y = 2x + 14.
Let's first convert the time interval to hours. There are 60 minutes in an hour, so 30 minutes is equivalent to 0.5 hours.
After x hours, the candle will have burned down by 2x inches (since it burns 1 inch every 0.5 hours).
If y is the total height of the candle, then we can write the equation:
y - 2x = 14
We can solve for y:
y = 2x + 14
So the height of the candle after x hours is given by the equation y = 2x + 14.
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Select the correct answer.
Using long division, what is the quotient of 3z + 20z³ + 14x² + 17x + 30 and +6?
OA 32:³ 2x² + 2x - 5
О в.
OC.
OD. 3z² + 2x + 2
22³ + 142² + 17z + 30
3z³ + 2z² + 2x + 5
Reset
Next
The quotient of the division 3x⁴ + 20x³ + 14x² + 17x + 30 ÷ x + 6 is 3x³ + 2x² + 6x - 19
Evaluating the long division expressionsThe quotient expression is given as
3x⁴ + 20x³ + 14x² + 17x + 30 ÷ x + 6
The long division expression is represented as
x + 6 | 3x⁴ + 20x³ + 14x² + 17x + 30
So, we have the following division process
3x³ + 2x² + 6x - 19
x + 6 | 3x⁴ + 20x³ + 14x² + 17x + 30
3x⁴ + 18x³
--------------------------------
2x³ + 14x² + 17x + 30
2x³ + 12x²
-------------------------------------
6x² + 17x + 30
6x² + 36x
-------------------------------------
-19x + 30
-19x - 114
-------------------------------------
134
Hence, the quotient of the long division is 3x³ + 2x² + 6x - 19
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The answer should be
2x³ + 14x² + 17x + 30
Last week Deion ran a total of 32 miles. This week, he increased his running distance by 6. 4 miles. By what percentage did he increase the distance he ran? Please help waaaaaa
Deion increased the distance he ran by 20%.
To discover the percentage increase within the distance Deion ran, we need to first calculate the amount of increase.
The increase in distance that Deion ran this week compared to final week is:
6.4 miles
To find the proportion increase, we need to divide the increase by means of the original value (the distance he ran last week),
Then multiply by using a hundred to express the result as a percent.
The original price (last week's distance) is:
32 miles
Therefore, the percentage increase within the distance he ran is:
(6.4 miles / 32 miles) x 100% = 20%
So, Deion increased the distance he ran by 20%.
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Tell whether the given value is the solution of the inequality
The solution to the inequality given is false.
Why is the solution false ?To determine whether x = 5 is a solution of the inequality x + 3 > 12, we substitute x = 5 into the inequality and see if the resulting statement is true or false:
5 + 3 > 12
8 > 12
In this case, when we substitute x = 5 into the inequality, we get the statement 5 + 3 > 12, which simplifies to 8 > 12. This statement is false, since 8 is not greater than 12. Therefore, x = 5 is not a solution of the inequality x + 3 > 12.
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The full question is:
Tell whether the given value is a solution of the inequality X + 3 > 12; x = 5
Kira paid $15. 60 for 19. 5 centimeters of wire.
Find the unit price in dollars per centimeter.
If necessary, round your answer to the nearest cent.
HELP PLEASE!!! ASAP!!!
The unit price in dollars per centimeter is 80 cents.
:: Total wire length = 19.5 cm
:: Total amount paid = $15.60
Per unit price = [ (total amount paid) / (total wire length) ]
Per unit price = (15.60 / 19.5) $/cm
Per unit price = 0.8 ($/cm)
And as we know, $1 = 100 cents,
So,
$0.8 = 0.8 x 100 cents = 80 cents.
Therefore, the unit price in dollars per centimeter is 80 cents.
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NEED ASAP!
MATH I NEED TO PASS!!
Answer:
Step-by-step explanation:
Find area of all shapes and add
A(biggest rectangle) = Lw = 6*3 =18 there are 2 of those A=36
A(long skinny rectangle = Lw = 2*6 =12 there are 2 of those A=24
A(smallest) = Lw = 2*3=6 there are 2 of those A=12
Add it all up
A=36+24+12 = 72
I checked it 5 times. I keep getting 72
Cory and Dalia like to buy fruit at the farmers’ market on Sundays. One Sunday, Cory bought 4 apples and 6 oranges and paid $5.10. Dalia bought 2 apples and 5 oranges and paid $3.65.
What is the cost of 2 oranges?
Write the answer as a decimal to 2 places
The cost of two oranges is 1.1 dollars.
How to find the cost of two oranges?One Sunday, Cory bought 4 apples and 6 oranges and paid $5.10. Dalia bought 2 apples and 5 oranges and paid $3.65.
Therefore, using equation,
let
x = cost of each apples
y = cost of each oranges
Hence,
4x + 6y = 5.10
2x + 5y = 3.65
Multiply equation(ii) by 2
4x + 6y = 5.10
4x + 10y = 7.3
4y = 2.2
y = 2.2 / 4
y = 0.55 dollars
Therefore,
cost of 2 oranges = 0.55(2) = 1.1 dollars
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HELP match each one with either 1-4
Answer:
(4),(3),(1),(2),(2),(1)
Step-by-step explanation:
Mnemonic to memorize trigonometric ratios: SOH CAH TOA
(S=O/H C=A/H T=O/A)
Sine, Cosine, Tangent, Opposite to x, Adjacent to x, Hypotenuse
Cosecant = 1/Sine, Secant = 1/Cosine, Cotangent = 1/Tangent
Franklin is helping his aunt sew a lace border onto 2 quilts. Each quilt is 2. 2 meters wide by 2. 7 meters long. At the craft store, they buy a 20-meter roll of lace. To their surprise, they use up almost all of it. How many millimeters of lace do they have left after finishing the quilts?
The amount in millimeters of lace they have left after finishing the quilts is 400 millimeters.
Determine how much lace is needed for each quilt. Each quilt has a perimeter that we need to cover with lace. The perimeter is the sum of all sides of a rectangle, which is (2 x width) + (2 x length).
Each quilt is 2.2 meters wide and 2.7 meters long. So, the perimeter of one quilt is (2 x 2.2) + (2 x 2.7) = 4.4 + 5.4 = 9.8 meters.
Since there are 2 quilts, the total lace needed for both quilts is 9.8 meters x 2 = 19.6 meters.
They bought a 20-meter roll of lace. To find out how much lace is left, subtract the total lace used from the initial length of the roll: 20 meters - 19.6 meters = 0.4 meters.
To convert this to millimeters, multiply by 1,000: 0.4 meters x 1,000 = 400 millimeters.
So, Franklin and his aunt have 400 millimeters of lace left after finishing the quilts.
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Which is a solution to 2n = 16?
Answer:
3
Step-by-step explanation:
2x2=4
4x2=8
8x2=16
12 16 10 find d surface area of d solid
Sara drops a tennis ball and lets it bounce. She records the height of the ball after each of its bounces as an ordered pair, where x represents the number of bounces and y represents the height of the ball in inches. The ordered pairs she records are (1,8), (2,6), (3,2) and (4,1)
We can plot the points (1,8), (2,6), (3,2), and (4,1) on a graph by using a coordinate plane and the x and y-coordinates of each point.
To plot these points, we will use a coordinate plane, which is a two-dimensional graph with an x-axis and a y-axis. The x-axis represents the horizontal position, and the y-axis represents the vertical position. We will use the x-coordinate to determine the horizontal position of the point and the y-coordinate to determine the vertical position of the point.
For the first point, (1,8), we will start at the origin of the graph, which is the point (0,0). We will then move 1 unit to the right along the x-axis and 8 units up along the y-axis to plot the point.
For the second point, (2,6), we will start again at the origin and move 2 units to the right along the x-axis and 6 units up along the y-axis to plot the point.
We will repeat this process for the remaining points, (3,2) and (4,1), to plot all four points on the graph. Once all four points are plotted, we can connect them with a line to visualize the pattern of the ball's bounces.
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Complete Question:
Sara drops a tennis ball and lets it bounce. She records the height of the ball after each of its bounces as an ordered pair, where x represents the number of bounces and y represents the height of the ball in inches.
The ordered pairs she records are (1,8), (2,6), (3,2) and (4,1).
Plot the ordered points on the graph.
Ms. arrington has been raising money to take her classroom to the zoo. she has raised $580. the zoo has allowed all the adults to enter the zoo at a flat rate of $75 for all. if each student ticket costs $8.50, what is the maximum number of students allowed to attend the field trip?
The maximum number of students allowed to attend the field trip is 59.
To determine the maximum number of students allowed to attend the field trip, given the ticket cost and money raised, we'll need to follow these steps:
1. Subtract the adult ticket cost from the total money raised.
2. Divide the remaining amount by the cost of a student ticket.
Subtract the adult ticket cost from the total money raised.
$580 (money raised) - $75 (adult ticket cost) = $505 (remaining amount)
Divide the remaining amount by the cost of a student ticket.
$505 (remaining amount) / $8.50 (student ticket cost) = 59.41
Since we can't have a fraction of a student, we round down to the nearest whole number.
The maximum number of students allowed to attend the field trip is 59.
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Given the function g(a) = 6x^3 - 9x^2 - 36x, find the first derivative, g'(x).
The first derivative of g(a) is [tex]g'(x) = 18x^2 - 18x - 36.[/tex]
To find the first derivative of g(a), we need to use the power rule and the constant multiple rule.
First, we use the power rule to take the derivative of each term:
[tex]- The derivative of 6x^3 is 18x^2
- The derivative of -9x^2 is -18x
- The derivative of -36x is -36[/tex]
Next, we use the constant multiple rule to combine these derivatives:
g'(a) = 18x^2 - 18x - 36
Therefore, the first derivative of g(a) is [tex]g'(x) = 18x^2 - 18x - 36.[/tex]
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Robin records the height of her plant for 3 months. If the pattern continues, what algebraic expression can Robin use to find the plant's height for any month? What will the plants height be at 12 months
The plant's height at 12 months would be 38 inches.
How to calculate the height?Assuming the plant's height follows a linear pattern, Robin can use the equation y = mx + b, where y is the height of the plant, x is the number of months, m is the slope or rate of growth, and b is the y-intercept or initial height.
To find the equation, Robin can use the data from the three months:
Month 1: Height = 5 inchesMonth 2: Height = 8 inchesMonth 3: Height = 11 inchesUsing these data points, Robin can calculate the slope m:
m = (11-5)/(3-1) = 3 inches/month
Then, using the point-slope form of the equation, Robin can find the y-intercept b:
y - 5 = 3(x - 1)
y = 3x + 2
Therefore, the algebraic expression to find the plant's height for any month x is y = 3x + 2.
To find the plant's height at 12 months, Robin can substitute x = 12 into the equation:
y = 3(12) + 2 = 38 inches
So the plant's height at 12 months would be 38 inches.
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(co 4) from a random sample of 85 teens, it is found that on average they spend 31.8 hours each week online with a population standard deviation of 5.91 hours. what is the 90% confidence interval for the amount of time they spend online each week?
The 90% confidence interval for the amount of time that teens spend online each week is (30.761, 32.839) hours
To find the 90% confidence interval for the amount of time that teens spend online each week, we can use the following formula
CI = x ± z*(σ/√n)
where
x is the sample mean
σ is the population standard deviation
n is the sample size
z is the z-score associated with the desired confidence level
In this case, we have
x = 31.8 hours
σ = 5.91 hours
n = 85
z = 1.645 (for a 90% confidence level, using a z-table or calculator)
Plugging in these values, we get
CI = 31.8 ± 1.645*(5.91/√85)
Simplifying, we get
CI = 31.8 ± 1.039
We can interpret this interval as saying that if we were to take many random samples of 85 teens and compute the confidence interval for each sample, about 90% of these intervals would contain the true population mean.
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A spotlight is mounted on the eaves of a house 20 feet above the ground. A flower bed runs between the house and the sidewalk, so the closest the ladder can be placed to the house is 15 feet. How long a ladder is needed so that an electrician can reach the place where the light is mounted
Answer:
Step-by-step explanation:
We can use the Pythagorean theorem to solve this problem. Let's call the length of the ladder "L". The ladder, the wall of the house, and the ground form a right triangle. The distance between the ladder and the house is the base of the triangle, which is 15 feet. The height of the triangle is the distance from the ground to the spotlight, which is 20 feet. The length of the ladder is the hypotenuse of the triangle.
Using the Pythagorean theorem, we have:
L^2 = 15^2 + 20^2
L^2 = 225 + 400
L^2 = 625
L = sqrt(625)
L = 25
Therefore, a ladder of at least 25 feet is needed for the electrician to reach the place where the light is mounted.
