The volume of the cylinder is 18.0864 cubic cm and the surface area of the cylinder is 39.1872 square cm.
What is a cylinder?
One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry.
We are given that the radius of the cylinder is 1.2 cm and the height is 4 cm.
So,
⇒ Volume = π[tex]r^{2}[/tex]h
⇒ Volume = π * [tex](1.2)^{2}[/tex] * 4
⇒ Volume = 3.14 * 5.76
⇒ Volume = 18.0864 cubic cm
Similarly,
⇒ Total surface area = 2πrh + 2π[tex]r^{2}[/tex]
⇒ Total surface area = 2π * 1.2 * 4 + 2π[tex](1.2)^{2}[/tex]
⇒ Total surface area = 2π * 4.8 + 2π * 1.44
⇒ Total surface area = 2π * (4.8 + 1.44)
⇒ Total surface area = 2 * 3.14 * 6.24
⇒ Total surface area = 39.1872 square cm
Hence, the volume of the cylinder is 18.0864 cubic cm and the surface area of the cylinder is 39.1872 square cm.
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What is the interest rate for $1000 investment at 16% simple interest for 20 yrs?
So far this year, the average monthly revenue at the Springtown Times is 69,314. That is 30% less than the monthly average was last year l. What was the average last year?
Answer:
The average monthly revenue last year would be 99,020.
Step-by-step explanation:
69,314 = 70%
69,314 ÷ 70 = 990.2 (this equals one percent of the revenue)
990.2 × 100 = 99,020
99,020 = 100%
What would solving this proportion tell you?
Answer:
how many fluid ounsous you need
Step-by-step explanation:
The recursive formula for an arithmetic sequence is: What is the 3rd term in the sequence? A. –14 B. –2 C. –5 D. –24
The answer is not listed in the choices given. None of the answer choices Match -20.
To find the third term in an arithmetic sequence, we need to use the recursive formula. The recursive formula for an arithmetic sequence is given as:
a(n) = a(n-1) + d
where a(n) represents the nth term in the sequence, a(n-1) represents the previous term, and d represents the common difference between terms.
Since we are looking for the third term, n = 3. We also need to know the value of a(2), which is the second term in the sequence. To find a(2), we use the recursive formula again:
a(2) = a(1) + d
We are not given the value of a(1), so we cannot directly calculate a(2). However, we are given the answer choices, so we can use them to work backwards.
If we assume that a(2) is equal to -5 (choice C), then we can find a(1) by using the recursive formula:
a(2) = a(1) + d
-5 = a(1) + d
If we assume that d = -3 (since the common difference between terms is the same), then we can solve for a(1):
a(1) = -5 + (-3)
a(1) = -8
Now that we know a(1) and d, we can use the recursive formula to find a(3):
a(3) = a(2) + d
a(3) = -5 + (-3)
a(3) = -8
However, none of the answer choices match -8. This means that our assumption for a(2) was incorrect. We can try the same process with the other answer choices to see if we get a matching answer.
If we assume that a(2) is equal to -14 (choice A), then we can find a(1) by using the recursive formula:
a(2) = a(1) + d
-14 = a(1) + d
If we assume that d = -3 (since the common difference between terms is the same), then we can solve for a(1):
a(1) = -14 + (-3)
a(1) = -17
Now that we know a(1) and d, we can use the recursive formula to find a(3):
a(3) = a(2) + d
a(3) = -14 + (-3)
a(3) = -17 - 3
a(3) = -20
Therefore, the answer is not listed in the choices given. None of the answer choices match -20.
In summary, to find the third term in an arithmetic sequence using the recursive formula, we need to know the previous term and the common difference between terms. If we are given answer choices, we can work backwards to find the missing information. However, we must check all answer choices to ensure that we have the correct solution.
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if $\frac ab$ rounded to the nearest trillionth is $0.008012018027$, where $a$ and $b$ are positive integers, what is the smallest possible value of $a b$?
If a/b rounded to the nearest trillionth is 0.008012018027, where a and b are positive integers, the smallest value of the a+b is 2013.
A mathematician would tell you that there cannot be such a number since it would violate the principles of mathematics. There cannot be a number n/2 since n is already the smallest if you have a number n, where n is the smallest integer after 0. Mathematicians dislike this since it implies that division itself fails.
A computer will truly respond to your question. Computers don't have an endless number of numbers, unlike the physical world, because they couldn't all fit. Each memory register in a computer has a set number of bits that are used to store numbers. Imagine having just three digits. 999 is the largest number you may possibly portray.
The continued fraction representations of the limits of the interval are
0.0080120180265 = [0; 124, 1, 4, 2, 1, 463872, 1, 1, 12, 1, 1, 41]
0.0080120180275 = [0; 124, 1, 4, 3, 545777, 2, 13, 1, 1, 1, 1, 2]
The simplest continued fraction (and therefore also the simplest ordinary fraction!) in that interval
is
[0; 124, 1, 4, 3] 16 1997 = = 0.00801201802704056084...
and the sum of its numerator and denominator is 2013.
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Complete question:
If a/b rounded to the nearest trillionth is 0.008012018027, where a and b are positive integers, what is the smallest possible value of a+b ?
Calculate the mean and mean absolute deviation of these two data sets and use that to compare the two sets of data.
Set A: 4,6,7,8,5,6
Set B: 5,7,4,8,9,9
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Robert is on a diet to lose weight before his Spring Break trip to the Bahamas. He is losing weight at a rate of 2 pounds per week. After 6 weeks, he weighs 205 pounds. Write and solve a linear equation to model this situation. There should be at least 3 lines of work.
Answer:
Let $x$ be the number of weeks Robert has been on his diet. We know that he loses 2 pounds per week and that he currently weighs 205 pounds. We can write this as an equation:
$2x = 205$
Solving for $x$, we get:
$x = 102.5$
This means that Robert has been on his diet for 102.5 weeks.
We can also use this information to create a linear equation to model the situation. The equation would be:
$y = 2x$
Where $y$ is Robert's weight in pounds and $x$ is the number of weeks he has been on his diet.
We can plug in $x = 102.5$ to get:
$y = 2 \cdot 102.5 = 205$
This shows that the equation accurately models the situation.
Step-by-step explanation:
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Find the perimeter of the triangle below. Write your final answer in Standard Form. Show all work including identifying your like terms.
Answer:
P = 14x² - 2x + 3------------------------------
Perimeter is the sum of side lengths:
P = a + b + cSubstitute side lengths into formula:
P = 10x² - 4 + x² + 2x + 1 + 3x² - 4x + 6 = (10x² + x² + 3x²) + (2x - 4x) + (-4 + 1 + 6) = 14x² - 2x + 37.
Write the equation of the piecewise function ƒ that is represented by its graph.
A.) [tex]f(x)=\left \{{{x^{3}, if x\ \textless \ 1} \atop {x, if x \geq 1}} \right.[/tex]
B.) [tex]f(x)=\left \{{{x^{3}, if x\ \textless \ 0} \atop {x^{2}, if x\geq 0}} \right.[/tex]
C.) [tex]f(x)=\left \{{{x^{3}, if x\ \textless \ 0} \atop {x, if x\geq 0}} \right.[/tex]
D.) [tex]f(x)=\left \{{{x, if x\ \textless \ 0} \atop {x^{3}, if x\geq 0}} \right.[/tex]
The piecewise function that represent the graph is A)f(x)=[tex]\left \{{ x^3 ,if{x < 1} \atop x,if {x\ge1}} \right.[/tex].
What is function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
In considering the definition of any piecewise function, the domain descriptions in the function definition must match the pieces shown in the graph.
Here, the right segment has no upper bound, so x > 1 is an appropriate description of its domain.
The left segment also has no upper bound , so x[tex]\ge[/tex] 1is an appropriate description of its domain.
The one answer choice that combines these domain descriptions is
A)f(x)=[tex]\left \{{ x^3 ,if{x < 1} \atop x,if {x\ge1}} \right.[/tex]
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Find the perimeter urgent
Answer:
24 ft
Step-by-step explanation:
The perimeter is the sum of a shape's side lengths.
We can add the given side lengths of this polygon to solve for its perimeter.
2 + 4 + 3 + 7 + 4 + 4 = 24 ft
Which graph shows the solution to the system of linear equations?
y = 2x
y = x + 2
a coordinate grid with one line that passes through the points 0 comma 0 and 1 comma 2 and another line that passes through the points 0 comma negative 2 and 1 comma negative 1
Two lines intersect at (2,4). The last choice listed, "a coordinate grid with one line that passes through the points 0,0 and 1,2 and another line that runs through the points 0,-2 and 1,-1," is the graph.
The given system of linear equations is y = 2x and y = x + 2. To find the solution to this system, we can set the two equations equal to each other:
2x = x + 2
Subtract x from both sides:
x = 2
Substitute x = 2 into either equation:
y = 2x = 2(2) = 4
Therefore, solution to system of linear equations is (2, 4).
To check our answer, we can graph the two lines y = 2x and y = x + 2 on a coordinate grid. The intersection point of the two lines will be the solution to the system.
The line y = 2x passes through the points (0,0) and (1,2). The line y = x + 2 passes through the points (0,2) and (1,3). We can plot these points and draw the lines to get the following graph:
Linear equation graph is attached.
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please help giving points and brainliest thx
The following descriptions of the function passing through (0,7) and (4,4) are true:
The slope of the function is -3/4 and the y-intercept is 7.
The function is linear and continuous.
y=-3/4x + 7 represents this function.
y = -4/3x + 9 represents this function.
What is function?In mathematics, a function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output. A function is often represented by a mathematical expression, formula or graph. Functions can be described using different notations, such as f(x), y = f(x), or y = g(u,v), and they can take various forms, such as linear, quadratic, polynomial, exponential, logarithmic, trigonometric, and many others.
Here,
To determine which descriptions of the function are true, we need to use the information given about the two points (0,7) and (4,4) to find the slope and y-intercept of the linear function that passes through them. Using the formula for the slope of a line:
slope = (4 - 7) / (4 - 0) = -3/4
So the slope of the function is -3/4.
To find the y-intercept, we can use the point-slope form of the equation of a line, which is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line. We can use either of the two points given:
y - 7 = (-3/4)(x - 0)
y - 7 = (-3/4)x
y = (-3/4)x + 7
So the y-intercept of the function is 7.
Using this information, we can now evaluate the given descriptions of the function:
y = 7x - 3/4: This represents the function, but the slope is incorrect (should be -3/4).
The function is decreasing: This is not true, since the slope is negative but less than -1.
y=-3/4x + 7: This represents the function, and the slope and y-intercept are both correct.
The slope of the function is -4/3 and the y-intercept is 9: This is not true, since the slope is -3/4 and the y-intercept is 7.
The function is increasing: This is not true, since the slope is negative.
The slope of the function is -3/4 and the y-intercept is 7: This is true, as shown by the calculations above.
y = -4/3x + 9: This represents a different function with a different slope and y-intercept.
The function is linear and continuous: This is true, since the function is a linear equation and is continuous over its domain.
The function is linear and discrete: This is not true, since the function is continuous over its domain.
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Use the graph to answer the question. Graph of polygon ABCDE with vertices at negative 3 comma 3, negative 3 comma 6, 1 comma 6, 1 comma 3, negative 1 comma 1. A second polygon A prime B prime C prime D prime E prime with vertices at 11 comma 3, 11 comma 6, 7 comma 6, 7 comma 3, 9 comma 1. Determine the line of reflection. Reflection across x = 4 Reflection across y = 4 Reflection across the x-axis Reflection across the y-axis
the line of reflection is the vertical line x = 7.Thus, if we reflect polygon ABCDE across the line x = 7, we get polygon A' B' C' D' E'.
To determine the line of reflection, we need to find the axis that maps each point of polygon ABCDE to its corresponding point on polygon A' B' C' D' E'.
If we observe the coordinates of the vertices of the polygons, we can see that the x-coordinates of the corresponding points are related by x' = 14 - x, where x is the x-coordinate of the point in polygon ABCDE. Similarly, the y-coordinates of the corresponding points are related by y' = y.
Now, if we reflect polygon ABCDE across the line of reflection, each point of polygon ABCDE will map to its corresponding point on polygon A' B' C' D' E' such that the distance between the line of reflection and the point is equal to the distance between the line of reflection and its image.
If we consider a point (x, y) in polygon ABCDE and its corresponding point (x', y') in polygon A' B' C' D' E', we can see that the line of reflection is the vertical line that passes through the midpoint of the segment joining (x, y) and (x', y').
We can find the midpoint of this segment by using the midpoint formula:
((x + x')/2, (y + y')/2)
Substituting the values of x and y in terms of x' and y', we get:
((14 - x' + x')/2, y/2) = (7, y/2)
Therefore, the line of reflection is the vertical line x = 7.
Thus, if we reflect polygon ABCDE across the line x = 7, we get polygon A' B' C' D' E'.
In summary, the line of reflection is x = 7.
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Use the quadratic formula to find both solutions to the quadratic equation given below
4x^2+3x-1=0
The solutions to the quadratic equation 4x² + 3x - 1 = 0 are: x = 1/2 and x = -1. None of the answer choices match these solutions, so none of the options provided are correct.
What is quadratic equation?it's a second-degree quadratic equation which is an algebraic equation in x. Ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form.
To use the quadratic formula, we need to first identify the values of a, b, and c in the quadratic equation:
ax² + bx + c = 0
In the given equation,
a = 4
b = 3
c = -1
Now, we can substitute these values into the quadratic formula:
[tex]$ \rm x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
Plugging in the values for a, b, and c gives:
x = (-3 ± sqrt(3² - 4(4)(-1))) / 2(4)
[tex]$ \rm x = \frac{ -3 \pm \sqrt{3^2 - 4(4)(-1)}}{2(4)}[/tex]
Simplifying inside the square root:
[tex]$ \rm x = \frac{-3 \pm \sqrt{9 + 16}}{8}[/tex]
[tex]$ \rm x = \frac{-3 \pm \sqrt{25}}{8}[/tex]
[tex]$ \rm x = \frac{-3 \pm 5}{8}[/tex]
Now, we have two solutions:
x = (-3 + 5) / 8 = 1/2
x = (-3 - 5) / 8 = -1
Therefore, the solutions to the quadratic equation 4x² +3x - 1 = 0 are:
x = 1/2 and x = -1
None of the answer choices match these solutions, so none of the options provided are correct.
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Three softball players discussed their batting averages after a game.
Probability
Player 1 four sevenths
Player 2 five eighths
Player 3 three sixths
By comparing the probabilities and interpreting the likelihood, which statement is true?
Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)
Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1)
Player 3 is more likely to hit the ball than Player 1 because P(Player 3) > P(Player 1)
Player 3 is more likely to hit the ball than Plaver 2 because P(Player 3) > P(Player 2)
A cylinder has a radius of 2 feet. Its volume is 37.68 cubic feet. What is the height of the cylinder?
Answer: H=3feet
Step-by-step explanation:
Answer: h ≈ 3 ft
Step-by-step explanation: The formula for volume of a cylinder is v = pi times radius squared times height (πr^2h).
To solve this we need to use the formula h = v/πr^2
h = 37.68/π2^2
h = 2.99848 ft
h ≈ 3 ft
(note: ≈ means approximately so the answer is estimated as 3 ft but the actual answer is 2.99848)
a lawyer commutes daily from his suburban home to his midtown office. the average time for a one-way trip is 24 minutes, with a standard deviation of 3.8 minutes. assume the distribution of trip times to be normally distributed. (a) what is the probability that a trip will take at least 1/2 hour? (b) if the office opens at 9:00 a.m. and the lawyer leaves his house at 8:45 a.m. daily, what percentage of the time is he late for work
Answer:
(a) To find the probability that a trip will take at least 1/2 hour (30 minutes), we need to find the area under the normal distribution curve to the right of 30 minutes. We can standardize the distribution using the formula z = (x - μ) / σ, where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.
z = (30 - 24) / 3.8 = 1.58
Using a standard normal distribution table or a calculator with a normal distribution function, we can find the probability that a trip will take at least 30 minutes is approximately 0.0571 or 5.71%.
(b) If the office opens at 9:00 a.m. and the lawyer leaves his house at 8:45 a.m. daily, he needs to arrive at the office before 9:00 a.m. to be on time. We can find the percentage of the time he is late for work by finding the area under the normal distribution curve to the right of 15 minutes (the difference between 8:45 a.m. and 9:00 a.m.), and then subtracting that value from 1 to get the percentage of the time he is on time or early.
z = (15 - 24) / 3.8 = -2.37
Using a standard normal distribution table or a calculator with a normal distribution function, we can find the probability that he is late for work is approximately 0.008 or 0.8%. Therefore, he is on time or early approximately 99.2% of the time.
A set of cloth napkins was originally priced at $4.99, but Zack waited to buy it until it was 45% off. If he paid 15% sales tax on the sale price, how much did he pay in total?
$
Solve for d.
8(d − 87) = 32
Answer:
d=91
Step-by-step explanation:
Answer: d=91
Step-by-step explanation:
First thing first, you have to use the distributive property. Distribute the 8 to the d-87.
(8*d) - (8*87) = 32 = 8d - 696= 32
Next, you have to add 696 to both sides of the equation:
8d-696 +696= 32+696 = 8d= 728
Last step is to divide both sides by 8:
8d/8 = 728/8 =
d= 91
We can check this by plugging the number 91 to the variable d in the equation:
(8*91) - (8 *87) = 32 = 728 - 696= 32
Marilyn moves 1/2 the remaining to the goal every second. if the goal if 50 yards away, how many seconds does it take to travel 49.5 yards? How to do?
It takes Marilyn approximately 6.64 seconds to travel 49.5 yards.
What is logarithm?A logarithm is the inverse operation of exponentiation. In other words, it is a way to find the exponent that a certain base must be raised to in order to produce a given number.
According to question:To solve the problem, you can use a geometric series formula. Let's say the remaining distance to the goal is d at time t. Then, Marilyn moves 1/2d every second, so after one second, the remaining distance is 1/2d, after two seconds, it's 1/4d, after three seconds, it's 1/8d, and so on.
So, the distance remaining at time t is given by the formula:
d(t) = d(0) * [tex](1/2)^t[/tex]
where d(0) is the initial distance remaining.
To find how long it takes to travel 49.5 yards, we need to solve for t when d(t) = 0.5 yards (since Marilyn moves half the remaining distance every second).
0.5 = d(0) * [tex](1/2)^t[/tex]
d(0) = 49.5 yards, so we have:
0.5 = 49.5 * [tex](1/2)^t[/tex]
Dividing both sides by 49.5:
0.01 = [tex](1/2)^t[/tex]
Taking the logarithm of both sides (using any base):
log(0.01) = log([tex](1/2)^t[/tex])
log(0.01) = t * log(1/2)
Solving for t:
t = log(0.01) / log(1/2) = 6.64 seconds (rounded to two decimal places)
Therefore, it takes Marilyn approximately 6.64 seconds to travel 49.5 yards.
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I want some help with this problem
The probability that the first spinner will land on 7 and the second spinner will land on C is 1/4. So correct option is D.
Describe Probability?Probability is a branch of mathematics that deals with the study of random events or phenomena. It provides a framework for quantifying uncertainty and making predictions based on data and observations.
Probability is typically expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. For example, the probability of flipping a coin and getting heads is 0.5, or 50%, since there are two equally likely outcomes (heads or tails).
The probability of an event can be determined by calculating the ratio of the number of favorable outcomes to the total number of possible outcomes. For example, the probability of rolling a 6 on a standard die is 1/6, since there is only one favorable outcome (rolling a 6) out of six possible outcomes (rolling a 1, 2, 3, 4, 5, or 6).
The probability that the first spinner will land on 7 and the second spinner will land on C is 1/4.
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Erica is swimming due north at a rate of 7 feet per second. If the current of the lake is 3 feel per second in the direction of S 75° W. find Erica's resultant speed and direction (as a true bearing).
This means that she is swimming with a speed of 4.27 feet per second in a direction that is 41.1° east of due north.
What is vector?A vector is a mathematical quantity that has both magnitude and direction. Vectors are used to represent physical quantities that have both magnitude (such as speed, force, or displacement) and direction (such as north, east, up, or down). Vectors can be represented graphically as arrows, where the length of the arrow represents the magnitude of the vector and the direction of the arrow represents the direction of the vector.
Here,
To find Erica's resultant speed and direction, we can use vector addition. We'll consider Erica's swimming speed as one vector and the current of the lake as another vector, and then find the vector sum of the two.
Let's denote Erica's swimming speed vector as A and the current vector as B.
Magnitude of A (Erica's swimming speed) = 7 feet per second
Direction of A = Due north, which can be represented as N or 0°
Magnitude of B (current of the lake) = 3 feet per second
Direction of B = S 75° W, which can be represented as 180° - 75°
= 105° in the clockwise direction from due north.
Now, we can add the two vectors A and B using vector addition.
To add vectors, we can break them down into their horizontal (x) and vertical (y) components, and then add the corresponding components separately.
A_x = A * cos(direction of A)
A_y = A * sin(direction of A)
B_x = B * cos(direction of B)
B_y = B * sin(direction of B)
Substituting the given values, we get:
A_x = 7 * cos(0°) = 7 * 1 = 7
A_y = 7 * sin(0°) = 7 * 0 = 0
B_x = 3 * cos(105°)
B_y = 3 * sin(105°)
Now, we can add the corresponding components:
Resultant x-component = A_x + B_x
Resultant y-component = A_y + B_y
Resultant x-component = 7 + 3 * cos(105°)
Resultant y-component = 0 + 3 * sin(105°)
Using a calculator, we can find the values of the x- and y-components. Let's assume the values to be:
Resultant x-component ≈ 3.23
Resultant y-component ≈ 2.97
Now, we can use these values to find the magnitude and direction of the resultant vector using trigonometry.
Magnitude of the resultant vector = √((Resultant x-component)² + (Resultant y-component)²)
Direction of the resultant vector = tan⁻¹(Resultant y-component, Resultant x-component)
Substituting the values, we get:
Magnitude of the resultant vector ≈ √((3.23)² + (2.97)²)
≈ 4.27 feet per second (rounded to two decimal places)
Direction of the resultant vector ≈ tan⁻¹(2.97, 3.23)
≈ 41.1° (rounded to one decimal place)
So, Erica's resultant speed is approximately 4.27 feet per second in the direction of 41.1° true bearing.
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EXPANDING BRACKETS -
3 (x + 4)
Answer:
[tex] \sf \: 3x + 12 [/tex]
Step-by-step explanation:
Now we have to,
→ Simplify the given expression.
The property we use,
→ Distributive property.
The expression is,
→ 3(x + 4)
Let's simplify the expression,
→ 3(x + 4)
→ 3(x) + 3(4)
→ (3 × x) + (3 × 4)
→ 3x + 12
Hence, the answer is 3x + 12.
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Here is a graph of f given by f(Θ) = tan(Θ). What are the Θ-intercepts of the graph of f? Explain how you know.
These intercepts are even multiple of π, such as 0, ±π, ±2π, etc.
how to find intercepts?The θ-intercepts of a function are the values of θ for which the function equals zero. the θ-intercepts of the graph of f(θ) = tan(Θ), we have to solve the equation tan(θ) = 0.
we know that the tangent function has zeros at θ = kπ, where k is an integer. the tangent function is undefined at odd multiples of π/2,
Therefore, the Θ-intercepts of the graph of f(θ) = tan(θ) are the values of θ that satisfy the equation tan(θ) = 0, which are θ = kπ for any integer k. These intercepts occur at every even multiple of π, such as 0, ±π, ±2π, etc.
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Max is tossing a snowball,
from 25 feet above ground
and it is thrown at a speed of
18 feet per second.
Determine how long it takes
Max's snowball to hit the
ground and find its maximum
height.
Step-by-step explanation:
We can use the kinematic equations of motion to solve this problem. Let's assume the initial velocity of the snowball is 18 feet per second and its initial height is 25 feet. Also, we know that the acceleration due to gravity is -32.2 feet per second squared (assuming downward direction as negative).
To find out when the snowball hits the ground, we can use the equation:
h = 25 + 18t - 16t^2
where h is the height of the snowball at time t. We want to find the value of t when h = 0 (since the snowball hits the ground at that point). Therefore, we can rewrite the equation as:
16t^2 - 18t - 25 = 0
Solving for t using the quadratic formula, we get:
t = (18 ± √(18^2 + 41625))/(2*16)
t = 2.25 seconds or -0.875 seconds
Since time cannot be negative, the snowball hits the ground after 2.25 seconds.
To find the maximum height the snowball reaches, we can use the fact that the maximum height occurs at the vertex of the parabolic trajectory. The x-coordinate of the vertex is given by:
t = -b/2a
where a and b are the coefficients of the quadratic equation. In this case, a = -16 and b = 18, so:
t = -18/(2*(-16)) = 0.5625 seconds
To find the corresponding height, we can substitute t = 0.5625 seconds into the equation for h:
h = 25 + 18(0.5625) - 16(0.5625)^2
h = 28.2656 feet
Therefore, the maximum height the snowball reaches is 28.2656 feet.
The diameter of a circle is 8 feet. What is the angle measure of an arc bounding a sector with area 6 square feet?
Answer:
Using chain of thought reasoning, the answer and explanation to the given math problem is as follows:
Step 1: Recognize that the arc's length can be calculated using the formula L = θ_arc*r, where L stands for the arc's length, θ_arc is the measure of the angle in radians, and r is the radius of the circle.
Step 2: We can calculate θ_arc by rearranging the formula to derive θ_arc = L/r. Assuming the arc's length is the same as the sector's perimeter, L = perimeter = 2πr, meaning that θ_arc = 2πr/r.
Step 3: Since the radius of the circle is 8 feet, θ_arc = 2π(8 feet/8 feet) = 2π.
Step 4: We then can calculate the angle measure of the arc bounding the sector. Calculate the area of the sector, A = θ/2πr^2. Rearranging the formula to derive θ = 2πr^2/A and inserting the given values yields θ = 2π(8^2 feet^2/6 square feet) ≈ 6.36 radians.
Answer:
The angle measure of an arc bounding a sector with area 6 square feet is 6.36 radians.
a small college has 1095 students. what is the approximate probability that more than five students were born on christmas day? assume that the birth rates are constant throughout the year and that each year has 365 days. (hint: use complements before implementing the normal approximation.)
The required probability of more than five students being born on Christmas Day as per total of 1095 students is approximately 0.0735.
Let X be the number of students in the college who were born on Christmas Day.
Birth rates are constant throughout the year,
Assume that X follows a binomial distribution with
n = 1095
and p = 1/365,
where n is the total number of students in the college
And p is the probability that a student is born on Christmas Day.
The probability of more than five students being born on Christmas Day can be written as,
P(X > 5) = 1 - P(X ≤ 5)
Use the normal approximation to the binomial distribution to estimate P(X ≤ 5)
And then subtract this value from 1 to obtain an estimate of P(X > 5).
Use the normal approximation,
First check if the conditions for using it are met.
For a binomial distribution with n trials and probability of success p, the mean and standard deviation are,
μ = np
σ = √(np(1-p))
here, we have,
μ = 1095 × (1/365)
= 3
σ = √(1095 ×(1/365) × (1 - 1/365))
≈ 1.73
Expected value is greater than 5 .
And the standard deviation is not too small ( σ > 1),
Use the normal approximation to the binomial distribution.
Using the continuity correction, we can rewrite P(X ≤ 5) ,
P(X ≤ 5) ≈ P(Z ≤ (5.5 - μ) / σ)
where Z is a standard normal variable.
Substituting the values for μ and σ, we get,
P(X ≤ 5) ≈ P(Z ≤ (5.5 - 3) / 1.73)
≈ P(Z ≤ 1.45)
≈ 0.9265
Using a standard normal table
P(Z ≤ 4.39) ≈ 0.9265
Probability of fewer than or equal to 5 students being born on Christmas Day is very close to 1.
This implies,
Estimation of the probability of more than five students being born on Christmas Day as,
P(X > 5)
≈ 1 - 0.9265
≈ 0.0735
This means that the probability of more than five students being born on Christmas Day is extremely small.
Conclude that it is unlikely that more than five students were born on Christmas Day.
Therefore, the probability of more than five students being born on Christmas Day is approximately 0.0735.
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For a fundraiser, the children in the art club made greeting cards and kept track of how many they produced.
How many children made fewer than 2 greeting cards?
0=2
1=5
2=4
3=1
4=6
There are 2 children who made 0 cards and 5 children who made 1 card.
Therefore, the total number of children who made fewer than 2 greeting cards is:
2 (children who made 0 cards) + 5 (children who made 1 card) = 7 children
From the given data, we can see how many children made a certain number of greeting cards:
- 2 children made 0 cards
- 5 children made 1 card
- 4 children made 2 cards
- 1 child made 3 cards
- 6 children made 4 cards
The question asks for the number of children who made fewer than 2 greeting cards. This includes children who made 0 or 1 card.
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a quality control specialist plans to sample 400 units from a shipment. they plan to reject the shipment if less than 10% of units are a desired color. suppose that in fact 12% of units are the desired color. what is the approximate probability that the shipment will be rejected? round your answer to two decimal places.
There is a 10.91% chance that the package will be refused.
The possibility that an event will occur is its probability, which is given as a number between 0 and 1.
Sample = 400 units
n = 400 units
If less than 10% of the units are the desired hue, the shipment will be rejected.
12% of the units are, in fact, the desired hue.
So, P = 12%
We can write it as
P = 0.12
Q = 1 - 0.12
Q = 0.88
σ = √PQ/n
Substitute the value
σ = √(0.12 × 0.88)/400
σ = √0.1056/400
σ = √0.000264
σ = 0.01625
Probability that the shipment will be rejected;
P(x < 10%) = P(x < 0.1)
P(x < 10%) = P([tex]Z_{0.1}[/tex])
[tex]Z_{0.1}[/tex] = (0.1 - 0.12)/0.01625
[tex]Z_{0.1}[/tex] = -0.02/0.01625
[tex]Z_{0.1}[/tex] = -1.231
P([tex]Z_{0.1}[/tex]) = 0.1091
P(x < 10%) = 0.1091
P(x < 10%) = 10.91%
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The polygons are regular polygons. Find the area of the shaded region.
PLEASE PLEASE HELP IM BEGGING
The area of the shaded region is equal to 280.6 ft².
How to determine the area of the shaded region?Based on the diagram of these regular polygons, the area of the shaded region of one triangle that makes up the hexagon can be calculated by determining the difference between the area of each of the equilateral triangles formed.
In Mathematics and Geometry, the area of an equilateral triangle with known side length (l) can be calculated by using the following mathematical equation;
Area of equilateral triangle = √3/4 × l²
The area of the shaded region of the triangle = √3/4 × l² - √3/4 × l²
The area of the shaded region of the triangle = √3/4 × (12)² - √3/4 × 6²
The area of the shaded region of the triangle = √3/4 × 144 - √3/4 × 36
The area of the shaded region of the triangle = 62.35 - 15.59
The area of the shaded region of the triangle = 46.76 ft².
Since the regular polygon is a hexagon, the area of the shaded region is given by;
Area of the shaded region = 6(46.76)
Area of the shaded region = 280.6 ft².
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