To test the convergence of the given infinite series, we can use the Alternating Series Test. The series is in the form: Σ((-1)^n * (arctan(n)/n^2)), for n = 1 to infinity.
The Alternating Series Test requires two conditions to be met:
1. The absolute value of the terms in the series must be decreasing: |a_n+1| ≤ |a_n|.
2. The limit of the terms in the series as n approaches infinity must be zero: lim (n→∞) |a_n| = 0.
For the given series, let's check these conditions: 1.The absolute value of the terms: |arctan(n)/n^2|. Since arctan(n) increases with n and n^2 increases faster than arctan(n), the ratio (arctan(n)/n^2) decreases as n increases. Therefore, this condition is met.
2. Now, we need to check the limit: lim (n→∞) |arctan(n)/n^2|. As n approaches infinity, the arctan(n) approaches π/2, and n^2 approaches infinity.
Therefore, the limit is (π/2)/∞ = 0, so the second condition is also met. Since both conditions are met, the Alternating Series Test confirms that the given series converges.
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"Complete question"
Apply Any Appropriate Testing Method To: ∞X N=1 (−1)Narctan N N2
Apply any appropriate Testing Method to:
∞X
n=1
(−1)narctan n
n2
Declan says, "To write an equivalent
fraction name for 5. I can write 5 as the
denominator and 1 as the numerator. "
Do you agree with Declan? Explain.
Declan's statement is technically correct, it is not a very helpful way to write an equivalent fraction for 5.
Declan's statement is mathematically correct, but it is not a useful way to write an equivalent fraction for 5 in most contexts.
In general, to write an equivalent fraction, we need to multiply or divide both the numerator and the denominator by the same nonzero number. This preserves the value of the fraction, but changes its form.
For example, to write an equivalent fraction for 5, we can multiply both the numerator and denominator by any nonzero number. Let's say we multiply both by 2:
5/1 = (5x2)/(1x2) = 10/2
So 10/2 is an equivalent fraction for 5.
However, if we follow Declan's approach and write 5 as the denominator and 1 as the numerator, we get:
5/1 = 1/5
This is indeed an equivalent fraction for 5, but it is not a particularly useful or common way to write an equivalent fraction. In general, we prefer to write equivalent fractions with a denominator that has some mathematical or practical significance, such as a power of 10 or a factor of the original denominator.
So while Declan's statement is technically correct, it is not a very helpful way to write an equivalent fraction for 5.
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Find the mass of each object. (Round answers to two decimal places.)
A thin copper wire 3.75 feet long (starting at a = 0) with density function given by
p(t) = 5x^2 + 4x lb/ft.
The mass of the copper wire is approximately 131.77 lb.
To find the mass of the copper wire, we will first need to calculate its mass per unit length using the given density function[tex]p(t) = 5x^2 + 4x lb/ft,[/tex] and then integrate the function over the length of the wire.
Write down the given density function: [tex]p(t) = 5x^2 + 4x lb/ft[/tex]
2. Write down the limits of integration, which correspond to the length of the wire:
a = 0, b = 3.75 feett.
Set up the integral to find the mass of the wire:
Mass = ∫[p(t) dt] from a to b.
Plug in the density function and limits:
Mass = ∫[tex][5x^2 + 4x dx][/tex]from 0 to 3.75
Integrate the function: Mass = (5/3)x^3 + 2x^2 | from 0 to 3.75
Substitute the upper limit and then subtract the result of the lower limit:
Mass =[tex][(5/3)(3.75)^3 + 2(3.75)^2] - [(5/3)(0)^3 + 2(0)^2][/tex]
Perform the calculations and round to two decimal places:
Mass ≈ 131.77 lb.
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determine the ordered pairs of....
[tex]6x - y > - 3[/tex]
and
[tex]4x + 3y < 4[/tex]
The ordered pairs of the system of inequalities are (1, 0) and (0, -5)
Determining the ordered pairs of the system of inequalitiesFrom the question, we have the following parameters that can be used in our computation:
6x - y > -3
4x + 3y < 4
The above expression is a system of linear inequality
That implies that we graph the inequalites in the system on the same plane and write out ordered pairs from the region that represent the solution of the system
Next, we plot the graph
See attachment for the graph of the inequality
The ordered pairs are (1, 0), (0, -5) and other pairs
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The length of a triangle is three times its width the perimeter of the rectangle is 24cmcalculate the area of the triangle
The area of the triangle is 6 cm².
Let's denote the width of the triangle as "w." According to the given information, the length of the triangle is three times its width, so the length can be expressed as "3w."
The perimeter of a rectangle is given by the formula: Perimeter = 2(length + width). In this case, the perimeter of the rectangle is given as 24 cm.
We can set up the following equation based on the given information:
24 = 2(3w + w)
Simplifying the equation:
24 = 2(4w)
12w = 24
w = 24/12
w = 2 cm
Now that we have the width of the triangle, we can find the length:
Length = 3w = 3 * 2 = 6 cm
The area of a triangle is given by the formula: Area = (base * height) / 2. In this case, the base of the triangle is the width (2 cm) and the height is the length (6 cm).
Area = (2 * 6) / 2
Area = 12 / 2
Area = 6 cm²
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Do You Understand?
1. How can you find the volume of the
china cabinet?
1 ft,
7 ft
3 ft
4 ft
2ft
The volume of the china cabinet is 21 cubic feet.
To find the volume of the china cabinet, we need to multiply its length, width, and height.
Since the dimensions are given in feet, we will use cubic feet as the unit of volume.
The length of the china cabinet is given as 1 ft, the width as 7 ft, and the height as 3 ft.
The volume can be calculated as follows:
Volume = length * width * height
Volume = 1 ft * 7 ft * 3 ft
Volume = 21 cubic feet
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(1 point) Use the linear approximation to estimate (-2.02)2(2.02)3 = Compare with the value given by a calculator and compute the percentage error: Error = %
the linear approximation, we estimated the value of (-2.02)^2 * (2.02)^3 as 31.68, and the percentage error compared to the calculator's value is approximately 0.1924%.
Let's break it down step-by-step:
1. Identify the function we want to approximate: f(x) = x^2 * (x+4)^3
2. Choose the point to approximate near Since we want to estimate f(-2.02), let's approximate near x = -2.
3. Compute the linear approximation (first-degree Taylor polynomial) at x = -2: f(-2) = (-2)^2 * (2)^3 = 4 * 8 = 32
4. Find the derivative of f(x): f'(x) = 2x(x+4)^3 + 3x^2(x+4)^2
5. Compute the derivative at x = -2: f'(-2) = 2(-2)(2)^3 + 3(-2)^2(2)^2 = -32 + 48 = 16
6. Use the linear approximation formula: f(-2.02) ≈ f(-2) + f'(-2)(-2.02 - (-2)) = 32 + 16(-0.02) = 32 - 0.32 = 31.68
Now, compare this approximation to the value given by a calculator: (-2.02)^2 * (2.02)^3 ≈ 31.741088. To compute the percentage error, use the formula:
Percentage Error = |(Approximate Value - Actual Value) / Actual Value| * 100%
Percentage Error = |(31.68 - 31.741088) / 31.741088| * 100% ≈ 0.1924%
So, using the linear approximation, we estimated the value of (-2.02)^2 * (2.02)^3 as 31.68, and the percentage error compared to the calculator's value is approximately 0.1924%.
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Solve the system of equations. 2x + 3y = 18 3x + y = 6 (9, 0) (3, 4) (1, 3) (0, 6)
X = 0 and Y = 6 are the answers to the equation system. The system's two equations are satisfied at the location (0, 6). Choice D
To solve the system of equations:
2x + 3y = 18
3x + y = 6
We can employ the substitution or elimination strategy. Let's solve this system via the process of elimination:
To make the coefficients of x in both equations equal, multiply the second equation by two:
2(3x + y) = 2(6)
6x + 2y = 12
Now we have the system of equations:
2x + 3y = 18
6x + 2y = 12
Next, by deducting the first equation from the second equation, we can remove the y term:
(6x + 2y) - (2x + 3y) = 12 - 18
6x + 2y - 2x - 3y = -6
4x - y = -6
4x - y = -6
y = 4x + 6
At this point, we can add this expression for y to one of the initial equations. Let's employ the first equation:
2x + 3(4x + 6) = 18
2x + 12x + 18 = 18
14x + 18 = 18
14x = 0
x = 0
Replacing x = 0 in the equation y = 4x + 6 now:
y = 4(0) + 6
y = 6
Thus, x = 0 and y = 6 are the answers to the system of equations. The system's two equations are satisfied at the location (0, 6). Basketball or baseball in option D is 5/6, or approximately 0.8333.
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Answer:
Option D, (0,6)
Step-by-step explanation:
took the test xx
1 ) If the supplement of an angle is 30 degrees more than the measure of the angle, what is the measure of the angle?
2) If the supplement of an angle is 12 degrees less than twice the measure of the angle, what is the measure of the angle?
a) If the supplement of an angle is 30 degrees more than the measure of the angle, the measure of the angle is 75 degrees.
b) If the supplement of an angle is 12 degrees less than twice the measure of the angle, the measure of the angle is 64 degrees.
a) Let x be the measure of the angle. The supplement of the angle is 180-x. According to the problem, the supplement of the angle is 30 degrees more than the measure of the angle. This can be written as:
180 - x = x + 30
Solving for x, we get:
2x = 150
x = 75
b) Let x be the measure of the angle. The supplement of the angle is 180-x. According to the problem, the supplement of the angle is 12 degrees less than twice the measure of the angle. This can be written as:
180 - x = 2x - 12
Solving for x, we get:
3x = 192
x = 64
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Which axis is point 5 located on?
Point 5 is located on the x-axis (horizontal one)
In which axis is the point 5 located on?On a general coordinate axis we have two axes.
The vertical one is called the y-axis, and here we put the outputs.
The horizontal one is called the x-axis, here we put the inputs.
Here we can see that point 5 (P5) is located on the horizontal axis, then the correct option is the first one, x-axis.
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If (2, 3) is a point on locus whose equation is ax + 2y = 16 and also show that (0, 8) is another point on the locus.
Quadrilateral abcd is inscribed in this circle.
find the measure of angle a and angle b if
m&c = 121-and m&d=93°
а
d
b.
121°
с
The measure of angle a is 59 degrees and the measure of angle b is 87 degrees. Based on the information given, we know that angles a and b are opposite angles of the quadrilateral abcd,
So they are supplementary (their sum is 180 degrees).
We also know that angles c and d are opposite angles of the quadrilateral abcd, and they are given in the problem. Using the fact that angles on the same side of a chord are equal, we can say that angles a and d are equal, and angles b and c are equal.
Therefore, we can set up the following equation:
a + d = 180 (because they are supplementary)
d = 121
a = d (because they are opposite angles of the quadrilateral)
b = c (because they are opposite angles of the quadrilateral)
c + d = 180 (because they are supplementary)
c = 93
Substituting the known values, we get:
a + 121 = 180
a = 59
b + 93 = 180
b = 87
Therefore, the measure of angle a is 59 degrees and the measure of angle b is 87 degrees.
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Pentagon
apothem = 7.3
side = 10.6
i need help immediately please help me show work
Answer:
Sure, I can help you with that!
To find the area of a regular pentagon, we can use the formula:
Area = (1/2) x apothem x perimeter
where apothem is the distance from the center of the pentagon to the midpoint of any side, and perimeter is the total length of all the sides.
So, to find the area of your pentagon, we can first calculate the perimeter:
Perimeter = 5 x side
Perimeter = 5 x 10.6
Perimeter = 53
Now, we can plug in the values for apothem and perimeter into the formula:
Area = (1/2) x apothem x perimeter
Area = (1/2) x 7.3 x 53
Area = 193.45
Therefore, the area of your pentagon is approximately 193.45 square units.
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Your name is Galileo Galilei, and you toss a weight upward at 16 feet per second from the top of the Leaning Tower of Pisa (height 186 ft). (a) Neglecting air resistance, find the weight's velocity as a function of time t in seconds. v(t) = Correct: Your answer is correct. ft/s (b) Find the height (in feet) of the weight above the ground as a function of time. s(t) =
(a) The weight's velocity as a function of time t in seconds is v(t) = 16 - 32.2t
(b) The height (in feet) of the weight above the ground as a function of time is s(t) = 186 + 16t - (1/2)(32.2)t^2
To find the weight's velocity and height as a function of time:
(a) The equation for velocity as a function of time is v(t) = v0 - gt,
where v0 is the initial velocity (in this case, 16 ft/s) and g is the acceleration due to gravity (32.2 ft/s^2).
Using this equation, we can find the weight's velocity as it travels upward:
v(t) = 16 - 32.2t
(b) The equation for height as a function of time is s(t) = s0 + v0t - (1/2)gt^2,
where s0 is the initial height (in this case, 186 ft).
Using this equation, we can find the height of the weight above the ground at any point in time:
s(t) = 186 + 16t - (1/2)(32.2)t^2
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A gym subscription runs several promotions. Customers can choose from the following offers.
Option A: 25% off an annual subscription of $308. 00
Option B: pay $29 per month
How much will a customer save by purchasing the annual subscription over paying per month?
a
$348
b
$231
c
$79
d
$117
A customer will save $117 by purchasing the annual subscription over paying per month. So the (d) $117 is the right answer.
To determine how much a customer will save by purchasing the annual subscription over paying per month, follow these steps:
Calculate the discounted annual subscription cost:
Option A: 25% off an annual subscription of $308.00
Discount = 25% of $308 = 0.25 * $308 = $77
Discounted Annual Subscription = $308 - $77 = $231
Calculate the total cost of the monthly subscription for one year:
Option B: Pay $29 per month
Total Monthly Subscription Cost = $29 * 12 months = $348
Calculate the savings:
Savings = Total Monthly Subscription Cost - Discounted Annual Subscription
Savings = $348 - $231 = $117
So, a customer will save $117 by purchasing the annual subscription over paying per month. Your answer is d. $117.
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_ x 10 = 3 1/2
what is in the blank help me pls
Answer:
x = 0.35
Step-by-step explanation:
We Know
x · 10 = 3 1/2
Find the missing number.
3 1/2 = 7/2 = 3.5
x · 10 = 3.5
x = 0.35
So, the answer is 0.35.
11. a bird makes a dive off a cliff to catch a fish in a lake. the path of the dive follows a
parabolic curve of the given function f(x) = (x-7)2 - 1 where f(x) represents the height of
the bird in meters, and x represents the time in seconds. how far was the fish from the bird?
The fish has located a horizontal distance of 7 meters away from the cliff.
How to find the distance between the bird and the fish?
To find the distance between the bird and the fish, we need to find the horizontal distance traveled by the bird during the dive. We can do this by finding the x-coordinate of the vertex of the parabolic curve, which represents the highest point of the dive.
The vertex of the parabolic curve of the given function f(x) = (x-7)^2 - 1 is at the point (7, -1). This means that the highest point of the bird's dive is reached at 7 seconds, and the bird is at a height of -1 meters at this point.
To find the distance traveled by the bird during the dive, we need to find the horizontal distance between the bird's starting point (the cliff) and the highest point of the dive (the vertex). The distance is given by the horizontal coordinate of the vertex, which is 7 seconds.
Therefore, the fish has located a horizontal distance of 7 meters away from the cliff, assuming that the bird started the dive from the edge of the cliff.
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At Sugar Creek Middle School, there are two sizes of lockers for the students: one size for the sixth-grade and seventh-grade students and a larger size for the eighth-grade students. Both sizes of lockers are 5 feet tall and 1 foot wide. The lockers for the younger students each have a volume of 5 cubic feet, while the lockers for the eighth-grade students each have a volume of 7.5 cubic feet.
How much deeper are the lockers for the eighth-grade students than the lockers for the younger students?
a decimal number that is larger than 0.0467 but smaller than 0.0468
Answer: .04671 - 0.04679
Step-by-step explanation:
Answer:
0.04675
Step-by-step explanation:
0.04675 > 0.0467
0.04675 < 0.0468
The coiling dragon cliff skywalk in china is $128$ feet longer than the length $x$ (in feet) of the tianmen skywalk in china. The world's longest glass-bottom bridge, located in china's zhangjiaji national park, is about $4. 3$ times longer than the coiling dragon cliff skywalk. Write and simplify an expression that represents the length (in feet) of the world's longest glass-bottom bridge
The expression that represents the length (in feet) of the world's longest glass-bottom bridge is 4.3x+550.4.
Let's denote the length of the Coiling Dragon Cliff Skywalk as y (in feet). According to the given information, we have:
y = x + 128
The length of the world's longest glass-bottom bridge is 4.3 times longer than the Coiling Dragon Cliff Skywalk, so we can write an expression for it as:
Length of the longest glass-bottom bridge = 4.3 * y
Now, we can substitute the expression for y from the first equation:
Length of the longest glass-bottom bridge = 4.3 * (x + 128)
To simplify, distribute the 4.3:
Length of the longest glass-bottom bridge = 4.3x + 550.4
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Find the y-component of this
vector:
42.2°
101 m
Remember, angles are measured from
the +x axis.
Y-component of the vector as shown in the diagram is 67.84 m in the direction of the negative y-axis.
What is a vector?Vector is a quantity that has both magnitude and direction.
Examples a vectors are
VelocityAccelerationDisplacementForceWeightMoment. Etc.To find the Y-component of the vector, we use the formula below.
Formula:
Y = dsinα................. Equation 1Where:
Y = Y-component of the vectord = Distance of the vector along the x-y planeα = Angle of the vector to the x-axisFrom the question,
Given:
d = 101 mα = (180+42.2) = 222.2°Substitute these values into equation 1
Y = 101sin222.2°Y = 67.84 mHence, the y component is 67.84 m.
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An a frame house has a front facade measuring 30' across and 20' in height what is the area of the facade
The area of the facade measuring 30' across and 20' in height is 300 square feet.
The front facade of an A-frame house is a triangular shape, with a base of 30 feet and a height of 20 feet. To calculate the area of the facade, we need to use the formula for the area of a triangle, which is 1/2 times the base times the height = 1/2 * b * h, where b is the base and h is the height.
In this case, the base is 30 feet and the height is 20 feet, so we can plug those values into the formula:
Area = 1/2 x 30 x 20
Simplifying the multiplication, we get:
Area = 300 square feet
Therefore, the area of the front facade of the A-frame house is 300 square feet.
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Determine the minimum and maximum value of the following trigonometric function.
f(x)=10sin(2/5x)+5
The minimum value of the function is -5 and the maximum value of the function is 15.
The minimum and maximum value of the given trigonometric function f(x)=10sin(2/5x)+5 can be determined by analyzing the amplitude and period of the sine function. The amplitude of the sine function is 10, which means that the maximum value of the function is 10+5=15 and the minimum value is -10+5=-5.
The period of the sine function is given by 2π/2/5=5π. This means that the function completes one full cycle every 5π units. To find the minimum and maximum values of the function, we need to evaluate it at the critical points of the function, which occur at intervals of 5π.
At x=0, the function has a value of 5+10sin(0)=15, which is the maximum value of the function. At x=5π/2, the function has a value of 5+10sin(2π/5)=5, which is the minimum value of the function.
At x=[tex]5π[/tex], the function has a value of 5+10sin(4π/5)=-5, which is the maximum value of the function. At x=15π/2, the function has a value of 5+10sin(6π/5) =5, which is the minimum value of the function.
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a school has 475 students.If the ratio of girls to boys is 2:3, how many boys are there?
Answer:
2x + 3x = 475
= 5x = 475
= x = 475/5
= x = 95
Answer:
285 boys
Step-by-step explanation:
2 + 3 = 5
475/5=95
Girls: 2 x 95= 190
Boys: 3 x 95 = 285
Check
285 + 190= 475
In a baseball game, a pop fly is hit, and its height in meters relative to time in seconds is modeled by the function h(t) = -4. 9t^2 + 8t + 1
The maximum height reached by the pop fly is approximately 3.27 meters.
How to find the maximum height reached by the pop fly?
The equation h(t) = -4.9t^2 + 8t + 1 models the height in meters of a pop fly hit in a baseball game as a function of time in seconds.
The coefficient of t^2 is negative (-4.9), which means that the graph of this function is a downward-facing parabola. This makes sense, as the ball will start at a certain height and then be pulled down by gravity as it moves through the air.
The coefficient of t is positive (8), which means that the height of the ball is increasing at first. This makes sense, as the ball is gaining altitude after being hit.
The constant term (1) represents the initial height of the ball when it was hit.
To find the maximum height reached by the pop fly, we can find the vertex of the parabola. The x-coordinate of the vertex is given by -b/2a, where a is the coefficient of t^2 and b is the coefficient of t. In this case, a = -4.9 and b = 8, so the x-coordinate of the vertex is:
x = -b/2a = -8/(2*(-4.9)) = 0.8163
To find the corresponding y-coordinate, we can plug this value of t into the equation:
h(0.8163) = -4.9(0.8163)^2 + 8(0.8163) + 1 = 3.27
Therefore, the maximum height reached by the pop fly is approximately 3.27 meters.
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Peter eats 3 carrot sticks, with 1 cup of peanut butter, p, every day before lacrosse practice. he practices 4 days a week.
select all the equivalent expressions that represents how much peter eats before practice in one week.
To find out how much Peter eats in one week (which is 7 days), we need to multiply this expression by 7.
How much Peter eats before practice in one week?Peter eats 3 carrot sticks and 1 cup of peanut butter before lacrosse practice every day, so in one day he eats:
3 + p
To find out how much he eats in one week (which is 7 days), we need to multiply this expression by 7:
7(3 + p)
Distributing the 7, we get:
21 + 7p
So the equivalent expressions that represent how much Peter eats before practice in one week are:
3 + 4p + 3p
4(3 + p)
21 + 7p
7(3p + 1)
So the correct answers are:
4(3 + p)
21 + 7p
7(3p + 1)
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An experiment is conducted with a coin. The results of the coin being flipped twice 200 times is shown in the table.
Outcome Frequency
Heads, Heads 75
Heads, Tails 40
Tails, Tails 35
Tails, Heads 50
What is the P(No Heads)?
85%
75%
37.5%
17.5%
The probability of no heads is given as follows:
P(No Heads) = 17.5%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The total number of outcomes is given as follows:
200.
The desired outcomes, those without heads, are Tails, Tails, which happened 35 times, hence the probability is given as follows:
p = 35/200
p = 0.175
p = 17.5%.
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Twenty-four pairs of adult brothers and sisters were sampled at random from a population. The difference in heights, recorded in inches (brother’s height minus sister’s height), was calculated for each pair. The 95% confidence interval for the mean difference in heights for all brother-and-sister pairs in this population was (–0. 76, 4. 34). What was the sample mean difference from these 24 pairs of siblings?
–0. 76 inches
0 inches
1. 79 inches
4. 34 inches
The sample mean difference from these 24 pairs of siblings is 1.79 inches.
To find the sample mean difference from these 24 pairs of siblings, you can use the given 95% confidence interval for the mean difference in heights, which is (-0.76, 4.34).
The sample mean difference is the midpoint of the confidence interval. To calculate this, add the lower bound (-0.76) and the upper bound (4.34) of the confidence interval, and then divide by 2:
(-0.76 + 4.34) / 2 = 3.58 / 2 = 1.79 inches
So, the sample mean difference from these 24 pairs of siblings is 1.79 inches.
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Mr. jackers was transporting a giraffe from one zoo to another. what is a reasonable amount of the weight of his cargo?
a. 200 lbs.
b. 400 lbs.
c. 1 ton
d. 2 tons
The reasonable amount of weight of his cargo Mr. Jackers while transporting a giraffe from one zoo to another is 1 ton and 2 tons. Options C and D are correct.
To arrive at a reasonable estimate, we can consider the average weight of a giraffe, which ranges between 2,600 lbs and 4,250 lbs for adult males and females, respectively.
Therefore, a reasonable amount for the weight of Mr. Jackers' cargo would be between 2,600 lbs and 4,250 lbs, which translates to either 1 ton or 2 tons.
Thus, options c and d are the only reasonable answers, with d (2 tons) being the safer choice.
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Offering brainiest to whoever can give me the answer fastest, a nice explanation, and the correct answer!
Box C has the smallest volume, followed by Box A, and Box B has the largest volume.
Explanation on how to get the least volumeFirst, we need to find the volume of each box.
Recall that the formula for volume of a box is given as:
V = length x height x width
For Box A,
V = 3 cm x 2 cm x 4 1/2 cm = 27 cm³
For Box B,
V = 2 1/3 cm x 3 cm x 5 cm = 7/3 cm x 3 cm x 5 cm = 35 cm³
For Box C,
V = 4 cm x 3 cm x 1 1/4 cm = 4 cm x 3 cm x 5/4 cm = 15 cm³
So, the order of the boxes by volume from least to greatest is: Box C, Box A, and Box B.
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Please help asap
0 = pi/3 radians. identify the terminal point and tan 0
An angle of 0 radians is an angle along the positive x-axis of the unit circle. Its terminal point is (1, 0).
The tangent of 0 radians is defined as the ratio of the y-coordinate to the x-coordinate of the terminal point, which is 0/1 = 0.
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