The parametric equations for the tangent line to the curve at the given point are x = 1 - 7e−7cos(6)t + 6e−7sin(6)t, y = -7e−7sin(6)t - 6e−7cos(6)t, and z = 1 - 7e−7t.
The given parametric equations are x = e−7t cos(6t), y = e−7t sin(6t), z = e−7t, and the point is (1, 0, 1).
We can find the tangent line in two steps. First, we'll find the slope at the given point (1, 0, 1). Second, we'll use the point-slope form of a line equation to find the equation of the tangent line.
At the given location, determine the slope.
We can find the slope by taking the partial derivative of each coordinate with respect to t.
∂x/∂t = -7e−7tcos(6t) + 6e−7tsin(6t)
∂y/∂t = -7e−7tsin(6t) - 6e−7tcos(6t)
∂z/∂t = -7e−7t
Evaluating these derivatives at t = 1, we find:
∂x/∂t = -7e−7cos(6) + 6e−7sin(6)
∂y/∂t = -7e−7sin(6) - 6e−7cos(6)
∂z/∂t = -7e−7
At the given point, x = 1, y = 0, and z = 1.
Thus, the slope of the tangent line is:
m = (∂x/∂t, ∂y/∂t, ∂z/∂t) = (-7e−7cos(6) + 6e−7sin(6), -7e−7sin(6) - 6e−7cos(6), -7e−7)
Use the point-slope form of a line equation to find the equation of the tangent line.
The point-slope form of a line equation is:
r(t) = r₀ + m*t
Where r₀ is the point and m is the slope.
Thus, the equation of the tangent line is:
r(t) = (1, 0, 1) + (-7e−7cos(6) + 6e−7sin(6), -7e−7sin(6) - 6e−7cos(6), -7e−7)*t
Simplifying, we find:
x = 1 - 7e−7cos(6)t + 6e−7sin(6)t
y = -7e−7sin(6)t - 6e−7cos(6)t
z = 1 - 7e−7t
Therefore, the parametric equations for the tangent line to the curve at the given point are x = 1 - 7e−7cos(6)t + 6e−7sin(6)t, y = -7e−7sin(6)t - 6e−7cos(6)t, and z = 1 - 7e−7t.
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The parametric equations for the tangent line to the curve with the given parametric equations at the point (1,0,1) are:
x = 1 + e^-7t * (-7cos(6t) + 6sin(6t))
y = e^-7t * (-7sin(6t) - 6cos(6t))
z = e^-7t
The tangent line at a given point on a curve is a line that is locally closest to the curve at that point. To find the tangent line, we need to first find the derivative of the curve at the given point and then use it to find the slope of the tangent line. In this case, the given curve is a parametric equation and we can find the partial derivatives with respect to the parameter t.
Next, we use the partial derivatives to calculate the slope of the tangent line at the given point. Finally, we use the slope and the given point to write the parametric equations of the tangent line.
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(b) In a continuous series, the average marks of some students is 40 and the sum of their marks (Efm) is 2000. Then find the number of students. श्रेणीहरुको औसत प्राप्ता 40 र तिनीहरूको
Answer:
50
Step-by-step explanation:
To find the number of students, we can use the formula: average = (sum of marks) / (number of students).
Substituting the given values: 40 = 2000 / number of students
Solving for the number of students: number of students = 2000 / 40 = 50
So, there are 50 students in the series.
A triangle has a base of 14 inches and a height of 11 inches find the area
Answer:
... correct answer is 77 inches...
Answer:
A = 77 inches squared
Step-by-step explanation:
To find the area of a triangle, we use the formula
A = 1/2 bh where b is the base and h is the height
A = 1/2 (14) * 11
A = 77 inches squared
4.07, 74, 4.70, 0.47, 7.40 smallest to biggest pls hurry 30mins 50points and brainliest
Answer: 0.47, 4.07, 4.70, 7.40, 74
Step-by-step explanation:
0.47, 4.07, 4.70, 7.4, 74
Answer:
0.47,4.07, 4.70, 7.40, 74
Step-by-step explanation:
In order the numbers from smallest to biggest, you can compare them pair-wise. For example, 0.47 is smaller than 4.07, so 0.47 is the smallest number. You can continue comparing the remaining numbers pair-wise to find the next smallest number, and so on.
Here is a more detailed explanation of how to order the numbers from smallest to biggest:
1. Compare 0.47 and 4.07. 0.47 is smaller than 4.07, so 0.47 is the smallest number.
2. Compare 4.07 and 4.70. 4.07 is smaller than 4.70, so 0.47, 4.07, and 4.70 are the smallest three numbers.
3. Compare 4.70 and 7.40. 4.70 is smaller than 7.40, so 0.47, 4.07, 4.70, and 7.40 are the smallest four numbers.
4. Compare 7.40 and 74. 74 is larger than 7.40, so 0.47, 4.07, 4.70, 7.40, and 74 are the smallest five numbers.
Therefore, the numbers from smallest to biggest are:0.474.074.707.4074Students
does not use
uses
Total
does not use
141
94
Parents
235
a) List the two variables in this table.
b) What is the observational unit?
uses
85
125
210
c) How many students total do not use drugs?
Total
226
219
445
d) What is the total number of student-parent pairs in this study?
Answer:
a) The two variables in this table are "students" and "parents".
b) The observational unit in this study is a student-parent pair.
c) The total number of students who do not use drugs is 141.
d) The total number of student-parent pairs in this study is 445.
Step-by-step explanation:
a) The two variables in this table are "students and parents" who do not use drugs and those who use drugs.
b) The observational unit in this study is a student-parent pair.
c) The total number of students who do not use drugs is 141.
d) The total number of student-parent pairs in this study is 445.
What is an observational unit?An observational unit is described as an entity for which data is collected and analyzed and enables conclusions to be drawn about its characteristics.
An observational unit is assigned a value based on the collected data.
On the other hand, we define a variable as the piece of information being collected from each observational unit.
Does not use Uses Total
Students 141 94 235
Parents 110 100 210
Total 251 194 445
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Which of the following is assumed for establishing the unbiasedness of Ordinary Least Square (OLS) estimates? A. The error term has an expected value of 1 given any value of the explanatory variable. B. The regression equation is linear in the explained and explanatory variables. C. The sample outcomes on the explanatory variable are all the same value. D. The error term has the same variance given any value of the explanatory variable.
The regression equation is linear in the explained and explanatory variables.
In order for Ordinary Least Squares (OLS) estimates to be unbiased, the regression equation must be linear in both the explained and explanatory variables. This means that the relationship between the dependent variable (what is being explained) and the independent variables (what is being used to explain the dependent variable) must be linear. This is important because it ensures that the estimated coefficients of the regression equation accurately reflect the true relationship between the variables. Additionally, the error term must have an expected value of 0, given any value of the explanatory variable, and have the same variance given any value of the explanatory variable. This ensures that the estimated coefficients do not suffer from bias and that the OLS estimates are unbiased.
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3.1 Area under the curve, Part I: Find the probability of each of the following, if Z~N(μ = 0,σ = 1).
(please round any numerical answers to 4 decimal places)
a) P(Z < -1.35) =
b) P(Z > 1.48) =
c) P(-0.4 < Z < 1.5) =
d) P(| Z | >2)
The Probability can be determine using z-Table. The z- table use to determine the area under the standard normal curve for any value between the mean (zero) and any z-score.
a) P(Z < -1.35) =0.8708
b) P(Z > 1.48) =0.5714
c) P(-0.4 < Z < 1.5) =0.000
d) P(| Z | >2)=0.3830
What is z-table?Z-Score Table. A z-table, also known as the standard normal table, provides the area under the curve to the left of a z-score. This area represents the probability that z-values will fall within a region of the standard normal distribution.
Given:
The given condition is Z~N(μ = 0,σ = 1).
(a)
Find the value for .P(Z < -1.35)
Here Z is less than 1 that means Z is negative. So it will lies it lies on left hand side of mid value.
Refer the table of Area Under the Standard Normal Curve.
Now,
Thus, the value of .P(Z < -1.35) =0.8708
(b)
Find the value for .P(Z > 1.48)
Here Z is positive. So it will lies it lies on right hand side of mid value.
Refer the table of Area Under the Standard Normal Curve.
Now,
Thus, the value of .P(Z > 1.48) =0.5714
(c)
Find the value for .) P(-0.4 < Z < 1.5)
Here Z is positive. So it will lies it lies on right hand side of mid value.
Refer the table of Area Under the Standard Normal Curve.
Now,
Thus, the value of .) P(-0.4 < Z < 1.5) =0.000
(d)
Find the value for .P(| Z | >2)
Here Z is mod of Z, it may be positive or negative. Consider the negative value of Z.
Refer the table of Area Under the Standard Normal Curve.
Consider the positive value of Z.
Refer the table of Area Under the Standard Normal Curve.
Now,
Thus, the value of .P(| Z | >2)=0.3830
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The probability distribution is calculated z-table.
What is z-table?Z-table is also known as standard normal table which is used to find the area under the curve to the left of a z-score.
(a)P(Z<-1.35)
Here Z value negative so it is lies left of the curve, using standard normal table , P(Z<-1.35) = 0.0885
(b)P(Z>1.48)
z value is positive it lies right of the curve, using standard normal table, area under the curve P(Z>1.48)= 0.9306
(c)P(-0.4 < Z < 1.5) = P(Z<1.5) - P(-0.4<Z)
= 0.9332 - 0.3446
= 0.5886
(d)P(| Z | >2), |Z| is both positive and negative we have,
P(| Z | >2) = P(-2 < Z <2)
= P(Z<2) - P(-2<Z)
= 0.9772 - 0.0228
= 0.9544.
Hence, (a)P(Z<-1.35) = 0.0885
(b)P(Z>1.48) = 0.9306
(c)P(-0.4<Z<1.5) = 0.5886
(d)P(|Z|>2) = 1.9544
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Jeff created the following shape to fill with skittles. He also wants to decorate the outside with Skittle wrappers. Find the surface area to determine the number of skittle wrappers he would need to save and volume to determine how the amount of Skittles he could fill it with
Show work please and thank you
The surface area of figure is 784 ft² and the volume of the figure is 576 ft³.
What is volume?
Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
The shape created by Jeff is a cube + square pyramid.
The height of square pyramid is = 3 ft
The sides of cube = 8 ft
The formula for volume of cube = (side)³
Volume of cube = (8)³
Volume of cube = 512 ft³
The formula for volume of square pyramid = (base)² × height / 3
Volume of square pyramid = (8)² × 3/3
Volume of square pyramid = 64 × 1
Volume of square pyramid = 64 ft³
Total volume of the figure -
Volume of cube + Volume of square pyramid
Total volume = 512 + 64
Total volume = 576 ft³
The formula for surface area of cube = 6(side)²
Surface Area of cube = 6 × (8)²
Surface Area of cube = 6 × 64
Surface Area of cube = 384 ft²
The formula for surface area of square pyramid = 6(side)²
Surface Area of square pyramid = (side)² + 2(side) √[{(side)²/4} + (height)²]
Surface Area of square pyramid = (8)² + 2(8) √[{(8)²/4} + (3)²]
Surface Area of square pyramid = 64 + 16 √[{64/4} + 9]
Surface Area of square pyramid = 80 √[16 + 9]
Surface Area of square pyramid = 80 √25
Surface Area of square pyramid = 80 × 5
Surface Area of square pyramid = 400 ft²
Total surface area of the figure -
Surface Area of cube + Surface Area of square pyramid
Total Surface Area = 384 + 400
Total Surface Area = 784 ft²
Therefore, the volume and surface area of the figure is 576 ft³ and 784 ft² respectively.
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CAN SOMEONE HELP WITH THIS?✨
The marginal revenue when q = 29 is 510 dollars.
How to find the marginal revenue?To find the marginal revenue we need to differentiate the revenue equation, here we know that:
R(q) = -5q² + 800q
Differentiating that, we will get:
R'(q) = MR(q) = 2*(-5)*q + 800
= -10q + 800
The marginal revenue when q = 29 is
MR(29) = -10*29 + 800 = 510
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Someone than Can solve this pleaseeee:)
The value of the functions are (f o g) (2) = 0 and (g o f) (2) = 4.
What are functions?
In mathematics, a function is an expression, rule, or law that specifies the relationship between an independent variable x and a dependent variable y.
y and x are related in such a way that there is a distinct value of y for each value of x, and this relationship is frequently represented as y = f(x). In other words, for the same x value, there cannot be more than one value for f(x).
We are given two functions, f(x) and g(x).
Their graphs are also given.
We are asked to solve the following questions using the given graphs.
1) (f o g) (2) = f( g(2) )
To solve this we have to first start with inner functions.
g(2) = value of y when x = 2
From the g(x) graph it is given that g(2) = 2 when x = 2
Now we substitute this in f( g(2) )
i.e f(2) = value of y when x = 2 = 0
From the f(x) graph it is given that f(2) = 0 when x = 2.
So (f o g) (2) = 0
2) (g o f) (2) = g( f(2) )
f(2) = 0 ( as mentioned above)
Substituting,
g( f(2) = g (0) = 4
So (g o f) (2) = 4
Therefore the value of the functions are (f o g) (2) = 0 and
(g o f) (2) = 4.
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. ¿Qué cantidad por concepto de interés simple mensual produce un capital de $ 500,000 al 8% anual de interés simple?
Answer:
$500.000 × 0.08 = $40,000
$40,000/12 = $3.333.33
Step-by-step explanation:
El interés simple mensual se puede calcular como una fracción del interés anual. Para calcular el interés simple mensual, primero debemos calcular el interés anual y luego dividirlo entre 12 para obtener el interés mensual.
El interés anual se puede calcular multiplicando el capital por la tasa de interés:
$500,000 × 0.08 = $40,000
Luego, para obtener el interés simple mensual, dividimos el interés anual por 12:
$40,000 / 12 = $3,333.33
Por lo tanto, un capital de $500,000 al 8% de interés simple generará $3,333.33 de interés simple mensual.
A spherical boulder Is 24 ft in diameter and weighs almost 6 tons. Find the volume. Use 3.14 for n.
Answer:
5425.92
Step-by-step explanation:
radius(r)=d/2
=24/2
=12ft
So,
Volume=πr^3
=(3.14*12^3)cubic feet
=5425.92cubic feet
Answer:
V≈7238.23 [ft³].
Step-by-step explanation:
1. formula of the required volume is
[tex]V=\frac{4}{3} \pi R, \ where \ R-radius.[/tex]
2. if diameter is 24 ft., then R=12 [ft] and the required volume is:
[tex]V=\frac{4}{3} *3.1415*12^3=7238.2294[ft^3].[/tex]
I NEED HELP RIGHT AWAY PLS HELP
You asked amusement park visitors the question "How
many times did
left the park.
you ride the Ferris wheel today?" as they
Four people said they rode a Ferris wheel
5 times.
Explain how this would be shown on a dot plot.
On a dot plot, the statement saying that Four people said they rode a Ferris wheel five times would be represented with four dots above the input five.
What is a dot plot?
A dot plot shows the number of times that each observation was accrued in a data-set, which the number of dots representing the number of observations of each input.
The parameters for this problem are given as follows:
Input: number of times people rode the Ferris wheel.Output: number of dots.Hence the statement would be represented with four dots above the input five.
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Suppose That \( R \) Is The Finite Region Bounded By \( Y=X, Y=X+1, X=0 \), And \( X=3 \). find the exact value of the volume of the object we obtain when rotating about the -axis.
Step-by-step explanation:
Find Object Volume Rotation
Suppose That \( R \) Is The Finite Region Bounded By \( Y=X, Y=X+1, X=0 \), And \( X=3 \). find the exact value of the volume of the object we obtain when rotating about the -axis.
The region R is a triangular region defined by the lines y = x, y = x + 1, x = 0, and x = 3. To find the volume of the object obtained by rotating this region about the x-axis, we can use the method of cylindrical shells.
The height of the cylindrical shell is given by the difference between y = x and y = x + 1, or 1 unit. The radius of the cylindrical shell is given by x. Therefore, the volume of the object is given by:
\begin{align*}
V &= \int_{x=0}^{x=3} \pi x^2 \cdot 1, dx \
&= \pi \int_{x=0}^{x=3} x^2, dx \
&= \pi \left[ \frac{x^3}{3} \right]_{x=0}^{x=3} \
&= \pi \left( \frac{27}{3} - \frac{0}{3} \right) \
&= 9\pi
\end{align*}
So the volume of the object is equal to 9π cubic units.
The value of a car in 2000 was $32,000 and it is decreasing in value at a rate of 16.3% per year.
a.) Write an equation that represents the situation for any amount of time from 2000.
b.) How much will the car be worth in 2035?
Answer:
see below
Step-by-step explanation:
a. amount of time = t
Value = 32000*(1-16.3%)^t
b. in 35 years Value = 32000*(1-16.3%)^35 = 63.17
Unit rates have a denominator with what number?
In a unit rate, the denominator is always 1.
Chantal draws a polygon with seven congruent sides and angles. name Chantal Shape.Is the shape a regular polygon
A polygon with seven congruent sides and angles is called HEPTAGON. In this case
What is a polygon?A polygon is a two-dimensional closed figure with three vertices, three angles, and at least three straight sides. The words "Poly" and "gon" both mean many and angle, respectively. A triangle, for instance, has three vertices, three sides, and three angles. Therefore, it qualifies as a polygon.
Chantal "draws a polygon with seven congruent sides and angles," according to the statement. Heptagon is the name for a polygon with seven identical sides and angles. This polygon is a regular one because all of its sides and angles are equal. A regular polygon must have equal side lengths and angles by definition.
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Use fraction strips to find each sum
2 6/10 + 1 3/5
Answer:
4 1/5
Step-by-step explanation:
6/10 = 3/5
2+1=3
3+6/5 = 4 1/5
5. The table below gives prizes and probabilities of winning (on a single $1 ticket) for the Multi-State Powerball lottery.
Find the expected value of the winnings for a single lottery ticket if the jackpot is $30 million. How much can you expect to win or lose each year if you buy 10 lottery tickets per week? Do you expect to win or lose this exact amount? Explain.
I attached the table
the expected value for the given data set will be 0.423
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given, a data set gives prizes and probabilities of winning (on a single $1 ticket) for the Multi-State Powerball lottery.
We have to determine the expected value of winnings when buying one ticket. This can be computed using the expected value formula.
Recall the formula for the expected value E for events A and B whose probabilities of occurring are P(A) and P(B), respectively:
E = (P(A)×value for A)+(P(B)×value for B)
Using the formula above and extending it to 99 events yields:
E(x) = (1/ 292, 201,338 * 30,000,000) + (1 / 11,688,053 * 1,000,000) + (1/913,129 * 50,000) + (1/ 36,525 * 100) + (1/14,494 * 100) + (1/ 580 *7) + (1 /701 * 7) + (1/92 * 4) + (1/ 38 * 4)
E = 0.423
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GIVING BRAILIEST TO THOSE WHO ANSWER CORRECT AND TRY. please help! thanks
Answer:
the answer is A
Step-by-step explanation:
use the formula y=mx+b
25.95 is the slope because its a constant arte of change and 50 is the y-intercept because you gain $50 in addition to the slope
Answer:
y=25.95x+50
Step-by-step explanation:
25.95 is the dependent variable, so it is the coefficient. The starting amount, or the y-intercept, is 50. This makes the equation y=25.95x+50.
1. Cisco Enterprises in Ontario purchased the following in a single month all-inclusive of taxes:
• 16,000 units of network routers at $79.25 each
• 12,000 units of wireless LAN adapters at $129.95 each
• 13,500 units of computer boards at $229.15 each
Assuming all purchases are taxable, calculate the total tax amount the company paid on their purchases only. Round off to 2 decimal places only.
The total tax that the business paid on its purchases only was 769720.25.
How should tax be defined?In order to pay for general public institutions, goods, and activities, local, state, and federal governments must collect mandated payments or charges from citizens and corporations.
We must first figure out the complete cost of the goods in order to determine the total taxable income the corporation paid
The cost of the 16,000 network routers is:
16,000 units x $79.25/unit = $1,268,000
The cost of the 12,000 wireless LAN adapters is:
12,000 units x $129.95/unit = $1,559,400
The cost of the 13,500 computer boards is:
13,500 units x $229.15/unit = $3,092,025
The total cost of all purchases is:
$1,268,000 + $1,559,400 + $3,092,025 = $5,919,425
To calculate the total tax amount, we need to multiply the total cost by the tax rate. Assuming a tax rate of 13%, the total tax amount is:
$5,919,425 x 0.13 = $768,527.25
Therefore, the total tax amount that the company paid on their purchases only is $768,527.25, rounded off to 2 decimal places.
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If the minute hand of a clock is $20^\circ$ behind the hour hand at this moment, then in $18$ minutes, the minute hand will be how many degrees ahead of the hour hand?
The solution is, the minute hand will be 87.7 degrees ahead of the hour hand.
What is Subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
here, we have,
Let's call the current position of the hour hand H and the current position of the minute hand M.
At the start, we have H = 0 and M = -20 degrees.
After 18 minutes, the minute hand will have moved 18 * 6 = 108 degrees, while the hour hand will have moved 18 * (6/60) = 0.3 degrees.
So the new position of the minute hand is M + 108 = 88 degrees,
and the new position of the hour hand is H + 0.3 = 0.3 degrees.
Therefore, the minute hand will be 88 - 0.3 = 87.7 degrees ahead of the hour hand.
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The circular blade on a saw has a diameter of 8.25 inches and rotates at 4300 revolutions per minute. (a) Find the angular speed of the blade in radians per minute. (Round your answer to three decimal places.)
radians/min
(b) Find the linear speed of the saw teeth (in inches per minute) as they contact the wood being cut. (Round your answer to one decimal place.)
in/min
Step-by-step explanation:
a) Find the angular speed of the blade in radians per minute:
The formula for angular speed is given by:
ω = 2 * π * f
where f is the frequency of rotation in revolutions per minute, and π is approximately equal to 3.14159.
Plugging in the values, we get:
ω = 2 * 3.14159 * 4300 revolutions per minute
ω = 26,957.1 radians per minute
Rounding to three decimal places, the answer is:
ω = 26,957.1 radians per minute = 26,957.1 radians/minute
b) Find the linear speed of the saw teeth (in inches per minute) as they contact the wood being cut:
The formula for linear speed (v) is given by:
v = ω * r
where ω is the angular speed in radians per minute, and r is the radius of the blade (half of the diameter).
Plugging in the values, we get:
v = 26,957.1 radians/minute * 4.125 inches
v = 111,542.7 inches per minute
Rounding to one decimal place, the answer is:
v = 111,542.7 inches per minute = 111,543 inches/minute
If m∠1=95°, find the measure of ∠8
Answer:
If m∠1=95°, then m∠8 can be found by using the Exterior Angle Theorem, which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. In this case, m∠8 = 180 - (m∠1 + m∠3) = 180 - (95° + 55°) = 30.
It's election day for a club. If a president and vice-president are elected, how many different combinations can be made among twelve people?
Answer:
24
Step-by-step explanation:
You multiply the number of positions (2), by the number of people (12).
A trucking company determined that the distance traveled per truck per year is normally distributed, with a mean of 40 thousand miles and a standard deviation of 12 thousand miles. Complete parts (a) through (c) below.
Question content area bottom Part 1
a. What proportion of trucks can be expected to travel between 23 and 40 thousand miles in a year? The proportion of trucks that can be expected to travel between 23 and 40 thousand miles in a year is enter your response here. (Round to four decimal places as needed.)
b. What percentage of trucks can be expected to travel either less than 30 or more than 60 thousand miles in a year? The percentage of trucks that can be expected to travel either less than 30 or more than 60 thousand miles in a year is enter your response here%. (Round to two decimal places as needed.)
c. How many miles will be traveled by at least 90% of the trucks?
The number of miles that will be traveled by at least 90% of the trucks is enter your response here miles. (Round to the nearest mile as needed.)
Therefore, standard deviation problem solution is at least 90% of the trucks can be expected to travel 55,36 miles or less per year.
What is Standard deviation?Statistics uses variance as a gauge of difference. The following equation of that number is used to determine the average variance in between data and the mean. It includes all data points in with its computations, in contrast to other numeric measures of variability, by comparing the value of each data point to the mean.
Here,
a.
z1 = (23 - 40) / 12 = -1.42
z2 = (40 - 40) / 12 = 0
P(-1.42 < z < 0) = 0.4199
So, approximately 0.4199 or 41.99% of trucks can be expected to travel between 23 and 40 thousand miles in a year.
b.
z1 = (30 - 40) / 12 = -0.83
z2 = (60 - 40) / 12 = 1.67
P(z < -0.83) + P(z > 1.67) = 0.2023 + 0.0475 = 0.2498
So, approximately 24.98% of trucks can be expected to travel either less than 30 or more than 60 thousand miles in a year.
c. Thus:
x = 40 + 1.28(12) = 55.36
So, standard deviation problem solution is at least 90% of the trucks can be expected to travel 55,36 miles or less per year.
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Divide to find two equivalent fractions 40/10
Two equivalent fractions is 16/4, 100/25
What is an equivalent fraction example?Equivalent fractions are two or more fractions that are all equal even though they have different numerators and denominators. For example, the fraction 1/2 is equivalent to (or the same as) 25/50 or 500/1000. Each time the fraction in its simplest form is 'one half'.
Given here : The two fractions 40/
Now the quotient is 40/10=4
Equivalent fractions are the fractions that have different numerators and denominators but are equal to the same value. For example, 2/4 and 3/6 are equivalent fractions, because they both are equal to the ½
Thus two equivalent fractions here are 16/4,100/25 both will equal to 4
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solve the right triangle!!!
The value of a and c in the right triangle are 38.28 and 66.89 respectively.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables using mathematical operations like addition, subtraction, multiplication, exponents
Trigonometric ratio is used to show the relationship between the sides and angles of a right angle triangle.
From the diagram:
sin(55.0892) = 54.855/c
c = 66.89
Also:
tan(55.0892) = 54.855/a
a = 38.28
The value of a and c are 38.28 and 66.89 respectively.
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Two observers are 500 ft apart on opposite sides of a flagpole. The angles of elevation from the observers to the top of the pole are 17° and 16°. Find the height of the flagpole.
When two observers on opposing sides of a flagpole are 500 feet apart, the height of the flagpole is 48.077 feet.
what is angles ?In Geometry and trigonometry, an aspect is a shape made up of two rays, referred to as the angle's sides, that converge at a center point termed as the angle's vertex. Two rays can create an angle in the region where they are arranged. Additionally, when two planes collide, an angle is created. Dihedral angles are what they are called. An angle is a possible structure for two rays or lines with only a common end in planar geometry. The English term "angle" originated from the Latin word "angulus," which meaning "horn." The vertex is the common endpoint of the opposite rays, also known as the side of the angle.
given
distance between two observer = 300 ft
angle of elevation to top pole = 17° and 16°
height of the flagpole = ?
now,
Let x be the distance of the pole
tan17° = h /x
x = h / tan17°
now,
tan20° = h / 500 - x
500 - x = h / tan16°
again applying
500 - 3.49h = 2.75h
h = 48.077 ft
When two observers on opposing sides of a flagpole are 500 feet apart, the height of the flagpole is 48.077 feet.
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I need the answer to this math problem
20pts!!
Answer:
9
Step-by-step explanation:
9 makes it so that each set becomes a whole number.
Suppose a student's grade for a course is weighted and based on three categories homework average, quiz average, and a project average.A) lithe quiz average is 80% of grade and the homework average is 20% of grade, what percentage of Students grade is their project average?B) Ifa student has a homework average of 95, a quiz average of 80, and a project average of 88, what would be students course grade? Round to nearest whole number.
The project average is 100% of the student's grade, and if the student has the given averages, their course grade would be 89%.
The project average is the only component of the student's grade that is not weighted. The homework average accounts for 20% of the grade, while the quiz average accounts for 80%. Therefore, the project average is 100% of the student's grade. If the student has the given averages, then their course grade can be calculated by multiplying the homework and quiz averages by their respective percentages and adding the two products. In this case, the student's course grade would be (95 * 0.2) + (80 * 0.8) + 88 = 89%. The student's course grade would then be rounded to the nearest whole number, which is 89%.
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