The required equation is tt = 48 km ÷ rr kilometers/hour
To write an equation that represents how many hours (tt) the 48 km trip will take if Saul bikes at a constant rate of rr kilometers per hour, we can use the formula for time:
time = distance ÷ speed
The distance Saul has to cover is 48 km, and he bikes at a constant rate of rr kilometers per hour.
Therefore, we can substitute these values into the formula above:
tt = 48 km ÷ rr kilometers/hour
This is the required equation.
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Determine the angle of rotation
Answer: b
Step-by-step explanation:
:)
Most Algebra 1 Formulas for needed for CST
The below would be most important Algebra 1 Formulas for CST.
Linear Equation:
\(Ax + By + C = 0\)
Equation of Straight Line or Slope:
\(y = mx+b\)
Point-slope form:
\(y-y_{1} = m(x-x_1)\)
Slope when 2 points are given:
\(m = \frac{(y_2 - y_1)}{(x_2-x_1)}\)
Quadratic Equation:
\(Ax^2 + Bx +C = 0\)
When lines are parallel:
Slope of both lines are equal. \(m_1 = m_2\)
When lines are perpendicular:
Slope of perpendicular lines are opposite reciprocals, meaning if the slope of a line \(l_1\) is \(\frac{1}{2}\). The line \(l_2\) perpendicular to \(l_1\) is \(-\frac{2}{1}\).
Work Formula:
Total Work Done = Number of Days \(\times\) Efficiency
where Efficiency is inversely proportional to Time Taken.
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A sample of a radioactive isotope had an initial mass of 360 mg in the year 1998 and
decays exponentially over time. A measurement in the year 2004 found that the
sample's mass had decayed to 270 mg. What would be the expected mass of the
sample in the year 2011, to the nearest whole number?
Answer:
193 mg
Step-by-step explanation:
Exponential decay formula:
\(A_t = A_0e^r^t\)where Aₜ = mass at time t, A₀ = mass at time 0, r = decay constant (rate), t = timeOur known variables are:
1998 to the year 2004 is a total of t = 6 years.The sample of radioactive isotope has an initial mass of A₀ = 360 mg at time 0 and a mass of Aₜ = 270 mg at time t.Let's solve for the decay constant of this sample.
\(270=360e^-^r^(^6^)\)\(270=360e^-^6^r\) \(\frac{3}{4} =e^-^6^r\)\(\text{ln} (\frac{3}{4} )= \text{ln}(e^-^6^r)\) \(\text{ln} (\frac{3}{4} )=-6r\) \(r=-\frac{\text{ln}\frac{3}{4} }{6}\) \(r=0.04794701\)Using our new variables, we can now solve for Aₜ at t = 7 years, since we go from 2004 to 2011.
Our new initial mass is A₀ = 270 mg. We solved for the decay constant, r = 0.04794701.
\(A_t=270e^-^(^0^.^0^4^7^9^4^8^0^1^)^(^7^)\) \(A_t=270e^-^0^.^3^3^5^6^2^9^0^7\)\(A_t=193.01982213\)The expected mass of the sample in the year 2011 would be 193 mg.
I will mark you brainlist and give 5 stars! Please help!
Answer:
9A-F
9B-EI
9C-FG
Step-by-step explanation:
Answer:
9A: Angle T
9B: Line IE
9C: Line FG
Step-by-step explanation:
rotate the pentagon EFGHI Respective to QRSTU
then just answer.
easy steps.
An Amtrak official obtains data on a particular day concerning the length of time (in minutes) that the metroliners leaving New York take to reach Philadelphia, with the following results:
93 89 91 87 91 89
Find the sample variance.
a. 3.6
b. 5.6
c. 6.8
d. 7.6
e. 4.4
The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.
The sample variance is a measure of how much the individual data points in a sample vary from the mean.
It is calculated by finding the average of the squared differences between each data point and the mean.
To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:
Calculate the mean (average) of the data set:
Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90
Subtract the mean from each data point and square the result:
(93 - 90)^2 = 9
(89 - 90)^2 = 1
(91 - 90)^2 = 1
(87 - 90)^2 = 9
(91 - 90)^2 = 1
(89 - 90)^2 = 1
Calculate the sum of the squared differences:
9 + 1 + 1 + 9 + 1 + 1 = 22
Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):
Variance = 22 / 5 = 4.4
It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.
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What is the value of numX when this program is executed? if 3 < 5 and 8 != 3: numX = 3 else: numX = 7 numX is .
Answer:
5
Step-by-step explanation:
Answer:
I think that the answer is 5
I hope this helps, have a wonderful day!
Step-by-step explanation:
Solve each inequality. Check your solution. (x/3) + 5 ≥ 1/6
The inequality given by (x/3) + 5 ≥ 1/6 has the solution x ≥ -29/2 or [-29/2 , +∞).
Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.
To solve an inequality is to find the values of x such that when we substitute that number for x we have a true statement.
Given the inequality (x/3) + 5 ≥ 1/6, subtract 5 from both sides.
(x/3) + 5 - 5 ≥ 1/6 - 5
x/3 ≥ -29/6
Multiply both sides by 3.
3(x/3) ≥ 3(-29/6)
x ≥ -29/2
To check, let x = -29/2
x = -29/2 ≥ -29/2
Substitute this value to the inequality.
(x/3) + 5 ≥ 1/6
(-29/2)/3 + 5 ≥ 1/6
1/6 ≥ 1/6
let x = -14,
x = -14 ≥ -29/2
Substitute this value to the inequality.
(x/3) + 5 ≥ 1/6
-14/3 + 5 ≥ 1/6
1/3 ≥ 1/6
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A dot plot going from 1 to 8. 1 dot is above 1, 4, 5, 7, and 8.
The mean for the data in the dot plot is 5. What is the absolute deviation for the data point at 7?
Answer:
2
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
Find the value of y
Answer:
y = 11°
Step-by-step explanation:
PR and QS and parallel lines and QR is a transversal.
Now,
5y = 55 (alternate interior angles)
y = 55/5
y = 11
I need help with school
Help me!!!
ln a certain clusters of school of 600 student the student can visit helu, park,both helu,park and neither. just as many visit both as many visit both as many visit neither. one quarter of those who visit park also visit helu. the total number who visit helu is 30 fewer than who visit park only. find how many visit helu only.
Answer:
this is your answer look it once.
Need help with some of my homework please
Answer:
A
Step-by-step explanation:
These are cross angles
Write an absolute value inequality to represent each situation:
A friend is planning a trip to Alaska. He purchased a coat that is recommended for outdoor temperatures from -15°F TO 45°F. Let t represent the temperature for which the coat is intended. Please show all steps too, please \(^v^)/
Answer:
I forgot about this app
Given: tan x- and x is in Quadrant IV. Find the exact values of sin (4), cos (4), and tan (4) without solving for x, when 0 ≤ x ≤ 360°. To enter the square root of a number, type "sqrt(a)". For example, type "sqrt(2)" to enter V2. a) sin (4) = cos (*) = tan (4) = b) c)
The exact values of sin (4), cos (4), and tan (4) are:
sin(4) = -√(1 - cos²(4))cos(4) = √(1 - sin²(4)) tan(4) = sin(4) / cos(4)Considering the trigonometric identities :
sin²(x) + cos²(x) = 1
tan(x) = sin(x) / cos(x)
Hence,
A.) sin(4):
Using the identity sin²(x) + cos²(x) = 1
sin²(x) = 1 - cos²(x)
sin(x) = ±√(1 - cos²(x))
Since x is in Quadrant IV, sin(x) is negative.
sin(4) = -√(1 - cos²(4))
B.) cos(4):
cos(x) = ±√(1 - sin²(x))
Since x is in Quadrant IV, cos(x) is positive.
cos(4) = √(1 - sin²(4))
C.) tan(4):
tan(4) = sin(4) / cos(4)
We can substitute the previously derived values of sin(4) and cos(4) into this equation.
Hence, the exact values of sin(4), cos(4), and tan(4) are :
sin(4) = -√(1 - cos²(4))
cos(4) = √(1 - sin²(4))
tan(4) = sin(4) / cos(4)
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A distribution in which all the values have the same frequency is called a(n) ______ distributiorectangularbimodalstandard.
A distribution in which all the values have the same frequency is called a rectangular distribution. This type of distribution is also known as a uniform distribution ,
because the probability of any given value occurring is equal to every other value in the distribution. Rectangular distributions can be represented graphically by a flat, straight line that runs across the entire range of values, indicating that each value has an equal chance of occurring.
This type of distribution is commonly used in probability and statistics, as well as in financial analysis and risk management. While rectangular distributions are relatively simple and easy to understand, they may not always accurately reflect the true nature of a dataset, particularly if there is a significant amount of variation or outliers.
It is important to note that bimodal and standard distributions have different properties and are not the correct terms for this scenario. Bimodal refers to a distribution with two distinct peaks, while standard distribution typically refers to a normal distribution with a mean of 0 and a standard deviation of 1.
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Problem 1 Part 1 a. For a gravel with D60 = 0.42 mm, D30=0.23 mm, and D10 = 0.15 mm, calculate the uniformity coefficient and the coefficient of gradation. Is it a well-graded or a poorly-graded soil? b. The following values for a sand are given: D10 = 0.28 mm, D30 = 0.39 mm, and D60 = 0.79 mm. Determine Cu and Ce, and state if it is a well-graded or a poorly-graded soil.
a. Cc = (0.23 mm)^2 / (0.42 mm * 0.15 mm) = 0.354.
b. Cc = (0.39 mm)^2 / (0.79 mm * 0.28 mm) = 0.256.
a. The uniformity coefficient (Cu) is calculated by dividing the D60 (effective size) by the D10 (coarsest size) of the gravel. In this case, the D60 is 0.42 mm and the D10 is 0.15 mm. Therefore, Cu = 0.42 mm / 0.15 mm = 2.8.
The coefficient of gradation (Cc) is calculated by dividing the square of the D30 (median size) by the product of the D60 and D10. In this case, the D30 is 0.23 mm. Therefore, Cc = (0.23 mm)^2 / (0.42 mm * 0.15 mm) = 0.354.
Based on the calculated values, we can determine the grading of the soil. A well-graded soil has a Cu value greater than 4 and a Cc value between 1 and 3. In this case, the gravel has a Cu value of 2.8, indicating that it is poorly graded.
b. To determine the Cu and Cc for the given sand, we can use the provided grain size distribution data.
Cu is calculated by dividing the D60 by the D10. In this case, the D60 is 0.79 mm and the D10 is 0.28 mm. Therefore, Cu = 0.79 mm / 0.28 mm = 2.82.
Cc is calculated by dividing the square of the D30 by the product of the D60 and D10. In this case, the D30 is 0.39 mm. Therefore, Cc = (0.39 mm)^2 / (0.79 mm * 0.28 mm) = 0.256.
Based on the calculated values, we can determine the grading of the soil. A well-graded soil has a Cu value greater than 4 and a Cc value between 1 and 3. In this case, the sand has a Cu value of 2.82, indicating that it is poorly graded.
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What is the slope? Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Step-by-step explanation:
Slope = (y2-y1)/(x2-x1)
Slope = (4-7)/(7-1)
Slope = -3/6
Slope = -1/2
Find the following, giving your answers
to 1 decimal place.
10 cm length
8 cm height
6 cm radius
a) The volume of the cone.
b) The curved surface area of the cone.
The volume of the cone is 1005.3 cubic centimeters. The curved surface area of the cone is 301.6 square centimeters.
a) The volume of the cone is 1005.3 cubic centimeters.
To calculate the volume of a cone, we use the formula V = (1/3)πr²h, where V represents the volume, π is approximately 3.14159, r is the radius of the base, and h is the height of the cone. By substituting the given values, we get V = (1/3) × 3.14159 × 6² × 8 = 1005.3 cubic centimeters.
b) The curved surface area of the cone is 301.6 square centimeters.
To determine the curved surface area, we use the formula A = πrl, where A represents the curved surface area, π is approximately 3.14159, r is the radius of the base, and l is the slant height of the cone. The slant height can be found using the Pythagorean theorem: l² = r² + h². Substituting the given values, we have l² = 6² + 8² = 100, resulting in l = 10. Plugging these values into the formula, we get A = 3.14159 × 6 × 10 = 301.6 square centimeters.
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represent the number of books a student buys at the next book fair. what is the expected value of
The following is the expected value of a number of books a student buys at the next book fair is 2.404 books.
How to determine a discrete probability distribution's expected value?The sum of each result of a discrete probability distribution times its corresponding probability is the distribution's anticipated value.The distribution is stated as follows based on the histogram provided by the picture just at end of the answer:P(X = 1) = 0.285P(X = 2) = 0.333P(X = 3) = 0.168P(X = 4) = 0.136P(X = 5) = 0.063P(X = 6) = 0.015The random variable b's expected value is then calculated as follows:
E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 E(X) = 2.404 books.
Thus, the expected value of discrete probability distribution is 2.404 books.
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The graph for the question is attached.
Consider the circle C of radius 8, centered at the origin. a. Find a parametrization for C inducing a counterclockwise orientation and starting at (8, 0). c(t) = ?, 0 ≤ t ≤ 2π b. Find a parametrization for C inducing a clockwise orientation and starting at (0, 8).
c(t) = ?, 0 ≤ t ≤ 2π c. Find a parametrization for C if it is now centered at the point (2, 4). c(t) = ?, 0 ≤ t ≤ 2π
The parametrization for C inducing a counterclockwise orientation and starting at (8, 0) is c(t) (8cos, 8sin) 0 ≤ t ≤ 2π, the parametrization for C inducing a clockwise orientation and starting at (0, 8) is c(t) (8cos, 8sin) 0 ≤ t ≤ 2π and parametrization for C if it is now centered at the point (2, 4) is C(t) = (4+ 8 cos, 2+ 8 Sin), 0 ≤ t ≤ 2π
The circle C of radius 8, centered at the origin, parametrization for C inducing a counterclockwise orientation and starting at (8, 0). c(t) :0 ≤ t ≤ 2π,
a) equation of the circle is x² + y² = 64.
starting point it (80) and orientation Counterclockwise.
c(t) (8cos, 8sin) 0 ≤ t ≤ 2π
b) Starting point is (0,8) and orientation is clockwise
c(t) (8cos, 8sin) 0 ≤ t ≤ 2π
c) equation of circle is (x-4)²+ (4-2)² - 64
For counterclockwise orientation
C(t) = (4+ 8 cos, 2+ 8 Sin), 0 ≤ t ≤ 2π
Therefore, the parametrization for C inducing a counterclockwise orientation and starting at (8, 0) is c(t) (8cos, 8sin) 0 ≤ t ≤ 2π, the parametrization for C inducing a clockwise orientation and starting at (0, 8) is c(t) (8cos, 8sin) 0 ≤ t ≤ 2π and parametrization for C if it is now centered at the point (2, 4) is C(t) = (4+ 8 cos, 2+ 8 Sin), 0 ≤ t ≤ 2π
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The double number line shows that 4 pounds of tomatoes cost $14. Draw these number lines on a separate sheet of paper. Draw tick marks and write labels to show the prices of 1, 2, and 3 pounds of tomatoes. Write your answers below.
If A = 30 degree and B = 60 degree , what is the value of sin(A+B). *
a) 0
b) 1/2
c) √3/2
d) 1
Answer:
I THINK it's B 1/2
Step-by-step explanation:
Sorry if wrong
Answer:
In this case, D
Step-by-step explanation:
Sin(30+60)=0.8939966636 which can be rounded to 0.89.
Now that we got that out of the way, we supposedly can follow the process of elimination.
It's clearly not A since we know the answer isn't equivalent to zero.
1/2 equals 0.5, meaning B's also not it.
We also know the answer isn't D, since 0.89 does not equal 1.
That only leaves C. Yet when check, just in case, √3/2 equals 1.22474487, meaning that's not the answer.
We've eliminated every answer so far, meaning we should go back and check our work. As I stated earlier, 0.8939966636 can be rounded to 0.89, but it can also be rounded to 1. Meaning, the closest answer to what we're looking for is D.
Of course, there could always be an error in the question itself, but unfortunately, there's no way to confirm that without asking your instructor or tutor.
I hope that helps.
chauncey billups, a current shooting guard for the los angeles clippers, has a career free-throw percentage of 89.4%. suppose he shoots six free throws in tonight's game. what is the standard deviation of free throws that billups will make
The standard deviation of the number of free throws that Chauncey Billups will make in tonight's game is approximately 0.726.
To calculate the standard deviation of free throws that Chauncey Billups will make in tonight's game, we need to use the following formula:
Standard Deviation (σ) = √(n * p * (1 - p))
where n is the number of trials (free throws) and p is the probability of success (making a free throw).
In this case, n = 6 (as Billups shoots six free throws) and p = 0.894 (as his career free-throw percentage is 89.4%).
Substituting the values into the formula, we get:
Standard Deviation (σ) = √(6 * 0.894 * (1 - 0.894))
Calculating this expression, the standard deviation is approximately 0.726.
Therefore, the standard deviation of free throws that Chauncey Billups will make in tonight's game is approximately 0.726.
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what is the least number of students who would have to take the exam to ensure that the class average is within 3 of 74 with probability of 95% using the central limit theorem? g
108 students would have to take the exam to ensure that the class average is within 3 of 74 with a probability of 95%.
To answer this question, we need to use the central limit theorem and the formula for the margin of error:
The margin of error = z * (standard deviation of the mean calculated from the sample)
where z is the z-score corresponding to the desired level of confidence (in this case, 95%), and the standard deviation of the sample mean is equal to the population standard deviation by the square root of the size n.
Let's assume that the population standard deviation is 10 (this is just an example value) and we want the class average to be within 3 of 74 with 95% probability. This means that the margin of error is 3, and we need to solve for the sample size.
First, we need to find the z-score that corresponds to a 95% confidence level. Using a z-score table, we find that the z-score is approximately 1.96.
Next, we can plug in the values into the margin of error formula:
3 = 1.96 * (10 / sqrt(n))
Solving for n, we get:
n = (1.96 * 10 / 3)^2 = 107.68
Since we can't have a fraction of a student, we need to round up to the nearest whole number, giving us a minimum sample size of 108 students to give the exam so that the average is within 3 of 74 with a probability of 95% using the central limit theorem.
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I want to know if my answer to these questions were right
From the triangle given,
a) To find cosθ,
\(\cos \theta=\frac{Adj}{Hyp}=\frac{a}{b}\)b) To find tanτ,
\(\tan \tau=\frac{Opp}{Adj}=\frac{a}{x+y}\)c) To find tan (θ+φ),
\(\tan (\theta+\Phi)=\frac{Opp}{Adj}=\frac{x+y}{a}\)d) To find sin μ,
\(\sin \mu=\frac{Opp}{Hyp}=\frac{a}{b}\)e) To find csc τ,
\(\csc \tau=\frac{1}{\sin \tau}=\frac{1}{\frac{a}{c}}=\frac{c}{a}\)f) To find sec (θ+φ),
\(\sec (\theta+\Phi)=\frac{1}{\cos (\theta+\Phi)}=\frac{1}{\frac{a}{c}}=\frac{c}{a}\)Answers given above.
At Manzana Grocery Store, apples cost $2.80 per pound. Maricela bought 2.7 pounds of apples. How much did she pay for the apples?
Answer:
7.56
Step-by-step explanation:
Yo Wassup? >:D
You answer is $6.00!
Hopefully this helps! :D
Plot the point (11, 7) on the coordinate plane.
Answer:
Step-by-step explanation:
When you're asked to plot a point on a coordinate plane just remember that the coordinate given is of the form \((x,y)\).
So, first, we need to plot 11 on the \(x\)-axis (the line going left to right, horizontal) then plot 7 on the \(y\)-axis (the vertical line)
So we first go 11 units to the right along the \(x\)-axis then go up 7 units along the \(y\)-axis.
Hope this helped.
Plot a point on a coordinate plane just remember that the coordinate given is of the form . Follow this simple steps and the image given below.
Identity the variable range .Determine the scale of the graph.Number and label each axis and title of the graph.Show the positive and negative x-axis and y-axisFirst , find the value of x on the x-axis . give x = 11 .Find the value of y on the y-axis . given y = 7.Mark the point x=11 in the positive x - axisMark the point y=7 in the positive y - axis,.After this meet the points by the help of scale and write the co-ordinates.For more details about graph plot click the link given below.
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Write the expreion for the perimeter of the rectangle. Perimeter: If the perimeter of the rectangle i 120 120 inche, what i the value of � x ? � = x= inche
The expression used for the perimeter of the rectangle is given by :
Perimeter = 2 ( x + 5 ).
The value of x for given perimeter and width is equal to 55 inches.
Let 'x' inches represents the length of the rectangle.
Width of the rectangle is equal to 5 inches
Expression used to represents the perimeter of the rectangle is
= 2 ( length + width )
= 2 ( x + 5 )
Perimeter of the rectangle = 120 inches
⇒ 120 = 2 ( x + 5 )
⇒ x + 5 = 120 / 2
⇒ x = 60 - 5
⇒ x = 55 inches
Therefore, the expression used to represents the perimeter of the rectangle is 2 ( x+ 5 ) and the value of x is equal to 55 inches.
The above question is incomplete , the complete question is:
Write the expression for the perimeter of the rectangle.
Perimeter=
If the perimeter of the rectangle is 120 inches with width 5 inches, what is the value of x representing the length of the rectangle?
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The inability to remember how Lincoln's head appears on a penny, or whether the water in the sink drains clockwise or counterclockwise, is most likely due to a failure in:
Creation
There is no other way
Chase plans to repaint some classroom bookcases. He has 1 4/7 gallons of paint. All of the bookcases are the same size and each requires 1/3 gallon of paint. How many bookcases will the custodian be able to repaint with that amount of paint?