The mean and standard deviation of the vehicle speed are 58.33 and 11.64 respectively.
The vehicle speed on a particular bridge in china has normal distribution.
5% represents the 5th percentile which is here, 39.18 m/h.
Since 10% travels more than 73.27 m/h, 90% travels less than 73.27 m/h.
So here the 90th percentile is 73.27 m/h.
Also the z-score, z = (x-μ)/σ, where μ is the mean of normal distribution and σ, the standard deviation.
So 39.18 corresponds to the z with p-value 0.05, i.e., z = -1.645 [from the normal tables]
Hence, z = (x-μ)/σ
⇒ -1.645 = (39.18 - μ)/σ
⇒ -1.645σ = 39.18 - μ
⇒ μ = 39.18 + 1.645σ ----------(1)
Also 73.27 corresponds to the z with p-value 0.9,i.e., z = 1.28.
Hence , z = (x-μ)/σ
⇒ 1.28 = (73.27 - μ)/σ
⇒ 1.28σ = 73.27 - μ
⇒ μ = 73.27 - 1.28σ ----------(2)
Equating (1) and (2), we get,
39.18 + 1.645σ = 73.27 - 1.28σ
2.925σ = 34.05
σ = 11.64
hence μ = 39.18 +1.645 x 11.64
⇒ μ = 58.33
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after 4 years what is a total amount of a compound interest investment of $30,000 at 2% interest compounded monthly?round to the nearest cent
Compound interest formula:
A = P (1+r/n)^nt
Where:
A = total amount
P = principal investment
r= interest rate in decimal form = 2/100 = 0.02
t= years
n= number of compounding periods in a year= 12
Replacing:
A = 30,000 (1+0.02/12)^4x12
A = 30,000 (1.001666667)^48
A= 32,496.45
5=3+a check
need the answer
Tommy earned $88.00 working for 5 hours. At this rate, how much will Tommy earn working for 12 hours?
At this rate, Tommy will earn $211.2 working for 12 hours.
The Unitary Method draws a relation between given data. Following the regular trend, information can be calculated. It is also called the 'Mango Method'.
Tommy earned $88.00 working for 5 hours.Tommy will earn $17.6 working for 1 hour.At this rate, Tommy will earn $211.2 working for 12 hours.
The Unitary Method is only valid for regular increases or decreases. Information about unity is drawn from given data, which is multiplied as required. It is widely used in the calculation of prices, amounts, etc.
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(No need to graph unless want to)Determine the period and asymptotes please grade 12 trig
SOLUTION:
The parent function is;
[tex]f(x)=sec(x)[/tex]The transformation applied is;
[tex]y=-2f(\frac{1}{4}x-\pi)+2[/tex]Graphing this, we have;
The period is the time to complete a cycle .
From the graph, the period is;
[tex]8\pi[/tex]The asymptotes are those lines for which sec x is undefined. those are lines where;
[tex][/tex]yeaa pls help this is past due
Answer: When you graph part a, it has a negative slope.
Step-by-step explanation:
Monica deposits $200 into a savings account that pays a simple interest rate of 4.4%. Paul deposits $300 into a savings account that pays a simple interest rate of 3.3%. Monica says that she will earn more interest in 1 year because her interest rate is higher. Is she correct? Justify your response.
Formula of simple interest rate:
[tex]S\mathrm{}I=\frac{P\times R\times T}{100}[/tex]Where,
[tex]\begin{gathered} P=\text{ Principal} \\ R=\text{ Rate} \\ T=\text{ Time} \end{gathered}[/tex]For Monica interest rate is:
[tex]\begin{gathered} S\mathrm{}I\mathrm{}=\frac{200\times4.4\times1}{100} \\ =8.8 \end{gathered}[/tex]For Paul interest rate is:
[tex]\begin{gathered} S\mathrm{}I\mathrm{}=\frac{300\times3.3\times1}{100} \\ =3\times3.3 \\ =9.9 \end{gathered}[/tex]No, Paul interest rate higher then Monic.
5/7 of the teaching staff in a certain primary school are females, what fraction of the staff are males
Answer: 2/7
Step-by-step explanation:
Substract 7/7 AKA the whole, by 5/7 tp get 2/7
2/7 is the fraction of males.
Inequalities in Two Triangles.
[?] < x < [ ]
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The inequality of the two triangle are 32° < x < 68° and the range of the value x is defined as x ≥ 4.
Inequality:
Inequality means the relationship between two values that are not equal is defined by inequalities which means they are not equal.
Given,
Here we have the two triangles with some angle values.
Now, we need to find the inequality of these triangle.
To find the inequality of the triangle first we have to write down the values provided, they are,
77, 11x - 33, 68°, 32°
Through this we have identified that, the value of x is lies in between 68° and 32°.
So, it ca be written as,
32° < x < 68°
The next this is to use the triangle inequality theorem, that is,
"The sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c."
Therefore, based on the given equation we have written it as,
11x - 33 ≥ 77
Subtract 33 on both sides then we get,
11x ≥ 44
Therefore, x ≥ 4.
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For the figure below, give the following
Answer:
Step-by-step explanation:
B
PLEASE HELP QUICKLY
What is the center of the hyperbola?
(y+3)^2/9 − (x−2)^2/2 = 1
Enter your answer by filling in the boxes.
The hyperbola has a center of (2, -3)
How to calculate the center of the hyperbola?The equation of the hyperbola is given as
(y + 3)²/9 − (x − 2)²/2 = 1
A hyperbola is generally represented as
(y - k)²/a² − (x − h)²/b² = 1
Where the coordinates of the center of the hyperbola is
Center = (h, k)
Next, we compare (y - k)²/a² − (x − h)²/b² = 1 and (y + 3)²/9 − (x − 2)²/2 = 1
From the comparison, we have
(h, k) = (2, -3)
This means that the center is (2, -3)
Hence, the coordinates of the center is (2, -3)
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-2x-7 > 1 or x - 2 ≥-1
The inequalities are solved below
What are inequalities?
A connection in mathematics that compares two numbers or other mathematical functions in an unequal way is known as an inequality. It is most frequently used to compare the sizes of two numbers on the number line. To indicate various sorts of inequalities, a variety of notations are employed. The following characteristics control inequalities. Any of these characteristics are also true if monotonic functions are restricted to strictly monotonic functions and all non-strict inequalities ( and ) are replaced by their equivalent strict inequalities ( and >). On each side of an inequality, a common constant c can be added to or removed from.
The inequalities are solved below
-2x-7>1 x-2≥-1
or, -2x>1+7 or, x≥-1+2
or, -x>8/2 or, x≥1
or, x<-4
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the length of a rectangle is 5 meters less twice it’s width. if the perimeter of the rectangular is 38 meters, then what is the value of the length
The length has a value of 9 meters
How to determine the length of the rectangle?From the question, we have the following parameters that can be used in our computation:
Length = 5 meters less twice it’s width
This means that
Length = 2Width - 5
The perimeter is given as
Perimeter = 38 meters
The perimeter is calculated as
Perimeter = 2 x (Length + Width)
So, we have
2 x (2Width - 5 + Width) = 38
Divide by 2
2Width - 5 + Width = 19
This gives
3Width= 21
Divide
Width - 7
Recall that Length = 2Width - 5
So, we have
Length = 2 * 7 - 5
Evaluate
Length = 9
Hence, the length is 9 meters
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Describe how to transform the graph of f(x)=x^2 into the graph of g(x)=4(3x-1)^2+5.
Please help me with this question! Thank You
The transformation from the graph of f(x) to g(x) is horizontal shift right 0.333 units and vertical shift is up 5 units.
The given functions are f(x) = x² and g(x)= 4(3x-1)²+5.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The transformation is
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Horizontal Shift: Right 0.333 Units
Vertical Shift: Up 5 Units
Reflection about the x-axis: None
Reflection about the y-axis: None
Vertical Compression or Stretch: Stretched
Therefore, the transformation from the graph of f(x) to g(x) is horizontal shift right 0.333 units and vertical shift is up 5 units.
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What is the image of ( − 8 , − 4 ) after a dilation by a scale factor of 1 4 4 1 centered at the origin?
The image of the point after the dilation is (-2, -1)
What is dilation?Dilation is the process of altering the side length of a shape or a function
How to determine the image of the points?From the question, the given parameters are:
Point = (-8, -4)
The scale factor of dilation is given as
Scale factor = 1/4
Mathematically, this transformation can be represented as
(x, y) = k(x, y)
Where k = 1/4 i.e. the scale factor
So, we have
(x, y) = (kx, ky)
This gives
(x, y) = (1/4x, 1/4y)
When represented as an equation, we have
Image = 1/4 * Point
Substitute the equation Point = (-8, -4) in the equation Image = 1/4 * Point
So, we have the following equation
Image = 1/4 * (-8, -4)
Evaluate the product
Image = (-2, -1)
Hence, the image is (-2, -1)
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A square has side length of 7.3 in. If the area is multiplied by 1/9, what happens to the perimeter. Please help!
Note that if the area of any figure is multiplied by a factor of a.
The perimeter will be multiplied by √a
From the problem, the are of the square is multiplied by 1/9, so we need to get the square root of that factor to get the factor for the perimeter.
[tex]\sqrt[]{\frac{1}{9}}=\frac{1}{3}[/tex]Therefore, the answer is C. multiplied by 1/3
a student group plans to donate school supplies for children in an orphanage. if notebooks that are normally 59 cents each are on sale two for 99 cents, how much can be saved by purchasing ten notebooks at the sale price?
The amount that can be saved by purchasing ten notebooks at the sale price is 95 cents.
What will the price be?The information stated that the notebook are in sale for 2 at 99 cents. The cost for each notebook will be:
= 99 cents / 2
= 49.5 cents
The amount they can be saved will be:
= (59 × 10) - (49.5 × 10)
= 590 - 495
= 95 cents
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Can someone help me with these two questions, I’m not sure if I’m correct or not.
5. The two triangles are similar. The value of x = 12.
6. The information cannot be used to show that the triangles are similar triangles.
How to Determine if two Triangles are Similar?Two triangles are similar to each other if they have the same shape but different sizes, in order words, they must have the same corresponding angle measures but different corresponding side lengths that are proportional to each other.
5. In the first figure, we see that there are two pairs of corresponding congruent angles (a pair of right angles and a pair of vertical angles in both triangles), but different corresponding side lengths.
Therefore, based on the AA similarity theorem that says two triangles are similar of they have two pairs of congruent sides, we can prove that both triangles are similar to each other.
Therefore:
x/9 = 20/15
15x = (9)(20)
15x = 180
15x/15 = 180/15
x = 12
6. The second image shows that the two triangles share a common side, which means they have a pair of corresponding sides that are congruent. Therefore, the information given cannot be used to prove they are similar triangles.
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Identify a pair of lines that looks parallel in the diagram.
pls help me
Lines f and g look to be parallel to each other.
Answer:
Lines G and F
Step-by-step explanation:
Parallel means never touching, and they usually run alongside eachother, that's why G and F look parallel.
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Select the correct answer. A circle with center O (0,0) has point B (4,5) on its circumference, which is joined by a line to O. What is the general form of the equation for the given circle centered at O(0, 0)? A. x2 + y2 + 41 = 0 B. x2 + y2 − 41 = 0 C. x2 + y2 + x + y − 41 = 0 D. x2 + y2 + x − y − 41 = 0
The general form of the equation: x2 + y2 − 41 = 0
The Correct option is (B).
Given,
A circle with center O (0,0) has point B (4,5) on its circumference
To find the what is the general form of the equation for the given circle centered at O(0, 0).
Now, According to the question:
How do you find the equation of a circle with center (0,0)?
x2 + y2 = r2 , and this is the equation of a circle of radius r whose center is the origin O(0, 0). The equation of a circle of radius r and center the origin is x2 + y2 = r2 .
The general form of the equation:
x2 + y2 − 41 = 0
Hence, The general form of the equation: x2 + y2 − 41 = 0
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what is the name of the function which has the form f(x)=mx+b, where m>0, and how can the graph of the function be described?
The correct option is D. i.e., Linear Function, Diagonal line which slants upward from left to right.
Given,
The function is :
f(x) = mx + b
and, where m> 0
Described the graph of the function and also write the name of the function:
Now, According to the statement is :
f(x) = mx + b , m > 0
It is an increasing line.
So, The correct option is D. i.e., Linear Function, Diagonal line which slants upward from left to right.
What is a increasing line in a graph?
If a linear graph is increasing then its gradient is positive, since when x increases by 1, y changes by a positive number. If a linear graph is decreasing, the gradient is a negative number.
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Zach submitted the work shown below when trying to simplify the expression 3 + 2(2x - 4) what mistake did he make and what is the correct simplified expression with correct steps
Answer:
The number “2” that is a outside the brackets multiplies both of the numbers inside the brackets.
Step-by-step explanation:
3+2(2x-4)
3+4x-8
4x-5
Select the conjecture with the rephrased statement of proof to show the diagonals of a parallelogram bisect each other.
BRO HELP ITS DUE TMRW WILL GIVE BRAINLIEST AND POINTS
Considering the given figure, the conjecture with the rephrased statement of proof to show the diagonals of a parallelogram bisect each other is: In parallelogram EFGH show EK is congruent to KG and F.K is congruent to KH
How to determine the correct rephrase of the proof about parallelogram diagonalsThe diagonals refer to the lines running between the two opposite ends of the parallelogram
Bisecting means sharing into two equal parts
congruent means a copy that is equal in dimension hence can be used in place of the other image
The diagonals of a parallelogram bisect each other means that the diagonals cut each other to form two equal parts such that each part is congruent to each other.
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i inserted a picture of the question answers to choices A 5/2B 2/5C -2/5D -5/2
If two lines are perpendicular, it means that the slope of one line is equal to the negative reciprocal of the slope of the other line. Given a value, a/b, the negative reciprocal of a/b is - b/a.
From the information given, the slope of the red line is 2/5. This means that the slope of the green line which is perpendicular to the red line is - 5/2
Option D is correct
462 people get on an empty train at a station. At the first stop, 234 more people get on the train, and 95 people get off. There are no more stops until the train reaches it final destination, where everybody gets off the train. How many people get off the train at the final destination?
Answer:
wow your so goood
Step-by-step explanation:
Find the perimeter and area of the figure, rounding to the nearest tent. Use 3.14 for pie 7 ft 25 ft 4 ft Perimeter = 89.12 feet Area = feet squared
According to the picture, you can find the area of the figure by susbtracting the area of the segments of the circles to the area of the rectangle. We can observe that these segments are a quarter of a circle, together they would be a complete circle, then to find the area of the figure we can substract the area of one of the circles to the area of the rectangle.
1. Find the area of the circle:
[tex]\begin{gathered} A=\pi r^2 \\ A=\pi(4)^2 \\ A=16(3.14) \\ A=50.24 \end{gathered}[/tex]2. Find the area of the rectangle:
To do it, you need to find the length and the width first, do it this way:
[tex]\begin{gathered} l=25+4+4=33 \\ w=7+4+4=15 \end{gathered}[/tex]Now, find the area of the rectangle:
[tex]\begin{gathered} A=l\cdot w \\ A=33\cdot15 \\ A=495 \end{gathered}[/tex]3. Find the area of the figure:
[tex]\begin{gathered} A=495-50.24 \\ A=444.76 \end{gathered}[/tex]The area of the figure is 444.76 feet squared.
Find the value of $x$ that makes this equation true:
\[2x + 5 = 1.99x + 22.\]
Please help quick!
The value of x that makes the equation 2x+5 = 1.99x + 22 is 1700
The equation is
2x+5 = 1.99x+22
First we have to rearrange the given term and combine the like terms, then we have to find the value of x
Move 1.99x to left hand side of the equation and move 5 to the right hand side of the equation
2x+5 = 1.99x+22
2x-1.99x = 22-5
We have to do the subtraction in like terms
(2-1.99)x = 22-5
0.01x = 17
Move the number 0.01 to the right hand side of the equation
x = 17/0.01
Division
x = 1700
Hence, the value of x that makes the equation 2x+5 = 1.99x + 22 is 1700.
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I will give 100 points!!
New Orleans is 2 feet about sea level, salton city has an elevation that is lower then New Orleans. What is a possible elevation in feet of salton city.
(Please give explanation!!)
Answer:
Salton City could have an elevation less than -2 or greater than 2 (depends on what u meant.
Step-by-step explanation:
Usually when u talk abt elevation, when it is lower than sea level, you write it with a negative sign. If you meant that new Orleans is 2 feet below sea level, the Salton City elevation could be anything less than -2. If you meant 2 feet above sea level, the New Orleans elevation could be anything above 2.
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CAN U PLSSSSSS HELP ME WITH THIS PROBLEM????
5. How many ways are there to distribute 10 indistinguishable candies among 4 different
children? Children may end up with no candies.
ive been struggling pls help
The probability that a random sample of n=40 oil changes results in a sample mean time of less than 20 minutes is 0.00714.
Given,
A random sample of n = 40
The mean time μ = 21.4
and, standard deviation is σ = 3.6 min
The z score (z) is given by the equation:
z = (x - μ) / σ / [tex]\sqrt{n}[/tex]
Substituting , the values we get
z = (20 - 21.4) / 3.6 /[tex]\sqrt{40}[/tex]
z = -2.45
Using the z table:
P(x < 20) = P(z < -2.45)= 0.00714
Hence, The probability that a random sample of n=40 oil changes results in a sample mean time of less than 20 minutes is 0.00714.
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What is the area of a triangle whose vertices are J(−2, 1), K(0, 3), and L(4, −1)?
Enter your answer in the box.
Based on the vertices of the triangle, the area of the triangle can be found to be 8 cm²
How to find the area of the triangle?First, find the lengths of JK, KL, and JL. When given vertices, you can find the length of a line by the formula:
= √ ( (x₂ - x₁)² + (y₂ - y₁)²)
The length of JK is therefore 2.83 units
The length of KL is therefore 5.66 units
The length of JL is therefore 6.32 units.
Given these units, the area of the triangle can be found by the formula:
= √ s(s - a) ( s - b) ( s - c)
Where:
s = semi perimeter
a, b, and c are the sides of the triangle which are JK, KL, and JL.
The semi-perimeter can be found by the formula:
= ( a + c + c) / 2
= 15.47 / 2
= 7.74
The area of the triangle is therefore:
= √ s(s - a) ( s - b) ( s - c)
= √ 7.74 (7.74 - 2.83) ( 7.74 - 5.66) ( 7.74 - 6.32)
= 8 cm²
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answer:
Well your answer is down below
Step-by-step explanation:
First as a Inequality −3(2x−5)<5(2−x)
Step 1: Simplify both sides of the inequality.
−6x+15<−5x+10
Step 2: Add 5x to both sides.
−6x+15+5x<−5x+10+5x
−x+15<10
Step 3: Subtract 15 from both sides.
−x+15−15<10−15
−x<−5
Step 4: Divide both sides by -1.
−x−1<−5−1 x>5
So your answer is x>5
hope this helps
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