The probability that an individual man’s step length is less than 2.2 feet is 0.10 or 10%
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation , the z-score of a measure X is given by:
Z = (X - mean)/S.D
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 2.8 feet and a standard deviation of 0.5 feet.
Find the probability that an individual man’s step length is less than 2.2 feet.
This is the p-value of Z when X = 2.2. So
Z = (2.2 - 2.8)/0.5
Z = 0.6/0.5 = 1.2
Z = 1.2
has a p-value of 0.10
Therefore, the probability that an individual man’s step length is less than 2.2 feet is 0.10 or 10%
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Last week, a coral reef grew 19.8 mm taller. Use the facts to
find how much this is in meters.
m
5
Conversion facts for length
1000 millimeters (mm) = 1 meter (m)
100 centimeters (cm) = 1 meter (m)
10 decimeters (dm) = 1 meter (m)
1 dekameter (dam) 10 meters (m)
1 hectometer (hm) = 100 meters (m)
1 kilometer (km) 1000 meters (m)
=
-
reducing fraction
[tex] \frac{15}{40} = \frac{3}{8} [/tex]
The reduced or lowest form of 15 / 40 is 3 / 8. The given statement is true.
First, let us understand about the reducing a fraction:
To express a fraction in the lowest terms, divide the numerator and denominator by the greatest common factor of the numerator and denominator.
We are given:
15 / 40 = 3 / 8
Let the LHS; 15 / 40
We need to write the following fraction in the lowest terms:
15 / 40
To write 15 / 40 in the lowest terms, we divide the numerator and the denominator by the greatest common factor of 15 and 40.
Since the factors of 15 are 1, 2, 3, 5, and 15 and the factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40, the greatest common factor of 15 and 40 will be 5.
So we will divide the numerator and the denominator of 15 / 40 by 5.
15 ÷ 5 = 3
40 ÷ 5 = 8
So, the reduced form of 15 / 40 is 3 / 8 which is 15 / 40 = 3 / 8.
Thus, the reduced or lowest form of 15 / 40 is 3 / 8. The given statement is true.
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Find the equation of the linear function represented by the table below in slope-
intercept form.
Answer:
Answer: (-3,0)
Step-by-step explanation:
-1 - 2 = -3
1+2=3
3+2=5
2 is the common thing between 2 and 4, 4 and 6, 6 and 8 so from -2 + 2 = 0
Which of the following has the markings of the given statements and any applicable
relationships, properties, definitions or theorems?
OR bisects PQS,
QR bisects POS 2PRO-ZSRQ
OR bisects POS 4PRO-SRG
OR bisects
Which variables would the scatter plot at the right be most likely to represent?
Question 2 options:
The number of people at a concert and the total concession sales
The number of guests at a hotel and the total water consumption
The number of siblings a person has and the person's GPA
The total number of miles driven and the total gallons of gas used
The variables that the scatter plot at the right would be most likely to represent is option C: The number of siblings a person has and the person's GPA.
What types of variables are allowed to be used in a scatter plot?To illustrate how much one variable affects another, scatter plots are tools that are often used to place data points on a horizontal as well as vertical axis.
A marker is used to represent each row in the data table, and the position of the marker depends on the values of the columns that are set up on the X and Y axes.
From the graph above, the Independent variables (siblings) are typically plotted on the horizontal axis, and dependent variables (Person's GPA) are typically plotted on the vertical axis.
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The illustration represents the positions of two planes on a radar screen at an airport control tower. The control tower is located at the origin. The radii of the circles are in miles.
Due to a problem on the ground, the pilots have been told to continue circling the airport and to maintain the same airspeed. The planes are located at the same altitude. Determine the equation of the circle on which the two planes are flying.
Answer:
0, 08Step-by-step explanation:
You want the equation of the circle shown on the radar screen as having a radius of 8 miles, centered at the origin.
Equation of a circleThe equation of a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
ApplicationYour circle is shown as having a radius of 8 miles. It is centered at the same origin where the control tower is located. That means we have ...
(h, k) = (0, 0)
r = 8
Using these values in the circle equation gives ...
(x -0)² +(y -0)² = 8²
PLEASE HELP IM SO DESPRATE !!!!!PLEASE MARK CORRECT ANSWER IN EXPLANATION:)
The expression below is a polynomial. wy^2(8y^3 - 2y^2 + 7y) It simplifies to 40y^5 - 10y^4 + 35y^3. What must be the value of w?
==================================================
Explanation:
The term wy^2 out front multiplies with each term inside the parenthesis (because of the distributive rule).
Let's multiply the outer term with the first term inside the parenthesis to get the following:
wy^2 times 8y^3 = 8wy^5
Compare 8wy^5 with 40y^5, and we see the coefficients 8w and 40 match up. Therefore, 8w = 40 solves to w = 5
-3[-4(3-10)-12]-2(-1)
Answer:
-46
Step-by-step explanation:
i hopethis helps you!!
What is the slope of the line that passes through the points (-1, 6)(−1,6) and (14, 3)(14,3)?
The slope of the line that passes through the points (-1, 6) and (14, 3) is - 1 / 5.
We know that the slope of a line is given by the formula,
m = (y₂ - y₁) / (x₂ - x₁)
where (x₂, y₂) and (x₁, y₁) are the coordinates of any point on the line of slope.
We are given the following points;
(-1, 6) and (14, 3)
substitute the given value in the slope formula, we will get;
m = (3 - 6) / (14 - (- 1))
m = - 3 / 14 + 1
m = - 3 / 15
m = - 1 / 5
So, the slope is - 1 / 5.
Thus, the slope of the line that passes through the points (-1, 6) and (14, 3) is - 1 / 5.
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Can you solve these two problems please
For the given angles , the measure of the missing angles are as follow:
a. m ∠POQ = 36° , m ∠POR = 62°
b. m ∠RST = 40°
As given in the question,
For the given angles , the measure of the missing angles are given as follow:
a. Q is in the interior of angle POR ,
Measure of angle POR = 2x -2
Measure of angle POQ = x + 4
Measure of QOR = 26°
From the given relation of the angles we have,
m ∠POQ + m ∠QOR = m ∠POR
⇒ x + 4 + 26° = 2x -2
⇒2x -x = (2+ 4+ 26)°
⇒ x= 32°
m ∠POQ = x + 4
= 32° + 4°
= 36°
m ∠POR = 2x -2
= 2(32) -2
= 62°
b. Q bisects angle RST
m ∠RSQ = 8x -12
m ∠RST = 10x
From the given relation we have,
8x -12 = (1/2)10x
⇒ 8x -12 = 5x
⇒8x -5x = 12
⇒3x =12
⇒ x= 4
m ∠RST = 10x
= 10(4)
= 40°
Therefore, for the given angles , the measure of the missing angles are as follow:
a. m ∠POQ = 36° , m ∠POR = 62°
b. m ∠RST = 40°
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solve for x
m = -12bx - 3 + 9x
Answer:
Below
Step-by-step explanation:
m = x ( -12b+9) - 3
m+ 3 = x (-12b+9)
x = (m+3) / ( -12b+9) 0r (m+3) / (9-12b)
g(x) = x¹¹ - 3x⁹ +2. I have to find the local minima using the second derivative test
x = √(27/11) is the local minima of the function g(x) = x¹¹ - 3x⁹ +2
Given, a function g(x) = x¹¹ - 3x⁹ +2
we have to find the local minima using the second derivative test.
first we differentiate the function,
g(x) = x¹¹ - 3x⁹ +2
g'(x) = 11x^10 - 27x^8
Now, putting g'(x) = 0
11x^10 - 27x^8 = 0
x^8(11x² - 27) = 0
Now, x = 0 or x = √(27/11)
After again differentiating the function we get
x = √(27/11) as the local minima of the function.
Hence, x = √(27/11) is the local minima of the function g(x) = x¹¹ - 3x⁹ +2
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12. Two functions are given below, one in equation form and the other in table form. Using these functions, give
the value of g (f (4)). Show how you arrived at your answer.
x
f(x)
-2
-1
0
3
4
12
7
9
19
6
g(x)=3.25x+6
The composition of the functions, when evaluated in x = 4, is:
g( f(4)) = 39
How to find the value of g(f(4))?Here we have two functions, one is a linear function:
g(x) = 3.25*x + 6
And the other is f(x), which is defined on a table.
We want to find the composition:
g( f(4)) = 3.25*f(4) + 6
Then we need to find the value of f(4), on the table we have the pair:
x f(x)
4 12
Which means that:
f(4) = 12
Replacing that we get:
g( f(4)) = 3.25*f(4) + 6
g( f(4)) = 3.25*12 + 6 = 39
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What is the solution to the system of equations?
-2x + 5y = -16
3x - 4y = 17
The solution of the system of equations is , x= -16 - 10/2 = 13
What is equations?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.A linear equation may have more than one variable. A linear equation is an equation in which the highest power of the variable is always 1.This is a second-order equation. In quadratic equations, at least one of the variables should be raised to exponent 2.According to our question-
-2x + 5y = -16 (3) = -6x + 15y = -48
3x - 4y = 17 (2) = 6x - 8y = 34
7y = -14
y= -14/7 = 2
-2x + 5(2) = -16
-2x + 10 = -16
x= -16 - 10/2 = 13
hence,The solution of the system of equations is , x= -16 - 10/2 = 13
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Marsha pays $25 each month for a car wash membership. Which of the following represents the total amount subtracted from her account after 4 months of having the membership?
A. −4|25| = −$100
B. 4|−25| = $100
C. |−25| − |4| = $21
D. |−25| − 4 = $21
Answer:
B. 4|−25| = $100
Step-by-step explanation:
Hope this helps!
What is the sum of all integers n that make this statement true?
-3n < 7n-20 < 3n
The notation a < b < c means that a < b and b < c must both be true at once.
We can simplify the inequality to:
-1/2 < -1/n < -1/5
The solutions are n = 3 and n =4, and the sum of these is equal to 7
How to get the sum?
We start with the inequality:
-3n < 7n - 20 < 3n
First, we need to solve this for n.
if we divide all the inequality by n, we will get:
-3 < 7 - 20/n < 3
Now we can subtract 7 in all the parts to get:
-3 - 7 < -20/n < 3 - 7
-10 < -20/n < -4
Fiinally, if we divide by 20 we get:
-10/20 < -1/n < -4/20
-1/2 < -1/n < -1/5
So if n is only an integer number, the values of n that make the inequality true are:
n = 3 and n = 4
Then the sum of these two values is:
sum = 3 + 4 =7
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find the slope of (1,2) and (7,-1)
Answer:
Slope (m) = -1/2 or -0.5
Hope that helps ! ^^
Answer:
m= - 1/2
The step-by-step explanation is in the screenshot below!
Write equations for the horizontal and vertical lines passing through the point (2, -6).
horizontal line: 0
vertical line:
Continue
0
00
X
0=0
3
The horizontal line passing through the point (2, -6) is y = -6 and the vertical line passing through the point (2, -6) is x = 2
We need to write equations for the horizontal and vertical lines passing through the point (2, -6)
For a vertical line the value of x will never change. This will be true for any value of y.
So, the equation for a vertical line passing through this point is:
x = 2
Similarly, for a horizontal line the value of y will never change. This is true for any value of x.
So, the equation for a horizontal line passing through this point is:
y = -6
Therefore, the horizontal line passing through the point (2, -6) is y = -6 and the vertical line passing through the point (2, -6) is x = 2
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Line m passes through points (3, 4) and (10, 8). Line n is parallel to line m. What is the slope of line n?
Answer:
4/7
Step-by-step explanation:
(8-4)/(10-3) = 4/7
parallel = same slope
Answer:
The slope of line n is 4/7
Step-by-step explanation:
First find the slope of line m
m = ( y2-y1)/(x2-x1)
m = (8 - 4)/(10 -3)
m = 4/7
Parallel lines have the same slope
The slope of line n is the same as slope of line m
The slope of line n is 4/7
Graph the function a ƒ(z) = 1/2 + 3.
the point (-4, f(-4)).
The graph of the function f(x) = 1/4x + 3 is attached below and the point (-x, f(-4) ) is pointed on it.
Graph:
Graph refers the visual representation of the function of set of data.
Given,
Here we have the function f(x) = 1/4x + 3
Now, we have to plot the function into the graph and we also plot the point (-4, f(-4)) on it.
By using the graphing calculator, we have plot the function f(x) = 1/4x + 3, then we get the graph like the following.
In order to point the (-4, f(-4)),
We have to find the value of f(-4), by apply the value of x as -4 in the given function then we get the values of the function as,
=> f(-4) = 1/4 (-4) + 3
=> f(-4) = -1 + 3
=> f(-4) = 2
Therefore, the point is (-4, 2).
Now we have to plot this point on the graph, and the point is on the line of the given function.
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In the accompanying diagram, parallel lines AB and CD are intersected by GH at E and F
respectively. If m
The measure of the angle AEG = 92°
What are corresponding angles?Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal. The opening and shutting of a lunchbox, solving a Rubik's cube, and never-ending parallel railway tracks are a few everyday examples of corresponding angles. These are formed in the matching corners or corresponding corners with the transversal.
∠CFH + ∠EFC = 180( angles on a straight line)
making ∠EFC subject and substituting ∠CFH = 2x + 20, we have
∠EFC = 180 - ( 2x + 20)
∠EFC = 180 - 2x -20
∠EFC = 160 - 2x
but ∠EFC = ∠BEF ( alternate angles are equal)
substituting their values
160 - 2x = 3x - 10
collect like terms
-2x - 3x = -10 - 160
-5x = -170
x = -170/-5
x = 34
Also ∠EFC = ∠AEG = 160 -2x ( corresponding angles are equal)
∠AEG = 160 -2X, but x = 34
∠AEG = 160 - 2(34)
∠AEG =160 - 68 = 92°
In conclusion, The value of the ∠AEG = 92°
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Caroline invested $80,000 in an account paying an interest rate of 8 1/8% compounded
daily. Qasim invested $80,000 in an account paying an interest rate of 7 3/4/%
compounded quarterly. After 10 years, how much more money would Caroline have
in her account than Qasim, to the nearest dollar?
PLEASE HELP!
Caroline have $7901.5 more in her account than Qasim when they both invest together compounded for 10 years.
What is compound interest?Compound interest is when an amount receives interest on top of it each time interest is paid on the original amount. The principal (original) sum and the interest that has already accrued over the course of previous periods are used to calculate compound interest.
here,
Caroline invested $80,000 in an account paying an interest rate of 8 1/8% compounded daily for 10 years,
A=P(1+r/n)^n/t
=$180,266.48
Caroline invested $80,000 in an account paying an interest rate of 8 1/8% compounded daily for 10 years,
A=P(1+r/n)^n/t
=$172,365.02
The difference between amounts,
=$180,266.48-$172,365.02
=$7,901.46
When they both invest which is compounded for 10 years, Caroline has $7901.5 more in her account than Qasim.
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Answer: 7901
Step-by-step explanation:
Please help! Explain how to find the slope and y-intercept by just looking at the equation y=1/3x-2. Then graph the equation and verify your answers.
Slope of the given equation is m = 1/3
intercept of the given equation = (0 , -2)
and the graph is attached below .
What is slope ?Slope is a number that describes the steepness of a line, usually determined by calculating the ratio of the vertical distance to the horizontal distance (rise) between two points. The slope of the line is the rate of increase in y for any given increase in x. slope indicates the slope of the line, i.e. how much y increases as x increases. The slope is constant (the same) everywhere along the straight line. One way to think of the slope of a line is to think of a roof or ski slope. Both the roof and the ski slopes can be very steep or quite flat. In fact, both ski slopes and roofs can be perfectly flat (horizontal) like lines. There are no perfectly vertical ski slopes or roofs, but lines are possible. You can usually tell visually which slope is steeper than the other. Indeed, the three slopes gradually become steeper.Calculationusing slope intercept formula
y = mx + b
we get
slope of the given equation ( y = 1/3 x - 2 )
is m = 1/3
if we put values either of x or y
we get intercepts as ( 0 , -2 )
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What is −11 + |−5| − |−15|?
A. −11
B. −9
C. −26
D. −21
Answer:
d) -21
Step-by-step explanation:
Given problem,
→ -11 + |-5| - |-15|
Let's solve the given problem,
→ -11 + |-5| - |-15|
→ -11 + 5 - 15
→ -11 - 10 = -21
Hence, the answer is -21.
Answer:
D. −21
Step-by-step explanation:
The bars either side of an expression or a value are the absolute value symbol.
"Absolute value" means how far a value is from zero.
Therefore, the absolute value of a number is its positive numerical value.
Given expression:
[tex]-11 + |-5| - |-15|[/tex]
Absolute values in the given expression:
[tex]| -5 | = 5[/tex][tex]| -15 | = 15[/tex]Therefore:
[tex]\begin{aligned} \implies -11 + |-5| - |-15|&=-11+5-15\\&=-6-15\\&=-21 \end{aligned}[/tex]
point(s) possible
A class consists of 30 women and 18 men. If a student is randomly selected, what is the probability that the student is a woman?
OA.
OB.
O C.
OD.
38
51005/3 19
48
Ne:
The probability that the student selected is 5/8.
According to the question,
We have the following information:
A class consists of 30 women and 18 men.
Now, total students in the class = Number of women + number of men
Total students = 30+18
Total students = 48
Now, the probability that the student is a woman:
Probability of an event = Number of women/total number of students
30/48
(More to know: probability of an event can not be greater than 1.)
Now, converting this into the simplest form by dividing both the numerator and denominator by 6:
5/8
Hence, the probability that the student selected is 5/8.
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A pilot needs to know if a plane with clear the tower. The plane will travel 1500 yards
before lifting off the ground to travel another 603 yards after which point the plane will be
directly over the tower. If the plane had continued on the runway, it is another 600 yards
to the control tower, which is 198 feet high.
Which statement best describes how to determine if the plane clears the tower?
The statement that best describes how to determine if the plane clears the tower is;
Use the Pythagoras Theorem where the distance to the tower is a leg of the right triangle and the distance in the air is the hypotenuse. Find the other leg. Convert to feet to compare to the tower height
Given,
The length the plane will travel before lifting = 1500 yards
The distance further the plane will travel after lifting off the ground = 603 yards
The horizontal distance from the point of lifting off the ground to control tower = 600 yards
The horizontal distance from the point of liftoff to the control tower, the height of the control tower, and the distance of the plane's path after takeoff create a right triangle with the following sides:
The distance of the path of the plane after lifting off the ground = The hypotenuse side of the triangle
The horizontal distance from the point of lifting off the ground to control tower and the height of the control tower = The two legs of the right triangle
Let h stand for the height of the control tower, x for the horizontal distance from the plane's liftoff point to the control tower, and R for the length of the plane's route after liftoff, and we obtain;
h = √(R² - x²)
We have;
R = 603 yards
x = 600 yards
∴ h = √(R² - x²) = h = √(603² - 600²) = 60.07 yards
The height of the control tower, h = 60.07 yards
1 yard = 3 feet
∴ 60.07 yards = 3 × 60.07 feet ≈ 180.22 feet
Therefore, given that the height of the control tower = 198 feet, the plane at the height of approximately 180.22 feet clears the tower.
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1/7+2/6 please help me
Answer:
10/21
Step-by-step explanation:
1/7+1/6=6/42+14/42
=(6+14)/42
=20/42
=10/21
Is x/4-y/3=1 a linear question and what is it in standard form
Answer:
Step-by-step explanation:
so I believe the question is
[tex]\frac{1}{4}[/tex]X - [tex]\frac{1}{3}[/tex]Y=1
and we want to know if that is linear, and what the standard form for the equation would be
let's move a few things around using our algebra skillz
[tex]\frac{1}{4}[/tex]X-1 = [tex]\frac{1}{3}[/tex]Y
[tex]\frac{3}{4}[/tex]X-3 = Y
y = [tex]\frac{3}{4}[/tex]x-3 (in standard form y=mx+b)
y=[tex]\frac{3}{4}[/tex]x + (-3)
we can see that this does make a line, so it's linear, and it's in standard form now.
A baker makes 18 cakes in a 12-hour day.
How many does she make in a 60-hour week?
Lout
A baker makes 90 cakes in a 60-hour week
A baker makes 18 cakes in a 12-hour day.
So, the number of cakes she makes in an hour would be,
18/12 = 1.5 cakes/hour
We need to find the number of cakes she make in a 60-hour week.
Using unitary method we find the required number of cakes,
1.5 * 60 = 90
Therefore, a baker makes 90 cakes in a 60-hour week
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Calculate Sam’s regular pay amount overtime pay and gross pay for the first week of December
Step-by-step explanation:
that's a right answer u're working on sir appreciated