The standard deviation of X is $2.00.
Probability is the likelihood that a specific occurrence will occur. Probabilities can be written as proportions with a 0 to 1 or 0% to 100% range.
Let X be the amount one wins. If the die is 4 or 5, the amount one wins is $1. If the die is 6, the amount one wins is $4. If the die is 1, 2, or 3, the amount is $0. Then, the probability of winning from 1 to 6 is 1/6.
The value of the expected mean (μ) is,
[tex]\begin{aligned}\mu&=\sum X P(X)\\&=1\times \frac{1}{6}+1\times \frac{1}{6}+4\times \frac{1}{6}+0\times\frac{1}{6}+0\times\frac{1}{6}+0\times\frac{1}{6}\\&=\frac{6}{6}\\&=1\end{aligned}[/tex]
Therefore, the standard deviation (σ)is [tex]\begin{aligned}\sigma&=\frac{\sum(X-\mu^2)}{n}\\&=\frac{(1-1)^2+(1-1)^2+(4-1)^2+(0-1)^2+(0-1)^2+(0-1)^2}{6}\\&=\frac{12}{6}\\&=2\end{aligned}[/tex]
The answer is $2. The correct option is option E.
The complete question is -
In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5 you win $1, if the number of spots showing is 6 you win $4, and if the number of spots showing is 1, 2, or 3 you win nothing. Let X be the amount that you win. Use Scenario 6-2. Which of the following is the standard deviation of X? A. $1.00 B. $1.35 C. $1.41 D. $1.78 E. $2.00
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Use separation of variables to find the solution to the differential equation subject to the given initial condition.
dP/dt=0.07P, P(0)=30
The solution to the differential equation subject to the given initial condition is log P = 0.07t + log(30)
Differential equation in which the variables can be separated from one from one another are called separable differential equations
A general form to write a separable differential equation is
dy/dx = f(x)g(y)
where the variable x and y can be separated from each other
According to the question,
We have to solve dP/dt=0.07P by using separation of variable
=> dP/dt=0.07P
Dividing P both sides and multiplying dt
=> dP / P = 0.07 dt
Now Integrating both the sides
=> [tex]\int\limits {\frac{1}{P} \, dP = \int\limits {0.07} \, dt[/tex]
=> log P = 0.07t + c ------(1)
It is given that P(0)=30
which means at t = 0 , the value of P = 30
Substituting t = 0 and P = 30
log(30) = 0 + c
=> c = log(30)
Substituting the value of c back to equation (1)
log P = 0.07t + log(30)
=> log(P / 30) = 0.07t is our solution
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Find an equation of the ellipse that has center −3, 5, a major axis of length 8, and endpoint of minor axis 0, 5.
Equation of the ellipse that has center −3, 5, a major axis of length 8, and endpoint of minor axis 0, 5 is (x+3)²/25+(y-5)²/16=1
What is Ellipse?An ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.
Given,
center −3, 5,
Major axis of length 8
Endpoint of minor axis 0, 5.
Standard form of equation for an ellipse with vertical major axis:
(x-h)²/b²+(y-k)²/a²=1, a>b
(h,k)=(x,y) coordinates of center.
(-3, 5) are coordinates of centre
given length of vertical major axis:=8=2a=4
a=4
a²=16
Length of minor axis=b=5
b²=25
Hence, equation of the ellipse that has center −3, 5, a major axis of length 8, and endpoint of minor axis 0, 5 is (x+3)²/25+(y-5)²/16=1
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Convert the following Fahrenheit degrees to Celsius.
a. 104°F
b. 41°F
c. 131°F
d. 95°F
Answer:
A) 40
B) 5
C) 55
D) 35
Step-by-step explanation:
The formula is:
[tex]\frac{(F - 32)5}{9}[/tex]
F is the temperature in Fahrenheit.
A)
[tex]\frac{(104-32)5}{9}[/tex]
40
B)
[tex]\frac{(41-32)5}{9}[/tex]
5
C)
[tex]\frac{(131-32)5}{9}[/tex]
55
D)
[tex]\frac{(95-32)5}{9}[/tex]
35
how do you Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
The slope of the line is 9/13 according to the given line.
What is a slope?The same number is given for every two different points on the same line when the ratio is stated as a quotient ("rise over run"). On a falling line, there is a negative "rise." In a diagram that depicts a roof or a road as a description or a design, the line may be practical as established by a road surveyor.
The steepness, incline, or grade of a line can be approximated by the slope's absolute value. The slope of a line in the plane including the x and y axes is typically symbolized by the letter m and is defined as the difference in the y coordinate by the equivalent difference in the x coordinate between two different places on the line. The following equation encapsulates this:
Slope=rise/run
Rise=y₂-y₁
=-1-(-10)
=9
Run=x₂-x₁
=9-(-4)
=13
Therefore, slope=9/13
Hence, the slope of the line is 9/13.
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Determine the Type II error if the null hypothesis, H0, is: researchers claim that 65% of college students will graduate with debt. Select the correct answer below:
a.The researchers cannot conclude that greater than or less than 65% of college students will graduate with debt when, in fact, 65% will graduate with debt.
b.The researchers cannot conclude that 65% of college students will graduate with debt when, in fact, more or less than 65% of college students will graduate with debt.
c.The researchers cannot conclude that 65% of college students will graduate with debt when, in fact, 65% of college students really will graduate with debt.
d.The researchers cannot conclude that greater than or less than 65% of college students will graduate with debt when, in fact, greater than or less than 65% of college students will graduate with debt.
Since type I error is to reject the null hypothesis when null is true that's why the Correct option is C.
The researchers believe that more than or less than 65% of college students will graduate with debt, when in fact, 65% will.
The null hypothesis is true if the experimental result matches the predicted theoretical result. The null hypothesis is disproved and we examine an alternative one if there are any variations in the observed parameters between the samples. The null hypothesis was rejected, which opens the door for additional study but does not imply that the first experimentation was flawed. Usually, the null hypothesis is used to gauge the strength of the evidence.
Hence we get the required answer and the correct option is c.
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how can a translation and a rotation be used to map δhjk to δlmn?
The correct statement regarding how can a translation and a rotation be used to map triangle HJK to triangle LMN is given as follows:
Translate K to N and rotate about K until HK lies on the line containing LN.What are the translation and the rotation?
The translation just changes the position of the figure, hence it has to be among equivalent vertices of the triangles.
The equivalent vertices are given as follows:
H and L.K and N.J and M.The equivalent sides are given as follows:
HK and LN.
Thus the rotation is about K until HK lies on the line containing LN, and the third option is correct.
Missing InformationThe problem is given by the image shown at the end of the answer.
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A banquet hall charges $1500 to rent the hall and $85 per guest that attends.
Write an algebraic expression that represents the cost, C, of holding a party in this banquet hall given the number of guests, n.
The algebraic equation representing cost can be given as C= 85n+1500.
What is an equation in one variable and power one?
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers and x is a variable. This equation has only one solution which can be found by separating the constant and variable terms in the equation.
We are given that A banquet hall charges $1500 to rent the hall and $85 per guest that attends.
Let the number of guests be n
Hence, The equation can be given as
C = 85n+1500
Where C is the cost, n is the number of guests attending.
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PLS HELP
Complex numbers are used to describe current (1), voltage (E),
and impedance (Z). Impedance is the opposition to current.
The relation between these three variables is demonstrated by
the formula for Ohm's Law:
E = (I)(Z)
Given:
I = (3 + 3i)
Z = (2+2i)
find E
E=
The relation between these three variables is demonstrated by
the formula for Ohm's Law: E = (I)(Z) is 12i.
What is Ohm's Law?
According to Ohm's law, the resistance of the circuit and the current or energy travelling through the resistance are both exactly proportional to the voltage or potential difference between two places. V=IR is the equation for Ohm's law.According to Ohm's Law, assuming the temperature and other physical parameters don't vary, the current flowing through a conductor is precisely proportional to the potential difference applied across its ends. Through a resistor, current is inversely proportional to the voltage difference.
(3+3 i)(2+2 i)
Apply complex arithmetic rule: (a+b i)(c+d i)=(a c-b d)+(a d+b c) i
=(3 .2-3. 2)+(3 .2+3 . 2) i
Simplify [tex]$(3 \cdot 2-3 \cdot 2)+(3 \cdot 2+3 \cdot 2) i: \quad 12 i$[/tex]
[tex]$=12 i$[/tex]
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a is an infinitesimally stochastic matrix (i.e., its rows sum to zero). prove that e at is a stochastic matrix.
A stochastic matrix A's steady state is an eigenvector w with eigenvalue 1, such that the elements are positive and add up to 1. The theorem of Perron-Frobenius...
A square matrix A is stochastic if all of its entries are nonnegative, and the elements of each column total to 1. If all of the elements in a matrix are positive integers, the matrix is positive.
A stochastic matrix is a square matrix with probability vector columns. A probability vector is a numerical vector with entries that are real values ranging from 0 to 1 and whose sum equals 1.
(Stochastic processes, mathematics) A square matrix of rows of nonnegative real values, with each row adding up to A Markov chain's transitions are described by its element in the 'th row and 'th column, which describes the probability of moving from state to state in one time step.
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Put 51, -59, -1, and -98 in order
from least to greatest.
-1
51 -59
Submit
-98
I don't know this yet >
Answer:
Step-by-step explanation:
x>y
-x<-y
98>59
-98<-59
59>1
-59<-1
any negative value <any positive value (including 0)
combining
-98<-59<-1<51
When attempting to do his homework Mark incorrectly uses the addition property of equality below which statement would correct Mark's error?
The addition property of equality states that if two values are equal to a third value, then they are also equal to each other. In this case, 4 is equal to 5+2, so 4 must also be equal to 2+5. However, Mark wrote the equation incorrectly, so the correct statement would be 4 = 5 + 2.
Mark incorrectly uses the addition property of equality, below which statement would correct Mark's error?Mark's statement: 4 = 2 + 5Correct statement: 4 = 5 + 2The addition property of equality is a key concept in mathematics, and it is important to understand and use it correctly. In this case, 4 is equal to 5+2, so the correct statement would be 4 = 5 + 2. This is because the addition property of equality states that if two values are equal to a third value, then they are also equal to each other. Therefore, Mark's statement of 4 = 2 + 5 was incorrect, and the correct statement was 4 = 5 + 2. Understanding and applying the addition property of equality is essential for success in math.
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the Celisius and the Fahrenight temperature scales are relased by the equation c=5/6 (F-32) expresses F in terms of C.
Answer:
F = (9/5)C + 32
Step-by-step explanation:
C = 5/9(F-32) **you wrote the fraction wrong in your question, it's 5/9, not 5/6
C = (5F)/9 - 160/9
C + 160/9 = (5F)/9
9C + 160 = 5F
(9C + 160)/5 = F
F = (9/5)C + 32
Answer: F = (6C/5) + 32
To express F in terms of C, rearrange the equation to isolate 'F'.
Inverse OperationsTo rearrange the equation, we want 'F' to be by itself. To move numbers to the other side, we do the other pair of inverse operation to both sides. This cancels out what we don't need while keeping the left and right sides equal.
Pairs of inverse operations
Multiply ⇔ DivideAdd ⇔ SubtractCalculate[tex]\displaystyle { C = \frac{5}{6}*(F-32) }[/tex] Start with the equation in the question.
[tex]\displaystyle { C = \frac{5*(F-32)}{6} }[/tex] Rewrite. This is the same as the question.
[tex]\displaystyle { 6C = \frac{5*(F-32)}{6}*6 }\\[/tex] Multiply both sides by 6.
[tex]\displaystyle { 6C = 5*(F-32) }[/tex] Cancelled out 6 on the right.
[tex]\\\displaystyle { \frac{6C}{5} = \frac{5*(F-32)}{5} }[/tex] Divide both sides by 5.
[tex]\displaystyle { \frac{6C}{5} = (F-32) }[/tex] Cancelled out 5 on the right.
[tex]\displaystyle { \frac{6C}{5} = F-32 }[/tex] We don't need the brackets if 'F - 32' is alone.
[tex]\displaystyle { \frac{6C}{5}+32 = F-32+32 }[/tex] Add 32 to both sides.
[tex]\displaystyle { \frac{6C}{5}+32 = F }[/tex] Cancelled out 32 on the right.
[tex]\displaystyle { F = \frac{6C}{5}+32 }[/tex] Keep lone variables on the left side.
Therefore, the equation to convert Celsius to Fahrenheit is:
[tex]\displaystyle { F = \frac{6C}{5}+32 }[/tex]
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A rectangle has a length of 42 centimeters and a width of 18 centimeters. What
is the area of the rectangle, in square meters?
The area of the rectangle, in square meters, is 7.56 meters².
What is rectangular shape?Rectangles are quadrilaterals having four equal vertices and parallel sides that are equal to one another.
Given;
a rectangle has a length of 42 centimeters,
and a width of 18 centimeters.
To find the area of the rectangle:
We multiply the length of the rectangle by the width of the rectangle.
Use formula,
The area of the rectangle = length x width
Substitute the value of length and width
The area of the rectangle = 42 x 18
The area of the rectangle = 756 cm².
To change centimeter to meter:
We have the rate of change,
1 centimeter = 0.01 meter
756 centimeters = 0.01 x 756 meters
756 centimeters = 7.56 meters
Therefore, the area of the rectangle = 7.56 meters².
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In the figure below, N is between M and O, and O is between N and P . If MP=16, NP=13 , and MO=9 , find NO.
NO= ?
MP = 16 ,, where NP = 13
therefore : MP - NP = MN <=> MN = 16 - 13 <=> MN = 3
MP = 16 ,, where MO = 9
therefore : MP - MO = OP <=> 16 - 9 = MO <=> MO = 7
MO = 7 & MN = 3
therefore : MO - MN = NO <=> NO = 7 - 3 <=> NO = 4
Doreen Schmidt is a chemist. She needs to prepare 24 ounces of a 10% hydrochloric acid solution. Find the amount of 12 % solution and the amount of 16% solution she should mix to get this solution
Find the matrix A representing the reflection about the line L in R^2 which consists of all scalar multiples of the vector [6 3]. A = []
the matrix A, which is composed of all scalar multiples of the vector [6 3], and represents the reflection about the line L in R2.A = [[-6/7, 9/7],[9/7, 6/7]]
Let L be the line in R^2 which consists of all scalar multiples of the vector [6 3], then the equation of the line is y= (3/6)x.
We need to find the matrix A which represents the reflection about the line L.
Let (x1, y1) be any point on the line L and let (x2, y2) be its reflection about the line L.
Now, we know that the slope of the line L is 3/6, hence the slope of the normal to the line L is -6/3.
So, the equation of the normal to the line L is y = -(6/3)x. Now, we can use the point-slope form of the line equation to calculate the equation of the line passing through (x1, y1) and its reflection (x2, y2).
The line that connects (x1, y1) and (x2, y2) has the following equation:
y-y1 = (y2-y1)/(x2-x1) (x-x1)
=> y-y
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what’s 10.37304 rounded to the nearest hundredth?
Answer:
10.37
Step-by-step explanation:
3 in the thousandths place is lower than 5 therefore you have to turn the thousandths into a 0 and don't change the forenumber
Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line.
x y
9 7.38
9 6.75
12 13.08
9 7.42
11 7.56
13 8.53
7 5.93
4 5.33
12 8.1
6 6.46
5 5.44
According to the data provided, the regression line equation is given by
y=2.83+0.52x. The non-linear characteristics of data is ignored by the regression line.
What do you mean by regression line?The most popular statistical method for simulating a link between two sets of variables is linear regression. As a result, a linear regression equation that can be applied to data is created.
What is the formula to calculate the line regression?The required formula is:
[tex]y= a + b_{yx}x[/tex]
[tex]b_{yx} = \frac {n \sum xy - \sum x \sum y}{n \sum x ^ {2} - (\sum x) ^ {2}}[/tex]
[tex]a = \bar y - b_{yx} \bar x[/tex]
[tex]\bar x = 8.81 \\\bar y = 7.45\\\sum x ^ {2} =947\\\sum xy = 770.95[/tex]
[tex]b_{yx} = 0.52[/tex]
[tex]a=2.83[/tex]
y=2.83+0.52x .
In scatter plot, Non-linear characteristics is ignored by the regression line.
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Find the value of X that makes m n
8
x = 6
9
x=7
10
x= 15
see explanation in image
because you know that m and n are parralell you can use the vertical angle theorem as well as the fact that lines in a straight angle add to 180
if you have any questions just comment
A combat jet is flying at 750 mph, at 40,000 feet above the ground. It needs to descend all the way to 100 meters above the ground in order to engage the target, which is an oil depot several miles ahead. It descends along a diagonal, maintaining a constant speed of 750 mph along the diagonal. Ground radar at the oil depot shows the jet approaching along the horizontal at 738 mph. How fast is the jet descending vertically, in mph?
After solving the equation the jet is descending vertically at 12 mph.
What is Pythagorean Theorem?The Pythagorean Theorem is a mathematical statement that states that in a right triangle the sum of the squares of the lengths of the two sides that make up the right angle are equal to the square of the length of the hypotenuse. This theorem is named after the ancient Greek mathematician, Pythagoras. It can be expressed as the equation: a2 + b2 = c2, where 'a' and 'b' are the lengths of the two sides adjacent to the right angle and 'c' is the length of the hypotenuse. The Pythagorean Theorem is a fundamental tool used in geometry and trigonometry, and it is used to calculate the lengths of the sides of a right triangle. It can also be used to calculate the distances between two points or to calculate the area of a triangle.
The jet is descending at 12 mph. This can be calculated by using the Pythagorean Theorem. Since the jet is approaching the oil depot horizontally at 738 mph and descending diagonally at a constant speed of 750 mph, we can use the Pythagorean Theorem to calculate the vertical component of the jet's descent.
750^2 = 738^2 + x^2
x = √(750^2 - 738^2)
x = 12 mph
Therefore, the jet is descending vertically at 12 mph.
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In the figure below, points N, K, J, and H lie in plane Z.
Points L and M do not lie in plane Z.
For each part below, fill in the blanks to write a true statement.
L
N
Z
M
(a) K, , and are distinct points that are
collinear.
(b) LM and , are distinct lines that
intersect.
(c) Point N and line are coplanar.
(d) Another name for plane Z is plane.
Points H, J and K are collinear and I'll choose K, J, and H as the non-collinear points
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
Points H, J and K are collinear as they are on the same line. Pick either K or K to fill out the answer box. I'll go with point K.
it through. Imagine if the flat piece of paper could revolve about this axis (like a propeller). The fact that the points are not all on the same line ensures that we build exactly one individual plane.
I'll choose K, J, and H as the non-collinear points to give the object the name Plane KJH. There may be further options.
Hence, Points H, J and K are collinear and I'll choose K, J, and H as the non-collinear points
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At Kamari's Sweet Treats, cookies are packaged in boxes of 8. Depending on the cookie flavor, the most a box can cost is $16.
Let x represent how much each cookie costs. Which inequality describes the problem.
a x / 8 < 16
b 8 + x ≥ 16
c 8 x ≤ 16
d x − 8 ≤ 16
The inequality that describes the problem is C. 8x ≤ 16
Which inequality describes the problem?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
Since Kamari's Sweet Treats, cookies are packaged in boxes of 8 and the most a box can cost is $16. This will be:
8x ≤ 16
The correct option is C.
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Find the Maclaurin series for f(x) = xe^2x and its radius of convergence. Use only the definition of a Maclaurin series.
The Maclaurin Series of xe²ˣ: x + 2x² + 2x³+ 4/3x⁴+ 2/3x⁵ +....
Given that,
f(x) = xe^2x
Taylor series of function f(x) at a is defined as:
f(x) = f(a) + f'(a)/1!/(x-a) +f''(a)/2! (x-a)² +....
Maclaurin series of Function F(x) is a Taylor series of Function f(x) at: a=0
f(x) = f(0) + f'(0)/1! /(x) +f''(0)/2!/ (x)² +....
Apply the Maclaurin Formula
= 0 +d/dx (xe²ˣ)(0)/1! x + d²/dx² (xe²ˣ)(0)/2! x² +....
Evaluate the derivatives :
= 0 + 1/1! x + 4/2! x² + 12/3! x³ + ...
Refine :
= x + 2x² + 2x³+ 4/3x⁴+ 2/3x⁵ +....
So, the Maclaurin series for f(x) = xe^2x is x + 2x² + 2x³+ 4/3x⁴+ 2/3x⁵ +....
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The population of bears on a nature preserve was 95 last year.This year , the population increased by 20% . what is the new bear population on the preserve
Answer:
114
Step-by-step explanation:
120% of 95 = 1.2 × 95 = 114
Winnie, a waitress, holds a 5.0-N tray stacked with twelve 3.5-N dishes in one hand. The
length of her arm from her hand to her elbow is 30.0 cm and her bicepts exert a force 5.0 cm
from her elbow, which acts as a fulcrum. How much force must her biceps exert to allow her to
hold the tray?
The force exerted by her biceps to allow her hold the tray is 282 N.
What is force?Force is the product of mass and acceleration.
To calculate the force the biceps must exert to allow her hold the tray, we use the formula below.
Formula:
Fd = F'd'....................... Equation 1Where:
F = Weight of the tray and the platesd = Distance of her hand to her elbowF' = Force exerted by the biceptsd' = Distance of her biceps to the elbow.From the question,
Given:
F = 5+12(3.5) = 47 Nd = 30 cmd' = 5 cmSubstitute these values into equation 1 and solve for F'
47×30 = F'×5F' = 47×30/5F' = 282 NHence, the force exerted by her biceps is 282 N.
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what is the slope of the line through the points (-2,4) and (1,2)
Answer:
The slope is [tex]\frac{-2}{3}[/tex]
Step-by-step explanation:
An order pair is in the form (x y). The slope is the change in y over the change in x. From the 2 points our y's are 2 and 4. From the 2 points our x's are 1 and -2. to find the change you subtract.
[tex]\frac{2-4}{1 - -2}[/tex] = [tex]\frac{-2}{1 + 2}[/tex] [tex]\frac{-2}{3}[/tex]
where is root 19??????
Answer:
4.358
Step-by-step explanation:
sqrt(19) = 4.358
Suppose U1, U2, ..., Un are independent random variables and for every i = 1, ..., n, Ui has a uniform distribution over [0, 1].
(a) Find the probability density function of M = max(U1, ..., Un). (We solved the case n = 2 in class. This a generalization.)
(b) Define Z = min(U1, ..., Un). Find the c.d.f. and the p.d.f of Z. (Hint: write the event {Z > z} in terms of random variables U1, ..., Un.)
The probability density function will be expressed as f_M(x) = n * x^(n-1) and cumulative density function is f_Z(z) = n * (1-z)^(n-1).
To find the probability density function of M, we need to find the probability that M takes on a particular value x, which is equal to the probability that all of the random variables U1, ..., Un are less than or equal to x. Since the Ui are independent, this probability is equal to the product of the individual probabilities that each Ui is less than or equal to x. Since each Ui has a uniform distribution over [0, 1], the probability that Ui is less than or equal to x is simply x. Therefore, the probability that M takes on a particular value x is equal to x^n.
This means that the probability density function of M is given by:
f_M(x) = n * x^(n-1)
for x in the range [0, 1].
For the second part of the question, we want to find the cumulative distribution function (c.d.f.) and probability density function (p.d.f.) of Z = min(U1, ..., Un). We can find the c.d.f. of Z by finding the probability that Z is less than or equal to a particular value z. This is equal to the probability that all of the random variables U1, ..., Un are greater than or equal to z. Since the Ui are independent, this probability is equal to the product of the individual probabilities that each Ui is greater than or equal to z. Since each Ui has a uniform distribution over [0, 1], the probability that Ui is greater than or equal to z is simply 1-z. Therefore, the probability that Z is less than or equal to z is equal to (1-z)^n.
This means that the cumulative distribution function of Z is given by:
F_Z(z) = (1-z)^n
for z in the range [0, 1].
To find the probability density function of Z, we can differentiate the cumulative distribution function with respect to z. This gives us:
f_Z(z) = n * (1-z)^(n-1)
for z in the range [0, 1].
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Since Scotty started doing his workout plan Janet has been inspired to set herself and go to do more exercises and walk a little more each day she has decided to walk 10 m more every day on day 20 she walked 800 M how many meters will she walk on today 21 on day 60
They walk 810 m on 21 day and 1,200 m on 60th day.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
She has decided to walk 10 m more every day on day 20 she walked 800 m.
Now,
Since, She has decided to walk 10 m more every day on day 20 she walked 800 m.
Hence, The amount of meters she walk everyday can be given as a linear function, and, the rate of variation is a constant (10 m/day):
⇒ 10 m / day
This constant (10 m/day) is the slope of the linear function.
And, We know that;
One point of the linear function (D(20) = 800) and the slope, so we can calculate the y-intercept:
⇒ D (t) = 10t + b
⇒ 800 = 10 × 20 + b
⇒ 800 - 200 = b
⇒ b = 600
So, The equation become;
⇒ D (t) = 10t + 600
Hence, For day t = 21;
⇒ D (21) = 10 x 21 + 600
⇒ D (21) = 810 m
And, For day t = 60;
⇒ D (60) = 10 x 60 + 600
⇒ D (60) = 1,200 m
Thus, They walk 810 m on 21 day and 1,200 m on 60th day.
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A college statistics professor has office hours from 9.00 AM: to 10.30 AM. daily sample of waiting times to see the professor (in minutes 10, 12,20, 15,17,10, 28,35, 28, 19,27, 25,22, 33, 37,14,21,20 Assuming & = 7.84, find the 99.74% confidence interval for the population mean. Round to two decima places_ a. 20.55 to 24.05 minutes b. 17.05 to 27.55 minutes c. 18.8 to 25.8 minutes d. 19.5 to 35. minutes
We are given the following data set:
10, 12,20, 15,17,10, 28,35, 28, 19,27, 25,22, 33, 37,14,21,20
Standard deviation = 8.043
Confidence level = 1 - Significance Level = 1 - 99.74% = 4.56% = 0.0456
