Answer:
c or b
Step-by-step explanation:
What way can you simplify this equation?
Answer: 8√2
Step-by-step explanation:
Thomas has devised a scheme for splitting up the test and training set. For each row from coordinates : • Rows for Stanford students have a 50% chance of being placed in the train set and 50% chance of placed in the test set. • . Rows for Berkeley students have a 80% chance of being placed in the train set and 20% chance of placed in the test set.Given that a row is in the test set, what is the probability that it corresponds to a Stanford student? Assign that probability to prob_furd. Hint: Remember that there are 77 Berkeley students and 23 Stanford students in coordinates Hint 2: Thomas' last name is Bayes (15 points)
The probability that a row in the test set belongs to a Stanford student is 0.4167.
Given that,
Thomas has come up with a plan for dividing the training and test set. From the coordinates, for each row:
Students from Stanford have a 50% chance of being assigned to the test set and a 50% chance of being assigned to the train set for their rows.
20% of Berkeley students' rows are assigned to the test set, while 80% are assigned to the train set.
We have to find what is the probability that a row in the test set belongs to a Stanford student.
We know that,
Let us define events are as
B: Student in the coordinate is Berkeley student
S: Student in the coordinate is Stanford student
Tr: Rows is in the train set
Ts: Rows is in the test set
Since there are 77 Berkeley student and 23 Stanford student in coordinate
Hence,
P(B) = Probability that Student in the coordinate is Berkeley student
= 77/(77+23) = 77/100 = 0.77
P(S) = Probability that Student in the coordinate is Stanford student =23/(77+23) = 23/100 = 0.23
Conditional probability,
P(Ts|B) = Probability that Student placed in the test set when the student is Berkeley student = P(Ts|B) = 0.20
P(Ts|S) = Probability that Student placed in the test set when the student is Stanford student = P(Ts|S) = 0.5
Required probability,
Given that a row is in the test se, Probability that it corresponds to a Stanford student =
Probability of Stanford students = P(S|Ts) =
By Bayes theorem,
P(S|Ts) = P(Ts|S)×P(S)/P(Ts|S)×P(S)+P(Ts|B)×P(B)
P(S|Ts) = 0.22×0.5/0.22×0.5+0.20×0.77
P(S|Ts) = 0.4167
Therefore, The probability that a row in the test set belongs to a Stanford student is 0.4167.
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A line's y-intercept is 9, and its slope is 5. What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
y=____ x +____
The equation of the line that has a slope of 5 and y-intercept of 9 will be y = 5x + 9.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The slope of the line is 5. Then the equation is given as,
y = 5x + c
The y-intercept of the line is 9. Then the equation of the line is given as,
y = 5x + 9
The equation of the line that has a slope of 5 and y-intercept of 9 will be y = 5x + 9.
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Find the missing side and angle measures in triangle ABC. Round your answers to the neFind the missing side and angle measures in triangle ABC. Round your answers to the nearest tenth.arest tenth. Scalene triangle ABC with side AC labeled 23 and side BC labeled 15. Angle A measures 40 degrees. The measure of angle B is approximately . The measure of angle C is approximately . The length of side AB is approximately units.
Answer:
B = 80.3°, C = 59.7°, AB = 20.2B = 99.7°, C = 40.3°, AB = 15.1Step-by-step explanation:
You want the solution to scalene triangle ABC with AC = 23, BC = 15, and ∠A = 40°.
Law of SinesWhen two sides of a triangle are given, along with an angle not between them, the Law of Sines can be used to solve the triangle. It tells you ...
sin(B)/AC = sin(C)/AB = sin(A)/BC
When the given angle is opposite the shortest given side, there are generally 2 solutions.
Applicationsin(B)/23 = sin(40°)/15 . . . . . fill in given values to find angle B
B = arcsin(23/15·sin(40°)) = 80.3° or 99.7°
Angle C will have the value that makes up the difference from 180°:
C = 180° -40° -{80.3°, 99.7°} = {59.7°, 40.3°}
The length of side AB can be found using the same Law of Sines proportion:
AB = BC·sin(C)/sin(A) = 15/sin(40°)·sin({59.7°, 40.3°})
AB = {20.2, 15.1}
The solutions are ...
B = 80.3°, C = 59.7°, AB = 20.2B = 99.7°, C = 40.3°, AB = 15.1Arguably, the second solution is not a "scalene" triangle. It is (nearly) isosceles. (See the comment below.)
__
Additional comment
Since answers are requested to be rounded to tenths, both solutions are scalene triangles. If we rounded to integers, then only the first solution would be a scalene triangle.
: question 13 a teacher has decided to implement a curve to calculate grades for her class. her class average grade is a 65,
The minimum grade require to get grade of B is 78.6.
In the given that;
μ = 65 (average grade)
σ = 20 (standard deviation)
X ≈ N(μ, σ^{2})
Let c be the minimum grade to required to get grade of B
Percentage of data below c = 10% + 15% + 50% =75%
If we convert the percentage to probability = 75%/100% = 0.75
Now to get the value of c we solve the equation
P(X < c) = 0.75
⇒P{(X-μ)/σ < (c-μ)/σ)=0.75
Here z = (X-μ)/σ follows normal (0,1)
z is the standard normal variable
⇒P(z<(c-μ)/σ)=0.75
⇒P(z< (c-65)/20)=0.75
From z table we get, (c-65)/20 = 0.68
⇒(c-65)/20 = 0.68
⇒c= 78.6
So, minimum grade require to get grade of B is 78.6.
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The right question is given below:
Please solve the question in Image
Answer:
y(0.1) = 0.05, y(0.2) = 0.09
what is modified Euler method?Modified Euler's method is a numerical method used to solve ordinary differential equations (ODEs). It is a variation of Euler's method that is more accurate than the original, but still relatively simple to implement. It works by taking a single iteration of the Euler method, then using the midpoint between the current and previous points to calculate the next point in the sequence. This is done in order to reduce the error.
Solution
We have, y(0) = 0
dy/dt = 1 – y
h = 0.1
Using modified Euler's method,
y(0.1) = y(0) + (1/2) h (f(t0, y0) + f(t0 + h, y0 + hf(t0, y0)))
= 0 + (1/2) (0.1) [(1 - 0) + (1 - 0 + 0.1)]
= 0.05
Similarly,
y(0.2) = 0.1 + (1/2) (0.1) [(1 - 0.05) + (1 - 0.1 + 0.1)]
= 0.0975
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Solve the simultaneous equations
Show clear algebraic working.
7x+2y=5.5
3x-5y=17
Answer:
(1.5, - 2.5 )
Step-by-step explanation:
7x + 2y = 5.5 → (1)
3x - 5y = 17 → (2)
multiplying (1) by 5 and (2) by 2 and adding will eliminate y
35x + 10y = 27.5 → (3)
6x - 10y = 34 → (4)
add (3) and (4) term by term to eliminate y
41x + 0 = 61.5
41x = 61.5 ( divide both sides by 41 )
x = 1.5
substitute x = 1.5 into either of the 2 equations and solve for y
substituting into (1)
7(1.5) + 2y = 5.5
10.5 + 2y = 5.5 ( subtract 10.5 from both sides )
2y = - 5 ( divide both sides by 2 )
y = - 2.5
solution is (1.5, - 2.5 )
Questions 6-10. Suppose Calvin Cordozar Broadus, Jr. (aka Snoop Doggy Dogg) is
considering moving his family to Manhattan. His real estate agent has managed to locate a
penthouse apartment that overlooks Central Park for $2.4 million. He will have $2.1 million
from the sale of his current home as a down payment. Snoop would like to finance the
remainder of the cost and his banker has presented two options: a 30-year fixed-rate
mortgage at 8% or a 20-year fixed-rate mortgage at 7.5%.
How much will snoop have to finance?
Answer:
The price of the Penthouse is $2.4 million
Down Payment is $2.1 Million
So the amount that must be financed is $2.4 million - $2.1 million = $0.3 million or $300,000
Step-by-step explanation:
I thought of a number. If I add 30/7 to it, then subtract 22/7 from the result, and then subtract that difference from 59/7, I get 19/7. What is my number
Answer: 10
Step-by-step explanation:
x + 30/7-22/7-59/7 = 19/7
Add 59/7 to both sides:
x + 30/7-22/7 = 19/7 + 59/7
Add 22/7 to both sides
x + 30/7 = 19/7 + 59/7 + 22/7
Subtract 30/7 from both sides
x = 19/7+59/7+22/7-30/7
Simplify
x = 10
What is the maturity date of a loan taken out on June 6, for 73 days?
The number of days in June is 30
The number of days in July = 31
The number of days in August = 31
The maturity date for a loan taken out on June 6 for 73 days is August 28.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The date on which the loan was taken = June 6.
The number of days for the loan to mature = 73 days.
Now,
The number of days in June is 30
The number of days in July = 31
The number of days in August = 31
Now,
There are (30 - 6) = 24 days remaining in the month of June.
So,
24 + 31(July) = 45 days.
Now,
73 - 45 = 28 days need to be taken from August.
So,
45(July) + 28(August) = 73 days.
This means,
The maturity date is August 28.
Thus,
The maturity date for a loan taken out on June 6 for 73 days is August 28.
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Find the slope and y- intercept of the line -x + y = -10
Answer:
y-intercept | -10
slope | 1
Step-by-step explanation:
plane curve | Cartesian equation -x + y = -10 | y-intercept
slope
y-intercept | -10
slope | 1
A sample of 200 g of an isotope decays to another isotope according to the function A(t}=200 e^{-0.054t}, where t is the time in years.
(a) How much of the initial sample will be left in the sample after 25 years?
(b) How long will it take the initial sample to decay to half of its original amount?
(a) After 25 years, about ? g of the sample will be left.
(Round to the nearest hundredth as needed.)
According to exponential equation 52 g sample will be left in the sample after 25 years
What is exponential equation?
The exponential function may be a function denoted by f(x)=\exp or e^. Unless otherwise fixed, the term usually refers to the positive-valued operate of a true variable
Main Body:
Given =
A(t}=200 e^{-0.054t}
A)
t = 25 years
A(25}=200 e^{-0.054*25}
A(25}=200 e^{-1.35}
A(25}=200 *0.26
A(25}= 52 g
B) A = 100
A(t}=200 e^{-0.054t}
100 =200 e^{-0.054t}
e^{-0.054t} = 1/2
taking logarithm on both sides , we get
t = 12.83 years
Hence the value for each parts are as follows.
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2) Solve for m: 2.6m = 8.06
Answer: m = 3.1
Step-by-step explanation:
To solve for m you must divide 2.6m by 2.6m. Therefore, you must do the same on the other side of the equation.
2.6m/2.6m = 8.06/2.6m
m= 3.1
[tex]m=3.1.[/tex]
Step-by-step explanation:1. Write the equation.[tex]2.6m = 8.06[/tex]
2. Divide by 2.6 in both sides of the equation.[tex]\frac{2.6}{2.6} m=\frac{8.06}{2.6}\\ \\(1)m=\frac{8.06}{2.6}\\ \\m=\frac{8.06}{2.6}[/tex]
3. Simplify the fraction.[tex]m=\frac{8.06}{2.6}\\ \\m=3.1[/tex]
4 Verify the answer by substituting the calculated value by x in the original equation.[tex]2.6(3.1) = 8.06\\8.06=8.06[/tex]
That's correct!
5. Express the final result.[tex]m=3.1.[/tex]
An alloy is a combination of two or more metals. A certain alloy of metal is made up
of copper and tin. The relationship between the number of grams of copper in the
alloy, x, and the number of grams of tin in the alloy, y, is represented by the graph
below.
What is the constant of proportionality as shown in the
graph?
Amount of tin (in grams)
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.2
0.4
0.6
Amount of copper (in grams)
0.8
The constant of proportionality of the given linear graph is; 3/5
What is the constant of proportionality?The constant of proportionality is defined as the ratio of two proportional values that is said to be in a constant value.
Now, in this case where we have a graph, the constant of proportionality is equivalent to the slope of the graph.
The slope will be gotten using two coordinates (x₁, y₁) and (x₂, y₂) with the formula;
m = (y₂ - y₁)/(x₂ - x₁)
Let us use two coordinates on the graph (0.5, 0.3) and (1, 0.6)
m = (0.6 - 0.3)/(1 - 0.5)
m = 0.3/0.5
m = 3/5
This is same as the constant of proportionality.
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In a multiple regression problem involving two independent variables, if b1 is computed to be +2.0. It means that a. the estimated mean of Y increases by 2 units for each increase of 1 unit of X1, without regard to X2.
b. the estimated mean of Y increases by 2 units for each increase of 1 unit of X1. holding X2 constant.
c. the estimated mean of Y is 2 when XI equals zero.
d. the relationship between X1 and Y is significant
In multiple regression problem with two independent variables, value of one varible , b₁ is 2 then it means that the estimated mean of Y increases by 2 units for each increase of 1 unit of X₁, holding X₂ constant. So, second option is correct option.
Multiple Regression: Multiple regression is a statistical technique that can be used to analyze the relationship between a single dependent variable and multiple independent variables. The goal of multiple regression analysis is to use independent variables with known values to predict the value of each dependent value.
Y = b₁x₁+ b₂x₂ + … bₙxₙ + a
Here Y is the dependent variable, and X₁,…,Xₙ are the n independent variables. In calculating the weights, a, b₁,…,bₙ,
In the multiple regression b1 shows the coeffcient of independent variable X₁ in fitted model.
Here b₁ =+2.0 shows that for each unit increase in X₁, dependent variable Y is increased by 2 keeping other things constant.
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Find the value of q for which the equation
qx² - 6x + 18 = 0
has one repeated real root
q = ______
Answer:
q = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
given a quadratic equation in standard form
ax² + bx + c = 0 ( a ≠ 0 )
then the nature of the roots can be found using the discriminant
Δ = b² - 4ac
• if b² - 4ac > 0 then roots are real and irrational
• if b² - 4ac = 0 then the roots are real and equal
• if b² - 4ac < 0 then the roots are not real
qx² - 6x + 18 = 0 ← is in standard form
with a = q , b = - 5 , c = 18
for one repeated (equal) real root , then
b² - 4ac = 0 ( substitute values )
(- 6)² - (4 × q × 18) = 0
36 - 72q = 0 ( subtract 36 from both sides )
- 72q = - 36 ( divide both sides by - 72 )
q = [tex]\frac{-36}{-72}[/tex] = [tex]\frac{1}{2}[/tex]
What is the slope of the line?
What is the equation for the line? y = ________
is the graph proportional? Y or N
The slope of line is -3, the equation of line is y=-3x+2 and the graph is not proportional.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
From the given graph let us take two points (0, 5) and (1,2).
m=2-5/1=-3.
Now let us find the y intercept.
2=-0+b
2=b
So the equation of line is y=-3x+2.
As the graph is not passing through the origin, then the graph is not proportional.
Hence, -3 is the slope of line and y=-3x+2 is the equation of line and the graph is not proportional.
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Suppose that the functions g and h are defined as follows.
g(x)=5-4 x²
h(x)=5-4 x
(b) Find all values that are NOT in the domain of g/h
If there is more than one value, separate them with commas.
By using the concept of function, it can be calculated that-
a) [tex]\frac{g}{h}(-3) = -\frac{31}{17}[/tex]
b) The point [tex]\frac{5}{4}[/tex] is not in the domain of [tex]\frac{g}{h}[/tex]
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here,
a) The given functions are
g(x) = 5 - 4x²
h(x) = 5 - 4x
[tex]\frac{g}{h}(x) = \frac{g(x)}{h(x)} = \frac{5-4x^2}{5-4x}[/tex]
[tex]\frac{g}{h}(-3) = \frac{g(-3)}{h(-3)} = \frac{5 - 4(-3)^2}{5 - 4(-3)} = -\frac{31}{17}[/tex]
b) [tex]\frac{g}{h}(x)[/tex] is not defined if 5 - 4x = 0
[tex]\frac{g}{h}(x)[/tex] is not defined if [tex]x = \frac{5}{4}[/tex]
So the point [tex]\frac{5}{4}[/tex] is not in the domain of [tex]\frac{g}{h}[/tex].
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Determine if a triangle exists with the given side lengths.
3, 6, 2
Answer:
Not a triangle.
Criteria for it to be a triangle:
3 = A
6 = B
2 = C
A + B > C
B + C > A
A + C > B
What this says, is that if you add any two sides of the triangle, it needs to be bigger than the one you left out.
3 + 6 > 2 This one works
6 + 2 > 3 This one works
3 + 2 > 6 This one doesn't work because 5 is less than 6
Since the last one didn't work, it's not a triangle.
Deshaun wants to attend a college that will cost $25,600 for the first year. His uncle gave him a special gift of $2500 to use toward the cost. Deshaun plans to attend the college in 7 years. How much must Deshaun save each month to have enough for the first-year cost?
Answer:
$275
Step-by-step explanation:
25600-2500=23100 how much is left to pay
7*12=84 months left till college
23100/84=275 he would have to save per month
1. The first letter of the suspect's name matches the variable with the greatest value.
7J=105 OR g-16=2
The name starts with letter g as the variable has highest value.
What is variable?
A variable is associate degree alphabet or term that represents an unknown variety or unknown worth or unknown amount. The variables square measure specially utilized in the case of algebraical expression or pure mathematics.
Main body:
according to question:
7j = 105
simplifying the value , we get
j = 105/7
j = 15
similarly
g - 16 = 2
simplifying the value , we get
g = 18
value of g is greater than j .
Hence the name starts with letter g.
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Which proportion could be used to prove that HJ || KL?
The correct proportion used to prove that HJ || KL is [tex]\frac{GK}{HK} = \frac{GL}{LJ}[/tex].
What is the proportion theorem of two similar lines?
According to this theorem, if you draw a line parallel to one side of a triangle that divides the other sides into two separate points, the line will proportionally divide the other sides. In addition, a line is parallel to the third side if it divides any two triangle sides in the same ratio.
We have,
HJ || KL
If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.
And in the given triangle, HJ is parallel to KL, So HJ divided the two sides in proportion, that is
[tex]\frac{GK}{HK} = \frac{GL}{LJ}[/tex]
The correct option is the fourth option.
So, The correct proportion could be used to prove that HJ || KL
[tex]\frac{GK}{HK} = \frac{GL}{LJ}[/tex]
Hence, the correct proportion used to prove that HJ || KL is [tex]\frac{GK}{HK} = \frac{GL}{LJ}[/tex].
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Which answer choice correctly complete the sentence?
Asking the “Did you Check” questions is an important step in the Problem Solving Plan because you can
A.
determine if your answers are
reasonable.
B. organize your thoughts.
C. understand the problem better.
D. define your strategy easier.
The Chungs recorded their monthly budget in a table. Complete the table. The first category is done for you.
7. Create a circle graph of the Chungs' budget.
To view the circle graph (pie chart) of the chungs' budget check the attached file.
What is pie chart?
A pie chart is a graphical representation technique that displays data in a circular-shaped graph.
Pie charts are often used to represent sample data with data points belonging to a combination of different categories.
Chung's budget in percentage:
Charity = 30/2145 x 100%
= 1.39%
= 1.4%
Clothes = 185/2145 x 100%
= 8.62%
Entertainment = 178/2145 x 100%
= 8.29%
Food = 424/2145 x 100%
= 19.76%
Rent = 1050/2145 x 100%
= 48.95%
Transportation = 213/2145 x 100%
= 9.93%
Others = 65/2145 x 100%
= 3.03%
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Write the following expression in simplest form.
the expression quantity negative three fifths times x minus 7 end quantity minus quantity negative 12 plus three tenths times x end quantity
negative nine tenths times x plus 5
negative nine tenths times x plus negative 5
three over 10 times x plus 5
three over 10 times x plus negative 19
The following expression (-3/5)x-7-(-12)+(3/10)x can be written in the simplest form as -3/10x+5( three over 10 times x plus 5). So, option c is correct.
What is meant by an expression?An expression or mathematical expression is a finite arrangement of symbols that are well-formed in line with context-dependent criteria. To help define the logical grammar and order of operations, mathematical symbols can be used to represent variables, operations, functions, brackets, punctuation, and grouping. A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, or variables. Mathematicians have the ability to multiply, divide, add, and subtract. The following is the structure of an expression: Expression, number/variable, and mathematical operator.
(-3/5)x-7-(-12)+(3/10)x
-3/5x-7+12+3/10x
-6/10x-7+12+3/10x
-3/10x+5
Three over 10 times x plus 5
Therefore, the following expression (-3/5)x-7-(-12)+(3/10)x can be written in the simplest form as -3/10x+5( three over 10 times x plus 5).
Hence, option c is correct.
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Ahmed is planning to cook his family dinner and needs to purchase several food items. He is able to purchase these items either at the local grocery store or the farmer's market. Given in the table are the items and their prices.
Grocery Store Farmer's Market
8 tomatoes for $14 10 tomatoes for $16.50
4 cups of mozzarella cheese for $4.40 3 cups of mozzarella cheese for $3.45
12 eggs for $2.40 7 eggs for $1.75
Part A: Choose one of the food items offered at the grocery store and the farmer's market and determine the unit price of the item at each location. Show all necessary work, including the name of the item chosen. (6 points)
Part B: Based on your answer in part A, which location offers a better deal? Explain. (4 points)
Answer: Better Deals: for tomatoes--Farmer's Mkt., for cheese--Grocery, for eggs--Grocery
Step-by-step explanation:
Unit prices:
tomatoes: $14/8 = $1.75/tomato (grocery); $16.50/10 = $1.65 (farmers)
cheese: $4.40/4 = $1.10/cup (grocery); $3.45/3 = $1.15 (farmers)
eggs: $2.40/12 = $0.20/egg (grocery); $1.75/7 = $0.25/egg (farmers)
Really need help on this
We need to see how far the figure has moved in translation and directions and angles in rotational transformation.
What is transformation?
A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
Given is a triangle ABC,
In translation transformation, the original image is congruent to the transformed one hence, we need to see how far the shape has moved to the left or right and how many it has moved up or down.
In rotational transformation, the original figure is not necessarily congruent to the image hence, we need to see direction (clockwise CW or counterclockwise CCW) angle in degrees and Center point of rotation (turn about what point)
Hence, we need to see how far the figure has moved in translation and directions and angles in rotational transformation.
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The angle below measures 2.4 radians, and the circle centered at the angle's vertex has a radius 3 units long. 2.21 (x, y) 11 2.4 rad Determine the exact coordinates of the terminal point (2,y). • 2 = cos(2.4) * Preview • y= sin(2.4)
The exact coordinates of the terminal point (x,y) is = (-2.212185 , 2) .
In the question ,
it is given that ,
the measure of the angle in the figure is = 2.4 radians ,
From graph ,
we can see that the y - coordinate is = 2 unit , So , y = 2 .
Now , for the x - coordinate ,
we draw a right triangle ABO ,
where the height is 2 units and hypotnuse is = 3 units (radius) ,
the angle 2.4 radian in degree is = 137.51° ,
So , from the trigonometric ratio ,
Cos(θ) = base/hypotnuse ,
Cos(137.51) = x/3 ,
x = 3*Cos(137.51)
x = 3*(-0.737395)
x = -2.212185
Therefore , the exact point (x,y) is = (-2.212185 , 2) .
The given question is incomplete , the complete question is
The angle below measures 2.4 radians, and the circle centered at the angle's vertex has a radius 3 units long. Determine the exact coordinates of the terminal point (x , y) .
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Complete the table to make a proportional relationship between distance and time.
The missing value of the distance is 8.4 feet
Direct Proportion:The relationship between two values when their ratio equals a constant number is known as a direct proportion or direct variation.
If a and b are in direct proportion then the relation can be represented as
=> a = kb [ where k is constant ]
Here we have
Distance 6 feet - -
Time 15 sec - 21 sec
As we know,
Distance will be directly proportional to Time
=> Distance ∝ Time
=> Distance = K (Time)
=> Distance/Time = k
Where k is the proportionality constant
By the above calculations
If Distance and Time are directly proportional then Distance/Time must be a constant
Now use the above condition to get the missing value
At a distance of 6 feet and a time of 15 sec
=> Distance/Time = 6/15
Let the missing value is x, and the time is 21 sec
=> Distance/Time = x/21
As we Distance/time will be constant
=> 6/15 = x/21
=> 6(21) = x(15)
=> x = 126/15
=> x = 8.4
Therefore,
The missing value of the distance is 8.4 feet
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A machine is designed to dispense 20 mg of d-desoxyephedrine into each capsule of a medicine. 13
pills are tested, and it's found that they have a mean drug content of 20.2 mg, with a standard
deviation of 2.4 mg. To a 1% level of significance, can it be asserted that the standard deviation of
the process (in general) is over 2 mg?
[Assume that the drug contents of all the pills are normally distributed.]
Answer: To answer this question, we need to perform a hypothesis test. The null hypothesis is that the standard deviation of the process is 2 mg or less, and the alternative hypothesis is that the standard deviation of the process is over 2 mg.
To test this hypothesis, we need to calculate the test statistic, which is the z-score. The z-score tells us how many standard deviations a given data point is from the mean. In this case, the z-score is calculated by subtracting the mean of the sample from the hypothesized mean of the population, and dividing that difference by the standard deviation of the sample:
z = (20.2 - 20) / 2.4 = 0.1
Since the z-score is positive, we know that the mean of the sample is greater than the hypothesized mean of the population. However, we need to compare this z-score to the critical value to determine whether it is statistically significant.
The critical value is the z-score that marks the cutoff between the region of acceptance and the region of rejection of the null hypothesis. For a 1% level of significance, the critical value is the z-score that marks the 99th percentile of the normal distribution. Since the normal distribution is symmetrical, this means that the critical value is 2.58 standard deviations from the mean.
Since the z-score we calculated is less than the critical value, we cannot reject the null hypothesis. This means that we cannot assert that the standard deviation of the process is over 2 mg at a 1% level of significance.