The integer for vector 1 {2,6,-7}, integer for vector 2 is 10,8,-14}, integer for vector 3 is {4,12,-14}, integer for vector 4 is {14,-2,-7} and integer for vector 5 is {22,0,-14}. (all these vectors are in span {V1 and V2})
List five vectors in Span {v_1, v_2}?
1) V1+v2={8,2,-7 }+{-6,4,0 }
={2,6,-7}
2) 2v1+v2={16,4,-14}+{-6,4,0}
={10,8,-14}
3)2v1+2v2={16,4,-14}+{-12,8,0}
={4,12,-14}
4)V1-v2={8,2,-7}-{-6,4,0}
={14,-2,-7}
5)2v1-v2={16,4,-14}-{-6,4,0}
={22,0,-14}
All of these vectors are contained within the span.
{v1,v2}={av1+bv2:ab∈r}
A matrix is a rectangular variety of ordered numbers (real or complex) or functions .Assume we want to express the following information about Ram and his two friends Rohan and Yash's possession of pens and pencils:
Ram has 20 pens and 7 pencils,
Rohan has 15 pens and 5 pencils,
Yash has 12 pens and 3 pencils
Now, this could be arranged in tabular form as follows,
⎢20 7⎢
⎢15 5⎢
⎢12 3⎢
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HI, i am in 7th grade i really need help this question is confusing
At the start, the water level of the river was 12 centimeters below its normal water level.
After a day of rain, the water level of the river increased by 18 centimeters.
The next 8 days were dry, and the water level of the river dropped by 2.6 centimeters each day.
Enter a numerical expression representing the water level after the 9 -day period.
What is the value of the expression you entered in part A?
What does the value in part B mean in the situation?
The changes in the river water level with reference to the normal water level in the 9-day period is analyzed as follows;
Part A: The numerical expression representing the water level after the 9-day period is; -12 + 18 - 8 × 2.6
Part B; -12 + 18 - 8 × 2.6 = -14.8
Part C; The meaning of -14.8 is that the water level after the 9-day period is 14.8 centimeters below the normal water level.
What is a mathematical expression?A mathematical expression is a collection of numbers and, or variables and operators combined according to the rules of mathematical operations.
Part A
The water level of the river at the start = 12 centimeters below its normal level
The amount by which the water level increases after a day of rain = 18 centimeters
The amount by which the water level reduces in the next 8 days = 2.6 centimeters per day
The numerical expression that represents the water level in the 9-day period is therefore;
-12 + 18 - 8 × 2.6
Part B
The value of the expression -12 + 18 - 8 × 2.6 is; -12 + 18 - 8 × 2.6 = -14.8
Part C
The meaning of the value -14.8 is that the water level after the 9-day period is 14.8 centimeters below the the normal water level of the river
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Identify the type of angle shown
A. Alternate exterior angles
B. Same side interior angles
C. Corresponding angles
D. Alternate interior angles
Help!!!
Answer:
A. Alternate exterior angles
Step-by-step explanation:
Alternate exterior angles are congruent angles that are outside the parallel lines. That is why their name is alternate exterior angles since they are exterior from parallel lines.
Simplify the expression.
the linear expression quantity negative 1 over 5 times r minus 6 minus 5 over 7 times r end quantity minus the linear expression quantity negative 3 over 5 times r plus 8 end quantity
negative 53 over 35 times r minus 2
negative 11 over 35 times r minus 2
negative 11 over 35 times r plus negative 14
3 over 35 times r plus negative 14
After solving the equation, the value obtained will be equal to negative 11 over 35 times r plus negative 14. Hence, option C is correct.
What is an expression?If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.
The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. To include terms in an expression, a mathematical operation like reduction, addition, multiplication, or division is used.
As per the given statement in the question,
The equation will be,
(-1/5r - 6 - 5/7r) - (-3/5r) - 8
Rearrange the equation with like terms,
-1/5r - 5/7r + 3/5r - 8 - 6
(-7r - 25r + 21r)/35 -14
=-(11/35)r - 14.
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f the toss of a coin comes down heads, you win two dollars. if it comes down tails, you lose fifty cents. how much would you expect to gain after 21 tosses (in $ dollars)? $ .
In each toss, the expected value is the probability of winning multiplied by the amount won, minus the probability of losing multiplied by the amount lost. The probability of winning is 1/2, or 0.5, and the probability of losing is also 1/2, or 0.5. The amount won is $2, and the amount lost is $0.50. So the expected value of each toss is 0.5 * $2 - 0.5 * $0.50 = $0.75.
Therefore, after 21 tosses, you would expect to gain an amount equal to 21 * $0.75 = $<<21*0.75=15.75>>15.75.
What does basic probability mean in math?The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.
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A boat travels 80 miles downstream in 4 hours. It makes the return trip, against the current, in twice the time. What is the speed of the current? (Remember: rate x time = distance)
[Please show and explain how you solved this word problem.]
By solving simultaneous linear equation, it can be calculated that
Speed of the current is 5 miles/hour
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Here a simultaneous linear equation needs to be solved
Let the speed of boat in still water be x miles/hour and speed of stream be y miles/hour
Speed of the boat downstream = (x + y) miles/hour
Speed of the boat upstream = (x - y) miles/hour
A boat travels 80 miles downstream in 4 hours
x + y = [tex]\frac{80}{4}[/tex]
x + y = 20 .... (1)
A boat travels 80 miles upstream in 8 hours
x - y = [tex]\frac{80}{8}[/tex]
x - y = 10 .... (2)
Subtracting (2) from (1)
2y = 10
y = [tex]\frac{10}{2}[/tex]
y = 5 miles/hour
Speed of the current is 5 miles/hour
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A local store is keeping track of service times. The table below shows the number of customers served and the time it took.
Answer: It appears to take the same amount of time to serve each customer
It takes 40 minutes to serve 10 customers.
Step-by-step explanation:
It appears to take the same amount of time to serve each customer
To find the number of minutes it takes
Divide the number of times by the number of customers
16/4 = 4
it takes 4 minutes to serve 1 customer
Find the number of time it takes to serve 10 customer
10*4=40
It takes 40 minutes to serve 10 customers.
2x(x+4)+7=(x+8)+2x(x+1)+122x(x+4)+7=(x+8)+2x(x+1)+12
Answer:
x = (-10 + sqrt(180)) / 8
= -1.25 + 0.75 * sqrt(5)
x = (-10 - sqrt(180)) / 8
= -1.25 - 0.75 * sqrt(5)
Step-by-step explanation:
To solve the given equation, we need to combine like terms and isolate the variable on one side of the equation. The given equation is:
2x(x+4)+7=(x+8)+2x(x+1)+12
We can start by expanding the parentheses on the left-hand side to obtain:
2x^2 + 8x + 7 = x + 8 + 2x^2 + 2x + 12
We can then combine like terms on both sides of the equation to get:
4x^2 + 10x - 5 = 0
To solve for x, we can use the quadratic formula, which states that the solutions of the equation ax^2 + bx + c = 0 are given by:
x = (-b +/- sqrt(b^2 - 4ac)) / 2a
In the given equation, we have a = 4, b = 10, and c = -5, so the solutions are:
x = (-10 +/- sqrt(10^2 - 4 * 4 * (-5))) / 2 * 4
= (-10 +/- sqrt(100 + 80)) / 8
= (-10 +/- sqrt(180)) / 8
This gives us two solutions:
x = (-10 + sqrt(180)) / 8
= -1.25 + 0.75 * sqrt(5)
x = (-10 - sqrt(180)) / 8
= -1.25 - 0.75 * sqrt(5)
These are the two solutions of the given equation. Note that we could also write the solutions in a simplified form by factoring the quadratic and using the zero product property, but the quadratic formula is generally more reliable and easier to use.
Mabel buys a television
priced at $84.75. If the
sales tax is 8%, how
much will Mabel pay for
the television?
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Answer:
Mabel will pay $91.53 for the television.
Step-by-step explanation:
To calculate the total cost of the television including sales tax, we first need to calculate the amount of sales tax by multiplying the price of the television by the sales tax rate. This gives us $84.75 * 0.08 = $6.78 in sales tax.
To find the total cost of the television, we add the price of the television to the sales tax amount. This gives us $84.75 + $6.78 = $91.53.
Therefore, Mabel will pay $91.53 for the television.
Two idewalk in a park are repreented by line on a coordinate grid. Two point on each of the line are hown in the table. Sidewalk 1 x y 0 3 2 7 Sidewalk 2 x y 1 5 3 3 (a) Write the equation for Sidewalk 1 in lope-intercept form. (b) Write the equation for Sidewalk 2 in lope-intercept form. (c) I the ytem of equation conitent independent, coincident, or inconitent? Explain. (d) If the two idewalk interect, what are the coordinate of the point of interection? Ue the ubtitution method and how your work
a) The equation is: y = 2x + 3. b) The equations are :Point - slope form: y - 5 = -(x - 1).Slope - intercept form: y = -x + 6. c) The systems are consistent independent. d) The point of intersection is (1, 5).
Linear function
A linear function is defined in slope-intercept formula by the rule presented as follows:
y = mx + b.
In which:
m is the constant rate of change of the function, called slope.
b is the value of y when x = 0, called intercept.
For Sidewalk 1, it is found that:
When x increases by 2, y increases by 4, hence the slope is of m = 2.
When x = 0, y = 3, hence the intercept is of b = 3.
Then the rule is:
y = 2x + 3.
For Sidewalk 2, when x changes by 2, y decays by 2, hence the slope is:
m = -2/2 = -1.
The line goes through point (1,5), hence the equation in point-slope form is:
y - 5 = -(x - 1).
Combining the like terms, the slope-intercept form is:
y - 5 = -x + 1
y = -x + 6.
Since the two lines have different slopes, the system is consistent independent.
The x-coordinate of the intersection is:
-x + 6 = 3 + 2x.
3x = 3
x = 1.
The y-coordinate is:
-x + 6 = -1 + 6 = 5.
Hence the intersection point is:
(1, 5).
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Please help quick show work and explain
The height of the ball after x seconds is given by the quadratic function presented as follows:
y = -16t² + 8t + 4.
This is a concave down parabola, hence the vertex of the function is the maximum point.
The coefficients of the quadratic function are given as follows:
a = -16, b = 8, c = 4.
Then the x-coordinate of the vertex is given as follows:
x = -b/2a = -8/-32 = 0.25.
The maximum height of the ball is given as follows:
y = -16(0.25)² + 8(0.25) + 4 = -1 + 2 + 4 = 5 feet.
The ball hits the ground when:
y = 0.
Hence:
-16t² + 8t + 4 = 0.
Solving the quadratic equation, the positive solution is given as follows:
t = 0.809 seconds.
The graph of the quadratic function is given by the image shown at the end of the answer.
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Suppose that you are rolling a six sided dice. Let A-get a 3 What is P(A^C)? 2/6
4/6 5/6 1/6 3/6
Answer:
5/6 (option 3)
Step-by-step explanation:
[tex]P(A^C)[/tex] is asking what the complement of A is. This means we are asking what the probability of NOT getting A is. This would be 1 - P(A).
P(A) = The probability of getting a 3 = 1/6
We can solve for the probability of the complement of the A and get:[tex]P(A^C) = 1 - P(A) = 1 - \frac{1}{6} = \frac{5}{6}[/tex]
Thus, the answer is 5/6 (which I believe is the 3rd option you are given)
2. If the distance travelled by a rickshaw in one hour is 10 km, then the distance travelled by the same rickshaw with the same speed in one minute is:
Answer:
166 meters/minute
Step-by-step explanation:
get speed in m/sec by multiplying 10 with 5/18
=
2.7m/sec
multiply it by 60 to get meters/minute
=
166 meters/minutes
Answer: 10/60, so 1/6 of a km of km per minute
Step-by-step explanation:
Translate the sentence into an inequality. The sum of 8 and y is greater than or equal to 17.
Answer:
8+y[tex]\geq[/tex]17
Step-by-step explanation:
In coordinate plane the point A(-4,8) B(10,1) and C(-2,-7) are reflected over the y-axi to the point A , B ,C repectively what are the coordinate of A, B, and C
The distance formula can be used to determine this distance. The formula d = (x 2 x 1 ) 2 + (y 2 y 1 ) 2 can be used to describe the distance that separates the two points (x 1, y 1) and (x 2, y 2).
Which coordinate sequence is correct?The y-coordinate comes after the x-coordinate in every case. The coordinate grid below demonstrates that the ordered pairs (3,4) and (4,3) are two distinct points!
How are XY coordinates written?Coordinates are written as (x, y), with the x-axis point being written first and the y-axis point following. The expression "along the corridor, up the stairs" may be used to remind some children of this, instructing them to follow the x axis first and then the y.
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What i mr Portillo cat weigh 6 kilogram her dog weigh 22 kilogram more than her cat
The total weight of Mrs. Portillo's cat and the dog is 34 kilograms.
Mathematical operations:The mathematical operations known as operators focus on particular activities, such as adding, taking away, adding multiple times and dividing equally, etc.
The four fundamental operations in Maths are
1. Addition
2. Subtracting
3. Multiplications
4. Divisions
Here we use Addition to solve the problem
Here we have
Cat's weight = 6 kilograms
Her dog weighs 22 kilograms more than her cat
Weight of dog = Cat's weight + 22 kilograms
= 6 kilograms + 22 kilograms
= 28 kilograms
Total weight of Mrs. Portillo's cat and dog = 6 + 28 = 34 kilograms
Therefore,
The total weight of Mrs. Portillo's cat and the dog is 34 kilograms.
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Complete Question:
What is the total weight of her cat and dog? Mrs. Portillo's cat weighs 6 kilograms her dog weighs 22 kilograms more than her cat.
which type of rigid transformation is the equivalent of two reflections across intersecting lines?
a. glide reflection
b. rotation
c. reflection
d. none of these
Answer:
a
Step-by-step explanation:
The equivalent of two reflections across intersecting lines is a glide reflection.
A glide reflection is a combination of a translation and a reflection. It involves moving an object along a line, and then reflecting the object across the same line. Since a reflection is an isometry (a transformation that preserves the distance between points), a glide reflection is also an isometry.
In contrast, a rotation is a transformation that involves turning an object around a fixed point, and a reflection is a transformation that involves flipping an object across a mirror line. Neither of these transformations is equivalent to two reflections across intersecting lines.
Therefore, the correct answer is (a) glide reflection.
2.6 sq. cm X 3.1 cm
Answer 8.06 X 10-8 M*4
Step-by-step explanation: No Explanation Just Answer srry could think of a way to say it.
Arturo is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if he spins a spinner with 5 equal-sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday, spins a spinner with four equal-sized sections labeled Red, Green, Blue, Orange, and rolls a fair die in the shape of a cube that has six sides labeled 1 to 6?
There are 6 different possible outcomes.
What is probability ?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
The party which calls the coin's side wins.
We find it because when we turn a coin very often, humans get half the heads and half the tails.
The chances of swinging the head are 1/2 , and the chances of swinging the tail are 1/2 .
Total outcomes = 2×5×6
= 60
So the final answer is 60
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Which pair of points represents a line segment with a slope of and a length of 15 units?
By using slope, it can be calculated that
(-8, -5) and (1, 7) represents a line with slope of [tex]\frac{4}{3}[/tex] and length 15 units
What is slope of a line?
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
For the first option
(-11, 7) and (1, -2)
Slope = [tex]\frac{-2-7}{1 - (-11)}[/tex]
= [tex]-\frac{9}{18}[/tex]
= [tex]-\frac{1}{2}[/tex]
First option is wrong
For the second option
(-2, -6) and (4, 2)
Slope = [tex]\frac{2 - (-6)}{4 - (-2)}[/tex]
= [tex]\frac{8}{6}[/tex]
= [tex]\frac{4}{3}[/tex]
Length =
[tex]\sqrt{(4 - (-2))^2 + (2-(-6))^2}\\\sqrt{36+64}\\\sqrt{100}\\[/tex]
10 units
Second option is wrong
For the third option
(-3, -2) and (9, 7)
Slope = [tex]\frac{7 - (-2)}{9 - (-3)}[/tex]
= [tex]\frac{9}{12}[/tex]
= [tex]\frac{3}{4}[/tex]
Third option is wrong
For the fourth option
(-8, -5) and (1, 7)
Slope = [tex]\frac{7 - (-5)}{1 - (-8)}[/tex]
= [tex]\frac{8}{6}[/tex]
= [tex]\frac{4}{3}[/tex]
Length =
[tex]\sqrt{(1 - (-8))^2 + (7-(-5))^2}\\\sqrt{81+144}\\\sqrt{225}\\[/tex]
15 units
Fourth option is correct
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Solve the following inequality algebraically: negative 2 less-than startfraction x over 3 endfraction 1 less-than 5 a. negative 9 greater-than x greater-than 12 b. negative 9 less-than x less-than 12 c. negative 2 less-than x less-than 5 d. negative 2 greater-than x greater-than 5
The solution to the inequality algebraically is -9 < x < 12
How to solve the inequality algebraicallyFrom the question, we have the following parameters that can be used in our computation:
negative 2 less-than startfraction x over 3 endfraction 1 less-than 5
Express the statement using numbers and expressions
So, we have the following representation
-2 < x/3 + 1 < 5
Subtract 1 from all sides of the inequality
This gives
-3 < x/3 < 4
Multiply through the inequality by 3
So, we have
-9 < x < 12
Hence, the solution is -9 < x < 12
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Answer:
b. Negative 9 less-than x less-than 12
Step-by-step explanation:
You want to apply the filter() function to the variables Cocoa. Percent and Rating. Add the code chunk that lets you filter the data frame for chocolate bars that contain at least 75% cocoa and have a rating of at least 3. 9 points. Filter(Cocoa. Percent >= 75, Rating >= 3. 9)What value for cocoa percent appears in row 1 of your tibble? a. 80% b. 75% c. 88% d. 78%
Answer:
A
Step-by-step explanation: here ya go <3
The velocity v of an object dropped from a tall building is given by the formula v = √64d where d is the distance the object has dropped. Solve the formula for d.
The solution for d in the equation v = √64d is d = v²/64
How to determine the solution for d in the equation?From the question, we have the following parameters that can be used in our computation:
v = √64d
Take the square root of both sides
So, we have the following representation
v² = 64d
Divide both sides of the equation by 64
So, we have the following representation
v²/64 = d
Rewrite as
d = v²/64
Hence, the value of d is d = v²/64
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how do u solve x+5y=20 and -2x+7y=45 by elimination
Answer:
x = -5; y = 5
Step-by-step explanation:
x + 5y = 20
-2x + 7y = 45
Multiply both sides of the first equation by 2 to get 2x. Write the second equation below it and add the equations. 2x and -2x add to zero eliminating the x terms.
2x + 10y = 40
-2x + 7y = 45
-----------------------
17y = 85
y = 85/17
y = 5
Now use substitution in the first original equation to find x.
x + 5y = 20
x + 5(5) = 20
x = -5
Answer: x = -5; y = 5
A circle has a diameter of 20 ft. What is the area?
Show or explain your reasoning.
Lots of love for the ones who helps!! <3
The area of a circle is given by the formula:
area = pi * r^2
where pi is a constant approximately equal to 3.14 and r is the radius of the circle.
To find the area of the circle, we first need to find the radius. The radius is half the diameter, so the radius of the circle is 20/2 = 10 feet.
Plugging this value into the formula, we get:
area = 3.14 * 10^2 = 3.14 * 100 = 314 square feet
So the area of the circle is 314 square feet.
Answer:
100π, or about 312. Could also be 314.16 if it needs to be rounded.
Step-by-step explanation:
First, the area of a circle is πr^2
To find radius, it's diameter/2.
So the radius is 20/2 which is 10.
With this, we plug it in: π(10)^2 = π100 = 100π.
That is an exact answer. For a rounded answer, assume π = 3.14.
3.14*100 = 314 sqr feet.
However, it you want to round the final answer, 100π is around 314.159265359 thus making rounding to the nearest hundredth 314.16.
Multiple choice math
I believe it would be the first answer choice
a.5n^2
n^2 being "the square of a number"
5n^2 is just multiplying 5 and n^2
in other words the product of the square of a number and 5
The right triangle on the right is a scaled copy of the right triangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.
The scale factor will be 1/4.
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The right triangle on the right is a scaled copy of the right triangle on the left.
Now,
Since, The right triangle on the right is a scaled copy of the right triangle on the left.
Hence, The ratio of their similar sides is equal to the scale factor.
So, We get;
⇒ 2 / 8 = 1 / 4
And, 2 / 8 = 1 / 4
Thus, The scale factor = 1/4.
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Ahok purchaed 15. 5kg rice and 3. 250kg ugar from the upermarket. Find the total weight of hi purchae
Using simple mathematical operations we know that Ashok purchased rice and sugar which together weights 18.75kg.
What are mathematical operations?A mathematical function known as just an operation converts zero or more input values into a precisely defined output value.
A quantity of operands affects the operation's arity.
Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are all referred to as PEMDAS (from left to right).
So, we know that:
Ashok purchased 15.5kg of rice and 3.25 kg of sugar.
Now, the total weight of rice and sugar Ashok purchased is:
15.5 + 3.25
18.75kg
Therefore, using simple mathematical operations we know that Ashok purchased rice and sugar which together weights 18.75kg.
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If a hypothesis test is significant at level α = 0.05, then what is known for the P-value?P-value > 0.01P-value ≤ 0.05P-value ≤ 0.01P-value > 0.05
If a hypothesis test is significant at level α = 0.05, then the P-value is less than or equal to 0.05 or P-value ≤ 0.05.
The P-value is a measure of the strength of the evidence against the null hypothesis. It is the probability of obtaining a test statistic at least as extreme as the one observed, assuming that the null hypothesis is true. If the P-value is less than or equal to the significance level α, it means that the observed evidence is unlikely to have occurred by chance under the null hypothesis, and we can reject the null hypothesis in favor of the alternative hypothesis.
For example, if the P-value of a hypothesis test is 0.03, it means that there is a 3% chance of obtaining the observed test statistic (or a more extreme one) if the null hypothesis is true. Since this is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis.
Hence, if a hypothesis test is significant at level α = 0.05, then P-value ≤ 0.05.
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relationship between f(x) , f’(x) , f’’(x) at x
Refer to the photo taken.
The larget taco contained approximately 1 kg of onion for every 6. 6 kg grilled teak. The total weight of thee two ingredient wa 617. 3 kg. How many kilogram of each ingredient were ued?
The largest taco contained approximately 1 kg of onion for every 6. 6 kg grilled teak. then Amount of grilled steak used: 6.6 (79.17) = 538.356 kg
What is a unit amount in math?
When a price is expressed as a quantity of 1, such as $25 per ticket or $0.89 per can, it is called a unit price. If you have a non-unit price, such as $5.50 for 5 pounds of potatoes, and want to find the unit price, divide the terms of the ratio
1 k + 6.6 k = 617.3
Where “k” is a constant value, a multiplier.
Solving for k:
7.8 k = 617.3
k = 617.3 /7.8
k= 79.17
So:
Amount of onion used:
1 (79.17) = 79.17 kg
Amount of grilled steak used:
6.6 (79.17) = 538.356 kg
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