Answer:
D. The input force is equal to the output force
Step-by-step explanation:
A pulley changes the direction of the applied force, but does not change its magnitude. The mechanical advantage is the ratio of output force to input force, so must be 1 when the force magnitude does not change.
Which of the following is NOT a formula for determining complementary probability? O Ploutcome) = 1- P(-outcome) O P(outcome) - P(-outcome) = 1 O P(outcome) + P(-outcome) =1 O P(-outcome) = 1 - P(outcome)
Answer:
P(outcome) - P(-outcome) = 1
Step-by-step explanation:
Given
Let the complementary probabilities be represented with P(outcome) and P(-outcome)
Required
Determine which of the options do not show complementary probabilities
In probability, complementary probability sums up to 1
i.e.
[tex]P(outcome) + P(-outcome) = 1[/tex]
Hence option C is correct
Make P(outcome) the subject of formula
[tex]P(outcome) = 1 - P(-outcome)[/tex]
Hence, option A is correct
Make P(-outcome) the subject of formula
[tex]P(-outcome) = 1 - P(outcome)[/tex]
Hence, option D is correct
So, from the list of given options,
[tex]P(outcome) - P(-outcome) = 1[/tex] is incorrect
The characteristic polynomial of a 5 × 5 matrix is given below. Find the eigenvalues and their multiplicities. 2) λ5 - 24λ4 + 189λ3 - 486λ2
The eigenvalues of the 5 x 5 matrix are 0 (multiplicity: 2), 6 (multiplicity: 1), 9 (multiplicity: 1) y 1 (multiplicity: 1).
The eigenvalues of the 5 x 5 matrix are represented by the roots of the characteristic polynomial. The multiplicity of a eigenvalue is the number of times that a root is repeated.
Now we proceed to determine the roots of the characteristic polynomial by algebraic means:
[tex]p = \lambda^{5}-24\cdot \lambda^{4}+189\cdot \lambda^{3}-486\cdot \lambda^{2}[/tex]
[tex]p = \lambda^{2}\cdot (\lambda^{3}-24\cdot \lambda^{2}+189\cdot \lambda -486)[/tex]
[tex]p = \lambda^{2}\cdot (\lambda -6)\cdot (\lambda - 9)\cdot (\lambda - 1)[/tex]
The eigenvalues of the 5 x 5 matrix are 0 (multiplicity: 2), 6 (multiplicity: 1), 9 (multiplicity: 1) y 1 (multiplicity: 1).
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The fourth term of an arithmetic
progression is one less than twice the
second term - If the sixth term is 7
find the first term
[tex] \huge{ \underline{ \underline{ \bf{ \orange{Solution:}}}}}[/tex]
Let the first term of the AP be a and the common difference of the AP be d
We know the formula for finding the nth term,
[tex] \large{ \boxed{ \rm{a_n = a + (n - 1)d}}}[/tex]
Here,
an = nth term of the APn = number of terms of APBy using formula,
a4 = a + 3da2 = a + da6 = a + 5dAccording to given condition,
⇛ a4 = 2a2 - 1
⇛ a + 3d = 2(a + d) - 1
⇛ a + 3d = 2a + 2d - 1
⇛ a - 2a + 3d - 2d = -1
⇛ -a + d = -1
⇛ a - d = 1
Then,
⇛ a = d + 1-----------(1)
It is given that, a6 = 7
⇛ a + 5d = 7
Putting a from eq.(1),
⇛ d + 1 + 5d = 7
⇛ 6d + 1 = 7
⇛ 6d = 6
⇛ d = 6/6 = 1
Putting value of d in eq.(1),
⇛ a = 1 + 1 = 2
⛈ First term of the AP(a) = 2
━━━━━━━━━━━━━━━━━━━━
Write the ratio as a ratio of whole numbers using fractional notation 15 hours to 40 hours simplified fraction
Answer:
3/8
Step-by-step explanation:
Since it is 15/40 hours originally, what we need to do is just simplify this fraction.
The numerator and denominator are both divisible by 5.
3/8
Can someone please help me with these questions! Please explain to me how to do it as well!
Thank You!
Answer:
(2) (-2, 4), (3, 9)
(3) (-2, 4), (1, 1)
Step-by-step explanation:
My favorite way to answer questions like this is to use a graphing calculator to find the points of intersection. The attached shows the points of interest.
If you want to solve this by hand, equate the expressions for y, then solve the resulting quadratic using any of the methods you know. Once you find the x-values, put those in either equation to find the y-value.
__
(2) x^2 = y = x+6
x^2 -x -6 = 0 . . . . put in standard form
(x -3)(x +2) = 0 . . . . factor
x = 3 or -2 . . . . . find the x-values that make the factors zero
y = x^2 = 9 or 4
The points are (3, 9) and (-2, 4).
__
(3) x^2 = -x +2
x^2 +x -2 = 0 . . . . standard form
(x +2)(x -1) = 0 . . . factored
x = -2 or 1 . . . . . . .zeros
y = x^2 = 4 or 1
The points are (-2, 4) and (1, 1).
_____
Comment on factoring
When you consider the factored form and its expanded equivalent, ...
(x +a)(x +b) = x^2 +(a+b)x +ab
you see that the coefficient of the linear term (a+b) is the sum of factors of the constant term (ab). Your knowledge of multiplication tables will often help you factor equations easily. You need to pay attention to signs.
In problem 2, we want factors of -6 that have a sum of -1:
-6 = (-1)(6) = (-2)(3) = (-3)(2) = (-6)(1)
These factor pairs have sums of 5, 1, -1, -5. The pair whose sum is -1 is the one we're looking for: -3 and 2. So, the factors in problem 2 are (x-3)(x+2).
__
In problem 3, we want factors of -2 that have a sum of +1:
-2 = (-1)(2) = (-2)(1)
These factor pairs have sums of 1, -1. So, the second pair is the one of interest: -2 and 1. That makes the factors be (x-2)(x+1).
Simplify 3m4-2+8
A.8m4
B.9m4
C.3m+244
D.3m+284
Answer:
[tex]3m^4 - 2 + 8 = 3(m^4 + 2)[/tex]
Step-by-step explanation:
Given
[tex]3m^4 - 2 + 8[/tex]
Required
Simplify
[tex]3m^4 - 2 + 8[/tex]
Subtract 2 from 8
[tex]3m^4 - 2 + 8 = 3m^4 + 6[/tex]
Factorize
[tex]3m^4 - 2 + 8 = 3(m^4 + 2)[/tex]
The expression cannot be further simplified;
Hence;
[tex]3m^4 - 2 + 8 = 3(m^4 + 2)[/tex]
None of the options answers the question
The mayor of a town has proposed a plan for the construction of a new bridge. A political study took a sample of 800 voters in the town and found that 67% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is over 63%. Make the decision to reject or fail to reject the null hypothesis at the 0.05 level.
Answer:
We have to reject null hypothesis
Step-by-step explanation:
n = 800
P* = sample proportion = 0.67
Alpha = 0.05
Null hypothesis h0: proportion = 63%
Alternate hypothesis h1: proportion > 64%
Test statistics:
Z = (p* - P)/√pq/n
Z = 0.67 - 0.64/√0.63x0.37/800
= 0.67 - 0.63/0.017
=0.04/0.017
= 2.352
At 0.05 the critical value of z = 1.645
We compare z calculated and z critical value.
2.352 is greater than 1.645 therefore we take the decision to reject the null hypothesis at 0.05 level of significance.
The percentage of residents that supports construction is greater than 63%
A man drove 8 miles directly east from his home, made a left turn at an intersection, and then traveled 8 miles due north to his place of work. If a road was made directly from his home to his place of work, what would its distance be? ______ miles
Answer:
11.3 miles
Step-by-step explanation:
We can use the pythagorean theorem to find the distance from his home to work, since the 3 roads form a right triangle where the new road is the hypotenuse.
a² + b² = c²
8² + 8² = c²
128 = c²
= approx. 11.3 miles
The distance between his home and his work of place is 11.31 miles.
Given,
A man drove 8 miles directly east from his home, made a left turn at an intersection, and then traveled 8 miles due north to his place of work.
A road was made directly from his home to his place of work.
We need to find what would its distance be in miles,
How to construct direction?We have,
North
West <----- ⇅ -------> East
South
What is the Pythagorean theorem?In a right triangle,
The square of the hypotenuse is equal to the sum of the square of the other two sides.
Find the direction of the given statement.
A man drove 8 miles directly east from his home:
8 miles
Home ------------------->East
Made a left turn at an intersection, and then traveled 8 miles due north to his place of work:
North Work
⇅ Left
⇅ 8 miles
Home ------------------->East
⇅
Right
If a road was made directly from his home to his place of work:
Work
Home North
West <------------------⇅ --------------->East
South
A (Work)
/ ║
/ ║
/ ║ 8 miles
/ ║
(Home) B /___________║C
8 miles
Find the distance between home and place of work.
AB = distance between home from work
Applying the Pythagorean theorem.
AB² = BC² + AC²
AB² = 8² + 8²
AB² = 64 + 64
AB² = 128
AB = ±√128
The distance can never be negative here so,
√128 = 11.31
AB = 11.31 miles.
Thus the distance between his home and his work of place is 11.31 miles.
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choose all the equations for which x=2 is a solution
a. x+3=5
b. x+2=8
c. x+1=1
d. x-2=4
e. x-7=-5
Answer:
Option A and Option E
Step-by-step explanation:
Option A.
x + 3 = 5
(x + 3) - 3 = 5 - 3
x = 2
Option B.
x + 2 = 8
(x + 2) - 2 = 8 - 2
x = 6
Option C.
x + 1 = 1
(x + 1) - 1 = 1 - 1
x = 0
Option D.
x - 2 = 4
(x - 2) + 2 = 4 - 2
x = 2
Option E.
x - 7 = -5
(x - 7) + 7 = -5 + 7
x = 2
Therefore, Option (A) and Option (E) are the correct options.
In the episode pertaining to the discovery of radium, all of the hypotheses turned out to be true.
a. true
b. false
Answer:
In the episode pertaining to the discovery of radium, it is false that all of the hypotheses turned out to be true.
There are some hypotheses in the episode thay turned out to be false.
What is the value of x? A. 36 B. 12 C. 32 D. 28
Answer:
the answer is D I hope this helps
What is the value of the y-coordinate of point A
Answer: [tex]-\dfrac{1}{2}[/tex]
Step-by-step explanation:
The coordinate at -30° (-30° = 330°) = [tex]\bigg(\dfrac{\sqrt3}{2},-\dfrac{1}{2}\bigg)\\[/tex]
the x-value is [tex]\dfrac{\sqrt3}{2}[/tex]
the y-value is [tex]-\dfrac{1}{2}\\[/tex]
Answer:
-0.5
Step-by-step explanation:
find the fraction below that is equivalent to 3/4
Answer:
6/8 9/12 15/20 12/16 and alot more
Step-by-step explanation:
Can't explain
Answer:
the answer is 6/8
[tex] {2}^{x + 2} = 9 \times ( {2}^{x} ) - 2[/tex]
How is this solved pls
Answer:
[tex]x = 1 - log_{2}(5) [/tex]Step-by-step explanation:
[tex] {2}^{x + 2} = 9 ( {2}^{x} ) - 2[/tex]Using the rules of indices
That's
[tex] {x}^{a + b} = {x}^{a} \times {x}^{b} [/tex]So we have
[tex] {2}^{x + 2} = {2}^{x} \times {2}^{2} = 4( {2}^{x} )[/tex]So we have
[tex]4( {2}^{x}) = 9( {2}^{x} ) - 2[/tex]Let
[tex] {2}^{x} = y[/tex]We have
4y = 9y - 2
4y - 9y = - 2
- 5y = - 2
Divide both sides by - 5
[tex]y = \frac{2}{5} [/tex]But
[tex] {2}^{x} = \frac{2}{5} [/tex]Take logarithm to base 2 to both sides
That's
[tex] log_{2}( {2}^{x} ) = log_{2}( \frac{2}{5} ) [/tex][tex] log_{2}(2) ^{x} = x log_{2}(2) [/tex][tex] log_{2}(2) = 1[/tex]So we have
[tex]x = log_{2}( \frac{2}{5} ) [/tex]Using the rules of logarithms
That's
[tex] log( \frac{x}{y} ) = log(x) - log(y) [/tex]Rewrite the expression
That's
[tex]x = log_{2}(2) - log_{2}(5) [/tex]But
[tex] log_{2}(2) = 1[/tex]So we have the final answer as
[tex]x = 1 - log_{2}(5) [/tex]Hope this helps you
Dean has a piece of wood that is 3/4 of a foot long, He
needs to cut pieces of the wood into 1/16 of a foot long, How
many pieces can Dean cut? How do you know?
Answer:
1. 12 pieces of wood
2. How to determine the number of pieces of wood Dean cut is by dividing the total length of wood by length of each piece of wood
Step-by-step explanation:
Total length of wood=3/4 of a foot
He needs to cut pieces of the wood into 1/16 of a foot long
How many pieces can Dean cut
Let x= number of pieces of wood Dean needs to cut
x=Total length of wood / length of each piece
=3/4 ÷ 1/16
=3/4 × 16/1
=48/4
=12 pieces
Number of pieces of the wood Dean can cut =12 pieces
How to determine the number of pieces of wood Dean cut is by dividing the total length of wood by length of each piece of wood
That is,
3/4 ÷ 1/6
Then follow the procedures in question 1
What is the vertex of the graph of f(x) = |x - 13|+ 11
Answer:
The vertex is located at the point (13, 11)
Step-by-step explanation:
When this equation is graphed, the vertex falls on this point on the graph. Hope this helps!!!
HELP!!!!! What is the slope of a line with the equation 3x+7?
Answer:
m=3
Step-by-step explanation:
The equation of the line is in slope-intercept form, or:
y=mx+b
where m is the slope and b is the y-intercept. The slope is multiplied by x and the y-intercept is added or subtracted from that.
The equation of the line is:
y=3x+7
3 and x are being multiplied, therefore 3 is the slope. 7 is added to 3x, therefore 7 is the y-intercept.
The slope is 3, or 3/1. Therefore, on a graph, the line will rise 3 up, then run 1 to the right.
The slope of the line is 3.
George has a triangle-shaped garden in his backyard. He drew a model of this garden on a coordinate grid with vertices A(4, 2), B(2, 4), and C(6, 4). He wants to create another, similar-shaped garden, A′B′C′, by dilating triangle ABC by a scale factor of 0.5. What are the coordinates of triangle A′B′C′?
Answer:
A' (2, 1)
B' (1, 2)
C' (3, 2)
Step-by-step explanation:
Scale factor = 0.5
A(⁴₂ ) → A'([tex]\frac{1}{2} * 4\\\frac{1}{2} * 2[/tex]) = (²₁ ) ∴ A'(2, 1)
B(²₄ ) → B'([tex]\frac{1}{2} * 2\\\frac{1}{2} * 4[/tex]) = (¹₂ ) ∴ B'(1, 2)
C(⁶₄ ) → C'([tex]\frac{1}{2} * 6\\\frac{1}{2} * 4[/tex]) = (³₂ ) ∴ C'(3, 2)
does anyone know this?
Answer: about 270
Step-by-step explanation:
If you look closely at 200 ml, you will see that there are 5 evenly spaced bars. This tells us that 200-300 ml is split by 20s. Counting the bars, you reach 260, but it goes almost halfway past it. Therefore, we get 270 since 270 is halfway past 260 and 280.
Evaluate the expression x+43x when x = 2
a.316
b.34
c.1
d.2
Answer:
88
Step-by-step explanation:
We are given the expression:
x+43x
and asked to evaluate when x=2. Therefore, we must substitute 2 in for x.
x + 43 x (plug 2 in for each x )
2+43(2)
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Multiply 43 and 2 first.
2+ (43*2)
2+ 86
Add 2 and 86.
88
The expression x+43x when evaluated for x=2 is 88.
Answer:
1
Step-by-step explanation:
11
Solve the following equation when a =4 and b=7. 5a2_11b+9=
Can you help me with the answer if you know?
Answer:
12
Step-by-step explanation:
a = 4 and b = 75a² - 11b + 9 = ?-------------
Plugging in values of a and b and simplifying to get answer:
5a² - 11b + 9=5*4² - 11*7 + 9=5*16 - 77 + 9 =80 - 77 + 9 =3+ 9 = 12Answer is 12
Identify the careers that match the descriptions:
Makes sure products meet safety regulations:
Operates equipment to cook meat for packaging in soup cans
Classifies eggs based on size and quality
Operates a large oven in a factory to bake bread before packaging
Operates equipment that mixes ingredients together to make candy
Options:
Agricultural Inspector
Food Baking Machine Operator
Food Batchmaker
Grader or sorter
Food cooking machine operator
Answer:
1. agricultural inspecter
2. food-cooking machine operator
3. grader or sorter
4. food-baking machine operator
5. food batchmaker
Step-by-step explanation:
i got this correct on ED2021
The correct order is agricultural inspector, food-cooking machine operator, grader, or sorter. food-baking machine operator, food matchmaker.
What is food processing?The process of turning agricultural materials into food or transforming one type of food into the next is referred to as transformation.
It is given that:
For the descriptions:
Makes sure products meet safety regulations - agricultural inspector.
Operates equipment to cook meat for packaging in soup cans - food-cooking machine operator.
Classifies eggs based on size and quality - grader or sorter.
Operates a large oven in a factory to bake bread before packaging - food-baking machine operator.
Operates equipment that mixes ingredients together to make candy - food matchmaker.
Thus, the correct order is agricultural inspector, food-cooking machine operator, grader, or sorter. food-baking machine operator, food matchmaker.
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PORFAVOR ALLUDENME :( El estanque de combustible de un automóvil contiene x litros de gasolina, se consumen 25 litros en un primer viaje y 4/19 del resto en un segundo viaje, conservando finalmente 3 litros de gasolina. ¿Qué ecuación modela la situación planteada? a. 25 menos x menos estilo en línea fracción 4 entre 19 fin estilo paréntesis izquierdo 25 menos x paréntesis derecho igual 3 b. x menos 25 menos estilo en línea fracción 4 entre 19 fin estilo por 25 igual 3 c. x menos 25 menos estilo en línea fracción 4 entre 19 fin estilo paréntesis izquierdo x menos 25 paréntesis derecho igual 3 d. x menos 25 menos estilo en línea fracción 4 entre 19 fin estilo paréntesis izquierdo x más 25 paréntesis derecho igual 3
Responder:
c. x menos 25 menos estilo en línea fracción 4 entre 19 fin estilo paréntesis izquierdo x menos 25 paréntesis derecho igual 3
Explicación paso a paso:
Dado lo siguiente:
Cantidad original de gasolina en el tanque de combustible = x
Gasolina consumida en el primer viaje = 25 litros
Gasolina restante después del primer viaje = (x - 25) litros
Gasolina consumida en el segundo viaje = 4/19 de lo que queda, es decir;
(4/19) * (x - 25)
Gasolina restante después del segundo viaje = 3 litros
Cantidad inicial - cantidad consumida en el primer viaje - 4/19 de la cantidad restante después del primer viaje = 3
La gasolina que queda después del segundo viaje se puede modelar mediante la ecuación:
x - 25 - 4/19 (x - 25) = 3
Inequalities with > or < symbols are graphed with a dashed line. Inequalities with an ≥or ≤ symbol line are graphed with a solid line. When graphing the inequalities in the example above. Which inequality would you graph using a dashed line? Select all that apply A B C D
Answer:
b and c
Step-by-step explanation:
both are just greater than or less than
Plssssssssssss help and fast
Answer:
Graph 11, 14, and 15 are proportional
But I'm not 100% sure ;>;
Which of the following is the correct equation for the Pythagorean Theorem, where a and b are the side lengths and c is the length of the hypotenuse?
A. a^2-b^2=c^2
B. (a+b)^2=c^2
C.(a-b)^2=c^2
D. a^2+b^2=c^2
Answer:
[tex]\huge \boxed{ \mathrm{D.} \ \ a^2 +b^2 =c^2}}[/tex]
Step-by-step explanation:
The correct equation for the Pythagorean theorem is:
[tex]\Rightarrow \ \ a^2 +b^2 =c^2[/tex]
c is the length of the hypotenuse of the right triangle
a and b are the side lengths of the right triangle
The opposite of 11 is 11. True False
Answer:
FALSE. The opposite of 11 is -11.
A theater wants to build movable steps that they can use to go on and off the stage. They want the steps to have enough space inside so they can also be used to store props. How much space is inside the steps? Give an exact answer (do not round).
Answer:
0.045
Step-by-step explanation:
khan
The required amount of the space available is 0.045 cubic meter.
Space inside the steps to be determine.
What is volume?Volume, is defined as the mass of object per unit density.
The required space = 0.3*0.4*0.5 - 0.15*0.5*0.2
= 0.06 - 0.015
= 0.045 cubic meter
Thus, the required amount of the space available is 0.045 cubic meter.
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how would you demonstrate the understanding of estimating a non perfect square? Estimate 388 to the nearest whole number.
Answer:
20
Step-by-step explanation:
Square root of 388=19.6977156
20
Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. Identify the P-value.
Answer:
hello your question has some missing parts below is the missing part
Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean.
Identify the p-value.
Source DF SS MS F p
Factor 3 13.500 4.500 5.17 0.011
Error 16 13.925 0.870
Total 19 27.425
A) 0.011 B) 4.500 C) 5.17 D) 0.870
answer : p-value = 0.011 ( A )
Step-by-step explanation:
using this information
Source DF SS MS F P
Factor 3 13.500 4.500 5.17 0.011
Error 16 13.925 0.870
Total 19 27.425
significance level = 0.05
given that the significance level = 0.05
and
F statistics are given as : F = 5.17 , F critical = 3.25
hence the p-value = 0.011
from the analysis the p-value is less than the significance level is lower than the significance level