If a + b ≤ 8 and a = 2, then b ≤ 5.Which of the following would be a counterexample?
Answers
Answer:
The correct counterexample is \(b \leq 6\).
Step-by-step explanation:
We proceed to demonstrate the validity of given implication by direct demonstration and use of our knowledge in algebra:
1) \(a + b \leq 8\) Given.
2) \(a = 2\) Given.
3) \(2+b \leq 8\) 2) in 1)
4) \(2 + b +(-2) \leq 8 +(-2)\) Compatibility with addition.
5) \(b+[2+(-2)]\leq 6\) Commutative and associative properties/Definition of subtraction
6) \(b \leq 6\) Existence of additive inverse/Modulative property/Result.
This contradicts what implies the given proposition. The correct counterexample is \(b \leq 6\).
Related Questions
if you get this right i will cash-app 5$.
Answers
Answer: A
Step-by-step explanation:
I graphed it using my graphing calculator. the maximum point is -2, 9. f(x) means y so graphing just requires you to type the equation into a calculator and replace the f(x) with y. sorry if that doesnt make sense. no money
A car is 160 inches long. A truck is 75% longer than the car.
How long is the truck?
Answers
what is the coefficient of x in 4x⁵5+6x²-7x-9
Answers
Answer:
-7
Step-by-step explanation:
Place in standard form.
4x⁵+6x²-7x-9
The coefficient of the x-value is -7.
Hope this helps!
\(4x 5 5+6x 2 −7x−9\)
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of any constant term is 0. The derivative of anorthit's naxn−1
\(5×20x 5−1 +2×6x 2−1 −7x 1−1\)
Multiply 5 by 4×5.
\(100x 5−1 +2×6x 2−1 −7x 1−1\)
Subtract 1 from 5.
\(100x 4 +2×6x 2−1 −7x 1−1\)
Multiply 2 by 6.
\(100x 4 +12x 2−1 −7x 1−1\)
Subtract 1 from 2.
\(100x 4 +12x 1 −7x 1−1\)
Subtract 1 from 1.
\(100x 4 +12x 1 −7x 0\\\)
For any term t, t 1=t.
\(100x 4 +12x−7x 0\)
For any term t except 0, t 0=1.
\(100x 4 +12x−7\)
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20 POINTSSS!!
Which of the following sets of Real Numbers are Counting Numbers?
A. { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }
B. { 1, 2, 3, 4 ... }
C. { 0, 1, 2, 3, 4 ...}
D. { ...-2, -1, 0, 1, 2 ... }
Answers
Answer:
option D. {......-2, -1, 0, 1, 2 ......}
two independent, completely accidental scientific discoveries will be required to plan a space elevator. the first, negative gravity, we believe will take an average of 10 years to happen. the second, monofilament cables, we believe will take an average of 6 years to take place. a) what is the probability monofilament cables will be discovered within the next 10 years? b) what is the probability both discoveries will take place within the next 20 years?
Answers
The probability that monofilament cables will be discovered during the next ten years and that both discoveries will occur within the next twenty years are, respectively, 0.811 and 0.833.
X = time taken to discover Negative gravity
Y = time taken to discover Monofilament Cables
X follow exponential distribution with mean = 10
Y follow exponential distribution with mean = 6
a)P(Y < y) = 1- e^(-y/mean)
P(Y < 10)
= 1 - e^(-10/6)
= 0.8111
The probability monofilament cables will be discovered within the next 10 years is 0.8111
b)P(X <20 ,Y < 20)= P(X < 20)P(Y < 20)
= (1 - e^(-20/10)) (1 - e^(-20/6))
= 0.8338
The probability both discoveries will take place within the next 20 years
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A backpack that normally sells for $39 is on sale for $25. Find the
percent of change.
Answers
Answer: To find the discount, simply multiply the original selling price by the %discount:
ie: 39 x 33/100= $12.87
So, the discount is $12.87.
Step-by-step explanation: To find the sale price, simply minus the discount from the original selling price:
ie: 39- 12. 87= 26.13
So, the sale price is $26.13
2. A number 'a' is equal to the square of the number 'b' plus three times the
number'c
o Write a formula for 'a'
Answers
Answer:
a = b² + 3c
Step-by-step explanation:
The square of the number b is b² and 3 times c is 3c , then
a = b² + 3c
HELP!!!
A car manufacturer collects data on the number of gallons of gasoline left in the gas tank after driving for different numbers of miles. The manufacturer creates a scatter plot of the data and determines that the correlation coefficient is −0.92.
Select each true statement based on this correlation coefficient.
A.) There is a weak correlation between the number of miles driven and the gallons of gasoline left in the tank.
B.) There is a negative correlation between the number of miles driven and the gallons of gasoline left in the tank.
C.) There is no correlation between the number of miles driven and the gallons of gasoline left in the tank.
D.) There is a linear correlation between the number of miles driven and the gallons of gasoline left in the tank.
E.) There is a strong correlation between the number of miles driven and the gallons of gasoline left in the tank.
Answers
The statement that is true about the variables analyzed is that there is a negative correlation between the number of miles driven and the gallons of gasoline left in the tank.
What is correlation?This refers to the relation or connection between two or more variables. In this case:
Amount of gasolineNumber of milesWhat does -0.92 mean?This has the sign -, which shows the correlation is negative. This implies that as the number of miles increase the amount of gasoline decreases.
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please help!! if you could show work too that would be amazing :))
Answers
Answer:
Was there suppose to be a attached image?
Challenge The Bells are adding a new room to their house. The room will be a cube with volume 4,096
ft³. They are going to put in hardwood floors, and the contractor charges $5 per square foot. How much
will the hardwood floors cost?
The hardwood floors will cost $
Answers
Answer:
$1280
Step-by-step explanation:
You want the cost of flooring a cubic 4096 ft³ room at $5 per square foot.
DimensionsEach dimension (length, width, height) of the room is the edge length of a cube with a volume of 4096 ft³.
V = s³
4096 = s³
∛4096 = s = 16 . . . . feet
AreaThe floor area is the square of the edge length:
A = s²
A = (16 ft)² = 256 ft²
CostAt $5 per square foot, the cost of flooring will be ...
($5/ft²)(256 ft²) = $1280
The hardwood floors will cost $1280.
NEED HELP ASAP Which is an equivalent expression for (52 • 34)3?
15 18
56 • 312
52 • 312
55 • 37
Answers
The expression that is equivalent to the expression given as (52 • 34)3 is 5^4 • 3^12
How to determine the equivalent expression?The expression is given as:
(52 • 34)3
Rewrite properly as:
(5^2 • 3^4)^3
Expand the expression
(5^2)^2 • (3^4)^3
Evaluate the products of the exponents
(5^4) • (3^12)
Remove the brackets
5^4 • 3^12
Hence, the expression that is equivalent to the expression given as (52 • 34)3 is 5^4 • 3^12
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Answer:
its 5^6 x 3^12
Find the values of a and b please I will mark brainliest. (make sure to show your work)
Answers
Answer:
a = 29
b = 20
Step-by-step explanation:
2a - 1 = 57
+ 1 + 1
2a = 58
/ 2 / 2
a = 29
2a - 1 + 7b - 17 = 180
2 (29) - 1 + 7b - 17 = 180
58 - 1 + 7b - 17 = 180
57 + 7b - 17 = 180
7b + 40 = 180
- 40 - 40
7b = 140
/ 7 / 7
b = 20
Express the form 1:n
Give n as a decimal
20 : 4
Answers
Answer:
1 : 0.2 is the answer I think
Solve each system.
[x-3 y =-1 -6 x+19 y =6 ]
Answers
The system of equations [x - 3y = -1 and -6x + 19y = 6] can be solved, resulting in x = -1 and y = 0.
To solve the system of equations [x - 3y = -1 and -6x + 19y = 6], we can use the method of substitution or elimination.
Let's solve it using the method of elimination.
First, we can multiply the first equation by 6 and the second equation by -1 to eliminate the x terms.
This gives us [6x - 18y = -6 and 6x - 19y = -6].
Now, subtracting the first equation from the second eliminates the x terms, leaving us with -y = 0. Solving for y, we find y = 0.
Substituting this value back into the first equation, we get x - 3(0) = -1, which simplifies to x = -1.
Therefore, the solution to the system of equations is x = -1 and y = 0.
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if you cant read it it says : Use the distributive property for the expression 4(m + 7) - 6(4-) and simplify
Answers
Explanation
The distributive property tells us how to solve expressions in the form of a(b + c)
\(a(b+c)=ab+ac\)Then,
Step 1
apply distributive property operate
\(\begin{gathered} 4(m+7)-6(4-m) \\ 4\cdot(m)+4\cdot7-6(4)+6(m) \\ 4m+28-24+6m \end{gathered}\)
Step 2
add similar terms
\(\begin{gathered} 4m+28-24+6m \\ 10m+4 \end{gathered}\)so, the answer is
\(D)10m+4\)I hope this helps you
given the maxwell distribution derive an expression for the most probable speed c* [see pci 3.2 p.18 for how to do this]
Answers
The most probable speed of gas molecules describes by the Maxwell-Boltzmann distribution is the speed at which distribution graph reaches its maximum. Thus, if we know the formula of this distribution, we just need to consider the derivative to be equal to zero.
According to the Maxwell Boltzmann energy distribution, the most probable energy is Ep = kT^2.
The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution of molecular speeds.
This predictable Maxwell-Boltzmann distribution, after its originators, who calculated it based on kinetic theory, and it has since confirmed experimentally.
The Boltzmann distribution shows the distribution of molecular energies in a sample of a gas at a given temperature.
Given question is incomplete.
The graphs above show Maxwell-Boltzmann distributions for one-mole samples of Ar(g). Graph 1 shows the distribution of particle energies at 600 k. A student predicts that if the samples are combined in an insulated container and thermal equillibrium is attained, then the most probablie particle energy will be between the most probable energy in graph 1 and the most probable energy in graph 2. Which of the following is the best justification for the student's claim?
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Please help me with imaginary numbers.
Answers
Answer:
i³².1
i²⁵.i
i⁸⁶.-1
i⁵¹.-i/0
If A and B are events with P(A) = 0.6, P(A OR B)0.98, PCA AND B)0.02, find P(B)
Answers
We are given the following:
\(\begin{gathered} P\mleft(A\mright)=0.6 \\ P\mleft(A,orB\mright)=0.98 \\ P(A,\text{and }B)=0.02 \\ \\ \text{For Mutually }Exclusive,\text{ we have:} \\ P\mleft(A,orB\mright)=P\mleft(A\mright)+P\mleft(B\mright)=0.98 \\ \Rightarrow0.6+P(B)=0.98 \\ P\mleft(B\mright)=0.98-0.6=0.38 \\ P\mleft(B\mright)=0.38 \\ \\ \text{For Mutually }Inclusive,\text{ we have:} \\ P(A,orB)=P(A)+P(B)-P(A,\text{and }B) \\ 0.98=0.6+P(B)-0.02 \\ P(B)=0.98+0.02-0.6 \\ P(B)=1-0.6 \\ P(B)=0.4 \\ \\ For\text{ Independent Events, we have:} \\ P(A,\text{and }B)=P(A)\times P(B) \\ 0.02=0.6\times P(B) \\ P(B)=\frac{0.02}{0.6} \\ P(B)=0.033 \end{gathered}\)The answer for P(B) would therefore be determined by the type of events that A & B are
what is the s10 for arithmetic sequence 25,20,15,10
Answers
Answer:
S₁₀ = 25
Step-by-step explanation:
the sum to n terms of an arithmetic sequence is
\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
here a₁ = 25 and d = a₂ - a₁ = 20 - 25 = - 5 , then
S₁₀ = \(\frac{10}{2}\) [ (2 × 25) + (9 × - 5)]
= 5(50 - 45)
= 5 × 5
= 25
The temperatures of two cities were measured at the same time. The
temperature in city A was 60 degrees and rose at a constant rate of 2
degrees per hour.
The temperature in city B was 40 degrees and rose at a constant rate
of 10 degrees per hour.
Enter the number of hours it took for the temperature to be the same in
both cities.
Answers
Answer:
2.5 hours
Step-by-step explanation:
60+2t=40+10t
hope this helps, have a great day :)
SOMEONE HELP PLZ!!!!!!
Answers
Answer:b
Step-by-step explanation:
Mr. Paulsen challenges Olivia and Angelica to move figure ABCDE onto figure
A'B'C'D'E' using a series of two different transformations. They give two different
answers
Answer the questions to investigate ways to transform ABCDE
1. Olivia finds a combination of two different transformations that moves ABCDE
onto A'B'C'D'E' What is one way she might have done this?
Write your answer in the space below.
Answers
Answer:
Step-1 : Reflect the original figure around the x-axis.
Step-2 : Slide the new figure 7 units to the right.
Answer:
Olivia finds a combination that moves figure ABCDE onto figure A"B"C"D"E".
She may have reflected it over the x-axis and then translated it right 10 units.
Angelica reflected the figure over the y-axis and translated it up 8 units. Her transformed figure is in the correct location, but facing the wrong direction
1/4=3/?? please help fast
Answers
Answer:
3/12
Step-by-step explanation:
multiply numerator and denominator by 3
hope it helped!!!
Please solve the equation
-4(2z+6)-12=4
Answers
Step by Step:
-4(2z+6)-12=4
-8z-36=4
-8z-4+36
-8z=40
z=-5
Which fraction converts to a repeating decimal number? A. B. C. D. E.
Answers
Answer: 1/3
Step-by-step explanation:
Answer:
it 1/12
Step-by-step explanation:
how do I solve an equation with different variables on both sides? here is an example.
solve for x
9x – 2c = k
Answers
Answer:
Step-by-step explanation:
9x - 2c = k
9x = k + 2c
x = (k + 2c)/9
Volume of a cone rh, curved surface area of a cone = xr!] [Volume of a spheresurface area of a sphere 4ar']
The solid is formed from a hemisphere of radius rcm fixed to a cone of radius rcm and height hem. The volume of the hemisphere is one third of the volume of the solid.
(a) Find h in terms of r
(b) The slant height of the cone can be written as Vk cm, where k is an integer.
Find the value of k
(c) Find an expressionin terms of r and x, for the total surface area, in cm², of the solid
Answers
Answer:
Long solution
Step-by-step explanation:
(a) Let the height of the cone be h cm. The volume of the hemisphere is given by (1/2)(4/3)πr³ = (2/3)πr³. The volume of the solid is the sum of the volumes of the hemisphere and the cone, which is (2/3)πr³ + (1/3)πr²h. Since the volume of the hemisphere is one third of the volume of the solid, we have:
(2/3)πr³ = (1/3)πr²h
Simplifying, we get:
2r = h
Therefore, h is expressed in terms of r as h = 2r.
(b) The slant height of the cone can be found using the Pythagorean theorem. Let l be the slant height, then we have:
l² = r² + h²
Substituting h = 2r, we get:
l² = r² + (2r)² = 5r²
Taking the square root of both sides, we get:
l = r√5
Since k is an integer, we can write:
l = Vk cm, where k is an integer
Comparing the two expressions, we get:
Vk = r√5
Therefore, the value of k is k = ⌊r√5⌋, where ⌊x⌋ denotes the largest integer less than or equal to x.
(c) The total surface area of the solid is the sum of the curved surface area of the cone, the curved surface area of the hemisphere, and the area of the circular base of the cone. We have:
Curved surface area of the cone = πr l = πr(r√5) = πr²√5
Curved surface area of the hemisphere = 2πr²
Area of the circular base of the cone = πr²
Therefore, the total surface area of the solid, in cm², is given by:
πr²√5 + 2πr² + πr² = (πr²)(√5 + 3)
Evaluate the expression. 9.12-5.28÷3.52
Answer
Answers
Answer:
=7.62
Step-by-step explanation:
i need help answering with steps
-40-2(3m+1/2) =7m-2
Answers
Answer:
Step-by-step explanation:
-Start by distributing the 2, -2(3m+1/2).
-Getting -6m-1, your equation should look like -40-6m-1=7m-2
-Combine -40 and -1 to get -41, and then add the -6m to the other side.
-The equation should look like -41=13m-2. Add the 2 to the -41 to get -39.
-Now, we have -39=13m. divide both sides by 13 to get m=-3.
3. Determine an exact value for the following expression
{sec π/4 cos 2π/3}/{tan π/6 csc 3π/4}
Answers
The exact value for the following expression {sec π/4 cos 2π/3}/{tan π/6 csc 3π/4} is - \(\sqrt{3} /2\)
The expression is given that
{sec π/4 cos 2π/3}/{tan π/6 csc 3π/4}
Here we have to use the trigonometric functions
Find the each values of the term
sec π/4 = 1 / cos π/4
= 1 / (1 / \(\sqrt{2}\) )
= \(\sqrt{2}\)
Next term is cos 2π/3
cos 2π/3 = -1 / 2
Next term is tan π/6
tan π/6 = \(\sqrt{3}\) / 3
Next term is csc 3π/4
csc 3π/4 = \(\sqrt{2}\)
Substitute the values in the expression
{sec π/4 cos 2π/3}/{tan π/6 csc 3π/4}
= ( \(\sqrt{2}\) × (-1/2) ) / ( \(\sqrt{3}\) / 3 × \(\sqrt{2}\))
= - \(\sqrt{3} /2\)
Hence, the exact value for the following expression {sec π/4 cos 2π/3}/{tan π/6 csc 3π/4} is - \(\sqrt{3} /2\)
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