The two statements a iff b and (not a) iff (not b) has been explained
The two statements are known as biconditionals, which state that two statements are true if and only if each other.
"a iff b" means that "a" is true if "b" is true, and "a" is false if "b" is false. In other words, "a" and "b" have the same truth value.
"(not a) iff (not b)" means that "not a" is true if and only if "not b" is true, and "not a" is false if and only if "not b" is false.
Therefore, these two statements are equivalent because they express the same idea: "a" and "b" have the same truth value. If "a" is true, then "b" is true, and if "a" is false, then "b" is false. Similarly, if "b" is true, then "a" is true, and if "b" is false, then "a" is false.
These statements are true in cases where both "a" and "b" have the same truth value. If both are true or both are false, then the statements are true. If "a" is true and "b" is false, or vice versa, then the statements are false.
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Given two points of a line, slope=
change in___
Over
change in___
Keiko was working with a new function, g(x). He wrote down the following steps for g(x):
• Add 5.
• Divide by 2.
• Cube it. (Find the third power.)
Multiply by 6.
a. What is the equation for g(x)? What is the output when 3 is put in?
b. Help Keiko write down the steps (in words) of the inverse machine, g¹(a), and then write its equation.
c. Verify that your equation in part (b) correctly "undoes" the output of g(x) in part (a).
a.) The equation for g(x) is g(x) = 6((x+5)/2)³and output is 384.
b.) The inverse machine, g¹(a), we need to undo each of the four steps in reverse order is g¹(a) = [tex]((a/6)^{(1/3)})*[/tex]2 - 5
c.) To verify that g¹(a) correctly "undoes" the output of g(x), we can plug in the output of g(3) (384) into g¹(a) and see if we get 3 as the result is 3.
What is Function?
A function is a mathematical rule that takes one or more inputs (also called independent variables or arguments) and produces a single output (also called a dependent variable or function value). In other words, a function is a relationship between the inputs and the output, where each input produces a unique output.
Functions can take many different forms and can be used to describe a wide variety of mathematical and real-world phenomena.
a. The equation for g(x) is:
g(x) = 6((x+5)/2)³
When 3 is put in for x, the output is:
g(3) = 6((3+5)/2)³= 6(4)³ = 384
b. To find the inverse machine, g¹(a), we need to undo each of the four steps in reverse order:
Undo step 4: Divide a by 6.Undo step 3: Take the cube root of the result from step 1.Undo step 2: Multiply the result from step 2 by 2.Undo step 1: Subtract 5 from the result from step 3.Putting this in equation form, we get:
g¹(a) = [tex]((a/6)^{(1/3)})[/tex]*2 - 5
c. To verify that g¹(a) correctly "undoes" the output of g(x), we can plug in the output of g(3) (384) into g¹(a) and see if we get 3 as the result:
g¹(384) =[tex]((384/6)^{(1/3)})[/tex]*2 - 5 =[tex](64^{(1/3)})[/tex]2 - 5 = 42 - 5 = 3
Since the output of g¹(a) is 3 when we input the output of g(x), we can conclude that g¹(a) correctly undoes the output of g(x).
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What number is exactly halfway between 61 and 547?
Answer:
304
Step-by-step explanation
it was on my quiz
Answer:
The number 304 is exactly halfway between 61 and 547.
Step-by-step explanation:
To find the halfway point between two given numbers we can simply add them together then divide them by 2.
Note:
let [tex]N[/tex] be the number that is halfway
[tex]N=\frac{547+61}{2}[/tex]
[tex]N=\frac{608}{2}[/tex]
[tex]N=304[/tex]
The height of a hill, h(x), in a painting can be written as a
function of x, the distance from the left side of the
painting. Both h(x) and x are measured in inches.
h(x) = -(x)(x-13)
Mark this and return
4
What is the height of the hill in the painting 3 inches from
the left side of the picture?
O 6 inches
O
13 inches
O 30 inches
O 150 inches
Save and Exit
Next
Submit
The height of the hill in the painting 3 inches from the left side of the picture is 30 Inches. Option C
How to determine the height
From the information given, we have that;
h(x) represents the height of a hill, h(x), in a paintingx represents the distance from the left side of the paintingBoth the height and the distance are measured in inchesWe also have that the function is;
h(x) =-(x)(x-13)
Given that the distance is 3 inches
Substitute the values, we have;
h(3)= -(3)(3-13)
substract the values
h(3) = (-3)(-10)
multiply the values
h(3) = 30 inches
Hence, the value is 30 inches
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Scatter plot, 8 grades help please!!!
Answer: 4 people
Step-by-step explanation:
As you can see the money spent is on one side of the graph and the people attending on the other. Try to go along the line of where 60 is and find where the line meets the line on 60. Look down and you can see 4.
In the figure, ACCB. D is a point on AB such that CD AB.
Prove that x = y.
Answer: x = y
Step-by-step explanation:
x and y are angles with vertical sides, and angles with vertical sides are always equal
2) Jane wants to buy some compost. Both Suttons Shop and Greens Garden Shop sell compost. Suttons Shop Bags of compost 20 litres £2.25 each bag £3.25 for 2 bags Jane needs 140 litres of compost. She wants to buy all the compost from the same shop. She wants to buy the compost as cheaply as possible. Which shop should Jane buy the compost from? You must show all your working. Greens Garden Shop Bags of compost 70 litres £4.99 each bag
The cheapest option for Jane is to buy from Suttons Shop, as the total cost is £12, whereas, at Greens Garden Shop, the total cost is £9.98.
To determine the cheapest option, we need to calculate the cost of purchasing 140 liters of compost from each shop.
First, we'll calculate the cost at Suttons Shop:
Jane needs 140 liters of compost, so she needs 140 / 20 = 7 bags of compost.
If she buys 1 bag of compost, it will cost her £2.25.
If she buys 2 bags of compost, it will cost her £3.25.
Since she needs 7 bags of compost, she can buy 3 sets of 2 bags (6 bags) and 1 bag.
So the cost of 6 bags will be 3.25 x 3 = £9.75, and the cost of 1 bag will be 2.25.
The total cost of 7 bags at Suttons Shop will be 9.75 + 2.25 = £12.
Next, we'll calculate the cost at Greens Garden Shop:
Jane needs 140 liters of compost, so she needs 140 / 70 = 2 bags of compost.
Each bag at Greens Garden Shop costs £4.99.
So the total cost of 2 bags at Greens Garden Shop will be 4.99 x 2 = £9.98.
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To raise money for a charity, a Year 10 class has decided to organise a school
luncheon. Tickets will cost $6 each. The students have negotiated a special deal for
delivery of drinks and pizzas, and they have budgeted $200 for drinks and $250 for
pizzas. If they raise $1000 or more, they qualify for a special award.
a) write an equation to represent this situation.
b) solve the equation to find the number of tickets they must sell to qualify for the award. explain your answer.
The equation that represents this situation is $6t - $450 ≥ $1000.
The number of tickets that should be sold is 242.
How many tickets should be sold?The form of the equation is:
total revenue - total cost ≥ $1000
(cost of one ticket x number of tickets sold) - cost of pizza and drinks ≥ $1000
($6 x t) - ($200 + $250) ≥ $1000
$6t - $450 ≥ $1000
$6t ≥ $1000 + $450
$6t ≥ $1450
t ≥ $1450 / 6t
t ≥ 242
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a square with area is inscribed in a square with area with one vertex of the smaller square on each side of the larger square. a vertex of the smaller square divides a side of the larger square into two segments, one of length , and the other of length . what is the value of ?
The value of is equal to the length of the side of the larger square minus the sum of the lengths of the two segments.
The value of is equal to the length of the side of the larger square minus the sum of the lengths of the two segments. This is because the area of the smaller square inscribed in the larger square is equal to the product of the side lengths of the smaller square. If a vertex of the smaller square is located on the side of the larger square, the side of the larger square is divided into two segments with one segment having length and the other having length . The side length of the larger square is then equal to the sum of the lengths of the two segments plus the side length of the smaller square, which is . Therefore, the side length of the larger square minus the sum of the lengths of the two segments is equal to the side length of the smaller square, or the value of is equal to two segments.
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`h\left(x\right)=\frac{1}{2}x-14`
`h\left(-4\right)=`
Answer:
-16
Step-by-step explanation:
[tex]h\left(x\right)=\frac{1}{2}x-14\\h\left(-4\right)=-4/2-14=-2-14=-16[/tex]
Write a quadratic equation with -1 and 5 as its roots
A quadratic equation with -1 and 5 as its roots is x^2 - 4x - 5 = 0 by multiplying the terms.
The roots of a quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation.
Derive factor from the roots
x = -1 and x = 5
x + 1 = 0 and x - 5 = 0
Now, (x+1)(x-5) = 0
x(x - 5) + 1(x - 5) = 0
x^2 - 5x + x - 5 = 0
x^2 - 4x - 5 = 0
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how many four-digit numbers are made up of four consecutive numbers from 1-9 in some order, like 5342 or 7658?
There 144 four digit numbers are made up of four consecutive numbers from 1 to 9
We can approach this problem by counting the number of ways we can choose four consecutive numbers from 1-9 and then arranging them in a four-digit number.
Here we have to use combination
There are 6 possible sets of four consecutive numbers in the range 1-9
= {1,2,3,4}, {2,3,4,5}, {3,4,5,6}, {4,5,6,7}, {5,6,7,8}, and {6,7,8,9}.
For each set, there are 4! = 24 ways to arrange the four numbers into a four-digit number.
So the total number of four-digit numbers made up of four consecutive numbers from 1-9 is:
6 sets × 24 arrangements per set = 144
Therefore, there are 144 such four-digit numbers.
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A bouncy ball is dropped such that the height of its first bounce is 5 feet and each
successive bounce is 68% of the previous bounce's height. What would be the height
of the 9th bounce of the ball? Round to the nearest tenth (if necessary).
I know, I answer quick. What do you expect I'm Johnny Sins to help you with your homework. :)
Anyways,
The height of the nth bounce can be calculated using the formula:
h_n = h_1 * 0.68^(n-1)
Where h_1 is the height of the first bounce, h_n is the height of the nth bounce, and 0.68 is the percentage of the height lost with each successive bounce.
Substituting the given values, we have:
h_9 = 5 * 0.68^(9-1)
h_9 = 5 * 0.68^8
h_9 = 5 * 0.265
h_9 = 1.325
So the height of the 9th bounce would be approximately 1.3 feet, rounded to the nearest tenth.
_________________________________________________________
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simplify 3 to the -2 power
Answer: 0.1 decimal 1/9 fraction
Step-by-step explanation:
Answer:
0.1 or 1/9 i think so but I am sure
Question 2 1 pts In a density curve, proportion of data is represented by area above the curve area under the curve: the shape of the curve: intervals of values on the vertical axis_ intervals of values on the horizontal axis. the length of the curve: Question 3 1 pts Which ONE of the following is a correct classification of shapes of density curves? All v Symmetric Uniform Normal All - Nonsymmetric Bell = Normal AIl = Nonsymmetric Symmetric - Normal AII + Bell 7 Symmetric Normal All v Symmetric Bell v Normal All + Uniform Bell 7 Normal
In a density curve, the proportion of data is represented by the area under the curve. So option B is correct.
What is Density curve?The probability that an observation chosen at random falls within a given interval is represented by the area under a density curve, which is a smooth representation of a probability distribution. As a result, the area under the curve between the respective points is proportional to the percentage of data that falls inside a given range.
The area under the curve that directly represents the proportion of data. The intervals of values on the vertical and horizontal axes are used to plot the curve and are important for interpreting the graph, but they do not directly represent the proportion of data. The length of the curve is not relevant for determining the proportion of data, as it can vary depending on the scaling of the graph.
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πrl,
curved surface area of a cone =
where r is the radius and is the slant height.
Work out the total surface area of the cone
shown below.
Give your answer to 1 d.p.
33 m
6 m
The total surface area of this cone is equal to 735.1 square meters.
How to calculate total surface area of a cone?Mathematically, the total surface area (TSA) of a cone can be calculated by using this mathematical expression:
Total surface area (TSA) of a cone = πr(l + r)
Where:
l represents the slant height of the cone.r represents the radius of the cone.Substituting the given parameters into the total surface area (TSA) (SA) of a cone formula, we have the following;
Total surface area (TSA) of a cone = πr(l + r)
Total surface area (TSA) of a cone = 3.142 × 6 × (33 + 6)
Total surface area (TSA) of a cone = 3.142 × 6 × (39)
Total surface area (TSA) of a cone = 735.1 square meters.
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Help me please!!!!!!!
Answer: 1/m^2n^2
Step-by-step explanation: when dividing powers, we subtract.
so, the top would all cancel out
and we would be left with only m^-2n^-2.
to get rid of the negative we put the number into the denominator.
so m^-2n^-2 would become 1/m^2n^2.
A city's population is currently 365,000. If the population doubles every 24 years, what will the population be 96 years from now?
Answer: 5,840,000
Step-by-step explanation:
96/24=4
365,000x2x2x2x2=5,840,000
or
365,000 x 2^4=5,840,000
Point W is located at (-5, -3). Select all of the following that are 5 units away from point W
These are the four points that are exactly 5 units away from point W. To find points that are 5 units from point W, which is located at (-5, -3).
To find points that are 5 units from point W, which is located at (-5, -3), we need to find all points that are a distance of 5 units away from (-5, -3) using the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the distance between two points) is equal to the sum of the squares of the lengths of the other two sides
Given a point (x, y), the distance between that point and point W can be found using the formula:
distance = sqrt((x + 5)^2 + (y + 3)^2)
Setting this distance equal to 5 and solving for x and y, we get the following points:
(0, -8), (-10, -8), (0, 2), and (-10, 2).
These are the four points that are exactly 5 units away from point W.
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is (, ) = 3 − 32 an harmonic function? if yes, then find a corresponding analytic function ()
No, f(x, y) = 3x - 3y^2 is not a harmonic function.
A harmonic function is a twice continuously differentiable function f(x, y) that satisfies the Laplace equation:
∂²f/∂x² + ∂²f/∂y² = 0.
Let's check if f(x, y) = 3x - 3y^2 satisfies the Laplace equation:
∂²f/∂x² = ∂/∂x(3) = 0
∂²f/∂y² = ∂/∂y(-6y) = -6
∂²f/∂x² + ∂²f/∂y² = 0 + (-6) = -6 ≠ 0
Since the Laplace equation is not satisfied, f(x, y) = 3x - 3y^2 is not a harmonic function.
As for finding a corresponding analytic function, an analytic function is a function that is locally given by a convergent power series. Since f(x, y) is not a harmonic function, there is no corresponding analytic function.
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Factor 26r³s
O 13(2r³s + 475-37²54)
037²s(27+ 47³-38³)
O 13r²(2rs + 4r3 – 384)
O 13r²(26r³s + 527-5-39²4)
+5275-39724. What is the resulting expression?
The resulting expression of the algebraic expression is 13r²(2rs + 4r³ - 3s⁴).
option C.
What is the resulting expression of the algebraic expression?The resulting expression of the algebraic expression given as
26r³s + 52r^(5) - 39r²s⁴
can be determined by finding the highest common factor here and factorize out.
The highest common factor of the letters is r²
Factors of 26 = 1, 2, 13, 26
Factors of 39 = 1, 3, 13, 39
Factors of 52 = 1, 2, 4, 13, 26, 52
The highest common factor for the 3 numbers is 13.
Thus, in total, the highest common factor for the algebraic expression is 13r².
Finally, we have;
13r²(2rs + 4r³ - 3s⁴)
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The complete question is below:
Factor 26r³s + 52r^(5) - 39r²s⁴
Determine if the two are equivalent.choose 3 different values for x and complete the table.Explain your reasoning.X
2(x + 5) + 3x
5x + 10
Answer:
The expressions are identical, as shown by two methods: 1) equation rearrangement and 2) mathematical calculations.
Step-by-step explanation:
2(x + 5) + 3x
Let's simplify this expression.
2(x + 5) + 3x
2x + 10 + 3x [remove parentheses]
5x + 10 [combine like terms]
This matches the other expression.
5x + 10
Several values of x are calculated for both expressions and are shown on the attached table. Each expression results in the same value for a given value of x. This comparison also holds for negative numbers.
There are 5 slices of pepperoni pizza, 1 slice of sausage pizza, and 3 slices of cheese pizza left. Without looking, Douglas took a slice of pizza, ate it, and then took another slice.
What's the probability of Douglas eating two of the same kinds of pizza?
Answer:
Step-by-step explanation:
well if there are 5 pepperoni pizzas that means that he eats 2 meaning he has 3 pepperoni slices of pizza.
Mr. Lopez must drive 340 miles to
attend an origami convention. His
car averages 28 miles per gallon and so far he has traveled 102 miles. How much gasoline must be left in his tank if he wants to complete the trip without stopping?
made
The quantity of gasoline that must be left in his tank if he wants to complete the trip without stopping is 8.5 gallons of gasoline.
What is the slope-intercept form?Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x represents the quantity of gasoline.y represents the total distance.c represents the y-intercept or initial value.In this context, an equation that models the situation is given by:
y = mx + c
340 = 28x + 102
28x = 340 - 102
28x = 238
x = 238/28
x = 8.5 gallons of gasoline.
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Someone help fast I need the answer (In a live class)
Answer:
216 in^3
Step-by-step explanation:
Volume = 6 in. * 4 in. * 9 in. = 216 in^3
Find the missing variable and indicated
angle measure.
D
X =
7x°
62°
F
E
m
K
Answer:
x = 4
The missing angle is 28°
Step-by-step explanation:
7x + 62 = 90 These angles are complementary which means that they add to 90°
7x + 62 = 90 Subtract 62 from both sides of the equation
7x = 28 Divide both sides by 7
x = 4
In a class & 60 students the most number of students who passed Ga is 6 more than the number that passed fante. Every student passed at least one of the two subjects and 8 students passed both subjects (1) How many students passed Ga?
Answer: 37
Step-by-step explanation:
let x be the number of students who pass "fante". Then the number of students who passed "Ga" will be x + 6.
with the added information that 8 students passed both we can say:
(x + x + 6) - 8 = 60
2x + 6 = 68
2x = 62
x = 31
.: x + 6 = "only Ga pass" = 37
The question does not make it clear if it is asking for students who *only* passed Ga, or students who passed Ga + those who passed both. I'll assume the former though. Otherwise the answer would be 37 + 8 = 45 students
A water well is composed of 28 cements rings with 1.4 m of diameter and 0.2 m height if labour of cost for digging out the well is RS.500 per cubic meter and cost of cement ring is 2500
The total cost of the cement rings for the water well is RS. 70,000. This cost is only for the cement rings and does not include the cost of labour for digging the well.
What is the total cost of the cement rings for the water well?The cost of each cement ring is given as RS. 2500. Since there are 28 cement rings used in the water well, the total cost of the cement rings can be calculated as follows:
Total cost of cement rings = Cost of each cement ring x Number of cement rings used
Total cost of cement rings = 28 x 2500 = RS. 70,000
Volume of the well = [tex]\mathrm{ \pi r^2h = \pi (0.7)^2(5.6) = 9.768m^3 }[/tex]
Cost of digging out the well = 500 x 9.798 = RS. 4,899
Total cost of the well = RS. 74,899
Total cost of cement rings = 2500 x 28 = RS. 70,000
Therefore, the total cost of the cement rings for the water well is RS. 70,000. This cost is only for the cement rings and does not include the cost of labour for digging the well.
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A survey was conducted among a group of employees to find the average time they spent online each day. The answers of the employees (in minutes) are shown in the box. 25, 45, 60, 30, 35, 20, 40, 45, 15, 30 Which of these scales would be most appropriate on the y -axis to represent this data on a bar graph? Responses
An appropriate scale for the y-axis would be to have each unit represent 5 minutes of time.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Since the data represents the average time employees spent online, the y-axis of the bar graph should represent time in minutes.
To choose an appropriate scale for the y-axis.
we need to consider the range of values in the data set.
The lowest value is 15 minutes
and the highest value is 60 minutes
Range of values is 60 - 15 = 45 minutes.
It's best to choose a scale that divides the range of values into equal intervals.
One possible option is to use a scale where each unit represents 5 minutes of time. This would allow us to represent the data accurately without making the bars too small or too large.
Therefore, an appropriate scale for the y-axis would be to have each unit represent 5 minutes of time.
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LB =
Round your answer to the nearest hundredth.
B
?
CT
5
4
A
C
3
Measure of angle B is 36.87°.
What are Trigonometric Functions?Trigonometric functions are defined as the real functions or the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.
Given is a right angled triangle.
We have to find measure of angle B.
Cosine of an angle in a right angled triangle is equal to the ratio of it's adjacent side to the hypotenuse.
Hypotenuse = AB = 5
Adjacent side to B = CB = 4
Cos B = 4/5
∠B = Cos⁻¹ (4/5)
= 0.6435 radians
= 36.87°
Hence the measure of the angle B is 36.87°.
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