A conditional statement has the same truth value as Contrapositive
How to complete the statement?From the question, we are to determine which type of conditional statement has the same truth value as the original statement
As a general rule, if the truth value of an original statement is True, the truth value of the contrapositive would also be true
Similarly;
If the truth value of an original statement is false, the truth value of the contrapositive would also be false
Hence, a conditional statement has the same truth value as contrapositive
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A pizza maker sells either whole pizzas or pizza by the slice. A slice of pizza is 1/8 of a pizza. How many whole pizzas would 113 slices of pizza make? Express your answer as a mixed number. Explain your answer.
Answer:
Here is your answer
Step-by-step explanation:
113/8= 14 and 1/8th
If the radius of a circle is 5, what is the diameter?
Answer:
d=10
d=2r=2·5=10
help
I will be using your answer in the question so follow the prompt carefully.
Answer:
1/5 as a fraction can be turned into 20/100. (Multiply the top and bottom by 20). 20/100 can be turned into 0.2.
0.2 multiplied by something will end up as 20% of the original value. So 0.2 and 20% are the same.
Therefore, they are all equal.
Step-by-step explanation:
1/5 as a fraction can be turned into 20/100. (Multiply the top and bottom by 20). 20/100 can be turned into 0.2.
0.2 multiplied by something will end up as 20% of the original value. So 0.2 and 20% are the same.
Therefore, they are all equal.
Find four solutions of the equation. Write the solutions as ordered pairs. 3x-y=-6
Solving the Question
We're given:
3x-y=-6Find 4 solutionsWe can start by isolating one of the variables, like y:
[tex]3x-y=-6\\-y=-3x-6\\y=3x+6[/tex]
Now we can find four solutions by plugging in any number for x:
[tex]y=3x+6\\y=3(1)+6\\y=3+6\\y=9[/tex]
First solution: (1,9)
[tex]y=3x+6\\y=3(2)+6\\y=6+6\\y=12[/tex]
Second solution: (2,12)
[tex]y=3x+6\\y=3(3)+6\\y=9+6\\y=15[/tex]
Third solution: (3,15)
[tex]y=3x+6\\y=3(4)+6\\y=12+6\\y=18[/tex]
Fourth solution: (4,18)
Possible AnswersFirst solution: (1,9)
Second solution: (2,12)
Third solution: (3,15)
Fourth solution: (4,18)
NEED HELP WITH INEQUALITY PLEASE!!!!!!!!!!!!!!!!!!
Answer:
D
Step-by-step explanation:
If the light build can be 50 and less, the sign needs to be ≤ because it means less than or equal to.
SOLVE THE Word problem involving average rate of change
Answer:
[tex]{ \rm{rate \: of \: change = \frac{R _{2}(t) - R _{1}(t) }{t _{2} - t _{1}} }} \\ [/tex]
For 0 < t < 10; 226.6 < R(t) < 205.6
[tex]{ \rm{ = \frac{205.6 - 226.6}{10 - 0} }} \\ \\ { \rm{ = - \frac{21}{10} }} \\ \\ = { \rm{ - 2.1}} \\ \\ = 2.1[/tex]
Negative indicates an inverse proportionality, or decrease in temperature
For 30 < t < 50; 157.6 < R(t) < 119.6
[tex] = { \rm{ \frac{119.6 - 157.6}{50 - 30} }} \\ \\ = { \rm{ - \frac{38}{20} }} \\ \\ = { \rm{1.9}}[/tex]
The dance committee consisted of 10 students. The committee will select three officers at random. What is the probability that Alice, David, and Carlene are selected?
The probability that Alice, David, and Carlene are selected is 1/120.
What is meant by probability?
Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.
3 people can be chosen from 10 people in 10C3 ways and Alice, David, and Carlene can be chosen in only one way.
10C3 = 10! / (10 - 3)! 3!
= (10 [tex]*[/tex] 9 [tex]*[/tex] 8 [tex]*[/tex] 7!) / (7! [tex]*[/tex] 3 [tex]*[/tex] 2 [tex]*[/tex] 1)
= 120
So, the number of possible outcomes is 120 and the number of favorable outcomes is 1. Therefore, the probability is 1/120.
The probability that Alice, David, and Carlene are selected is 1/120.
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What is the squared root of 56 minus the squared foot of 189?
The squared root of 56 minus the squared root of 189 is -6.26 .
The square root of any number is equal to the number squared to give the original number. In mathematics, the square root function is defined as a one-to-one function that takes a positive number as input and returns the square root of the given input number.The square root symbol is usually represented by '√'. It's called a radical. To represent the number 'x' as a square root, this symbol can be written as "√x"We have given an statement that squared root of 56 minus the squared root of 189 which can be represented in expression as
[tex]\sqrt{56} -\sqrt{189}[/tex] ..(1)
Prime factorization 56 is given by
[tex]\sqrt{56} =\sqrt{2\times2\times2\times7} \\\sqrt{56} =2\sqrt{14} \\\sqrt{56} =2\times3.74\\\sqrt{56} =7.48[/tex]
Prime factorization 189 is given by
[tex]\sqrt{189} =\sqrt{3\times3\times3\times7} \\\sqrt{189} =3\sqrt{21} \\\sqrt{189} =3\times4.58\\\sqrt{189} =13.74[/tex]
Putting above values in equation (1) , we get
[tex]\sqrt{56} -\sqrt{189}=7.48-13.74\\\sqrt{56} -\sqrt{189}=-6.26[/tex]
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Tamara is creating a model of a rectangle. She has 26 inches of yellow ribbon to use for the border of the rectangle. She wants the length, l, to be 3 inches greater than the width, w. Which system of equations could Tamara use to find the dimensions of a rectangle that uses all of the ribbon?
A system of equations. 2 l plus 2 w equals 26. 3 l equals w.
A system of equations. 2 l plus 2 w = 26. l equals 3 w.
A system of equations. 2 l plus 2 w equals 26. l equals w plus 3.
A system of equations. 2 l plus 2 w equals 26. l plus 3 equals w.
The systems of equations which Tamara can use to find the dimensions of a rectangle that uses all the ribbons is;
2l + 2w = 26l = w +3System of equationsIf follows from the task content that the systems of equations which best models the situation and can be used to find the dimensions is required.
Hence, since the perimeter of a rectangle is; P = 2l +2w.
2l + 2w = 26Also, the length of the rectangle is 3 inches greater than its width, we have;
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Ifs= unit and A = 12s², what is the value of A, in square units?
square unit(s). (Input whole number only.)
The value of A is 3 square unit
A square number is a number multiplied by itself. This can also be called 'a number squared'. The symbol for squared is ².
Formula: s²= s x s
given that, the question is testing the concept of substitution.
A=12s^2
If s=1/2,
Substituting s with 1/2 we get;
A=12(1/2)^2
=12×1/4
=3
The answer is 3 unit squared. There is no fraction in the answer.
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Answer:
A has a value of 3 square units.
Step-by-step explanation:
Any number multiplied by itself is a square number. This is also referred to as "a number squared." 2 represents the squared sign.
Equation: s2=s x s
As a result, the question is putting the idea of substitution to the test.
A=12s^2
If s=1/2,
Substituting s with 1/2 we get;
A=12(1/2)^2
=12×1/4
=3
The answer is 3 unit squared. There is no fraction in the answer.
A question paper has two parts, a and b, each containing 10 questions. if a student has to choose 7 from part a and 4 from part b, in how many ways can he choose the questions?
Combinations exist ways to select elements from a collection in mathematics where the order of the selection exists irrelevant. He can choose the question in 28 ways.
What is meant by combinations?
Combinations exist mathematical operations that count the number of potential configurations for a set of elements when the order of the selection exists is irrelevant. You can select the components of combos in any order.
The combination formula is used to determine how many options there are for choosing things from a collection so that the order in which they are chosen is irrelevant. Combination, to put it simply, is the choosing of items or things from a bigger group when the order doesn't important.
Given: Number of questions in part A = 10
Number of questions in part B = 10
A student chooses 7 from part A and 4 from part B
Required number of ways = ( 10C7 × 10C4) × ( 10C3 × 10C6)
= 5040 × 24/ 6 × 720
= 28
He can choose the question in 28 ways.
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How do you find the square root of the following WITHOUT a calculator:
1. Square root of 2 890 000
2. Square root of 0.000004
Answer:
1. you can think that 289000= 17×17(=289)x100x100, so the result is √289x√100x√100=17 x 10x10=1700
2. 0.000004= 4x10^-6, so the Square root Is √4 x√10^-6= 2x 10^-3
Find the value of x.
Answer:
1 15 degrees
Step-by-step explanation:
Exterior angle is equal to sum of opposite interior angles
At a little-known vacation spot, taxi fares are a bargain. A36 -mile taxi ride takes 42 minutes and costs $25.20. You want to find the cost of a 47 - taxi ride. What unit price do you need?
Answer:
it will cost $32.9 for a 47 mile taxi ride
Step-by-step explanation:
Since 36 miles takes 42 minutes and Costa $25.20 then 47 miles taxi rides will take
42/36 = per minute = 1.17
1.17 × 47 = 54.83
In order to find cost per minute = $25.2/42 = 0.6
then 54.83 × 0.6 = $32.898
∴it will cost $32.9 for a 47 mile taxi ride
Determine whether each statement is always, sometimes, or never true. (Lesson 1-5 )
If two angles are supplementary, then one of the angles is obtuse.
If two angles are supplementary, then one of the angles is obtuse: Never TRUE
What do we mean by obtuse angles?An obtuse angle is one that is less than 180 degrees but greater than 90 degrees. Obtuse angle degrees include 110°, 135°, 150°, 179°, 91°, and others. As a result, all angles ranging from 90° to 180° are obtuse. The hypothesis that if two angles are supplementary, one is obtuse and the other acute is false. This is due to a situation in which two angles are supplementary but neither is acute or obtuse. When we have two right angles, we get this. A supplementary angle cannot be formed by two obtuse angles. Obtuse angles are defined as angles that are greater than 90° in length. The sum of two obtuse angles will be larger than 180°. When we add obtuse angles, the property of supplementary angles is violated.Therefore, the statement "if two angles are supplementary, then one of the angles is obtuse" is never TRUE.
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Write the equation of each line in standard form.
slope =-1 ;(-3,3)
The standard equation for the given slope is x + y = 0.
These are two methods for finding the equation of a line given a point and slope. Create the equation y = mx + b using the m given in the problem and the b you just solved. Point-slope form = y-y1 = m (x-x1), where (x1, y1) is the specified point and m is the specified slope. "x" and "y" remain as variables.
y = 3 and x = -3 and m = - 1
To find b, we will plug in the known parameters listed above.
3 = −1(-3) +b
To solve for b, move 3 to the other side of the equation.
3=3+b
b=0
Standard form equation:
y = -x + 0
x + y = 0
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Here is the picture it says xxxxxxxxxxxxxxxxxxx
Answer:
Step-by-step explanation:
given: 5^3/5^7
= 1/5^(7-3)
= 1/5^4
= 1/625
final answer: 1/625
Answer:
[tex]5^{-4}[/tex]
Step-by-step explanation:
using the rules of exponents
• [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]
• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
given
[tex]\frac{5^{3} }{5^{7} }[/tex]
= [tex]5^{(3-7)}[/tex]
= [tex]5^{-4}[/tex]
= [tex]\frac{1}{5^{4} }[/tex] ← if required with a positive exponent
Use the given statement to find the measure of numbered angle.
∠1 and ∠ form a linear pair and m ∠2=67 .
The answer is ∠1 = 113°
Linear Pair :
When two lines meet at a single point, a pair of linear angles is created. If the angles follow the point where the two lines cross, they are considered to be linear. A linear pair's angles add up to 180° in every case.
Now as per the question the given angle is
∠2 = 67°
It is also given that ∠1 and ∠2 form a linear pair. Therefore it means that the sum of both the angles will be 180°
∠1 + 67° = 180°
Now subtracting 67 from both sides we will get :
∠1 = 180 - 67 = 113°
Therefore, ∠1 = 113°
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Which input value produces the same output value for
the two functions?
O x=-3
O x=-1
O x=0
O x = 1
x = -2 is input value produces the same output value for the two functions .
What are the function's input values?
The domain of the function is the collection of input values. The range of the function is the collection of output values.
What input and output functions are used?
The fundamental functions for input and output are getchar, putchar, puts, scanf, and printf. To transfer single characters, utilize the first two functions, getchar and putchar.
Which four sorts of functions are there?
Four main categories can be used to classify different sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.
The input value which produces the same input .
value for two function is x = -2
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In Triangle ABC, the measure of angle B is 50 degrees. Select all (there may be one or more) possible measure angles of A and C if ABC is a right triangle.
By using angle sum property, The value of ∠ A = 40° and ∠ C = 90°
A triangle's total angle is 180°.
Using angle sum property,
∠A+∠B+∠C = 180°
assuming B = 50°
replacing in the formula
∠A+50+∠C = 180°
Due to the triangle's right angle, A+90=180-50
∠A = 130° - 90
∠ A = 40°
The angles A and C must be more than 90 degrees since the ABC is a right triangle.
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Complete question -In triangle ABC, the measure of angle B is 50 degrees. Select all possible values for the measures of A and C if ABC is an right triangle. m\angle∠A= 58 degrees; m\angle∠C= 72 degrees m\angle∠A= 100 degrees; m\angle∠C= 30 degrees m\angle∠A= 80 degrees; m\angle∠C= 50 degrees m\angle∠A= 60 degrees; m\angle∠C= 70 degrees m\angle∠A= 90 degrees; m\angle∠C= 40 degrees m\angle∠A= 105 degrees; m\angle∠C= 25 degrees
Answer:
m∠A = 40°, m∠B = 75°, m∠C = 65° (A)
m∠A = 136°, m∠B = 28°, m∠C = 16° (B)
m∠A = 60°, m∠B = 60°, m∠C = 60° (E)
Step-by-step explanation:
i did the assignment and got it wrong at first then it showed me the right answers
Write an explicit and a recursive formula for each arithmetic sequence. -3,0,3,6, . . . . .
The recursive formula is a(n) = a(n-1) + 3 while the explicit formula is a(n) = 3n - 6.
In an arithmetic sequence, the following applies:
a(n) = a(n-1) + d (This is the recursive formula)
a(n) = a(1) + (n-1) . d ( This is the explicit formula)
Where:
a(n) = nth term
a(n-1) = (n-1)th term
d = common difference
a(1) = the first term
The given sequence is:
-3, 0, 3, 6, ....
The common difference (d) = 0 - (-3) = 3
Hence, the recursive formula is:
a(n) = a(n-1) + 3
Note that a(1) = -3. Hence, the explicit formula is:
a(n) = a(1) + (n-1) . d
a(n) = -3 + (n-1) . 3
a(n) = -3 + 3n - 3
a(n) = 3n - 6
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Suppose you are stacking boxes in levels that form squares. The numbers of boxes in successive levels form a sequence. The figure at the right shows the top four levels as viewed from above.
c. Suppose you are stacking a total of 285 boxes. How many levels will you have?
There is need of total of 9 levels to stack 285 boxes.
What is a sequence ?A sequence can be taken as the set of numbers having a particular order for all the terms or we can say that arrangement of numbers in some order is known as sequence.
Some examples for sequence are :
2,4,6,8,10,12
3,9,27,81,243
What is recursive sequence ?The recursive sequence is the sequence in which any term in the sequence can be find with the help of previous term of that sequence.
In a sequence , first term always known as initial term.
and difference between two terms are known as common difference. It is denoted by d.
General form of sequence is :
[tex]a_1,a_2,a_3,----,a_n[/tex]
where , [tex]a_n[/tex] = last term in sequence.
According to question,
Also, number of boxes at level recursively n =[tex]a_{n-1} + n^2[/tex]
The formula to find number of level for 285 boxes is :
[tex]a_n > =285[/tex]
now, find each level
[tex]a_1 = 1 , a_2 = 1 + 2^2 = 5 , a_3 = 5+3^2 = 14,\\a_4 = 14 + 4^2 = 30\\a_5 = 30 + 5^2 = 55\\a_6 = 55 + 6^2 = 91\\a_7 = 91 + 7^2 = 140\\a_8 = 140 + 8^2 = 204\\a_9 = 204 +9^2 = 285[/tex]
thus, to stack 285 boxes total numbers of level are 9.
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The complete question is :
Suppose you're stacking boxes in levels which make squares. The numbers of boxes in each successive levels make a sequence. The figure show top four levels as view from top or above.
a. How many boxes of same size would need for next lower level?
b. How many boxes of same size would need to add the 3 levels?
c. Suppose you are stacking 285 boxes. Then, how many total levels will you have?
b. Use summation notation to write the related series for a triangle with 10 cans in the bottom row.
The series that is related to a triangle with 10 cans in the bottom row can be expressed in summation notation as [tex]\sum\limits^{10}_{n=1} {n}[/tex]
Let us consider the simpler triangle formed by stacking cans as in the attached picture.
As we can see in the picture, if the bottom row contains 3 cans, then the triangle will have 3 rows. The number of cans in each row decreases by 1. We can expand this idea for a triangle with 10 cans in the bottom row.
In this case, there will be 10 rows and the number of cans in each row decreases by 1.
10th row : 10 cans
9th row : 9 cans
and so on.
We can express the number of all cans in this triangle as a series, starting from the top row (the first row):
1 + 2 + 3 + ... + 10
The explicit formula of the nth term is: a(n) = n.
Hence, in the summation notation, it can be written as:
[tex]\sum\limits^{10}_{n=1} {a(n)} = \sum\limits^{10}_{n=1} {n}[/tex]
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Write an explicit formula for each sequence. Then generate the first five terms. a₁ =4, r=0.1
The given geometric sequence, with first term = 4 and ratio = 0.1, has the formula for its nth term: a(n) = 4 . 0.1ⁿ⁻¹. The first five terms are: 4, 0.4, 0.04, 0.004, 0.0004
The formula of the nth term of a geometric sequence is:
a(n) = a₁ . r^(n-1)
with a₁ is the first term and r is the ratio. In a geometric sequence, the ratio is constant and equal to a(n)/a(n-1).
In the given problem, a₁ =4, r=0.1, therefore:
a(n) = a₁ . r^(n-1)
a(n) = 4 . 0.1ⁿ⁻¹
To find the first five terms, replace n with 1, 2, 3, 4, and 5.
a₁ = 4
a(2) = 4 . 0.1²⁻¹
= 4 . 0.1¹ = 0.4
a(3) = 4 . 0.1³⁻¹
= 4 . 0.1² = 0.04
a(4) = 4 . 0.1⁴⁻¹
= 4 . 0.1³ = 0.004
a(5) = 4 . 0.1⁵⁻¹
= 4 . 0.1⁴ = 0.0004
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Racha of Meghna’s cat has fleas, Her veterinarias recommended a treatment plan that includes combing out her cats fur every day. Meghna kept track of the number of fleas that she removed from her cats while combing them, on day 0, the day she started the treatment, she removed a total of 87 fleas. On day 6, she removed a total of 14 fleas. If Meghna keeps up the treatment and the number of fleas can be modeled by an exponential function, approximate the number of fleas she should expect to remove from the cats on Day 14, write the exponential function and show your work
The approximate number of fleas she should expect to remove from the cats on Day 14 is 1
How to approximate the number of fleas she should expect to remove from the cats on Day 14?The given parameters are
Function type: exponential function
Day 0 = 87
Day 6 = 14
An exponential function is represented as
y = ab^x
Where
y = a, when x = 0
This means that a = 87
So, we have
y = 87b^x
Day 6 = 14 means that
When x = 6, y = 14
So, we have
87b^6 = 14
This gives
b^6 = 0.161
Take the 6th roots of both sides
So, we have
b = 0.74
Subsitute b = 0.74 in y = 87b^x
y = 87(0.74)^x
On day 14, we have
y = 87(0.74)^14
Evaluate
y = 1.28
Approximate
y = 1
Hence, the approximate number of fleas she should expect to remove from the cats on Day 14 is 1
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Every day, the Randolph Pet Store uses 2/3 of a bag of dog food to feed the dogs. How many days will 1 1/3 bags of dog food last?
Write your answer as a fraction or as a whole or mixed number.
this qestion is hard hope you can it get it right and dont just geuss
The correct option that proves that angles 1 and 2 are supplementary is; B: Angles 1 and 4 form a Linear Pair and angles 4 and 8 are congruent as corresponding angles.
How to prove supplementary angles?
Supplementary angles are two angles whose measures add up to 180° . The two angles of a linear pair are always supplementary.
Now, looking at the given image, we can see a total of 8 angles formed from the transverse lines.
Angles 1 and 4 can be classified as Linear Pairs because Linear pair of angles are formed when two lines intersect each other at a single point.
Similarly, angle 4 and angle 8 are classified as corresponding angles because Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal
Thus, the correct option that proves that angles 1 and 2 are supplementary is; B: Angles 1 and 4 form a Linear Pair and angles 4 and 8 are congruent as corresponding angles.
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volume=1/8π ft r=1/3ft what is the height?
Answer:
Need to know the shape of object (cylinder, cone, etc)
Part 3 of 3 Graph the equation y=49x, where y represents the distance traveled over time, z, in hours is the relationship proportional? How many miles from home is the family after 5 hours?
Refer to the graph below for the graphical representation of the given equation y = 49x.
What is an equation, exactly?An equation, in its most basic form, is a mathematical statement that proves two mathematical expressions appear to be equal.The expressions 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14.Graph:
A diagram (such as a series of one or more points, lines, line segments, curves, or areas) that depicts the variation of one variable in comparison to another. A grouping of all points whose coordinates satisfy a given relationship (such as a function).Refer to the graph given below for the equation y=49x.
Therefore, the graph of the given equation y=49x is shown below.
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Write a recursive definition for each sequence. 2,-4,8,-16, . . . .
A recursive definition of the given Geometric progression is: [tex]a_{n}=a_{n-1}r[/tex], with a₁ = 2 and n > 1.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Now,
Given: 2, -4, 8, -16, ...
Here, [tex]r = \frac{-4}{2} = -2[/tex] and a₁ = 2.
Thus, a recursive formula for this geometric progression can be: [tex]a_{n}=a_{n-1}r[/tex], with a₁ = 2 and n > 1.
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