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Contrapositive represents the implication of conditional statement to the logical statement if p then q to be false where as contradiction we prove that our supposition is false that implies the given condition is true.

Comparison in the proof of contrapositive and contradiction:

Contrapositive represents the hypothesis is true that implies conclusion is also true or the conclusion is false that implies hypothesis is also false.

Example of contrapositive: For any integer a , b a + b ≥ 17 , a≥9 , b≥ 9.

Using contrapositive :

If a < 9 , b < 9 then a + b < 17

a < 9, b < 9 consider a ≤8 , b≤8

a + b = 8 + 8

        = 16

        < 17

It proves a < 9 , b < 9 then a + b < 17 implies ,when  a≥9 , b≥ 9 then

a + b ≥ 17 .

Contradiction : Here we suppose the statement which is against the required statement and prove it wrong which implies our given statement is true.

Example: For any integer a, a²  is even then a is even .

Here we assume a is an odd integer then prove it wrong.

Therefore, comparing contrapositive and contradiction provides contrapositive is conditional to logical and contradiction required to our supposition is wrong.

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Answer:

The answer is Graph B. you could also plug it in demos and it will give you the answer.

Answer:

Irrational Number is the answer

Answer:

\( \sqrt{11 + 10} = \sqrt{22} = 4.69041576 \)

THIS IS IRRATIONAL

Step-by-step explanation:

The correct answer is irrational and the reason for that is the decimals for sqrt of 22 are non-recurring, are non-terminating and lastly it cannot be expressed in a form of a fraction.

I hope this makes sense

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Answer: So, the sales tax on the item is $49.

Step-by-step explanation:

The sales tax rate is already given as 14%. It is stated that the item costs $350 before tax, and the sales tax rate is 14%. Therefore, the sales tax amount can be calculated by multiplying the cost of the item by the tax rate:

Sales tax amount = $350 * 14% = $350 * 0.14 = $49

So, the sales tax on the item is $49.

13 degrees mPQT = 1 degree in internal angle .

An illustration of an internal angle?

mPQR=25 degrees , mRQT=11 degrees.

mPQT=PQR-RQT

MPQT=25-11=13 degrees

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Answer:

Angle 3 = 95° (vertically opposite angles)

Angle 2 and 4 = 180 - 95

= 85° (adjacent angles on straight line)

Angle 5 = 180 - 144

= 36° (adjacent angles on straight line)

Angle 6 = 180 - angle 3 - angle 5

= 180 - 95 - 36

= 49° (sum of angles in triangle=180)

Angle 1 = 180 - 90 - angle 6

= 180 - 90 - 49

= 41° (sum of angles in triangle=180)

Angle 7 = 180 - 38 - angle 5

= 180 - 38 - 36

= 106° (sum of angles in triangle=180)

1 and 1/6

1 and 1/12

1 and 1/10

1 and 1/4

Hope this helps! a

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Sarah spends reading 30 min + \(0.05 min^{2}\).

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. To assist identify the sequence of operations and other features of logical syntax, mathematical symbols can denote numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.

However, in modern mathematics, and particularly in computer algebra, formulae are considered expressions that may be evaluated as true or false based on the values assigned to the variables in the expressions.

The problem is in a mathematical expression.

30 min+3s min did Sarah spend reading

Convert s to min

.30min+3s min× 1min/60s

Cancel the common units and simplify.

Cross-cancel units.

30 min + \(0.05 min^{2}\)

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Answer:

Answer: positive

Step-by-step explanation:

Answer:

-19x

Step-by-step explanation:

Answer:

− 19x

Step-by-step explanation:

Let's simplify step-by-step.

− 12x − 7x

= − 12x + − 7x

Combine Like Terms:

= − 12x + − 7x

=( − 12x + −7x )

= − 19x

Hope it helps,

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Answer:

96 ft²

Step-by-step explanation:

SA = 2bh/2 + Ph

SA = 2(4)(3)/2 + (3 + 4 + 5)(7)

SA = 12 + 84

SA = 96

Answer: 96 ft²

After 18 years, the investment compounded periodically (quarterly) will be worth $1,230.23 more than the investment compounded annually.

Compounded interest refers to the interest system that charges interest on both principal and accumulated interest.

The period of compounding in a year determines the worth of the future value.

The future value can be ascertained using an online finance calculator as follows:

Interest periods: = 4 times yearly (Quarterly)

Principal = $5,000

Annual interest rate = 9%

Number of years: 18

N (# of periods) = 72 quarters (18 years x 4)

I/Y (Interest per year) = 9%

PV (Present Value) = $5,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $24,815.83

Total Interest = $19,815.83

Interest periods: = Annually

N (# of periods) = 18 years

I/Y (Interest per year) = 9%

PV (Present Value) = $5,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $23,585.60

Total Interest = $18,585.60

Difference in Future Values $1,230.23 ($24,815.83 - $23,585.60)

Thus, an investment compounded periodically earns more than an investment compounded annually.

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Answer:

  x ≈ 2.09590327429

Step-by-step explanation:

You want the solution to 3^x = 10 using logarithms.

Taking logarithms of both sides of the given equation, we have ...

  x·log(3) = log(10)

Dividing by the coefficient of x gives ...

  x = log(10)/log(3)

  x ≈ 2.09590327429

__

Additional comment

If the logarithm to the base 10 is used, then this becomes ...

  x = 1/log₁₀(3)

The meaning of "log( )" varies with the context. In high-school algebra, it usually means "log₁₀( )". In other contexts, it may mean "ln( )", the natural logarithm.

For the purpose here, it doesn't matter what base the logarithms have, as long as log(10) and log(3) are to the same base.

<95141404393>

The approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.

To evaluate the equation 3^x = 10 using logarithms, we can take the logarithm of both sides of the equation. The most commonly used logarithm is the base 10 logarithm, also known as the common logarithm (log).

Taking the log of both sides, we get:

log(3^x) = log(10)

Now, we can apply the logarithmic property that states log(a^b) = b * log(a). Applying this property to the left side of the equation:

x * log(3) = log(10)

Next, we can divide both sides of the equation by log(3) to isolate the variable x:

x = log(10) / log(3)

Using a calculator, we can evaluate the right side of the equation:

x ≈ 1.46497

Therefore, the approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.

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Answer:

  x = 1

Step-by-step explanation:

You want to know the value of x in the trapezoid with adjacent angles (43x+2)° and 135°.

The two marked angles can be considered "consecutive interior angles" where a transversal crosses parallel lines. As such, they are supplementary.

  (43x +2)° +135° = 180°

  43x = 43 . . . . . . . . . . . . . . divide by °, subtract 137

  x = 1 . . . . . . . . . . . . . . . divide by 43

The value of x is 1.

__

Additional comment

Given that the figure is a trapezoid, we have to assume that the top and bottom horizontal lines are the parallel bases.

<95141404393>

Th two-way relative frequency table has been attached at the end of the solution. The relative frequencies were obtained by dividing each frequency by the total number of students (325).

Frequency refers to the number of times that a particular event or value occurs within a specific dataset or sample. In statistics, frequency is often used to represent the distribution of values in a dataset, and it can be displayed using tools such as frequency tables, histograms, or frequency polygons.

90 students are in a club and play a sport.

140 total students play a sport.

Therefore, 140 - 90 = 50 students play a sport but are not in a club.

The total number of students who play a sport is 140 + 50 = 190.

200 total students are in a club.

Therefore, 200 - 90 = 110 students are in a club but do not play a sport.

The total number of students who do not play a sport is 325 - 190 = 135.

The relative frequency of students who play a sport and are in a club is 90/325 = 0.277.

This table tends to show the proportion of students in each category and how they overlap with the other category. For example, we can see that 27.7% of the students play a sport and are in a club, while 15.4% of the students do not play a sport but are in a club. We can also see that 21.5% of the students play a sport but are not in a club, while 35.4% of the students do not play a sport and are not in a club.

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Explanation:

Note that 2^4 = 16 is one less than 17.

Because of this nature of being 1 less, we can say the remainder of 16/17 is -1 because it comes up one short.

In terms of modular arithmetic, we can say,

\(2^4 \equiv 16 \ (\text{mod } 17)\\\\2^4 \ \equiv -1 (\text{mod } 17)\\\\\)

Then let's raise both sides to the 20th power. I'm picking 20 because 20*4 = 80 which will help build toward 81

\(2^4 \equiv -1 \ (\text{mod } 17)\\\\\left(2^4\right)^{20} \equiv (-1)^{20} \ (\text{mod } 17)\\\\2^{20*4} \equiv 1 \ (\text{mod } 17)\\\\2^{80} \equiv 1 \ (\text{mod } 17)\\\\\)

Lastly, we'll multiply both sides by 2 to get to the final answer

\(2^{80} \equiv 1 \ (\text{mod } 17)\\\\2*2^{80} \equiv 2*1 \ (\text{mod } 17)\\\\2^{1}*2^{80} \equiv 2 \ (\text{mod } 17)\\\\2^{1+80} \equiv 2 \ (\text{mod } 17)\\\\2^{81} \equiv 2 \ (\text{mod } 17)\\\\\)

So if we were to divide 2^81 over 17, then we get some quotient and a remainder of 2

Answer:

A

Step-by-step explanation:

A is the asymptotes of the function

Answer:

x = -2.

y = 3.

Step-by-step explanation:

If y = 3x + 9

Substitute this value for y in the first equation.

4x + 5(3x + 9) = 7

4x + 15x + 45 = 7

19x = 7 - 45

19x = -38

x = -38/19

x = -2.

with this value of x, substitute -2 in the second equation

y = 3(-2) + 9

y = -6+9

y = 3.

check if your values are all correct

4(-2) + 5(3) = 7

-8 + 15 = 15 - 8 = 7

Correct!

Answer:

lighter bag weighs 1 \(\frac{83}{100}\)

heavier bag weighs 3 \(\frac{3}{100}\)

Step-by-step explanation:

let x = weight of lighter bag

let x+6/5 = weight of heavier bag

2x + x+6/5 = 6 3/4

3x + 6/5 = 27/4

3x = 27/4 - 6/5

3x = 111/20

x = 111/20 ÷ 3

x = 1 83/100

x+ 6/5 = 3 3/100

Factor of polynomial m are 0,   6n⁴.

What is polynomial in maths?

A polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients, and it only uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of the variables. The polynomial x2 4x + 7 is an illustration of one with a single indeterminate x.

= 30m³n⁴ - 5m⁴

= 5m³(6n⁴ - m )

let 5m³(6n⁴ - m ) = 0

       5m³ = 0

         m = 0

 6n⁴ - m = 0

      m =   6n⁴

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Answer:

Step-by-step explanation:

Option C 1/5 is the correct answer

The input (x) that satisfies the condition of being multiplied by 6 and then Subtracted by 80 to give the same value as the output is 16.

The input as "x." According to the given information, the input (x) is multiplied by 6 and then subtracted by 80, resulting in the output. In mathematical terms, this can be expressed as:

Output = (6 * x) - 80

The problem states that the input and output are the same. Therefore, we can set up the equation:

x = (6 * x) - 80

To solve for x, we'll rearrange the equation and isolate the variable:

x - 6 * x = -80

Combine like terms:

-5 * x = -80

Divide both sides by -5:

x = (-80) / (-5)

Simplifying the division:

x = 16

Hence, the input (x) that satisfies the condition of being multiplied by 6 and then subtracted by 80 to give the same value as the output is 16.

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The 98% confidence interval for the mean of the population is ( 11832.583 , 12371.417) with upper control limit --> 12371.417 and Lower control limit, 11832.583..

A random sample of the monthly incomes from a random sample of 20 workers in a factory.

Sample size, n = 20

Standard deviations, σ = $518

confidence interval, CI = 98%

Here, Population has a normal distribution,

we compute a 98% confidence interval for the mean of the population. let'X' be random variable for monthly incomes of workers in factory.

Formula for confidence interval for the mean is

X-bar ± Zα/2 (σ/√n) --(*)

Now, at 98% confidence interval, α = 0.98

α/2 = 0.49 , using Z-table , Zα/2 is 2.326.

Monthly Income record is

11621 12367 12030 12135 12561 11453 12313 11561 12424 12346 11591 12032 11562 12224 12850 11802 12360 12519 11960 12337

X- bar = sum of all monthly incomes/20

= 12,102

Confidence interval for the mean is 12,102 ± 2.326( 518/√20)

= 12,102 ± 269.417

= ( 11832.583 , 12371.417)

Hence, required confidence interval is ( 11832.583 , 12371.417).

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Answer:The reciprocal of 2/3 is 3/2. The product of 2/3 and its reciprocal 3/2 is 1.

Step-by-step explanation:

simplification of expression will be g - 2

Our expression is  g - 16/4 + 2

16/4 = 4

so we c will write it as

g - 4 + 2

which can be further simplified to

g - 2

Therefore, our simplified expression comes out to be g - 2.

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Answer:

11 dimes 20 nickels

Step-by-step explanation:

Only combo that makes $2.10

-y⁴ + 4y

hope it helps...!!!