find the total cost to the nearest cent, $58 bill; 20% tip​

The given statement "A successful proof can indeed turn a conditional statement into a theorem.'' is true because a successful proof can transform a conditional statement into a theorem by providing a logical and rigorous demonstration of its truth based on the given hypothesis.

In mathematics, a conditional statement is a proposition that asserts a relationship between two or more mathematical objects or concepts. It consists of a hypothesis and a conclusion.

A conditional statement is typically expressed in the form "If A, then B," where A represents the hypothesis and B represents the conclusion.

To establish a conditional statement as a theorem, one needs to provide a valid proof that demonstrates the truth of the statement. A proof is a logical argument that follows a series of logical deductions from axioms, definitions, and previously established theorems.

When a proof is successfully constructed for a conditional statement, it provides rigorous justification for the truth of the conclusion based on the given hypothesis.

By demonstrating the logical validity and coherence of the argument, the proof confirms the truth of the conditional statement and establishes it as a theorem.

The process of proving a conditional statement involves carefully reasoning through logical steps, utilizing mathematical principles and logical inference rules.

It requires precise and accurate reasoning, ensuring that each step in the proof is valid and consistent with the underlying mathematical framework.

Once a conditional statement has been proven, it is elevated to the status of a theorem. Theorems are fundamental results in mathematics that have been rigorously proven and hold true within a given mathematical system.

They serve as building blocks for further mathematical investigations and form the foundation of mathematical knowledge.

In summary, a successful proof can transform a conditional statement into a theorem by providing a logical and rigorous demonstration of its truth based on the given hypothesis.

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Answer:

shorter leg = 6 cm

Step-by-step explanation:

let n be the shorter leg then n + 2 is the longer leg.

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

n² + (n + 2)² = 10² , that is

n² + n² + 4n + 4 = 100

2n² + 4n + 4 = 100 ( subtract 100 from both sides )

2n² + 4n - 96 = 0 ( divide through by 2 )

n² + 2n - 48 = 0 ← in standard form

(n + 8)(n - 6) = 0 ← in factored form

equate each factor to zero and solve for n

n + 8 = 0 ⇒ n = - 8

n - 6 = 0 ⇒ n = 6

However , n > 0 then n = 6

the shorter leg is 6 cm long

Answer:

5x - 2 = 7

5x = 7 + 2

5x = 9 (divide both sides by 5 to get x)

5x/5 = 9/5

x = 1.8

Step-by-step explanation:

Answer:

The width is 35 cm.

The length is 25 cm.

Step-by-step explanation:

Answer:

-2(4x-5)

Step-by-step explanation:

The cοοrdinates οf the fοurth vertex are (4,-1).

Tο find the fοurth vertex οf the parallelοgram, we need tο use the fact that οppοsite sides οf a parallelοgram are parallel and have the same length. We can use the given three vertices tο determine the vectοr representing οne οf the sides οf the parallelοgram. Then, we can extend that vectοr tο find the fοurth vertex.

Let's take the vectοrs representing twο adjacent sides οf the parallelοgram:

v1 = (-4,1) - (-2,-5) = (-2,6)

v2 = (6,-7) - (-4,1) = (10,-8)

Since οppοsite sides οf a parallelοgram are parallel, v1 and v2 must be parallel. This means that we can find the fοurth vertex by adding v1 tο the third vertex, (6,-7):

v4 = (6,-7) + v1 = (6,-7) + (-2,6) = (4,-1)

Therefοre, the cοοrdinates οf the fοurth vertex are (4,-1).

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Complete question:

Three vertices of a parallelogram are shown in the figure below. Give the coordinates of the fourth vertex.

Answer:

Leslie has 13 quarters and 23 half-dollars.

Step-by-step explanation:

You can write the following equations from the information given and considering that a quarter is $0.25 and half-dollar is $0.50:

x+y=36 (1)

0.25x+0.50y=14.75 (2), where:

x=amount of quarters

y=amount of half-dollars

First, you can isolate x in (1):

x=36-y (3)

Then, you can replace (3) in (2):

0.25(36-y)+0.50y=14.75

9-0.25y+0.50y=14.75

0.25y=5.75

y=5.75/0.25

y=23

Finally, you can replace the value of y in (3) to find the value of x:

x=36-23

x=13

According to this, the answer is that Leslie has 13 quarters and 23 half-dollars.

The coordinate point (x,y) = (3√2,0) represents the square root of 18 on the x-axis

The expression is given as:

x = √18

Express 18 as the product of 9 and 2

x = √9 * 2

Take the square root of 9

x = 3√2

This means that we plot the following coordinate point to represent the square root of 18 on the x-axis

(x,y) = (3√2,0)

See attachment for the plot

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The 2 decimal places for beta, 4 decimal places for firm-specific

variance, and 3 decimal places for covariance.

To calculate the beta of your portfolio, you need to determine the

weighted average beta of the individual assets in your portfolio.

The beta of a security measures its sensitivity to changes in the market.

By multiplying the weight of each asset by its beta and summing these

values, you can calculate the portfolio beta.

The formula for portfolio beta is:

Portfolio Beta = (Weight of Asset A * Beta of Asset A) + (Weight of Asset B

* Beta of Asset B) + ...

To calculate the firm-specific variance of your portfolio, you need to

subtract the market variance from the portfolio variance.

Firm-specific variance represents the risk that is specific to the individual

assets in your portfolio.

The formula for firm-specific variance is:

Firm-specific variance = Portfolio variance - Market variance

Lastly, to calculate the covariance between the portfolio and the market

index, you need to multiply the weight of each asset by its beta and sum

these products.

The formula for covariance is:

Covariance = (Weight of Asset A * Beta of Asset A) + (Weight of Asset B *

Beta of Asset B) + ...

Remember to not round your intermediate calculations, but round your

final answers to 2 decimal places for beta, 4 decimal places for firm

specific variance, and 3 decimal places for covariance.

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The inequality that models the scenario is the first one:

$24 + $2*n ≤ $37

Solving that we conclude that Eli can buy at most 6 notebooks.

We know that Eli wants to buy a calculator that costs $24 and some notebooks, such that each notebook costs $2.

Then If Eli buys the calculator and n notebooks the total cost will be:

$24 + $2*n

We know that Eli has a total of $37 to spend, so that is the maximum amount he can spend. Thus, we can write the inequality:

$24 + $2*n ≤ $37

So the correct option is the first one.

Now also let's solve the inequality for n.

$24 + $2*n ≤ $37

$2*n  ≤ $37 - $24

$2*n ≤ $13.

n ≤ $13/$2

n ≤ 6.5

So Eli can buy at most 6 notebooks.

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Answer:

1. The formula for the area of a circle is given by A = πr^2, where r is the radius of the circle. To find the area of the 12" pizza, we first need to find the radius:

r = 12 / 2 = 6 inches

The area of the pizza is then:

A = πr^2 = π * 6^2 = 36π square inches

2. To find the radius of a pizza that is 25% larger, we can first find the amount by which the radius will increase:

increase = 6 * 0.25 = 1.5 inches

The new radius will then be:

new_r = 6 + 1.5 = 7.5 inches.

Step-by-step explanation:

Answer:

113.1, 8

The equation to find the area of a circle is:

Now we can input 12 into the equation:

To find the radius of a pizza that is %25 larger, we can use this equation:

Well, that's a good question! If we were to multiply by 0.25, the radius would get smaller, instead of bigger. We add the 1.0 because we have to add the original radius, not just the added length.

Fitting the radius into the equation:

Therefore, the area of the pizza is 113.1, and the radius of a pizza that is %25 larger is 8.

The range of x are;

1. x < -30

2. x > 8

3. x > 15

4. x < -2

A relationship between two expressions or values that are not equal to each other is called 'inequality.

1. -130 > 50x +20

-130-20> 50x

-150 > 50x

-150/50 > x

-30 > x

x < -30

2. -8(x-3) < -40

-8x +24< -40

collect like terms

-8x < -64

x > -64/-8

x > 8

3. 2x - 22 > 8

collect like terms

2x > 30

divide both sides by 2

x > 30/2

x > 15

4. -35 < -5(x+9)

-35 < -5x -45

collect like terms

10 < -5x

-2 > x

x < -2

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The raid caused a significant impact on the organization, as it ranked 14th in a job satisfaction survey conducted by an external entity.

Stark Industries, a renowned company, recently experienced a raid. The raid caused a significant impact on the organization, as it ranked 14th in a job satisfaction survey conducted by an external entity.

The raid likely led to a decrease in employee morale, affecting their overall satisfaction within the company. Such incidents can create an atmosphere of insecurity and anxiety, making employees feel uncertain about their workplace environment and job stability.

The decrease in job satisfaction might be attributed to concerns regarding safety, trust, and the company's ability to provide a secure and fulfilling work experience.

It is crucial for Stark Industries to address the aftermath of the raid promptly, ensuring transparency, supporting affected employees, and taking necessary steps to restore confidence and enhance job satisfaction within the organization.

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Answer:

672 had dark hair, 592 had blond hair, and 48 had red hair

Step-by-step explanation:

To solve this problem, we need to first find the total number of people for each hair color based on the given ratio.

Let's start by finding the common factor that we can use to scale the ratio up to the total number of people, which is 1,312:

42 + 37 + 3 = 82

We can then divide 1,312 by 82 to get the scaling factor:

1,312 ÷ 82 = 16

This means that for every 16 people, there are 42 with dark hair, 37 with blond hair, and 3 with red hair.

To find the actual number of people with each hair color in the town meeting, we can multiply the scaling factor by the number of people for each hair color in the ratio:

Dark-haired people: 42 × 16 = 672

Blond-haired people: 37 × 16 = 592

Red-haired people: 3 × 16 = 48

Therefore, there are 672 people with dark hair, 592 people with blond hair, and 48 people with red hair at the town meeting.

The 80% confidence interval estimate for the average browsing time is approximately 12.648572 minutes to 14.548572 minutes.

To construct an 80% confidence interval estimate of the average browsing time for the population of crownfashion.com visitors this week, we can use the following formula:

Confidence Interval = \(\bar{X}\) ± Z \(\times\)  (σ/√n)

Where:

\(\bar{X}\) is the sample mean (average browsing time) = 13.6 minutes,

Z is the Z-score corresponding to the desired confidence level (80% confidence level corresponds to a Z-score of 1.28),

σ is the population standard deviation = 5.2 minutes,

n is the sample size = 49.

Plugging in these values, we can calculate the confidence interval as follows:

Confidence Interval = 13.6 ± 1.28 \(\times\) (5.2/√49)

Simplifying the expression:

Confidence Interval = 13.6 ± 1.28 \(\times\) (5.2/7)

Confidence Interval = 13.6 ± 1.28 \(\times\) 0.742857

Confidence Interval = 13.6 ± 0.951428

The lower bound of the confidence interval is 13.6 - 0.951428 = 12.648572, and the upper bound is 13.6 + 0.951428 = 14.548572.

Therefore, the 80% confidence interval estimate for the average browsing time is approximately 12.648572 minutes to 14.548572 minutes.

The margin of error indicated by the interval is half of the width of the confidence interval, which is (14.548572 - 12.648572) / 2 = 0.95 minutes.

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The approximate volume of the sphere is 6.01 ft³.

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

Where r is the radius of the sphere and π is the mathematical constant pi (approximately equal to 3.14).

Given that the surface area of the sphere is 16 square feet.

First, we determine the radius r:

Surface area = 4πr²

Hence

16 = 4πr²

Dividing both sides by 4π, we get:

r² = 16/4πr

r = √( 16/4πr )

r = 1.128 ft

Plugging in the value of r that we just found, we get:

Volume =  (4/3)πr³

Volume =  (4/3) × 3.14 × (1.128 ft)³

Volume =  6.01 ft³

Therefore, teh volume is 6.01 ft³.

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Answer:

11

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

4+11+ (-4)

The cubic inches in a cubic meter is 61,023.7 cubic inches as 1 cubic meter is 1000000 cubic centimeters and 1 cubic centimeter is  0.0610237 cubic inches

To find the number of cubic inches in a cubic meter using the concept of measurements, we need to use the conversion factors as follows:

1 inch = 2.54 cm1

meter = 100 cm

We need to convert the meter to centimeters, so we multiply the meter value by 100. Then we cube the result to obtain the cubic meter value in cubic centimeters. Finally, we convert cubic centimeters to cubic inches by dividing the value by 16.387

Here's the complete solution:

1 meter = 100 cm

1 meter³ = (100 cm)³

1 meter³ = (100)³ cm³

1 meter³ = 1,000,000 cm³

1 cm³ = 0.0610237 in³

Therefore, 1 meter³ = 1,000,000 cm³

1 m³ = 1,000,000 cm³ x (0.0610237 in³ / cm³)

1 m³ = 61,023.7 in³

Answer: 61,023.7 cubic inches are in a cubic meter.

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The measure of an angle if the measures of its two adjacent supplementary angles at up to 100 is 130.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

Given,

The measures of its two adjacent supplementary angles at up to 100.

We are aware of:

x + y = 180°

x + z = 180°

y + z = 100°

Combining the first two equations:

2x + y + z + 360° For the product of y + Z, substitute 100°.

Since 2x + 100° = 360°, both sides must be reduced by 100°.

Divide both sides by 2 to get 2x = 260°.

x = 130° .

The measure of an angle if the measures of its two adjacent supplementary angles at up to 100 is 130.

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Answer:

Triangle ABC ~ DAC

Step-by-step explanation:

If you would like a full explanation let me know and I'll try my best.  

ABC ~ DAC

Step-by-step explanation:

yw

A sample size of 76 would be required to estimate the population mean with a margin of error of 4 and a 98% level of confidence.

To determine the sample size required to estimate the population mean with a specific margin of error and level of confidence, we can use the formula:

n = (Z * σ / E)²

where

n = required sample size

Z = Z-score corresponding to the desired level of confidence

σ = standard deviation of the population

E = desired margin of error

here, we have that

the standard deviation (σ) is given as 15,

the margin of error (E) is 4 and

the level of confidence is 98% and For a 98% confidence level, the Z-score is approximately 2.33.

Plugging the values into the formula:

n = (2.33 * 15 / 4)²

n = (8.7375)²

n ≈ 76.34

n = 76

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Step-by-step explanation:

sqrt(50) = sqrt(25×2) = 5×sqrt(2)

Answer:

(-1, -6),  (7, 0) , and  (11, 3)

Step-by-step explanation:

3x - 4y = 21        Solve the equation for y

3x - 21 = 4y      

(3x - 21)/4 =  y  

Now use the ordered pair and find the true ordered pair

  (-1, -6)     [ (3)(-1) - 21]/ 4 ;    (-3 -21)/4 ;  (-24)/4 = -6     True

   (7, 0)     [(3)(7) -21]/4 ; (21 - 21)/4;  0/4 = 0     True

   (11, 3)    [(3)(11) - 21]/4;  (33 - 21)/4; 12/4 = 3    True

    (-3 ,3)   [(3)(-3) - 21]/4  (-9 -21)/4 ; -30/4  = -7.5   No

Step-by-step explanation:

5x+4<16

or,5x<16-4

or,5x<12

or,x<12÷5

or,x<12/5

or,x<2.4

:.x<2.4

Answer:

hope it helps.

Using the doubling time and exponential growth formulae, the population of annual plants will be 4,000 after 42 years, assuming a constant rate of increase and an initial population size of 500.

To answer your question, we will use the doubling time formula and exponential growth formula. Given that the doubling time of a population of annual plants is 14 years, the initial size is 500, and we want to know the population size after 42 years, we can follow these steps:

1. Determine the number of doubling times within 42 years: Since the doubling time is 14 years, we can calculate the number of doubling times by dividing the total time (42 years) by the doubling time (14 years):
  Number of doubling times = 42 / 14 = 3

2. Calculate the growth factor using the doubling time: In exponential growth, the population size increases by a growth factor. Since the population doubles in 14 years, the growth factor (g) is 2 (doubled).

3. Apply the exponential growth formula: The formula for exponential growth is P(t) = P0 * g^t, where P(t) is the population size at time t, P0 is the initial population size, g is the growth factor, and t is the number of doubling times.

4. Plug in the given values and solve for P(t): We know the initial population size (P0) is 500, the growth factor (g) is 2, and the number of doubling times (t) is 3. So the formula becomes:
  P(t) = 500 * 2^3

5. Calculate the population size after 42 years: P(t) = 500 * 8 = 4000

In conclusion, using the doubling time and exponential growth formulae, the population of annual plants will be 4,000 after 42 years, assuming a constant rate of increase and an initial population size of 500.

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The best measure of center for the data is Option D: The median, and it equals 8.

What is median?

In mathematics, the middle number in a sorted list of numbers is referred to as the median. By arranging the numbers, the middle number can be discovered. Ascending order is used to arrange the numbers. The middle number in the ordered set of numbers is referred to as the data set's median.

The best measure of center for this data is the median because the data is skewed and has outliers.

The median is the middle value when the data is arranged in order, which is less sensitive to outliers than the mean.

To find the median, we need to count the number of data points and find the middle value -

1, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9

We have 11 data points, so the median is the 6th value -

Median = 8

Therefore, the best measure of center for the data is the median, and its value is 8.

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Answer:

A. 150

Step-by-step explanation:

Calculate the probability of landing on an odd number: 1/2.

Multiply the probability by the number of trials: (1/2) * 300.

Simplify the expression: 150.

Therefore, a reasonable prediction is that the event of landing on an odd number will occur 150 times out of the 300 rolls of the fair 6-sided die.

A permutation is an arrangement of outcomes in which the order does matter.

A combination is an arrangement of outcomes in which the order does not matter.

In this case, for example, the password HI is different from the password IH. In both cases, the outcomes (letters H and I) are the same, but the order of them changes the arrangement (the password). Therefore, the problem involves a permutation because the order of letters selected does matter

Three pairs of negative x- and y-coordinates that lie on the line y = 3x + 4:

1. x = -2, y = -2

2. x = -3, y = --5

3. x = -5, y = -11

Here are three pairs of negative x- and y-coordinates that lie on the line y = 3x + 4:

1. x = -2, y = -2:

When x is -2, y = 3(-2) + 4 = -6 + 4 = -2. So the point (-2, -2) lies on the line y = 3x + 4.

2. x = -3, y = -5:

When x is -3, y = 3(-3) + 4 = -9 + 4 = -5. So the point (-3, -5) lies on the line y = 3x + 4.

3. x = -5, y = -11:

When x is -5, y = 3(-5) + 4 = -15 + 4 = -11. So the point (-5, -11) lies on the line y = 3x + 4.

In all three pairs of coordinates, the x-coordinate is negative, and the corresponding y-coordinate is also negative, and they all satisfy the equation y = 3x + 4.

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Answer:

n=-3

Step-by-step explanation:

11(n – 1) + 35 = 3n

expand left side

11n-11+35=3n

Add-11 to 35

11n+35-11=3n

11n+24=3n

subtract 24 from both sides

11n+24-24=3n-24

11n=3n-24

subtract3n from both sides

11n-3n=3n-24-3n

8n=-24

divide both sides by 8

8n/8=-24/8

n=-3

Answer:

Step-by-step explanation:

\(11(n -1) + 35 = 3n\\n =? \\11n -11 +35=3n\\Collect-like-terms\\11n-3n=-35+11\\4n =-24\\divide -both-sides-of-the-equation\\n = \frac{-24}{4} \\n = -6\\\\\)