Roberto paid $35.75 for dinner at a restaurant, plus an additional $7.15 tip. What percent of the bill did he pay as a tip? Round to the nearest percent, if necessary.

The factorization of the given expression \(\rm x^2+10x+21\) is (x+3)(x+7) the option first is correct.

It is given that the expression \(\rm x^2+10x+21\)

It is required to find which expression is the factorization of the given expression, the options are:

a) (x + 3)(x + 7)

b) (x + 4)(x + 6)

c) (x + 6)(x + 15)

d) (x + 7)(x + 14)

Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.

We have an expression:

\(\rm x^2+10x+21\)

\(\rm x^2+7x+3x+21\)  

Breaking 10x into 7x and 3x because the multiplication of 7x and 3x is \(\rm 21x^2\) and the addition is 10x.

\(\rm x^2+7x+3x+21\\\\\rm x(x+7)+3(x+7)\\\\\rm (x+7)(x+3)\)or

\(\rm (x+3)(x+7)\)

Thus, the factorization of the given expression \(\rm x^2+10x+21\) is (x+3)(x+7) the option first is correct.

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According to the question  the marine science class after attempting each day for the first 5 days the probability of the event occurring is 0.3 or 30%.

To calculate the probability of an event, we need the total number of favorable outcomes and the total number of possible outcomes. Let's assume we have 10 possible outcomes and 3 favorable outcomes.

In this case, the probability (P) of the event occurring is calculated as:

P = favorable outcomes / total outcomes

Substituting the values:

P = 3 / 10

P = 0.3 or 30%

So, the probability of the event occurring is 0.3 or 30%.

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Based on the amount of Nacho cheese corn chips and the calories per gram, the calories per party bag is 1,094.6 calories

First, convert ounces to grams:

= 1 ounce is 28.3495 grams

Party bag in grams:

= 15 x 28.3495

= 425.243 grams

The amount of calories is:

= 425.243 x 28.6% x 9

= 1,094.6 calories

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Answer:

10 hours

Step-by-step explanation:

Given that time taken to clean the garden by Abe and Bianca together = 6 hours.

So, in 1 hour both can clean 1/6 of the garden.

Let Abe can clean the garden in x hours, as Bianca took 5 hours less than Abe took, time taken by Bianca alone to clean the garden = x-5 hours.

Therefore, in 1 hour Abe can clean 1/x portion of the garden while Bianca can clean 1/(x-5) portion of the garden.

Together, Abe and Biana can clean \frac 1 x + \frac {1}{x-5} portion of garden in 1 hour.

As both can clean 1/6 portion of the garden in 1 hour together, so

\(\frac 1 x + \frac {1}{x-5} = \frac 1 6 \\\\\Rightarrow \frac {2x-5}{x(x-5)}= \frac 1 6 \\\\\Rightarrow x^2 - 5x = 6(2x-5) \\\\\Rightarrow x^2 - 5x = 12x-30 \\\\\Rightarrow x^2 - 17x +30= 0 \\\\\Rightarrow x^2 - 15x-2x +30= 0 \\\\\Rightarrow x(x-15) -2(x +15)= 0 \\\\\Rightarrow (x-2)(x-15)= 0 \\\\\Rightarrow x-2=0 \;or\; x-15=0 \\\\\Rightarrow x = 2 \;or\; x=15.\)

Now, if x=2, then the time taken by Bianca x-5 = 2-5=-3 hours (negative) which is not possible.

For x= 15, time taken by Bianca = x=5=15-5=10 hours.

Hence, the time taken by Bianca alone to clean the garden is 10 hours.

Answer:

Step-by-step explanation:

1. Sherelle's reasons for saying that the 1916 coin is most likely in her bag:

She might argue that she is older than Venita and therefore more likely to have inherited the coin from their grandmother.

She might claim that she has a special connection to their grandmother and was entrusted with the coin as a keepsake.

Sherelle might suggest that she has been collecting coins for a longer time than Venita and is more likely to have come across the 1916 coin in her collection.

Venita's reasons for saying that the 1916 coin is most likely in her bag:

She might argue that she has a strong interest in history and specifically coins, making her more likely to have acquired the 1916 coin through her own efforts.

Venita might claim that she has been studying and researching coins extensively, including the history and value of different years, making her more aware of the significance of the 1916 coin.

She might suggest that she recently found the 1916 coin at a coin shop or auction and specifically placed it in her bag for safekeeping.

Considering the information provided, it is difficult to determine with certainty whose bag is more likely to contain the 1916 coin. Both Sherelle and Venita present valid arguments based on their personal circumstances and interests. Without additional information, it is impossible to make an accurate judgment. It would be helpful to investigate further or ask their grandmother directly to determine the true location of the 1916 coin.

2. To find the five-number summary and construct the box-and-whisker plots for each data set, we need to arrange the numbers in ascending order.

Sherelle's data set: 26, 39, 56, 58, 60, 62, 65, 66, 66, 68, 71, 72, 72, 73, 74, 75, 81, 83, 84, 85

Venita's data set: 44, 45, 51, 51, 53, 53, 55, 57, 58, 62, 65, 66, 69, 69, 70, 73, 75, 77, 78, 79

Now we can find the five-number summary for each data set:

Sherelle's data set:

Minimum: 26

First quartile (Q1): 58

Median (Q2): 68

Third quartile (Q3): 75

Maximum: 85

Venita's data set:

Minimum: 44

First quartile (Q1): 53

Median (Q2): 65

Third quartile (Q3): 73

Maximum: 79

Sherelle might give the following reasons for saying that the 1916 coin is most likely in her bag:

Higher frequency of older coins: If Sherelle's bag has a higher proportion of older coins in general, it increases the likelihood of finding a coin from 1916. She could argue that her bag contains more coins from earlier years, making it more probable to have a coin from 1916.

Coin distribution pattern: If Sherelle's bag follows a pattern where the older coins tend to be grouped together, she may believe that the 1916 coin is more likely to be in her bag. She might argue that her bag contains a cluster of coins from the early 1900s, increasing the chance of having the specific 1916 coin.

On the other hand, Venita might give the following reasons for saying that the 1916 coin is most likely in her bag:

Higher randomness in coin selection: If Venita's bag has a more diverse mix of coins from various years, she could argue that the chances of having the 1916 coin are higher. She might claim that her bag includes a wider range of years, making it more likely to contain the specific coin from 1916.

Equal probability: Venita might believe that since the coin is equally likely to be in either bag, the probability is 50/50. She may argue that there is no reason to assume the 1916 coin is more likely to be in Sherelle's bag.

Considering the information provided, it is difficult to determine which bag is more likely to contain the 1916 coin. Without additional information about the distribution or characteristics of the coins in each bag, it would be purely speculative to make a definitive conclusion. Both Sherelle and Venita have their own reasons, but ultimately, it is a matter of chance unless further information is available.

The range of the function f(x) = log5x is (-∞, +∞).The function f(x) = log5x represents the logarithm base 5 of x. To determine the range of this function, we need to consider the possible values that the logarithm can take.

The range of the logarithm function y = log5x consists of all real numbers. The logarithm function is defined for positive real numbers, and as x approaches 0 from the positive side, the logarithm approaches negative infinity. As x increases, the logarithm function approaches positive infinity.

The range of the function is the set of all possible output values. In this case, the range consists of all real numbers that can be obtained by evaluating the logarithm

log5(�)log 5 (x) for �>0 x>0.

Since the base of the logarithm is 5, the function log5x will take on all real values from negative infinity to positive infinity. Therefore, the range of the function f(x) = log5x is (-∞, +∞).

In other words, the function can output any real number, ranging from negative infinity to positive infinity. It does not have any restrictions on the possible values of its output.

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Answer: All real numbers

Step-by-step explanation:

Edge

a) For this study of hypothesis testing, we should use a z-test for a population proportion.

b) The null and alternative hypotheses would be:

H₀ : p = 0.17

H₁ : p ≠ 0.17

c) The test statistic is z = -1.527

d) The p-value = 0.127

e) The p-value is greater than α.

f) Based on this, we should fail to reject the null hypothesis.

g) Thus, the final conclusion is that the data suggest the population proportion is not significantly different from 17% at α = 0.10, so there is statistically insignificant evidence to conclude that the population proportion of millionaires who can wiggle their ears is different from 17%.

a) The problem asks us to determine whether to use a z-test or t-test for a population proportion.

b) H₀: p = 0.17, H₁: p ≠ 0.17. These are the null and alternative hypotheses for the test, where p represents the population proportion of millionaires who can wiggle their ears.

c) We use a z-test for this problem, and the test statistic is z = -0.49.

d) The p-value for the test is 0.625, which is greater than the level of significance α = 0.10.

e) Since the p-value is greater than α, we cannot reject the null hypothesis. The appropriate inequality sign is ">=".

f) Therefore, we should fail to reject the null hypothesis.

g) The final conclusion is that the data suggest the population proportion is not significantly different from 17% at α = 0.10, so there is statistically insignificant evidence to conclude that the population proportion of millionaires who can wiggle their ears is different from 17%.

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The question is -

Only about 17% of all people can wiggle their ears. Is this percent different for millionaires? Of the 391 millionaires surveyed, 78 could wiggle their ears. What can be concluded at the α = 0.10 level of significance?

a) (Fill in the blank with either z-test or t-test.) For this study, we should use a __________ for a population proportion.

b) (Fill in the blanks.) The null and alternative hypotheses would be (use p to denote the population proportion):

H₀ : _____ _____ _____ (Please enter a decimal for the 3rd blank.)

H₁ : _____ _____ _____ (Please enter a decimal for the 3rd blank.)

c) The test statistic is _____ = _____ (Choose between z ot t for the first blank; please show your answer to 3 decimal places for the 2nd blank.)

d) The p-value = _____. (Please show your answer to 3 decimal places.)

e) (Fill in the blank with the appropriate inequality sign.)The p-value is _____ α

f) Based on this, we should __________ the null hypothesis (select an answer from the following list):

g) Thus, the final conclusion is that ...

The data suggest the population proportion is significantly different from 17% at = 0.10, so there is statistically significant evidence to conclude that the population proportion of millionaires who can wiggle their ears is different from 17%.

The data suggest the population proportion is not significantly different from 17% at = 0.10, so there is statistically significant evidence to conclude that the population proportion of millionaires who can wiggle their ears is equal to 17%.

The data suggest the population proportion is not significantly different from 17% at = 0.10, so there is statistically insignificant evidence to conclude that the population proportion of millionaires who can wiggle their ears is different from 17%.

It is possible for a valid argument to have a false conclusion as long as at least one premise is false.

When the premises are genuine, validity guarantees a true conclusion; when the premises are wrong, validity provides no assurance. Even in a legitimate argument, faulty premises might lead to either a true or erroneous conclusion. In many cases, it was chance rather than reasoning that led to the correct conclusion.

Avoid including: Important evidence or analysis that was not provided in the main body for a stronger conclusion paragraph.Generic closing phrases (for example, “In conclusion…”)Weak remarks that undercut your argument (for example, “There are valid points on both sides of this debate.”)

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Answer:

A number that can be made by dividing two integers (an integer is a number with no fractional part). The word comes from "ratio". But π (pi) is not a rational number, it is an "Irrational Number".

Step-by-step explanation:

mark me please

Answer:

Since rational numbers are all numbers that can be written as a fraction, and includes positive numbers, negative numbers and the 0. We can conclude that since -3.4 can be written as a fraction it is a rational number.

On solving the provided question, we can say that  - he need 56  answers he need to get correct if he want a grade of 80 percent on a test with 70 questions

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. It has no measuring systems. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) * 100%.

Assuming that all of the questions are equally weighted, 56 is equal to 80% of 70. (.80)(70)=56

Therefore, 56 out of 70 is the lowest number you may get correct, or 80%.

\(70-56=14\)

So, the maximum number of questions you may omit is 14.

As an alternative, if you desire 80% accuracy, you can have no more than 20% errors.

20% of 70 \(= .20)(70) = 14\)

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Answer:

Step-by-step explanation:

Answer:

n the immediate aftermath of a national election, exit polls offer the best glimpse of what the electorate looked like – who voted for whom and what seemed to drive their choices.

Traditionally, the exit polls have been a collaborative effort of a consortium of major media organizations, involving interviews with a representative sample of thousands of voters as they leave polling places across the nation. In this election, concerns about the pandemic helped drive an unprecedented number of Americans to vote early or by mail. By Nov. 3, more than 100 million Americans had already voted. To account for these voters, this year’s exit polls include data from telephone interviews with a representative sample of people who voted early or by mail. In all, the national exit poll includes interviews with 15,590 voters. It is important to note that these data will be updated, so the numbers below should be considered preliminary, reflecting the exit polls reported as of Nov. 4.

Step-by-step explanation: can you give me brilent

The reflexive closure of a relation on a set is the smallest reflexive relation that contains the original relation. In other words, it is the addition of pairs that ensure every element in the set is related to itself. To form the reflexive closure, we need to add pairs that relate each element in the set to itself.

To form the reflexive closure of relation r on the set {0, 1, 2, 3}, we need to add ordered pairs that ensure every element in the set is related to itself. In other words, we need to add pairs of the form (x, x) for each element x in the set that is not already present in relation r.

In this case, the reflexive closure of relation r would require adding the following ordered pairs: (0, 0), (1, 1), (2, 2), and (3, 3). These pairs ensure that every element in the set {0, 1, 2, 3} is related to itself, making the relation reflexive. These pairs ensure that every element is related to itself, satisfying the reflexivity property.

By adding these additional ordered pairs, we have modified relation r to include reflexivity, as every element now has a direct relation to itself in the set.

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Answer:

What? Retype the question below and ill answer it, but this isnt answerable.

Step-by-step explanation:

What is \redD{\text{A}}Astart color #e84d39, start text, A, end text, end color #e84d39 rounded to the nearest ten? What is \redD{\text{A}}Astart color #e84d39, start text, A, end text, end color #e84d39 rounded to the nearest hundred?

Like what kind of language is this ;--;

Answer:

you are correct'v'

Step-by-step explanation:

in the first column it adds the next odd number, 1, 3, 5,7

and in the 2nd it mutiplies by 2 so it would be faster by a whole lot

Step-by-step explanation:

mark me as the brainliest

Answer: The number of sides of the shape.

The angles between the sides of the shape.

The length of the sides of the shape.

Step-by-step explanation:

To find the eigenvalues of matrix A, we need to solve the equation det(A - λI) = 0, where λ is the eigenvalue and I is the identity matrix.

Given matrix A:

A = |1 0 1|

   |0 1 1|

   |1 1 0|



We subtract λI from A:

A - λI = |1-λ   0    1  |

          |0    1-λ   1  |

          |1    1    -λ |

Taking the determinant of A - λI:

det(A - λI) = (1-λ)[(1-λ)(-λ) - 1] - [(0)(-λ-1) - (1)(1)] + [1 - 0 + (1-λ)(1)]  

           = (1-λ)[-λ^2 + λ - 1] - 1 + [1 - λ + 1 - λ^2]

           = -λ^3 + 2λ^2 - 2λ

To find the eigenvalues, we set the determinant equal to zero:

-λ^3 + 2λ^2 - 2λ = 0

This is a cubic equation, which can be factored or solved using numerical methods to find the eigenvalues.

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The Maclaurin polynomials of orders n=0, 1, 2, 3, and 4 for the function 5/(1+x) are P0(x) = 5, P1(x) = 5 - 5x, P2(x) = 5 - 5x + 5x^2, P3(x) = 5 - 5x + 5x^2 - 5x^3, and P4(x) = 5 - 5x + 5x^2 - 5x^3 + 5x^4, respectively.

The Maclaurin polynomials are a way to approximate a function using a polynomial expansion centered at x = 0. The Maclaurin polynomial of order n for a function f(x) is given by Pn(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3 + ... + (f^n(0)/n!)x^n, where f'(0), f''(0), f'''(0), ..., f^n(0) are the derivatives of f(x) evaluated at x = 0.

In this case, the given function is f(x) = 5/(1+x). To find the Maclaurin polynomials of orders n=0, 1, 2, 3, and 4, we evaluate the function and its derivatives at x = 0 and substitute them into the general formula for the Maclaurin polynomials.

For n=0, P0(x) = 5, as f(0) = 5.

For n=1, P1(x) = 5 - 5x, as f(0) = 5 and f'(0) = -5.

For n=2, P2(x) = 5 - 5x + 5x^2, as f(0) = 5, f'(0) = -5, and f''(0) = 10.

For n=3, P3(x) = 5 - 5x + 5x^2 - 5x^3, as f(0) = 5, f'(0) = -5, f''(0) = 10, and f'''(0) = -30.

For n=4, P4(x) = 5 - 5x + 5x^2 - 5x^3 + 5x^4, as f(0) = 5, f'(0) = -5, f''(0) = 10, f'''(0) = -30, and f^4(0) = 120.

These Maclaurin polynomials provide polynomial approximations of the given function 5/(1+x) for different orders. The higher the order (n), the more terms are included in the polynomial expansion, resulting in a more accurate approximation of the original function around x = 0.

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43³/₄% can be expressed as a decimal to give 43.75%, which can be pronounced as forty-three point seventy-five percent.

A decimal value is a number that contains a whole and a fractional part.

Mathematically, decimal values are expressed using the decimal sign (.).

43³/₄%, which is a fractional value that can be changed into a decimal value thus:

= 43% + ³/₄%

= 43% + 0.75%

= 43.75%

Thus, 43³/₄%, which is forty-three-three-fourth percent, can be expressed as a decimal to give 43.75%.

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The solution to the equation is t = log(146)/8, and the approximate value of t is 0.270.

To solve the equation 0.5 *\(10^{8t}\) = 73 for t, we can first simplify the left side of the equation by dividing both sides by 0.5 * 10^8:

\(10^{8t}\) = 146

Next, we can take the logarithm of both sides of the equation using base 10:

\(log(10^{8t}) = log(146)\)

Using the property of logarithms that says \(log(a^{b} ) = b*log(a)\), we can simplify the left side of the equation:

8t * log(10) = log(146)

Since log(10) = 1, we can further simplify the equation:

8t = log(146)

Finally, we can solve for t by dividing both sides by 8:

t = log(146)/8

t = 2.164/8

The approximate the value of t as:

t ≈ 0.27054410

Therefore, the solution to the equation is t = log(146)/8, and the approximate value of t is 0.270.

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Answer:

4

Step-by-step explanation:

Answer:

\(x\leq 6\)

Step-by-step explanation:

The line given passes through two points. These are (-6,0) and (0,-8).

Remember that two lines are perpendicular if the product of their slopes is -1. So, the first thing we're going to do is to find the slope of the line given.

The slope between two points (x1,y1) and (x2,y2) can be found using the formula:

If we replace our values:

To find other perpendicular line to this one, we have to find a number which multiplication with -4/3 is -1.

This number is clearly 3/4. Because

Therefore, the slope of the perpendicular line must be 3/4, and the original slope is -4/3.

If we graph this:

The Standard Form of the polynomial function 3x^2 4x + 7x^3 + 1 is 7x^3 +3^2 +4x + 1

The meaning of the Standard Form of polynomial function can be explained as when the terms are in this equation or functions are be written in descending order of exponents.

This is usually done starting from the from left to right, we were given the function as :3x^2 +4x + 7x^3 + 1  , then let us arrange it as:

7x^3 +3^2 +4x + 1

Therefore, the Standard Form of polynomial function is 7x^3 +3^2 +4x + 1 .

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There is a 25% chance that a flight between New York City and Chicago will take between 97 and 98 minutes.

Since the time to fly between New York City and Chicago is uniformly distributed between 96 and 100 minutes, the probability of a flight being between any two times is proportional to the length of the time interval between those two times.

To find the probability that a flight is between 97 and 98 minutes, we need to calculate the length of the time interval between those two times, which is 1 minute.

Then, we divide the length of the interval by the length of the entire time range (100-96 = 4 minutes) to obtain the probability of a flight being between 97 and 98 minutes: Probability = 1 minute / 4 minutes = 0.25 or 25%.

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Answer:

Step-by-step explanation:

To find the area of the circle use the formula pi r^2, r is the radius, so half the diamiter. D/2 = 20.

Now we use pi r^2 = pi * 400

So answer is A.

Answer:

Option A 400x m²

Step-by-step explanation:

We know that the diameter of a circle is double of the radius.

So the radius will be 40/2 m = 20 m i.e half of the diameter.

According to the question let the pi be x.

Area of a circle

πr²

= x×20m×20m

= 400x m²

Hence option A is correct.

Answer:

∠ C ≈ 73.7°

Step-by-step explanation:

using the sine ratio in the right triangle

sin C = \(\frac{opposite}{hypotenuse}\) = \(\frac{AT}{CT}\) = \(\frac{48}{50}\) , then

∠ C = \(sin^{-1}\) ( \(\frac{48}{50}\) ) ≈ 73.7° ( to the nearest tenth )

Answer:

A. 30 minutes

Step-by-step explanation:

30 minutes - strength training

90 minutes - treadmill

The new image would be smaller in sample size than the original image.

For example, if the scale factor is 0.5, the new image will be half the size of the original image. To determine the exact size of the new image, the scale factor is multiplied with the width and height of the original image. For example, if the original image is 200 x 100 pixels, and the scale factor is 0.5, the new image will be

(200 x 0.5) = 100 x (100 x 0.5)

= 50 pixels.

The same concept applies when the scale factor is a decimal. For example, if the scale factor is 0.75, the new image will be three-quarters the size of the original image. In this case, the new image would be

(200 x 0.75) = 150 x (100 x 0.75)

= 75 pixels.

In summary, when the scale factor is less than 1, the new image will always be smaller than the original image, depending on the scale factor. The exact size of the new image can be determined by multiplying the width and height of the original image with the scale factor.

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