While cooking a stew, Michelle used

6

12

of a shaker of salt and

1

12

of a shaker of pepper. How much more salt did Michelle use?

The probability of finding a sample mean (Y¯) of 1.5 ounces or more when the liquor tax has no impact on consumption (µ = 0). To determine this probability, we would use the Central Limit Theorem and the z-score formula.

Since the population mean (µ) is 0, we'll need to know the population standard deviation (σ) and the sample size (n) to proceed. Without these values, it's impossible to provide an exact probability. However, I can explain the general process.

First, you would calculate the standard error (SE) using the formula SE = σ / √n. Next, you would find the z-score, which is the difference between the sample mean (Y¯) and the population mean (µ) divided by the standard error: z = (Y¯ - µ) / SE.

Once you have the z-score, you can look it up in a standard normal distribution table or use a calculator to find the probability associated with it. In this case, you're looking for the probability of finding a sample mean of 1.5 ounces or more, which corresponds to the area to the right of the z-score in the distribution.

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The mean will be the middle number or 12.1.

According to our question-

The median is the middle number  in the data set when the data set is written from least to greatest.

least to greatest 4.8, 6.9, 12.1, 14.8, 16.2

Hence, The mean will be the middle number or 12.1.

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Answer:

V = 396 cubic inches

Step-by-step explanation:

width = w; length = l; height = h; volume = V; area of smallest face = a

base units are inches

w = 2 + l

h = l - 5

Height is smallest and length is second smallest (h = l -, l = l, w = l +), so a is for h and l.

a = h × l = (l - 5) × l

36 = l^2 - 5l ==> l^2 - 5l - 36 = 0

Factor ==> (l - 9) × (l + 4) = 0

l = 9 and l = -4

Since length cannot be negative, 9 is the only Real answer.

l = 9

h = l - 5 = 9 - 5 = 4

w = 2 + l = 2 + 9 = 11

Volume of rectangular prism/box is length times width times height.

V = l × w × h = 9 × 11 × 4 = 396

The volume of the box with the given dimensions is;

Volume = 396 in³

Let us denote the properties of the box as follows;

Length of box = l

Width of box = w

Height of box = h

Area of the smallest face of box = a  

We are told that the width is 2 inches more than the length. Thus;

w = 2 + l

We are told that the height is 5 inches less than its length. Thus;

h = l - 5

Since length is smaller than width but bigger than height, the height and length are the 2 smallest faces

Thus,

a = h × l

plugging in the relevant values gives;

a = (l - 5) × l

a = l² - 5l

We are told that the area of the two smallest faces is 36 in². Thus;

l² - 5l = 36

l² - 5l - 36 = 0

Using online quadratic equation solver, we have; l = 9 inches

Plugging in 9 for h in; h = l - 5  

h = 9 - 5

h = 4

Also, plugging in 9 for l into; w = 2 + l, we have;

w = 2 + 9

w = 11

Volume of box is given by;

Volume = length × width × height

Volume = 9 × 11 × 4

Volume = 396 in³

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The total cost is the sum of the pizza and the tip. The value of the tip is 15% of the cost of the pizza. Percentage is expressed in terms of 100. The value would be

15/100 * 39 = 5.85

The total cost would be

39 + 5.85 = 44.85

Rounding to the nearest cent, it becomes $44.90

Answer:

44.90 gotta round the the nearest cent

If \(h^{-1}(x)\) is the inverse of \(h(x)\), then

\(h\left(h^{-1}(x)\right) = x\)

Given that \(h(x)=-(x-2)^2+7\), we have

\(h\left(h^{-1}(x)\right) = -\left(h^{-1}(x)-2\right)^2 + 7 = x\)

Solve for the inverse :

\(-\left(h^{-1}(x)-2\right)^2 + 7 = x \\\\ -\left(h^{-1}(x)-2\right)^2 = x-7 \\\\ \left(h^{-1}(x)-2\right)^2 = 7-x \\\\ \sqrt{\left(h^{-1}(x)-2\right)^2} = \sqrt{7-x} \\\\ \left|h^{-1}(x)-2\right| = \sqrt{7-x}\)

At this point, we have two possible solutions:

• If \(h^{-1}(x)\ge2\), then \(\left|h^{-1}(x)-2\right| = h^{-1}(x)-2\). Continuing with the equation, we have

\(h^{-1}(x) - 2 = \sqrt{7-x} \\\\ h^{-1}(x) = 2 + \sqrt{7-x}\)

• Otherwise, if \(h^{-1}(x)<2\), then \(\left|h^{-1}(x)-2\right|=-\left(h^{-1}(x)\right)=2-h^{-1}(x)\), in which case

\(2-h^{-1}(x) = \sqrt{7-x} \\\\ h^{-1}(x) = 2 - \sqrt{7-x}\)

Both solutions are simultaneously incompatible. For instance, when x = 0 we have \(h^{-1}(0)=2+\sqrt7\) using the first solution, and \(h^{-1}(0)=2-\sqrt7\) using the second one. Choosing one over the other depends on how you restrict the domain.

(A) If we want to stick with the first solution, we would required that x ≥ 2. In other words, we would have \(h(x)\) defined only when x ≥ 2; then \(h\left(h^{-1}(x)\right)\) is defined only when \(h^{-1}(x)\ge2\), so that ...

(B) ... the inverse is

\(\boxed{h^{-1}(x)=2+\sqrt{7-x}}\)

(C) The domain of the inverse is the same as the range of the original function, and vice versa.

• Domain: we have for all x that

\(-(x-2)^2 \le 0\)

so

\(-(x-2)^2 + 7 \le 7\)

which means the range of \(h(x)\), and hence the domain of \(y=h^{-1}(x)\), is

\(\left\{y \mid y \le 7\}\)

• Range: we get this immediately from the domain restriction we chose earlier,

\(\left\{x \mid x \ge 2\}\)

See the attached plot - \(h(x)\) is shown as a dashed orange curve; \(h(x)\) with the restricted domain is shown in blue; the inverse \(h^{-1}(x)\) corresponding to the restricted \(h(x)\) is shown in green; the other inverse is shown with a dashed red curve. You can see a geometrical properties of inverses: if you mirror the blue curve along the dotted line (y = x), you would get the green curve.

The solution for l4  is  mathematically given as

L_{4}=0.5431

\(&\text { Given } f(x)=a \cos ^{2}(x) \quad\left[\frac{\pi}{8}, \frac{\pi}{2}\right] \text { \& } n=4\\\\&\Delta a=\frac{b-a}{n}=\frac{\pi / 2-\pi / 8}{9}=\frac{3 \pi}{32}\\\\&x_{0}=\pi / 8, x_{1}=\frac{\pi}{8}+\frac{3 \pi}{32}=\frac{7 \pi}{32}\\\\&x_{2}=\frac{5 \pi}{16}, \quad x_{3}=\frac{13 \pi}{32}, x_{4}=\pi / 2\\\\&f\left(x_{0}\right)=f(1 / 8)=0.8535\\\)

\(&f\left(x_{1}\right)=f\left(\frac{7 \pi}{32}\right)=0.5975\\\\\&f\left(x_{2}\right)=f\left(\frac{5 \pi}{16}\right)=0.3086\\\\\&f\left(a_{3}\right)=f\left(\frac{13 \pi}{32}\right)=0.0842\\\\\&L_{4}=\sum_{k_{0}^{=0}}^{3} f\left(x_{k}\right) \Delta x\\\\&=\Delta \\\\x\left[f\left(x_{0}\right)+f\left(x_{1}\right)+f\left(x_{2}\right)+f\left(x_{3}\right)\right]\\\\\&=\frac{3 \pi}{32}[0.8535+0.5975+0.3056+0.0842]\\\\&L_{4}=0.5431\)

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CQ

The complete Question is attached below

Explanation cannot be summarized in one row as it requires multiple factors and considerations to determine the asymptotes of different functions.

In order to find the horizontal and vertical asymptotes of a function, we need to analyze its behavior as x approaches infinity or negative infinity.

In the given question, we are provided with multiple functions (a) to (h) and asked to find their asymptotes, if any exist.

To find the horizontal asymptote, we look at the highest degree term in the numerator and denominator.

If the degrees are equal, the horizontal asymptote is the ratio of their coefficients.

If the degree of the numerator is greater, there is no horizontal asymptote.

For vertical asymptotes, we examine the values of x that make the denominator zero.

These values represent vertical lines that the graph approaches but never crosses.

By analyzing the given functions based on these criteria, we can determine whether they have horizontal or vertical asymptotes, if any.

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The business has a savings account that earns initially invested approximately $3,455 in 1991.( C: $3,455).

The business initially invested in 1991, we need to use the given information and the formula provided.

The formula F = P(1 + R)²T is used to determine the final amount in the savings account.

Given information:

The business had $4,000 in the account at the end of 1996.

The annual interest rate is 3%.

The time in years is (1996 - 1991) = 5 years.

To solve for the initial investment amount (P):

F = P(1 + R)²T

$4,000 = P(1 + 0.03)²5

Now for P:

$4,000 = P(1.03)²5

Dividing both sides of the equation by (1.03)²5:

P = $4,000 / (1.03)²5

Calculating the value:

P ≈ $3,455.47

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Answer:

18

Step-by-step explanation:

18 because -3×(-2)=6

6×3=18

The pairs of days and heights that could also be included in the table is given as follows:

The slope-intercept linear function that defines the plant's height after x days is given as follows:

y = mx + b.

The coefficients of the function are given as follows:

Then, considering the table given at the end of the answer, the equation that gives the height after x days is of:

y = 2x + 10.

The possible pairs are given at the beginning of the answer, for example, on day 9, the expected height is of:

y = 2(9) + 10 = 28 in.

The table is given by the image shown at the end of the answer.

The problem is incomplete, hence the pairs were calculated considering the table at the end of the answer. For a different table, you should follow the same procedure, identifying the equation and then testing the pairs.

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The length of side LJ is 12.41.

Since triangle XYZ is similar to triangle JKL, we know that the corresponding sides are proportional. This means that the ratio of the lengths of the sides in triangle XYZ to the corresponding sides in triangle JKL is constant. We can use this fact to solve for the length of side LJ.

Let k be the constant of proportionality. Then we have:

XY / JK = YZ / KL = ZX / LJ = k

Substituting the given values, we have:

8.7 / 13.05 = 7.8 / KL = 8.2 / LJ

Solving for KL and LJ, we get:

KL = (7.8 x 13.05) / 8.7 = 11.70

LJ = (8.2 x 13.05) / 7.8 = 12.41

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Answer:

220 yards

Step-by-step explanation:

15*1760 = 26,400

26,400/120 = 220

Answer:

after simplifying, we get,

23/6

Step-by-step explanation:

(2/3+5/2-7/3)+(3/2+7/3-5/6)

We simplify,

\((2/3+5/2-7/3)+(3/2+7/3-5/6)\\(2/3-7/3+5/2)+(3/2+7/3-5/6)\\(5/2-5/3)+(9/6+14/6-5/6)\\(15/6-10/6)+((9+14-5)/6)\\(15-10)/6+(23-5)/6\\5/6+18/6\\(5+18)/6\\23/6\)

If you have 367 people there are at least 2 that were born on the same day of the year.There must be at least 2 that were born on the same day of the year.

To prove by contradiction that if you have 367 people, there are at least 2 that were born on the same day of the year, follow these steps:

1. Assume the opposite of what we want to prove, i.e., all 367 people were born on different days of the year.

2. We know that there are only 365 possible days in a year (ignoring leap years). So, if 367 people were all born on different days, that would mean there are at least 367 unique days in a year.

3. This assumption contradicts the fact that there are only 365 days in a year, which is a contradiction.

4. Since we've reached a contradiction, our original assumption must be incorrect.

Thus, if you have 367 people, there must be at least 2 that were born on the same day of the year.

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The opposite of the assumption (i.e., what you want to prove) must be true.

Assume that there are 367 people and none of them were born on the same day of the year.

There are 365 days in a year, so if no two people were born on the same day, then the first person could have been born on any day, the second person could have been born on any of the remaining 364 days, the third person could have been born on any of the remaining 363 days, and so on.

Therefore, the number of possible ways for 367 people to be born on different days of the year is: 365 x 364 x 363 x ... x 2 x 1 / (367 x 366 / 2)

Simplifying this expression gives: 365 x 364 x 363 x ... x 2 x 1 / 183,055

This is a very large number, approximately equal to 2.8 x 10^782.

However, this is greater than the total number of people who have ever lived on Earth, which is estimated to be around 108 billion.

Therefore, it is impossible for 367 people to be born on different days of the year, and our initial assumption must be false.

Thus, we can conclude that if you have 367 people, there are at least 2 that were born on the same day of the year.

Step 1: Assume the opposite of what you want to prove.

Step 2: Use logical reasoning to derive a consequence of the assumption.

Step 3: Show that the consequence is inconsistent with what is known to be true.

Step 4: Conclude that the assumption must be false, and therefore, the opposite of the assumption (i.e., what you want to prove) must be true.

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Answer:

A: 82.5

Step-by-step explanation:

Average score of the 4 regular tests = (78 + 72 + 74 + 88)/4 = 78

We are told;

- the regular tests account for 40% of the final grade.

- final exam counts for 20%

- project counts for 10%

- homework counts for 30%

Thus;

weighted mean grade = (40% × 78) + (20% × 79) + (10% × 88) + (30% × 89) = 82.5

0 represents the surface level of the swimming pool.

The height of the slide in relation to 0 is +10 feet.

Part A: In this situation, 0 represents the surface level of the swimming pool on the number line, acting as a reference point between the depth of the water and the height of the slide.

Part B: The height of the slide in relation to 0 is +10 feet. This means the slide is 10 feet above the surface level of the swimming pool.

Part C: To mark the level of the bottom of the pole on the number line, Kayla should mark it at -3 since the bottom of the pole is at a depth of 3 feet below the surface level of the pool.

This is determined by using the negative value to represent the depth below the surface (0).

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Answer:

x

Step-by-step explanation:

An inverse function does the opposite of the non-inverted function.

For example,

\(\text{if } f(x) = x +3,\text{ then } f^{-1}(x) = x - 3\)

and if we input 3 into the function:

\(f(3) = 3 + 3 = 6\)

but then apply the inverse function to the result:

\(f^{-1}(6) = 6 - 3 = 3\)

we end up with what we started with.

Answer:

Easy there ya go

Step-by-step explanation:

center: -1

radius: 3

equation of the circle: 3 X -1

Answer:

Eric drove 28 7/11 miles with 1 gallon of gas.

Step-by-step explanation:

You just use long division and do 315 divided by 11, and you should get 28R7 so you just turn that R7 into 7/11.

Have a nice rest of your day :)

Answer:

1.3

Step-by-step explanation:

Hope this is correct, if not sorry

The value of the derivatives of f df(x, y, z)/dx + df(x, y, z)/dy is 20, when x = 1, y = 1, and z = 1.

To determine df/dt using the chain rule, we need to compute the partial derivatives of f with respect to x, y, and z, as the derivatives of x(t), y(t), and z(t) with respect to t.

We are given that the function as f (x, y, z)= 3x² + xyz + 4y³ z²

To Find df(x, y, z)/dx + df(x, y, z)/dy when x = 1, y = 1, and z = 1.

f (x, y, z)= 3x² + xyz + 4y³ z²

Therefore,

df(x, y, z)/dx = 6x + yz

df(x, y, z)/dy = xz + 12y² z²

Now we have;

df(x, y, z)/dx + df(x, y, z)/dy

6x + yz + xz + 12y² z²

When x = 1, y = 1, and z = 1 then we get;

6 + 1 + 1 + 12

= 20

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Answer:

rational number.......

Answer:

Step-by-step explanation:

It's a terminating decimal fraction.

Answer:

I hope this is helpful (2x-3)(3x+5)

Step-by-step explanation:

(2x-3)(3x+5)

6x2-9x+10x-15

6x2+x-15

Answer:

your answer is 3x+5

Step-by-step explanation:

on edge 2021

The volume of the given solid, with the boundaries, is given as follows:

661.5 cubic units.

The volume of the solid is obtained using a double integral.

The equation for the solid is given as follows:

7x + 9y + z = 63.

z = 63 - 7x - 9y.

The coordinate planes bound the plane, hence:

Hence the double integral that is used to obtain the volume of the solid is given as follows:

\(V = \int_{0}^{9}\int_{0}^{7 - \frac{7x}{9}} 63 - 7x - 9y dydx\)

The inner integral is given as follows:

\(I = \int_{0}^{7 - \frac{7x}{9}} 63 - 7x - 9y dy\)

Which, applying the Fundamental Theorem of Calculus, has the result given as follows:

\(I = -98x + \frac{49x^2}{9} - \frac{(7x + 63)^2}{18} + 441\)

Then the volume of the solid is given by the outer integral as follows:

\(V = \int_{0}^{9} \left(-98x + \frac{49x^2}{9} - \frac{(7x + 63)^2}{18} + 441\right) dx\)

Which has a numeric value of:

661.5 cubic units.

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1. P-adic Numbers:

P-adic numbers are a specialized alternative not commonly used as a continuity strategy in mathematics. They are an extension of the real numbers that provide a different way of measuring and analyzing numbers. P-adic numbers are based on a different concept of distance, known as the p-adic metric. This metric assigns a measure of closeness or distance between numbers based on their divisibility by a prime number, p. P-adic numbers have unique properties and can be useful in number theory, algebraic geometry, and other branches of mathematics. However, they are not typically employed as a continuity strategy in practical applications.

2. Nonstandard Analysis:

Nonstandard analysis is a mathematical framework that provides an alternative approach to calculus and analysis. It introduces new types of numbers called "infinitesimals" and "infinite numbers" that lie between the standard real numbers but are infinitely smaller or larger than any real number. Nonstandard analysis allows for more rigorous treatment of infinitesimal quantities and provides a different perspective on limits, continuity, and differentiation. While nonstandard analysis has theoretical implications and can provide valuable insights in mathematical research, it is not commonly used as a continuity strategy in practical applications where standard analysis and calculus are more prevalent.

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Answer: (x, y) → (x, y - 7)

Step-by-step explanation:

Answer:

14 remainder  2

Step-by-step explanation:

Step 1: Take the first digit of the dividend. ...

Step 2: Then divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and write the difference below.

Step 4: Bring down the next number (if present).

Step 5: Repeat the same process.

Answer:

14.334

Step-by-step explanation:

86/6=14.3333333….

\(\frac{1820728291}{14285714286}\)