A restaurant bill is $25, and a 20 percent tip should be given to the waiter. Which expression can be used to find the total amount that will be paid?

Answer: x = - 4

Step-by-step explanation:

7-2x=1

PEMDAS

so add 7 to both sides

-2x=8

divide by -2 from both sides

x=-4

Answer:

x = -2

Step-by-step explanation:

Let's find the required value of x,

→ 7 - 2x = 11

→ -2x = 11 - 7

→ -2x = 4

→ x = -4/2

→ [ x = -2 ]

Therefore, the value of x is -2.

Answer:

1) .8³ = .512 = 51.2%

2) .2³ = .008 = .8%

3) 1 - .8³ = 1 - .512 = .488 = 48.8%

4) 1 - .2³ = 1 - .008 = .992 = 99.2%

1) The probability that the player makes a free throw is 80%, or 0.8. Since each free throw is an independent event, the probability of making all three free throws is calculated by multiplying the individual probabilities together: 0.8 * 0.8 * 0.8 = 0.512, or 51.2%.

2) The probability that the player misses a free throw is the complement of making a free throw, which is 1 - 0.8 = 0.2. Again, since each free throw is independent, the probability of missing all three free throws is calculated by multiplying the individual probabilities together: 0.2 * 0.2 * 0.2 = 0.008, or 0.8%.

3) The probability that the player misses at least one free throw is the complement of making all three free throws. So, it is 1 - 0.512 = 0.488, or 48.8%.

4) The probability that the player makes at least one free throw is the complement of missing all three free throws. So, it is 1 - 0.008 = 0.992, or 99.2%.

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Therefore, the probability that a person with blue hair isn't invited is 49/50 or approximately 0.98.

Probability is a measure of the likelihood that an event will occur. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. In other words, probability represents the proportion of times an event is expected to occur in a large number of repetitions of the same situation. For example, the probability of rolling a six on a fair six-sided die is 1/6, since there is one favorable outcome out of six possible outcomes.

Here,

Assuming that the invitation is randomly given to one of the 50 friends, the probability that a person with blue hair isn't invited can be found as follows:

Let B be the event that a friend has blue hair, and let I be the event that the friend is not invited. Then, we need to find the probability of the event not(B ∩ I), which represents the event that a person with blue hair isn't invited.

We can use the formula for conditional probability to express this as:

P(not(B ∩ I)) = P(not(I) | B) * P(B)

where P(B) is the probability of a friend having blue hair, and P(not(I) | B) is the conditional probability of not being invited given that the friend has blue hair.

From the given information, we know that there are 12 friends with blue hair out of 50 total friends. Therefore, P(B) = 12/50.

To find P(not(I) | B), we need to know the number of friends with blue hair who are not invited. This number is not given, so we have to make an assumption.

If we assume that the invitation is given randomly without any bias towards or against friends with blue hair, then the probability of a friend with blue hair not being invited is the same as the probability of any friend not being invited, which is:

P(not(I)) = 1 - P(I) = 1 - 1/50 = 49/50

Then, the conditional probability we need is:

P(not(I) | B) = P(not(I) ∩ B) / P(B)

P(not(I) | B) = P(not(I)) / P(B)

P(not(I) | B) = (49/50) / (12/50)

P(not(I) | B) = 49/12

Now we can substitute these values into the formula for P(not(B ∩ I)):

P(not(B ∩ I)) = P(not(I) | B) * P(B)

P(not(B ∩ I)) = (49/12) * (12/50)

P(not(B ∩ I)) = 49/50

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The average value of f(x,y) = 2x²y over the given rectangle R is approximately 6.42.

To find the average value of f(x,y) = 2x²y over the given rectangle R with vertices (-2,0), (-2,5), (2,5), and (2,0), we need to integrate f over R and divide by the area of R.

First, we can find the area of R using the formula for the area of a rectangle, which is length times width. The length of R is 4 units and the width is 5 units, so the area of R is 4 × 5 = 20 square units.

Next, we can integrate f(x,y) over R by setting up a double integral of f over R, which is ∫∫R 2x²y dA.

We can evaluate this double integral using iterated integration. First, we integrate with respect to y from 0 to 5: ∫\(0^5\) 2x²y dy = x²(5²) = 25x².

Next, we integrate with respect to x from -2 to 2: ∫-2² 25x² dx = (25/3)(2³ - (-2)³) = 128.33.

Finally, we divide the value of the double integral by the area of R to get the average value of f over R: (1/20)(128.33) = 6.42.

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Answer

What grade are u in because I never seen that before!

Here's how you can use the Trapezoidal Rule to approximate the integral of the function \(f(x) = \frac{1}{{(25+x^2)}^{\frac{3}{2}}}\) from -2 to 2 in MATLAB:

```matlab

a = -2;    % Lower limit

b = 2;     % Upper limit

n = 1000;  % Number of subintervals (increase for higher accuracy)

h = (b - a) / n;   % Step size

x = a:h:b;         % Generate evenly spaced x values

y = 1 ./ (25 + x.^2).^1.5;  % Evaluate the function at x

approximation = h * (sum(y) - (y(1) + y(end)) / 2);  % Trapezoidal Rule approximation

fprintf('Approximation: %.6f\n', approximation);

```

1. We define the lower limit `a` as -2, the upper limit `b` as 2, and the number of subintervals `n` as 1000 (you can adjust `n` for higher accuracy).

2. We calculate the step size `h` by dividing the range (`b - a`) by the number of subintervals (`n`).

3. We generate an array `x` of evenly spaced values from `a` to `b` using the step size `h`.

4. We evaluate the function `f(x)` at each point in `x` and store the results in the array `y`.

5. Finally, we use the Trapezoidal Rule formula to approximate the integral by summing the values in `y` and adjusting for the endpoints, multiplying by the step size `h`.

The Trapezoidal Rule approximation for the integral of the function \(f(x) = \frac{1}{{(25+x^2)}^{\frac{3}{2}}}\) from -2 to 2 is the value calculated using the MATLAB code above.

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The lengths of LV and OE are 15cm, and the lengths of LD and EV are 3√7 cm and 9/√7 cm, respectively.

Since LOVE is a kite, LV and OE are perpendicular bisectors of each other. Let the length of LD be x, and the length of EV be y. Then, we can use the Pythagorean theorem and the fact that the diagonals bisect each other to set up two equations:

x² + (LV/2)² = DV²/4

y² + (OE/2)² = LE²/4

Simplifying each equation and substituting the given values, we get:

x² + (LV/2)² = 81/4

y² + (OE/2)² = 225/4

We also know that the diagonals bisect each other, so we can set up another equation:

LV/2 + OE/2 = LO = VE

Substituting the given value for LE, we get:

LV/2 + OE/2 = 15

Solving this equation for one of the variables, we get:

LV = 30 - OE

Substituting this expression into the first equation above, we get:

x² + ((30 - OE)/2)² = 81/4

Simplifying and rearranging, we get:

OE² - 60OE + 675 = 0

Using the quadratic formula, we get:

OE = (60 ± √(3600 - 2700)) / 2

OE = 15 or 45

If OE = 15, then LV = 30 - 15 = 15, and we can solve for x and y:

x² + 7.5² = 81/4

y² + 7.5² = 225/4

Solving these equations, we get:

x = 3√7

y = 9/√7

If OE = 45, then LV = 30 - 45 = -15, which is impossible for a length. Therefore, the solution is:

LV = OE = 15

x = 3√7

y = 9/√7

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Complete question:

LOVE is a kite. LV and OE are diagonals. The segments DV = 9cm and LE = 15cm are given. Find the lengths of the other segments of the diagonals, DV, OE, and LV.

The puddle is 29.8 feet away from his residence.

The angle of depression is the angle formed by the horizontal line and the horizontal line's observation of the item.

From the given diagram, we need to calculate the distance of the puddle from his house. This is the adjacent side of the triangle.

Using trigonometry identity;

tan 40 = opposite/adjacent

tan 40 = 25/d

d = 25/tan40

d = 29.8 feet

Hence the distance of the puddle from his house is 29.8 feet

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The probability that the average height of the sample men is greater than 69.5 inches is approximately 0.9772 or 97.72%.

To find the probability that the average height of the sample men is greater than 69.5 inches, we will use the Central Limit Theorem and the z-score formula.
Identify the given values:
  - Population mean (μ) = 70 inches
  - Population standard deviation (σ) = 2.5 inches
  - Sample size (n) = 100
  - Sample mean (\(\bar{x}\)) = 69.5 inches.

According to the Central Limit Theorem, the distribution of sample means will be approximately normally distributed with mean μ and standard deviation σ/√n.

Calculate the standard deviation of the sample means \((\sigma \bar{x} )\)
\((\sigma \bar{x} ) = \sigma /\sqrt{n }\)

= 2.5/√100

= 2.5/10

= 0.25
Calculate the z-score using the formula:
\(z = ([\bar{x}- \mu )/\sigma\bar{x}\)

= (69.5 - 70)/0.25 = -0.5/0.25

= -2
Use a z-table or calculator to find the probability that a z-score is greater than -2:
  P(z > -2) = 1 - P(z ≤ -2) = 1 - 0.0228 = 0.9772.

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The equation of the tangent plane to z=x**2−y**2 at the point (x,y)=(2,1) is z = 4x - 2y - 5 and to z=3x-2y at (x,y)=(4,3) is z = 3x - 2y + 6.

The partial derivatives of z with respect to x and y must first be found in order to determine the equation of the tangent plane to the surface z=x**2-y**2 at the point (x,y)=(2,1):

Z/Y = -2Y, and Z/X = 2X.

After that, we can use the expression for a plane's point-normal form, which is given by:

z - z0 Equals n · (x - x0, y - y0) (x - x0, y - y0)

where n is the plane's normal vector and (x0, y0, z0) is a location on the plane. We know the normal vector is given by because we want the tangent plane: n = <∂z/∂x, ∂z/∂y, -1>

The normal vector is therefore n = 4, -2, -1> at the location (2,1). Also known is the equation z0 = f(2,1) = 22 - 12 = 3. Consequently, the expression of the tangent plane's solution is:

z - 3 = <4, -2, -1> · (x - 2, y - 1) (x - 2, y - 1)

z - 3 = 4(x - 2) (x - 2) - 2(y - 1) (y - 1) - (x - 2) (x - 2)

z = 4x - 2y - 5

(b) We must first determine the partial derivatives of z with respect to x and y in order to obtain the equation of the tangent plane to the surface z=3x-2y at (x,y)=(4,3):

∂z/∂x = 3 ∂z/∂y = -2

Then, we can use the point-normal form of the equation of a plane, which is denoted by the formula: z - z0 = n (x - x0, y - y0), where (x0, y0, z0) is a point on the plane and n is the normal vector to the plane. Due to our desire for the tangent plane, we are aware that the normal vector is given by: n = z/x, z/y, -1.

The normal vector is therefore n = 3, -2, -1> at the location (4,3). Additionally, we are aware of the fact that z0 = f(4,3) = 3(4) - 2(3) = 6 for the given number (4). In light of this, the tangent plane equation is

z - 6 = <3, -2, -1> · (x - 4, y - 3)

z - 6 = 3(x - 4) - 2(y - 3) - (x - 4)

z = 3x - 2y + 6

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Answer:

20.48

Step-by-step explanation:

Answer:

60 or 60:1 (Depending on the answer choices)

Step-by-step explanation:

160 feet = 1920 inches (160 * 12)

\(\frac{1920}{32} = \frac{60}{1}\)

The scale factor required will be 1:60 or 60:1 (actual:movie or movie:actual).

The scale factor is the simplest ratio between the actual and the model's size of the same object.

In the question, we are informed that in a movie, a child who was 32 inches tall was ''blown up'' to be 160 feet tall.

We are asked to determine the scale factor needed for the props in the movie.

To find the scale factor, we first find the size of the child in the movie in inches.

Size = 160 feet = 160*12 inches = 1920 inches.

Now, the scale factor is calculated as the ratio of the actual size to the size in the movie, that is,

Scale factor = 32:1920 = 32/1920 = 1:60.

Therefore, the scale factor required will be 1:60 or 60:1 (actual:movie or movie:actual).

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As the y-intercept increases, the graph of the line shifts up;

As the y-intercept decreases, the graph of the line shifts down

There are two perspectives on this issue. The graphical technique would be the first method.

If we merely alter the y-intercept, the slope remains unchanged;

The vertical axis is the y-axis;

A higher or lower y-intercept can be obtained by shifting the line's point of intersection with the y-axis, respectively.

Now, using algebraic reasoning, a line has the general form of the following equation:

When x = 0, the y-intercept is essentially computed as follows:

y = b:

The graph shifts up or down depending on how much we change the b value, which also affects how much the y value changes.

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Answer:

since sum means addition it would be c because the it represents to the sum of w and 4

Answer: C

The sum is the solution when you add two (or more) numbers together. So, the sum of w and 4 can be written as w+4.

:)

Assume a particular solution of the form )e^-x and  the values of A, B, and C that satisfy the equation.

1. To prove that z(x) = 2f(x) + zg(x)

is a particular solution of the given differential equation,

substitute z(x) into the equation and show that it satisfies the equation.

2. To show that W[y1, y2](x) = W[z1, y2](x) + W[y2, z2](x),

use the properties of the Wronskian and the fact that y1(x) = z1(x) - z2(x).

3. To find the general solution of y'' - 14y' + 49y = xe^7x,

assume a particular solution of the form y_p = Ax^2e^7x

find the values of A that satisfy the equation. Then, find the complementary solution by solving the homogeneous equation y''

- 14y' + 49y = 0.

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Based on this sample, the best estimate for the number of people in the town that read the local newspaper is d. 4500.

Using this formula

Number of people=(Population-Random sample)/Random sample× Number of people that read local newspaper

Let plug in the formula

Number of people=(15,200-200/200)×60

Number of people=(15,000/200)×60

Number of people=75×60

Number of people=4500

Inconclusion the best estimate for the number of people in the town that read the local newspaper is d. 4500.

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Answer:

x = 28

Step-by-step explanation:

4x-16 = 2(x+20)

4x-16 = 2x+40

Divide 2x from each side:

2x-16 = 40

Add 16 to each side:

2x = 56

Divide each side by 2:

x = 28

Answer: y=0.392x2 - 5.583x +21.167

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

You have to add 4 on both sides to get X by itself. Then, you solve for X by multiplying the Denominator.

Answer:

10

Step-by-step explanation:

To find 1/4 of 40, is the same as dividing 40 into four parts (each of the four parts become 1/4 of the whole). 40/4=10.

Answer:

\(\frac{\partial f}{\partial x} = -70+7\cdot y\), \(\frac{\partial f}{\partial y} = 12+7\cdot x\), \(\frac{\partial f}{\partial x} (1,-1) = -77\), \(\frac{\partial f}{\partial y}(1,-1) = 19\)

Step-by-step explanation:

Let \(f(x,y) = 9000-70\cdot x +12\cdot y +7\cdot x \cdot y\), then the first partial derivatives of this multivariate function are, respectively:

\(\frac{\partial f}{\partial x} = -70+7\cdot y\) (1)

\(\frac{\partial f}{\partial y} = 12+7\cdot x\) (2)

Now we evaluate the partial derivatives at \((x,y) = (1, -1)\):

\(\frac{\partial f}{\partial x}(1,-1) = -70+ 7\cdot (-1)\)

\(\frac{\partial f}{\partial x} (1,-1) = -77\)

\(\frac{\partial f}{\partial y}(1,-1) = 12+7\cdot (1)\)

\(\frac{\partial f}{\partial y}(1,-1) = 19\)

I think it's D.

???????????????????????????????????????????

Answer:

A

Step-by-step explanation:

We can calculate the equation of the lines based on two points. First line m:

y = ax +b

where a is the slope and b is the y-intercept. To find the slope we use the x and y of the points as:

a = \(a = \frac{y_1-y_2}{x_1-x_2} = \frac{4- -32}{2- -4} = \frac{36}{6} = 6.\)

So:

y = 6x + b

we can find the y intercept by substituting the x and y for one of the points:

solving for b:

b=-32-(6)(-4)= -8.

So the equation is:

y = 6x - 8.

We can change it to:

y + 8 = 6x

8 = 6x - y.

So it’s (A).

Hope that helps!

Answer:

B I think

Step-by-step explanation:

The AP Statistics formula sheet is illustrated below.

An Advanced Placement (AP) Statistics class, you may be wondering if there is a formula sheet available to help you study and prepare for exams.

The formula sheet includes formulas and equations that are commonly used in statistics, such as measures of central tendency, standard deviation, probability, hypothesis testing, and regression analysis. These formulas are essential for understanding statistical concepts and solving problems in real-world applications.

It's important to note that while the formula sheet is available during the AP exam, it does not include every formula that you will need to know. You will still need to have a solid understanding of statistical concepts and be able to apply them to new situations.

In addition to the formula sheet, it's also helpful to practice working with data sets, analyzing graphs and charts, and interpreting results.

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Ketone or aldehyde has a carbonyl absorption at lowest frequency.

To determine which compound has a carbonyl absorption at the lowest frequency (lowest wavenumber), we need to compare the compounds and their carbonyl groups. The carbonyl absorption frequency is influenced by the type of carbonyl group (e.g., ketone, aldehyde, ester, or amide) and the presence of electron-donating or electron-withdrawing groups attached to the carbonyl carbon.

In general, electron-donating groups (EDGs) lower the carbonyl absorption frequency, while electron-withdrawing groups (EWGs) increase it. So, to find the compound with the lowest carbonyl absorption frequency, look for a carbonyl group with the highest number of electron-donating groups and the lowest number of electron-withdrawing groups attached to the carbonyl carbon.

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Answer:

10

Step-by-step explanation:

She gave 1/5 to her sister,

now 1/5 of 20 is 20/5 = 4

so she is left with 16

then she gives 3/8 of these 16 to her friend

3/8 of 16 is (16)(3)/(8) = 6

after giving away these 6, she is left with 10 candies

According to the rectangle plot, the total length of fence that Farmer Ted will use can be expressed in terms of x as 2x + 432/x.

Now, the problem asks us to find the total length of fence that Farmer Ted will use to enclose the rectangle and divide it into two equal parts using another fence parallel to one of the sides. To solve this problem, we need to first visualize the rectangle and understand what's happening.

Next, we need to enclose the rectangle with a fence. This means we need to find the perimeter of the rectangle, which is the total length of all its sides. The perimeter of a rectangle can be found by adding up the lengths of all its sides:

Perimeter = 2x + 2y

Now we have two smaller rectangles with dimensions x by y/2. The total area of both rectangles is still 216 square meters, so we can set up an equation to solve for y:

(x)(y/2) + (x)(y/2) = 216

Simplifying this equation, we get:

xy = 216

We can now use this equation to solve for y in terms of x:

y = 216/x

We can substitute this value for y in the equation for the perimeter of the original rectangle:

Perimeter = 2x + 2y

Perimeter = 2x + 2(216/x)

Simplifying this equation, we get:

Perimeter = 2x + 432/x

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Answer:

The large sandwiches be 45

And, the small sandwiches be 90

Step-by-step explanation:

The computation is shown below:

Let us assume the large sandwiches be x

And, the small sandwiches be 2x

Now the equation would be

5x + 4(2x) = $585

5x + 8x = $585

13x = $585

x = 45

So, the large sandwiches be 45

And, the small sandwiches be 90

Exponential smoothing is a popular forecasting technique used to predict future trends in time-series data. It works by assigning weights to historical data points, with more recent data points receiving higher weights. The level of smoothing is controlled by a smoothing parameter called alpha, which ranges between 0 and 1. As alpha increases, the influence of older data points decreases, and the model becomes more reactive to recent changes in the data.

When alpha is high, the exponential smoothing model group of answer choices tends to produce sluggish forecasts. This is because the model gives more weight to recent data points, which can cause it to overreact to short-term fluctuations in the data. As a result, the model may miss important trends or patterns in the data that would have been captured by a more balanced weighting scheme.

On the other hand, when alpha is low, the model tends to be more stable and less reactive to short-term changes in the data. This can be useful for predicting long-term trends or for smoothing out noisy data sets.

In summary, the choice of alpha in an exponential smoothing model depends on the characteristics of the data and the goals of the forecast. A high alpha value may be appropriate for short-term forecasting or for data sets with high volatility, while a low alpha value may be more suitable for long-term forecasting or for data sets with low volatility.

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