Bob went out to dinner and paid a 15% tip on a $20 meal? How much is the total bill?

9514 1404 393

Answer:

  $18.48

Step-by-step explanation:

If we assume the account earned simple interest, the amount is given by the formula ...

  I = Prt . . . . interest on principal P at annual rate r for t years

  1.155 = P·0.0125·5

  P = 1.155/0.0625 = 18.48

Jake initially deposited $18.48 as his principal.

_____

Additional comment

The amount $1.155 is an unusual specification for an amount of money. If you mean $1,155.00, then the principal amount is likewise multiplied by 1000: $18,480.

Answer:

He uses 23 balloons for each of the 28 events.

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

I divided 644 by 28. There are 644 balloons and you want to split

(divide) into the same number of balloons with none left over. Look for those key words to tell you what type of math your doing. Hope this helps!

Answer:

50 and 80 or 65 and 65

Step-by-step explanation:

two angles in an isosceles are the same.

Answer:

94.6-18.8=75.8

75.8 is the answer

Step-by-step explanation:

Hope this helps

May i get braineist pls?

Answer:

117.5

Step-by-step explanation:

hope this helps! have a great day

The angle R corresponds to the angle E.

This comes from the fact that they are alternate interior angles.

The jogger is 3 km away from the starting point and is located at an angle of 45 degrees counter-clockwise from the east axis.

To calculate the distance from the starting point, we can use the Pythagorean theorem. The jogger first runs 5 km east, then 6 km northwest, and finally 3 km south.

The distance traveled east and west cancels out, as they are in opposite directions. So we only need to consider the north-south distance.

The north-south distance is the sum of the distances traveled north (0 km) and south (3 km), which gives us a total distance of 3 km.

Therefore, the jogger is 3 km away from the starting point.

To determine the direction from the starting point, we can use trigonometry. We can consider the east direction as 0 degrees, and measure angles counter-clockwise from the east axis.

Since the jogger traveled northwest, which is halfway between north and west, the angle from the east axis would be 45 degrees (45°).

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Solving for Cartesian product n(B), we have n(B) = 72 / 24 = 3.

The Cartesian product is a mathematical operation that takes two sets and produces a set of all possible ordered pairs of elements from both sets.

In other words, if A and B are two sets, their Cartesian product (written as A × B) is the set of all possible ordered pairs (a, b) where a is an element of A and b is an element of B.

For example, if A = {1, 2} and B = {3, 4}, then A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}.

By the question.

We know that n (Ax B) represents the number of elements in the set obtained by taking the Cartesian product of sets A and B.

Using the formula for the size of the Cartesian product, we have:

n (Ax B) = n(A) x n(B)

Substituting the given values, we get: 72 = 24 x n(B)

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We prove that both side are equal.

In the given question,

The given expression is 16p + 8 = 2(8p+4).

We have to prove that both side are equal.

To solve this question we use have to follow some rule.

Some Rules are

In this given question to solve the expression we firstly solve the bracket.

To solve this question we use Distributive Property

In this property a(b+c) = ab+ac

Solving the expression

16p + 8 = 2×8p+2×4

16p + 8 = 16p+8

Hence, we prove that both side are equal.

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Answer:

59

Step-by-step explanation:

3x=177

3x represents the # of arrow he can shoot at once every time

177 represents the total # of arrow he has

Answer:

59

Step-by-step explanation:

177/3=59

So, the volume of the snowball is decreasing at a rate of approximately 2,130.51 cm^3/min when the radius is 15 cm.

When dealing with problems involving rates and volumes, it's important to remember the formula for the volume of a sphere, which is V = (4/3)πr^3.
Now, we know that the radius of the snowball is decreasing at a rate of 0.3 cm/min, which means dr/dt = -0.3 cm/min (the negative sign indicates that the radius is decreasing). We want to find the rate at which the volume of the snowball is decreasing, or dV/dt.

To do this, we'll need to use the chain rule of differentiation. That means we'll need to differentiate the volume formula with respect to time:

dV/dt = d/dt[(4/3)πr^3]

= 4πr^2 (dr/dt)

= 4π(15)^2 (-0.3)

= -678π cm^3/min

Note that we plugged in r = 15 cm because that's the radius when we're trying to find the rate of volume change. Also, since we're looking for a positive rate, we'll take the absolute value of the answer:

|dV/dt| = 678π cm^3/min

So, the volume of the snowball is decreasing at a rate of approximately 2,130.51 cm^3/min when the radius is 15 cm. I hope that helps! Let me know if you have any other questions.

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1   Y is distributed as N(aμ + b, a^2σ^2), as desired.

2  We have shown that under these conditions, E[XY] = E[X]E[Y].

To prove that Y is distributed as N(aμ + b, a^2σ^2), we need to show that the mean and variance of Y match those of a normal distribution with parameters aμ + b and a^2σ^2, respectively.

First, let's find the mean of Y:

E(Y) = E(aX + b) = aE(X) + b = aμ + b

Next, let's find the variance of Y:

Var(Y) = Var(aX + b) = a^2Var(X) = a^2σ^2

Therefore, Y is distributed as N(aμ + b, a^2σ^2), as desired.

We can use the definition of covariance to prove that E[XY] = E[X]E[Y]. By the properties of expected value, we know that:

E[XY] = ∫∫ xy f(x,y) dxdy

where f(x,y) is the joint probability density function of X and Y.

Then, we can use the fact that X and Y are independent to simplify the expression:

E[XY] = ∫∫ xy f(x) f(y) dxdy

= ∫ x f(x) dx ∫ y f(y) dy

= E[X]E[Y]

where f(x) and f(y) are the marginal probability density functions of X and Y, respectively.

Therefore, we have shown that under these conditions, E[XY] = E[X]E[Y].

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To cut a 14-inch pizza into three equal area pieces using two parallel cuts placed symmetrically from the center, each piece will have an area of 150.

As we need to cut a 14-inch pizza into three pieces of equal area using two parallel cuts, we have to follow the steps given below

:Step 1: Cut the pizza with a line that goes through the center of the pizza and marks its diameter. This cut separates the pizza into two equal halves.

Step 2: The second cut needs to be made parallel to the first cut and needs to be at a distance of approximately 1/3 the diameter of the pizza from the first cut.

Step 3: Then, the pizza will be separated into three equal area pieces as required. As we have to cut the pizza into three equal area pieces, the area of each piece will be 150 square inches.

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Answer:

Use the slope formula to find the slope of a line given the coordinates of two points on the line. The slope formula is m=(y2-y1)/(x2-x1), or the change in the y values over the change in the x values.

The answer is true

Answer:

235$

Step-by-step explanation:

85+2x=555

-85         -85

      2x=470

2x/2x     460/2x

235

so the freshman class raised 235$

Answer:

10000

here you gooooooooo

Answer:

100x100=10000

The Fourier transform of the function \(\(f(x) = e^{-\alpha |x|} \cos(\beta x)\)\), where \(\(\alpha > 0\)\) and \(\(\beta\)\) is a real number, is given by: \(\[F[f] = \hat{f}(\xi) = \frac{2\pi}{\alpha^2 + \xi^2} \left(\frac{\alpha}{\alpha^2 + (\beta - \xi)^2} + \frac{\alpha}{\alpha^2 + (\beta + \xi)^2}\right)\]\)

In the Fourier transform, \(\(\hat{f}(\xi)\)\) represents the transformed function with respect to the variable \(\(\xi\)\). The Fourier transform of a function decomposes it into a sum of complex exponentials with different frequencies. The transformation involves an integral over the entire real line.

To derive the Fourier transform of \(\(f(x)\)\), we substitute the function into the integral formula for the Fourier transform and perform the necessary calculations. The resulting expression involves trigonometric and exponential functions. The transform has a resonance-like behavior, with peaks at frequencies \(\(\beta \pm \alpha\)\). The strength of the peaks is determined by the value of \(\(\alpha\)\) and the distance from \(\(\beta\)\). The Fourier transform provides a representation of the function f(x) in the frequency domain, revealing the distribution of frequencies present in the original function.

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Answer:

  53°

Step-by-step explanation:

You want the measure of angle DAC in rhombus ABCD with angle BAC marked as 53°.

Each diagonal of a rhombus bisects its vertex angles.

  ∠DAC = ∠BAC = 53°

Answer:

y = x + 3

Hope it helps!!!!

In linear regression, the variance around the regression line represents the variability of the dependent variable (response variable) that is not explained by the regression model.

It measures the dispersion of the actual data points around the predicted values from the regression line.

The variance around the regression line can vary with different values of the predictor variable. This is because the relationship between the predictor variable and the response variable may not be constant across the entire range of the predictor variable. In other words, the spread or dispersion of the data points around the regression line may change as the predictor variable changes.

By examining the residuals (the differences between the observed values and the predicted values from the regression line) and calculating their variances, you can assess the variability of the data points around the regression line. This variability is an important aspect of understanding the goodness of fit of the regression model and the accuracy of the predictions.

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The volume of the box in shape of a rectangular prism is solved to be

716 inches³

Three-dimensional object with six faces is called a rectangular prism (two at the top and bottom and four are lateral faces).

The prism has rectangular-shaped faces on each side. As a result, there are three sets of matching faces in this picture. Rectangular prisms are sometimes known as cuboids due to their shape.

In the given problem the formula used for volume of prism is

= length * width * height

= 358 * 1/2 * 4

= 716 inches³

The prism has a volume of 716 inches³

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The volume of the rectangular prism with a length of 358 inches, width of 1/2 inches and a height of 4 inches is 716 in³.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is width, h is height and l is length.

Given that;

Plug the given values into the above formula and simplify.

V = w × h × l

V = 1/2 in × 4 in  × 358 in

V = 716 in³

Therefore, the volume of the box is 716 in³.

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Answer:

This is gebber gabber but yes

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

AB+BC= AC

13+2= 15

Answer:

1/2

Step-by-step explanation:

Slope equals rise over run. To find this use two points that land evenly on the graph then count how ever many spaces up and then to the side. In this case, it goes up 1 and right 2, so put that into fraction form, 1/2, and that is your answer.

Answer:

1/2

Step-by-step explanation:

The greatest number of 24 inch pieces the carpenter can cut from 6 boards of wood is 51.

A carpenter needs to cut 24-inch pieces of wood from a board that is 17 feet in length.

Therefore, the greatest number of 24 inches pieces the carpenter can cut from 6 of these boards of wood can be calculated as follows:

let's convert from feet to inches.

17 feet = 204 inches

1 board = 204 inches

6 board = ?

cross  multiply

length of 6 board = 204 × 6

length of 6 board = 1224 inches

Hence,

greatest number of 24 inch that can be cut from 6 boards = 1224 / 24

greatest number of 24 inch that can be cut from 6 boards = 51

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The student can complete 25/34 of the science project per hour based on their current rate of progress.

To determine the fraction of the project the student can complete per hour, we divide the number of completed parts by the time taken.

The student has completed 25 parts of the science project in 34 hours. To find the fraction completed per hour, we divide the number of completed parts (25) by the number of hours (34).

Therefore, the fraction of the project completed per hour is 25/34. This means that for every hour of work, the student completes approximately 25/34 of the project. This fraction represents the rate or efficiency at which the student is progressing on the project, indicating how much work is accomplished in a given unit of time.

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The cost C (in dollars) for ordering and storing x units is C = 4x + 100,000 x. We can calculate it in the following manner.

The minimum cost of the order size can be obtained by differentiating the given expression of the cost C (in dollars) with respect to x and equating it to 0.

So, we have C(x) = 4x + 100,000/x

Differentiating both sides with respect to x, we get: C′(x) = 4 - 100,000/x²C′(x) = 0 for minimum C(x)∴ 4 - 100,000/x² = 0

Thus, we have x² = 100,000/4= 25,000

Order size x = ± 25,000

Taking positive value for the order size, we get:x = 25000

Therefore, the order size that will produce a minimum cost is 25,000. Answer: 25,000.
To find the minimum cost, we need to minimize the function C(x) = 4x + 100,000/x. To do this, we will find the critical points by taking the derivative of the function and setting it to zero.

dC/dx = 4 - 100,000/x^2

Now, set dC/dx = 0:

4 - 100,000/x^2 = 0

Add 100,000/x^2 to both sides:

4 = 100,000/x^2

Now, multiply both sides by x^2:

4x^2 = 100,000

Divide both sides by 4:

x^2 = 25,000

Take the square root of both sides:

x = sqrt(25,000)

x ≈ 158.11

Since we need to round to the nearest whole number, the order size that will produce a minimum cost is 158 units.

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