Chrissie likes to tip a server in a restaurant a minimum of 25%. She and her friend have a lunch bill that is
$18.26. Chrissie says the tip will be $4.44. Her friend says that is not a minimum of 25%.
Tell who is correct, then complete the explanation
?
25% of $18.26 =
$18.26 = $
The tip should be at least $

Answer:

300 girls, 200 boys

Step-by-step explanation:

To find boys: 500 x 0.4 = 200

To find girls: 500 x 0.6 = 300

60% girls

The rotation that that translates AWXY to AW'X'Y' is a 45° anticlockwise rotation. See the attached image for details.

Rotation in math refers to the change in the angle of a geometric shape around a central axis on a point on the geometric plane such that it's original coordinates are modified but it's size or shape.

Hence, it is correct to state that The rotation that that translates AWXY to AW'X'Y' is a 45° anticlockwise rotation.

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Answer:

(23*2)+s

Step-by-step explanation:

Answer:

2(23+s)

Yep there ya goo

To compute the double integral by changing the order of integration and making y the outer integration variable, the value of the double integral by changing the order of integration is 1/6.

∫∫ R f(x,y) dA
where R is the region of integration and dA represents the area element.
In this case, we are given the integral in problem 7:
∫ from 0 to 2√2 ∫ from y/2 to 2-y/2 (2x-y) dx dy
To change the order of integration, we need to rewrite the limits of integration for x and y in terms of the other variable.
First, let's sketch the region R. We see that R is the trapezoidal region bounded by the lines y = 0, y = 2, x = y/2, and x = 2 - y/2.
Next, let's write the limits of integration for x in terms of y. From the equations of the bounding lines, we can see that x ranges from y/2 to 2 - y/2. So, we have:
∫ from 0 to 2 ∫ from y/2 to 2-y/2 (2x-y) dx dy
= ∫ from 0 to 2 ∫ from y/2 to 2-y/2 2x dx dy - ∫ from 0 to 2 ∫ from y/2 to 2-y/2 y dx dy
= ∫ from 0 to 2 [x^2]y/2 to 2-y/2 dy - ∫ from 0 to 2 [y^2/2]y/2 to 2-y/2 dy
= ∫ from 0 to 2 ( (2-y/2)^2 - (y/2)^2 )/2 dy - ∫ from 0 to 2 ( (2-y/2)^3 - (y/2)^3 )/6 dy
= ∫ from 0 to 2 ( 3/4 - y/4 ) dy - ∫ from 0 to 2 ( 7/12 - y/8 ) dy
= [ 3y/4 - y^2/8 ] from 0 to 2 - [ 7y/12 - y^2/16 ] from 0 to 2
= ( 6 - 0 )/4 - ( 14/3 - 0 )/2
= 3/2 - 7/3
= 1/6
Therefore, the value of the double integral by changing the order of integration is 1/6.

To compute the double integral by changing the order of integration and making y the outer integration variable, you need to follow these steps:
1. Identify the given double integral: Since the actual integral from question 7 is not provided, I will use a general double integral as an example: ∬f(x, y)dxdy, where f(x, y) is a given function and the limits for x and y are given as a ≤ x ≤ b and c ≤ y ≤ d.
2. Change the order of integration: To change the order of integration, you will rewrite the double integral by swapping the differential terms and their respective limits. For our example, it becomes ∬f(x, y)dydx with limits of e ≤ y ≤ f and g ≤ x ≤ h. Note that you'll need to adjust the new limits according to the problem you're working on.
3. Evaluate the inner integral: Next, you'll integrate f(x, y) with respect to the inner integration variable (in this case, y). You'll get a function in terms of x: F(x) = ∫f(x, y)dy with limits e to f.
4. Evaluate the outer integral: Finally, integrate F(x) with respect to the outer integration variable (x) and use the limits g to h: ∫F(x)dx from g to h.
By following these steps, you will have successfully computed the double integral by changing the order of integration and making y the outer integration variable.

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Using complementary angles, it is found that the solution to the trigonometric equation is of x = 20.

Complementary angles are two angles whose measures add to 90º.

If two angles a and b are complementary, we have that the sine of one is the cosine of other, that is:

\(\sin{a} = \cos{b}\)

In this problem, the equation is:

\(\sin{(2x)} = \cos{(x + 30)}\)

Hence, they are complementary, which means that:

\(2x + x + 30 = 90\)

\(3x = 60\)

\(x = \frac{60}{3}\)

\(x = 20\)

The solution to the trigonometric equation is of x = 20.

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Answer:

$5745.03

Step-by-step explanation:

A = 4250(1 + 0.044)7 = $5745.03

The required amount in the Mai accounts after 7 years will be $5745.03.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Amount = principal[1 + r/n]ⁿᵃ

Here,

Principal = 4250, rate = 4.4%, Time = 7 ,
Amount = 4250[1 + 0.044]⁷
Amount = $5745.03

Thus, the required amount in the Mai accounts after 7 years will be $5745.03.

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The value of P((A ∩ B) ∪ (C ∪ D ∩ E))' is approximately 0.1571. the probability that component A is not working given that the system works is approximately 0.001.

To calculate the values in Part 1 and Part 2, we'll use basic probability rules and formulas.

Given: P(A) = P(B) = 0.77, P(C) = P(D) = P(E) = 0.85

Part 1: We want to find the probability of the complement of the event (A ∩ B) ∪ (C ∪ D ∩ E), denoted as P((A ∩ B) ∪ (C ∪ D ∩ E))'.

Using De Morgan's law, the complement of a union is the intersection of complements:

P((A ∩ B) ∪ (C ∪ D ∩ E))' = P((A ∩ B)') ∩ (C ∪ D ∩ E)'

The complement of an intersection is the union of complements:

P((A ∩ B)') ∩ (C ∪ D ∩ E)' = (P(A') ∪ P(B')) ∩ (P(C') ∩ P(D') ∩ P(E'))

Substituting the given probabilities:

P((A ∩ B)') ∩ (C ∪ D ∩ E)' = (1 - P(A)) ∪ (1 - P(B)) ∩ (1 - P(C)) ∩ (1 - P(D)) ∩ (1 - P(E))

Calculating the values:

P(A') = 1 - P(A) = 1 - 0.77 = 0.23

P(B') = 1 - P(B) = 1 - 0.77 = 0.23

P(C') = 1 - P(C) = 1 - 0.85 = 0.15

P(D') = 1 - P(D) = 1 - 0.85 = 0.15

P(E') = 1 - P(E) = 1 - 0.85 = 0.15

Now, we calculate the final probability:

P((A ∩ B)') ∩ (C ∪ D ∩ E)' = (0.23 ∪ 0.23) ∩ (0.15 ∩ 0.15 ∩ 0.15)

                          = 0.23 ∩ 0.15 = 0.1571 (rounded to 4 decimal places)

Therefore, the value of P((A ∩ B) ∪ (C ∪ D ∩ E))' is approximately 0.1571.

Part 2: We want to find the probability that component A is not working given that the system works, denoted as P(A' | System Works).

Using the conditional probability formula:

P(A' | System Works) = P(A' ∩ System Works) / P(System Works)

To calculate the numerator:

P(A' ∩ System Works) = P(A' ∩ B' ∩ C' ∩ D' ∩ E')

                    = P(A') ∩ P(B') ∩ P(C') ∩ P(D') ∩ P(E')

                    = 0.23 ∩ 0.23 ∩ 0.15 ∩ 0.15 ∩ 0.15  = 0.0002634 (rounded to 7 decimal places)

To calculate the denominator:

P(System Works) = 1 - P(A' ∪ B' ∪ C' ∪ D' ∪ E')

= 1 - (P(A') ∪ P(B') ∪ P(C') ∪ P(D') ∪ P(E')) = 1 - (0.23 ∪ 0.23 ∪ 0.15 ∪ 0.15 ∪ 0.15) = 1 - 0.66 = 0.34

Now, we calculate the final probability:

P(A' | System Works) = P(A' ∩ System Works) / P(System Works)

= 0.0002634 / 0.34 = 0.0007735 (rounded to 7 decimal places)

Therefore, the probability that component A is not working given that the system works is approximately 0.001.

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The complete question is:<The reliability (probability of working) of each component is specified as follows and the components work or fail independently. P(A) = P(B) = 0.77 P(C) = P(D) = P(E) = 0.85 A B с DHE Part 1 What is the value of P((ANB) U(CODn E))' (Enter your answer with 3 decimal digits.) 0.1571 100% Part 2 What is the probability that the component A is not working given that the system works? (Enter your answer with 3 decimal digits.) Hint: Think of a conditional probability definition.>

The answer is 3.  

Hope this helps!

A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a test of significance

Statistical Test

A statistical test provides a mechanism for making quantitative decisions about a process or processes. The intent is to determine whether there is enough evidence to reject a conjecture or hypothesis about the process.

A test of significance is a formal procedure for comparing observed data with a claim (also called a hypothesis), the truth of which is being assessed. The claim is a statement about a parameter, like the population proportion p or the population mean µ.

Hypothesized Probability Distribution

To hypothesis test with the binomial distribution, we must calculate the probability, p , of the observed event and any more extreme event happening. We compare this to the level of significance α . If p>α then we do not reject the null hypothesis. If p<α we accept the alternative hypothesis.

The test is a statistical test .The test is used to accept or reject an hypothesis. The statistical test that has the above features is the test of significance

Then the statistical test is the test of significance.

A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a test of significance

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Answer: The awnser is 45 degrees

Step-by-step explanation:

As you can see there are two z's which equal to 90 degrees and one z eqquals to 45 degrees.

Answer:

x = -2

Step-by-step explanation:

m(x) = 4x+15; m(x) = 7

7= 4x+15

7-4x=15

-4x=15-7

-4x=8 / :(-4)

x= -2

297 mm is  nearest millimetre complete this statement .

The definition of convert units?

1 cm = 10mm

the length of a sheet of paper = 29.7 cm

the nearest millimetre = 29.7 * 10 = 297 mm

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The equation "ax2 = y," which has one solution unless a = 4, and none unless a = 4, has a solution. x = √(-4ay) / (2a) restricted by the condition that y be negative.

We may use the quadratic formula to determine the solutions to an equation for various values of an to construct a solution to the equation "ax² = y," which has no solution when a = 4 & just one solution in all other cases.

According to the quadratic formula, the answers to the problem "ax2 + bx + c = 0" are provided by

x = (-b +/- √(b² - 4ac)) / (2a)

In this formula, if we add "ax² = y," we obtain

x = (-0 +/- √(0² - 4ay)) / (2a)

which simplifies to

x = √(-4ay) / (2a)

If a = 4, the equation becomes

x = √(-16y) / 8

The equation has no solutions if y is positive because the value of (-16y) is fictitious. The value of (-16y) is real if y is negative, but the equation is still unsolvable since x cannot have a negative value. As a result, when a = 4, the problem has no solutions.

The equation has a single solution provided by any other value of a.

x = √(-4ay) / (2a)

For example, if a = 3, the equation becomes

x = √(-12y) / 6

Since √(-12y) is imaginary if y is positive, the problem has no solutions. If y is negative, √(-12y) has a real value, and there is only one solution to the problem.

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The transformation rule that describes the rotation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

The rule that describes the transformation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

To understand this, let's apply the transformation rule to each vertex of the original parallelogram ABCD:

Point A (2, 5) becomes A' (-5, 2).

Point B (5, 4) becomes B' (-4, 5).

Point C (5, 2) becomes C' (-2, 5).

Point D (2, 3) becomes D' (-3, 2).

By applying the transformation rule, we observe that the x-coordinate of each point becomes the negative of the original y-coordinate, and the y-coordinate becomes the original x-coordinate.

This transformation is a 90-degree counterclockwise rotation about the origin (0, 0) on the coordinate plane. The image parallelogram A'B'C'D' is obtained by rotating the original parallelogram ABCD by 90 degrees counterclockwise.

Visually, this transformation can be seen as the original parallelogram being rotated around the origin, where the x-axis becomes the y-axis, and the y-axis becomes the negative x-axis.

Therefore, the transformation rule that describes the rotation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

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Answer:

$566,700 to the nearest dollar.

Step-by-step explanation:

This is a geometric series with nth term = a1r^(n-1) where common ratio r

= 1.15 and first term a1 = 245000

So in its 7th year the profit will be 245000^ 1.15^(7-1)

= 566699.8876.

Interior Angle is 180n = 375 - x in given question.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

To determine the number of sides in a convex polygon given the sum of all but one of its interior angles, we can use the formula:

Sum of interior angles = (n - 2) * 180 degrees,

where n represents the number of sides in the polygon.

In this case, the sum of all but one of the interior angles is missing, so we need to subtract one interior angle from the total sum before applying the formula.

Let's denote the missing interior angle as x. Therefore, the sum of all but one of the interior angles would be the total sum minus x.

Given that the stamina is 15, we can express the equation as:

(15 - x) = (n - 2) * 180

Simplifying the equation, we have:

15 - x = 180n - 360

Rearranging the terms:

180n = 15 - x + 360

180n = 375 - x

Now, we need more information or an equation to solve for the number of sides (n) or the missing interior angle (x).

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Finding the slope of the linear equation, we will see that she buys 7 cans per week.

We know that she buys a constant number of cans per week, then this can be modeled with a linear equation.

Remember that the general linear equation is written as:

y = a*x +b

Where a is the slope, in this case, this gives how many cans she buys per week.

We know that if a line passes through two points (x₁, y₁) and (x₂, y₂) the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Here we have two points of the form (week, cans)

(5, 29) and (9, 57)

Then the slope is:

a = (57 - 29)/(9 - 5)

a = 7

She buys 7 cans per week.

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If the area of the base of the rectangular prism is 36.8 in2 and the height is 8.5 in, the volume is

The measurement of three-dimensional space is volume. It is frequently quantified numerically by various imperial or US customary units, SI-derived units, or both.

V=Bh, where B is the base area and h is the height, is the formula for a prism's volume. Volume (V) = base area height of the prism is the formula for calculating the volume of a rectangular prism.

Volume = l w h is another way to state this equation, where l is the prism's length, w is its width, and h is its height.

Volume = base x height

V = 36.8 x 8.5 = 312.8

Therefore, the volume of the rectangular prism is

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Answer:

To find the confidence interval for the mean weight of all baby Orca whales, we can use the following formula:

Confidence interval = estimate ± (critical value) × (standard error)

where:

estimate = sample mean

critical value = the value from the t-distribution that corresponds to our desired confidence level and degrees of freedom

standard error = standard deviation of the sample divided by the square root of the sample size

First, we need to calculate the sample mean and standard deviation:

Sample mean:

x = (425 + 454 + 380 + 405 + 395) / 5 = 411.8 pounds

Sample standard deviation:

s = sqrt(((425 - 411.8)^2 + (454 - 411.8)^2 + (380 - 411.8)^2 + (405 - 411.8)^2 + (395 - 411.8)^2) / 4) = 28.6 pounds

Next, we need to find the critical value from the t-distribution with degrees of freedom (n - 1) and our desired confidence level of 98%. With a sample size of 5, our degrees of freedom is 4. Using a t-table or a calculator, we find the critical value to be 3.747.

Finally, we can calculate the confidence interval:

Confidence interval = 411.8 ± 3.747 × (28.6 / sqrt(5)) = 411.8 ± 45.1

Rounded to the nearest tenth of a pound, the confidence interval is:

Confidence interval = 411.8 ± 45.1 = [366.7, 456.9]

Therefore, we can say with 98% confidence that the true mean weight of all baby Orca whales is between 366.7 and 456.9 pounds

The inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is: w ≥ 10

To find the inequality that can be used to determine the number of weeks it can take for the animal shelter to meet its fundraising goal, we need to consider the total expenses and donations.

Let's break down the expenses and donations:

Expenses:

Annual rental = $2,500

Weekly expenses = $450

Donations:

One-time donation = $125

Pledged donations per week = $680

Let w represent the number of weeks it takes for the shelter to meet its goal.

Total expenses for w weeks = Annual rental + Weekly expenses * w

Total expenses = $2,500 + $450w

Total donations for w weeks = One-time donation + Pledged donations per week * w

Total donations = $125 + $680w

To meet the goal, the total donations must be greater than or equal to the total expenses. Therefore, the inequality is:

Total donations ≥ Total expenses

$125 + $680w ≥ $2,500 + $450w

Simplifying the inequality, we have:

$230w ≥ $2,375

Dividing both sides of the inequality by 230, we get:

w ≥ $2,375 / $230

Rounding the result to the nearest whole number, we have:

w ≥ 10

Therefore, the inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is:

w ≥ 10

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This result is approximate.

=========================================================

Explanation:

mu = 750 = mean

sigma = 75 = standard deviation

The raw scores or x values are x = 750 and x = 825

Let's compute the z score for each x value

z = (x - mu)/sigma

z = (750 - 750)/75

z = 0

and

z = (x - mu)/sigma

z = (825 - 750)/75

z = 1

Therefore P(750 ≤ x ≤ 825) is equivalent to P(0 ≤ z ≤ 1) in this context.

Use a z score table to determine that

P(z ≤ 0) = 0.5

P(z ≤ 1) = 0.84314 approximately

So,

P(a ≤ z ≤ b) = P(z ≤ b) - P(z ≤ a)

P(0 ≤ z ≤ 1) = P(z ≤ 1) - P(z ≤ 0)

P(0 ≤ z ≤ 1) = 0.84314 - 0.5

P(0 ≤ z ≤ 1) = 0.34314 approximately

The value 0.34314 then converts to 34.314% which rounds to 34%

Or you could use the empirical rule as shown below. The pink section on the right is marked 34% which is approximate. This pink section is between z = 0 and z = 1.

Roads that are well-maintained, dry, and free from hazards are generally less likely to result in traction loss.

The likelihood of losing traction depends on various factors such as road conditions, weather, vehicle type, and driver behavior. However, in general, roads that are well-maintained, dry, and free from debris or hazards are less likely to result in traction loss. Additionally, roads with good grip surfaces, such as asphalt or concrete, tend to provide better traction compared to unpaved or slippery surfaces. It's important to drive cautiously and adapt to the specific conditions of the road to minimize the risk of losing traction.

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The length of the third side of a right triangle can be found using the Pythagorean Theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

The Pythagorean Theorem can be written as follows:

a^2 + b^2 = c^2

where a and b are the lengths of the two shorter sides of the triangle, and c is the length of the hypotenuse.

To find the length of the third side, we can simply plug in the lengths of the other two sides into the equation. For example, if the lengths of the two shorter sides are 3 cm and 4 cm, then the length of the hypotenuse is:

c^2 = 3^2 + 4^2 = 9 + 16 = 25

Taking the square root of both sides, we get:

c = sqrt(25) = 5 cm

Therefore, the length of the third side of the triangle is 5 cm.

It is important to note that the Pythagorean Theorem only works for right triangles. If the triangle is not a right triangle, then the Pythagorean Theorem cannot be used to find the length of the third side.

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When we measure a ECG waveform the large boxes represents 0.2 seconds.

To determine the measurements of the big box on ECG paper, we need to consider the standard calibration of ECG paper.

In most ECG papers, the standard calibration is as follows:

These measurements allow for accurate interpretation of the ECG waveform and analysis of heart activity.

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To find the number of bicycles that must be manufactured to minimize the cost, we need to determine the value of x that corresponds to the minimum point of the cost function C(x).

We can find this by taking the derivative of C(x) with respect to x and setting it equal to zero. Let's differentiate C(x):

C'(x) = 6x - 1500

Now we set C'(x) = 0 and solve for x:

6x - 1500 = 0

6x = 1500

x = 250

Therefore, the number of bicycles that must be manufactured to minimize the cost is 250 bicycles.

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If 150 town residents were asked about their age and yogurt , then the probability that a randomly selected customer prefers Swirl if age is at least 25 years old is 0.66 .

let X be = the selected customer that prefers swirled yogurt or is at least 25 years old ;

The sum of all the customers that are "at least 25 years old" = 21 + 30 + 24 = 75 ;

the sum of all the customers that " like Swirl Yogurt" is = 24 + 24 = 48 ;

the total number of residents = 150 students ;

So , the probability is calculated as : ( 75+48 -24)/150 = 0.66 .

Therefore , the required probability is 0.66 .

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The given question is incomplete , the complete question is

The 150 residents of the town of wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. the results are displayed next.

     Age                               Chocolate      Vanilla      Swirl

under 25 years old                  22                 29             24

at least 25 years old                21                  30             24

What is the probability a randomly selected customer prefers Swirl Yogurt given he or she is at least 25 years old ?

The value of x is x=7.

A triangle is a polygon with 3 sides.

Given, the measures of the interior angles of the triangle are 60°, 70°, and 6x+8.

Since the sum of the measures of the interior angles of a triangle is 180°, it follows:

60+ 70+ 6x+8 = 180

138 + 6x =180

6x = 180-138

6x = 42

x = 42/6

x = 7

Hence, the value of x is x=7.

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Therefore, there are 6,227,020,800 different ways a deck of cards can be arranged when only the values of the cards matter and their suits are irrelevant.

In the case where only the values of the cards matter and their suits are irrelevant, and there are effectively only 13 distinct cards, the number of different ways a deck of cards can be arranged can be calculated using the concept of permutations. Since there are 13 distinct cards, each card can occupy one of the 13 positions in the deck. The first card has 13 options, the second card has 12 options (as one card has been placed), the third card has 11 options, and so on, until the last card has only one option left.

Therefore, the number of different ways the deck can be arranged is given by:

13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 13!

Using the factorial notation, the number of different ways a deck of cards can be arranged in this case is 13!.

Calculating 13! gives:

13! = 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 6,227,020,800

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