The ratio of girls to boys is 3:5 . If there are 15 boys in the classroom, how students are there total?

Shortest distance from the point (2, 0, -3) to the plane x + y + z = 1 is √3 units.

To find the shortest distance between a point and a plane, we can use the formula:

distance = |ax + by + cz + d| / √(a² + b² + c²)

where a, b, and c are the coefficients of the plane's equation, d is the constant term, and (x, y, z) is the coordinates of the point.

In this case, the plane is x + y + z = 1, so a = 1, b = 1, c = 1, and d = -1. The point is (2, 0, -3), so x = 2, y = 0, and z = -3. Plugging in these values, we get:

distance = |1(2) + 1(0) + 1(-3) - 1| / √(1² + 1² + 1²)

= 3 / √3

= √3

Therefore, the shortest distance from the point (2, 0, -3) to the plane x + y + z = 1 is √3 units.

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Answer:

Developing a research topic is difficult when your trying to make sure it ties in all the information you need to prove your points and give reasoning

Step-by-step explanation:

The height of the building is 71 meters.

We can solve this problem using the similar triangles. The height of the building can be determined by setting up the following proportion:

(the height of pole) / (length of pole's shadow) = (height of building) / (length of building's shadow)

Substituting the given values:

2.8 / 1.49 = (height of building) / 37.5

To find the height of the building, we can cross-multiply and solve for it:

(2.8 * 37.5) / 1.49 = height of building

Calculating the expression on the right side:

(2.8 * 37.5) / 1.49 ≈ 70.7013

Rounding to the nearest meter, the height of the building is approximately 71 meters.

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Answer:

Thanks

Step-by-step explanation:

n Quadrant I, both the x– and y-coordinates are positive; in Quadrant II, the x-coordinate is negative, but the y-coordinate is positive; in Quadrant III both are negative; and in Quadrant IV x is positive but y is negative

Answer:

quadrant 4

Step-by-step explanation:

quadrant 1 is positive x positive y

quadrant 2 is negative x  positive y

quadrant 3 is negative x negative y

quadrant 4 is positive x negative y  

The triangle with the lengths 2m, 5m and 6m is not a right triangle, as the lengths do not form a Pythagorean triple.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The sum of the two smaller sides squared is given as follows:

2² + 5² = 4 + 25 = 29.

The square of the largest side is of:

6² = 36.

As 29 is different of 36, the Pythagorean Theorem is not respected, and thus the triangle is not a right triangle.

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Claire fed Folly at 2 pm, gave Folly to Max at 2:10 pm. Folly belonged to either Max or Claire at 2:05 pm. Neither Mar nor Claire fed Folly at 2 pm or 2:05 pm. The event occurred between 1:55 pm and 2:05 pm. At 2 pm, Max took Folly from Claire. Folly wasn't hungry at 2 pm but was at 3 pm.

1. student(Mar) ∧ ¬pet(Mar)2. fed(Claire, Folly, 2pm) ∧ gave(Claire, Folly, Max, 2:10pm)3. (belongs(Folly, Max, 2:05pm) ∨ belongs(Folly, Claire, 2:05pm))4. ¬(fed(Mar, Folly, 2pm) ∨ fed(Claire, Folly, 2pm) ∨ fed(Mar, Folly, 2:05pm) ∨ fed(Claire, Folly, 2:05pm))5. between(2pm, 1:55pm, 2:05pm)6. ¬hungry(Folly, 2pm) ∧ hourLater(Folly, 2pm, 3pm)

1. Student(Mar) ∧ ¬Pet(Mar)2. Fed(Claire, Folly, 2pm) ∧ Gave(Claire, Folly, Max, 2:10pm)3. BelongsTo(Folly, Max, 2:05pm) ∨ BelongsTo(Folly, Claire, 2:05pm)4. ¬(Fed(Mar, Folly, 2pm) ∨ Fed(Claire, Folly, 2pm) ∨ Fed(Mar, Folly, 2:05pm) ∨ Fed(Claire, Folly, 2:05pm))

5. Between(2:00pm, 1:55pm, 2:05pm)6. Gave(Max, Folly, Claire, 2pm) ∧ ¬Hungry(Folly, 2pm) ∧ Hungry(Folly, 3pm)

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Answer:

P times R times T

5000 times 4 times 8,

divided by hundred.

Therefore the answer is = 160 dollars

Answer:

Step-by-step explanation:

We can solve this in either of two approaches:  Mathematically or Graphically.

Mathematically

y=-(3/4)(x-4)^2+12  where y is the height of the ball, and x is the time, in seconds.

We want to know how many seconds for the height to be 0, so y=0.

0 = -(3/4)(x-4)^2+12

-12 = -(3/4)(x-4)^2

12*(4/3) = (x-4)^2

16 = (x-4)^2

x = 8 and 0 (the initial point).]

It will reach the ground in 8 seconds

Graphically

Plot the function and find the time, x, when the graph passes through the x axis (after t = 0).  Attached.

Answer: 9

Step-by-step explanation:

If 19 students take history, 12 take economics and 5 take both:

19-5 = 14 students that take only history

12-5 = 7 students that take only economics

Therefore total number of students who either history, economics or history and economics: 14 + 7 + 5 = 26

Therefore students who take neither: 35 - 26 = 9

students who take neither: 35 - 26 = 9.

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

In a class of 35 students, 19 take history and

12 take economics. If 5 take both subjects,

now,

If 19 students take history, 12 take economics and 5 take both:

19-5 = 14 students that take only history

12-5 = 7 students that take only economics

Therefore total number of students who either history, economics or history and economics: 14 + 7 + 5 = 26

Therefore students who take neither: 35 - 26 = 9

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Alicia's estimate of the surface area of the rectangular prism is not reasonable based on her miscalculation of the volume.

To determine whether Alicia's estimate of the surface area of the rectangular prism is reasonable, we first need to check if her calculation of the volume of the rectangular prism is correct.

The formula for calculating the volume of a rectangular prism is:

Volume = length x width x height

Substituting the given values in the formula, we get:

Volume = 11 meters x 5.6 meters x 7.2 meters

Volume = 449.28 cubic meters

As we can see, Alicia's estimate of 334 cubic meters is significantly lower than the actual volume of the rectangular prism, which is 449.28 cubic meters. Therefore, her estimate of the surface area is likely to be incorrect as well.

It is also important to note that the problem statement asks about the estimate of the surface area, not the volume. However, since the formula for calculating the surface area of a rectangular prism also involves the dimensions of length, width, and height, it is highly likely that Alicia's estimate of the surface area would also be incorrect given her miscalculation of the volume.

In conclusion, Alicia's estimate of the surface area of the rectangular prism is not reasonable based on her miscalculation of the volume.

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The probability that none of the ten freshmen graduates from the local community college is approximately 0.006 or 0.6%.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

Assuming that the probability of each freshman graduating is independent of the others, the probability that none of the ten freshmen graduates is -

\(P = (0.6)^{10}\)

= 0.0060466176

Here, we are using the fact that the probability of a freshman not graduating is 1 - 0.4 = 0.6.

So, the probability value is obtained as 0.006 or 0.6%.

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We can solve this problem using a system of linear equations, have in mind the expression for simple interest:

Let x be the principal invested on the first account.

Let y be the principal invested on the second account.

We can solve the system by the method of substitution, isolate the variable y in equation (1):

Now, substitute (1) into equation (2) to get x-value:

Austin invested $16,000 on the first account.

Then, substitute the x-value in the equation (1) to get y-value:

Austin invested $14,000 on the second account.

The probability that the ace of diamonds and a black card will come is 1 / 51 .

Case A :

probability of first getting an ace of diamonds = 1 / 52

probability of getting a black card given first card is ace of diamond = 26 / 51

Hence , probability that the ace of diamonds and a black card will come is  ( 1 / 52 ) * ( 26 / 51 ) = ( 1 / 102 )

Case B :

probability of first getting a black card = ( 26 / 52 )

probability of getting an ace , given first card is a black card = ( 1 / 51 )

Hence , the probability that the ace of diamonds and a black card will come is  ( 26 / 52 ) * ( 1 / 51 ) = ( 1 / 102 )

P ( A ∪ B ) = P ( A ) + P (B ) + P ( A ∩ B )

                  = ( 1 / 102 ) + ( 1 / 102 )

                = 1 / 51 .

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Answer:

See Explanation

Step-by-step explanation:

The question has missing details; as the radius or an attachment of the hemisphere is not given.

However, I'll solve on a general terms.

The volume of a hemisphere is: \(V = \frac{2}{3}\pi r^3\)

Take for instance

\(r = 14.9cm\)

The volume becomes:

\(V = \frac{2}{3} * 3.142 * 14.9^3\)

\(V = \frac{2 * 3.142 * 14.9^3}{3}\)

\(V = \frac{20787.151516}{3}\)

\(V = 6929.051cm^3\)

So, all you need to do is plug in the value of radius in the formula.

The linearized equation around its equilibrium position is given as;f(x) = -4.8(x - 1.39)

The given equation is x² + 2x* + 2x² - 12x + 10 = 0.

It needs to be linearized around its equilibrium position.

Linearizing the given equation around its equilibrium position x0, we have;

f(x) = f(x0) + f'(x0)(x - x0)

Where f(x) = x² + 2x* + 2x² - 12x + 10

The equilibrium position is the point where f(x) = 0.

Hence, f(x0) = 0.

Thus, x² + 2x* + 2x² - 12x + 10 = 0⇒ 3x² - 6x = -10⇒ x² - 2x + (2.33) = 0(x-1)² = 0.77x - 0.77 or

x = 1 + (0.77)/(2) or x = 1.39

Hence, the equilibrium position x0 = 1.39.

Substitute x0 = 1.39 in the equation and simplify to get f'(x0):

f(x) = x² + 2x* + 2x² - 12x + 10

f(x) = 3.84 - 8.34 + 10

f'(x0) = f'(1.39) = -4.8

Therefore, the linearized equation around its equilibrium position is given as;f(x) = -4.8(x - 1.39)

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The formula or equation used to determine the slope of a straight line is as follows:

m = (Y₂-Y₁)/(X₂-X₁)

An equation is about two expressions, either arithmetic or algebraic, that are related with a "=" sign that indicates equality of expressions.

Equations can be graphed, they are used to model many problems and theories.

The straight lines are characterized by a finite succession of points, when they have an inclination they adopt a slope value different from 0, and to determine that slope it is necessary to know two points of the line and use the following equation:

m = (Y₂-Y₁)/(X₂-X₁)

Where the points are:

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Answer:

2%

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

Here is your answer

HOPE IT IS USEFUL

47 degrees

Step-by-step explanation:

Answer:

i believe the answer is 47 degrees

288 dinner specialist

1 Appetizer = 3  C₁

1 Salad = 2  C₁

1 Entree = 4  C₁

1 Side dish = 3  C₁

1 desert = 4 C₁

Total =  3  C₁ * 2  C₁ *  4  C₁ * 3  C₁ * 4 C₁

=3* 2 * 4 * 3 * 4

= 288 dinner specialist

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an occurrence is a number between 0 and 1, with 1 representing certainty and 0 representing impossibility. The higher the likelihood of an event, the more likely it is to occur. A straightforward illustration is tossing a fair (impartial) coin. Since there are no other conceivable outcomes and the coin is fair, the odds of both the possibilities, "heads" and "tails," are equally likely to occur. As a result, the probability of either occurrence is half.

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Answer:

Baguette is very important

Step-by-step explanation:

they don't have bidet but baguette

Answer:

honestly i think its a pretty country, its pretty nice and wish i could go.  

Step-by-step explanation:

The standard deviation of the monthly amount charged is 346.41

Step 1: Identify the values of a and b, where [a , b] is the interval over which the continuous uniform distribution is defined.

Since it takes between 300 and 1500 minutes to be seated at the restaurant, we have:

a = 300

b = 1500

Step 2: Calculate the variance using the formula Var(x) = \(\frac{(b-a)^{2} }{12}\)

Using the formula for the variance and the values identified in step 1

(a = 300 , b = 1500), we have:

Var(x) = \(\frac{(b-a)^{2} }{12}\)

         = \(\frac{(1500 - 300)^{2} }{12}\)

         = 1440000/12

         = 120,000

the variance is 120,000

Step 3: Calculate the standard deviation by taking the square root of the variance. σ = \(\sqrt{Var(x)}\)

The standard deviation is the square root of the result from step 2 (variance = 120,000)

σ = \(\sqrt{Var(x)}\)

σ = \(\sqrt{120000}\)

   = 346.41

The standard deviation of the monthly amount charged is 346.41

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Answer:

1)

2/5 ≠ 10/15= 2/3 not equivalent

3/7 ≠ 6/7  not equivalent

9/7 = 1 2/7 = 9/7 equivalent

2)

a) 50/75 = 25*2/25*3= 2/3

b) 65/105 = 5*13/5*21= 13/21

c) 18/81 ​= 9*2/9*9= 2/9

The probability that George drove given that he is late is approximately 0.355 or 35.5%.

Let's call the event of George being late "L". The problem is asking for P(Drives | L), which is the probability that George drove given that he is late.

We can use Bayes' theorem to find this probability:

P(Drives | L) = P(L | Drives) * P(Drives) / P(L)

P(L | Drives) is the probability that George is late given that he drove, which is given as 55%.

P(Drives) is the prior probability that George drives, which is given as 20%.

P(L) is the overall probability that George is late, which can be found by summing up the individual probabilities of George being late for each mode of transportation and weighting it by the corresponding prior probability of using that mode of transportation:

P(L) = P(L | Walks) * P(Walks) + P(L | Cycles) * P(Cycles) + P(L | Drives) * P(Drives) + P(L | Bus) * P(Bus)

P(L | Walks) is the probability that George is late given that he walks, which is given as 15%.

P(Cycles) is the prior probability that George cycles, which is given as 30%.

P(Bus) is the prior probability that George takes the bus, which is given as 40%.

P(L | Bus) is the probability that George is late given that he takes the bus, which is given as 20%.

Substituting these values into the formula for P(L) and simplifying:

P(L) = 0.15 * 0.10 + 0.10 * 0.30 + 0.55 * 0.20 + 0.20 * 0.40

= 0.155

Finally, substituting the values for P(L | Drives), P(Drives), and P(L) into the formula for P(Drives | L) and simplifying:

P(Drives | L) = 0.55 * 0.20 / 0.155 = 0.55 / 0.155 = 3.548

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The article titled "The comparisons of data mining techniques for the predictive accuracy of probability of default of credit card clients" by Yeh and Lien (2009) explores the different variables or factors that could impact the probability of default, such as income, credit history, and demographic information.

Yeh and Lien (2009) aim to compare these techniques and determine which ones provide the most accurate predictions.
Predictive accuracy refers to how well a model or technique can accurately predict an outcome or event. In this case, the authors are interested in predicting the probability of default for credit card clients. Probability refers to the likelihood or chance of something happening. In the context of credit card clients, it refers to the likelihood of a client defaulting on their credit card payments.
The study compares various data mining techniques to assess their predictive accuracy for determining the probability of default. These techniques may include algorithms, statistical models, or machine learning methods. The factors that could impact the probability of default, such as income, credit history, and demographic information etc. are analyzed in the article.
By comparing the different techniques, the authors aim to identify which one provides the most accurate predictions. This information can be useful for credit card companies or financial institutions to assess the creditworthiness of their clients and make informed decisions regarding credit limits, interest rates, or loan approvals.

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Hence, in answering the stated question, we may say that We can travel slope intercept down 3 units and right 1 unit to acquire another point on the line because the slope is -3.

The intersection point in mathematics is the point on the y-axis where the slope of the line intersects. a point on a line or curve where the y-axis intersects. The equation for the straight line is Y = mx+c, where m represents the slope and c represents the y-intercept. The intercept form of the equation emphasises the line's slope (m) and y-intercept (b). The slope of an equation with the intercept form (y=mx+b) is m, and the y-intercept is b. Several equations can be reformulated to seem to be slope intercepts. When y=x is represented as y=1x+0, the slope and y-intercept are both set to 1.

We must solve for y in order to find the slope-intercept form of the equation:

6x + 2y = 4

2y = -6x + 4

y = -3x + 2

As a result, the slope is -3 and the y-intercept is 2.

To graph the line, first plot the y-intercept at the point (0, 2). The slope can then be used to find another point on the line. We can travel down 3 units and right 1 unit to acquire another point on the line because the slope is -3.

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Answer:

The triangles are not similar

Step-by-step explanation:

We can see that TU and EU are equal in length but SU and DU are not hence they are not similar

Answer:

c 136 degrees

Step-by-step explanation:

Answer:232 inch^2

Step-by-step explanation:to solve, add the surface area of each side. Remember, there are 3 pairs of sides and the pairs have equal area. Area =length x length. So we have 2x(8x2)+2x(2x10)+2x(10x8) in square inches.