An arts academy requires there to be 4 teachers for every 100 students and 3 tutors for every 30 students. How many students does the academy have per teacher? Per tutor? How many Tito’s does the academy need if it has 110 students?

The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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The given events are mutually exclusive events.

Since we know that,

Two occurrences are said to be mutually exclusive in probability theory if they cannot occur at the same time or concurrently.

In other words, discontinuous events are those that are mutually exclusive. If two occurrences are regarded discontinuous, the likelihood of both happening at the same time is zero.

If A and B are the two occurrences, then the probability of their disjoint is stated as:

P (A and B) = 0 for the probability of a disjoint (or mutually exclusive) event.

The given events are;

Event A: Drawing a face card from a deck of cards.

Event B: Drawing a 5 from a deck of cards

These are mutually exclusive, because a face card is not a 5 and a 5 is not a face card, both occurrences are mutually exclusive.

When you draw a card from a deck, it can only be one card with one value, therefore it can't be a face card and a 5.

As a result, the occurrence of one event precludes the occurrence of the other.

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Answer:

3,975.16 United States Dollar

Step-by-step explanation:

The Pythagoras theorem is not applicable in 24, 22, and 40 thus (D) will be not the side of the right angle triangle.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.

The Pythagoras theorem is given as,

Hyp² = base² + perp²

Since the hyp is the biggest side thus it can be said to be as,

Biggest side² = (smaller side 1)² + (smaller side 2)²

In the  24, 22 and 40,

40² ≠ 22² + 24² thus it will not right an angle triangle,

Hence "In 24, 22, and 40, the Pythagorean theorem is not applicable so it will be not a right angle triangle".

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The race horse's speed is approximately 256 furlongs per fortnight.

To determine the race horse's speed in furlongs per fortnight, we need to convert both the distance and time units to their respective values.

1 furlong is equal to 180 yards, so the horse's speed in yards per second (7 yards/second) can be converted to furlongs per second:

Speed in furlongs per second = (7 yards/second) / (180 yards/furlong) = 7/180 furlongs/second

Next, we need to convert the time from seconds to fortnights. Since a fortnight is a time period of two weeks, and there are 7 days in a week, a fortnight consists of 14 days:

Time in seconds per fortnight = (14 days/fortnight) * (24 hours/day) * (60 minutes/hour) * (60 seconds/minute) = 1,209,600 seconds/fortnight

Finally, we can calculate the horse's speed in furlongs per fortnight by multiplying the speed in furlongs per second by the time in seconds per fortnight:

Speed in furlongs per fortnight = (7/180 furlongs/second) * (1,209,600 seconds/fortnight) = 46,080/180 furlongs/fortnight ≈ 256 furlongs/fortnight

The race horse's speed is approximately 256 furlongs per fortnight.

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Answer:

ΔGAS ≅ ΔIOL By the Angle-Angle-Side (AAS) rule of congruency

Step-by-step explanation:

The given information are;

Statement                                  \({}\)                               Reason

Segment \(\overline {SA}\) is congruent to \(\overline {OL}\)              \({}\)As shown in the diagram provided

∠SAG is congruent to ∠LOI               \({}\)       As shown  in the diagram provided

∠SGA is congruent to ∠LIO               \({}\)       As shown  in the diagram provided

Therefore, ΔGAS ≅ ΔIOL By the Angle-Angle-Side (AAS) rule of congruency

Given that the the number of interior angles of triangle = 3 and the sum of the interior angles of a triangle = 180°, the third angle can be defined by specifying the measure of two of the angles

Therefore, the Angle-Angle (AA) rule of similarity can be used to prove the congruency of two triangles when they have one side of each triangle which are congruent.

Answer:

∆GAS ≅ △IOL By rule ASA, AAS

Step-by-step explanation:

By looking at the triangle, you can see two little quarter-circle things inside the triangle (I don't know what they are called). That means it has 2 angles.  We already know that it can't be SSS or SAS because we have 2 angles, as I said.

If you look at the triangle's sides, you can see that there is a side with a dash on it. That means that it is a side in ASA, AAS, etc. So there we go. We've figured it out. There is one side and two angles.  Therefore, our answer is ASA or AAS

The value of y when x = 4 is 3.

In this given condition statement, if x is greater than 5, the value of y is 1. If x is less than 5, there is an additional condition.

If x is less than 3, the value of y is 2.

Otherwise, if x is not less than 3, the value of y is 3. Lastly, if x is equal to 5, the value of y is 4.

In the case of x = 4, x is less than 5 but not less than 3.

Therefore, the condition statement within the else condition is satisfied, resulting in the value of y being 3.

This means that when x is equal to 4, the value of y equals 3 as per the given conditions.

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Answer:

5

Step-by-step explanation:

Let the number of children who rode the bus be C and the number of adults who rode the bus be A. Here's how to solve this problem:

Step-by-step explanation: We are given the following information:

Total number of passengers = 1000 Children's fare = $0.50. Adult fare = $1.75. Total revenue from fares = $1500. Let C be the number of children who rode the bus during the morning shift. Therefore, the number of adults who rode the bus will be (1000 - C). The total revenue from fares is given as:$0.50 × C + $1.75 × (1000 - C) = $1500. Simplifying this equation gives us: 0.5C + 1750 - 1.75C = 1500-1.25C = -250C = 200. Therefore, the number of children who rode the bus is C = 200. Therefore, the number of adults who rode the bus is:1000 - C = 1000 - 200 = 800.

Therefore, the number of adults who rode the bus during the morning shift is 800.

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Step-by-step explanation:

3y + 4) - (2y - 7)

=3y-2y-7+4

=y-3

Answer:

y+11

Step-by-step explanation:

Distribute and remove parentheses.

3y + 4 - 2y +7

Combine Like-Terms:

y + 11

Answer:

Un ejemplo de una recta numérica es lo que un estudiante de matemáticas puede usar para encontrar la respuesta a las preguntas de suma y resta. Una línea recta, teóricamente que se extiende hasta el infinito en direcciones tanto positivas como negativas desde cero, que muestra el orden relativo de los números reales.

explanation:

what is the number line

An example of a number line is what a math student can use to find the answer to addition and subtraction questions. A straight line, theoretically extending to infinity in both positive and negative directions from zero, that shows the relative order of the real numbers.

Combining the complementary and particular solutions, the general solution is y(x) = C1e²ˣ+ C2e⁻²ˣ+ Ax² + Bx + C + De⁻ˣ.

To find the general solution for y'' - 4y = 4x² + 10e⁻ˣ using undetermined coefficients, we first identify the complementary and particular solutions.

The complementary solution, yc(x), is obtained from the homogeneous equation y'' - 4y = 0. This leads to the characteristic equation r² - 4 = 0, which has roots r1 = 2 and r2 = -2. Therefore, yc(x) = C1e²ˣ + C2e⁻²ˣ.

For the particular solution, yp(x), we assume a form of Ax² + Bx + C + De⁻ˣ. Differentiate yp(x) twice and substitute it into the given equation. Then, solve for the undetermined coefficients A, B, C, and D.

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Answer:

D

Step-by-step explanation:

a) The logarithmic regression equation is y = -2.37 + 0.76 ln x b) the value of the investment after 12 years is approximately $11,270.

A regression equation is a mathematical formula used to model the relationship between a dependent variable (Y) and one or more independent variables (X). The goal is to find the line of best fit that describes the relationship between the variables, allowing for predictions or estimations to be made.

In linear regression, the equation takes the form Y = a + bX, where a is the y-intercept, b is the slope, X is the independent variable, and Y is the dependent variable. The regression equation can be used to calculate the expected value of Y for a given value of X, or to estimate the value of X that corresponds to a given value of Y.

a) To find the logarithmic regression equation, we need to find values for a and b in the equation y = a + b ln x that best fit the given data. We can use a calculator or software to do this, but here is one way to do it by hand:

Let's start by writing the given data in the form (x, y):

(2600, 1)

(2812, 3)

(3041, 5)

(3289, 7)

(3557, 9)

Next, we can use the formulas for the mean of x, y, ln x, and y ln x:

¯x = (2600 + 2812 + 3041 + 3289 + 3557) / 5 = 3060

¯y = (1 + 3 + 5 + 7 + 9) / 5 = 5

¯ln x = (ln 2600 + ln 2812 + ln 3041 + ln 3289 + ln 3557) / 5 ≈ 7.886

¯y ln x = (1 ln 2600 + 3 ln 2812 + 5 ln 3041 + 7 ln 3289 + 9 ln 3557) / 5 ≈ 37.002

Using these means, we can find b:

b = [¯y ln x - ¯y ¯ln x] / [¯ln x^2 - (¯ln x)^2] ≈ 0.764

Finally, we can use b and one of the data points to find a:

1 = a + 0.764 ln 2600

a ≈ -2.366

Therefore, the logarithmic regression equation is:

y = -2.37 + 0.76 ln x

b) To find the value of the investment after 12 years, we plug x = 12 into the regression equation and solve for y:

y = -2.37 + 0.76 ln 12 ≈ 11.27

Therefore, the value of the investment after 12 years is approximately $11,270.

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The value of x =26°, m∠p =116°, m∠q=21°, m∠r=43°

What is an angle?

An angle is formed when two lines meets at the same vertex. It is measured by degree. Based on the measurements angles are of three types.

Consider POR as a triangle.

Given that m∠p=5x-14, m∠q=x-5, m∠r=2x-9.

In triangle the sum of the angle is 180°, then

m∠p + m∠q +m∠r =180°

⇒5x-14+x-5+2x-9 = 180°

⇒8x-28=180°

⇒x=26°

then, m∠p=5x-14 = 5(26)-14 = 116°

m∠q=x-5 = 26-5=21°

m∠r=2x-9 = 2(26)-9=43°

Hence, the value of x =26°, m∠p =116°, m∠q=21°, m∠r=43°

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The yy-component of vector a a is -y-direction, which is equal to 0 m/s2.the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.

Given a vector, a⃗ a→ = (5.0 m/s2, −y−direction)Find the yy -component of the given vector a⃗ a→.Solution: The yy-component of the given vector a⃗ a→ = -y-directionTo find the yy-component of the given vector a⃗ a→, we have to take the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.Therefore, the yy-component of vector a⃗ a→ is :a_yy = -y-direction = (-1)(0) = 0 m/s²  Answer: 0 m/s².

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The yy-component of vector a⃗ a→ is -y-direction.

The yy-component of a vector represents the magnitude of the vector in the y-direction.

In this case, the vector a⃗ a→ is given as (5.0 m/s2, −y-direction).

Since the yy-component is the magnitude in the y-direction, the yy-component of the vector a⃗ a→ is -y-direction.

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Answer:

sometimes

Step-by-step explanation:

You can never divide a non-zero number, such as 3 or 7, by zero. However, you can divide zero by zero, so the answer is sometimes.

Hope this helped! :)

Answer:

sometimes

Step-by-step explanation:

Answer:

8 and 2

Step-by-step explanation:

I don't know if its right btw

Answer:

12x + 7 is the answer

Step-by-step explanation:

Answer:

5.6667in

Step-by-step explanation:

I can't show you the diagram at the moment but I hope that helps.

Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .

Answer: 3.5

Step-by-step explanation:

DE for T(t): \frac{\partial^0 T(t)}{\partial t^0} = 0 This implies that the function T(t) does not depend on t.

Given partial differential equation for u(x, t):t³urx + xUxt − xu₁ = 0DE for X(x): = 0• DE for T(t): 0 Here, t is the time and x is the position. In the given partial differential equation, the first term is with respect to x, second term is with respect to t and the third term is constant with respect to both x and t.t³urx + xUxt − xu₁ = 0 We can simplify the above partial differential equation by expressing it using the variables as follows: t^3 \frac{\partial u}{\partial x} + x \frac{\partial u}{\partial t} - xu_1 = 0 DE for X(x): \frac{\partial^0 X(x)}{\partial x^0} = 0.

This implies that the function X(x) does not depend on x. DE for T(t): \frac{\partial^0 T(t)}{\partial t^0} = 0 This implies that the function T(t) does not depend on t.

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(a) To plot the point (6, 1/3, 1/6), we first convert to Cartesian coordinates as follows:

x = r sinφ cosθ = 6(1/3)cos(1/6π) ≈ 2.991

y = r sinφ sinθ = 6(1/3)sin(1/6π) ≈ 0.499 z = r cosφ = 6 cos(1/3π) ≈ 5.196

Therefore, the rectangular coordinates of the point (6, 1/3, 1/6) are approximately (2.991, 0.499, 5.196).

(b) To plot the point (3, 7/2, 37/4), we first convert to Cartesian coordinates as follows:

x = r sinφ cosθ = 3(1/2)cos(37/8π) ≈ -1.149

y = r sinφ sinθ = 3(1/2)sin(37/8π) ≈ -1.172 z = r cosφ = 3 cos(7/4π) ≈ -1.097

The rectangular coordinates of the point (3, 7/2, 37/4) are approximately (-1.149, -1.172, -1.097).

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Answer:

Well, I think that the 50% coupons would give you only 50% off of your entire purchace. Not 100% off.

Step-by-step explanation:

The predicted values of A, B, C, and D are: A = 595B = -0.5C = 600D = $6350, therefore, the correct option is IC.

Given,

Mean of X = 600

Standard deviation of X = 10

Mean of Y = $5000

Standard deviation of Y = 1000

Correlation r= 0.9

Future value of X = 595

Z score of X = (X- Mean of X) / Standard deviation of X= (595-600) / 10 = -0.5

Using the formula, Predicted y = average of y+ r* (Z score of X)* standard deviation of y

Predicted y = $5000 + 0.9 * (-0.5) * 1000 = $4750

The predicted value of Y for X = 595 is $4750.

Now, to find the values of A, B, C, and D; we need to calculate the Z score of X = 615 and find the corresponding predicted value of Y.

Z score of X = (X- Mean of X) / Standard deviation of X= (615-600) / 10 = 1.5

Predicted y = average of y+ r* (Z score of X)* standard deviation of y

Predicted y = $5000 + 0.9 * (1.5) * 1000 = $6350

The predicted value of Y for X = 615 is $6350.

Hence, the values of A, B, C, and D are: A = 595B = -0.5C = 600D = $6350

Therefore, the correct option is IC.

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Answer:

∠ACB = 72

Step-by-step explanation:

OAD is straight line.

∠DAB +  ∠OAB  = 180

142 + ∠OAB  = 180

          ∠OAB = 180 - 142

          ∠OAB =  38

ΔAOB is isosceles triangle. OA = OB = radius

∠OAB = ∠OBA = 38   {angles opposite to equal sides or equal}

In ΔAOB ,

∠OAB + ∠OBA + ∠AOB = 180   {Anlge sum property of triangle}

   38 + 38 + ∠AOB = 180

               76 + ∠AOB = 180

                       ∠AOB = 180 - 76

                       ∠AOB = 104

THe angle subtended by an arc of a circle at the center is double the angle subtended by it at any point on the remaining part of the circle

∠AOB =  2*∠ACB

∠ACB = ∠AOB/2

         = 104/2

∠ACB = 72

The area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

a. To find the area to the right of z = -1 for the standard normal distribution, we need to calculate the cumulative probability using the standard normal distribution table or a statistical calculator.

From the standard normal distribution table, the area to the left of z = -1 is 0.1587. Since we want the area to the right of z = -1, we subtract the left area from 1:

Area to the right of z = -1 = 1 - 0.1587 = 0.8413

Therefore, the area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

b. To answer this question, we would need additional information about the mean and standard deviation of the annual salaries for first-year college graduates. Without this information, we cannot calculate specific probabilities or make any statistical inferences.

If we are provided with the mean (μ) and standard deviation (σ) of the annual salaries for first-year college graduates, we could use the properties of the normal distribution to calculate probabilities or make statistical conclusions. Please provide the necessary information, and I would be happy to assist you further.

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Answer:

1.  (12,−5)⋅(5,6)

2. (−5,8)+(2,4)

3. (12,−5)−(5,6)

There are 450 triangles, we can pick that do not form an equilateral triangles when 15 dots are evenly spaced on the circumference of a circle.

Let's calculate the total no. of possible triangles, it depends on the combination. To make a triangle, we have to choose 3 dots out of 15.

Here, we will use the combination rule to find out the possible triangles,Thus, the total number of possible triangles = 15C3                                                                      = (15.14.13) / (1.2.3) = 455

Note that an equilateral triangle would be formed by connecting 3 equally spaced dots.

For an equilateral triangle, out of 15 dots, there would be 15 - 3 = 12 dots that will not be connected.

And 12/3 = 4 dots would be between any two connecting dots.

Taking 1st connecting dot, the second connecting dot would be

1 + 4 + 1 = 6th

Similarly, the third connecting dot would be 6 + 4 + 1 = 11th

So, the following connecting dots will form equilateral triangles: (1, 6, 11); (2, 7, 12); (3, 8, 13); (4, 9, 14); (5, 10, 15);

After applying the combination rule we found the total number of the possible triangle and there are 5 equilateral triangles:

So, there are 455 - 5 = 450 triangles that are not equilateral triangles.

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