The tendency to perceive meaningful patterns in random sequences of outcomes often leads us to underestimate the extent to which outcomes result from.

The coordinates of the point on the unit circle corresponding to a central angle of 21 degrees are (0.93, 0.36), which is answer choice c.

The point on the unit circle corresponding to a central angle of 21 degrees can be found using the trigonometric functions sine and cosine.

In this case, the x-coordinate is equal to the cosine of the angle and the y-coordinate is equal to the sine of the angle.

Converting degrees to radians, we have:

x = cos(21) = 0.93

y = sin(21) = 0.36

A unit circle in mathematics is a circle with a radius of one, or one unit. The unit circle is frequently the circle with radius 1 that is located at the origin (0, 0) in the Cartesian coordinate system on the Euclidean plane, notably in trigonometry.

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With the help of standard deviation we can conclude our answer.

acc to our question-

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Answer:

that would be 12.5

Step-by-step explanation:

The probability that at least one number cube show a 2, given that the sum is even is 5/36   .

In the question ,

it is given that ,
two standard cube are rolled ,

we have to find the probability that at least one number cube show a 2, given that the sum is even ,

we know that on rolling two dice ,

the total number of outcomes is = 36 ,

the outcomes in which one cube shows 2 are ,

{ (1,2) , (2,2) , (2,3) , (2,4) , (2,5) , (2,6) , (2,1) , (3,2), (4,2) , (5,2) ,(6,2) }

and the outcomes in which the sum is even is :

{ (2,2) , (2,4) , (2,6), (4,2) , (6,2) }

So , the number of favorable outcomes is = 5 ,

So , the probability is = 5/36

Therefore , the required probability is = 5/36 .

The given question is incomplete the complete question is

You roll two standard number cube . What is the probability that at least one number cube show a 2, given that the sum is even ?

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Answer:

56

Step-by-step explanation:

according to the sum of the exterior angles of  a polygon, we get that the exterior angles of this polygon add up to 360

so our equation is: 9x-31+7x-2+4x+33=360,

the -31-2+33 cancel out,

and combining like terms gives us: 20x=360

so x=18,

from here we know that DCE equals to 180-7x+2, because it is an exterior angle, therefore the angle is 180-126+2, which is 56

The required equation that is perpendicular to the line y = -¾ x - 14 and goes through the point (0, 13) is 3x + 4y = 52 .

Given equation is y = - 3/4 - 14

this is of the form y = mx + c

on comparing, m= - 3/4

And the points given are x = 0 and y =13

thus as we know that the equation of the line is

y - y₁ = m ( x- x₁ )

On substituting the values mentioned above we see that

y - 13 = - 3/ 4 ( x - 0 )

4 y - 52 = - 3 x

and on rearranging we get :

3x + 4y = 52

Thus the required equation that is perpendicular to the line y = -¾ x - 14 and goes through the point (0, 13) is 3x + 4y = 52 .

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The total number of combinations of the numbers 1 through 10, using only 5 integers, that can combine to add up to 15 is the product of the number of ways in which we can choose 5 integers out of 10 and the number of ways in which we can divide these 5 integers into 4 parts such that their sum is 15. This is equal to 252 × 21 = 5292. The total number of combinations is 5292.

We can use a combination formula which is given by C(n,r) = n! / (r! * (n-r)!).Here, n is the total number of integers available (10 in this case) and r is the number of integers we are choosing (5 in this case).So, we can choose any 5 integers out of 10 in C(10,5) ways which is equal to 252.
Then, we need to find the number of ways in which these 5 integers can combine to add up to 15. We can use a stars and bars method to do that.Let's assume that we have 5 stars representing the 5 integers we chose. Now, we need to divide these stars into 4 parts using 3 bars, such that the sum of stars on the left of the first bar, between the first and second bars, between the second and third bars, and on the right of the third bar, adds up to 15.Each bar divides the stars into two groups.
So, we can say that we are placing 3 identical objects (bars) in a row of 5 identical objects (stars). Using a combination formula, the number of ways in which we can place 3 identical objects in a row of 5 identical objects is C(5+3-1, 3-1) = C(7, 2) = 21.So, the total number of combinations of the numbers 1 through 10, using only 5 integers, that can combine to add up to 15 is the product of the number of ways in which we can choose 5 integers out of 10 and the number of ways in which we can divide these 5 integers into 4 parts such that their sum is 15.

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Answer:

15.2

Step-by-step explanation:

She makes 31% of her foul shots

she took 49 shots

the number of foul shots is 31% of 49 shots

=31% * 49

=0.31 * 49

= 15.19

The answer to the question is that we cannot determine the rate of change of the expected GPA with respect to the SAT score without additional information.

The partial rate-of-change function needed to answer this question is the partial derivative of G(h, s) with respect to s, denoted as ∂G/∂s.

Using the chain rule of differentiation, we can write:

∂G/∂s = (∂G/∂h) x (dh/ds) + (∂G/∂s)

where dh/ds is the rate of change of high school GPA with respect to SAT score.

To evaluate the partial derivative at (h,s) = (3.6, 1104), we need to compute both ∂G/∂h and dh/ds at that point. However, the problem does not provide any information about the functional form of G(h, s) or the relationship between high school GPA and SAT score. Without that information, it is not possible to calculate the partial rate-of-change function or the requested derivative.

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Key takeaways of Cross Tab and Scatter plots (Reflecting on visual models):

We can develop insights and knowledge about our world by manipulating and visualizing data, in particular by finding patterns. Cross Tab is a powerful method of data analysis that helps to compare the relationship between two or more variables. The scatter plot is one of the most effective tools to visualize two-variable data.

The main takeaways from cross-tabulation and scatter plots include:

In conclusion, both cross-tabulation and scatter plots are effective tools for data analysis that can help to identify patterns and relationships between variables. When investigating two columns of data we can observe patterns of different values that move together (are correlated). We cannot know for certain the cause of the correlation.

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Answer: just graph it using the x and y coordinate points

Step-by-step explanation:

Answer:

(-4, -2)

Step-by-step explanation:

Rewrite the equations to make y the subject, so that it's easier to calculate the points on each line:

Equation 1

x - y = -2

⇒ x + 2 = y

⇒ y = x + 2

Equation 2

2x - 3y = -2

⇒ 2x + 2 = 3y

⇒ y = (2/3)x + 2/3

Calculate 2 points on each line:

Equation 1  (blue line on attached graph)

Substitute x = 0 and x = -2 into Equation 1 to create 2 points:

x = 0:   y = 0 + 2  ⇒ (0, 2)

x = -2:   y = -2 + 2  ⇒ (-2, 0)

Plot the points and draw a line through them.

Equation 2 (red line on attached graph)

Substitute x = 2 and x = -1 into Equation 1 to create 2 points:

x = 2:   y = (2/3)(2) + 2/3  ⇒ (2, 2)

x = -1:   y = (2/3)(-1) + 2/3  ⇒ (-1, 0)

Plot the points and draw a line through them.

Solution

The solution is the point where the two lines intersect.

Therefore, the point of intersection is (-4, -2)

Chords and arcs

YM is the chord of the circle and it has a length of 12 in

The perpendicular VL bisects the chord in V.

To prove the above statement, please note that triangles VYL and VLM are similar because they have one side in common and the second side of the same length (the radius of the circle).

Let's work with any of those triangles, for example, VLY. It's a right triangle in V. The hypotenuse of the triangle is the radius, one leg is the given distance of 5 in and the other leg is half the length of the chord (6 in).

Thus, applying Pythagora's Theorem:

Thus, the radius is

r=7.8 in

Option b.

The given statement, "O D. 3.8 seconds describes the translation of the graph y=3(x+5)2 - 1 to the graph of" implies that the original graph of y=3(x+5)2 - 1 has undergone a transformation.

Specifically, the new graph is the result of translating the original graph by some amount in the horizontal direction. The time period for this translation is 3.8 seconds. It's important to note that this statement doesn't provide any further information on the nature or direction of the translation.

However, it is clear that the transformation has caused the new graph to be different from the original graph in terms of its position along the x-axis.
The term "translation" in the context of graphs refers to the process of moving a function or its graph from one position to another without changing its shape or orientation. In this case, the given function is y = 3(x + 5)^2 - 1.

The graph of this function is a parabola that opens upward. The translation describes the transformation from the graph of the basic quadratic function y = x^2 to the graph of the given function. The translation can be described as a horizontal shift of 5 units to the left and a vertical shift of 1 unit downward.

This is because the function y = 3(x + 5)^2 - 1 has the form y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola. In this case, the vertex is (-5, -1), indicating the described translation.

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Answer:

7 students in each van and 52 students in each bus.

Step-by-step explanation:

v = no of students in van, b = no of student in bus

High school A ⇒ 3v + 6b = 333 ---------- Equation (1)

High school B ⇒ 11v + 6b = 389 ------------ Equation (2)

Solve equation (1) & (2) simultaneously :

11v + 6b = 389

3v + 6b = 333

----------------------- MINUS

8v + 0 = 56

v = 56 / 8

v = 7

Put v = 7 into Equation (1) to get b:

3v + 6b = 333

3 (7) + 6b = 333

21 + 6b = 333

6b = 312

b = 312 / 6

b = 52

So there are 7 students in each van and 52 students in each bus.

Answer: 41/20

Step-by-step explanation:

3/8+(-3/8)=0

4/5+5/4=16/20+25/20

16/20+25/20=41/20

41/20

Answer:

(C)On a coordinate plane, 2 rays form an angle. One ray sits on the x-axis.

Step-by-step explanation:

In the coordinate plane, an angle is said to be in standard position when its value is stated with respect to the x-axis.

Therefore, for an angle to be in a standard position, one of its rays must be on the x-axis.

From the given options, only Option C has a ray that sits on the x-axis. Therefore, it is the only angle in standard position.

Answer:

C

Step-by-step explanation:

Number of students at preschool are four-years-old in the program is 6

If 16 students are four-years-old, then the remaining students must be older than four. Let's call the number of older students "x". Then the total number of students is

16 + x

Now we know that 3/8 fraction of the total students attend the full-day program. So we can set up an equation

3/8 (16 + x) = number of students in full-day program

To solve for the number of four-year-old's in the program, we need to find 3/8 of the number of four-year-old's (16). We can do this by multiplying 16 by 3/8

16 x 3/8 = 6

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Answer: 5

Step-by-step explanation: with these problems you're supposed to add all the numbers and then you divide it by the number you're asking to find the probability of so 10/2=5

The probability that the dial stops on a red slice, when it is spun and stops on a slice at random is 1/5.

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

A spinner with 10 equally sized slices has 2 red slices, 4 yellow slices, and 4 blue slices.

The total number of slices is 10 and the total number of favorable outcome to get a red slice is 2. Thus, the probability that the dial stops on a red slice is,

\(P=\dfrac{2}{10}\\P=\dfrac{1}{5}\)

Thus, the probability that the dial stops on a red slice, when it is spun and stops on a slice at random is 1/5.

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f(x) and g(x) are not closed under subtraction because when subtracted, the result will be a polynomial, the correct option is B.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.

Given f(x) and  g(x) two polynomial functions in the standard form of the polynomial,

According to Closure Property, when something is closed, the output will be the same as the input.

The polynomials f(x) and g(x) can be seen in the image.

On subtracting the two polynomials, the output will be a polynomial and so it is closed under subtraction.

Therefore, The reason why f(x) and g(x) are not closed under subtraction is that the outcome of subtraction will be a polynomial, making option B the best choice.

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Complete question:

The fraction of days the cafetaria offered an apple as a fruit choice is 6/10. The equivalent form of decimal is 0.6, the equivalent form of fraction is 3/5, and the equivalent form of percentage is 60%.

A fraction is a ratio of two numbers, mathematically expressed as a/b where a is the numerator and b is the denominator. That mathematical expression is the common form of fraction. Fractions can take a number of forms, such as decimal and percentage.

Decimals are numbers that consist of two parts, which are the whole number part and the fractional part. 0.6 is the decimal form of fraction 6/10.

Percentage is a relative value that indicates hundredth parts of a quantity. 60% is the percent form of fraction 6/10.

Finally, we can simplify 6/10 to get 3/5:  \(\frac{6}{10} =\frac{6\div 2}{10\div 2}=\frac{3}{5}\).

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Approximately 15,418.646 cubic feet of rice are in the silo when it is 34% full.

To calculate the approximate volume of rice in the silo when it is 34% full, we need to find the volume of a cylindrical segment.

First, let's calculate the height of the rice-filled portion. If the silo is 40 feet tall and it is 34% full, the height of the rice-filled portion is 34% of 40 feet, which is 0.34 * 40 = 13.6 feet.

Now, let's calculate the radius of the rice-filled portion. The diameter of the silo is 16 feet, so the radius is half of the diameter, which is 16 / 2 = 8 feet.

Using the formula for the volume of a cylindrical segment:

V = (1/3) * π * h * (3r^2 + h^2)

where V is the volume, π is approximately 3.14159, h is the height of the rice-filled portion, and r is the radius of the rice-filled portion.

Plugging in the values:

V = (1/3) * 3.14159 * 13.6 * (3 * 8^2 + 13.6^2)

Calculating this expression gives us:

V ≈ 3.14159 * 13.6 * (3 * 64 + 184.96)

≈ 3.14159 * 13.6 * (192 + 184.96)

≈ 3.14159 * 13.6 * 376.96

≈ 15418.646 cubic feet

Therefore, approximately 15,418.646 cubic feet of rice are in the silo when it is 34% full.

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Answer: 5π/3 (5,236)

Step-by-step explanation: Length of the whole circle arc is 2πr, in this case it is 12π. 50° is 50/360 = 5/36 part of the arc, so we can multiply 12π by 5/36 to get an answer. 12π * 5/36 = 5π/3.

Answer:

Step-by-step explanation:

Answer: He will need 49 tiles.

Step-by-step explanation:

Given: The patio will measure 13.5 feet by 43 feet.

Area of patio = 13.5 feet x 43 feet [Area = length x width]

= 580.5 sq. feet

Since area of each concrete tile = 12 sq. inch

Number of concrete tiles required to cover patio = (Area of patio) ÷ (area of each concrete tile)

= 580.5 ÷ 12

= 48.375 sq. inch ≈49

Answer:

Correct

not mutually exclusive events 1 to 12 and red

Correct

mutually exclusive events 1 to 12 and 25 to 36

Correct

not mutually exclusive events 1 to 18 and odd

Correct

mutually exclusive events black and red

Correct

not mutually exclusive events even and black

Step-by-step explanation:

Given:

Thus, the answer of 4/5 divided by 1/10 is 8.

Answer: 20

Step-by-step explanation: 7x+40=180

40-180=140

7x=140

140/70.

Answer:

lateral surface area of the triangular prism = 128 cm²

Step-by-step explanation:

Answer:

The answer is B) 1440cm

Step-by-step explanation:

The equation for finding the lateral surface area of a triangular prism is Al=(A+B+C)h

Therefore you would plug in the numbers to get (10+21+17)30=Al

Once you solve the equation, you should get 1440 as your answer.

Hope this helped :)

If two trains leave towns 978 miles apart at the same time and travel toward each other and one train travels 21 miles per hour faster than the other and if they meet in 6 hours, then the rate of the faster and slower train will be 92mph and 71 mph respectively.

To determine the rate or speed of each train, an algebraic expression can be used.

As one train travels 21 miles per hour faster than the other, consider x to be the speed of the train that travels slower. In this case, an algebraic expression can be given as,

6x + 6(x + 21) = 978

Here, (x + 21) represents the speed of the faster train

6x + 6x + 126 = 978

12x = 978 - 126

12x = 852

x = 852 ÷ 12

x = 71

x + 21 = 71 + 21 = 92

Hence, the rate of the faster train is 92 miles per hour and the rate of the slower train is 71 miles per hour.

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Answer:

10 miles

Step-by-step explanation:

So we know that it flies 5/8 of a mile in 1/16 of an hour. So after flying 5/8 of a mile 16 times, we will reach an hour. So we can do 5/8*16 and we get our answer of 10. So the bee will have traveled ten miles.

Step-by-step explanation:

We are given a theta degree measure of sin in a specific interval. We are asked to find half of that degree measure.

The interval it ask us to find it in is between 2 pi and 5 pi over 2.

That is 360 degrees to 450 degrees. If you use reference angles, that is between the 0 degrees and 90 degrees. So that means our measure is going to be in the 1st quadrant.

Replace x with theta

\( \sin( \frac{x}{2} ) = + - \sqrt{ \frac{1 - \cos(x) }{2} } \)

We dont know cos x but we can use the pythagorean trig theorem to find cos x.

\( \sin {}^{2} (x) + \cos {}^{2} (x) = 1\)

\( \sin {}^{2} ( \frac{4}{5} ) + \cos {}^{2} (x) = 1\)

\( \frac{16}{25} + \cos {}^{2} (x) = 1\)

\( \cos {}^{2} (x) = 1 - \frac{16}{25} \)

\( \cos {}^{2} (x) = \frac{9}{25} \)

\( \cos(x) = \frac{3}{5} \)

Cosine in 1st quadrant is positive so 3/5 is cos x.

Replace 3/5 for cos x.

\( + - \sqrt{ \frac{1 - \frac{3}{5} }{2} } \)

\( + - \sqrt{ \frac{2}{10} } \)

The answer is

\( + - \sqrt{ \frac{2}{10} } \)