a college food court surveyed students to see how many drink tea and how many drink soda. the venn diagram below shows the results. (each number gives the number of students who fall into that venn diagram category.) (a) how many of the students drink soda? (b) how many of the students drink tea or soda (or both)? (c) how many of the students do not drink both tea and soda?

The answer is option (C), that is, the events of rolling a fair die two times are independent. The events are neither disjoint nor exclusive.

When rolling a fair die two times, one can get any one of the 36 possible outcomes equally likely. Let A be the event of obtaining an even number on the first roll and let B be the event of getting a number greater than 3 on the second roll. Let’s see how the outcomes of A and B are related:

There are three even numbers on the die, i.e. A={2, 4, 6}. There are four numbers greater than 3 on the die, i.e. B={4, 5, 6}. So the intersection of A and B is the set {4, 6}, which is not empty. Thus, the events A and B are not disjoint. So option (A) is incorrect.

There is only one outcome that belongs to both A and B, i.e. the outcome of 6. Since there are 36 equally likely outcomes, the probability of the outcome 6 is 1/36. Now, if we know that the outcome of the first roll is an even number, does it affect the probability of getting a number greater than 3 on the second roll? Clearly not, since A∩B = {4, 6} and P(B|A) = P(A∩B)/P(A) = (2/36)/(18/36) = 1/9 = P(B). So the events A and B are independent. Thus, option (C) is correct. Neither option (A) nor option (C) can be correct, so we can eliminate options (D) and (E).

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Answer:  Any equation that is of the form y = -3/4x + b, where b is a real number, will be parallel to y = -3/4x - 2.

Step-by-step explanation:

A parallel line has the same slope as the original line.  Therefore, if the equation of the original line is y = mx+b, m (the slope) will remain the same, while b can change.

The equation  y = -3/4x - 2 has the same slope -3/4, represents a line which is parallel to the line y=-3/4 x -2

A function that can be represented in the form of y =mx +c, is called a Linear Function. where m is the slope and c is the y-intercept.

The slope of the given line can be found as;

A parallel line has the same slope as the original line.  Thus, if the equation of the original line is y = mx+b, m (the slope) will remain the same, while b can change.

Any equation that is of the form y = -3/4x + b,

where b is a real number, will be parallel to the equation.

y = -3/4x - 2.

m = -3/4

The equation  y = -3/4x - 2 has the same slope -3/4, represents a line which is parallel to the line y=-3/4 x -2

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Answer:

B. substitute for X in first equation

The value of the expression \(4\frac{1}{10}\times-4\times\frac{5}{12}\) is \(-6\frac{5}{6}\).

A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.

The given, expression is \(4\frac{1}{10}\times-4\times\frac{5}{12}\).

= (41/10) × (- 4) × (5/12).

= (41×-4×5)/(10×12).

= (-820/120).

= - 82/12.

= - 41/6.

= \(-6\frac{5}{6}\).

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Answer:

x = 2 or 3

Step-by-step explanation:

Diagonal of a rhombus bisects the vertex angles. So,

\(x^{2} =5x-6\)

\(=> x^{2} -5x + 6 = 0\)

Lets factorise the eqn.

\(=> x^{2} - 2x - 3x + 6 = 0\)

\(=> x (x - 2) -3(x-2)\)

\(=> (x-2)(x-3) = 0\)

Here x will have 2 values.

1) \(x-2=0\)

\(=> x =2\)

2) \(x - 3 = 0\)

\(=> x = 3\)

Answer:

28

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

180-152=28

28 _________

Answer:

20 cause when According to Sciencealert, the longest math equation contains around 200 terabytes of text. Called the Boolean Pythagorean Triples problem, it was first proposed by California-based mathematician Ronald Graham, back in the 1980s.The Navier-Stokes equation, for me is the hardest of all. This is the full Navier-Stokes equation in conservative form. It looks pretty simple, but as one will dig in, they will notice why it is the hardest one.

Answer:

DF=28 AC=64 CF=32

Step-by-step explanation:

Given :-

Solution :-

>> 2x + 5 < x + 1 / 4

>> 4 (2x + 5) < x + 1

>> 4 × (2x + 5) < x + 1

>> 8x + 20 < x + 1

>> 8x - x < 1 - 20

>> 7x < 1 - 20

>> 7x < -19

>> x = -19 / 7

\(\boldsymbol{\sf{2x+5 < \dfrac{x+1}{4} }}\)

Multiply the two sides of the equation by 4. Since 4 is > 0, the direction of inequality remains the same.

          \(\boldsymbol{\sf{8x+20 < x+1 }}\)

Resta x en los dos lados.

              \(\boldsymbol{\sf{8x+20-x < 1 }}\)

Combine 8x and −x to get 7x.

                \(\boldsymbol{\sf{7x+20 < 1 }}\)

Subtract 20 on both sides.

                 \(\boldsymbol{\sf{7x < 1-20 \ \ \longmapsto \ \ [To \ subtract] }}\)

                  \(\boldsymbol{\sf{7x < -19 }}\)

Divide the two sides by 7. Since 7 is >0, the direction of inequality remains the same.

                     \(\boldsymbol{\sf{x < -\dfrac{19}{7} } }\)

As the end result, it is not simplified or divided, then

                               \(\blue{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \ x < -\frac{19}{7} }}}}\)

ヘ( ^o^)ノ＼(^_^ )If you want to learn more about mathematics, I share this link to complement your learning:

Answer: 46.2m

Side A = 7m

Side B = 19m

Side C = 20.2m

Side A + Side B + Side C = ABC

7 + 19 + 20.2 = 46.2m

Answer: 845

Step-by-step explanation: so you divide 24 by 20,280. 24 goes into 202 how many times then from there on u get your answer

Here's a possible implementation of the function.

A fraction represents a part of a whole or a ratio between two quantities. It consists of a numerator (top number) and a denominator (bottom number) separated by a fraction bar. The numerator represents the number of equal parts being considered, while the denominator represents the total number of equal parts in the whole. Fractions can be written in various forms, such as mixed numbers, improper fractions, or decimals.

Here,

The function uses NumPy's random.choice function to simulate Emily running through the experiment 210 times and recording her guesses. It then calculates the proportion of times Emily guessed a hand correctly, and uses this to compute the standard normal deviate (also known as the z-score) of the proportion, which is a measure of how many standard deviations away from the expected proportion the observed proportion is. The statistic is then simply this z-score, which we can use to test the null hypothesis that Emily's guesses are no better than chance.

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Answer: i believe its B

Step-by-step explanation:

thats what i would put

FAIR DATE is both in NP and NP-hard, we can conclude that FAIR DATE is NP-complete.

To prove that FAIR DATE is NP-complete, we need to show two things: (1) FAIR DATE is in NP, and (2) FAIR DATE is NP-hard.

1. FAIR DATE is in NP:
We can easily verify a potential solution for FAIR DATE in polynomial time. Given subsets A* and B*, we can check if the sum of the bills in A* equals c_A and the sum of the bills in B* equals c_B. This verification can be done in O(n) time for Alice's bills and O(m) time for Bob's bills, where n and m are the number of bills Alice and Bob have, respectively.

2. FAIR DATE is NP-hard:
To show that FAIR DATE is NP-hard, we need to reduce a known NP-complete problem to it. Let's choose the PARTITION problem for this reduction. In the PARTITION problem, given a set S of integers, we need to determine if there exists a subset S' of S such that the sum of the elements in S' is equal to half the sum of all elements in S.

Reduction: Given an instance of PARTITION, we can create an instance of FAIR DATE as follows:
- Let Alice's bill be the set A = S, and c_A = 1/2 * (sigma_a ∈ A, a).
- Let Bob's bill be the set B = {}, and c_B = 0.

Now, if there exists a subset A* of A such that sigma_a ∈ A* a = c_A, then this subset is the solution to the PARTITION problem as well. Conversely, if there is a solution to the PARTITION problem, then there exists a subset A* such that sigma_a ∈ A* a = c_A.

Since we can perform this reduction in polynomial time, FAIR DATE is NP-hard.


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Answer:

A. 87.5 mi

Step-by-step explanation:

1 in : 17.5 mi       Multiply both sides of the ratio by 5

5 in : 87.5 mi

Answer:

because its bad for branding the person who did that was a ldiot

Step-by-step explanation:

The solution set of the example inequality, 2•x + 3 ≤ -3, is the option;

A possible inequality that can be used to get one of the options, (the inequality is not included in the question) is as follows;

Solving the above inequality, we have;

2•x + 3 ≤ -3

2•x ≤ -3 - 3 = -6

2•x ≤ -6

Therefore;

x ≤ -6 ÷ 2 = -3

x ≤ -3

Which gives;

-∞ < x ≤ -3 in interval notation is (-∞, -3]

The solution set of the inequality, 2•x + 3 ≤ -3, is therefore the option;

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Rounding up to the nearest integer, we get a sample size of 1068. Therefore, the answer is 1068.

To find the required sample size, we need to use the formula for the margin of error of a proportion:

Margin of error = z*sqrt(p(1-p)/n)

where z is the z-score for the desired level of confidence, p is the estimated proportion, and n is the sample size.

Since we want the confidence interval to have a width of 0.06, the margin of error should be 0.03. Also, since the scientists believe that about half of all people with the blood disorder will benefit from the drug, we can estimate p as 0.5. Finally, we can use a z-score of 1.96 for a 95% confidence interval.

Substituting these values into the formula, we get:

0.03 = 1.96sqrt(0.5(1-0.5)/n)

Solving for n, we get:

n = (1.96/0.03)^20.5(1-0.5) = 1067.11

Rounding up to the nearest integer, we get a sample size of 1068. Therefore, the answer is 1068.

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If O is the intersection point of the perpendicular bisectors of line segments DE and EF, then O is the center of the circle that passes through the three points.  

1: Draw line segments DE and EF. Since the question states that the points D, E, and F are not on a line, we can assume that these three points form a triangle. So, we will draw line segments DE and EF as shown in the diagram below.

2: Construct the perpendicular bisectors of DE and EF.A perpendicular bisector is a line that passes through the midpoint of a line segment and is perpendicular to it. We can construct the perpendicular bisectors of line segments DE and EF using a straight edge and a compass. After constructing the perpendicular bisectors, we label the point of intersection O.

3: Explain why point O is the center of the circle that passes through the three points.Since the perpendicular bisectors of DE and EF intersect at point O, we know that point O is equidistant from points D and E, and also equidistant from points E and F. This means that O is equidistant from all three points D, E, and F.

Hence, O is the center of the circle that passes through these three points.

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Answer:

24

Step-by-step explanation:

18/3=6 6*4=24

The value of x for the similar triangles is equal to 24.

The triangles are similar, this implies that the length x cm of the bigger triangle is similar to the length HJ = 18 cm of the smaller triangle

and the length DF = 16 cm of the bigger triangle is similar to the length JG = 12 cm of the smaller triangle

so;

x/18 = 16/12

12x = 18 × 16 {cross multiplication}

12x = 288

x = 288/12 {divide through by 12}

x = 24 cm

Therefore, the value of x is equal to 24 cm for the similar triangles.

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Answer:

The given three sides can not form a triangle.

Step-by-step explanation:

Given three sides:

Length of first side = 7.7 cm

Length of second side = 4.0 cm

Length of third side = 1.7 cm

To find:

Whether these three sides can possibly be the three sides of a triangle ?

Solution:

Here, we can use the property of sides of a triangle:

The sum of the lengths of any two sides must be greater than the length of third side.

Now, let us try to verify this property.

Length of first side + Length of second side = 7.7 + 4.0 = 11.7 cm which is greater than the length of third side i.e. 1.7 cm

Length of first side + Length of third side = 7.7 + 1.7 = 9.4 cm which is greater than the length of second side i.e. 4.0 cm

Length of second side + Length of third side = 4.0 + 1.7 = 5.7 cm which is not greater than the length of first side i.e. 7.7 cm

Therefore, the property does not hold true.

It can be concluded that, the given three sides can not form a triangle.

Answer:

isyllus is correct

they can not from a triangle

Step-by-step explanation:

Answer:

Since the sample size is n=10 we can find the first quartile taking in count the first 5 observations from the data set ordered and we have this:

33  60  62  63  69

\( Q_1 =62\)

We can find the third quartile taking in count the last 5 observations from the data set ordered and we have this:

70  74  79 107 119

\( Q_3 =79\)

And finally the median can be calculated with the average of the two moddlie values and we got:

\( Median= \frac{69+70}{2} =69.5 \)

And the IQr would be:

\( IQR = 79-62= 17\)

Step-by-step explanation:

Assuming that 2 is not part of the data we have:

74, 63, 69, 62, 33, 79, 70, 60, 107, 119

We can sort the values on increasing order and we got:

33  60  62  63  69  70  74  79 107 119

Since the sample size is n=10 we can find the first quartile taking in count the first 5 observations from the data set ordered and we have this:

33  60  62  63  69

\( Q_1 =62\)

We can find the third quartile taking in count the last 5 observations from the data set ordered and we have this:

70  74  79 107 119

\( Q_3 =79\)

And finally the median can be calculated with the average of the two moddlie values and we got:

\( Median= \frac{69+70}{2} =69.5 \)

And the IQr would be:

\( IQR = 79-62= 17\)

(A) Circular orbits of stable particles are possible at radii greater than three times the Schwarzschild radius for the non-rotating spherically symmetric mass.

This represents the radius of a black hole's event horizon, within which nothing can escape. The Schwarzschild radius is the event horizon radius of a black hole with mass M.

M can be calculated using the formula: r+ = 2Mwhere r+ is the radius of the event horizon.

(B)  1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ R. This is the required expression.

Tau is the proper time of the particle moving around a circular orbit. Hence, by making use of the formula given above:1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ dt.

(C) Time passes differently in different gravitational fields, and it follows that the period as measured at infinity should be larger than that measured by the particle.

The principle of equivalence can be defined as the connection between gravitational forces and the forces we observe in non-inertial frames of reference. It's basically the idea that an accelerating reference frame feels identical to a gravitational force.

(D) The period of the orbit as measured by an observer at infinity is 16π M^(1/2) and the period of the orbit as measured by the particle is 16π M^(1/2)(1 + 9/64 M²).

The period of orbit as measured by an observer at infinity can be calculated using the formula: T = 2π R³/2/√(M). Substitute the given values in the above formula: T = 2π (8M)³/2/√(M)= 16π M^(1/2).The period of the orbit as measured by the particle can be calculated using the formula: T = 2π R/√(1-3M/R).

Substitute the given values in the above formula: T = 2π (8M)/√(1-3M/(8M))= 16π M^(1/2)(1 + 9/64 M²).

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To find the sum of the vertex angles in various polygons, we need to sketch the polygons and then calculate the sum. For a hexagon, octagon, and dodecagon, the sums of the vertex angles are 720°, 1,080°, and 1,800°, respectively.

a. Hexagon: A hexagon is a polygon with six sides. To find the sum of the vertex angles, we can divide the hexagon into triangles. Since each triangle has an interior angle sum of 180°, the hexagon can be divided into four triangles. Therefore, the sum of the vertex angles in a hexagon is 4 * 180° = 720°.

b. Octagon: An octagon is a polygon with eight sides. Similar to the hexagon, we can divide the octagon into triangles. Dividing it into six triangles, each with an interior angle sum of 180°, the sum of the vertex angles in an octagon is 6 * 180° = 1,080°.

c. Dodecagon: A dodecagon is a polygon with twelve sides. Dividing it into ten triangles, each with an interior angle sum of 180°, the sum of the vertex angles in a dodecagon is 10 * 180° = 1,800°.

Therefore, the sum of the vertex angles in a hexagon is 720°, in an octagon is 1,080°, and in a dodecagon is 1,800°.

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Find the sum of the vertex angles of the following polygons---

a. A hexagon

b. An octagon

c. A dodecagon.

The person who gets to say the last number, 1000, will be Person 6.

In this scenario, we have seven people sitting in a circle and counting clockwise. The goal is to determine which person will say the last number when they reach 1000. To solve this problem, we can use the concept of modular arithmetic.

When dividing 1000 by the total number of people (7), we get a quotient of 142 and a remainder of 6 (1000 = 142*7 + 6). This means that after completing 142 full rounds of counting, the group will have reached the number 994 (142*7). In the next round, they will continue counting from 995 to 1000.

Since the remainder is 6, it indicates that the last number (1000) will be spoken by the person sitting 6 positions after the first person in the circle (clockwise). In other words, Person 1 says numbers 1, 8, 15, and so on, while Person 6 will say 6, 13, 20, and so on.

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True. The 3px, 3py, and 3pz orbitals are similar in shape but differ in their orientation or direction.

The p orbitals are one type of orbital that corresponds to the angular momentum number l = 1. These p orbitals are designated as 3px, 3py, and 3pz to indicate their orientations along the x, y, and z axes, respectively.

The p orbitals have a  shape with a node at the nucleus. They consist of two lobes of electron density, one on either side of the nucleus, separated by a region of zero electron density. The lobes are oriented along the designated axes. The 3px orbital points along the x-axis, the 3py orbital points along the y-axis, and the 3pz orbital points along the z-axis. Although they have different orientations, their shapes and sizes are the same.

So, while the 3px, 3py, and 3pz orbitals differ in their orientation in space, they share the same overall shape and size.

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Answer: C (324)

Step-by-step explanation:

He is making $54 a day working 6 hours a day. 54 x 6 = 324 meaning in 6 days he would make $324.

Answer:

C. 324 thats the answer my cousin solved this