There are 36 students on the debate team at a school. There are 6 seniors, 12 juniors,
10 sophomores, and 8 freshmen on the team. The coach is going to select 4 students at random to participate in
the next debate. Calculate the probability that all 4 students are sophomores.
O 0.0036
O 0.0060
O 0.0084
O 0.2778

Answer: it would be C

Step-by-step explanation: have a good day

Answer:

t is less than 0

Step-by-step explanation:

An open dot indicates that the number it is on is not included in the inequality, meaning it would not be less than or equal to.

Answer:

  $28

Step-by-step explanation:

Each round trip will be double the price of a one-way trip, so will be ...

  2 × $3.50 = $7.00

Diego and his 3 friends will require a total of 4 round-trip tickets for a cost of ...

  4 × $7.00 = $28.00

The graph which correct shows an image and pre-image after reflecting across the line; y = -x as required in the task content is; Option 1.

It follows from the task content that the answer choice which correctly represents an image ajd pre-image after reflecting across the line; y = -x.

First it is noteworthy to know that the line; y = -x is one which passes through the origin and has a negative slope of; -1.

On this note, by observation; when the line y = -x is drawn; the graph which represents the image and pre-image after reflecting across the line; y = -x is; Option 1.

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Answer: The answer is 8/5

Answer:

Each person gets 8/5 part of cookie

Answer:

y

Step-by-step explanation:

4y=6 sorry thats all i know

The probability of the event for the given odds in favor (4 to 7) is found as 4/11.

To continue solving, we must represent the ratio as a fraction.

Thus, we have the depiction shown below.

Odds ratio equals 4/7

We use the following equation to translate the aforementioned odd's expression into a probability expression.

This is displayed as

P = (Odds + 1)/(Odds).

Replace the unknown values in the equation above.

The following equation is what we have.

P = (4/7)/(4/7 + 1)

Analyze the amount

This results

P = (4/7)/(11/7)

Put the quotient in product form.

P = (4/7) * (7/11)

Evaluate

P = 4/11

Thus, the probability of event for the given odds in favor (4 to 7) is found as 4/11.

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Using the lexicographic ordering 5 tuples we get that option b and d is correct.

The lexicographic ordering of 5-tuples means that we compare the elements of each tuple from left to right, and as soon as we find a pair of elements that differ, we say that the tuple with the smaller element is less than the other tuple.

Using this ordering, we can compare the given tuples as follows:

a. (3,1,10,17,2) < (3,1,10,20,1) is true because the fifth element of the first tuple (2) is smaller than the fifth element of the second tuple (1).

(5,1,10,17,2) < (5,0,101,2,2) is false because the second element of the first tuple (1) is greater than the second element of the second tuple (0).

Therefore, option (a) is not correct.

b. (3,1,10,17,2) > (3,1,10,20,1) is false because the fifth element of the first tuple (2) is smaller than the fifth element of the second tuple (1).

(5,1,10,17,2) < (5,0,101,2,2) is true because the second element of the first tuple (1) is smaller than the second element of the second tuple (0).

Therefore, option (b) is correct.

c. (3,1,10,17,2) < (3,1,10,20,1) is true because the fifth element of the first tuple (2) is smaller than the fifth element of the second tuple (1).

(5,1,10,17,2) > (5,0,101,2,2) is true because the second element of the first tuple (1) is greater than the second element of the second tuple (0).

Therefore, option (c) is not correct.

d. (3,1,10,17,2) > (3,1,10,20,1) is false because the fifth element of the first tuple (2) is smaller than the fifth element of the second tuple (1).

(5,1,10,17,2) > (5,0,101,2,2) is true because the second element of the first tuple (1) is greater than the second element of the second tuple (0).

Therefore, option (d) is correct.

So the correct answer is (b) and (d).

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Answer:

There would be 6 boys.

Step-by-step explanation:

Hope this helps:)

Answer:

36 boys

Step-by-step explanation:

The question says that for every 7 girls there are 6 boys in the class. Using this line of reasoning we can say this:

For every 14 girls, there are 12 boys

For every 21 girls, there are 18 boys

For every 28 girls, there are 24 boys

For every 35 girls, there are 30 boys.

For every 42 girls, there are 36 boys.

You can see the pattern here, and there are 36 boys in that class.

Answer:

median: 6

Range: 9

Mode: 7

Step-by-step explanation:

Answer:

a) 6

b) 0

c) 7

Step-by-step explanation:

a) the middle number in a sorted ascending or descending order.

b) the difference between the highest number and the lowest

c) The most frequent number

The row of table reveals the x-intercept could be second ( -4, 0).

The x-intercept of a function of variable x ( y = f(x) ) form is an intersection fo the x-axis and the curve of the function.

The x-intercept for a function y = f(x) is a solution to the equation f(x) = 0 because at that value of x, the function f(x) lies on x-axis where y is 0.

Values of x-intercept for a function f(x) are also called roots or solution of f(x) = 0 equation.

We have to find Which row of table reveals the x-intercept.

Thus, We can conclude that the second row shows the unit rate.

Hence, the row of table reveals the x-intercept could be second ( -4, 0).

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Hope this helps the answer is 97!

Answer:

x = 19

Step-by-step explanation:

you can set up a proportion among corresponding sides:

2x -14 = 18

   32        24

18 /24 can be reduced to 3/4

2x - 14 = 3

   32        4

cross-multiply:  4(2x - 14) = 32(3)

                          8x - 56 = 96

                          8x = 152

                           x = 19

Answer:

eight

Step-by-step explanation:

There are eight different rays that can be formed from five collinear points.

Collinear points are defined as points that are along a straight line represented by a collinear. Because a straight line may be drawn continuously between any two points, they are always collinear.

If five points are collinear, it means they lie on a single straight line.

The number of rays is determined by n collinear points

In general, for n collinear points, there are 2(n−1) different rays.

As per the question, substitute the value of n = 5 for the above formula,

⇒ 2(5−1)

⇒ 2 x 4

⇒ 8

Thus, there are eight different rays can be formed from five collinear points.

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Answer:

The 95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program = ( -0.293, 0.023)

Step-by-step explanation:

The formula for confidence interval for the difference between the proportions is given as:

p1 - p2 ± z × √p1 (1 - p1)/n1 + p2(1 - p2)/n2

From the question

We have two groups.

Group 1 = For women

A survey found that 37 of 74 randomly selected women

p1 = x/n1

n1 = 74

x1 = 37

p1 = 37/74

p1 = 0.5

Group 2 = For Men

A survey found out that 47 of 74 randomly selected men follow a regular exercise program

p2 = x/n1

n2= 74

x2 = 47

p2 = 47/74

p2 = 0.6351351351 ≈ 0.635

z = z score for 95% Confidence Interval = 1.96

The confidence interval for the difference between the proportions is given as:

p1 - p2 ± z × √p1 (1 - p1)/n1 + p2(1 - p2)/n2

0.5 - 0.635 ± 1.96 × √0.5 (1 - 0.5)/74 + 0.635(1 - 0.635)/74

-0.135 ± 1.96 × √(0.5 × 0.5)/74 + (0.635× 0.365)/74

-0.135 ± 1.96 × 0.08068750209663572

-0.135 ± 0.158147504109406

Hence:

= -0.135 - 0.158147504109406

= -0.2931475041

Approximately = -0.293

= -0.135 + 0.158147504109406

= 0.0231475041

Approximately = 0.023

Therefore, the 95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program = ( -0.293, 0.023)

Answer:

  x²/2166784 +y²/2159989 = 1

Step-by-step explanation:

The relationship between the semi-axes and the eccentricity of an ellipse is ...

  e = √(1 -b²/a²)

In order to write the desired equation we need to find 'b' from 'e' and 'a'.

__

Squaring the equation for eccentricity gives ...

  e² = 1 -b²/a²

Solving for b², we have ...

  b²/a² = 1 -e²

  b² = a²(1 -e²)

Using the given values, we find ...

  b² = 1472²(1 -0.056²) = 2166784(0.996864) ≈ 2159989

The desired equation is ...

  x²/2166784 +y²/2159989 = 1

Projectile B begins its descent 1 seconds before Projectile A does.

In Mathematics and Geometry, the y-intercept of any graph or table such as a quadratic equation or function, generally occurs at the point where the value of "x" is equal to zero (x = 0).

By critically observing the table shown in the image attached above, we can reasonably infer and logically deduce the following y-intercept of Projectile A:

y-intercept = (0, 44).

Maximum height = (4, 300).

When t = 0, the y-intercept of Projectile B can be calculated as follows;

h(t) = -16t² + 96t

h(0) = -16(0)² + 96(0)

h(0) = 0.

For the maximum height, we have:

h(t) = -16t² + 96t

h'(t) = -32t + 96

32t = 96

t = 96/32

t = 3

Difference in time = 4 - 3

Difference in time = 1 seconds.

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The word problem is : Mansi has total 81 rupees in her pocket. She wants to buy chocolates for her classmates to distribute on the occasion of her birthday. She has 152 students in her class. She buys two chocolates for her bestfriends of total rupees 6 and for classmates buys chocolates which are of ½ rupees each. Find how many remaining classmates where there in her class ?

According to the given expression, the word problem can be given as:

Mansi has total 81 rupees in her pocket. She wants to buy chocolates for her classmates to distribute on the occasion of her birthday. She has 152 students in her class. She buys two chocolates for her bestfriends of total rupees 6 and for classmates buys chocolates which are of ½ rupees each. Find how many remaining classmates where there in her class ?

So according to the question the expression can be made, that is,

Let number of remaing student in her class be x

Then,   1/2x + 6 =81

We will be solving this linear equation as follows,

             1/2x = 81 – 6

             1/2x = 75

                x = 75 * 2

                x = 150

Hence she has total of 152 students in her class out of which 2 are her best friends and 150 are her classmates.

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Answer:

x = 5

AB = 14 units

Step-by-step explanation:

From the picture attached,

In the given triangles ΔAEB and ΔCDB,

AE║CD and ED is a transverse,

∠EAB ≅ ∠DCB [Alternate interior angles]

AE║CD and AC is a transverse,

∠AEB ≅ ∠CDB [Alternate interior angles]

ΔAEB ~ ΔCDB by AA property of the similarity of two triangles.

Therefore, corresponding sides of these triangles will be proportional.

\(\frac{\text{AE}}{\text{CD}}=\frac{\text{BE}}{\text{BD}}=\frac{\text{AB}}{\text{BC}}\)

\(\frac{\text{BE}}{\text{BD}}=\frac{\text{AB}}{\text{BC}}\)

⇒ \(\frac{7}{4}=\frac{2x+4}{x+3}\)

⇒ 7x + 21 = 8x + 16

⇒ 8x - 7x = 21 - 16

⇒ x = 5

AB = (2x + 4)

     = 10 + 4

     = 14 units

Answer:

Set your calculator to Degree mode.

a² = 17² + 20² - 2(20)(17)cos(89°)

a² = 677.13236

a = 26.0 in.

sin(89°)/26.02177 = (sin B)/17

sin B = 17sin(89°)/26.02177

B = 40.8°

C = 50.2°

Answer:

x^2 -9

Step-by-step explanation:

(x + 3)(x − 3)

FOIL

first x*x =x^2

outer -3x

inner 3x

last -3*-3 =-9

Add together

x^2 -3x+3x -9

Combine like terms

x^2 -9

Answer:

3/5 = 12/20

Step-by-step explanation:

5 x 4 = 20 so mulyiply 3 x 4 to get 12

Step-by-step explanation:

please mark me as brainlest

The general form of the equation for the given circle centered at O(0, 0) include the following: B. x^2 + y^2 − 41 = 0

Mathematically, the general (standard) form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²  

Where:

Next, we would determine the radius of this circle by using the distance formula as follows;

Radius, r = √[(4 - 0)² + (5 - 0)²]

Radius, r = √(16 + 25)

Radius, r = √41

Substituting the given parameters into the general form, we have;

(x - h)² + (y - k)² = r²  

(x - 0)² + (y - 0)² = (√41)²  

x² + y² = 41

x² + y²- 41 = 0

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Complete Question:

Select the correct answer. A circle with center O (0,0) has point B (4,5) on its circumference, which is joined by a line to O. What is the general form of the equation for the given circle centered at O(0, 0)?

a. x^2 + y^2 + 41 = 0

b. x^2 + y^2 − 41 = 0

c. x^2 + y^2 + x + y − 41 = 0

d. x^2 + y^2 + x − y − 41 = 0

Answer:

Step-by-step explanation:

6x² - 10x + 21x - 35 = 6x² + 11x - 35

6x² - 6x² + 11x - 11x - 35 + 35 = 0

0 = 0

The equation is an identity. Its solution set is {all real numbers}.

819 in base five is equal to 13134.

Base five is a positional numeral system used in mathematics, having 5 as its base or radix. This means that it represents any real number using five different symbols, often the digits 0, 1, 2, 3, and 4. The ones place is represented by the digit on the right, the place of the five by the digit to the left, the twenty-fives place by the digit after that, and so on. Each digit in base five represents a multiple of a power of five.

To write 819 in base five:

Repeat steps 1-3 with the remainder (194):

Repeat steps 1-3 with the remainder (69):

Repeat steps 1-3 with the remainder (19):

The remainder (4) is less than 5, so write it down in the 5^0 place (rightmost digit).

Combine all the digits: 13134.

Therefore, 819 in base five is equal to 13134.

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