The following two-way table describes student'safter school activities. Find the probability that arandomly selected student either does sports orworks.GradeSportsMusic/DramaWorkSophomore2073Junior20132.255Senior5P(Sports U Work) = [?]Round to the nearest hundredth.

The number of handshakes altogether exists 45.

In mathematics, there are two alternative methods for dividing up a collection of components into subsets: combination and permutation. The subset's components can be arranged in any sequence when used together. The components of the subset are arranged in a particular order in a permutation.

A combination in mathematics is a choice of elements from a set with distinct members, where the order of the choices is irrelevant.

Combinations are a mathematical method for calculating the number of alternative arrangements in a collection of objects where the order of the selection is irrelevant. You are free to choose any combination of the things.

Given:

Number of people in the conference = 10

Each person shakes hands with others.

The total number of handshakes \($={ }^n \mathrm{C}_2$\)

Total number of handshakes \($={ }^{10} C_2=(10 \times 9) / 2=45$\) handshakes.

The complete question is:

At the end of a meeting all the ten people present shake hands with each other once. The number of handshakes altogether is

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Answer: b

Step-by-step explanation: graph b is correct hope it helps

The key features of this quadratic relation y = -3x² - 24x - 36 include;

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped.

Since the leading coefficient (value of a) in the given quadratic function y = -3x² - 24x - 36 is negative 16, we can logically deduce that the parabola would open downward and the x-intercept (roots) is given by the ordered pair (-6, 0) and (-2, 0).

When x = 0, the y-intercept can be determined as follows;

y = -3x² - 24x - 36

y = -3(0)² - 24(0) - 36

y = -36

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(-24)/2(-3)

Axis of symmetry, Xmax = -4

For the vertex, we have:

y(-4) = -3x² - 24x - 36

y(-4) = -3(-4)² - 24(-4) - 36

y(-4) = 12

In conclusion, the quadratic function has a maximum value at 12.

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Answer:

for x = −11y/16+ 21/16

for y = 16x/11 +21/11

Step-by-step explanation:

Step-by-step explanation:

we will draw 30⁰ angle first and then we will bisect it then it will become 15⁰ angle

Your well-wisher

Answer:

There are 40 apples in the basket.

This is because 5 apples to 3 pears have a difference of 1.66666667 when dividing 5 by 3 to show the ratio difference. Then, all you do is multiply this number by the number of total pears which would look like 24 x 1.66666667 = 40.

I hope this helped you, have an amazing day! :)

Answer:

look at the picture i sent please

Answer:

6.25 is the answer

Step-by-step explanation:

Answer:

Im not sure but I think it is 172! I hope this helped!!

Step-by-step explanation:

In the given case, each loaf of bread contains 25/18 cups of flour.

To find how many cups of flour are in each loaf of bread, we need to divide the total amount of flour by the number of loaves.

First, let's convert the mixed numbers to improper fractions:

\(2 2/3 cups = 8/3 cups\)

\(1 1/2 cups = 3/2 cups\)

Next, we can add the two fractions to find the total amount of flour:

8/3 cups + 3/2 cups = (16/6 + 9/6) cups = 25/6 cups

So, the recipe requires 25/6 cups of flour to make 3 loaves of bread.

To find the amount of flour in each loaf, we divide 25/6 cups by 3:

(25/6 cups) / 3 = 25/18 cups

Therefore, each loaf of bread contains 25/18 cups of flour.

Alternatively, we could simplify the mixed numbers at the beginning:

2 2/3 cups = 8/3 cups

1 1/2 cups = 6/4 cups

Then we can add the fractions:

8/3 cups + 6/4 cups = (32/12 + 18/12) cups = 50/12 cups

Finally, we can divide by 3 to find the amount of flour in each loaf:

(50/12 cups) / 3 = 25/18 cups

So the answer is the same.

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The perimeter of the regular nonagon will be; 840.7 units

The in-radius of the regular nonagon is given as:

Radius, r =17

The perimeter is then calculated by:

P = 18r/Tan(π/9)

Substitute 17 for r;

P = 18(17)/Tan(π/9)

Evaluate the product of 18 and 17;

P =  306/Tan(π/9)

Evaluate the quotient

P =  840.7

Hence, the perimeter of the regular nonagon = 840.7 units

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Answer:

24000

Step-by-step explanation:

6/5×20000

=24000

The dimension of the rectangular of a norman window will be 1.6803*3.3606.

What is the area of Rectangle?

In any quadrilateral which have equal and parallel opposite sides is considered to be a rectangle. It is also called as a polygon with four sides and the four angles that are all 90 degrees each. A rectangle is a shape with only two dimensions. The product of the length and the breadth calculates its area. The length of the diagonals of any rectangle are equal in length. Thus, the length of the diagonals can be calculated easily using the Pythagoras theorem where, the diagonal is considered to be the hypotenuse.

Let r represents the radius, and b be the breadth.

Then, perimeter = 3.14*r+2r+2b = 12

For the dimension needed for the most light to enter we need to maximize the area.

Hence, area of the window : area of the semicircle + area of the rectangle

= \(\frac{3.14*r^2}{2} + 2rb\)

= \(12r - (\frac{3.14+4}{2}) r^2\)

A'(r) = 0

Therefore, \(r=\frac{12}{3.14+4}\) which is nearly equal to 1.6803m

From this value of r we can calculate the value of b to be;

b= 1.6803m

Thus, a= 3.606m

Thus the required dimension is : 1.6803*33606

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Answer:

33 and 17

Step-by-step explanation:

Answer:

Step-by-step explanation:

The biggest angle in the triangle is opposite the largest side, which is how they actually relate to one another. The right answer is D.

A triangle's characteristics are:

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The value of cos(2α + β) using trigonometric identities is; -1.0155

We are given;

α = sin⁻¹(4/5)

β = tan⁻¹(12/5)

Thus;

sin α = 4/5

tan β = 12/5

From trigonometric ratios, we can say that;

cos α = 3/5

sin β = 12/13

cos β = 5/13

We know from trigonometric identities that  cos (a + b) = cos a cos b - sin a sin b.

Thus;

cos(2α + β) = cos 2α cos β - sin 2α sin β

Thus;

cos(2α + β) = 2(3/5) * (5/13)) - ((2 * 4/5 * 12/13))

= 0.4615 - 1.477

= -1.0155

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Answer:

The ratio of cosine X = 12 : 13

Step-by-step explanation:

Given;

∠Y=90°

length WY = 5

length XW = 13

length YX = 12

Check the image uploaded for the solution.

hypotenuse is

Brooklyn needs to invest $432.43, rounded to the nearest ten dollars.

To determine how much Brooklyn needs to invest in an account that pays a continuously compounded interest rate, we can use the formula:

A = \(Pe^(^r^t^)\)

where A is the future value of the account, P is the principal investment, e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.

In this case, we want the future value of the account to be $640, the interest rate is 3.5% (or 0.035 as a decimal), and the time is 9 years. We can substitute these values into the formula and solve for P:

640 = \(Pe^(^0^.^0^3^5^*^9^)\)

640 = Pe^0.315

P =\(640/e^0^.^3^1^5\)

P = 432.43

Therefore, to have a future value of $640 in 9 years with a continuously compounded interest rate of 3.5%.

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Answer:

5) \(y=\frac{7}{2}x\)

6) \(y=\frac{1}{4}x\)

Step-by-step explanation:

k in this equation represents the slope of the line. To find the slope of a line, pick 2 points that land perfectly on the grid and find the vertical and horizontal distance between them. The vertical distance is the 'rise', and the horizontal distance is the 'run'. Given those two numbers, you can calculate the slope:

\(k=\frac{rise}{run}\)

A more precise definition is:

\(k=\frac{y2-y1}{x2-x1}\)

5)

You can use whichever 2 points you want here. I'll use the 2 outermost points:

(x1, y1) = (2, 7)

(x2, y2) = (8, 28)

Now, to find the distance between them, subtract the position of the first point from the second point. Vertical distance first, subtract the y-coordinates:

\(28-7=21\)

The rise is 21.

Horizontal distance, subtract the x-coordinates:

\(8-2=6\)

Slope is 'rise over run' as I wrote above, so you can now write the slope and the equation of the line:

\(k=\frac{21}{6}\\\\k=\frac{7}{2}\\\\y=\frac{7}{2}x\)

6)

I'll pick the 2 outermost points again:

(x1, y1) = (8, 2)

(x2, y2) = (24, 6)

This time, I'll just plug all 4 values directly into the 2nd formula I wrote at the top.

\(k=\frac{y2-y1}{x2-x1}\\\\k=\frac{6-2}{24-8}\\\\k=\frac{4}{16}\\\\k=\frac{1}{4}\\\\y=\frac{1}{4}x\)

Answer: $44.55

Step-by-step explanation:

$45 times the 10% sales tax equals $49.50

$49.50 minus the 10% discount equals $44.55

the value of variable x in the rhombus is Option (c) 25.

A parallelogram is a particular instance of a rhombus. opposite sides and angles of the rhombus are parallel and equal. The rhombus has equal-length sides on each side, and its diagonals meet at right angles to form its shape as square. The rhombus is sometimes called as a diamond or rhombus.

Let O be the intersection point of the line AC and the line BD in the rhombus.

This two lines intersect at a 90° angle in the center. ( Property of Rhombus)

∠AOD=90°

∠AOD+∠OAD+∠ODA=180° (triangle sum property)

90°+x+x+40°=180°

2x=180°-130°

x=25

Hence the value of x=25.

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The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

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Step-by-step explanation:

Sum of all interior angles = 900°

A+B+C+D+E+F+G=900

120+B+148+90+142+130+129=900

B=900-759

B=141°

Answer:

Red grapes.

Step-by-step explanation:

If you find how much one bag of each grape cost which is:

$13.00 ÷ 5 = 2.60 (1 bag of red grapes)

$5.08 ÷ 2 = $2.54 (1 bag of green grapes)

See the price and you'll know it is red grapes.

Answer: D

Step-by-step explanation:

it goes up by one in sides , count the sides

Answer:

49°

Step-by-step explanation:

arc AB subtends a central angle of 98°

Let O be the center of the circle.

∠OAB = ∠OBA = (180°-98°)/2 = 41°

Assuming that BC  is tangent to the circle, ∠OBC = 90°

∠ABC = ∠OBC - ∠OBA = 90° - 41° = 49°

To match the graphs of cylinders a and b to cylinders P and Q, we need to analyze the relationship between the height of the water and the volume of water in each cylinder.

Cylinder P would correspond to graph b, while Cylinder Q would correspond to graph a.

The reasoning behind this is as follows:

Cylinder P, corresponding to graph b, shows a steeper increase in height with increasing volume. This indicates that the water level rises quickly as more volume is added, suggesting that the cylinder has a smaller cross-sectional area. Since height is directly proportional to volume for a cylinder, a smaller cross-sectional area would result in a higher rise in height for the same volume of water.

Cylinder Q, corresponding to graph a, shows a slower increase in height with increasing volume. This implies that the water level rises more gradually as more volume is added, indicating a larger cross-sectional area. A larger cross-sectional area would result in a smaller increase in height for the same volume of water.

In summary, the steeper graph b matches Cylinder P with a smaller cross-sectional area, while the gentler graph a matches Cylinder Q with a larger cross-sectional area.

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Answer:

8x - 2

Step-by-step explanation:

2x + 3 - (5 - 6x) ← distribute parenthesis by - 1

= 2x + 3 - 5 + 6x ← collect like terms

= (2x + 6x) + (3 - 5)

= 8x + (- 2)

= 8x - 2

Answer:

4= 0 is two one real solution.