A football team consists of 20 each freshmen and sophomores, 15 juniors, and 10 seniors. Four players are selected at random to serve as captains. Find the probability that

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Option (d) is the correct choice.

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.

A parallelogram has the following qualities:

The opposing sides are equally spaced and parallel.

Angles on either side are equal.

The following or neighboring angles are supplemental.

All of the angles will be at right angles if any one of them is a right angle.

The two diagonals cut across one another.

For more questions on Parallelogram

https://brainly.com/question/3050890

#SPJ4

Answer:

33=2x+y, 48=3x+y

Step-by-step explanation:

Sorry my internet isn't working well. Go to math-way and put that in and it will give you the answer :)

Answer:

h=10

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

3/7 = h/14- 2/7

3/7=h/14 - 4/14

7/14 - 4/14 = 3/7

(4/14 is the same as 2/7)

Answer:

C

Step-by-step explanation:

Y - 4 = -2x + 10 Multiply -2 to the inside the brackets

Y = -2x + 14 Add the 4 over

Answer:

[tex]x = 11[/tex]

Step-by-step explanation:

[tex] \frac{12x + 8 - 4x + 4}{2} = 50[/tex]

[tex] \frac{8x + 12}{2} = 50[/tex]

[tex]8x + 12 = 100[/tex]

[tex]8x = 88[/tex]

[tex]x = 11[/tex]

Answer:

9 brownies

Step-by-step explanation:

Since we are not given the total number of batches. Let us assume the total batches is 81

If each brownie is 1/9 of a batch, number of brownie made will be equivalent to:

Amount of brownie made = 1/9 × 81

Amount of brownie made = 81/9 = 9 brownies

Hence he made 9 brownies

The measure of m∠1 = 85 degrees and m∠2 = 15 degrees.

The correct answer is option D: ∠1 = 85°, m∠2 = 15°.

What is the right triangle?

A right-angle triangle is a triangle that has one of its angles 90 degrees. The sum of angles in a right triangle is 180 degrees.

To find the measures of angles 1 and 2, we can use the fact that the sum of the angles in a triangle is 180 degrees.

We know that angles 1, 2, and 3 form a triangle, so we can write:

m∠1 + m∠2 + m∠3 = 180

Substituting the given values, we get:

m∠1 + m∠2 + 80 = 180

Simplifying, we get:

m∠1 + m∠2 = 100

We also know that angles 2, 3, and 4 form a triangle, so we can write:

m∠2 + m∠3 + m∠4 = 180

Substituting the given values, we get:

m∠2 + 80 + 85 = 180

Simplifying, we get:

m∠2 = 15

Substituting this value in the first equation, we get:

m∠1 + 15 = 100

Simplifying, we get:

m∠1 = 85

Therefore, the measure of m∠1 = 85 degrees and m∠2 = 15 degrees.

The correct answer is option D: ∠1 = 85°, m∠2 = 15°.

To learn more about the right triangle visit:

https://brainly.com/question/29869536

#SPJ1

Answer:

Step-by-step explanation:

The measure of m∠1 = 85 degrees and m∠2 = 15 degrees.

The correct answer is option D: ∠1 = 85°, m∠2 = 15°.

What is the right triangle?

A right-angle triangle is a triangle that has one of its angles 90 degrees. The sum of angles in a right triangle is 180 degrees.

To find the measures of angles 1 and 2, we can use the fact that the sum of the angles in a triangle is 180 degrees.

We know that angles 1, 2, and 3 form a triangle, so we can write:

m∠1 + m∠2 + m∠3 = 180

Substituting the given values, we get:

m∠1 + m∠2 + 80 = 180

Simplifying, we get:

m∠1 + m∠2 = 100

We also know that angles 2, 3, and 4 form a triangle, so we can write:

m∠2 + m∠3 + m∠4 = 180

Substituting the given values, we get:

m∠2 + 80 + 85 = 180

Simplifying, we get:

m∠2 = 15

Substituting this value in the first equation, we get:

m∠1 + 15 = 100

Simplifying, we get:

m∠1 = 85

Therefore, the measure of m∠1 = 85 degrees and m∠2 = 15 degrees.

The correct answer is option D: ∠1 = 85°, m∠2 = 15°.

To learn more about the right triangle visit:

brainly.com/question/29869536

#SPJ1

Answer:

Hi.

three fifth of 200 is 120.

The amount of the proposed increase is, Rs 1071.4

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The annual gym subscription for a single member is Rs.1000,

And, An annual family membership is Rs.1500.

Here, A single membership increased cost 5/7 of a family membership.

Hence, The increased cost = 5/7 of 1500

                                          = 1071.4 Rupees

Learn more about the divide visit:

https://brainly.com/question/28119824

#SPJ1

The ladder touches the building at 4.53 meters right angle triangle vertical distance from the ground.

The triangle that has one 90 degrees angle is called right-angled triangle. The Pythagorean theorem is applicable for right-angled triangle.

What is the height of the point where the ladder touches the building A ladder leans up against a building at an angle of 65 degrees with the ground. the length of ladder = 5 meters

we understand that the ladder, building and ground together formed a right-angled triangle. The right angle is in between the building and ground. The length of ladder acts as a hypotenuse of this triangle. If we consider the angle 65 degrees,

then sin 65° = opposite side length / hypotenuse here, opposite side length = the required length we need to determine sin 65° × hypotenuse = opposite side opposite side = 0.9063 × 5 =4.53 meters

the ladder touches the build at 4.53 meters vertical distance from the ground.

To learn more about right angle triangle visit:

brainly.com/question/3772264

#SPJ1

Answer:

the answer would be seven hundred

8,000

700

60

5

hope this helps :)

The value of 7 in the number represents 100th place.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

The precise position of a number within a series is assigned a value by a place-value system.

The given number is 8765 in the number 7 is representing 100th place. The expanded form of the number can be written as:-

8765 = 8000 + 700 + 60 + 5

Here in the expanded form, it is observed that 7 is the 100th place of the number.

Therefore, the value of 7 in the number represents the 100th place.

To know more about the place value system follow

brainly.com/question/2004114

#SPJ2

Answer:

x = 48

Step-by-step explanation:

If the two angles are supplementary then their sum must be 180 degrees

x + 34 + 2x + 2 = 180

3x + 36 = 180 subtract 36 from both sides

3x = 144 divide both sides by 3

x = 48

Answer:

Yes, Rudy is correct

Explanation:

Number of sides of a hexagon = 6

The sum of all interior angles of a polygon with n sides  = (n-2)*180

Here, since a regular hexagon has 6 sides, n = 6

= (6 - 2)*180

= 4*180

= 720 degrees

Hope it helps :)

Have a great day!

Answer:

B. 73°

Step-by-step explanation:

Answer:

I believe this is the only answer I got from you bro.

hope it helps.

A logarithmic function is a type of inverse function.

A logarithmic function is a type of inverse function that is commonly used in mathematics and science. It is typically written in the form of y = log base b (x), where b is the base of the logarithm, and x is the input value. The most common bases for logarithms are 10 (common logarithm) and e (natural logarithm).

The logarithmic function is the inverse of the exponential function with base b. This means that if y = log base b (x) then x = b^y

One way to describe a logarithmic function is to say that it represents the exponent to which the base number must be raised in order to produce the input value x. For example, log base 10 of 100 is 2, because 10^2 = 100.

Another way to describe a logarithmic function is to say that it is a way of expressing very large or small numbers in a more manageable form. For example, instead of expressing a number like 10^9 as 1 billion, it can be expressed as 9 using a logarithm to base 10.

It is also important to note that logarithmic function have some key characteristics such as:

The domain of a logarithmic function is x>0, since the logarithm of a non-positive number is undefined.

The range of a logarithmic function is all real numbers.

The graph of a logarithmic function has a vertical asymptote at x=0, since the logarithm of a non-positive number is undefined.

A logarithmic function is increasing over its domain and concave down.

The x-intercept of the graph is (1,0), since the logarithm of 1 is always 0.

Overall, logarithmic functions are mathematical tools that allow us to simplify the representation and manipulation of very large and small numbers, and are used in many areas of science and engineering.

To learn more about logarithms visit: brainly.com/question/30085872

#SPJ4

Answer:

Diagonals of a kite are perpendicular.

Answer:

D

Step-by-step explanation:

A Gradient is also called a slope of a line, which represents how steep a line is.

Formula of slope: Vertical difference ÷ Horizontal difference

For a slope to be zero, the line must be horizontal.

Based on the question given, we can deduce that D is a horizontal line and therefore the slope is zero.

Answer:

Step-by-step explanation: We will determine if ratios are proportional using cross multiplication.

first, we will check option (a)

12/15 =5/4

12*4 = 15*5

48 is not equal to 75. So, these are not proportional.

now, we will check option (b)

15/12 = 5/4

15*4 = 12*5

60 = 60.

as the left-hand side is equal to the right-hand side.

So, option (b) is correct.

Answer:

[tex]\textsf{B)} \quad \dfrac{15}{12}\; \textsf{and}\;\dfrac{5}{4}[/tex]

Step-by-step explanation:

If two fractions are equal, they form a proportion.

Therefore, to determine if two ratios form a proportion, rewrite the fractions so that their denominators are the same, then compare.

[tex]\textsf{A)}\quad \dfrac{12}{15}\; \textsf{and}\;\dfrac{5}{4} \implies \dfrac{12 \times 4}{15\times 4}\; \textsf{and}\;\dfrac{5\times 15}{4\times 15}\implies \dfrac{48}{60}\; \textsf{and}\;\dfrac{75}{60}[/tex]

As the two fractions are not equal, they do not form a proportion.

[tex]\textsf{B)} \quad \dfrac{15}{12}\; \textsf{and}\;\dfrac{5}{4}\implies \dfrac{15}{12}\; \textsf{and}\;\dfrac{5 \times 3}{4 \times 3}\implies \dfrac{15}{12}\; \textsf{and}\;\dfrac{15}{12}[/tex]

As the two fractions are equal, they form a proportion.

[tex]\textsf{C)} \quad \dfrac{6}{5}\; \textsf{and}\;\dfrac{4}{5}[/tex]

The denominators of these two fractions are already the same.

Therefore, as the two fractions are not equal, they do not form a proportion.

[tex]\textsf{D)} \quad \dfrac{5}{6} \; \textsf{and}\;\dfrac{4}{5}\implies \dfrac{5\times 5}{6\times 5} \; \textsf{and}\; \dfrac{4\times 6}{5\times 6}\implies \dfrac{25}{30}\; \textsf{and}\;\dfrac{24}{30}[/tex]

As the two fractions are not equal, they do not form a proportion.

Projective tests are created so that the test taker cannot tell what they are testing for.

To learn more about Projective tests refer to:

https://brainly.com/question/20221937

#SPJ4

Answer:

Step-by-step explanation:

To find the number Katherine should multiply the prices on the tags by to find the price she would have to pay before tax, we need to calculate the inverse of the discount percentage, which is 1 - (discount percentage / 100).

Given that the discount is 3% and we want to find the price after the discount, that means:

1 - (3/100) = 1 - 0.03 = 0.97

So, the number Katherine should multiply the prices on the tags by to find the price she would have to pay, before tax, in one step, is 0.97. Multiplying the price of an item by 0.97 is equivalent to subtracting 3% from the original price, which is the same as finding the final price after the discount.

For example, if an item is priced at $10, Katherine can multiply this by 0.97 to find that the final price she would have to pay before tax is $9.7

10*0.97 = 9.7

The measures of the angles of the triangles are

The measure of ∠B = 80.3°

The measure of ∠C = 59.7°

The length of side AB = 20.2 units

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of side AC = 23

The measure of side BC = 15

The measure of ∠A = 40°

From the law of sines , we get

( sin A ) / a = ( sin B ) / b = ( sin C ) / c

Substitute the value of A and a in the equation , we get

sin ( 40 )° / 15 = sin B / 23

On simplifying the equation , we get

sin B = ( 23/15 ) x sin ( 40 )°

Now , m∠B = 80.27°

So , the measure of angle ∠B = 80.3°

And ,

The interior angles of a triangle is 180°

So , The measure of angle ∠C = 180° - ( 80.3° + 40° )

On simplifying the equation , we get

The measure of angle ∠C = 59.7°

Now ,

From the law of cosines , c² = a² + b² - 2ab ( cos C )

Substitute the value of a , b and cos C in the equation , we get

c² = 15² + 23² - 2 ( 15 ) ( 23 ) cos ( 59.7 )°

On simplifying the equation , we get

c² = 225 + 529 - 348.12363

c² = 405.87

Taking square roots on both sides of the equation , we get

c = 20.156

c = 20.2 units

Therefore, the measure of side AB = 20.2 units

Hence , the measures angles of triangle is solved

To learn more about triangles click :

https://brainly.com/question/16739377

#SPJ1

Answer:

Father age is 40 and Son age is 16

Step-by-step explanation:

Let Father be x and Son be y.

If their ratio of their age is 5:2 then

Find Y:

2x = 5y

Find X

Answer:

Multiply the x by 5 to get the y

Answer:

smaller/ less than

Answer:

less than

Step-by-step explanation:

On a number line, the values go from least to greatest, left to right. So if you go towards the left, the number is decreasing.