If a person draws 2 cards at random from a standard deck of 52 cards, what is the probability that they get 2 aces?

Look at the picture.

This is isosceles triangle. Therefore, the angles at the base are congruent.

m∠ BAC = m∠ABC.

We know, the sum of the measures of the angles in a triangle is equal 180°.

Therefore:

m∠BAC + m∠ABC + m∠ACB = 180°

2m∠ABC + 120° = 180°     subtract 120° from both sides

2m∠ABC = 60°     divide both sides by 2

m∠ABC = 30°

m∠MCB = 90° → ΔMCB is a right triangle (30 - 60 - 90).

The sides of that triangle are in proportion: 1 : √3 : 2.

Therefore MC : BC : MB = 1 : √3 : 2

MC = 12 → BC = 12√3 and MB = 2 · 12 = 24

ΔCDB is the right triangle (30 - 60 - 90) too.

Therefore CD : BD : BC = 1 : √3 : 2

CD = 1/2 BC → CD = 1/2(12√3) = 6√3

BD = CD√3 → BD = 6√3(√3) = 6(3) = 18

AB = 2BD therefore your answer is:

AB length is 24 cm

Given length CM = 12 cm

and length CB = 12 sqrt 3

sin 60 ° = CB / BM

1/2 sqrt 3 = 12 sqrt 3 / BM

BM = 1/2 sqrt 3 * 12 sqrt 3

BM = 18 cm

sin 30 ° = CM / MA

1/2 = 12 / MA

MA = 1/2 * 12

MA = 6 cm

So, the length of AB is BM + MA = 18 cm + 6 cm = 24 cm

A triangle is the name of a shape made from three sides in the form of a straight line and three angles. The mathematician Euclid who lived around 300 BC found that the sum of the three angles on a triangle on a flat plane was 180° degrees. This allows us to calculate the magnitude of one angle when the other two angles are known.

According to the length of the sides:

According to the biggest angle:

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Details

Class: Middle/High School and College

Subject: Mathematics

Keyword: degrees, angles, triangle

Answer:

24.7619048 %

Step-by-step explanation:

The percent spent on food

food/total

520/2100

.247619048

This is in decimal form

Multiply by 100 to change it to percent

24.7619048 %

Answer:

Step-by-step explanation:

The given congruent triangles △QXR and △NYC mean that corresponding sides and angles are equal. Hence, line segment QX equals NY and angle Y equals angle X.

The symbols △QXR and △NYC stand for two triangles which are mentioned to be congruent. Congruency in triangles means they have the same size and shape. This implies that the corresponding sides and angles of the two triangles are equal.

a) As per the congruency of the triangles, line segment QX in triangle △QXR would be congruent to corresponding segment in triangle △NYC, which is NY. Hence, line segment QX = NY.

b) Referring to the same principle, angle Y in triangle △NYC should be equal to its corresponding angle in triangle △QXR. Considering the order of the letters in triangles, angle Y would correspond to angle X. Hence, angle Y = angle X.

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The letter X shown ''Point and Line Symmetry''.

What is Line segment?

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

Given that;

The letter is X.

Now,

We know that;

A point symmetry is defined as a type of symmetry in which a geometrical figure is divided into two equal and symmetrical parts by a central point.

Thus, Letter X has Point symmetry.

And, The line symmetry is defined as a type of symmetry that divides a geometrical figure into two equal and symmetrical parts.

Thus, Letter X has Line symmetry.

Therefore, The letter X shown ''Point and Line Symmetry''.

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[tex]6x-14=2-10x\qquad\text{add 14 to both sides}\\\\6x=16-10x\qquad\text{add 10x to both sides}\\\\16x=16\qquad\text{divide both sides by 16}\\\\\boxed{x=1}[/tex]

[tex]Check:\\\\6x-14=6(1)-14=6-14=-8\\\\2-10x=2-10(1)=2-10=-8\\\\CORRECT[/tex]

Answer:

x=1

Step-by-step explanation:

6x-14=2-10x

First step is to add 10x to each side

6x+10x-14=2-10x+10x

16x-14=2

Now add 14 to each side

16x-14+14=2+14

16x=16

Divide each side by 16 to isolate x

16x/16 =16/16

x =1

Answer:

The probability will be 2/7.

Hope this helps :D

The probability that the event will fail to occur is 7:9 .

Given that the odds against an event is 2:7 or 2/7.

The meaning of odds against an event is the ratio of the number of times the respective event does not happen compared to the number of times the event occur .

So for the given problem, it refers that for every 2 occurrences that the event does not occur there will be 7 occurrences that it will happen.  

Thus the total number of occurrences of the event is (2 + 7) = 9

This means that the event will occur definitely 2 times in every 9 times total outcome.

The probability that the event will occur is 2/9 or 2:9 .  

Therefore the probability that the event will fail to occur is 1 - 2/9 = 7/9 or 7:9 .

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Answer:

20% was evaporated

Step-by-step explanation:

Formula:

((New value-old value)/(old value))*100

((2-2.5)/(2.5))*100 = 20

Answer:

20% of the water evaporated

Step-by-step explanation:

We know that 500,000 evaporated because 2,500,000-2,000,000 is 500,000.

100% - 2,500,000

500,000 - x%

2,500,000/500,000 = 100/x

x=(500,000)(100)/2,500,000

x= 20%

20% of the water evaporated.

It's a linear function. We need only two points to the plotting of the graph.

[tex]5x-y=5\qquad\text{subtract 5x from both sides}\\\\-y=-5x+5\qquad\text{change the signs}\\\\y=5x-5\\\\for\ x=0\to y=5(0)-5=0-5=-5\to(0,\ -5)\\\\for\ x=1\to y=5(1)-5=5-5=0\to(1,\ 0)[/tex]

Answer:

original size of Jay's bread dough is raised to 220%

Step-by-step explanation:

Let 1 be the original size of the bread

her bread dough is 11/5 of its original size.

[tex]1* \frac{11}{5} = 2.2[/tex]

The original size of the bread is raised to 2.2

To get percentage we multiply by 100

2.2*100 = 220%

original size of Jay's bread dough is raised to 220%

Answer:

Question one 186

Question two 240

Step-by-step explanation: You multiply the variable (the letter) by the number that the person is using

Answer:

1. 186

2. 240

Step-by-step explanation:

1. D =3w+60

D =3(42)+60

D =186

2. I =48t

I =48(5)

I =240

Answer:

176 km/88 liters = 2 km/liter

(250 km)(1 liter/2 km) = 125 liters

Answer:

Maximum (250,125) Answer

Step-by-step explanation:

This is more of a graphing problem than it is anything else.

Begin by graphing all 4 given equations.

When you do that, mark the intersection points of at least 2 lines. In this case it is exactly 2 lines for each intersecting point.

6x + 4y <= 2000 and 2x + 4y <= 1000 intersect at (250,125)

x=>0 and y=>0 intersect at (0,0)

6x + 4y <=2000 and x => 0 intersect at 333.333

2x + 4y <=1000 and y>=0 intersect at  0,250.

Any other intersection points fall outside the range of the givens. The shaded part we are interested in is sort of a very dark green/blue. It is the interior of the quadrilateral determined by the 4 vertices that are marked.

Now all you have to do is determine the maximum point using P=15x + 12y

For 0,0                 P = 15*0 + 12,0 = 0

For 0,250            P = 15*0 + 12*250 = 3000

For 333.3333,0   P = 15*333.3333 + 12*0 = 5000 rounded.

For 250,125        P = 15*250 + 12*125 = 5250  Which is the maximum

Answer (250,125) produces the maximum value Answer

To determine the maximum value of the objective function P in a linear programming problem, one must graph the constraints to find the feasible region and then use the corner-point method to evaluate P at each vertex of this region.

The problem presented is a linear programming problem where we need to find the maximum value of the objective function P, given by P = 15x + 12y, subject to certain constraints involving x and y which must both be non-negative. To solve this problem, we will graph the constraints to find the feasible region and then use the corner-point method to evaluate the objective function at each vertex of this region to determine which gives the maximum value.

Answer:

The probability of choosing an A student is 58% (0.58 or 29/50)

Step-by-step explanation:

The fact that 23 students are boys and 27 are girls is irrelevant to the question so we can ignore that.

There are 50 students in all and out of these students 15 boys and 14 girls made an A.

We can first add 15+14 which equals 29. So 29 students out of 50 made in A on the exam.

29/50 equals 0.58 or 58%.

91.8 ft above sea level

Answer:

12.5 hours

Step-by-step explanation:

15/6 is 2.5. 2.5 is how many hours per worker. 5 times 2.5 is 12.5 hours

Answer:

3.00 = original price * (1-.4)

or

3 = original price*.6

Step-by-step explanation:

We know the cost after the discount.

Price after discount = original price - original price * discount rate

Factoring out the original price

Price after discount = original price (1- discount rate)

We know the price after discount = 3.00  and the discount rate =.40

Substituting these values in

3.00 = original price * (1-.4)

3 = original price*.6

Divide each side by .6

3/.6 = original price

5.00 = original price

Answer:

x=5

Step-by-step explanation:

5x-6=19

first you add 6 to both sides now you have 5x=25 then you divide by 5 on both sides then you get x=5

Question

5x-6=19 what is the variable

Answer:

Step-by-step explanation:

5x - 6 = 19

5x = 19 + 6

5x = 25

x = 25 : 5

x = 5

[tex]f(x)=x^2-2x;\ g(x)=6x+4\\\\(f+g)(x)=f(x)+g(x)\\\\(f+g)(x)=0\Rightarrow(x^2-2x)+(6x+4)=0\\\\x^2+(-2x+6x)+4=0\\\\x^2-4x+4=0\\\\x^2-2x-2x+4=0\\\\x(x-2)-2(x-2)+0\\\\(x-2)(x-2)=0\iff x-2=0\\\\\boxed{x=2}[/tex]

Josh needs 3 and one-eighth feet of plywood to finish building his deck. This conclusion is derived from multiplying the amount of plywood he currently has (5/8 feet) by 5.

The problem stated tells us that Josh has five-eighths of a foot of plywood and he needs five times that amount to finish building the deck. We can solve this problem by performing a simple multiplication operation. The method to solve it would be: 5/8 (amount of plywood Josh has) * 5 (amount of plywood required) = 25/8 = 3 1/8 feet. Therefore, Josh needs 3 and one-eighth feet of plywood to finish building his deck.

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The uppercase T means "transpose". A matrix transpose is where you swap the rows and columns. Anything that is row becomes a column, and vice versa. What this means is that instead of a row vector, you end up with a column vector. The dimensions are important so you can properly multiply matrices.

Answer:

<1 =33

<2 = 147

<4 = 147

Step-by-step explanation:

Angle 1 equals angle 3 because they are vertical angles.  Vertical angles are opposite angles made by two intersecting lines.

<1 = <3

<1 = 33

Angle 2 and <3 are supplementary angles because they form a straight line.  The add to 180 degrees

<2 + <3 = 180  

<2 + 33 = 180

Subtract 33 from each side

<2 +33-33 = 180-33

<2 = 147

Angle 2 equals angle 4 because they are vertical angles

<2 = <4

<4 = 147

Answer:

[tex]n=241[/tex]

Step-by-step explanation:

We are given

[tex]5x^2+nx+48[/tex]

Let's assume it can be factored as

[tex]5x^2+nx+48=(5x-s)(x-r)[/tex]

now, we can multiply right side

and then we can compare it

[tex]5x^2+nx+48=5x^2-5rx-sx+rs[/tex]

[tex]5x^2+nx+48=5x^2-(5r+s)x+rs[/tex]

now, we can compare coefficients

[tex]rs=48[/tex]

[tex]5r+s=-n[/tex]

[tex]n=-(5r+s)[/tex]

now, we can find all possible factors of 48

and then we can assume possible prime factors of 48

[tex]48=-+(1\times 48)[/tex]

[tex]48=-+(2\times 24)[/tex]

[tex]48=-+(3\times 16)[/tex]

[tex]48=-+(4\times 12)[/tex]

[tex]48=-+(6\times 8)[/tex]

Since, we have to find the largest value of n

So, we will get consider larger value of r because of 5r

and because n is negative of 5r+s

so, we will both n and r as negative

So, we can assume

r=-48 and s=-1

so, we get

[tex]n=-(5\times -48-1)[/tex]

[tex]n=241[/tex]

Statement: Two planes intersect to form a point

This is false. Two planes intersect to form a single straight line.

-----------------

Statement: two lines intersect to form a point

This is true assuming the two lines have different slopes

-----------------

Because the first statement is false, the overall argument is false.

Final answer:

The intersection of two planes is a line, not a point, which makes the statement false. Two lines intersecting in a point is true provided they are not parallel.

Explanation:

The statement that the intersection of two planes is a point is false. According to geometric principles, specifically the line of intersection of two planes, when two planes intersect, they do so along a line, not just a single point. This line of intersection is represented by the points where their respective great circles cross. The intersection of two lines, however, is indeed a point, provided that the lines are not parallel. This is in agreement with Theorem 1, which states that two straight lines of a plane have either one point or no point in common; similarly, two planes have no point in common or a straight line in common.

Relevant Theorems on Intersections

Theorem 1 and Theorem 2 outline the foundational concepts regarding intersections in geometry. Understanding these theorems helps explain why two intersecting planes result in a line and not a single point.

Answer:

The solution of the inequality is [tex](-2.5,\infty)[/tex].

Step-by-step explanation:

The given inequality is

[tex]-3x<7.5[/tex]

If an inequality divided by a negative number,then the sign of inequality change. Divide both sides by -3.

[tex]\frac{-3x}{-3} >\frac{7.5}{-3}[/tex]

[tex]x >-2.5[/tex]

Therefore the solution of the given inequality is all real numbers greater than -2.5.

In interval notation it can be defined as

[tex](-2.5,\infty)[/tex]

Answer:

x > −2.5

Step-by-step explanation:

i got the correct answer

Answer:

see below  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

$23.95 x 2 = $47.90

$100 - $47.90 = $52.10

$52.10 ÷ .34 = 153.23 miles can be driven  

If you need to round the number will be 153 miles

[tex]A(n)=-3+(n-1)(-2.2)=-3+(n)(-2.2)+(-1)(-2.2)\\\\A(n)=-3-2.2n+2.2=-0.8-2.2n\\\\\text{Substitute n = 1, n = 4, n = 10}:\\\\A(1)=-0.8-2.2(1)=-0.8-2.2=-3\\\\A(4)=-0.8-2.2(4)=-0.8-2.2(4)=-0.8-8.8=-9.6\\\\A(10)=-0.8-2.2(10)=-0.8-22=-22.8[/tex]

Answer:

12

Step-by-step explanation:

So the ratio is 5:2, so we can set up a proportion! So there are 12 sweaters.

Answer:

17.2°

Step-by-step explanation:

using the tangent ration in the right triangle

tan y° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{19.1}{14.1}[/tex], hence

y = [tex]tan^{-1}[/tex]([tex]\frac{19.1}{14.1}[/tex]) ≈ 53.6°

tan x° = [tex]\frac{14.1}{19.1}[/tex], hence

x = [tex]tan^{-1}[/tex]([tex]\frac{14.1}{19.1}[/tex]) ≈ 36.4°

y - x = 53.6° - 36.4° = 17.2°

Answer:

D) y -x = Approximate 17.1 degree.

Step-by-step explanation:

Given : Triangle .

To find :  Approximate value of y - x.

Solution : We have given a right angle triangle with

Opposite side = 19.1 in.

Adjacent side = 14 .1 in.

Tan( y ) = [tex]\frac{Opposite}{adjacent}[/tex].

Plug the values

Tan( y ) = [tex]\frac{19.1}{14.1}[/tex].

tan(y) = 1.354.

Taking tan inverse both sides.

y = [tex]tan^{-1}(1.354)[/tex].

y = 53.55 degree.

Now, by the sum of angle of triangles is 180 degree.

Angle c + angle y + angle  x = 180.

Plug the variable

90 + 53.55 + x = 180.

83.55 + x = 180

On subtracting both sides by 83.55

x = 36.45 degree

Then ,

y - x = 53 .55 - 36 . 45

y - x = 17.2

Approximate 17.1 degree

Therefore, D) y -x = Approximate 17.1 degree.

Answer:

t = 0.35, t = 5.65

Step-by-step explanation:

You are given h = 30t - 5t^2. Put this in standard form order (ax^2 + bx + c) by switching the two terms.

h = -5t^2 + 30t

Now you want to find all the values of t for which the rocket's height is 10 meters, so your equation will be equal to 10 instead of h, because 10 is the height you are solving for.

10 = -5t^2 + 30t

Make the entire equation equal to 0 by subtracting 10 from both sides.

0 = -5t^2 + 30t - 10

To solve this quadratic equation, the easiest way would be to use the quadratic formula: [tex]\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Identify your a, b, and c values in the standard form equation (a = -5, b = 30, c = -10) and substitute these values into the quadratic formula.[tex]\frac{-(30)\pm\sqrt{(30)^2-4(-5)(-10)} }{2(-5)} \rightarrow \frac{-30\pm\sqrt{900-200=700} }{-10} \rightarrow \frac{-30\pm\sqrt{700} }{-10}[/tex]

We have (-30 ± sqrt 700)/-10.

Use a calculator to input the two solutions and solve for them; (-30 + sqrt 700)/-10 and (-30 - sqrt 700)/-10.

[tex]\frac{-30+\sqrt{700} }{-10} = 0.35[/tex]

[tex]\frac{-30- \sqrt{700} }{-10} =5.65[/tex]

The quadratic formula is used to solve the equation h = 30t - 5t^2 when h is set to 10 meters, yielding two times at which the rocket's height is 10 meters: approximately 0.59 seconds and 3.41 seconds.

10 = 30t - 5t2

Moving all terms to one side we get:

5t2 - 30t + 10 = 0

To simplify, we divide the entire equation by 5:

t2 - 6t + 2 = 0

Now we can apply the quadratic formula:

t = √ (62 - 4*1*2) )/ (2*1)

Calculating under the square root, we get:

t = (6 √ (36 - 8) )/ 2

t = (6 ± √28) / 2

Thus, the two solutions for t are:

t = (6 + √28) / 2 and t = (6 - √28) / 2

Rounded to the nearest hundredth, the values of t are approximately 0.59 s and 3.41 s. The rocket reaches a height of 10 meters at these two instances during its flight - once when ascending and once when descending.