A card player selects 2 cards from a deck of 52 cards at random without replacement. The deck contains 4 aces.

What is the probability that both cards the player selects are aces?

Answer:

Step-by-step explanation:

Given that:

[tex]y^2 (y^2-4) = x^2(x^2 -5)[/tex]

at point (0, -2)

[tex]\implies y^4 -4y^2 = x^4 -5x^2[/tex]

Taking the differential from the equation above with respect to x;

[tex]4y^3 \dfrac{dy}{dx}-8y \dfrac{dy}{dx}= 4x^3 -10x[/tex]

Collect like terms

[tex](4y^3 -8y)\dfrac{dy}{dx}= 4x^3 -10x[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{4x^3 -10x}{4y^3-8y}[/tex]

Hence, the slope of the tangent line m can be said to be:

[tex]\dfrac{dy}{dx}= \dfrac{4x^3 -10x}{4y^3-8y}[/tex]

At point (0,-2)

[tex]\dfrac{dy}{dx}= \dfrac{4(0)^3 -10(0)}{4(-2)^3-8-(2)}[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{0 -0}{4(-8)+16}[/tex]

[tex]\dfrac{dy}{dx}= 0[/tex]

m = 0

So, we now have the equation of the tangent line with slope m = 0 moving through the point (x, y) = (0, -2) to be:

(y - y₁ = m(x - x₁))

y + 2 = 0(x - 0)

y + 2 = 0

y = -2

Answer:

The only true statement is:

"The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution."

Step-by-step explanation:

First, some definitions.

A system of linear equations has infinite solutions if both equations define the same line, has no solutions if we have two parallel lines, has one solution in all the other cases.

Where two lines are parallel if we can write them as:

a*x + b*y = c

a*x + b*y = d

where c and d are different numbers.

Now we can analyze the given statements:

a)

6x - 5y = 8

12x - 10y = 16

has no solution?

If we divide both sides of the second equation by 2, we get:

(12x - 10y)/2 = 16/2

6x - 5y = 8

We get the first equation, then both equations define the same line, thus the system has infinite solutions, then the statement is false.

b)

7x + 2y = 6

14x + 4y = 16

has infinite solutions?

Let's divide the second equation by 2, then we get:

(14x + 4y)/2 = 16/2

7x + 2y = 8

If we rewrite our system of equations, we get:

7x + 2y = 6

7x + 2y = 8

These are parallel lines, thus, this system has no solutions.

So the statement is false.

c)

8x - 3y = 10

16x - 6y = 22

has no solution?

Again, let's divide the second equation by 2 to get:

(16x - 6y)/2 = 22/2

8x - 3y = 11

If we rewrite our system:

8x - 3y = 10

8x - 3y = 11

These are parallel lines, thus the system has no solutions, so this statement is correct.

d)

9x + 6y = 14

18x + 12y = 26

Has infinite solutions?

Dividing the second equation by 2 we get:

(18x + 12y)/2 = 26/2

9x + 6y = 13

So the equations are different (are parallel lines again) so this system has not infinite solutions.

Then the statement is false.

Answer:

The answer to your question is the third choice.

Step-by-step explanation:

a)          6x - 5y = 8

          12x - 10y = 16

We observe that these lines are the same so they have infinite solutions.

b)

           7x + 2y = 6

          14x + 4y = 16

These lines are parallel because they have the same slope, so they do not cross, there is no solution.

c)

            8x - 3y = 10

           16x - 6y = 22

These lines are parallel because they have the same slope, so they do not cross, there is no solution.

d)

           9x + 6y = 14

          18x + 12y = 26

These lines are parallel because they have the same slope, so they do not cross, they do not have an infinite number of solutions.

Answer:

z=1.96

Step-by-step explanation:

Using normal distribution table or technology, 97.5% corresponds to z=1.959964, generally denoted z=1.96, or 1.96 standard deviations above the mean.

(above value obtained from R)

Answer:

Profit % on skates = 8.7 %

Step-by-step explanation:

Step 1 : Find cost price of skates

Cost price of helmet = £45

Let cost price of skate be = x

Selling price = £224

Cost price = (x + 45)

Total profit % = 40%

[tex]Profit \% = \frac{Selling \ price - cost \ price }{Cost \ price} \times 100[/tex]

[tex]\frac{40}{100} = \frac{224 - (x + 45)}{(x + 45)}\\\\40(x+ 45) = 100(224 - (x +45))\\\\40(x + 45) = 22400 - 100(x + 45)\\\\40(x +45) + 100(x+ 45) = 22400\\\\140(x + 25) = 22400\\\\x + 45 = \frac{22400}{140}\\\\x = 160 - 45 = \£ \ 115[/tex]

Total cost price = 45 + 115 = £160

Step 2 : Selling price of Helmet

Cost price of Helmet = £45

Let selling price of helmet be = y

Profit % of helmet = 120 %

[tex]Profit \% = \frac{selling \ price - cost \ price}{cost \ price}[/tex]

[tex]\frac{120}{100} = \frac{y -45}{45}\\\\\frac{120 \times 45}{100} = y -45\\\\54 = y - 45\\\\99 = y[/tex]

Step 3 : Selling price of skates

Total selling = selling price of helmet + selling price of skates

224 = 99 + selling price of skates

224 - 99 = selling price of skates

125 = selling price of skates

Step 4 : Profit percentage on skates

Cost price of skate = £ 115

Selling price of skate = £ 125

[tex]Profit \% \ on \ skates = \frac{selling\ price- cost \ price }{cost \ price} \times 100[/tex]

                           [tex]= \frac{125-115}{115} \times 100\\\\=\frac{10}{115} \times 100\\\\= 8.7 \%[/tex]

Answer:

4x^2 + 2x + 4

Step-by-step explanation:

5x^2 + 2x + 4 - x^2

4x^2 + 2x + 4

Answer:

2(2x^2 + x + 2)

Step-by-step explanation:

5x^2+2x + 4-x^2

Re arrange so like terms are next to each other

Keep the same symbol that is at the front of the term when moving it

5x^2 - x^2 + 2x + 4

We will just do the first part first

5x^2 - x^2

5x^2 - 1x^2 (is the same thing as above)

So because they are like terms (are both x^2)

We can just minus 1 from 5

5-1=4

So 4x^2

Now the equation is

4x^2 + 2x + 4

This is as small as it gets but you can also bring it to this

4, 2 and 4 all are divisible by 2 so

2(2x^2 + x + 2)

Answer:

10km per hour

Step-by-step explanation:

Distance = speed * time

speed = distance/time

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

Distance traveled

25 + 30 + 35 = 90 km

Time

2 + 3 + 4 = 9 hours

Average peed

90/9 = 10km per hour

Answer:

First find the SA of the triangular figure

4 x 3 = 12 cm^2 (the triangles on the sides)

2 x 3 = 6 cm^2 (the back square)

2 x 5 = 10 cm^2 (the slanted square)

*I'm not sure if this question includes the bottom of the triangle but here it is anyways

4 x 2 = 8 cm^2

Including the bottom the SA of the triangular figure is:

12 + 6 + 10 + 8 = 36 cm^2

Find the SA of the rectangular shape

4 x 2 = 8 cm^2 (the bottom square)

2 x 6 = 12 x 2 = 24 cm^2 (the sides)

4 x 6 = 24 x 2 = 48 cm^2 (the front and back)

Add them up

8 + 24 + 48 = 80 cm^2

If you wanted to find the SA of the whole figure it would be:

12 + 6 + 10 + 8 + 24 + 48 = 108 cm^2

Hope this helps!

Answer:

P = $98.77

Step-by-step explanation:

FV = p (1+i)^n -1

            i

pv = 700,000

i = .075/12 = .00625

n = (66 - 15)* 12 = 612

700,000 = P (( 1 + .00625)^ 612 -1 /.00625

4375 = P (1.00625)^612 -1)

P = $98.77

Answer:

page 1:

51 years

$98.78

639546.64 (i think)

Page 2:

213 months

17.8 years

321 months

26.8 years

1128.9 months

88.8 years

I would probably choose the second plan because it's rather unlikely that i live past 90

Step-by-step explanation:

page 1

Let's assume the payments are at the end of the month

66-15= 51 years

effective rate: .075/12=.00625

[tex]700000=x\frac{(1+.00625)^{51*12}-1}{.00625}\\x=98.77973387[/tex]

which i guess we can round to 98.78

700000-98.78*(51*12)= 639546.64

This number is really really high and so maybe you want to double check it

page 2

effective rate: .051/12=.00425

[tex]700000=5000\frac{1-(1+.00425)^{-n}}{.00425}\\.405=(1+.00425)^{-n}\\log_{1.00425}.405=-n\\n=213[/tex]

213 months

213/12= 17.8 years

[tex]700000=4000\frac{1-(1+.00425)^{-n}}{.00425}\\.25625=(1.00425)^{-n}\\log_{1.00425}.25625\\n=321[/tex]

321 months

321/12=26.8 years

[tex]700000=3000\frac{1-(1+.00425)^{-n}}{.00425}\\.008333333=(1.0045)^{-n}\\log_{1.0045}.00833333=-n\\n=1128.9[/tex]

1128.9 months

1128.9/12= 94.1 years

1066 months

1066/12= 88.8 years

Answer:

The cost per printer is $240 and the cost per computer is $530

Explanation:

Make the equation from both parts of the problem and solve them.

Answer:

[tex]\displaystyle x \approx 9.9[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

Identify variables

Angle θ = 64°

Opposite Leg = x

Hypotenuse = 11

Step 2: Solve for x

No, x²+y²= 9 does not represent y as a function of x.

For x= 0,

y²= 9

=>y= ±3,

i.e y has two values +3 and -3

Since single value of x , there are two values of y

For an equation or relation to be function every element in domain( every value of x) there should one distinct value or image in co-domain (one value of y)

Answer:

maybe if u translate it in English

Step-by-step explanation:

it wouldv been helpful if u mind?

Answer:

22°

63°

m<H=22°

m<G=63°

Problem 1

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

Work Shown:

For any triangle, the three angles always add to 180

For any isosceles triangle, the base angles are congruent. The base angles are opposite the congruent sides. We see that angle O = angle H.

O+H+T = 180

H+H+T = 180

2H+T = 180

2H+22 = 180

2H = 180 - 22

2H = 158

H = 158/2

H = 79

=======================================================

Problem 2

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

Work Shown:

We'll use the same ideas as problem 1.

In this case, angle O = angle D = 63 since they are the base angles opposite the congruent sides.

D+G+O = 180

63+G+63 = 180

G+126 = 180

G = 180-126

G = 54

Answer:

4/10 but simplified = 2/5

Step-by-step explanation:

Add the marbles up, there are 4 green, so it's 4/10

But if you simplify it, it would be 2/5

I hope this helped!

Answer:

The probability is [tex]\frac{24}{70}[/tex].

Step-by-step explanation:

topping options available: four vegetables, two meats, and two cheeses

Number of topping on one pizza = 4

Getting two vegetables = (4 C 2)

Getting one meat = (2 C 1)

Getting one cheese = (2 C 1)

Choosing 4 toppings out of 8 = (8 C 4)

probability that the pizza is ordered with exactly two vegetables, one meat, and one cheese

[tex]\frac{(4C2)\times (2C1)\times (2C1)}{(8C4)}\\\\\frac{6\times 2\times 2}{70}\\\\\frac{24}{70}[/tex]

Answer:

x = -5y

Step-by-step explanation:

x = ay

-10 = 2a

a = -5

x = ay

-15 = 3a

a = -5

x = ay

-25 = 5a

a = -5

Answer:

what is the question?

Step-by-step explanation:

answer the question

The slope formula is the changes of two y-values over/to the changes of two x-values.

[tex] \large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }[/tex]

Substitute two given points in the formula to find the slope. The m-term represents the slope from y = mx+b.

[tex]\large{m = \frac{10 - ( - 8)}{2 - 10} } \\ \large{m = \frac{10 + 8}{ - 8} } \\ \large{ m = \frac{18} { - 8} \longrightarrow \frac{9}{ - 4} } \\ \large \boxed{m = - \frac{9}{4} }[/tex]

Answer

Hope this helps and let me know if you have any doubts!

Answer:

m=-9/4

Step-by-step explanation:

Hi there!

The formula for the slope (m) calculated from two points is given as (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are points

we are given the two points (2,10) and (10,-8)

to avoid any confusion, let's label the values of the points

x1=2

y1=10

x2=10

y2=-8

now substitute into the formula:

m=(-8-10)/(10-2)

subtract

m=(-18)/(8)

simplify (reduce to lowest terms)

m=-9/4

Hope this helps!

Answer:

how old are you gghhjjzetstu9u

Answer:

4 ft

Step-by-step explanation:

let's find radius first

radius=diameter/2

=6/2

=3 ft

radii=3 ft

Now by using pythagoras theorem

a^2 + b^2 = c^2

3^2 + 3^2 =AB^2

9+9=AB^2

18=AB^2

[tex]\sqrt{18}[/tex] AB

4.24 =AB

4 ft =AB (after converting to nearest foot)

Answer:

B-2

Step-by-step explanation:

To find the constant of dilation take the lead of EF and divide it by the length of AB to get (6/3)=2

Answer:

3 feet

Step-by-step explanation:

A = l x w                    Formula

18.9 = 6.3 x w           Substitution

18.9/6.3 = w              Division

3 = w                         Solution

Step-by-step explanation:

the answer is in the image above

Answer:

Kindly check explanation

Step-by-step explanation:

The hypothesis :

H0 : μ = 3000

H0 : μ ≠ 3000

The test statistic :

(xbar - μ) ÷ (s/√(n))

xbar = 3500

μ = 3000

σ = 300

n = 30

(3500 - 3000) ÷ (350/√(30))

Test statistic = 7.824

Df = 30 - 1 = 29

Tcritical at 0.01 = 2.462

Test statistic > critical value ; we reject H0 ; and concluded that there is significant evidence that

μ ≠ 3000

Answer:

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.

Answer:

f(d)=0.1d^2+d+2

Step-by-step explanation:

t(d)=−0.2d2+4d+12

a(d)=−0.3d2+3d+10

how many more teenagers than adults attend the festival on any day?

==>

f(d) = t(d) - a(d)

=0.1d^2+d+2

Answer:

The coordinates of point E are (7,8).

Step-by-step explanation:

Point E:

Is given by (x,y).

DE: EF = 2:3.

This means that, for both coordinates x and y:

[tex]E - D = \frac{2}{2+3}(F-D)[/tex]

[tex]E - D = \frac{2}{5}(F-D)[/tex]

x-coordinate:

x-coordinate of D: 1

x-coordinate of F: 16

[tex]E - D = \frac{2}{5}(F-D)[/tex]

[tex]x - 1 = \frac{2}{5}(16-1)[/tex]

[tex]x - 1 = 2*3[/tex]

[tex]x = 7[/tex]

y-coordiante:

y-coordinate of D: 4

y-coordinate of F: 14

[tex]E - D = \frac{2}{5}(F-D)[/tex]

[tex]y - 4 = \frac{2}{5}(14-4)[/tex]

[tex]y - 4 = 2*2[/tex]

[tex]x = 8[/tex]

The coordinates of point E are (7,8).

Answer:

you will remember none of the words.

Step-by-step explanation:

10%of hundred words is 10.

students attend school for 5 days in a week.So if one is to forget 10 words out of 100 words every day for two weeks after a test,one loses all words.

5×10=50

for two weeks=

50×2=100.