Is the quotient of (-5) ÷ (-7) a rational number

Answer:

2 time 5 squared is simplified form of 60 they both get the end result of 7.4

Step-by-step explanation:

Answer:

The correct answer is second option

2√15

Step-by-step explanation:

From the attached question we can see that,

√60

To find the value of √60

We know that, 60 = 4 * 15

and √4 = 2

Therefore √60 can be written as,

√60 = √(4 * 15)

 = 2√15

The correct answer is 2√15

Therefore the correct option is second option.

√60 = 2√15

Answer:

an increase then a pause then anotha increase

Step-by-step explanation:

Hold on I have that answer

Answer:

The numerical value of circumference is greater than the numerical value of area

Step-by-step explanation:

Given

circumference= 2π

formula for circumference of circle is 2πr

hence r of given circle is 1

formula for area of circle is πr^2

putting r=1 in above equation

Area of given circle= π(1)^2

                               = π

As 2π>π

The numerical value of circumference is greater than the numerical value of area!

Answer:

The quotient is (10x - 5) and the reminder is -50 ⇒ 1st answer

Step-by-step explanation:

* Lets solve the long division by easiest way

∵ (10x² - 85x - 10)/(x - 8)

∵ (10x² - 85x - 10) is the dividend

∵ (x - 8) is the divisor

- Divide the first term of the dividend by the first term of the divisor

∴ 10x² ÷ x = 10x ⇒ first term of the quotient

- Multiply 10x by the the divisor

∴ 10x(x - 8) = 10x² - 80x

- Subtract the answer from the dividend

∴ (10x² - 85x - 10) - (10x² - 80x) =

# 10x² - 10x² = 0

# -85x - -80x = -85x + 80x = -5x

# -10

∴ (10x² - 85x - 10)/(x - 8) = 10x + (-5x - 10)/(x - 8)

* Repeat the same steps again with the new dividend -5x - 10

- Divide the first term of the dividend by the first term of the divisor

∴ -5x ÷ x = -5 ⇒ second term of the quotient

- Multiply -5 by the divisor

∴ -5(x - 8) = -5x + 40

- Subtract the answer from the dividend

∴ (-5x - 10) - (-5x + 40) =

# -5x - -5x = -5x + 5x = 0

# -10 - 40 = -50

∴ (-5x - 10)/(x - 8) = -5 + -50/(x - 8)

∴ (10x² - 85x - 10)/(x - 8) = 10x - 5 + -50/(x - 8)

- The quotient is the answer of the division

∴ The quotient is (10x - 5) and the reminder is -50

Answer:

The quotient is 10x - 5 and the reminder is -50

Step-by-step explanation:

Answer:

y<2x-4

y<-2x

Step-by-step explanation:

Since we are dealing with and inequality we need to remember the following tips.

We no obtain values from inequalities, we obtain ranges.

If y<f(x), the range of variable y resides below de graph of f(x), but if y>f(x), the range is above.

y<2|x-1|-2​

Gives two functions.

first'

y<2(x-1)-2 if x>1 and

y<-2(x-1)-2 if x<1

First equation turns in y<2x-4 and the second y<-2x

Two line going in different directions

5x=45

divide by 5 for 5x and 45 to get the answer

5x/5= 45/5

x=9 ( Answer)

The solution to the equation 5x = 45 is x = 9.

To solve the equation 5x = 45, you want to find the value of x that satisfies the equation.

Here's how you can solve it step by step:

Step 1: Start with the equation 5x = 45.

Step 2: To isolate x, divide both sides of the equation by 5. This step cancels out the multiplication by 5 on the left side of the equation.

(5x) / 5 = 45 / 5

Simplifying further:

x = 9

Explanation: In Step 2, when you divide both sides of the equation by 5, you are essentially undoing the multiplication operation on the left side.

By dividing both sides by the same number, you maintain the equality of the equation.

On the left side, the 5s cancel out, leaving you with just x. On the right side, 45 divided by 5 equals 9.

Thus, x = 9 is the value that satisfies the equation.

Therefore, the solution to the equation 5x = 45 is x = 9.

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ANSWER

The correct a sweet is 7

EXPLANATION

The given algebraic expression is;

[tex]f(x) = - 3 {x}^{3} - 4x[/tex]

To evaluate this function for f means, we should substitute x=-1 wherever we see x in the given expression.

[tex] f( - 1) = - 3 { (-1 )}^{3} - 4( - 1)[/tex]

[tex]f( - 1) = - 3 { (-1 )} - 4( - 1)[/tex]

This simplifies to

[tex]f( - 1) = 3 + 4[/tex]

[tex]f( - 1) = 7[/tex]

The correct answer is 7

Answer:

9x^2-4

Step-by-step explanation:

use FOIL

9x²-4 is represented by the factorization.

Writing a number or other mathematical object as the result of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics.

Given

(3x+2)(3x - 2)

= 9x² + 6x - 6x -4

= 9x² -4

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Answer:

0

Step-by-step explanation:

From the graph of the function f(x) we have:

        When f(x)=0  ,   x= -1.8

By looking at the graph we observe that the graph first increases in the interval (-∞,-1.2) and then it decreases in the interval (-1.2,0.6) and then again it increases in the interval (0.6,∞).

Hence, the graph of the function is neither strictly increasing nor strictly decreasing in the whole of the real line.

Also, when x=0 the value of the function is: f(x)=5

( Since, the graph passes through the point (0,5) )

Also, when f(x)=0

then x= -1.8

( Since, the graph of the function passes through the point (-1.8,0) )

Answer:

32 × 2 = 64

Step-by-step explanation:

x is being multiplied by 2 so it would be half of 64.

Answer:

x = ± 8

Step-by-step explanation:

Given

x² = 64 ( take the square root of both sides )

x = ± [tex]\sqrt{64}[/tex] = ± 8 ← note plus or minus

[ since 8² = 64 and (- 8)² = 64 ]

that is incorrect. you would have to do $3.00 divided by 60 which is equal to 0.05. therefore, each crayon costs 0.05. the way you can check that this is right is to do 0.05 multiplied by 60 which will get you to $3.00

Answer:

3.00 is the correct answer

Answer:

x=9 and x=-2

Step-by-step explanation:

GFC = 9 => 9(x²-6x-16) =0

9(x-8)(x+2) = 0

x-b=0    x+2= 0

x=8 and x = -2

Solving the quadratic equation, it is found that the company needs to sell 8 products for the net income to be equal $0.

It is given by:

f(x) = 9x² - 54x - 144.

It can be simplified as follows:

f(x) = 9(x² - 6x - 16)

Then:

f(x) = 9[(x + 2)(x - 8)]

It has a net income equals to 0 when:

f(x) = 0, hence:

The amount of products sold is positive, hence, the company needs to sell 8 products for the net income to be equal $0.

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Answer:

  98 ft²

Step-by-step explanation:

There are a couple of ways you can think about this one. Perhaps easiest is to treat it as a square with a triangle cut out of it. The cutout triangle has a base (across the top) of 14 ft and a height of 14 ft, so its area is ...

  A = (1/2)(14 ft)(14 ft) = 98 ft²

Of course the area of the square from which it is cut is ...

  A = (14 ft)² = 196 ft²

So, the net area of the two triangles shown is ...

  A = (196 ft²) - (98 ft²) = 98 ft²

_____

Another way to work this problem is to attack it directly. Let the base of the left triangle be x. Then the base of the right triangle is 14-x, and their total area is ...

  A = A1 + A2 = (1/2)(x ft)(14 ft) + (1/2)((14-x) ft)(14 ft)

We can factor out 7 ft to get ...

  A = (7 ft)(x ft + (14 -x) ft)

  A = (7 ft)(14 ft) = 98 ft²

Answer:

a)  4x +7y =100             b)  4x = 100-7y

Step-by-step explanation:

students = 4x

teachers  = 7y

4x +7y = 100

4x =100 -7y

Final answer:

The equation is solved to determine the number of students Mr. Bean gave money to as 2.

Explanation:

a) Equation:

Let x be the number of students and y be the number of teachers Mr. Bean gave money to.

Equation: 4x + 7y = 100

b) Solving the equation:

Given that Mr. Bean only gave out $100, we substitute this into the equation:

4x + 7y = 100

4x + 7(14-x) = 100

4x + 98 - 7x = 100

98 - 3x = 100

-3x = 2

x = -2/-3 = 2/3

Therefore, Mr. Bean gave money to 2 students.

Learn more about Equation solving here:

Answer: 78.85 ft

Step-by-step explanation:

 Based on the information provided in the exercise, you can draw the right triangle attached, wheree "x" is the height of the tree.

You need to remember the following identity:

[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]

By definition:

[tex]\alpha+108\°=180\°[/tex]

Then, this is:

[tex]\alpha=180\°-108\°\\\alpha =72\°[/tex]

In the right triangle shown in the figure, you can identify:

[tex]opposite=75\\hypotenuse=x[/tex]

Then, you need to substitute the corresponding values into  [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]:

 [tex]sin(72\°)=\frac{75}{x}[/tex]

Now, you can solve for "x":

[tex]xsin(72\°)=75\\\\x=\frac{75}{sin(72\°)}\\\\x=78.85\ ft[/tex]

Answer:

answer is 25t I DID THE TEST!!

Answer: 25F i did the test

Step-by-step explanation:

Hey there! :)

(0, 2) & (-1, -2)

Slope-intercept form is : y=mx+b , where m=slope, b=y-intercept

First, we must find the slope using the slope formula, which is :

m = y2-y1/x2-x1

Where y2 = -2 ; y1 = 2 ; x2 = -1 ; x1 = 0

Now, let's plug and chug! :)

m = (-2 - 2) / (-1 - 0)

Simplify.

m = -4/-1 --> Therefore, our slope is : m = 4

Now that we have the slope, we can plug this (and our original coordinates) into point-slope form, which is : y - y1 = m(x - x1) -> use the coordinates (0, 2)

y - 2 = 4(x - 0)

Simplify.

y - 2 = 4x

Add 2 to both sides.

y = 4x + 2

Hope this helped! :)

Answer:

Step-by-step explanation:

[tex]k\in\mathbb{Z}\\\\\sin x=0\iff x=180^ok\\\\\cos x=0\iff x=90^o+180^ok\\\\\tan x=0\iff x=180^ok\\\\\cot x=0\iff x=90^o+180^ok\\\\\csc x\neq0\ \text{for}\ x\in\mathbb{R}-\{180^ok\}\\========================\\\\\sin270^o\neq0\\\\\cos90^o=\cos(90^o+180^o\cdot0)=0\\\\\tan0^o=\tan(180^o\cdot0)=0\\\\\csc(-180^o)\neq0\\\\\cos(-90^o)=\cos(90^o-180^o)=\cos(90^o+180^o\cdot(-1))=0\\\\\cot270^o=\cot(90^o+180^o)=0[/tex]

Answer:

cos90° = 0°, tan0° = 0°,cos(-90°) = 0°, cot270° = 0°

Step-by-step explanation:

Answer:

The coordinates of C are (5 , 2)

The slope of CD is 3

The coordinates of D are (6 , 5) and (4 , -1)

Step-by-step explanation:

* Now lets study the problem

- The ends points of line AB are A = 2 , 3) and B = (8 , 1)

- CD is the perpendicular bisector of AB, and C lies on AB

- That means:

# C is the mid-point of AB

# The slope of AB × the slope of CD = -1 (one of them is a multiplicative

  inverse and additive inverse of the other)

-Ex: the slope of one is a/b, then the slope of the other is -b/a

* The mid-point between two points (x1 , y1) and (x2 , y2) is:

  [(x1 + x2)/2 , (y1 + y2)/2]

∵ C is the mid-point of AB

∴ C = [(2 + 8)/2 , (3 + 1)/2] = [10/2 , 4/2] = (5 , 2)

* The coordinates of C are (5 , 2)

- The slope of a line passing through points (x1 , y1) and (x2 , y2) is:

 the slope = (y2 - y1)/(x2 - x1)

∴ The slope of AB = (1 - 3)/(8 -2) = -2/6 = -1/3

∵ CD ⊥ AB

∴ The slope of CD × the slope of AB = -1

∴ The slope of CD = 3

* The slope of CD is 3

- The length of a line passing through points (x1 , y1) and (x2 , y2) is:

 the length = √[(x2 - x1)² + (y2 - y1)²]

∵ The length of CD = √10

∵ Point D is (x , y)

∴ (x - 5)² + (y - 2)² = (√10)²

∴ (x - 5)² + (y - 2)² = 10 ⇒ (1)

∵ The slope of CD is (y - 2)/(x - 5) = 3 ⇒ by using cross multiply

∴ (y - 2) = 3(x - 5) ⇒ (2)

- Substitute (2) in (1)

∴ (x - 5)² + [3(x - 5)]² = 10 ⇒ simplify

* [3(x - 5)]² = (3)²(x - 5)² = 9(x - 5)²

∴ (x - 5)² + 9(x - 5)² = 10 ⇒ add the like terms

∴ 10(x - 5)² = 10 ⇒ ÷ 10 both sides

∴ (x - 5)² = 1 ⇒ take √ for both sides

∴ x - 5 = ± 1

∴ x - 5 = 1 ⇒ add 5 to both sides

∴ x = 6

* OR

∴ x - 5 = -1 ⇒ add 5 to both sides

∴ x = 4

- Substitute the values of x in (2)

∴ y - 2 = 3(6 - 5)

∴ y - 2 = 3 ⇒ add 2

∴ y = 5

* OR

∴ y - 2 = 3(4 - 5)

∴ y - 2 = -3 ⇒ add 2

∴ y = -1

* The coordinates of D are (6 , 5) and (4 , -1)

Answer and Step-by-step explanation:

Answer:

The coordinates of C are (5 , 2)

The slope of CD is 3

The coordinates of D are (6 , 5) and (4 , -1)

Step-by-step explanation:

* Now lets study the problem

- The ends points of line AB are A = 2 , 3) and B = (8 , 1)

- CD is the perpendicular bisector of AB, and C lies on AB

- That means:

# C is the mid-point of AB

# The slope of AB × the slope of CD = -1 (one of them is a multiplicative

 inverse and additive inverse of the other)

-Ex: the slope of one is a/b, then the slope of the other is -b/a

* The mid-point between two points (x1 , y1) and (x2 , y2) is:

 [(x1 + x2)/2 , (y1 + y2)/2]

∵ C is the mid-point of AB

∴ C = [(2 + 8)/2 , (3 + 1)/2] = [10/2 , 4/2] = (5 , 2)

* The coordinates of C are (5 , 2)

- The slope of a line passing through points (x1 , y1) and (x2 , y2) is:

the slope = (y2 - y1)/(x2 - x1)

∴ The slope of AB = (1 - 3)/(8 -2) = -2/6 = -1/3

∵ CD ⊥ AB

∴ The slope of CD × the slope of AB = -1

∴ The slope of CD = 3

* The slope of CD is 3

- The length of a line passing through points (x1 , y1) and (x2 , y2) is:

the length = √[(x2 - x1)² + (y2 - y1)²]

∵ The length of CD = √10

∵ Point D is (x , y)

∴ (x - 5)² + (y - 2)² = (√10)²

∴ (x - 5)² + (y - 2)² = 10 ⇒ (1)

∵ The slope of CD is (y - 2)/(x - 5) = 3 ⇒ by using cross multiply

∴ (y - 2) = 3(x - 5) ⇒ (2)

- Substitute (2) in (1)

∴ (x - 5)² + [3(x - 5)]² = 10 ⇒ simplify

* [3(x - 5)]² = (3)²(x - 5)² = 9(x - 5)²

∴ (x - 5)² + 9(x - 5)² = 10 ⇒ add the like terms

∴ 10(x - 5)² = 10 ⇒ ÷ 10 both sides

∴ (x - 5)² = 1 ⇒ take √ for both sides

∴ x - 5 = ± 1

∴ x - 5 = 1 ⇒ add 5 to both sides

∴ x = 6

* OR

∴ x - 5 = -1 ⇒ add 5 to both sides

∴ x = 4

- Substitute the values of x in (2)

∴ y - 2 = 3(6 - 5)

∴ y - 2 = 3 ⇒ add 2

∴ y = 5

* OR

∴ y - 2 = 3(4 - 5)

∴ y - 2 = -3 ⇒ add 2

∴ y = -1

* The coordinates of D are (6 , 5) and (4 , -1)

The circumference of the circle with a diameter of 16 units is approximately 50.26544 units.

To find the circumference of a circle, you can use the formula C = πd, where C represents the circumference and d is the diameter of the circle. In this case, the diameter of the circle is given as 16 units.

Substituting the value into the formula, we have C = π(16). Using the value of π (pi) as approximately 3.14159, we can calculate the circumference.

C = 3.14159 x 16 = 50.26544 units.

Therefore, the circumference of the circle with a diameter of 16 units is approximately 50.26544 units.

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Answer:

domain; x<0 or x>0

Step-by-step explanation:

We have been given the following function;

f(x) = 2x + 6/x^2 + 5x + 6

We need to evaluate the values of f(x) for the following domain values;

{-3, -2, 0, 2, 3}

f(-3) = 2(-3) + 6/(-3)^2 + 5(-3) + 6

      = -43/3

f(-2) = 2(-2) + 6/(-2)^2 + 5(-2) + 6

      = -6.5

f(0) = 2(0) + 6/(0)^2 + 5(0) + 6

     = undefined

f(2) = 2(2) + 6/(2)^2 + 5(2) + 6

     = 21.5

f(3) = 2(3) + 6/(3)^2 + 5(3) + 6

     = 83/3

The function is real and defined for every value of x in its domain except where x = 0 . This is a point of discontinuity.

Find the attachment below;

Answer:

4

Step-by-step explanation:

Count

The provided scenario that relates to the equation y = 2x + 5 involves starting with 5 chickens on a farm and then doubling the number each month.

For the farm scenario with chickens, the number of chickens each month is not 2 times the number in the month before plus five, but rather 2 times the previous month's number. This does not fit the equation y = 2x + 5, where x would represent time in months and y would represent the total number of chickens.

In Nina's book-selling scenario, for each book she sells, she earns $2 plus a $5 tip. This fits the equation perfectly, where x represents the number of books Nina sells and y represents her total earnings. So, for Nina's scenario, Yes, it models the equation.

The temperature scenario also fits the equation y = 2x + 5, where x represents the number of hours after 8:00 AM and y represents the temperature in degrees Celsius. Thus, for every hour, the temperature increases by 2 degrees, starting from 5 degrees at 8:00 AM. So, for the temperature scenario, Yes, it models the equation.

Second from top down

Answer:

1.what number should be added to both sides of the equation? 1

2. how many of the solutions to the equation are positive? one, x=3.031

3.what is the approximate value of the greatest solution to the equation rounded to the nearest hundredth? 3.03

Step-by-step explanation:

The question is on solving for quadratic equations using the completing square method

The equation given is ;

4x²+8x+27=88...........rewrite the equation

4x²+8x+27-88=0

4x²+8x+-61=0...................divide every term of the equation by 4

4x/4²+8x/4+-61/4=0/4

x²+2x-15.25=0..................rewrite the equation as;

x²+2x=15.25.......................complete square on both sides

x²+2x+ (2/2)²= 15.25 +(2/2)²

x²+2x+1 = 15.25+1

x²+2x+1=16.25................factorize the left hand side

(x+1)²=16.25.....................eliminate the root on the left hand side

x+1=±√16.25

x+1= ± 4.031

solutions

x+1= +4.031

x= +4.031-1 =3.031

or

x+1= -4.031

x= -4.031-1 = - 5.031

Answer:

The first box is 1, the second box is 1, and the third box is 3.03

Step-by-step explanation:

Answer:

Step-by-step explanation:

The circumference of a circle = 2*pi * r

so 16 pi yards = 2 * pi * r

Divide both sides by 2

16 pi/2 = 2*pi * r /2

8*pi =  pi * r    

Divide both sides by pi

8 * pi / pi = pi * r / pi

r = 8

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

Surface Area = 4 pi * r^2

r = 8

Surface Area = 4 * pi * 64

Surface Area = 256 * pi

The surface area of the sphere is [tex]\( 256\pi \)[/tex] square yards.

To find the surface area of a sphere given its great circle circumference, we can use the relationship between the circumference and the radius of the sphere.

The formula for the circumference of a great circle of a sphere is:

[tex]\[ C = 2\pi r \][/tex]

We can solve for the radius r

[tex]\[ 16\pi = 2\pi r \][/tex]

r = 8

Next, we use the formula for the surface area A of a sphere:

[tex]\[ A = 4\pi r^2 \][/tex]

Substitute  r = 8  into the formula:

[tex]\[ A = 4\pi (8)^2 \][/tex]

[tex]\[ A = 256\pi \][/tex]

Therefore, the surface area of the sphere is [tex]\[ A = 256\pi \][/tex] square yards.

Answer: distance = rate x time

Step-by-step explanation: divided by distance then multiply by rate

Six Is 2/5 Of 15

6 Is 40% Of 15

Answer:

2/5, 40%

Step-by-step explanation:

When we ask "six is what fraction of 15?", we're asking this: how much of 15 does 6 take up? Just looking at a picture of it, if we have 15 pieces of a whole cake, 6 of those pieces take up a little less than half of that total. We represent this with the fraction 6/15. Now, 6 and 15 have something in common, too: they can both be divided by 3. Take a look at the second picture now. Notice that when we divide the total number of parts and the number of pieces by the same number, the amount those pieces take up stays exactly the same. Since 6 divided by 3 is 2 and 15 divided by 3 is 5, we can say that 6/15 = 2/5, and we can't go any further than that.

Percents are just a special kind of fraction; ones that have 100 in their denominator (the word "percent" literally means "for each 100"). We also have a special way of writing percents: 6/100 would be written as 6%, 50/100 would be 50%, and 100/100 would be 100%.

Remember when I showed how fractions can be equal to each other if you can divide both number by the same thing? You can do the same thing in the other direction: you can create equivalent fractions by multiplying both numbers by the same number.

So, we want to go from 2/5 to ?/100 (we don't know what number ? is yet!) but how do we get there? Well, remember, for two fractions to be equal, you have to multiply both the top and bottom by the same number. Whatever we multiply 5 by to get 100, we'll have to multiply 2 by to get that ?

Well 5 × 20 = 100, so 20 seems to fit the bill, and multiplying 2 × 20 gets us 40, making our fraction 2/5 = 40/100, which we'd write as 40%.

So 6 is 2/5 of 15, which is the same as 40% of 15!

Answer:

b) There is translation 3 units to the right and 1 unit up

c) The domain is {x I x > 3}

   The equation of the asymptote is x = 3

Step-by-step explanation:

* Lets revise the rule of the translation

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

* Now lets solve the problem

b) ∵ f(x) = [tex]log_{2} (x-3)+1[/tex]

∵ The parent function is [tex]log_{2} x[/tex]

∴ x is changed to (x - 3), that means there is a translation 3 units

  to the right

∵ We add the parent function by 1, that means there is a translation

  1 unit up

* There is translation 3 units to the right and 1 unit up

c) To find the domain of the function, find the values of x which

    make the function undefined

∵ [tex]log_{2}(0)[/tex] is undefined

∴ x - 3 can not be 0

∵ x - 3 = 0 ⇒ add 3 to both sides

∴ x = 3

∴ The domain of the function is all real number greater than 3

* The domain is {x I x > 3}

∵ x can not be 3

∴ There is a vertical asymptote, its equation is x = 3

* The equation of the asymptote is x = 3

# Look to the attached graph for more understand for the domain

  and the equation of the asymptote

In a standard shuffled deck of 52 cards, half of the cards are black and half of the cards are red: (26 black cards, 26 red cards).

Since we are interested in pulling a black card first, the probability is 26/52.

Without replacing the card we have chosen, we are left with 51 total cards in the entire deck (25 black cards, 26 red cards).

Now that we want to pull a red card, we know that the probability will be 26/51.

Since we are interested in both events occurring simultaneously, we must multiply the probability of the first by the probability of the second, aka: (26/52) * (26/51)

The answer we are given is 0.2549

The probability of picking a black card and then a red card from a standard deck without replacement is 13/51.

To calculate the probability of selecting a black card and then a red card from a standard deck without replacement, we need to consider the sequence of the two events. Initially, the deck contains 26 black cards (spades and clubs) and 26 red cards (diamonds and hearts). The probability P(A) of picking a black card first is 26/52 or 1/2.

After one black card has been removed, there are now 51 cards left in the deck with 26 red cards remaining. The probability P(B) of then picking a red card is 26/51. To find the overall probability of both events happening in sequence, we multiply the probabilities:

[tex]P(A and B) = P(A) \times P(B) = (\frac{1}{2}) \times (\frac{26}{51})[/tex]

This simplifies to P(A and B) = [tex](\frac{26}{102})[/tex] which can be further simplified to [tex](\frac{13}{51}).[/tex]