A box contains six cards. Three of the cards are black on both sides, one card is black on one side and red on the other, and two of the cards are red on both sides. You pick a card uniformly at random from the box and look at a random side. Given that the side you see is red, what is the probability that the other side is red? Express your answer as a common fraction.

Triangle is always 180 degrees because the sum of all angles in a triangle is 180 degrees. This is known as the "Triangle Angle Sum Theorem." The theorem states that the sum of all angles in a triangle is equal to 180 degrees.

1. A triangle is a three-sided polygon with three angles.

2. The sum of the three angles in any triangle must be 180 degrees.

3. This is known as the Triangle Angle Sum Theorem.

4. The Triangle Angle Sum Theorem states that the sum of the angles in a triangle must equal 180 degrees.

5. It does not matter which angles the triangle has, the sum will always equal 180 degrees.

6. This theorem is based on the fact that the sum of the angles in any triangle is equal to two right angles or 180 degrees.

7. The Triangle Angle Sum Theorem can be proven by drawing a triangle, and then measuring and adding the three angles.

8. The sum of the three angles will always equal 180 degrees.

9. Therefore, triangle is always 180 degrees.

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The answer to 7^2 is 49. This means that 7 is multiplied by itself two times. To solve the given problem following steps should be followed :

Step 1: To calculate the value of 7 power 2, we need to use the exponentiation operator (^).

Step 2: The operator is written as 7^2, which is read as "seven to the power of two".

Step 3: We can calculate the value of 7 power 2 by multiplying 7 by itself 2 times.

Step 4: 7 × 7 = 49

Therefore, 7 power 2 = 49.

An expression known as "power" is defined as the process of repeatedly multiplying a value or integer. An is often a power where n is the exponent and an is the base.

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The Complete is showing the length of the fence and the cost.

Length of fencing  4  6      7    9  10

Cost:                       36 54  63 81  90

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

Length of fencing  4  6  7  x  10

Cost:                       36 y z 81 w

Now, Using proportion

4/ 36 = 6/y

4y = 36(6)

y = 54

and, 4/36 = 7/z

4z = 36 (7)

z = 63

and, 4/36 = x /81

x = 9

and, 4/36 = 10/w

360 = 4w

w= 90

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The equation of the line is 3x + y - 11 = 0.

The slope-intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point.

First we find the slope of the line y=-3x+10 by placing it into slope-intercept form:

y = -3 x + 10

Therefore, the slope of the line is m= -3

Now since the equation of the line with slope m passing through a point

(x₁ ,y₁) is y-y₁ = m(x-x₁)

Here the point is (1,8) and slope is m= -3, therefore, the equation of the line is:

y - 8 = -3(x - 1)

y - 8 = -3x +3

3x + y - 11 = 0

Hence, the equation of the line is 3x + y - 11 = 0.

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Answer:

Slope=-3.333/2.000=-1.667

X-intercept= -13/5 = -2.60000

Y-intercept= -13/3 = 14.33333

Ericka’s mistake is in ''Step 2.''

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Ericka was solving an exponential equation, and upon finishing, she realized her answer was incorrect when she substituted -5 back into her original equation.

Now,

Since, Ericka was solving an exponential equation.

Clearly, The equation is,

⇒ 5 ⁹ˣ⁺⁶ = 25³ˣ ⁻ ²⁴

Step 1;

⇒ 5 ⁹ˣ⁺⁶ = 25³ˣ ⁻ ²⁴

⇒ 5 ⁹ˣ⁺⁶ = 5 ² ⁽³ˣ ⁻ ²⁴⁾

Step 2;

⇒ 9x + 6 = 2 (3x - 24)

So, Ericka’s mistake is in Step 2.

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Answer:

9

Step-by-step explanation:

27 divided by 3 equal 9

Answer:

10^11

Step-by-step explanation:

This question helps you practice some exponent rules. To "fix" a negative exponent you push it across the fraction bar. The 10^-3 on the bottom becomes a 10^3 on the top. See image.

Then, when you have 10^8 • 10^3, that is when you are multiplying, you add the exponents.

10 ^ (8+3)

= 10^11

see image

A total of 785 planks Andy Mann needs to order to make sure he has enough to complete the fence.

As the planks are 10cm wide to the nearest cm.

The total length of the fencing is = 75 m

From above, we can conclude that,

Range of the planks' lengths: 9.5 cm <= Plank's length < 10.5 cm

Range of fencing needed: 74.5 m <= Fence length < 75.5 m

We should consider the worst-case scenario where all the planks are 9.5 cm.

To complete the job, he only needs 74.5 m in total.

So, the total number of planks needed for completing the Job will be

= (74.5 * 100) / 9.5 = (7.84210*100) = 784.210

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Answer:

2√14

Step-by-step explanation:

√56 = √4 × √14

which is

2√14

Answer:

Yes, it would be 225%.

Step-by-step explanation:

If 20/20= 100% you can evenly take out 200% because there is 45/20.

That leaves you with the 5/20.

5/20= 25%.

If we add those two percentages 200% + 25%= 225%.

I hope that made sense lol, have a great day!

The reason to choose problem B over A is simple -  it is more relatable to them.

Problem A involves dinosaurs, which may be more interesting to students than the abstract concept of creating an area with rope. Additionally, the use of feet as a unit of measurement in Problem A may be more familiar to students than inches.

Finding a number that represents the quantity of anything is called measurement. An accepted quantity that is used to represent a physical quantity is called a measurement unit. Let's learn about some of the standard units used to measure physical quantities.

The inch, foot, yard, and mile are the fundamental units of length and distance measurement in the English system. The rod, furlong, and chain are additional length units.

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Roberto paid 16.7% of the bill as a tip.

To find the percent of the bill Roberto paid as a tip, you can use the formula: (tip / total bill) x 100 = tip percentage

In this case, the tip was $7.15 and the total bill was $35.75 + $7.15 = $42.90. We know the formula to calculate percentage share of an item to total items.

Plugging these values into the formula:

(7.15 / 42.90) x 100 = 16.7 %

Roberto paid 16.7% of the bill as a tip, rounded to the nearest percent.

Thus, we know Roberto paid 16.7% of the bill as a tip.

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The person who has the most number 1 in UK is Elvis Presley. He has a total of 21 number 1 which is the highest in history.

The UK Singles Chart is a chart which numbers musician on the basis of their songs and their sales and streams it  was created in 1969. The records and statistics listed here, however, date back to 1952 .

The song which charted the charts was Old Town Road which was recently remixed and launched by Lil Nas X.

Elvis Aaron Presley or more commonly known as Elvis, was an American singer and actor. He dubbed the "King of Rock and Roll", and is now regarded as one of the most significant cultural figures of the 20th century.

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Remembering the ratio of 1: 3: 2 and understanding that the smallest side length is always opposite the shortest angle (30°) and the longest side length is always opposing the greatest angle (90°) can help you recall the 30-60-90 triangle principles.

According to the 30-60-90 triangle theorem, the hypotenuse is twice as long as the shorter leg. Additionally, the sides of this particular triangle have a ratio of 1:2: [tex]\sqrt{3}[/tex].

A 30-60-90 triangle can have three sides, and if you only know one, you can use shortcuts to discover the other two. The three scenarios you encounter when performing these computations are as follows:

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5W = 24D is the expression that represents the change in the rate of dosage as per the weight.

A mathematical expression is a sentence that includes numbers, variables, or both. The equal symbol is never used in expressions. Here are a few phrases as examples. A mathematical statement stating the equality of two expressions is known as an equation.

Given the relation between dosage and the weight of a medicine

               Children's Fever Medicine

                (given every 4-6 hours, as needed)

Weight:     24 lbs         36+ lbs         48+lbs          60+lbs         72+ lbs

Dosage:    5 mL         7.5 mL          10 mL             12.5 mL           15 mL

ratio of weught and dose

24/5 = 36/7.5 = 48/ 10 = 60/12.5 = 75/15

=> 4.8 = 4.8 = 4.8 = 4.8 = 4.8

Since weight is directly proportional to the dosage

let W be the weight of the child and D be the Dose of the medicine

Thus, Relation between them:

=>W/D = 24/5

=> 5W = 24D

Therefore, The formula that describes the change in dosage rate in relation to weight is 5W = 24D.

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The mean of the walleye 'W' for the given number of walleye and its probability to represent that 30% chances are of walleye is equal to 1.4.

As given in the question,

Let 'W' is the random variable represents the number of walleye.

'P(W)' represents its probability

The values are given as follow:

W      :        0                        1                       2

P(W)  :        0.09                0.42                  0.49

Mean of the walleye 'W' is given by :

= W₁P(W₁) + W₂P(W₂) + W₃P(W₃)

= ( 0 ×  0.09 )  + ( 1 × 0.42 ) + ( 2 × 0.49 )

= 0 + 0.42 + 0.98

= 1.4

Therefore, the mean of the walleye 'W' for the given number of walleye and its probability is given by 1.4.

The above question is incomplete , the complete question is :

Eva loves to go fishing. Each time she catches a fish, there is a 70% chance that it is a northern pike and a 30% chance it is a walleye. Let W be the random variable that represents the number of walleye Eva gets

if she catches 2 fish.

W      :        0                        1                       2

P(W)  :        0.09                0.42                  0.49

Calculate the mean of W.

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The sum of first 20 terms of the AP will be -206.25

As in AP, let us assume that the "a" be the first term and 'd' be the common difference.

So, the value of nth term can be determined by using formula: a_n=a+(n-1)d, where, n = number of terms, and d = common difference.

So, the value of 19th terms = a+(19-1)d = a+18d = -5 -----(i)

And the value of 15th term = a+(15-1)d = a+14d = -7(1/2) ----(ii)

Now subtracting (ii) from (i),

We will get,

4d = 2(1/2)

=>4d = 2.5

=>d = (2.5/4) = 0.625

Now putting value of "d" in (i)

We will get,

a+(18*0.625) = -5

a=-5-11.25 = -16.25

We have, the formula for finding the sum of terms:

Sum of terms can be determined by using formula:

Sum = (n/2) × [2a + (n-1)d]

Here, n = 20, a = -16.25, d = 0.625

We will get sum of first 20 terms as:

[tex](n/2)\times [2a + (n-1)d]\\(20/2) \times [2 \times -16.25+(20-1)0.625]\\[/tex]

10[-32.5+11.875]

=10(-20.625) =-206.25

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A system of equations for this problem can be written as:

x + y = 10 (1) equation for the total number of herbs planted

0.50x + 0.25y = 3 (2) equation for the total cost of the herbs

Where x is the number of basil plants and y is the number of mint plants.

Using substitution, we can solve the system of equations.

Solving equation (1) for x, we get x = 10 - y

Substituting this into equation (2) we get:

0.50(10 - y) + 0.25y = 3

5 - 0.50y + 0.25y = 3

5 = 0.75y + 3

0.75y = -2

y = -2/0.75 = -8/3

So, Eden planted -8/3 mint plants, which doesn't make sense, as a fraction of plant are not possible. This implies that either the number of plants or the amount spent are incorrect or something is missing in the problem description.

Answer:

x = 3.1 as a decimal or x = 28/9 as a fraction

Step-by-step explanation:

Answer:

34 + 23 = 57

57 - 5 = 52

Therefore, she has 52 toy horses.

Answer:

  1.033×10⁴

Step-by-step explanation:

You want the quotient 40.79÷0.003949​ using log tables.

The log of a quotient is the difference of logs:

  log(a/b) = log(a) -log(b)

It can work well to start by writing the numbers in scientific notation:

  log(40.79) = log(4.079×10¹) = 1 +log(4.079) = 1.6106

  log(0.003949) = log(3.949×10⁻³) = -3 +log(3.949) = -3 +0.5965

Then the log of the quotient is ...

  log(40.79/0.003949) = 1.6106 -(-3 +0.5965) = 4.0141

The antilog of this number will be ...

  antilog(4.0141) = 10⁴ × antilog(0.0141) ≈ 1.033×10⁴

With our 4-digit log tables, 4 significant figures is the best we can expect.

The quotient is about 1.033×10⁴.

__

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Answer:

Step-by-step explanation:

To find the y-intercept, we can use the slope-intercept form of a linear equation which is y = mx + b, where m is the slope of the line, and b is the y-intercept.

Since the line passes through the points (2, -2.5) and (4, -2), we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

To find the slope(m) we can use the rise over the run formula ,

m = (y2 - y1) / (x2 - x1) = (-2 - (-2.5)) / (4 - 2) = -0.5

then we can substitute the values in point-slope form

y - (-2.5) = -0.5 (x - 2)

And now we can use x = 0,

y = -0.5(0-2) -2.5 = 1.5

so the y-intercept of the line is 1.5

On solving the provided question, we can say that the equation of the expression is given by y = 6x + 50

Equations with graphs as the unknowns are known as graph equations. The concept of isomorphism is one of the key issues in graph theory. When are two graphs identical, we inquire? Different graph equations may be used to express the aforementioned graphs.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is utilized. A lot of specialists, such as air traffic controllers, architects, computer programmers, and carpenters, employ equations on a daily basis.

From the table we can see that if the equation be

y = mx + c

for x = 0 y = 50

c = 50

again from x = 1 and y = 56

m = 6

So the equation of the expression is given by y = 6x + 50

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If Ahmad took 200 mg of medication and the function [tex]f(t) = 200e^{-0.4t}[/tex] can be used to determine the amount of medication, then He will have only 50 mg of medication left in his system after (c) 3.47 hours .

The Function that is used to determine the amount of medication, f(t), still in his system after t hours. is given as [tex]f(t) = 200e^{-0.4t}[/tex] ,

we have to find the after how many hours there will be only 50 mg of medication left ;

we need to substitute f(t) as 50 ;

we get ;

⇒ [tex]50 = 200e^{-0.4t}[/tex] ;

⇒ [tex]\frac{50}{200} =e^{-0.4t}[/tex] ;

⇒ [tex]\frac{1}{4} =e^{-0.4t}[/tex]

On solving further ,

we get ;

⇒ [tex]t=3.4657..[/tex] hours ;

So , t≈ 3.47 hours .

Therefore , After 3.47 hours there will be 50 mg of medication left .

The given question is incomplete , the complete  question is

Ahmad took 200 mg of a medication. The function [tex]f(t) = 200e^{-0.4t}[/tex] can be used to determine the amount of medication, f(t), still in his system after t hours. To the nearest hundredth, after how much time will Ahmad have only 50 mg of medication left in his system ?

(a) 4.37 hours

(b) 7.47 hours

(c) 3.47 hours

(d) 3.74 hours

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The expression that represents the perimeter of the rhombus is 2d√17

How to determine the expression that represents the perimeter of the rhombus?

From the question, we have the following parameters that can be used in our computation:

The length of one diagonal of a rhombus is 4 times the length of the other diagonal.

This means that

Length 1 = 4 * Length 2

From the question, we have

Let d be the length of the shorter diagonal.

This means that

Length 1 = 4d

Length 2 = d

The perimeter of the rhombus from the diagonals is calculated as

P = 2√(Length 1² + Length 2²)

Substitute the known values in the above equation, so, we have the following representation

P = 2√((4d)² + d²)

Evaluate the exponents

P = 2√(16d² + d²)

So, we have

P = 2√(17d²)

Evaluate the exponents

P = 2d√17

Hence, the perimeter is 2d√17

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The quotient of 1.782 × 10⁹ and 8.1 × 10⁶ in scientific notation is 2.2 × 10². The result is obtained by using the quotient rule.

Several rules for exponents are

Find the quotient of 1.782 × 10⁹ and 8.1 × 10⁶!

Dividing the first number by the second using the quotient rule, it would be

= (1.782 × 10⁹) / (8.1 × 10⁶)

= (1.782/8.1) × (10⁹/10⁶)

= 0.22 × 10⁹⁻⁶

= 0.22 × 10³

In scientific notation, we should write a.b × 10ⁿ, where 1 ≤ a < 10 and n is an integer.

So,

0.22 × 10³ = 2.2 × 10²

Hence, the result of 1.782 × 10⁹ divided by 8.1 × 10⁶ in scientific notation is 2.2 × 10².

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No, 12, 20, and 16 do not form a Pythagorean triple. A Pythagorean triple is a set of three whole numbers, a, b, and c, such that a^2 + b^2 = c^2.

To determine if 12, 20, and 16 form a Pythagorean triple, we can substitute each number into the equation and solve for c.

Start by substituting 12 for a, 20 for b, and 16 for c:

12^2 + 20^2 = 16^2

144 + 400 = 256

544 ≠ 256

Since 544 does not equal 256, the numbers do not form a Pythagorean triple. We can also verify this by calculating the square of c to see if it is equal to the sum of the squares of a and b.

Start by substituting 12 for a, 20 for b, and 16 for c:

a^2 + b^2 = c^2

12^2 + 20^2 = c^2

144 + 400 = c^2

544 = c^2

Taking the square root of both sides:

√544 = √c^2

23.2 ≠ c

Since 23.2 does not equal c, the numbers do not form a Pythagorean triple.

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The polynomial 5x³ 4x² 7x has three terms, with the highest degree being 3, which makes the degree of the polynomial 3. The polynomial can be written as 5x³ + 4x² + 7x.

1. Identify the polynomial: 5x³ + 4x² + 7x

2. Count the number of terms: 3

3. Find the highest degree (the largest exponent): 3

4. The degree of the polynomial is 3.

The degree of a polynomial is the highest degree of its terms. A polynomial is a mathematical expression consisting of one or more terms with coefficients and exponents. In this case, the polynomial is 5x³ + 4x² + 7x. This polynomial has three terms, and the highest degree is 3, which makes the degree of the polynomial 3. This means that the largest exponent of the terms is 3. To calculate the degree of a polynomial, simply count the number of terms and identify the highest degree, which is the largest exponent. If the polynomial has only one term, then the degree is the exponent of that term

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