A jar contains 10 red marbles numbered 1 to 10 and 8 blue marbles numbered 1 to 8. A marble is drawn at random from the jar. Find the probability of the given event, please show your answers as reduced fractions. (a) The marble is red. P(red) s (b) The marble is odd-numbered. Plodd)- (c) The marble is red or odd-numbered. P(red or odd) - (d) The marble is blue or even-numbered.

Answer:

x = 76

Step-by-step explanation:

-4(x-26) = -4x + 104

-4x + 104 = -200

-4x = -304

x = 76

The solution of the equation is x= 76.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given, equation –4(x – 26) = –200

–4(x – 26) = –200

-4x + 104 = -200

-4x = -200-104

-4x = -304

x = 304/4

x= 76

Therefore, the solution of the equation is x= 76.

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Option A:

This is false because a number's opposite is the number in negatives. The product of a number and it's opposite is sometimes not 1.

Option B:

This is true because 0's opposite will be 0.

Option C:

This is true because the opposite of a negative number will always result as a positive number.

Option D:

This is true. Let's take an example of -1.

-1 => opposite => 1

Both numbers will be one away from 0. Thus, this is true.

We can now conclude that B,C,D are correct.

Hoped this helped.

\(BrainiacUser1357\)

R = 1/e^3, is the radius of convergence of the given power series.

Assuming the given power series is:

∑(k=0 to ∞) (k(z-1))^3

We can use Theorem 2 to find the radius of convergence. The theorem states that for a power series of the form:

∑(n=0 to ∞) c_n (z-z_0)^n

The radius of convergence is given by:

R = 1 / lim sup |c_n|^(1/n)

In this case, we have c_k = k^3, and z_0 = 1. So we can rewrite the series as:

∑(k=0 to ∞) c_k (z-1)^k

where c_k = k^3. Then, using Theorem 2, we have:

R = 1 / lim sup |c_k|^(1/k)

= 1 / lim sup k^(3/k)

= 1 / e^3

The Radius of Convergence Theorem states that for any power series, there exists a non-negative real number called the radius of convergence, such that the series converges absolutely for all values of x within a distance of the radius of convergence from the center of the series, and diverges for all values of x outside that distance.

Therefore, the radius of convergence is R = 1/e^3.

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Answer: a+c=27,126

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

Discount= $30 - $24 = $6

Discount%= \(\frac{6}{30}\) × \(\frac{100}{1}\) = 20%

The unknown angle x in the triangle is 80 degrees

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

The triangle

The unknown angle x is calculated using the sum of angles in a triangle theorem

So, we have

x + 60 + 40 = 180

Evaluate the like terms

x + 100 = 180

So, we have

x = 80

Hence, the unknown angle x is 80 degrees

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Answer:

y = - 5x + 16

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (3, 1 ) and (x₂, y₂ ) = (4, - 4 )

m = \(\frac{-4-1}{4-3}\) = \(\frac{-5}{1}\) = - 5 , then

y = - 5x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (3, 1 )

1 = - 5(3) + c = - 15 + c ( add 15 to both sides )

16 = c

y = - 5x + 16 ← equation of line

Answer:

14.

Step-by-step explanation:

-67 - (-81)=14

Therefore , the solution of the given problem of triangle comes out to be the relationship between s,t and u is u²= t²+s².

Given that it has three sides and three vertices, a triangle qualifies as a polygon. It is a fundamental geometric figure. Triangle ABC is the term used to refer to a triangle containing the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.

Here,

Given : Triangle STU is a right triangle.

Thus,

We find :

sides s,t and u

the relationship between them is :

As it is a right triangle

So,

According to the pythagoras theorem,

=>u²= t²+s²

Therefore , the solution of the given problem of triangle comes out to be the relationship between s,t and u is u²= t²+s².

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Statement                Reason

m∠A ÷ 5 = m∠B       1. Given

m∠B = 20                 2. Given

m∠A ÷ 5 = 20           3. Substitution

m∠A = 100                4. Multiplication property of equality

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

m∠A ÷ 5 = m∠B  ____(1)

m∠B = 20 _____(2)

Substitute (2) in (1)

m∠A ÷ 5 = 20

m∠A / 5 = 20

Multiply 5 on both sides.

m∠A = 5 X 20

m∠A = 100

Thus,

Statement                Reason

m∠A ÷ 5 = m∠B       1. Given

m∠B = 20                 2. Given

m∠A ÷ 5 = 20           3. Substitution

m∠A = 100                4. Multiplication property of equality

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Answer: There are two real roots

Step-by-step explanation: Terms in this set (6) If the discriminant of a quadratic equation is 4, which statement describes the roots? B. There are two real roots.

As of discriminant of the quadratic equation is 4, then we find that there two real and distinct roots.

In a quadratic equation, the discriminant of the quadratic formula indicates the nature of the two roots of the polynomial. Main characteristics are described below:

According to the statement, the discriminant of the quadratic equation is 4, then we find that there two real and distinct roots.

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Hey there!

16 + 2 * 36

= 16 + 36 * 2
= 16 + 36 + 36

= 16 + 2 * 6^2

= 16 + 72

= 88

Thus, your answers could possibly be:

• 16 + 36 * 2
• 16 + 72
• 16 + 2 * 6^2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

0.04 mol/ Liter

Step-by-step explanation:

If you have 8.1 grams of NaOH in 5 L of solution, what is the molarity? (Round answers to the nearest hundredth)

The formula for molarity = Number of moles/ Volume in Liters

Step 1

Find the Number of moles of NaOH

We find the Molar mass of NaOH

Na = 23, O = 16, H = 1

Molar mass = 23 + 16 + 1 = 40 g/mol

Grams of NaOH in the solution = 8.1 grams

Number of moles = Mass/Molar mass

= 8.1 g/40 g/mol

= 0.2025 moles

Step 2

Molarity = 0.2025moles/ 5 L

= 0.0405 mol/ Liter

Approximately = 0.04 mol/L

Answer:

1.2

Step-by-step explanation:

24/25 ÷ 4/5

Change the numbers from division to decimals. PS: this is the same thing just written much easier.

0.96/0.8

1.2

To find the value of the effective spring constant (k), we are given the masses of oxygen (16.0 atomic mass units) and carbon (12.0 atomic mass units). We will use this information to determine the value of k.

The effective spring constant (k) is a measure of the stiffness of the spring and is usually given in units of force per unit length or mass per unit time squared. In this case, we need to determine k based on the masses of oxygen and carbon.

To find k, we can use the formula for the effective spring constant in a molecular vibration system, which is given by:

K = (ω^2)(μ)

Where ω is the angular frequency of the vibration and μ is the reduced mass of the system.

Since we are given the masses of oxygen and carbon, we can calculate the reduced mass (μ) as follows:

Μ = (m1 * m2) / (m1 + m2)

Where m1 and m2 are the masses of oxygen and carbon, respectively.

Using the given masses:
M1 = 16.0 atomic mass units (oxygen)
M2 = 12.0 atomic mass units (carbon)

We can substitute these values into the equation for μ:

Μ = (16.0 * 12.0) / (16.0 + 12.0)
= 192.0 / 28.0
≈ 6.857 atomic mass units

Now, to find the value of k, we need the angular frequency (ω) of the vibration. Unfortunately, the angular frequency is not provided in the given information. Without the angular frequency, we cannot determine the exact value of k.

Therefore, we can calculate the reduced mass (μ) using the given masses of oxygen and carbon, but we cannot find the value of k without the angular frequency.

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The greatest common divisor of 660 and 73 expressed as a linear combination of 660 and 73 is 1 = 4(63) - 37(73).

To find the greatest common divisor of 660 and 73, we will use the extended Euclidean algorithm.

Step 1: Begin by dividing 660 by 73.660 ÷ 73 = 9 R 63

Step 2: The remainder of the previous division becomes the divisor and the divisor becomes the dividend.73 ÷ 63 = 1 R 10

Step 3: The remainder of the previous division becomes the divisor and the divisor becomes the dividend.63 ÷ 10 = 6 R 3

Step 4: Repeat the process again by making the divisor the previous remainder and the dividend the previous divisor.10 ÷ 3 = 3 R 1

Step 5: Repeat the process again by making the divisor the previous remainder and the dividend the previous divisor.3 ÷ 1 = 3 R 0Since the remainder is 0, we have found the greatest common divisor, which is 1.

Now, we'll express it as a linear combination of 660 and 73. We need to work backwards using the remainders obtained from the division process.

We have:1 = 3 - 1(3)1 = 3 - 1(10 - 3(3))1 = 4(3) - 1(10)1 = 4(63 - 9(73)) - 1(10)1 = 4(63) - 37(73)

Therefore, the greatest common divisor of 660 and 73 expressed as a linear combination of 660 and 73 is:1 = 4(63) - 37(73).

The greatest common divisor of 660 and 73 expressed as a linear combination of 660 and 73 is 1 = 4(63) - 37(73).

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Answer:

x = 2

y = 0

Step-by-step explanation:

Here are the simultaneous equations:

\(y=2-x\\6x+5y=11\\x+2y=2\\2x+y=1\\\)

There are only two unknown values, so only two equations are needed to find the answer. I will use these:

\(y=2-x\\x+2y=2\)

Substitute the first equation into the y in the second equation:

\(x+2(2-x)=2\)

Simplify

\(x+4-2x=2\\x=2\)

Use the value of x to find y in equation 1:

\(y=2-x\\y=2-2\\y=0\)

The probability that the spinner lands on yellow and the coin toss is tails is 9/10.

What is probability?

Probability shows the likelihood of an event happening.  it can be calculated by dividing the number of outcomes of an event by the total number of possible outcomes or sample space. Probability is equal to '1' when the event is certain to occur. i.e P =1. It is less than '1' when it is not likely to occur. i.e P< 1

Probability P=no. outcomes/total no. of the possible outcomes

From the question;

No of blue=1

No of yellow=9

No. of total possible outcome=10

Therefore the probability that the spinner lands on yellow and the coin toss is tails P= 9/10.

           P= 9/10                            

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The area of the overlap between two strips of width 1 that overlap at an angle of a can be expressed as 2 - 2cos(a).

To determine the area of the overlap between the two strips, we can consider the shape formed by the overlapping region. The overlapping area can be visualized as a parallelogram, where the two sides of the parallelogram are the two strips of width 1 and the included angle is a.

The formula to calculate the area of a parallelogram is given by A = base * height. In this case, the base is the width of one of the strips, which is 1, and the height can be calculated as the projection of the other strip onto the first strip.

The projection of the second strip onto the first strip can be determined by considering the cosine of the angle a. The height of the parallelogram is equal to the length of the projection, which is given by cos(a).

Therefore, the area of the overlap is given by A = 1 * cos(a) = cos(a).

However, this only represents one side of the overlapping region. Since there are two sides to consider, the total area of the overlap is equal to 2 * cos(a).

To express the answer in a different form, we can use the trigonometric identity cos(a) = 1 - 2sin²(a/2). Substituting this identity into the formula, we have:

Area of overlap = 2 * (1 - 2sin²(a/2))

                       = 2 - 4sin²(a/2)

                       = 2 - 2(2sin²(a/2))

                       = 2 - 2cos(a)

Thus, the area of the overlap between the two strips in terms of the angle a is given by 2 - 2cos(a).

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The inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

        ≤ : less than or equal to

        ≥ : greater than or equal to

        < : less than

        > : greater than

        ≠ : not equal to

Given is the maximum load for a certain elevator is 2000 pounds. The total weight of the passengers on the elevator is 1400 pounds. A delivery man who weighs 243 pounds enters the elevator with a crate of weight [w].

        1400 + 243 + w ≤ 2000

        w + 1643 ≤ 2000

        w + 1643 ≤ 2000

        w ≤ 2000 - 1643

        w ≤ 357

Therefore, the inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

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Here's an explanation to help you understand the problem. Remy stands on the dock represented by point C. He plans to swim from C to A, then from A to B, and then from B back to C. Now, from Remy to the swim route AB¯¯¯¯¯¯¯¯, the shortest distance is 60 meters, which is measured from C to D.

From the diagram ,AC = x meters and BD = y meters Since Remy swims from C to A and then to B, he swims a distance equal to AB. Thus, the total distance that he swims can be given as follows: AB + BA + BC, where BA is equal to 2x, and BC is equal to 2y.Then, the distance that Remy swims can be given by AB + 2x + 2yNow, we know that Remy swims from C to D at a distance of 60 meters. Therefore, we can represent x in terms of y using the Pythagorean theorem as shown below:x² + y² = 60² ... (Equation 1)Also, we know that Remy plans to swim back to point C. Therefore, the total distance that he will swim is given by: AB + 2x + 2y + AC Substituting AB with 2x, we have:4x + 2y + AC ... (Equation 2)Also, substituting Equation 1 into Equation 2, we get:4x + 2y + √(3600 - y²)Simplify the expression by multiplying both sides by 2:8x + 4y + 2√(3600 - y²)Now, substituting 2x with AB and 2y with BD, we get:2(AB) + AB + 2(BD) + BD + 2√(3600 - y²)Simplify the expression:4AB + 4BD + 2√(3600 - y²)Therefore, the total distance that Remy swims is equal to:4AB + 4BD + 2√(3600 - y²)Therefore, the correct answer is 4AB + 4BD + 2√(3600 - y²).

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Answer:

sorry i cant help

Step-by-step explanation:

Answer:

156.

Step-by-step explanation:

130/5 = 26.

130 + 26 = 156.

Answer:

See below

Step-by-step explanation:

\(2e)15-4x=10x+45\)

Solve:

\(15-4x=10x+45\\-4x-10x=45-15\\-14x=30\\ \boxed {x=-\dfrac{15}{7}}\)\(3(x+1)=21\)

Check:

\(15-4 \left(-\dfrac{15}{7} \right)=10\left(-\dfrac{15}{7} \right)+45\)

\(15+\dfrac{60}{7} \right)=-\dfrac{150}{7} +45\)

\(\dfrac{210}{7} =30\)

\(30=30\)

\(3a) 3(x+1)=21\)

Solve:

\(3(x+1)=21\\3x+3=21\\3x=18\\x=6\)

\(3b) 2+3(x+1)=6x\)

\(2+3x+3=6x\\5=3x\\\)

\(x=\dfrac{5}{3}\)

\(3c) -2(2x-3)=-2\)

Solve:

\(-2(2x-3)=-2\\-4x+6=-2\\-4x=-8\\x=2\)

Answer: B

Hope this helps :)

The interest Lisa's friend had to pay is $34.15. Hence, the correct option is (c) $34.15.

Given that Lisa lent for 5 months $2,980 at a simple-interest rate of 2.75% per annum, we have to calculate the amount of interest Lisa's friend had to pay.

Using the simple interest formula we can determine the amount of interest earned over a given time period that depends on the principal amount, the interest rate, and the duration of the loan as follows:

I = P x R x T

Where, P is the principal amount;R is the interest rate;T is the time in years;I is the simple interest earned by the lender

Using the above formula, we get I = $2,980 × 2.75% × 5/12

= $34.15.

Therefore, the interest Lisa's friend had to pay is $34.15. Hence, the correct option is (c) $34.15.

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Answer:

trinomial

Step-by-step explanation:

a monomial has 1 term

a binomial has 2 terms

A trinomial has 3 terms

a² + a - 6 ← has 3 terms so is a trinomial and also a polynomial