A number cube with the numbers 1 through 6 is rolled. The probability of rolling an odd or even number is 1. What is the likelihood of rolling an odd or even number?

Answer: It is I believe because that's how scientific notation looks likes

Step-by-step explanation:

Answer:

3\(\sqrt{3}\)\(\sqrt[4]{2}\)

Step-by-step explanation:

(3^3 * 2^(1/2))^1/2 = 3^(3/2) * 2^(1/4) = 3* 3^(1/2) * 2^(1/4)

Answer:

4:3.

Step-by-step explanation:

Number of boys = 12 and number girls = 16.

Ratio girls to boys = 16:12

= 4:3.

Given:

The recursive formula is:

For n = 2, 3, 4, ...

There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.

1. SSS (side, side, side)-If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

2. SAS (side, angle, side) -If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

3. ASA (angle, side, angle)-If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

4. AAS (angle, angle, side)-If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

5. HL (hypotenuse, leg)

This one applies only to right angle triangles

From the figure,

HL stands for "Hypotenuse, Leg" (the longest side of a right-angled triangle is called the "hypotenuse", the other two sides are called "legs")

It means we have two right-angled triangles with

It doesn't matter which leg since the triangles could be rotated.

For example: From fig(2)

is congruent to fig(3)

If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.

The additional information need to know in order to prove the two triangles congruent using HL is the hypotenuses to be congruent.

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Answer:

The answer is below

Step-by-step explanation:

The question is not complete. But I would show you how to solve the problem.

Two events A and B are said to be independent if the occurrence of event A does not affect the occurrence of event B and vice versa. P(A and B) = P(A) * P(B).

Two events A and B are said to be mutually exclusive if event A and event B cannot occur at the same time. P(A and B) = 0.

Two events A and B are said to be complementary when event A occurs if and only if event B does not occur and vice versa.

the area under the standard normal curve between z = -2.9 and z = 0.28 is approximately 0.0014 (rounded to four decimal places).

The given values for z are z = -2.9 and z = 0.28. We need to find the area under the standard normal curve between these values.

To find this area, we can use the standard normal distribution table. This table lists the areas under the standard normal curve for different z-values. However, we need to make some adjustments to use this table because our values are negative.

Let's first find the area between z = 0 and z = 2.9, and then subtract this area from 0.5 to get the final answer.0.5 - P(0 ≤ z ≤ 2.9) = 0.5 - [0.49865] (from the standard normal distribution table)

= 0.00135

Therefore, the area under the standard normal curve between z = -2.9 and z = 0.28 is approximately 0.0014 (rounded to four decimal places).

Hence, the correct option is, Area ≈ 0.0014.

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Michael’s child is going to college in 13 years. If he saves $ 7,000 a year at 9% compounded annually. Therefore,  the amount available for Peter's child education will be $147,330.55.

Given that Michael is saving $7,000 per year for his child's education which will occur in 13 years. If the interest rate is 9% compounded annually,

The problem of finding the amount of money Michael will have saved in 13 years is a compound interest problem.

In this case, the formula for calculating the future value of the annuity is: $FV = A[(1 + r)n - 1] / r

where: FV is the future value of the annuity, A is the annual payment,r is the annual interest rate, and n is the number of payments.

Using the above formula; the future value of Michael's savings is:

FV = 7000[(1 + 0.09)^13 - 1] / 0.09= 7000(1.09^13 - 1) / 0.09= 147,330.55

Therefore, the amount available for Peter's child education will be $147,330.55.

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384,000 bacteria would be present at the end of 7 hours if it doubles itself every hour.

Initial number of bacteria=3000

Number of bacteria at the end = initial number of bacteria * (base)ⁿ

where, n= number of hours

Number of bacteria at the end=3000*2⁷

                                                    =3000*128

                                                     =384,000

Therefore, there will be 384000 bacteria at the end of seven hour if the bacteria doubles itself every hour.

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Answer:

(2x+3y)^2

= (2x)^2 + 2(2x)(3y) + (3y)^2

= 4x^2 + 12xy + 9y^2

Answer:

4x^2 12xy +9y^2

Step-by-step explanation:

(2x+3y)^2

(2x+3y)(2x+3y)

FOIL

4x^2 + 6xy+6xy + 9y^2

4x^2 12xy +9y^2

Therefore , the solution of the given problem of median comes out to be

a)z-score = 1.50 b)age 34 has SD=1.5 and C. option B correct.

Specify median.

The value that exactly falls in the center of an ordered dataset is the median value. A central tendency measure or average is the difference between both the lowest and highest 50% of the data. The methods for calculating the median and mode vary according to whether you have had an odd or perhaps even number of data points.

Here,

Given : mean age is 36.

Standard deviation = 3.5

a) z - score = (34 - 28.3)/3.8 = 1.50

b) Interpretation:

An age of 34 is about 1.50 standard deviations above the mean.

c) Option B is correct.

Therefore , the solution of the given problem of median comes out to be

a)z-score = 1.50 b)age 34 has SD=1.5 and C. option B correct.

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Answer:

1,3

Step-by-step explanation:

If a coordinate point is at (4, 2) and is translated down 3 units and right 1 unit, what is its new coordinate point?

4-3=1

2+1=3

(1,3)

Answer: (-1,5)

Step-by-step explanation:

Based on the information provided, it can be determined that there are 120 steps visible on the escalator at any given time.

Assume that there are x total steps, e for the escalator speed, and b for Bob's pace.

Bob noticed 75 stairs and climbed the entire escalator in the time it took him to ascend it. As a result, the escalator must have added an extra x + 75 steps.

Let e and b be the speeds of the escalator and Bob, respectively.

Alice took 150 steps at a speed of (3b-e) step rate as she descended the stairs.

Bob took 75 steps at a speed of (b+e) each step as he ascended.

Since, Al and Bob were walking the same distance at a time , we have,

150(3b-e) = 75(b+e)  

Solving  these two equation we get ,  e/b = 3/5

Thus while Bob took 75 steps to go up, the escalator contributed an extra

3/5 * 75 = 45 steps

Finally, there is a total of 75+45=120 steps in the length of the escalator.

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As a result, such a system is said to have no solutions or to be incompatible.

The system of inequalities y < 6 and y > 2 is incompatible, implying that it has no solutions. The first inequality y < 6 is satisfied by any value of y less than 6, whereas the second inequality y > 2 is satisfied by any value of y greater than 2.

The only way to combine these two inequalities into a valid solution would be if y were both less than 6 and greater than 2 simultaneously, but that is not feasible since there is no number that is both less than 6 and greater than 2 at the same time.

As a result, the solution set of the system is empty, or in other words, it has no solutions.

A system of linear equations with no solutions can be referred to as an inconsistent system.

It is characterized by the fact that the graphs of the equations never intersect, implying that there is no point of intersection that satisfies both equations simultaneously.

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Hi 

yes. It's a proportional situation.

proportionnal situation is modelize by f(x) = a(x).

Which fix coefficient, which is here is 126 and X is the number of years.

The solution of the equation x^ay! + 5xy + (4 + x)y = 0, where x > 0, can be represented as a power series of the form y = ΣCnx^n, where C0 = 1 and Cn = 0 for n = 1, 2, 3, ...

To find the solution of the equation x^ay! + 5xy + (4 + x)y = 0, we can represent the solution as a power series expansion of the form y = ΣCnx^n, where Cn is the coefficient of x^n and n ranges from 0 to infinity. Plugging the power series into the equation, we get:

x^a*(ΣCnx^nn!) + 5x*(ΣCnx^n) + (4 + x)(ΣCn*x^n) = 0

We can then collect the terms with the same powers of x:

ΣCnx^(n+a)n! + Σ5Cnx^(n+1) + Σ(4 + x)Cnx^n = 0

For the equation to hold true for all powers of x, each term with the same power of x must be zero. Therefore, we can determine the coefficients Cn for each power of x. For n = 0, the term ΣCnx^a0! simplifies to C0x^a0! = C0*x^a. Since the equation must hold for all x > 0, the coefficient C0 must be non-zero. Therefore, C0 = 1. For n = 1, the term Σ5Cnx^2 simplifies to 5C1x^2 = 0. Therefore, C1 = 0. Similarly, for n = 2, 3, 4, ... , the terms involving Cn will also be zero, as they are multiplied by powers of x. Hence, the solution of the equation x^ay! + 5xy + (4 + x)y = 0 can be represented as y = C0x^a = x^a, where a is a positive real number, and the coefficients Cn are zero for n = 1, 2, 3, ....

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Let the original cost be \( x\).

Profit= $187-x$

The profit is 120%, which means:

$\frac{(187-x)}{x}\times 100 = 120$

Solve to get:

$x=\frac{187\times 5}{11}=85$

Answer:

(3, \(\frac{1}{8}\) )

Step-by-step explanation:

Hi there,

To find the answer to this question, you can simply use a graphing calculator to graph this function. When looking at the values of points along the function, we find that (3, \(\frac{1}{8}\) ) is one of the answer choices.

Hope this answer helps.

Cheers.

Answer.

Use the sum-product pattern. (a*2 − 9  + 20)

                                                   (a*2 −4a-5a + 20)

Common factor from the two pairs. (a*2 − 4a − 5a + 20)

                                                             ( a − 4 ) − 5 ( a − 4 )

Rewrite in factored form. a( a − 4 ) − 5 ( a − 4 )

                                              ( a − 5 ) ( a − 4 )

Answer:

No, it does not meet the goal. 2 hours and 10/24

Given:

The function is

\(f(x+2)=2x+3\)

To find:

The value f'(4).

Solution:

We have,

\(f(x+2)=2x+3\)

Putting \(x+2=t\) and \(x=t-2\) we get

\(f(t)=2(t-2)+3\)

\(f(t)=2t-4+3\)

\(f(t)=2t-1\)

Differentiate with respect to t.

\(f'(t)=2(1)-0\)

\(f'(t)=2\)

At \(t=4\), we get

\(f'(4)=2\)

Therefore, the value of f'(4) is 2.

Answer: Cam did not use a zero place holder for the x^3 term

Step-by-step explanation:

sin(4π3) = sin(240 degrees) = -√3/2 found using the trigonometric ratios of right-angled triangle.

Sine of a positive acute angle: sin(4π3)

The sine of an acute angle is the ratio of the length of the opposite side to the length of the hypotenuse of a right-angled triangle.

Consider a right-angled triangle ABC, with an acute angle α, opposite side length O and hypotenuse length H. We can express the sine of angle α as sin(α) = O/H.

For a positive acute angle, the sine is always positive since the opposite side is positive and the hypotenuse is positive. In the case of sin(4π3), we can determine the exact value by first converting it to degrees. Recall that 2π radians is equivalent to 360 degrees.

Therefore, 4π3 radians is equivalent to 240 degrees. We can then use the unit circle to find the sine of 240 degrees.

The unit circle is a circle of radius 1 with its center at the origin of the coordinate plane. Any point on the circle can be expressed as (cos θ, sin θ) where θ is the angle formed between the x-axis and the terminal side of the angle in standard position.

In the case of 240 degrees, the terminal side is in the third quadrant and forms a 60-degree angle with the x-axis.

This means that the point on the unit circle corresponding to 240 degrees is (-1/2, -√3/2).

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Answer:

13,860

Step-by-step explanation:

List all prime factors for each number.

Prime Factorization of 11 shows:

11 is prime.

Prime Factorization of 35 is:

5 x 7

Prime Factorization of 36 is:

2 x 2 x 3 x 3

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 3, 3, 5, 7, 11

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 3 x 3 x 5 x 7 x 11 = 13860

LCM(11, 35, 36) = 13,860

The face value of the non-interest-bearing note for the woman's loan should be approximately $500.26. The face value of the non-interest-bearing note for the man's loan should be approximately $2417.91.

To find the face value of a non-interest-bearing note, we can use the formula:

Face Value = Proceeds / (1 - Discount Rate * (Days to Maturity / 360))

1. Calculation for the woman's loan:

Proceeds = $485

Discount Rate = 13.22%

Days to Maturity = 80 (from April 10 to June 29)

Face Value = $485 / (1 - 0.1322 * (80 / 360))

Face Value = $485 / (1 - 0.1322 * 0.2222)

Face Value = $485 / (1 - 0.0294)

Face Value = $485 / 0.9706

Face Value = $500.26 (approximately)

Therefore, the face value of the non-interest-bearing note for the woman's loan should be approximately $500.26.

2. Calculation for the man's loan:

Amount needed = $2350

Discount Rate = 14.4%

Days to Maturity = 70 (from July 10 to September 18)

Face Value = $2350 / (1 - 0.144 * (70 / 360))

Face Value = $2350 / (1 - 0.144 * 0.1944)

Face Value = $2350 / (1 - 0.0279)

Face Value = $2350 / 0.9721

Face Value = $2417.91 (approximately)

Therefore, the face value of the non-interest-bearing note for the man's loan should be approximately $2417.91.

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The value of x will be; x = 4

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that the equation 6x-9 = 15

Here, we need to solve for x;

Add 9 to both sides

6x-9+9 = 15+9

6x = 24

x = 24/6

x = 4

Therefore, the solution will be as;

x = 4

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Using the concept of proportions, the value of x in the similar triangle is 3.55

Similar triangles are two or more triangles that have the same shape but may differ in size or location. They have the same angles and corresponding sides that are in proportion to each other.

In this problem, we can find the value of x when we take the ratio of similar sides in the given triangle.

This can be expressed mathematically as;

16 / 5x - 3 = 39 / 36

Cross multiply both sides and solve for x

16 * 36 = (5x - 3) * 39

576 = 195x - 117

576 + 117 = 195x

693 = 195x

x = 693 / 195

x = 3.55

The value of x is 3.55

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36 motorcycles were repaired during the month.

To solve this problem, we can use the formula for the total number of wheels of a vehicle, which is equal to the number of vehicles multiplied by the number of wheels per vehicle. In this case, the number of wheels per vehicle is 4 since both autos and motorcycles have 4 wheels each. This formula can be expressed as: Wheels = Vehicles × Wheels per Vehicle.

We can substitute the given values of the total number of wheels (336) and the number of wheels per vehicle (4) into the formula, and solve for the number of vehicles (V): Wheels = Vehicles × Wheels per Vehicle → 336 = Vehicles × 4 → Vehicles = 336 ÷ 4 → Vehicles = 84.

Since we know that both autos and motorcycles were repaired, and the total number of vehicles was 84, we can use the information that 120 vehicles were repaired to solve for the number of motorcycles (M) that were repaired.

If the total number of vehicles was 84, and 120 vehicles were repaired, then the number of motorcycles that were repaired must be equal to the difference between the total number of vehicles and the total number of autos, which is 120 - 84 = 36.

Therefore, 36 motorcycles were repaired during the month.

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Answer:

X = 3/2.

Step-by-step explanation:

Please refer to the attachment given above.

The value of x in the equation 2\(^{(2x)}\) = 2³ is 1.5.

To find the value of x in the equation 2\(^{(2x)}\) = 2³, we can use the property of exponents that states: If two exponential expressions have the same base and are equal, then their exponents must be equal.

In this case, we have 2\(^{(2x)}\) = 2³. Since the bases are the same (both are 2), we can equate the exponents:

2x = 3

Now, to solve for x, divide both sides by 2:

x = 3/2

So, the value of x is 3/2 or 1.5.

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