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Solution:

Probability of the second outcome occurring is 1-p

Explanation:

In an experiment with only two outcomes, the probabilities of both outcomes must add up to 1.

This means that if the first outcome has a probability of p, the second outcome must have a probability of 1-p.

Therefore, the equation for this situation would be: p + (1-p) = 1Solving for p, we get: p = 1 - (1-p) = 1 - 1 + p = p.

Therefore, the probability of the first outcome occurring is simply p, as given in the question.

The probability of the second outcome occurring is 1-p.

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The probability of the first outcome, p, is equal to the total probability of all outcomes, minus the probability of the second outcome, p2. So, p = 1 - p2.

In an experiment with only two outcomes, the sum of the probabilities of the two outcomes must equal 1. This means that if the first outcome has a probability of p, the second outcome must have a probability of 1-p.

Therefore, the probability of the first outcome, p, can be found by subtracting the probability of the second outcome, p2, from 1:
p = 1 - p2

So, if you know the probability of the second outcome, you can find the probability of the first outcome by subtracting it from 1.

For example, if the probability of the second outcome is 0.3, the probability of the first outcome would be:
p = 1 - 0.3 = 0.7

So the probability of the first outcome is 0.7.

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Recall that the discriminant of a quadratic equation:

is:

Also, if:

Now, notice that the discriminant of the given equation is:

Simplifying the above result we get:

Since 24>0, we get that the given equation has 2 different real roots.

Answer: The given equation has 2 different real roots.

So, the volume of the can in cubic centimeters is 61.99 cm^3. If we round to the nearest tenth, the volume of the can is 62 cm^3.

A can of soda can be modeled as a right cylinder, which is a three-dimensional geometric shape with two circular bases that are connected by a curved surface. The volume of a cylinder can be calculated using the formula:

V = πr^2h

Where V is the volume, π is a constant (approximately equal to 3.14), r is the radius of the base and h is the height of the cylinder.

Given that the radius of the can is 2.6 cm and the height is 9.2 cm, we can substitute these values into the formula:

V = π (2.6 cm)^2 (9.2 cm)

To get the area of the base we need to square the radius and multiply by π, and then multiply it by the height to get the volume.

V = π * 6.76 * 9.2 = 61.99 cm^3

So the volume of the can in cubic centimeters is 61.99 cm^3. If we round to the nearest tenth, the volume of the can is 62 cm^3. This means that the can can hold 62 cubic centimeters of liquid.

It's worth noting that this is an approximation and the real value of π is not 3.14. Also, this answer is based on the assumption that the can is a perfect cylinder with no other gaps or spaces.

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Based on the given data, there is not enough evidence to suggest a significant difference in the average number of words spoken per day between male and female students at this university at a significance level of 0.05.

The critical value will be:

= ✓(55)(7520²) + (55)(9108²))/(56 + 56 - 2))

≈ 8285.89

t = (16177 - 16569) / (8285.89 * ✓(1/56 + 1/56))

≈ -0.4704

The critical value for a two-tailed test with α = 0.05 and df = 110 is approximately ±1.983.

Since the absolute value of the test statistic (0.4704) is less than the critical value (1.983), we fail to reject the null hypothesis.

Therefore, based on the given data, there is not enough evidence to suggest a significant difference in the average number of words spoken per day between male and female students at this university at a significance level of 0.05.

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Dante deposited $5,000 into an account with an annual interest rate of

3.5%. He plans to deposit an additional $200 each year, just after the

interest is compounded. His balance will be $9,838.44 after 16 years.

It displays the actual percentage rate of interest owed on any outstanding debts, including credit card debt and loans.

Because it takes compounding effects into account, the effective annual interest rate is the real interest rate on an investment or loan. The rate increases as the compounding periods get more frequent. Advertisements for loans or savings accounts may include both the nominal interest rate and the effective yearly interest rate. The rate that should be used to compare loan and investment rates of return is the effective annual interest rate.

We can substitute the known values into the formula and calculate the final balance:

A = $5,000 (1 + 0.035)¹⁶

We can calculate the final balance by using a calculator, or we can use the formula of compound interest:

A = P(1 + r/n)ˣ

where, A= Amount

P= Principle($5,000 )

x= Time(16 years)

n= Rate(3.5%)

A = $5,000 (1 + 0.035/1)¹⁶

Now we can add the $200 deposit each year for 16 years:

A = $5,000 (1 + 0.035)¹⁶ + $200 × 16

A = $9,838.44

Dante's balance will be $9,838

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The bowl of Kashi cereal has a total of 93 calories

Each gram of carbohydrates provides 4 calories, and each gram of fat provides 9 calories. To calculate the total calories in the bowl of Kashi cereal, we need to determine the calories from carbohydrates and fat separately and then add them together.

Calories from carbohydrates

Total carbohydrates = 25g

Fiber = 4g

Net carbohydrates = Total carbohydrates - Fiber = 25g - 4g = 21g

Calories from carbohydrates = Net carbohydrates x 4 calories/gram

Calories from carbohydrates = 21g x 4 calories/gram

Calories from carbohydrates = 84 calories

Calories from fat

Fat = 1g

Calories from fat = Fat x 9 calories/gram

Calories from fat = 1g x 9 calories/gram

Calories from fat = 9 calories

Total calories = Calories from carbohydrates + Calories from fat

Total calories = 84 calories + 9 calories

Total calories = 93 calories

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Answer:

801.66

Step-by-step explanation:

calculator

Answer:

801.6632653061

Step-by-step explanation:

.......

By using the quotient of powers property, we will see that the value of n must be 6.

Here we want to solve the equation below:

2.3 × 10^9 = (1 × 10^3)(2.3 × 10^n)

For the exponent n.

To fo so, we can start by dividing both sides by the first factor on the right side.

2.3 × 10^9 = (1 × 10^3)(2.3 × 10^n)

(2.3× 10^9)/(1 × 10^3) = 2.3 × 10^n

Remember the quotient between powers of the same base:

a^n/a^m = a^{n - m}

Then we will get:

(2.3× 10^9)/(1 × 10^3) = 2.3 × 10^n

(2.3/1)×(10^9/10^3) = 2.3 × 10^n

Now we can use the property written above:

2.3×10^{9 - 3} = 2.3 × 10^n

2.3×10^6 = 2.3×10^n

There we can see that the value of n must be 6.

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Answer:

degree is 2

standard form is

-x^2+2x-8

classification is trinomial

leading coeff is -1

hope i helped

Step-by-step explanation:

Answer:

y = 2x -12  to find any equation to the perpendicular line  x=0

Step-by-step explanation:

find the slope to the original line using the slope formula , then take the opposite reciprocal = -1/2

The x- and y-coordinates of the center of mass are; (20, 0)

The center of mass is the location where the sum of the relative position of the masses in a mass distribution is zero. It is the point where force can be applied on the distributed mass without causing a rotation of the system.

The mas of the steel plate = 800 g = 0.8 kg

The base length of the isosceles triangular plate = 20 cm = 0.2 m

The height of the isosceles triangular plate = 30 cm = 0.3 m

Considering a small strip of height, dx and width, I, we get

Area of small strip, dA = I·dx

Density of the plate for a unit thickness, ρ = M/A

Density of the small strip of mass dm = dm/dA

Considering the density of the plate as uniform, we get;

\(\displaystyle {\frac{dm}{dA} =\frac{M}{A}\)

Therefore;

\(\displaystyle {dm=\frac{M}{A}\times dA}\)

The area of the triangular plate, A = (1/2) × 0.2 m × 0.3 m = 0.03 m²

Mass of the plate, M = 0.8 kg

Therefore;

\(\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx}\)

The width of the small strip, I, located at a distance x from the vertex of the triangular plate, using similar triangles, indicates;

\(\dfrac{I}{20} = \dfrac{x}{30}\)

\(I=20\times \dfrac{x}{30} = \dfrac{2}{3} \cdot x\)

Therefore;

\(\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx} = \frac{0.8}{0.03}\times \dfrac{2}{3} \cdot x\cdot dx}\)

The center of mass, \(x_{cm}\), can be obtained with the formula; \(\displaystyle {x_{cm} = \dfrac{1}{M} \cdot \int\limits {x} \, dm }\)

Therefore; \(\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx }\)

\(\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx } = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx\)

\(\displaystyle {x_{cm} = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0\)

\(\displaystyle {x_{cm} = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0=\frac{200}{9} \times \frac{0.027}{3} =0.2\)

The location of the x-coordinate center of mass, \(x_{cm}\) = 0.2 m = 20 cm from the vertex, which is the same location as the x-coordinate of the centroid of the plate of uniform density.

The plate is symmetrical about the x-axis, therefore, the y-coordinate of the center of mass is along the x-axis, which is \(y_{cm}\) = 0

The coordinate of the center of mass = (0.2, 0)

Part of the question requires the location of the coordinate of the center of mass of the triangular plate

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15a) To evaluate the power series ∑((-1)^(2n) * 7^(32) * (2n)! * 9^(2n+1)), we can break it down term by term.

The term can be written as follows:

((-1)^(2n) * 7^(32) * (2n)! * 9^(2n+1))

Let's start evaluating each part of the term:

1. (-1)^(2n) = 1 for all values of n, since any even power of -1 is 1.

2. 7^(32) is a constant term that remains the same for all values of n.

3. (2n)! represents the factorial of 2n. It is the product of all positive integers from 1 to 2n.

4. 9^(2n+1) can be simplified as (9^2)^n * 9. Since (9^2) is a constant, it remains the same for all values of n.

Now, let's substitute these values back into the power series:

∑((-1)^(2n) * 7^(32) * (2n)! * 9^(2n+1))

= ∑(1 * 7^(32) * (2n)! * (9^2)^n * 9)

The series can be simplified further by factoring out the constants:

= 7^(32) * 9 * ∑((2n)! * (9^2)^n)

Now we have a power series in the form of ∑(c * a^n), where c and a are constants. We can use the properties of power series to evaluate it.

However, it seems that there might be a typo in the given expression as the factorial term (2n)! and the exponent of 9^(2n+1) both have an odd power of 2n. Please verify and provide the correct expression if there is a mistake.

15b) To evaluate the power series ∑((-1)^n * 3^(n+1) * (n!)^2 / 5^n), we can follow a similar approach.

The term can be written as follows:

((-1)^n * 3^(n+1) * (n!)^2 / 5^n)

1. (-1)^n alternates between 1 and -1 for even and odd values of n, respectively.

2. 3^(n+1) is a constant term that changes as n increases.

3. (n!)^2 represents the square of the factorial of n.

4. 5^n is a constant term that remains the same for all values of n.

Now, let's substitute these values back into the power series:

∑((-1)^n * 3^(n+1) * (n!)^2 / 5^n)

= ∑((-1)^n * 3^(n+1) * (n!)^2 * (5^-1)^n)

Simplifying further:

= ∑((-1)^n * 3^(n+1) * (n!)^2 * (1/5)^n)

Now we have a power series in the form of ∑(c * a^n), where c and a are constants. We can use the properties of power series to evaluate it.

15c) To evaluate the integral of √(x^3) * sin(x^2) dx using power series, we can expand the function sin(x^2) as a power series.

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Step-by-step explanation:

Let's find the difference between 7508 and the other numbers.

A. 5706 - 7508 = -1802

B. 6993 - 7508 = -515

C. 8108 - 7508 = 600

D. 8522 - 7508 = 1014

E. 1050 - 7508 = -6458

If we do not take +ve / -ve into account,

the closest number to 7508 = the smallest difference

which in this case, is B, 6993.

Answer:

B. 6993

Step-by-step explanation:

hope this helps :)

The value of the 5000th term is 44995.

Given, an arithmetic sequence k starts 4, 13, and we are required to calculate the value of the 5,000th term. Arithmetic sequence: An arithmetic sequence is a sequence in which each term is equal to the previous term plus a constant value, known as the common difference, denoted by d.

Formula: The nth term in an arithmetic sequence is given by the formula: `an=a1+(n-1)d`Here,a1 = 4,  d = 13 - 4 = 9We need to find the 5000th term, so n = 5000.Therefore, the value of the 5000th term, an is given by:an = a1 + (n - 1)d= 4 + (5000 - 1)9= 4 + 44991= 44995

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Answer:

In order of the questions asked, the answers are, C, D, A, C

Step-by-step explanation:

After three half-lives have elapsed, 12.5% of the original nuclide remains, so the answer is C.

if 17 % is daughter nuclide, then 83% is parent nuclide, so , the answer is D

the isotope for dating organic remains is A. carbon-14

for 25% of original, 2 half-lives must have passed, so we get (2)(5730) = 11460

so the answer is C

Let's begin by finding the mean of the data

Mean = 48.9

Next, we calculate the absolute value of the difference between each data value and the mean, we have:

|data value – mean|

|46 - 48.9| = 2.9

|47 - 48.9| = 1.9

|56 - 48.9| = 7.1

|48 - 48.9| = 0.9

|46 - 48.9| = 2.9

|52 - 48.9| = 3.1

|57 - 48.9| = 8.1

|52 - 48.9| = 3.1

|45 - 48.9| = 3.9

Next, we sum up the absolute values of the differences (from above) & divide by the number of data values, we have:

MOD = 8 (to the nearest whole number)

The equation of the line in slope-intercept form is,

where,

m = slope

The equation of the line given is,

Let us now rearrange the equation in the slope-intercept form in order to obtain the slope.

Therefore,

We were told the point is parallel to the equation of the line.

The rule for parallelism is,

The formula to calculate for the equation of a line given one point is,

Given

Substitute and simplify

Hence, the equation of the line in slope-intercept form is

Answer:

A, D, C, F, B, G

Step-by-step explanation:

The correct order of the given expressions is:

1: (1.93 x 10⁷) - (9.7 x 10⁶)

3: (1.93 x 10⁷) - (0.97 x 10⁷)

6: (1.93 - 0.97) x 10⁷

2: 0.96 x 10⁷

4: 10/10 (0.96 x 10⁷)

7: (1.93 x 10⁷) - 10/10 (9.7 x 10⁶)

8: 9.6 x 10⁶

In mathematics, an expression is a combination of one or more numbers, variables, and mathematical operations that can be evaluated to produce a value or result.

The correct order to perform the subtraction operation is:

Write out the problem: (1.93 x 10⁷) - (9.7 x 10⁶)

Subtract the second number from the first number (ignoring the scientific notation): (1.93 - 0.97) x 10⁷

Simplify the subtraction to get the result in scientific notation: 0.96 x 10⁷. Convert the result to standard scientific notation: 9.6 x 10⁶.

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There are at least two group means that are significantly different from one another, according to the alternative hypothesis (H a). The alternative hypothesis is adopted if the outcome is statistically significant.

You can use ANOVA to determine whether differences between data sets are statistically significant. It functions by examining the levels of variance present within each group using samples drawn from each.

The likelihood that the mean of a sample taken from the data will be different owing to chance increases if there is a lot of variance (spread of data away from the mean) among the data groups.

In addition to examining the variance within the data groups, ANOVA also considers sample size (the smaller the sample, the lower the likelihood that outliers will be randomly selected from it) and sample mean differences (the greater the difference between the sample means, the greater the likelihood that an outlier will be randomly selected from it).

hence, The alternative hypothesis is adopted if the outcome is statistically significant.

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Answer:

1. No solution

2. All real numbers

3. Always true

Step-by-step explanation:

Answer: look at the picture and you will see the answer, for the numbers 3 -2(5+6n)<6(8-2n) it all real numbers are solutions.

Step-by-step explanation: hope this help

Step-by-step explanation:

Area=(a+b)/2 x h

a=6x+3

b=4x-5

h=-5x+10

Area= -25x^2+55x-10

Answer:

Step-by-step explanation:

We are being asked for times, so we can express the rate in terms of seconds per meter.

  (15 seconds)/(14 meters) = (15/14) seconds per meter = 1 1/14 seconds/meter

__

1) It will take Robot A 1 1/14 seconds to go 1 meter.

2) it will take Robot A 4 2/7 seconds to go 4 meters. (4 times as long)

Answer:

She earned 260 dollars

Step-by-step explanation:

If you multiply 9 by 10 you get 90 then do the same to the rest of the numbers then add them you get your answer.

Answer:

(x-y)(x-y)(x-y)= x²-yx+x²-yx-yx+y²-yx+y²

2x²-4yx+2y²

(y-x)(y-x)= y²-yx-yx+x²

y²-2yx+x²

-(y²-2yx+x²) = -y²+2yx-x²

2x²-4yx+2y²-y²+2yx-x²= x²-2yx+y²

or

(x−y−1)(x−y)² ≡ x³−x²+3xy²+2xy−y³−y²−3yx³

The statement using absolute value notation will be x - 78 ≤ 22.

The student will pass the test which scores 22 points for the number 78

Absolute values are any digit's value without taking the sign into an account. Therefore, all negative numbers will be regarded as positive for absolute value. The absolute value of -5, for instance, will be 5, whereas that of -7, will be 7.

In essence, the absolute value calculates the distance from zero. Putting an absolute value on something does not imply that they are the same number but that they are the same distance from 0.

Le the score of student be = x

Forming the absolute value notation -

This can be expressed as,

x - 78 ≤ 22.

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Answer:

N=CD C=2-3 sentance

Step-by-step explanation:

Answer:

Waves transfer energy, but not matter.

Waves transfer energy from one point to another without moving matter.

i hoped this helped

Total attempt = 90

Successful throws = 81

Unsuccessful = Total attempt - Successful

= 90 - 81

=> 9

To calculate the percentage of unsuccessful, we will use the formula:

Answer:

-10

Step-by-step explanation:

-5(2) - 4(-1) - 8 +2(2)

Answer:

-10

Step-by-step explanation:

-5(2)-4(-1)-8+2(2)=

-10+4-8+4=-10

-×- is +

-×+ is -