A skydiver falls 144 feet in three seconds. How far does the skydiver fall per second?

The half-life of a substance is the amount of time it takes for half of the substance to decay or disintegrate. The half-life formula is used to calculate the amount of a substance that remains after a certain amount of time has passed.

To understand the half-life formula, it is important to first understand the concept of radioactive decay. Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting ionizing particles and radiation. This process results in the nucleus becoming more stable, often by converting into a different element.

The half-life formula is typically represented as t1/2. The t1/2 represents the half-life of the substance, and the number following it represents the number of half-lives that have passed. The formula can be used to calculate the remaining amount of a substance after any number of half-lives. For example, if the half-life of a substance is 10 days and 20 days have passed, the formula would be used to calculate the remaining amount of the substance after 2 half-lives (20 days / 10 days per half-life = 2).

The formula is typically used in the context of radioactive decay, but it can be used for other types of decay as well. In physics and chemistry, the half-life of a substance is commonly used to measure the stability of a substance and predict how long it will remain stable. The half-life formula can also be used to calculate the rate of decay of a substance, which is useful for understanding how a substance will behave over time.

In short, the half-life formula is used to calculate the remaining amount of a substance after a certain amount of time has passed, based on the substance's half-life. It is a useful tool for understanding the stability and rate of decay of a substance, and it is widely used in physics, chemistry, and other sciences.

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If the equation Ax = b has multiple solutions, we can conclude that the transformation represented by matrix A is not one-to-one and not invertible.

If the equation Ax = b has more than one solution for some b, it implies that the transformation represented by matrix A is not invertible or not bijective.

To justify this, let's consider the implications of the equation having multiple solutions. If there are multiple solutions to Ax = b, it means that there are different vectors x₁ and x₂ that satisfy the equation. In other words, there exist two distinct inputs that produce the same output when multiplied by A. This violates the condition of a one-to-one transformation, which states that each input should have a unique output.

Furthermore, if A is not invertible, it means that there is no unique inverse matrix A⁻¹ that can be used to recover the original input x from the output b. Invertibility is a characteristic of one-to-one transformations, as it ensures that the transformation can be reversed to obtain the original input.

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Step-by-step explanation:

let m2 be x

then m1 = 4x

Since, m1+m2 = 115

therefore x + 4x = 115

5x = 115

x = 23

so , m2 = 23°

Answer:

Step-by-step explanation:

Let m2 be x

Then m1 will be= 4x

A/Q

--> m1+m2= 115

    4x+x= 115

    5x= 115

    x=115/5

    x= 23

--> m2= 23 degree

--> m1= 4x

        = 4*23

        = 92 degree

Answer:

thhe answer would only be 3 feet

Step-by-step explanation:

Yes, I can find the slope of a line and type the correct code. The SLOPE function will return the slope of the linear regression line that best fits the data.

The slope of a line is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. The formula for finding the slope of a line is (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line.

The slope is a measure of how steep the line is. It can be positive, negative, zero, or undefined. The code for finding the slope of a line in ALL CAPS with no spaces is SLOPE.

To use this function in Excel, you need to provide the range of x-values and the range of y-values.

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On solving the provided question, we can say that - here in the given equation we got x- 1 = 0; x = 1, y = 2

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

y = 2x +1

y = 3x - 1

x- 1 = 0

x = 1, y = 2

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Answer:

2 girls for every 1 boy or 2:1

Step-by-step explanation:

Theres x2 girls for every boy so it would be 2:1.

2.74 would be your answer

The parametric equations for the curve are:

x = -5t^3 - 3t

y = t

To find parametric equations for the curve x = -5y^3 - 3y, we can set y as the parameter and express x in terms of y.

Let y = t, where t is the parameter.

Substituting y = t into the equation x = -5y^3 - 3y:

x = -5(t^3) - 3t

The interval for the parameter values depends on the context or specific requirements of the problem. If no specific interval is given, we can assume a wide range of values for t, such as all real numbers.

So, the correct answer is:

A. x = -5t^3 - 3t, y = t

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Here's link to the answer:

tinyurl.com/wpazsebu

Answer:

a=4.2

Step-by-step explanation:

The constant is 1.4 bc if u divide the numbers in y with the x that corresponds them, it will be 1.4

ex. 2.80 divided by 2 is 1.4

ex. 5.60 divided by 4 is 1.4

This means that

2×1.4 is 2.80

4×1.4 is 5.69 so

3×1.4 is 4.2

After solving the given expression that is 11 feet 7 inches plus 14 feet 6 inches plus 35.5 inches plus 30 inches plus 6 feet 10 inches is 460.5.

Given that,

We have to find what is 11 feet 7 inches plus 14 feet 6 inches plus 35.5 inches plus 30 inches plus 6 feet 10 inches.

We know that,

1 feet is equal to 12 inches.

So,

We can write as

11 feet 7 inches plus 14 feet 6 inches plus 35.5 inches plus 30 inches plus 6 feet 10 inches.

11f 7in+ 14f 6in +35.5in+ 30in + 6f 10in

11(12)+7in+14(12)+6+35.5+30+6(12)+10

132+7+168+6+35.5+30+72+10

460.5

Therefore, After solving the given expression that is 11 feet 7 inches plus 14 feet 6 inches plus 35.5 inches plus 30 inches plus 6 feet 10 inches is 460.5.

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The monthly payment amount is approximately $129.45.

To find the payment amount and finance charge for the loan, we can use the formula for calculating monthly loan payments and finance charges.

The formula to calculate the monthly loan payment amount is given by:

\[ P = \frac{{r \cdot PV}}{{1 - (1+r)^{-n}}} \]

where:

P = monthly payment amount

r = monthly interest rate (APR divided by 12 months and 100 to convert it to a decimal)

PV = present value or loan amount

n = total number of payments

Given:

Loan amount (PV) = $4800

APR = 12%

Monthly payments (n) = 24

To calculate the monthly interest rate (r), we divide the annual percentage rate (APR) by 12 and convert it to a decimal:

\[ r = \frac{{12\%}}{{12 \cdot 100}} = \frac{{0.12}}{{12}} = 0.01 \]

Substituting the values into the formula, we have:

\[ P = \frac{{0.01 \cdot 4800}}{{1 - (1+0.01)^{-24}}} \]

Calculating this equation will give us the monthly payment amount.

To calculate the finance charge, we can subtract the loan amount (PV) from the total amount paid over the loan term (P * n).

Let's calculate these values:

\[ P = \frac{{0.01 \cdot 4800}}{{1 - (1+0.01)^{-24}}} \]

\[ P = \frac{{48}}{{1 - (1+0.01)^{-24}}} \]

\[ P = \frac{{48}}{{1 - 0.62889499777}} \]

\[ P \approx \frac{{48}}{{0.37110500223}} \]

\[ P \approx 129.4532449 \]

To calculate the finance charge, we can subtract the loan amount (PV) from the total amount paid over the loan term:

Total amount paid = P * n

Total amount paid = $129.45 * 24

Total amount paid = $3106.80

Finance charge = Total amount paid - PV

Finance charge = $3106.80 - $4800

Finance charge = $-1693.20

The finance charge is approximately -$1693.20. The negative sign indicates that the borrower will be paying less than the loan amount over the loan term.

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Answer:

x=48

Step-by-step explanation:

4x-12=180

+12

4x=192

/4

x=48

11 1/4

Step-by-step explanation:

the yards have to be converted to feet

1 yards = 3 feet

5 yards x 3 = 15 feet

Area of a rectangle = length x width

15 x 2 1/4

15 x 9/4 = 33 3/4

33 3/4 x 1/3 = 135 /12 = 11 1/4

Answer:

2x+8=3x-2

8=x-2  

x=10'

the answer is 10

Step-by-step explanation:

sorry i didnt put an answer at the start

i was in a rush

The amount of simple interest on a $1250 loan at 6.5% simple interest for 3 years would be $243.75.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

From the given information, P = $1250, r = 6.5 and t = 3.

Therefore, SI = (1250×6.5×3)/100.

SI = 12.5×6.5×3.

SI = $243.75

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Answer: {-2, -0.5, -1.5, 0}

Step-by-step explanation:

The key things we need to recognize is that we are extracting the numbers covered by the red line. This line does not include all values from -2 to 4, though. The white dot means that part of the inequality is x < 4.

Therefore, the answer is every number that fits in the equality:

\(-2 \leq x < 4\)

This includes -2 and every number up to 4, but NOT 4.

I hope this helps, if you need anything explained let me know.

Answer:

Point C i think is: (33/8, 0)

Step-by-step explanation:

I hope this helps -w-

Answer:

B; The second answer

Step-by-step explanation:

The question is asking about the associative property of addition. This involves the rearranging of the parenthesis. If you were to solve the given equation, and solve the the answer, then you will get the same answer. In this property, it says that you will get the same result if you were to move/switch the parenthesis from the values; This means that order doesn't matter.

No, it is not possible to obtain a negative value for the ss, variance, or standard deviation. They represent the amount of spread in data, and the values are always positive or zero.

Sum of squares (SS) measures the deviation of each data point from the mean of the set, squared. The formula for SS is:

SS = Σ (X - μ)^2

Variance is the average of the sum of squares, and it is calculated by dividing the SS by the degrees of freedom (n-1), where n is the number of data points in the set:

Variance = SS / (n - 1)

Standard deviation is the square root of variance and it is a measure of how far each data point is from the mean of the set:

Standard deviation = √Variance

Since both variance and standard deviation are based on the sum of squares, which is always non-negative, variance and standard deviation are also always non-negative.

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Answer:

There is no separation (distance) between the first y-intercept (6) and the second (6).

Step-by-step explanation:

We'll assume that the table shows points on a straight line.

If we go from x = 2 to x = 8 (an increase of 6), the corresponding y values go from y =2 to y = -10 (a decrease of 12).  Thus, the slope of the line represented by the table is

m = rise / run = -12/6, or m = -2.

We need to find the equation of the line represented by the table, so that we can know the y-intercept.  Start with y = mx + b and substitute -2 for m:

y = -2x + b.  We arbitrarily choose an ordered pair from the table, such as (11, -16).  Here we substitute 11 for x and -16 for y:

-16 = -2(11) + b, or

-16 = -22 + b, which yields b = 6.

This is the same y-intercept as the '6' in the given f(x) = -2x + 6.  So:  There is no separation (distance) between the first y-intercept (6) and the second (6).

The shape of the sampling distribution of sample means it approaches a normal distribution. (option d).

The shape of the sampling distribution of sample means is determined by the size of the sample. As the sample size increases, the shape of the distribution approaches a normal distribution. This is known as the Central Limit Theorem (CLT).

The CLT states that, regardless of the population's distribution, the sampling distribution of sample means will be approximately normal as the sample size increases. This means that even if the population is not normally distributed, the distribution of the sample means will still be normal as long as the sample size is large enough.

The reason for this is that as the sample size increases, the variability of the sample means decreases. This is because the sample means tend to cluster around the population mean, making the distribution more concentrated and less spread out. As a result, the distribution becomes more symmetrical and bell-shaped, resembling a normal distribution.

Therefore, the correct answer to the multiple-choice question is d) it approaches a normal distribution.

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The probability that he/she neither receives a text message nor an email during any weekend afternoon be 0.3000.

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Using the method for the union of two sets, we can calculate the number of students who receive either a text message or an email (or both) based on the above data:

Number of students who receive either a text message or an e-mail = Number of students who receive a text message + Number of students who receive an e-mail - Number of students who receive both

= 1364 + 857 - 470

= 1751

The proportion of students who don't receive either a text message or an email divided by the total sample of students is the probability that a student will not receive either:

P(neither T nor E) = (2500 - 1751) / 2500

= 749 / 2500

= 0.2996

Rounding to four decimal places:

P(neither T nor E) = 0.2996 ≈ 0.3000

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the discrepancy between the sample mean and the claimed protein content is due to chance error in the measurements

To determine whether the discrepancy between the sample mean and the claimed protein content of 4 grams can be due to chance error in the measurements, we can perform a hypothesis test.

The null hypothesis, H0, is that the true mean protein content is equal to 4 grams. The alternative hypothesis, Ha, is that the true mean protein content is less than 4 grams.

Using a one-tailed t-test with a significance level of 0.05 and four degrees of freedom (n-1=5-1=4), we calculate the t-value to be -1.386. The critical t-value for a one-tailed test at a significance level of 0.05 and four degrees of freedom is -2.132.

Since our calculated t-value of -1.386 is greater than the critical t-value of -2.132, we fail to reject the null hypothesis. This means that we do not have enough evidence to conclude that the true mean protein content is less than 4 grams. Therefore, it is possible that the discrepancy between the sample mean and the claimed protein content is due to chance error in the measurements.

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