Mr. Donley drove 504 km in each direction on a vacation
trip. The average rate going was 14 km/h faster than the
rate returning. The total time for the entire trip was 21
hours. Find the average rate for each direction.

The cliff divers dive headfirst from the top of cliff. 1/2 or 0.5 second is the time period will the diver's height exceed that of the cliff.

An object that moves along the vertical axis due to gravitational acceleration is called a free-falling object. The free fall position is given by the following equation of motion:

yₜ = y₀ + v₀t + 1/2(at²)

Where y₀--> the initial height of the object

v₀--> the initial velocity

t --> time

a --> the acceleration due to gravity and is equal to a = g = - 32.2 ft²/sec

We have given that,

Initial velocity of divers , v₀ = 8 feet/sec

Initial Height of top of cliff , s₀ = 87 feet

position function, s(t) = - 16t²+ v₀t +s₀

Plugging all known values in above position function,

s(t) = -16 t² + 8t + 87

The the diver's height exceed that of the cliff means, s(t) > 87

=> -16 t² + 8t + 87 > 87

Subtract 87 from both sides, we get

-16t^2 + 8t > 0 , now we solve this inequality by changing it in a equality,

-16 t² + 8t = 0

=> -8 t( 2t - 1) = 0 => -8t = 0 , 2t -1 = 0

=> either t = 0 or t = 1/2

So the first half second, the person is above the height of the cliff.

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Complete question:

Use the position function s(t)-16t2+ vot +so position, t time) to answer the following: Divers in Acapulco, Mexico, dive headfirst at 8 feet per second from the top of a cliff 87 feet above the Pacific Ocean. During which time period will a diver's height exceed that of the cliff? (vo initial velocity, so initial.

The total length of ribbon that Leah bought is equal to 358.4 inches.

In Mathematics, measurement can be defined as an act or process through which the size, weight, magnitude, quantity, volume (capacity), dimensions (length and width), or distance traveled by a physical object or body is taken, especially for the purpose of an experiment.

In order to determine the total length of ribbon that was purchased by Leah, we would have to multiply the length of the strips of ribbon by the length of each of the strips as follows;

Total length of ribbon = Length of the strips of ribbon × Length of each of the strips

Substituting the given parameters into the formula, we have;

Total length of ribbon = 32 × 11.2 inches

Total length of ribbon = 358.4 inches.

In this context, we can reasonably infer and logically deduce that total length of ribbon that was purchased by Leah is equal to 358.4 inches.

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The last term is 300

The sum of all the terms is 15150.0

The average of all the terms is 151.5

Here is an example solution in Python that follows the given pseudocode:

# Prompt for and read the first term

first_term = int(input("Enter first term: "))

# Prompt for and read the common difference

common_difference = int(input("Enter common difference: "))

# Prompt for and read the number of terms

number_of_terms = int(input("Enter number of terms: "))

# Calculate the last term

last_term = first_term + (number_of_terms - 1) * common_difference

# Calculate the sum of all the terms

sum_of_terms = number_of_terms * (first_term + last_term) / 2

# Calculate the average of all the terms

average_of_terms = sum_of_terms / number_of_terms

# Display the results

print("The last term is", last_term)

print("The sum of all the terms is", sum_of_terms)

print("The average of all the terms is", average_of_terms)

If you run this code and enter the values from the sample run (first term: 3, common difference: 3, number of terms: 100), it will produce the following output:

The last term is 300

The sum of all the terms is 15150.0

The average of all the terms is 151.5

The program prompts the user for the first term, common difference, and number of terms. Then it calculates the last term using the given formula. Next, it calculates the sum of all the terms and the average of all the terms using the provided formulas. Finally, it displays the calculated results.

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Step-by-step explanation:

* start by finding the gradient/ slope of the line using the two points*

after finding the gradient you can now use the formula/ equation of any straight line which is *y = m×x + c*

The number of additional gifts Jeff can buy with the remaining cost is 1.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

As per the given,

Total cost = $15 + $20 = $35

Total spent = $50

Remaining = $50 - $35 = $15

Since one gift cost $10

Thus, 15/10 = 1.5 since the number of gifts will be the whole number so it will be round to bottom 1 gift.

Hence "With the money still available, Jeff can purchase 1 more present".

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Answer:

1:55

Step-by-step explanation:

3:40 - 1:45= 1:55

\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\qquad \tt \rightarrow \:x = -3 \)

____________________________________

\( \large \tt Solution \: : \)

\(\qquad \tt \rightarrow \: CD + DE = CE\)

\(\qquad \tt \rightarrow \: x + 10 + x + 4 = 8\)

\(\qquad \tt \rightarrow \: 2x + 14 = 8\)

\(\qquad \tt \rightarrow \: 2x =8 - 14\)

\(\qquad \tt \rightarrow \: 2x = - 6\)

\(\qquad \tt \rightarrow \: x = - 3\)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

\(\huge \boxed{\sf x=-3}\\\\\\\displaystyle \sf CD+DE=8 \\\\x+10+x+4=8\\\\2x+14=8\\\\Subtracting\ 14\ from\ each\ side\\\\ 2x+14-14=8-14\\\\2x=-6\\\\ Dividing\ each\ side\ by\ 2 \\\\ \frac{2x}{2} =\frac{-6}{2} \\\\x=-3\)

Answer:

P(factor of 90) = 5/6

Step-by-step explanation:

When you roll a 6 sided die, it can land showing a 1, 2, 3, 4, 5 or 6. All these numbers except for 4 are factors of 90.

That is 1 goes into 90.

2 goes into 90.

3 goes into 90.

4 does not go into 90.

5 goes into 90.

6 goes into 90.

So 5 out of the 6 sides show a number that goes into 90.

5 of 6 numbers are factors of 90.

So, P(factorof90)

= 5/6

Step-by-step explanation:

1.

Let's say she starts on a Monday(first day).

She walked 10min on Monday

She then starts increasing the number of minutes each day by "2".

So

Tuesday --- 12min

Wednesday--- 14min

Thursday --- 16min

Friday --- 18min

Saturday --- 20min

Sunday ---- 22min

Total = 10 + 12 + 14 + 16 + 18 + 20 + 22

= 112minutes

She walks 112minutes in one week.

2.

Since each 8 cans are consumed per day

...

200cans would be consumed in

200/8 = 25days.

We can drag the particles in mass/grams measurement to the corresponding descriptions as follows:

1.  1.6744 × 10⁻²⁴: Two electrons and 0ne proton

2. 5.021 × 10⁻²⁴: Two protons and one neutron

3. 5.0224 × 10⁻²⁴: One proton and two neutrons

4. 3.3484  × 10⁻²⁴: One electron, one proton, and one neutron

To match the measurements to the descriptions first note that one neutron is 1.6749 × 10⁻²⁴. One proton is equal to  1.6726 × 10⁻²⁴ and one electron is equal to  9.108 × 10⁻²⁸.

To obtain the right combinations, we have to add up the particles to arrive at the constituents. So, for the figure;

1.6744 × 10⁻²⁴, we would

Add 2 electrons and one proton

= 2(9.108 × 10⁻²⁸) + 1.6726 × 10⁻²⁴

= 1.6744 × 10⁻²⁴

The same applies to the other combinations.

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In the standard curve for nitrophenol generated for use in this experiment, the nitrophenol concentration is reported on the x - axis.

What is standard curve?

A calibration curve, sometimes referred to as a standard curve, is a common technique used in analytical chemistry to compare an unknown sample to a group of standard samples with known chemical concentrations.

In order to calculate the nitrophenol concentration in mole/ml based on absorbance readings, the standard curve is drawn.

Based on the optical density, or OD410, or absorbance at 410 nm, this standard curve of absorbance is used to calculate the quantity of nitrophenol.

Therefore, the nitrophenol concentration is displayed on the x axis of the standard curve.

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The future value (A) is approximately 5610.2 for the given investment and annu $4000 for 5 years at 7% compounded annually

To find the compound amount and compound interest rate for the given investment, we can use the formula for compound interest:

(a) The compound amount in the account after 5 years can be calculated using the formula:

A = P(1 + r/n)^(nt)

Where A is the compound amount, P is the principal (initial investment), r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Given that the principal (P) is $4000, the interest rate ® is 7%, and the interest is compounded annually (n = 1), and the investment is for 5 years (t = 5), we can plug these values into the formula:

A = 4000(1 + 0.07/1)^(1*5)

A = 4000(1 + 0.07/1)^(1*5)

= 4000(1 + 0.07)^(5)

= 4000(1.07)^(5)

≈ 4000(1.402551)

≈ 5610.20

Therefore, the future value (A) is approximately 5610.2

Calculating this expression will give us the compound amount after 5 years.

(b) The compound interest earned can be calculated by subtracting the principal from the compound amount:

Compound interest = Compound amount – Principa

This will give us the total interest earned over the 5-year period.

By evaluating the expressions in (a) and (b), we can determine the compound amount and the compound interest earned for the given investment.

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The statement "the interquartile range is least influenced by an outlying value in the data set" is true.

The range is simply the difference between the maximum and minimum values in a data set.

The variance is a measure of the spread of a data set, and is calculated by finding the average of the squared differences between each data point and the mean of the data set.

The interquartile range, on the other hand, is a measure of the spread of the middle 50% of the data set. It is calculated by finding the difference between the upper quartile and the lower quartile.

Because the interquartile range only takes into account the middle 50% of the data, it is less influenced by outliers than the range and variance. This is because outliers can greatly impact the range and variance, but have little effect on the interquartile range.

In conclusion, the interquartile range is a more robust measure of spread for a data set, as it is less influenced by outliers.

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Answer:The first issue one most notice is the words “at least” We are trying to find the probability of at least 2 girls.

The five possible outcomes for girls are 0,1,2,3,4. The odds of 1 girl out of 4 is .25 and the odds of 1 boy out of 4 is .25 (same as the odds of 3 out of 4 girls). Therefore the odds of 1 OR 3 girls must be .5 because 1 girl and 3 girls each has a .25 probability. If the probability of (1 OR 3 girls) equals .5, then the probability of 2 girls must be a different number.

The probability of 2 or more girls, is the sum of the probability of 4 girls (.06125)(—-.5 to the 4th power—— ), plus the probability of 3 girls (.25)——(the same as the probability of 1 boy)—- plus the probability of 2 girls. Since we know the probability of zero boys is .0625 (again, .5 to the 4th power) and the probability of 1 boy is .25 (the same as the probability of 3 girls )———then the probability of 2 girls is ((1 minus (the sum of the probability of 0 OR 1 boys) plus the (sum of the probability of 3 or 4 girls)), or 1-((.0625+.25)+(.0625+.25)), or .375. We had to derive the probability of two from the other known probabilities. Therefore .375+.25+.0625=.6875 is the probability of both AT LEAST 2 girls and also NO MORE than 2 boys. Notice this adds up to 1.375 because the probability of the central number 2 (i.e., .375) appears on both sides.

Answer:

7/3

Step-by-step explanation:

3t^2 - 7t

T(3t-7)

T=0, 3t-7=0,.: t=7/3

The zeros are t=7/3

2root5y^2 +y-3 root 5

Pls does the root affect y tooo.

a) The logistic equation for this problem is L dP/dt = P(1 - P/L), where L = 2000 and Po = 100.

b)  The maximum reproduction rate is 0.03465 times the current population.

a. The logistic equation for this problem is:

L dP/dt = P(1 - P/L)

where L is the carrying capacity of the lake, P is the current population, and dP/dt is the rate of change of the population over time.

We know that at t = 0, P = 100, and one year later at t = 1, P = 200. So we can use this information to find k, which is the growth rate coefficient:

P(t) = L / (1 + (L / Po - 1) * exp(-kt))

200 = L / (1 + (L / 100 - 1) * exp(-k))

200 = L / (1 + (L - 100) * exp(-k))

200 + 200L - 20000 = L * (1 + (L - 100) * exp(-k))

200L -\(L^2\) * exp(-k) + 200L * exp(-k) - 10000 * exp(-k) = 0

\(L^2\) - 400L + 5000 = (L - 200)^2 - 30000

\((L - 200)^2\) = 35000

L = 200 + sqrt(35000) ≈ 223.6

So L ≈ 223.6, and we can use this to find k:

2000 = 223.6 / (1 + (223.6 / 100 - 1) * exp(-k))

20000 + 2000L - 2236 = L * (1 + (L - 100) * exp(-k))

2236 - \(L^2\)  * exp(-k) + 2236 * exp(-k) - 100 * exp(-k) = 0

\(L^2\) - 4472L + 220000 = 0

(L - 2000)(L - 100) = 0

So either L = 2000 or L = 100. We know that L ≠ 100, since we know that the population stabilizes at 2000 after a long time. Therefore, L = 2000, and we can solve for k:

k = -ln((L / Po - 1) / (1 + (L / Po - 1))) / t

k = -ln((2000 / 100 - 1) / (1 + (2000 / 100 - 1))) / 1

k ≈ 0.0693

Therefore, the logistic equation for this problem is:

L dP/dt = P(1 - P/L)

dP/dt = 0.0693P(1 - P/2000)

b. The maximum reproduction rate occurs when the population is halfway to the carrying capacity, or P = L/2. At this point, the equation becomes:

dP/dt = 0.0693P(1 - 0.5)

dP/dt = 0.03465P

Therefore, the maximum reproduction rate is 0.03465 times the current population. For example, if the current population is 1000, the maximum reproduction rate is 34.65 fish per year.

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Full Question : Logistic Equation: L dP dt P(1-2). P() = L - Po Po 1+ 4e ki Where A 1. Fish population in a lake grows according to the logistic law. The initial population of 100 fish and year later it was 200. After a long time fish population stabilized at 2000.

a. Write down the logistic equation for this problem.

b. What is the maximum reproduction rate (fish/year)?

Answer: Yes

Step-by-step explanation:

Yes area should be right because you are finidng how much it covers which would be area. A way I used to remember it was you looking for the AREA it covers so that awnser is area! Hope that helped!

We're trying to find \(s(t(-7))\).

\(t(-7)=3(-7)\)

\(t(-7)=-21\)

\(s(-21)=2-(-21)^2\)

\(s(-21)=2-441\)

\(s(-21)=-439\)

Hope this helps.

頑張って!

A subset of the population used by statisticians to make predictions about a population is called a sample. In statistical analysis, it is usually not practical or feasible to study an entire population, hence a representative sample is selected instead.

The sample is selected based on specific criteria that must be met, such as age, gender, income, location, or any other relevant factors that might affect the population being studied.
The sample must be a true representation of the population, which means it should be chosen randomly and without any bias. This is important because if the sample is not representative of the population, then any conclusions drawn from it may not be accurate or applicable to the population as a whole.
Once the sample is selected, statisticians use various methods to analyze and interpret the data collected from it. The results obtained are then used to make inferences and predictions about the entire population. These predictions can be used to inform policies, decisions, or actions that affect the population.
In conclusion, a sample is a subset of a population that is selected by statisticians to make predictions about the population. It must be representative, randomly selected, and without any bias to ensure accurate results.

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Answer:

4t

Step-by-step explanation:fssSVfg

Jessica’s friend tried to find the side length of a square garden, but made a mistake:

24 x + StartFraction 12 over 13 EndFraction = 4 (6 x + StartFraction 12 over 13 EndFraction) = Side length = 6 x + StartFraction 12 over 13 EndFraction

Can you identify and correct her error?

The average IQ test score would be 100.

What is a normal distribution?

A probability distribution that is symmetric about the mean or average is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the average value occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

Average IQ Score

A score of 100 is regarded as the average IQ on various tests. The majority of results (68%) are within one standard deviation of the mean (that is, between 85 and 115). This indicates that the average result is within plus or minus 15 points for almost 70% of test takers.

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Answer:

27 :)

Step-by-step explanation:

$27 it D

Step-by-step explanation:

Step-by-step explanation:

1/6 ÷ 1/2

=1/6 × 2

=1/3

Hope it helps you

The equivalent equation for the height, h, of a triangle in terms of area, A, and base, b is h = 2A / b

The area of a triangle when given the height and base can be represented as follows:

area of triangle = 1 / 2 bh

where

b = base

h = height

Therefore, the equivalent equation for the height, h, of a triangle in terms of area, A, and base, b can be represented as follows:

A = area

b = base

h = height

A = 1 / 2 bh

Therefore, making height the subject of the formula,

cross multiply

2A = bh

divide both sides by b

2A / b = h

h = 2A / b

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Answer:

X = -3, y = -8

Please see the link to view the Graph:

Answer:

Yes, it is a right triangle

Step-by-step explanation:

Because 6, 8 and 10 are Pythagorean triplets.

Answer:

no

Step-by-step explanation:

It is a scalene triangle. Right triangles have a right angle and have two congruent sides, like an isosceles.

Answer:

Factor GCF: 3x(2x⁴ - 5x + 4)

Step-by-step explanation:

Simply take out the greatest variable first and then take out the GCF of the numbers to find out factored GCF.

The correlation between x and z would be a strong positive relationship when the correlation between x and y is 0.9 and the correlation between y and z is 0.9.

A correlation can be defined as statistical terminology which is used as a measure to indicate the relationship that exists between two or more variables.

This ultimately implies that, correlation can be used to statistically measure and predict the level of fluctuation between two or more variables in relation to one another.

A positive correlation can be defined as a terminology that is used to described a scenario (situation) in which two variables move in the same direction because they are in tandem.

In this context, we can infer and logically deduce that the correlation between x and z would be a strong positive relationship when the correlation between x and y is 0.9 and the correlation between y and z is 0.9.

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