In (a) and (d), the -1 is a reciprocal, as -1 is being multiplied by f(p) or f(p⁻¹) respectively, and the solutions for p are p = 2 and p = -7/3 respectively. In (b) and (c), the -1 is an inverse, as it is part of the inverse of f(p), and the solutions for p are p = 7 and p = 5/3 respectively.
(a) f(p) = 5 is not an inverse or a reciprocal. To solve for p, we can use the equation f(p) = 5 and solve for p. We do this by subtracting 2 from both sides of the equation to get 3p = 3, and then dividing both sides by 3 to get p = 1.
(b) f⁻¹(p) = 5 is an inverse and we can solve for p using the equation f⁻¹(p) = 5. To do this, we subtract 2 from both sides to get 3p = 3, and then divide both sides by 3 to get p = 1.
(c) (f(p))⁻¹ = 5 is a reciprocal and we can solve for p using the equation (f(p))⁻¹ = 5. To do this, we first divide both sides of the equation by 5 to get 1/f(p) = 1. Then, we multiply both sides by f(p) to get f(p) = 5. Finally, we subtract 2 from both sides to get 3p = 3, and then divide both sides by 3 to get p = 1.
(d) f (p⁻¹) = 5 is not an inverse or a reciprocal. To solve for p, we can use the equation f (p⁻¹) = 5 and solve for p. We do this by multiplying both sides of the equation by p⁻¹ to get f(p) = 5p⁻¹. Then, we subtract 2 from both sides to get 3p = 5p⁻¹ - 2, and then multiply both sides by 3 to get 9p = 5p⁻¹ - 6. Finally, we add 6 to both sides to get 9p + 6 = 5p⁻¹, and then divide both sides by 4 to get p = 1.
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Paul wins 1500 metres in 4,67m (a) Estimate his average speed in metres per minute
Answer:
293.1596091
Step-by-step explanation:
Average speed= speed/time
average speed= 1500/4.67
if 2x ≤ g(x) ≤ x4 − x2 2 for all x, evaluate lim x→1 g(x).
The limit value is equal to 2 .
Given,
2x ≤ g(x) ≤ [tex]x^{4}[/tex] − x² + 2
According to sandwich theorem,
g(x)≤ f(x) ≤ h(x)
[tex]\lim_{x \to \ a} g(x) = \lim_{x \to \ a} h(x) = L[/tex]
Then,
L= [tex]\lim_{x \to \ a} f(x) = L[/tex]
Here we have,
2x ≤ g(x) ≤ [tex]x^{4}[/tex] − x² + 2
And so if we take the limit as x→1; then
[tex]\lim_{x \to \ 1} 2x = 2\\\\ \lim_{x \to \ 1} x^{4} - x^{2} + 2 = 2\\[/tex]
Thus we can apply the sandwich theorem,
[tex]\lim_{x \to \ 1} g(x) = 2[/tex]
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Correct expression:
2x ≤ g(x) ≤ [tex]x^{4}[/tex] − x² + 2
Which statement best describes the values of a and b in the regression model?
In the power regression model, a represents the initial value and b represents the growth factor.
In the power regression model, a represents the growth factor and b represents the initial value.
In the exponential regression model, a represents the initial value and b represents the growth factor.
In the exponential regression model, a represents the growth factor and b represents the initial value.
Answer:
this question to this question is 2
what is the solution to this system of equations
Answer:
[tex](-1, -2)[/tex]
Step-by-step explanation:
In this problem, we are asked to solve a system of equations given two equations each containing two variables: x and y. We can solve it using the substitution method.
First, we need to solve for a variable in terms of the other using one of the equations. I will solve for x in the first equation.
[tex]4x-7y=10[/tex]
↓ add [tex]7y[/tex] to both sides
[tex]4x=7y+10[/tex]
↓ divide both sides by 4
[tex]x=\dfrac{7y+10}{4}[/tex]
Now that we have solved for x in terms of y, we can substitute the solved x-value into the bottom equation.
[tex]3x + 2y = -7[/tex]
↓ substitute in solved x-value
[tex]3\left(\dfrac{7y+10}{4}\right) + 2y = -7[/tex]
↓ distribute 3
[tex]\dfrac{21y+30}{4}\right) + 2y\left(\dfrac{4}{4}\right) = -7\left(\dfrac{4}{4}\right)[/tex]
↓ rewrite all terms as fractions over 4
[tex]\dfrac{21y+30 + 8y}{4}\right)= -\dfrac{28}{4}[/tex]
↓ cancel denominators
[tex]29y+30= -28[/tex]
↓ isolate y's
[tex]29y = -28 - 30[/tex]
↓ simplify
[tex]29y= -58[/tex]
↓ divide both sides by 29
[tex]y = -2[/tex]
Now that we have solved exactly for y, we can solve for x using the substitution value we solved for earlier.
[tex]x=\dfrac{7y+10}{4}[/tex]
↓ substitute in y-value
[tex]x=\dfrac{7(-2)+10}{4}[/tex]
↓ simplify numerator
[tex]x=\dfrac{-14+10}{4}[/tex]
[tex]x=\dfrac{-4}{4}[/tex]
[tex]x = -1[/tex]
Finally, we can put the solved x and y values into a Cartesian coordinate in the form (x, y).
[tex](-1, -2)[/tex]
The local newspaper has letters to the editor from 60 people. If this number represents 8% of all of the newspaper's readers, how many readers does the newspaper have?
There are the newspaper has 750 readers.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
For example, If Misha obtained a score of 67% on her exam, that corresponds to 67 out of 100. It is expressed as 67/100 in fractional form and as 67:100 in ratio form.
If the number of letters to the editor is 60, and it represents 8% of all of the newspaper's readers, we can find the total number of readers by dividing the number of letters by the percentage as a decimal:
60 / 0.08 = 750
So the newspaper has 750 readers.
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The total number of readers the newspaper have is 750.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, The local newspaper has letters to the editor from 60 people and it is 8% of the total readers.
let, The total number of readers be 'x'.
Therefore, 60 is 8% of 'x' which can be numerically expressed as,
(8/100)×x = 60.
0.08x = 60.
x = 60/0.08.
x = 750.
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What are the domain and range of this relation? (8,-5) (2, 1) (6,2) (-1, 6) (-10, 1)
Answer: Domain Is always the x-input, while range will be the y-output.
Step-by-step explanation:
domain- -10,-1,2,6,8
Range- -5,1,2,6
2. If i have 3 bags of fertilizer that covers 150 square feet and 2 bag of fertilizer that covers 175 square feet . How many total square feet. How many total square feet can it cover with these total bags of fertilizer.
Answer:
If you have 3 bags of fertilizer that cover 150 square feet and 2 bags of fertilizer that cover 175 square feet, the total number of square feet that can be covered is:
3 bags x 150 square feet/bag = 450 square feet
2 bags x 175 square feet/bag = 350 square feet
450 square feet + 350 square feet = 800 square feet
So with these total bags of fertilizer, it can cover 800 square feet.
Step-by-step explanation:
round 4.2101 to the nearest hundredth
Answer:
4.21
Step-by-step explanation:
The hundredths place is the second number after the decimal. when rounding, you want to look at the number after. In this case the number after 1 is 0 which is lower than 5. Since it's lower than 5 we will keep the number the same.
Say the number after 1 was 7. Then we would round up and make the 1 into a 2. Any number above 5 you round up and add one to the number. If the number after is below 5, the number doesn't change.
Hope that made sense! :)
Answer:
4.21
Step-by-step explanation:
In this case, the hundredths place is 1 (4.2101, bold number is the hundredths place.) To round it you need to look at the number to the right of it which is 0, and if the number to the right of it is between 0-4 you keep the hundredths place the same and remove any numbers to the right of the hundredths place. Leaving you with 4.21. I hope this makes sense!
Hi can someone check my work for me! im unsure of my answers, please tell me if get any wrong! PLEASE HELP ASAPPP
Answer:
Step-by-step explanation:
all of them are correct!!!!! Great Job!!!!!
Please help with precal problem?
The population of the world was 5.7 billion in 1995 and increases according to the exponential growth model where the growth rate is assumed to be 2%. When will the population double?
P(t) = P₁ (1+r)t
A) 2012
B) 2027
C) 2029
D) 2030
E) None of these
Answer:
D) 2030
Step-by-step explanation:
You want to know when the population will double from its value in 1995 if it increases at 2% per year.
MultiplierThe multiplier for t years is given as (1 +r)^t. We want to find t such that this value is 2 when r = 0.02.
2 = 1.02^t
log(2) = t·log(1.02)
t = log(2)/log(1.02) ≈ 35.003
The year the population doubles will be ...
1995 + 35.003 = 2030.003
The population will double in year 2030, choice D.
<95141404393>
What is the range of the given function?
{(–2, 0), (–4, –3), (2, –9), (0, 5), (–5, 7)}
{x | x = –5, –4, –2, 0, 2}
{y | y = –9, –3, 0, 5, 7}
{x | x = –9, –5, –4, –3, –2, 0, 2, 5, 7}
{y | y = –9, –5, –4, –3, –2, 0, 2, 5, 7}
Answer: [tex]\{y|y=-9, -3, 0, 5, 7\}[/tex]
Step-by-step explanation:
The range is the set of [tex]y[/tex]-values.
30,000,000,000,000 IN SCIENTIFIC NOTATION
The answer is 3.0 x 10^13
Answer: [tex]3x10^1^3[/tex]
Explanation: When writing a number in scientific notation, the decimal point should be placed or moved until the coefficient is higher than 1 and less than 10.
Which statement is true? answer choices.
a. 4 liters 300 milliliters > 4,000 milliliters. b. 4 liters 300 milliliters < 4,000 milliliters.
Accordingly, 1 ml (milliliter) is just 1/1,000 of a liter. Consequently, 1 ml is less than 1 l.
What is the difference between liters and milliliters?Small quantities of liquid are measured in milliliters. Liters can be used to measure bigger amounts of liquid. 1 ml is equal to 0.001 liter, or 1000 milliliters. The symbol for a milliliter is either ml or mL.
The metric prefix "m" stands for "milli," which denotes "1/1,000 of" in English. Accordingly, 1 ml (milliliter) is just 1/1,000 of a liter. Consequently, 1 ml is less than 1 l.
The smallest metric unit, the milliliter, measures the tiniest amount of liquid and is a thousandth of a litre. So, 1 liter is equal to 1000 milliliters.
Therefore, the correct answer is option b. 4 liters 300 milliliters < 4,000 milliliters.
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Expand & simplify 4 ( p + 6 ) + 3 ( p − 2 )
Expanding and simplifying the expression:
4 ( p + 6 ) + 3 ( p − 2 ) = 4p + 24 + 3p - 6
= 7p + 18
So, the simplified expression is 7p + 18.
Answer:
[tex]4(p + 6) + 3(p - 2) \\ \longrightarrow \: 4p + 24 + 3p - 6 \\ solving \: the \: like \: terms \: together \: we \: get \\ \longrightarrow \:\boxed{ 7p + 18}[/tex]
hope helpful! :)
The figure below is a square. Find the length of side x to the nearest tenth.
Answer:
3.7
Step-by-step explanation:
The length of the diagonal of a square is [tex]\sqrt{2}[/tex] times the side length.
[tex]\implies x=\sqrt{7}\sqrt{2} \approx 3.7[/tex]
A family’s expenses are $1,200. One parent makes $850. Must the other earn $400 for both incomes to equal expenses?
A ray is 23 feet below sea level, what is its elevation?
The elevation of the ray is -23 feet below the sea level
How to determine the elevatin of the rayFrom the question, we have the following parameters that can be used in our computation:
Elevation = 23 feet below the sea level
The elevation of a location is its height above a certain reference point, typically sea level.
If a location is 23 feet below sea level, its elevation is -23 feet.
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Sam saved $35 buying the suit at a 20% off sale what was the regular price of the suit
find the open intervals over which the function is increasing or decreasing. write the answers in interval notation.
Given a quadratic function y = 36 - x² , the intervals over which the function is increasing is: (-∞ , 0) and the intervals over which the function is decreasing is: (0, ∞).
The standard form of a quadratic function is given by:
f(x) = ax² + bx + c
If a > 0, the graph of the function opens upward and the extreme point is the minimum one.
If a < 0, the graph of the function opens downward and the extreme point is the maximum one.
In this case, the function is: y = 36 - x²
Since the coefficient of the quadratic term is negative, or a < 0, then the graph opens downward and has a maximum point.
y = 36 - x² is already in the form of perfect square, hence, we can immediately compute:
x-intercepts : (-6,0) and (6,0)
y-(intercept = maximum point = (0, 36)
Before the maximum point, the function is increasing, while after the maximum point, the function is decreasing.
Hence,
increasing interval = (-∞ , 0)
decreasing interval = (0, ∞)
Your question is incomplete, most likely, it was:
Find the open intervals over which the function is increasing or decreasing. write the answers in interval notation.
y = 36 - x²
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Rabia doe not currently have a job, but declined a job offer becaue he feel her kill merit better pay and a better poition. Which term can be ued to decribe Rabia? Check all that apply. Cyclically unemployed
dometically unemployed
frictionally unemployed
tructurally unemployed
till employed
unemployed
Rabia is currently classified as unemployed, option .D since she has no job and has declined a job offer.
She falls into the category of frictionally unemployed, which means she is unemployed due to the time it takes to find a job that meets her qualifications and salary needs.
This is different from someone who is cyclically unemployed, which means they are out of work due to economic conditions, or someone who is structurally unemployed, which means they are out of work due to changes in technology or other factors that eliminated their job.
Rabia is still employed in the sense that she is actively seeking employment, but she is not employed in the sense that she has no job.
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Simplify: 6(x + 5) =
Answer:
You want to multiply the 6 to the numbers inside the parythesis:
6 * x = 6x
6 * 5 = 30
6x + 30
Step-by-step explanation:
Hope it helps! =D
Answer:
6x + 30
Step-by-step explanation:
1. 6(x + 5)
2. 6x+30
Can you help solve the question attached
a) The best estimate for the probability of landing on black is,
= 11/50
b) This is the best estimate because it involves the largest number of trials.
What is the probability?The Probability in mathematics is the possibility of an event in time. In simple words how many times that incident is happening in any given time interval.
Given:
Gemma spun a spinner a total of 200 times and worked out the estimated probability of it landing on black after different numbers of spins.
Her results are shown in the table below.
a) The best estimate for the probability of landing on black is,
= 11/50
b) This is the best estimate because it involves the largest number of trials.
Therefore, all the required values are given above.
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The density, d, of an object can be found by using the formula d=[tex]\frac{m}{v}[/tex], where m is the mass of the object and v is its volume. What is the density of an object that has a mass of 73,430 kilograms and a volume of 7 [tex]m^{3}[/tex]
The density of an object is 10490kg/m^3.
How to find the density?Density is like rate. It tells you how much of a thing is available for each unit other thing which contains the first thing.
Density = (Total amount available)/(total space which contains that amount)
Given;
The mass of object= 73,430 kilograms
The volume of object= 7m^3
Now
D=mass/volume
D=73430/7
D=10490
Therefore, the density will be 10490kg/m^3.
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Clara is training for a race in the summer. Every day she jogs the same number of miles. She also rides her bicycle 5.5 miles each day. During a 5-mile training period, she jogs and rides a total of 50 miles. How many miles does Clara jog each day during training
The required number of miles Clara jogs each day during training is 4..5 miles.
What is Miles?You can anticipate that it will take between 1 and 2.5 minutes to travel one mile because the majority of roads have speed limits between 25 and 60 mph. Do not allow algebra cause you to lose focus on the road! Also keep in mind how crucial it is to properly insure your vehicle.
According to question:Let miles does Clara jog each day during training be x.
During a 5-day training period, she jogs and rides a total of 50 miles.
5x + 5(5.5) = 50
5x + 27.5 = 50
5x = 50 - 27.5
5x = 22.5
x = 4.5 miles.
Thus, Clara jogs 4.5 miles each day.
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At a construction job for a gallery there are 33 painters. Of these painters, 21 of them
are painting the interior of the gallery. What percent of these painters are painting the
interior? Round your answer to the nearest tenth if necessary.
Answer:
63.6%
Step-by-step explanation:
21 out of 33 is what we are working with here. Divide.
21/33
= 0.636363...
Times by 100 to change from a decimal to a percent (you know "per cent" means "per hundred")
= 63.636363...
Round to the nearest tenth as per the instructions.
= 63.6%
the video describes a helping behavior study conducted by john darley and bibb latané. in their study, the number of people present in the room with the participant served as which variable?
In the study conducted by John Darley and Bibb Latané, the number of people present in the room with the participant served as an independent variable, as it was manipulated by the researchers to observe its effects on helping behavior.
Specifically, the researchers examined how the presence of other people in the room would affect whether or not the participant would choose to help in a given situation. By changing the number of people present in the room, the researchers were able to measure the effects of diffusion of responsibility on helping behavior.
Diffusion of responsibility is a phenomenon in which individuals are less likely to help a victim when they are in the presence of other people, as they assume that someone else will take responsibility. Therefore, the number of people present in the room was an important variable in the study, as it allowed the researchers to measure how the presence of others affected helping behavior.
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A fair coin is tossed 10 times, which of the following outcomes are contradict to the law of large numbers?A)FIVE HEADS ARE OBSERVEDB) NO TAILS ARE OBSERVEDC) SIX HEADS ARE OBSERVEDD) TWO TAILS ARE OBSERVEDE) NONE OF THE ABOVE
The outcome that contradict the law of large numbers is option E) NONE OF THE ABOVE.
The law of large numbers states that as the number of trials in a random experiment increases, the average of the results will approach the expected value.
A) FIVE HEADS ARE OBSERVED: This outcome is not contradictory to the law of large numbers as it is possible to have five heads in ten tosses of a fair coin, and as the number of trials increases, the average of heads will approach the expected value of 0.5.
B) NO TAILS ARE OBSERVED: This outcome is not contradictory to the law of large numbers as it is possible to have no tails in ten tosses of a fair coin, and as the number of trials increases, the average of tails will approach the expected value of 0.5.
C) SIX HEADS ARE OBSERVED: This outcome is not contradictory to the law of large numbers as it is possible to have six heads in ten tosses of a fair coin, and as the number of trials increases, the average of heads will approach the expected value of 0.5.
D) TWO TAILS ARE OBSERVED: This outcome is not contradictory to the law of large numbers as it is possible to have two tails in ten tosses of a fair coin, and as the number of trials increases, the average of tails will approach the expected value of 0.5.
E) NONE OF THE ABOVE: None of the above outcomes are contradictory to the law of large numbers as each of them is possible in ten tosses of a fair coin and as the number of trials increases, the average of heads and tails will approach the expected value of 0.5.
Therefore, the answer is E) NONE OF THE ABOVE.
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Simplify the expression by using the distributive property. -(2g + c) = ?
A patient who weighs 65 kg is scheduled to receive 75 mg/kg of her medicine. How much mg should the patient receive?
The patient will receive 4875mg
How do drug calculations with weight?Some drugs, particularly those for children, may be administered based on the individual’s body weight (kg) or body surface area (m2). Simply multiply the dose by the weight to get the needed dose, which can then be used in other formulas. A single dosage of medication containing 2mg/kg is necessary.
The force of gravity pressing down on an item is measured by its weight. It is determined by the mass of the item and the acceleration due to gravity, which is 9.8 m/s2 on Earth. Weight is calculated using the formula F = m 9.8 m/s2, where F is the object’s weight in Newtons (N) and m is the object’s mass in kilograms. Assume the active substance’s optimal dose is 2 mg/kg of body weight.
Given:
the weight of the patient is: 65kg
he is asked to receive 75 mg/kg of her medicine
therefore, she will have to consume 65*75mg
Finally, the patient will get 4875 mg
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Four angles in the quadrilateral Q have the ratio 2: 3: 3: 2. Give the names of the
two possible types of quadrilateral that Q could be.
Answer:
Parallelogram, Rhombus or a regular trapezium.
Step-by-step explanation:
Since all the units add up to 10 units, which is a factor of 180 degrees, all quadrilaterials work in this case as all quadrilaterals must have angles summing up to 180 degrees.
I might be wrong though. :(
