The required generalization that can be made is at least half of the trout in both lakes measure between 12 and 18 inches. Therefore, option B is the correct.
What is the interquartile range?The Interquartile Range (IQR) formula is a measure of the middle 50% of a data set. The smallest of all the measures of dispersion in statistics is called the Interquartile Range. The difference between the upper and lower quartile is known as the interquartile range.
Given that, a wildlife biologist captured and released 34 trout's from two different lakes and measured them to the nearest inch.
Interquartile range (IQR), The IQR is the range of the middle 50% of values in a data set. To calculate the IQR, we first need to find the quartiles of the data set.
In the given question we have 3 IQR data sets that jointly vary from 10 to 17 by this we can conclude that, at least half of the trout in both lakes measure between 12 and 18 inches.
Therefore, option B is the correct.
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In a Pew Research Poll, 287 out of 522 randomly selected US men were able to identify Egypt when it was highlighted on a map of the Middle East. When 520 randomly selected US women were asked, 233 were able to do so. Construct a 98% confidence interval for the true proportion of US men and US women (m-w) who can identify Egypt on a map.
answer choices
(0.0384, 0.1650)
(0.0301, 0.1733)
(0.0413, 0.1621)
(0.0510, 0.1524)
Answer:
(0.0301, 0.1733)
Step-by-step explanation:
[tex]\displaystyle CI=(\hat{p}_1-\hat{p}_2)\pm z\sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1}+\frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}\\\\\\CI_{98\%}=\biggr(\frac{287}{522}-\frac{233}{520}\biggr)\pm 2.326\sqrt{\frac{\frac{287}{522}(1-\frac{287}{522})}{522}+\frac{\frac{233}{520}(1-\frac{233}{520})}{520}}\\\\\\CI_{98\%}\approx\{0.0300,0.1734\}[/tex]
Hence, the best choice is (0.0301, 0.1733) which tells us that we are 98% confident that the difference between the two proportions of men and women who successfully found Egypt on the map when highlighted is between 0.0301 and 0.1733
a student estimated their mass to be 82.0 kg. upon stepping on the scale at the doctor's office, the actual (accepted) mass of 83.8 kg was recorded. use the formula on page 4 of lab 3v to calculate the % error of the student's estimated mass. remember to take the absolute value in the numerator and to round off to the proper degree of certainty. the unit that should be reported is % (use the symbol, do not type out the word).
The percentage error of the student's estimated mass is 2.15%.
What is the percentage error?The percentage or percent error is the difference between the estimated value and the actual value divided by the actual value, multiplied by 100.
The estimated mass of the student = 82.0 kg
The actual mass of the student = 83.8 kg
Absolute error = Actual Value - Estimated Value
= 1.8 kg (83.8 - 82.0)
Percentage error = Actual Value - Estimated Value /Actual Value x 100
= 2.15% (1.8/83.8 x 100)
Thus, we can conclude that the student's estimate contains a 2.15% error.
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Need helping solving this problem
The cost of the burger and the cost of an order of fries to Lynn would be :
Cost of burgher - $3.00Cost of fries - $ 1. 60How to find the cost ?From the problem, we know that Lynn spent $20.00 and purchased 4 hamburgers and 5 orders of fries. Similarly, we know that Ricardo spent $41.20 and purchased 10 hamburgers and 7 orders of fries, which gives us the equations:
4h + 5f = 20
10h + 7f = 41.20
Using substitution, we can express h in form of f to be :
4h + 5f = 20
4 [ ( 3 f + 1. 20 ) / 2] + 5 f = 20
6 f + 2 . 40 + 5 f = 20
11 f = 17. 60
f = $ 1. 60
We can then find the cost of hamburgers using the first equation :
4h + 5f = 20
4h + 5 ( 1. 60 ) = 20
4h + 8 = 20
4h = 12
h = $ 3
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given a set of data that is skewed-right, there is at least % of the data within 3 standard deviations. use either chebyshev's theorem or the empirical rule to fill in the blank with the best answer:
The set of data that is skewed-right, there is at least 99.7% of the data within 3 standard deviations.
What Is the Empirical Rule?A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, almost all observed data will lie within three standard deviations (denoted by ) of the mean or average (denoted by ).
Some points about standard deviation using Empirical Formula:
In accordance with the Empirical Rule, 99.7% of data that are found to have a normal distribution fall within 3 standard deviations of the mean.According to this formula, 68% of the data are within one standard deviation of the mean, 95% are within two standard deviations, and 99.7% are within three standard deviations.Learn more about Empirical Formula here:
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What is the value of x?
Enter your answer in the box.
Answer:
x = 54
Step-by-step explanation:
See picture below :)
a rectangle below has an area 84 cm saquered, what is half of the rectangle area?
Hello I’m having a hard time with question
[-1.5, 3.5] and [-2, infty) are the range and domain of the equation.
Determining the domain and range of a quadratic functionQuadratic function are functions that have a leading degree of 2.
The domain of the function are values that lies along the x-axis of the graph. Hence the domain of the curve will be [-1.5, 3.5]
The range of the function are values that lies along the y-axis of the graph. Hence the domain of the curve will be [-2, infty)
Hence the range and domain of the graph are [-1.5, 3.5] and [-2, infty)
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use the multiplier method to increase £258 by 43%
Answer:
43% * 258 = 110.94 (£110.94 is 43% of £258) 258 + 110.94 = 368.94
Step-by-step explanation:
Which statement BEST matches the image. Cannot be used more than once.
>
>
soda
soda
soda
A
↑
orange juice
A
orange juice
. A
1. Inefficient / Underutilization
2. Impossible / Unobtainable
3. Technological advances in
production
4. Efficient Production
Financial plan - The cost of a jug of squeezed orange is $2.00 and the cost of pop is $1.00. These information propose that Sharon is augmenting her utility from the given fixed spending plan
What is financial plan make sense of?A written financial program offers you a quantifiable objective to strive for. By monitoring your progress, you can eliminate doubt or uncertainty regarding your choices and make necessary adjustments to help you get past potential roadblocks.
Budgeting is the most crucial first step in financial planning. Making a budget is fairly simple; keeping one is more challenging! What matters is having the self-control to take the time as well as care to track and reconcile your spending in some way.
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Mary invests $600 in a high-interest savings account. In the first year, the value of her savings increases by 8%. In the second year, there is a further increase of 8%. What is the total value of her investment after two years? Round your answer to the nearest dollar.
Answer:
Therefore, the total value of Mary's investment after two years is $700.
Step-by-step explanation:
To calculate the total value of Mary's investment after two years, we need to calculate the value of the investment after the first year, and then use that value to calculate the value after the second year.
In the first year, the value of the investment increases by 8%, so the value after the first year is:
Value after first year = $600 + 8% of $600
Value after first year = $600 + 0.08 * $600
Value after first year = $648
In the second year, the value of the investment increases by another 8%, so the value after the second year is:
Value after second year = Value after first year + 8% of Value after first year
Value after second year = $648 + 0.08 * $648
Value after second year = $699.84
Rounding to the nearest dollar, the total value of Mary's investment after two years is:
Total value after two years = $700
From a deck of regular playing cards, one card is chosen at
random. Find the probability the card is a diamond or a face card.
The probability that now the card is indeed a diamond or a face card is [tex]\frac{11}{26}[/tex].
What are probability and examples?The probability that any random event will occur is referred to as probability. This expression is used to calculate the likelihood that a given event will occur. When we fling a coin into the air, as an illustration. Probability: P(A) = f / N calculates the probability that an event will take place. Ratios and probability are related, but the former determines the latter. When calculating the likelihood of an event, it is necessary to know the probability of that event.
When we find the probability, we obtain:
A typical deck of cards contains 52 cards. There are 12 face cards, known as the Kings, Queens, and Jacks, because there are four suits. There are a total of 13 diamonds, of which 3 are previously counted face cards. Hence, there are 10 diamonds that are faceless.
So, total Diamond & face card =22
Probability =[tex]\frac{22}{52}[/tex]=[tex]\frac{11}{26}[/tex].
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Difference Quotient Problem
The difference quotient expression for the given function is
[tex]\frac{f(x+h)-f(x)}{h} =\frac{\sqrt{(x+h+1)(x+h-1)}-\sqrt{(x+1)(x-1)} }{h}[/tex]
Difference Quotient Formula:The expression in single-variable calculus is usually referred to as the difference quotient.
[tex]\frac{f(x+h)-f(x)}{h}[/tex]
When taken to the limit as h gets closer to zero, h frac f(x+h)-f(x)h, which gives the derivative of the function f.
The slope of a secant line passing through the curve of f(x) is measured by the difference quotient.
Consider the difference quotient formula,
[tex]\frac{f(x+h)-f(x)}{h}[/tex]
Evaluate the function at x = x + h
replace the variable x with (x + h) in the given expression
[tex]f(x+h)=\sqrt{(x+h)^2-1}[/tex]
simplify the result ,
[tex]f(x+h)=\sqrt{(x+h+1)(x+h-1)}[/tex]
find the components of the definition,
[tex]f(x+h)=\sqrt{(x+h+1)(x+h-1)}[/tex]
[tex]f(x)=\sqrt{(x+1)(x-1)}[/tex]
plug in the components,
[tex]\frac{f(x+h)-f(x)}{h} =\frac{\sqrt{(x+h+1)(x+h-1)}-\sqrt{(x+1)(x-1)} }{h}[/tex]
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true/false. problem 3-1a (static) determine accrual-basis and cash-basis revenues and expenses (lo3-1, 3-2) required: for each transaction, determine the amount of revenue or expense, if any, that is recorded under accrual-basis accounting and under cash-basis accounting in the current period.
Answer:
true
Step-by-step explanation:
cause I’ve done this before
During the course of your examination of the financial statements of Trojan Corporation for the year ended December 31, 2021, you come across several items needing further consideration. Currently, net income is $100,000. An insurance policy covering 12 months was purchased on October 1, 2021, for $24,000. The entire amount was debited to Prepaid Insurance and no adjusting entry was made for this item in 2021. During 2021, the company received a $4,000 cash advance from a customer for services to be performed in 2022. The $4,000 was incorrectly credited to Service Revenue. There were no supplies listed in the balance sheet under assets. However, you discover that supplies costing $2,750 were on hand at December 31, 2021. Trojan borrowed $70,000 from a local bank on September 1, 2021. Principal and interest at 9% will be paid on August 31, 2022. No accrual was made for interest in 2021.
Answer: $3,700 or $90,650
Step-by-step explanation:
Answer:
3,700
Step-by-step explanation:
i thibk thisisthay answer
An engine supplies 110 hp to an electric generator, and the generator delivers 90 hp of electrical power. What is the
efficiency of the generator?
(Type a whole number or decimal rounded to two decimal places as needed)
Answer:
the efficiency of the generator is 81.82%.
Step-by-step explanation:
The efficiency of a generator is defined as the ratio of the electrical power output to the mechanical power input. In this problem, the electrical power output is given as 90 hp, and the mechanical power input is the power supplied by the engine, which is 110 hp. Therefore, the efficiency of the generator can be calculated as follows:
Efficiency = Electrical power output / Mechanical power input
Efficiency = 90 hp / 110 hp
Simplifying the fraction, we get:
Efficiency = 0.8182
To convert this decimal to a percentage, we multiply by 100:
Efficiency = 0.8182 * 100
Rounding to two decimal places, we get:
Efficiency = 81.82%
Therefore, the efficiency of the generator is 81.82%.
The proportion of people who respond to a certain mail-order solicitation is a random variable X having the following density function 2(x+3) 0
The question you have indicated appears incomplete. However, here is a very similar example that uses the same logic and principles of probability and proportion. In this case, the proof is given below.
What is the rationale for the above response?a.
Given: f(x) = 2(x+2)/5 , 0 <x< 1
Calculating P(0 <X< 1)
P(0 <X< 1) = ∫ f(x) dx {0.1}
Substitute 2(x+2)/5 for f(x)
P(0 <X< 1) = ∫ 2(x+2)/5 dx {0.1}
P(0 <X< 1) = 2/5 ∫(x+2) dx {0.1}
Integrate with respect to x
P(0 <X< 1) = 2/5 (x²/2+2x) {0.1}
P(0 <X< 1) = 2/5 (1²/2+2(1))
P(0 <X< 1) = 2/5 (½+2)
P(0 <X< 1) = 2/5 * 5/2
P(0 <X< 1) = 1 ----- Proved
b.
Here we're to solve for P(¼<X< ½)
P(¼<X< ½) = ∫ f(x) dx {¼,½}
Substitute 2(x+2)/5 for f(x)
P(¼<X< ½) = ∫ 2(x+2)/5 dx {¼,½}
P(¼<X< ½) = 2/5 ∫(x+2) dx {¼,½}
P(¼<X< ½) = 2/5 (x²/2+2x) {¼,½}
P(¼<X< ½) = 2/5 [ (½²/2+2(½)) - (¼²/2+2(¼))]
P(¼<X< ½) = 2/5 [(⅛+1)-(1/32 + ½)]
P(¼<X< ½) = 0.2375
The probability that more than ¼ but fewer than ½ of the people contacted will respond to this type of solicitation is 0.2375
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Full Question:
The proportion of people who respond to a certain mail-order solicitation is a continuous random variable X that has the density function f(x) = 2(x+2)/5 , 0 <x< 1, 0, elsewhere.
(a) Show that P(0 <X< 1) = 1.
(b) Find the probability that more than ¼ but fewer than ½ of the people contacted will respond to this type of solicitation.
let $pqr$ be an equilateral triangle, centered at $o.$ a point $x$ is chosen at random inside the triangle. find the probability that $x$ is closer to $o$ than to any of the vertices. (in other words, find the probability that $xo$ is shorter than $xp,$ $xq,$ and $xr.$)
The probability that $xo$ is shorter than $xp,$ $xq,$ and $xr.$ is,
⇒ 1/3
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Given that;
Let $pqr$ be an equilateral triangle, centered at $o$ a point $x$ is chosen at random inside the triangle.
Hence, The probability that $xo$ is shorter than $xp,$ $xq,$ and $xr.$ is,
⇒ 1/3
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g bar graphs (aka. column charts) with error bars are used to show the comparison between two variables, not the relationship.truefalse
True. bar graphs (aka. column charts) with error bars are used to show the comparison between two variables, not the relationship.
What are error bars?A confidence intervals bar chart (shown as red lines)
In graphs, error bars are used to graphically show data variability and to denote error or uncertainty in reported measurements. They provide a basic indication of a measurement's accuracy or, alternatively, how far the true (error-free) value may deviate from the reported value. The standard deviation of uncertainty, the standard error, or a specific confidence range (such a 95% interval) are frequently represented as error bars. Due to the fact that these values are not the same, the measure chosen needs to be specified clearly in the graph or supporting text.
According to the definition the statement is true.
True. bar graphs (aka. column charts) with error bars are used to show the comparison between two variables, not the relationship.
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perform the calculation 50°21' - 38°48'
Answer:
11° 33'
Step-by-step explanation:
[tex]21' = \left(\dfrac{21}{60}\right)^\circ = \left(\dfrac{7}{20}\right)^\circ \\50^\circ 21' = 50 \dfrac{21}{60}\; degrees\\\\38^\circ 48' = 38 \dfrac{48}{60} \;degrees[/tex]
Break
[tex]50 \dfrac{21}{60} = 49 + 1 \dfrac{21}{60}\\[/tex]
[tex]1 \dfrac{21}{60} = \dfrac{1 \times 60 + 21}{60} = \dfrac{81}{60}[/tex]
Therefore
[tex]50^\circ21' - 38^\circ48' = 49\dfrac{81}{60} - 38\dfrac{48}{60}[/tex]
Subtract the whole numbers:
49 - 38 = 11
Subtract the fractions:
[tex]\dfrac{81}{60} - \dfrac{48}{60} = \dfrac{33}{60} = 33'[/tex]
So
50°21' - 38°48' = 11° 33'
May grave 1/5 of her property to her son and 1/3 to her daughter. what fraction of her left property is left
The fraction of May's property that is left is 7/15.
What is a fraction?A fraction is a value derived in such a way that it is a part of a given initial value. An example is one third of 12 is 4. In this case, 4 is a fraction of 12.
Considering the given question, we have;
let the total property of May be represented by 1, so that
fraction left after giving 1/5 to her son = 1 - 1/5
= (5 - 1)/ 5
= 4/ 5
The fraction left after giving 1/5 of her property to her son is 4/ 5.
So that;
the fraction left after she gave 1/3 to her daughter = 4/ 5 - 1/ 3
= (12 - 5)/ 15
= 7/ 15
Therefore, the fraction of her property left is 7/ 15.
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Which of the following results in the difference of two squares?
Answer:
Step-by-step explanation:
(3x + 7y)(3x - 7y) FOIL
9x² -49y² yes, this is difference of two squares
(2x - 7y)(2x - 7y) FOIL
4x² -14x -14x +49y²
4x² -28x + 49y² not difference of two squares
9x²(5x - 7) Distribute the 9x²
45x³ - 63x² not difference of two squares because one term is cubed
(6x - 4y)² Distribute the square term
36x² - 16y² yes, difference of two squares
About 217,000 high school students took the AP Statistics exam in 2017. The free-response section of the exam consisted of five open-ended problems and an investigative task. Each free-response question is scored on a 0 to 4 scale (with 4 being the best). For one of the problems, a random sample of 30 student papers yielded a mean score of x =1.267 and a standard deviation of 1.230. a. Find and interpret the standard error of the mean. b. Construct and interpret a 90% confidence interval to estimate the true mean score on this question.
The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.
What is a confidence interval?The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.
The confidence interval formula is [tex]\bar x\pm t\frac{s}{\sqrt{n}}[/tex].
Where, [tex]\bar x[/tex] is the sample mean, t is the critical value, n is the sample size and s is the standard deviation for the sample.
Here,
[tex]\bar x[/tex] =1.267, s=1.23, n=30
The standard error is Se= 1.23/√30
= 0.2246
Item a:
The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.
Item b:
Using a t-distribution calculator, considering a confidence level of 0.99 with 30 - 1 = 29 df, the critical value is t = 2.7564.
[tex]\bar x\pm tS_c[/tex]
[tex]\bar x+ tS_c[/tex] =1.267-2.7564(0.2246) =0.6479
[tex]\bar x- tS_c[/tex] =1.267+2.7564(0.2246) =1.8861
Therefore, the 99% confidence interval to estimate the true mean score on this question is (0.6479, 1.8861). It means that we are 99% that the true mean score of all students in this question is between 0.6479 and 1.8861.
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A small-scale model of a submarine is being designed with the stabilizing wings and rudder to be added later. The fuselage is a cylinder of length 30 inches with a radius of 5 inches. The bow (front) is a semi sphere ( half of a sphere) that fits on one end of the cylinder. The stern (back) is a cone on the tail end that has a height of 6 inches. Calculate the volume and surface area of the new solid.
If a medium-scale model was required at 8x the scale of the small model, What is the overall length from back to the tip? What is the new surface area? What is the new Volume?
The Volume of Solid is 2,773.66 inch³ and Surface Area is
2,552.82 inch².
What is Surface Area?Surface area is the amount of space covering the outside of a three-dimensional shape.
Given:
Cylinder: Height = 30 inch, Radius = 5 inch
Semi sphere: radius = 5 inch
Cone: Height = 6 inch, radius = 5 inch, l= √r² + h² = 7.81 inch
Now, The Volume solid
= Volume of Semi sphere + Volume of Cylinder + Vol. of Cone
= 2/3 πr³ + πr²H + 1/3 πr²h
= πr² (2/3 r + H + 1/3 h)
= 3.14 x 5 x 5 (2/3(5) + 30 + 1/3 (6))
= 78.5 x ( 10/ 3 + 30 + 2)
= 2,773.66 inch³
Now, the Surface Area of Solid
= SA (Cylinder+ S. Sphere + Cone)
= πr²H + 2πr² + 1/3 πrl
= πr (rH + 2r + 1/3l)
= 3.14 x 5 (150 + 10 + 2.60)
= 2,552.82 inch²
Now, the model is increased by 8 times then the dimensions are:
Cylinder: Height = 240 inch, Radius = 40 inch
Semi sphere: radius = 40 inch
Cone: Height = 48 inch, radius = 40 inch, l= √r² + h² = 62.48 inch
and, Now, The Volume solid after dilation
= Volume of Semi sphere + Volume of Cylinder + Vol. of Cone
= 2/3 πr³ + πr²H + 1/3 πr²h
= πr² (2/3 r + H + 1/3 h)
= 3.14 x 40 x 40 (2/3(40) + 240 + 1/3 (48))
= 78.5 x ( 10/ 3 + 30 + 2)
= 1,420,117.33 inch³
Now, the Surface Area of Solid
= SA (Cylinder+ S. Sphere + Cone)
= πr²H + 2πr² + 1/3 πrl
= πr (rH + 2r + 1/3l)
= 3.14 x 5 (1200 + 80 + 20.82)
= 163, 382. 992 inch²
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This problem refers to triangle ABC. If B = 150°, C = 20°, and c = 21 inches, find b. (Round your answer to the nearest whole number.)
b = ? in
Answer:
Step-by-step explanation:
To solve for b, we can use the law of sines, which states that in any triangle ABC:
a/sin(A) = b/sin(B) = c/sin(C)
Here, we are given B = 150°, C = 20°, and c = 21 inches. We can solve for the remaining angle A by using the fact that the angles of a triangle add up to 180°:
A + B + C = 180°
A = 180° - B - C
A = 180° - 150° - 20°
A = 10°
Now we can use the law of sines to solve for b:
a/sin(A) = b/sin(B)
a = c * sin(A)/sin(C) = 21 * sin(10°)/sin(20°)
b = a * sin(B)/sin(A) = 21 * sin(10°)/sin(20°) * sin(150°)/sin(10°)
b = 21 * sin(150°)/sin(20°)
Using a calculator, we get:
b ≈ 41 inches (rounded to the nearest whole number)
Therefore, the length of side b is approximately 41 inches.
You pick a card at random. 4 5 6 7 8 What is P(not prime)?
the probability of selecting a card that is not prime from the set {4, 5, 6, 7, 8} is 0.6 or 60%.
How we solved?
To determine the probability of selecting a card that is not prime from the set {4, 5, 6, 7, 8}, we first need to identify which numbers in the set are prime.
The prime numbers in the set are 5 and 7, so the non-prime numbers are 4, 6, and 8.
The total number of cards in the set is 5.
Therefore, the probability of selecting a non-prime card is:
P(not prime) = number of non-prime cards / total number of cards
P(not prime) = 3 / 5
P(not prime) = 0.6 or 60%
So the probability of selecting a card that is not prime from the set {4, 5, 6, 7, 8} is 0.6 or 60%.
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The vertices of a rectangle are at (-4,2),(3,2),(3,-2), and (-4,-2). What is the length of the longer side of the rectangle?
The longer side of the rectangle is the side that connects the points (-4,2) and (3,2), which have the same y-coordinate, so it is a horizontal line.
The length of this side is the distance between the x-coordinates of these two points, which is:
3 - (-4) = 7
Therefore, the length of the longer side of the rectangle is 7 units.
Use the verticals line test to determine if y is a function of x in the graph
Which of the following statements is correct?
a) y is a function of x
B) y is not a function of x
Using the vertical line test we conclude that y is not a function of x.
How to use the vertical line test?When we have the graph of a relation, the vertical line test says that if we draw a vertical line over the graph and it intercepts the graph in more than one point, then the graph does not represent a function.
Here we have the graph of a circle, and there are multiple lines that intercept the graph twice (for example the line x = 0)
So we can conclude that this is not a function, thus, the correct option is A.
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Calculus please help
f(x) is discontinuous.
Since LHS ≠ RHS ≠ f(x).
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
here, we have,
We have,
f(x) = x + 1, for x ≤ 2
f(x) = 2x - 1, for 1 < x < 2
f(x) = x - 1, for x < 1
Now,
A x = 1
LHS of f(x) = lim f((h - 1)) = (h - 1 - 1) = 0 -2 = -2
RHS of f(x) = lim f(h + 1) = (2(h + 1) - 1) = 2h + 2 - 1 = 0 + 1
f(1) = x + 1 = 1 + 1 = 2
We see that,
LHS ≠ RHS ≠ f(x)
So,
f(x) is not continuous, it is discontinuous.
Thus,
f(x) is discontinuous.
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The complete question.
Show that the following functions are continuous or discontinuous at x = 1.
f(x) = x + 1, for x ≤ 2
f(x) = 2x - 1, for 1 < x < 2
f(x) = x - 1, for x < 1
Use a direct proof to show that the product of two rational numbers is rational.
We have shown that the product of two rational numbers is rational.
What is Number system?A number system is defined as a system of writing to express numbers.
Let a and b be two rational numbers, such that:
a = p/q
b = r/s
where p, q, r, and s are integers and q, s are non-zero.
We need to show that the product ab is also a rational number.
We have:
ab = (p/q) x (r/s)
= (p x r) / (q x s)
Since p, q, r, and s are all integers,
ab = m/n
where m = p x r and n = q x s.
Since both m and n are integers and n is non-zero ,we can conclude that ab is a rational number.
Therefore, we have shown that the product of two rational numbers is rational.
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Which best describes the rate at which Mandy used up her bags of dog food?
OA. 6 bags per day
OB. 2/3 bags per day
OC. 4 bags per day
OD. 3/2 bags per day
The rate at which Mandy used up her bags of dog food is 2/3 bags per day
What is unit rate?
A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.
Slope = change in y /change in x
Here, Slope = change in bags of food/ /change in days
form the graph = 4/6 = 4 bags per 6 days
4/6 simplifies to 2/3
=> 2/3 bags per day
The rate at which Mandy used up her bags of dog food is 2/3 bags per day
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