The total amount of money Carol originally invested is £22,000 in the bank account.
What is compound intrest?Compound interest is interest that is calculated not only on the initial amount of money invested or borrowed, but also on any accumulated interest from previous periods.
This results in exponential growth or accumulation of interest over time.
Let X be the amount that Carol originally invested in the account.
After 1 year, the amount of money in the account will be X(1+0.025) = X(1.025).
After Carol withdrew £1000, the amount of money in the account will be X(1.025) - £1000.
After 2 years (i.e. on 1st January 2016), the amount of money in the account will be (X(1.025) - £1000)(1+0.025) = (X(1.025) - £1000)(1.025).
We know that the amount of money in the account on 1st January 2016 was £23,517.60, so we can write the equation:
(X(1.025) - £1000)(1.025) = £23,517.60
Expanding the left-hand side and simplifying, we get:
X(1.025)² - £1000(1.025) = £23,517.60
X(1.025)² = £24,567.63
Dividing both sides by (1.025)², we get:
X = £22,000 (rounded to the nearest pound)
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The complete question is -
On the 1st of January 2014, Carol invested some money in a bank account. The account pays 2.5% compound interest per year. On the 1st of January 2015, Carol withdrew £1000 from the account. On the 1st of January 2016, she had £23 517.60 in the account. Work out how much Carol originally invested in the account?
Determine the length of HK
Step-by-step explanation:
that height splits GK (32) into 2 parts :
8 and 32-8 = 24
then we use the geometric mean theorem for right-angled triangles
height = sqrt(p×q)
with p and q being the parts of the Hypotenuse.
so,
height = sqrt(8×24) = sqrt(192)
and now we can use Pythagoras
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs,
to get HK.
HK² = height² + 24² = 192 + 576 = 768
HK = sqrt(768)
convert 69 3/4% to a fraction in the lowest terms
Answer:The fraction 69 3/4% is a mixed fraction
69 3/4% to a fraction in lowest term is 27603/400
How to simplify the fraction?
The fraction is given as:
69 3/4%
Rewrite the fraction as:
69 + 3/400
Add the fractions
(400 * 69 + 3)/400
Evaluate the sum
27603/400
The above fraction cannot be further reduced.
Hence, 69 3/4% to a fraction in lowest term is 27603/400
Juan is constructing picture frames to create a collage on his bedroom wall. He constructs a square frame with side lengths of x inches. He constructs another frame with the same length, but a width that is 3.5 inches longer than the square frame. The area of the new, rectangular frame can be determined by the following expression.
please look at the picture attached then answer!
Select the best description of the term 3.5x.
A. the area of the original picture frame
B. the area of the new picture frame
C. the width of the new picture frame
D. the increase in area of the new frame
Answer:
The correct answer is D. the increase in area of the new frame.
Step-by-step explanation:
Hope this helps you!!
Find the standard normal area for each of the following Round your answers to the 4 decimal places
The standard normal areas are given as follows:
P(1.22 < Z < 2.15) = 0.0954. P(2 < Z < 3) = 0.0215.P(-2 < Z < 2) = 0.9544.P(Z > 0.5) = 0.3085.How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.Considering the second bullet point, the areas are given as follows:
P(1.22 < Z < 2.15) = p-value of Z = 2.15 - p-value of Z = 1.22 = 0.9842 - 0.8888 = 0.0954.P(2 < Z < 3) = 0.0215 = p-value of Z = 3 - p-value of Z = 1 = 0.9987 - 0.9772 = 0.0215.P(-2 < Z < 2) = p-value of Z = 2 - p-value of Z = -2 = 0.9772 - 0.0228 = 0.9544P(Z > 0.5) = 1 - p-value of Z = 0.5 = 1 - 0.6915 = 0.3085.More can be learned about the normal distribution at https://brainly.com/question/25800303
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4u^2(a-3)+q(a-3)=
please answer
The simplified expression is (4u^2 + q)(a-3).
To simplify the expression 4u^2(a-3) + q(a-3), we can factor out the common factor (a-3) from both terms:
4u^2(a-3) + q(a-3) = (4u^2 + q)(a-3)
This is the factored form of the expression.
The value of the expression depends on the values of u, a, and q. When (a-3) is factored out, it remains as a common factor, while the terms 4u^2 and q are combined into a single term (4u^2 + q).
The abbreviated expression is therefore (4u2 + q)(a-3).
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Can Anyone Help?
A poster is to have a total area of 245cm2. There is a margin round the edges of 6cm at the top and 4cm at the sides and bottom where nothing is printed.What width should the poster be in order to have the largest printed area?
The poster should have width ____ cm
Answer: The poster should have width 17.50 CM
Step-by-step explanation:
Given that boasted I have a total area 245 cm square area of a poster is 200 and 45 20 m square. And it is in the rectangle format. So we know that the poster is always in the rectangle format and the area of rectangular area is equal to L N T W. So 245 will be equal to Ln tW. From this. We need to find L. So L is equal to 245 divided by W. Now consider the diplomatic representation of the poster. So it has mentioned that there is a margin around the edges of six cm at the top. This is 6cm and four cm at the sites. All the four sides 3 sides are four cm. So from this we need to find land and the doctor posted area that is printed area. The first wine printed with www. Z. Quilter. Now let this be total birth will be W. And this will be four and this will be four. Therefore posted with will be we need to find this part alone. So W -4 -4 will give the this part with. So W -4 -4. So post printed with PW will be equal to W -8. Similarly printed lunch will be equal to The total length is already we have found 245 by W. And we need to find this part length. So we have to subtract six and four from the total length so that that will give them this part length, So -6 -4. So printed length will be equal there 245 Divided by W -10. And we know that formula for area of a rectangle. Urz D is equal to L W. Now substitute the printed with and printed length in the area formula. We have to find the printed area. So Printed area Zeke Walter W -8 into 245 Divided by W -10. To simplify this, we get 325 minus 10. W -100 and 30,960 W. to the power of -1. Now fine D A by D. T. Not D D. This is D. W. So this is equal to differentiation of constant alma zero, this is minus 10 plus 900 and 60 W. to the power of -2 and equate this to be equal to zero. We out to find the maximum width so D A by D W is equal to zero, therefore minus 10 1960 W. To the power of -2 will be equal to zero. To simplify this, we get them maximum with value the W is equal term I wrote off 196. Therefore the value of W. Z quilter plus or minus 14. We will neglect the negative values since we cannot be negative. So one we assume the positive values. So what will be equal to 14 and length will be equal to 245 divided by 14, So which will be equal to 17.50 centimeters. And they have concluded that At W is equal to 14 cm and lunch will be equal to 17.50 cm needed to print the largest area. I hope you found the answer to school. Thank you.
The base of a triangle is 3 inches shorter than its height. Its area is 275 square inches. Set up a quadratic equation and solve to find its base and height.
Answer: hope its help
Let's start by assigning variables to the unknown quantities in the problem. Let h be the height of the triangle in inches, and let b be the base of the triangle in inches.
According to the problem, the base of the triangle is 3 inches shorter than its height. This can be expressed as:
b = h - 3
The formula for the area of a triangle is:
A = (1/2)bh
We are given that the area of the triangle is 275 square inches, so we can substitute these values into the formula to get:
275 = (1/2)(h)(h-3)
Simplifying the right-hand side, we get:
275 = (1/2)(h^2 - 3h)
Multiplying both sides by 2 to eliminate the fraction, we get:
550 = h^2 - 3h
Rearranging this equation to standard quadratic form, we get:
h^2 - 3h - 550 = 0
Now we can solve for h using the quadratic formula:
h = (-b ± sqrt(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -3, and c = -550, so we can substitute these values into the formula to get:
h = (-(-3) ± sqrt((-3)^2 - 4(1)(-550))) / (2(1))
Simplifying the expression inside the square root, we get:
h = (3 ± sqrt(2209)) / 2
We can ignore the negative solution since height must be positive, so we get:
h = (3 + sqrt(2209)) / 2 ≈ 29.04
Now that we know the height of the triangle is approximately 29.04 inches, we can use the equation b = h - 3 to find the length of the base:
b = 29.04 - 3 = 26.04
Therefore, the base of the triangle is approximately 26.04 inches, and the height is approximately 29.04 inches.
Step-by-step explanation:
a. Provide two independent events that you know the probability of.
b. Explain how you know these events are independent.
c. Find the probability that they both occur.
a. Provide two dependent events.
b. Explain how you know these events are dependent.
c. Explain why these dependent events might require a different method for calculating the probability of both events occurring.
1. a. Rolling fair die, Flipping fair coin ; b. does not affect the occurrence of the other event; c. 1/4; 2. a. Picking red card, Picking another red card; b. affects the probability of the second event, c. use of conditional probability.
Describe Probability?Probability can be used to make predictions, analyze data, and make informed decisions in a wide range of fields, including science, economics, finance, engineering, and social sciences. It is often used in conjunction with statistical methods to make inferences about populations based on samples, and to test hypotheses about the relationships between variables.
There are many different types of probability, including classical probability, empirical probability, subjective probability, and conditional probability. Probability theory also includes concepts such as random variables, probability distributions, and statistical inference.
1. a. Two independent events:
Rolling a fair die and getting an even number.
Flipping a fair coin and getting heads.
b. These events are independent because the occurrence of one event does not affect the occurrence of the other event. In other words, the outcome of rolling the die does not influence the outcome of flipping the coin, and vice versa.
c. The probability of both events occurring is found by multiplying the individual probabilities of each event.
P(getting an even number on a die) = 3/6 = 1/2
P(getting heads on a coin) = 1/2
P(rolling an even number on a die AND flipping heads on a coin) = (1/2) * (1/2) = 1/4
2. a. Two dependent events:
Picking a red card from a standard deck of playing cards.
Picking another red card without replacing the first card.
b. These events are dependent because the occurrence of the first event affects the probability of the second event. If a red card is picked on the first draw, there are fewer red cards remaining in the deck for the second draw, which changes the probability of picking another red card.
c. The probability of both events occurring in this case would require the use of conditional probability. We would need to find the probability of picking a red card on the second draw given that a red card was picked on the first draw. This conditional probability would be affected by the number of red cards remaining in the deck after the first draw, which changes with each draw.
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What is the difference between the longest and
shortest pieces of scrap wood?
The difference in length between the two pieces of scrap wood is 7/8 inches.
What is the difference between the longest and shortest pieces of scrap wood?
To get the difference we just need to take the difference between the two lenghs.
Remember that we only have pieces of scraph wood if we have an "x" over the correspondent value in the line diagram.
By looking at it we can see that the longest pice measures 5 inches, while the shortest one (there are two of these) measure (4 + 1/8) inches.
The difference is:
5 - (4 + 1/8) = 7/8
The longest piece is 7/8 inches longer.
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Twelve of the workers received the following salaries: three of them earn P12,500 a month, four of them earn P11,000; twoearn P10,500 and the rest earn P9,000 a month. What is the median salary of the workers?
The median salary of the workers is P11,000.
What is median?In statistics, the median is a measure of central tendency that represents the middle value of a data set when the data set is ordered from least to greatest (or vice versa). If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, the median is the average of the two middle values. The median is used as a measure of central tendency when the data set has outliers or is not normally distributed.
How to calculate median?To calculate the median of a set of numbers:
Put the numbers in order from lowest to highest.If the number of items in the list is odd, the median is the middle number. For example, if the list is 3, 5, 7, 9, 11, the median is 7.If the number of items in the list is even, the median is the average of the two middle numbers. For example, if the list is 4, 6, 8, 10, the median is (6 + 8)/2 = 7.In the given question,
To find the median salary of the workers, we need to arrange the salaries in order from lowest to highest.
The salaries are:
P9,000, P9,000, P10,500, P10,500, P11,000, P11,000, P11,000, P11,000, P12,500, P12,500, P12,500, P12,500
There are 12 workers, so the median salary will be the average of the 6th and 7th salaries when arranged in order.
Median salary = (P11,000 + P11,000)/2
= P11,000
Therefore, the median salary of the workers is P11,000.
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Given a regular pentagon, what is the value of p?
A) 54º
B) 13º
C) 27º
Question 8 (2 points)
A survey asked 1,000 people if they invested in Stocks or Bonds for retirement. 700
said they invested in stocks, 400 said bonds, and 300 said both.
How many invested in just stocks?
Note: consider making a Venn Diagram to help solve this problem.
700
300
400
none
300 is the correct answer.
-3+b> 7 OR b +9 <17.
The solution to the compound inequality -3+b> 7 OR b +9 <17 is given as follows:
b < 8 or b > 10.
How to solve the compound inequality?The inequality for this problem is defined as follows:
-3+b> 7 OR b +9 <17.
The or operation means that the we must solve each operation separately, and then the solution set to the compound inequality is given by the union of the solution set of each of the inequalities.
The solution set for the first inequality is given as follows:
-3+b> 7
b > 10.
The solution set for the second inequality is given as follows:
b + 9 < 17
b < 8.
Hence the solution for the entire inequality is of:
b < 8 or b > 10.
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Letsha wants to produce 80 pages information books for school project. She can have this done at local printing company at R0.35 per page.
Answer:
if u want total price then,
=Rs.35×80=Rs.2800
16) Critique the sample method and the survey used by the guild. You’ll want to use some of the following words in your critique: sample, bias, random, response-bias, undercoverage, non-response, voluntary response.
Answer:
The critique of the sample method and survey used by the guild is as follows:
Sample: The sample used in the survey is not representative of the entire population. The survey was conducted only among the guild members, and hence it does not represent the views of non-members. This type of bias is called undercoverage bias.Bias: The survey seems to suffer from selection bias, where the participants who responded may not represent the entire population. This type of bias is known as response bias. It is possible that the members who chose to participate in the survey have different views from those who did not respond. Furthermore, the survey did not specify how the participants were selected, and hence there may be other types of bias present in the survey.Randomness: The survey did not use random sampling, which is a fundamental principle of survey research. A random sample ensures that every member of the population has an equal chance of being selected, which increases the representativeness of the sample.Non-Response: The survey did not address the issue of non-response bias, where participants who choose not to respond may have different views from those who respond. The survey did not specify the response rate, and hence it is unclear how many members chose to participate in the survey.Voluntary response: The survey seems to be a voluntary response survey, where members chose to participate voluntarily. This type of survey is known to suffer from bias because participants who respond are usually more motivated or have stronger opinions than those who do not respond.In summary, the survey used by the guild suffers from various types of bias, which may affect the validity and generalizability of the results. To improve the validity and reliability of the survey, the guild should use random sampling and address issues such as non-response and response bias.
Help me please.
Whoever answers right gets brainliest
Answer:y=x-5
Step-by-step explanation:this is the answer for sure
Answer:
[tex]y=x-5[/tex]
Step-by-step explanation:
Notice for every X you do increase your Y by 1, this is the slope must be 1, to check you can use the slope equation with any two points
[tex]m= \frac{-4-(-3)}{1-(2)} =-1[/tex]
The lets use one point and the line equation:
[tex]y-yo=m(x-xo)[/tex]
[tex]y+4=-1(x-1)[/tex]
Solving for Y you can obtain
[tex]y=x-5[/tex]
You can input any X value and check the Y value to be sure, for example, for X=3 you can check Y=3-5=-2. In the table for X=3 the Y value is -2, so this checks.
We can use the formula =rS12.6 to relate a ball's surface area S (in square centimeters) to its radius r (in centimeters). Suppose a ball has a radius of 12.04 centimeters. What is its surface area?
Carry your intermediate computations to at least four decimal places, and round your answer to the nearest tenth.
The surface area of the sphere ball is 1817.74 square centimeters.
What is surface area?Every geometric shape has a different surface area formula, but the goal of all of them is to determine the total area occupied by all of the objects' faces. While the lateral surface area is calculated to determine the area occupied by the shape's curved surface, the total surface area takes into account all faces of the 3D shape, including the flat and curved surfaces. The area of the bases is excluded. One 3D shape called a sphere has just one round surface and no flat base.
Given that the surface area is related using the relation r = √(S/12.6).
Also, the value of r = 12.04, substituting the value we have:
(12.04) = √(S/12.6)
Squaring on both sides:
Hence. the surface area of the ball is approximately 1817.74 square centimeters.
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The complete question is:
in nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by
The correct option is (C). In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by: ΔY = f(x₁ + ΔX₁, X₂ + ΔX₂, ..., Xk + ΔXk) - f(x₁, X₂, ..., Xk)
where ΔX₁, ΔX₂, ..., ΔXk are the changes in the respective explanatory variables. This equation represents the change in Y due to a simultaneous change in all the explanatory variables by ΔX₁, ΔX₂, ..., ΔXk. Option (C) represents the same equation in a slightly different notation. Option (A) only considers one explanatory variable, and option (B) does not include the baseline value of the function. Therefore, option (C) is the correct answer.
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Complete question:
In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by
A. ΔY= f(x₁ +Xq, X2, Xx) = f(Xq, X2....XK). 1 1'
B. ΔY = F(X,+ ΔX₁₁ X2, Xx) - F(X₁₁ X2, Xk). ---
C. ΔY = f(x,+ ΔX₁₁ X₂ + ΔX2, Xx+ ΔX x) - F(X₁₁ X2, Xx). 1°
D. ΔY = f(x₁ +Xq, X2, Xk).
12. Reason A data set is represented by the box plot shown. Between which two values would the middle 50% of the data be found? Explain.
The middle 50% data of the boxplot will be calculated between the value of 7 to 14.
Explain about the box plot?The variation in information is shown using a boxplot, which is a standardized method based on a five-number summary ("minimum," first quartile ("Q1"), median ("Q3"), and "maximum"). It can reveal information about your outliers' values. Boxplots can also show you exactly securely your data is grouped, whether or not your data is skewed, and whether or not your data is symmetrical.The data set ranges are:
4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17
Divide the given data in 4 quartiles Qs;
Q1 = 4 - 6
Q2 = 7 - 10
Q3 = 11 - 14
Q4 = 15 - 17
Thus, 50% data will be lying in Q2 and Q3.
Range - 7 - 14
Thus, the middle 50% data of the box plot will be calculated between the value of 7 to 14.
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Jaydon has twice as much as cristiano .Ozias has $25 less than Cristiano .The three children have $195 altogether.How much money does Ozias have
Upon letting x variable be the amount of money Cristiano has. Cristiano has $55, Ozias has $30, Jaydon has $110
What is meant by variables?A variable is a symbol used to represent an unknown or changing value in an equation or expression. Variables can take on different values and are used to solve equations, simplify expressions, and model real-world situations.
According to the question
Let us use variables to represent the amount of money each child has:
Let x be the amount of money Cristiano has.
Then Jaydon has twice as much, that is 2x
And Ozias has $25 less than Cristiano, that is x - $25.
We know that the three children have a total of $195, so we can make an equation:
x + 2x + (x - $25) = $195
Simplify and solve for x:
4x - $25 = $195
4x = $220 x = $55
So Cristiano has $55, Jaydon has twice as much or $110, and Ozias has $25 less than Cristiano.
So Ozias has $55-$25= $30.
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You are crossing two pea plants. One is heterozygous for yellow. The second pea plant is homozygous for green. Use "G/g" as the letter to represent the gene for this problem.
The result of the cross breeding between the heterozygous and homozygous pea plant is the offspring will have a 50% chance of inheriting the dominant "G" allele and displaying yellow color, and a 50% chance of inheriting the recessive "g" allele and displaying green color.
What is the result of crossbreeding?In this problem, the heterozygous pea plant with yellow color is represented as "Gg" (where "G" is the dominant allele for yellow color and "g" is the recessive allele for green color). The homozygous pea plant with green color is represented as "gg" (where both alleles are recessive).
When these two plants are crossed, their offspring will inherit one allele from each parent, which will determine their phenotype (observable trait).
The possible combinations of alleles that the offspring can inherit from their parents are:
Gg x gg
Gametes from the Gg plant: G, gGametes from the gg plant: g, gPossible genotypes of offspring: Gg, gg (50% chance for each)Possible phenotypes of offspring: yellow (Gg) or green (gg) in a 1:1 ratioTherefore, in this cross, the offspring will have a 50% chance of inheriting the dominant "G" allele and displaying yellow color, and a 50% chance of inheriting the recessive "g" allele and displaying green color.
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The price of a mortgage is calculated using the present value of future cash flows, which includes an interest payment, CC, a principal payment, PrinPrin, the number of periods until the mortgage is to be paid off, tt, and a required rate of return, kk.
Mathematically, the general price movement of mortgages can be modeled as which of the following?
ΔPM=f(k)ΔPM=f(k)
ΔPM=f(Δk,ΔPrin)ΔPM=f(Δk,ΔPrin)
ΔPM=f(Δk,ΔC)ΔPM=f(Δk,ΔC)
ΔPM=f(Δk)
What are the type of securities that are issued to financial institutions where the funds are used to increase liquidity in the secondary mortgage market by financing the origination of mortgages? Check all that apply.
Private-label pass-through securities
Government National Mortgage Association (Ginnie Mae) mortgage-backed securities
Federal Home Loan Mortgage Association (Freddie Mac) participation certificates
Federal National Mortgage Association (Fannie Mae) mortgage-backed securities
The mathematical model that represents the general price movement of mortgages is: ΔPM = f(Δk, ΔPrin, ΔC)
Where ΔPM is the change in the price of the mortgage, Δk is the change in the required rate of return, ΔPrin is the change in the principal payment, and ΔC is the change in the interest payment.
This means that the change in the price of a mortgage is a function of the change in the required rate of return, the change in the principal payment, and the change in the interest payment.
The securities that are issued to financial institutions to increase liquidity in the secondary mortgage market by financing the origination of mortgages are:
Government National Mortgage Association (Ginnie Mae) mortgage-backed securitiesFederal Home Loan Mortgage Association (Freddie Mac) participation certificatesFederal National Mortgage Association (Fannie Mae) mortgage-backed securitiesFinancial institutions may also receive private-label pass-through securities, although these are not guaranteed by government entities like Ginnie Mae, Freddie Mac, or Fannie Mae.
They are not backed by the government, but by private institutions, which can make them riskier.
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every nonzero real number has a reciprocal. zero does not have a reciprocal. therefore, zero is not a nonzero real number
The given argument is Valid because the conclusion follows the argument logically.
The argument is that "Every nonzero real number has a reciprocal. Zero(0) does not have a reciprocal. Therefore, zero is not a non-zero real number."
The argument can be expressed in logical form as:
⇒ Premise 1: For every nonzero real number x, there exists a reciprocal 1/x.
⇒ Premise 2: Zero does not have a reciprocal.
⇒ Conclusion: Therefore, zero is not a nonzero real number.
This argument is valid because the conclusion logically follows from the premises.
The premises establish that every nonzero real number has a reciprocal, and that zero does not have a reciprocal.
The conclusion then follows logically, as zero is explicitly excluded from the set of nonzero real numbers based on the definition of a reciprocal.
Therefore, the argument is valid.
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The given question is incomplete, the complete question is
Is The Following Argument Valid Or Invalid?
Every nonzero real number has a reciprocal. Zero does not have a reciprocal. Therefore, zero is not a nonzero real number.
given a function f(x), find the critical values and use the critical values to find intervals of increasing/deacreasing, maxes and mins.
The critical values, the intervals of increasing or decreasing and the maximum and minimum points of the f(x) is (-1.5, -16), x < -1.5 and x = -1.5 and for b (4,6) and (2,10), (2,4).
A) Critical values
We will find out the critical value by solving for f ' (x) = 0
therefore, taking the derivative of given function we get,
f ' (x) = 4(2x) + 12 = 0
= 8x + 12 = 0
therefore, 8x = -12
x = -12/8
x= -1.5
x = -1.5 is the only critical value in x-coordinate. Now to determine the y-coordinate, simply put the value of x in the function f(x) = 4x2 + 12x - 7
we get, f(-1.5) = 4(-1.5)2 + 12 (-1.5) - 7
= 4(2.25) - 18 - 7
= 9 - 25 = -16
therefore, the critical value of the function f(x) = 4x2 + 12x - 7 is (-1.5, -16)
f(x) =x3 - 9x2 + 24x - 10.
Intervals of increasing and decreasing function is i.e. f decreases for
x < -1.5.
Therefore, f has minimum value at x = -1.5.
B) Critical values
We will find out the critical value by solving for f ' (x) = 0
therefore, taking the derivative of given function we get,
f '(x) = 3x2 - 9(2x) + 24
= 3x2 - 18x + 24 = 0
therefore, 3 ( x2 - 6x + 8) = 0
i.e x2 - 6x + 8 = 0
(x-4) (x-2) = 0
So, x = 4 or x = 2 are the two critical values in x-coordinate. Now to determine the y-coordinate, simply put the values of x in the function f(x) =x3 - 9x2 + 24x - 10
we get, Substituting x = 4
f(4) = 43 - 9 (4)2 +24 (4) -10
= 64 - 144 + 96 - 10
= 6
Now, Substituting x = 2
f(2) = 23 - 9(2)2 + 24(2) - 10
= 8 - 36 + 48 - 10
= 10
Therefore, the critical values of the function f(x) =x3 - 9x2 + 24x - 10 are (4,6) and (2,10).
Intervals of increasing and decreasing functions is f decreases in (2,4).
therefore, f has minimum at x = 4 and maximum at x = 2.
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Complete question:
For each function determine: i) the critical values ii) the intervals of increasing or decreasing iii) the maximum and minimum points.
a. f(x) = 4x²+12x–7 (3 marks)
b. F(x) = x°-9x²+24x-10 (3 marks)
The table shows some points on the graph of exponential function g(x)
0 1 2 3 4 g(x) 1 3 9 27 81 What is the range of g?
the range of g is all positive numbers greater than or equal to 1. In set-builder notation, we can write the range of g as {g(x) | g(x) ≥ 1}.
How to solve and what is graph?
The range of a function refers to the set of all possible output values. Looking at the table, we can see that the output values of g(x) increase rapidly as x increases.
In fact, the output values of g(x) are the result of raising 3 to the power of x, which means that g(x) can never be negative. Therefore, the range of g is all positive numbers greater than or equal to 1. In set-builder notation, we can write the range of g as {g(x) | g(x) ≥ 1}.
A graph is a visual representation of data or mathematical functions. It is a diagram made up of points, lines, and curves that show the relationship between different variables or data points.
Graphs are used to display and analyze data, to illustrate trends and patterns, and to communicate complex information in an easily understandable way. There are many different types of graphs, including bar graphs, line graphs, pie charts, scatter plots, and more, each suited to different types of data and analysis.
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What is the probability that someone who does not take vitamins is a female? Round to three decimal places.
Female
Male
Total
(1 point)
O 0.374
O 0.139
O 0.080
O 0.626
Takes vitamins
248
145
193
Does not take vitamins
40
67
107
Total
288
212
500
Answer:
A) 0.374
Step-by-step explanation:
Let event A be that the person is female.
Let event B be that the person does not take vitamins.
[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]
Therefore, from the given table:
[tex]\sf P(A) = \dfrac{288}{500}=0.576[/tex]
[tex]\sf P(B) = \dfrac{107}{500}=0.214[/tex]
[tex]\sf P(A \cap B)=\dfrac{40}{500}=0.08[/tex]
To calculate the probability that someone is female (Event A), given that they do not take vitamins (Event B), use the conditional probability formula for A given B:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Conditional Probability formula}\\\\A given B:\\\\$\sf P(A|B)=\dfrac{P(A \cap B)}{P(B)}$\\\end{minipage}}[/tex]
[tex]\sf \implies P(A|B)=\dfrac{0.08}{0.214}=0.374\;(3\;s.f.)[/tex]
Pls help! Due tmrrww!!
Answer:
1. basement: 1,4,7,10,13
middle : 2,5,8,11,14
top: 3,6,9,12,15
2. you just need to skip count ten times then we will have 30. so she lives in apartment 30.
Step-by-step explanation:
Does the expression 56x+40y-48z=8(7x+5y-6z)
For all values of x, y, and z, the expression 56x + 40y - 48z = 8(7x + 5y - 6z) holds true.
Explain expression using an example.As an illustration, the phrase x + y is one where x and y are terms with an addition operator in between. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables.
Indeed, for all values of x, y, and z, the expression 56x + 40y - 48z = 8(7x + 5y - 6z) holds true.
We can simplify both sides of the equation to understand why:
56x + 40y - 48z = 8(7x + 5y - 6z)
56x + 40y - 48z = 56x + 40y - 48z
As we can see, the equation is true for all values of x, y, and z because both sides are identical.
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(√3 + √3)²=
F) 12
G) 9
H) 6
J) 3
K) None of these
Answer:
F) 12
Step-by-step explanation:
To answer, we use the perfect square formula:
(a + b)² = a² + 2ab + b²
(√3 + √3)² = (√3)² + 2(√3)(√3) + (√3)²
Simplify:
√3² = 3
2(√3)(√3) = 2 x (√3)² = 2 x 3 = 6
Plug in:
(√3 + √3)² = 3 + 6 + 3 = 12
If a drug has a concentration of 5.315 mg per 3.743 mL, how many mL are needed to give 4.719 gram of the drug? Round to 1 decimal.
Answer:
888.4 mL.
Step-by-step explanation:
To solve this problem, we can use the following formula:
Amount of drug (in mg) = concentration (in mg/mL) × volume (in mL)
We are given the concentration of the drug as 5.315 mg per 3.743 mL. To find the volume of the drug needed to give 4.719 g, we need to rearrange the formula to solve for volume:
Volume (in mL) = amount of drug (in mg) ÷ concentration (in mg/mL)
First, we need to convert 4.719 g to mg by multiplying by 1000:
4.719 g × 1000 mg/g = 4719 mg
Now we can substitute the given concentration and the calculated amount of drug into the formula and solve for volume:
Volume (in mL) = 4719 mg ÷ 5.315 mg/mL
Volume (in mL) ≈ 888.5 mL
Therefore, approximately 888.5 mL of the drug are needed to give 4.719 g. Rounded to 1 decimal, the answer is 888.4 mL.