Answer:
The difference between the square of their ages is 219----------------------------
Let the husband's age be h and wife's age be w.
The difference of their age is 3 and sum is 73:
h - w = 3h + w = 73The difference between the squares is:
h² - w² = Difference of squares(h + w)(h - w) = Identity for difference of squares73*3 = Substitute219 AnswerAnswer:
219
Step-by-step explanation:
H-W=3
H+W =73
2H=76
H=38
W=35
38² -35² = 219
identify the correct unit fraction to multiply by the second term to create a common denominator for the rational expression below:
(2x^(2)-16)/(x^(2)-4)-(x 4)/(x-2)
The correct unit fraction to multiply by the second term to create a common denominator is [tex](x+2)/(x+2)[/tex]
To find a common denominator for the given rational expression, we need to identify a unit fraction that can multiply the second term so the denominators of both terms will be the same.
The denominators of the two terms are [tex]x^2-4[/tex] and [tex]x-2[/tex]. To find a common denominator for these terms, we can multiply the second term [tex](x+2)/(x+2)[/tex] which is a unit fraction because it is equal to 1.
Multiplying the second term by [tex](x+2)/(x+2)[/tex] gives us:
[tex](x 4)/(x-2) * (x+2)/(x+2) = (4x(x+2))/(x^2-4)[/tex]
Now both terms have a common denominator [tex]x^2-4[/tex]. Thus the correct unit fraction to multiply by the second term to create a common denominator is [tex](x+2)/(x+2)[/tex]
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24-hour digital clock is gaining three minutes every hour,if you set it to the correct time at 6 p.m. on Saturday,when will it show the correct time again?
after 20 hours the clock will show 3*20 = 60 min = 1 hr more
since the clock is analogue after 12 hours it will show the same time hat is 6 am and 6 pm are shown the same way.
after 20*12 = 240 hr = 10 days the clock will show 12 hr more but since 6 am and 6 pm are shown the same after 240 hr = 10 days the clock will show the correct time again.
the correct time will be shown on Monday 6 pm.
Find the intervals on which the given function is increasing and the intervals on which it is decreasing. (Enter your answers using interval notation.) h(x) = (x + 2)^2 x (x-7)^1/3
The intervals on which the function is increasing are: (-∞, -2) and (7, ∞), and the intervals on which the function is decreasing are: (-2, 7). In interval notation, this is written as (-∞, -2), (7, ∞) and (-2, 7).
The given function is h(x) = (x + 2)^2 x (x-7)^1/3. This is a polynomial function with two terms. The first term, (x + 2)^2, is a quadratic function, and the second term, (x-7)^1/3, is a cube root function.
We can use the derivative of the function to determine the intervals on which the function is increasing and decreasing. Taking the derivative of the function yields: h'(x) = 2(x + 2)(x - 7)^1/3 + (x + 2)^2 x (1/3)(x - 7)^-2/3. Setting the derivative equal to zero, we can solve for x and find where the function is not increasing or decreasing. Solving this equation yields x = -2 and x = 7, the points of inflection.
Therefore, the intervals on which the function is increasing are: (-∞, -2) and (7, ∞), and the intervals on which the function is decreasing are: (-2, 7). In interval notation, this is written as (-∞, -2), (7, ∞) and (-2, 7).
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P(a)=.40 p(b)=.50 P(A
and b )=.10. Whats p(b/a)
Answer:
The probability of (B|A) is 0.25 which is correct option(B).
What is probability?
The probability is defined as the possibility of an event is equal to the ratio of the number of outcomes and the total number of outcomes.
P(A)=0.40
P(B)= 0.50
P(A ∩ B) = 0.10
In order to find the probability of (B|A),
Condi
Step-by-step explanation:
Please help, ignore the 7
Answer: 17
Step-by-step explanation:it goes -1 then x2 so after ten is 9 then 18 then 17
What are the coordinates of the point on the directed line segment from ( − 10 , 9 ) (−10,9) to ( − 4 , 3 ) (−4,3) that partitions the segment into a ratio of 1 to 5 help plss
We can find the coordinates of the point that partitions a line segment into a ratio of 1 to 5 by using the formula:
(x, y) = (x1 + r * (x2 - x1), y1 + r * (y2 - y1))
Where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment, and r is the ratio of the distance from the starting point to the point of interest, to the total distance of the line segment. In this case, r = 1/(1 + 5) = 1/6.
We know the coordinates of the two endpoints of the line segment:
(x1, y1) = (-10, 9)
(x2, y2) = (-4, 3)
So, we can substitute these values into the formula and find the coordinates of the point that partitions the line segment into a ratio of 1 to 5:
(x, y) = (-10 + (1/6) * ((-4) - (-10)), 9 + (1/6) * (3 - 9))
= (-10 + (1/6) * (-6), 9 + (1/6) * (-6))
= (-10 -1/6, 9 -1)
= (-10/6 -1/6, 3/2 -1)
= (-16/6, 3/2 -1)
= (-8/3,-1/2)
So, the coordinates of the point on the directed line segment from (-10, 9) to (-4, 3) that partitions the segment into a ratio of 1 to 5 is (-8/3,-1/2)
It is important to notice that this point is a vector and not a point in the Cartesian plane
Use the algebraic tests to check for symmetry with respect to both axes and the origin.
y = x^4 - x^2 + 3
Axis of Symmetry: This function is not symmetric with respect to the x-axis, y-axis, or the origin.
To check for symmetry with respect to both the x-axis and the y-axis, we need to check whether the function is even or odd. To do this, we can substitute -x for x in the equation and check if the equation remains the same.
y = x^4 - x^2 + 3
y = (-x)^4 - (-x)^2 + 3
y = x^4 - x^2 + 3
Since the equation remains the same, the function is neither even nor odd and therefore is not symmetric with respect to either the x-axis or the y-axis.
To check for symmetry with respect to the origin, we need to check if the equation is symmetric when x and y are both substituted with -x or -y.
y = x^4 - x^2 + 3
y = (-x)^4 - (-x)^2 + 3
y = x^4 - x^2 - 3
Since the equation is not the same, the function is not symmetric with respect to the origin.
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Find the area
…………………………
Answer:
118
Step-by-step explanation:
18*4=72
8+3*2=22
8*3=24
72+22+24=118
5 Now, perform each of the calculations indicated. Please refer to the financial formulas section of the instructions for Major Assignment 3, where you will find the equations for the Compound Interest Formula,
Future Value of Periodic Payments Formula, and Loan Payment Formula to use for the final calculation in the Sponsorship, Fundraising, and Loan Payment sections below, respectively. Important Note: for these
calculations, you MUST use direct calculation formulas, and you MAY NOT use built-in Excel functions to calculate these values.
Format all amounts (in the gold-shaded cells) as Currency with the $ symbol and 2 decimal places, and all n and t entries (in the green-shaded cells) as Number with 0 decimals.
Bring your 5-year projected budget total
forward from the Project Budget and Projection
sheet
8 Loan Payment (determine the
5-year projected budget total is brought forward from the Project Budget and Projection sheet, using an Excel formula.
How can you determine a recurring payment's future value?
P is equal to PMT [((1 + r)n - 1)/r]
Taking into account a certain amount of compounded interest earnings that progressively accumulate during the measurement period, this figure represents the sum that a stream of future payments will increase to.
One of the financial functions, FV, determines the investment's future value using a constant interest rate. Future Value (FV )can be used with either a series of regular, recurring payments or a single, one-time payment. To determine the future worth of a sequence of payments, use the Excel Formula Coach.
Your interest rates correctly match the corresponding entries from the table for theyears and months given.Your 5-year projected budget total is brought forward from the Project Budget andProjection sheet, using an Excel formula.
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if there is sufficient evidence to reject the null hypothesis, we conclude that the alternate hypothesis is true
if there is not sufficient evidence to reject the null hypothesis, we conclude that the null hypothesis might be true, but we never conclude that the null hypothesis is true
If there is sufficient evidence to reject the null hypothesis, we conclude that the alternate hypothesis is true. if there is not sufficient evidence to reject the null hypothesis, we conclude that the null hypothesis might be true, but we never conclude that the null hypothesis is true
if there is not sufficient evidence to reject the null hypothesis, we conclude that the null hypothesis might be true, but we never conclude that the null hypothesis is true
This statement is describing the process of hypothesis testing in statistics. In hypothesis testing, a null hypothesis is a statement that there is no significant difference between two sets of data or no relationship between two variables. An alternate hypothesis is a statement that there is a significant difference or relationship.
When conducting a hypothesis test, a researcher will collect data and use statistical methods to determine the likelihood that the null hypothesis is true given the data. If the likelihood is low, the researcher will reject the null hypothesis and conclude that the alternate hypothesis is true. If the likelihood is high, the researcher will fail to reject the null hypothesis, but this does not necessarily mean that the null hypothesis is true. It means that the data is not strong enough to reject the null hypothesis.
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what is the converse of the following conditional statement? "if two angles form a linear pair, then they are supplementary angles." if two angles are supplementary angles, then they form a linear pair. if two angles do not form a linear pair, then they are not supplementary angles." if two angles are not supplementary angles, then they do not form a linear pair. two angles form a linear pair if and only if they are supplementary angles.'
If two angles form a linear pair, then they are supplementary.
This is because it is not necessary for angles to form a linear pair for them to be supplementary. Angles can be supplementary even if they do not form a linear pair.
if two angles do not form a linear pair, then they are not supplementary angles
Supplementary angles do not have to be , whereas a linear pair must be adjacent and create a straight line. So, if two angles do not form a linear pair, then they are not supplementary .
if two angles are not supplementary angles, then they do not form a linear pair. Supplementary angles do not have to be adjacent, whereas a linear pair must be adjacent and create a straight line. So, , supplementary angles are not always linear pair . However, linear pairs are always supplementary.
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If two angles form a linear pair, then they are supplementary.
This is because it is not necessary for angles to form a linear pair for them to be supplementary. Angles can be supplementary even if they do not form a linear pair.
if two angles do not form a linear pair, then they are not supplementary angles
Supplementary angles do not have to be , whereas a linear pair must be adjacent and create a straight line. So, if two angles do not form a linear pair, then they are not supplementary .
if two angles are not supplementary angles, then they do not form a linear pair. Supplementary angles do not have to be adjacent, whereas a linear pair must be adjacent and create a straight line. So, , supplementary angles are not always linear pair . However, linear pairs are always supplementary.
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Which of the following is most likely the next step in the series?
The geometric figure which is most likely the next step in the series include the following: C. heptagon.
What is a series?In Mathematics, a series can be defined as a sequence of real and natural numbers in which each term differs from the preceding term by a constant numerical quantity.
By critically observing the given series, we can logically deduce that the first geometric figure represent a square with four (4) sides, the second geometric figure represent a pentagon with five (5) sides, the third geometric figure represent a hexagon with six (6) sides. This ultimately implies that, each of the sides of the geometric figure increases by one (1).
In this context, the next geometric figure in the series must be a heptagon with seven (7) sides.
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Liliana has $3.60 in nickels and quarters in her backpack. She has 18 more nickels than quarters. How many coins of each type does she have?
Answer: Liliana has 9 quarters and 27 nickels.
Step-by-step explanation:
Let's call the number of quarters Liliana has "q" and the number of nickels she has "n".
From the problem, we know that:
n = q + 18 (because she has 18 more nickels than quarters)
We also know that the total value of the coins is $3.60. We can use the following equation to find the total number of coins:
(0.25 * q) + (0.05 * n) = 3.60
Now we can substitute the first equation into the second equation to get:
(0.25 * q) + (0.05 * (q + 18)) = 3.60
Simplifying this equation:
0.25q + 0.05q + 0.90 = 3.60
0.30q = 2.70
q = 9
So Liliana has 9 quarters. We can use the first equation (n = q + 18) to find the number of nickels she has:
n = 9 + 18
n = 27
Which means, Liliana has 9 quarters and 27 nickels.
a p-value of 0.04 obtained from a two-tailed t-test means that there is a % chance that the obtained results are due to . given the conventional significance level, you would reject the hypothesis.
A p-value of 0.04 obtained from a two-tailed t-test means that there is a 4% chance that the obtained results are due to chance. Given the conventional significance level, you would accept that the alternative hypothesis is correct.
If the null hypothesis is correct and the study is conducted several times and exactly as it was intended to be done, the P=0.04 indicates that.
In statistical hypothesis testing, it is necessary to state the alternative hypothesis, which is the statistical difference, and the null hypothesis, which is the absence of any statistical difference between the groups.
The test statistic, which is a uniformly scaled quantitative measure of the group difference, is then calculated.
The test statistic result is expected to be modest under the null hypothesis, but there is a small risk that it could accidentally be large. Once we get the test statistic, we use the test statistic to compute the p-value.
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The complete question is:
A p-value of 0.04 obtained from a two-tailed t-test means that there is a ____ % chance that the obtained results are due to _______. Given the conventional significance level, you would accept that the _________ hypothesis is correct.
segment vu is parallel to segment lm. find the missing length. segment vu is parallel to segment lm. find the missing length. 44 27 24 39
The missing length of segment VU is 33.49.
The formula for finding the missing length of two parallel lines is given below:
L = L1 + (L2 - L1) * (L3/L4)
Where L1 is the length of one line, L2 is the length of the other line, L3 is the known length of the first line, and L4 is the known length of the second line.
In this problem, L1 is the length of segment LM and L2 is the length of segment VU. We know that L3 is 24 and L4 is 39.
Using the formula, we can calculate the missing length of segment VU as follows:
L = 44 + (27 - 44) * (24/39)
L = 44 + (-17) * (0.61538)
L = 44 - 10.51
L = 33.49
Therefore, the missing length of segment VU is 33.49.
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What is 6 x 3/5 as a fraction
Answer:
18/5 or 3 3/5
Step-by-step explanation:
Turn 6 into a fraction -> 6/1
Hence, 6/1 × 3/5
Multiply the numerators and denominators.
(6×3)/(1×5) = 18/5
Simplify = 3 3/5
Answer:
= 18/5
Step-by-step explanation:
6 × 3 = 18
Then:
6 × 3/5
= 18/5
...
A group of adult males has foot lengths with a mean of 28.02 cm and a standard deviation of 1.35 cm. Use the range rule of thumb for identifying significant values to identify the limits separating values that are significantly low or significantly high. Is the adult male foot length of 31.1 cm significantly low or significantly high? Explain.
The bounds of non-unusual measures are given as follows:
Lower bound: 25.32 cm.Upper bound: 30.72 cm.Hence an adult male foot length of 31.1 cm is significantly high, as it is greater than the upper bound.
What is the range rule of thumb?The range rule of thumb states that measures that are more than two standard deviations from the mean in a data-set are considered unusual.
Considering the mean and the standard deviation for this problem, the bounds are given as follows:
Lower bound: 28.02 - 2 x 1.35 = 25.32 cm.Upper bound: 28.02 + 2 x 1.35 = 30.72 cm.More can be learned about the range rule of thumb at https://brainly.com/question/15825971
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PLEASEHELP WITH PROBLEMS
In order to maximize profit the firm should produce 4 or 5 units.
The marginal revenue and the marginal cost are the same at quantity 6.
The marginal revenue curve and the marginal cost curve cross at a quantity 6.
The firm loses in a competitive industry because marginal revenue is decreasing as quantity increases.
The industry is in a long-run equilibrium.
True.
The graph is given below.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Marginal cost = Change in cost / Change in Quantity
Marginal Revenue = Change in Revenue / Change in Quantity
Profit = Marginal revenue - Marginal cost
Now,
Quantity Total cost Marginal cost Total revenue Marginal revenue Profit
0 5 0
(6 - 5)/(1 - 0) = 1 (6 - 0)/(1 - 0) = 6 (6 - 5) = 1
1 6 6
(8 - 6)/(2 - 1) = 2 (12 - 6)/(2 - 1) = 6 (6 - 2) = 4
2 8 12
(11 - 8)/(3 - 2) = 3 (18 - 12)/(3 - 2) = 6 (6 - 3) = 3
3 11 18
(15 - 11)/(4 - 3) = 4 6 (6 - 4) = 2
4 15 24
(20 - 15)/(5 - 4) = 5 6 (6 - 5) = 1
5 20 30
(26 - 20)/(6 - 5) = 6 6 (6 - 6) = 0
6 26 36
(35 - 26)/(7 - 6) = 9 6 (6 - 9) = -3
7 35 42
We see from the table,
There is no profit when the quantity is 6 and 7.
So,
In order to maximize profit the firm should produce 4 or 5 units.
Now,
From the table,
The marginal revenue and the marginal cost are the same at quantity 6.
The marginal revenue curve and the marginal cost curve cross at a quantity 6.
Now,
The firm loses in a competitive industry because marginal revenue is decreasing as quantity increases.
Now,
Since the marginal cost is the same.
The industry is in a long-run equilibrium.
True.
Now,
The marginal cost equation.
y = x + 0.5
i.e
(0.5, 1) and (1.5, 2)
y = mx + c
m = (2 - 1)/(1.5 - 0.5) = 1/1 = 1
1 = 1 x 0.5 + c
c = 1 - 0.5
c = 0.5
The marginal revenue equation.
y = 6
i.e
(0.5, 6) and (1.5, 6)
m = 0
6 = 0 x 0.5 + c
c = 6
The graph is given below.
Thus,
The statement is given above.
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convert 1.2 meters to millimeter. please remember to use significant figures. do not answer in scientific notation.
Millimeter and meter are units of length. 1.2 meters are equal to 1200.O millimeters. Significant figures means writing all the certain digit along with an uncertain or estimated digit.
The SI unit of length is meters. There are different units like millimeters, centimeters, kilometers, inches etc. All these values are interconvertible.
1 Meter = 100 centimeters
1 centimeter = 10 meter
So 1 meter = 100× 10 = 1000 millimeter.
So 1.2 meter = 1.2× 1000 = 1200 millimeters.
1200 has only two significant. To increase the number of significant figures we can add two decimal places. 1200.00 have 6 significant figures.
So 1.2 meters is 1200.00 millimeter.
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Consider a one-sample two-sided z-test for a population proportion. Given that conditions for inference are met, which of the following is closest to the P-value for a test statistic of -1.86 ? A. 0.0157 B. 0.0314 C. 0.0628 D. 0.9371 E. 0.9686
The closest value to the P-value for a test statistic of -1.86 is 0.0628. Hence, option C is the correct answer to this question.
The P-value for a test statistic of -1.86 in a one-sample two-sided z-test for a population proportion can be found using a standard normal table or a calculator with a built-in function for z-scores. It represents the probability of obtaining a test statistic as extreme or more extreme than the one observed, under the assumption that the null hypothesis is true.
In this case, the test statistic of -1.86 is on the left tail of the standard normal distribution, since it is negative and represents a deviation to the left of the mean. To find the P-value, we would need to look up the area under the standard normal curve to the left of -1.86.
Using a standard normal table, we can see that the area under the curve to the left of -1.86 is approximately 0.0314. However, since this is a two-sided test, we also need to consider the area in the right tail, which is also 0.0314. Therefore, the P-value for a test statistic of -1.86 in a one-sample two-sided z-test for a population proportion is approximately 0.0314 + 0.0314 = 0.0628.
Hence, the answer to the P-value is 0.0628.
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Bethany runs 3 days a week four miles each day. How many miles does she run in 16 weeks?
Answer:
48 miles in 16 weeks dtWhich relation is not a function?
OAX 126 18 24 36
y 6 12 6 30 24
B. ((7,3), (3, 7), (1, 5), (5, 4), (0, 6))
OC ((6.5) (3, 2), (2, 4), (6, 3), (1, 0))
OD
23
C ((6.5) (3, 2), (2, 4), (6, 3), (1, 0)) , this relation is not a function
Which relation is not a function?C ((6.5) (3, 2), (2, 4), (6, 3), (1, 0)) is not a function because it does not pass the vertical line test.
The vertical line test states that if a vertical line crosses the graph of a relation more than once, then the relation is not a function.
In this example, a vertical line drawn at x=6.5 will cross the graph twice, at (6.5, 3) and (6.5, 2).
Since a vertical line passes the graph twice, it does not pass the vertical line test and is not a function.
The theory used in this question is the Vertical Line Test,
which states that if a vertical line crosses the graph of a relation more than once, then the relation is not a function.
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C ((6.5) (3, 2), (2, 4), (6, 3), (1, 0)) , this relation is not a function
What relationship doesn't function?Because C ((6.5) (3, 2), (2, 4), (6, 3), and (1, 0) fail the vertical line test, they are not functions.
According to the vertical line test, a relation is not a function if a vertical line crosses its graph more than once.
A vertical line drawn at x=6.5 in this example will cross the graph twice at (6.5, 3) and (6.5, 2).
A vertical line fails the vertical line test and is not a function because it traverses the graph twice.
The Vertical Line Test is the hypothesis employed in this query.
which implies that a vertical line crossing a relation's graph more than once is a sign that the relation is not a function.
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PLEASE HELP SOON! :)
Multiply and simplify. ( 4x - 7 ) ( x + 5 )
What is the answer? Fill in the blanks in standard form, from left to right.
4x^? + ?x-?
blank 1: enter number
blank 2: enter number
blank 3: enter number
Q. 2
Multiply and simplify. ( 6x - 5y ) ( 2x^2 - 7xy - 8y^2 ) What is the answer?
1. 12x^3 - 52x^2y - 13xy^2 + 40y^3
2. 12x^3 - 42x^2y - 48xy^2 + 40y^3
3. 12x^3 - 10x^2y - 35xy^2 + 40y^3
4. 12x^3 - 42x^2y - 35xy^2 + 40y^3
Answer:
The answer to your question is no 1 that is
12x^3 - 52x^2y - 13xy^2 + 40y^3
After examining the reciprocal identity for sect, explain why the function is undefined at
certain points.
The function is undefined for those values of x where the denominator is zero.
What informs the function to be undefined?The reciprocal identity for sine, cosine, and tangent states that:
sin(x) = 1/csc(x)
cos(x) = 1/sec(x)
tan(x) = 1/cot(x)
It is important to note that csc, sec, and cot are only defined for values of x where the denominator is not equal to zero.
For example, csc(x) is defined as 1/sin(x), so it is undefined for x = kπ where k is any integer and sin(x) = 0.
Similarly, sec(x) is defined as 1/cos(x) and is undefined for x = (k+1/2)π where k is any integer and cos(x) = 0. Finally, cot(x) is defined as 1/tan(x) and is undefined for x = kπ where k is any integer and tan(x) = 0.
Therefore, the reciprocal identity for sine, cosine, and tangent is only defined for certain input values, and it is undefined for those values of x where the denominator is zero.
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What is the measurement of the angle shown below? O O 150° 60° ○ 30° 10 20 30 0 170 150 150 140 130 120 180° 249 848 60 90 100 110 120 130 140 150 80 70 60 50 $ ata
150°
Because it is not acute it cant be 30°
let $n$ be a positive integer such that every digit in $n$ is a $1$ or a $2,$ and $n$ is divisible by both $4$ and $9.$ what is the smallest possible value of $n?$ https://web2.0calc/questions/
The smallest possible number with digits 1 and 2, divisible by 4 and 9 is 22212.
A number that is divisible by both 4 and 9 must be divisible by their least common multiple (LCM), which is 36. To find the smallest possible value of n such that every digit is a 1 or a 2 and the number is divisible by 36, we can start with the smallest possible number that is divisible by 36 and only contains 1s and 2s, which is 11112.
As the number is divisible by 4 and contains only 1 and 2, the last two digits is 12. Now it is divisible by 9 so sum of digits is 9 or multiple of 9.
1 + 2 = 3
So we need digits sum equal 9-3 = 6 to be divisible by 9, so number is 22212.
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( HELP ME PLS )
315% of 26.2 is what?
Answer:
Solution:
315 percent of 26.2=82.53
Step-by-step explanation:
To calculate 315 percent of the number 26.2, we must create a ratio from which we can easily determine the value we are looking for.
First we create two simple equations with data that we know.
26.2 equals 100%, so we can save it as 26.2 = 100%
The value we are looking for can be called x
Now we know that x is 315 of the output value, so we can write it as x = 315.
So we have two simple equations:
1) 26.2=100%
2) x=315%
When we compare these two equations, we get:
26.2/x=(100%)/(315%)
Now we just have to solve the simple equation.
We calculate 315 percent of 26.2 :
26.2/x=100/315
(26.2/x)*x=(100/315)*x
26.2=0.31746031746032*x
26.2/0.31746031746032=x
82.53=x
x=82.53
Solution:
315 percent of 26.2=82.53
Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function.
(a) f(x) = log2(x) (b) g(x) = ∜x (c) h(x) = 2x^3/(1 - x^2) (d) u(t) = 1 - 1.1t + 2.54t^2 (e) v(t) = 5^t (f) w(θ) = sin θ cos^2 θ
(a) log₂(x) is a logarithmic function, (b) ∜x is a root function, (c) 2x^3/(1 - x^2) is a rational function, (d) 1 - 1.1t + 2.54t^2 is a polynomial of degree 2, (e) 5^t is an exponential function and (f) sin θ cos^2 θ is a trigonometric function.
A power function has the form f(x) = x^n, where n is a constant.
A root function has the form f(x) = √x or f(x) = x^(1/n), where n is a constant.
A polynomial is an algebraic function that can be written in the form f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_2 x^2 + a_1 x + a_0, where a_i are constants and n is the degree of the polynomial.
A rational function is a function that can be written as the ratio of two polynomials, i.e., f(x) = (p(x))/(q(x)), where p(x) and q(x) are polynomials and q(x) ≠ 0.
An algebraic function is a function that can be expressed as the solution to a polynomial equation, i.e., it can be written as a polynomial, a root, or a combination of polynomials and roots.
A trigonometric function is a function that involves the ratios of sides in a right triangle, such as sine, cosine, tangent, etc.
An exponential function has the form f(x) = a^x, where a is a positive constant greater than 1.
A logarithmic function has the form f(x) = logₐx, where a is a positive constant greater than 1.
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In science class, Farah uses a graduated cylinder with water in it to measure the volume of some marbles. After dropping in 4 marbles, the height is 10 mL. After dropping in 6 marbles, the height is 11 mL. How much does the height increase for each marble? 0.5 mL How much water was in the cylinder before any marbles were dropped in? mL wwwww Submit
The volume of one marble is 0.5 ml and the water level before dropping the marbles is 8 ml.
Finding Volume by Water Displacement Method:The volume of an object is the amount of space occupied by the object within all boundaries. The volume of any geometrical shape can be calculated by the respective formula.
The Water Displacement Method is a method that is used to calculate the volume of any object without knowing the dimensions. If we drop the object into the water and the amount that can be displaced will be equal to the volume of the object.
Here we have
After dropping 4 marbles, the height of the water level is 10 ml
After dropping 6 marbles, the height of the water level is 11 ml
This means for 2 extra marbles the water level increase up to 1 ml
So, the Volume of the marble = 1 ml/2 = 0.5 ml
From the given data,
After dropping 4 marbles the water level is 10 ml
As we know the volume of 1 marble = 0.5ml
=> Volume of 4 marbles = 4 × 0.5ml = 2ml
The water level before dropping 4 marbles = 10 ml - 2 ml = 8 ml
Therefore,
The volume of one marble is 0.5 ml and the water level before dropping the marbles is 8 ml.
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In a classroom, there are 18 boys and 22 girls. What is the ratio of girls to boys? Always simplify ratios!!
The ratio of girls to boys would be = 11:9
what is a ratio?A ratio is defined as the expression that is used to show the relationship between two different variables.
The number of boys represented = 18 boys
The number of girls represented = 22 girls
To calculate the ratio of girls to boys the following is done;
22 : 18 ( divide through by 2)
11. : 9
Therefore the ratio of girls to boys in the classroom = 11:9
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