1.) A husband 3 years older than his wife. The Sum of their ages is 73 years. Calculate the difference between the square of their ages.​

Answer:

The answer to your question is no 1 that is

12x^3 - 52x^2y - 13xy^2 + 40y^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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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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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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The volume of one marble is 0.5 ml and the water level before dropping the marbles is 8 ml.

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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Answer: 17

Step-by-step explanation:it goes -1 then x2 so after ten is 9 then 18 then 17

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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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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The function is undefined for those values of x where the denominator is zero.

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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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

The geometric figure which is most likely the next step in the series include the following: C. heptagon.

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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C ((6.5) (3, 2), (2, 4), (6, 3), (1, 0)) , this 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

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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Answer:

118

Step-by-step explanation:

18*4=72

8+3*2=22

8*3=24

72+22+24=118

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.

5-year projected budget total is brought forward from the Project Budget and Projection sheet, using an Excel formula.

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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Answer:

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.

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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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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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.

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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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

...

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.

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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The bounds of non-unusual measures are given as follows:

Hence an adult male foot length of 31.1 cm is significantly high, as it is greater than the upper bound.

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:

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The ratio of girls to boys would be = 11:9

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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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:

150°

Because it is not acute it cant be 30°

(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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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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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