5/8 + 4/5 = 9/8 1 17/40 57/40 9/13​

Verifying the numbers states that a. Icm(60, 90).gcd(60, 90) = mn is right. The correct answer is option a)

To verify Icm(m,n).gcd(m, n) = mn, we need to calculate the least common multiple (Icm) and greatest common divisor (gcd) of each pair of numbers and then multiply them together to check if the product is equal to the product of the original numbers.

a. m = 60, n = 90

Icm(60, 90) = 180

gcd(60, 90) = 30

Icm(60, 90).gcd(60, 90) = 180 * 30 = 5400

m*n = 60 * 90 = 5400

Therefore, Icm(60, 90).gcd(60, 90) = mn is true.

b. m = 220, n = 1400

Icm(220, 1400) = 2200

gcd(220, 1400) = 20

Icm(220, 1400).gcd(220, 1400) = 2200 * 20 = 44000

m*n = 220 * 1400 = 308000

Therefore, Icm(220, 1400).gcd(220, 1400) ≠ mn is false.

c. m = 32.73.11, n = 23.5.7

Icm(32.73.11, 23.5.7) = 32.73.11.5.7 = 12789

gcd(32.73.11, 23.5.7) = 1

Icm(32.73.11, 23.5.7).gcd(32.73.11, 23.5.7) = 12789 * 1 = 12789

m*n = 32.73.11 * 23.5.7 = 2539623

Therefore, Icm(32.73.11, 23.5.7).gcd(32.73.11, 23.5.7) ≠ mn is false.

Therefore, the only true statement is option a. Icm(60, 90).gcd(60, 90) = mn.

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Answerc=2=2_2+

Step-by-step explanation:

The three angles at the bottom need to equal 180:

60 + 50 + ? = 180

Subtract the two known angles from 180.

The unknown angle = 70 degrees

Answer:

see explanation

Step-by-step explanation:

the equation of a line (linear equation) has slope- intercept form

y = mx + c ( m is the slope (gradient)) and c the y- intercept )

y = 12 + 2x or y = 2x + 12 ← is in slope- intercept form

with gradient m = 2

--------------------------------------------------------

the only graphs in linear form are

y = \(\frac{1}{2}\) x and y = 12 - x

the other 2 have an x² term which indicates they are quadratic

It will take approximately 538 years for 52.5 g of a 60.0 g sample of Argon-39 to decay to its daughter isotope.

The half-life of Argon-39 is given as 269 years. This means that in each half-life, the amount of Argon-39 is reduced by half.

Initially, we have a 60.0 g sample of Argon-39. To find the time it takes for 52.5 g (half of the initial amount) to decay, we need to determine how many half-lives it will take to reach that amount.

We can calculate the number of half-lives by dividing the initial amount by the final amount after decay: 60.0 g / 52.5 g = 1.143.

Since each half-life is 269 years, we can multiply the number of half-lives by the length of one half-life to find the total time: 1.143 * 269 years = 307.767 years.

Rounding to the nearest whole number, it will take approximately 538 years for 52.5 g of the Argon-39 sample to decay to its daughter isotope.

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Answer:

1000 cubic metre

Step-by-step explanation:

hopes it help

Answer:

solution,

length=10 cm

volume=?

now,

volume of cube=l×l×l

=10×10×10

therefore,the answer is 1000 cubic centimeter

Answer:

\(17\pi\)

Step-by-step explanation:

Circumference =  diameter x pi

Diameter = 17

So the Circumference is \(17\pi\)

Hope this helps :)

Have a nice day!

The declaration states that the value of Arc EFC = 253°.

A measure is indeed a quantitative concept used to express how large a collection is. Each unique measure represents a different method for determining how large a collection is. It would initially appear that a set's cardinality is the only logical way to determine its number.

We can tell we are working with a circular that has 360 degrees because of the connection.

We can infer that we have it if we look at that file.

Arc EFC

Arc CD

Arc DE

And everything together give us 360,

Arc EFC + Arc CD + Arc DE = 360

If we examine the figure again, we can see that the central angle of an intercepted arc is identical to the arc's measure.

Arc CD is 90 degrees since the central angle is 90 degrees given

Arc DE is 17 degrees

Arc EFC + Arc CD + Arc DE = 360

If we input all the figures

Arc EFC + 90 + 17 = 360

Arc EFC + 107 = 360

Arc EFC = 360 - 107

Arc EFC = 253

Therefore, Arc EFC = 253°

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The correct questions is:

Circle O, and are diameters. Arc ED measures 17°. Circle O is shown. Line segments F C and A E are diameters. Line segments C O and B O are radii. Point B is between points A and C, and point C is between points E and C. Angle D C is a right angle. What is the measure of Arc E F C? 107° 180° 253° 270°

Using the remainder theorem, the value of k in f(x) = 3x^2 + kx - 7 is 10

The given parameters are:

f(x) = 3x^2 + kx - 7

Divisor = x - 4

Remainder = 81

To solve for k, we use the remainder theorem

Set the divisor to 0

x -4 = 0

Add 4 to both sides of the above equation

x - 4 + 4 = 0 + 4

This gives

x = 4

Substitute x = 4 in the function f(x) = 3x^2 + kx - 7

f(4) = 3(4)^2 + k * 4 - 7

Evaluate the exponents

f(4) = 3 * 16 + k * 4 - 7

Evaluate the products

f(4) = 48 + 4k - 7

So, we have:

f(4) = 41 + 4k

The remainder is 81.

So, we have

41 + 4k = 81

Subtract 41 from both sides

4k = 40

Divide both sides of the above equation by 4

4k/4 = 40/4

Evaluate the division

k = 10

Hence, the value of k in f(x) = 3x^2 + kx - 7 is 10 using the remainder theorem

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The equation of the line through the midpoint of AB that is perpendicular to AB is y = (-1/12)x + 31/24 obtained by finding the midpoint of AB.

To find the equation of the line through the midpoint of AB that is perpendicular to AB, we can follow these steps:

Find the midpoint of AB.

The midpoint of AB can be calculated by taking the average of the x-coordinates and the average of the y-coordinates of points A and B.

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Given A = (3, -5) and B = (4, 7):

Midpoint = ((3 + 4) / 2, (-5 + 7) / 2)

= (7/2, 2/2)

= (7/2, 1)

So, the midpoint of AB is (7/2, 1).

Find the slope of AB.

The slope of a line passing through two points can be calculated using the formula:

Slope (m) = (y2 - y1) / (x2 - x1)

Given A = (3, -5) and B = (4, 7):

Slope (m) = (7 - (-5)) / (4 - 3)

= 12 / 1

= 12

So, the slope of AB is 12.

Find the negative reciprocal of the slope of AB.

The negative reciprocal of a slope is the negative value of the reciprocal of that slope.

Negative Reciprocal = -1 / Slope of AB

= -1 / 12

= -1/12

So, the negative reciprocal of the slope of AB is -1/12.

Find the equation of the line through the midpoint of AB perpendicular to AB.

Since we have the slope (-1/12) and the point (7/2, 1), we can use the point-slope form of a line to find the equation.

Point-Slope Form: y - y1 = m(x - x1)

Plugging in the values, we have:

y - 1 = (-1/12)(x - 7/2)

Simplifying and converting to slope-intercept form (y = mx + b):

y - 1 = (-1/12)x + 7/24

y = (-1/12)x + 7/24 + 24/24

y = (-1/12)x + 31/24

Therefore, the equation of the line through the midpoint of AB that is perpendicular to AB is y = (-1/12)x + 31/24.

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Answer:

0.125 = 1/8

Please mark me Brainliest; I need it to move onto the next level. =D

Answer:

D because even though the flat fee is 150 paying 5$ a hour it will cost less

William must make 1806 copies before his total cost is less than the photocopy store.

Let William made x copies from his home photocopier.

Now total cost of x copies = 0.12 x + 162.5

Total cost of x copies from the store = 0.21 x

Now his cost needs to be lower, so we form an inequality to solve this problem.

0.12x + 162.5 < 0.21x

or, 0.12x - 0.21x < -162.5

or, -0.09x < -162.5

or, x > 1805.56

Hence the minimum value of x will be 1806.

Therefore we can say that he needs to make at least 1806 copies.

The two sides of a mathematical equation having an inequality must be equal. In inequality, we compare several values in contrast to equations. The equal sign can be substituted with the less than (or less than as well as equal to), larger above (or greater to), or is not equal to signs.

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Answer:

the answer is -281

Step-by-step explanation:

x+57=-234

x= -57-234

x= -281

Answer:

x+57

x=234-57= 177 I hope it will help you please follow me

The discriminant is a mathematical tool used to determine the number of solutions of a quadratic equation.

The discriminant is calculated using the formula Δ = b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0. Once the discriminant is obtained, it can be used to determine the number of solutions based on its value.

1. If Δ > 0: The quadratic equation has two distinct real solutions. This means the equation intersects the x-axis at two different points.

2. If Δ = 0: The quadratic equation has one repeated real solution. This means the equation intersects the x-axis at a single point.

3. If Δ < 0: The quadratic equation has no real solutions. This means the equation does not intersect the x-axis and has complex solutions.

By utilizing the discriminant, a calculator or a person can quickly determine the number and nature of solutions for a quadratic equation without explicitly solving for the roots.

This information is useful in various mathematical and real-life applications, such as determining the points of intersection, analyzing the behavior of a system, or understanding the geometry of a quadratic function.

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Complete Question

What is discriminant in maths?

An area of mathematics that studies how competing parties interact is known as "game theory."

Game theory analyzes strategic decision-making in situations where multiple participants, known as players, make choices that affect each other's outcomes. It examines the interactions, strategies, and outcomes of these competitive or cooperative situations.

Game theory provides mathematical models and frameworks to analyze various scenarios, such as conflicts, negotiations, auctions, voting systems, and economic markets. It studies the behavior of rational players, their objectives, and the choices they make to maximize their own outcomes, considering the actions and reactions of other players.

The field of game theory explores concepts such as strategies, payoffs, Nash equilibrium, dominant strategies, and cooperative or non-cooperative games. It aims to predict and understand the behavior and outcomes of competitive situations and provides insights into decision-making, resource allocation, and the dynamics of interactions between individuals, organizations, or even nations.

Overall, game theory serves as a valuable tool in various disciplines, including economics, political science, psychology, and computer science, to analyze and model situations where competing parties interact.

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Answer:

Step-by-step explanation:

Here's the long division of (2x³ + 3x² + 4x + 2) ÷ (x + 2):

2x^2 - x + 6

x + 2 | 2x^3 + 3x^2 + 4x + 2

- (2x^3 + 4x^2)

--------------

- x^2 + 4x

- (- x^2 - 2x)

-------------

6x + 2

- (6x + 12)

--------

-10

Therefore, the quotient is 2x^2 - x + 6, and the remainder is -10.

The quotient represents the result of the division of the polynomial (2x³ + 3x² + 4x + 2) by the divisor (x + 2). In particular, the quotient 2x^2 - x + 6 represents the quadratic polynomial that, when multiplied by the divisor x + 2, gives the dividend 2x³ + 3x² + 4x + 2.

In other words, we have:

(2x³ + 3x² + 4x + 2) = (x + 2)(2x^2 - x + 6) - 10

The remainder -10 indicates that the division is not exact, and that there is a "leftover" term of -10 when we try to divide the polynomial (2x³ + 3x² + 4x + 2) by (x + 2).

\(\\ \sf\longmapsto \dfrac{3p}{5}+\dfrac{8}{5}=1\)

\(\\ \sf\longmapsto \dfrac{3p+8}{5}=1\)

\(\\ \sf\longmapsto 3p+8=5\)

\(\\ \sf\longmapsto 3p=5-8\)

\(\\ \sf\longmapsto 3p=-3\)

\(\\ \sf\longmapsto p=\dfrac{-3}{3}\)

\(\\ \sf\longmapsto p=-1\)

Based on the information given in the question, the number of packages that was bought will be 7.

From the information given, there are 5 pairs of scissors in one package and Hill bought 35 scissors for students in her art class, therefore, the number of packages will be:

= 35/5

= 7

In conclusion, the number of packages will be 7 packages.

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Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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The Mean Absolute Deviation (MAD) of the given data set is approximately 7.5.

To find the mean and the Mean Absolute Deviation (MAD) of the given data set, follow these steps:

Step 1: Calculate the Mean

To find the mean (average) of a data set, add up all the values and divide the sum by the total number of values.

Mean = (10 + 15 + 20 + 25 + 30 + 35) / 6

Mean = 135 / 6

Mean = 22.5

So, the mean of the given data set is 22.5.

Step 2: Calculate the Mean Absolute Deviation (MAD)

To find the MAD, follow these steps:

Find the difference between each data point and the mean.

Take the absolute value of each difference.

Find the mean of these absolute differences.

Let's calculate the MAD:

|10 - 22.5| = 12.5

|15 - 22.5| = 7.5

|20 - 22.5| = 2.5

|25 - 22.5| = 2.5

|30 - 22.5| = 7.5

|35 - 22.5| = 12.5

Now, find the mean of these absolute differences:

MAD = (12.5 + 7.5 + 2.5 + 2.5 + 7.5 + 12.5) / 6

MAD = 45 / 6

MAD ≈ 7.5

So, the Mean Absolute Deviation (MAD) of the given data set is approximately 7.5.

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The equation of the line for the given graph is y = - 4x + 110.

1)We can calculate the slope of the given line by,

m = (y2 - y1)/(x2 - x1)

where, (x1, y1) are the initial points and (x2,y2) are the final points of the line.

here, (x1, y1) = (5,90)

and, (x2,y2) = (0,110)

so,

m = (110 - 90)/(0 - 5) = -4

therefore, the equation of the line will be,

y = - 4x + 110

where 110 is the y-intercept of the line

2) Slope is the rate of change of the dependent variable with respect to the independent variable.

Here we can say that the slope shows the decrease in the balance of the savings accounts with respect to the weeks.

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there are approximately 34 boys in the introductory geology course.

To determine the number of boys in the introductory geology course, we need to calculate the ratio of boys to girls and use the total number of students enrolled.

The given ratio states that there are six boys for every five girls. This can be expressed as 6 boys : 5 girls.

Let's assume the number of boys in the course is represented by B and the number of girls is represented by G.

According to the given information, we can set up the following equation:

6 boys / 5 girls = B / G.

Since the total number of students enrolled in the course is 374, we can write another equation:

B + G = 374.

To solve these equations simultaneously, we can use the concept of proportion.

From the first equation, we can rewrite it as:

6G = 5B.

Now we can substitute this expression into the second equation:

B + G = 374

5B + 6B = 374

11B = 374

B = 374 / 11

B ≈ 34.

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To find the derivative of f(x) = sin(4x)cos(5x), we can apply the product rule of differentiation. Let's denote u = sin(4x) and v = cos(5x).

Using the product rule, the derivative f'(x) can be calculated as follows:

f'(x) = u'v + uv'

Taking the derivatives of u and v, we have:

u' = 4cos(4x)

v' = -5sin(5x)

Now substituting these values into the derivative formula, we get:

f'(x) = (4cos(4x))(cos(5x)) + (sin(4x))(-5sin(5x))

Simplifying further:

f'(x) = 4cos(4x)cos(5x) - 5sin(4x)sin(5x)

Therefore, the correct answer is: f'(x) = 4cos(4x)cos(5x) - 5sin(4x)sin(5x).

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Answer:

1. Simplify each side of the equation by removing parentheses and combining like terms.

2. Use addition or subtraction to isolate the variable term on one side of the equation.

3. Use multiplication or division to solve for the variable.

The equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

What are parallel lines?

Parallel lines are coplanar infinite straight lines that do not intersect at any point in geometry. Parallel planes are planes that never meet in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance.

To find an equation for the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5),

We use the equation of a line: v = v₀ + tv₁

where v₀ and v₁ are points on the line and t is a real number.

Substitute the given points in for v₀ and v₁: v = (0, 1, −8) + t(6, 7, −5)

This equation of the plane is Ax + By + Cz = D, where A, B, C, and D are constants to be determined.

Equate the components:

0x + 1y - 8z = D....(1)

6x + 7y - 5z = D...(2)

Now, we subtract equation (1) from (2) and we get

6x - 0x + 7y - 1y - 5z + 8z = 0

6x + 6y + 3z = 0

Hence, the equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

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Answer:

Let l = length of rectangle

w = width of rectangle

l = w + 2

(l - 3)(w + 4) = lw + 49

(w - 1)(w + 4) = (w + 2)w + 49

w² + 3w - 4 = w² + 2w + 49

w = 53, l = 55

The width of the rectangle is 53 cm., and the length of the rectangle is 55 cm.

ANSWER

C. 50 > x + 12.50

EXPLANATION

We have that the price of each t-shirt is the same and the pair of shorts cost $12.50.

Let the price of the t-shirts John bought be x.

We have that John did not speand more than $50.

This means that, if we add the prices of the t-shirts and the pair of shorts, it must be less than $50.

Therefore, the inequality is:

x + 12.50 < 50

This is not among the options, but we can rewrite it as:

50 > x + 12.50

That is the answer. Option C.

The number of balls, given the ratio of white balls to yellow balls that could not be in the bag is C. 42 balls.

The number of balls that could not be in the bag, given the ratio of white balls to yellow balls, is the number that would not give a whole number when multiplied by the ratio of white balls to yellow balls.

26 balls :

= 3 / ( 10 + 3 white balls ) x 26

= 3 / 13 x 26

= 6 balls

39 balls :

= 3 / 13 x 39

= 9 balls

42 balls :

= 3 / 13 x 42

= 9.69 balls

There therefore cannot be 42 balls.

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Options for this question include: