The LCM of three numbers is 7920 and their GCD is 12. Two of the numbers are 48 and 264. Using factor notation find the third number if one of its factors is 9.

Answer:

Therefore, the base-6 representation of 1407 is 1303.

Step-by-step explanation:

To convert the decimal numeral 1407 to base 6, we can use the following steps:

Divide 1407 by 6 and store the quotient and the remainder.

Repeat the division process with the quotient until the quotient is 0.

Write down the remainders in the reverse order to get the base-6 representation of 1407.

So, the steps would look like this:

1407 ÷ 6 = 234 with a remainder of 3

234 ÷ 6 = 39 with a remainder of 0

39 ÷ 6 = 6 with a remainder of 3

6 ÷ 6 = 1 with a remainder of 0

1 ÷ 6 = 0 with a remainder of 1

Writing down the remainders in the reverse order, we get: 1407(10) = 1303_6.

Therefore, the base-6 representation of 1407 is 1303.

The lateral surface area of a cylinder can be calculated using the formula 2πrh, where r is the radius of the circular base and h is the height of the cylinder. Using the given value of π as 3.14 and rounding to the nearest whole number, the formula becomes: Lateral surface area = 2 × 3.14 × 8 × 18Lateral surface area = 904.32The lateral surface area of the cylinder is 904.32 square units.

The lateral surface area of a cylinder is the area of the curved surface that connects the two circular bases of the cylinder. It can be calculated using the formula 2πrh, where r is the radius of the circular base and h is the height of the cylinder. To find the lateral surface area of the given cylinder, we need to first identify the values of r and h. From the problem statement, we know that the value of π is 3.14.

We are also told to round our answer to the nearest whole number. Using the given formula, we have: Lateral surface area = 2πrh where r is the radius of the circular base and h is the height of the cylinder.  From the problem statement, we are not given the radius of the cylinder directly. However, we are given the diameter of the cylinder, which is 16. The radius is half of the diameter, so the radius can be calculated as: r = d/2 = 16/2 = 8 units We are also given the height of the cylinder as 18 units. Substituting these values in the formula, we get: Lateral surface area = 2 × 3.14 × 8 × 18Lateral surface area = 904.32 square units Rounding to the nearest whole number, the lateral surface area of the cylinder is 904 square units.

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The product of the volume and total surface area of the given right conical frustum is approximately 146520π². To find the product of the volume and total surface area of a right conical frustum, we first need to determine the individual values of volume and surface area.

The volume of a frustum can be calculated using the formula:

V = (1/3)πh(r₁² + r₂² + r₁r₂),

where h is the height of the frustum, r₁ and r₂ are the radii of the larger and smaller bases, respectively.

In this case, we are given that the radii of the larger and smaller bases are 12 and 9 units, respectively. We also know that the two bases are 4 units apart, which means the height of the frustum is 4 units.

Substituting the given values into the formula, we have:

V = (1/3)π(4)(12² + 9² + 12*9)

 = (1/3)π(4)(144 + 81 + 108)

 = (1/3)π(4)(333)

 = (4/3)π(333)

 ≈ 444π cubic units

Now, let's move on to calculating the total surface area of the frustum. The formula for the total surface area is:

A = π(r₁ + r₂)ℓ + πr₁² + πr₂²,

where ℓ is the slant height of the frustum.

Since the frustum is a right frustum, the slant height ℓ can be found using the Pythagorean theorem:

ℓ = √(h² + (r₁ - r₂)²)

Substituting the given values, we have:

ℓ = √(4² + (12 - 9)²)

 = √(16 + 9)

 = √25

 = 5

Now we can calculate the total surface area:

A = π(12 + 9)(5) + π(12²) + π(9²)

 = π(21)(5) + π(144) + π(81)

 = 105π + 144π + 81π

 = 330π square units

Finally, to find the product of the volume and total surface area, we multiply the two values:

VA = (444π)(330π)

  ≈ 146520π²

Therefore, the product of the volume and total surface area of the given right conical frustum is approximately 146520π².

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Given:

The figure and dimensions of the triangular prism.

The base is an isosceles triangle

To find:

The area of the triangular prism.

Solution:

The area of a triangle is:

\(A_1=\dfrac{1}{2}\times base\times height\)

The base of the triangle is 24 cm and the height is 35 cm. So, the area of a triangular base (in sq. cm) is:

\(A_1=\dfrac{1}{2}\times 24\times 35\)

\(A_1=12\times 35\)

\(A_1=420\)

The bases of the triangular prism are same. So, the area of the other triangular base is \(A_2=420\) sq. cm.

The sides of the base triangle are 37 cm, 37 cm and 24 cm. So, the perimeter of the base triangle is:

\(P=37+37+24\)

\(P=98\)

Now, the curved surface area of the prism is:

\(A_3=P\times h\)

Where, P is the base perimeter and h is the height of the prism.

The base perimeter of the triangular prism is 98 cm and the height is 48 cm. So, the curved surface area is:

\(A_3=98\times 48\)

\(A_3=4704\)

Now, the total  area of the triangular prism is:

\(A=A_1+A_2+A_3\)

\(A=420+420+4704\)

\(A=5544\)

Therefore, the area of the given triangular prism is 5544 sq. cm.

Answer: The first or the second point (- 2, - 3) or (- 2, 1)

Step-by-step explanation:

Ok, a relation (x, y) is a function only if, for each value x in the domain, we have only one value y in the range such that:

f(x) = y.

Here we have the pairs:

(- 2, - 3), (- 2, 1), (- 4, 3), (0, 4), (1, 1), and (2, 3).

Here, for the value x = -2, we have two different values of y.

y = 1 and y = 3.

So this is not a function, then if we want that this relation becomes a function, we must remove the first or the second point.

Answer:

I think B

Step-by-step explanation:

The value of segment BC = 9.8 and the value of BD = 7 in the given right triangle ABC.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

Given that the length of the segment CA = 14.

As BD is the bisector of line CA we have:

CD = 7 and

DA = 7

Given that angle C = 45 degrees.

Then,

tan C = opposite side/ adjacent side

tan (45) = BD / 7

1 (7) = BD

BD = 7

Using the Pythagorean Theorem we have:

BC^2 = BD^2 + CD^2

Substituting the values of BD = 7 and CD = 7 we have:

BC^2 = 7^2 + 7^2

BC^2 = 49 + 49

BC = 9.8

Hence, the value of segment BC = 9.8 and the value of BD = 7 in the given right triangles ABC.

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The Volume of the cylinder is 90π cubic inches.

The volume of a right circular cylinder, we can use the formula:

Volume = π * r^2 * h

Where π is the mathematical constant pi (approximately 3.14159), r is the radius of the cylinder's base, and h is the height of the cylinder.

In this case, the radius is given as 3 inches and the height is given as 10 inches. Let's substitute these values into the formula:

Volume = π * (3^2) * 10

      = π * 9 * 10

      = 90π cubic inches

Therefore, the volume of the cylinder is 90π cubic inches.

In the answer choices provided:

a. 30π in³

b. 60π in³

c. 90π in³

d. 120π in³

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Answer:

Just simple calculator work which is around 33.3333 infinite or rounded 33.3 times.

Step-by-step explanation:

Calculator

Answer:

5/18

Step-by-step explanation:

The total number of horses present is 9

The probability that the first selected horse is tan is 4/9

So , now for the second choice , we are left with 8 total horses of which 5 is brown

The probability is 5/8

So the joint probability is the product of this two

That will be;

5/8 * 4/9 = 5/18

Answer:

C

Step-by-step explanation:

for Japan and South Korea it's more about high tech industry and services. but they also import all the resources other countries lack.

Answer:

K is -12/5

k is also 28/5

Step-by-step explanation:

Here, we want to solve the equation

|5k-8| = 10(2)

5k-8 = 20

5k = 20 + 8

5k = 28

k = 28/5

or

5k-8 = -20

5k = -20 + 8

5k = -12

k = -12/5

Answer:

37.5 Units

Step-by-step explanation:

The exercise involves finding the product C = AB, where matrix A is given by [2 9] and matrix B is given by [3 6 1]. We need to perform the matrix multiplication to obtain the resulting matrix C.

Let's calculate the matrix product C = AB step by step:

Matrix A has dimensions 2x1, and matrix B has dimensions 1x3. To perform the multiplication, the number of columns in A must match the number of rows in B.

In this case, both matrices satisfy this condition, so the product C = AB is defined.

Calculating AB:

AB = [23 + 912 26 + 94 21 + 95]

[103 + 612 106 + 64 101 + 65]

Simplifying the calculations:

AB = [6 + 108 12 + 36 2 + 45]

[30 + 72 60 + 24 10 + 30]

AB = [114 48 47]

[102 84 40]

Therefore, the product C = AB is:

C = [114 48 47]

[102 84 40]

In summary, the matrix product C = AB, where A = [2 9] and B = [3 6 1], is given by:

C = [114 48 47]

[102 84 40]

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Answer:

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The type of variable that represents the names of the automobile manufacturers would be the categorical variable.

A variable is defined as the quantity that may change within the context of a mathematical problem, research work or an experiment.

There are various types of variables that include the following:

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The account would be worth approximately $62,420.80, which includes both the initial investment of $36,000 and the accumulated interest.

Assuming that the $200 has been added each month for the past 15 years, the total amount of money invested would be $200 x 12 months x 15 years = $36,000.
To calculate the amount of money earned from the 4% interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the principal (the initial investment), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
Plugging in the values, we get:
A = $36,000(1 + 0.04/12)^(12*15)
Simplifying, we get:
A = $36,000(1.0033)^180
A = $36,000(1.7328)
A = $62,420.80
Therefore, after 15 years, the account would be worth approximately $62,420.80, which includes both the initial investment of $36,000 and the accumulated interest.

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The balance of the account after 15 years is given as follows:

$49,218.

The balance of an account, considering periodic deposits, is given as follows:

\(B = \frac{P\left(\left(1 + \frac{r}{n}\right)^{nt}-1\right)}{\frac{r}{n}}\)

The meaning of each parameter is given as follows:

The parameter values for this problem are given as follows:

P = 200, r = 0.04, n = 12, t = 15.

Hence the balance of the account after 15 years is given as follows:

\(B = \frac{P\left(\left(1 + \frac{r}{n}\right)^{nt}-1\right)}{\frac{r}{n}}\)

\(B = \frac{200\left(\left(1 + \frac{0.04}{12}\right)^{12 \times 15}-1\right)}{\frac{0.04}{12}}\)

B = 49,218.

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Answer:

171 \(in^2\)

19.5 \(in^2\)

Step-by-step explanation:

To find the area of a parallelogram, one uses the following formula,

\(A=(base)(hieght)\)

Substitute in the given values, and find the area of the parallelogram.

1.

Base = 16

Hieght = 11

 \(Area=(base)(height)\\= (11)(16)\\=176\)

2.

Base = 1.5

Hieght = 13

\(Area=(base)(hieght)\\=(1.5)(13)\\=19.5\)

Answer: 11.6

Step-by-step explanation: plug in x for 4. 3.2(4)-1.2 = 11.6

Mathematical proofs are used to prove or disprove mathematical statements.

The theorems to use are:

From the question, we have: \(\triangle ABC\)

This means that, ABC is a triangle

Also, we have:

BP || AC

This means that lines BP and AC are parallel

So, the following angles are congruent by alternate angle theorem

The angles on a straight line add up to 180 degrees.

So, we have:

\(\angle 4 + \angle 1 + \angle 5 = 180\)

By substitution, the above equation becomes

\(\angle 2 + \angle 1 + \angle 3 = 180\)

Rewrite the equation as:

\(\angle 1 + \angle 2 + \angle 3 = 180\)

Hence, the statement that \(\angle 1 + \angle 2 + \angle 3 = 180\) has been proved

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The fish population, initially weighing 2 million tons, is being depleted by fishing at a rate of 14 million tons per year. At this rate, all the fish will be gone in approximately 251 years. This rate can be calculated by equating the rate of increase due to the proportionality constant with the fishing rate.

To maintain a constant mass of fish, the fishing rate should be adjusted to remove fish at a constant rate. This rate can be calculated by equating the rate of increase due to the proportionality constant with the fishing rate.

By setting the rate of increase equal to zero, we find that the fishing rate should be approximately 2.667 million tons per year. This would ensure that the mass of fish remains constant.

The rate of increase of the fish population is proportional to its mass, with a proportionality constant of Sy. This can be expressed as dM/dt = Sy, where dM/dt represents the rate of change of mass over time.

In this case, dM/dt is given as -14 million tons per year because fishing removes fish from the population.

To find the time it takes for all the fish to be gone, we can use the formula:

t = (M0 - M) / (-dM/dt)

where t is the time in years, M0 is the initial mass of fish, M is the final mass (0 in this case), and -dM/dt is the fishing rate.

Substituting the given values, we have:

t = (2 million tons - 0) / (-14 million tons/year) = 2/14 = 0.143 years

Converting this to years, we get:

t = 0.143 years * 365 days/year = 52.195 days ≈ 52 years

Therefore, all the fish will be gone in approximately 251 years.

To maintain a constant mass of fish, the fishing rate should be adjusted to remove fish at a constant rate. Since the rate of increase is proportional to the mass of fish, we can set the rate of increase equal to zero and solve for the fishing rate.

0 = Sy

Solving for y, we find that y = 0.

Now we can use the formula for the fishing rate, which is -dM/dt. Since y = 0, we have:

-dM/dt = 0

dM/dt = 0

Therefore, the fishing rate should be approximately 2.667 million tons per year to maintain a constant mass of fish.

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Answer:

37.50

Step-by-step explanation:

2/5x + 15 = 30

2/5x = 15

x = 15 ( 5/2)

x = 37.50

When you add a fitting this new model, the estimated coefficient for height must be Different, but still positive.

If there is a  positive correlation but negative regression coefficient it means that the influence or the effect of the intercorrelations that exist between the independent variables may be negative when there is a positive correlation coefficient that exist between the variable and the dependent variable.

Therefore  When you add a fitting this new model, the estimated coefficient for height must be Different, but still positive.

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Suppose you have an SLR model for predicting IQ from height. The estimated coefficient predictor for age to create an MLR model. After for height is positive. Now, we add a fitting this new model, the estimated coefficient for height must be:

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The length οf diameter οf the given sphere is 18m.

A sphere is a three-dimensiοnal οbject which is rοund in shape. It has nο edges οr vertices. The sphere can be defined in three axes, thοse are x-axis, y-axis and z-axis.

The given diagram is a sphere.

Given that,

The surface area οf the sphere is  1017.36 m²

Fοrmula fοr surface area οf the sphere = 4πr² where r is the radius and π=3.14

Equating both we get,

4πr² = 1017.36

[ dividing bοth sides by 4 ]

⇒πr² = (1017.36)/4

⇒πr² = 254.34

[putting the value of π]

⇒r² = 254.34/ 3.14

⇒r² = 81

⇒r =± 9

As radius cannot be a negative value so we take r=9

Sο the radius οf the sphere is 9 m

Diameter = 2× radius =2×9= 18m

Hence, diameter οf the given sphere is 18m.

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In a case whereby A group of students formed a circle during a game. The circumference of the circle was about 43.96 feet, and the diameter of the circle was 14 feet the expression that best represents the value of pi is  43.96 feet/ 14 feet.

The concept that will be use here is Circumference. we were given Circumference of the circle  as 43.96 feet

where the Diameter of the circle is  14 feet, then we can find the Circumference of the circle  as( πd)

Then ( πd) = 43.96 feet

π= 43.96 feet/ 14 feet

Therefore, option C is correct.

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The linear equation is z = 450 - 30 x, where z is the number of pages Lourdes has left to read after x days

We need to write a linear equation to represent the number of pages

Lourdes has left the number of pages to read after x days

Lourdes reads 30 pages each day

Lourdes will read for x days

The number of pages Lourdes will read in x day = 30 x

The left pages will be the difference between the total pages of the

book and the pages Lourdes read.

After 9 days Lourdes completes 3/5 of the total number of pages.

So the  number of pages Lourdes reads after 9 days = 30×9 = 270 pages.

Let The total number of pages in the book = y

Therefore 3/5 × y = 270.

So y = 270 × (5/3) = 450 pages.

The total number of pages in the book = 450 pages.

Lourdes will read 30 x in x days

The number of pages left = 450 - 30 x

Assume that z represents the number of pages Lourdes has left to read after x days

z = 450 - 30 x

The linear equation is z = 450 - 30 x, where z is the number of pages Lourdes has left to read after x days

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The choose a. 3x+12

\(( \frac{f}{g} )(x) = \frac{3 {x}^{2} - 48 }{x - 4} = \frac{3( {x}^{2} - 16) }{x - 4} \\ \\ = \frac{3(x - 4)(x + 4)}{x -4} \\ \\ = 3(x + 4) \\ = 3x + 12\)

I hope I helped you^_^

After evaluating (f/g)(x) is equal to 3x + 12.

The correct option is (A).

An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable (the dependent variable). Functions may be found everywhere in mathematics, and they are essential for building physical connections in the sciences. The modern definition of function was first proposed in 1837 by the German mathematician Peter Dirichlet: A variable y is said to be a function of the independent variable x if there is a correlation between them such that a rule determines a particular value of y whenever a numerical value is assigned to x.

As per the given data:

We are given two functions, f(x) and g(x)

f(x) = 3x² - 48

g(x) = x - 4

We have to find out (f/g)(x).

For finding out  \(\frac{f}{g}(x)\):

= f(x) / g(x)

= \(\frac{3x^2 - 48}{x - 4}\)

= \(\frac{3(x^2 - 16)}{x-4}\)      {a² - b² = (a + b)(a - b)}

= \(\frac{3(x-4)(x+4)}{(x-4)}\)

= 3(x+4)

= 3x + 12

Hence, after evaluating (f/g)(x) is equal to 3x + 12.

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The probability:  P(A, A) if two cards are randomly selected with replacement is one ninth. Option B

You should be aware that probability is the chance of occurance of an event.  the probability of an event is written thus

P(E) = Number of required outcome divided by the total number of possible outcomes

The possible outcomes are the spelling the word ADD,

The probabilities are 1/3, 1/3, 1/3 respectively.

So, P(A, A) if two cards are randomly selected with replacement will be

P(A, A) = 1/3 * 1/3

Therefore the probability of the event is 1/9

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Answer: one ninth i took the test

Step-by-step explanation:

Number of strings of seven hexadecimal digits that do not have any repeated digits and at least one repeated are required. The hexadecimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.

Number of strings of seven hexadecimal digits that do not have any repeated digits. There are sixteen different digits.The first digit can be any one of the sixteen different digits. Hence, the first digit can be chosen in 16 ways. Once the first digit has been chosen, there are only fifteen remaining digits. Hence, the second digit can be chosen in 15 ways. Similarly, the third digit can be chosen in 14 ways, the fourth digit can be chosen in 13 ways, and so on. Thus, the number of ways that a string of seven hexadecimal digits can be formed without any repeated digits is given by 16×15×14×13×12×11×10 = 111, 767, 040

Number of strings of seven hexadecimal digits that have at least one repeated digit is required. There are two ways to approach the solution of this problem:By finding the number of strings that do not have any repeated digits and subtracting this from the total number of strings of seven hexadecimal digits.By counting the number of strings that have at least one repeated digit directly.

Method 1 : To find the number of strings that do not have any repeated digits, we have found in part (a) to be 111, 767, 040. The total number of strings of seven hexadecimal digits is 167, 772, 160. Hence, the number of strings of seven hexadecimal digits that have at least one repeated digit is given by:167, 772, 160 – 111, 767, 040 = 56, 005, 120

Method 2 :By counting the number of strings that have at least one repeated digit directly, we shall apply the principle of inclusion and exclusion. Let A1, A2, A3, A4, A5, A6, A7 denote the events that the first, second, third, fourth, fifth, sixth and seventh digits repeat, respectively. The number of strings in which only the first and second digits repeat is 16×15×14×13×12×11×1 = 24,883,200. Similarly, the number of strings in which only the first and third digits repeat is 24, 883, 200. There are fifteen possible pairs of distinct digits and for each such pair, there are 10 ways to place the two digits into the seven positions, i.e., ten different arrangements of the pair of digits. Hence, the number of strings in which exactly two digits repeat is given by 15×10×16×15×14×13×1 = 56,160,000. There are six different ways in which three distinct digits can be selected from sixteen. For each choice of three distinct digits, there are three possible ways that the digits can be arranged in the string. This gives a total of six×3×16×15×14×1×1×1 = 60,480. There are no strings with four or more distinct digits repeating. Thus, by the principle of inclusion and exclusion, the number of strings of seven hexadecimal digits with at least one repeated digit is given by24, 883, 200+24, 883, 200−56, 160, 000+60, 480=56,005,120

The number of strings of seven hexadecimal digits that do not have any repeated digits is 111, 767, 040. The number of strings of seven hexadecimal digits that have at least one repeated digit is 56, 005, 120.

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Answer:

2x-10

Step-by-step explanation:

Multiply BOTH x and -5 by 2

Answer:

2x-10

Step-by-step explanation:

2(x-5)

2*x - 2*5

2x-10

Hope u mark me as the brainliest!

Answer:

Step-by-step explanation:

The distance between two points can be found by using the formula

\(d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ \)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-4,-1) and (-3,-1)

The distance between them is

\(d = \sqrt{ ({ - 4 + 3})^{2} + ({ - 1 + 1})^{2} } \\ = \sqrt{ ({ - 1})^{2} } \\ = \sqrt{1} \)

We have the final answer as

1 unit

Hope this helps you