define a positive integer n to be a factorial tail if there is some positive integer m such that the decimal representation of m! ends with exactly n zeroes. how many positive integers less than 1992 are not factorial tails?

A function that depends on another function is referred to as a composite function.

Let's say the price of an item is $1

Scenario #1 - 40% off $1  = 40 cents OFF

The discounted price = 60 cents

Now the 10% off of 60 cents

60-6 = 54 cents.

Scenario #2 - 10% of $1

The discounted price = 10 cents

100(cents) - 10 = 90 cents

Now the 40% off of 90 cents

90-36 = 54 cents

Let's try another value to confirm

Let's say the price of an item is $2

Scenario #1  - 40% off $2 = 80 cents OFF

200-80= 120 = $1.20

Now the 10% off of $1.20

120-12= 108 = $1.08

Scenario #2 - 10% off $2 = 20 cents OFF

200-20 = 180= 1.80

Now the 40% off of $1.80

180-72 = 108 = 1.08

The complete question is,

A store offers a discount of 40 off any one regular-priced item. employees also get 10% off any purchases. in which order should the discounts apply so that the employee pays the least amount?

A. Employee discount then store discount

B. They are both the same

C. Store discount then employee discount

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The true statement is:

The asymptote of g(x) is the asymptote of f(x) shifted three units down.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x) = [tex](2/5)^x[/tex]

and, g(x) ==  [tex](2/5)^x[/tex] - 3

Now, Using translation the '-3' in g(x) shows the Vertical Translation down by 3 units.

Hence, The asymptote of g(x) is the asymptote of f(x) shifted three units down.

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The volume of this rectangular prism is (x+5) * (x+1) * x = x^3 + 6x^2 + 6x + 5.

Rectangular Prism:

A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four lateral faces). All the faces of the prism are rectangular in shape. Hence, there are three pairs of identical faces here.

The Volume of a Rectangular Prism Formula is,

The volume of a Rectangular Prism (V) = l × b × h

Where,

“b” is the base length of the rectangular prism

“l” is the base width of the rectangular prism

“h” is the height of the rectangular prism

The formula for the volume of a rectangular prism is length x width x height. So, the volume of this rectangular prism is (x+5) * (x+1) * x = x^3 + 6x^2 + 6x + 5.

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By using the properties of real numbers the given expression can be written as  -8y.

What is solving an expression?

Another word for "solving a math problem" is "simplifying an expression." When you simplify an expression, your goal is essentially to make it as simple as you can. There shouldn't be any additional multiplying, dividing, adding, or subtracting to be done at the conclusion.

Given:

The given expression is, [tex]\frac{4}{3}(-6y)[/tex]

According to the distributive property of real numbers, if a, b, c are three real numbers the,

a(bc) = (ab)c

Using the associative property of multiplication, the given expression can be written as,

[tex]\frac{4}{3}(-6y) = (\frac{4}{3}*(-6))*y \\\frac{4}{3}(-6y) = (\frac{-24}{3} )*y\\\frac{4}{3}(-6y) = -8y[/tex]

Hence, by using the properties of real numbers the given expression can be written as  -8y.

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The solution to the given initial-value problem is  x(t) = c1(e-ωt - eωt) = 2c1 sin ωt

The given initial-value problem is a second-order differential equation: d2x dt2 + ω2x = f0 sin ωt, x(0) = 0, x '(0) = 0

First, we can solve the homogeneous equation d2x dt2 + ω2x = 0 using the method of characteristic equation. The characteristic equation is r2 + ω2 = 0, which has two solutions r1 = -ω, r2 = ω.

The general solution to the homogeneous equation can be expressed as:

x(t) = c1e-ωt + c2eωt

Next, we can solve the non-homogeneous equation d2x dt2 + ω2x = f0 sin ωt. Since the right-hand side of the non-homogeneous equation has a sinusoidal form, we can use the method of variation of parameters to solve it.

The particular solution can be expressed as:

x(t) = A sin ωt + B cos ωt

By substituting the initial conditions, we can get:

A = 0, B = 0

Therefore, the solution to the given initial-value problem is:

x(t) = c1e-ωt + c2eωt

The constant c1 and c2 can be determined by the initial conditions:

x(0) = c1 + c2 = 0

x'(0) = -ωc1 + ωc2 = 0

Therefore, c1 = -c2 and c1 + c2 = 0.

Hence, the solution to the given initial-value problem is:

x(t) = c1(e-ωt - eωt) = 2c1 sin ωt

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The rate of change of the angle of elevation is -2π/3 radians/second.

We can use the tangent ratio to solve this problem. Since the rope is attached to the boat, we can draw a right triangle with the rope as the hypotenuse. The angle of elevation is the angle formed by the rope and the horizon.

The pulley is 5 feet above the water level, so the length of the opposite side (the side adjacent to the angle) is 5 feet. The length of the hypotenuse is 12 feet, since the boat is 12 feet from the dock.

Using the tangent ratio, we can calculate the angle of elevation:

tan(θ) = opp/hyp = 5/12

θ = arctan(5/12) = 0.927 rad

Now, since the rope is being pulled in at 3 ft/sec, the length of the hypotenuse is decreasing at a rate of 3 ft/sec. Therefore, the rate of change of the angle of elevation is:

rate of change of θ = -(3 ft/sec) / (12 ft) = -2π/3 radians/second

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For keyboard navigation, use the up/down arrow keys to select an answer is (b) 373.33

By letting users know where they are while they use the keyboard to browse a page, keyboard focus aids keyboard accessibility. Even those who have trouble using a touchpad or mouse can use a computer thanks to keyboard navigation.

The sequence in which interactive objects acquire keyboard focus is crucial for keyboard users navigating the page. The order of the keyboard navigation must be reasonable and obvious by default. This typically means that it moves from left to right and from top to bottom of the page.

This typically means that the header appears first, followed by the main navigation, page navigation, and finally the footer. The web page's source code determines this navigation order as well as the reading order for screen readers.

For keyboard navigation, use the up/down arrow keys to select an answer is (b) 373.33

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Answer:

tenth

Step-by-step explanation:

The age of my sister and her three children in 4 years will be 70 years

The age is added in 6 years to get 90 years> the addition is done as follows

Sister + 6 + Child1 + 6 + Child2 + 6 + Child3 + 6 + Child4 + 6 = 90 years

Sister + Child1 + Child2 + Child3 + Child4 + 6 + 6 + 6 + 6 + 6 = 90

Sister + Child1 + Child2 + Child3 + Child4 + 6 * 5 = 90

Sister + Child1 + Child2 + Child3 + Child4 = 90 - 30

Sister + Child1 + Child2 + Child3 + Child4 = 60

In 4 years the age will be

Sister + Child1 + Child2 + Child3 + Child4 + 4 * 5 = 90

Sister + Child1 + Child2 + Child3 + Child4 = 90 - 20

Sister + Child1 + Child2 + Child3 + Child4 = 70

in 4 years the ages will be 70 years

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Grade 7 maths includes integers, shapes, and symmetry etc. that is incorporated with the earlier study of previous grades.

Grade 7 math covers many topics, including: number sense and operations, geometry, data analysis, probability and statistics, expressions and equations, and problem solving. Number sense and operations involves understanding the properties of integers, rational numbers, and real numbers, and how to use them in operations and equations. Geometry focuses on understanding the properties of shapes and angles, and how to measure, construct, and classify them. Data analysis involves collecting, organizing, and interpreting data, as well as understanding the concept of probability. Expressions and equations involves solving equations and manipulating algebraic expressions. Finally, problem solving involves using the knowledge from all of the topics to solve real-world problems. Grade 7 math builds on the fundamentals learned in earlier grades, and is essential for success in math classes in the future.

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The number of cupcakes and brownies Fwam could have purchased is 1.75b + 4.50c ≤50.

The word "inequality" is used in mathematics to refer to expressions that relate variables (for example the prices of different products) using symbols that are different from =, which is used in equations. Due to this, inequalities might have numbers, letters representing variables, and symbols such as ≤, <, >.

1. List the variables

b = cupcakes

c = brownies

4.50 = price of the cupcakes

1.75 = price of the brownies

50 = total money

2. Relate the variables

1.75b + 4.50c ≤50

Each product should be multiplied by its price

The total money can be equal to or less than 50 (≤)

The products should be added

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The people who are interviewed constitute a convenience sample.

If the survey company is interviewing anyone who is available in the shopping mall without using any systematic method for selecting the participants, it would be considered a convenience sample.

In a convenience sample, the sample is selected based on ease of access to the participants, and it may not be representative of the entire population. This type of sampling can lead to bias in the sample, as the views of people who happen to be available in the mall at the time may not be representative of the views of the entire population.

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The sample correlation coefficient, is represented as  r, measures the strength of correlation  and direction of the linear relationship between two variables. It ranges from -1 to 1. The closer the coefficient is to -1, the stronger the negative correlation, the closer it is to 1, the stronger makes the  positive correlation reach towards its closer and the closer towards to the expectancy to 0, the weaker the correlation.

The correlation coefficient does not indicate the cause and effect relationship between the variables, just the association between them.

A positive correlation tells us  that as one variable increases with respective its the other variable also increases, and a negative correlation means that as one variable increases with respective to its the other variable decreases.

So, the value of the sample correlation coefficient between the  rates of admit and the -yr grad rate . rate can indicate if these variables are positively or negatively done as  correlated and how strong is this correlation occurs.

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(a) A system of two equations, x=2 and y=3, is needed to express (2,3) in R2. (b) No, only two equations can express (2,3) in R2. (c) The maximum number of distinct equations that can be added is three. (d) Yes, the general form for the equations is x-2=0, y-3=0, and z=0.

(a) The smallest number of equations you would need is two. The system of linear equations would be:

x + 2y = 6

2x + 4y = 12

(b) Yes, you can add one more equation to the system in (a) so that the new system still has the unique solution (2,3). The equation would be:

3x + 6y = 18

(c) The maximum number of distinct equations you can add to your system in (a) to still maintain the unique solution (2,3) is three. The equations would be:

x + 2y = 6

2x + 4y = 12

3x + 6y = 18

(d) Yes, there is a general form for the equations in (c). The general form is:

ax + by = c, where a, b, and c are constants.

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[tex] \sf \frac{2x}{5} = 4 \\ \sf \: 2x = 4 \times 5 \\ \sf \: 2x = 20 \\ \sf \therefore \: x = 10[/tex]

Answer: X stands for 10

Step-by-step explanation:

If we subsitute X for 10, and convert 2/5 to 0.4 we get, 10x0.4 = 4

To convert a fraction to a decimal, you simply divide the numerator by the denominator.

Answer: the answer is negative  5

Step-by-step explanation:

If Last year, Christine had $20,000 to invest. The amount that she invest in each account is First account $16,000 and Second account: $4,000.

Let x represent the amount Christine invested in an account that paid 8% interest

Let y represent  the amount Christine invested in an account that paid 10% interest

x + y = 20,000    

.8x + .010y = 1920

Multiply each sides of this equation by 100 to  remove  the decimal points.

8x + 10y = 192,000

8(20,000-y) + 10y = 192,000

160,000 - 8y + 10y = 192,000

2y = 32,000

y = 32,000/2

y = $16,000

So,

x = 20,000 - 16,000

x = $4000

Therefore the First account is $16,000 and Second account is $4,000.

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a) The velocity and position functions are given as follows:

b) The particle is at rest when: t = kπ, k = ± 1, ± 2, ± 3, ...

The acceleration function for this problem is defined as follows:

a(t) = cos(t).

The velocity function is the integral of the acceleration function, hence it is given as follows:

v(t) = sin(t).

(as the integral of cos(t) is sin(t).)

The particle will be at rest when:

v(t) = 0.

Hence:

sin(t) = 0

t = arcsin(0)

t = kπ, k = ± 1, ± 2, ± 3, ...

The position function is the integral of the velocity function, hence it is given as follows:

s(t) = -cos(t) + 3.

As:

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The surface area of the hemispherical vessel is 715.92 square centimeter and the cost to paint is Rs. 3579.62.

An object's surface area is the total area that all of its surfaces occupy. Different 3D shapes in geometry have various surface areas. There are two groups for the surface area:

Surface area of the lateral Surface that is curved Surface area overall.

Given that the external diameter of the hemispherical vessel is 16cm, hence the radius is 8cm.

The internal diameter of the hemispherical vessel is 12cm, hence the radius is 6cm.

The total surface area of the vessel is given by the following formula:

[tex]SA= 2\pi R^2 + 2\pi r^2 + \pi (R^2 - r^2)\\\\SA= 2(3.14)(8)^2 + 2(3.14)(6)^2 + (3.14)(8^2 - 6^2)\\\\SA= 401.92 + 226.08 + 87.92\\\\SA= 715.92[/tex]

The total surface area of the vessel is 715.92 square centimeters.

The cost to paint 1 square centimeter is Rs. 5, hence the cost to paint 715.92 square centimeters is:

C = (715.92)(5)

C = 3579.6

Hence, the cost to paint 715.92 square centimeters is Rs. 3579.62.

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Answer:

Sin A / A = Sin B / B         Law of Sines

Sin 73 / X = Sin 59 / 18     Application of Law of Sines

X = Sin 73 / Sin 59 * 18 = .956 / .857 * 18 = 20.1

The total number of starting lineups (of 5 players) can coach yells lot make, if the starting lineup can't contain both bob and yogi is 672.

An official list of the players who will take part in the event when the game starts is known as a starting lineup in sports. The players who are in the starting lineup are frequently referred to as starters, while the rest are known as bench players or replacements.

Case 1: Bob starts (and Yogi doesn't). In this case, the coach must choose 4 more players from the 10 remaining players (remember that Yogi won't play, so there are only 10 players left to select from). Thus there are 10C4 lineups that the coach can choose.

⇒ ¹⁰C₄ = 10!/4!(10-4)! = 10!/4!6!

⇒ ¹⁰C₄ = (10*8*9*7)/(4*3*2*1)

⇒ ¹⁰C₄ = 210

Case 2: Yogi starts (and Bob doesn't). As in Case 1, the coach must choose 4 more players from the 10 remaining players. So there are 10C4 lineups in this case.

⇒ ¹⁰C₄ = 210

Case 3: Neither Bob nor Yogi starts. In this case, the coach must choose all 5 players in the lineup from the 10 remaining players. Hence there are 10C5 lineups in this case.

⇒ ¹⁰C₅ = 10!/5!(10-5)! = 10!/5!5!

⇒ ¹⁰C₅ = (10*8*9*7*6)/(5*4*3*2*1)

⇒ ¹⁰C₅ = 252

To get the total number of starting lineups, we add the number of lineups in each of the cases:

Case 1 + Case 2 + Case 3

= 210 + 210 + 252 = 672

The total number of starting lineups (of 5 players) can coach yells lot make, if the starting lineup can't contain both bob and yogi is 672.

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Simplest radical form means the radical form of a number or algebraic expression in simplest terms.

The simplest radical form of the square root of 16 is √16. Generally, the radical form of the square root of a number can be written, if we know the prime factorization of a number. Thus, the prime factorization of 16 is 2×2×2×2.

Square root of 16 is +4 or -4. Since -4 is not a natural number, the square root can be described as an integer.

16 (sixteen) is the natural number following 15 and preceding 17. 16 is a composite number, and a square number, being 42 = 4 × 4.

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Answer: We can find the inequalities. One inequality has a line with y-intercept 2 and slope -1. The inequality is y >= -x + 2.

Step-by-step explanation:

Note that after the expression 2x³-5x²-19x+42, has been factorized, we have (x−2)(x+3)(2x−7).

Factorization or factoring in mathematics is the process of expressing a number or any mathematical object as a product of numerous factors, generally smaller or simpler objects of the same sort.

The polynomial 2x³-5x²-19x+42 can be factorized by using the rational root test. To apply this test first we need to find at least one rational zero.

In this case one rational zero is x=2.

This means that we can divide polynomial 2x³-5x²-19x+42 by x−2 (the factor theorem)

That is:

2x³-5x²-19x+42/ x-2

= 2x² - x - 21, this means that

2x³-5x²-19x+42 =  (2x² - x - 21) * (x-2)

From the above, our constants are given as:

a = 2, b = -1 and c = 21

Multiply the constant terms by the leading coefficient.

a *x = -42

Find out two number that multiply to a*c = -42 and add b = -1

Next we identify all pairs of numbers with a product of -42. They are:

Next we find all factor pair that sum up to b = -1. It is given as 6 +-7 which is identical to item 8 above.

Next, replace the middle term -1x with 6x-7x to get:

(2x²  −x−21) * (x-2) =(2x²  +6x−7x−21) * (x-2)

If we thus apply factoring by grouping, and factor 2x out of the first group and -7 out of the second group, we have: (2x-7) (x+3) (x-2).

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Full Question:

Factorise 2x³-5x²-19x+42

By using trigonometric relations, we can see that the angle x on the right triangle is:

x = 62.96°

On the image, we can see a right triangle, and we want to find the value of x, which is the measure of an angle on the right triangle.

On the given triangle we can see that the hypotenuse measures 77 units, and the adjacent cathetus to the angle has a measure of 35.

Then we can use the trigonometric relation:

cos(x) = (adjacent cathetus)/(hypotenuse)

Replacing the values that we know:

cos(x) = 35/77

Now we can apply the inverse cosine function in both sides:

Acos(cos(x)) = Acos(35/77)

x = Acos(35/77) = 62.96°

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The probability that in the next game of serenity bowls, her score will be between 183 and 218 is 73.14%

Given that,

Mean = 195

Standard deviation = 14

Thus, the probability between 183 and 218 is the ρ value of z when x = 195

Subtracting by the ρ value of z when x = 183

so, x = 218

z = 218-195/14 = 1.64

when x = 183

z = 183-195/14= -0.85

Thus, z value is 1.64 then the probability is 0.94950 and when z value is -0.85 then the probability is 0.21886

Now, 0.94950 - 0.21886 = 0.73064

Therefore, The probability that in the next game of serenity bowls, her score will be between 183 and 218 is 73.14%

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Equating the total costs of the two rental companies, they would cost the same amount after 625 driving miles.

An equation is a mathematical statement that claims that two or more mathematical expressions are equivalent or equal.

Equations use the equation symbol (=) to depict the equality of the expressions.

                                  Company A    Company B

Fixed rental charge         $75                 $100

Rental charge per mile  $0.07              $0.03

Let the number of miles driven = m

Total cost of Company A's rental = 75 + 0.07m

Total cost of Company B's rental = 100 + 0.03m

For the cost to be the same, 75 + 0.07m = 100 + 0.03m.

Solving for m:

75 + 0.07m = 100 + 0.03m

0.07m - 0.03m = 100 - 75

0.04m = 25

m = 625

Thus, for the two car companies' rental cost to be the same amount, one would rent a car for 625 miles.

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To make the polynomial monic, divide even by leading term first.

Then, in order to create an equation even without linear element, replace x = y a12 for the supplied values of x2 + a1x + a0.

A monic polynomial in algebra is a univariate polynomial with a single variable and a leading coefficient of 1. Its leading coefficient is the highest degree nonzero coefficient.

x3=y3 and y2=x2+xy+y2.

Finding a common denominator allows us to determine that x2 + y2 + xy=1 if xy+yx=1.

By multiplying by xy:

x2+y2=−xy

move every term to the left:

x2+xy+y2=0

Consequently, x3y3=(xy)(x2+xy+y2)=(xy)

x/y+y/x+1=0

=>(x²+y²+xy)/xy=0/1

=>x²+xy+ y²=0——(1)

Now, Since,x³-y³=(x-y)(x²+xy+y²)

=>x³ -y³=(x-y)(0). [from equation (1)]

=>x³ -y³=0,Ans.

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Answer:

Step-by-step explanation:

The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the polynomial is 4w - 1. The highest power of the variable w is 1, so the degree of the polynomial is 1.Therefore, the correct answer is A) 1