question: 49a+26+11–3–6

The prove of given limit lim θ → 0 ( sin θ / θ ) = 1 is shown in below.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

⇒ lim θ → 0 ( sin θ / θ ) = 1

Here, The form of given limit is 0/0, so we can apply the L - Hospital Rule.

⇒ lim θ → 0 ( sin θ / θ ) = 1

Take LHS;

⇒ lim θ → 0 ( d/dθ (sin θ)/ dθ/dθ )

⇒ lim θ → 0 ( cos θ / 1 )

⇒ ( cos 0 )

⇒ 1

⇒ RHS

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Answer:

Step-by-step explanation: infinity or undefined.

Tim received 8 SMS on Monday, 4 emails on Thursday, and 0.52 of the communications were emails, which is the solution to (a), (b), and (c).

When two sets of data are joined and their frequencies are combined, a composite bar chart is utilized. Two pieces of data—emails and texts—are included in this inquiry, but they both fall under the same heading, "messages." With regard to question (a), it is clear from the diagram that Tim got 8 texts on Monday. In order to answer question (b), we must determine how many emails Tim received on Thursday. To do this, we must look at the bar for Thursday and divide the total number of texts by the total number of messages to determine the number of emails received. 15-11=4, indicating that Tim received 4 emails on Thursday.

given

Tim for five days, total the emails received, and then determine the percentage of emails relative to messages.

Total messages: 14+16+14+15+14=73.

Emails totaled: 6 + 10 + 10 + 4 + 8 = 38

Email to message ratio is equal to 0.52.

Emails made up 0.52 of the messages, therefore.

Tim got 8 texts on Monday, 4 emails on Thursday, and 0.52 of the messages were emails, according to an analysis of the composite bar chart we used to determine the answers to the three questions.

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The complete question is :- The composite bar chart Messages received shows the number of messages Tim received each day for five days.

a) How many texts did Tim receive on Monday?

b) How many emails did Tim receive on Thursday?

c) In total, what fraction of the messages were emails?

Give your answer in its simplest form.

Answer:

42

Step-by-step explanation:

2 + 3(5) + 5(5)

2 + 15 + 25

Which equals..

42

Answer:

42

Step-by-step explanation:

IF b=5

Now,

2+3b+5b

=. 2 + 3*5 + 5*5

=. 2 + 15 + 25

=. 42

[tex] \longmapsto \: =25/35 [/tex]

[tex] \longmapsto \: =5/7[/tex]

[tex] \longmapsto \: =5:7[/tex]

The answer which we get after calculating from the data given is that  Larry has 15 dollars more than Lenny.

Let the amount which Lenny is having be x

then the amount which Larry is having will be (2/5)x

and on combining them it makes $35 .

Which means,  x + 2x/5 = 35

On simplifying this equation we will get ,

(7/5)x= 35   ,

multiplying both the sides by 5/7

x= (5/7)*35 = $25

Therefore , Lenny is having 4 25.

So Larry must be having ,  $(35 - 25) = $10

So , we can conclude that Lenny has more dollars. The difference is of 15 dollars.

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Therefore , the solution of gross pay problem is 62% is this of her gross wage.

Hannah's take home pay of percentage 785 is 62.8% of her gross wage of 1250. This can be calculated by dividing 785 by 1250 and multiplying the answer by 100.

Here,

62.8% is the same as 0.628.

This can be calculated by dividing 785 by 1250.

To get the answer to the nearest whole percentage, we round up 0.628 to 0.63 which is 63%.

This means that Hannah's take home pay of 785 is 63% of her gross wage of 1250.

63% is the answer to the question: what percentage is Hannah's take home pay of her gross wage? This is correct to the nearest whole percentage.

To summarise, Hannah's take home pay of 785 is 63% of her gross wage of 1250, correct to the nearest whole percentage.

Hannah's take-home pay is 62.8% of her gross wage. This percentage is the result of taxes and other deductions taken by her employer.

Knowing this percentage can help Hannah better understand how much money she is taking home each week and how much money is being withheld from her paychecks.

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The equation to find the root of the statement given in the question is , 12x = 2x - 24.

Let the number of tamp which Ritu have be x

Then the number of tamp which Raj have be 2x = 24

Now as Ritu has 6 times more than Raj , 6( 2x) = 24 x 6

Therefore, the required equation becomes,

12x = 2x - 24

=> 10x = 24

=> x = 2.4 answer.

An equation is a mathematical statement which is made up of constants , variables and operators. There are two parts of an equation which are equated using the equal sign . The right hand and the left hand side of the equation.

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Yes, it is a perfect square trinomial.

Perfect squares are numbers that are the product of a number multiplied by itself. Examples of perfect squares include 4 (2 x 2), 9 (3 x 3), 16 (4 x 4), 25 (5 x 5), 36 (6 x 6), 49 (7 x 7), and 64 (8 x 8). Perfect squares are also referred to as "square numbers" or "whole-number squares."

The equation X² + 10X + 25 can be factored into (X + 5)²,

which is a perfect square trinomial. In general, a perfect square trinomial is any polynomial of the form A² + 2AB + B² where A and B are constants or variables.

This is because such a polynomial can be factored into (A + B)².

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A polynomial in which the degrees of all the variables is 0 is called a zero degree polynomial .

The zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero.

For example- 6 x 0 , − 9 a 0.

Polynomial

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division .

Degree of polynomial

The degree of a polynomial is defined as the highest exponent of a monomial within a polynomial. Thus, a polynomial equation having one variable which has the largest exponent is called a degree of the polynomial .

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a) The average rate of change of a function over an interval is the change in the function's output (f(b) - f(a)) divided by the change in the function's input (b - a). So, to find the average rate of change of f over the interval -4 <= x <= 3, we can use the formula:

(f(3) - f(-4)) / (3 - (-4)) = (sqrt(25 - 9) - sqrt(25 - 16)) / (3 - (-4)) = (-2sqrt(7) + 4sqrt(3)) / 7

b) To find the derivative of f(x), we need to use the power rule and the chain rule. The power rule states that the derivative of x^n is nx^(n-1), and the chain rule states that the derivative of f(g(x)) is f'(g(x)) * g'(x).

So, the derivative of f(x) = sqrt 25 - x^2 is:

-2x

c) To find the equation of the line tangent to the graph of f at x = -3, we need to use the point-slope form of a line, which is:

y - y1 = m(x - x1)

where m is the slope of the line (which is f'(-3) = -6), (x1, y1) is the point on the graph where the line touches (which is (-3, f(-3)) = (-3, sqrt(25 - 9) = 2sqrt(7))

so we have: y - 2sqrt(7) = -6(x + 3)

d) To check if g(x) is continuous at x = -3, we need to check if the limit of g(x) as x approaches -3 exists and is equal to g(-3).

Since g(x) = f(x) for -5 <= x <= -3 and g(x) = x + 7 for -3 <= x <= 5, we have:

g(-3) = f(-3) = sqrt(25 - 9) = 2sqrt(7)

and the limit of g(x) as x approaches -3 is:

lim x->-3 g(x) = lim x->-3 (x + 7) = -3 + 7 = 4

Since g(-3) = 2sqrt(7) and lim x->-3 g(x) = 4, g(x) is not continuous at x = -3.

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The required money to be invested in order to save $5000 is $4677.26.

The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.

The principal for each interval is the sum of interest And the principal for the previous interval.

Suppose the amount to be invested be P.

The rate of interest for monthly compounding is given as 4.5/12 = 0.375%.

Time is given as 18 months.

This implies number of time period is 18.

Plug n = 18, r = 0.375% and A = 5000 in A = P(1 + r/100)ⁿ as,

⇒ 5000 = P(1 + 0.375/100)¹⁸

⇒ P = 4677.26

Hence, the amount of money that should be invested is obtained as $4677.26.

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The object will hit the ground after 5.01 seconds.

When an object is propelled upward from ground level with an initial velocity of 80.1 feet per second then its height h in feet t seconds later is giving by the equation,

h= -16t^2+ (80.1)t

When the object hit the ground, the height of the object h would be zero.

To find: time (t) when h = 0

Substitute h = 0 in given equation.

h = -16t^2+ (80.1)t

0 = -16t^2+ (80.1)t

16t^2 -  (80.1)t = 0

t (16t - 80.1) = 0

t = 0  or  16t - 80.1 = 0

t = 0   OR   t = (80.1)/16

t = 0 OR t = 5.01

Therefore, it will hit the ground after 5.01 seconds.

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Therefore , the solution of the given problem of equation comes out to be  the error range for x is [1250, 1350].

A mathematical equation is a formula that uses the equal sign (=) to connect two statements and express equality. A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The equal sign is a crucial part of mathematical formulas, especially equations. Algebra is frequently utilized in equations. Algebra is used in mathematics when it is difficult to determine a precise quantity.

Here,

Given: Some material has a length of 8.3 meters

We have provided a number, x, that has been rounded to two significant numbers with the supplied error.

Next, we must determine the x error interval.

​It is necessary for x to have a value that is both bigger than or equal to 1250 and less than or equal to 1300.

i.e.,1250 ≤ x ≤ 1300 ---(1)

2. The value of x is more than 1300 but not equal to 1350.

1300  ≤ x ≤ 1350--- (2)

When (1) and (2) are combined, we obtain

1250≤ x ≤ 1350

As a result, 1350 is not part of the error-interval for x.

As a result, the interval notation is [1250, 1350].

As a result, the error range for x is [1250, 1350].

Therefore , the solution of the given problem of equation comes out to be  the error range for x is [1250, 1350].

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On solving the provided question, we can say that number 12 is the smallest natural number is abundant

Natural numbers are those employed in mathematics for counting and ranking. Cardinal numbers are the ones used for counting, and ordinal numbers are the ones used for organizing. The natural numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11... are the ones to use while counting or sorting them. Integer a sum that consists of integers and zero. not using decimals or fractions. Integers are not fractions or decimals. Although all integers are integers (as are all natural numbers), not all integers are also integers or natural numbers. For instance, the integer -5 is both an integer and a natural number, but it is neither.

number 12 is the smallest natural number is abundant

factor of 12 = 1,2,3,4,6,12,

1~1

2>1

3>1

4>2+1

.............

10> 1+2+5

11>1

therefore, number 12 is the smallest natural number is abundant

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Complete question: A natural number is abundant if it is less than the sum of its proper divisors. What is the smallest abundant number?

The probability that the product has a shelf life of at least 1 week and at most 2 weeks is 0.30.

Potential is described by probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability is a concept in mathematics that helps predict the likelihood of certain events. Probability generally refers to the degree to which something is likely to occur.

A standard normal variable with a mean of 0 and a variance of 1 can be created from a normally distributed random variable with a defined mean and variance.

Thus, The probability that the product has a shelf life of at least 1 week and at most 2 weeks is 0.30.

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quadrilateral with both pairs of opposite sides congruent

What is a parallelogram?

A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.

Having two sets of parallel sides makes a quadrilateral a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size. Additionally, the internal angles on the same transverse side are supplementary. 360 degrees are equal to the total of all internal angles.

If both pairs of opposite sides of a quadrilateral are congruent , then the quadrilateral is a parallelogram.

So, the option  I only is correct

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Yes, [tex]9x^2-30x +25[/tex]  is a perfect square trinomial.

A perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial of the form [tex]ax^2 + bx + c[/tex] meets the requirement [tex]b^2 = 4ac[/tex], it is said to be a perfect square.

Two of your terms will be perfect squares in a perfect square trinomial. This trinomial is not a perfect square trinomial if it lacks two perfect square terms. The square root of each perfect square word should now be determined, combine the two square roots, then multiply the result by two.

This trinomial is a perfect square. The only thing left to determine is whether the middle term matches when you square (3x-5) because both [tex]9x^2=(3x)^2\ and\ 25=52[/tex] are perfect squares. The minus sign was used to at least produce a negative coefficient for the middle term.

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The function be f(x) = (6) then growth factor for the given equation (b) = 6.

Quantity grows exponentially over time. It happens when a quantity's instantaneous rate of change with regard to time is proportional to the quantity itself.

A function called exponential growth illustrates an expansion within a population that happens at the same pace across time. When a population's per capita growth rate remains constant across time, regardless of population size, exponential growth occurs, causing the population to grow exponentially as the population increases.

The general exponential growth function is given by :-

[tex]$f(t)=A b^t$[/tex] , where A is the initial amount , b is the growth factor and t is the time period.

The given function : [tex]$f(x)=(6)^x$[/tex]

When we compare it to the general exponential equation , we get

The growth factor for the given equation (b) = 6.

The complete question is:

Consider the function f(x) = (6)x. What is the value of the growth factor of the function?

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The function be f(x) = (6) then growth factor for the given equation (b) = 6.

Quantity grows exponentially over time. It happens when a quantity's instantaneous rate of change with regard to time is proportional to the quantity itself.

A function called exponential growth illustrates an expansion within a population that happens at the same pace across time. When a population's per capita growth rate remains constant across time, regardless of population size, exponential growth occurs, causing the population to grow exponentially as the population increases.

The general exponential growth function is given by :-

F(t) = AB^t, where A is the initial amount , b is the growth factor and t is the time period.

The given function : f(t) = (6)^x

When we compare it to the general exponential equation , we get

The growth factor for the given equation (b) = 6.

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The complete question is:

Consider the function f(x) = (6)x. What is the value of the growth factor of the function?

Answer: The Sale price is $196

Step-by-step explanation:

We can start by converting 30% to a decimal 0.3, then we will multiply the $280 by the decimal (280*0.3 = $84) This means it is marked down by $84, so to get the sale price we subtract the mark down by the original price, ($280-$84 = $196).

Answer:

The suit's sale price is $196.

Step-by-step explanation:

⭐What is "mark down"?

To find the sale price, we need to form an equation representing the given situation.

MARK DOWN:

original price - (mark down percentage)(original price) = sale price

Substitute the known values.

280 - (0.3)(280) = sale price

Compute.

280 - 84 = sale price

∴ $196 = sale price

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There are five different types of Time complexity analysis:

The computational complexity that describes the amount of computer time required to run an algorithm is known as time complexity in computer science. The time complexity of an algorithm is commonly estimated by counting the number of elementary operations performed by the algorithm, assuming that each elementary operation takes a fixed amount of time to perform.

As a result, the time required and the number of elementary operations performed by the algorithm are assumed to be proportional. Because the running time of an algorithm varies among different inputs of the same size, the worst-case time complexity, which is the maximum amount of time required for inputs of a given size, is commonly considered.

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To find the equation of a vector given a point and direction, you need to find the components of the vector and plug them into the equation: v = (x, y, z).

The equation of a vector is typically written like this:

v = (x, y, z)

To find the equation of a vector given a point and direction, you need to find the components of the vector and plug them into the equation. For example, let's say you are given the point (1,2,3) and the direction of the vector is (2,3,4). The components of the vector, v, would be x = 2, y = 3, and z = 4, so the equation for that vector would be:

v = (2, 3, 4)

To find the equation of a vector given a point and direction, you need to find the components of the vector and plug them into the equation: v = (x, y, z).

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The degree of the given polynomial is 4.

A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer. A polynomial comprises constants and variables, but we cannot perform division operations by a variable in polynomials.

The given polynomial is y=3x²-7x⁴+5-9x.

a) The polynomial in standard form is -7x⁴+3x²-9x+5.

b) The degree of the polynomial is 4.

c) The number of terms in the polynomial are 4.

d) Use the degree and the leading coefficient to determine the behavior.

Falls to the left and falls to the right

e) Use the derivative to find the maximum and minimum.

(−0.78859507, 11.25584002) is a local maxima

f) Here the y-intercept is (0, 5)

g) The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x. x≈−1.33755842,0.5797309.

h) Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain.

Domain: (−∞,∞),{x|x∈R}

i) Range: (−∞,11.25584002],{y|y≤11.25584002}

Therefore, the degree of the given polynomial is 4.

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One cheese sandwich costs $1.4 and one bottle of water costs $1.8.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

Let x be the cost of cheese sandwiches and y be the cost of one bottle of water.

3x+2y=7.8

5x+4y=14.2

(3x+2y=7.8)*2

6x+4y=15.6

5x+4y=14.2

x=$1.4

y=$1.8

The cost of one cheese sandwich is $1.4 and that of one bottle of water is $1.8.

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Suppose the average yearly salary of an individual whose final degree is a​ master's is ​$ 41 thousand less than twice that of an individual. the average yearly salary of an individual with each of these final degrees is: $50,000 (Bachelor's degree) and $59,000 (Master's degree )

Let x represent the average yearly salary of an individual with the bachelor's degree

Let (2x-41000) represent the   average yearly salary of an individual with the master's degree

Let the sum of these salaries = 109000

So, x + (2x-41000) = 109000

Simplify and solve:

3x = 109000 + 41,000

3x = 150,000

Divide both side by 3x

x= 150,000/3

x = 50,000 (Bachelor's degree)

So,

(2x-41000)

= 2(50,000) - 41,000

=100,000 - 41,000

= $59,000 (Master's degree )

Therefore the average yearly salary is $50,000 (Bachelor's degree) and $59,000 (Master's degree )

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The processing capability for the size of the Santa rounded to three decimal places is 1.07.

CP (Process Capability) is a statistical measure that compares the performance of a process to the specifications of that process. It can be calculated using the formula:

CP = (USL - LSL) / (6 * standard deviation)

Where:

USL = Upper Specification Limit (3.5 + 0.9) = 4.4 cm

LSL = Lower Specification Limit (3.5 - 0.9) = 2.6 cm

Standard deviation = 0.28 cm

Substituting these values into the formula:

CP = (4.4 - 2.6) / (6 * 0.28) = 1.8 / 1.68 = 1.07

So, CP rounded to three decimal places is 1.07

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Step-by-step explanation:

y = 2x + 1 -------- (I)

y = 4x + 6 --------(ii)

from eqn (I)

y = 2x + 1

sub y = 2x + 1 in eqn (ii)

2x + 1 = 4x + 6

2x - 4x = 6 - 1

-2x = 5

x = -5/2

sub x = -5/2 in eqn (I)

y = 2(-5/2) + 1

y = -5 + 1

y = -4

Therefore, (x, y) = (-5/2, -4)