Write and exponential function in the form y=ab^x that goes through points (0,15) and (2,240)

The unit circle's radius is 1, that is 1 is the radius of the circle.

45 degrees' sine, cosine, and tan values are

[tex]sin \ 45^0=\frac{1}{\sqrt{2} }[/tex]

[tex]cos\ 45^0=\frac{1}{\sqrt{2 } }[/tex]

[tex]tan \ 45^0 =1[/tex]

Due to the fact that all angles are smaller than,

the reference angle coincides with the specified angle. In the first quadrant, 45 degrees is the reference angle, and sine, cosine, and tangent are all positive trigonometric functions.

In the second quadrant, sine is positive, cosine is negative, and tan is positive. In the fourth quadrant, sine and tan are negative, cosine is positive.

In the case of a unit circle, the cosine sine of the angle formed by the horizontal line is used to represent the unit circle's coordinates.

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The resulting equation is 14√3x - 47 = 0.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 8 is an equation.

We have,

√3x + 4 = 1 + √3x -11

√3x + 4 = √3x - 10

Squaring both sides

(√3x + 4)² = (√3x - 10)²

3x² + 16 + 8√3x = 3x² - 20√3x + 100

16 - 100 + 8√3x + 20√3x = 0

28√3x - 94 = 0

2(14√3x - 47) = 0

14√3x - 47 = 0

Thus,

14√3x - 47 = 0 is the resulting equation.

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When both sides of the given equation are squared, the resulting equation is x = 20.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The equation is given in the question, as follows:

√(3x+4) = 1+√(3x-11)

Squaring both sides of the equation:

3x + 4 = (1 + √(3x - 11))²

Expanding the square on the right side:

3x + 4 = 1 + 2√(3x - 11) + (3x - 11)

Simplifying the above equation, we get

196 = 12x - 44

12x = 196 + 44

12x = 240

x = 20

So the value of x that satisfies the equation is 20.

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The value of x and y in the given triangle is 4 and 6 respectively.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

The two triangles are similar. Using the rule of similar triangles we have:

4/ 6 = y / y+3

4(y + 3) = 6y

4y + 12 = 6y

12 = 2y

y = 6

Similarly, using the rule of similar triangles we have:

4/6 = x/6

(4)(6) = 6x

24 = 6x

x = 4

Hence, the value of x and y in the given triangle is 4 and 6 respectively.

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The the function to estimate the average age of employee of a company is A(s)=0.285s + 59  , then the average age of employee in 2003 is 65.27 and in 2009 is 66.98

To estimate the average age of an employee in 2003, we need to find the value of A(s) when s = 22  ;

because the number of years between 2003 and 1981 is = 22 years ;

So , A(22) = 0.285×22 + 59 = 65.27  ;

The average age of an employee in 2003 is approximately 65.27.

To estimate the average age of an employee in 2009,

we need to find the value of A(s) when s = 28

because the number of years between 2009 and 1981 is = 28 years ;

So , A(28) = 0.285×28 + 59 = 66.98  ;

The Average age of employee in 2009 is approximately 71.48.

The given question is incomplete , the complete question is

The function​ A(s) given by ​A(s)=0.285s + 59  can be used to estimate the average age of employee of a company in the year 1981 to 2009. Let​ A(s) be the average age of an​ employee, and "s" be the number of year since​ 1981; that​ is, s=0 for 1981 and s=9 for 1990. What is the average age of the employee in 2003 and in​ 2009 ?

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Answer: B. 309.

Step-by-step explanation: The discriminant of the quadratic equation 7x^2 - 13x - 5 = 0 is D = b^2 - 4ac, where a = 7, b = -13, and c = -5.

Plugging in the values, we get:

D = (-13)^2 - 4 * 7 * -5 = 169 + 140 = 309

Therefore, the answer is B. 309.

Answer:B.309 I hope this helps you

Step-by-step explanation:

7x^2-13x-5=0

Identify the coefficients , and of the quadratic equation

something like this

a=7 b=-13, c=-5

Evaluate the discriminant by substituting a=7, b=-13 and c=-5 into the expression b^2-4ac

Something like this

(-13)^2-4 time 7( -5)

Simplify the expression then you get your answer

309

To solve the inequality, we need to get the variable on one side and the constant on the other side. We can start by multiplying both sides of the inequality by 3:

[tex]4a ≥ 6[/tex]

Now, we can divide both sides by 4:

[tex]a ≥ \frac{3}{2}[/tex]

The solution to this inequality is all values of a that are greater than or equal to 3/2. We can represent this on a number line as:

(-infinity, -1.5) U [1.5, infinity)

Where ( -infinity, -1.5) represents all values less than -1.5 and [1.5, infinity) represents all values greater than or equal to 1.5.

Note that the solution can also be represented as a >= 1.5.

Answer:

4a/3≥ 2

4a/3*3≥ 2*3

4a≥6

4a/4≥6/4

a≥3/2

On a number line, you would plot 3/2 with a filled in hole. The arrow you would draw to is the one that goes to the positive side, to the right. That's how to plot it.

Step-by-step explanation:

The equation of line a is given as follows:

y = 3x - 2.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The parallel line is defined as follows:

3x - y + 1 = 0.

In slope-intercept format, it is given as follows:

y = 3x + 1.

Hence the slope of line a is given as follows:

m = 3.

(as parallel lines have the same slope).

The intercept is the same as the line 11x + 3y + 6 = 0, hence:

3y + 6 = 0

3y = -6

y = -2

b = -2.

Hence the line a is defined as follows:

y = 3x - 2.

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John made at the end $357 for building cabinets

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

To solve this problem we must perform the following algebraic operations with the given information

Information about the problem:

Total money will be as follow:

Total = 36*$8.50 + 17*$3

Total = $306+$51

Total = $357

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the 12th term of the geometric sequence will be 97656250.

What is geometric sequence?

The sequence where each word is varied by another by a common ratio is known as a geometric progression or geometric sequence. When we add a constant (which is not zero) to the term before it, the sequence's subsequent term is created. The following symbols stand in for it: a, ar, ar2, ar3, ar4, etc.

Geometric Progression (GP), a form of sequence in mathematics, is a series in which each subsequent term is created by multiplying each preceding term by a set integer, known as a common ratio. A geometric sequence of integers that follows a pattern is another name for this development.

The terms are given 2,10,50...

a = 2

r = 10/2 = 5

The 12th term will be= 2*(5)[tex])^{11}[/tex] = 2 * 48828125= 97656250

Hence, the 12th term of the geometric sequence will be 97656250.

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Answer: The length of one side of the triangular-shaped walking path is 330 feet.

Step-by-step explanation:

The perimeter of the triangular-shaped walking path is 990 feet, and the length of one side is represented by x. We can write an equation to find x using the formula for the perimeter of a triangle:

P = a + b + c

Where P is the perimeter, and a, b, and c are the lengths of the sides of the triangle. Since one of the sides is represented by x, the equation can be written as:

990 = x + x + x

Simplifying the equation, we can find the value of x:

990 = 3x

Dividing both sides by 3, we get:

330 = x

So the length of one side of the triangular-shaped walking path is 330 feet.

Answer:

The rate of interest per annum is 3%.

Step-by-step explanation:

The rate of interest per annum is 3%.

This can be calculated using the formula:

Simple Interest = (Principal x Rate x Time) / 100

In this case, we know that the Simple Interest = $54 and the Principal = $800, Time = 3 years.

So, we can rearrange the formula to solve for the Rate:

Rate = (Simple Interest x 100) / (Principal x Time)

Plugging in the given values, we get:

Rate = (54 x 100) / (800 x 3)

Rate = 3%

Answer:

36-30:[26-100:(10-12:b)]=6 - 10417845.

Correct option is E, The slope of a line perpendicular to y = -10/4 x + 5 is 4/10

The slope of the parallel line is undefined and the slope of the perpendicular line is 0.

Yes, the slope of a line perpendicular to the line 10x + 4y = 20 is indeed -4.

To find the slope of a perpendicular line, we can find the negative reciprocal of the slope of the original line.

The slope of line 10x + 4y = 20 can be found by solving for y and writing the line in slope-intercept form (y = mx + b), where m is the slope.

By solving for y in the equation 10x + 4y = 20:

10x + 4y = 20

4y = -10x + 20

y = -10/4 x + 20/4

y = -10/4 x + 5

So the line is in the form y = -10/4 x + 5, which is the slope-intercept form of a line where the slope (m) is -10/4 and the y-intercept (b) is 5.

Now, to find the slope of a line perpendicular to this line, we need to find the negative reciprocal of the slope of this line. The negative reciprocal of -10/4 is 4/10.

hence,. the slope of a line perpendicular to y = -10/4 x + 5 is 4/10

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If I lose half each week there is no value to reach "0" so we approximate the value to be less than 1, and the weekly amount is:

7 weeks

   Fractions are also called fractional numbers and are defined as an expressed numerical value that denotes a division and is expressed in the form:

x/y

Where:

x = numerator or dividing

y = denominator or divisor.

If the initial value we have is $100 and we determine its half, which is one week of expenses, we are left with the following:

$100 * 1/2 = $50

$50 * 1/2 = $25

$25 * 1/2 = $12.5

$12.5 * 1/2 = $6.25

$6.25 * 1/2 = $3.125

$3.125 * 1/2 = $1.5625

$1.5625 * 1/2= $0.78125

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The equation that matches the number of bacteria in the population after 2 hours is [tex]y = 300 * 2^2[/tex], where y is the number of bacteria and [tex]2^2[/tex] is the exponential term representing the doubling of the bacteria every hour.

In the lab experiment, the population of bacteria is doubling every hour, so after 2 hours, the number of bacteria will be 2 times the initial number of bacteria for each of the 2 hours, or [tex]2^2[/tex] times the initial number of bacteria.

So, the equation for the number of bacteria after 2 hours is [tex]y = 300 * 2^2[/tex], where y is the number of bacteria and 300 is the initial number of bacteria. This equation calculates the number of bacteria in the population after 2 hours by multiplying the initial number of bacteria by 2 raised to the power of the number of hours the bacteria has been doubling, or [tex]2^2[/tex] in this case.

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From given data, equation of line will be x - 2y = -16.

To find points on the line y = mx + b, choose x and solve the equation for y, or. choose y and solve for x.

The two-point form of a line is used for finding the equation of a line given two points (x1,y1) ( x 1 , y 1 ) and (x2,y2) ( x 2 , y 2 ) on it. The two point-form of a line is:y−y1=y2−y1x2−x1(x−x1) y − y 1 = y 2 − y 1 x 2 − x 1 ( x − x 1 ) OR y−y2=y2−y1x2−x1(x−x2) y − y 2 = y 2 − y 1 x 2 − x 1 ( x − x 2 ) .

It's called this because it clearly identifies the slope and the y-intercept in the equation. The slope is the number written before the x. The y-intercept is the constant written at the end. Let's look at an example: y = 3x + 2.

Given,

x represent how old the baby is in weeks

y represent the baby's weight in pounds.

At 2 weeks old, baby Nellie weighed 9 pounds. When she was 8 weeks old, she weighed 12 pounds.

⇒ (2,9)

⇒ (8,12)

Equation of line will be = y - yo = m (x - xo)

= y - 9 = 1/2 (x - 2)

= 2y - 18 = x - 2

= x - 2y = -16

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Answer:

y=1/5x

That's the answer with the other point at (0,0)

Step-by-step explanation:

Answer:

The expression for the truck's position in terms of t would be xtruck = t × vtruck, where vtruck is the truck's velocity. The expression for the car's position in terms of t would be xcar = t × vcar + x0, where vcar is the car's velocity and x0 is the car's initial position. For the vehicles to eventually meet, these two equations must be equal, so vtruck = vcar + (x_0/t).

Answer:

A) (3x + y)^4:

The Binomial Theorem states that for any real numbers a and b, and any positive integer n, the expansion of (a + b)^n is given by the sum of n terms of the form:

C(n,k)a^(n-k)b^k

where C(n,k) is the binomial coefficient (n choose k).

So, expanding (3x + y)^4:

(3x + y)^4 = C(4,0)(3x)^4(y)^0 + C(4,1)(3x)^3(y)^1 + C(4,2)(3x)^2(y)^2 + C(4,3)(3x)^1(y)^3 + C(4,4)(3x)^0(y)^4

Using the binomial coefficients:

C(4,0) = 1, C(4,1) = 4, C(4,2) = 6, C(4,3) = 4, C(4,4) = 1

Expanding the terms:

(3x + y)^4 = 1(3x)^4(y)^0 + 4(3x)^3(y) + 6(3x)^2(y)^2 + 4(3x)(y)^3 + 1(y)^4

= 1(81x^4) + 4(27x^3y) + 6(9x^2y^2) + 4(3xy^3) + 1(y^4)

= 81x^4 + 108x^3y + 54x^2y^2 + 12xy^3 + y^4

B)

The Binomial Theorem states that for any real numbers a and b and any positive integer n, the expansion of (a + b)^n is given by:

(a + b)^n = C(n, 0)a^n * b^0 + C(n, 1)a^(n-1) * b^1 + C(n, 2)a^(n-2) * b^2 + ... + C(n, n-1)a^1 * b^(n-1) + C(n, n)a^0 * b^n

where C(n, k) represents the binomial coefficient, which can be calculated as n! / (k! (n - k)!).

Applying this to (x - 2y)^6, we get:

(x - 2y)^6 = C(6, 0)x^6 * (-2y)^0 + C(6, 1)x^5 * (-2y)^1 + C(6, 2)x^4 * (-2y)^2 + ... + C(6, 5)x^1 * (-2y)^5 + C(6, 6)x^0 * (-2y)^6

Expanding each term:

C(6, 0) = 6! / (0! 6!) = 1

C(6, 1) = 6! / (1! 5!) = 6

C(6, 2) = 6! / (2! 4!) = 15

C(6, 3) = 6! / (3! 3!) = 20

C(6, 4) = 6! / (4! 2!) = 15

C(6, 5) = 6! / (5! 1!) = 6

C(6, 6) = 6! / (6! 0!) = 1

Now we can substitute each value into the equation:

(x - 2y)^6 = 1x^6 - 12x^5 * 2y + 90x^4 * (-2y)^2 - 360x^3 * (-2y)^3 + 720x^2 * (-2y)^4 - 720x * (-2y)^5 + 1 * (-2y)^6

Answer:

(x - 2y)^6 = x^6 - 12x^5 * 2y + 90x^4 * (-2y)^2 - 360x^3 * (-2y)^3 + 720x^2 * (-2y)^4 - 720x * (-2y)^5 + (-2y)^6.

Answer:

The marked price of the torchlight is Rs. 1960.

Step-by-step explanation:

The marked price (MP) of a torchlight is 40% more than the cost price (CP), so we can calculate the MP using the formula:

MP = CP + (CP x 40%)

The cost price of the torchlight is Rs. 1400, so the marked price is:

MP = 1400 + (1400 x 40%) = 1400 + 560 = 1960

The shopkeeper is selling the torchlight at a 20% discount, so we can calculate the selling price (SP) using the formula:

SP = MP - (MP x 20%)

The marked price of the torchlight is Rs. 1960, so the selling price is:

SP = 1960 - (1960 x 20%) = 1960 - 392 = 1568

So the marked price of the torchlight is Rs. 1960.

The measure of ∠C found using central angle and intercepted angle relationship is 50°.

What is central angle and intercepted arc of a circle?

An angle with its vertex at the circle's centre and both of its endpoints are on circle is said to be central angle. The angle's intercepted arc's ends are the same as the circle's endpoints. A circle's circumference includes an arc. Therefore, an intercepted arc is an arc that is created when one or more chords or line segments intersect a circle and come together at a vertex.

Given,

∠AFE = 150°

arc BD =  50°

External angle formed outside a circle,

= 1/2 ( major arc -  minor arc )

Major arc = intercepted arc AE =  central angle ∠AFE = 150°

Minor arc = arc BD =  50°

Therefore external angle ∠C = 1/2(150-50) = 50°

Hence 50° is the measure of ∠C.

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The averages are less variable as compare to the individual outcomes is a true statement as individual value spread in wide range.

The averages are less variable compare to individual values.

Therefore, the individual values are more variable than averages is a true statement.

The given question is incomplete, I answer the question in general according to my knowledge:

Averages are less variable than individual outcomes is a true statement ? Give reason?

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The number of casual jeans sold was 81 and the number of dress jeans sold was 40.5 (rounded to 41).

        $45x + $55x/2 = $4,060

        $45x + $55x/2 = $4,060

        $45x + $55x/2 = $4,060

        $100x/2 = $4,060

        $100x = $8,120

        x = 81

So from above calculation, we got that the number of casual jeans sold was 81 and the number of dress jeans sold was 81/2 = 40.5 (rounded to 41).

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The complement of 0.87 is calculated by subtracting the given number from 1. Mathematically, this can be expressed as 1 - 0.87 = 0.13.

The complement of any number x is calculated by subtracting x from 1. This means that the complement of 0.87 is 0.13.

The complement of a number is used to find the remaining portion of a whole. For example, if the given number is 0.87, then the complement of 0.87 is 0.13. This means that 0.87 is 87% of the whole and 0.13 is the remaining 13%. Thus, the complement of 0.87 is 0.13.

Complements can also be used to find the probability of something happening. For example, if the probability of an event occurring is 0.87, then the probability of it not occurring is 0.13. This is because the sum of the probabilities must equal 1 (100%). Therefore, the complement of 0.87 is 0.13.

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Step-by-step explanation:

Elaine spent 6.30 + px dollars on her purchase and Elena spent 4.15 + 4p dollars on her purchase. To find how much more Elaine spent, we can subtract Elena's total cost from Elaine's total cost: (6.30 + px) - (4.15 + 4p) = (6.30 - 4.15) + (px - 4p) = 2.15 + (px - 4p) = 2.15 + p*x - 4p. This is the simplified expression for how much more Elaine spent than Elena.

Question 1 should be chosen first to maximize your expected reward.

To maximize the expected reward, we need to calculate the expected reward for each question, taking into account the probability of getting the answer right and the reward for a correct answer.

For Question 1, the expected reward is 0.8 * $100 = $80, since you have an 80% chance of getting the answer right and earning a reward of $100.

For Question 2, the expected reward is 0.5 * $200 = $100, since you have a 50% chance of getting the answer right and earning a reward of $200.

Since the expected reward for Question 1 is higher than the expected reward for Question 2, you should choose Question 1 first to maximize your expected reward.

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Answer:

B

Step-by-step explanation:

[tex]x = \frac{2}{3}\pi r^{3}[/tex]

The objective is to isolate r and make r the subject of the equation:

Cross-multiplication is applied:

[tex]= 2\pi r^{3}= 3x[/tex]

The variables and number multiplied with [tex]r^{3}[/tex] are transferred to the other side of the equation:

[tex]= \pi r^{3} = \frac{3x}{2}[/tex]

[tex]= r^{3} = \frac{3x}{2\pi}[/tex]

Cube root is applied to both sides of the equation to get rid of the cube:

[tex]= \sqrt[3]{r^{3}} = \sqrt[3]{\frac{3x}{2\pi}}[/tex]

[tex]r = \sqrt[3]{\frac{3x}{2\pi}}[/tex]

The function that is non-linear is (a) q = 8p³ + 9

From the question, we have the following parameters that can be used in our computation:

The list of options

As a general rule

Linear functions are functions with the highest power of 1

All but option (a) have a degree of 1

Hence. q = 8p³ + 9 is not linear

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The quadratic function f(x)= 3x2 - 2x + 5 has an average rate of change from x = -2 to x = 0 of - 14.

Qualities and their permutations, theorems and surrounding structures, morphologies and their placements, and locations where they can be encountered are all included in the study of mathematics. The association between a group of inputs, of which each has a related output, is referred to as a "function." A function is a relationship between inputs and outputs where each input produces a single, unique result. Every function has a domain and a requires great, often known as a scope. F is typically used to denote functions (x). An x is the input. Based on the following criteria, there are four primary categories of functions that are available: on procedures, one-to-one functions, several more functions, within functions, and on functions.

given

The slope formula, (y2-y1)/, states that the average rate of change is the ratio of the change in y to the change in x.

(x2-x1) We have f(x), which is equivalent to byt but instead of y.

f(-2) - f (0)  /   -2

= f(14+4 + 5 ) + 5 / -2

28 / - 2

= -14

The quadratic function f(x)= 3x2 - 2x + 5 has an average rate of change from x = -2 to x = 0 of - 14.

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