Work out:
2 x 2.2 x 10^12 × 1.5 × 10^12/
2.2 x 10^12 - 1.5 x 1012
Give your answer in standard form correct to 3 significant figures.

Answer: Yes

Step-by-step explanation:

3 is a factor of 81 because on dividing 81 by 3, we get no remainder and 27, that is, the quotient in this division, which is also a factor of 81.

The length of segment FB is given as follows:

FB = 4 in.

The theorem used to solve this problem is given as follows:

A line parallel to one side of a triangle divides the other two proportionately, as similar triangles are formed.

The parallel segments in this problem are given as follows:

DF, EF and AB.

Hence the proportional side lengths are given as follows:

Meaning that the length of segment FB is obtained as follows:

3/4 = 3/FB

FB = 4 in.

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The data have a mean of 200 and a standard deviation of 5, with 95% of the data falling between 190 and 210.

Mean = 200

5 is the standard deviation.

10 divided by two standard deviations

Lower Boundary = Mean – Two SDs = 200 – 10 = 190

Upper Boundary = Mean + Two SDs, which is 200 + 10 = 210.

As a result, 190 through 210 should contain 95% of the data.

The data provided indicate that the data set's mean is 200 and its standard deviation is 5. Accordingly, the range of the data for 95% of the samples should be between 190 and 210, with 200 serving as the average. Due to the fact that for a set of data with a normally distributed distribution, around 95% of the values should be within two standard deviations of the mean, this is the case. Two standard deviations from the mean of 200 would be 190 and 210 since 5 is the standard deviation. As a result, these two figures should encompass 95% of the data.

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The complete question is

a+given+data+set+is+normally+distributed+with+a+mean+of+200+and+a+standard+deviation+of+5.+++which+two+values+does+95%+of+the+data+fall+between 190 and 210.

The exact doubling time calculation provides a more accurate estimate of how long it will take a given value to double.

Approximate Doubling Time:

5% - 14 Years

10% - 7 Years

15% - 5 Years

20% - 4 Years

Exact Doubling Time:

5% - 14.2 Years

10% - 6.93 Years

15% - 4.77 Years

20% - 3.58 Years

Approximate doubling times are calculated by dividing 72 by the percentage rate of growth. This method assumes a consistent rate of growth, which is not always the case. The exact doubling time can be calculated by using the formula T=ln(2)/ln(1+r) where r is the rate of growth. This formula accounts for the compounding effect of the growth rate, which is not taken into account in the approximate calculation. For example, for a 5% annual growth rate, the approximate doubling time is 14 years, but the exact doubling time is 14.2 years. The exact doubling time calculation provides a more accurate estimate of how long it will take a given value to double.

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The temperature is a function of time, as there is a single temperature for each instant of time.

A relation represents a function when each input value is mapped to a single output value.

For the set in this problem, we have that:

As there are no repeated inputs, the temperature is in fact a function of time.

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By Solving by factorization method of equation 5x² - 3x - 2 = 0

x = 1 , [tex]\frac{-2}{5}[/tex]  

Given data :

Given equation is, 5x² - 3x - 2 = 0

Solving by factorization method,

5x² - 3x - 2 = 0

5x² - 5x + 2x - 2 = 0

( 5x + 2 ) ( x -*1 ) = 0

x = 1 , [tex]\frac{-2}{5}[/tex]

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False

If it doesn't have an equal sign ( = ), it's not an equation. It would be considered an expression.

Answer: False

Step-by-step explanation:

According to the above, the fractions numbers would be: 0.8 = 4/5, 2.34 = 117/50, and 1.25 = 5/4.

To convert a decimal to a fraction, we must write the decimal number as a numerator and its place value as the denominator. Also, if there is a number to the left of the decimal point, we leave that number as an integer. According to the above, the fractional numbers would be:

Those fractions are simplified.

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The value of x that makes triangles DEF ~ XYZ is -2. 25

It is important to note that perpendicular lines are equal to each other

From the triangles given, let us equate their perimeter one to another, we get;

8 + 10 + 3(x -1 ) = 7. 5 + 4 + x-1

expand the bracket

18 + 3x - 3 = 11. 5 + x - 1

collect like terms

3x - x = 10. 5 - 15

Add or subtract the collected like terms, we get;

2x = 4. 5

Now, make 'x' the subject from the equation

x = 4.5/2

Divide the values

x = -2. 25

Hence, the value is -2. 25

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The statement "if a > √n and b > √n, then n ≠ ab" is saying that if two positive integers, a and b, are both greater than the square root of another positive integer n, then the product of a and b is not equal to n. This statement can be proven by contradiction.

Suppose the opposite is true, and that n = ab, where a and b are positive integers such that a > √n and b > √n. Then, because n = ab, we have n/a = b and n/b = a. But because both a and b are greater than the square root of n, we have √n < a and √n < b. This leads to a contradiction, because it means that n/a = b > √n, but √n is the largest possible value of b such that b < n/a.

Thus, we have proven that if a > √n and b > √n, then n cannot equal ab, and our original statement is true.

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The function f·g(x) for the functions f(x)=4x-5 and g(x)=2x+8 is 8x²+22x-40.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

7) The given functions are f(x)=2x+3 and g(x)=x²-3x-6.

Here, f·g(x) =f(x)×g(x)

f·g(x) = (2x+3)×(x²-3x-6)

f·g(x) = 2x(x²-3x-6)+3(x²-3x-6)

f·g(x) = 2x³-6x²-12x+3x²-9x-18

f·g(x) = 2x³-3x²-21x-18

8) The given functions are f(x)=4x-5 and g(x)=2x+8

f·g(x) =f(x)×g(x)

f·g(x) = (4x-5)×(2x+8)

f·g(x) = 4x(2x+8)-5(2x+8)

f·g(x) = 8x²+32x-10x-40

f·g(x) = 8x²+22x-40

Therefore, the function f·g(x) for the functions f(x)=4x-5 and g(x)=2x+8 is 8x²+22x-40.

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Answer: I don't know if this is what you wanted, but two ways to represent 4/5 are 0.8 and 4 divided by 5.

Step-by-step explanation:

4/5 = 8/10

8/10 = 0.8

fraction symbol means to divide.

I hope this helps!

(a)  The function f: r -> r is not one-to-one (injective) since there are two separate inputs (2 and -2) that have the same result. It is defined as f (x) = x2 - 4x + 9. (9).

(b)  The element (-1) that occurs in the codomain of the function f: r -> r, which is defined by f (x) = x2 - 4x + 9, prevents the function from being onto (surjective).

As a result, neither one-to-one nor onto are applicable to the function

f: r -> r defined by f (x) = x2 - 4x + 9.

According to the Question

We must demonstrate that if a function f(x1) = f(x2), then x1 = x2 in order to establish whether the function is one-to-one (injective). To put it another way, no two unique inputs produce the same outcome.

We must demonstrate that there exists an x in the domain of f such that f(x) = y for every element y in the codomain of f in order to establish if a function f is onto (surjective). Alternatively expressed, each output in the codomain has an associated input in the domain.

For the function f: r → r defined by f (x) = x^2 - 4x + 9, we can easily see that it is not one-to-one since f(2) = f(-2) = 9.

It is also not onto, as the codomain of f is all real numbers and there is no real number x such that f(x) = -1.

So, we can conclude that the function f: r → r defined by f (x) = x^2 - 4x + 9 is neither one-to-one nor onto.

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this arithmetic sequence will be 10, 14, and 18.

What is arithmetic sequence?

There are two approaches to defining an arithmetic sequence. It is a "series where the differences between every two succeeding terms are identical" (or) In an arithmetic sequence, "each term is obtained by adding a fixed number (positive or negative or zero) to its preceding term." The series where the common difference between any two next terms stays constant is known as the arithmetic sequence. Let's go through what a sequence is once again. A collection of numbers that follow a pattern is referred to as a sequence.

The first term of an arithmetic sequence is 6

common difference 2/3.

a2 = a+d = 6+4 =10

a3= a+8 =14

a4=a+12 =18

Hence this arithmetic sequence will be 10, 14, and 18.

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The new price for each pillow case is Php 27.50.

The concept used in this problem is markup pricing, where a certain percentage is added to the cost price of a product to arrive at the selling price.

Markup is the difference between a product's selling price and cost as a percentage of the cost. For example, if a product sells for $125 and costs $100, the additional price increase is ($125 – $100) / $100) x 100 = 25%.

As given, Mr. Mosquera plans to add 10% to the original price which is Php 25. 00 each,

Php 25 * 10/100

= Php 2.50 for each pillow case.

So, the new price for each pillow case is

Php 25 + Php 2.50

= Php 27.50.

Therefore, the new price for each pillow case is Php 27.50.

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Mr. Mosquera ' price for each pillow is 27.50 php. His price for each pillow is 27.50 php.

Here, these values are given,

Total no. of pillows = 50

Original price of each pillow = 25.00 php

Original price of 50 pillows= 125000 php

After, planning to add 10% to the original price'

New price of pillow will increase after adding 10% to the previous price.

New price of each pillow became 25+ 25 of 10%

= 25+ 25 × 10/100

= 25+ 5/2

= 55/2

=27.50 php

New price of each pillow became 27.50 php.

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The slope of lines a, b, c, and d are 1/3, 1/4, 1/3, and -4 respectively. Line a is parallel to line c. Line b and line d are perpendicular to each other.

What is a line?

A line is an object in geometry that is infinitely long and has neither width nor depth nor curvature. Since lines can exist in two, three, or higher-dimensional spaces, they are one-dimensional objects. The term "line" can also be used to describe a line segment in daily life that has two points that serve as its ends.

The slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is m = (y₂ - y₁)/(x₂ - x₁).

Line a passes through points (-1,4) and (5,6).

The slope of line a is (6-4)/(5-(-1)) = 2/6 = 1/3

Line b passes through points (-1,1) and (3,2).

The slope of line b is (2-1)/(3-(-1)) = 1/4

Line c passes through points (-3,-2) and (3,0).

The slope of line c is (0-(-2))/(3-(-3)) = 2/6 = 1/3

Line d passes through points (1,6) and (3,-2).

The slope of line d is (-2-6)/(3-1) = -8/2 = -4.

The slopes of line a and line c are the same, thus line a is parallel to line c.

If two lines are perpendicular to each other, then the product of therir slope is -1.

The product of slopes of line b and line d is

1/4 × (-4) = -1

Thus line b and line d are perpendicular to each other.

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The value of c at which the function is continuous is 5/6.

For a function to be continuous at a point, the left and right limit of the function must exist and be equal at that point. In this case, the point is x = -5.

The function f(x) = c for x = -5, f(x) = 4 for x = 1, and f(x) = (x^2 - 25) / (x + 5)(x - 7) for x ≠ -5 and x ≠ 7.

To determine the value of c, we need to find the limit of f(x) as x approaches -5 from the left and from the right.

From the left, we have:

lim x→−5− f(x) = lim x→−5− (x^2 - 25) / (x + 5)(x - 7) = 5/6

From the right, we have:

lim x→−5+ f(x) = 5/6

For the function to be continuous at x = -5, we must have:

lim x→−5− f(x) = lim x→−5+ f(x) = c

c = 5/6

--The question is not readable, answering to the question below--

"For what value of c is the function continuous at x = -5?

f (x) = c for x=-5; f(x)=4 for x=1; f(x) = x^2-25 / (x+5)(x-7) otherwise"

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15

Step-by-step explanation:

20/8 =2.5

6x2.5=15

therefore, 15

Coefficient of x on 4(3x+5) is 12

A coefficient refers to a number or quantity placed with a variable. It is usually an integer that is multiplied by the variable and written next to it.

To find the co-efficient of x in 4(3x+5)

Expand the bracket

4(3x+5) = 12x + 20

From 12x + 20

The co-efficient of x in 12, That is the number with the variable x

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Yes, that's correct. When a figure is dilated from the origin, each ordered pair of the figure is transformed according to the rule

What is dilation in maths ?

A dilation is a function f from a metric space M into itself that fulfils the identity d=rd for all locations x, y in M, where d is the distance between x and y and r is some positive real number.

Yes, that's correct!

When a figure is dilated from the origin, each ordered pair of the figure is transformed according to the rule (x, y) → (kx, ky), where k is the scale factor. The scale factor determines the size of the dilation; if k > 1, the dilation increases the size of the figure, while if 0 < k < 1, the dilation decreases the size of the figure. If k = 1, the figure remains unchanged.

It's important to note that dilations preserve the orientation of the figure and can be thought of as a non-uniform scaling of the figure.

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The value of g(f(-5)) is 5.

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)= |2x+ 9|

Now, g(f(-5))

f(-5) = |2(-5)+9|

       = |-10 + 9|

       = |-1|

       = 1

and, g(f(-5)) = g(1)

So, from the graph we can see that the value of g(1) is 5.

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The student's final grade in three significant digits is 247.

Significant Figures refer to the number of important single digits from 0 to 9 in the coefficient of the expression that conveys the message accurately. These significant figures help engineers or scientists in asserting the quantity of any measurement, length, volume, or mass. For example, 453 has three significant figures.

The two main applications to understand significant figures are - Precision and Accuracy. Let's learn how these two terms play an important role in real-life situations when it comes to the concept of significant figures.  

Precision - The closeness between two or more quantities to each other under the same condition is called precision. In precision, the level of measurement when repeated gives the same result and the individual measurement agrees to each other.

Accuracy - The closeness between the measurement and the accurate number is called accuracy. Accuracy helps in providing consistent results with no error along with accuracy in the result.

The final grade of the student would be equal to the sum of the grades obtained in the quizzes, exams, and final.

So, the total grades = 92 + 76+ 79 = 247

Calculating this to three significant digits, we get 247.

Thus, the student's final grade in three significant digits is 247.

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The arc length of the circle will be 0.35 units.

Using the formula Length of an Arc = r x θ, where is in radians, one can determine the arc length of a circle given its radius and central angle. Arc length is equal to Arc = θ × (π/180) × r, where r is the radius in degrees.

Given that a circle has a radius of 3. An Arc in this circle has a central angle of 20 degrees.

The length of the arc of the circle will be calculated as:-

Arc = θ × (π/180) × r

Arc = 20 x  (π/180) × 3

Arc = 0.35 units

Therefore, the arc length of the circle will be 0.35 units.

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The probability that a muffin picked at random contains raisins is 3/5.

The probability that a muffin picked at random contains raisins is calculated as follows:

The number of muffins that are not frozen = 30 - 14

The number of muffins that are not frozen = 16

The number of muffins that are not frozen but contain raisins = 16 - 4

The number of muffins that are not frozen but contain raisins = 12

The total number of muffins that contain raisins = 12 + 6

The total number of muffins that contain raisins = 18

The probability that a muffin contains raisins, P(contain raisins) = 18/30

P(contain raisins) = 3/5

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The slope for the function f(t) = 3 - 3/5t at point (3/5, 2) is 5/3.

What is slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

The given function is - f(t) = 3 - 3/5t.

The data points are - (3/5, 2)

Rewrite the function -

f(t) = 3 - 3/5 t^-1

Differentiate with respect to t. Use the difference rule.

d/dt (3) - d/dt (3/5 t^-1)

Use the constant rule and the constant multiple rule.

0 - 3/5 d/dt (t^-1)

Use the power rule.

-3/5(-1)t^(-1 - 1)

3/5t^-2

Now plug in 3/5 for t on the derivative in order to find the slope at point (3/5, 2).

3/5(3/5)^-2

3/5(5/3)^2

3/5 × 25/9

5/3

Therefore, the slope value is 5/3.

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Find the slope of the graph of the function at the given point.

Function Point f(t) = 3 - 3/5t (3/5, 2)

-pi is the  phase shift of y = -cos ( 1/2 x + pi/2 )

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The given function is y = -cos ( 1/2 x + pi/2 )

Standard form of the cosine function is y=acos(bx+c)+d

Phase shift is -c/b

b=1/2 and c is pi/2

Now phase shift=-(pi/2)/(1/2)

=-pi

Hence, -pi is the  phase shift of y = -cos ( 1/2 x + pi/2 )

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The difference quotient of f(8 + h) - f(8) / h = x³ + 3x²h + 3xh³ + h³ - 512 / h.

When you hear the phrase "difference quotient formula," what comes to mind? Difference and quotient resemble the slope formula in appearance. Yes, the difference quotient formula does really provide the slope of a secant line drawn to a curve. What is a secant line? A line that joins any two points on a curve is known as the secant line.

Given that the function is f(x) = x³

The value of f(8 + h) = (x+ h)³ = x³ + 3x²h + 3xh³ + h³

The value of f(8) = (8)³ = 512

Substituting the value of f(8 + h) and f(8) we have:

f(8 + h) - f(8) / h = x³ + 3x²h + 3xh³ + h³ - 512 / h

Hence, the difference quotient of f(8 + h) - f(8) / h = x³ + 3x²h + 3xh³ + h³ - 512 / h.

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Based on the formula [tex]C (t) = 0.8 (1.2)^{t}[/tex] it is expected for the concentration of organisms to increase over time (third option).

To determine how the formula or function affects the number of organisms, let's use two different times in order to compare the results:

C (t) = 0.8 (1.2)^{t}

Let's find out the concentration of organisms with the times 2 and 5:

2:

C (t) = 0.8 (1.2)^{2}

C (t) = 0.8 x 1.44 = 1.152

5:

C (t) = 0.8 (1.2)^{5}

C (t) = 0.8 x 2.48 = 1.99

Based on this, it can be concluded that as time increases the concentration increases too.

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The actual temperature after the freezer was on for five minutes could be 18ºF or 12ºF

What is a graph ?

Graph can be defined as visual representation of the data through the given ordered pairs .

First, you must find the y-value returned by the line in the graph for a time (x) of five minutes, and then use the deviation of 3º to conclude the range of the real temperature.

1. y- value at x = 5 min.

The trend line (blue line in the graph) passes through the point (5,15), which means that it predicts a temperature of 15ºF when the time (x) is 5 minutes, or five minutes after the freezer was turned on.

2. Actual temperature value

It is stated that the temperature was actually three degrees from what the trend line shows, that means that the actual temperature could be 3ºF more or 3ºF less than the predicted temperature of 15ºF.

Mathematically:

Temperature = 15ºF ± 3ºF

Temperature = 15ºF + 3ºF or 15ºF - 3ºF

Temperature = 18ºF or 12ºF

Therefore, The actual temperature after the freezer was on for five minutes could be 18ºF or 12ºF

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Answer:

6a + 12b + 18c

Step-by-step explanation:

Distribute 6 to all numbers in the parenthesis.

(6(a) + 6(2b) + 6(3c))

[6a + 12b + 18c]