Answer:
Step-by-step explanation:
To find the left-hand derivative of f at x = 4, we need to evaluate:
f′−(4) = limh→0−f(4+h)−f(4)h
Since f(x) = 0 for x ≤ 0 and f(x) = 5 - x for 0 < x < 5, we have:
f(4 + h) = 0 for h < -4
f(4 + h) = 5 - (4 + h) = 1 - h for -4 < h < 1
f(4 + h) = undefined for h > 1
Therefore, we can rewrite the limit as:
f′−(4) = limh→0−f(4+h)−f(4)h = limh→0−(1 - h) - 0h = -1
To find the right-hand derivative of f at x = 4, we need to evaluate:
f′+(4) = limh→0+f(4+h)−f(4)h
Using the same reasoning as before, we can rewrite the limit as:
f′+(4) = limh→0+(5 - (4 + h)) - 0h = -1
Since the left-hand derivative and the right-hand derivative are equal, we can conclude that f'(4) exists and is equal to:
f'(4) = f′−(4) = f′+(4) = -1
Therefore, the derivative of f at x = 4 is -1.
A rectangular picture frame is 6 inches wide and 10 inches tall. You want to make
the area 7 times as large by increasing the length and width by the same amount.
Find the number of inchey by which each dimension must be increased.
Step-by-step explanation:
let length and width be increased by x>0
(10+x)(5+x)=6×10×5
50+10 x+5x+x²=300
x²+15x-250=0
x²+25 x-10x-250=0
x(x+25)-10(x+25)=0
(x+25)(x-10)=0
x=-25(rejected),10
so x=10
so both the dimensions should be increase by 10 inches.
(X1,y1) point slope Equation
The point slope equation with the point (x1, y1) is given as (y - y1) = m (x - x1).
What is point slope equation?As a line has length but no width, it is a one-dimensional figure in geometry. A line is constructed from a collection of points that can be stretched indefinitely in opposite directions. In a two-dimensional plane, it is determined by two points. In a two-dimensional coordinate plane, there are various ways to express line equations. The general or standard form of the equation of a line, the slope-intercept form, and the point-slope form are the three most often used ways. The point-slope form, as its name implies, combines a line's point with the straight-line slope. The equations of infinite lines with a specified slope can be written, however when we specify that the line passes through a certain point, we obtain a singular straight line.
The point slope equation with the point (x1, y1) is given by the formula:
(y - y1) = m (x - x1)
Here, (x1, y1) are the coordinates of the point on the graph.
m is the slope of the line.
Hence, the point slope equation with the point (x1, y1) is given as (y - y1) = m (x - x1).
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Lin has 2 small baking pans each
Answer:The volume would be 8,341,984
Step-by-step explanation:
the right isosceles triangle pqr has vertices p(3,3),, q(3,1) and r(x,y) and is rotated 90 degress counterclowise about the origin. find the missing vertex of the triangle.
The right isosceles triangle PQR has vertices p(3,3), q(3,1) and r(x,y) and is rotated 90 degrees counterclockwise about the origin. the missing vertex of the triangle is r (5, 1)
What is isosceles triangle?An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.
Properties are:
In a triangle, the angles that face the two equal sides are likewise equal.
An isosceles triangle has one base and two equal sides, which are known as the legs and the base, respectively.
Since the triangle is isosceles, the two legs have equal length. The coordinates of two vertices are given:
P(3,3)
Q(3,1)
Assuming that PQ and QR are the legs of equal length, the distance between Q and R must be the same as the distance between P and Q
d = √[(3-3)² + (3-1)²
d = 2
Therefore, the coordinates of r is: (5, 1)
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Solve: 3|x|+4≥1. Write your solution in interval notation
The solution of the inequality 3|x|+4≥1 in interval notation is {x | -1 ≤ x ≤ 1}.
What is interval notation?An interval on a number line can be represented using interval notation. It is a method of representing subsets of the real number line, in other words. The numbers in between any two particular provided numbers are referred to as an interval. For instance, the interval containing 0, 5, and all values between 0 and 5 is the set of numbers x satisfying 0 x 5.
Given that the inequality is:
3|x|+4≥1
Subtract 4 from both sides of the equation:
3|x| + 4 - 4 ≥ 1 - 4
3 |x| ≥ -3
Divide 3 from both sides of the equation:
|x| ≥ -1
We know that, |x| can be written as x and -x thus,
x ≥ -1
-x ≥ -1 or x ≤ 1
Hence, the solution of the inequality 3|x|+4≥1 in interval notation is {x | -1 ≤ x ≤ 1}.
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Write the point-slope form of the lines equation satisfying the given conditions then use the point-slope form of the equation to write the slope-intercept form of the equation
y = 4. is the equation of the line in slope intercept form.
Equation of a line in point slope formThe formula for calculating the equation of a line in point slope form is expressed as:
y - y0 = m(x - x0)
where:
m is the slope
(x0, y0) is the point on the line
Using the coordinate points (-3, 4) and (2, 4). The slope is calculated as:
Slope = 4-4/2-(-3)
Slope = 0/5
Slope = 0
The required equation will therefore be expressed as:
y - 4 = 0(x - 2)
y - 4 = 0
y = 4
Hence the slope-intercept form of the equation is y = 4.
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Use this table to answer the question. Round to 2 decimal places.
Car Plane Train Total
Green 120 250 500 870
Blue 150 350 750 1250
Yellow 170 200 450 820
Red 200 300 300 800
Brown 220 450 320 990
Total 860 1550 2320 4730
What percent of the total are made up of Yellow Trains?
Trains make up approximately 49.04% of the total journeys across all modes of transportation.
We must divide the total number of train trips by the total number of trips made using all modes of transportation, then multiply the result by 100 to get the percentage that trains make up of the total.
There have been 2320 train trips overall, and there have been 4730 trips overall using all forms of transportation.
Trains therefore account for the following proportion of the total:
(2320 / 4730) x 100% = 49.04%
Train travel thus accounts for roughly 49.04 percent of all travels made using all modes of transportation.
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This is a set notation I need the number of elements
The number of elements in the complement of the union set of A and B is given as follows:
12.
How to solve the operations with sets?The universal set is given as follows:
S = {1, 2, 3, ... , 23, 24, 25}.
The union between two sets is composed by the elements that belong to at least one of the sets, hence the union of sets A and B is given as follows:
A U B = {2, 3, 4, 6, 8, 12, 13, 14, 16, 18, 22, 24, 25}.
The number of elements in the union set is of:
13.
The complement of a set is composed by all the elements that belong to the universal set but to not belong to the set. As the union of A and B has 13 elements, and the universal set has 25 elements, the number of elements of the complement is given as follows:
25 - 13 = 12.
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A union charges monthly dues of $5.00 plus $0.15 for each hour worked during the month. A union member's dues for March were $31.40. How many hours did the union member work during the month of March?
The union member worked 176 hours during the month of March.
What is dues?Dues are the payment or obligation required by law or custom, it is like a monthly payment, fees or charges made by organizations.
Let h be the number of hours worked during the month of March by the union member.
According to the problem statement, the union charges monthly dues of $5.00 plus $0.15 for each hour worked during the month.
So, the total dues for the month of March can be expressed as -
Total dues = $5.00 + $0.15 x h
It is also given that the union member's dues for March were $31.40.
Set up an equation using this information as follows -
$31.40 = $5.00 + $0.15 x h
To solve for h, isolate the variable on one side of the equation.
Start by subtracting $5.00 from both sides -
$31.40 - $5.00 = $0.15 x h
Simplifying the left side gives -
$26.40 = $0.15 x h
To solve for h, divide both sides by $0.15 -
h = $26.40 / $0.15
h = 176
Therefore, the number of hours is 176.
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Find partial decomposition of (x+6)/[x^2(x^2+2)]
Answer:
Step-by-step explanation:
[tex]\frac{x+6}{x^2(x^2+2)} =\frac{A}{x} +\frac{B}{x^2} +\frac{Cx+D}{x^2+2} \\x+6=Ax(x^2+2)+B(x^2+2)+(Cx+D)x^2\\equating~co-efficients ~of~same~powers~of~x\\0=A+C (of~x^3)\\0=B+D (of~x^2)\\1=2A (of~x)\\A=1/2\\6=2B (constant~term)\\B=6/2=3\\C=-A=-1/2\\D=-B=-3\\\frac{x+6}{x^2(x^2+2)} =\frac{1}{2x} +\frac{-3}{x^2} +\frac{-\frac{1}{2} x-3}{x^2+2}[/tex]
Some values of f(x) are given in the table. Find the value of f-¹ (6).
Kristina paid mortgage interest of $6,320.00 and Medical Expenses of $$19,500.00 during 2022. Her GROSS INCOME was $32,500.
19. How much did she save by
itemizing her deductions?
Answer:
$448.25
Step-by-step explanation:
For her medical expenses, it has to be more than 7.5% of her gross income of $32,500 => 7.5% of $32,500 = $2437.5.
so her deduction for medical expenses is $19,500 - $2437.50 = $17,062.5
so her total itemized deduction is $6,320.00 + $17,062.50 = $23,382.50
Given Kristina will file a single so her standard deduction for 2022 is $12,950.
If she uses standard deduction, her taxable income is 32,500 - 19,500 = 13,000
For the first 10,000 taxed at 10% so it is 10,000 x 10% = $1,000
The next $3000 taxed at 12% = $360
Her total tax is $1,000 + $360 = $1,360
If she uses itemized deduction, her taxable income is 32,500 - 23,382.50 = 9117.5
For the first 10,000 taxed at 10% so it is 9117.5 x 10% = $911.75
The tax saved is $1,360 - $911.75 = $448.25
Hope this helps.
The stem and leaf plot shows the number of laps around a track
that several teams walked as part of a fund-raiser for the library.
The teams that walked more than 50 laps raised an extra $100 for
the library.
What fraction of the teams raised this extra money?
The fraction of the teams that raised the extra money, given the number of teams laps needed to be walked, is D. 1 / 3
How to find the fraction ?To find the fraction of teams that raised the extra money, you need to count the number of teams who were able to walk more than 50 laps. The number of teams who walked more than 50 laps walked:
53, 63, 63, and 65 miles so 4 teams did so.
The total number of teams is the number of leafs which is 12 teams.
The fraction of teams who raised the extra money is :
= 4 teams / 12 total teams
= ( 4 ÷ 4 ) / ( 12 ÷ 4 )
= 1 / 3
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if a student is randomly chosen, find the probability that the student is male or earned grade a. leave your answer as a reduced fraction.
The expression to obtain the final probability as a reduced fraction.
What is fraction?A fraction is a mathematical representation of a part of a whole or a part of a group. It consists of two numbers separated by a horizontal line, where the number on the top is called the numerator, and the number at the bottom is called the denominator. The numerator represents how many parts are being considered, and the denominator represents the total number of equal parts that make up the whole or group. Fractions can be written in various forms, such as proper fractions, improper fractions, and mixed numbers, and can be added, subtracted, multiplied, and divided using specific rules and techniques.
We cannot provide a specific numerical answer without more information on the gender and grade distribution of the students. However, we can use the following formula to calculate the probability that a student is either male or earned grade A:
P (male or grade A) = P(male) + P (grade A) - P (male and grade A)
The probability of selecting a male student and the probability of selecting a student who earned a grade A are two independent events, so we can add their probabilities. However, we need to subtract the probability of selecting a male student who also earned a grade A, since we don't want to count that student twice.
If we have the probabilities of each event, we can plug them into the formula and simplify the expression to obtain the final probability as a reduced fraction.
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which polynomial represents the dividend for the division problem shown?
The dividend is 3x³ + 0x² - 1x - 1, which is option A.
Describe Polynomial?In algebra, a polynomial is an expression consisting of variables (also known as indeterminates) and coefficients, which are combined using the operations of addition, subtraction, multiplication, and non-negative integer exponents. For example [tex]2x^2 - 3x + 1[/tex] is a polynomial of degree 2 with three terms.
The term "polynomial" comes from the Greek words "poly" (meaning "many") and "nomial" (meaning "term"). Polynomials are used in many areas of mathematics and science, including calculus, physics, and engineering.
Polynomials are classified by their degree, which is the highest exponent in the polynomial. For example, the polynomial [tex]2x^3 + 3x^2 - x + 5[/tex] is a cubic polynomial, because it has a degree of 3. Polynomials can also be classified by the number of terms they have. For example, a polynomial with only one term is called a monomial, while a polynomial with two terms is called a binomial.
Polynomials have many important properties, such as the fact that the sum and product of two polynomials is also a polynomial. Polynomials can also be factored into simpler polynomials, which can be useful in solving equations and finding roots.
Overall, polynomials are a fundamental concept in algebra and play an important role in many areas of mathematics and science.
The dividend is the product of the divisor and the quotient plus the remainder. In this problem, the divisor is -3x+7 and the quotient is[tex]3x^2-7x+9[/tex]. Using polynomial long division, we get:
[tex]3x^2 - 4x + 2[/tex]
[tex]-3x + 7 | 3x^3 + 0x^2 - 1x - 1[/tex]
[tex]-3x^3 + 7x^2[/tex]
[tex]-7x^2 - 1x[/tex]
[tex]-(-7x^2 + 16x)[/tex]
[tex]-15x - 1[/tex]
[tex]-(-15x + 35)[/tex]
[tex]-36[/tex]
Therefore, the dividend is [tex]3x^3 + 0x^2 - 1x - 1[/tex], which is option A.
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Simplify the expression 3/5x+x
Answer:3x+5x
Step-by-step explanation:
3x÷5 +x
3x+5x(multiply each term by 5)
Find the value of y.
y
3 cm
9 cm
2 cm
y = [?] cm
Enter a decimal rounded to the nearest tenth.
4.3cm is the measure of the unknown side
Secant secant theorem of a circleAccording to the theorem, the product of the measurements of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment if two secant segments are drawn to a circle from an exterior point.
Applying the rule to the question;
3(y+3)= 2(2+9)
3y + 9 = 22
Subtract 9 from both sides
3y = 22- 9
3y = 13
y = 13/3
y = 4.3cm
Hence the measure of y to the nearest tenth is 4.3cm
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In a controlled lab environment some organisms exhibit growth over a specific period. Suppose a certain organism starts out weighing 16 mg and grows to 46 mg over a 5 hour period.
Find a linear model (equation of line) that describes the growth of the organism for the time period given.
Hint x is the number of hours and y is the weight
A linear model (equation of line) that describes the growth of the organism for the time period given is y = 46/5(x) + 16.
What is the slope-intercept form?Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Based on the information provided, we have the following equation that represents the relationship between the number of hours and the weight;
y = mx + c
y = 46/5(x) + 16
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A wall is to be constructed by using tiles, each of the tile's dimensions are 10cm by 20cm by 0.67cm. What is the volume of each tile?
Responses
96.2 cm³
44.7 cm³
200 cm³
134 cm³
The volume of each tile is 134 cm³.
Describe Volume of Cuboid?The volume of a cuboid is the amount of space it occupies in three-dimensional space. A cuboid is a three-dimensional geometric shape with six rectangular faces, where each face has perpendicular edges to two other adjacent faces. The formula for calculating the volume of a cuboid is V = l x w x h, where V is the volume, l is the length of the cuboid, w is the width of the cuboid, and h is the height of the cuboid.
To calculate the volume of a cuboid, first measure its length, width, and height. Then, multiply the length by the width and the height, and then multiply the result by the height again. This gives the volume of the cuboid in cubic units, such as cubic inches, cubic centimeters, or cubic meters.
For example, if a cuboid has a length of 5 cm, a width of 3 cm, and a height of 2 cm, the volume can be calculated as follows:
V = l x w x h
V = 5 cm x 3 cm x 2 cm
V = 30 cubic centimeters
Therefore, the volume of the cuboid is 30 cubic centimeters.
The volume of each tile can be calculated by multiplying its length, width, and height:
Volume = 10 cm × 20 cm × 0.67 cm = 134 cm³
Therefore, the volume of each tile is 134 cm³.
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An economy car weighs 400 pounds more than the compact car. How much does the economy car weigh.
Compact car 1 ton
Answer:
The economy car weighs 800 pounds.
find the 7th term of G.P :1/6,1/3,2/3
Answer:
10 2/3
Step-by-step explanation:
The common ratio is 2. Each term is being multiply by 2 to get to the next term.
To find the 7th term you take the first term and multiply that by the common ratio to the n-1 or 6th power.
[tex]1/6(2)^{6}[/tex] = 10 2/3
Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of mu equals 1.1
kg and a standard deviation of sigma equals 4.5
kg. Complete parts (a) through (c) below
The amounts of weight that male college students gain during their freshman year are normally distributed with a mean of μ equals 1.1 then the probability is 0.9979.
What is probability?Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is the measure of the likelihood of an event occurring divided by the number of possible outcomes. Probability is used to determine the chances of a particular outcome occurring and can range from 0 to 1.
a) What is the probability that a randomly selected male college freshman will gain more than 5.6 kg?
To answer this question, we can use the z-score formula to calculate the z-score for a gain of 5.6 kg. The z-score formula is:
z = (x - μ) / σ
where x is the gain of 5.6 kg, μ is the mean of 1.1 kg, and σ is the standard deviation of 4.5 kg.
Therefore, z = (5.6 - 1.1) / 4.5 = 2.8
The probability that a randomly selected male college freshman will gain more than 5.6 kg is 1 - the cumulative probability of a z-score of 2.8. This can be found using a z-table. The probability is 0.9979.
b) What is the probability that a randomly selected male college freshman will gain between 1.1 kg and 5.6 kg?
To answer this question, we can use the z-score formula to calculate the z-scores for a gain of 1.1 kg and a gain of 5.6 kg.
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What is NOT an examples of a medium?
A. Photographs
B. Newspaper articles
C. Cookbook
D. Paintings
Answer:
Step-by-step explanation:
In the context of communication, a medium is a substance or material through which information or messages are conveyed from a sender to a receiver. Examples of media include photographs, newspaper articles, paintings, videos, radio broadcasts, and so on. These media carry information from the person or organization that created them to the people who consume them, whether it be to inform, entertain, or educate.
A cookbook, on the other hand, may not be considered a medium in the same way as the other options, as it is not primarily used to convey information or messages from a sender to a receiver. While a cookbook contains information, such as recipes and instructions for preparing food, this information is not usually communicated from one person to another in the same way as, for example, a photograph or a newspaper article. A cookbook is more like a reference book or guidebook, which people use to obtain information rather than as a means of transmitting information.
All of the options given could be considered examples of media. However, if we interpret "medium" as a substance or material through which something is transmitted or conveyed, then "cookbook" might not be considered a medium. A cookbook is a book that provides instructions on how to prepare food and does not necessarily serve as a substance through which information is transmitted or conveyed. So the answer would be C. Cookbook.
Answer:
C. Cookbook
Step-by-step explanation:
The other answer choices represent examples of communication medium. A communication medium is a system or channel through which information disseminated to others.
A cookbook is a set of instructions for a specific task and therefore does not fall under the generalized category of medium.
Write the sum using summation notation, assuming the suggested pattern continues.
2, -10, 50, -250, +…
Answer:
The sum using summation notation can be written as: Σn = 2 + (-10) + (50) + (-250) + (1250).
Hannah is taking out a loan in the amount
of $12,000. Her choices are a 3-year loan
at 6% simple interest and a 5-year loan at
7.5% simple interest. What is the difference
in the amount of interest Hannah would
have to pay on these two loans?
A. $2,290
B. $2,340
C. $2,410
D. $2,470
Answer:
Step-by-step explanation:
For the 3-year loan at 6% simple interest:
Interest = Principal x Rate x Time
Interest = 12,000 x 0.06 x 3
Interest = $2,160
For the 5-year loan at 7.5% simple interest:
Interest = Principal x Rate x Time
Interest = 12,000 x 0.075 x 5
Interest = $4,500
The difference in the amount of interest Hannah would have to pay on these two loans is:
$4,500 - $2,160 = $2,340
So the answer is (B) $2,340.
Please help me solve this question on trigonometry.
The trigonometric ratios are given as follows:
a) cos(y) = -0.94.
b) sin(x) = 0.94.
How to obtain the angle measures?The tree bisects an angle into two equal angle measures, one of which is of 70º and the other of which is of x.
Hence the measure of x is given as follows:
x = 70º.
The sine is given as follows:
sine of 70 degrees = 0.94.
The sum of the measures of the internal angles of a triangle is of 180º, hence the missing internal angle is of 20º.
An internal angle is supplementary with it's external angle, hence the value of y is given as follows:
y = 180 - 20
y = 160º.
Then the cosine is of:
cosine of 160 degrees = -0.94.
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The figure shows the graph of the function.
f(x)=
The domain are the possible input while the range are the possible output of a function.
(a) The domain = [-√2, √2], the range = [0, 2]
(b) The domain = [-1, 1], the range = [0, 1]
(c) The domain = [-1, 1], the range = [0, -1]
(d) The domain = [0, 2], the range = [0, 1]
(e) The domain = [-(2 + √2), (√2 - 2)], the range = [0, 2]
Reasons:
The given functions can be expressed by the equation; (-x + 1)·(x + 1) = -x² + 1
Therefore, we have;
(a) y = f(x) + 1 = -x² + 1 + 1 = -x² + 2
The x-intercept of the above function are, x = √2, and x = -√2
Which gives;
The domain = [-√2, √2]
The range = [0, 2]
(b) y = 3·f(x) = 3 × (-x² + 1) = -3·x² + 3
At the x–intercepts, we have;
-3·x² + 3 = 0
x = ±1
The domain = [-1, 1]
The maximum value of y is given at x = 0, therefore;
= -3 × 0² + 3 = 3
The range = [0, 1]
(c) y = -f(x) = -(-x² + 1) = x² - 1
At the x–intercepts, x² - 1 = 0
x = ± 1
The domain = [-1, 1]
The minimum value of y is given at x = 0, which is y = -1
The range = [0, -1]
(d) y = f(x - 1) = -(x - 1)² + 1 = -x² + 2·x
At the x–intercepts, we have; -x² + 2·x = 0, which gives;
(-x + 2)·x = 0
Which gives, x = 0, or x = 2
The domain = [0, 2]
The maximum value of y is given when x = -b/(2·a) = -2/(2×(-1)) = 1
y = f(1) = -1² + 2×1 = 1
Therefore;
The range = [0, 1]
(e) y = f(x + 2) + 1 = (-(x + 2)² + 1) + 1 = -x² - 4·x - 2
At the x–intercepts, we have; -x² - 4·x - 2 = 0, which gives;
x = -(2 + √2) or x = x = √2 - 2
The domain = [-(2 + √2), (√2 - 2)]
The maximum value of y is given when x = -4/(2)) = -2
Which gives;
-(-2)² - 4·(-2) - 2 = 2
The range = [0, 2]
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Evaluate the expression 1/3x^2 for x=6
Please help
Solve only this problem :
Write an expression for the number of years after which there will be 15,000 dollars in the account.
The time is about 122 years and 9 months after which there will be 15,000 dollars in the account.
What is an exponential function?Mathematical functions with exponents include exponential functions. f(x) = bˣ, where b > 0 and b 1, is a fundamental exponential function.
Given:
An expression,
1[tex](e)^{0.034t}[/tex] model the balance, in thousands of dollars, where t is time.
(a).
0.034 represents the rate at which the function is expressed.
So,
0.034t = log(15000)
t = log(15000)/0.034
t = 122.826213502 in years.
t = 122 years, 9 months.
Therefore, t = 122 years, 9 months.
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Giorgio offers the person who purchases an surpriseunce bottle of Allure two free gifts, chosen from the following: an umbrella, a 1-ounce bottle of Midnight, a feminine shaving kit, a raincoat, or a pair of rain boots. If you purchased Allure, what is the probability you randomly select an umbrella and a shaving kit in that order?
a.
0.00
b.
1.00
c.
0.05
d.
0.20
Therefore , the solution of the given problem of probability comes out to be the required probability is 0.05 or 1/20 and the correct option is c.
What does the probability technique actually suggest?Probability theory is an area of mathematics that focuses on calculating the probability that a claim is valid or that a specific event will occur. Chance can be represented by any number between zero and 1, where range 1 is typically used to convey certainty and 0 is frequently used to denote possibility. The probability that a specific event will occur is displayed in a probability diagram.
Here,
The probability of randomly selecting an umbrella and a shaving kit in that order is equal to the probability of selecting an umbrella (with probability 1/5) multiplied by the probability of selecting a shaving kit from the remaining gifts (with probability 1/4,
since one gift has already been chosen and removed from consideration).
Therefore, the probability of selecting an umbrella and a shaving kit in that order is:
=>(1/5) x (1/4) = 1/20 or 0.05
So if you purchased Allure, the probability of randomly selecting an umbrella and a shaving kit in that order as your two free gifts is 1/20 or 0.05.
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