There are 7 % of Americans over age 100 who were there in 2000 and the number of Americans growing by 54% over age 100 changed in 2000.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
The number of Americans over age 100 can be approximated by
[tex]P(t) = 0.07e^{0.54t}[/tex]
where is P(t) measured in millions and t is measured in decades.
Also, t = 0 corresponds to 2000.
⇒ [tex]P(t) = 0.07e^{0.54t}[/tex]
Substitute the t = 0 in the above function, and we get
⇒ [tex]P(t) = 0.07e^{0.54\times0}[/tex]
⇒ P(t) = 0.07 e°
⇒ P(t) = 0.07
Convert decimals into fractions, and we get
⇒ P(t) = 7 / 100
This represents 7 out of 100 which is 7 % of Americans over age 100 who were there in 2000.
Thus, the number of Americans growing by 54% over age 100 changed in 2000.
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Using FUNCTION NOTATION, assume you are given the function: y = 3x - 2. This can be rewritten as ________ = 3x - 2, since y can be replaced with _______.
The complete statement is:
This can be rewritten as _f(x)_ = 3x - 2, since y can be replaced with _f(x)__.
How to use function notation?A general relation is written as:
y = something that depends of x.
This is a relation that relates the variable y with the variable x, where we define x as the input and y as the output.
If this is a function, we can use the notation:
y = f(x).
(or any letter of x, f(x) is the most common notation used)
in this case, we have:
y = 3x - 2
And in function notation, this will be writen as:
f(x) = 3x - 2
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A company has 40 salespeople. A board member at the company asks for a list of the top 5 salespeople, ranked in order of effectiveness. How many such rankings are possible?
The number of rankings that are possible when the company has 40 salespeople is 78960960.
What is permutation?Based on the information given, permutations will be used. The formula is illustrated thus:
Permutations = n! / (n – r)!
N is the number of things you are choosing from,
r is the number of items.
“!” is a factorial of a number
The company has 40 salespeople and the board member at the company asks for a list of the top 5. This will be;
= 50! / (40 - 5)!
= 40! / 35!
= 40 × 39 × 38 × 37 × 36
= 78960960
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In a math class , there are 14 girls and 16 boys. Which of the following ratios does NOT represent between girls and boys?A. 14:16B. 14/16C. 7 to 8D. 2:9its not college mathematics its middle school
No. of girls = 14
No. of Boys =16
Therefore the ratio, from girls to boys is,
[tex]\frac{14}{16}[/tex]Which can also be written as,
[tex]\begin{gathered} 14\colon16 \\ 7\text{ to 8} \end{gathered}[/tex]Therefore, the wrong ratio is option D.
That is,
[tex]2\colon9[/tex]So, the answer is option D.
In which pair do both decimals represent rational numbers? O A. 9.0032812373025549382... and 0.12333.. OB. 0.115 and 0.12333... O C. 3.10382947305718274... and 0.123 O D. 9.0032812373025549382... and 0.115
Rational numbers can be formed by dividing 2 integers. It can be represented in this format x/y where y is not 0. Rational numbers, in decimal form are not repetitive and unending.
Therefore,
Find the length of the sloping side of the roof. Give your answer to the nearest foot. Show your work.
Given:
The triangle having two similar angles.
This is the isosceles traingle.
Draw the altitude to the given traingle,
D divides the side BC into two equal side having length,
[tex]\begin{gathered} \frac{45}{2}=22.5 \\ BD=22.5\text{ and DC=22.5} \end{gathered}[/tex]Now, use the tan ratio for right triangle ABD,
[tex]\begin{gathered} tan15^{\circ}=\frac{AD}{BD} \\ 0.268=\frac{AD}{22.5} \\ AD=6.02=6\text{ f}eet \end{gathered}[/tex]Using the pythagorean theorem,
[tex]\begin{gathered} AB^2=AD^2+BD^2 \\ =6^2+22.5^2 \\ =542.25 \\ =23.286 \\ =23.3 \end{gathered}[/tex]The length of the sloping side of the roof is 23.3 feet.
Althea needs 134 ounces of cold cuts for a party. How many pounds and ounces does she need?
The number of pounds and ounces that we have in 134 ounces is; 8 pounds 6 ounces
How to carry out units conversion?
We know that in units conversion, there are different units and their conversion rates. For example;
1 meters = 100 cm
1000 meters = 1 kilometer
1000 grams = 1 kilograms
100 cents = 1 dollar
Now, we want to convert ounces to pounds.
The conversion rate for ounces to pounds is;
1 ounce = 0.0625 pounds
We are given 134 ounces of cold cuts for a party. Converting that to pounds gives us;
134 * 0.0625/1 = 8.375 pounds
Now, we want it in pounds and ounces and so we convert the decimal part to ounces
1 pound = 16 ounces
0.375 pounds = 0.375 * 16/1 = 6 ounces
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Kaj needs to order some new supplies for the restaurant where she works. The restaurant needs at least 736 knives. There are currently 155 knives. If each set on sale contains 12 knives, what is the minimum number of sets of knives Kaj should buy?
Hence, the minimum number of sets of knives kaj should buy is 48 sets.
Given this, a restaurant must have at least 736 knives.
At the moment, it possesses 155 knives.
Every set includes 12 knives.
Let the number of knife sets be.
Reason: Minimum number of sets indicates ≥
This means ≤ the maximum amount of sets
Step: 2
In light of the inquiries,
[tex]155+s*12\geq 736[/tex]
[tex]12s\geq 736-155[/tex]
[tex]12s\geq 581[/tex]
[tex]s\geq \frac{581}{12}[/tex]
[tex]s\geq 48.42[/tex]
Step 3: Count the number of knife sets [tex]s\geq 48.42[/tex]
that is greater than or equal to 48
Therefore, the required minimum is 48 sets of knives.
What are sets?
In mathematics, a set is a well-defined collection of objects. Sets are named and represented using capital letters. In the set theory, the elements that a set comprises can be any kind of thing: people, letters of the alphabet, numbers, shapes, variables, etc.
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100 points asap and brainliest
Answer:
68
Step-by-step explanation:
i would appreciate so much if you could answer this and atleast explain a little how you did it (optional)
Answer:
a.
Fee of whole band = Fee of writer + guitarist + singer
Fraction of fee of whole band = 4/12 + 1/12 + 1/12
= 4+1+1/12
=6/12
=1/2
b.
Fee of writer= 4/12 of £3000
=3000 × 4/12
= £1000
Fee of singer= 1/12 of £3000
= 3000 × 1/12
= £250
Fee of guitarist= Fee of singer
= £250
A car that travels from Las Vegas to Los Angeles averages about 60 mi/h. The distance from Las Vegas to Los Angeles is 270 miles. Write a function to represent the distance d remaining on the trip t hours after departure.
The distance remaining is given by the equation d = 270 - 60t
How to solve an equation?Speed is the ratio of distance travelled to time taken. It is given by:
Speed = distance / time
Let d represent the distance from Las Vegas to Los Angeles and t represent the remaining time after departure.
A car travels from Las Vegas to Los Angeles at about 60 mi/h. The distance from Las Vegas to Los Angeles is 270 miles.
Hence distance remaining is:
d = 270 - 60t
The distance remaining is d = 270 - 60t
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A quiz consists of two true false questions and two multiple-choice question with three choices each. How many different sets of answers are there?There aredifferent sets of answers.
We know that
• There are two true/false questions.
,• There are two multiple-choice questions with three choices each.
In the true/false questions, there are 4 ways to answer since each question has only two choices.
In the multiple-choice questions, there are 6 ways to answer since there are 3 choices per question.
Therefore, there are 10 ways to answer in total.Help me rewrite this problem to satisfy the provided boxes please
EXPLANATION
Since we have the expression:
Removing the parentheses:
[tex]5x^2+6x+5+6x^2-6x-5[/tex]Rearranging terms:
[tex]5x^2+6x^2+6x-6x+5-5[/tex]Adding like terms:
[tex]11x^2+0x+0[/tex]The final expression is as follows:
[tex]undefined[/tex]7x — 9y = 12—7x – 7y = -28
In order to solve this system of equations, we can add both equations, this way we can find the value of y and then the value of x:
[tex]\begin{gathered} \begin{cases}7x-9y=12 \\ -7x-7y=-28\end{cases} \\ 7x-9y-7x-7y=12-28 \\ -16y=-16 \\ y=\frac{-16}{-16}=1 \\ \\ 7x-9=12 \\ 7x=21 \\ x=\frac{21}{7} \\ x=3 \end{gathered}[/tex]So the solution to this system is (3, 1).
Determine whether the function has a minimum or maximum value and then find that value.()=−^2+2−7
Given function is
[tex]f(x)=-x^2+2x-7[/tex]Now,
[tex]\begin{gathered} f(x)=-(x^2-2x+7) \\ =-(x^2-2x+1+6) \\ =-\lbrack(x-1)^2+6\rbrack \\ =-(x-1)^2-6 \end{gathered}[/tex]Being a perfect square,
[tex](x-1)^2\ge0[/tex]Therefore,
[tex]-(x-1)^2\leq0[/tex]So,
[tex]f(x)\leq-6[/tex]Theerfore, the maximum value of the given function is -6.
A coordinator will select 5 songs from a list of 8 songs to compose an event's musical entertainment lineup. How many different lineups are possible?
The number of lineups possible is the combination of selecting 5 songs from 8 songs.
8C5 = 56.
What is combination?A combination is a mathematical way that evaluates the number of possible arrangements within a collection of items, leaving behind of the order of selection. A combination can select items in any order. Combinations can be confused with permutations Water is a combination of hydrogen and oxygen. The car interior is available in various color combinations. The formula for combinations is nC_r = n/(r!*(n - r)!), where n is the number of items and r is the number of items selected at once. Let's look at an example of how combinations are calculated. There are 10,000 possible combinations of the numbers 0-9 in a 4-digit codeTo learn more about combination from the given link:
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Nathan loved learning about earthquakes in science class. He told his brother that up until a 7.8-magnitude earthquake hit Nepal in 2015, Mount Everest had been moving northeast at a rate of 7.7×10
–
6 centimeters per minute. What would be the most appropriate unit for Nathan to use instead of centimeters per minute?
The most appropriate unit for Nathan to use instead of centimeters per minute is centimeters per year.
What is an earthquake?An earthquake simply means a rapid motion of the solid layer of the Earth.
In this case, Nathan told his brother that up until a 7.8-magnitude earthquake hit Nepal in 2015, Mount Everest had been moving northeast at a rate of 7.7×10^-6 centimeters per minute.
Since the year is being discussed, the unit should be based on the year.
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Is the answer correct if no please let me know
Answer: 57
Given:
[tex]S_n=4n-3[/tex]We are asked to find the 15th term, meaning n = 15
[tex]S_n=4n-3[/tex][tex]S_{15}=4(15)-3[/tex][tex]S_{15}=60-3[/tex][tex]S_{15}=57[/tex]Therefore, the 15th term is 57.
Let f(x) = 2x^2 – 3 and g(x) =x+1/2Find the value of (fof )(-1)A -1B-3C 0.5D 95
HELP PLEASE.
Either Table A or Table B shows a proportional relationship.
Plot the points from the table that shows a proportional relationship.
( If you can, can you save the image as and edit it it will help me out a lot)
Answer: Table A has a proportional relationship
See the diagram below
==================================================
Explanation:
Table A has a proportional relationship because all the points are on the same straight line. That line in this case is y = 2x
Whatever x is, multiply it by 2 and you'll get the y value
Example: If x = 4, then y = 2*x = 2*4 = 8 which gives the point (4,8)
Another phrase for "proportional relationship" is "direct variation".
Kali just started a new sales floor job to save for college. She earns 15.75 plus a flat fee of 50 . She wants to earn between 200 and 400 . The following inequality represents her earning potential
200 ≤ 15.75x + 50 ≤ 400 Solve the inequality PLEASE HELP ASAP HELP I WILL GIVE BRAINLIEST AND 100 POINTS
!!
The solution for the inequality is 11.746 ≤ x ≤ 24.44
Kali earns a 15.75 plus a flat fee of 50 from her job.
She wants to earn between 200 and 400.
Let 'x' denote her earning potential.
Then the inequality for her earning potential is given by,
200 ≤ 15.75x + 50 ≤ 400
We solve this inequality for x.
Subtract 50 from the inequality,
⇒ 200 -15 ≤ 15.75x ≤ 400 -15
⇒ 185 ≤ 15.75x ≤ 385
Divide by 15.75,
⇒ 11.746 ≤ x ≤ 24.44
is the solution for the inequality.
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Find the midpoint of the line segment with endpoints (13,-14) and (-13, 10).
Answer:
(0, -2)
Step-by-step explanation:
Add the x value and divide by 2
[tex]\frac{13-13}{2}[/tex] = [tex]\frac{0}{2}[/tex] = 0
Add the y value and divide by 2
[tex]\frac{-14 + 10}{2}[/tex] = [tex]\frac{-4}{2}[/tex] = -2
Mr. Thomatos thinks that {3, 8} and [3, 8] represent the same set of values Is Mr. Thomatos correct? Why or why not? Explain. (giving brainliest)
{3,8} give the values of set that implies the set has two elements 3 and 8. [3,8] give the range of values that can be used in any functions with values from 3, 4, 5, 6, 7, 8 both 3 and 8 included.
What is set?Sets are collections of well-defined objects or elements in mathematics. A set is denoted by a capital letter symbol, and the number of elements in a finite set is denoted by the cardinal number of a set enclosed in a curly bracket{...}.
What is Function?A function is defined as a relationship between a set of inputs that each have one output. A function is a relationship between inputs in which each input is related to exactly one output. Every function has a domain and a codomain, as well as a range.
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The radius of a circle is 14 cm. Find its circumference in terms of pie
Explanation.
The question wants us to determine the circumference of the circle.
Circumference of a circle simply means the perimeter of a circle, and the formula to be used is
[tex]\begin{gathered} C=2\pi r \\ where \\ r=radius=14cm \end{gathered}[/tex]At a party, there are 30 men, 16 of whom are without dates, and 30 women, none of of whom are without dates. Find the probability of picking someone at random and getting a person who is a woman or without a date?
For this type of probability question, there are different ways to solve the same question but let's analyze the situation and calculate as simple as possible.
For our question, there are two parts, the first one first is the probability to pick someone who is a woman. Once there are 60 people of which 30 are women, it means this probability is 30/60. Let's keep this probability.
Now let's move on to the second part. The situation where we pick someone who is without a date. once there are 60 people and all 30 women have a date and 16 men also have a date it means 30 + 16 - 60 = 14 people does not have a date. So the probability to pick someone without a date is 14/60.
Now once we have analyzed the two parts of the question, and we have two probabilities all we need is to sum our probabilities, as follows:
But why do we sum and do not multiply? Because we use the proposition OR at "Find the probability of picking someone at random and getting a person who is a woman OR without a date" If the proposition was AND we would have multiplied both probabilities.
Given: f(x) =x^2 + 6x + 5Find the x and y value of the vertex (turning point)And what are the zeros of the parabola?
Solution: X-value of vertex=-3
Y-value of vertex=-4
Zeros of the parabola: X=-5 and x=-1
Analysis
We can find the x-coordinate of the vertex, calculating -b/2a. First, we identify the a and b values of y=ax^2+bx+c of your quadratic equation.
b=6
a=1
[tex]\begin{gathered} -\frac{b}{2a}=-\frac{6}{2(1)}=-3 \\ \\ After\text{ we find x-coordinate, we can find y-coordinate of the vertex replacing x-value.} \\ f(x)=x^2+6x+5\text{ = }^^(-3\text{ }^2)+6(-3)+5 \\ f(x)\text{ = 9}-18+5 \\ f(x)=-4 \end{gathered}[/tex]Now, let's find the zeros of the parabola. We factorize the quadratic equation:
[tex]\begin{gathered} f(x)=x^2+6x+5 \\ f(x)=(x+5)(x+1) \\ Let^{\prime}s\text{ equal to zero} \\ (x+5)(x+1)=0 \\ (x+5)=\text{ 0 }(x+1)=0 \\ x=-5\text{ }x=-1 \end{gathered}[/tex]I need help with 3x-2y=24 find the y and x intercept and the slope
3x-2y=24
3x - 2y + 2y = 24 +2y Adding 2y to both sides of the equation
3x - 24 = 2y + 24 - 24 Subtracting 24 from both sides of the equation
(3x - 24)/2= 2/2y Dividing by 2 on both sides of the equation
3/2x - 12 = y
From this form of the equation we deduce the slope (coefficient of x) is 3/2 and the y-intercept is equal to -12.
To find the x-intercept, we replace y= 0 in the equation and isolate x
3/2x - 12 = 0
3/2x - 12+12 = 0+12 Adding 12 to both sides of the equation
x= 12/(3/2) Isolating x
x= 8
The x-intercept is 8
please help
Which graph represents the solution set of the system of inequalities?
{y≥12x+1y>−x−2
Responses
A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. A solid line passing through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 0 comma 1 end ordered pair. The region below the solid line and above the dashed line is shaded.
Image with alt text: A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. A solid line passing through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 0 comma 1 end ordered pair. The region below the solid line and above the dashed line is shaded.,
A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair negative 5 comma 3 end ordered pair. A solid line passing through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair 0 comma 1 end ordered pair. The region above the solid line and above the dashed line is shaded.
Image with alt text: A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair negative 5 comma 3 end ordered pair. A solid line passing through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair 0 comma 1 end ordered pair. The region above the solid line and above the dashed line is shaded.,
The graph that represents the system of inequalities is the graph attached below.
How to Determine the Graph of a System of Inequalities?The graph that would represent the system of inequalities must be two lines that intersect each other and have the exact slope and y-intercept of each of the lines on the graph.
Determine the slope and y-intercept of each of the inequalities, and also determine their boundary lines based on which inequality sign they have.
The line that represents the inequality, y ≥ ½x + 1, will be a solid line that has a slope of ½, and a y-intercept of 1.
The second line that represents the inequality, y ≥ -x - 2, will be a dashed line that has a slope of 1, and a y-intercept of -2.
Therefore, the graph that represents the features stated above for both lines is shown in the diagram below.
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I don’t understand this paper and our sub has no idea, nor the other students so if someone could help me, that would be great.
By Angle-Angle theorem similarity ΔABC is similar to ΔA'B'C'.
Given two triangles are ABC and A'B'C'.
What is a dilation?Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.
1) Triangle ABC is reduced to triangle A'B'C'
∠ABC=∠A'B'C'=90°
∠BAC=∠B'A'C'
So, by AA similarity
ΔABC≈ΔA'B'C'
2) Triangle ABC is enlarged to triangle A'B'C'
∠ABC=∠A'B'C'
∠BAC=∠B'A'C'
So, by AA similarity
ΔABC≈ΔA'B'C'
Therefore, by Angle-Angle theorem similarity ΔABC is similar to ΔA'B'C'.
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What is the slope and y-intercept?
y=-5x+6
Options:
Blank # 1
Blank # 2
3. Given: B is the midpoint of AC, AD = CD
Prove:
DAB = LDCB
Statements
1)
2) AB=CB
3) DB DB
4)
5) ZDAB=2DCB
A
1)
2)
3)
5)
Reasons
D
B
C
Using the congruency of the triangle we can prove all the conditions.
What do you mean by congruencey of the triangle?The dimensions of the sides and angles of two or more triangles determine whether they are congruent. A triangle's size and shape are determined by its three sides and three angles, respectively. Two triangles are said to be congruent if pairings of corresponding sides and corresponding angles are equal. They are the exact same size and form.
D is the midpoint of AC
so AB = BC
and also AD = CD
so the triangle ADB is congruent to triangle CDB
Therefore,
angle ADB = angle CDB
angle ABD = angle CBD
angle BAD = angle BCD
Using congruency of the triangle.
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