Answers
The time taken for the population to reach 26.6 million is 2 years while the population in year 2000 is 18.5 million.
What is the population growth?We can be able to define population growth as the process by which the population of an area is increasing. We know that the increase or the decrease of population would have to be an exponential function.
Given that we have the function A =18.5e^0.1708t where A is the population after a given time from year 2000 and t is the number of years after year 2000. It then follows that 18.5 million refers to the population of the united states as at year 2000.
We now have;
26.6 =18.5e^0.1708t
26.6/18.5 = e^0.1708t
1.44 = e^0.1708t
ln(1.44) = 0.1708t
t = ln(1.44)/ 0.1708
t = 2 years
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Related Questions
find the x and y of the graph of 3x +2y=15. State each answer as an integer or an improper fraction in simplest form.
Answers
Answer:
Step-by-step explanation: To find the x let y=0
We substitute into the equation 3x+2y=15
3x+2 *0=15
3x=15
x=15/3=5
To find the y let x=0
we substitute into the equation x =0
3*0+2y=15
2y=15
y=15/2
Type the expression as a radical.
Answers
Step-by-step explanation:
in a fraction as exponent the numerator defines the pure exponent of the base, and the denominator gives the degree of root of the base.
so, this is
[tex] \sqrt[5]{y^{3} } [/tex]
Answer:
[tex] \sqrt[5]{ {y}^{3} } [/tex]
Step-by-step explanation:
When converting an expression with a fractional exponent to its radical form, the base number goes inside the radical(which means it becomes the radicand) along with the numerator(which remains an exponent). Whereas the denominator of the exponent becomes the index, or what dictates whether the radical is a square root, cube root, etc.
EX:
[tex] {y}^{ \frac{a}{m} } = \sqrt[m]{ {y}^{a} } [/tex]
I need help with this
Answers
Answer:
D
Step-by-step explanation:
5*1 = 5
5*2 = 10
5*3 = 15
5*4 = 20
5*5 = 25
3. Laurie uses yellow and white tiles to create a pattern.
a) Make a table of values to show the number of yellow tiles in relation to the figure number.
b) Describe the relationship between the number of yellow tiles and the figure number.
c) Develop an expression and an equation to model the number of yellow tiles. Explain what each part of the equation represents.
d) How many yellow tiles are in Figure 24?
e) Which figure number has 176 yellow tiles? Verify your answer.
f) Is it possible to have a figure with 54 yellow tiles? Show how you know.
Answers
a) Figure 1 2 3
Number of tiles 8 12 16
b) The number of tiles is 8 more than 4 times of 1 less than the number of figure.
c) The equation of model the number of yellow tiles is y = 4x + 4.
d) The number of tiles in figure 24 is 100.
e) Figure 43 has 176 yellow tiles.
f) No.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
Given that
the number of yellow tile in figure 1 is 8.
The number of yellow tile in figure 2 is 12.
The number of yellow tile in figure 3 is 16.
(a) The table is
Figure 1 2 3
Number of tiles 8 12 16
(b)
The number of tiles increase at a constant rate.
The rate is (12 - 8) = (16 - 12) = 4
The relation with the figure and number of tiles is
The number of tiles is = 4 + (the number of figure - 1)4
C)
Assume that y represents total number of tiles.
x = Number of figure
Rewrite "The number of tiles is = 4 + (the number of figure - 1)4" in term of x and y:
y = 8 +(x - 1)4
y = 8 + 4x -4
y = 4x + 4
d) Putting x = 24 in y = 4x + 4
y = 4×24 + 4
y = 96 + 4
y = 100
e)
Putting y = 176 in y = 4x + 4
176 = 4x + 4
Subtract 4 from both sides:
172 = 4x
Divide both sides by 4
x = 43
f)
Putting y = 54 in y = 4x + 4
54 = 4x + 4
Subtract 4 from both sides:
50 = 4x
Divide both sides by 4
x = 50/4
The value of x is not a whole number. Thus it is not possible that a figure has with 54 yellow tiles.
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PLEASE HELP ME WITH THIS QUESTION
Draw an example of a polynomial with
-Degree of 5
-Positive lead coefficient
-Zeros at -5, -2, 0, 3, 6
Answers
The required polynomial is x⁵ - 2x⁴ - 35x³ + 36x² + 180x.
What is a polynomial?A polynomial is an algebraic expression.
A polynomial of degree n in variable x can be written as,
a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.
Given, We have to construct a polynomial of degree 5, a positive lead
co-efficient and zeros or roots are -5, -2, 0, 3, 6.
If roots are -5, -2, 0, 3, 6 factors are (x + 5), (x + 2), (x + 0), (x - 3), (x - 6).
∴The required polynomial is (x + 5)(x + 2)(x + 0)(x - 3)(x - 6).
= x(x + 5)(x + 2)(x - 3)(x - 6).
= (x² + 5x)(x² - 3x + 2x - 6)(x - 6).
= (x² + 5x)(x² - x - 6)(x - 6).
= (x² + 5x)(x³ - 6x² - x² + 6x -6x + 36).
= (x² + 5x)(x³ - 7x²+ 36).
= x⁵ - 7x⁴ + 36x² + 5x⁴ - 35x³ + 180x.
= x⁵ - 2x⁴ - 35x³ + 36x² + 180x.
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Which side lengths form a right triangle?
Choose all answers that apply:
A
B
4, 8, 12
2, √/5,3
2,2, √8
Answers
Based on the Pythagorean theorem, the set of side of lengths that will form a right triangle are:
2, √5, 3
2, 2, √8
What are the Side Lengths that can Form a Right Triangle?Based on the Pythagorean theorem, any set of side lengths that will form a right triangle would have the following relationship:
b² = a² + c², where b is the longest side or the hypotenuse of the right triangle and "b and c" are the lengths of the legs of the triangle.
For side lengths, 4, 8, and 12, we have:
12² = 4² + 8²
144 = 16 + 64
144 = 80 [not true, cannot form a right triangle]
For side lengths, 2, √5, 3, we have:
3² = (√5)² + 2²
9 = 5 + 4 [true, this set will form a right triangle]
For side lengths, 2, 2, √8, we have:
(√8)² = 2² + 2²
8 = 4 + 4
8 = 8 [true, this set will form a right triangle]
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Determine the degree measure of one angle of a 45-sided regular polygon.
Answers
The measure of an interior angle (in degrees) of an [tex]n[/tex]-sided regular polygon is [tex]\frac{180(n-2)}{n}[/tex].
[tex]n=45 \implies \frac{180(n-2)}{n}=\boxed{172^{\circ}}[/tex]
The degree measure of one angle of a 45-sided regular polygon is 172°.
What is an angle measure?When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
Here, the polygon has 45 sides.
To find the measure of an interior angle of a regular polygon,
we make use of the formula for each angle = (n - 2) × 180 / n.
The formula calculated is only valid in cases of regular-sided polygons.
n = 45 substituting the value of n to the formula.
(n - 2) × 180 / n
= 180 ( 45-2) / 45
= 180 x 43 / 45
= 7740 / 45
= 172°
Therefore, the measure of one angle is 172°.
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A recipe requires 1 1/4 cups of sugar for every 1/3 of a cup of salt. What is the unit rate of salt to sugar in the recipe?
Answers
Answer:
3 3/4 cups of sugar per cup of salt
Step-by-step explanation:
To find the unit rate of salt to sugar in the recipe, we need to divide the number of cups of sugar by the number of cups of salt. In this case, the unit rate of salt to sugar is 1 1/4 cups of sugar divided by 1/3 of a cup of salt, which can be simplified to 3 3/4 cups of sugar per cup of salt.
Answer:
The unit rate of cups per teaspoon is 1 1/3
Step-by-step explanation:
-A recipe calls for 2 by 3 cup of sugar for every 1 by 2 teaspoon of vanilla.
Based on the above information, the calculation is as follows:
=(2/3)/(1/2)
=(2/3)/(1/2)
=(2/3)x(2/1)
=(2x2)/(3x1)
=(4/3)
= 1 1/3
The_______states that the part equals the percent multiplied by the whole
Answers
The percentage equation states that the part equals the percent multiplied by the whole.
What is percent?
A percentage is a number that indicates how much is 100 and can also be expressed as a decimal or fraction.
What is Percentage Equation?
Percentage equations allow you to find parts or ratios of amounts (or wholes). Percentages are specified with a % sign after the number of hundredths.
The formula for percentage equation is given below
Percent=(Part/Whole)x100
Example: 45 is 60% of what number?
Modifying the above percentage equation, we get
Whole= (Part/Percent) x 100
⇒Whole= (45/60) x 100
⇒Whole= (3/4) x 100
⇒Whole= 3 x 25
⇒Whole= 75
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Determine whether the following function is a polynomial function. If the function is a polynomial function, state its degree. If it is not, tell why not. Write the polynomial in standard form. Then identify the leading term and the constant term. f(x) = 2x+x5
Answers
Therefore the given function is a polynomial function consisting of the constant 0 and the leading term 1.
What is polynomial function?A polynomial function is a function in an equation that only employs non-negative integer powers or only positive integer exponents of a variable, such as in a quadratic equation, cubic equation, etc. For instance, the polynomial 2x+5 has an exponent of 1.
Here,
Exponents are positive integers for the polynomial function given.
The positive integer 2x has an exponent of 1.
[tex]x^{5}[/tex], where is a positive integer with exponent 5, and.
Real numbers like 5 and 1 are among the coefficients in the function.
Consequently, a polynomial describes the function.
Having a degree of 5, it is a polynomial.
A polynomial is written in standard form by beginning with the term with the highest exponent and writing the remaining terms in descending order of terms with lower exponents.
Standard form for the polynomial is f(x)=2x+ [tex]x^{5}[/tex].
consisting of the constant 0 and the leading term 1.
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Jody takes out a 30-year mortgage for $300,000 at 3.524% APR. Her monthly payment is $1,350. She pays $186,175 in interest over those 30 years.
What is the total amount she will pay for the house?
Answers
If her monthly payment is $1,350. She pays $186,175 in interest over those 30 years. The total amount she will pay for the house will be $ 672175.
What is APR?The full name of APR is the annual percentage rate. It is defined as the percentage rate applied on borrowing money in the form of interest but APR is applied annually.
It is given that, Jody takes out a 30-year mortgage for $300,000 at 3.524% APR. Her monthly payment is $1,350. She pays $186,175 in interest over those 30 years.
1 year = 12 month
30 year = 360 month
We have to find the total amount she will pay for the house,
Total amount = Monthly payment × 360 + intreast over 30 years
Total amount =1,350 × 360 + 186,175
Total amount =$ 672175
Thus, if her monthly payment is $1,350. She pays $186,175 in interest over those 30 years. The total amount she will pay for the house will be $ 672175.
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What is the equation in slope-intercept form of the line that passes through the point (3,4) and is parallel to the line represented by y=3x−2?
y=3x+7y
y=3x−5y
y=−3x+5y
y=−3x−7
Answers
The equation in slope-intercept form of the line that passes through the point (3,4) and is parallel to the line represented by y=3x−2 is y = 3x - 5.
How to represent equation in slope intercept form?The equation of a line can be represented in slope intercept form, point slope form, standard form and general form.
Linear equation in slope intercept form is as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the line that passes through the point (3,4) and is parallel to the line represented by y = 3x −2.
parallel lines have the same slope.
Therefore, the slope of the line is 3.
The y-intercept can be found as follows:
using (3, 4)
y = 3x + b
4 = 3(3) + b
b = 4 - 9
b = -5
Therefore, the equation in slope intercept form is y = 3x - 5.
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Twenty-five people in a survey were asked to give their current checking account balances. Use the balances shown in the following list to complete the frequency distribution table.
$220
$337
$29
$60
$201
$519
$462
$290
$131
$572
$227
$111
$124
$509
$331
$306
$439
$28
$504
$431
Fill in the missing information.
Class Intervals
Class Frequency
(Account Balances) (Number of People)
$0-$99
$431
$83
$451
$417
$341
CIP
Answers
Twenty-five people in a survey were asked to give their current checking account balances and the frequency = 4.
What is frequency and example?
The frequency of a particular data is the number of times the data value occurs. We represent the frequency of a data value by f. For example, if five students got an A in science, and then the grade A is said to have a frequency of 5.Given that;
Class intervals Class frequency
(Account Balance) (No of people)
$0 - $99 ?
Entries in this ($0 - $99) range are $29 , $60 , $28 , $83 = 4
Therefore, class frequency (no of people) = 4
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Topic: Simplifying Fractions
Progress:
The movement of the progress bar may be uneven because questions can be worth more or less (including zeroj depending on your answer
Simplify to lowest terms and find an equivalent fraction that has a denominator of 32.
Submit
Test
Pass
Question : 9782
Save and close
Answers
The equivalent fraction for 12/16 will be A. 3/4, 24/32
How to calculate the fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.
It should be noted that equivalent fraction for 12/16 will be found by reduction to lowest term. This will be:
12/16 = 3/4
Also multiply the numerator and denominator by 8 will give 24/32. In conclusion, the correct option is A.
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Below are two parallel lines with a third line intersecting them.
Answers
Answer: 132 degrees
Step-by-step explanation:
Because the lines are parallel, and the line intersecting them is straight, the angle on top should be the same as the angle on the bottom.
So that makes x=132
PLEASE ANSWER CLEARLY
Aisha is working two summer jobs, making $7 per hour babysitting and $8 per hour landscaping. Last week Aisha worked 2 more hours babysitting than hours landscaping and earned a total of $134. Write a system of equations that could be used to determine the number of hours Aisha worked babysitting last week and the number of hours she worked landscaping last week. Define the variables that you use to write the system.
Answers
The number of hours Aisha worked babysitting and landscaping last week is 7.9 hours and 9.9 hours respectively
Step-by-step explanation:
What is the solution to this equation
x^2+4x-12=0
Answers
Answer:
x = 2 or –6
Step-by-step explanation:
x² + 4x –12 = 0
x² +6x –2x –12 = 0
x(x + 6) –2( x + 6) = 0
(x–2)(x+6)= 0
x–2= 0
x= 2.
x+6= 0
x= –6
x = 2 or –6
SDSADASDASDADASDASDA
Answers
Answer:
ong
Step-by-step explanation:
Evan added -2 1/2+4 and got six 1/2 draw arrows on the number line to represent the problem and explains Evans error
Answers
Evan made a mistake to add. As the sign of 4 positive and the sign of [tex]2\frac{1}{2}[/tex]. The subtraction operation must be performed for this.
What is a number line?
The horizontal straight lines in mathematics known as number lines are where integers are arranged in equal intervals. A number line can be used to represent every number in a sequence. The endpoints of this line go on forever.
The given expression is
[tex]-2\frac{1}{2}[/tex] +4
It can be written as 4 [tex]-2\frac{1}{2}[/tex] .
Now perform the subtraction operation:
= 4 - 5/2
= (8-5)/2
=3/2
= [tex]1\frac{1}{2}[/tex]
The number line that represents the given operation is attached below.
Evan added 4 and [tex]2\frac{1}{2}[/tex] which is incorrect way.
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64 - (-2)⁵ ÷ 2³ + (-1)³ · (0.5)²
Answers
To solve this expression, we need to use the rules of order of operations, which dictate the order in which mathematical operations should be performed. The order of operations is typically abbreviated using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Using the order of operations, we can solve the expression as follows:
64 - (-2)⁵ ÷ 2³ + (-1)³ · (0.5)²
= 64 - (-2)⁵ ÷ 8 + (-1)³ · 0.25
= 64 - (-32) ÷ 8 + (-1)³ · 0.25
= 64 + 32 + (-1)³ · 0.25
= 96 + (-1)³ · 0.25
= 96 + (-1) · 0.25
= 96 - 0.25
= 95.75
Therefore, the final result of the expression is 95.75
Pronghorn Company purchased a delivery truck for $26,000 on January 12022. The truck has an expected salvage value of $1.280 and is expected to be driven 103,000 miles over its estimated useful life of 10 years. Actual miles driven were 12,700 in 2022 and 10,200 in 2023
compute the depreciation expense using
A) Striaght-line Method
B) Units Of Activity Method
C) Declining Balance method
Answers
The computation of the depreciation expense using the following methods are as follows:
2022 2023
A) Straight-line Method $2,472 $2,472
B) Units Of Activity Method $3,048 $2,448
C) Declining Balance method $5,200 $4,160
What is the depreciation expense?The depreciation expense is the periodic recognition of the cost for a long-term asset over its useful life.
The costs of long-term assets are spread over their estimated life through depreciation, depletion, or amortization.
The various depreciation methods include:
Straight-line methodUnit-of-activity methodDouble-declining-balance methodSum-of-the-years-digit methodModified accelerated recovery systems (MACRS).The cost of the delivery truck on January 1, 2022 = $26,000
Expected salvage value = $1,280
Depreciable amount = $24,720
Estimated useful life = 103,000 miles or 10 years
Depreciation Expenses:
Straight-line method = $2,472 annually ($24,720/10)
Units of activity method per mile = $0.24 ($24,720/103,000)
2022 = $3,048 (12,700 x $0.24)
2023 = $2,448 (10,200 x $0.24)
Declining-balance method rate = 20% (100/10 x 2)
2022 = $5,200 ($26,000 x 20%)
2-23 = $4,160 ($20,800 x 20%)
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Water boils at a minimum temperature of 100 degrees Celsius. Which inequality represents this scenario? 100 > b 100 < b 100 ≤ b 100 ≥ b
Answers
The inequality which represents the range of temperature at which water boils is 100 ≤ b thus, option (C) is correct.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given,
Water boils at a minimum temperature of 100 degrees Celsius.
Suppose b is the temperature at which water boils.
100 ≤ b
Hence "The inequality which represents the range of temperature at which water boils is 100 ≤ b".
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The formula v(t)=14t+29 represents the cost of renting a moving van. The variable t represents the number of hours the moving van is rented for. If the cost of renting the
moving van is $439, how many hours was it rented for? Round to the nearest whole number.
Answers
Answer:
29 hrs
Step-by-step explanation:
439 = 14t + 29
439-29 = 14t
410 = 14t
t = 410/14
t= 29.28
t = 29
Cupcakes are packed six to a box Abby only buys full boxes of cupcakes give two possible numbers of cupcakes that she could buy?
Answers
Two possible numbers are 6 and 12.
6 would mean she bought one box, and 12 would mean she bought 2 boxes.
Find the slope of the line that goes through the given points
(-5-10) and (-6, -1)
Answers
Answer:
-9
Step-by-step explanation:
(y2-y1)/(x2-x1)
[tex]\frac{(-1--10)}{(-6--5)}[/tex]=-9
Assuming that a personal space is 3ft squared. Estimate how many people can fit into a circular arena a diameter of 100 yards?
Answers
Answer
2617.
Step-by-step explanation
To estimate the number of people that can fit into a circular arena with a diameter of 100 yards, we first need to find the area of the arena. To do this, we can use the formula for the area of a circle, which is equal to pi times the radius squared. Since the diameter of the arena is 100 yards, the radius would be half of that, or 50 yards. Plugging this value into the formula for the area of a circle, we get:
Area = pi * 50^2
Since pi is approximately equal to 3.14, we can plug this value into the equation to get:
Area = 3.14 * 50^2
This simplifies to:
Area = 3.14 * 2500
Which gives us an area of approximately 7850 square yards.
Since one person requires a personal space of 3 square feet, we can divide the total area of the arena by 3 to find the number of people that can fit in the arena. This gives us:
7850 square yards / 3 square feet/person = 2616.666... people
Rounded to the nearest whole number, this means that approximately 2617 people could fit in the circular arena with a diameter of 100 yards.
PLEASE HLEP I WILL MARK U BRANLIEST I REALLY NEEED HELPPPP
Answers
Answer:
Step-by-step explanation:
-1<x<0
x<0
so x is negative.
Hence -x is positive.
and -1<x
or
x>-1
or
x+1>0
x+5=x+1+4>0+4
hence x+5 is positive.
x is negative .
∴x-2 is negative.
f(x)=(+)×(+)×(+)×(-)=-
B
1. In a triangle∆ABC, if DE is parallel to BC, AD
DB
=
3
4
and AC = 15 cm, then the length AE is:
(a) 45 (b) 23/7 (c) 1 (d) 45/7
Answers
The length of the segment AE on the triangle is 45/7
How to determine the length of AE?From the question, we have the following parameters that can be used in our computation:
DE parallel to BC,
Also, we have
AD/DB=3/4
The above parameters mean that
AD/AB = AE/AC
Also, we know that
AB = AD + DB
From the ratio values, we have
AB = 3 + 4
Evaluate the sum
AB = 7
Updating the initial ratio, we have
AE/15 = 3/7
Multiply both sides by 15
So, we have the following representation
AE = 15 * 3/7
Evaluate the products
AE = 45/7
Hence, the length of AE is 45/7
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Question 1 options: James is observing the population of the fish he put into a pond. He built a pond and populated it with 900 fish. The population of the fish doubles every year.
Answers
The equation by using x represent the number of years and y represent the number of fish is y=900×(2)ˣ.
Given that,
James is keeping an eye on the fish population in the pond he created. He constructed a pond and added 900 fish to it. Every year, the fish population doubles.
We have to find the equation by using x represent the number of years and y represent the number of fish.
We know that,
We get
Number of fish at starting =900
Number of fish after 1 year =900×2=1800
Number of fish after 2 year =1800×2=3600=900×(2)²
Number of fish after 3 year =3600×2=7200=900×(2)³
So,
Here we can see that the number of fish are in Geometric progression (G.P) with a=900 and r=2
So,
Tₙ=arⁿ⁻¹
We get
y=900×(2)ˣ
Therefore, The equation by using x represent the number of years and y represent the number of fish is y=900×(2)ˣ.
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6. order from least to greatest. 0.4,4/6,40.5%,11/25
Answers
Answer:
Answer:
Step-by-step explanation:
[tex]0.4, 40.5, \frac{11}{25}, \frac{4}{9}[/tex]
Step-by-step explanation:Given numbers :
[tex]0.4, 40.5, \frac{11}{25}, \frac{4}{9}[/tex]
Let's convert percent and fraction into like decimals.
[tex]\frac{4}{9}\ = 0.444[/tex]
We know that to convert percentage into decimals, we need to divide it by 100, we get
[tex]40.5 = \frac{40.5}{100} = 0.405[/tex]
[tex]\frac{11}{25} = 0.400[/tex]
Now , placing the above decimal numbers in order from least to greatest
[tex]0.400, 0.405, 0.440, 0.444[/tex]
[tex]=0.4, 40.5, \frac{11}{25}, \frac{4}{9}[/tex]