The calculation that tells us the year the population can be expected to reach 100 million is log 2/log 1.02 + 2000.
i.e
x = log 2/log 1.02 + 2000
Option B is the correct answer.
What is a function?A function is defined as a relation between a set of inputs having one output each.
The inputs are called the domain of the function.
The outputs are called the range of the function.
We have,
P(x) = 50 x [tex]1.02^x[/tex]
P(x) = Number of population in millions after x years
For 100 million populations we have,
100 = 50 x [tex]1.02^x[/tex]
Divide both sides by 50.
100/50 = [tex]1.02^x[/tex]
2 = [tex]1.02^x[/tex]
Putting log on both sides.
log 2 = x log 1.02
x = log 2 / log 1.02
Since x is the number of years after 2000 we have,
x = log 2/log 1.02 + 2000
Thus,
The calculation that tells us the year the population can be expected to reach 100 million is log 2/log 1.02 + 2000.
i.e
x = log 2/log 1.02 + 2000
Option B is the correct answer.
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A concession stands sells drinks and hotdogs the number of drinks sold is five more than four times the number of hotdogs sold the stands sells 500 items how many hotdogs were sold
Answer:120
Step-by-step explanation:
What is it called when two numbers have a product of one
Answer: Reciprocals
Explanation isn't really needed but reciprocals are basically
Example:
3/4's reciprocal is 4/3 and multiplying 3/4 x 4/3 = 1
There is lightning rod on the top of a building. From a location 500 feet from the base of the building, the angle of elevation to the top of the building is measured to be 36°. From the same location, the angle of elevation to the top of the lightning rod is measured to be 38°. Find the height of the lightning rod. To earn full credit please share a diagram and include all your work and calculations
To better analyze the problem, let us draw an illustration:
To determine the height of the lightning rod, we have to determine the height of the building and the height of the building + lightning rod using the given angles and distance from the base.
Let's solve for the height of the building itself first. Use the 36-degree angle.
[tex]tan36=\frac{height\text{ }of\text{ }the\text{ }building}{distance\text{ }from\text{ }the\text{ }building}[/tex]Let's plug in the data to the function above and solve for the height of the building.
[tex]\begin{gathered} tan36=\frac{x}{500ft} \\ 500tan36=x \\ 363.2713ft=x \end{gathered}[/tex]Therefore, the height of the building itself is 363.2713 ft.
Moving on to the height of the building + lightning rod, use the tangent function still but this time, use the 38-degree angle.
[tex]\begin{gathered} 500tan38=x \\ 390.6428=x \end{gathered}[/tex]Therefore, the height of the building + lightning rod is 390.6428ft.
So, to determine the height of the lightning rod only, let's subtract the two calculated heights.
[tex]\begin{gathered} lightning\text{ }rod=390.6428ft-363.2713ft \\ lightning\text{ }rod=27.3715\approx27.37ft \end{gathered}[/tex]Answer:
The height of the lightning rod is approximately 27.37 ft.
1 Type the correct answer in each box. Use numerals instead of words, Consider this quadratic equation, x2 + 2x + 7 = 21 The number of positive solutions to this equation is The approximate value of the greatest solution to the equation, rounded to Reset
Answer:
The number of positive solutions to this equation is;
[tex]1[/tex]The approximate value of the greatest solution to the equation is;
[tex]2.87[/tex]Explanation:
Given the equation;
[tex]x^2+2x+7=21[/tex]Let us subtract 21 from both sides;
[tex]\begin{gathered} x^2+2x+7-21=21-21 \\ x^2+2x-14=0 \end{gathered}[/tex]We can now solve for x using the quadratic formula;
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]from the equation;
[tex]\begin{gathered} a=1 \\ b=2 \\ c=-14 \end{gathered}[/tex]substituting;
[tex]\begin{gathered} x=\frac{-2\pm\sqrt[]{2^2-4(1)(-14)}}{2(1)} \\ x=\frac{-2\pm\sqrt[]{4+56}}{2} \\ x=\frac{-2\pm\sqrt[]{60}}{2} \end{gathered}[/tex]so, we have;
[tex]\begin{gathered} x=\frac{-2\pm\sqrt[]{60}}{2} \\ x=\frac{-2+\sqrt[]{60}}{2} \\ x=2.87 \\ \text{and} \\ x=\frac{-2-\sqrt[]{60}}{2} \\ x=-4.87 \end{gathered}[/tex]Therefore, the number of positive solutions to this equation is;
[tex]1[/tex]The approximate value of the greatest solution to the equation is;
[tex]2.87[/tex]Identify the 25th term of an arithmetic sequence where a1 = −7 and a18 = 95
The 25th term is 137
Explanation:[tex]\begin{gathered} \text{Given:} \\ a_1\text{ = -7} \\ a_{18}\text{ = 95} \\ a_{25}\text{ = ?} \end{gathered}[/tex]To get the 25th term, we need to find the common difference.
An arithmetic sequence is given as:
[tex]\begin{gathered} a_n=a_1\text{ + (n - 1)d} \\ \text{where a}_1\text{ = first term} \\ n\text{ = number of terms} \\ d\text{ = co}mmon\text{ difference} \end{gathered}[/tex]The formula for the 18th term will be used to find the common difference:
[tex]\begin{gathered} \text{where n = 18} \\ a_{18}=a_1\text{ + (18 - 1)(d)} \\ 95\text{ = -7 + 17d} \\ 95\text{ + 7 = 17d} \\ 102\text{ = 17d} \\ d\text{ = }\frac{102}{17} \\ d\text{ = 6} \end{gathered}[/tex]Now we can find the 25th term:
[tex]\begin{gathered} \text{where n = 25} \\ a_{25}=a_1\text{ + (25 - 1)d} \\ a_{25}=a_1\text{ + 24d} \\ a_{25}=\text{ -7 + 24(6) }=\text{ 144 - 7} \\ a_{25}=\text{ }137 \end{gathered}[/tex]The 25th term is 137
A rectangular pool is surrounded by a walk 3 meters wide. The pool is 5 meters longer than its width. If the total area of the pool and walk is 270 square meters more than the area of the pool, find the dimensions of the pool.
The length and width of the rectangular pool are respectively; Length = 22 meters and Width = 17 meters
What is the area of the rectangle?Area of the pool which is a rectangle has the formula;
A = Length(L) * Width(w)
Let the width of the pool = x
Then the length will = (x + 5)
Since the walkway is 3 meters wide, It means that the overall dimensions will be (x + 6) by (x + 5 + 6) or (x + 11)
Total area - pool area = 270
Thus;
(x + 11) * (x + 6) - x(x + 5) = 270
x² + 11x + 6x + 66 - x² - 5x = 270
17x - 5x + 66 = 270
12x + 66 = 270
12x = 270 - 66
x = 204/12
x = 17
Length of pool = x + 5 = 17 + 5 = 22 meters
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The winner of a card game is the person closest to 0.The second place player was 8 points behind.If the winner had a score of -3 then what was the score for 2nd place?
ANSWER:
-11
STEP-BY-STEP EXPLANATION:
We have that the winner has a score of -3, and the second place, 8 points behind, therefore, the score of the second place would be:
Therefore:
[tex]-3-8=-11[/tex]The score is -11
if a population of a town decreases by 5% every 3 years would it be exponential ?
Yes, the population would be exponential.
What are exponents?
Exponentiation is a numerical technique denoted by the symbol bn that involves two integers, the base b and the exponent or power n, and is spoken as "b (raised) to the (power of) n." Exponentiation corresponds to repeated multiplication of the base when n is a positive integer: bn is the product of multiplying n bases. Typically, the exponent is displayed as a superscript to the right of the base. In such scenario, bn is referred to as "b raised to the nth power," "b (raised) to the power of n," "the nth power of b," "b to the nth power," or simply "b to the nth."
Yes, the population would be exponential.
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can someone solve this?2 > -3t - 10and is it an open or closed circle?
Given data:
The given inequality is 2> -3t-10.
The given inequality can be written as,
[tex]\begin{gathered} 2>-3t-10 \\ 12>-3t \\ 4>-t \\ t>-4 \end{gathered}[/tex]Thus the value of t is (-4, ∞), and it is open interval.
Pluto has a diameter of 1,413 miles. What does this distance equal in kilometers?
(1 mile = 1.6 kilometers)
A. 12,761 km
B. 2,275 km
C. 3,476 km
D. 143,042 km
Answer:
B
Step-by-step explanation:
since 1 mile is 1.6 kilometers we multiply 1,413 with 1.6 and it equals 2260.8
And since 1.6 was a approximation the closest answer is B
Hopes this help please mark brainliest
simplify the equation
The simplified expression of the equation given as (x² - 16)/(x² -2x - 3) ≤ 4 is 3x² -8x + 4 ≥ 0
How to simplify the equation?From the question, we have the following parameters
(x² - 16)/(x² -2x - 3) ≤ 4
Multiply both sides of the expression by (x² -2x - 3)
So, we have the following representation
(x² -2x - 3) * (x² - 16)/(x² -2x - 3) ≤ 4 * (x² -2x - 3)
Evaluate the products in the above expression
So, we have the following equation
(x² - 16) ≤ 4 * (x² -2x - 3)
Open the brackets
This gives
x² - 16 ≤ 4x² -8x - 12
Collect the like terms in the above expression
So, we have the following equation
0 ≤ 3x² -8x +4
Rewrite the expression as
3x² -8x + 4 ≥ 0
Hence, the simplified expression of the equation is 3x² -8x + 4 ≥ 0
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3/4=6/x proportionsolve for x
5) x = 8
Explanation:[tex]\frac{3}{4}=\frac{6}{x}[/tex]cross multply:
[tex]\begin{gathered} 3\times\text{ x = 4 }\times\text{ 6} \\ 3x\text{ = 24} \end{gathered}[/tex]divide both sides by 3:
[tex]\begin{gathered} \frac{3x}{3\text{ }}=\text{ }\frac{\text{24}}{3} \\ x\text{ = 8} \end{gathered}[/tex]A triangle has sides of length 7 centimeters, 5.6 centimeters, and 4.2 centimeters. What is the perimeter?
The perimeter of the triangle is 16.8 cm.
What is a triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane. According to the sides of a triangle rule, the lengths of any two sides of a triangle must add up to more than the length of the third side.So, the perimeter of the triangle:
Formula: P = a + b + cWhere a = 7, b = 5.6 and c = 4.2.Now, substitute the values in the formula as follows:
P = a + b + cP = 7 + 5.6 + 4.2P = 16.8Therefore, the perimeter of the triangle is 16.8 cm.
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which expression is equivalent to. -2(5x + 3y)
A. 3y(5x - 2)
B 5x(-2+3y)
c -10x - 6y
-10x + 3y
The -2 multiplies each every term in the brackets. meaning -2 will multiply 5x and also 3y
[tex] = - 2(5x) - 2(3y) \\ = - 10x - 6y[/tex]
OPTION C MATCHES AS THE SOLUTION.
GOODLUCK
1,3/5,9/25 find the 8th term
Answer:
2187/78125
Step-by-step explanation:
T(n) = 3^(n-1) / 5^(n-1)
Choose a sequence of similarity transformations that maps ABC to DEF
A similarity transformation is one or more rigid transformations (reflection, rotation, translation) followed by a dilation.
When a figure is transformed by a similarity transformation, an image is created that is similar to the original figure
In this case, the sequence of transformation that maps ABC to DEF is as follow:
• Reflection across the x-axis
,• A scale factor of 2
It is a reflection across the x-axis because the image is turned upside down and it is enlarged because:
[tex]\frac{DE}{AC}=\frac{4}{2}=2[/tex]Hence Option A is correct
Given mn, find the value of x.
t
(9x+7)°
(10x-10)°
(9x+7=10x-10)
All terms are shifted to the left:
(9x+7-(10x-10))=0
Parentheses are used to compute terms: +(9x+7-(10x-10)), so:
9x+7-(10x-10)
the Function Domain determination
9x-(10x-10)
+7
We eliminate parenthesis.
9x-10x+10+7
All the numbers and variables are added together.
-
1x+17
Returning to the equation
+(-1x+17)
We eliminate parenthesis.
-1x+17=0
We shift every term that contains x to the left and every other term to the right.
-x=-17 \sx=-17/-1 \sx=+17
Relation of degrees of polynomials:How can you determine an equation's degree?
The degree of a term in the polynomial expression is expressed as a + b if a and b are the exponents of the many variables in a term.
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help meeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
33
Step-by-step explanation:
you are scamming everyone. why?
17. 17. The scores for a math test are shown below, ordered from smallest to largest. 60 61 62 63 63 64 64 65 66 66 66 69 72 72 72 74 75 80 82 84 86 86 87 87 89 89 90 93 94 98 Fill out the stem and leaf plot below for this data. Enter the leaves separated by commas (ex: 1,1,2,3). Stems Leaves
Answer:
Filling the values we have;
Explanation:
Given the data on the given table, we want to fill them in a stem leaves plot.
The tens values would be in the stems while the unit values will be written in their corresponding leaves.
Filling the values we have;
Please help me with this : For the coordinate grid to the right, identify a pair of congruent figures. Then determine a congruence transformation that maps the preimage to the congruent image.
SOLUTION:
From the image;
The congruent triangles are;
[tex]\Delta ZTF\cong\Delta BQY[/tex]2. The transformation that maps these triangles is;
[tex]T(-5,-1)\circ r_{(180^o,O)}(\Delta ZTF)[/tex]This means triangle ZTF was translated 5 units to the left and 1 unit down and rotated 180 degrees about the origin to get triangle BQY,
At the bicycle shop there are 23 bicycles and 18 tricycles. Each bicycle has 2 wheels, and each tricycle has three wheels. How many wheels are there at the bicycle shop?
Answer:
There are 100 wheelsStep-by-step explanation:
GivenNumber of bicycles = 23,Number of tricycles = 18Total number of wheels23*2 + 18*3 = 46 + 54 = 100For jewelry prices in a jewelry store, state whether you would expect a histogram of the data to be bell-shaped, uniform, skewed left, or skewed rightChoose the correct answer below."O UniformO Skewed rightSkewed leftO Bell shaped+
For jewelry prices in a jewelry store, histogram of the data will be bell-shaped .
Which does NOT represent a valid argument?Anyone who buys a boat will go water skiing.Ivan bought a boat.Ivan will go water skiing.Everyone who went to the football gamecheered.Maria cheered.Maria went to the football game.If the Nationals win the playoffs, then I will behappy.O if I am happy, then I will have a party.If the Nationals win the playoffs, then I will have aparty.Everyone who studies Geometry will pass theSOL.Everyone who passes the SOL will be exemptfrom the exam.Everyone who studies Geometry will be exemptfrom the exam,
the statement that does not represent a valid arguement is,
Everyone who went to the football game cheered.
Maria cheered.
Maria went to the football game.
how can you represent all the solutions y=2x
All the solutions of the equation y=2x can be represented by the points in the straight line.
We are given an equation. The equation is linear in nature. The equation is given below :
y = 2x
An equation is a mathematical statement that includes the sign 'equal to' between two expressions with equal values.
We can see that the equation is a straight line. A line is an endlessly long object with no breadth, depth, or curve in geometry. Lines are thus one-dimensional objects, even if they can exist in two, three, or higher dimensions. All the solutions to the equation can be represented by the coordinates of the points that satisfy the equation of line. The graph is attached below.
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Sue learned to sing a total of 10 pieces over the course of 5 weeks of voice lessons. After 8
weeks of voice lessons, how many pieces will Sue be able To sing total?
Answer:
2 pieces per week. 10 pieces/ 5 weeks. 16 pieces for 8 weeks. ? 16 pieces total.
Step-by-step explanation:
Need help asap extra points
The most appropriate choice for equation of line in slope intercept form will be given by-
[tex]8x - 5y = 26[/tex] is the required equation of line.
What is equation of line in slope intercept form?
General form of equation of line in slope intercept form is given by
y = mx + c where m is the slope of the line and c is the y intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept
The distance from the origin to the point where the line cuts the x axis is the x intercept
Here,
[tex]8x - 5y = 4\\5y = 8x - 4\\y = \frac{8}{5}x - \frac{4}{5}[/tex]
Slope of [tex]8x - 5y = 4[/tex] is [tex]\frac{8}{5}\\[/tex]
Slope of the line parallel to the given line = [tex]\frac{8}{5}[/tex]
The line passes through (2, -2)
Equation of line =
[tex]y - (-2) = \frac{8}{5}(x - 2)\\5y + 10 = 8x -16\\8x - 5y = 16+10\\8x - 5y = 26[/tex]
This is the required equation of line.
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Hope you help me, I need help with the check part
1.- 3(x - 2) = 15
Solve for x 3(x - 2)/3 = 15/3
Simplifying x - 2 = 5
(x - 2) = 15/3
(x - 2) = 5
x - 2 = 5
x = 5 + 2
x = 7
Check. Substitute the value of x in the original equation and solve it
3(7 - 2) = 15
3(5) = 15
15 = 15 As the two value are the same, the solution of x is
correct.
2.- 4y + 9 - 7y = -6
Solve for y
Simplify like terms
4y - 7y + 9 = -6
- 3y + 9 = -6
-3y = -6 - 9
-3y = -15
-3y/-3 = -15/-3
y = 5
Check
4(5) + 9 - 7(5) = -6
20 + 9 - 35 = -6
29 - 35 = -6
-6 = -6 The solution is correct because both numbers are the same.
How many thousands are in 50,000
ANSWER
50
EXPLANATION
We want to know how many thousands there are in 50,000
To do this, we have to find what we will multiply by 1000 to get 50,000
That is:
[tex]\begin{gathered} x\cdot\text{ 1000 = 50000} \\ \Rightarrow\text{ x = }\frac{50000}{1000} \\ x\text{ = 50} \end{gathered}[/tex]The answer is 50.
4x^(2)+4=20 solve by using square roots
Explanation
We are told to resolve the quadratic equation
[tex]4x^2+4=20[/tex]To do so, we will have to collect like terms
[tex]\begin{gathered} 4x^2=20-4 \\ 4x^2=16 \end{gathered}[/tex]Then we will divide both sides by 4
[tex]\begin{gathered} \frac{4x^2}{4}=\frac{16}{4} \\ \\ x^2=4 \end{gathered}[/tex]Thus the value of x will be obtained using square root
[tex]\begin{gathered} x=\pm\sqrt{4} \\ x=\pm2 \end{gathered}[/tex]Therefore, the values of x are: x=2, x=-2
Find the difference of (4y2 - 2y - 5) and (y² - y + 8).4у2 - 3у - 133у2 - у - 135y2 - 3y + 33у2 - 3у + 3
We must find the difference between the following polynomials:
[tex]\begin{gathered} f_1(y)=4y^2-2y-5, \\ f_2(y)=y^2-y+8. \end{gathered}[/tex]The difference between the polynomials is obtained by subtracting the coefficient of terms with equal power of y:
[tex]\begin{gathered} f_1(y)-f_2(y) \\ =\left(4y^2-2y-5\right)-\left(y^2-y+8\right) \\ =\left(4y^2-y^2\right)+\left(-2y+y\right)+\left(-8-5\right) \\ =3y^2-y-13. \end{gathered}[/tex]Answer3y² - y - 13
