The number of years until the town will have 100 students is given as follows:
22.68 years.
How to model the situation?A decaying exponential function is modeled as follows:
y = a(1 - r)^x.
In which:
a is the initial value.r is the decay rate.The parameter values for this problem are given as follows:
a = 320, r = 0.05.
Hence the function is given as follows:
y = 320(0.95)^x.
The time it will take for the population to have 100 students is x when y = 100, hence:
100 = 320(0.95)^x
(0.95)^x = 100/320
(0.95)^x = 0.3125
x log(0.95) = log(0.3125)
x = log(0.3125)/log(0.95)
x = 22.68 years.
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Help me solve this Simultaneous equation assignment
Answer:
Case 1 : x = - 2, y = 3
Case 2 : x = 5. y = 2
Step-by-step explanation:
Case 1
5y + x = 13 --------> Eq 1
y - x = 5 ---------> Eq 2
Add both Eq 1 and y,
5y + x = 13
y - x = 5
________
6y + 0 = 18
6y = 18
y = 18/6
y = 3
Substitute y = 3 in Eq 2,
3 - x = 5
3 - 5 = x
- 2 = x
x = - 2
Hence,
x = - 2
y = 3
Case 2
2x + y = 12 ---------> Eq 1
6x + 5y = 40 -----------> Eq 2
Multiply Eq 1 with 3,
3(2x + y = 12)
6x + 3y = 36 --------> Eq 3
Eq 2 - Eq 3,
6x + 5y = 40
- 6x - 3y = - 36
_____________
0 + 2y = 4
2y = 4
y = 4/2
y = 2
Substitute y = 2 in equation 1,
2x + 2 = 12
2x = 12 - 2
2x = 10
x = 10/2
x = 5
Hence,
x = 5
y = 2
write an equation of the line that passes through the given points and is perpendicular to the given line
The equation of the line parallel to the line is y = -4x + 10
The equation of the line perpendicular to the line is y = 1/4x +3/2
Using the point (1, 6) and (2, 2) on the line to get the slop:
Slope = 2-6/2-1
Slope = -4/1
Slope = -4
The equation is written in point slope form as y-y0 = m(x-x0)
Substitute a point and the given slope for the equation parallel to the line
y - 2 = -4(x-2)
y - 2 = -4x + 8
y+4x = 10
Hence the equation of the line parallel to the line is y = -4x + 10
The needed slope for the perpendicular line is 1/4.
Substitute a point and the given slope for the equation parallel to the line
y - 2 = 1/4(x-2)
4(y - 2) = x - 2
4y - 8 =x -2
4y = x + 6
y = 1/4x + 3/2
Hence the line perpendicular to the line is y = 1/4x + 3/2
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The following question may be like this:
write an equation of the line that passes through the given points and is perpendicular to the given line.
Solve for x. Write the equation and show ALL STEPS to solve.
(3x - 3)"
AP
(2x+13)"
Answer:
x = 16
Step-by-step explanation:
(2x+13)° = (3x-3)° [vertically opposite angles]
2x + 13 = 3x - 3
2x - 3x = -3 - 13
-x = -16
∴ x = 16
the gardener has 75 shrubs to plant in 4 rows.
If he planted an equal number in each row, there were _____ shrubs left over.
if possible explain why you got this answer please :)
Help..
select all the coordinates that represent a point on the line.
0,2
0,6
2,6
3,1
4,1
6,×
Answer:
Okay so 6,0 3,1 4,1 and 0,2
Step-by-step explanation:
So take 3,1 you would go over 3 on the x axes and up 1 on the y axes
16. Rylan claimed that adjacent angles are complementary.
Draw an example that supports Rylan's statement and draw a
counterexample that shows her statement is not always true.
The example of adjacent angles that are complementary and those that are non-complementary are given as attached.
What are adjacent and Non-Adjacent angles?When two adjacent angles have a similar vertex and side, they might be complementary or supplementary angles.
If the total of neighboring angles equals 90 degrees, then they are complementary. If the total of neighboring angles equals 180 degrees, they are complementary to one another.
Non-adjacent Complementary Angles: Two angles that are not next to each other are non-adjacent complementary angles. AOB and XOY are non-adjacent angles since they share neither a vertex nor an arm. They also add up to 90°. As a result, these two angles are non-adjacent complimentary.
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in ten dollars more than Sara. How much money did Lisa and Joe put towards the gift?
Answer:
20
Step-by-step explanation:
10$ by lisa
10$ by joe
so, 20$ money did lisa and joe put towards the gift
you can answer any 12 questions from a total of 14 questions on an exam. in how many different ways can you select the question?
In 420 ways different ways can you select the question.
you can answer any 12 questions from a total of 14 questions on an exam
At least 8 questions, including 3 from the last section, must be attempted out of the 5 questions in part and the 7 questions in part 2.
There are three choices.
&% from part 2; (1)3 from part 1
= ⁵C 3 × ⁷ C 5
= 3!(5−3)!/5! × 5!(7−5)!/7!
= 2/5×4 ×= 2/7×6
=5×2×7×3
=210 ways
(2)4 from part 1 & 4 from part 2
= ⁵C 3 × ⁷ C 5
=4!(5−4)!/5!
×= 4!(7−4)!/7!
=5×= 3×2×1/7×6×5
=5×7×5
=175 ways
(3)5 from part 1 & 3 from part 2
= ⁵C 3 × ⁷ C 5
= 5! 0!/5!
×= 3!(7−3)!/7!
=1×= 3×2/7×6×5
=35 ways
Total number of ways =210+175+35
420 ways
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which set represents a Pythagorean triple
A. 1,2,3
B.9,12,16
C. 30,40,50
D.38,44,49
The set that represents a Pythagorean Triple is given as follows:
C. 30,40,50
What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
For item c, we have that:
30² + 40² = 50²
900 + 1600 = 2500
2500 = 2500.
Which is a true statement, hence item c represents the Pythagorean Triple in the context of this problem.
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Draw a sketch to help with this problem. From Tracey's house
to John's house is 0.5 kilometers. From John's house to school is 0.8
kilometer. Tracey rode from her house to John's house and then to
school. Later she rode from school to John's house to her house.
Altogether, how far did Tracey ride?
Answer:
2.6 km
Step-by-step explanation:
You want the total distance from Tracey's house to John's house to school, and back again, when the distance from Tracey's to John's is 0.5 km, and the distance from John's to school is 0.8 km.
TotalThe total distance will be the sum of the parts:
Tracey's to John's: 0.5 kmJohn's to school: 0.8 kmschool to John's: 0.8 kmJohn's to Tracey's: 0.5 kmTotal distance = (0.5 +0.8 +0.8 +0.5) km = 2(0.5 +0.8) km = 2(1.3 km)
= 2.6 km
Tracey rode 2.6 km altogether.
The ticket price to a concert is $65 plus an additional (d) dollars service fee per ticket. The total cost for four people to attend the concert is $308. Calculate the cost of the service fee charged for each ticket.
SHOW HOW YOU DID IT PLEASE!!!
Answer: d=12
Step-by-step explanation:
4(65)+ 4d=308
multiply 65 by 4
260+4d=308
move the constant to the right
4d=308-260
calculate
4d=48
divide both sides
d=12
HELP!! ASAP! 60 POINTS
This diagram shows right triangular prism UVWXYZ.
What is the volume of UVWXYZ? If necessary, round your answer to the nearest tenth.
In the diagram which shows right triangular prism UVWXYZ, the volume of UVWXYZ can be expressed in nearest tenth as 750 cm^3.
How can the the volume of UVWXYZbe calculated?The concept that will be used here is volume. In mathematics, 'Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m3, cm3, in3
√ (12.5^2 -7.5^2) =10 cm
The volume can be calculated as : (1/2 * 7.5 * 10 *20
=750 cm^3
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what number is an integer
An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface Z or blackboard bold \mathbb {Z}.
A rectangular garden has a walkway around it. The area of the garden is 2(5.5x + 3.5). The combined area of the garden and the walkway is 2.5(8x + 6). Find the area of the walkway around the garden as the sum of two terms.
The total of the two terms that represent the length of the garden's walkway: 26x + 28
Explain the features of term rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional form. The rectangle's longer side is its length, while its shorter side is its breadth.A walkway around a rectangular garden.
The garden's size is 4(4.5 x + 1.5) square meters.The garden's and the walkway's combined area is 5.5(8 x + 4).Simplifying each equation.
Area of the garden : 4(4.5 x + 1.5) = 18x + 6
Combined area: 5.5(8 x + 4) = 44x + 22
Thus,
Area of walkway = Combined area - Area of the garden
= 44x + 22 - 18x + 6
= 26x + 28
Thus, the total of the two terms that represent the length of the garden's walkway: 26x + 28
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A rectangle has an area of 15 square millimeters. The width of the rectangle is 3 millimeters.
Answer:
5 millimeters
Step-by-step explanation:
15 = 3x
5 = x
A 6-kg bowling ball sits on top of a building that is 120 meters tall.
The potential energy of the ball will be 7200 Joules.
What is potential energy?The energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors.For small height changes, gravitational potential energy can be computed using - E = mgh.Given is a 6-kg bowling ball sits on top of a building that is 120 meters tall.
We can write the potential energy of the ball as -
E = mgh
E = 6 x 10 x 120
E = 60 x 120
E = 7200 Joules
Therefore, the potential energy of the ball will be 7200 Joules.
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6. The graph of an exponential function is
shown. Write an equation for the function.
manu (3,13.5)
(2,4.5)
(1, 1.5)
olismolensando
On soloing the provided question, we can say that an equation from the graphs for the function. 3x + 13.5y = 4.5 and x+1.5y = 2
What is graphs?Mathematicians use graphs to logically represent or chart facts or values. Typically, a graph point will show the relationship between two or more objects. A graph is a non-linear data structure made up of nodes, or vertices, and edges. The nodes, also known as vertices, should be joined with glue. This graph's vertices are 1, 2, 3, and 5, while its edges are 1, 2, 1, 3, 2, 4, and 2.5. (3.5). (4.5). Graphical depictions of exponential growth in statistical charts (bar charts, pie charts, line charts, etc.). triangle-shaped logarithmic graph.
an equation for the function.
3x + 13.5y = 4.5
and x+1.5y = 2
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an airline has six flights from new york to california and seven flights from california to hawaii per day. if the flights are to be made on separate days, how many different flight arrangements can the airline offer from new york to hawaii?
The total number of different flight arrangements the airline can offer from New York to Hawaii is 42.
The Flight ArrangementsThe airline has 6 flights from New York to California and 7 flights from California to Hawaii per day. Therefore, the total number of different flight arrangements the airline can offer from New York to Hawaii is 6 x 7 = 42.
The airline has the capability to offer 42 different flight arrangements for travel from New York to Hawaii by combining the number of flights available per day from New York to California (6) with the number of flights available per day from California to Hawaii (7). This calculation is done by multiplying the number of flights from New York to California by the number of flights from California to Hawaii.
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The height of the trapezoid is 5 cm
The area of trapezoid is 47.5 cm².
What is trapezoid?A quadrilateral having only two sides parallel.The area of a trapezoid is the half of the product of sum of its parallel sides to the height of that trapezoid (the distance between those parallel sides).
Thus, if we have:
Length of its parallel sides = 'a' and 'b' units respectively
Perpendicular distance between its parallel sides = 'h' units,
Then, we get:
[tex]A = \dfrac{1}{2}\times(a+b) \times h \: \rm unit^2[/tex]
Given;
trapezoid has two bases that measure 11 cm and 8 cm.
a= 11 cm, b= 8 cm
Now, height= 5
A = (½* height) x (Sum of the bases)
A= 1/2 * ( 11 + 8) * 5
A= 95/2
Therefore, the Area trapezoid will be 47.5 cm²
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The complete question is;
A trapezoid has two bases that measure 11 cm and 8 cm. The height of the figure is 5 cm. What is the area of the trapezoid?
What is the name of the relationship between Angle 1 and Angle 4?
Answer: alternate exterior angles
Step-by-step explanation:
They are equals if the two intersected lines by the transversal are parallel. In the figure, angles 1 and 4 are alternate exterior angles. Angles that are on opposite sides of the transversal of two other lines.
Brad's mother says she was tested for HCG during her last two doctor visits. On March 21, her
HCG level was 200 mlU/ml (milli-international units per milliliter). Two days later, her HCG
level was 392 mIU/ml.
a. Assuming that the model for HCG levels is of the form y = ab', write an equation that
models the growth of HCG for Brad's mother's pregnancy.
The required function is 200 (1.4)ˣ = 5, where the value of x is calculated to be -11.
The given function is y = a bˣ
x₁ = 0, y₁ = 200
x₂ = 2, y₂ = 392
Let us determine a, b.
a b⁰ = 200
a b² = 392
a = 200
200 b² = 392
b² = 392/200 = 49/25 = 7/5 = 1.4
So, the function is y = 200 (1.4)ˣ
Now, let us determine x for y = 5,
200 (1.4)ˣ = 5
(1.4)ˣ = 0.25
Taking log on both sides,
log (1.4)ˣ = log 0.025
x log 1.4 = log 0.025
x = log 0.025/log 1.4
x ≈ -11
This means the embryo was implanted on March 10th and she visited the doctor 11 days later.
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a particular person in america uses 395.0 gallons of water in a given day. how many liters of water is this?
395 gallons will contain 1,495.075 L of water.
A gallon is a unit of liquid measure equal to eight pints. It is approximately 4.546 litres in the United Kingdom.
It is about 3.785 litres in the United States.
To convert litres to gallons, for example, a quart is somewhat less than a litre and 4 litres is slightly more than 1 gallon. 1 litre equals 0.264 gallon (a little more than a quart), and 4 litres equals 1.06 gallon.
One US gallon is approximately 3.79 litres;
one imperial gallon is approximately 4.55 litres.
The dry gallon in the United States is roughly 4.41 litres. As a result, one gallon, regardless of kind, is always larger than one litre.
One gallon contains 3.785 L of water,
Hence 395 gallons will contain 3.785395 3.785×395 Liters of water,
ie, 3.785395 = 1,495.075 L of water.
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Describe the symmetries of a rhombus and prove that the set of symmetries forms a group. Give Cayley tables for both the symmetries of a rectangle and the symmetries of a rhombus. Are the symmetries of a rectangle and those of a rhombus the same?
The symmetries of a rectangle and those of a rhombus are not the same, as the rectangle has two additional symmetries.
A rhombus is a quadrilateral with all sides of equivalent length, and it has the accompanying symmetries:
Identity symmetry: The rhombus stays unaltered when reflected about its center.
Rotational symmetry: The rhombus stays unaltered when pivoted 180 degrees about its center.
Reflective symmetry: The rhombus stays unaltered when reflected about its two diagonals.
These symmetries structure a gathering under the operation of the organization of symmetries. A gathering is a bunch of components with a twofold operation (for this situation, the creation of symmetries) that fulfills the cooperative, identity and converse properties.
The arrangement of symmetries of a rhombus fulfills these properties, making it a group.
The Cayley table for the symmetries of a rhombus is as per the following:
E R1 R2 R3
R1 E R3 R2
R2 R3 E R1
R3 R2 R1 E
Where E addresses the identity symmetry, R1 addresses the 180-degree turn symmetry, R2 addresses the symmetry around one diagonal, and R3 addresses the symmetry about the other diagonal.
Then again, the symmetries of a rectangle are:
Identity symmetry: The rectangle stays unaltered when reflected about its center.
Rotational symmetry: The rectangle stays unaltered when pivoted 180 degrees about its center.
Reflective symmetry: The rectangle stays unaltered when reflected about its two vertical and two horizontal axis.
The Cayley table for the symmetries of a rectangle is as per the following:
E R1 R2 R3 R4
R1 E R3 R2 R4
R2 R3 E R1 R4
R3 R2 R1 E R4
R4 R4 R4 R4 E
Where E addresses the identity symmetry, R1 addresses the 180-degree turn symmetry, R2 addresses the symmetry around one vertical axis, R3 addresses the symmetry around one horizontal axis and R4 addresses the symmetry about the two diagonals.
We can see that the arrangement of symmetries of a rectangle and those of a rhombus are not something similar.
The rectangle has two additional symmetries, the symmetry around one vertical and one horizontal axis, which are not present in the rhombus.
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Choose the correct graph of LMN below.
After clockwise rotation 90°, we obtain vertices of image as (-2, -2), (-4, -5) and (2, -4). Therefore, option C is the correct answer.
What is rotation rule of 90°?Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).
Given that, triangle LMN with vertices L(2, -2), M(5, -4) and N(4, 2).
After clockwise rotation 90° we get
Here, L(2, -2) →L'(-2, -2)
M(5, -4) →M'(-4, -5)
N(4, 2) →N'(2, -4)
Therefore, option C is the correct answer.
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a 5 ft tall girl stands on level ground the sun is 25 degrees above the horizon how long is her shadow
The girl has a shadow of 10.72 ft if she has a 5 ft tall and the sun is 25 degrees.
CALCULATION THE GIRL SHADOWBased on the given conditions, formulate:5 ÷ tan (25°)
Find angles from the level ground of the sun5 ÷ tan (25°)
Calculate5 ÷ 0.466308
Calculate10.722527
TANGENT RATIOWhen measuring the area of a right shadow, the ratio of the opposite side to the adjacent side is known as the tangent ratio. Right angle can have their angles and sides determined using tangent ratios, just as sine and cosine ratios.
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amy uses 41-cent stamps and 6-cent stamps to mail a gift card to a friend. if the postage is $1.77, how many of each stamp did amy use?
If Amy uses 41-cent stamps and 6-cent stamps to mail a gift card to a friend worth of $1.77 , then the number of 41 cent stamp used is 3 and the number of 6 cent stamps used is 9 .
Let the number of 41 cents stamps used in postage is = x ;
let the number of 6 cents stamps used in postage is = y ;
the amount 41 cents in dollars is = $0.41 ;
and amount 6 cents in dollars is = $0.06 ;
Amy used 41-cent stamps , 6-cent stamps to pay $1.77 in postage
it is represented in equation form as ⇒ 0.41x + 0.06y = 1.77
Multiplying on both sides by 100 , we get
⇒ 41x + 6y = 177 ;
⇒ y = (177 - 41x)/6 ;
We will test for corresponding values of x and y to satisfies this equation and the number of stamps must be whole numbers.
If x = 1 , then y = 26.66
If x = 2 , then y = 15.83
If x = 3 , then y = 9
If x = 4 , then y = 2.16 .
the only values that shows a whole number is : If x = 3 , then y = 9 .
Therefore , Amy used "3" 41-cents stamps and "9" 6-cent stamps .
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Long division ? ?????
Answer: 37.5
Step-by-step explanation: To find this, we must move the decimal place one spot over. It would now look like this:
300. ÷ 8
Now for the division look at the attachment. In the end, you've should've got 37.5. To check if that's right, you'd multiply 0.8 and 37.5. Then again, you should get 30. I hope this helped!
Could someone help me on this problem please thank you if you do!
Answer:
the third graph
Step-by-step explanation:
1. increase - then you know the line has to go upwards. so only first &3rd lines are potentially correct answer
2. look at the Y axis markings, first one goes from 5 to 11, it increased by 6. so it's not right.
answer is the 3rd one.
the administration team compiled test results for those who had been tested for strep throat in a random sample of 400 sick patients who had been tested. the following relative frequency table shows the data. positive negative total has the flu 54% 6% 60% does not have the flu 8% 32% 40% total 62% 38% 100% based on the data, what is the ratio of false positives to true positives? 6 over 32 8 over 6 8 over 54
The ratio of false positives to true positives is 8 over 54.
According to the Question
Results of a strep throat test performed on a sample of 400 ill people are displayed in the table's data. People who have the flu and those who don't are separated into two categories. The patients are then separated into groups based on whether they tested positive or negative for strep throat within each of these categories.
We must first define what a true positive and a false positive are in order to calculate the ratio of false positives to true positives. A patient who tests positive for strep throat but does not actually have the illness is said to have a false positive. The 8% of patients in this instance who tested positive for strep throat but did not have the flu would fall under that category. A patient who tests positive for strep throat and truly has the illness is said to have a true positive. That would be the 54% of patients who tested positive for both the flu and strep throat in this instance.
We divide the percentage of false positives (8%) by the percentage of true positives (54%), which gives us the ratio of false positives to true positives.
As a result, the ratio becomes 8% / 54%, or 8/54.
It's critical to remember that this ratio is dependent on the sample and test performed and may not be the same for different populations or testing methodologies.
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what term is used to describe this type of survey in which the people surveyed consist of those who decided to respond? what is wrong with this type of sampling method
Part A: The respondents in the population are a voluntary response sample.
Part B: The responses may not reflect the opinions of the general population
The total number of internet users in those is 1072 people.
The percentage of the total number of people that chose to respond is 38%
We can note that this survey does not compel the population to respond to the survey. These responses are given by the voluntary respondents.
Another point is that a voluntary response sample is a sample that consists of participants who are interested to participate in a sample group voluntarily.
In this type of survey, the people who are supposed to decide to provide voluntary responses to the survey are called voluntary response samples.
The percentage of those that chose to respond to this survey which is 38% is less than half of the total population. This result shows that the responses may not reflect the opinions of the general population.
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