Answer:
d
Step-by-step explanation:
This is an example of the distributive property, a(b-c) = a(b) - a(c)
a=t, b=14, c=5
t(14-5) = t(14) - t(5)
This exercise uses, the population growth model
A culture starts with 8300 bacteria, After 1 hour the count is 10,000 .
(a) Find a function that models the number of bacteria n(t) after t hours. (Round your r value to three decimal places.)
n(t)=8300(1)
(b) Find the number of bacteria after 2 hours. (Round your answer to the nearest hundred.)
17485.75 x bacteria
(c) After how many hours will the number of bacteria double? (Round your answer to one decimal place.)
50times
P is equal to 8700% for population x time in hours.
What is population growth model?P is equal to 8700% for population x time in hours. 2Ae%5E%28kx%29
K's model must be solved. ln%28p%29=ln%288700%29%
2Bkx%2Aln%28e%
29\skx%
2A1=ln%28p%29-ln%288700%
29\sk=%281%
2Fx%29%
28ln%28p%29-ln%288700%29%29
Replace the point (1,10000).
k=%281%
2F1%29%
28ln%2810000%
29-ln%288700%
29%
29\sk=ln%2810000%
29-ln%288700%
29 k=0.13926, which you might only desire to three or maybe even two significant figures.
You may just enter 10000% if you want p after two hours.
And it SHOULD be the same as 8700% (2810000%2F8700%).
Just give it a shot and see, 2Ae%5E%280.139%2A2%29. More particular, the model is highlighted by p=8700%. 2Ae%5E%280.139% 2Ax%29% 29.
Determine how long to double x.
Take the logs on both sides, then find x.
To put it more simply, start with this form: 2=1%2Ae%5E%280.13926%2Ax%29
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The buying rate and selling rate of £1 fixed by Nepal Rastra Bank are Rs. 132.50 and Rs. 133.80 respectively. If the bank buys £5000 and sells it, what is the profit in NRs?
The profit in RS. will be 6500 if the bank buys £5000 and sells it.
What is Profit ?
In mathematics, the gain from any business operation is referred to as the profit. Every time a shopkeeper sells a product, his goal is to make a profit by getting something from the customer. In essence, he earns a profit when he sells the item for more money than it cost.
Here, buying rate = £1 = 132.50
and, Selling rate = £1 = 133.80
The bank has bought £5000, that means the rate on the date of buying will be £1 = 132.50.
So, Cost price = £5000 × 132.50. = Rs.662500
Similarly, If he sells it, the rate on the date of selling will be £1 = 133.80.
So, Selling price = £5000 × 133.80 = Rs.669000
We know that, Profit = Selling price - Cost price
= 669000 - 662500
= 6500.
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Functions are in the world all around us. You have used functions to model phenomena and to make predictions. Mathematically, you can add, subtract, multiply, and divide functions, and you can also create a composition of functions.
A composition of functions occurs when you evaluate one function using another function, or even with the same function. A composition of functions is useful when a change in one function will create a change in another function, which, in turn, affects a third function. For example, suppose that humans build a housing development on land that was previously used as a corn field. This change in land usage causes the number of birds in the area to decrease, which causes the number of mosquitos to increase. You could model the increase in the number of mosquitoes as a function of the number of birds in the area, which is a function of the number of humans that live on that land.
You can also use the composition of functions to show that one function is the inverse of another function. Recall that the graphs of inverse functions are reflections of each other over the line. Think about these ideas as you read through the scenario below.
Last night it started raining as Hiba was closing up the store where she works. By 3 am, the roof of the store developed a small hole and water began to leak onto the sales floor. The water created a circular puddle on the floor. At any time, t, in minutes, the radius of the puddle increases by 0.1 cm. The rain continued through the night, but stopped by the time the morning shift arrived at the store at 7 am.
When the employees arrived at work, the leak and water puddle were discovered. The employees cleaned up the water puddle and placed a tall circular bucket underneath the leak, which was still slowly dripping. The capacity of the bucket can be expressed as. By 10 am, the amount of water in the bucket is.
Function composition is only one way to combine existing functions. Another way is to carry out the usual algebraic operations on functions, such as addition, subtraction, multiplication and division.
What is composition function ?The procedure known as "function composition" in mathematics takes two functions, f and g, and creates a function, h = g f, such that h(x) = g(f(x)).The combination of two functions to create a third function is known as function composition. Simply using the first function's output as the input for the second function is how it works.The function g is applied in this operation on the outcome of applying the function f to x. In other words, a function that maps x in domain X to g(f(x)) in codomain Z is produced by composing the functions f: X Y and g: Y Z. It makes sense that z would be a function of x if z were a function of y and y was a function of x. The resulting composite function is designated as (g f )(x) = g(f(x)) for all x in X, and is written as g f: X Z. [nb 1]Find the attachment of answer
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Look at the transformation of a 2-dimensional shape on the coordinate plane.
(x, y)→(−y,−x)
Which statement is true?
In the transformation of a 2-dimensional shape on the coordinate plane. (x, y) → (-y, -x), the statement which is true is that: d. Transformation preserves distance and angle measure both.
What is a transformation?In Mathematics, a transformation can be defined as the movement of a point from its original (initial) position to a final (new) location. This ultimately implies that, when an object is transformed, all of its points would be transformed as well.
Based on the transformation rule (x, y) → (-y, -x), we can reasonably infer and logically deduce that it represents or models a rotation of the geometric shape, followed by a reflection, which both preserves distance and angle measure based on these transformation rules:
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Complete Question:
Look at the transformation of a 2-dimensional shape on the coordinate plane. (x, y) → (-y, -x). Which statement is true?
a. Transformation preserves only distance.
b. Transformation preserves only angle measures.
c. Transformation preserves neither distance nor angle.
d. Transformation preserves distance and angle measure both.
Lydia and Claudia have the same number of charms in their collections. Lydia started with 6 charms and bought 3 more packs. Claudia started with 9 charms and bought 2 more packs. If each pack had x charms, which equation be used to find x?
A. x=(2+3)-(6+9)
B. x=6+3+9+2
C. 6x+3=9x+2
D. 3x-2x=6+9
E. 3x+6=2x+9
The equation that can be used to find x is
3x + 6 = 2x + 9
Option E is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Lydia started with 6 charms and bought 3 more packs.
Claudia started with 9 charms and bought 2 more packs.
If each pack had x charms.
This can be written as,
Lydia:
Number of charms = 6 + 3x
Claudia:
Number of charms = 9 + 2x
Now,
Lydia and Claudia have the same number of charms in their collections.
This can be written as,
6 + 3x = 9 + 2x
3x + 6 = 2x + 9
Thus,
The equation that can be used to find x is
3x + 6 = 2x + 9
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if somthing costid 64 dolers and thay sold it for 90% of the originol price how much wold it be
?
Answer:
6.40
Step-by-step explanation:
For this we will divide,
look below for a explanation
Purchase Price:
$64
Discount:
(64 x 90)/100 = $57.60
Final Price:
64 - 57.60 = $6.40
if I can vaccinate 10 people in 2 hours. how many people will I get vaccinated in 5 hours?
y=the number of people being vaccinated
x= the number of hours
Answer:
25 people
Step-by-step explanation:
10 people will be vaccinated for 2hrs
10 = 2
y people will be vaccinated for 5hrs
y = 5
(To find y we need to cross multiply)
10 = 2
y = 5
2y= 50
y=50/2
y=25
:- 25 people will be vaccinated in 5hrs.
Lets check if our answer is correct let us make 5 hrs our unknown x
10 = 2
25 = x
(cross multiply)
25×2=10x
50=10x
x=5hrs
so our answer is correct.
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What is the measure of a base angle of an isosceles triangle if the measure of the vertex angle is 80 less than the sum of the measures of the base angles?
Answer: 65 °
Step-by-step explanation:
Let x = measure of a base angle
Base angles of an isosceles triangle are equal
Sum of interior angles of a triangle is always 180:
x + x + (2x - 80) = 180
4x - 80 = 180
4x = 260
x = 65
what do you call a destroyed angle worksheet answers
Answer:
Step-by-step explanation:
A destroyed angle is called to as a rect-angle.
It's a pun on the "wreck"tangle
If the boundary line is dashed and the graph is shaded below the line what inequality do we use and why?
Answer: <
Step-by-step explanation:
If the boundary line is dashed, it means we will use < or > because it is not equal to, so that rules out ≤ or ≥.
Next, if the graph is shaded below the line we will use < because the graph is less than.
please help!
Jocelyn has a points card for a movie theater.
She receives 25 rewards points just for signing up.
She earns 12.5 points for each visit to the movie theater.
She needs at least 170 points for a free movie ticket.
Write and solve an inequality which can be used to determine v, the number of visits Jocelyn can make to earn her first free movie ticket.
Answer:
25 + 12.5v ≤ 170
Step-by-step explanation:
WHAT WILL YOU WEAR?
You are getting ready for Thanksgiving dinner and trying to find the perfect outfit. You want to wear your new sweater from Infinity21. The manufacturer advertises that this sweater is most comfortable to wear when the temperature satisfies |t-56| ≤6 degree: Fahrenheit. The weaather report says it will be 53°F on Thanksgiving Day at mealtime.
Can you wear your new sweater comfortably?
By solving a linear inequation, it can be concluded that
The sweater can be worn comfortably
What is a linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by > . < , ≤, ≥
A one degree inequation is known as linear inequation.
Here, the given linear inequation is
[tex]|t - 56| \leq 6\\t - 56 \geq -6 \ or \ t - 56 \leq 6\\t \geq 56 - 6 \ or \ t \leq 56+6\\t \geq 50 \ or \ t \leq 62\\50 \leq t \leq 62[/tex]
As 53° F lies between 50 and 62, the sweater can be worn comfortably
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Can the two triangles be proven congruent by SAS explain?
Yes, two triangles can be proven congruent by SAS(Side angle side) congruence.
What is SAS Congruence?If any pair of comparable sides and their included angles are the same in both triangles, then the triangles are said to be congruent.
There are five ways to determine whether two triangles are congruent. It's one of them (SAS). Congruent Triangles provides a list. If any two comparable sides and their included angle in both triangles are same, then the triangles are congruent.
Why does this matter?
Due to the congruence of the triangles:
Third sides also have identical angles.
the other two complementary angles are equal
Two triangles, congruent since all three sides are the same length, but one flipped and rotatedCongruent triangles can be turned and/or mirror images of each other (reflected).
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what is the range of the function on the graph all real numbers
The required range is [0,∞]
All values, or inputs, constitute a function's domain, while all values, or outputs, constitute its range.
When examining a graph, the range of the function is from up to down, and the domain refers to all of the values on the graph from right to left.
Therefore , the range of the function on the graph of all real numbers extends from zero to positive infinity.
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Given the inflation model C(t)=C0(1+r)t and given that a boat that currently sells for $385,290 sold for $142,700 7 years ago, what has the average annual rate of inflation been for the past 7 years? Round to two decimal places.
1,384,190...............
What is the rule of proof?
The rules of proof is that every statement should be justified and never assume things when proofing in contradiction
The basic rules of proofs are as followings:
Each assertion should be legitimate.A support can allude to earlier lines of the verification, the speculation as well as recently demonstrated explanations from the book.Cases are frequently expected to finish a proof which has proclamations with an "or" in them.A logical inconsistency is reached when an assertion goes against any of the speculations, an earlier line of the confirmation, or any well established truth .A proof by logical inconsistency is possibly finished when a logical inconsistency has been arrived at for each situation.On the off chance that you can't find a defense and you are certain it is valid, you might wish to compose a separate verification as an after thought to demonstrate that support and afterward apply it to your unique circumstanceDuring a proof you might present new factors by saying "Let x be..."To know more about Proof here
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The questions are in the picture
The linear function is of:
P(t) = 3265t + 34687.
Using the linear function, the estimate for 2016 is of:
54,277.
The exponential function is of:
P(t) = 34687(1.0941)^t.
Using the exponential function, the estimate for 2016 is of:
59,499.
What is the linear function?The linear function is defined as follows:
P(t) = mt + b.
The coefficients of the function are given as follows:
m is the slope, representing the yearly change in the population.b is the intercept, representing the population in 2010.In the context of this problem, these parameters are given as follows:
m = 37,952 - 34,687 = 3265.b = 34,687.Hence the function is:
P(t) = 3265t + 34687.
2016 is 6 years after 2010, hence the estimate is given as follows:
P(6) = 3265(6) + 34687 = 54,277.
What is the exponential function?The exponential function is defined as follows:
P(t) = ab^t.
In which the coefficients are given as follows:
a is the population in 2010.b is the rate of change.Hence the parameters are given as follows:
a = 34687.b = 37952/34687 = 1.0941.Hence the function is of:
P(t) = 34687(1.0941)^t.
Then the estimate for the year of 2016 is of:
P(6) = 34687(1.0941)^6 = 59,499.
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A recipe for flapjacks uses only syrup, butter and oats, in the ratio 1: 2: 3
a) Trevor makes some flapjacks using this recipe and uses 200g of syrup.
(i) What quantity of butter should he use? _________g
(ii) What quantity of oats should he use? _________g
b) Using this recipe, 150g of syrup are needed to make 8 flapjacks. Find the quantity of oats needed to make 16 of these flapjacks.
Answer: _____g
By using Unitary method, it can be calculated that
a) Quantity of butter Trevor uses = 200 [tex]\times[/tex] 2 = 400 g
Quantity of oats Trevor uses = 200 [tex]\times[/tex] 3 = 600 g
b) 900 g of oats is required to make 16 flapjacks
What is Unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here Unitary method will be required
a) Let Trevor use x g Syrup, 2x g butter and 3x g oats
Trevor uses 200 g syrup
So x = 200
i) Quantity of butter Trevor uses = 200 [tex]\times[/tex] 2 = 400 g
ii) Quantity of oats Trevor uses = 200 [tex]\times[/tex] 3 = 600 g
b) To make 8 flapjacks 150 g of syrup is used
To make 1 flapjack [tex]\frac{150}{8}[/tex] g of syrup is used
To make 16 flapjacks [tex]\frac{150}{8} \times 16[/tex] g of syrup is used
To make 16 flapjacks 300g of syrup is used
To make 16 flapjacks 300 [tex]\times[/tex] 3 g of oats is used
To make 16 flapjacks 900 g of oats is used
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Luke and Cade have started running. Luke runs 15 more than three times the number of miles Cade runs. Together they run a total of 63 miles. Write an equation to determine the number of miles Luke and Cade ran.
*
1 point
3x + 15 = 63
x + 15 + 3x = 63
x - 15 + 3x = 63
3x - 15 = 63
The Linear equation that represents the above situation is given by
x + 3x + 15 = 63
Linear Equation:A linear Equation is a Mathematical expression that is used to calculate an unknown number of values or any unknown quantity. Here we use variables to represent the unknown numbers.
Here given that
Luke and Cade have started running
Luke runs 15 more miles than thrice of that of number of miles Cade runs
Since we don't know the number of miles run by Cade
Let us assume that Cade runs x miles
=> Number of miles run by Cade = x miles
From the given data,
The number of miles run by Luke will be = 3x + 15
=> Number of miles run by Luke and Cade = x + 3x + 15
Given that the total mile run by Luke and Cade = 63 miles
=> x + 3x + 15 = 63
Therefore,
The Linear equation that represents the above situation is given by
x + 3x + 15 = 63
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what are the 12 kinds of polygons
The 12 kinds of polygons are:
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Hendecagon
Dodecagon
Tridecagon
Tetradecagon
Polygons:
A polygon is a closed shape figure that has a minimum of three sides and three vertices.
Poly → many
gon → angle
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Graph -7x+5y=35−7x+5y=35minus, 7, x, plus, 5, y, equals, 35.
Answer:
835786543225644323567
convert 1/2 into a decimal
Answer:0.5
Step-by-step explanation:
here you go
How do you know if a graph has two solutions?
If the line intersects the parabola in two places, then two solutions are true for both equations.
We graph both equations in the same coordinate system to visually solve a system of linear equations. The intersection of the two lines is where the system's answer will be found. The point where the two lines join is (-3, -4), which is where this equation system's solution lies.
There are no solutions that hold for both equations if the equations' graphs do not meet (for instance, if they are parallel). There are an infinite number of solutions that hold for both equations if the equations' graphs are identical.
Two solutions hold for both equations if the line crosses the parabola twice.
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You read 6 chapters. Each chapter has 8 pages. Your brother reads the same number of pages. His chapters have 12 pages. How many chapters does your brother read?
The sixth chapter's Brother 0.66 pages were read.
How to calculated the chapters in 12 pages?According to the order of operations, you should perform multiplication and division first, going from left to right, before adding and subtracting.
Add and subtract from left to right while continuing to multiply and divide. the next step is to add and subtract from left to right.
Assumed the question is how many pages are in each chapter.
Let it be x:
6x + 8 = 12
6x = 4
x = 4 /6
x = 0.66.
The sixth chapter's Brother 0.66 pages were read.
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help me i dont get this at all
Answer: 18
D
Step-by-step explanation:
The constant of proportionality is y/x, not x/y, which is what your friend found.
X= 1
y=18
18/1=18
André planted a cedar hedge 15 years ago (currently it's the start of the 16th year). The
hedge is now 3 metres high. The cedars grew an average of 12 cm per year. How tall were
the cedars when he planted them?
The height of the cedars when they were planted by André, found using the formulas for arithmetic progression is 1.32 meters
What is an arithmetic progression?An arithmetic progression is a number sequence that consists of numbers that have a constant or common difference between consecutive term of the sequence.
The year André planted the cedar hedge tree = 15 years ago
The present height of the hedge = 3 meters = 300 cm
The average rate at which the cedars grew = 12 cm per year
The height of the cedar hedge when André initially planted the them can be found by representing the situation using an arithmetic progression formula or as follows;
The nth term of an arithmetic progression, aₙ, can be found using the formula; aₙ = a₁ + (n - 1)·d
Where;
a₁ = The initial height of the tree
d = The amount the tree grows each year = 12 cm
n = The number of years ago, the tree was planted
When n = 15, we get;
a₁₅ = 3 meters = 300 cm
Therefore;
300 = a₁ + (15 - 1) × 12
a₁ = 300 - (15 - 1) × 12 = 132
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Chelsey puts twelve colored pieces of chocolate candy in a bag. Three pieces are green, four pieces are yellow, two pieces are purple, and three pieces are red. She draws one piece of candy from the bag at a time and eats it.
problem A: What is the probability that Chelsey will draw out three pieces of candy in this order: red, green, yellow?
Problem B: What is the probability that Chelsey will draw out three pieces of candy in this order: green, yellow, red?
problem C: What is the probability that Chelsey will draw out three pieces of candy in this order: yellow, red, green?
problem D: Make a conclusion about how the order in which she draws out the red, green, and yellow pieces affects the probability.
The probability for each event are
[A] - 36/1320
[B] - 36/1320
[C] - 36/1320
[D] - The probability doesn’t change in any order.
What is a expression? What is a mathematical equation? What is Probability?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. The formula to calculate the probability of occurrence of an event 'A' can be written as -P(A) = n(A)/n(S)
where -
n(A) = Number of outcomes favorable to event A.
n(S) = Total number of outcomes
We have Chelsey who puts twelve colored pieces of chocolate candy in a bag. Three pieces are green, four pieces are yellow, two pieces are purple, and three pieces are red. She draws one piece of candy from the bag at a time and eats it.
[A] -
{3/12} x {3/11} x {4/10} =
36/1320
[B] -
{3/12} x {4/11} x {3/10}
36/1320
{C} -
{4/12} x {3/11} x {3/10}
36/1320
D) The probability doesn’t change in any order.
Therefore, the probability for each event are -
[A] - 36/1320
[B] - 36/1320
[C] - 36/1320
[D] - The probability doesn’t change in any order.
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Look at the pattern.
72, 67, 62, 57
Which of these is the rule for the pattern?
a
b
d
subtract 5
add 5
subtract 9
add 9
Answer:
Subtract 5
Step-by-step explanation:
72 , 67, 62, 57,..
Each term is obtained by subtracting 5 from the previous term.
72 - 5 = 67
67 - 5 = 62
62 - 5 = 57
5 2/3 divided by 2 1/8 Perform the indicated operation.
Answer: 2 and 2/3
Step-by-step explanation: To divide these mixed numbers, I would first rewrite them as improper fractions.
You should be familiar with how do this and if you aren't, send me a comment below and I can give you a quick review.
So 5 and 2/3 becomes 17/3 and 2 and 1/8 becomes 17/8.
This gives us 17/3 ÷ 17/8.
When we divide fractions, we just change the division sign
to multiplication and take the reciprocal (flip) the second fraction.
So we have 17/3 · 8/17.
before multiplying, we can cross-cancel the 17's by dividing by their greatest common factor of 17 to get 1.
So we have 1/3 · 8/1 which is 8/3.
Now since 3 goes into 8 twice, our we have 2 as our whole fraction.
Since there is 2/3 left over, we have a fraction of 2/3.
So our final answer is 2 and 2/3.
A certain triangle has a 30° angle and a 60° angle. Which must be a true
statement about the triangle?
OA. The longest side is 3 times as long as the shortest side.
OB. The second-longest side is twice as long as the shortest side.
OCTwo sides of the triangle have the same length.
Sons
D. The longest side is twice as long as the shortest side.
Answer:
D. The longest side is twice as long as the shortest side.
Step-by-step explanation:
Given one angle is 30° and another is 60°, the third must be 90°, making a Special 30-60-90 triangle. In a 30-60-90 triangle, the hypotenuse (longest side) is twice (two times) as long as the shortest side.
