Select all the correct locations on the table.
Classify each situation as an exponential growth, exponential decay, or linear relationship.
A catering company purchased a delivery van
for $25,000. After 2 years, the value of the van
was $17,500. After 4 years, the value of the van
was $12,250.
At the beginning of the day, a laptop had 100%
battery life. After 3 hours, the laptop had 60%
battery life. After 6 hours, it had 20% battery life.
A tiger reserve had an initial population of
20 tigers. After 5 years, the population was
30 tigers. After 10 years, the population was
45 tigers.
exponential growth
exponential decay
linear
Answers
The required answer choices are (i)exponential decay (ii) linear and (iii) exponential growth
What are exponential growth and exponential decay?
Quantities that fluctuate quickly are subject to exponential growth and decay. The idea of geometric progression has been used to infer exponential growth and decay. Exponential growth or exponential decay are terms used to describe quantities that vary exponentially rather than continuously.
From question,
1) The first question is like, initially delivery van price is $25,000 after 2 years, the value of the van becomes $17,500
This means it is decaying. The difference between the initial price and after 2 years price is $7500.
To be linear, further after 2 years, or from start after 6 years, the price should be $10000. But it is given to be $12250.
Thus exponential decay.
2) In the second, Initially, a laptop had 100% battery life. After 3 hours, the laptop has 60% battery life. Thus the loss in 3 hours is (100 - 60) = 40%.
After 4 hours, the loss is (60 -20) = 40%
As the loss is the same in equal intervals of time, the decay is linear.
3) In the third one, A tiger reserve had an initial population of 20 tigers.
After 5 years the population was 30 tigers, thus the growth is (30-20) =10.
After 10 years, the population was 45 tigers. Thus the growth is (45-30) = 15.
Thus the increase is non-linear, and so is exponential growth.
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Related Questions
Did I solve the absolute value right, when solving I used [tex]\sqrt{(5)^2+(0)^2}[/tex]
which I only got 5, but I feel like that felt a little too easy and wanted to make sure i answer this question right.
Answers
Answer:
(-5, 0)
|z| = 5
Step-by-step explanation:
Complex numbers can be represented on an Argand diagram.
The x-axis is called the real axis and the y-axis is called the imaginary axis.
The complex number z = x + iy is represented on the diagram by the point P(x ,y), where x and y are Cartesian coordinates.
Therefore, the complex number z = -5 can be represented on the Argand diagram by the point:
(-5, 0)The absolute value of a complex number is the magnitude of its corresponding vector.
For a complex number z = x + iy, the absolute value is given by:
[tex]|z|=\sqrt{x^2+y^2}[/tex]
Therefore, the absolute value of complex number z = -5 is:
[tex]\implies |z|=\sqrt{(-5)^2+(0)^2}[/tex]
[tex]\implies |z|=\sqrt{25+0}[/tex]
[tex]\implies |z|=\sqrt{25}[/tex]
[tex]\implies |z|=5[/tex]
Rewrite the linear expressions by factoring out the greatest common factor.
-x – 10
Answers
According to the given statement the greatest common factor is -1(x+10).
What is an example of a linear expression?Examples involving linear equations are 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3. The concept of linear equations, the including that for linear equations involving one parameter, two independent variables, or three variables, and examples of each will all be explored in detail in this article.
How should a linear expression be written?A linear equation has the slope-intercept form y = mx + b. When x is 0, the integers m and b provide the line's slope (m) and also the value of y. (b). It y-intercept is indeed the value that y has when x is 0 because (0,y) is the point at which the line crosses the y-axis.
Briefing:= -x – 10
= -1(x+10)
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The barometric air pressure in inches of mercury at a distance of x miles from the eye of a severe hurricane is given by f(x)=0.48 ln (x+2)+27. How far from the eye is the pressure 28 inches of mercury?
The pressure of 28 inches of mercury occurs about miles from the eye of the hurricane.
(Round to the nearest whole number as needed.)
Answers
For the given function, f(x)=0.48 ln (x+2)+27. The distance is 6.004 from the eye is the pressure of 28 inches of mercury.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that the function is, f(x)=0.48 ln (x+2)+27
f(x)=28
28 = 0.48 ln (x+2)+27
0.48 ln(x+2)=28-27
ln(x+2)=1/0.48
ln(x+2)=2.08
[tex]\rm x+2 = e^{2.08}[/tex]
x+2 = 8.004
x=8.004 - 2
x=6.004
Thus, for the given function, f(x)=0.48 ln (x+2)+27. The distance is 6.004 from the eye is the pressure of 28 inches of mercury.
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What is the slope of the line on this graph?
Enter your answer in the box.
Answers
to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} \implies \cfrac{-6}{2 +1} \implies \cfrac{ -6 }{ 3 } \implies \text{\LARGE -2}[/tex]
Answer:
The slope is 2
Step-by-step explanation:
To find the slope you divide the rise by the run. Rise being how many units it goes up or down) (run being how many units it goes to the side).
In this case the rise is -2 and the run is -1.
See in the picture, for every 2 units the line goes down, it moves one unit to the right.
so, -2/-1= 2
The odds on (against) your bet are 3
to 7
.
If you bet $49
and win, how much will you gain?
Answers
Answer:
No more than 10 dollars
Step-by-step explanation:
Facts!
Pls help I need done quickly I am overdue
Answers
so, to find the answer you times the 2 bottom rows together so in this picture is is 4 x 7 which equals 28
hope this helps :)
A farmer needs to pack 2,903 apples into crates to ship to supermarkets. Each crate can hoid
only 30 apples. Choose true or false for each statement.
A. The farmer needs 96 crates to ship out all apples. True or False
B. The farmer needs 97 crates to ship out all the apples. True or False
C. At least one of the crates will not be filled to capacity. True or False
D. To determine the number of crates needed, divide 30 by 2,903. True or False
Answers
A farmer needs to pack 2,903 apples into crates to ship to supermarkets. Each crate can hold only 30 apples. Choose true or false for each statement.
A. The farmer needs 96 crates to ship out all apples. False
B. The farmer needs 97 crates to ship out all the apples. True
C. At least one of the crates will not be filled to capacity. True
D. To determine the number of crates needed, divide 30 by 2,903. False
Answer:
A. False, you will need another crate in order for all of the apples to be shipped to the supermarkets.
B. True, this will hold all of the apples with some extra space left in the last crate.
C. True, 2,903 divided by 30 is 96.76666666666667. Meaning that one of them won't have exactly 30 apples.
D. False, you divide 2,903 by 30.
There are 9 bottles of juice on a shelf. Each serving of juice is of a bottle.
How many servings of juice are there in the bottles on the shelf?
Enter your answer in the box.
servings
PLEASE HELP IM DOING A TEST
Answers
The number of servings of juice in the bottles on the shelf is 135
How to determine the number of servings of juice in the bottles on the shelf?From the question, we have the following parameters that can be used in our computation:
Bottles = 9
Serving of juice per bottle = 15
This means that
The number of servings of juice in the bottles on the shelf = Bottles x Serving of juice per bottle
So, we have
The number of servings of juice in the bottles on the shelf = 9 * 15
Evaluate
The number of servings of juice in the bottles on the shelf = 135
Hence, the servings is 135
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Complete question
There are 9 bottles of juice on a shelf. Each serving of juice is 15 of a bottle.
How many servings of juice are there in the bottles on the shelf?
Specific entries in a two dimensional array dataMatrix are identified by a logical index array logicalSelect. Assign the first numSelected of the selected elements to an array selectedData. Ex: If dataMatrix is [-2, 3, 6; 5, 78, 44; 9, -3, -53], logicalSelect is [ 1, 0, 0; 0, 0, 1; 1, 1, 1], and numSelected is 4, then selectedData is [-2; 9; -3; 44].
Answers
The first numSelected of the selected elements to an array selectedData is assigned in the programme.
Explain the term two dimensional array?Although the data are still saved linearly in memory, a two-dimensional array is a type of data structure that consists of a set of cells arranged in a two-dimensional grid, much like a table with columns and rows.The program for the given condition is-
function selectedData = SelectLogicalN( dataMatrix, logicalSelect, numSelected )
% SelectLogicalN: Return the first numSelected values of input 2D
% array dataMatrix indexed by localSelect indexing array.
%Inputs: dataMatrix - input data matrix (2D array)
%logiccalSelect - logical indexing array, can be 2D or linear
%numSelected - number of indexed elements to return in selectedData%
%Outputs: selectedData - column vector of logically indexed elements to return
dataMatrix = dataMatrix(logical(logicalSelect));
% assign tempSelected with logically indexed elements of dataMatrixtemp
Selected = dataMatrix
% find the size of tempSelected
s=size(tempSelected);
% remove the last element from the temp
SelectedselectedData =tempSelected
(1:s-1)end
Thus, the first numSelected of the selected elements to an array selectedData is assigned in the programme.
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arrange the following five girls in order starting from the youngest
sue is older than ria but younger than jill one other girl separates jill and Michelle in age . Michelle is neither the youngest nor the eldest . Paula is the youngest.
need help fast
Answers
Answer:
Step-by-step explanation:
Sue is older than Ria, but Ria is younger than Jill. Ria is the middle of the three. Paula is the youngest. So the order would be Paula, Ria, Michelle, Jill, and Sue. Hope this was correct and hoped it helped. :)
Coin's family has driven 318 miles in 6 hours. If they continue at this rate how far will they travel during the next 4 hours. complete the proportional statement with the selections.
Answers
Hello,
I hope you and your family are doing well!
To solve this problem, you need to set up a proportion using the information given in the problem. Let x represent the number of miles the family will travel during the next 4 hours. The proportion will look like this:
318 miles / 6 hours = x miles / 4 hours
To solve for x, you can cross-multiply and solve the equation:
318 miles / 6 hours = x miles / 4 hours
6 hours * 318 miles = 4 hours * x miles
1848 miles = 4x miles
x = 462 miles
Therefore, if the family continues at the same rate, they will travel a total of 462 miles during the next 4 hours.
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Select all the true statements given that APQR= ASTU.
A. PO= ST
B. PQ= TU
C. mLR =mLU
D. MLP = m
E. ML0= m
Answers
The true statements that satisfy ΔPQR ≅ ΔSTU are PQ = ST, m∠R = m∠U, and m∠Q = m∠T.
What is congruence?
In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Here, we have
Given
ΔPQR is congruent to ΔSTU
We have to find a true statement that satisfies the given condition.
We concluded that PQ = ST, m∠R = m∠U, and m∠Q = m∠T.
Hence, the true statements that satisfy ΔPQR ≅ ΔSTU are PQ = ST, m∠R = m∠U, and m∠Q = m∠T.
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Consider all three-digit numbers that can be created from the digits 0-9 where the first and last digits must be even and no digit can repeat. Assume that numbers can start with 0. What is the probability of choosing a random number that starts with 6 from this group? Enter a fraction or round your answer to 4 decimal places, if necessary.
Answers
The probability of choosing a random number that starts with 6 from this group is 1/5 Or 0.2.
What are permutation and combination?A permutation is an arrangement of things where order matters, AB and BA are two different permutations.
The combination is a selection of things where order does not matter, AB and BA are the same combinations.
Given, All three-digit numbers that can be created from the digits 0-9.
So, The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 total of 10 digits.
No. of even digits is 4 and the number of odd digits is 5.
The total number of 3 digits that can be formed where the first and last digits must be even and no digit can repeat and can start with 0 is,
= 5×10×4.
= 200.
The number of digits starts with 6 in this group is,
= 1×10×4.
= 40.
∴ The probability of choosing a random number that starts with 6 from this group is (40/200) = 1/5 Or 0.2
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evaluate for the value of sum and x after the following code is executed. sum is initialized to 4. x is initialized to 2.
Answers
The value of the given sum after the execution of code segment is equal to 16.
As given in the question,
Using attached code segment.
Given values are:
num1 = 6
num2 =4
num3 =10
Value of sum after execution of code segment is given by:
num1 < num2
⇒ 6< 4 which is false.
Else num3 = num2
⇒ num3 = 4
num2≥ num3
⇒4 ≥ 4
True as 4 =4
num1 = num2 + num3
= 4 + 4
= 8
Final sum = num1 + num2 + num3
= 8 + 4 + 4
= 16
Therefore, using code segment the value of the sum is equal to 16.
The given question is incomplete, I answer the question in general according to my knowledge:
What is the value of sum after the code segment is executed?
code segment is attached:
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Complete the explanation of how the parameter b horizontally stretches or compresses the graph of y=(b x)² when 0
Answers
By using the concept of stretch, it can be concluded that -
When 0 < b < 1, the graph of y = [tex](bx)^2[/tex] is stretched horizontally by a factor of b
What is stretch?
Stretch is a mathematical transformation in which an object enlarges in one direction only.
y = [tex](\frac{1}{2}x)^2[/tex] is a horizontal stretch of y = [tex]x^2[/tex] by a factor of 2
y = [tex](\frac{1}{3}x)^2[/tex] is a horizontal stretch of y = [tex]x^2[/tex] by a factor of 3
y = [tex](\frac{1}{4}x)^2[/tex] is a horizontal stretch of y = [tex]x^2[/tex] by a factor of 4
So when 0 < b < 1, the graph of y = [tex](bx)^2[/tex] is stretched horizontally by a factor of b
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Answer the questions below to explain what kind of function would better model the data, linear or exponential.
function would better model the data because as x increases, the
y values change . The of this function is approximately
Answers
The linear model would be a better model for the given function.
What are linear models?
A response variable can be described in terms of a linear combination of predictor variables using linear models. The response ought to be continuous and at least roughly regularly distributed. Although these models are widely used, they are unable to handle clearly discrete or skewed continuous data.
In the table, we see that as x increases, y values change in a steady manner. The slope of this function is approximately 1860.
We use straight lines to visually illustrate linear relationships. Typically, a linear model has two parameters: the slope, also known as the growth factor or rate of change, and the y-intercept, often known as the beginning value. The linear model can be expressed as a linear function, y = mx + b or y=mx+b, where m is the slope and b is the y-intercept.
So, we get the slope as 1860.
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If $900 is invested at 3%, compounded monthly, the future value S at any time t (in years) is given by the following.S = 900(1.0025)^12tHow long (in years) will it take for the amount to double? (Round your answer to one decimal place.)
Answers
Number of years it will take for the amount to double is 23 years
The principal amount = $900
The interest rate = 3%
The interest is compounded monthly
The given equation is
S = 900(1.0025)^12t
Where S is the final amount
t is the time period in years
The final amount is the double of principal amount
Final amount = 2 × 900
= $1800
Substitute the values in the equation
1800 = 900(1.0025)^12t
1.0025^12t = 1800/900
1.0025^12t = 2
Then value of t = ln(2) / 12ln (1.0025)
Divide the numbers
= 23.13b years
Therefore, the time period is 23 years
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UV ≅ ST, QR ≅ PQ, QT ≅ QU, and PV ≅ RS. Complete the proof that ∠V ≅ ∠S.
Answers
The two column proof in completed as follows
Statement Reason
1 line UV ≅ line ST Given
2 line QR ≅ line PQ Given
3 line OT ≅ line OU Given
4 line PV ≅ line RS Given
5 PT = PQ + QT Additive Property of Length
6 RU = QR + QU Additive Property of Length
7 PY = QR + QU Substitution
8 PT = RU Transitive Property of Equality
9 TV = UV + TU Additive Property of Length
10 SU = ST + TU Additive Property of Length
11 TV = ST + TU Substitution
12 SU = TV Transitive Property of Equality
13 ΔSUR ≅ ΔVTP SSS
14 ∠V ≅ ∠S CPCTC
What is congruency of triangle?Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules
Some of the rules include
Side - Side - Side = SSSSide - Angle - Side = SASAngle - Side - Angle = ASA Angle - Angle - Side = AAS Hypotenuse and one leg = HLThe problem requires the prove by Side - Side - Side = SSS rules to ensure that the the triangles are congruent
The SSS have it that the two triangles being compared should have their three sides being are equal then the triangles are congruent
Achieving the SSS rules then by Corresponding Parts of Congruent Triangles are Congruent CPCTC theorem ∠V ≅ ∠S
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read the proof given AB//DE prove ABC EDC:
Answers
Answer:
AA similarity theorem.
Step-by-step explanation:
Solve for x.
36=27^x+10
Answers
Answer:
x = In(26)/In(27)
Step-by-step explanation:
26=27^(x)
take the logarithm of both sides
x = In(26)/In(27)
Answer:
This is a bit late but I believe the answer is
Step-by-step explanation:
x = In (26)/3In (3).
Im very sorry if this turns out to be wrong.
The formula A=23.1 е⁰⁰¹⁵²⁺ models the pollution of US state, a, in millions ,t years after 2000.
A. What was the population of the state in 2000 ?
b. When will the population of the state reach 28.3 million?
a. In 2000 , the population of the state was million.
Answers
Answer:
a) 23,1 milions
b) en 2013 - 2014
Robin worked his 40 regular hours last week plus 20 overtime hours at the time-and-a-half rate. His gross pay was $16,203. What is his regular hourly rate?
Answers
Answer:
His rate is a whopping $231.47 per hour.
:)
Step-by-step explanation:
We can conclude that.
[tex]r*t_1=p_{reg}[/tex] is the gross pay from his regular hours.
[tex]1.5r*t_2=p_{ovt}[/tex] is the gross pay from his overtime hours.
So all together we can say
[tex](r*t_1)+(1.5r*t_2)=p[/tex]
We are looking for his hourly rate.
Lets solve for [tex]r[/tex].
Multiply the terms in the parenthesis.
[tex]rt_1+1.5rt_2=p[/tex]
Factor [tex]r[/tex] out of [tex]rt_1[/tex].
[tex]r(t_1)+1.5rt_2=p[/tex]
Factor [tex]r[/tex] out of [tex]1.5rt_2[/tex].
[tex]r(t_1)+r(1.5t_2)=p[/tex]
Factor [tex]r[/tex] out of [tex]r(t_1)+r(1.5t_2)[/tex].
[tex]r(t_1+1.5t_2)=p[/tex]
Divide each term in [tex]r(t_1+1.5t_2)=p[/tex] by [tex]t_1+1.5t_2[/tex] and simplify.
[tex]\frac{r(t_1+1.5t_2)}{t_1+1.5t_2} =\frac{p}{t_1+1.5t_2}[/tex]
Simplify the left side. Cancel the common factor of [tex]t_1+1.5t_2[/tex]
[tex]r=\frac{p}{t_1+1.5t_2}[/tex]
Now we have an equation to find his regular hourly rate.
We are given
[tex]p=16203[/tex]
[tex]t_1=40[/tex]
[tex]t_2=20[/tex]
Lets plug these numbers into our equation for [tex]r[/tex].
[tex]r=\frac{16203}{40+1.5*20}[/tex]
[tex]r=\frac{16203}{70}[/tex]
[tex]r=231.47[/tex]
5. Table Item For parties of 6 or more people
at a certain restaurant, a tip of 18% is
automatically included on the bill.
Select yes or no to indicate whether or not
each of the following tip amounts is correct
for an 18% gratuity on each subtotal.
(Lesson 3)
subtotal: $129.50
tip: $23.27
subtotal: $98.40
tip: $17.71
subtotal: $142.17
tip: $22.75
yes
no
Answers
Answer:
Look at images
Step-by-step explanation:
it doesn't let me put the full image
1. Is H nonempty? 2. Is H closed under addition? If it is, enter CLOSED. If it is not enter two vectors in H whose sum is not in H. using a comma separated list and syntax such as <1,2,3>, <4,5,6>. 3. Is H closed under scalar multiplication? If it is, enter CLOSED. If it is not enter a scalar in R and a vector in H whose product is not in H, using a comma separated list and syntax such as 2, <3,4,5>. 4. Is H a subspace of the vector space V? You should be able to justify your answer by writing a complete, coherent, and detailed proof based on your answers to parts 1-3.
Answers
As per the concept of vector, the subspace of the vector is < 3, 4, 5>
The term vector is defied as the geometric entity that has both magnitude and direction.
Here we have to find the given vector <1, 2 , 3> and < 3, 4, 5> subspaces by using the vector formula.
Let us consider V = R³ and let H be the subset of V of all points on the plane 7x+4y+6z=0.
By looking into the given equation, we have identified that H is a non empty set.
And here be looking into the given vector, the second one is always the subspace. Based on this, the resulting subspace is written as,
=> < 3, 4, 5>
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Claim: Most adults would erase all of their personal information online if they could. A software firm survey of 526
randomly selected adults showed that 61% of them would erase all of their personal information online if they could. Find
the value of the test statistic.
The value of the test statistic is
(Round to two decimal places as needed.)
Answers
The value of the test statistic rounded to two decimal places is equal to 5.05.
What is a sample proportion?In Mathematics, a sample proportion can be defined as the proportion of individuals in a sample that have a specified characteristic or trait.
For a claim that most adults would erase all of their personal information online if they could, the appropriate null hypothesis and alternative hypothesis would be given by this mathematical expression:
H₀: p ≤ 0.5.
Ha: p > 0.5.
How to calculate the value of the test statistic?Mathematically, the test statistic for the z-test of a population proportion can be calculated by using this mathematical expression;
[tex]z=\frac{\hat{p} \;- p}{\sqrt{\frac{p(1\;-p)}{n } } }[/tex]
Where:
z represents the test statistic.p^ represents the sample proportion.n represents the sample size.p represents the population proportion.Substituting the given parameters into the formula, we have;
z = (0.61 - 0.5)/√(0.5(1 - 0.5)/526)
z = (0.11)/√(0.5(0.5)/526)
z = (0.11)/√(0.25/526)
z = 0.11/0.0218
z = 5.05.
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if sandy earns $5.00 an hour at her new job, how much will she make after 12 hours?
Answers
12 hour = x,
Cross multiply
1*x = 5 * 12
X = 60 $
Answer: $60.00
Step-by-step explanation: If we want to find how much money she makes in 12 hours, we must use the information we got for how much she makes in 1 hr, and apply that to make a proportional relationship. So, it would look like this:
[tex]\frac{5}{1}[/tex] = [tex]\frac{?}{12}[/tex]
Now, using cross multiplying, we multiply 1 x 12 and 5 x 12 to get $60. I hope this helped.
A bag contains 12 red, 3 blue, and 5 yellow marbles, what is the probability of drawing a blue or yellow marble?
Answers
Answer:
the chance to pull a blue marble is 3/20
the chance to pull a yellow marble is 5/20
Triangle A B C is an isosceles triangle. Find the missing angles and side measures.
- Angle A =?
- Angle C=?
- Side A C=?
Answers
The value of ∠ A = 40°,∠C = 70° and AC = 12
What is value ?
Value in mathematics can refer to a number of closely related ideas. A mathematical value can generally be any specific mathematical object. This is most frequently a number in elementary mathematics, such as a real number like or an integer like 42.
Depending on where it is in the number, each digit has a different value, which is referred to as value. We figure it out by multiplying the digit's place value by its face value. Place value plus face value equals value. Consider the number 45, for example. Here, the fourth digit is in the tens column.
If triangle is isosceles it means the two sides and angles are equal
∴ BC = AC
AC = 8 cm
A + B + C = 180
A = 180 - 70 -70
∠A = 40°
∠C = 70°
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shiloh is sharing jelly beans. The jar has a ratio 36:32 if shiloh keeps the ratio the same and gives his friend 7 pink jellybeans, how many green jellybeans should he also share
Answers
Answer:
5.89 green jelly beans or we would round down to the nearest whole jellybean, 5.
Step-by-step explanation:
I am assuming that the ration is 36:32 pink:green so we need 7:?
36/32
7/ (36/32) =5.8947
Write and find the general solution of the differential equation that models the verbal statement. Evaluate the solution at the specified value of the independent variable.
The rate of change of P is proportional to P. When t = 0, P = 8,000 and when t = 1, P = 5,200. What is the value of P when t = 6?
Be sure to:
1) Write the differential equation (use k for the constant of proportionality)
2)Solve the differential equation
3) Evaluate the solution at the specified value of the independent variable. (Round your answer to three decimal places.)
Answers
1) The differential equation is: dP/dt=kP
2) P(t)=8000[tex]e^{-0.28t}[/tex]
3) The solution at the specified value of the independent variable is 1490.991
What is meant by differential equation?In practical contexts, derivatives frequently represent the rates of change of physical quantities, and the differential equation establishes a relationship between the two. As a result of the frequent occurrence of these correlations, differential equations are widely employed in a wide range of disciplines, including engineering, physics, economics, and biology.
Only the simplest differential equations can be resolved explicitly, but many aspects of a given differential equation's solutions can be determined without doing an exact calculation.
1) The differential equation is: dP/dt=kP
Here k is the proportionality constant
2) Now, we have to solve the differential equation on dP/dt=kP
∫dP/P=∫kdt+lnP₀
lnP₀=kt+lnP₀
lnP/P₀=kt
P=P₀[tex]e^{kt}[/tex]
Here P₀ is the constant of integration.
P(t)=P₀[tex]e^{kt}[/tex]
And they have given that,
P(0)=8000=P₀e⁰
P₀=8000
P(1)=5200
5200=8000[tex]e^{k}[/tex]
k=-2log(2)+log(3)≈ -0.28
Therefore, the required function is:
P(t)=8000[tex]e^{-0.28t}[/tex]
3) Now, we have to put t=6 in the above equation:
P(6)=8000[tex]e^{-0.28*6}[/tex]
P(6)=1490.991
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