[tex]P(t)=3400e^{0.04t}\implies 68000=3400e^{0.04t}\implies \cfrac{68000}{3400}=e^{0.04t} \\\\\\ 20=e^{0.04t}\implies \log_e(20)=\log_e(e^{0.04t})\implies \log_e(20)=0.04t \\\\\\ \ln(20)=0.04t\implies \cfrac{\ln(20)}{0.04}=t\implies 74.89\approx t[/tex]
that's about 74 years and 325 days more or less.
based on the exponential equation which is really a continuously compounding equation with an initial value of 34000 in 1994, so 74 years later that'd be 1994 + 74 = 2068, then we add the 325 days to that, well, that's pretty much in November in 2069.
Select the correct answer.
Stephanie is exploring the key features of the functions ƒ (z) = and g(z) = 4=+5
She says that the graphs of the two functions will have the same vertical asymptote but different horizontal asymptotes because she ca
define function g as a transformation of function f and g(x) = f(x) + 4. Which statement is true?
O A. Stephanie correctly rewrote g(x) as a transformation of f(x), and she described the asymptotes of the two functions
correctly.
OB. Stephanie correctly rewrote g(x) as a transformation of f(x), but she described the asymptotes of the two functions
incorrectly.
OC. Stephanie rewrote g(x) as a transformation of f(x) incorrectly, but she described the asymptotes of the two functions
correctly.
O D. Stephanie rewrote g(x) as a transformation of f(x) incorrectly, and she described the asymptotes of the two functions
incorrectly.
Answer:
A. Stephanie correctly rewrote g(x) as a transformation of f(x), and she described the asymptotes of the two functions correctly.
Step-by-step explanation:
The statement is true because, g(x) = f(x) + 4 is indeed a transformation of f(x) by shifting the graph 4 units up, and because the horizontal asymptote is determined by the highest degree term in the function, which in this case is the same for both functions, so the two functions will have the same vertical asymptote, but the horizontal asymptote is determined by the leading coefficient which is different for both functions, so the two functions will have different horizontal asymptotes.
a(b-c)=de Solve for c
Answer:
Step-by-step explanation:
a(b - c) = de
b - c = de/a
-c = de/a - b
c = b - de/a
Pls mark as brainliest. Cheers
What type of proofs did Julie and Samuel use
What else is part of the problem?
NO LINKS!!
Find the area of this shape.
Answer:
54 units²---------------------------------
It is a combination of 3 rectangles.
All dimensions are given apart from the middle one. The missing dimension is:
6 - 2 = 4 unitsThe total area is:
8*2 + 5*4 + 6*3 = 16 + 20 + 18 = 54 units²Please please look at the picture and answer the question thank you
Answer:
[tex]\boxed{-2 < x\le1}[/tex]
Representation on number line is in attached image.
Notice that -2 has an unfilled circle and 1 has a filled circle. Important
Step-by-step explanation:
The given inequality is
[tex]2 < 4x+10\le14[/tex]
Subtract 10 throughout:
[tex]2-10 < 4x+10-10\le14-10\\\[/tex]
[tex]-8 < 4x\le4[/tex]
Divide throughout by 4:
[tex]-2 < x\le1[/tex]
Answer: [tex]\boxed{-2 < x\le1}[/tex]
This is represented on the number line as follows: Notice the use of the
Please help with geometry question!!!
Answer:
x = 14EG = 9Step-by-step explanation:
You want the missing length EG and the corresponding value of x in isosceles triangle DEF with midline GH of length 6 parallel to base DF of length 12.
MidlineThe length of segment GH is half the length of segment DF (6/12 = 1/2), so we know that corresponding sides EG and ED have the same ratio:
EG/ED = 1/2
2EG = ED . . . . . . . . . . . . multiply by 2·ED
2(x -5) = (x-5)+9 . . . . . . substitute given values
2x -10 = x +4 . . . . . . . . simplify
x = 14 . . . . . . . . . . . . . add 10-x
Then the length of EG is ...
EG = 14 -5 = 9
Solve system using elimination 2x+9y=20
-4x-18y=-15
Answer: Which is impossible, indicating that the system is inconsistent. Therefore, based on the analysis performed with the elimination method, the system has no solution.
Step-by-step explanation:
2x + 9y = 20-4x - 18y = -15Multiplying the first equation by 2 we get:
4x + 18y = 40-4x - 18y = -15Now, once we have amplified the original equations, the sum of the first equation and the second equation leads to:
4x + 18y +(-4x - 18y) = 40 - 15⇒ 0=25Which is impossible, indicating that the system is inconsistent. Therefore, based on the analysis performed with the elimination method, the system has no solution.
0.006375 g = _________ mcg?
Answer:
6375 mcg
Step-by-step explanation:
hopes this helps :)
The total sales of a particular model of calculator on three days are $180, $414 and $306 respectively. Find the greatest possible price of the calculator.
Answer:
To find the greatest possible price of the calculator, we can use the information given about the total sales.
We know that the total sales of the calculator on three days are $180, $414, and $306. We can assume that the calculator is sold at a single price p on all three days, and the total number of calculators sold is x, y and z respectively.
So, we can set up the following equation:
px = $180 (1)
py = $414 (2)
p*z = $306 (3)
From (1) and (2) we can say x < y and from (2) and (3) we can say y > z
so the greatest possible price of the calculator will be the one from equation (2)
p = $414 / y
Therefore, the greatest possible price of the calculator is $414 / y.
It is important to note that we don't know the actual numbers of calculators sold, but we know that y is greater than x and z, and that is why we can say that the greatest possible price of the calculator is $414 / y.
What is the value of 5 to the 4th power
5 raised to the fourth power (written as 5^4) is equal to 5 multiplied by itself 4 times. Mathematically, it can be written as:
5^4 = 5 * 5 * 5 * 5 = 625
So, the value of 5 to the fourth power is 625.
I hope this helps :)
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{5^4}[/tex]
[tex]\mathsf{= 5 \times 5 \times 5 \times 5}[/tex]
[tex]\mathsf{= 25 \times 25}[/tex]
[tex]\mathsf{= 625}[/tex]
[tex]\huge\text{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\mathsf{625}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
find the y-intercept(s) of f(x)=(3x+4)^(4)(x-5)^(5)
The y - intercept of the function f(x) = (3x + 4)⁴(x - 5)⁵ is (0, -800,000)
What is Y - Intercept of EquationWhen an equation's graph crosses the y-axis, that location is known as the y-intercept. When x = 0, it is y's value.
A linear equation's constant term serves as a representation for the y-intercept. The y-intercept of the equation y = 2x + 3 is 3, for instance. This indicates that the coordinate plane point (0, 3) is at y = 3 when x = 0.
y= mx + b, where m is the slope and b is the y-intercept, is another way to express a linear equation.
For instance, the equation y = -2x + 5 can be written as y = -2x + 5, and since the y-intercept is 5, the point (0, 5) is on the graph of the equation.
The y-intercept of an equation, or the value of y when x = 0, is the point at which the graph of the equation crosses the y-axis. It can be represented by b in the slope-intercept form of a linear equation as well as by the constant term in the equation.
In the function given;
f(x) = (3x + 4)⁴(x - 5)⁵
Substitute the value of 0 for x and solve to find the y - intercept.
f(0) = (3(0) + 4)⁴(0 - 5)⁵
f(0) = -800000
The value of y - intercept(s) is (0, -800000)
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The y-intercept of the function f(x) = (3x + 4)^4(x - 5)^5 is given as follows:
-800,000.
How to obtain the y-intercept of a function?The function for this problem is defined as follows:
f(x) = (3x + 4)^4(x - 5)^5
Graphically, the y-intercept of a function represents the value of y assumed by the function when the graph of the function crosses the y-axis.
Hence, algebraically, the y-intercept of a function is given by the numeric value of the function when the input x assumes a value of zero.
The numeric value of the function at x = 0 is calculated replacing the two instances of x in the function by zero, hence the y-intercept of the function is defined as follows:
f(0) = (3(0) + 4)^4(0 - 5)^5
f(0) = 4^4 x (-5)^5
f(0) = -800,000.
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What is the sum of 4 and -9? What does that tell you about the temperature at
the weather station?
The sum of numbers 4 and - 9 is, - 5.
And, A weather station is a collection of instruments that measure atmospheric conditions to help study the weather and climate of a specific location.
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that;
The numbers are,
⇒ 4 and - 9
Now, Sum of the numbers 4 and - 9 as;
⇒ 4 + (-9)
⇒ 4 - 9
⇒ - 5
Thus, The sum of numbers 4 and - 9 is, - 5.
And, A weather station is a collection of instruments that measure atmospheric conditions to help study the weather and climate of a specific location.
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A hiker walks at a speed of 3 2 5 kilometers per hour. How many kilometers will the hiker walk in 5 hours
Answer:
17 km----------------------------------------
The distance is the product of the speed and time.
Given:
Speed = 3 2/5 km/h,Time = 5 hours.Find the distance:
3 2/5 × 5 = 3 × 5 + 2/5 × 5 =15 + 2 = 17 kmQuestion 1
For your 15th birthday, your grandma puts $100 in a savings account for you, and
tells you that you cannot take it out until your 20th birthday. If the account she has
chosen has an interest rate of 3% compounded semiannually, how much money will
you have when you turn 20?
O $109.35
O $103.00
O $122.75
1 pts
O $116.05
Answer:
116.05
Step-by-step explanation:
15 to 20 = 5 years
compound semiannually = 10 time
annual rate 3% = 1.5% for every 6 mos
so 100*(1+1.5%)^10 =116.05
find the average of the numbers 11, 20, 13, and 16
The average of the numbers 11, 20, 13, and 16 is 15
Why is average called mean?The average may be calculated by dividing the total number of values by the sum of all the numbers. An average of the values in a sample of data may be used to determine a mean. In other words, the arithmetic mean is another name for an average. A mean is a term used to describe the average.
Why do we calculate the average?Finding an average helps us understand a general pattern of behavior or trend. For example, knowing Mrs. Mansell's average shopping expenditure helps us understand whether she typically spends a lot or little money, and knowing Keiran's average spelling score helps us understand how proficient he typically is.
In the above question:-
The average of the numbers 11, 20, 13, and 16 is
15
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Please look at the picture and answer the question thank you
Answer:
-2x^2+5y^3+
Step-by-step explanation:
Margie has 64 rectangular steppingstones to arrange in an array in her backyard . How many arrays can Margie make with the 64 steppingstones
If Margie has 64 rectangular steppingstones to arrange in an array in her backyard. The number of arrays that Margie can make with the 64 steppingstones is: 2 × 32, 4 ×16, 8 × 8.
How to find the number of array:Given data:
Rectangular steppingstones to arrange in an array =64
In order to determine the number of arrays we have to find the number that will give us 64 when multiply.
The number that will gives us 64 as the answer when multiply are:
2 × 32 = 64
4 ×16 = 64
8 × 8 = 64
The arrays are 3 which are:
2 × 32
4 ×16
8 × 8
Therefore we can conclude that the number of array that Margie can make with the 64 steppingstones is: 2 × 32, 4 ×16, 8 × 8.
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Expresa estas fracciones como un número mixto realizando para ello la división correspondiente
The representation of the fraction 10/8 as a mixed number is given as follows:
[tex]\frac{10}{8} = 1\frac{1}{5}[/tex]
How to convert a fraction to mixed number?The fraction in this problem is given as follows:
10/8.
A mixed number is composed by two parts, as follows:
Integer part.Fractional part.The integer part and the fractional part are defined as follows:
Integer: quotient of the numerator by the denominator.Fractional part: remainder of the fraction divided by the divisor.For the division of 10 by 8, we have that:
The quotient is of 1.The remainder is of 2.Then the mixed number is given as follows:
[tex]1\frac{2}{10}[/tex]
The fraction 2/10 can be simplified as 1/5, hence the simplified representation is given as follows:
[tex]1\frac{1}{5}[/tex]
Missing Information and TranslationThe problem asks to represent the fraction 10/8 as a mixed number
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What is AE?
Enter you answer in the box.
Answer:It means almost everywhere
Step-by-step explanation:
The value of AE is, 10 units.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Here, From the given figure we can see that two triangle ABE and DEC are similar.
Therefore, The ratio of corresponding sides are equal.
Hence, From figure we get,
⇒ ED/AE = CD/AB
Substitute all the values, we get;
⇒ (x + 6)/(2x + 6) = 8/10
⇒ 10(x + 6) = 8(2x + 6)
⇒ 10x + 60 = 16x + 48
⇒ 16x - 10x = 60 - 48
⇒ 6x = 12
⇒ x = 2
So, The value of AE is,
AE = 2x + 6
AE = = (2 × 2 ) + 6
AE = 4 + 6
AE = 10
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What is an equation of the line that passes through the points ( − 1 , − 5 ) and (1,3)?
The equation of the line that passes through the points ( − 1 , − 5 ) and (1, 3) is y = 4x - 1
How to find the equation of the lineThe slope, m of the linear function is calculated using the points on the graph (-1, -5) and (1, 3)
m = (y₀ - y₁) / (x₀ - x₁)
m = (-5 - 3) / (-1 - 1)
m = (-8) / (-2)
m = 4
equation passing through point (1, 3)
(y - y₁) = m (x - x₁)
plugging in the points
y - 3 = 4 * (x - 1)
y - 3 = 4x - 4
y = 4x - 4 + 3
y = 4x - 1
The equation of the line passing through points (-1, -5) and (1, 3) is written as y = 4x - 1
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Suppose that you made repeated measurements of your height. If you used good technique, would you expect the range of measurements to be large or small? Explain your answer.
Answer:
Step-by-step explanation:
If you used good technique, you would expect the range of measurements to be small. Good technique would include using a measuring instrument that is calibrated correctly, measuring in the same position and at the same time of day, and being consistent in how you position your body during the measurement. All of these factors would help to reduce the amount of measurement error and therefore lead to a smaller range of measurements.
answer for 10 points
Answer:
30 = 2·2·3
48 = 2·2·2·2·3
GCF = 6 (2·3)
LCM = 240 (2·3·5·8)
Step-by-step explanation:
help me with this answer
Answer:
f(1) = 7
Step-by-step explanation:
f(1) has x = 1 in the interval x < 2 with f(x) = - 2x + 9 , then
f(1) = - 2(1) + 9 = - 2 + 9 = 7
pls help. I've been stuck on this question and I just cannot find the answer. Pls help
Answer:
(g+f)(x/4) = x^2/16 + 3x/4
Step-by-step explanation:
To find (g+f)(x/4), we must first find the expressions for g(x) and f(x) and then add them together.
g(x) = x^2 + 4
f(x) = 3x - 4
So (g+f)(x) = g(x) + f(x) = x^2 + 4 + 3x - 4 = x^2 + 3x + 0
Now we can substitute x/4 for x in the expression:
(g+f)(x/4) = (x/4)^2 + 3(x/4) + 0
Multiplying it out
(g+f)(x/4) = (x^2/16) + (3x/4) + 0
so (g+f)(x/4) = x^2/16 + 3x/4
Juan's Cafe has regular coffee and decaffeinated coffee. This morning, the cafe served 70 coffees in all, 70% of which were regular. How many regular coffees did the cafe serve?
The cafe served 49 regular coffees.
How to calculate thisYou can use the proportion of regular coffees to the total number of coffees to find out how many regular coffees were served.
If 70% of the coffees served were regular, that means that 100-70 = 30% of the coffees served were decaffeinated.
To find out how many regular coffees were served, you can use the following proportion:
(Number of regular coffees) / (Total number of coffees) = 70% / 100%
You can then cross-multiply and solve for the number of regular coffees:
Number of regular coffees = (70/100) * (Total number of coffees)
Given the Total number of coffees = 70, you can substitute that and get:
Number of regular coffees = (70/100) * 70 = 49
Therefore, the number of regular coffees which the cafe served was 49.
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help help help help help
Answer:
[tex]3x^{2}[/tex] + x + 6
Step-by-step explanation:
Prove AB || CD and BC || AD
The indicated congruency of the angles ∠BEC and ∠AED (∠BEC ≅ ∠AED) and ∠BEA and ∠CED (∠BEA ≅ ∠CED), according to the alternate interior angles postulate, shows that [tex]\overline{AB}[/tex]║[tex]\overline{CD}[/tex] and [tex]\overline{BC}[/tex]║[tex]\overline{AC}[/tex] are parallel.
What are parallel lines or segments?Two segments on a plane are parallel if the distance between the segments remain the same, through the lengths of the segments.
The specified details of the dimensions of the segments in ABCD are;
Segments [tex]\overline{AC}[/tex] bisects segment [tex]\overline{BD}[/tex] and vice versa
Required to prove that [tex]\overline{AB}[/tex] ║ [tex]\overline{CD}[/tex] and [tex]\overline{BC}[/tex] ║ [tex]\overline{AD}[/tex]
The two column consisting of the statements and reasons to prove that the specified sides are parallel is presented as follows;
Step [tex]{}[/tex] Statement Reasons
1. [tex]{}[/tex] [tex]\overline{AC}[/tex] and [tex]\overline{BD}[/tex] bisect each other Given
2. [tex]{}[/tex] [tex]\overline{BE}[/tex] ≅ [tex]\overline{ED}[/tex] and [tex]\overline{CE}[/tex] ≅ [tex]\overline{AE}[/tex] Definition of bisected segments
3. ∠BEC ≅ ∠AED and ∠BEA ≅ ∠CED Vertical angles theorem
4. [tex]{}[/tex] ΔBCE ≅ ΔADE and ΔBEA ≅ ΔCED SAS congruency rule
5. [tex]{}[/tex] ∠EBC ≅ EDA and ∠EBA ≅ ∠EDC CPCTC
6. [tex]{}[/tex] [tex]\overline{AB}[/tex] ║ [tex]\overline{CD}[/tex] and [tex]\overline{BC}[/tex] ║ [tex]\overline{AD}[/tex] Converse of alt. int. ∠s theorem
The details of the reasons in the above table are;
Vertical angles theorem
The vertical angle theorem states that the vertical angles formed by two intersecting straight lines are congruent.
SAS congruency rule
The SAS (acronym for Side-Angle-Side) congruency rule states that if two sides and an included angle in one triangle are congruent to two sides and an included angle in a second triangle, the two triangles are congruent
CPCTC
CPCTC is an acronym for Corresponding Parts of Congruent Triangle are Congruent.
Converse Alt, Int, ∠s theorem
The converse of the alt. int. ∠s (abbreviation for alternate interior angles) theorem state that if the the alternate interior angles formed by two lines and a common transversal are congruent, then the two lines are parallel
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Meryl pays £400 into her sister's South African bank account. How much ister receive if the current exchange
Answer:
8232 South African Rand
Step-by-step explanation:
The question cuts off at "if the current exchange" so the exchange rate is not specified. At the time of writing this answer, the echnage rate from one sterling pound to South African Rand is 1=20.58. So, we just need to multiply 20.58*400 to get 8232.
A large western state consists of 2051 million acres of land
Approximately 56% of this land is federally owned. Find the
number of acres that are not federally owned
million acres
How much would you need to invest in a money market account if you would like to have $5,000 in the account at the end of 3 years? The account provides an APR of 5% compounded monthly.
Answer:
To calculate the amount you would need to invest in a money market account to have $5,000 at the end of 3 years, we can use the formula for future value of an investment:
FV = PV(1+r)^n
where FV is the future value of the investment, PV is the present value of the investment, r is the interest rate (expressed as a decimal), and n is the number of compounding periods.
In this case,
FV = $5,000 (future value)
r = 5% (APR) = 0.05 (as a decimal)
n = 3 years * 12 (months) = 36
So we can use the formula:
PV = FV / (1 + r)^n
PV = $5,000 / (1 + 0.05)^36
PV ≈ $3,716.76
So you would need to invest $3,716.76 in the money market account to have $5,000 in the account at the end of 3 years.
