The value of the exponential function (-1) will be equal to f(-1) = -0.02.
What is an exponential function?The mathematical expression f(x)=exp or e^x denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to complex numbers or adapted to other mathematical objects.
Given that f(x) is an exponential function where f(-3) = 11 and ƒ(4) = 55. The value of the exponential function will be calculated as,
[tex]y=ax^b[/tex]
[tex]11=a(-3)^b\\55=a(4)^b[/tex]
Calculate the value of constants,
log5 = blog(4 / 3)
b = 0.7 / 0.125
b = 5.6
The value of 'a' will be,
11 = a(-3)⁵°⁶
a = -0.02
The exponential function f(-1) will be calculated as,
f(-1) = -0.02(-1)⁵°⁶
f(-1) = -0.02
Therefore, the value of the exponential function (-1) will be equal to f(-1) = -0.02.
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Solve 2x-7 = 3x-2(x+8) for x
Answer:
x = -11
Step-by-step explanation:
2x - 7 = 3x - 2x - 18
2x - 7 = x - 18
collect like terms
2x - x = 7 - 18
x = -11
sin cos tan
( )
0
7
ans
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One side of a rectangle is 24 m longer than four times another side. Find the length of the sides, given that
the area of the rectangle is 1408 m². Enter both sides, separated by a comma.
Length of the sides:
Question Help: D Post to forum
1
m
Length= 80 and width = 16 cm in the rectangle .
What is rectangle?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.let side = x cm
= x( 24 + 4x) = 1408
= 24x + 4x² = 1408
⇒ 4x² + 24x - 1408 = 0
4 ( x² + 6x - 352 ) = 0
x² + 6x - 352 = 0
x² + 22x - 16x - 352 = 0
x( x + 22 ) - 16 ( x + 22) = 0
( x - 16 ) ( x + 22 ) = 0
x= 16 , -22
we take x = 16 because distance never be negative
length = 16 + 4 * 16 = 80 cm
width = 16 cm
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The table below shows a proportional relationship between h and j.
h
18
27
48
j
6
9
16
Find the constant of proportionality from h to j. Express
your answer as a fraction in reduced terms.
As per the proportional relationship, the constant of the proportionality is 1/3
Proportional relationship
A relationship is said to be proportional if each pair of data values are related in the same way, by multiplying by a factor.
The standard form of proportional relationship is written as.
y = k x
where k refers the constant of proportionality.
Given,
The table shows the proportional relationship between h and j.
Now, we need to find the constant of proportionality from h to j and we have to express the answer as a fraction in reduced terms.
We know that the standard form of the proportionality is written as,
y = k x
So, here y takes the value of j and x takes the values of h.
Then we have to take the points as (18, 6) and apply t on the standard form to get the value of k,
=> 6 = k (18)
Here we need the value of k, so move the number to the other side then we get,
=> k = 6/18
When we reduce this, then we get,
=> k = 1/3
Therefore, the constant of proportionality is 1/3.
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Consider the equation and the following ordered pairs: (−3,y) and (x,2). y=−3x−1 Step 1 of 2 : Compute the missing x and y values so that each ordered pair will satisfy the given equation. Answer Keyboard Shortcuts Complete the table below. x y row 1−3 Answer row 2 Answer 2
Using the equation y = -3x - 1, the missing values are in the ordered pairs, (−3,y) and (x,2), are: x = -1 and y = 8.
How to Compute Missing Values that Satisfies an Equation?An algebraic equation is an expression that has variables. The values of those variables, when plugged into the equation would make the equation true.
Given the equation, y = -3x - 1, substitute x = -3 into the equation to find y:
y = -3(-3) - 1
y = 9 - 1
y = 8
The missing value in the ordered pair is: (-3, 8).
To find the missing value of x in (x, 2), substitute y = 2 into the equation, y = -3x - 1:
2 = -3x - 1
2 + 1 = -3x
3 = -3x
3/-3 = x
x = -1
The missing value is (-1, 2).
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Mrs B invested $30,000, part at 5%, part at 8%. The total interest on the investment was $2100, how much did she invest at each rate?
(Please show working)
Answer:
$10,000 invested at 5%
$20,000 invested at 8%
Step-by-step explanation:
1. Let x = the amount of money invested at 5%, and y = the amount of money invested at 8%.
x + y = 30,000 (the total amount invested)
0.05x + 0.08y = 2,100 (the total interest earned)
2. Solve the system by whatever method you choose.
What is the equation in slope-intercept form of the line that passes through the point (2, -1) and is perpendicular to the line represented by y=x+4?
y=32-4
y=3x+4
y=-32-2
y=-3x+2
The slope-intercept form is
y = - x + 1
Given points are (2, - 1)
and y = x + 4
The product of slopes of perpendicular lines is - 1
so , m = - 1/1 = -1
y = mx + b-1 = (-1) (2) + b -1 = -2 + b-1 + 2 = b b = 1∴ y = -1 (x) + b
y = - x + 1
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Daniel has invested $300 in an annuity each month, earning 4% interest for 20 years.
Sarah has invested $150 in an annuity each month, earning 4% interest for 40 years.
Which of the following must be true?
Answer: daniel and sarah will deposit the same amount
←
Suppose a bunny farm initally has 20 bunnies. After 2 years the population grew to 80 bunnies.
A) Find f(T)=mT+b, where f(T) is the bunny population after every 2 months. Answers must be in Exact Form, Round 3 decimals, and Change of Base
B) What is the bunny population after 16 weeks?
C) How many months will it take for the bunny population to reach 300 bunnies? Answers must be in Exact Form, Round 3 decimals, and Change of Base
A) The bunny population after every 2 months is f(T)=5T+20
B) The bunny population after 16 weeks is x=29.205
C) The number of months that the bunny population to reach 300 bunnies is 112 months.
What is meant by population?All nationals present in, or temporarily absent from, a country, as well as aliens permanently settled in a country, are characterized as population. This indicator depicts the average number of people who live in a given location. The annual changes in population caused by births, deaths, and net migration during the year are referred to as growth rates.
Given,
0 months -------- 20 bunnies
2 years ------- 80 bunnies
In two years, bunnies are increased by,
=80-20
=60
2 years ------>60
1 year ------>30
A) f(T)=mT + b
1 year -----> 12 months -----> 30 bunnies
12/6 months ------>30/6 bunnies
2 months -----> 5 bunnies
f(T)= initial population+ increased population in two months
f(T)=20+5
f(T)==25
f(T)= 2.5T+20
f(T)=5T+20
Where T =time in months
B) For 10 years ------> 10 bunnies
52 weeks -------->30 bunnies
16 weeks ------?
x=(16*30)/52
x=29.205
C) 1 month -------> 2.5 bunnies
? ---------------->280 bunnies
x=280/2.5
x=112 months
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Answer:
A) The bunny population after every 2 months is f(T)=5T+20
B) The bunny population after 16 weeks is x=29.205
C) The number of months that the bunny population to reach 300 bunnies is 112 months.
What is meant by population?
All nationals present in, or temporarily absent from, a country, as well as aliens permanently settled in a country, are characterized as population. This indicator depicts the average number of people who live in a given location. The annual changes in population caused by births, deaths, and net migration during the year are referred to as growth rates.
Given,
0 months -------- 20 bunnies
2 years ------- 80 bunnies
In two years, bunnies are increased by,
=80-20
=60
2 years ------>60
1 year ------>30
A) f(T)=mT + b
1 year -----> 12 months -----> 30 bunnies
12/6 months ------>30/6 bunnies
2 months -----> 5 bunnies
f(T)= initial population+ increased population in two months
f(T)=20+5
f(T)==25
f(T)= 2.5T+20
f(T)=5T+20
Where T =time in months
B) For 10 years ------> 10 bunnies
52 weeks -------->30 bunnies
16 weeks ------?
x=(16*30)/52
x=29.205
C) 1 month -------> 2.5 bunnies
? ---------------->280 bunnies
x=280/2.5
x=112 months
Beverly has a bag of marbles that weighs 30 grams. She knows that each marble weighs 1.5 grams and the bag weighs 1.5 grams. Which equation could she use to determine how many marbles are in the bag? Select all that apply. (1.5)x + 1.5 = 30 30 – x = 2(1.5) (1.5)(30) = 1.5x 1.5 + x = 30 1.5x = 30 – 1.5
Answer:
1.5x = 30 - 1.5
Step-by-step explanation:
30 grams minus the weight of the bag 1.5
1.5x x is the number of marbles and the bag so take 1 out and you have an answer which is 28.5 19 marbles
Given f of x is equal to the quantity x plus 6 end quantity divided by the quantity x squared minus 9x plus 18 end quantity, which of the following is true?
f(x) is decreasing for all x < 6
f(x) is increasing for all x > 6
f(x) is decreasing for all x < 3
f(x) is increasing for all x < 3
The correct statement of the expression (x + 6) / ( x² - 9x + 18 ) is f(x) is increasing for all x > 6
How to determine the correct statementInformation given in the question
f of x is equal to the quantity x plus 6 end quantity divided by the quantity x squared minus 9x plus 18 end quantity
This is written as (x + 6) / ( x² - 9x + 18 )
factorizing the denominator gives
(x + 6) / {( x - 6)( x - 3)}
In the denominator
At x = 6 and at x = 3 the equation will result to infinity which is a very high value. hence:
f(x) is decreasing for all x < 6: contains x = 3 and result to a higher value
f(x) is decreasing for all x < 3: will result to negative numbers which will end up increasing
f(x) is increasing for all x < 3: contains values which will be decreasing like x = 4
Therefore the correct option is f(x) is increasing for all x > 6
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SOMEONE PLEASE HELP!
I WILL GIVE BRAINLIEST TO THE FIRST CORRECT ANSWER!! Just Need Help!!!
A fish tank has a capacity of 154L.
What is the volume of the fish tank?
The volume of the fish tank required = 0.154 m^3.
A fish tank has a capacity = 154L.
Capacity of fish tank in Litre = Volume of the fish tank in meter cube
So the volume of the fish tank required in cubic meter.
For the volume we required a conversion of litre into meter cube.
Cubic meters and liters are two common metric units of volume.
1 cubic meter is 1000 liters.
To convert liters to cubic meters, you simply need to move the decimal point three places to the left. In other words, divide a value in liters by 1000 to get an answer in cubic meters.
1L = 0.001 m^3
So 154L = 0.154 m^3
So the volume of the fish tank required = 0.154 m^3.
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Represent the following expressions as a power of the number a where a ≠ 0: (a^3)^-2. PLEASE ANSWER I WILL GIVE BRAINLYEST
Answer:
a^-6 or 1/a^6
Step-by-step explanation:
(a³)-²
=a^-6
=1/a^6
According to the local weather report, the probability of rain in Chicago on October 14 is 57%.
The fraction that represents the percentage of 57% is presented as follows:
57/100.
How to convert a percentage to a fraction?A fraction is represented by the division of a term x by a term y, according to the equation presented as follows:
Fraction = x/y.
The terms are know as numerator and denominator, respectively, as follows:
Numerator: the top term of the fraction, in our example x, is called the numerator of the fraction.Denominator: the bottom term of the fraction, in our example y, is called the denominator of the fraction.For a percentage of a%, the equivalent fraction is obtained as follows:
The numerator is the percentage of a.The denominator is of 100.Hence, for a percentage of 57%, as is the case in this problem:
The numerator is 57.The denominator is 100.Hence the fraction is:
57/100.
Missing InformationThe problem asks to represent the percentage as a fraction.
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Given the position function:
s(t) = sin t
where t is measured in seconds and
s is measured in feet, find the
average velocity on the interval [0, π].
If you cut a sheet of paper in half, stack one piece on top of the other, cut those in half, stack all the pieces together, repeating this process 20 times, how high will the stack of paper be?
The stack of paper will have the height of 1048576 papers
How to determine how high the stack of paper will be?
The first cut will produce 2 papers, the second cut will produce 4 papers, the third cut will produce 8 papers and the fourth cut will produce 16 papers.
If you examine the stages of cut and the number of papers, the relationship between them is:
1st cut: number of papers = 2¹ = 2
2nd cut: number of papers = 2² = 4
3rd cut: number of papers = 2³ = 8
4th cut: number of papers = 2⁴ = 16
nth cut: number of papers = 2ⁿ
So if the process is repeated 20 times, the number of papers will be:
Number of paper = 2²⁰ = 1048576
Therefore, the stack of paper will be as high as 1048576 papers
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Sam is driving on the highway. He begins the trip with 12 gallons of gas in his car. The car uses up one gallon of gas every 35 miles.
Let G represent the number of gallons of gas he has left in his tank, and let D represent the total distance (in miles) he has
traveled. Write an equation relating G to D, and then graph your equation using the axes below.
equation and graph attached
Which rule describes the transformation
R₀, 270° is the rule that describes the transformation
How to determine the rule that describes the transformation?
Rotation simply means turning. In a cartesian plane, if a point P, whose position vector is (x,y), is rotated through θ° about the origin, the position of the image P' is
a. (-y, x) for θ = 90°
b. (-x, -y) for θ = 180°
c. (y, -x) for θ = 270°
Given the: Triangle RST with vertices R(2, 0), S(4, 0), and T(1, -3). And the image of triangle RST after a rotation has vertices R'(0, -2). S'(0, -4), and T(-3, -1)
From the given vertices it is obvious that the relation between preimage and image is defined as
(x, y) => (y, -x)
Therefore, the rule that describes the transformation is (y, -x) for θ = 270° (i.e. when the figure rotates 270° counterclockwise). So the third option (R₀, 270° ) is the answer.
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Work out the values of a, b, c and d.
Justify each of your answers.
In the given circle, the values of required angles are as follow:
a = 51°, b = 28° , c = 31°, and d = 70°.
As given in the question,
In the given circle,
As we know by theorem , angles formed in the same arc are congruent.
Angle a° and angle 51° is formed in the same arc XY .
⇒ Value of a = 51°
Angle b° and angle 28° is formed in the same arc ZY .
⇒ Value of b = 28°
Angle c° and angle 31° is formed in the same arc WX .
⇒ Value of c = 31°
Angle d° and angle 70° is formed in the same arc WZ .
⇒ Value of d = 70°
Therefore, in the given circle the values of required angles are as follow: a = 51°, b = 28° , c = 31°, and d = 70°.
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4.
Consider the following diagram:
What is the value of m?
56°
m
68°
According to the solving the Angle m = 124
What is the name for a straight angle?An angle with something like a vertex point at 180 degrees is considered to be a straight angle in geometry. Basically, it produces a straight line with sides that are turned away from the vertex. "Flat angles" is another term for it.
How do you see a straight angle?A straight line appears to have a straight angle. Here's an illustration of a straight angle. a straight line that has a half circle in the middle and at the top to symbolize a straight angle.
According to the given data:The sum of all angles in triangle = 180.
Angle A = 56
Angle B = 68
Angle C =
A + B + C = 180
56 + 68 + C = 180
124 + C = 180
C = 180 - 124
C = 56
if Angle C = 56
so we know the property of straight angle:
= Angle m + 56 = 180
Angle m = 180 - 56
Angle m = 124
According to the solving the Angle m = 124
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kind of suck help please ? brianslest
Answer:
[tex]d=7[/tex]
[tex]a_9=59[/tex]
Step-by-step explanation:
If the first term of a sequence is [tex]3[/tex] and the second term is [tex]10[/tex], then each successive term in the sequence is [tex]7[/tex] more than the previous term. The common difference is [tex]7[/tex] ( [tex]d=7[/tex] ).
The formula representing the arithmetic sequence is:
[tex]a_n=7n-4[/tex]
Therefore, the ninth term in the sequence is:
[tex]a_9=7(9)-4[/tex]
[tex]a_9=63-4[/tex]
[tex]a_9=59[/tex]
Ken spends $344.76 before tax at a hardware store. If the sales tax rate in his city is 7.5%, what is the total cost of his purchase? Round to the nearest cent if necessary.
Answer:
$370.62
Step-by-step explanation:
Ken spends $344.76 before tax at a hardware store. If the sales tax rate in his city is 7.5%, what is the total cost of his purchase? Round to the nearest cent if necessary.
7.5% = 0.075
0.075 * $344.76 = $25.857 in tax so:
cost + tax
$344.76 + $25.857 = $370.617
rounded: $370.62
A certain disease has an incidence rate of 0.2%. If the false negative rate is 8% and the false positive rate is
1%, compute the probability that a person who tests positive actually has the disease.
Give your answer accurate to at least 3 decimal places
According to the solving the probability will be 0.159.
What is probability?The area of mathematics known as probability deals with numerical assessments of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
In statistics, what exactly is a probability?A probability is a number that expresses the possibility or likelihood that a specific event will take place. In addition to being expressed in percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and 1.
According to the given data:The incidence rate is = 0.2% or 0.002
The false negative rate is = 8% or 0.008
The false positive rate is = 1% or 0.001
The probability is
0.01*(1-0.002) + 0.95*0.002
= 0.00998 + 0.0019 = 0.01188
Probability that a person who tests positive actually has the disease would be represented as:
Let the probability be represented by = p
p * 0.01188 = 0.95 * 0.002
p = 0.0019/0.01188
p = 0.159
Hence, probability is 0.159
According to the solving the probability will be 0.159.
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What Did the Baby Porcupine Say
When It Backed Into a Cactus?
each
Answer:
As baby porcupine is backed into cactus, so the spines of cactus will feel like spines of mother porcupine. So the baby porcupine will give call to its mother.
Step-by-step explanation
He said hi Ma.
3. Analyze and Persevere The height of
an experimental plant after x days can be
represented by the formula 3(4x + 2) The
height of a second plant can be represented
by the formula 6(2x + 2). Is it possible that
the two plants will ever be the same height?
Explain.
their pr
Р
$1
Two plants will never be of the same height.
Given, the height of an experimental plant after x days can be
represented by the formula 3(4x + 2).
The height of a second plant can be represented by the formula 6(2x + 2).
We have to state that will the two plants ever be of the same height,
Let assume that, the height of two plants be same,
So, 3(4x + 2) = 6(2x + 12)
On simplifying, we get
12x + 6 = 12x + 72
On subtracting 12x from both the sides, we get
12x + 6 - 12x = 12x + 72 - 12x
6 ≠ 72
It is an absurd condition, so we do not have any solution for x.
So, the two plants will never be of the same height.
Hence, two plants will never be of the same height.
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Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $25 and same-day tickets cost $15. For one performance, there were 55 tickets sold in all, and the total amount paid for them was $1025. How many tickets of each type were sold?
Answer:
advance: 20same-day: 35Step-by-step explanation:
You have tickets that sell for $25 and $15, and you sold 55 tickets for $1025. You want to know the number of each sold.
SetupLet 'a' represent the number of advance tickets sold. Then 55-a is the number of same-day tickets sold. The total revenue is ...
25a +15(55 -a) = 1025
Solution10a + 825 = 1025 . . . . . simplify
10a = 200 . . . . . . . . . . subtract 825
a = 20 . . . . . . . . . . . divide by 10; the number of advance tickets
55 -20 = 35 . . . . the number of same-day tickets
20 advance tickets and 35 same-day tickets were sold.
Graph the following features:
Y-intercept=1
Slope- -2/3
The graph with the y-intercept of 1 and a slope of -2/3 is added as an attachment
What are linear equations?Linear equations are equations whose slopes are constant average rates of change.
How to graph the equation of the line?The given parameters are
y-intercept, c = 1Slope, m = -2/3A linear equation is represented as
y = slope * x + y-intercept i.e. y = mx + c
Substitute the known values in the above equation
So, we have the following equation
y = -2/3x + 1
Hence. the linear equation is y = -2/3x + 1
See attachment for the graph
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there are 32 steps in one floor of a tower max lives .he climbs 6 floors of his building. if he clims 6 floor every day , how many steps does he climb every week
Answer:
1,344
Step-by-step explanation:
First, find how many steps he climbs every day
32*6=192
Now, multiply that by 7 to see how many he climbs in a week
192*7=1,344
In Alex's drawer she has 10 pairs of socks, 8 of which are white, and 9 tee shirts, 2 of which are white.
The probability of choosing a white pair of socks is
The probability of choosing a white tee shirt is
The probability of both being white is
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Total socks= 10
White socks= 8
Total T- shirts= 9
White T- shirts = 2
Now, The probability of choosing a white pair of socks is
= 8/10
= 4/5
and, The probability of choosing a white tee shirt is
= 2/9
and, The probability of both being white is
= 4/5 x 2/9
= 8/45
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Tim needs 6 lb of a metal that contains 54 % silver. If Tim combines one metal with 29%
silver, and another with 80 % silver, how much of each metal does Tim need?
After solving the Algebraic expression we gets Tim needs 3.05 lbs. and 2.95 lbs. Metal.
What is algebra ?Algebraic expressions are constructed using integer constants, variables, and the addition, subtraction, multiplication, and division operations of basic arithmetic.
To form the Algebraic expression
Let x be the quantity of silver at 29% and y the quantity at 80%
Then x*28% + y*61% = 6*54%
and x + y = 6
Let y = 6-x then
29*x + (6-x)*80= 324
29*x + 480- 80*x = 324
51*x = 156 and x = 156/51 = 3.05 lbs.
so y = 6 - x = 2.95 lbs.
Hence,
Tim needs 3.05 lbs. and 2.95 lbs. Metal.
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