The base in the exponential function is greater than 1 because exponential growth is defined as a constant multiplication of the original value, rather than a constant addition as in linear growth. A base greater than 1 results in a growth rate that increases over time, while a base less than 1 results in a growth rate that decreases over time.
THE EXPONENTIAL FUNCTIONThe exponential function is written as bˣ, where b is the base and x is the exponent. The base is the number that is being multiplied by itself a certain number of times, as determined by the exponent.
A base greater than 1 means that the value of the function is increasing at an increasing rate. This is because as the exponent (x) increases, the base (b) is being multiplied by itself more and more times, leading to a larger and larger result. This is known as exponential growth.
On the other hand, a base less than 1 means that the value of the function is decreasing at an decreasing rate. This is because as the exponent (x) increases, the base (b) is being multiplied by itself more and more times, leading to a smaller and smaller result. This is known as exponential decay.
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Briefly, describe the distribution in context. Recall, categorical variables are summarized by counts and/or percents
Thus, distribution is a function that shows the possible values for a variable and how often they occur and categorical values are summarized by counts and/or percents
In statistics, the distribution is a function that shows the possible values for a variable and how often they occur.
The distribution of a data set is the shape of the graph when all possible values are plotted on a frequency graph. Usually, we are not able to collect all the data for our variable of interest. Therefore we take a sample. This sample is used to make conclusions about the whole data set.
The categorical variable is a data in which individuals are placed into groups or categories.
One way to summarize categorical data is to simply count (frequency), or tally up, the number of individuals that fall into each category. Another way is to show the percentage of individuals who fall into each category, thereby creating a relative frequency.
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Write the standard form of the equation of the line trough the given point with the given slope.
Step-by-step explanation:
we use the point-slope approach :
y - y1 = m(x - x1)
m is the slope, and (x1, y1) is a point on the line.
so,
1.
y - 2 = 7(x - 1) = 7x - 7
y = 7x - 5
2.
y - -1 = -1×(x - 3) = -x + 3
y + 1 = -x + 3
y = -x + 2
3.
y - 5 = -4(x - -2) = -4x - 8 (3x a "-" is a "-" for 8)
y = -4x - 3
4.
y - 5 = 5/3 × (x - 3) = 5x/3 - 5
y = 5x/3 or 5/3 × x
Answer:
1. [tex]7x-y=5[/tex]
2. [tex]x+y=2[/tex]
3. [tex]4x+y=-3[/tex]
4. [tex]5x-3y=0[/tex]
Step-by-step explanation:
Since we already know the slope and the coordinates of one point, first use the point-slope form to create an equation.
[tex]y-k=m(x-h)[/tex]
[tex]y-2=7(x-1)[/tex]
[tex]y-2=7x-7[/tex]
[tex]7x-y=5[/tex]
[tex]y+1=-1(x-3)[/tex]
[tex]y+1=-x+3[/tex]
[tex]x+y=2[/tex]
[tex]y-5=-4(x+2)[/tex]
[tex]y-5=-4x-8[/tex]
[tex]4x+y=-3[/tex]
[tex]y-5=\frac{5}{3} (x-3)[/tex]
[tex]y-5=\frac{5}{3}x-5[/tex]
[tex]3y-15=5x-15[/tex]
[tex]5x-3y=0[/tex]
A 4-column table with 3 rows. The first column has no label with entries students, teachers, total. The second column is labeled wear glasses with entries 32, 4, 36. The third column is labeled do not wear glasses with entries 97, 2, 99. The fourth column is labeled total with entries 129, 6, 135.
Which statements are correct about the two-way frequency table? Check all that apply.
The correct statements about the two-way frequency table are:
Option C, and Option E.
According to the statement
we have to check that the given statement is applicable or not on the given conditions.
So, For this purpose
The two-way frequency table is
In Mathematics and statistics, A two-way frequency table is a tabular method for displaying relative data for two categories of variables. (See the attached).
the given options are:
Option A the row categories are "wears glasses"
Option B and "do not wear glasses."
Option C two teachers do not wear glasses.
Option D thirty-six students wear glasses.
Option E a total of 6 teachers were polled.
So, The correct statements about the two-way frequency table are:
Option C, and Option E.
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Answer: the corret answer is A, C and E
if 3n+2 is an odd number which of the following is an even number
A. 3n
B. 3n + 4
C. 3n + 3
D. (3n)²
Answer: 3n+3
Step-by-step explanation:
Adding 1 to an odd number results in an even number.
A spherical balloon is inflated so that its volume is increasing at the rate of 3 ft3/min. How fast is the diameter of the balloon increasing when the radius is 1 ft
When an spherical balloon volume is increasing at the rate of [tex]3ft^3/min[/tex] then the diameter of the balloon is increasing [tex]\frac{3}{2\pi }ft /min[/tex]
How can we find the rate of change of balloon's diameter ?
The volume of a spherical balloon is [tex]v=\frac{4}{3} \pi r^3[/tex]
In form of diameter we can write as
[tex]v=\frac{4}{3} \pi (\frac{D}{2} )^3\\=\frac{1}{6} \pi D^3[/tex]
Now we will differentiate both sides wrt to [tex]t[/tex] we get
[tex]\frac{dv}{dt} =\frac{1}{6} \pi 3D^2 \frac{dD}{dt} \\\frac{dD}{dt} =\frac{2}{\pi D^2} \frac{dv}{dt} \\\\when r=1\\D=2ft[/tex]
Given in the question [tex]\frac{dv}{dt} =3ft^3/min[/tex]
thus when we substitute the values we get
[tex]\frac{dD}{dt} =\frac{2}{\pi *2^2} (3)\\\frac{dD}{dt}=\frac{3}{2\pi } ft/min[/tex]
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Find the missing angle.
The missing angle of the right trapezoid is 126°.
Quadrilaterals
There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. The trapezoid is a quadrilateral that presents at least one set of parallel sides and the sum of the internal angles is 360°. The trapezoid classifications are:
Right trapezoid - it presents two right angles.Isosceles trapezoid - it presents the congruent non-parallel sides.Scalene trapezoid - it is one in which the non-parallel sides are not congruent.From the figure, it is possible to see that the image has two right angles. Thus, you have a right trapezoid.
Therefore, from the sum of internal angles, you can find the missing angle:
u+54+90+90=360
u=360-234
u=126
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Which rule describes the translation below? on a coordinate plane, triangle s t u is shifted 3 units down and 5 units to the left to form triangle s prime t prime u prime. (x, y) right-arrow (x minus 5, y minus 3) (x, y) right-arrow (x 5, y 3) (x, y) right-arrow (x minus 3, y minus 5) (x, y) right-arrow (x 3, y 5)
am bad at this type of geomtry
pls haIp
x =x=x, equals
^\circ
∘
degrees
Answer:
15
Step-by-step explanation:
The blue angle and the yellow angle form a linear pair, so they are supplementary (angle measures add up to 180).
180 - 165 = 15
what is the scale factor from ABC to DEF
Answer:
the scale factor from triangle ABC to triangle DEF would be 8
Step-by-step explanation:
the triangle DEF was actually flipped from triangle ABC
1.line AB corresponds to line EF
AB = 6 , and EF = 48
we multiply 6 by "8" to get to 48
2.line BC corresponds to line ED
BC = 6 , and ED = 48
we multiply 6 by "8" to get to 48
3.line AC corresponds to line FD
AC = 6 , and FD = 48
we multiply 4 by "8" to get to 32
I hope this help
PLEASE HELP FAST!!! Find the surface area of the composite figure. Round your answer to the nearest tenth if necessary.
Using the surface area formula for rectangular and triangular prism, the surface area of the composite figure is: 444 m².
What is the Surface Area of the Composite Figure?Total surface area = surface area of the top triangular prism + surface area of the bottom rectangular prism - area of the surface both share together.
Surface area of the top triangular prism = (S1 + S2+ S3)L + bh = (10 + 10 + 16)5 + (16)(6) = 276 m².
Surface area of the bottom rectangular prism = 2(wl + hl + hw) = 2·(5·16+4·16+4·5) = 328 m²
Area of the surface both share together = 2(16)(5) = 160 m²
Total surface area = 276 + 328 - 160 = 444 m².
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help me w this pls thanks
Answer:
Perimeter: 4+[tex]\pi \\[/tex] mm
Area: [tex]\pi[/tex] mm^2
Step-by-step explanation:
Perimeter:
90/360 * 4[tex]\pi \\[/tex] +2 + 2 = 4+ [tex]\pi \\[/tex]
Area:
90/360 * 4[tex]\pi[/tex] = [tex]\pi[/tex]
Answer: 7.14 mm and 3.14 mm²
Step-by-step explanation:
The perimeter of a figure is the total length on the outside of the figure. A regular circle has a perimeter of [tex]2\pi r[/tex], where r is the radius and [tex]\pi[/tex] is an irrational constant, approximately 3.14.
Due to the right angle, we know that this is a quarter circle, as it is a quarter of 360°, or a full circle. Hence, the curved portion of the quarter circle is [tex]\frac{1}{4}* 2\pi r[/tex] or [tex]\frac{1}{2} \pi r[/tex]. The radius is 2 mm, so this value is
[tex]\frac{1}{2} \pi*2=\pi[/tex]
However, this isn't the total perimeter, as there are straight edges in the figure too. Both edges are radii of the whole circle, so both would be 2mm. Their total is
[tex]2+2=4[/tex]
By adding [tex]\pi[/tex] to 4 we get [tex]\pi +4[/tex] or 7.14 mm.
The area is the total space enclosed by a figure. The total area of a whole circle is [tex]\pi r^2[/tex], where r is still the radius. Since this is a quarter circle, it would take up a quarter of the area, or [tex]\frac{1}{4} \pi r^2[/tex]. We can plug in 2 for r and solve to get the area.
[tex]\frac{1}{4}\pi*2^2\\\frac{1}{4}\pi*4\\\pi[/tex]
Hence, the area is [tex]\pi[/tex], or around 3.14 mm².
HELP ASAP
You work at a canning factory that's producing cans for a new brand of soup. You need to decide what size the cans should be. The soup cans can have a radius of either 2 in, 2.5 in, 3 in, or 3.5 in. The cans need to hold a volume of exactly 90 in3. The company wants the cans to be no more than 5 inches tall, and it wants the cans to have the greatest lateral surface area possible so it can print more information on the side of the cans.
To solve this problem, you will fill in this table with the surface area and volume of each cylinder:
a. First, calculate the height each can must be, given the radius and volume.
b. Now calculate the lateral surface area for each possible can.
c. Based on the requirements for the can, which can should you make?
Answer:
The answers are in the image
Step-by-step explanation:
The solution is in the attached image
If f(x)=2x-6, which of these is the inverse of f(x)?
○ A. f-¹(x) = 1 +6
X-6
○ B. f-¹(x) = x=6
2
○ C. f-¹(x) = X+6
2
○ D. f¹(x) = -6
Answer:
f-¹(x) = (x + 6)/2
Step-by-step explanation:
Replace f(x) with y.
y = 2x – 6
Interchange x and y.
x = 2y – 6
Solve for y.
y = (x + 6)/2
Replace y with f-¹(x)
f-¹(x) = (x + 6)/2
Use the following information to answer the question. The economic impact of an industry, such as sport fishing, can be measured by the retail sales it generates. In 2006, the economic impact of great lakes fishing in states bordering the great lakes had a mean of $318 and a standard deviation of $83.5. Note that all dollar amounts are in millions of dollars. Assume the distribution of retail sales is unimodal and symmetric. (Source: National Oceanic and Atmospheric Administration). For what percentage of great lakes states would you expect the economic impact from fishing to be between $234.5 and $401.5 (in millions of dollars)? ( Hint use the empirical rule)
The percentage of great lakes states would we expect the economic impact from fishing to be between $234.5 and $401.5 is 50%.
Given that mean is $318 , standard deviation is $83.5 and confidence interval is $234.5 and $401.5.
We have to calculate the percentage of great lakes that we would expect the economic impact from fishing to be between $234.5 and $401.5.
Because we have not given the sample size taken so we will use any test.We are using z test.
We know that,
z=X-μ/σ
where μ is population mean and σ is population standard deviation.
We cannot find p value between $234.5 and $401.5. We have to find the p value between $234.5 and $318 and then add the p value between $318 and $401.5 by calculating.
P value between $234.5 and $318:
z=234.5-318/83.5
=-83.5/83.5
=-1
p value of -1 is 0.1587
P value between $318 and $401.5:
z=401.5-318.5/83.5
=83.5/83.5
=1
p value of z=1 is 0.3413
Total p value=0.1587+0.3413
=0.5
Total percentage=0.5*100
=50%
Hence the percentage that we would expect the impact to be between $234.5 and $401.5 is 50%.
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What is the slope of line m? please help
An urn contains 11 balls, 3 white, 3 red, and 5 blue balls. Take out two balls at random, without replacement. You win $1 for each red ball you select and lose a $1 for each white ball you select. Let X be the random variable that notes the amount you win. Find the probability mass function (pmf) of X.
Let X be the number of times you win.
The total number of ways to select 2 balls (order does not matter) =>
The number of ways so that two balls are white:
= 3/55
The number of ways so that two balls are red:
= 3/55
The number of ways so that one ball is red, one is white:
= 9
The number of ways so that two balls are blue:
= 10
i.e. p = 10+9/55 = 19/55
The number of ways so that one ball is blue, one is white:
p = 15/55 = 3/11
The number of ways so that one ball is blue, one is red:
15/55 = 3/11
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the diffrence of 3-7p^2+11(4+n)
The expression 3 - 7p² + 11(4 + n) to find an example of each kind of expression is;
The first value is a number, 3 = constantThe second value, -7p² = factorThe third value, 11(4 + n) = binomial and monomial valuesExpression3 - 7p² + 11(4 + n)
The expression has 3 parts
3-7p²11(4 + n)3 - 7p² + 11(4 + n)
= 3 - 7p² + 44 + 11n
= 47 + 7p² + 11n
Complete question:
Use the expression 3 — 7p2 + 11(4 + n ) to find an example of each kind of expression
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The padlock for your gym locker uses a 3 number sequence to open the lock. If
the numbers go from 1 to 22, how many different sequences are there on the dial
without repeating a number?
Answer:
9,240
Step-by-step explanation:
For the first number, there are 22 numbers available to choose from. For the second number, there are 21 numbers available, since the first number cannot be the same as the second number. And for the last number, there are 20 remaining numbers to choose from. So, there are 22*21*20=9240 possible sequences.
Which expressions are equivalent to 2(4f+2g)-
choose three answers
A. 8f+2g
B. 2f(4 + 2g)
C. 8f+4g
D. 4(2f+g)
E. 4f+4f+4g
Can someone please help me
Answer:-2.4+3.2t
Step-by-step explanation:
-3.6+1.2-1.9t+5.1t
= -2.4+3.2t
A machine manufactuers 300 nails a day. how many did it produce in the month of april 2007
The machine produces 3000 nails in the month of April 2007.
Production of Nails in the Month of April
According to the given information,
Number of nails manufactured per day by the machine, x = 300
And, we know that April is the fourth month of a year which has total 30 days.
Hence, number of days the machine is manufacturing nails in the month of April, y = 30
So, the number of nails that will be produced by the machine in the month of April is given by,
N = Number of nails produced per day × Number of days in April
N = xy
N = 300 × 30
N = 9000
Therefore, the machine produces 9000 nails in the April month of year 2007.
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Brett had 3/4 of a family sized pizza. he gave each of his brothers half of this. what fraction of the pizza was each brother given?
Answer:
[tex]\frac{3}{8}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}[/tex] * [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex]
in this triangle, cosA/cosB =
AB = 4.24
BC= 3
AC = 3
<C 90deg.
Answer:
1
Step-by-step explanation:
[tex]\cos A=\frac{3}{4.24} \\ \\ \cos B=\frac{3}{4.24} \\ \\ \frac{\cos A}{\cos B}=1[/tex]
There are 5,280 feet in a mile. Gary walked 220 feet to the bus stop, and the bus took him a quarter of a mile to school. What is the ratio of his distance walking to.the distance he rode the bus
The ratio of distance travelled by walking to distance travelled by bus is 1 : 6.
What is ratio?When two quantities of the same units are compared, the ratio is what shows how much of one quantity is included in the other.
Total no. of Feet in a Mile = 5280
Distance Gary walked to the bus stop = 220 feet
Distance travelled by bus = 1/4 mile = (1 / 4)*5280 = 1320 feet
Ratio of distance walking to distance by bus = 220 / 1320 = 1 : 6
Hence, the ratio of distance travelled by walking to distance travelled by bus is 1 : 6.
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A wall is in the shape of a trapezoid. The lengths of the parallel bases are 8 feet and 20 feet. The height of the room is 8 feet. How much paint is needed to cover the wall? 80 ft2 112 ft2 160 ft2 224 ft2
The amount of paint needed to cover the wall is 112 square feet
How to determine the amount of paint?The given parameters are:
Parallel bases = 8 feet and 20 feet
Height = 8 feet
The area is calculated as:
Area = 0.5 * (Sum of parallel bases) * Height
So, we have;
Area = 0.5 * (8 + 20) * 8
Evaluate
Area = 112
Hence, the amount of paint needed to cover the wall is 112 square feet
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Find the interval in which the function is positive.
f(x)=x²-7x + 10
1. (-∞0, 2)
II. (2,5)
III. (5,00)
O I, II
O I, III
O II, III
O II only
Answer:
(b) I, III
Step-by-step explanation:
The correct answer can be chosen based on your knowledge of the shape of the graph of f(x).
General shapeThe leading coefficient of this quadratic function being positive tells you the graph will be a parabola that opens upward. The left branch of the parabola will extend to positive infinity, as will the right branch.
If there are x-intercepts, the x-values between those will be where the graph has crossed the x-axis and function values are negative.
Specific shapeThe answer choices suggest that x=2 and x=5 are x-intercepts of the function's graph. These can be checked, if you like, by evaluating f(2) and f(5).
f(2) = 2² -7·2 +10 = 4 -14 +10 = 0
f(5) = 5² -7·5 +10 = 25 -35 +10 = 0
This means the function will be positive for x < 2 and for x > 5. These intervals are described by I and III.
PLEASE HELP FAST!!! Find the surface area of the composite figure. Round your answer to the nearest tenth if necessary.
The surface area of the composite figure is 524 square meters
Surface area of a figureThe given composite figure is made up of a triangular prism and a rectangular prism. The surface area of the figure is given as:
Surface area = 2(16*5+5*4+16*4) + (16*6) + 2(50)
Take the sum
Surface area = 2(80+20+64) + 96 + 100
Surface area = 2(164) +196
Surface area = 328 + 196
Surface area = 524 square meters
Hence the surface area of the composite figure is 524 square meters
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PLEASE HELP HURRYYYYY
Answer:
See below
Step-by-step explanation:
Looks like positive linear to me....slope is up and to the right (positive) and the line drawn shows it ot be approx linear
Silicone implant augmentation rhinoplasty is used to correct congenital nose deformities. The success of the procedure depends on various biomechanical properties of the human nasal periosteum and fascia. An article reported that for a sample of 20 (newly deceased) adults, the mean failure strain (%) was 26.0, and the standard deviation was 3.4. (a) Assuming a normal distribution for failure strain, estimate true average strain in a way that conveys information about precision and reliability. (Use a 95% confidence interval. Round your answers to two decimal places.)
The true average strain in a way that conveys information about precision and reliability is 27.314.
Given that sample size is 20, mean is 26%, standard deviation is 3.4, confidence level is 95%.
We have to calculate the true average strain in a way that conveys information about precision and reliability.
We have to use t test in our problem because sample size is less than 30.
Weknow that,
t=x bar-μ/s[tex]\sqrt{n}[/tex]
where μ is sample mean,
s is sample standard deviation.
Degree of freedom=n-1
=20-1
=19
T value at 95% confidence interval=1.7281
put the values in the formula of t given above.
1.7291=x bar-26/3.4/[tex]\sqrt{20}[/tex]
1.7291=xbar-26/3.4/4.47
1.7291= x bar-26/0.76
1.7291*0.76=x bar-26
1.314=x bar-26
x bar=26+1.314
x bar=27.314
After rounding it will be 27.31
Hence the true average strain in a way that conveys information about precision and reliability is 27.31%.
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PLEASE I NEED HELP SO BADLY
Answer:
[tex]3y^{2} -3y-5[/tex]