The exponential function illustrated as f(x)=50(1.02)^x has a growth rate of 2%.
What is the growth rate in the function?The exponential function is a mathematical function that is represented by e^x. Unless otherwise specified, the term refers to a positive-valued function of a real variable, though it can be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras.
In this case, the function is given as:
f(x)=50(1.02)^x
It should be noted 1 + 2% = 1.02 which us the value in the parentheses.
In conclusion, the growth rate is 2%.
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Which of the following shapes could be formed by taking a longitudinal section perpendicular to the base of a rectangular prism?
The longitudinal section perpendicular to the base of a rectangular prism is a rectangle.
What is a three dimensional shape?A three dimensional shape is a shape that has length, width and height. Examples of three dimensional shapes are cone, cylinder, prism and pyramid.
A two dimensional shape is a shape that have both length and width. Examples of two dimensional shape are circle, rectangle, square.
A rectangular prism is a three-dimensional shape, having six faces, where all the faces are rectangles.
The longitudinal section perpendicular to the base of a rectangular prism is a rectangle.
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Evaluate f(-3) for f(x) = 2^x
a. 1/8
b. -8
c. 8
d. -6
Answer:
A
Step-by-step explanation:
f(-3) = 2^-3
to get rid of a negative in an exponent, move the whole thing to the denominator.
1/(2^3)
2^3 = 2×2×2
1/(2×2×2)
1/8
PLEASE I REALLY NEED HELP ON THIS QUESTION QUICKLY
Answer:
4/7
Step-by-step explanation:
[tex]\frac{6}{7} times \frac{2}{3}[/tex] 6x2=12
7x3=21
[tex]\frac{12}{21} = \frac{4}{7}[/tex]
True or false: f(x) is a function
Answer Section 1. <3
Heyy, I'm sunny and I'm here to help you :)
(P.S: answer in explanation)
----------------------------------------------------------------------------------------------------------
Explanation Section:
It is false
If f(x) is a function , then for each value of x there should be a single y values
For input 0 there is a output 0
for input 10, the output is 2
for input 15, output is 3
For input 5, we have two output 1 and 3
for single input 5, the function cannot have two outputs 1 and 3
So this f(x) is not a function
Bye! - SunnyBunny <3
Carly takes three steps to walk the same distance as jim walks in four steps. each of carly’s steps covers 0. 5 metres. how many metres does jim travel in 24 steps?
The distance travelled by Jim in 24 step is 9 miles by unitary method.
According to the given question.
The number of steps travelled by Jim = 24
Also, it is given that "Carly takes three steps to walk the same distance as Jim walks in four steps".
Therefore, by unitary mehod we can say that
The number of steps walked by Carly = 3 × (24/4) = 3 × 6 = 18
So, the distance travelled by Carly in 18 steps
= 18 × 0.5miles
= 9 miles
Since, the Carly's 18 steps is equals to Jim's 24 steps.
Therefore, the distance travelled by Jim in 24 step is 9 miles.
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A basketball is shot into the air. its height is represented by the polynomial equation h(t) = –16t2 35t 5, where h is the height of the basketball at t seconds. what is the height of the basketball at 0.5 seconds?
The height of the basketball at 0.5 seconds will be = 26.5
What is a polynomial equation?A polynomial equation is an equation where a polynomial is set equal to zero. i.e., it is an equation formed with variables, non-negative integer exponents, and coefficients together with operations and an equal sign. It has different exponents. The highest one gives the degree of the equation.
Example of a polynomial equation is: 2x2 + 3x + 1 = 0, where 2x2 + 3x + 1 is basically a polynomial expression which has been set equal to zero, to form a polynomial equation.
According to the given equation if we put value in it we will follow the following steps -
[tex]h(t) = - 16t^{2} + 35t+ 5\\ h(0.5) = -16(0.5)^{2} + 35(0.5) + 5\\h(0.5) = -16(0.25) + 17.5 + 5\\h(0.5) = 4 + 17.5 + 5\\h(0.5) = 26.5\\[/tex]
Therefore, the height of the basketball at 0.5 s will be 26.5
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Answer:
Is the question supposed to be (1.5), if so then the answer would be 21.5
Step-by-step explanation:
ht=-16t^2+35t+5
h(1.5)=-16(1.5)^2+35(1.5)+5
=21.5
Bentley's family took a road trip to the Grand Canyon. Bentley fell asleep 59% of the way through the trip. If the total length of the trip was 300 miles, how many miles had they travelled when Bentley fell asleep?
Answer:177
Step-by-step explanation:so for short, you need to multiply the 300 miles with the 59 precent we have and divide it to 100 this provides us the answer of miles he slept through the road trip
The number of miles they had travelled when Bentley fell asleep is 177 miles.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, Bentley fell asleep 59% of the way through the trip.
The total length of the trip was 300 miles.
The number of miles
= 59% of 300
= 59/100 ×300
= 59×3
= 177 miles
Therefore, the number of miles they had travelled when Bentley fell asleep is 177 miles.
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please help I'm so tired and I need to turn this in tomorrow
Considering the given box plots, it is found that:
a) They had the same IQR.
b) Athlete A went on the shortest training ride.
c) Athlete B went on more rides longer than 35 miles.
d) Athlete B had a greater median distance.
What is a box plot?It is a plot that focuses the interquartile range of the population, which is the difference between the third and the first quartile, but gives a five number summary of the population, composed by these following measures.
The smallest value.The first quartile.The median.The third quartile.The highest value.Hence, for Athlete A, we have that:
The smallest value is 12.The first quartile is 27.The median is of 29.The third quartile is 34.The highest value is of 45.IQR: 34 - 27 = 7.For Athlete B, we have that:
The smallest value is 18.The first quartile is 32.The median is of 37.The third quartile is 39.The highest value is of 41.IQR: 39 - 32 = 7.Hence:
a) They had the same IQR.
b) Athlete A went on the shortest training ride.
c) Athlete B went on more rides longer than 35 miles(as it is less than his median).
d) Athlete B had a greater median distance.
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Consider two forces of 17 and 42 pounds both acting in the horizontal direction on a single object. find the resultant force acting on the object. magnitude = direction angle =
The forces have a magnitude of 59 pounds, and their direction angles are zero.
What is the magnitude of force?The total amount of forces exerted on an object is referred to as the magnitude of force. The strength of the force increases when all the forces are pulling in the same direction. The force's strength reduces when forces are exerted on an item from different angles.When two forces operating on a body in opposite directions along the same line of action are equal in magnitude, they cancel one another out. When two forces operating on a body in opposite directions along the same line of action are equal in magnitude, they cancel one another out.According to this formula, the amount of net force acting on an item is equal to the mass times the acceleration of the object.Magnitude is a term that refers to size or importance. The depth of the Grand Canyon serves as an illustration of magnitude. The scope of the hunger crisis in the world serves as an illustration of magnitude. A measurement of the energy released by an earthquake, as shown on the Richter scale (geology).Two forces of 17 and 42 pounds act horizontally on an object.
i.e
F1 = 17 pounds
F2 = 42 pounds
As the magnitude of the force represents the sum of all the forces
The direction is the same
Magnitude : 17 + 42 = 59 pounds
The Direction angles : 0
As they have the same direction so angle will be 0.
The forces have a magnitude of 59 pounds, and their direction angles are zero.
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Answer:59 and 0
Step-by-step explanation:
EDGE
PLEASE HELP IM STUCK PLS
Answer:
The slope is -3.
Step-by-step explanation:
The slope is the Rise/Run between the two points. The change in y for every change in x. Take the two points and calculate the:
RISE = (-6 - 3) = -9
RUN = (8 - 5) = 3
Rise/Run, or slope, is = -9/3 or -3
I graphed a line with slope of -3 and then added 18 to force the line to intersect the two given points.
Find the midpoint of the line segment joining points A and B.
A(6-7); B(4,3)
Answer: [tex]\Large\boxed{Midpoint=(5,~-2 )}[/tex]
Step-by-step explanation:
Given information
[tex](x_1,~y_1)=(6,~-7)[/tex]
[tex](x_2,~y_2)=(4,~3)[/tex]
Given the midpoint formula
[tex]Midpoint=(\dfrac{x_1+x_2}{2} ,~\dfrac{y_1+y_2}{2} )[/tex]
Substitute values into the given formula
[tex]Midpoint=(\dfrac{(6)+(4)}{2} ,~\dfrac{(-7)+(3)}{2} )[/tex]
Simplify values on the numerator
[tex]Midpoint=(\dfrac{10}{2} ,~\dfrac{-4}{2} )[/tex]
Simplify the fractions
[tex]\Large\boxed{Midpoint=(5,~-2 )}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Can someone point out in which step I made a mistake in and what the mistake was? (I know the answer is 1,980, but I somehow managed to get 360 using these steps which seem logical, and I don't know where I went wrong).
The value of the product expression 6 * 330 is 1980
How to evaluate the product?The product expression is given as:
6 * 330
Express 330 as the product of 33 and 10
6 * 330 = 6 * 33 * 10
Express 33 as the product of 3 and 11
6 * 330 = 6 * 3 * 11 * 10
Evaluate the product of 6 and 3
6 * 330 = 18 * 11 * 10
Evaluate the product of 11 and 10
6 * 330 = 18 * 110
Evaluate the product of 18 and 110
6 * 330 = 1980
Hence, the value of the product expression 6 * 330 is 1980
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Alan's bamboo plant adds some flair to his apartment. In four weeks, Alan has trimmed a total of inches off the top of the plant. What is the rate of change in the plant's height in terms of inches per week? Ignore the growth rate of the plant.
The rate of change in the plant's height in terms of inches per week will be 1 2/3 inches.
How to calculate the rate?Rate of change is used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable.
The calculation for the rate of change is simple in that it takes the current value of a stock or index and divides it by the value from an earlier period.
The change in y (y being the height of the plant) over 4 weeks was 6 2/3 inches and there are four weeks. Therefore, the average height will be:
= 6 2/3 ÷ 4
= 1 2/3 inches
The average rate of change of the plant growth per week was 1 2/3 inches.
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Complete question:
Alan's bamboo plant adds some flair to his apartment. In four weeks, Alan has trimmed a total of 6 2/3 inches off the top of the plant. What is the rate of change in the plant's height in terms of inches per week? Ignore the growth rate of the plant.
a.+1 2/3B)-1 2/3C)+3/5D)-5/2
Find the sum of 10 x 2 + 7 x + 6 10x 2 +7x+6 and 6 x + 5 6x+5.
The sum of the given expression expressed as a quadratic equation is 10x^2 + 13x + 11
Sum of expressionsExpressions are equations separated by mathematical signs. This expressions are known to contains certain unknowns
Given the following expression
10x^2 +7x+6 and 6x + 5
We are to take the sum of both expression to have:
f(x) = 10x^2 +7x+6 + 6x + 5
Collect the like terms
f(x) = 10x^2 + 7x + 6x + 6 + 5
f(x) = 10x^2 + 13x + 11
Hence the sum of the given expression expressed as a quadratic equation is 10x^2 + 13x + 11
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Which of the following ordered pairs lies on the graph of h(x) = -2x squared?
(1, 4)
(1, -4)
(1, -2)
By direct evaluation we conclude that the point (x, y) = (1, - 2) lies on the graph of the quadratic equation h(x) = - 2 · x². (Correct choice: C)
What ordered pair lies on the curve generated by a given function?
In this problem we have three ordered pairs to be checked on a given function by direct evaluation, a ordered pair lines on the curve of function if and only if the x-value of the ordered pair leads to the y-value by evaluating in the function. Now we proceed to evaluate each of the three points at the function presented in the statement:
(x, y) = (1, 4)
h(1) = - 2 · 1²
h(1) = - 2
By direct evaluation we conclude that the point (x, y) = (1, - 2) lies on the graph of the quadratic equation h(x) = - 2 · x². (Correct choice: C)
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You are given an expression for the volume of the rectangular prism. determine an expression for the missing dimension. v=4x^3 5x^2-32x-33 and the dimensions are (x 1)and (x 3)
A certain type of thread is manufactured with a mean tensile strength of kilograms and a standard deviation of kilograms. How is the variance of the sample mean changed when the sample size is
In the case above:
(a) If there is an increased from 64 to 196, then the variance decreases.
(b) If there is a decreased from 784 to 49, then the variance increases.
What occurs if the variance increases?Standard Error is known to be the square root of the variance. if a given variance increases, so its standard error also.
Since the standard error takes place in the denominator, hence, if the standard error increases, the variance goes up.
Therefore, In the case above:
(a) If there is an increased from 64 to 196, then the variance decreases.
(b) If there is a decreased from 784 to 49, then the variance increases.
See full question below
A certain type of thread is manufactured with a mean tensile strength of 78.3 kilograms and a standard deviation of 5.6 kilograms. How is the variance of the sample mean changed when the sample size is (a) increased from 64 to 196? (b) decreased from 784 to 49?
What is the variance about?
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im having trouble with this question! pls help
Using a proportional relationship, it is found that the unit rate of change is of 9.
The relation d = 9t is graphed at the end of the answer.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
In this problem, we have d as a function of t, hence the relationship is:
d = kt.
When t increases by 0.2, d increases by 1.8, hence the constant is given as follows:
k = d/t = 1.8/0.2 = 9
The relation d = 9t is graphed at the end of the answer.
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Which expression is equivalent to the given expression?
Assume the denominator does not equal zero.
a^3b^5 / a^4b
A. b^4 / a
B. a / b^4
C. 1 / ab^4
D. ab^4
The expression which is equivalent to the given expression by means of evaluation using the laws of indices is; Choice A; b⁴/a.
Which of the answer choice represents an expression which is equivalent to the given expression?The given expression according to the task content is; a³b⁵/a⁴b.
It therefore follows from the laws of indices that each variable can be evaluated by means of their exponents as follows;
a^(3-4)b^(5-1)
Consequently we have;
b⁴/a.
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How many solutions does the equation −3y 3y 4 = 4 have? none infinitely many one four
A given linear equation has infinitely many solutions.
What is a linear equation?There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that make a linear equation true and plot those values on a coordinate grid.As much as possible, reduce the equation to y = mx + b. Verify the exponents in your equation. It is nonlinear if it has exponents. Your equation is linear if there are no exponents in it.The definition of a linear equation is an equation with a maximum degree of one.Given: −3y 3y 4 = 4
3y+4=3y+4
The given linear equation satisfies any value of 'y'.
So, A given linear equation has infinitely many solutions.
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how many rectangles of different sizes can be formed from 36 identical rectangles
The number of rectangles of different sizes can be formed from 36 identical rectangles is 5
Number of rectangles
From the question, we have proofs of;
Total number of identical squares = 36
Now, let the measurement of the side of each square be 1 unit
We have that the formula for area of a square is;
Area of a square = Side × Side square units
We have the area of the square to be;
Area of each square = 1×1 = 1 square units
This is so because the rectangles are identical both in length and width
Let's find the area of the identical squares
Area of total 36 identical squares
= 36×1 square units
= 36 square units
So Area of the rectangle = length × breadth square units
if the rectangles are formed from 36 identical squares then their areas are the same
Total area of required rectangles = 36 square units
It can be written as;
36 = length × breadth
36 = 1×36 36 = 2×1836 = 3×1236 = 4×936 = 6×6(1,36) , (2,18),(3,12),(4,9),(6,6) are the different rectangles formed from 36 identical squares
Total rectangles = 5
Thus, the number of rectangles of different sizes can be formed from 36 identical rectangles is 5
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Please helppppp!!
Question #1 (Question un ) : What is the smallest positive integer k such that k/660 can be expressed as a terminating decimal?
Give BRAINLIST IF ANSWER!!!!!
Answer:
k = 33
Step-by-step explanation:
Terminating decimal numbers: Decimals that have a finite number of decimal places.
For a decimal to be terminating, the factors of the denominator must only contain 2 and/or 5. As 2 and 5 are prime numbers, use prime factorization to rewrite the denominator.
Prime factorization of 660:
⇒ 660 = 2 × 2 × 3 × 5 × 11
⇒ 660 = 2² × 3 × 5 × 11
Therefore:
[tex]\implies \sf \dfrac{k}{660}=\dfrac{k}{2^2 \cdot 3 \cdot 5 \cdot 11}[/tex]
The fraction will only be a terminating decimal if both 3 and 11 in the denominator are canceled out. To do this, their lowest common multiple must be the numerator:
⇒ LCM of 3 and 11 = 3 × 11 = 33
[tex]\implies \sf \dfrac{33}{660}[/tex]
[tex]\implies \sf k=33[/tex]
Therefore, the smallest positive integer k such that k/660 can be expressed as a terminating decimal is 33.
Answer:
33
Step-by-step explanation:
Select the equation of a straight line that is perpendicular to the line y = 3x - 2.
A y = 3x - 5
B 3y=x+2. C y=- -3x-2 D y= -x/3+2 E y=1\3x-2
[tex]y = mx + b \\ y = nx + c \\ for \: the \: two \: lines \: to \: be \: perpendicular \\ m.n = - 1[/tex]
[tex]m = 3 \\ \\ 3n = - 1 \\ n = \frac{ - 1}{3} [/tex]
Answer: D[tex]y = \frac{ - x}{3} + 2[/tex]
Suppose that 4 ≤ f '(x) ≤ 5 for all values of x. what are the minimum and maximum possible values of f(8) − f(3)?
The minimum value of f(8) - f(3) is 20.
The maximum value of f(8) - f(3) is 25.
In the question, we are given that, 4 ≤ f'(x) ≤ 5 for all values of x.
Taking the given inequality as (i).
We are asked to find the minimum and maximum possible values of f(8) - f(3).
We multiply (i) by dx throughout, to get:
4dx ≤ f'(x)dx ≤ 5dx.
To find this, we integrate (i) in the definite interval [8, 3] with respect to dx, to get:
[tex]\int_{3}^{8}4dx \leq \int_{3}^{8}f'(x)dx \leq \int_{3}^{8}5dx\\\Rightarrow [4x]_{3}^{8} \leq [f(x)]_{3}^{8} \leq [5x]_{3}^{8}\\\Rightarrow 4*8 - 4*3 \leq f(8)-f(3) \leq 5*8 - 5*3\\\Rightarrow 20 \leq f(8) -f(3) \leq 25[/tex]
Thus, the minimum value of f(8) - f(3) is 20.
The maximum value of f(8) - f(3) is 25.
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Gilbert plans to invest $14 000 into two types of bonds. one bond yields 8% interest each year and the other bond yields 12% interest each year. he needs to earn $1400 each year to consider the investment successful. how much should he invest in each bond?
invest in each bond = $7000
What is Profit and Loss?An income statement, also known as a profit and loss account, is one of a company's financial statements and displays the company's receipts and outlays for a specific time period. It explains how revenues are converted into net income or net profit.
According to the given data:
Let n be the amount invested at 8%
the amount invested at 12% would be : 14000-n
so,
8n+12(14000-n) = 1400
8n + 168000 - 12n = 1400 * 100
4n + 168000 = 140000
n = 28000/4
= 7000
Therefore,
At 12% amount invested
= 14000 - 7000
= $7000
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When we make inferences about the difference of two independent population proportions, what assumptions do we need to make? mark all that apply.
When we make inferences about the difference of two independent population proportions, we assume that it is a random sample, and the number of successes and failures are at least 15 in each group.
Two independent proportions tests involve comparing the proportions of two unrelated datasets.
For these two datasets to be regarded as an independent population, the following must be true or assumed to be true
The datasets must represent a random sampleEach dataset must contain at least 15 successes and failuresHence, the above highlights are the assumptions of two independent population proportions.
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what is the parent function of g(x) = 3cos (x + 180°) + 1
The parent function of the function g(x) = 3cos (x + 180°) + 1 is f(x) = cos(x)
What are parent functions?Parent functions are the basic function that represents the entire family of that function family
How to determine the parent function?The function is given as;
g(x) = 3cos (x + 180°) + 1
As a general rule, the parent function of any function is the basic equation of the function family
The basic equation of the function g(x) = 3cos (x + 180°) + 1 is f(x) = cos(x)
Hence, the parent function of the function g(x) = 3cos (x + 180°) + 1 is f(x) = cos(x)
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if x : y = 0.75 : 0.90 and y : z = 1/3 : 1/4
(A) simplify the ratio x : y and y : z
(B) find x : y : z
Step-by-step explanation:
x:y=0.75:0.90
Here,
Dividing by the value of y=0.90,
x:y=0.75/0.90:0.90/0.90
=5/6:1
Similarly,
y:z=1/3:1/4
Dividing by 1/3,we get,
y:z=1:3/4
Now,
X:y:z=5/6:1:3/4
Multiplying by both value of y,0.90×1/3=3/10
x:y:z=5/6×3/10:1×3/10:3/4×3/10
By solving this,
x:y:z=1/4:3/10:9/40Mia, Keela And Michelle are selling girl scout cookies.In all they have sold $800 worth of cookies. Mia sold 57 boxes, Keela sold 28 boxes and Michelle sold 15 boxes. How should the girls split the money so that they earn the same fraction as the boxes of cookies that they sold? Should Mia and Michelle get the same amount of money? Why Or Why not?
Answer:
the money should be split as per each girl sold. total boxes sold is 100.
Step-by-step explanation:
total boxes sold is 100. Mia sold 57/100 keela 28/100 and Michelle 15/100.
mia=456$
keela=224$
michelle=120$
calculated as boxes sold/100 x 800$
find the size of each of the angles marked with letter
Answer:
angle l = 115
angle k = 115
angle j = 114
angle i = 66
Step-by-step explanation:
angle l = it is opposite to 115 so its the same
angle k = opposite opposing angles with angle l
angle j = 180-66=114 (between 2 parallel lines the sum of 2 angles is 180)
andle i = 180-114=66 (straight line = 180 degrees so subtract angle j to get i)
