The rate of change of base is 5 cm/min.
The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity. In simple terms, in the rate of change, the amount of change in one item is divided by the corresponding amount of change in another. The rate of change formula gives the relationship describing how one quantity changes in relation to the change in another quantity.
Let us assume that
h = height of the triangle
[tex]\frac{dh}{dt}[/tex] = rate of increase of height = 1 cm/min
A = Area of triangle
[tex]\frac{dA}{dt}[/tex] = rate of increase of area = 13 cm²/min
Area of traingle, A = 1/2*(b*h)
When A = 12 cm² and h = 4 cm,
Put in above formula,
12 = 1/2 * (b)(4)
∴ b = 6 cm
A = 1/2 * b*h
[tex]\frac{dA}{dT} = \frac{1}{2}h\frac{db}{dt} + \frac{1}{2}b\frac{dh}{dt} \\\\13 = \frac{1}{2}*4* \frac{db}{dt} + \frac{1}{2}*6*1\\\frac{db}{dt} = 5 cm/min[/tex]
Thus, rate of change of base is 5 cm/min.
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An item on sale costs 45% of the original price. The original price was $39.
Use the ALEKS calculator to find the sale price.
$0
X
S
The sales price of the item is $17.55
How to determine the sales priceFrom the question, we have the following parameters that can be used in our computation:
Sales price = 45% of the original price
The original price = $39
The above parameters mean that
Sales price = 45% * original price
Substitute the known values in the above equation, so, we have the following representation
Sales price = 45% * $39
Evaluate
Sales price = $17.55
Hence, the sales price is $17.55
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50th term: –9, 2, 13, 24, 35, ... ______________
Answer: :/ listen to the lesson
Step-by-step explanation:
Answer: the 50th term is 530
Step-by-step explanation:
it increases by 11 each time so 11*49
539 subtract by nine since it starts at -9
530
Please helpp absolute value
-|f| = -16
A) no solution
B) one solution
C) two solution
help me pleaseeeeeeeeeeeeeeeeeeeeee!!!!!!!!!!!!!!!!
Answer:
5% of $1100 = 55
Year given = 7
So, 55 × 7 = 385
She would get after 7 years all total = (1100 + 385) = $1485
A city is building a fence around a rectangular playground. If the perimeter of the playground is 90 feet and the length of one side of the fence is 26 feet, what is the width of the playground?.
We can conclude that the width of the rectangular ground is 19ft.
What is a rectangle?A quadrilateral with all of its angles equal, or right angles, is a rectangle.
In addition to having all equal angles, a square also has all equal sides. Therefore, a special case of a square is a rectangle.
To put it another way, a rectangle can also be a square.
So, we know that:
The perimeter of the rectangular ground is 90ft.
The length of the rectangular ground is 26ft.
Now, the width will be:
Perimeter of rectangle formula: P = 2(l+w)
Now, put the values and substitute as follows:
P = 2(l+w)
90 = 2(26+w)
90 = 52 + 2w
2w = 90 - 52
2w = 38
w = 38/2
w = 19ft
Therefore, we can conclude that the width of the rectangular ground is 19ft.
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If a researcher wants to use a control group whose participants receive a placebo pill as well as an experimental group whose participants receive a new treatment medication, which type of statistical test is most appropriate for analyzing the results and why?.
The t-test is appropriate because it can handle small sample sizes and is robust to violations of normality assumptions.
What are Statistical Tests?Mathematical statistical tests are techniques for data analysis and drawing conclusions about a population from a sample. These tests employ mathematical formulae and probability theory to assess if a participant's result is statistically significant, implying that it is unlikely to have happened by chance. Comparing two or more groups, figuring out how variables relate to one another, and assessing the accuracy and validity of data may all be done using statistical tests. They are frequently used to derive inferences from experimental or observational data in disciplines including psychology, economics, and sociology.The outcomes of these tests are used to determine whether to accept or reject a hypothesis and can offer important insights into the underlying patterns and relationships in data.
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What is the rate of change of the function Y= -3/2x + 2 PLEASE HELP I MEED HELP ASAP
Answer:
-3/2
Step-by-step explanation:
rate of change is slope
w(5)=w(-5) true or false
Answer: False
Step-by-step explanation:
w(5) = 5w
w(-5) = -5w
These aren't the same expressions.
Hope this helps!!! :)
In which choice is y a function of x?
A (-2, 3), (0, 2), (-1, 1), (0, 0)
B. (4, 1), (1, 4), (-4, 1), (1, 4)
C. (4, 1), (4, 2), (4,3), (4,4)
D. (0, 2), (1, 1), (3, 0), (0, -2)
Answer:
B. (4, 1), (1, 4), (-4, 1), (1, 4)
Step-by-step explanation:
A mixed number is a number consisting of a whole number and a proper fraction.
It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 1 × 4 = 4. In the following intermediate step, it cannot further simplify the fraction result by canceling. In other words - four minus one quarter is fifteen quarters.
Which relation is not a function?
Answer: C, the table.
Step-by-step explanation:
In a function, there can only be one output (y) per input (x), but you can have multiple inputs (x) per one output (y).
Using this logic, we see that the answer is;
C
one year, the population of a city was 359,000. several years later it was 420,030. find the percent increase.
Answer:
17%
Step-by-step explanation:
Hello factor the polynomial completely with steps please
The factor form of the cubic equation y = x³ + 3 · x² + x + 3 is y = (x² + 1) · (x + 3).
How to factor a cubic equation
In this problem we find a cubic equation, that is, a polynomial of the form:
y = a · x³ + b · x² + c · x + d
Where a, b, c, d are the real coefficients of the polynomial. Herein we must use algebra properties to find the factor form of the expression:
y = a · Π (x - rₙ) for n = {1, 2, 3, ..., m - 1, m}
Where:
a - Lead coefficient.m - Grade of the polynomial.First, write the entire equation:
y = x³ + 3 · x² + x + 3
Second, use distributive property of real mumbers:
y = x² · (x + 3) + 1 · (x + 3)
Third, use distributive property of real numbers once again:
y = (x² + 1) · (x + 3)
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Which expressions are equivalent to this expression? y + y + y + 3z
The expressions that are equivalent to the expression y + y + y + 3z are 3y + 3z and 3(y + z)
How to determine the expressions that are equivalent?From the question, we have the following parameters that can be used in our computation:
y + y + y + 3z
To start with, expressions that are equivalent are expressions that have equal values when evaluated
Using the above as a guide, we have the following:
Evaluate the like terms in y + y + y + 3z
So, we have the following representation
y + y + y + 3z = 3y + 3z
Factor out 3 from the expression
So, we have the following representation
y + y + y + 3z = 3(y + z)
Hence, the equivalent expressions of y + y + y + 3z are 3y + 3z and 3(y + z)
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Write the following expression using an exponent. (2y-9) (2y-9) (2y-9) (2y-9) (2y-9)
For the given expression the exponent would be [tex](2y-9)^5$[/tex].
What is an exponent?
An exponent is a number that indicates how many times a base number should be multiplied by itself. For example, in the expression 2³, the base is 2 and the exponent is 3. The exponent indicates that the base should be multiplied by itself 3 times, so the value of the expression is 2 * 2 * 2 = 8.
The given expression is
= (2y-9) (2y-9) (2y-9) (2y-9) (2y-9)
Exponent expression = [tex](2y-9)^5$[/tex]
Hence, for the given expression the exponent would be [tex](2y-9)^5$[/tex].
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For the given expression the exponent would be (2y-9)⁵.
What is an exponent?
An exponent is a number that indicates how many times a base number should be multiplied by itself. For example, in the expression 2³, the base is 2 and the exponent is 3. The exponent indicates that the base should be multiplied by itself 3 times, so the value of the expression is 2 * 2 * 2 = 8.
The given expression is
= (2y-9) (2y-9) (2y-9) (2y-9) (2y-9)
Exponent expression = (2y-9)⁵
Hence, for the given expression the exponent would be (2y-9)⁵.
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I am purchasing a smart TV for $648.
I have a coupon for 40% off.
Find the sale price.
Answer:
$1080
Step-by-step explanation:
Since we have 40% off 60 percent of the price is $648 so we can make ratios
60/100=648/x
Cross multiply
60x=100(648)
60x=64800
/60. /60
x=1080
Sales price is $1080
Hopes this helps please mark brainliest
For each equation, determine whether it is linear.
(a) y=4
Equation
(b) y=-4x²+3
(c) y=7x+2
(d) y=-x
Is the equation linear?
Yes
No
Answer:
(a) yes
(b) no
(c) yes
(d) yes
Step-by-step explanation:
You want to know which of these equations is linear.
y = 4y = -4x² +3y = 7x +2y = -xLinear equationFor the purpose here, we will define a linear equation as one that graphs as a straight line. (Other definitions may give different answers.)
In general, a linear equation will have a highest degree of 1. (It may be 0.)
The equation of choice (b) has degree 2, so is not a linear equation.
GraphThe attached graph shows the only equation that is not linear is choice (b).
__
Additional comment
In some branches of mathematics, an equation of the form y = mx+b is not a linear equation. In basic algebra, that is the model of a linear equation, for any values of m and b.
Mr. Reynolds is a car salesman. He makes a salary of $55,000 a year. He
also earns a commission of of his total sales for the year. This year, Mr.
Reynolds has a sales total of $295,200. Write and evaluate a function to find
Mr. Reynolds's total earnings for the year.
Answer:you speak French pls
Step-by-step explanation:
:::
Order these numbers from least to greatest: 0, 1,
1
2
8
610
9
49
100
11
20
1
13
Answer:
100
Step-by-step explanation:
I did the test
Please help me quick !!
A food truck did a daily survey of customers to find their food preferences. The data is partially entered in the frequency table. Complete the table to analyze the data and answer the questions:
Likes hamburgers Does not like hamburgers Total
Likes burritos 39 77
Does not like burritos 95 33
Total 134 205
Part A: What percentage of the survey respondents liked hamburgers but do not like burritos? Show all work. (3 points)
Part B: What is the marginal relative frequency of all customers who like hamburgers? Show all work. (3 points)
Part C: Which category has the lowest joint relative frequency? Show all work. (4 points)
a) The percentage of the survey respondents liked hamburgers but do not like burritos is of: 46.34%.
b) The marginal relative frequency of all customers who like hamburgers is of: 0.6537.
c) The lowest joint frequency is not liking neither of hamburgers or burritos.
How to obtain frequencies and percentages?The relative frequency is obtained as the division of the number of desired outcomes by the number of total outcomes.
The percentage is calculated as the multiplication of the relative frequency by 100%.
From the table given by the image at the end of the answer, the total number of people in the survey is of:
77 + 128 = 134 + 71 = 205.
The percentage for item a is then calculated as follows:
95/205 x 100% = 46.34%.
The relative frequency for item b is then calculated as follows:
134/205 = 0.6537.
The joint frequencies are found completing the table, considering the sums for the rows and columns, as follows:
Like both: 134 - 95 = 39.Like burritos but not hamburgers: 38.Like hamburger and do not like burritos: 95.Do not like both: 71 - 38 = 33. -> lowest.Missing InformationThe table is given by the image shown at the end of the answer.
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How many gallons of rocket fuel containing 80% liquid oxygen must be mixed with 250 gallons containing 40% liquid oxygen to produce a mixture containing 70% oxygen? PLSSSS EXPLAIN!!!!
750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity
We need to find how many gallons of 80%
8x, since we don't know how many gallons
mixed with 250 gall of 40%: 0.40(250)
and we want a mix at 70%. The mix will include the 0.8x and the 0.4(250) Like this:
8x+0.4(250)=0.7x+0.7*250
Multiply on both sides of the equation
0.8x+100= 0.7x+175 Subtract 100 on both sides
0.8x= 0.7x+75
Subtract 0.7 on both sides
0.1x= 75
Divide both sides by 0.1
x= 750
You need 750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.
Hence, 750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.
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y = 1/4x+1 y =1/4x-1
How many solutions does this system
of equations have?
Answer:
3
Step-by-step explanation:
3 because you have to find x, you have to find x and y and then the overall answer
The given system of equations,
y = 1/4 x + 1
y = 1/4 x - 1
has no solution.
Given a system of equations.
There are two equations in the system.
We have to find the number of solutions for the system if it exists.
Consider the equations,
y = 1/4 x + 1
y = 1/4 x - 1
Since both the equations are in y value, they are equal.
1/4 x + 1 = 1/4 x - 1
1/4 x - 1/4 x = -1 - 1
0 = -2
This is not possible.
This means that the given system has no solution.
Hence the given system of equations has no solution.
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Suppose a sightseeing tour company charges $7.50 for each hour you rent a motorized scooter, plus a non-refundable fee of $45. Write an equation that represents the total cost, y, of renting the scooter in relation to the number of hours, x.
An equation that plots the total cost, y, of renting the scooter against the duration, x is y=7.50x+45
What is meant by an equation?3x - 5 = 16 is an illustration of an equation. By solving for x, we discover that the variable's value is 7, or x = 7. By deleting parenthesis and merging related terms, you can simplify either side of an equation and obtain the solution. Together with the variables for which the equation must be solved, the values of the variables that must satisfy the equality to compose the answer are referred to as the unknowns. Equations can be categorized as identities or conditional equations. An identity holds true regardless of the value given to the variables. A conditional equation's variables can only have specific values that produce the truth.
Given,
You must pay a non-refundable $45, plus $7.50 per hour, to rent a motorized scooter from a sightseeing tour company.
The equation is y=7.50x+45
Therefore, a formula that plots the total cost, y, of renting the scooter against the duration, x is y=7.50x+45.
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What are the domain and range of the function f(x)= x^2-3x-28/x+4?
The domain will be D:{x ∈ R| x ≠ 4} and the range will be R:{y ∈ R| y ≠ 11}. Then the correct option is A.
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The function is given below.
f(x) = (x² - 3x - 28) / (x + 4)
Simplify the function, then we have
f(x) = (x² - 7x + 4x - 28) / (x + 4)
f(x) = [x(x - 7) + 4(x - 7)] / (x + 4)
f(x) = [(x + 4)(x - 7)] / (x + 4)
f(x) = x - 7
The Domain of the function is all real numbers except 4. And the range of the function is all real numbers except 11.
The domain will be D:{x ∈ R| x ≠ 4} and the range will be R:{y ∈ R| y ≠ 11}. Then the correct option is A.
The diagram is given below.
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find a recurrence relation for the number of bit strings of length n that contain three oconsecutive 0
A recurrence relation is an equation in mathematics that states that the nth term of a series of numbers is equal to some combination of the terms that came before it.
What is recurrence relation ?A recurrence relation is an equation in mathematics that states that the nth term of a series of numbers is equal to some combination of the terms that came before it.
For a parameter k that is independent of n, only k preceding terms of the sequence frequently occur in the equation; this number k is known as the order of the relation.
The rest of the series can be determined by continually using the equation if the values of the first integers in the sequence have been provided.
The nth term in linear recurrences is equivalent to a linear function of the k prior terms. The Fibonacci numbers' recurrence is a well-known example.
Hence, A recurrence relation is an equation in mathematics that states that the nth term of a series of numbers is equal to some combination of the terms that came before it.
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Add the equations.
3x - y = -5
7x + y=15
A. -4x = 10
B. -4x = -20
C. 10x = 10
D. 10x-2y = -20
The addition of the given system of equations is 10x = 10.
What is system of equations?
A set of one or more equations involving numerous variables is referred to as a system of equations. The variable mappings that satisfy all component equations are the solutions to systems of equations, or the points where the components of these equations intersect.
Consider the given system of equations
3x - y = -5 ..(1)
7x + y = 15 ..(2)
We have to find the addition of this equations.
Add equation (1) and equation (2).
3x - y = -5
+ 7x + y = 15
____________
10x + 0 = 10
Hence, the addition of the given system of equations is 10x = 10.
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◄) Cora's city took a survey about a plan for a new park. The city surveyed 5,000 people
84% of the people surveyed liked the plan for the park. How many people liked the plan?
Consider the following points on the graphs of y = sin(x) and y = sin(2x), with the added vertical dashed lines:
What are c and d in that order?
From the given graphs the values of c and d are, c = 0.53,
d = 0.95.
What is sinusoidal wave?
A mathematical curve defined in terms of the sine trigonometric function, of which it is the graph, is known as a sine wave, sinusoidal wave, or simply sinusoid. It is a smooth periodic function and a particular kind of continuous wave.
Let the graphs of y = sin(x) and y =sin(2x) are given.
From this graphs we have to find the value of c and d.
First from y = sin(x) to find the value of 'a'.
consider the point [tex](a, -\frac{4}{5})[/tex]
⇒
[tex]sin(a) = -\frac{4}{5} \\a = sin^-^1(-\frac{4}{5})\\ a = -53.13[/tex]
Now to find the value of 'c'.
Plug a = -53.13 in y = sin(2x)
[tex]sin(2a) = c\\sin(2(-53.13)) = 0.52622\\sin2a= 0.53[/tex]
Hence, the value of 'c' is c = 0.53.
Now to find the value of d.
First y = sin(x) to find the value of b.
Consider, the point [tex](b, \frac{5}{13})[/tex]
⇒
[tex]sinb = \frac{5}{13} \\b = sin^-^1(\frac{5}{13})\\ b = 22.62[/tex]
Now to find value of d.
Plug b = 22.62 in y = sin(2x)
[tex]sin(2b) = d\\sin(2(22.62)) = 0.95138\\sin(2b) = 0.95[/tex]
So, the value of 'd' is 'd = 0.95'.
Hence, from the given graphs the values of c and d are, c = 0.53,
d = 0.95.
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28% adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is (a) exactly three, (b) at least four, (c) less than eight.
The probability distribution that the number of U.S. adults who favor the use of unmanned drones by police agencies is
(a) exactly three :-= 0.251
(b) at least four:-= 0.445
(c) less than eight:-= 0.994
What is probability distribution?
The probabilities of any random occurrence are determined by the probability distribution. It is sometimes described as a collection of potential results from any random experiment depending on the underlying sample space. A set of real numbers, a set of vectors, or a set of any other things might make up these settings. It is a component of statistics and probability.
The outcome of an experiment whose results cannot be anticipated is known as a random experiment. Imagine that we can't foresee whether a coin will land on its head or its tail when we throw one. An outcome is a potential outcome of a random experiment. The collection of results is known as a sample point.
X ~ Bin ( n , p)
Where n = 12 , p = 0.28
Binomial probability distribution is
P(X) = nCx * px * ( 1 - p)n-x .
a)
P(X = 3) = 12C3 * 0.283 * ( 1 - 0.28)9
= 0.251
b)
P(X >= 4) = 1 - P(X <= 3)
= 1 - [ P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) ]
= 1 - [ 12C0 * 0.280 * ( 1 - 0.28)12 +12C1 * 0.281 * ( 1 - 0.28)11 +12C2 * 0.282 * ( 1 - 0.28)10 +12C3 * 0.283 * ( 1 - 0.28)9 ]
= 0.445
c)
P(X < 8) = 1 - P(X >=8)
= 1 - [ P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) ]
= 1 - [ 12C8 * 0.288 * ( 1 - 0.28)4 +12C9 * 0.289 * ( 1 - 0.28)3 +12C10 * 0.2810 * ( 1 - 0.28)2 +
12C11 * 0.2811 * ( 1 - 0.28)1 +12C12 * 0.2812 * ( 1 - 0.28)0 ]
= 0.994
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Montoya has carefully cut out a perfectly square section of graph
paper. She counts all the blocks in the square, then takes a square root
of this number. Will Montoya's square root equal the number of
blocks in one side of the graph-paper square? Explain.
Answer: Yes, Montoya's square root will equal the number of blocks in one side of the graph-paper square.
Step-by-step explanation: The square root of a number is the number that, when multiplied by itself, produces the original number. For example, the square root of 16 is 4, because 4 * 4 = 16.
If Montoya has cut out a perfectly square section of graph paper, the number of blocks in the square will be the same as the number of blocks in one side of the square multiplied by the number of blocks in the other side of the square. In other words, the number of blocks in the square will be the square of the number of blocks in one side of the square.
Therefore, when Montoya takes the square root of the number of blocks in the square, she will get the number of blocks in one side of the square.
For example, if Montoya's square has 4 blocks on each side, the number of blocks in the square will be 4 * 4 = 16, and the square root of 16 will be 4, which is the number of blocks in one side of the square.
x² + 13x + 12 factorise
x²+ 12x + 1x + 12
x(x+12) + 1(x+12)
(X+1) (X+12)