As per kinematic theory, when any object is moving on a rough surface, the friction force will act on the surface. And the friction force is in the opposite direction to the motion of the object.
Using kinematic formulas, the acceleration speed can be calculated:
[tex]v^{2} = u^{2} +2as[/tex]
As per the given data,
The initial speed of the skater [tex](u) = 12m/s[/tex]
The width of the pitch on the rough ice [tex](s) = 7.0 mt[/tex]
The final speed of the skater [tex](v) = 6.0m/s[/tex]
Substituting these values in the kinematic formula, we get
[tex]a = \frac{v^{2}-u^{2} }{2s}[/tex]
[tex]a = \frac{6^{2}-12^{2} }{14}[/tex]
[tex]a=- 7.71 m/s[/tex]
Therefore the calculated acceleration on the rough ice is [tex]-7.71m/s[/tex]
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f(x) = x + 4x³, find the value of f(-1)
We get the value of f ( - 1 ) as - 5 for the function f (x) = x + 4 x³.
We are given a function:
f (x) = x + 4 x³
A function from a set X to a set Y assigns to each element of X exactly one element of Y.
We need to find the value of f ( - 1 )
We will do this by substituting the value of x as - 1
Put x = -1, we get that:
f ( x = -1 ) = ( - 1 ) + 4 ( - 1 )³
f ( - 1 ) = - 1 + 4 ( - 1 )
f ( - 1 ) = - 1 - 4
Simplifying the function:
f ( - 1 ) = - 5
Therefore, we get the value of f ( - 1 ) as - 5 for the function f (x) = x + 4 x³.
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Han made some hot chocolate by mixing 4 cups of milk with 6 tablespoons of cocoa. How many cups of milk per tablespoon of cocoa is that?
Answer:
24
Step-by-step explanation:
4 x 6 = 24
Given g(x) = 1/3 (2x-1) 2, what is the value of g(8)?
By evaluating in x = 8 we can see that the value of g(8) is 45.
How to evaluate the function g(x)?
Here we have the function:
g(x) = (1/3)*(2x - 1)^2
We want to get the value of g(8), this means that we need to evaluate the function in x = 8.
To do this, we just need to replace the variable "x" in the equation by the number 8.
We will get:
g(8) = (1/3)*(2*8 - 1)^2 = (1/3)*(15)^2 = 3*15 = 45
g(8) = 45
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Find the equation of a line parallel to\hspace{4px}x-3y=3\hspace{4px}x−3y=3that passes through the point (-3,-5)(−3,−5).
Answer:
something
Step-by-step explanation:
something
The equation of the line is x - 3y = 12 which is parallel to the line x - 3y = 3 and passes through (-3, -5).
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The equation of the line is:
x - 3y = 3
Parallel to the above line:
x - 3y = c
Plug x = -3 and y = -5
-3 + 15 = c
c = 12
x - 3y = 12
Thus, the equation of the line is x - 3y = 12 which is parallel to the line x - 3y = 3 and passes through (-3, -5).
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Can someone please help with this? I need step by step on how to solve
Answer:
8
Step-by-step explanation:
You times 4 by 4 since it's squared =16
You have to times 2 by 2 by 2 like this=8
2x2=4 4x2=8
then subtract them= 16-8= 8
put it over the line where 4 and 2 were
after you subtract 5 and 3= 2
than times 2 by the squared= 2x2= 4
times the 2 with 4= 8
put the 8 under the line so you can divide it
8 divided by 8 is 1
lastly, add 7 and 1= 8
=8
the answer is eight
four squared is 16 and two cubed is eight so sixteen minus eight is eight then five minus three is two then you would figure out what 2 squared us and its four so two times four is eight so the first part is eight over eight which is one and one plus seven in eight
Shureka Washburn has scores of 62, 82, 62, and 68 on her algebra tests.
a. Use an inequality to find the scores she must make on the final exam to pass the course with an average of 71 or higher, given that the final exam counts as two tests.
b. Explain the meaning of the answer to part (a).
Shureka's present scores of 62, 82, 62, and 68, and a passing score of 71 or higher gives;
The score she must make in her final exam is x ≥ 152Which inequality can be used to represent the final score?Shureka's scores are 62, 82, 62, 68
Grade with which Shureka will pass the course = 71
Number of test her final exam is equivalent to = 2
Let x represent her score in her final exam, we have;
[tex] \frac{62 + 82 + 62 + 68 + x}{4 + 2} \geqslant 71[/tex]
Which gives;
62+82+62+68+x ≥ 71 × (4+2) = 426
274 + x ≥ 426
x ≥ 426 - 274 = 152
x ≥ 152
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What are the intercepts for the function y=-x-1 graphed bellow
Answer:
The intercept is - 1.
Hope this helps :)
Step-by-step explanation:
In the function y = - x - 1 the initial value which is the y-intercept is - 1, and the line intercepted at -1 on the y-axis. Also, the line on the graph also intercepted at - 1 on the x-axis too. So the interceptes is - 1.
Im not understanding this, Can someone help ?
1. Write a word description of the set.
S={January, June, July}
Answer:
X:X is the same as the letter J
A director of a company notices that there is a nonlinear
relationship between the company's sales revenue and
customer satisfaction. Here are the data for the past six
months.
Sales Revenue
(Millions of $)
1.5
4
6
8
10
11
Customer Satisfaction
(Scale: 1-100)
78
75
62
50
35
15
Examine the scatterplots provided in this graphic.
Which one correctly displays these data?
O Scatterplot A
O Scatterplot B
O Scatterplot C
O Scatterplot D
Answer:
O Scatterplot C
Step-by-step explanation:
Sales Revenue
(Millions of $)
1.5
4
6
8
10
11
Customer Satisfaction
(Scale: 1-100)
78
75
62
50
35
15
Examine the scatterplots provided in this graphic.
Which one correctly displays these data?
Consecutive numbers are whole numbers that follow in order such as 7, 8, 9 10, 11, 12. find three consecutive numbers such as the sum of the first and third is 118
The three consecutive numbers are 58, 59 and 60.
Consecutive numbers are the numbers that follow each other continuously in a sequence from smallest number to largest number.
Let the first number = x
Let the second number = y
And Let the third number = z
As given in the question that the sum of the first and third number is 118, So we can write mathematically as
x + z = 118
The first and third numbers are 58 and 60 and their sum is 118.
The second number automatically will be 59.
So, the three consecutive numbers are 58, 59 and 60.
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Which integer is greater, -5 or -7 ?
Answer:-5
Step-by-step explanation:
Listen
Maikel has a pitcher filled with 18.5 ounces of lemonade. She pours 6.4 ounces into a glass for herself.
Write an addition equation that represents the amount of lemonade left in the pitcher.
Enter your answer as an addition equation, like this: 42+(-53)=-11
The equation that represents the amount of lemonade left in the pitcher will be.(18.5 - 6.4) = 12.1
How to calculate the equation?From the information given, Maikel has a pitcher filled with 18.5 ounces of lemonade and she pours 6.4 ounces into a glass for herself.
Therefore, the equation that represents the amount of lemonade left in the pitcher will be:
= Total amount - amount poured
= 18.5 - 6.4
= 12.1
Therefore the amount left will be 12.1 ounches
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factor this 4r³ - 3r²-4r +3
Answer:
(4r - 3)(r + 1)(r - 1)
Step-by-step explanation:
In order to factor the polynomial [tex]\sf 4r^3 - 3r^2 - 4r + 3[/tex], we can use various factoring methods.
In this case, we can use grouping.
Let's break down the expression and factor it step by step:
Group the terms in pairs:
(4r^3 - 3r^2) +(-4r + 3)
Factor out the greatest common factor from each group:
[tex]\sf r^2(4r - 3) - 1(4r - 3)[/tex]
Notice that both groups have a common factor of (4r - 3): and keeping remaining in bracket
[tex]\sf (4r -3)(r^2-1)[/tex]
Now, the expression r² - 1 can be factored further using the difference of squares:
(r + 1)(r - 1)
So, the fully factored form of the polynomial 4r³ - 3r² - 4r + 3 is:
(4r - 3)(r + 1)(r - 1)
Multiply the number by 4 add 12 to the product divide the sum by 2 subtract 6 from the quotient a. 4, 10, 20, 30 b. 1, 2.5, 5, 7.5 c. 2, 5, 10, 15 d. 5, 10, 15, 20
According to the given information multiply the integer by four, add 12 to the product, divide the sum by two, and subtract 6 from the quotient.
The correct option is A.
How do you solve the equations in order?In both mathematics and computer programming, the order of operations refers to a set of guidelines on which operations to do first in order to evaluate a certain mathematical expression. The order of operations is a rule that outlines the proper steps to take when analyzing a mathematical equation. We can recall the PEMDAS steps in the following order:
parentheses, exponents, multiplication and division (from Left to right), addition, and subtraction (from left to right).
The term BODMAS is used in the UK (Brackets, Orders, Divide, Multiply, Add, Subtract).
BDMAS is a term used in Canada (Brackets, Exponents, Divide, Multiply, Add, Subtract).
The equation ((4x+12)2)-6 leads to the result 2x, demonstrating that the answer is in multiples of 2.
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solve the equation n-6= -12
Answer: It is -6
Step-by-step explanation:
1. Add 6:
n - 6 +6 = -12 +6
2. Simplify and complete:
n = -6
Solve the equation by completing the square.
x2 − 10x + 26 = 8
Fill in the values of a and b to complete the solutions.
The values of a and b are:
a = 5 + √7
b = 5 - √7
Given data
x2 − 10x + 26 = 8
How to solve by completing x2 − 10x + 26 = 8 the squareTransform the equation to standard quadratic equation by equating to zero
x2 − 10x + 26 = 8
x2 − 10x + 26 - 8 = 0
x2 − 10x + 18 = 0
x2 − 10x + 18 + 5^2 - 5^2 = 0
x2 − 10x + 25 = 25 - 18
(x-5) (x-5) = 7
(x-5)^2 = 7
(x-5) = √7
x = 5 + √7
x = 5 - √7
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Find The Next Three Terms of the geometric sequence 4,2,1,1/2,...
Thank You...
Step-by-step explanation:
1/4, 1/8, 1/16. :)
You're welcome :)
Drag the tiles to the boxes to form correct pairs.
Consider functions fand g.
f (x) = 1 - ²
g(x)
Evaluate each combined function, and match it to the corresponding value.
ہے
4
= √11 - 4x
√3-3
√15
-3√3
(g- f)(-1)
(g. f)(2)
(g + f)(2)
(4) (-1)
0
The numeric values of the functions are given as follows:
[tex](g - f)(-1) = \sqrt{12}[/tex](g x f)(2) = 9.(g + f)(2) = 0.[tex]\frac{f}{g}(-1) = 0[/tex]How to find the numeric value of a function/expression?To find the numeric value of a function, we replace each instance of the variable by the desired value.
For this problem, the functions are given as follows:
f(x) = 1 - x².[tex]g(x) = \sqrt{11 - x}[/tex]At x = -1, the values are given as follows:
f(-1) = 1 - (-1)² = 1 - 1 = 0.[tex]g(-1) = \sqrt{11 - (-1))} = \sqrt{12}[/tex]Hence:
[tex](g - f)(-1) = g(-1) - f(-1) = \sqrt{12}[/tex][tex]\frac{f}{g}(-1) = \frac{f(-1)}{g(-1)} = \frac{0}{\sqrt{12}} = 0[/tex]At x = 2, the values are given as follows:
f(2) = 1 - (2)² = 1 - 4 = -3.[tex]g(2) = \sqrt{11 - 2} = \sqrt{9} = 3[/tex]Hence:
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A $400 deposit for 7 years at a compound interest rate of 2%
Answer:
$459.47
Hope this helps!
Sunil deposited $400 in an
account. After one and a half
years he withdrew his money and
had earned $78 in interest. What
is the simple interest rate on the
account?
3
The simple interest rate on the account is 13%
Here Sunil deposited $400 for one and a half years, and the interest he gets is $78. He deposits in at the simple rate of interest.
We know that the simple interest formula is
Simple interest = Principle × time × rate/ 100
It is given that,
simple interest = $78
time = 1 [tex]\frac{1}{2}[/tex] year = 3/2 year
Principle = $400
Let the rate of interest be r
So we have
78 =( 400 × 3/2 × r )/100
r =( 78 × 2×100) / (400 × 3)
r = 39%
Therefore the simple interest rate on the account is 13%.
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in recent years, the numbers of cell phones and the numbers of pirates have both increased, so there is a correlation, or association, between those two variables. therefore, pirates cause increases in cell phones
Final answer:
When two variables are correlated or associated, it does not necessarily follow that one of the variables is the root cause of the other. Correlation does not always indicate cause.
What are the three forms of mathematical correlations ?The link between variables is described by correlation. It can be characterized as strong or weak, as well as positively or negatively.
Positive correlation occurs when two variables change in the same direction. There are three fundamental forms of correlation. The two variables fluctuate in opposite directions when there is a negative correlation. No association or meaningful connection exists between the two variables, hence there is no correlation.
The correlation coefficient aids in determining how closely two variables are related in a single figure. Finding the crucial variables that other factors depend on and comprehending economic behavior are both facilitated by correlation analysis.
Explanation:
A correlation test determines whether two variables are related. Nevertheless, just because two variables are traveling together does not necessarily mean they are connected. This is why the phrase "correlation does not indicate causation" is used frequently.
As two factors are connected or related, it does not necessarily imply that one of the variables is the main cause of the other. Correlation not always show cause.
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Find the location of X.
Coordinate of X is [tex]-18[/tex] .
Section formulas are used to find the coordinates of the point that bisects a line segment (external or internal) at a specified ratio. When a point on a line segment divides it into two line segments, the formula used to determine the coordinates of that point is called the section formula. Suppose we have a point P(x,y) that divides a line segment in the ration m : n at points marked as A[tex](x_1,y_1)[/tex] and B [tex](x_2,y_2)[/tex] the , section formula is given by [tex]P(x,y)=(\frac{mx_2+nx_1}{m+n} ,\frac{my_2+ny_1}{m+n} )[/tex]It is given that coordinate of W ( -22, 0) and Y(-2,0) and X is the point which divides the line segement WY in ratio 1 : 4.
By using section's formula , we get
[tex](x,y)=(\frac{1(-2)+4(-22)}{1+4} , \frac{1(0)+4(0)}{1+4} )\\\\(x,y)=(\frac{-2-88}{5} ,\frac{0}{5} )\\\\(x,y)=(\frac{-90}{5} ,0)\\\\(x,y)=(-18,0)[/tex]
On comparing we get the location of X
-18
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Anita states that in her experience, a jar can hold 288 marbles. How accurate is Anita’s statement? Explain.
The statement that is made by Anita is not accurate.
Is the statement true?We know that a statement can only be true if it could be proven beyond every reasonable doubt. If the statement can not be proven, then it is a mere assertion. It does not hold water empirically and it can not be the basis for argumentation. It is just a mere guess and may not in any way be thought to reflect the reality of the situation.
In this case, the statement that has been made by Anita is that a jar can hold 288 marbles. How accurate is Anita’s statement. This statement can not be backed by any kind of empirical proof because the marbles were not counted individually. The statement is at best probable and may not reflect the actuality of the situation.
Hence the statement that has been made by Anita is a mere guess and it does not reflect the actual number of the marbles that are found in the container.
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Ordinarily, these two tests, confirmations and estimating allowance for doubtful accounts, focus on which primary concerns and audit objective(s) for accounts receivable?
Existence and value - Are the accounts for the AR really there, and can they be collected.
What are accounts receivable?Money owed to a business in the near future is represented by the asset account known as accounts receivable on the balance sheet. When a business permits a customer to pay for its products or services on credit, accounts receivable are generated. Similar to accounts receivable, accounts payable tracks money that is due as opposed to money that will be collected. The ratio of accounts receivable to sales outstanding or days sales outstanding can be used to determine how strong an organization's AR is. To determine when the AR will really be received, a turnover ratio study might be performed.
Briefing:Existence is an audit affirmation that the auditor must examine to ensure that all accounts receivable are present.
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A square-shaped pool has an area of 169 square meters. Find the approximate length of each side of the pool.
The value of the side length of the square-shaped pool is 13 meters
How to determine the lengthThe formula for calculating the area of a square is expressed as;
Area = a^2
Where 'a' is the side length of the square.
It is important to note the properties of a square, they include;
The four sides are equalAll the angles are equalEach interior angle is 90 degreesNow, substitute the value of the area into the formula, we have;
169 = a^2
To determine the value of a, find the square root of both sides
√169 = √a^2
13 meters = a
Thus, the value of the side length of the square-shaped pool is 13 meters
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4. Which equation is perpendicular to the line y = 3 and passes through the point (-1,3)
The equation that is perpendicular to the line is x = -1
How to determine the equation that is perpendicular to the line?The line equation is given as
y = 3
The point is also given as:
(x, y) = (-1, 3)
A linear equation is represented as
y = mx + c
Where m represents the slope
This means that y = 3 can be represented as
y = 0x + 3
So, the slope is 0
Since the slope is 0, the equation of the perpendicular line must be
x = xt
Where
(xt, y) = (-1, 3)
By comparison, we have
x = -1
Hence, the equation that is perpendicular to the line is x = -1
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what is 52 divide by 7540
Answer:
145 I think
Step-by-step explanation:
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a pesticide manufacturer is developing a new type of organic pesticide for a particular plant. to study the effectiveness of the new pesticide, a large sample of young plants is collected. the sample is then separated into many groups of two plants based upon age, size and soil type so that plants with similar characteristics are grouped together. one of the two plants in each group is randomly chosen and administered the pesticide, while both plants are placed in a controlled environment and are exposed to the possibility of attack from the target pests. the plants are inspected regularly over a 3 month period and the results are recorded for comparison.
The following scenario is a good example of a matched-pairs experiment.
What do we mean by matched pairs experiment?A matched pairs design is a type of experimental design in which study participants are matched based on key variables, or shared characteristics, related to the study's topic. Then, one member of each pair is assigned to the control group, and the other to the experimental group. A diet study involving 100 people is one example. Each subject would be matched with another of comparable age and weight. The pairs would then be divided into study groups, with each subject assigned to an opposing study group, diet or no diet.So, the given situation of a pesticide manufacturer is a perfect example of a matched-pairs experiment.
Therefore, the following scenario is best described as an example of a matched-pairs experiment.
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The correct question is given below:
A pesticide manufacturer is developing a new type of organic pesticide for a particular plant. To study the effectiveness of the new pesticide, a large sample of young plants is collected. The sample is then separated into many groups of two plants based upon age, size and soil type so that plants with similar characteristics are grouped together. One of the two plants in each group is randomly chosen and administered the pesticide, while both plants are placed in a controlled environment and are exposed to the possibility of attack from the target pests. The plants are inspected regularly over a 3 month period and the results are recorded for comparison.
This scenario is best described as an example of...
Find the complement of the set given that u = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. (enter your answers as a comma-separated list.) {x | x is in n and x < 6}
A = { 0,6,7} is the complement of the set given.
What is the set in math?
Any grouping of items (elements) in mathematics and logic, whether or not they are mathematical (such as numbers and functions). A list of all the members of a set, wrapped in braces, is a typical way to represent a set. Even older than the concept of number is the intuitive conception of a set.What is sets and its types?
A set is referred to as a well defined group of objects. These things are referred to as set elements. Various sets are categorized based on how many components they include. Sets are essentially a grouping of unique components of the same type.Given U = { 0,1 , 2 , 3, 4,5,6,7 }
Let set A = { x/x < 6 and x ∈ NI}
A = { 1,2,3 ,4,5}
∴ AC = Complement of A = { 0,6,7}
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