Based on the numbers to be divided of 1,060 ÷ 33 to get a quotient, the mixed number in the simplest form is 32¹/₂ .
How to find the quotient?Finding the quotient of two numbers means that one of the numbers would have to divide the other number.
The quotient in this case is:
= 1,060 ÷ 33
= 32.1212
To convert this to mixed number, divide the decimal portion by the relevant power of 10:
= 32 + 1212/10,000
= 32 + 4/32
= 32 + 1/8
= 32¹/₂
In conclusion, the quotient of 1,060 ÷ 33 is 32¹/₂ .
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There will be 4 floats in a parade. the parade organizers are trying to determine the order in which the floats should appear. how many different orders are possible?
Using permutation, there are a total of 24 different orders possible.
If there are a total of 4 floats in a parade then the number of possible orders = 4!
If we further calculate it we will get,
4 x 3 x 2 x 1 = 24
So there are a total of 24 possible orders in which the floats should appear.
The concept used here is the number of arrangements and the technical term used for it in mathematics is a permutation. A permutation is a mathematical calculation that involves finding the number of ways a particular set can be arranged.
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Mrs. Jenkins gave her class the function f(x)=(x-5)(x+1). Four students made a claim about the function. Each student's claim is below.
• Annie: The x-intercepts are (5,0) and (1,0)
•Jacob: The y-intercept is at (-5,0)
• Neil: The vertex is at (2, -9)
•Zoey: The midpoint between the x-intercepts is at (-2,0)
Which student's claim about the function is correct?
The only student with the correct claim about the given quadratic equation is; Neil: The vertex is at (2, -9)
How to identify the features of a quadratic function?We are given the quadratic function;
f(x) = (x - 5)(x + 1)
1) The x-intercepts of the quadratic function are simply the roots of the quadratic function. Now, the roots are at; (5, 0) and (-1, 0). Thus, Annie's claim is not correct.
2) The y-intercept is the point at which x = 0. Thus;
f(0) = (0 - 5)(0 + 1)
f(0) = -5
y-intercept is at; (0, -5)
Thus, Jacob is wrong.
3) The x-coordinate of the vertex is;
x = -b/2a
The equation is; x² - 4x - 5
Vertex = -(-4)/(2 * 1) = 2
y-coordinate is;
y = 2² - 4(2) - 5
y = -9
Thus, Jacob is correct
4) Zoey is incorrect because she didn't properly find the midpoint of the x-intercepts.
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Which statement explains why one source is the most reliable? The Squawkbook post is the most reliable source because ConcernedCitizen was at the meeting. The Local Reader article is the most reliable source because it shows a photograph of the lots. The Squawkbook post is the most reliable source because it provides the author’s opinion of the council. The Local Reader article is the most reliable source because the author offers a neutral reporting of facts.
HELP PLEASE
The statement that explains why one source is the most reliable is D. The Local Reader article is the most reliable source because the author offers a neutral reporting of facts.
What are reliable sources?Reliable sources are necessary for reliable information. A trustworthy source will offer a "complete, well-reasoned hypothesis, argument, etc. based on substantial evidence," according to UGA Libraries.
Scholarly, peer-reviewed articles and books are examples of widely regarded sources. trade publications, professional books, etc.
It should be noted that a reliable source should be based in facts and should not be biased.
Therefore, the correct option is D.
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Write an equation that represents the line.
Use exact numbers.
[tex]\displaystyle\\Answer:\ \frac{7}{5}x +\frac{34}{5}[/tex]
Step-by-step explanation:
[tex]\displaystyle\\(-7,-3)\ \ \ \ (-2,4)\\\\\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} \\\\x_1=-7\ \ \ \ \ x_2=-2\ \ \ \ y_1=-3\ \ \ \ \ y_2=4\\\\\frac{x-(-7)}{-2-(-7)} =\frac{y-(-3)}{4-(-3)}\\\\\frac{x+7}{-2+7}=\frac{y+3}{4+3} \\\\\frac{x+7}{5} =\frac{y+3}{7} \\\\[/tex]
Multiply both parts of the equation by 7:
[tex]\displaystyle\\7(\frac{x+7}{5} )=y+3\\\\7(\frac{1}{5} x+\frac{7}{5} )=y+3\\\\\frac{7}{5}x +\frac{49}{5} =y+3\\\\\frac{7}{5}x +\frac{49}{5} -3=y+3-3\\\\\frac{7}{5}x +\frac{49}{5}-3=y\\\\\frac{7}{5}x +\frac{49-3(5)}{5} =y\\\\\frac{7}{5}x +\frac{49-15}{5} =y\\\\\frac{7}{5}x +\frac{34}{5} =y\\\\So,\ y=\frac{7}{5}x +\frac{34}{5}[/tex]
geometry, is this correct?
Answer:
I think this is correct.
Step-by-step explanation:
-23x² + x² - 6x + 10 + 2x²
Step-by-step explanation:
what do you need to do ?
the only thing we can do here without any further information is simplification if the expression:
-23x² + x² - 6x + 10 + 2x²
now we group ask the terms of the same variable exponents :
-23x² + x² + 2x² - 6x + 10
-20x² -6x + 10
we could do
2×(-10x² - 3x + 5)
but I personally don't find this more simplified that the previous form.
help, please! 25 points! :)
The properties of the function are:
Its shape is an absolute functionIt has a domain of all real valuesIt has a range of real values greater than or equal to 0Vertex at (0, 0)How to make a table of values for the following equationThe absolute value equation of the function is given as
y = |x|
On the incomplete table of values, we do not have any x values
So, we can make use of any x value
To do this, we make use of the following x values
x = -3, -1, 0, 1 and 3
Next, we substitute x = -3, -1, 0, 1 and 3 in the equation y = |x|
So, we have:
y = |-3| = 3
y = |-1| = 1
y = |0| = 0
y = |1| = 1
y = |3| = 3
When represented on a table of values, we have
x | y
-3 | 3
-1 | 1
0 | 0
1 | 1
3 | 3
How to make the graph the equationNext, we plot the graph of the absolute value equation
See attachment for the graph of the absolute value equation
From the graph of the absolute value equation, we have the following properties:
Domain: All set of real valuesRange: All set of real values greater than or equal to 0Vertex: (0, 0)Shape: Absolute value equationRead more about absolute value equation at
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find the indicated probability. in one town, 72% of adults have health insurance. what is the probability that 7 adults selected at random from the town all have health insurance?
The radius of a sphere is 14 cm. The cost of
painting the surface of sphere is ₹25 per
square cm. If the radius of sphere is increased
by 10%, then the cost of painting is increased
by 20%. What is the percentage increase in
the total cost of painting per square cm?
(a) 54.27%
(b) 20.3%
(d) 45.2%
(c) 2.58%
The total cost of painting per cm will be 45.2% i.e. option(d).
Total cost of painting = Rate × Surface area of sphere
We know the radius is increases by 10%.
Thus, the Surface area will change by 21%
using formula a + b + (a × b)/ 100
The total change in cost of painting will be
= 20+21 +(20x21)/100
= 45.2%.
What is surface area?
The total area of all faces (or surfaces) on a 3D form is the surface area. For example:
There are six rectangular faces of a cuboid.
Add the areas of each of the cuboid's six faces to determine its surface area.
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A soccer team played 24 games and won 16.
What is the ratio of the number of wins to the number of losses?
Answer: 8:16
24(games)-16(wins)=8. 8=the losses
Step-by-step explanation:
Please answer the questions
The numeric values for the given functions are as follows:
1. g(-4) = -21.
2. f(-1) = 3.
How to find the numeric value of a function or of an expression?To find the numeric value of a function at input x = a, we replace each instance of the variable x in the function by the desired value of a.
For item 1, function g(x) is defined as follows:
g(x) = -x² - 5.
We want to find the numeric value at x = -4, hence the lone instance of x is replaced by -4 as is shown below:
g(-4) = -(-4)² - 5 = -16 - 5 = -21.
Hence g(-4) = -21 is the numeric value.
For item 2, the function f(x) is given as follows:
f(x) = -3(1 - x - 3x²).
To find the numeric value at x = -1, both instances of x have their values replaced by -1, hence the numeric value will be given as follows:
f(-1) = -3(1 - (-1) - 3(-1)²) = -3(1 + 1 - 3) = 3.
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(extra credit) suppose you have a well-balanced "super coin" with three sides or outcomes equally likely: head, middle, and tail. (the super coin is a die with opposite faces showing head, middle, and tail) you tossed this super coin two times.
Possible outcomes are Head, Middle, and Tail.
Since all outcomes are equally likely, the probability of each event is same, therefore
P(Head) = P(Middle) = P(Tail)
= 1/3
P(B|A) is 1/3
P(C|A) is 2/3
A and B are independent
A and C are not independent
Part a
Finding the sample space, S
S = { (HH), (HM), (HT), (MH), (MM), (MT), (TH), (TM), (TT) }
Part b
Finding P(B|A) and P(C|A):
n(B and A) = no. of outcomes in which the first toss is Middle and second toss is Tail = 1
n(A) = Total no. of events in which the first toss is Middle = 3
Therefore, P(B|A) = 1/3
n(C and A) = no. of outcomes in which the first toss is Middle and total no. of heads is zero = 2
n(A) = Total no. of events in which the first toss is Middle = 3
Therefore, P(C|A) = 2/3
Part c
Finding if A and B are independent, or if A and C are independent
Two events A and B are said to be independent when the occurrence of one event does not affect the occurrence of the other event and vice versa. In case of independent events,
P(A) = P(first toss is Middle) = 3/9 =1/3
P(B) = P(second toss is Tail) = 3/9 = 1/3
P(A and B) = P(first toss is Middle and second toss is Tail) = 1/9
P(A)*P(B) = (1/3)*(1/3)
= 1/9 = P(A and B)
Hence, we can say that events A and B are independent.
For A and C, we have,
P(A) = P(first toss is Middle) = 3/9
P(C) = P(total no. of Heads is 0) = 4/9
P(A and C) = P(first toss is Middle and total no. of heads is 0) = 2/9
P(A)*P(C) = (3/9)*(4/9)
= 4/27 P(A and C)
Hence, events A and C are not independent.
The question was incomplete, the complete question is:
(Extra Credit) Suppose you have a well-balanced "super coin" with three sides or outcomes equally likely: Head, Middle, and Tail. (the super coin is a die with opposite faces showing Head, Middle, and Tail) You tossed this super coin two times
a) Describe the sample space using the notation HM for example, if the results are Head first, and Middle second.
Let;
A = event the first toss is Middle,
B = event the second toss is Tail, and
C = event the total number of Heads is 0.
b) Find
P(B|A)
P(C|A)
c) Are A and B independent? YES, NO, Why?
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For which value of x is 12/x not a rational number
0
0.1
2
-1/2
Because we can't divide by zero, the correct option is x = 0.
For which value of x the quotient is not a rational number?
Here we have the quotient:
12/x
We want to find a value of x such that it is not a rational number, where a rational number is any number that can be written as the quotient of two integers.
Here is a trick, remember that we can't divide by 0, so if we choose x = 0, technically we can't take the quotient, so in that case we wouldn't have a rational number.
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solve for x
9x + 11
10x + 5
Answer: top: x= 2 bottom: x= -5
Step-by-step explanation: First you need to get rid of everything on the x side, so for example on the top one you would do 9-9 to get 0 so that x is by itself and then you also have to 11-9 because whatever you do to one side you have to do to the other. And then 11-9=2 so you are left with x= 2.
Consider the following graph of g(x). Write a formula for g(x) that describes the transformations performed on the basic function.
The formula for function g(x) that describes the transformations performed on the basic function f(x) = |x| is g(x) = - ( |x| + 4 )
As per the question statement, we are given a basic function f(x) = |x| and we are supposed to find the formula for function g(x) that describes the transformations performed on the basic function f(x) = |x|.
Solution is as follows:
Reflected about X - axis and translated 4 units down to X - axis.
Basic function y = |x| - 2
Transformed function g(x) = - ( |x| + 4 )
Reflected across y = -2
Function: A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).To learn more about functions, click on the link given below:
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Compare problems 1 and 2. What similarities do you see? What differences do you
notice?
(Algebra/geometry terms)
In the picture there are 2 problems. The similarity is they two have to find 2 question. The difference is given question are different.
Given that,
In the picture there are 2 problems.
We have to find the difference and similarities of question in the picture.
The similarities are they 2 are word problems.
Another similarity is they two have to find 2 question.
1. How much money for 10 days and How many days to collect the money $1.05?
2.How much gallon of water need for 50 minutes and How much time take to fill the pool?
Another similarity is they two have to justified the answer in a mathematical model.
Now,
The difference is,
First question has given sisters and money problem where as the second has given pool and gallon water problem.
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The moon is 2.4 x 10^5 miles from earth. Venus is 1.59 x 10^8 miles from the earth. How much further, in miles, is Venus than the moon from earth.
The Venus is at a distance of [tex]1.5876 * 10^8[/tex] further away from the earth than the moon
We have given that
The Distance of moon from the earth(in miles)= a= [tex]2.4 * 10^5[/tex] miles
The Distance of venus from the earth(in miles)= b = [tex]1.59 * 10^8[/tex] miles
What is distance?The distance between two objects that are not points is usually defined to be the smallest distance among pairs of points from the two objects.
Now,
Let the distance from which venus is further away from the earth than the moon be x
So, x = b - a
x = [tex]1.59 * 10^8-2.4 * 10^5[/tex]
x = [tex]1590 * 10^5 - 2.4*10^5[/tex]
x = [tex](1590 - 2.4)*10^5[/tex]
x = [tex]1587.6*10^5[/tex]
x = [tex]1.5876 * 10^8[/tex]
Therefore, venus is at a distance of [tex]1.5876 * 10^8[/tex] further away from the earth than the moon.
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Area of the shaded part
In the picture, there is a square and a shaded region inside the square. The shaded portion has a 13.76 square meter area.
Given that,
In the picture, there is a square and a shaded region inside the square.
We have to find the shaded portion area.
The side of the square is 8cm.
Now,
First we see the unshaded region on the square is there are 4 unshaded regions.
In the figure u can see there is a unshaded region we named that has tile 1, tile2, tile 3, and tile 4.
If we restock them we can see that we got a circle with that 4 tiles.
Now, the side is 8 cm then the 1 tile will be of 4 cm.
So, the radius of the circle is 4 cm.
In the other picture we can see that the area of the shaded region is equal to area of square- area of circle.
Area of the shaded region =s²-πr²
Area of the shaded region =8²-π(4)²
Area of the shaded region =64-π(16)
Area of the shaded region =64-16π
Area of the shaded region =64-16(3.14)
Area of the shaded region =64-50.24
Area of the shaded region =13.76
Therefore, The shaded portion has a 13.76 square metre area.
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if RS = ST and ST = 2UV then RS = 2UV
It is true given the above logical analysis to state that RS = 2UV. This is known as a conditional statement also known as an If-then-statement.
What is a conditional statement?A conditional statement (also known as an If-Then Statement) is a statement that begins with a hypothesis and ends with a conclusion.
A conditional statement can also be defined as "If this happens, then that will happen." A conditional statement's hypothesis is the first, or "if" element. While the "Then" is the Conclusion.
Hence, the hypothesis from the above statement is:
IF RS = ST and ST = 2UV [Hypothesis]
Then RS = 2UV [Conclusion]
Put differently we can say
A → B and B→C; then
A → C.
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Let f(p) be the average number of days a house stays on the market before being sold for price p in $1,000s. Which statement best describes the meaning of f(150)? (2 points)
This is the average number of days the house stayed on the market before being sold for $150,000.
The house sold on the market for $150,000 and stayed on the market for an average of 150 days before being sold.
The house sold for $150,000.
The house stayed on the market for an average of 150 days before being sold.
A statement which best describes the meaning of function f(150) is that: A. This is the average number of days the house stayed on the market before being sold for $150,000.
What is the average rate of change?The average rate of change can be defined as a type of function that is used for describing the average rate at which a quantity either decreases or increases with respect to another quantity.
What is a function?A function simply refers to a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable (x-value) to an output variable (y-value or f(x)).
In this scenario, the function f(150) can be evaluated as follows:
Function f(150) = 150 × p
Function f(150) = 150 × $1,000.
Function f(150) = $150,000
Therefore, the function f(150) simply means the average number of days this house stayed on the market before it was then sold for $150,000.
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5/8 divided by 2 1/10
Answer:
0.29761904761
Step-by-step explanation:
Brainlest, Please!
Answer:
25/84
Step-by-step explanation:
1. 2 1/10 is mixed number fraction so convert it into an improper fraction.
~ Multiply whole number and denominator and add the numerator of 1
~ Improper fraction: 21/10
2. So, new equation is (5/8) / (21/10)
3. Use the Keep, Change, Flip method:
~ Keep the 5/8
~ Change division to multiplication
~ Flip the improper fraction to 10/21
4. Solve the equation:
~ (5/8) x (10/21) = 50/ 168
5. Reduce fraction:
~ By 2
~ 25/84
2 questions standard algorithm division WRITE ON PAPER OR USE DIGITAL NOTEPAD
50 POINTS
lol its easy 2 questions
Answer:
Step-by-step explanation:
Which relation is also a function?
Answer:
answer is D prettyy sure
13y-5=9y+27
What is y?
Answer:
y=8
Step-by-step explanation:
Find f (g (x)) for the functions f (x) = x+2 and g (x) = x²
Answer:
f(g(x) ) = x² + 2
Step-by-step explanation:
to find f(g(x) ) substitute x = g(x) into f(x)
f(g(x) )
= f(x²)
= x² + 2
Jake, Aliya and Lucy each vegetable patch. Jake's vegetable patch has a m², of h. Aliya's vegetable patch has a m², of 3h + 7. Lucy's vegetable patch has a m², of 5h. In total, their vegetable patch an area greater than 79 Write and solve an inequality possible values of h
The most appropriate choice for Linear Inequation and area will be given by-
value of h > 8.
What is Linear Inequation and area?
Linear Inequation involves comparision between two values with the help of <, >, [tex]\leq[/tex], [tex]\geq[/tex].
Area of a 2D shape is the total space taken by that shape.
Here ,
Area of vegetable patch of Jake = [tex]h[/tex] [tex]m^{2}[/tex]
Area of vegetable patch of Aliya = ([tex]3h + 7[/tex]) [tex]m^{2}[/tex]
Area of vegetable patch of Lucy = [tex]5h[/tex] [tex]m^{2}[/tex]
Total area of vegetable patch of Jake, Aliya and Lucy
= [tex](h + 3h+7+5h)[/tex] [tex]m^{2}[/tex]
= [tex](9h+7)[/tex] [tex]m^{2}[/tex]
By the problem,
[tex]9h + 7 > 79\\9h > 79 - 7\\9h > 72\\h > \frac{72}{9}\\ h > 8[/tex]
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What is the least common multiple of 32, 48, and 16?
The least common multiple of 32, 48, and 16 is 96
How to calculate the least common multiple ?The first step is to get the prime factors of each number
The prime factors of 32 are 2, 2, 2, 2 and 2.
The prime factors of 48 are 2, 2, 2, 2 and 3
The prime factors of 16 are 2,2,2 and 2
The least common multiple of 32, 48 and 16 can be calculated as follows
2 × 2 × 2 × 2 × 2 × 3
= 32 × 3
= 96
Hence the least common multiple of 32, 48, and 16 is 96
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Which factor do 9x2 + 24x + 16 and 9x2 - 16 have in common?
O 3x-4
0 3x + 16
O 3x + 4
9x²
Answer:
3x + 4
.................
The factor 3x + 4 have common in both the given expressions.
What is common factor?A whole number that is a factor of two or more numbers is referred to as a common factor. The largest factor that will divide into two or more numbers is known as the highest common factor (HCF). The smallest multiple shared by two or more numbers is known as the lowest common multiple (LCM).
The given expressions are,
[tex]9x^2 + 24x + 16, 9x^2 - 16[/tex]
The expression [tex]9x^2 + 24x + 16[/tex] is of the form [tex](a + b)^2[/tex]
where [tex]a = 3x , b = 4[/tex]
Therefore, [tex]9x^2 + 24x + 16 = (3x + 4)^2.[/tex]
The expression [tex]9x^2 - 16[/tex] is of the form [tex]a^2 - b^2[/tex].
It can be written as, [tex]a^2 - b^2 = (a - b)(a + b)[/tex]
Here, [tex]a = 3x , b = 4[/tex]
Therefore,
[tex]9x^2 - 16 = (3x - 4)(3x + 4)[/tex]
So, in both the expressions the factor (3x + 4) is common.
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a + 1/4 = -6
Please help explain it to me I just want to understand it. I learned it today.
Answer: a = 6 and 1/4
Step-by-step explanation:
you subtract the 1/4 to the other side and theres your answer
Find the distance between each pair of points
Answer:
7.071068 ≈ 7.07
Step-by-step explanation:
The distance, d, between 2 points (x1, y1) and (x2, y2) is given by the formula
[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
The two points as determined from the graph are (1, 5) and (2, -2)
[tex]d = \sqrt {(2 - 1)^2 + (-2 - 5)^2}[/tex]
[tex]d = \sqrt {(1)^2 + (-7)^2}[/tex]
[tex]d = \sqrt {{1} + {49}}[/tex]
[tex]d = \sqrt {50}[/tex]
[tex]d = 7.071068[/tex]