Answer: The student's estimate is off by 12%
28.007 x 10² = _____
28.007 x 10² = _2800.7_
[tex] \red{ {10}^{2} } = 100 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = \red{100} \times 28.007 \: \: multiply \: the \: numbers \\ = \green {2800.7}\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:[/tex]
that's all :)
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[tex] \: \Large \mathbb{SOLUTION:}[/tex]
[tex] \: \: \text{28.007 × 10² }[/tex]
[tex] \: \: \text{Calculate the power}[/tex]
[tex] \: \: \text{28.007 × 100 }[/tex]
[tex] \: \: \text{Calculate the product or quotient}[/tex]
[tex] \: \: \text{\underline{\underline{2800.7}}}[/tex]
A rectangle PQRS is dilated about the origin to form a new rectangle P ’Q ’R ’S ’, as shown. What is the scale factor of the dilation?
Answer:
3
Step-by-step explanation:
Point p was on -1, 2
Point p' was on -3, 6
IF you divde p' by p you get 3, so the dialation is 3.
what are the zeros of the expression (x-5)(2x+7)
The zeroes of the expression are 5 and -3.5.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The zeroes of the expression can be found by equating the factors of the given expression with 0. Therefore, the zeroes of the expression are,
x - 5 = 0
x = 5
2x + 7 = 0
2x = -7
x = -7/2
x = -3.5
Hence, the zeroes of the expression are 5 and -3.5.
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√-100=____ + _____i
Answer:
[tex]10 + 1i[/tex]
Step-by-step explanation:
[tex]i = \sqrt{-1}[/tex]
[tex]\sqrt{-100} = \sqrt{100} * \sqrt{-1}[/tex]
[tex]\sqrt{-100} = 10 + 1i[/tex]
y is less than -2 in inequality notation
Given statement 'y is less than -2 ' in inequality notation would be, y < -2
In this question we have been given a statement 'y is less than -2'
We need to write given statement in inequality notation.
We know that, an inequality is a mathematical expression where two non-equal mathematical expressions or numbers are compared.
We know that we use '<' notation for less than.
Consider given statement:
y is less than -2.
⇒ y < -2
Therefore, given statement 'y is less than -2 ' in inequality notation would be, y < -2
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Convert 5.764764764 ... to a rational expression in the form of a over b , where b ≠ 0
If x = 5.764764764…, then 1000x = 5764.764764764…, so that
1000x - x = 5764.764764764… - 5.764764764…
999x = 5759
x = 5759/999
Kara's Custom Tees experienced fixed costs of $800 and a variable cost of $3 per shirt. Write an equation that can be used to determine the total costs encountered by Kara's Custom Tees when x shirts are produced. Then, determine the total cost of producing 75 shirts.
The total cost of producing 75 shirts will be $1050.
It is given that Kara's Custom Tees experienced fixed costs of $800 and variable cost of $3 per shirt.
We have to find an equation and also the total cost of producing 75 shirts.
What is algebra ?
Algebra is the branch that deals with various symbols and the arithmetic operations such as addition , multiplication , etc.
As per the question ;
Fixed cost = $ 800
and
Variable cost per shirt = $3.
If x shirts are produced then ; then equation will be ;
= 800 + 3x
And total cost of 75 shirts will be ;
= 800 + 3 × 75
= 800 + 225
= $ 1050
Thus , the total cost of producing 75 shirts will be $1050.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Write an inequality for the graph.
The inequality for the graph is given by y > | x - 5 | + 1 .
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.
A graphical representation of an inequality in 2 dimension refers to as the region above or below the graph.
Given the graph of an inequality we write the required inequality using translation properties of a graph.
The parent function of the graph can be written as y > | x |.
the graph of y > | x | is attached below.
The following steps are used to write the inequality:
Now for the vertical shift of 1 unit of the graph we replace the y value with y-1. Therefore the new inequality becomes y-1> |x| or , y = | x | +1Now for the horizontal shift of 5 units of the graph we replace the x with x-5 , Therefore the graph becomes y > | x - 5 | + 1Hence the required inequality for the graph is given by y > | x - 5 | + 1
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A town's population is 42,975 . About 125 people move out of the town each month. Each month, 175 people on average move into town. A nearby town has a population of 45,225. It has no one moving in and an average of 175 people moving away every month. In about how many months will the populations of the towns be equal? Write an equation to model the situation. Then solve the equation and answer the question.
The number of months when they will be equal is 45 months.
How to calculate the equation?The equation for the first town will be:
= 42975 + 125x
The equation for the second town will be:
= 45225 + 175x
The number of months when the populations of the towns will be equal will be:
42975 - 125x = 45225 - 175x
- 125x + 175x = 45225 - 42975
50x = 2250
x = 2250 / 50
x = 45
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Which of the following describes a situation in which the total distance a baseball player travels is zero meters from his starting point? (5 points)
Situation (B) best describes how a baseball player travels a total distance of zero meters from his starting point, that is, the player runs 3 meters forward and then 3 meters in the opposite direction.
What is the distance?Distance is a numerical or quantifiable measurement of the distance between two objects or points. The distance can refer to a physical length or an estimate based on other criteria in physics or everyday usage (e.g. "two counties over"). Because spatial thinking is a rich source of conceptual metaphors in human thought, the term is also frequently used figuratively to mean a measurement of the amount of difference between two common pieces (such as statistical distance between probability distributions or edit distance between text strings) or a degree of detachment (as exemplified by the distance between people in a social network). The concept of a metric space is used in mathematics to formalize most such notions of distance, both physical and metaphorical.According to the options:
Options (A), (C), and (D) is wrong as there the basketball travels some sought distance from the starting point. It is only in option (B) in which the total distance of the baseball player comes to 0 as he runs 3 meters forward and then runs 3 meters in the opposite direction.Therefore, situation (B) best describes that the total distance a baseball player travels is zero meters from his starting point that is, the player runs 3 meters forward and then runs 3 meters in the opposite direction.
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The complete question is given below:
Which of the following describes a situation in which the total distance a baseball player travels is 0 meters from his starting point? (5 points)
a) The player runs 4 meters forward and then runs 3 meters in the opposite direction.
b) The player runs 3 meters forward and then runs 3 meters in the opposite direction.
c) The player runs 3 meters forward and then runs 4 meters in the opposite direction.
d) The player runs 3 meters forward and then runs 0 meters in the opposite direction.
Use the graph of
f(x) = x3
to write an equation for the function represented by each graph.
Answer:
y = - x³ - 3x² - 3x - 4
Step-by-step explanation:
!!!!!!
The function represented in the graph is -
[tex]y\ =\ -\left(x+0.9\right)^{3}-3.3[/tex]
What is a exponent? What is logarithmic function?In mathematics, if -
xⁿ = k
then -
[n] is called exponent
[x] is called base.
Logarithm is the inverse function to exponentiation. That means the logarithm of a number [x] to the base [b] is the exponent to which [b] must be raised, to produce [x]. We can write -
[tex]y = log_{e}x[/tex]
We have the function as -
f(x) = x³
Refer to the graph of the function in the modified form. The function after being translated is same as the one given in the question. The function after translation is -
[tex]y\ =\ -\left(x+0.9\right)^{3}-3.3[/tex]
Therefore, the function represented in the graph is -
[tex]y\ =\ -\left(x+0.9\right)^{3}-3.3[/tex]
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Convert the decimal below to a fraction in simplest form.
0.166
(166÷2)
______
(1000÷2) = 83/500
Jill's plant is 15 inches tall and grows 0.25 inches each week, Mox's plant is 18 inches fall and grows 0.25 inches each week. At this rate, will Jill's plan! ever be faller than Max's Explain
Can please anyone help me with this
Answer:
Step-by-step explanation:
im not sure but yea
the ratio to the number of adults to the number of chirldren at a restaraunt is 3 to 7 whats a equavielent fraction
The equivalent fraction is: 3/7 or 6/14 or 15/35
What is an equivalent fraction?Equivalent fractions are those that, despite their visual differences, reflect the same value. You will have consumed half of a cake, for instance, if you have one, divide it into two equal pieces, and then eat one of the pieces.
Given:
Ratio of number of adults to that of children = 3:7
3 : 7 = 3/7
There can be 'n' number of equivalent fractions for this fraction, such as: 3/7, 6/14, 15/35
Hence, The equivalent fraction is: 3/7, 6/14, 15/35
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an aaba form can be repeated to create a larger form; when b and a are repeated after the first aaba, it is called a
An AABA form can be repeated to create a larger form; when b and a are repeated after the first AABA, it is called a "partial reprise". The BA or ABA sections of the AABA structure are repeated in the majority of partial reprises.
What is reprise?The term "reprise" is derived from the French word "repris," which means "act of taking back." The word is also derived from the Latin word "reprendre," which means "taken up again." The term is typically used in music, but it can refer to any continuation of an action.
Various uses of reprise in musics are given below-
Music that is classical: Reprises are most prevalent in the sonata form's recapitulation section.Music for films: Characters and settings are given specific motifs by film composers. These motifs reappear throughout the film.Theatrical musicals: Repetition is used in musical theater as scenarios develop and characters reappear.Jazz: Repetition is used by jazz musicians in a head-solo-head music format. The players begin with a pre-composed segment labeled the head, then break off towards solos influenced by that head, & finish with a reprise of a initial theme.Rock and pop: Pop and rock are created on repetition, and whenever a tune, vocal hook, or entire chorus is repeated, we can call it a reprise.To know more about pop music, here
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the set of differentiable real-valued functions f on the interval .0; 3/ such that f 0 .2/ d b is a subspace of r.0;3/ if and only if b d 0.
The condition [tex]f^{\prime}(2)[/tex] = 0 to form a subspace of [tex]\mathbb{R}^{(0,3)}[/tex] is that f ∈ S is that otherwise, S wouldn't be closed under addition and thus would not be a subspace of [tex]\mathbb{R}^{(0,3)}[/tex].
What is additive identity?An identity element (like 0 in the collective of whole numbers under operation of addition) that leaves unaffected any element that it is added in a provided mathematical system.
Now, for the given question.
I'd just like to comment on the paragraph about intuition as well as the additive identity: That instinct is incorrect.
First, we could perhaps define a object that we need to confirm is a subspace of [tex]\mathbb{R}^{(0,3)}[/tex] in a more precise manner than the translation in which it is initially presented. We want to look at a set, S.
Where,
[tex]S=\left\{x, f \mid 0 < x < 3, f \in \mathbb{R}^{(0,3)} \wedge f^{\prime}(x)=0\right\}[/tex]
We are specifically tasked with having to prove the restriction just on derivative of f, which is best accomplished in the manner made reference.
The fact that S, as described above, describes a functional space explains why my initial intuition about problem is ultimately incorrect. I was hindering myself by viewing it solely as a geometric space.
As a result, I missed the fact that zero function (the additive identity in such a functional space) is indeed a natural member of S.
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The complete question is-
I'm working my way through Axler's "Linear Algebra Done Right", and I've run into a proposition that I don't understand. Namely:
The set of differentiable real-valued functions f on the interval (0, 3) such that [tex]f^{\prime}(2)[/tex] = b is a subspace of [tex]\mathbb{R}^{(0,3)}[/tex] if and only if b = 0.
My intution is that this has something to do with the fact that a subspace requires an additive identity, but that because the domain of the differentiable functions is open and exludes 0, we have to make some concessions (i.e. [tex]f^{\prime}(2)[/tex] = 0), though I'm unsure of how to work up a proof that backs this.
Why must [tex]f^{\prime}(2)[/tex] = 0 to form a subspace of [tex]\mathbb{R}^{(0,3)}[/tex]?
a medical researcher obtains a sample of adults suffering from diabetes. she randomly assigns people to a treatment group and to a placebo group. the treatment group receives a medication over a period of three months and the placebo group receives a placebo over the same time frame. at the end of three months the patients' symptoms are evaluated.
This is an example of an experimental study since the researcher chose who would get medicine and who would receive a placebo.
What is Experimental Study?a quantitative research technique that controls other pertinent variables while observing the effects of changes in the study's key variables The Impact of Product Modularity on Supplier Integration: A Multi-Objective Approach2 provides further information. In experimental research, participants are randomly divided into distinct groups (such as experimental and control groups) in order to ascertain the causal relationship between a given condition (an independent variable) and a certain outcome (dependent variable).An illustration of an experimental research on the subject would be to assign people at random to either spend 10 minutes on their page as the experimental treatment, or spend the same amount of time on other websites (control group).
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annie measured a city park and made a scale drawing. the scale of the drawing was 1 millimeter : 4 meters. the soccer field is 28 millimeters long in the drawing. how long is the actual field?
Answer:
Step-by-step explanation:
34 millimeter
whats the pattern of 1,1,11,6,6,16,11,11,21,16
The pattern is 1, 1, 11, 6, 6, 16, 11, 11, 21, 16, 16, 26.
Given,
The pattern: 1, 1, 11, 6, 6, 16, 11, 11, 21, 16.
Here,
First and second term:
1,1 = same number repeat for two times.
Third term:
11 = preceding term + 10
That is, 1 + 10 = 11: That is the third term.
As follows:
Fourth and fifth term:
6, 6 = same number repeat for two times.
Sixth term:
6 + 10 = 16
Seventh and eighth term:
11, 11 = same number repeat.
Ninth term:
11 + 10 = 21
Tenth term is given: 16
Now we have to find eleventh and twelth terms:
Tenth and eleventh should be same number repeat for two times:
16, 16
Twelth term:
16 + 10 = 26.
Now we can complete the pattern:
1, 1, 11, 6, 6, 16, 11, 11, 21, 16, 16, 26.
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Xochitl earned $94.80 at her job when she worked for 4 hours. What was her hourly
wage, in dollars per hour?
Answer: $23.70/hr
Step-by-step explanation:
x= hourly wage
4= the number of hours worked
$94.80=total earned
4x=$94.80
x=$94.80/4
x= $23.70/hr
She earned $23.70 per hour
consider a traingle of base 1 cm and height 1 cm.on the same base and on the same side, second traingle is drawn with half the previous height.if this process continues as many times as possible what will be the total area of all the traingles thus formed????
As n approaches infinity, the area of the triangle decreases until it equals 1, resulting in a triangle of area 1.
What is a geometric summation equation?Every term in a geometric sequence has a fixed relationship to the term before it. A popular representation of a geometric sequence containing the initial term a, the common ratio r, and a finite number of terms is a, a*r, a*r₂, ..., a*r(ₙ₋₁).
According to given value;
The area of first triangle =(1)*(1)*(1/2)=1/2
The area of second triangle =(1/2)*(1/2)
=(1/2)²
The area of third triangle =(1/2)²*(1/2)=(1/2)³
The area of [tex]n^{th}[/tex] triangle = (1/2)ⁿso the total area of all triangle is formed;=(1/2)+(1/2)²+(1/3)³+.......+(1/2)ⁿ
=(1)-(1/2ⁿ)
The formula of geometric summation equation;= a₁-(1-qⁿ)/(1-q)
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A rectangular hotel room has a perimeter of 72 feet. Its area is 320 square feet. What are the dimensions of the room?
Answer
Step-by-step explanation:
Please help me it doesn't have to be quickly just help
Answer:
3 to the power of 3
Step-by-step explanation:
Answer:
1. 8x
2.4x^2
3.3^x
Step-by-step explanation:
I took the test
the teacher separated her class of fifty-eight students into two groups. one group has 6 more than thrice as many students as the other group. how many students are in each group?
Students in one group is 45
Students in another group is 13
teacher separated her class of fifty-eight students into two groups
Number of groups =2
one group has 6 more than thrice as many students as the other group
Let one group has x students
another group has y students
x+ y = 58 . . . . . 1
x= 6+3y
Substitute x= 6+3y in . . . 1
6+3y +y = 58
4y=52
y=13
x=6+3y=6+3(13)
= 6+39
= 45
Students in one group is 45
Students in another group is 13
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Diana usually drives at an average rate of 30 mph. If Diana drives at an average rate of x mph, how long will it take her to get to Tony's house?
Diana drives for two hours at a speed of 30 mph, covering a total distance of 60 miles to get to Tony's house.
What exactly is average speed?Average speed is described as the ratio of a body's total distance traveled to the total time required to reach its destination.The total distance covered by the element in a given time interval is the average speed. A scalar quantity is average speed. It is depicted by magnitude and lacks direction.Diana drives for two hours at a speed of 30 miles per hour.
To calculate the distance she will travel
Average speed = total distance / total time
Total time = two hours and the average speed = 30 mph
30 mph = total distance / two hours
Total distance = 30 × 2
Total distance = 60 miles
Therefore, Diana drives for 2 hours at a speed of 30 mph, so the total distance traveled is 60 miles to get to Tony's house.
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what’s the answer to this???
you have to find where it increases, decreases, and where it’s constant….
help..
HELPP PLEASE 70 POINTS
What are the values of (-2)^4 and -2^4?
8 and -8
16 and 16
-8 and -8
16 and -16
A portion of the periodic table is shown below. Which column of elements would be most likely to chemically combine with sodium in a 1:1 ratio?
Step-by-step explanation:
chlorine cl when combines with sodium na
Nacl will form so chlorine