The expression in scientific notation is given as follows:
3.5 x 10³.
What is scientific notation?A number in scientific notation is given by:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex].
For this problem, the expression is given by:
[tex]\frac{5 \times 10^2 \times 4.2 \times 10^4}{6 \times 10^3}[/tex]
When two factors of a multiplication have the same base and different exponent, we keep the base and add the exponents, hence:
[tex]10^2 \times 10^4 = 10^6[/tex]
5 x 4.2 = 21, hence the expression is:
[tex]\frac{5 \times 10^2 \times 4.2 \times 10^4}{6 \times 10^3} = \frac{21 \times 10^6}{6 \times 10^3}[/tex]
When we divide two terms with the same base and different exponents, we keep the base and subtract the exponents, hence:
[tex]\frac{21 \times 10^6}{6 \times 10^3} = 3.5 \times 10^3[/tex]
Which is the simplified expression.
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HELP!!! what is the quadratic formula????
The distance from arias home to the science museum is 0.72 mile which fraction is equivalent to this distance in miles.
The fraction which is equivalent to this distance in 0.72 mile of science museum from Arias home is 18/25.
What is described as a fraction?Fractions are defined as a numerical value that represents a portion of a whole.
A fraction is a portion or section of any quantity taken from the whole, which can be any number, a constant set, or a thing.Every fraction has a numerator or a denominator divided by a horizontal bar recognized as the fractional bar.The denominator represents the number of parts into which the whole has also been subdivided. It is positioned below the fractional bar in the bottom section of the fraction.The numerator specifies how many fractional sections are depicted or selected. It is positioned above the fractional bar in the upper portion of the fraction.For the given question.
The distance from the science museum to Arias home is 0.72 mile.
As, we have to 2 significant figures on the right of the decimal.
Then, remove the decimal and divide the number by 100.
= 72/100
Now, divide the numerator and denominator by 4 , we get;
= 18/25
Therefore, the distance between the Arias home and the science museum in fraction is written as 18/25.
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Find the area of the region enclosed by the curves y = 7 sin x and y = sin(7x) , 0 < x
The area of the region enclosed by the curves y = 7sin x and y = sin(7x) , 0 < x < π is 13.7 square units.
Given the equation of the curves:
y = 7sin x and y = sin(7x)
Now, we have to find the area between the curves .
Area between y = 7sin x and y = sin(7x) ,
A = ∫[7sin(x) - sin(7x)]dx
⇒ A = [-7cos(x) + 1/7 cos(7x)]
⇒ A = [-7cos + 1/7 cos(7)] - [-7cos(0) + 1/7 cos(0)]
Since cos(π) = -1 ; cos(7) = -1 ; cos(0) = 1
⇒A = [-7(-1) + 1/7 * (-1)] - [-7 * 1 + 1/7 * 1]
⇒A = 7- 1/7 + 7 - 1/7
⇒A = 14 - 2/7
⇒A = 96/7
⇒A = 13.7 units
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Lola has 4 1 2 cups of rice. she uses 3 4 of the rice to make sushi rolls for dinner. she uses the rest of the rice to make rice pudding for dessert. how much rice does lola use for the rice pudding?
Lola used 15/4 or [tex]3 \frac{3}{4} [/tex] cups of rice for pudding.
Amount of rice Lola has = [tex]4 \frac{1}{2} [/tex] cups
Converting from mixed fraction to improper fraction
Amount of rice Lola has = (2×4 + 1)/2
Amount of rice Lola has = 9/2 cups
Now, to find the amount of rice used for rice pudding, we will simply subtract the rice left with her after being used for sushi rolls.
Amount of rice used for pudding = Amount of rice Lola has - Amount of rice used to make sushi rolls
Amount of rice used for pudding = 9/2 - 3/4
Performing subtraction to find the amount of rice used for pudding
Taking LCM we get 4
Amount of rice used for pudding = (9×2 - 3)/4
Amount of rice used for pudding = (18 - 3)/4
Amount of rice used for pudding = 15/4
In mixed fraction, the amount of rice used for pudding = [tex]3 \frac{3}{4} [/tex]
Hence, Lola used 15/4 or [tex]3 \frac{3}{4} [/tex] cups of rice for pudding.
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how many terms are in 7w +2g+3 + 8w
Answer: 4! Terms are numbers with letters, letters, or simple numbers in an equation! Hope this helps!
Answer:
4
Step-by-step explanation:
The numbers count as terms, but anything else doesn't
When drawing a line, use
_____ to show that the line continues endlessly in both directions. (Fill in the blank)
when drawing a line use arrows to show that the line continues endlessly in both directions.
Travis wrote five checks to the employees of his business, each for $225. if the original balance in his checking account was $890, what is his new balance?
Travis's checking account new balance, after wrote five checks to the employees of his business is - $235
To solve this problem, we have to state the equation using the information of the problem
Information about the problem:
Original balance= $890Check amount of each employer= $225No. of checks= 5Final balance = ?Calculating the checks total amount Travis wrote to the employees of his business:
Total amount for his employers = Check amount of each employer * No. of checks
Total amount for his employers = $225 * 5
Total amount for his employers = $1125
Calculating the final balance, we have:
Final balance = Original balance - Total amount for his employers
Final balance = $890 - $1125
Final balance = - $235
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
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Find the value of y is x = -3
y = 4x² + 2x - 9
Simplify 150\sqrt{150}
150
The required solution of the given expression is 12.247.
What is expression?An expression is a set of terms combined using the operations +, – , x or ÷. An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An expression is in simplest form when no terms can be combined.
Given:
The given expression is
[tex]\frac{150}{\sqrt{150} } \\[/tex]
Simply or simplification is reducing the expression/fraction/problem in a simpler form. A fraction is in simplest form if the top and bottom have no common factors other than 1.
The process of making something less complicated and therefore easier to do or understand, or the thing that results from this process.
According to given question we have
[tex]\frac{150}{\sqrt{150} } \\[/tex]
We know that the square root of 150 is 12.247.
By putting the value we have
150/12.247
= 12.247.
Therefore, the required solution of the given expression is 12.247.
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If the sample variance for a frequency distribution consisting of hourly wages was computed to be 10, what is the sample standard deviation?
The sample standard deviation is (B) $3.16.
What is the sample standard deviation?The sample standard deviation is defined as the root-mean-square of the differences between observations and the sample mean: A significant deviation is defined as two or more standard deviations from the mean. The lowercase Greek letter (sigma) for the population standard deviation or the Latin letter s for the sample standard deviation is most commonly used in mathematical texts and equations to represent standard deviation. For example, if the sample variance for a frequency distribution of hourly wages is 10 and the sample standard deviation is $3.16.Therefore, the sample standard deviation is (B) $3.16.
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The complete question is given below:
If the sample variance for a frequency distribution consisting of hourly wages was computed to be 10, what is the sample standard deviation?
A. $4.67
B. $3.16
C. $1.96
D. $10.00
Find the circumference
and the area of a circle with radius 9 m.
Use the value 3.14 for and do not round your answers. Be sure to include the correct units in your answers.
Answer:
56.52m is the circumference. The area is 254.34[tex]m^{2}[/tex]
Step-by-step explanation:
The equation for the circumference of a circle is c=2πr with r being the radius. So 2(3.14)(9)=56.52m. The area equation for a circle is A=π[tex]r^{2}[/tex] so it would be (3.14)(9)^2 or (3.14)(81) which equals 254.34[tex]m^{2}[/tex]
Rory has 3 pounds of ground turkey to make meatballs.He uses 3/8 pound per to make 6 meatballs. How many 1/8 pound meatballs can Rory make with the remaining turkey?
He can make 2 meat balls from the remaining turkey.
Total pounds of ground turkey available = 3 pounds.
Turkey used to make 6 meat ball = 3 / 8 of 3 pounds = 9 / 8 pounds
Turkey used to make 1 meat ball = 9 / 8 ÷ 6 = 3 / 16
1 / 8 meat = 1/ 8 of 3 = 3 / 8 pound of meat.
Number of meatballs made = 3 / 8 × 16 / 3 = 2
Therefore, he can make 2 meat balls from the remaining turkey.
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martin can read 4 pages in 7 minutes. at this rate,how long will it take him to read 9 pages
Answer:
5.14 minutes
Step-by-step explanation:
4 pages / 7 minutes = 0.57 minutes per page
0.57 minutes/pg * 9 pages = 5.14 minutes
If everyone in a class scored 100 on a quiz, what is the standard deviation of quiz scores?
The standard deviation of quiz scores is 0.
What is the standard deviation?The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values of the set tend to be close to the mean (also known as the expected value), whereas a high standard deviation indicates that the values are spread out over a larger range.To find the standard deviation:
Let, the number of students = nx = 100Mean = n×x/n=xVariance = [tex]\frac{\sum(\bar{x}-x)^2}{n}[/tex]Variance = (x₁ - x)² + (x₂ - x)² + (x₃ - x)²/nV = 0Standard variance = √0Therefore, the standard deviation of quiz scores is 0.
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help!!! 50 points!!!!
Answer:
Less than and -97
Step-by-step explanation:
Answer: -17
Step-by-step explanation:
find the value by using the systematic of expressions then exponent it then factorize it by using prime numbers
-w + 4(w + 3) = -12
Answer:
Step-by-step explanation:
-w + 4(w + 3) = -12
Expand: -w + 4w + 12 = -12
3w + 12 = -12
3w = -12-12
3w = -24
w = -8
Select from the drop-down menu to correctly identify the property shown. 3.8+(−4.8+(−6.2))=(3.8+(−4.8))+(−6.2) Choose...
The property of real numbers that was applied in the equation, 3.8+(−4.8+(−6.2))=(3.8+(−4.8))+(−6.2), is known as the: distribution property of multiplication.
What is the Distribution Property?The distribution property of multiplication is one of the properties of real numbers which states that, given that a(c + d), then we would have:
a(c) + a(d) = ac + ad.
Given the expression, 3.8+(−4.8+(−6.2)), applying the distribution property of multiplication will give us:
(3.8+(−4.8))+(−6.2).
Therefore, the property of real numbers that was applied in the equation, 3.8+(−4.8+(−6.2))=(3.8+(−4.8))+(−6.2), is known as the: distribution property of multiplication.
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Help me please
Two step equation.
1. -15 = -4m + 5
2. 10 - 6v = -104
3. 8n + 7= 31
4. -9x - 13 = -103
5 and six are on the picture
4 12 ➗ 1 12
what is the quotient?
The quotient of the fraction 4/12 ÷ 1/12 is 4.
What do we mean by fractions?A fraction is a small part of a larger whole.In arithmetic, the number is expressed as a quotient, which is the numerator divided by the denominator.In a simple fraction, both are integers.A complex fraction has a fraction in the numerator or denominator.In mathematics, there are three major types of fractions.The three types are proper fractions, improper fractions, and mixed fractions.Fractions are terms with a denominator and a numerator.So, evaluation of 4/12 ÷ 1/12:
4/12 ÷ 1/124/12 × 12/1 (Reciprocal)4/1 (12 - 12 cancel)4Therefore, the quotient of the fraction 4/12 ÷ 1/12 is 4.
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help me with this ques. (need solution and answer both) thanks so much <3
Answer:
1.) 27a^11 + 18a^9 -72a^7
2.) 6p^4q^3 - 10p^3q + 4p^2q3
Step-by-step explanation:
1.) Distribute and do the math
-9a^5 x (-3a^6) - 9a^5 X (-2a^4) - 9a^5 x 8a^2
27a^11 + 18a^9 -72a^7
2.) Distribute and do the math
2pq^2q x 3p^2q^2 - sp^2q x 5p + 2p^2q x 2q^2
6p^4q^3 - 10p^3q + 4p^2q3
A "size 7" shoe is about 1.4 x 10-¹ meters long. The circumference of the earth is about meters 1.06 x 10^7 around the equator. How many shoes, end-to-end, would it take to wrap around the equator? Show how you expanded and used the Giant One.
Number of shoes needed to wrap around the equator = 7.57 x10⁷
The length of a size 7 shoe = 1.4 x 10-¹ m
The circumference of the Earth around the equator = 1.06 x 10^7 m
We know that here, the circumference around the equator will be equal to the number of shoes times the length of each shoe.
So to find the number of shoes, we should divide the circumference of the Earth by the length of one shoe.
Hence, number of shoes end-to-end needed to wrap around the equator = 1.06 x 10⁷ / 1.4 x 10-¹
= 7.57 x10⁷
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Describe all numbers x x that are at a distance of 6 6 from the number 12 12. express this using absolute value notation.
The absolute value notation will be |x - 12| = 6
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
The absolute function is given as
f(x) = | x |
All numbers x is at a distance of 6 from the number 12. Then the equation will be
|x - 12| = 6
Simplify the equation, then we have
For x ≥ 0, then the value of x will be
x - 12 = 6
x = 18
For x < 0, then the value of x will be
- x + 12 = 6
x = 6
The absolute value notation will be |x - 12| = 6
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I need help! Ignore the stuff on top and bottom
Answer:
Starting from the left, the points are plotted as:
-4.5, -√16,-4, √1, 80/25, 7/2.
*PLS HELP*
Chris buys p pairs of pants and 4 more shirts than pairs of pants. Shirts cost $13 each and pairs of pants
cost $27 each. What does each term in the expression 27p + 13(p+4) represent? What does the entire
expression represent?
The term 27p represents the (select)
The term 13(p+4) represents the (select)
The expression 27p +13(p+4) represents the (select)
Answer:
The term 27p represents the total cost in dollars of pants
The term 13(p+4) represents the total cost in dollars of shirts
The expression 27p+13(p+4) represents the overall cost in dollars of the shirts and pants Christ buys
Step-by-step explanation:
Disclaimer: if the owner can include the options, I can give a better answer.
We know each pair of pants is $27. Since each pair of pants costs $27, we can say the total cost in dollars of pants is equal to 27*P. For each pair of pants Chris buys, he buys 4 shirts. P+4 is the total number of shirts Chris will buy. The price of these shirts in dollars is $13. So we can assume the total cost in dollars of shirts will be 13(P+4). The total expression is the total amount in dollars Chris spends.
Find the square root.
√16
√16 = ?
Mia uses the formula πr2 to find the area of a circle. What is πr2 an example of?.
πr2 is an example of a (D) model.
What exactly is a model?A mathematical model is a system description that makes use of mathematical concepts and language.The process of developing a mathematical model is known as mathematical modeling.Natural sciences (physics, biology, earth science, chemistry), engineering disciplines (computer science, electrical engineering), and non-physical structures such as the social sciences all use mathematical models (such as economics, psychology, sociology, and political science).The use of statistical equations to solve problems in business or military operations is a large part of the field of operations research.Mathematical models are used in music, linguistics, and philosophy (for example, intensively in analytic philosophy).A model is, for example, the πr2 method for calculating the area of a circle.
Therefore, πr2 is an example of a (D) model.
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The complete question is given below:
Mia uses the formula πr2 to find the area of a circle. What is πr2 an example of?
A. a robot
B. a car
C. a telescope
D. a model
What is the product of (−3)(18) • (−5)?
Answer:
The product of (-3)(18) * (-5) is 270.
Step-by-step explanation:
(-3)(18) * (-5)
Multiply -3 and 18.
(-54) * (-5)
Multiply -54 and -5. When multiplying 2 negative numbers, the result will become positive.
270.
Answer:
270
Step-by-step explanation:
BODMAS
Brackets, Order, Division, Multiplication, Addition, Subtraction.
(-3)(18) is basically (-3) • (18)
No more expressions within brackets so we go by order from left to right of the equation.
(-3) • (18) = (-54)
(-54) • (-5) = 270
Hope this helps! ^^
Which values are in the range of the function f(x) = -2x + 4 with a domain of (-6,0,6)
The range of the function is x∈[(-8 ,16)]
It is required to find the range.
What is function?A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
Given:
Since f(x) = -2x + 4 is linear, its limit values correspond to the limits imposed by the domain (in this case x∈[(-6 ,6)]
By put the value of x in the given function we get,
f(-6) = -2(-6) + 4
=12+4
=16
f(6) = -2*6 + 4
=-12+4
=-8
So the range is -8<x<16.
Therefore, the range of the function is x∈[(-8 ,16)]
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please help with 7, 9 and 11!! i am stuck on problems
7) (x, TU, TB) = (4, 8, 13)
9) (x, RS, MN) = (8, 41, 41)
11) (AB, BC, AC) = (42, 42, 84)
What are the values of the variable x and the lengths of the line segments?
In this question we have three cases of colinear line segments, each of them can be solved by using definitions from Euclidean geometry and algebraic handling:
Case 7 - TU = 2 · x, UB = 3 · x + 1, TB = 21
TB = TU + UB
21 = 2 · x + 3 · x + 1
21 = 5 · x + 1
5 · x = 20
x = 4
Then, the lengths of each line segment are:
TB = 21
TU = 2 · 4
TU = 8
UB = 3 · 4 + 1
UB = 13
The solutions are (x, TU, TB) = (4, 8, 13).
Case 9 - RS = 3 · x + 17, MN = 7 · x - 15
RS = MN
3 · x + 17 = 7 · x - 15
4 · x = 32
x = 8
And the lengths of each line segment are:
RS = MN = 41
The solutions are (x, RS, MN) = (8, 41, 41).
Case 11 - AB = 2 · x - 8, BC = x + 17
AB + BC = AC
AB = BC
2 · x - 8 = x + 17
x = 25
And the lengths of each line segment are:
AB = 2 · 25 - 8
AB = 42
BC = AB
BC = 42
AC = 42 + 42
AC = 84
The solutions are (AB, BC, AC) = (42, 42, 84).
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five more than the product of two and a number,
decreased by seven;
evaluate when a = 8
Key Words
five
more than
product
two
a number
decreased by
seven
Replace With
5
+
x
2
a
7
Write and evaluate the expression. Then, complete the
statements.
First, write the expression
Second,
Third,
The answer is
8 in for the variable, a.
by using