Answers
We can simplify the expression by using exponent properties, and we will see that the correct option is the fourth option.
How to simplify the expression?Remember the exponent property:
[tex]\frac{a^n}{a^m} = a^{n - m}[/tex]
Here we have the expression:
[tex]\frac{83.9*10^{12}*2.87*10^{-3}}{3.76*10^2}[/tex]
We can reorder this to get:
[tex]\frac{83.9*10^{12}*2.87*10^{-3}}{3.76*10^2} = \frac{83.9*2.87}{3.76}*\frac{10^{12}*10^{-3}}{10^2}[/tex]
The right side can be simplified to:
[tex]\frac{83.9*2.87}{3.76}*\frac{10^{12}*10^{-3}}{10^2} = 64.04*10{12 - 3 - 2} = 64.04*10^{7}[/tex]
Now, we can move the decimal point one time to the left and increase the exponent by one, so we get:
[tex]6.404*10^8[/tex]
Then we conclude that the correct option is the last one (where I rounded the expression to only 3 values after the decimal point).
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Related Questions
Helppppppo points to give
Answers
a) The point (2, -7/5) is not a point on the graph?
b) The value of f(x) when x is 1 is -1/3 and the point on the graph is (1, -1/3)
c) The value of x for f(x) = 2 is 22 and the point on the graph is (22, 2)
d) The domain of x is all real values of x ≠ 10
e) The x intercept is -2
f) The y intercept is -1/5
What is a Function?Function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output and not one input for two outputs.
Analysis:
a) To test if the point (2, -7/5) is a point on the graph, we put in x = 2 into the function,
f(2) = 2+2/2-10 = 4/-8 = -1/2 ≠ -7/5. Therefore (2, -7/5) is not a point on the graph.
b) if x = 1, f(1) = 1 +2 / 1-10 = 3/-9 = - 1/3
The point on the graph is (1, -1/3)
c) if f(x) = 2, then 2 = x+2/x-10
2(x-10) = x+2
2x -20 = x+2
2x-x = 2+20
x = 22, the point on the graph is (22, 2)
d) The domain of the function is such that the denominator would not be zero.
so if x - 10 ≠ 0
Then the values of x ≠ 10 are the domain of the function.
e) The x intercept of the graph is the point at which f(x) = 0
0 = x+2/x-10
x+2 = 0
x = -2. The x-intercept is -2.
f) the y-intercept is such that x = 0
0+2/0-10 = 2/-10 = -1/5
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A bus covered a distance of 331.25 km in 25 L of diesel. Find the distance covered by the bus in 1 L of diesel . please do answer in copy
Answers
Answer:
13.25km
Step-by-step explanation:
25 Litres = 331.25km
1 Litre =
[tex] \frac{331.25}{25} \\ = 13.25km[/tex]
Answer:
13.25 km
Step-by-step explanation:
25 litres = 331.25 km
1 litre =
331.25
25
=13.25 km
What is the range of the function y=3√x+8?
-∞xy<∞
-8
0≤y<∞
2≤y<∞
Answers
The range of the function the as given in the equation is; -∞ ≤ y < ∞.
What is the range of the function?It follows from the task content that the function given is; y=3√x+8.
On this note, it follows that the range of the function is the set of all possible outputs, y values and in this case is; -∞ ≤ y < ∞.
It therefore follows that the range of the function is as indicated above as all X-values (domain) must be positive and the square root of x yields a positive or negative real number.
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Name this triangle by its sides and angles. This is a(n) ____________________ triangle. a triangle with one right angle and three non-congruent sides obtuse, isosceles obtuse, scalene right, scalene right, isosceles
Answers
Answer:
c
Step-by-step explanation:
Tyler spent 17,700 seconds completing a 1,000 piece puzzle.
How many hours is this equivalent to? Answer choices are rounded
to the nearest hour.
O 288 hours
O 20 hours
5 hours
O124 hours
Answers
Explained
I divided 17,700 by 60 seconds to get minutes
Then I divided by 60 minutes to get hours
4.916 hours rounded to 5 hours
What the 29th square number?
Answers
Answer: 841
Step-by-step explanation:
29×29=841
The ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3. If an elephant weighs 3200 pounds on Planet A, find the
elephant's weight on Planet B.
The elephant's weight on Planet B is….. lb.
Answers
A ratio shows us the number of times a number contains another number. The elephant's weight on Planet B is 96 pounds.
What is a Ratio?A ratio shows us the number of times a number contains another number.
The ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3.
Weight on Planet A/ Weight on planet B = 100 / 3
Now, the weight of the elephant on planet A to Planet B will be,
elephant's weight on Planet A/elephant's weight on Planet B = 100 / 3
elephant's weight on Planet B = (3 ×3200)/100
elephant's weight on Planet B = 96 pounds
Hence, the elephant's weight on Planet B is 96 pounds.
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Which of the following could be the ratio between the lengths of the two legs of a 30-60-90 triangle?
Check all that apply.
Answers
Answer:c
options A and B
Step-by-step explanation:
the ratio between the lengths of the two legs of a 30-60-90 triangle
General ration of 30-6- 90 degrees triangle is
x : xsqrt(3) : 2x
When x=1 the ratio becomes 1 : 1 sqrt(3)
when x= 2sqrt(3) the ratio becomes
It becomes
Two sides of 30-60-90 triangle cannot be equal
so option c and option D are not possible
sqrt(2) is also not possible because we have sqrt(3) in general ratio
PLS MARK ME AS BRAINLIEST.
Which of the following equations has the solution x = all real numbers?
O 4(3-x) + 7x = 4x + 12 + 2x
O 4(4-x) + 6x = x + 16 - 4x
O 3(4-x) + 6x = 4x + 12 - x
O 4(3-c) + 6x = 3x + 8x
Answers
Answer: 3(4-x) + 6x = 4x + 12 - x
Step-by-step explanation:
For the solution to be all real numbers, the left hand has to be identical to the right hand side.
1) [tex]4(3-x)+7x=12-4x+7x=12+3x[/tex], so wrong.
2) [tex]4(4-x)+6x=16-4x+6x=16+2x[/tex], so wrong.
3) [tex]3(4-x)+6x=12-3x+6x=12+3x=4x+12-x[/tex], so correct.
4) Wrong variable, so eliminate immediately.
Please help!!! Suppose we have two functions...
Answers
Answer:
4
Step-by-step explanation:
To find f(-1)g(-1) which is f(-1)*g(-1), first, we must find what are values of f(-1) and g(-1) first which can be found by substituting x = -1 in both functions.
[tex]\displaystyle{f(-1)=(-1)^2+1}\\\\\displaystyle{f(-1)=1+1 = 2}[/tex]
Now we know that f(-1) is 2, next, we find g(-1).
[tex]\displaystyle{g(-1) = 3(-1)+5}\\\\\displaystyle{g(-1)=-3+5 = 2}[/tex]
Now we know that g(-1) is 2 too. Since the question wants to find f(-1)g(-1), therefore 2*2 = 4.
Hence, the answer is 4.
Answer:
D) 4
Step-by-step explanation:
Given functions:
f(x) = x² + 1
g(x) = 3x + 5
Here, we're asked to find the value of both functions when the value of x is -1. Then, we multiply the functions in order to find the value of f(-1)•g(-1).
Note: f(-1) • g(-1) is equivalent to (f • g)(-1).
Method 1: f(-1) • g(-1)
Find the value of each function when x = -1.
f(-1) = (-1)² + 1 ⇒ f(-1) = 1 + 1 ⇒ f(-1) = 2
g(-1) = 3(-1) + 5 ⇒ g(-1) = -3 + 5 ⇒ g(-1) = 2
Multiply the functions together.
f(-1) • g(-1) ⇒ 2 • 2 ⇒ 4
Method 2: (f • g)(-1)
First, multiply the functions.
⇒ (x² + 1) • (3x + 5) [ Simplify using the Distributive Property: (a + b) • (c + d) = ac + ad + bc + bd. ]
⇒ x²(3x) + x²(5) + 1(3x) + 1(5)
⇒ 3x³ + 5x² + 3x + 5
Now, substitute -1 as the value of x.
⇒ 3(-1)³ + 5(-1)² + 3(-1) + 5 [ Exponents first. }
⇒ 3(-1) + 5(1) -3 + 5 [ Multiply the numbers. ]
⇒ -3 + 5 - 3 + 5 [ Simplify. ]
⇒ 4
Therefore, the product of both functions when x = -1 is 4.
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One jar filled with honey weighs 120 grams and one empty jar with half filled honey jar weighs 150 grams what is the weight of the jar
Answers
Answer:
90 grams
Step-by-step explanation
Full = 120
half filled + empty = 150
half of 120 = 60
Therefore, a jar weighs 150 - 60
= 90 grams
Use the demoivres theorem
Answers
By de Moivre's theorem,
[tex]\left(\cos\left(\dfrac\pi6\right) + i \sin\left(\dfrac\pi6\right)\right)^{18} = \cos\left(\dfrac{18\pi}6\right) + i \sin\left(\dfrac{18\pi}6\right) \\\\ ~~~~~~~~ = \cos(3\pi) + i \sin(3\pi) = \boxed{-1}[/tex]
The value of the given complex number is -1
De'moivres theorem
Given the polar form of a complex number expressed as:
[tex](cos\theta + isin\theta)^n\\[/tex]
This can also be expressed according to the de moivre's theorem as;
[tex]=(cos\theta + isin\theta)^n\\\\=(cosn\theta+isinn\theta)[/tex]
Given the expression below;
[tex](cos\frac{\pi}{6} + isin\frac{\pi}{6} )^{18}\\(cos18\cdot\frac{\pi}{6} + isin18\cdot\frac{\pi}{6} )\\(cos3\pi + isin3\pi)\\=-1[/tex]
Hence the value of the given complex number is -1
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Pls Help! Geometry
How much will the molding cost?
Answers
Answer: $412.50
Step-by-step explanation:
The area of the square formed by combining the painting and the molding is [tex](25)(28)=700[/tex] square inches.
The area of the painting itself is [tex](22)(25)=550[/tex] square inches.
Therefore, the area of the molding is [tex]700-550=150[/tex] square inches, and thus costs [tex](150)(2.75)=\$412.50[/tex]
What is this expression in simplified form?
Answers
Answer:
See below
Step-by-step explanation:
= (-7)(11)(√(3*10) ) = - 77 √(30)
Compare the graph of m(x) = 0.7x² + 4 with the graph of n(x) = x².
The graph of m(x) is narrower.
Both graphs open upward.
Both have the axis of symmetry x = 1.
The vertex of m(x) is (0, 4); the vertex of n(x) is (0, 0).
The graph of m(x) is wider.
Both graphs open upward.
Both have the axis of symmetry x = 0.
The vertex of m(x) is (0, 4); the vertex of n(x) is (0, 0).
The graph of m(x) is wider.
Both graphs open downward.
Both have the axis of symmetry x = 0.
The vertex of m(x) is (0, 4); the vertex of n(x) is (0, 0).
The graph of m(x) is narrower.
Both graphs open upward.
Both have the axis of symmetry x = 1.
The vertex of m(x) is (0, 4), the vertex of n(x) is (0, 2).
Answers
Answer:
B.) The graph of m(x) is wider.
Both graphs open upward.
Both have the axis of symmetry x = 0.
The vertex of m(x) is (0, 4); the vertex of n(x) is (0, 0).
Step-by-step explanation:
When the coefficient before x² is greater than 1, the curve of the graph is narrower. When the coefficient is less than 1, the curve of the graph is wider.
When the coefficient in front of x² is positive, the graph opens upwards. When the coefficient is negative, the graph opens downwards.
The axis of symmetry is the "x" value which divides the curve into two equal sections. Their axis of symmetry are both x = 0 because their vertexes (the lowest point of the curve) are both at x = 0.
The vertex can be found by plugging x = 0 into both of the equations and then solving. The resulting value is the "y" position of the vertex.
m(0) = 0.7(0)² + 4 n(0) = (0)²
m(0) = 0 + 4 n(0) = 0
m(0) = 4
Therefore, the vertexes are m(x) = (0,4) and n(x) = (0,0).
Answer:
Step-by-step explanation:
m(x) =.7x^2 + 4
n(x) = x^2
In the graph below
green = m(x)
blue = n(x)
Answer:
Just look at the graph belowBoth graphs open upward.The vertex of m(x) is (0, 4); the vertex of n(x) is (0, 0).The graph of m(x) is wider.Find the y intercept of the line on the graph
Answers
Answer: y = -1
Step-by-step explanation:
When x = 0, y = -1
Also, you can think about it as when the graph of the line passes the y axis
PLS HELP ME 17 MIN LEFT Solve the following equation: one third plus one third equals
one third,
two sixths,
two thirds,
or three thirds.
Answers
15. Which one of the following is a geometric sequence?
O A. 0, 1, 2, 3,...
O B. 2, -3, 92, -18/4
O C. -7, 10, 23, 36, ...
O D. 8, 4, 2, 1, 1/2, ¹/4....
Answers
PLEASE ANSWER
Consider the data set displayed on the following box plot.
Which of the following statements about the data set are true? Select all that apply.
A.The interquartile range is 10.
B.There is one outlier.
C.There are no outliers.
D.The data is skewed.
E.The interquartile range is 8.
F.There are two outliers
G.The data is symmetric.
Answers
The true statements are:
The interquartile range is 10.
The data is skewed.
What are the true statements?A box plot is used to study the distribution and level of a set of scores
The end of the first whisker represents the minimum number and the end of the second whisker represents the maximum number.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile. The interquartile range is the difference between the first and third quartile.
Interquartile range = 9 - (-1) = 10
A box plot is negative skewed because the median is not at the center of the box.
An outlier would be within: (Q1 - 1.5 * IQR or Q3 + 1.5 * IQR).
- 1 - (1.5 x 10 ) = -16
9 + (1.5 x 10) = 24
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Which of the following is the best buy?
a 6 oz box of rice for $0.90
a 12 oz box of rice for $1.93
a 16 oz bag of rice for $2.42
a 9 oz box of rice $1.25
Answers
The $1.25 one for 9 Oz box of rice would be the best buy.
How to find the Unit Price?To get the best buy among the given items and prices, we need to find the unit price. Thus, the formula is;
Unit price = Price/Quantity
A) Unit Price = 0.90/6 = 0.15
B) Unit Price = 1.93/12 = 0.15083
C) Unit price = 2.42/16
Unit Price = 0.15125
D) Unit Price = 1.25/9 = 0.138
The $1.25 one for 9 Oz box of rice would be the best buy.
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Which term describes the set of all possible input values for a function? O A. Range OB. Input O C. Output OD. Domain SUBMI
Answers
Answer:
D. domain
Step-by-step explanation:
domain is set of x-values
range is set of y-values
Input is the set of x-values, so it is the domain.
Peter received a $15 tip on a meal that cost $130. What percent of the meal cost was the tip?
11.5%
21%
18.5%
14%
Answers
130x=1500
X=11.5%
Which of the following equations have complex roots?
Answers
Answer:
D
Step-by-step explanation:
Subtracting 2 from both sides and then dividing both sides by 3 gives that x² = -2/3, which indicates the roots are complex.
how much is 0.54/0.2
Answers
Answer:
2.7 is the answer!!
Step-by-step explanation:
hope this helps :)
in the x-y plane, what is the y- intercept of the graph of the equation y=6 (x-1/2) (x+3)
Answers
The y-intercept on the x-y plane is (0, -9).
How to get the y-intercept?To get the y-intercept we just need to evaluate in x = 0.
Here we have:
y = 6*(x - 1/2)*(x + 3)
Evaluating the given equation in x = 0 we get:
y = 6*(0 - 1/2)*(0 + 3) = -9
Then the y-intercept on the x-y plane is (0, -9).
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Answer:
-9
Step-by-step explanation:
7. Write a general formula to describe the variation: x varies directly with the cube of y; x = 8 when y = -8.
Answers
Answer: it should be this M=kb^3/B^2
Step-by-step explanation:
Drag each graph to the correct location on the table. The points on the graphs represent relations. Classify these relations according to whether or not they are functio 1-3 -2 -1 3. -40 2 1 -2 -3 1 2 Function -3 -2 -1 -1 -2 3 D 2 3 -3 2 101 -1 3 1240 1 24 2 10 3 Not a Function Drag each graph to the correct location on the table . The points on the graphs represent relations . Classify these relations according to whether or not they are functio 1-3 -2 -1 3. -40 2 1 -2 -3 1 2 Function -3 -2 -1 -1 -2 3 D 2 3 -3 2 101 -1 3 1240 1 24 2 10 3 Not a Function
Answers
Answer:
Function: BNot a function: A, CStep-by-step explanation:
A relation is a function if there is only one y-value for each x-value. If you can draw a vertical line on the graph that intersect more than one point, the relation is not a function. (This is the "vertical line test.")
ApplicationGraph A: there are 3 y-values associated with x=2. Not a function.
Graph B: passes the vertical line test: A function.
Graph C: there are 2 y-values at each of x=1 and x=2. Not a function.
??????????????????????????????
Answers
[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{2x-20}{3}=2x \end{gathered}$}[/tex]
Multiply both sides of the equation by 3.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 2x-20=6x \end{gathered}$}[/tex]
Subtract 6x on both sides.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 2x-20-6x=0 \end{gathered}$}[/tex]
Combine 2x and −6x to get −4x.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -4x-20=0 \end{gathered}$}[/tex]
Add 20 to both sides. Any value plus zero results in its same value.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -4x=20 \end{gathered}$}[/tex]
Divide both sides by −4.
[tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{20}{-4} \end{gathered}$}[/tex]
Divide 20 by −4 to get −5.
[tex]\large\displaystyle\text{$\begin{gathered}\sf x=-5 \ \ \to \ \ \ Answer \end{gathered}$}[/tex]
{ Pisces04 }[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation: }[/tex]
[tex]\mathbf{\dfrac{2x - 20}{3} = 2x}[/tex]
[tex]\huge\textbf{SIMPLIFY IT or DISTRIBUTE:}[/tex]
[tex]\mathbf{\dfrac{2}{3}x - \dfrac{20}{3} = 2x}[/tex]
[tex]\huge\textbf{SUBTRACT 2x to BOTH SIDES:}[/tex]
[tex]\mathbf{\dfrac{2}{3}x - \dfrac{20}{3} - 2x = 2x - 2x}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{- \dfrac{4}{3}x - \dfrac{20}{3} = 0}[/tex]
[tex]\huge\textbf{ADD }\boxed{\rm{\bf \dfrac{20}{3}}}\huge\textbf{ to BOTH SIDES:}[/tex]
[tex]\mathbf{-\dfrac{4}{3}x - \dfrac{20}{3} + \dfrac{20}{3} = 0 + \dfrac{20}{3}}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{-\dfrac{4}{3}x = \dfrac{20}{3}}[/tex]
[tex]\huge\textbf{MULTIPLY }\boxed{\rm \bf {\dfrac{3}{-4}}}\huge\textbf{ to BOTH SIDES:}[/tex]
[tex]\mathbf{\dfrac{3}{-4}\times\dfrac{-4}{3}x = \dfrac{3}{-4}\times\dfrac{20}{3}}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{x = -5}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = -5}}}\huge\chekmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
John deposits a certain amount that is compounded continuously at 8% interest. Find the number of years it takes to double the amount.
Answers
Answer:
about 8.66 years
Step-by-step explanation:
The multiplier of account value when interest is compounded continuously is ...
k = e^(rt)
where r is the annual interest rate, and t is the number of years.
SetupWe want to find t when k=2 and r=0.08. Putting these values in the formula gives ...
2 = e^(0.08t)
SolutionTaking logs of both sides, we have ...
ln(2) = 0.08t
t = ln(2)/0.08 = 0.693147/0.08 ≈ 8.66
It takes about 8.66 years to double the amount.
__
Additional comment
If the interest rate is expressed in integer numbers of percentage points (R%), then the doubling time is ...
t = 100·ln(2)/R ≈ 69.3147/R
Here, that is 69.3147/8 ≈ 8.66.
The "rule of 72" is used to estimate the doubling time for periodically compounded interest at rate R%. That rule tells you the time is t ≈ 72/R. For most interest rates and compounding frequencies in a reasonable range, this gives a time within a reasonable amount of error.
For continuously compounded interest, we have shown the doubling time in years is 69.3147/R. (The exact value of the constant is 100·ln(2).) For the purpose here, a constant of 69.3 gives an estimate accurate to 3 sf.
you have 32 tbsp of peppercorns you need 2 teaspoons to make one serving of cajun seasoning how many servings can u make
Answers
Answer:
48 servings
Step-by-step explanation:
3tsp=tbsp
32*3=96
96/2=48