[tex]\frac{2.4}{10^{4} }[/tex] is the simplest form of scientific notation.
What is notation?In mathematical notation, operations, unnamed numbers, relations, and any other mathematical objects are represented by symbols that are combined into expressions and formulae. Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, 650,000,000 can be expressed as 6.5 108 in scientific notation. A system of symbols for designating unique items. Example: In mathematics, the symbol "∞" stands for "infinity." There are many notations in mathematics.
Given Data
8.1×10^−7
3×10^−3
Dividing
[tex]\frac{8.1(10}{3(10}[/tex]⁷₃
[tex]\frac{8.1}{3}[/tex] × 10⁻⁷⁻⁽⁻³⁾
2.7 × 10⁻⁴
[tex]\frac{2.4}{10^{4} }[/tex]
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I have available 1500mg/250mL ordered is 1500mg to be given over 90 minutes. What is the pump setting?
What is the missing perfect square in this list?
81, 100, 121, ____, 169
A. 125
B. 160
C. 12
D. 144
Answer:
d 144
Step-by-step explanation:
Each number is the square starting with 10
10² = 100
11² = 121
12² = __?
13²=169
Coins are placed into a treasure chest, and each coin has a radius of 1.4 inches and a height of 0.0625 inches. If there are 230 coins inside the treasure chest, how many cubic inches of the treasure chest is taken up by the coins? Round to the nearest hundredth and approximate using π =3.14
A: 0.38 in²
B: 126.39 in³
C: 353.88 in³
D: 88.47 in³
The total volume taken by the coins is 88.47 cubic inches, so the correct option is D.
How many cubic inches are taken up by the coins?The coins are cylinders with a radius of 1.4 inches and a height of 0.0625 inches.
Remember that the volume of a cylinder is given by:
volume = (height)*pi*(radius)^2
Where pi = 3.14
Then here the volume of each coin is:
V = (0.0625 in)*3.14*(1.4 in)^2 = 0.384 in³
And there are 230 coins, so the total volume is:
V = 230*0.384 in³ = 88.47 in³
So the correct option is D.
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Answer: D: 88.47 in³
Step-by-step explanation: So what you want to do is first find the individual volume of the coins. Use the volume formula: V = πr^2h
Take 1.4 and times it by itself
1.4 x 1.4 = 1.96
Now multiply 1.96 by 0.0625
1.96 x 0.0625 = 0.1225
And times 0.1225 by pi, or in this case, 3.14
0.1225 x 3.14 = 0.38465
Now you have found the individual volume of each coin. You are trying to find how much space all of the coins take up together. The question says that there is 230 coins in total. So times 0.38465 by 230 to find how much space all the coins take up.
0.38465 x 230 = 88.4695 in³
Now round it to the nearest hundredth: 88.47 in³
That is your answer.
Also I took the same test and I picked 88.47 inches cubed and got it right.
Proof:
Have a good day :)))
Grant orders a $55 bouquet of flowers to be delivered to his sister. He pays the bill plus a 6.5% sales tax and a 15% tip on the total cost including tax. He also pays a $10 delivery fee that is charged after the tax and tip. How much change does he receive to the nearest cent, if he pays the delivery driver with a $100 bill?
The change that Grant received to the nearest cent after giving the delivery driver with a $100 bill is $ 32.6.
This is a question of percentages.
Given that:-
Price of bouquet of flowers = $ 55
Sales tax % = 6.5 %
Tip % = 15 %
Delivery fee= $10
We have to find the change that Grant received to the nearest cent after giving the delivery driver with a $100 bill.
Sales tax = (6.5/100)*55 = $3.575
$55 + $3.575 = $58.575
Tip = (15/100)*58.575 = $ 8.78625
Total money paid by Grant = 55 + 3.575 + 8.78625 = $ 67.36125 ≈ $ 67.4
Hence,
Change received by Grant = 100 - 67.4 = $ 32.6
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Need help on #3 Please help me on my hw
Factor the left hand side:
[tex]\begin{gathered} \frac{6}{6}\cdot\frac{1}{1+2x}\ne\frac{1}{1+12x} \\ \frac{1}{1+2x}\ne\frac{1}{1+12x} \\ \end{gathered}[/tex][tex]1+12x\ne1+2x[/tex]Subtract 2x from both sides:
[tex]\begin{gathered} 1+12x-2x\ne1+2x-2x \\ 1+10x\ne1 \end{gathered}[/tex]Sutract 1 from both sides:
[tex]\begin{gathered} 1+10x-1\ne1-1 \\ 10x\ne0 \end{gathered}[/tex]Divide both sides by 10:
[tex]\begin{gathered} \frac{10x}{10}\ne\frac{0}{10} \\ x\ne0 \end{gathered}[/tex]Therefore, the equation is correct for every x different from 0.
What is the correct answer
1) [tex]m\angle A=76^{\circ}[/tex] (given)
2) [tex]m\angle B=76^{\circ}[/tex] (base angles theorem)
3) [tex]m\angle BCA=28^{\circ}[/tex] (sum of angles in a triangle)
4) [tex]m\angle ECD=28^{\circ}[/tex] (vertical angles)
5) [tex]m\angle DEC=90^{\circ}[/tex] (perpendicular lines)
6) [tex]m\angle D=62^{\circ}[/tex] (sum of angles in a triangle)
Help me with question 2, thank you!
Given the function f(x):
[tex]f(x)=3x^2-5x-4[/tex]We will find the point on the given parabola where the slope of the tangent is horizontal
The horizontal line has a slope = zero
The slope of the line is the first derivative of the function
So, we will find the first derivative and equate it to zero
[tex]\begin{gathered} f^{\prime}(x)=0 \\ 3(2x)-5(1)-(0)=0 \end{gathered}[/tex]solve the equation to find (x):
[tex]\begin{gathered} 6x-5=0 \\ 6x=5 \\ x=\frac{5}{6} \end{gathered}[/tex]substitute with the value of (x) into the given function to find the y-coordinate
[tex]y=3(\frac{5}{6})^2-5(\frac{5}{6})-4=\frac{-73}{12}[/tex]So, the answer will be the point will be as follows:
[tex](x,y)=(\frac{5}{6},\frac{-73}{12})[/tex]See the following figure:
please help fast how do i what property do i need to solve this
h to the 3rd power g to the -7th power
Answer: the property needed to find this is negative exponents
Step-by-step explanation: find the reciprocal of g to the -7th power which would be 1 over g to the 7th power
Find the area of the polygon with the given vertices.
X(-1, 2), Y(-1, -3), Z(4, -3)
square units
Check the picture below.
how do you tun the area of a rectangle into its side lengths?
In order to find what factors could represent the length and the width, we need to factor the polynomial that represents the area.
To do so, first let's find the zeros a1 and a2, then we can factor as follows:
[tex]k(a-a_1)(a-a_2)[/tex]Where k is the coefficient of the quadratic term (so k = 12).
Using the quadratic formula, we have:
[tex]\begin{gathered} 12a^2+4a-5=0 \\ a_{}=\frac{-4+\sqrt[]{4^2-4\cdot12\cdot(-5)}}{2\cdot12} \\ a_1=\frac{-4+16}{24}=\frac{1}{2} \\ a_2=\frac{-4-16}{24}=-\frac{5}{6} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} 12(a-\frac{1}{2})(a+\frac{5}{6}) \\ =(2a-1)(6a+5) \end{gathered}[/tex]Therefore the factors are 2a-1 and 6a+5.
The support arm, AB, is
perpendicular to a line tangent to this curve on a roller coaster at the point of tangency B.
The equation of the tangent line to the curve at B is 3x + 2y = 28.
Find the equation of the support arm, AB.
B(4,8)
Lines perpendicular to tangents to curves, at
the point of tangency, are referred to as “normals.”
Answer:
[tex]y = \dfrac{2}{3}x + \dfrac{16}{3}}[/tex]
Step-by-step explanation:
The genera slope-intercept equation of a line is
y = mx + 8 where m is the slope and b the y-interecept
A perpendicular line will have a slope = -1/m ie the negative of reciprocal of the first line such that m x (-1/m ) = -1
The equation of the tangent line is
3x + 2y = 28.
1. Convert to slope-intercept form:
Subtract 3x from both sidesSo slope = -3/2
Reciprocal of -3/2 = -2/3
Negative of reciprocal = +2/3
Slope of a perpendicular line should be -1/3 and the resultant equation of the line(the support arm) should be:
y = (2/3)x + b
To calculate b for the complete line equation plug in the point B(4, 8) and solve for B
y = 8 when x = 4
=> 8 = (2/3)(4) + b
Switch sides: (does not change any signs)
8/3 + b = 8
Subtract 8/3 on both sides
b = 8 - 8/3
b = 24/3 - 8/3
b = 16/3
So equation of the support arm is
[tex]\boxed{y = \dfrac{2}{3}x + \dfrac{16}{3}}[/tex]
Choose the graph that represents the following set.
the whole numbers greater than 3
O
1 2 3 4 5 6 7 8 9 ...
-1 0 1 2 3 4 5 6 7
1011H
0 1 2 3 4 5 6 7 8
Answer:
option 3
It has a zero a set of whole no has 0 in it and it start after the no 3 as it says GREATER then 3.
Calculate your take-home pay (net pay) for the following situation. Gross Salary: $3,500 per month. You are paid once a month. Federal Income Tax Withholding = 20% of Gross Salary. State Income Tax Withholding = 12% of Gross Salary. Social Security Tax Withholding = 8.25% of Gross Salary. 401k Contribution = 4% of Gross Salary.
What is the amount of Federal Income Tax Withholding each month?
What is the amount of State Income Tax Withholding each month?
What is the amount of Social Security Tax Withholding each month?
What is the amount contributed to the 401k each month?
What is the net pay (take-home pay) each month?
What is the total take-home pay for a full-year?
Using proportions, the amounts are given as follows:
Federal Income Tax Withholding each month: $700.State Income Tax Withholding each month: $420.Social Security Tax Withholding each month: $288.75.Amount contributed to the 401k each month: $140.The take-home pay for the month is $1,951.25.The take-home pay for the year is $23,415.What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication or division.
One example of application is for percentage problems, as the equivalent amount can be found multiplying the equivalent decimal by the total amount.
The amount of Federal Income Tax Withholding each month is given by:
0.2 x 3500 = $700.
The amount of State Income Tax Withholding each month is given by:
0.12 x 3500 = $420.
The amount of Social Security Tax Withholding each month is given by:
0.0825 x 3500 = $288.75.
The amount contributed to the 401k each month is:
0.04 x 3500 = $140.
The take-home pay for the month is the $3,5500 subtracted by all the with holdings, hence:
3500 - (700 + 420 + 288.75 + 140) = $1,951.25.
A year has 12 months, hence the take-home pay for the year is given by:
12 x 1951.25 = $23,415.
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Use the drawing tool(s) to form the correct answers on the provided graph. F(x)=(x^4-16)(x^4+3x-18) Find the real zeros of the following function, and plot them on the graph.
The real zeros of the following function [tex]$\quad f(x)=\left(x^4-16\right)\left(x^2+3 x-18\right)$[/tex] are
2,-2,3,-6, and the graph is attached below
This is further explained below.
What are the Zeros?[tex]$\quad f(x)=\left(x^4-16\right)\left(x^2+3 x-18\right)$[/tex]
as we know the formula a^2-b^2=(a-b)(a+b)
[tex]\begin{aligned}x^4-16 &=\left[\left(x^2\right)^2-(4)^4\right]=\left(x^2-4\right)\left(x^2+4\right) \\&=\left((x)^2-(2)^2\right)\left(x^2+4\right) \\x^4-16 &=(x-2)(x+2)\left(x^2+4\right)\end{aligned}[/tex]
substituting it in equation (1) we get.
[tex]\begin{gathered}f(x)=(x-2)(x+2)\left(x^2+4\right)\left(x^2+3 x-18\right) \\\\\left(x^2+3 x-18\right)=x^2+6 x-3 x-18=x(x+6)-3(x+6) \\\\f(x)=(x-2)(x+2)(x-3)(x+6)\left(x^2+4\right) \\\\x^2+4=(x+2 i)(x-2 i)=\left[(x)^2-(2 i)^2\right] \\\\f(x)=(x-2)(x+2)(x-3)(x+6)(x+2 i)(x-2 i)\end{gathered}[/tex]
Real zuoes =2,-2,3,-6
imaginary zuroes =2 i,-2 i
In conclusion, In the question, we have to answer the real zeroes of the function f(x)
which is 2,-2,3,-6
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2. Ying sees this flyer. She decides to buy 12 of these boxes for her shoes. What total volume will these boxes occupy in her closet?
Step 1. Find the volume of just one box.
To find the volume V of one box, we multiply all of the dimensions of the box:
In this case, the volume of one box is:
[tex]V=29.5cm\times18cm\times9.5cm[/tex]The result is:
[tex]V=5,044.5cm^3[/tex]Step 2. We are told that Ying bought 12 boxes, so the total volume that the boxes occupy will be the volume of one box multiplied by 12:
[tex]12\times5,044.5cm^3=\boxed{60,534cm^3}[/tex]Answer:
[tex]\boxed{60,534cm^3}[/tex]PLSSS HELP MEEE
Classify quadrilateral RSTV. Support your answer by showing calculations.
The given quadrilateral RSTV is a kite.
What are quadrilaterals?The following characteristics apply to quadrilaterals, which are polygons.
It has four sides and four vertices surrounding four angles.A quadrilateral's interior angles add up to 360 degrees.To classify the quadrilateral calculate the length of its sides using the distance formula given as follows:
[tex]\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} }[/tex]
In the given quadrilateral RSTV,
RS = [tex]\sqrt{(2 - (-5))^{2} + (6 - 7)^{2} }[/tex] = [tex]\sqrt{50 }[/tex]
RV = [tex]\sqrt{(-4 - (-5))^{2} + (0- 7)^{2} }[/tex] = [tex]\sqrt{50}[/tex]
ST = [tex]\sqrt{(5 - 2)^{2} + (-3- 6)^{2} } = \sqrt{90}[/tex]
VT = [tex]\sqrt{(-3 - 0)^{2} + (5- (-4))^{2} } = \sqrt{90}[/tex]
The two adjacent sides of the quadrilateral are equal i.e. RS = RV and ST = VT.
A kite is a quadrilateral with two pairs of sides that are both the same length and are next to one another.
Therefore, the quadrilateral is a kite.
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If f(x) = 2x + 1 and g(x) = x 7, find (++ g)(x). h
Therefore Option B is correct
Please solve the question. I am leaving but I will refer the answer typed by you teacher tomorrow, as I am going to sleep. Bit please solve.
To rotate the figure 90 degrees clockwise about a point, every point(x,y) will rotate to (y, -x)
Step 1
[tex]\begin{gathered} Preimage\text{ of }triangle\text{ ABC} \\ A(1,3) \\ B(2,1) \\ C(1,1) \end{gathered}[/tex]Step 2
The new ordered pair of the image after rotation
[tex]\begin{gathered} \Delta A^{\prime}B^{\prime}C \\ A^{\prime}(3,-1) \\ B^{\prime}(1,-2) \\ C(1,-1) \end{gathered}[/tex]Step 3
Image of the coordinateStep
Step 4
Label of the points
Use front end rounding to round each number. Then add the rounded
numbers to get an estimated answer. Finally, find the exact answer.
35.25
197.39
+ 4.835
An estimated answer is 237.44 and the exact answer is 237.475.
The first number is 35.25.The second number is 197.39.The third number is 4.835.We need to use front end rounding to round each number and then add the rounded numbers to get an estimated answer.First, look only at the whole numbers and add the digits.35 + 197 + 4 = 236Next, look at the decimals and round them.0.25 is approximately equal to 0.2.0.39 is approximately equal to 0.4.0.835 is approximately equal to 0.84.Add the rounded decimals.0.2 + 0.4 + 0.84 = 1.44Now add the whole number part and the decimal part together.236 + 1.44 = 237.44An estimated answer is 237.44.Now we will calculate exact answer :35.25 + 197.39 + 4.835 = 237.475The exact answer is 237.475.To learn more about rounding off numbers, visit :
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Please explain step by step I do not explain this,
The value of f(1/2) for the given function f(x) = -3(4x² + 12) + 3/4(8x) - 2x is: -37. (None of the options are correct).
How to Evaluate a Function?If given a function, to evaluate the function for a given value of x, input the value of x in the equation and solve to evaluate the function.
Given the function, f(x) = -3(4x² + 12) + 3/4(8x) - 2x, to find the value of f(1/2), substitute x = 1/2 into the equation:
f(1/2) = -3(4(1/2)² + 12) + 3/4(8(1/2)) - 2(1/2)
Evaluate
f(1/2) = -3(4(1/4) + 12) + 3/4(4) - 1
f(1/2) = -3(1 + 12) + 3 - 1
f(1/2) = -3(13) + 2
f(1/2) = -39 + 2
f(1/2) = -37
The value of the function f(1/2) is: -37. (none of the given options are correct).
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Write a simplified expression for the right half of the equation that can be used to find the nth term in the sequence
Answer is;
[tex]a_n=3n[/tex][tex]\begin{gathered} \text{common difference (d) =6-3=3} \\ By\text{ formula, } \\ a_n=a+(n-1)d\text{ , where a=3} \\ a_n=3+(n-1)3 \\ a_n=3+3n-3 \\ a_n=3n \end{gathered}[/tex]f(x)=4x+6 and g(x)=1/2*f(x) What is the function rule for function g?
g(x) = _________________ x+ _____________________
g(x) is a dilation of scale factor 1/2 of f(x), and the rule is:
g(x) = 2x + 3
What is the rule for function g?
Here we have the function f(x) = 4x + 6 and the function g(x) that is defined as:
g(x) = (1/2)*f(x)
So g(x) is a vertical dilation of scale factor k = 1/2 of f(x).
Replacing f(x) in there we get:
g(x) = (1/2)*(4x + 6) = (4/2)*x + 6/2 = 2x + 3
The rule for g is:
g(x) = 2x + 3
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Members of a softball team raised $1186.50 to go to a tournament. They rented a bus
for $842.50 and budgeted $21.50 per player for meals. Write and solve an equation
which can be used to determine x, the number of players the team can bring to the
tournament.
The equation to determine the number of players the team can bring is $842.50 + $21.50y = $1,186.50
The team can bring 16 players to the tournament.
To go to a tournament, softball team members raised $1186.50 and rented a bus for $842.50, and the cost of meals of each player is $21.50.
Let y represent the number of players.
$842.50 + $21.50 × y = $1,186.50
$842.50 + $21.50 × y = $1,186.50
$842.50 + $21.50y = $1,186.50
Subtracting $842.50 from each side.
$21.50y = $1,186.50 - $842.50
$21.50y = $344
Divide both side of the equation by $21.50.
x = $344 / $21.50
x = 16 players
As a result, the team is allowed to enter 16 players into the competition.
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Hello I need help please :)
Given: The system of equations below...
[tex]\begin{gathered} y=2x-2 \\ -4x-y=26 \end{gathered}[/tex]To Determine: The value of x and y
Using substitution method, Substitute for y in the second equation
[tex]\begin{gathered} -4x-y=26 \\ -4x-(2x-2)=26 \\ -4x-2x+2=26 \\ -6x=26-2 \\ -6x=24 \\ x=\frac{24}{-6} \\ x=-4 \end{gathered}[/tex]Substitute for x in the first equation to solve for y
[tex]\begin{gathered} y=2x-2 \\ y=2(-4)-2 \\ y=-8-2 \\ y=-10 \end{gathered}[/tex]ence,
x = -4; y = -10
G
The equation for a projectile's height versus time is h(t) = -16+2 +Vot+to. A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 110 feet per second. After how many seconds does the ball attain its maximum height? Round to the nearest hundredth.
Given the equation of a projectile to be:
[tex]h(t)=-16t^2+v_0t+h_0[/tex]Initial height = 2 feet
Initial speed = 110 feet per second.
That is,
[tex]h_0=2,v_0=110\text{ f}eet\text{ per second}[/tex]Substitute the initial height and speed into the projectile equation,
[tex]h(t)=-16t^2+110t+2[/tex]The graph of the projectile is shown below:
From the graph, the time it takes the ball to attain maximum height to the nearest hundredth is 3.44 seconds
Find the scale factor from triangle A to triangle B:
From the figure of triangles, scale factor of A and B, the value of x = 3
According to the question, given that
when two triangle are same, then we easily get missing value x
From the figure, two triangle are similar in it thus,
[tex]\frac{x}{1}[/tex] = [tex]\frac{9}{3}[/tex] {property of triangles which are similar}
x = [tex]\frac{9}{3}[/tex] .
x = 3
Therefore, we get scale factor of triangle A and B, the missing value of missing x = 3.
What is a Scale Factor?Scale factor is the proportion of an original object's scale to a new one that is a representation of it but is a different size (bigger or smaller).
For example, if we have a rectangle of sides 4 cm and 6 cm, we can enlarge it by multiplying each side by a number, say 4. The new figure we get will be similar to the original figure, but all its dimensions will be twice that of the original rectangle.
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What’s the correct answer answer now for brainlist better he right
Answer:
they filter the air coming into the body
7 1
92. _ _ _
+6,39 0. ————
6,5 32
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Find the value of p in the inequality.
three fourths times p plus 8 is greater than or equal to 3
p is greater than or equal to negative twenty over three
p is less than or equal to negative twenty over three
p is greater than or equal to negative forty four over three
p is less than or equal to negative forty four over three
Value of p for given inequality of three fourths times p plus 8 is greater than or equal to 3 is p is greater than or equal to negative twenty over three.
As given in the question,
Given inequality:
Three fourths times p plus 8 is greater than or equal to 3 is written as
(3/4)p + 8 ≥ 3
Simplify inequality to get the value of p
(3p + 32)/4 ≥ 3
⇒ 3p + 32 ≥ 12
⇒ 3p ≥ 12 -32
⇒ 3p ≥ -20
⇒ p ≥ -20 /3
Therefore, value of p for given inequality of three fourths times p plus 8 is greater than or equal to 3 is p is greater than or equal to negative twenty over three.
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PLSSSS HELP Which number is not in the correct location?
We can conclude that the position of the number -7 in the provided Venn diagram is incorrect as -7 is an integer but, not a whole number.
What are whole numbers?Any positive number that does not contain a fractional or decimal component is referred to as a whole number. The numbers 0, 1, 2, 3, 4, 5, 6, and 7 are all whole numbers, for instance, as a result. -3, 2.7, or 3 12 are examples of non-whole numbers.Integers:
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers.As we can read the definitions whole numbers do not include negative numbers and integers do include negative numbers, so we can conclude that the number -7 in the given Venn diagram is not in the correct location.
Therefore, we can infer that the position of the number -7 in the provided Venn diagram is incorrect as -7 is an integer but, not a whole number.
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