15 nm converted into km gives 1·5 × [tex]10^{-11}[/tex] km.
A process involving numerous stages, multiplication or division, especially a conversion factor, can be referred to as Unit Conversion. Additionally, rounding and determining the number of significant digits may be necessary steps in the procedure.
For measuring various properties, including length, weight, capacity, and temperature, many units of conversion are employed. We can change the units of measurement in mathematics to better understand.
Unit conversions are used to represent an amount in a different unit.
We have to convert 15 nm into km.
1 nm = [tex]10^{-12}[/tex] km
15 nm = 15 × [tex]10^{-12}[/tex] km
= 1·5 × [tex]10^{-11}[/tex] km
Thus, 15 nm converted into km gives 1·5 × [tex]10^{-11}[/tex] km.
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More multiple choice math
Answer:
The System of inequalities shown is C.
the graph below shows the solution to which system of inequalities?
Answer: The correct answer is C
Step-by-step explanation: Let's find each equation without any inequalities first. We have a dotted line at y = 1, so we can already remove A and B. Now, a dotted line represents exclusivity and hence; it should not include the = sign.
The height (h) of an object after t seconds is given by the equation h=-2t²-9t+
56? In how many seconds will the object strike the ground?
Answer:
7/2 second
Step-by-step explanation:
The equation is: h= -2t²-9t+56
h = the height
We ask how many seconds the object will strike the ground. That means the h will be 0, and we have the equation!
0 = -2t^2 -9t + 56
First, we factor the equation and get
-(2t - 7) (t + 8) = 0
If any individual factor on the left side of the equation equals 0, the entire expression will be similar to 0. So we have the equations
2t - 7 = 0
t + 8 = 0
t = 7/2 and -8
Because a time can't be negative, so the answer is 7/2 second
So, the answer is in 7/2 seconds, the object will strike the ground.
.
Find the value of x in the triangle shown below.
8
3
Answer:
The answer should be 8.
Step-by-step explanation:
an2-25art 2 10) Which fraction represents 72-7-20 eXP expressed in simplest form? 2) X-5 X-4 3) x+5 4+4 4) 25 X + 20
The given fraction (x^2-25)/(x^2-x-20) expressed in simplest form is (x+5)/(x+4). (Option C)
A fraction is in simplest form if the numerator and denominator have no common factors other than 1. In order to solve the given fraction, the numerator and denominator must be factorized, and the common factor will be canceled out.
Factoring x^2 – 25 using the difference of squares formula that states that a^2 – b^2 = (a + b)(a - b)
x^2 – 25 = x^2 – 5^2 = (x + 5)(x – 5)
Factoring x^2 – x – 20,
x^2 – x – 20 = x^2 + 4x – 5x – 20 = x(x + 4) -5(x + 4) = (x + 4)(x – 5)
Hence, factor (x – 5) is there in both numerator and denominator, it is canceled out. Hence the fraction in the simplest form is:
(x + 5)(x – 5)/ (x + 4)(x – 5) = (x + 5)/(x + 4)
Note: The question is incomplete. The complete question probably is: What fraction represents(x^2-25)/(x^2-x-20) expressed in simplest form. A) 5/4 B) (x-5)/(x-4) C) (x+5)/(x+4) D)25/(x+20)
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Find two different sets of parametric equations for the rectangular equation. (Enter your answer in a list as [x = f(t), y = f(t)], [x = f(t), y = f(t)].) y = 6x - 1
The parametric equations of y = 6x -1 are [x = t, y = 6t - 1].
What are parametric equations?Parametric equations divide an equation into two or more equations, depending upon the variables in the original equation, both dependent and independent.
What does the variable t mean?In parametric equations we mostly use t as an independent variable and write all equations in terms of t.
To convert a rectangular equation in its parametric representation, the easiest way to do is to equate x with the variable t in the original equation. Now, our x is equal to t. Hence, the final answer is [x = t, y = 6t - 1].
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consider the following 3 statements about parametric equations: a. parametric equations are useful because they often describe curves in a more natural way than cartesian coordinates. b. the same curve can have several different parametric representation, thus parametric representation is not unique. c. parametric equations often describe curves that are not functions. a. only a is true. b. a and c are true. c. a and b are true. d. all three are true.
All three statement parametric equation are true so option D. all three are true is the correct option of the given statement.
What is the formula for a parametric equation?In parametric form, the x and y coordinates are defined as functions of t, which represent angles in this form: x = r cos t and y = r sin t, and so map the whole circle. These parametric equations are known as polar equations.
What are some instances when parametric equations are used?The position of a point on a Ferris wheel, for instance, can be represented graphically using parametric equations. The parametric equations can be used to model every aspect, including height above the ground, spin direction, and speed.
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a straight line passes through points (2,15) and (6,39) what is the y intercept?
Considering the expression of a line, the y intercept has a value of 3.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:
m= (y₂ - y₁)÷(x₂ - x₁)
Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, the value of the ordinate to the origin b can be obtained.
y intercept in this caseBeing (x₁, y₁)=(2,15) and (x₂, y₂)=(6,39), the slope m can be calculated as:
m= (39 - 15)÷(6 - 2)
m= 24÷ 4
m= 6
Considering point 1 and the slope m, you obtain:
15= 6×2 + b
15= 12 +b
15 - 12= b
3=b
Finally, the value of the y intercept is 3.
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40 times 3453 divided by 24=
Answer:
Step-by-step explanation:
57,555
Answer:5755
Step-by-step explanation: 40 X 3453 = 138,120
138,120 / 24 = 5755
how many different ways are there for 10 women and 6 men to stand in a line so that no two men stand next to each other? hint: first position the women and then consider possible positions for the men.
As per the combination method, the number of ways for 10 women and 6 men to stand in the line is 1,207,084,032,000
Combination method:
In statistics, combination method refers the method of selection of r items from a set of n items where the order of selection does not matter
Given,
Here we need to find how many different ways are there for 10 women and 6 men to stand in a line so that no two men stand next to each other.
Here we know that, first consider the positions of the women, then the positions of the men
Then the possible ways are there to arrange ten women in a row is
=> 10!=3628800.
For the given condition is no two men stand next to each other.
Therefore, we need to find how many ways we can arrange 6 men in the 11 possible places
=> 11P6 = 11×10×9×8×7×6 = 332640.
Therefore, the resulting number is
=> 3628800 × 332640 = 1,207,084,032,000
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help!! please and thanks!
Answer: Congruent
Step-by-step explanation:
Question 1 (Multiple Choice Worth 2 points)
(Evaluating Algebraic Expressions LC)
If w = 24, what is the value of 2w - 18?
Answer:
30
Step-by-step explanation:
2 multiplied by 24 = 48
48 - 18 = 30
The length of the base edge of a pyramid with a regular hexagon base is represented as x. The height of the pyramid is 3 times longer than the base edge. The height of the pyramid can be represented as.
The height of the pyramid can be represented ,as per the given details as 3x.
The volume is 3/2 times 3 x 3, and the hexagon base's area is six times greater than the equilateral triangle's.
A pyramid's base edge's length is equal to x units.
In other words, the pyramid's height is three times as long as its base edge.
The pyramid's height is equal to 3x
A three-dimensional structure with a polygon at its base is referred to as a pyramid. You must be familiar with The Great Pyramid of Giza, which was built using a similar framework. This structure has a distinct shape because each corner is connected to a single apex.
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Ava thinks of a number, v.
She squares her number and multiplies her result by 3.
Next, she divides this number by 4 and finally adds 9 to get an answer of
57,
Write an equation to describe this.
Answer:
Step-by-step explanation:i think she multiplyed 9x4 and got36. The next thing she did is added 3 i don’t know the rest for this
given: \overline{ac} \perp \overline{bd} ac ⊥ bd and \angle a \cong \angle c.∠a≅∠c. prove: \triangle abd \cong \triangle cbd△abd≅△cbd.
It has been proved that △ABC is congruent to △CBD (△ABC ≅ △CBD) under the SAS condition.
What is the congruency of the triangle?In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
Two triangles are said to be congruent if all the sides of a triangle are equal to all the corresponding sides of another triangle.
So, we have:
AC⊥BD and BD bisect AC
We have to prove:
△ABC ≅ △CBD
∠ADB = ∠CDB (Given: AC⊥BD)
BD = BD (Common side)
AD = CD (BD bisect AC)
So, △ABC ≅ △CBD under SAS condition.
Therefore, it has been proved that △ABC is congruent to △CBD (△ABC ≅ △CBD) under the SAS condition.
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Complete question:
Given: \overline{AC} \perp \overline{BD} AC ⊥ BD and \overline{BD} BD bisects \overline{AC}. AC. Prove \triangle ABD \cong \triangle CBD△ABD≅△CBD.
Find the domain and range.
The domain of the given function is (-∞, ∞), the rage of the function is (-∞, 1).
What is a function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The lowest to highest value of x-coordinate is the domain of the function.
The lowest to highest value of y-coordinate is the range of the function.
The highest point of the function is (2.5, 1).
The highest value of y-coordinate is 1.
Since the graph function can be expended to infinity, the lowest value of y-coordinate is -∞.
The range of the function is (-∞, 1).
Both ends of graph can be extended -∞ to ∞ for x-coordinate.
The domain of the function is (-∞, ∞).
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4. Car dealer Lisa Kovach paid 82% of a car's options totaling $3,098. She paid 85% on a base price of $15,480.
The destination charge was $890. What is the dealer's cost?
a. $13,158.00
b. $16,588.36
c. $18,020.36
d. $19.001.20
Part (c) is the correct option i.e. The total dealer's cost is $16588.36.
What is Percentage ?
Percentage, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolised as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
Given, Cost paid for car's options = 82 % $3,098 = $2540.36
Cost paid for base price = 85 % $15,480 = $13158.
Destination charge = $890
∴ The total dealer's cost will be :
= Cost paid for car's options + Cost paid for base price + Destination charge
= $2540.36 + $13158 + $890
= $16588.36.
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2. the shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days. about what percent of the products last between 9 and 15 days? about what percent of the products last between 12 and 15 days? about what percent of the products last 6 days or less? about what percent of the products last 15 or more days? 3. a line up for tickets to a local concert had an average (mean) waiting time of 20 minutes with a standard deviation of 4 minutes. what percentage of the people in line waited for more than 28 minutes? if 2000 ticket buyers were in line, how many of them would expect to wait for less than 16 minutes?
1) The percentage of the products last between 9 and 15 days is 68.26%.
2)The percent of the products last between 12 and 15 days is 34.13%.
3) The percentage of the people in line waited for more than 28 minutes 2.28%.
4) The percentage of the people wait for less than 16 minutes 15.87%
What is percent example?Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.
What is the number whose 20% is 150?
20% of 150 is 30.
1) µ = 12
sd = 3
a) P(9<X<15)=P
(\frac{9-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{15-\mu}{\sigma})
9-12\sP(\s15\s12
= P(-1 < Z < 1)
= P(Z < 1) - P(Z < -1)
= 0.8413 - 0.1587
= 0.6826
= 68.26%
b) P(12<X<15)=P
(\frac{12-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{15-\mu}{\sigma})
12 - 12\sP(\s15\s12
= P(0 < Z < 1)
= P(Z < 1) - P(Z < 0)
= 0.8413 - 0.5
= 0.3413
= 34.13%
c) P(X6) = P(frac X-mu sigma frac 6 mu sigma)
=P(Z<\frac{6-12}{3})
= P(Z < -2)
= 0.0228
= 2.28%
d) P(X>15)=P(frac X–mu–sigma>frac X–mu–sigma)
=P(Z>\frac{15-12}{3})
= P(Z > 1)
= 1 - P(Z < 1)
= 1 - 0.8413
= 0.1587
= 15.87%
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Question
.Jeff and Lauryn are long-distance runners.
Jeff's race time, based on his average pace, is represented by the equation y=9x, where x is the number of miles and y is the number of minutes.
Lauryn's average pace is represented in this graph.
If Jeff and Lauryn run a 10k (a 6.2-mile race), who will win? Why?
Select two answers: one for the winner of the race and one for the reason they won.
Responses
Lauryn's pace is 9 minutes per mile, so Jeff is slower at 10 minutes per mile.
Lauryn's pace is 9 minutes per mile, so Jeff is slower at 10 minutes per mile.
Lauryn wins.
Lauryn wins.
Lauryn's pace is 10 miles per minute, so Jeff is slower at 9 miles per minute.
Lauryn's pace is 10 miles per minute, so Jeff is slower at 9 miles per minute.
Lauryn's pace is 10 minutes per mile, so Jeff is faste
Lauryn's race time equation is y = 10x. Thus, Lauryn's pace is 10 minutes per mile, so Jeff is faster. Jeff will win.
How to determine who will win the race between Jeff and Lauryn?Given that:
Jeff's race time is represented by the equation y=9x
You will find Lauryn's race time equation in the graph:
The equation of the line is of the form y = mx
where m is the slope
m = 20-0 / 2-0 = 20/2 = 10
Thus, Lauryn's race time equation is y = 10x
For a 10k, the race time for Jeff will be:
y = 9x
y = 9×10 = 90 minutes
For a 10k, the race time for Lauryn will be:
y = 10x
y = 10×10 = 100 minutes
Therefore, Lauryn's pace is 10 minutes per mile, so Jeff is faster. Jeff wins.
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what is the equation of the function shown in the graph, given that the equation of the parent function is f(x)=(17)x?
The equation is shown in the graph as (C) g(x) = (1/7)^x - 4.
What are equations?A relationship between two terms on either side of an equal sign is described by a straightforward equation.
Additionally, addition, basic arithmetic, multiplication, and division are one or more of the four arithmetic calculations that simple equations undertake.
The system of equations can be expressed in three different ways: in point-slope form, standard form, and slope-intercept form.
So, the parent function is therefore known to be:
f(x) = (1/7)^x
Observe that the y-intercept results from evaluating this in zero:
f(0) = (1/7)^0 = 1
The graph's y-intercept is located at y = -3.
As a result, the function was translated downward by 4 units, bringing it to a point 4 units below the y-intercept of the parent function.
Thus, the graphed function is as follows:
g(x) = f(x) - 4
g(x) = (1/7)^x - 4
Therefore, the equation is shown in the graph as (C) g(x) = (1/7)^x - 4.
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Complete question:
What is the equation of the function shown in the graph, given that the equation of the parent function is f(x)=(1/7)^x ?
A. g(x)=(1/7)^x−3
B. g(x)=(1/7)^x−2
C. g(x)=(1/7)^x−4
D. g(x)=(1/7)^x+3
Solve the inequality. Graph your solution. $$ - 5.3 x > 21 |
The solution to the inequality - 5.3 + x > 21 is x > 26.3
In mathematics, inequality refers to a relation which makes a non-equal comparison between two numbers or other mathematical expressions. In other words, it is a relationship between two expressions or values that are not equal to each other. It is used generally used to compare two numbers on the number line by their size.
In order to solve the given inequality - 5.3 + x > 21, add 5.3 both sides.
- 5.3 + x + 5.3 > 21 + 5.3
x > 26.3
The solution means that the value of x is greater than 26.3. The solution is graphed on a number line.
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Write two expressions that are equivalent to -5/4x-3/4
Answer:
-10/8x-6/8
Step-by-step explanation:
Answer: -1.25x-0.75 or 1/4*(-5x-3)
Step-by-step explanation:
The first answer is converting the original expression into decimals (0.75 = 1/4). The second answer is factoring 1/4 out of the original expression (dividing each term by 1/4).
a) a research article described a simple random sample of 584 smokers who tried to quit smoking by using either a nicotine patch or e-cigarettes, fake cigarettes producing nicotine in water vapor form. after six months, 7.3% of those using e-cigarettes had stopped smoking, compared with 5.8% of those wearing the patch. to see if quitting result is significantly associated with the method used, which statistical inference procedure should we use? matched
To see if quitting result is significantly associated with the method used, which statistical inference procedure which should be used is the Chi-square test for two-way table.
A random sample of 584 smokers who attempted to quit smoking and were observed using the method they used to help themselves to achieve their goal was taken in order to determine whether there is a correlation between the percentage of people who successfully stop smoking and the method they used to do so (nicotine-patch or e-cigarettes). The percentage of subjects who successfully quit smoking after six months.
The t-test is not appropriate in this situation because the population mean is being tested by this statistic.
The percentage of participants who successfully quit smoking using either technique is the study's dependent variable.
The variable must be categorizable in order to do Chi-Square tests, and since the data can be arranged in a 2x2 table, all anticipated frequencies must be greater than 5.
The Goodness-to-Fit test seeks to determine if a population adheres to a particular theoretical model.
In this case, it's important to compare the percentage of smokers who were able to successfully stop using both methods and the percentage who were unsuccessful.
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A tile is in the shape of a rectangle.
It is 14 centimeters long and 3 centimeters wide.
What is its perimeter?
Answer: The perimeter is 34 cm
Step-by-step explanation:
14cm + 14cm = 28cm
3cm + 3cm = 6cm
28cm + 6cm = 34 cm
Answer:
34
Step-by-step explanation:
Perimeter is equal to :
Length + length + width + width
So theres two ways we can do this:
2(14) + 2(3)
OR
14 + 14 + 3 + 3
either way, solving will give us an answer of 34
Triangle ABC is dilated. The image is A'B'C'
Find the value of x.
Answer:
x = 2
Step-by-step explanation:
6 : 4 = 3 : x
x = 4 * 3 / 6
x = 4/2
x = 2
The value of x in the given figure is 2
What is dilation?Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape.
Given that, Triangle ABC is dilated into A'B'C'
We know that dilated triangles are similar
Hence, their corresponding sides are in equal ratio,
BC : B'C' = AC : A'C'
6 : 4 = 3 : x
x = 4 × 3 / 6
x = 4/2
x = 2
Hence, The value of x in the given figure is 2
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While training for a marathon, you consume at least 2200 calories a day. For one session of exercise, you consume 400 calories. How many calories do you consume for the rest of the day?
The amount of calories you consume for the rest of the day is 1800
How to determine the amount of calories you consume for the rest of the dayFrom the question, we have the following parameters that can be used in our computation:
Total amount of calories for a day = 2200 calories
Total amount of calories for one session = 400 calories
The above parameters can be represented as
Total amount of calories for one session + Total amount of calories for the end of the day = Total amount of calories for a day
Substitute the known values in the above equation, so, we have the following representation
400 + Total amount of calories for the end of the day = 2200
Evaluate the like terms
Total amount of calories for the end of the day = 2200 - 400
So, we have
Total amount of calories for the end of the day = 1800
Hence, the amount of calories is 1800
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Solve |2 +1| = 10x
{-9/2, 9/2}
{-11/2, 9/2}
{9/2, 11/2}
The solution to the equation |2 +1| = 10x is x = 3/10
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
|2 +1| = 10x
Evaluate the sum in the above equation
So, we have the following representation
|3| = 10x
Remove the absolute bracket in the above equation
So, we have the following representation
3 = 10x
Divide both sides by 10
This gives
3/10 = x
Rewrite as
x = 3/10
Hence, the solution is 3/10
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translate the description as an algebraic expression: half the difference of 2 and b
Marcus monthly salary is $1,500 plus 10% of sales. How much could Marcus earn per month with salary and 9% sales? Please explain your answer.
pls
If Marcus monthly salary is $1,500 plus 10% of sale, then he could earn 1500 + 0.09x per month with salary and 9% sales
Monthly salary of Marcus = $1500
The percentage incentives for sales = 10%
If the percentage of incentive for sales is 9 %
Consider the amount of sales is $x
Therefore the monthly salary of Marcus = Monthly salary of Marcus + (The amount of sales × 9/100)
Substitute the values in the equation
The monthly salary of Marcus = 1500 + (x×9/100)
Divide the numbers in the equation
= 1500 + (x × 0.09)
Multiply the numbers the numbers
= 1500 + 0.09x
Therefore, the monthly salary of Marcus will be 1500 + 0.09x
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Use substitution to determine which system is represented by the graph.
ty
(
20
-28 0
-20
Arc 29
20
X
The system of equations plotted on the graph are -
y = (-3/5)x + 9
y = - (1/2)x - 12
What is the system of equations?In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought
Given are two graphs as shown in the image.
The equation of line [1] can be written as -
y = {(9 - 0)/(0 - 15)}x + 9
y = (-9/15)x + 9
y = (-3/5)x + 9
The equation of line [2] can be written as -
y = {(12 - 0)/(0 + 24)}x - 12
y = - (1/2)x - 12
Therefore, the given system of equations is -
y = (-3/5)x + 9
y = - (1/2)x - 12
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