Using scientific notation, the length of the hydrogen atom is given as follows:
[tex]1.9 \times 10^{-10}[/tex]
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].
The diameter of a proton is given by:
[tex]1.9 \times 10^{-15}[/tex].
The hydrogen atom has an overall length of 100,000 times the diameter of the proton, hence the length is given by:
[tex]L = 100000 \times 1.9 \times 10^{-15} = 10^5 \times 1.9 \times 10^{-15} = 1.9 \times 10^{5 - 15} = 1.9 \times 10^{-10}[/tex]
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Graph the function g.
f(x) = -2(x-4)² +4
g(x) = f(x) - 1
O
Answer:
19
Step-by-step explanation:
fx=16+4
fx=20
gx= 20-1
gx=19
19
find the measure of the exterior angle x
The measure of the exterior angle x is 90°.
We need to find the measure of the exterior angle x.
What is the exterior angle theorem formula?An exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles.
Now, x°=∠A+∠B
⇒x°=30°+60°=90°
Therefore, the measure of the exterior angle x is 90°.
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Now, he wants to wrap it with wrapping paper. If the length of the shoebox measures 10 in, the width measures 5 in, and the height measures 3 in, how much wrapping paper does he need to cover the shoebox?
The amount of wrapping paper he need to cover the shoebox is 190 square inches
Surface area of a boxThe formula for calculating the surface area of a box is expressed as:
SA = 2(lw + wh + lh)
where
l is the length
w is the width
h is the height
Given the following parameters
l = 10in
w = 5in
h =3in
Substitute
S = 2(10*5 + 5*3 + 10*3)
S = 2(50+15+30)
S = 2(95)
S = 190 square inches
Hence the amount of wrapping paper he need to cover the shoebox is 190 square inches
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(3-0/4a)-(10-0.8a). Solve for a
An equation is formed of two equal expressions. The value of 'a' in the given equation is 6.452.
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given equation can be solved for 'a' as shown below,
[tex]\dfrac{(3-0)}{4a} = (10-0.8a)\\\\\dfrac{3}{4a} = (10-0.8a)\\\\[/tex]
0.75a = 10 - 0.8a
0.75a + 0.8a = 10
1.55a = 10
a = 6.452
Hence, the value of 'a' in the given equation is 6.452.
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scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 13. use empirical rule to determine the following:
a) what percentage of people has an IQ score between 61 and 139?
b) what percentage of people has IQ score less than 87 or greater than 113?
c) what percentage of people has an IQ score greater than 113?
Using the Empirical Rule, the percentages are given as follows:
a) 99.7%.
b) 32%.
c) 16%.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.Item a:
61 and 139 is within 3 standard deviations of the mean, hence the percentage is of 99.7%.
Item b:
87 and 113 is within one standard deviation of the mean, hence 68% of the data is within this interval and 100 - 68 = 32% of the data is outside this interval.
Item c:
Considering that the normal distribution is symmetric, and item b, this percentage is of 32%/2 = 16%.
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Step 6: Patterns can provide a clear understanding of mathematical relationships. This can be seen very clearly in the form of multiplication tables. 3 x 2; 3 x 3; 3 x 4 are clearly examples of the relationship pattern found in multiplication. Provide two more examples of relationship patterns found in mathematics. Describe the pattern in each case. (NB: Do not use the multiplication tables). (8) Step 6 : Patterns can provide a clear understanding of mathematical relationships . This can be seen very clearly in the form of multiplication tables . 3 x 2 ; 3 x 3 ; 3 x 4 are clearly examples of the relationship pattern found in multiplication . Provide two more examples of relationship patterns found in mathematics . Describe the pattern in each case . ( NB : Do not use the multiplication tables ) . ( 8 )
Two more examples of relationship patterns found in mathematics are Geometric sequences and Fibonacci numbers.
What are mathematical patterns?Mathematical patterns are a sequence of repeated arrangements of numbers, shapes, colors, letters, etc.
Mathematical patterns are usually abstract.
What is a geometric sequence?A geometric sequence is a sequence of non-zero numbers. The first number is the product of multiplying a previous number by a fixed, non-zero number, called the common ratio.
A Geometric sequence may look like: 2, 4, 8, 16, 32, 64, 128, ..., where the common ratio is 2.
What is a Fibonacci sequence?
A Fibonacci number starts with a zero, followed by a one, then by another one, and then by a series of steadily increasing numbers.
The rule of the Fibonacci sequence is that each number is equal to the sum of the preceding two numbers, for example, 0, 1, 1, 2, 3, 5, 8, 13.
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Trigonometry Maths Question
80 points up for grabs!
Will mark brainliest to whoever answers
Answer:
x = 35.537677791974°
y = 63.434948822922°
Step-by-step explanation:
let x be the measure of the angle of elevation of the sun.
tan(x) = 10/14
Then
x = tan⁻¹ (10÷14) = 35.537677791974°
………………………………………………
let y be the measure of the angle of elevation of the sun
where the shadow decreases to 5m.
tan(y) = 10/5 = 2
Then
y = tan⁻¹ (2) = 63.434948822922°
Answer:
a) 35.54°
b) 63.43°
Given following:
length of pole: 10 meterits shadow: 14 meterDetermining, the shadow is adjacent side and length of the pole is the opposite side. Hence, use the tan rule. Let the angle be x.
(a)
[tex]\sf tan(x) = \dfrac{opposite}{adjacent}[/tex]
[tex]\sf tan(x) = \dfrac{10}{14}[/tex]
[tex]\sf x = tan^{-1}(\dfrac{10}{14} )[/tex]
[tex]\sf x = 35.54^{\circ \:} \quad (rounded \ to \ nearest \ hundredth )[/tex]
(b) If the shadow decreases to 5 meter.
[tex]\sf tan(x) = \dfrac{opposite}{adjacent}[/tex]
[tex]\sf tan(x) = \dfrac{10}{5}[/tex]
[tex]\sf x = tan^{-1} (\dfrac{10}{5})[/tex]
[tex]\sf x = 63.43 ^\circ \quad (rounded \ to \ nearest \ hundredth)[/tex]
A rectangle is removed from a right triangle to create the shaded region shown below. Find the area of the shaded region.
The area of the shaded region is 29.5 square yards.
The following calculations are to be done:
Area of the triangle:
Base of the triangle is
= 5 + 4
= 9 yard.
Height of the triangle = 6 + 5
Height of the triangle= 11 yards.
The area of the triangle is,
[tex]\ Area \ of \ the\ rectangle=\frac{1}{2} \times height\times base[/tex]
[tex]\ Area \ of \ the\ rectangle=\frac{1}{2}\times 9\times 11[/tex]
= 49.5 square yards.
What is the formula for the area of a triangle?Area of the rectangle:
[tex]=Length\times width[/tex]
[tex]=4\times 5[/tex]
= 20 square yards.
Now finally the shaded region should be
= 49.5 square yards - 20 square yards
= 29.5 square yard
Therefore we can conclude that the area of the shaded region is 29.5 square yards.
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I NEED THE ANWERS QUICK PLS THANK YOU
Answer:
76 sqcm.
Step-by-step explanation:
2(5 x 2) + 2(5 x 4) + 2(4 x 2) = 2(10) + 2(20) + 2(8)
= 20 + 40 + 16
= 76
A sub sandwich shop offers 22 toppings to choose from. How many ways could a person choose a 4-topping sandwich?
a)26
b)88
c)7,315
d) 175,500
pleaseee help, will mark branliest
There are 7,315 different combinations, thus, the correct option is c
How many combinations are there?
If we have a set of N elements, the number of different combinations of K elements (such that K ≤ N) of these N elements that we can make is:
[tex]C(N, K) = \frac{N!}{(N - K)!K!}[/tex]
In this case we have K = 4 and N = 22, replacing that, we get:
[tex]C(22, 4) = \frac{22!}{(22 - 4)!*4!} = \frac{22*21*20*19}{4*3*2*1} = 7,315[/tex]
So there are 7,315 different combinations, thus, the correct option is c.
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In the diagram, line I and line m are parallel lines cut by transversal n.
b
a
n
m
The measure of both the interior angles are 70 and 110 degree.
What are Parallel Lines ?Lines they never intersect with each other and the distance between them always remains same are called parallel lines.
It is given that
Line l and m are parallel lines and are intersected by a transversal ,n
Interior angles of the same side are (2x−8) degree and (3x−7) degree
Applying the property of interior angles of parallel lines
2x -8 + 3x - 7 = 180 degree
5x -15 = 180
5x = 195
x = 39 degree
Both the angles have measure of
2 * 39 - 8 = 70 degree
3 * 39 -7 = 110 degree
Therefore the measure of both the angles are 70 and 110 degree.
The complete question is
Two parallel lines l and m are cut by a transversal n . If the interior angles of the same side of n are (2x−8) degree and (3x−7) degree , find the measure of each of these angles.
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-76 * a number minus 61 is equal to -89 less than the number
Answer: -211/76
Step-by-step explanation:
to solve this word problem equation, we need to first convert the words to numbers and variables we can solve for:
we can replace "a number" for a variable such as x
this gives:
-76·x-61=x+89
now all you have to do is solve the equation and you're done!
If f(x) = x³ - 2, find f(3).
[tex]f(x) = x {}^{3} - 2 \\ f(3) = 3 {}^{3} - 2 = 27 - 2 = 25[/tex]
[tex]f(3) = 25[/tex]
evaluate (-1 - 3²) - 4³/2
Answer:
-42
Step-by-step explanation:
You have to To subtract the fractions, then find the Least common denominator (LCD) and then combine.
pls brainliest Hope this helps have a nice day :>
[tex]\boldsymbol{(-1-3^{2})-\dfrac{4^{3} }{2} }[/tex]
Calculates 3 to the power of 2 and gets 9.
[tex]\boldsymbol{-1-9-\dfrac{4^{3} }{2} }[/tex]
Subtract 9 from −1 to get −10.
[tex]\boldsymbol{-10-\dfrac{4^{3} }{2} }[/tex]
Calculates 4 to the power of 3 and gets 64.
[tex]\boldsymbol{-10-\dfrac{64}{2} }[/tex]
Divide 64 by 2 to get 32.
[tex]\bf{-10-32 }[/tex]
Subtract 32 from −10 to get −42.
[tex]\bf{-42 \ \ \to \ \ \ Answer}[/tex]
{ Pisces04 }State. Probability sampling vs. non probability sampling
Probability sampling simply illustrates a scenario where the subjects of the population have an equal opportunity.
What is probability sampling?Probability simply means the likelihood of the occurence of an event.
In this case, in probability sampling, the subjects of the population have an equal opportunity.
In non-sampling, an equal opportunity isn't given.
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there are 32 students in a class and 20 of them own at least one pet
what fraction of class own pets?
give your answer in its simplest form.
Answer:
there 32 students and 20 have pets so you take 20 over 30 divide by 2 to get 10/16 then divide by 2 to get 5/8and that is the answer
31) Alana ordered jeans ($28) and a sweater ($35) from a catalog. The sales tax is 8%. The shipping charges came
to $6.58. What was the total amount she was charged?
O a.) $74.62
Ob.) $77.62
Oc.) $75.62
Answer:
a) $74.62
Step-by-step explanation:
Cost of both clothes = 28+35 = $63
Tax = 0.08*63 = $5.04
Shipping: $6.54
Add: 63+5.04+6.58 = 74.62
What is the length of the track, in miles, around turn A? Round your answer to three decimal places.
Answer:
?
Step-by-step explanation:
Please explain-WHAT TRACKS?
Answer:
5.275
Step-by-step explanation:
Got the answer from Emma on Gauth Math
Solve: −(23a−13)+53a=−4
Answer:
a = -17/30
Step-by-step explanation:
So the first step is to distribute the negative sign, if that's a bit confusing think of the negative sign as a -1 instead of just a negative sign, and then think of distributing that negative 1 to the 23a and -13.
Original Equation:
-(23a - 13) + 53a
Distribute negative sign
-23a + 13 + 53a
Group like terms:
(-23a + 53a) + 13
Simplify
30a + 13 = -4
Subtract 13 from both sides
30a = -17
Divide both sides by 30
a = -17/30
Which equation is a function of x? x = 5 x = y squared 9 x squared = y x squared = y squared 16
The equation which is a function of x is x²=y.
Given an equation that is a function of x.
A function may be a relation between a collection of inputs and a collection of permissible outputs with the property that every input is said to precisely one output.
If we input a value of x then we get the output f(x) = y, which is the function of x.
We are given four options out of which we are to pick the one which may be a function of 'x'.
The first option is x=5 in which no term of y is included and its a constant. So, option 1 is not correct.
The second option is x=y²+9 in which y contains a power 2. So, option 2 is not correct.
The third option is x²=y in which y contains power 1. So, option 3 is correct.
The fourth option is x²=y²+16 in which y contains a power 2. So, option 3 is not correct.
Hence, the equation which is a function of x is x²=y.
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what is w? 11w= 12 please be quick with the response.
Answer:
1.090909090909091
Step-by-step explanation:
12/11 = 1.090909090909091
W = 1.090909090909091
Answer:
w = [tex]\frac{12}{11}[/tex]
Step-by-step explanation:
11w = 12 ( isolate w by dividing both sides by 11 )
w = [tex]\frac{12}{11}[/tex]
The diameter of a circle is 48 meters. What is the angle measure of an arc 17 meters long?
simplest form IXL
Renee is correct. The equations are the same when the line goes through the origin. y = mx + b is a more general form of y = mx.
If the line goes through the origin, then b = 0, so y = mx + b is y = mx + 0 or y = mx.
The equations are the same when the line goes through the origin. y = mx + b is a more general form of y = mx. Therefore, Renee is correct.
The given statement is "The equations are the same when the line goes through the origin. y = mx + b is a more general form of y = mx".
What is the origin?The point where the reference axes in a coordinate system meet. The values of coordinates are normally defined as zero.
The equation of the line is y = mx + b.
If the line goes through the origin, then b = 0, so y = mx + b is y = mx + 0 or y = mx.
The equations are the same when the line goes through the origin. y = mx + b is a more general form of y = mx. Therefore, Renee is correct.
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14. Tasha is counting votes from a school election. There were 3 candidates running for treasurer, and students either voted for 1 of those 3 or they didn't vote at all. If there are 420 students in the school and half of them voted for Marcus, one- third of them voted for Mary, and one-seventh voted for Edward, how many students did not vote? (A) 10 (B) 20 (C) 42 (D) 105
Answer:
A) 10
Step-by-step explanation:
Votes for Marcus: 420/2 = 210 votes
Votes for Mary: 420/3 = 140 votes
Votes for Edward: 420/7 = 60 votes
Total number of votes: 210+140+60 = 410 votes
people who didn't vote: 420-410 = 10 people
x f(x)
0 24
1 12
2 6
3 3
The table represents an exponential function given by:
[tex]f(x) = 24*(1/2)^x[/tex]
Is the function exponential or quadratic?Here we have the table:
x f(x)
0 24
1 12
2 6
3 3
First, notice that for each unit that x increases, the value of f(x) decreases by its half.
This is clearly an exponential equation, whose base must be equal to (1/2).
And because when x = 0, f(0) = 24, we know that the initial value of the function is 24.
Then the exponential function is:
[tex]f(x) = 24*(1/2)^x[/tex]
Such that:
[tex]f(0) = 24*(1/2)^0 = 24\\\\f(1) = 24*(1/2)^1 = 12\\\\f(2) = 24*(1/2)^2 = 24*(1/4) = 6\\\\f(3) = 24*(1/2)^3 = 24*(1/8) = 3[/tex]
Concluding, the table represents an exponential function.
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Find the equivalent fraction of 12/25 having a.n=60 and b.
The equivalent fraction of 12/25 is 24/50
How to determine the equivalent fraction?The fraction is given as:
Fraction = 12/25
Multiply the fraction by 1
Fraction = 12/25 * 1
Express 1 as 2/2
Fraction = 12/25 * 2/2
Evaluate the product
Fraction = 24/50
Hence, the equivalent fraction of 12/25 is 24/50
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Two parallel lines are cut by a transversal. What is the measure of angle 6?
[tex]\huge\boxed{\textsf{D.}\ 57^\circ}[/tex]
We know that angles 1 and 2 are supplementary angles that add up to 180 degrees.
Solve for angle 2:
[tex]\begin{aligned}\angle1+\angle2&=180^\circ\\123^\circ+\angle2&=180^\circ\\123^\circ-123^\circ+\angle2&=180^\circ-123^\circ\\\angle2&=57^\circ\end{aligned}[/tex]
We also know that angles 2 and 6 are corresponding angles, so they are equal to each other. This means that angle 6 is also 57 degrees.
For more information on this topic, search the Internet. There are many great resources on transversal lines and angles out there that expand on the few details I shared here.
Pls help
Volume round to tenth
The volume of the cone to nearest tenth is 247. 12 cm ^3
How to determine the volumeNote that the shape is a cone
Volume for a cone =
[tex]\pi \: { {r}^{2} \frac{h}{3} } [/tex]
Given that radius = 5.3cm
height = 8.4cm
Substitute into the formula, we have
Volume = 3.142 × 5.3 × 5.3 × (8.4/3)
Volume = 3. 142× 28.09 × 2.8
Volume = 247. 12 cm ^3
Thus, the volume of the cone to nearest tenth is 247. 12 cm ^3
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The two lines below are parallel. If the slope of the red line is 3, what is the
slope of the green line?
Use the following image to solve the problem
Answer:
The distance is √17.
Step-by-step explanation:
the step is provided in the image....
I hope it was helpful