Based on the fact that Gordon has 1/2 gallons of paint and is able to fill up bowls in 7 tables, the number of gallons of paint each table has is 1/14 gallons of paint
How to find the number of gallons?Gordon has 1/2 gallons of paint and knows that this amount of paint can given each bowl in all 7 tables, a full bowl of paint.
The amount of paint that each bowl gets can therefore be calculated by the formula:
= Gallons of paint Gordon has / Number of tables
Solving for the paint each bowl has gives:
= 1/2 ÷ 7
= 1/2 x 1/7
= 1/14 gallons of paint
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Three times a number decreased by five ikbetween 41 and 58. Enter your answer in interval notation.Interval notation of valid valuesO No interval of valid values
Answer:
(-12, 21)
Explanation:
3 times a number decreased by 5 means 3x -5.
This number is between -41 and 58; therefore,
[tex]-41<3x-5<58[/tex]Now we solve for the unknown number x.
Adding 5 to the three sides gives
[tex]\begin{gathered} -41+5<3x-5<58+5 \\ -36<3x<63 \end{gathered}[/tex]finally, dividing the inequality by 3 gives
[tex]-12which in interval notation we write as [tex](-12,21)[/tex]the parenthesis indicates that the -12 and 21 are not included in the solution interval =.
1. The amount of time 26 students spend on their phones on a given day (rounded to the nearest
hour) is recorded as follows.
0, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 12
Create a dot plot of the information. *Be sure to label all necessary parts!
The amount of time 26 students spend on their phones represent by a dot plot:
take the smallest and highest data from the given record. i.e., 0 and 12.As the data given is: 0(1 time), 3(1 time), 4,4(2 times), 5,5(2 times), 6,6,6(3 times), 7,7,7,7(4 times), 8,8,8,8(4 times), 9,9,9(3 times), 10,10,10(3 times), 11,11(2 times) and 12(1 time) occurrence.divide the whole line between 0 to 12 representing the number of hours spent.start dotting out points with their respective data with the number of times one above another( if data is more than one)To learn more about dot plots, follow the below link:
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Answer:
See attachment.
Step-by-step explanation:
A Dot Plot is a graphical display of quantitative data consisting of dots plotted on a simple scale.
If a value occurs more than once, the dots are placed one above the other so that the height of the column of dots represents the frequency for that value.
Given data set:
{0, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 12}
Step 1Label the increments on the given line to include the range of data.
Label them -2 to 16 increasing in 1 unit.
Step 2Label the dot plot with a suitable title describing what the dot plot represents.
Place "Time students spent on their phones on one given day (nearest hour)" under the line.
Step 3Count the number of data points for each discrete category:
[tex]\begin{array}{|c|c|}\cline{1-2} \sf Category & \sf Frequency\\\cline{1-2} 0 & 1\\\cline{1-2} 3 & 1\\\cline{1-2} 4 & 2\\\cline{1-2} 5 & 2\\\cline{1-2} 6 & 3\\\cline{1-2} 7 & 4 \\\cline{1-2} 8 & 4 \\\cline{1-2} 9 & 3\\\cline{1-2} 10 & 3\\\cline{1-2} 11 & 2\\\cline{1-2}12 & 1\\\cline{1-2}\end{array}[/tex]
Draw a stack of dots that number high for each category.
(See attachment).
Let A = (3, 4) and B = (-2, -2). Find the coordinates of Q along the directed line segment AB so that the ratio of AQ to QB is 5 to 3.
The coordinates along the directed line segment is (-1/8, 1/4)
How to find the coordinates of the point along the directed line segment?The points are given as:
A = (3, 4)
B = (-2, -2)
The ratio on the segment can be represented as;
m : n = 5 : 3
So, we have the coordinates of the point Q that lies along the directed line segment to be
Q = 1/(m + n) * (mx2 + nx1, my2 + ny1)
So, we have:
Q = 1/(5 + 3) * (5 * -2 + 3 * 3, 5 * -2 + 3 * 4)
Evaluate
Q = (-1/8, 1/4)
Hence, the coordinates of the point Q is (-1/8, 1/4)
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What is the answer do this please
Answer:
r = 5%
Step-by-step explanation:
Formula : I=PRT
GIVEN:
I = 125
P = 5000
R = R
T = 6
125= (5000)(R)(0.5)
125=2500R
0.05=R
Interest rate = 0.05(100)
= 5%
Question 9
Write an equation to represent each relationship. Then solve the equation.
variable.
Fifteen more than twice the hours Carla worked last week is the same as three times the hours she worked this week decreased by 15. She worked the same number of hours each week. Howany hours did she work each week?
Answer:
x = 30
Step-by-step explanation:
2x + 15 = 3x - 15
--------------------------
2x + 15 = 3x - 15
-3x -3x
----------------------
-x + 15 = -15
-15 -15
-------------------
-x = -30
÷-1 ÷-1
----------------
x = 30
I hope this helps!
What is the slope in pages per hour? Number of Hours 2 4 6 8 Pages Completed 3 6 9 12
could you answer my question? thanks
a = 252, x = 7; y = 5925.13
Equation is given by the formula:
[tex]y\text{ = y}_0\cdot(1+r)^{^x}{}[/tex]where:
yo = the initial population; r = growth rate, x = time
In your case, yo = 252. And the grow rate is 57%, therefore the r = 0.57. Finally, the exponential equation has this form:
[tex]y\text{ = 252}\cdot1.57^x[/tex]Then, if we want to know what is the population after 7 days, we can evaluate this function:
[tex]y\text{ \lparen7\rparen = 252}\cdot1.57^7\text{ =5925.13}[/tex]solve inequality 10x+5 > 25
Solve the inequality for x.
[tex]\begin{gathered} 10x+5>25 \\ 10x+5-5>25-5 \\ 10x>20 \\ \frac{10x}{10}>\frac{20}{10} \\ x>2 \end{gathered}[/tex]Answer:
x > 2
Step-by-step explanation:
10x+5 > 25
Solve
Subtract 5 from each side
10x+5-5 > 25-5
10x > 20
Divide each side by 10
10x/10 > 20/10
x > 2
A jet engine close up produces sound at 152 decibels. What is the decibel reading of a pair of nearby jet engines? (Round your answer to the nearest decibel.)
If a jet engine close up produces sound at 152 decibels then the decibel reading of a pair of nearby jet engines is 168.62 decibel
A jet engine close up produces sound at 152 decibels
The the relative intensity of one jet engine = [tex]126^{152}[/tex]
The relative intensity of a pair of jet engines = 2× [tex]126^{152}[/tex]
The reading of a pair of nearby jet engine in decibel = 10log(The relative intensity of a pair of jet engines)
Substitute the values in equation
The reading of a pair of nearby jet engine in decibel = 10×log(2× [tex]126^{152}[/tex])
= 168.62 decibel
Hence, if a jet engine close up produces sound at 152 decibels then the decibel reading of a pair of nearby jet engines is 168.62 decibel
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Graph the image of the given triangle, reflected across the y-axis. Select the Polygon tool. Then, click the points of the triangle vertices to create the triangle by connecting the sides.
The image of the transformation are (2, -9), (-9, -7), (-7, -4)
How to perform the transformation?The coordinates of the triangle are given as
(-2, -9), (9, -7), (7, -4)
The transformation is given as
Reflection across the y-axis
This is represented as
(x, y) ⇒ (-x, y)
This means that the transformation is (-x, y)
When this rule is applied on the coordinates, we have
(2, -9), (-9, -7), (-7, -4)
Next, we plot the image of the transformation on a coordinate plane
See attachment for the image of the transformation
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When the plumber comes to my house to fix the leaky faucet, he charges a flat rate of $50 in addition to charging $22 per hour. If the final bill was $116, how long was the plumber at my house?
question in screenshot
The vertical and horizontal asymptotes for the graphed function are given as follows:
a) The vertical asymptotes are given at x = -1 and x = 2.
b) The horizontal asymptote is given at y = -1.
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator, and in the graph, they are represented by vertical dashed lines.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity, and in the graph, they are represented by horizontal dashed lines.In the context of this problem, we have that the asymptotes can be extracted from the graph as follows:
In item a, there are two vertical dashed lines, at x = -1 and x = 2, hence those are the vertical asymptotes of the graphed function.In item b, there is one horizontal dashed line, at y = -1, hence this is the horizontal asymptote of the graphed function.More can be learned about asymptotes at https://brainly.com/question/4138300
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Can someone explain this ???
The intersection point of the circle and the line is at-(2.68, 7.36).
What is defined as the equation of circle?A circle is a confined curve drawn from a fixed point known as the centre, with all points on the curve sharing the same distance as from centre point. (x-h)² + (y-k)² = r² is the equation for a circle with (h, k) centre and r radius.For the given question;
The equation of the line is; y = 2x + 2 ......eq 1
The centre of the circle (h,k) = (0,2)
The radius of the circle = 6 units.
This is the equation's standard form.
(x - h)² + (y - k)² = r²
Put the values in the formula;
(x - 0)² + (y - 2)² = r²
(x)² + (y - 2)² = r²
Put the value of y from eq 1.
(x)² + (2x + 2 - 2)² = 6²
(x)² + (2x)² = 36
Simplifying;
x = ±6/√5
But the intersection must be in first quadrant.
x = 6/√5 = 2.68
Put the value of x in eq 1.
y = 2x + 2
y = 2×2.68 + 2
y = 7.36
Thus, the coordinates of the intersection of the line and the circle are (2.68, 7.36).
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Suppose that there is a negative correlation between the variables k and l. If l is 150 when k is 7, which of these is most likely to be the value of l when k is 14.A. 300B. 150C. 75D. 225
Answer:Explanation:
C. 75
n cthe oomparison of variables, a negative correlation means that as the value of one of the variables increases, the value of the other variable decreases.
Given the variables k and l.
• L=150 when k = 7
,• L=? when k=14
The variable k has increased.
Thus, to satisfy the condition for a negative correlation, the variable, l must decrease.
Thus, the only likely possible value of l is 75.
Option C is correct.
6. This number is the same as sixty-eight and 830 thousandths.
The most appropriate choice for decimal will be given by-
The number is 68.830
What is decimal?
The type of numbers which has a whole number part and a fractional part and the whole number part is seperated from the fractional part by a decimal point is known as decimal.
Decimal can be terminating as well as non terminating
Terminating decimal numbers are those numbers which has finite number of figures after the decimal point.
Non terminating decimal numbers are those numbers which has infinite number of figures after decimal points.
Here,
The required number is the same as sixty-eight and 830 thousandths.
So, the number is 68.830
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name the property of a(b+(-b))=(b+(-b))a
The property of a(b+(-b))=(b+(-b))a is called as Commutative Property of Multiplication.
The Commutative Property in mathematics is a rule that allows interchange the order of terms or factors without any change in the end result.
In multiplication, we can interchange the factors without affecting the end result of multiplication. For example, 2 x 3 = 3 x 2 = 6
In addition, we can interchange the terms without affecting the summation result. For example, 2+3 = 3+2 = 5
But Commutative Property does not apply to subtraction or division.
For example, 2-3 != 3-2
or, 2/3 != 3/2
Hence the answer to the question is Commutative Property of Multiplication.
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From sin²x + cos²x = 1, prove other two identities
Answer:
[tex]{ \tt{ { \sin}^{2} x + \cos {}^{2}x = 1 }}[/tex]
- Divide through by cos²x ;
[tex]{ \tt{ \frac{ { \sin }^{2}x }{ \cos {}^{2} x} + \frac{ \cos {}^{2} x }{ { \cos }^{2} x} = \frac{1}{ { \cos }^{2}x } }} \\ \\ { \boxed{ \tt{ { \tan}^{2} x + 1 = { \sec }^{2} x}}}[/tex]
- Divide tgrough by sin²x;
[tex]{ \tt{ \frac{ { \sin }^{2}x }{ { \sin}^{2}x } + \frac{ \cos { }^{2}x }{ { \sin}^{2}x } = \frac{1}{ { \sin}^{2} x} }} \\ \\ { \boxed{ \tt{1 + { \cot }^{2}x = \csc {}^{2} x}}}[/tex]
Answer:
See below for proof.
Step-by-step explanation:
Given trigonometric identity:
[tex]\large\boxed{\sin^2x+\cos^2x =1}[/tex]
To prove the identity 1 + cot²x = cosec²x :
[tex]\boxed{\begin{aligned}\sin^2x+\cos^2x &=1\\\textsf{Divide by $\sin^2x$}\implies \dfrac{\sin^2x}{\sin^2x}+\dfrac{\cos^2x}{\sin^2x}& =\dfrac{1}{\sin^2x}\\1+\left(\dfrac{\cos x}{\sin x}\right)^2&=\left(\dfrac{1}{\sin x}\right)^2\\1+(\cot x)^2&=(\text{cosec}\: x)^2\\1+\cot^2x&=\text{cosec}\: ^2x\end{aligned}}[/tex]
To prove the identity tan²x + 1 = sec²x :
[tex]\boxed{\begin{aligned}\sin^2x+\cos^2x &=1\\\textsf{Divide by $\cos^2x$}\implies \dfrac{\sin^2x}{\cos^2x}+\dfrac{\cos^2x}{\cos^2x}& =\dfrac{1}{\cos^2x}\\\left(\dfrac{\sin x}{\cos x}\right)^2+1&=\left(\dfrac{1}{\cos x}\right)^2\\(\tan x)^2+1&=(\sec x)^2\\\tan^2x+1&=\sec ^2x\end{aligned}}[/tex]
Additional identities used:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Trigonometric Identities}\\\\$\tan \theta=\dfrac{\sin \theta}{\cos \theta}$\\\\$\cot \theta=\dfrac{\cos \theta}{\sin \theta}$\\\\$\csc \theta=\dfrac{1}{\sin \theta}$\\\\$\sec \theta=\dfrac{1}{\cos \theta}$\\\end{minipage}}[/tex]
A bookshelf has 7 shelves, each measuring 4 feet 3 inches in length.
The average width of a book is ; inch. How many books will the
shelves hold?
Answer:
I think its 64 please let me know if its wrong
What is the lowest value of the range of the function shown on the graph? A. - ∞B. - 2C. 0D. 3
-2
Explanations:The range of the function is a set of all the values of y on the graph
The lowest point of the graph on the y-axis is -2
Therefore, the lowest value of the range of the function shown on the graph is -2
In Mr. Stowe's math class, Katherine earned an 88 in the 1st quarter and a 94 in the end quarter. What is the percentage of increase? Round to the nearest hundredth.
Solve. (Enter your answer using interval notation.)
|3x + 15| > 21
Answer:
(-∞, -12), (2, ∞)
or
(-∞, -12) U (2, ∞)
Step-by-step explanation:
|3x + 15| > 21, |3x + 15| < -21
3x + 15 > 21, 3x + 15 < - 21
-15 -15 -15 -15
------------------ -------------------
3x > 6 3x < - 36
÷3 ÷3 ÷3 ÷3
------------ ------------------
x > 2 x < -12
(-∞, -12), (2, ∞)
or
(-∞, -12) U (2, ∞)
I hope this helps!
K
Suppose that a certain car has the following average operating and ownership costs.
Average Costs per Mile
Operating
$0.28
Ownership
50.74
a. If you drive 30,000 miles per year, what is total annual expense for this car?
b. If the total annual expense for this car is deposited at the end of each year into an IRA paying 8.5% compounded
nt
[(¹)
yearly, how much will be saved at the end of nine years? Use the formula A=
a. If you drive 30,000 miles per year, the total annual expense for this car is $ 30,600
(Round to the nearest dollar as needed.)
1
k
b. If the total annual expense for this car is deposited at the end of each year into an IRA paying 8.5% compounded
yearly, the amount saved at the end of nine years is $
(Round to the nearest dollar as needed.)
S
LIC
(0,0)
Total
$1.02
More
x
rrect: 1
Total annual expense= $8400
Saving= $622,834,634,198.44
What is compound interest?Compound interest is addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest. It is result of reinvesting interest, or adding it to the loaned capital rather than paying it out, or requiring payment from borrower, so that interest in the next period is then earned on principal sum plus previously accumulated interest. Compound interest is standard in finance and the economics.
Compound interest is contrasted with the simple interest, where previously accumulated interest is not added to the principal amount of the current period, so there is no compounding. The simple annual interest rate is interest amount per period, multiplied by the number of periods per year. The simple annual interest rate is also known as nominal interest rate (not to be confused with the interest rate not adjusted for inflation, which goes by the same name).
a)Total annual expense= total miles *average cost per mile
= 30,000* 0.28= $8400
b)Amount deposited in 9 years= 8400*9= $75,600
total amount after 9 years= FV= PM[tex][(1+r)^{n}-1]/r[/tex]
=8400* [tex][(1+8.5)^{9}-1]/8.5[/tex]
=$622,834,709,798.44
Savings=622,834,709,798.44 -75600= $622,834,634,198.44
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Lesly graphed two lines in order to find thesolution to a given system of equations.What is the solution?1.) (3, -8)2.) (-3, -8)3.) (8, 3)4.) (-8, -3)
The solution of the system of equation is the point where the 2 lines cross each other.
By looking at the graph, we can see that they cross each other at (-3,-8)
Correct option: 2
Since a sample is a subset of the population, the sample mean Incorrect Response is always smaller than the mean of the population. is always larger than the mean of the population. must be equal to the mean of the population. Correct Answer varies around the mean of the population.
Since a sample is a subset of the population the sample mean varies around the mean of the population.
What is a sample mean about?An average of a group of data is called a sample mean. A data set's central tendency, standard deviation, and variance can all be determined using the sample mean. A population average can be determined using the sample mean, among other things.
The statistic known as the sample mean is created by arithmetically averaging the values of a variable in a sample. The sample mean is an estimator of the expected value if the sample is taken from probability distributions with a common expected value.
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5(3x + 10)³ can be expanded and fully simplified
to give an expression of the form
ax³ + bx² + cx + d.
Work out the values of a, b, c and d
After simplified the equation we get
a=54
b= 540
c=1800
d=2000
What is simplified expression?
Solving a math problem is the same thing as simplifying an expression. You basically try to write an expression as simply as you can when you simplify it. At the conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to do. Take this formula, for instance: 4 + 6 + 5. To simplify an expression, create an equivalent expression without any terms that are similar. The expression will then be rewritten using the fewest terms possible. When confronted with the phrase 4x+5(3x12),
Sol-
2(3x+10)^3
=2(Bx)^3+3.(3x)^2.10+3.3x.10^2+10^3
=2(27x^3+270x^2+900x+1000)
=54x^3+540x^2+1800x+2000
So,
a=54
b=540
c=1800
d=2000
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PLEASE CAN SOMEONE HELP ME !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!a) Fully factorise 5y² + 13y + 6
b) Use your answer to part a) to solve
5y² + 13y+6=0
Answer:
(y +2)(5y +3)y = -2, -3/5Step-by-step explanation:
You want the factors of 5y² +13y +6, and the solutions to 5y² +13y +6 = 0.
a) FactorsThe quadratic ax²+bx+c with a leading coefficient a≠1 can be factored by considering the factors of the product 'ac' that have a sum of 'b'.
5·6 = 30 = (1)(30) = (2)(15) = (3)(10) = (5)(6)
The sums of these factor pairs are, respectively, 31, 17, 13, 11. The factor pair with a sum of 13 is (3)(10).
There are a couple of methods that can be used to apply this knowledge to the factorization of the quadratic. Perhaps the most straightforward is to write the quadratic as 4 terms, using the found values to rewrite the linear term as their sum:
5y² +13y +6 = 5y² +3y +10y +6 . . . . . . . . . 13 ⇒ 3 +10
Now, pairs of terms can be factored:
= y(5y +3) +2(5y +3)
= (y +2)(5y +3) . . . . . . . fully factored expression
b) SolutionThe solutions that makes the product of factors be zero will be the values of x that make the factors be zero. A product is only zero if one of the factors is.
y +2 = 0 ⇒ y = -2
5y +3 = 0 ⇒ y = -3/5
The solutions to the quadratic equation are y = {-2, -3/5}.
__
Additional comment
Another way to find the factors is this. For factors p, q that have a product of 'ac' and a sum of 'b', the factorization can be ...
(ay +p)(ay +q)/a
For the values in this problem, this would be ...
(5y +3)(5y +10)/5
The latter of these factors can be divided by 5, so this can be simplified to ...
(5y +3)(y +2) . . . . as above
Use the Chain Rule to find dw/dt. (Enter your answer only in terms of t.)[tex]w = xe^{y/z}, x = t^{4}, y = 2 - t, z = 5 + 5t[/tex]
[tex]{\Large \begin{array}{llll} w=t^4 e^{\frac{2-t}{5+5t}} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ 4t^3e^{\frac{2-t}{5+5t}}~~ + ~~\stackrel{\textit{\LARGE product rule}}{t^4 \stackrel{\textit{\large chain rule}}{e^{\frac{2-t}{5+5t}}\cdot \stackrel{quotient~rule}{\cfrac{(-1)(5+5t)~~ - ~~(2-t)(5)}{(5+5t)^2}}}} \\\\\\ 4t^3e^{\frac{2-t}{5+5t}}~~ + ~~t^4 e^{\frac{2-t}{5+5t}}\cdot \cfrac{(-5-5t)~~ - ~~(10-5t)}{(5+5t)^2}[/tex]
[tex]4t^3e^{\frac{2-t}{5+5t}}~~ + ~~t^4 e^{\frac{2-t}{5+5t}}\cdot \cfrac{-15}{(5+5t)^2} \implies t^3 e^{\frac{2-t}{5+5t}}\left[4- \cfrac{15t}{(5+5t)^2} \right] \\\\\\ t^3 e^{\frac{2-t}{5+5t}}\left[\cfrac{(100t^2+200t+100)-15t}{(5+5t)^2} \right]\implies t^3 e^{\frac{2-t}{5+5t}}\left[\cfrac{100t^2+185t+100}{(5+5t)^2} \right] \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} \cfrac{dw}{dt}=t^3 e^{\frac{2-t}{5+5t}}\left[\cfrac{100t^2+185t+100}{(5+5t)^2} \right] \end{array}}~\hfill[/tex]
simplify complex fraction PLEASE!!!!
[tex]\frac{16}{3} /\frac{22}{45}[/tex]
The simplified complex fraction is
120/11
This is further explained below.
What is a complex fraction?Generally, the complex fraction is
[tex]\frac{\left(\frac{16}{3}\right)}{\left(\frac{22}{45}\right)}[/tex]
Multiply the numerator by the reciprocal of the denominator.
[tex]\frac{16}{3} \cdot \frac{45}{22}[/tex]
Cancel the common factor of 2
[tex]$\frac{8}{3} \cdot \frac{45}{11}$[/tex]
Combine 8 and 15/11
=8*15/11
=120/11
In conclusion, The result can be shown as.
120/11
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Find the measure of the angle at the center of atom B inside the triangle
The measure of the angle having the question mark, found using the law of sines is ? ≈ 140°
What is the law of sines?The law of sines states that the sine of an interior angle of a triangle is proportional to the the length of the side opposite to the angle.
The given parameters are;
The radius of circle A = 6.4
The radius of circle B = 4.0
The radius of circle C = 3.0
The measure of angle at C = 24°
The length of the segment AB = 6.4 + 4 = 10.4
According to the law of sines, we have;
[tex]\dfrac{sin(A)}{a} = \dfrac{sin(B)}{b} = \dfrac{sin(C)}{c}[/tex]
Where;
a = The length of the side opposite angle ∠A
b = The length of the side opposite angle ∠B
c = the length of the side opposite angle ∠C
From the diagram, the side opposite angle ∠C, is AB, which by comparison indicates that when side c = AB = 10.4
c = 10.4
Similarly, the side opposite angle ∠A = a = BC = 4 + 3 = 7
a = 7
The known information are therefore; ∠C = 24°, a = 7, c = 10.4
[tex]\dfrac{sin(A)}{a} = \dfrac{sin(C)}{c}[/tex]
[tex]\dfrac{sin(A)}{7} = \dfrac{sin(24^{\circ})}{10.4}[/tex]
[tex]sin(A) = \dfrac{sin(24^{\circ})}{10.4}\times 7[/tex]
[tex]\angle A = arcsine \left( \dfrac{sin(24^{\circ})}{10.4}\times 7\right)[/tex]
∠A + ∠B + ∠C = 180° (angle sum property of a triangle)
∠B = 180° - (∠A + ∠C)
Which gives;
[tex]\angle B = 180^{\circ} -\left(24^{\circ} + arcsine \left( \dfrac{sin(24^{\circ})}{10.4}\times 7\right)\right) \approx 140^{\circ}[/tex]
The measure of the angle is ∠B ≈ 140°
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How many times greater is 4.65 x 108 than 7.5 x 106? Express your answer using
either standard notation or scientific notation.