Answer:
Step-by-step explanation:
The question will look like (3b)/(a^-2)
To simplify, note the (a^-2). It is a negative, so flip the placement of the monomial. Note that the term is located in the decimal, so when it is flipped, it goes to the numerator (vice versa if it is opposite)
(3b)/(a^-2) = (3b)(a²)
3a²b, or (A) is your answer choice
~
Answer:
Option A) 3a2b
Step-by-step explanation:
Given the following figure, what is the value of x? PLZ HELP ASAP WILL MARK BRAINIEST
Answer:
The value of x = 11
Step-by-step explanation:
It is given that, the figure shows a pentagon.
The sum of angle of pentagon = 540
So we can equate these 5 angles to 540
To find the value of x
13x + 6 + 9x - 6 + 92 + 12x + 84 = 540
34x + 166 = 540
34x = 540 - 166
34x = 374
x = 374/34 = 11
Therefore the value of x = 11
The percentage of people accessing the Internet increased from 61 % in 2000 to 87% in 2012. Describe the change as an absolute change in terms of percentage points.
Answer:
26%
Step-by-step explanation:
We are given that the percentage of people accessing the Internet increased from 61 % in 2000 to 87% in 2012.
So we can describe the change as an absolute change in terms of percentage points by calculating the difference in the two percentages:
Absolute change in terms of percentage = 87 - 61 = 26%
Therefore, there is a 26% absolute change in the percentage of people accessing the internet.
Answer: There is an absolute change of 2.16%.
Step-by-step explanation:
Since we have given that
Percentage of people accessing the internet in 2000 = 61%
Percentage of people accessing the internet in 2012 = 87%
So, there is an increment of some percentage, and we need to find that percent.
so, Absolute change in terms of percentage is given by
[tex]\dfrac{87-61}{2012-2000}\\\\=\dfrac{26}{12}\\\\=2.16\%\\[/tex]
Hence, there is an absolute change of 2.16%.
Determine the range of the function: (0,2)(2,4)(4,6)(6,8)(8,10) Options: A) y<_10 B) {2,4,6,8,10} C) 2<_y<_10 D) {0,2,4,6,8,10#
(0, 2), (2, 4), (4, 6), (6, 8), (8, 10)
The domain is the set of the first coordinates of the points.
The range is the set of the second coordinates of the points.
The domain = {0, 2, 4, 6, 8}
The range = {2, 4, 6, 8, 10}
Answer: B) {2, 4, 6, 8, 10}.The sum of two numbers is 52 . The smaller number is 16 less than the larger number. What are the numbers?
Let the Smaller Number be : S
Let the Larger Number be : L
Given : The Sum of Two Numbers is 52
⇒ S + L = 52 --------------- [1]
Given : The Smaller Number is 16 Less than Larger Number.
It Means if we Add 16 to the Smaller Number, It should be Equal to the Larger Number
⇒ S + 16 = L
⇒ S = L - 16 ------------------ [2]
Substituting Equation [2] in Equation [1], We get :
⇒ L - 16 + L = 52
⇒ 2L = 52 + 16
⇒ 2L = 68
⇒ L = 34
Substituting L = 34 in Equation [2], We get :
⇒ S = 34 - 16
⇒ S = 18
⇒ The Larger Number is 34
⇒ The Smaller Number is 18
The two numbers are 34 and 18; 34 being the larger number and 18 being the smaller number.
Explanation:This is a common type of problem in algebra called a system of linear equations. We can solve it step by step.
First, let's assign variables to the unknowns. Let's let 'x' be the larger number and 'y' be the smaller number. The problem gives us two equations: x + y = 52 and y = x - 16. Next, we can substitute the second equation into the first one. This gives us: x + (x - 16) = 52.Combine like terms to simplify the equation: 2x - 16 = 52.Add 16 to both sides to isolate '2x': 2x = 68.Finally, divide both sides by 2 to find the value of 'x': x = 34. By substituting 'x' into the second equation, we can also find 'y': y = 34 - 16 = 18.So, the larger number is 34 and the smaller number is 18.
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What is the effect on the graph of the function f(x) = x when f(x) is replaced with -1/2 f(x)?
A) vertical reflection over x-axis and vertical stretch
B) vertical reflection over x-axis and vertical compression
C) horizontal reflection over y-axis and horizontal stretch
D) horizontal reflection over y-axis and horizontal compression
Answer:
The correct option is B.
Step-by-step explanation:
The given function is
[tex]f(x)=x[/tex]
The new function is
[tex]g(x)=-\frac{1}{2}f(x)[/tex]
[tex]g(x)=-\frac{1}{2}x[/tex] .... (1)
It is in the form of
[tex]g(x)=mx[/tex] .... (2)
Where, m is a constant.
If m is negative, then there is a vertical reflection over x-axis. If the constant is greater than 1, we get a vertical stretch and if the constant is between 0 and 1, we get a vertical compression.
From (1) and (2), we get
[tex]m=-\frac{1}{2}[/tex]
Since the value of m is negative and absolute value of m is between 0 and 1, therefore the graph g(x) shows the vertical reflection over x-axis and vertical compression.
Option B is correct.
Final answer:
The graph of f(x) = x, when modified to -1/2 f(x), undergoes a vertical reflection over the x-axis and a vertical compression by a factor of 1/2, resulting in answer B.
Explanation:
When the function f(x) = x is replaced with -1/2 f(x), the effect on the graph is two-fold. Firstly, there is a vertical reflection over the x-axis because of the negative sign.
This means that the graph is flipped over the x-axis, with points that were above the x-axis now being below it, and vice versa.
Secondly, there is a vertical compression by a factor of 1/2 due to the multiplier of -1/2. This compresses the graph towards the x-axis, making it 'flatter' than the original graph of f(x) = x.
Therefore, the correct answer to the question is B) vertical reflection over the x-axis and vertical compression.
4 times a number is 8 more than 40. what is the number?
Answer:
The number is 12
Step-by-step explanation:
4 times a number is 8 more than 40
Write the equation
4n=40+8
4n =48
Divide each side by 4 to isolate n
4n/4 = 48/4
n = 12
i will give the brainliest
Answer:
option 3
Step-by-step explanation:
sin45° = 11/BC
=>1/√2 = 11/BC
=>BC = 11√2
For this case we must find the hypotenuse (H) or the BC side of the rectangular triangle shown in the figure.
We have to:
[tex]Tangent (B) = \frac {Cathet \ opposite} {Cathet \ adjacent}\\Tangent (45) = \frac {11} {BA}[/tex]
By clearing BA we have:
[tex]BA = \frac {11} {Tangent (45)}\\BA = \frac {11} {1}\\BA = 11[/tex]
The Pythagorean theorem, which states:
[tex]BC = \sqrt {(CA) ^ 2 + (BA) ^ 2}\\BC = \sqrt {(11) ^ 2 + (11) ^ 2}\\BC = \sqrt {(11) ^ 2 + (11) ^ 2}\\BC = \sqrt {2 * 11 ^ 2}\\BC = 11 \sqrt {2}[/tex]
Answer:
[tex]BC = 11 \sqrt {2}[/tex]
Option C
Social Science predicts that the population of barre, Vermont will double every 54 years. If the population in 1974 was 56000, in what year should we expect the population to reach 71000
Answer:
We should expect the population to reach 71000 in 1993.
Step-by-step explanation:
If the population will double every 54 years and the population in 1974 was 56000 people, then the function that represents this situation is
[tex]y=56000\cdot 2^{\frac{x}{54}},[/tex]
where x is time in years since 1974.
Nota that in 1974, x=0, then y=56000 and after 54 years the population will be [tex]y=56000\cdot 2^{\frac{54}{54}}=56000\cdot 2=112000.[/tex]
Therefore, you have to calculate x, when y=71000:
[tex]71000=56000\cdot 2^{\frac{x}{54}},\\ \\\dfrac{71}{56}=2^{\frac{x}{54}},\\ \\\dfrac{x}{54}=\log_2\dfrac{71}{56},\\ \\x=54\log_2\dfrac{71}{56}\approx 18.49[/tex]
Thus, we should expect the population to reach 71000 in 1993 (after full 19 years).
H= 62.4NS/33,000 solve for N
Answer:
N = 33,000H/(62.4S)
Step-by-step explanation:
Multiply the equation by the inverse of the coefficient of N.
... N = 33,000H/(62.4S)
Answer:
33,000
Step-by-step explanation:
How long will it take to fill the pool if two hoses are used, one that fills at a rate of 40 gallons per hour and one that fills at a rate of 60 gallons per hour?
Your selection is correct: 180 hours
Step-by-step explanation:The pool is apparently 18000 gallons (= 60 gal/h × 300 h). The combined flow from the two hoses is ...
... (40 gal/h) + (60 gal/h) = 100 gal/h
So, the time required with the two hoses is ...
... 18000 gal/(100 gal/h) = 180 h
Answer:
C) 180 hours
Step-by-step explanation:
Edge 2020
Theorem: The segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length. A two-column proof of the theorem is shown, but the proof is incomplete. A triangle with vertices A is at 6, 8. B is at 2, 2. C is at 8, 4. Segment DE with point D on side AB and point E is on side BC. Statement Reason The coordinates of point D are (4, 5) and coordinates of point E are (5, 3) By the midpoint formula Length of segment DE is Square root of 5 and length of segment AC is 2 multiplied by the square root of 5 By the distance formula Segment DE is half the length of segment AC By substitution Slope of segment DE is −2 and slope of segment AC is −2 Segment DE is parallel to segment AC Slopes of parallel lines are equal Which of the following completes the proof? By definition of congruence Addition property of equality By construction By the slope formula
The proof can be completed with the concept of the slope formula, which shows that two line segments with identical slopes equate to parallel lines. This fits perfectly in the context of the given two-column proof.
Explanation:In the provided incomplete two-column proof, the statement in question infers that the segment DE is parallel to segment AC because they have the same slope. The reason for this, which completes the proof, would be the slope formula. The slope formula allows us to calculate the steepness, incline, or gradient of a line segment defined by two points in a 2D space. When applied to segments DE and AC, it gives us identical values, indicating that the two line segments are parallel as per the theorem stating that parallel lines have equal slopes.
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To complete the proof, the correct answer is 'By the slope formula'
Explanation:To complete the proof, we need to show that the slopes of segment DE and segment AC are equal. By calculating the slopes using the slope formula, we can determine if they are indeed equal. Therefore, the correct answer is 'By the slope formula'.
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Don’t mind my college name, I’m really in 8th grade and I’m really frustrated in this one.
Answer:
its ok to be mad just take your time
and try i bet you can do this just put in some thinking time
Step-by-step explanation:
solve the equation. plesse help.
Answer:
x = 2
Step-by-step explanation:
[tex]11^{2x}=14641\\11^{2x}=11^4\\2x = 4\\x = 2[/tex]
please help me asap!
What is the best approximation of the length of segment QS? (Note: cos 80° = 0.17)
(Round your answer to the nearest tenth.)
Answer:
Length of the segment QS = 11.76 cm
Step-by-step explanation:
We are given with right angle triangle QRS
Angle S is 80 degree and RS = 2 cm
We need to find out QS
RS is adjacent to angle S, so we use cos formula
[tex]Cos (A) = \frac{adjacent}{hypotenuse}[/tex]
[tex]Cos (S) = \frac{RS}{QS}[/tex]
Plug in the angle and RS
[tex]Cos (80) = \frac{2}{QS}[/tex]
Given cos(80) = 0.17
[tex]0.17= \frac{2}{QS}[/tex]
Multiply by QS on both sides
0.17 * QS = 2
Divide by 0.17 on both sides
QS= 11.76470588
Length of the segment QS = 11.76 cm
1.) A video store is selling previously owned DVDs for 40% off the regular price of $15. What is the sale price of the DVDs? Show your work
2.) . Due to the increased rate of its rent, the Neat Novelties Store had to markup the cost of its helium balloons by 7%. The store’s original cost for a bunch of 8 primary-colored helium-filled balloons was $7.00. What was the selling price after markup? Show Work
3.) Cecil Home Builders are offering 10% off the option of finishing a basement on all the new homes they are currently building in the Miller Falls Subdivision. The original cost for the finished basement option is $12,000. What is the cost to the buyer after the discount? Show Work
Hi There!
------------------------------------------------
Question #1:
A video store is selling previously owned DVDs for 40% off the regular price of $15. What is the sale price of the DVDs?
40% = 0.4
15 * 0.4 = $6 (Discount)
15 - 6 = $9 (Sale Price)
Answer: $9
------------------------------------------------
Question #2:
Due to the increased rate of its rent, the Neat Novelties Store had to markup the cost of its helium balloons by 7%. The store’s original cost for a bunch of 8 primary-colored helium-filled balloons was $7.00. What was the selling price after markup?
7% = 0.07
7 * 0.07 = $0.49 (Increase)
7 + 0.49 = $7.49 (Price after Increase)
Answer: $7.49
------------------------------------------------
Question #3:
Cecil Home Builders are offering 10% off the option of finishing a basement on all the new homes they are currently building in the Miller Falls Subdivision. The original cost for the finished basement option is $12,000. What is the cost to the buyer after the discount?
10% = 0.1
12,000 * 0.1 = $1,200 (Discount)
12,000 - 1,200 = $10,800 (Price after Discount)
Answer: $10,800
------------------------------------------------
Hope This Helps :)
Devonte opens a savings account by making a deposit of $249.45. Every week, he deposits another $31.75 in the account. Which expression shows the amount of money that will be in the account 'w' weeks after the account is opened?
To find the total you would need to multiply the 31.75 by w to get the total amount of his weekly deposits, then that would get added to the initial amount of 249.45
The equation would be 249.45 + 31.75w
249.45 +31.75w
Step-by-step explanation:When w = 0, the amount is 249.45. This eliminates the first two choices.
When w = 1, the amount is 31.75 greater than 249.45. This eliminates the last choice.
The remaining choice is the correct one:
... 249.45 +31.75w
It shows the account balance is initially 249.45 and increases with increasing w at the rate of 31.75 per week.
Round the numbers to the nearest cent and then to the nearest dollar. 23. $62.756 24. $38.415
Answer:
23. $ 62.76 to the nearest cent
$63.00 to the nearest dollar
24. $ 38.42 to the nearest cent
$38.00 to the nearest dollar
Step-by-step explanation:
When we round to the nearest cent we round the second number after the decimal. We look at the third number after the decimal. If it is 5 or above we round up.
When we round to the nearest dollar, we round the number befroe the decimal. We look at the number after the decimal. If it is 5 or above we round up.
23. $62.756 we round the 5 so we look at the 6 6>= 5 so we round up
$ 62.76 to the nearest cent
$62.756 we round the 2 so we look at the 7 7>= 5 so we round up
$63.00 to the nearest dollar
24. $38.415 we round the 1 so we look at the 5 5>= 5 so we round up
$ 38.42 to the nearest cent
$38.415 we round the 8 so we look at the 4 4< 5 so we leave alone
$38.00 to the nearest dollar
mark wants to buy a skateboard that costs $65. he plans to save $5 per week. how many weeks will it take him to save $65
Answer:
13 weeks
Step-by-step explanation:
65=5w
w=65/5
w=13
Final answer:
It will take Mark 13 weeks to save $65 for the skateboard by saving $5 each week.
Explanation:
Mark wants to buy a skateboard that costs $65. He plans to save $5 per week. To calculate how many weeks it will take him to save $65, we divide the total cost of the skateboard by the amount Mark can save per week.
Here's the calculation:
Total cost of the skateboard: $65
Amount Mark saves each week: $5Number of weeks needed to save $65: $65 ÷ $5 = 13 weeksTherefore, it will take Mark 13 weeks to save enough money to buy the skateboard.
Can someone help me figure out the answer?
Answer:
f(t) = 5×0.87^t
Step-by-step explanation:
The general form for an exponential function described in this fashion is ...
... f(t) = (starting value) × (1 + (percent change))^t
Here, the "percent change" is -13%, or -0.13.
Then the value (1 + percent change) is (1 + (-0.13)) = 0.87. Putting this and the starting value into the form above, we have ...
... f(t) = 5 × 0.87^t
n trapezoid STUV, SW is an altitude. Which is equivalent to the measure of angle m + n + p if m angle VSW = 65 degrees?
Answer:
The measure of angle m+n+p is equivalent to 205° (Fourth option)
Step-by-step explanation:
In a quadrilateral, the sum of the interior angles must be equal to 360°:
S=m+n+p+m<VSW+m<WST=360°
m<VSW=65°
Like SW is an altitude, m<WST=90°
Replacing the known values in the formula above:
m+n+p+65°+90°=360°
Adding like terms:
m+n+p+155°=360°
We want m+n+p, then subtracting 155° both sides of the equation:
m+n+p+155°-155°=360°-155°
m+n+p=205°
Answer:
4th Option is correct.
Step-by-step explanation:
Given: STUV ia a trapezoid that is ST is parallel to UV
SW is altitude that is m∠ SWV = 90°
m∠ VSW = 65°
To find: measure of m + n + p
Since, ST is parallel to UV.
⇒ n + p = 180° because Sum of Interior Angle on the same side of traversal is 180°
Now, In ΔSVW
∠SVW + ∠SWV + ∠WSV = 180° (Angle sum property of triangle)
m + 90° + 65° = 180°
m + 155 = 180
m = 180 - 155
m = 25°
Thus, m + n + p = 25 + 180 = 205°
Therefore, 4th Option is correct.
In ΔABC, AD and BE are the angle bisectors of ∠A and ∠B and DE ║ AB . If m∠ADE is with 34° smaller than m∠CAB, find the measures of the angles of ΔADE.
Answer:
ADE = 34°
Step-by-step explanation:
To solve a question in which a shape is described, the first step must be to draw a diagram based on the information provided. Based on the information provided in a diagrammatic form, it can be seen clearly that lines DE and BA are parallel. Therefore, angle ADE and DAB are equal. It is also mentioned that line AD is the bisector of angle CAB. From the information provided, below correlations are determined.
CAB - 34 = ADE
ADE = DAB
DAB = DAC
CAB = DAB + DAC
This gives:
CAB = 2xDAB = 2xADE
When the above equations are reduced,
CAB - 34 = ADE
2xADE - 34 = ADE
ADE = 34°
6(t-2)-76=-142 solve for t
Answer:
t= -9
Step-by-step explanation:
Add 76 to both sides
6(t-2)= -142+76
Simplify -142+76 to -66
6(t-2)=-66
Divide both sides by 6
t-2= -66/6
Simplify 66/6 to 11
t-2= -11
Add 2 to both sides
t= -11+2
Simplify -11+2 to -9
t= -9
I hope this helps you
An eccentric clockmaker built three different clocks. The first clock was a five-minute clock designed with an alarm set to sound each time the hand reached the number 2. The second clock was a six-minute clock designed to sound each time the hand reached the number 3. The third clock was a seven-minute clock designed to sound each time the hand reach the number 4. The clockmaker started the clocks simultaneously on day, and each clock began to sound at its appropriate time. Was there a time when all three clocks sounded their alarms together? If so, tell when it occurred and explain why. If not, explain why not.
Answer:
Yes, there was a time when the three alarms sounded together. It occurred 3 hours and 27 minutes after the clocks were started, and every 3 hours 30 minutes after that.
Step-by-step explanation:
We assume the clocks are numbered 1–5 on the 5-minute clock, 1–6 on the 6-minute clock, and 1–7 on the 7-minute clock. Then the alarm on each clock goes off 3 minutes before the clock repeats its timing action.
The least common multiple of the clock times is 5·6·7 = 210 minutes, or 3 1/2 hours. All clocks will simultaneously be 3 minutes before their repeat at 3 minutes before this 210-minute period is up.
That is, the clocks will simultaneously alarm 207 minutes after being started, and every 210 minutes after that.
_____
Comment on clock face numbering
If the clock faces are numbered 1–12, so the 5-minute clock alarms 5·(2/12) minutes = 50 seconds after being started, for example, then the alarms can never sound together. The clocks will come together at least once on any/every multilple of 1 minute, but not on any/every multiple of 10 seconds.
Problem 3 among the cast aluminum parts manufactured on a certain day, 80% were flawless, 15% had only minor flaws, and 5% had major flaws. find the probability that a randomly chosen part
a.has a flaw (major and minor).
b.has no major flaws.
Answer:
A) P(flaw) = 0.2
B) P(No major flaws) = 0.95
Step-by-step explanation:
A)To find the probability of flaws, we can find the probability of no flaws first by dividing by 100:
P(no flaw) = [tex]\frac{80}{100}[/tex] = 0.8
So then:
P(flaw) = 1 - P(no flaw) = 1 - 0.8 = 0.2
P(flaw) = 0.2
B)First, we need to find the probability of major flaws:
P(major flaws) = [tex]\frac{5}{100} = 0.05[/tex]
P(Major flaws) = 0.05
So to find the probability of no major flaws:
P(No major flaws) = 1 - P(major flaws) = 1 - 0.05 = 0.95
P(No major flaws) = 0.95
According to known percentages, it can be concluded that the probability a part has a flaw is 20% (0.20), and the probability a part has no major flaws is 95% (0.95).
Explanation:This question is about probability in Mathematics. Specifically, it's based on the principles of probability distribution. Given that we know the percentages for flawless, minorly flawed, and majorly flawed parts, we can calculate the requested probabilities as follows:
The probability that a part has a flaw (major or minor) is the sum of the probabilities of a part having minor flaws and major flaws, so 15% + 5% = 20%, or 0.20 when expressed as a decimal.The probability of a part having no major flaws includes both flawless parts and parts with minor flaws. Therefore, its probability equals 80% + 15% = 95%, or 0.95 in decimal form.Learn more about Probability here:https://brainly.com/question/22962752
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Please answer ASAP!! which of the following is closest to 0.25 and why?
A) 9/40 B)5/16 C) 9/32 D) 0.28 E) 15/64
Answer:
E) 15/64
Step-by-step explanation:
To compare the numbers, it works best to express them all using a common denominator. One possibility is 1600, another is 1,000,000.
9/40 = 360/1600
5/16 = 500/1600
9/32 = 450/1600
0.28 = 448/1600
15/64 = 375/1600
The number we're comparing to is 0.25 = 400/1600, so we want to find the closest number to 400 in the set ...
... {360, 500, 450, 448, 375}.
The magnitude of the differences of these numbers from 400 is ...
... {40, 100, 50, 48, 25}.
Clearly, the last number, 15/64 = 375/1600 has the smallest difference from 0.25.
Hey there!
“Which of the following is closest to[tex]0.25[/tex] and why?”
Options
A. [tex]\frac{9}{40}[/tex]
B. [tex]\frac{5}{16}[/tex]
C.[tex]\frac{9}{32}[/tex]
D. [tex]0.28[/tex]
E. [tex]\frac{15}{64}[/tex]
Process of elimination
Well,
Option A can’t be your answer because, [tex]\frac{9}{40}[/tex]equals [tex]0.225[/tex] in decimal form
Option B can’t be your answer because [tex]\frac{5}{16}[/tex] equals [tex]0.3125[/tex] in decimal form
Option C can’t be your answer because [tex]\frac{9}{32}[/tex] equals [tex]0.234375[/tex] in decimal form
Option D. Could be your answer because it’s a tad bit closer by a tad bit but let’s check for option E
Option E can but can’t be your because[tex]\frac{15}{64}[/tex] equals [tex]0.234375[/tex]
This leaves us with [tex]\boxed{OptionE. \frac{15}{64} }[/tex] as your result
Good luck on your assignment and enjoy your day
~LoveYourselfFirst:)
Suppose you have 15 muffins. How many muffins ate left after you give a friend 1/3 of them
Answer:
10 muffins
Step-by-step explanation:
If you give away 1/3 of your muffins
1/3 * 15 = 5
You will give away 5 muffins
15 -5 =10
You will have 10 muffins left
Christy and Seth are measuring water in a rectangular prism. They know the volume of the container. Christy suggests that they solve for the width of the prism. Transform the formula to find the volume of a rectangular prism to solve for width (w). Solve for w: V = lwh
Answer:
d) V/(lh) = w
Step-by-step explanation:
The appropriate solution divides the equation by the coefficient of w, which is lh. In answer selection (d), that is done by first dividing by l, then by h.
_____
Comment on the solution
One could just divide by l·h and be done with it.
Ella collects 50 bottles to recycle. Of the bottles she collects, 19 are plastic and the rest are glass.
A.) What percent of the bottles are plastic?
B.) What percent of the bottles are glass?
*Please Show Work*
38% of the bottles Ella collects are plastic and the remaining 62% are glass. Percentage is calculated by dividing the part by the whole and then multiplying by 100.
Explanation:Ella has 50 bottles in total, out of which 19 are plastic. To find out what percentage of bottles are plastic, we use the formula:
Percentage = (Part/Whole) * 100
Substitute the given values into the formula we get:
Percentage of plastic bottles = (19/50) * 100 = 38%
For the percentage of glass bottles, we first need to find out how many bottles are glass. As the total number of bottles are 50 and 19 of these are plastic, we subtract 19 from 50 to find the number of glass bottles:
Total glass bottles = 50 - 19 = 31
Now we can find out what percentage of bottles are glass using our formula:
Percentage of glass bottles = (31/50) * 100 = 62%
So, 38% of the bottles Ella collects are plastic and 62% are glass.
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What is the value of sin 0 given that (-3,7) is a point on the terminal side 0
Answer:
[tex]\frac{7\sqrt{58}}{58}[/tex]
Step-by-step explanation:
[tex]\\\text{Given that a point on the terminal side of }\theta \text{ is }(-3,7)\\\\\text{so the terminal side is in Quadrant II}\\\\\text{In the right triangle OMN, using Pythagorean theorem, we get}\\\\\text{ON}=\sqrt{(MN)^2+(OM)^2}\\\\\Rightarrow ON=\sqrt{(7)^2+(-3)^2}\\\\\Rightarrow ON=\sqrt{49+9}\\\\\Rightarrow ON=\sqrt{58}\\[/tex]
[tex]\\\text{we know that in Quadrant II, sine and cosecant are positive.}\\\text{so using the trigonometric ratios, we get}\\\\\sin \theta=\frac{\text{Opposite }}{\text{Hypotenus}}\\\\\Rightarrow \sin \theta=\frac{7}{\sqrt{58}}\\\\\Rightarrow \sin \theta=\frac{7\sqrt{58}}{58}\\[/tex]