Solve this equation in the
given domain: 0
*give answer in radians*
3 sin (2x-4)=2
There should be 4 answers.
look at attached photo
Answers
Answer: 2.294524311274043, 4.294524311274043, 6.294524311274043 and 8.294524311274043 radians.
Step-by-step explanation: We can start by isolating the sin function on one side of the equation:
sin (2x-4) = 2/3
Next, we can use the inverse sine function (sin^-1) to find the value of 2x-4:
2x-4 = sin^-1(2/3)
We know that the domain of the inverse sine function is [-1,1], so the value of 2/3 falls in that range. To find the value of x, we can add 4 to both sides and divide both sides by 2:
x = (sin^-1(2/3) + 4) / 2
The value of sin^-1(2/3) is approximately 0.5890486225480862 radians and that's the first solution in the range [0, pi], and we can add multiples of pi to get the other solutions.
x = (0.5890486225480862 + 4) / 2 = 2.294524311274043 radians (in the range [0, pi])
x = (0.5890486225480862 + 4 + pi) / 2 = 4.294524311274043 radians (in the range [pi, 2pi])
x = (0.5890486225480862 + 4 + 2pi) / 2 = 6.294524311274043 radians (in the range [2pi, 3pi])
x = (0.5890486225480862 + 4 + 3pi) / 2 = 8.294524311274043 radians (in the range [3pi, 4*pi])
So there are four solutions to this equation: 2.294524311274043, 4.294524311274043, 6.294524311274043 and 8.294524311274043 radians.
[tex]3\sin(2x-4)=2\implies \sin(2x-4)=\cfrac{2}{3}\implies 2x-4=\sin^{-1}\left( \cfrac{2}{3} \right) \\\\\\ 2x=\sin^{-1}\left( \cfrac{2}{3} \right)+4\implies x=\cfrac{\sin^{-1}\left( \frac{2}{3} \right)+4}{2} \\\\\\ x=\cfrac{\sin^{-1}\left( \frac{2}{3} \right)}{2}+2\implies x\approx\cfrac{0.73}{2}+2\implies \stackrel{II~Quadrant}{x\approx 2.365}\hspace{5em}\stackrel{III~Quadrant}{\stackrel{\frac{\pi -0.73}{2}+2}{x\approx 3.206}}[/tex]
Related Questions
Companies A and B provide housekeeping services. The charges are shown in the table. After how many hours will Company A be cheaper than Company B?
Answers
After the first 3 hours, Company A will be cheaper than Company B, based on a system of equations.
What is a system of equations?A system of equations or simultaneous equations refers to two or more equations whose solutions are computed concurrently or simultaneously.
Company A Company B
First-hour charge $28 $20
Subsequent half hour $10 $12
Subsequent one-hour $20 $24 ($12 x 2)
Let one hour of housekeeping service after the first-hour charge = x
Company A's total charge for x hours = 28 + 20x ... Equation 1
Company B's total charge for x hours = 20 + 24x ... Equation 2
For the costs to become equal:
28 + 20x = 20 + 24x
-4x = -8
x = 2
For the first 3 hours (2 + 1) of housekeeping service, the costs for both companies are equal.
Thus, after the first 3 hours of service, Company A's charges become cheaper than Company B's.
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Which is the graph of the piecewise function f(x)?
f(x) = StartLayout Enlarged left-brace 1st row 1st column negative x + 1, 2nd column x less-than-or-equal-to 0 2nd row 1st column x + 1, 2nd column x greater-than 0 EndLayout
On a coordinate plane, a piecewise function has 2 connecting lines. The first line goes from (4, 5) down to (0, 1). The second line goes from (0, 1) up through (4, 5).
On a coordinate plane, a piecewise function has 2 connecting lines. The first line goes from (4, 5) down to (1, 0). The second line goes from (1, 0) up through (4, 3).
On a coordinate plane, a piecewise function has 2 connecting lines. The first line goes from (negative 5, negative 4) up to (0, 1). The second line goes from (0, 1) down through (4, negative 3).
On a coordinate plane, a piecewise function has 2 connecting lines. The first line goes from (negative 4, negative 5) up to (1, 0). The second line goes from (1, 0) down through (4, negative 3).
Answers
The graph of the piece-wise function for this problem is given by the image presented at the end of the answer.
What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input of the function.
The two definitions for the function in this problem are given as follows:
Left of x = 0: y = - x + 1 -> decreasing line.Right of x = 0: y = x + 1 -> increasing line.Both of the lines will meet at the y-intercept of y = 1, as shown in the image presented at the end of the answer.
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Answer: The first one
Step-by-step explanation:
On a coordinate plane, a piecewise function has 2 connecting lines. The first line goes from (4, 5) down to (0, 1). The second line goes from (0, 1) up through (4, 5).
Basically it should look like a wide V staring at point 1 on the y axis facing upwards.
PLSSS HELP IF YOU TURLY KNOW THISSSS
Answers
Answer:
x = 15
Step-by-step explanation:
Because the first part is division.... x/5, you'd want to multiply by that same number to get X alone. So you'd multiply by 5
Because of that
x = (3)(5)
x = 15
[tex]\dfrac{x}{5} =3[/tex]
Multiply both sides by 5:
[tex](\dfrac{x}{5} )\times5=(3)\times5[/tex]
[tex]\fbox{x = 15}[/tex]
Evaluate the expression.
4×(7×5)
=
Answers
Answer:
4x(7x5) = 4x(35)
To evaluate the expression, we must first perform the operations inside the parentheses. In this case, 7x5 = 35. Then we can multiply 4 with that result, which gives us 4x35 = 140. So the final value of the expression is 140.
Answer: 140
Step-by-step explanation:
4 x (7 x 5)
7 x 5 = 35
4 x 35
= 140
A radar gun meaured the peed of a baeball at 5 mile per hour. If the baeball wa going 4.2 mile per hour, what wa the percent error in thi meaurement?
Answers
The percent error in this measurement would be 16%.
1. Calculate the difference between the measured speed and the actual speed: 5 mph - 4.2 mph = 0.8 mph
2. Calculate the percent error: (0.8 mph / 4.2 mph) x 100 = 19.05%
3. Round to the nearest whole number: 19.05% = 19%
The percent error in this measurement is 19%, which means that the measured speed was 19% higher than the actual speed.
This can be caused by a variety of factors, including the radar gun being set to an incorrect sensitivity, the speed of the ball being too high for the radar gun to accurately measure, or the radar gun not being able to accurately detect the speed of the ball due to environmental factors such as wind or lighting.
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In the triangle below, what is the tangent of 30°?
O A.
OB.
-IN
B. √3
OC. 2
O D. 1
60°
2
13
30°
Answers
Answer:
B
Step-by-step explanation:
tangent formula is the line facing the angle divided by the shorter one. so 1/root3
Answer:
Option B.
[tex]tan(30)=\frac{1}{\sqrt{3} }[/tex]
Step-by-step explanation:
We can use SOH CAH TOA to find our answer.
In this acronym, O is the opposite side, A is the adjacent side, and H is the hypotenuse.
TOA is for tangent.
So we can say the tangent of angle x is the opposite side divided by the adjacent side.
[tex]tan(x)=\frac{O}{A}[/tex]
In this triangle we are given
[tex]O=1\\A=\sqrt{3} \\H=2[/tex]
Therefore
[tex]tan(30)=\frac{1}{\sqrt{3} }[/tex]
choose the correct answer below. a. false. the method for selecting a cluster sample is to order a population in some way and then select members of the population at regular intervals. b. false. the method for selecting a systematic sample is to order a population in some way and then select members of the population at regular intervals. c. true.
Answers
The researcher could also use a random number generator to select the members of the sample, instead of selecting them at regular intervals.
The formula for calculating a systematic sample is p = (n/N) x 100, where p is the percentage of the population to be sampled, n is the sample size, and N is the total population size. For example, if a researcher wanted to sample 100 people from a population of 500, the formula would be p = (100/500) x 100 = 20%. This means that the researcher would select every fifth person in the population to be included in the sample. The researcher could also use a random number generator to select the members of the sample, instead of selecting them at regular intervals.
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at Freddy's, three steak burgers zzz and two orders of fries cost $18. Two steak burgers and three orders of fries cost $15.75. What is the cost for one steak burger? What is the cost of one order of feries
Answers
The cost of one steak burger is $4.5 and the cost of one order of fries is $2.25.
How to find a cost using equation?To find a cost using an equation, you need to first identify the variables involved in the equation.
Variables are values that can change, such as the price of an item or the quantity of an item. Next, you must determine the value of each variable.
Once you have all the values, plug them into the equation and solve for the cost. For example, if you have an equation where x is the cost, y is the quantity, and z is the price per item, you would plug in the values of y and z and solve for x.
The answer you get would be the cost of the item. Additionally, you can use the equation to find the cost of multiple items by changing the value of the variable y to represent the amount of items you need.
After plugging in the new values into the equation, you can solve for the cost of all the items.
Let x be the fries and y be the steak burgers.
From the following information, the equation are as follows:
2x + 3y = 18 ---------equation 1
3x + 2y = 15.75 -------equation 2
To find cost of one steak burger and cost of one order of fries,
Multiply by 3 in equation 1 and 2 in equation 2,
6x + 9y = 54 -------3
6x + 4y = 31.5 -----4
Subtracting the equation 3 and 4, we get
5y = 22.5
y = 22.5/5
y = 4.5
Substitute y=4.5 in eq 1,
2x + 3(4.5) = 18
2x = 4.5
x = 2.25
∴ The cost of one steak burger is $4.5
∴The cost of one order of fries is $2.25.
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how do you write 2.2616161… using bar notation
Answers
Answer:2.261 repeating sign on top
Step-by-step explanation:
2.261 repeating sign on top
Answer: 2.261 with the bar notation line over 61. Since I can't actually type it.
Step-by-step explanation: I hope this helps!
an organization will give a prize to a local artist. the artist will be randomly chosen from among 7 painters, 4 sculptors, and photographers. what is the probability that the artist chosen will be a painter or a 5 photographer? write your answer as a fraction.
Answers
The probability that the artist chosen will be a painter or a photographer is 3/4
What is probability?Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.
To solve this exercise the formula and the procedure that we have to use for probability is:
probability= (achieving success / possible outcomes)
Achieving success = 7 painters + 5 photographer = 12
Possible outcomes = 7 painters + 5 photographer + 4 sculptors = 16
Applying the formula to calculate the probability we get:
probability= (achieving success / possible outcomes)
probability= 12/16
Simplifying:
probability= 3/4
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Please help I dont know where to start
the standard deviation of a simple random sample of 40 calling times on a payphone is found to be 2. 6 minutes. Find the test statistic to test a claim that the standard deviation of all phone calls on a payphone is less than 2. 9 minutes. Use a 0. 05 significance level
32. 152
31. 348
48. 519
34. 966
Answers
Here we have to compare a standard deviation of test statistic with the expected standard deviation of the population. So a chi square test is used. The chi square value got after the calculations is 31.348.
It is a hypothesis testing method. Significance level is 0.05.
The equation for chi square is
Χ² = (n-1)s²/ σ₀²
Lets look into what each term means
n is the sample size which is 40
s² is the sample variance = 2.6²
σ² is the population variance =2.9²
X² = (40-1)×2.6²/ 2.9²
= 39× 6.76/ 8.41
= 31.3483947681
= 31.348
So the X² value is 31.348
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the sales tax rate is 7.8%.kiara buys a box of dirt priced at $150.24 what is the tax amount,round your number to the nearest penny
Answers
With a sales tax rate of 7.8%, the tax amount is $11.72.
How to determine the tax amount?A sales tax rate is the percentage of the sale price of a good or service that is added on as a tax. It is usually applied to the final purchase price of a product or service and is paid by the consumer at the time of purchase.
Since the sales tax rate is 7.8% and Kiara buys a box of dirt priced at $150.24. Thus, the tax amount can be determined as follows:
Tax amount = 7.8/100 × $150.24
Tax amount = $11.72
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find the interior angle of each regular polygon. Round your answer to the nearest tenth.
Answers
The interior angles of each regular polygon are 60 degree, 90 degree and 108 degree respectively.
What is interior angle of polygon and how to find?Interior Angle of a polygon = 180° – Exterior angle of a polygon. Method 3: If we know the sum of all the interior angles of a regular polygon, we can obtain the interior angle by dividing the sum by the number of sides. Interior Angle = Sum of the interior angles of a polygon / n.
To solve the given problem, it is necessary to know about the polygon. A polygon is a closed curve that consist a set of line segments connected together, such that there is a no intersection between the segments.
A regular polygon refers to a multi-sided convex figure where all the sides are equal in length and all the angles have equal degree measures.
For example: -
The triangle is a polygon that has 3 interior angles.The square is a polygon that has 4 interior angles.The pentagon is a polygon that has 5 interior angles.The formula for the interior angle of a regular polygon is given by,
= (n-2)*180/n
Here, n is the number of sides.
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11.5% of an amount is 782.
What is the original amount?
Answers
Answer:
15640
let me know If I got it!
a recent medical study reported that people who own pets have lower blood pressure than people who do not own pets. this led some doctors to believe that pet ownership has positive health benefits. however, more careful analysis of the data showed that the pet owners in the study exercised more and smoked less than those who did not own pets. this is an example of
Answers
confounding variables; the medical study did not control for other factors that could have caused the lower blood pressure in pet owners.
A confounding variable is an extraneous factor that can influence the results of a study. In this case, the medical study reported that people who owned pets had lower blood pressure than those who did not own pets. This led some doctors to believe that pet ownership had positive health benefits. However, further analysis of the data revealed that the pet owners in the study also exercised more and smoked less than those who did not own pets. This means that the pet ownership was not necessarily responsible for the lower blood pressure, but rather these other factors could have contributed to the results. Thus, the study lacked control for these confounding variables, which could have invalidated the results.
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whats the answer!! please asap
Answers
Answer:1/90
Step-by-step explanation:
-3x +4y = -5
-6x +8y = -10
Answers
Answer:
1. The equation you've provided is a linear equation in the form of y = mx + b, where m is the slope, x is the variable and b is the y-intercept.
The slope (m) of the line represented by this equation is -3/4, the y-intercept is -5/4 and x is a variable.
It is a representation of a straight line in the coordinate plane, where x and y are the coordinates. The line passes through the point (-5/4, 0) and the slope of the line is -3/4.
2.The equation you've provided is a linear equation in the form of y = mx + b, where m is the slope, x is the variable and b is the y-intercept.
The slope (m) of the line represented by this equation is -3/4, the y-intercept is -5/4 and x is a variable.
It is a representation of a straight line in the coordinate plane, where x and y are the coordinates. The line passes through the point (-5/4, 0) and the slope of the line is -3/4.
Please note that in the equation you provided -6x +8y = -10 the slope is -3/4 and y-intercept is -5/4.
How to find proportional parts in triangles and parallel lines?
Answers
If a line parallel to one side of a triangle contacts the other two sides of the triangle, the line proportionally splits these two sides. If DE = BC, then ADDB=AEEC.
If a line parallel to one side of a triangle contacts the other two sides, the two sides are proportionately divided.
The formula for a proportional equation is y = kx. The letters y and x denote the variables in the equation. The letter k represents the proportionality constant, which is fixed.
Because matching angles produce the AA similarity shortcut, when a line is drawn parallel to one side of a triangle, two similar triangles are generated. Because the triangles are comparable, the parallel line segments are proportionate segments.
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Martina made 3 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for all 3 necklaces was $11.10 . If the beads cost $1.80 for each necklace, how much did each pendant cost?
Answers
Answer:
1.9
Step-by-step explanation:
11.1 /3 =3.7 for beads + pendants per necklace
pendant =3.7-1.8 =1.9
Copy the problem, and write a Statement/Reason proof.
Answers
The problem is given as follows:
Prove: ΔLUZ ≅ ΔIDA
The triangles above can be said to be congruent because:
[tex]\overline{ZL}[/tex] ≅ [tex]\overline{AI}[/tex] (Corresponding sides)
[tex]\overline{LU}[/tex]≅ [tex]\overline{DI}[/tex] (Corresponding sides)
[tex]\overline{UZ}[/tex] ≅ [tex]\overline{AD}[/tex] (Corresponding sides)
It is also given that:
m ∠ ULZ ≅ m ∠ ADI
since
[tex]\overline{ZL}[/tex] ≅ [tex]\overline{AI}[/tex] (Corresponding sides)
[tex]\overline{LU}[/tex]≅ [tex]\overline{DI}[/tex] (Corresponding sides) and
m ∠ ULZ ≅ m ∠ ADI ;
We can thus conclude that the ΔLUZ ≅ ΔIDA
What is the meaning of congruent triangles?When two triangles are congruent, one can be moved (through one or more stiff movements) to coincide with the other. All congruent sides and angles will be found.
The triangles are congruent if two sides and the included angle of one triangle are congruent to the corresponding sections of another triangle. [Side - Angle - Side]
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Use your formula 1/2(a+b)h, to determine the height of a trapezoid with an area of 24 cubic centimeters and base lengths of 9 cm and 7 cm.
Answers
The height of the trapezoid with an area of 24cm² and base lengths of 9 cm and 7 cm is 3cm.
What is the height of the trapezoid?A trapezoid is simply a quadrilateral with at least one pair of parallel sides.
The area of a trapezoid is expressed as;
A = 1/2(a+b)h
Given that;
Area A = 24 cmBase side a = 9cmBase side b = 7cmHeight h = ?Plug in the values into the above formula and solve for h.
A = 1/2(a+b)h
A = 1/2(a+b)h
2A = (a+b)h
2A/(a+b) = h
h = 2A/(a+b)
h = ( 2 × 24cm² ) / ( 9cm + 7cm )
h = 48cm² / 16cm
h = 3cm
Therefore, the value of height h is 3cm.
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I need help! ……………….
Answers
Answer:
x = 140 degrees
Step-by-step explanation:
this polygon has 6 sides
to find the number of degrees of the six interior angles you can use this formula:
(n-2)*180 where 'n' equals the number of sides
(6-2)*180 = 4(180) = 720 degrees
starting with the 'x' angle and going clockwise, we have the following:
x + 90 + 104 + 123 + 155 + 108 = 720
x + 580 = 720
x = 720 - 580
x = 140
Over 40% of
Belorussian territory
is covered in forests,
this is why they have
a green stripe on
their flag is Belarus
is 80,153 mi? what
percentage is NOT
forests?
Answers
If 40% of Belorussian territory is covered in forests , and the total area is 80153 mi² , then the percent that is not covered in forests is 60% and land area is 48,091.8mi² .
the total land area of Belorussian territory is = 80153 mi² ;
the percent of land area covered in forest is = 40% ;
So , the percent that is not covered in Forest is = 100 - 40 = 60% ;
and the land area not covered in forest is = 60% of 80153 ;
= 0.6 × 80153 ;
= 48,091.8 .
Therefore , the percentage that is NOT forests is 60% .
The given question is incomplete , the complete question is
Over 40% of Belorussian territory is covered in forests, this is why they have a green stripe on their flag is Belarus total area is 80153 mi² , What percentage is NOT forests ?
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at a dance, there are 20 girls and 20 boys. how many ways are there to form 20 pairs consisting of 1 boy and 1 girl?
Answers
There are 400 different ways possible to form 20 pairs consisting of 1 boy and 1 girl
What is a combination?In mathematics, a combination or combinations are all the possible groupings that can be made of a given number of elements, without repeating them and regardless of the order in which they are found.
To solve this problem the formula and the combination procedure we must use is:
C(n/r) = n! / [(n-r)! *r!]
Where:
C(n/r) = combination
n = total number of objects
r = number of selected objects
! = factorial of the number
Information about the problem:
n(girl) = 20n(girl) = 1n(boy) = 20n(boy) =1Applying the combination formula we have:
C(n/r) = n! / [(n-r)! *r!]
C(20/1) = 20! / [(20-1)! *1!]
C(20/1) = 20! / [(19)! *1!]
C(20/1) = 20*19! / [(19)! *1!]
C(20/1) = 20/1!
C(20/1) = 20
Cgirl(20/1) * Cboy(20/1) = 20*20
Cgirl(20/1) * Cboy(20/1) = 400
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What is the value of x in this triangle?
Answers
Answer:
83 degrees
Step-by-step explanation:
Angles inside a triangle is what we called interior angles, which its sum should be equal to 180. Thus, the equation would be like this:
44 + 53 + x = 180
We simply re-arrange the equation to get the value of x.
x = 180 - (44 + 53)
x = 180 - 97
x = 83
Admission to a carnival costs $5. Tickets for games at the carnival costs $2 each.
defines a function in this situation. What does the function
1. The equation C = 5 + 2t
represent?
Answers
C=5+2t represents the total cost of attending the carnival: you pay an admission fee of $5 and then $2 for a ticket to play games.
C=5+2 T stands for the carnival's overall ticket price: $5 is the entrance cost, and $2 is the game ticket price.
To determine the inverse function of C(t), solve the following equation for "t" (the function and argument are switched in the inverse function):
t =(C - 5)/2
The number of games someone played during the carnival is represented by the inverse function.
[tex]t=\frac{C-2}{5}[/tex]is not the inverse function of C, according to. (t). In 2, the inverse function was discovered.
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Scientists want to investigate the effects caffeine on short term memory by randomly assigning 200 volunteers to intake 86mg of caffeine. remaining 200 volunteers to intake 86mg of a placebo. In context, what was the control used in this study?
Answers
A placebo is a medication or procedure that is given to a patient for psychological rather than physiological reasons.
The most typical sources of caffeine in nature are the cocoa, tea, and coffee plants. It functions by activating the central nervous system and brain, keeping you alert and delaying the development of fatigue.
Coffee has a maximum of 86 mg of caffeine per serving.
The highest daily dose of caffeine recommended by health authorities, excluding those who are pregnant or breastfeeding, is 400 mg for healthy individuals. Additionally, it is advised to consume no more than 200 mg of caffeine daily from all sources while pregnant or nursing.
Unwanted adverse effects might arise from placebos. Negative placebo effects, often referred to as nocebo effects, have been documented as nausea, drowsiness, and allergic reactions, including skin rashes.
Considering everything, it's clear that placebos aren't used in studies all that frequently. Therefore, the 86mg of placebo is employed in a regulated manner in the study.
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five cards were randomly drawn from a standard deck of cards. a) (two pairs) what is the probability that two cards are of the same rank, two are of an
Answers
If three cards are drawn from a standard deck of 52 cards , then the probability that all the cards are of same rank is 1/425 .
The number of cards in the standard deck is = 52 cards ;
thee cards are drawn from the deck ,
we have to find the probability that they all are of the same rank , that means ( e.g. all 3 are queens ) ;
we have to draw 3 cards from 4 suits. which means 1 card is taken from the 13 numbers.
the number of favorable outcomes (all from same rank) = ⁴C₃×13
= 52 ;
total number of outcomes is = ⁵²C₃ = 22100 ;
the required probability is = 52/22100 ;
= 1/425 .
Therefore , the probability that all 3 cards are of same rank is 1/425 .
The given question is incomplete , the complete question is
The three cards were randomly drawn from a standard deck of 52 cards.
What is the probability they are all the same rank ?
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Write 7.67 times 10 -² in standard notation.
Answers
7.67 times 10^-² in standard notation can be written as 0.0767.
To convert scientific notation to standard notation, you can simply move the decimal point to the left or right as many times as indicated by the exponent of the power of 10. In this case, the exponent is -2, so you move the decimal point 2 places to the left. The result is 0.0767.
Help me pls it’s due tomorrow and pls have a explanation!!
Answers
Answer: 16/24
Step-by-step explanation: You should convert 7/8 and 2/3 to get a common denominator, in this situation the common denominator is 24. You multiply 2/3 by 8 on both sides of the fraction and the same with 7/8 except with 3. When you convert it 7/8 becomes 21/24 which is the total amount of grapes she bought, the amount she used comes out to be 16/24.