6.2 × 10⁴ in decimal notation is simply 62,000.
In scientific notation, a number is expressed as the product of a decimal number between 1 and 10 and a power of 10.
Now, let's talk about converting a number in scientific notation to decimal notation. Decimal notation simply means expressing a number in the standard way, using digits and a decimal point. To convert a number in scientific notation to decimal notation, we just need to evaluate the product of the decimal number and the power of 10.
In the case of 6.2 × 10⁴, the decimal number is 6.2, and the power of 10 is 4. To evaluate the product, we simply move the decimal point in 6.2 four places to the right, since the power of 10 is positive. This gives us:
6.2 × 10⁴ = 62,000
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Complete Question:
Convert to decimal notation: 6.2 × 10⁴
Which point on the number line has the least absolute value?
The point with the least absolute value on the number line is always the point zero.
The absolute value of a number is the distance that number is from zero on the number line. Therefore, the point on the number line with the least absolute value is the point closest to zero. This point is located at zero itself, as it is the point on the number line that is equidistant from both the positive and negative numbers.
To further explain, consider the following examples:
- The point 3 is 3 units away from zero, but the point -3 is also 3 units away from zero.
- The point 5 is 5 units away from zero, but the point -5 is also 5 units away from zero.
- The point 0 is 0 units away from zero, making it the point with the least absolute value on the number line.
In conclusion, the point with the least absolute value on the number line is always the point zero.
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13. d(-8, 1), e(-3, 6), f(7,4), g(2, -1) (distance formula)
The distances between the points are approximately 7.07, 10.20, and 7.07.
To find the distance between the points d(-8, 1) and e(-3, 6), we use the distance formula:
distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Plugging in the values, we get:
distance = √[(-3 - (-8))^2 + (6 - 1)^2]
distance = √[5^2 + 5^2]
distance = √50
distance ≈ 7.07
To find the distance between the points e(-3, 6) and f(7, 4), we again use the distance formula:
distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Plugging in the values, we get:
distance = √[(7 - (-3))^2 + (4 - 6)^2]
distance = √[10^2 + (-2)^2]
distance = √104
distance ≈ 10.20
To find the distance between the points f(7, 4) and g(2, -1), we again use the distance formula:
distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Plugging in the values, we get:
distance = √[(2 - 7)^2 + (-1 - 4)^2]
distance = √[(-5)^2 + (-5)^2]
distance = √50
distance ≈ 7.07
So, the distances between the points are approximately 7.07, 10.20, and 7.07.
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complete question:
Determine the distance between DE, EF and FG.
D(-8, 1), E(-3, 6), F(7, 4), G(2, -1)
Find the exact values of sin 2. cos2u. and tan 2u using the double angle formulas Cos u =- 4/5 π/2 < u < π sin 2u = cos 2u= tan 2u =
The probability of drawing either a two or a ten from a standard deck of 52 cards is the sum of the probabilities of drawing a two and drawing a ten.
There are four twos and four tens in the deck, so the probability of drawing a two is 4/52 and the probability of drawing a ten is 4/52. Therefore, the probability of drawing either a two or a ten is:
4/52 + 4/52 = 8/52 = 2/13
The probability of drawing either a two or a club from a standard deck of 52 cards is the sum of the probabilities of drawing a two and drawing a club, minus the probability of drawing the two of clubs (since we have already counted it). There are four twos and 13 clubs in the deck, including the two of clubs. Therefore, the probability of drawing a two is 4/52, the probability of drawing a club is 13/52, and the probability of drawing the two of clubs is 1/52. Therefore, the probability of drawing either a two or a club is:
4/52 + 13/52 - 1/52 = 16/52 = 4/13
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2.
(03. 02 MC)
Kayla was at the surface of a swimming pool and recorded the following two measurements, in feet, on a number line:
−9, which represents the depth of water in the swimming pool
+10, which represents the height of the slide at the pool
Part A: What does 0 represent in this situation? (3 points)
Part B: Describe the height of the slide in relation to 0 in the situation. (3 points)
Part C: Kayla held a pole in the swimming pool. The bottom of the pole was at a depth of 3 feet. How should Kayla mark the level of the bottom of the pole on the number line? Explain how you determined this. (4 points)
0 represents the surface level of the swimming pool.
The height of the slide in relation to 0 is +10 feet.
Part A: In this situation, 0 represents the surface level of the swimming pool on the number line, acting as a reference point between the depth of the water and the height of the slide.
Part B: The height of the slide in relation to 0 is +10 feet. This means the slide is 10 feet above the surface level of the swimming pool.
Part C: To mark the level of the bottom of the pole on the number line, Kayla should mark it at -3 since the bottom of the pole is at a depth of 3 feet below the surface level of the pool.
This is determined by using the negative value to represent the depth below the surface (0).
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An appliance store manager noted that
sales varied directly with the amount of money
spent on advertising. If last week's sales were
$10,000 and $2000 was spent on advertising,
what should sales be during a week that $1200
was spent on advertising?
In the given problem, solving systematically, sales should be $6,000 during a week that $1,200 was spent on advertising.
How to Calculate the Sales?If sales vary directly with the amount of money spent on advertising, it means that the ratio of sales to advertising spending is constant. We can use this ratio to find out what sales should be during a week that $1200 was spent on advertising.
Let the ratio of sales to advertising spending be denoted by k. Then, we have:
k = sales / advertising spending
From the information given, we know that:
k = 10,000 / 2,000 = 5
This means that for every dollar spent on advertising, $5 in sales are generated.
To find out what sales should be during a week that $1200 was spent on advertising, we can use the ratio k:
sales = k * advertising spending
sales = 5 * 1200
sales = 6000
Therefore, sales should be $6,000 during a week that $1,200 was spent on advertising.
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Kyra bought a ""trick"" coin that lands on heads with a probability of 0. 4. Which frequency table would Kyra most likely generate by flipping the coin many times?
Don't mind the answer c because I don't know if that's right
Kyra's trick coin is more likely to generate a frequency table with a higher count of tails than heads, reflecting the 0.4 probability of landing on heads and the 0.6 probability of landing on tails.
Kyra's "trick" coin has a probability of 0.4 for landing on heads, meaning that it is more likely to land on tails. If Kyra flips the coin many times, she will likely generate a frequency table that shows a higher frequency of tails than heads.
A possible frequency table might look like this:
| Outcome | Frequency |
|---------|-----------|
| Heads | 40 |
| Tails | 60 |
In this table, the coin landed on heads 40 times and tails 60 times, representing the probability of 0.4 for heads and 0.6 for tails (since the total probability must equal 1). The more times Kyra flips the coin, the closer the relative frequencies will get to the actual probabilities. It's important to note that this is just an example, and the exact frequency counts may vary in practice due to randomness.
To summarize, Kyra's trick coin is more likely to generate a frequency table with a higher count of tails than heads.
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Help me please!
use either method to construct a line parallel to the given line through the given point. gl 3.1)
a lab 1 question 1
To construct a line parallel to a given line through a given point, there are two methods that can be used: the ruler and compass method or the parallel line equation method.
The ruler and compass method involves drawing a line through the given point that intersects the given line at a right angle. Then, using the compass, the distance between the given point and the intersection point is measured and transferred to a point on the given line. Finally, a line is drawn through the given point and the point on the given line to create a parallel line.
The parallel line equation method involves using the slope of the given line to find the slope of the parallel line. This is done by recognizing that parallel lines have the same slope. Then, using the point-slope equation of a line, the parallel line equation can be found by plugging in the given point and the calculated slope.
In summary, constructing a line parallel to a given line through a given point can be achieved using either the ruler and compass method or the parallel line equation method. Both methods are valid and can be used depending on personal preference and familiarity with the mathematical concepts involved.
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1. Simplify (Write each expression without using the absolute value symbol. )
|120+x| if x<-120
2. Simplify (Write each expression without using the absolute value symbol. )
|x-120| if x<-120
3. Simplify (Write each expression without using the absolute value symbol. )
|x-(-12)| if x>-12
4. Simplify (Write each expression without using the absolute value symbol. )
|x-(-12)| if x<-12
By solving each expression without using the absolute value symbol are:-
1. -x-120 if x<-120
2. -(x-120) if x<-120
3. x+12 if x>-12
4. -(x+12) if x<-12
To simplify each expression without using absolute value symbols, we need to determine the cases when the expression inside the absolute value bars is positive and negative. Then we can remove the absolute value bars and simplify the expression accordingly.
For the first expression, |120+x|, if x is less than -120, then x+120 will be negative. Therefore, we can simplify the expression as -x-120.
For the second expression, |x-120|, if x is less than -120, then x-120 will also be negative. Therefore, we can simplify the expression as -(x-120).
For the third expression, |x-(-12)|, if x is greater than -12, then x-(-12) is positive. Therefore, we can simplify the expression as x+12.
For the fourth expression, |x-(-12)|, if x is less than -12, then x-(-12) is negative. Therefore, we can simplify the expression as -(x+12).
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find the missing side length
Answer:
6.5
Step-by-step explanation:
Use pythagorean theorem:
[tex]a^{2} +b^{2} =c^{2}[/tex]
a=6
b=2.5
c=hypotenuse
[tex]6^{2} +2.5^{2} =c^{2}[/tex]
simplify
[tex]36 +6.25=c^{2}\\42.25=c^{2}[/tex]
take square root of both sides
[tex]c=6.5[/tex]
The missing side length is 6.5 units.
Hope this helps!
A plane leaves Singapore airport at 07:45 to fly to Sydney. The plane flies at an average speed of 757.2 km/h. The distance from Singapore to Sydney is 6310 km. The time in Sydney is 2 hours ahead of Singapore time. Calculate the local time when the plane arrives in Sydney. Give your answer in the form hours:minutes using the 24-hour clock.
The local time in Sydney when the plane arrives will be 18:58, or 6:58 PM on a 24-hour clock.
How to find arrival time for the plane?The time difference between Speed and Sydney is 2 hours, and the plane will take some time to fly from Singapore to Sydney at an Speed of 757.2 km/h over a distance of 6310 km.
The time it takes the plane to fly from Speed to Sydney can be calculated as:
time = distance / Speed= 6310 km / 757.2 km/h = 8.33Speed
So the plane will take 8.33 hours to fly from Singapore toSpeed
Now we need to add the 2-hour time difference between Singapore and Sydney to determine the local time in Sydney when the plane arrives.
07:45 (Singapore time) + 8.33 hours (flight time) + 2 hours (time difference) = 18:58
Therefore, the local time in Sydney when the plane arrives will be 18:58, or 6:58 PM on a 24-hour clock.
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fast pls
in When calculating 4-√x+15 what option you get x?-1 lim X>1 1 the process -1 A) lim (x + 1) (4 + V1 +15) -1 B) lim 21 (1+1) (4 - V1-15) C) lim 16 - 2 - 1)(4+r+15) D) lím 16-1 (12 - 1) (4 - Vr+15)
None of the options are correct, and the value of x is simply 1.
Start with the given expression: 4 - √x + 15
Substitute x with the limit value of 1: 4 - √1 + 15 = 18
Therefore, the limit of the given expression as x approaches 1 from the right is 18.
To verify this result using the provided options, we can simplify each option and check which one equals 18 as x approaches 1 from the right.
Option A simplifies to (2/√2) + 2, which equals √2 + 2, not equal to 18.
Option B simplifies to 2(4 - √15), which equals 2(4 - 3.87), approximately equal to 2.27, not equal to 18.
Option C simplifies to 3(4 + √15), which equals 3(4 + 3.87), approximately equal to 23.61, not equal to 18.
Option D simplifies to 3(3)(3), which equals 27, not equal to 18.
Therefore, none of the options are correct, and the value of x is simply 1.
none of the options are correct, and the value of x is simply 1.
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For the function f (x) x = 2 to r 2 to X = 2.001. . x3, find the slope of secant over the interval A. slope = 10. 001001 B. slope = 1.006001 C. slope 2. 001001 D. slope - 12. 006001
To find the slope of the secant over the interval from x=2 to x=2.001, we need to use the formula for the slope of a secant line:
slope = (f(2.001) - f(2)) / (2.001 - 2)
First, we need to find the values of f(2.001) and f(2):
f(2) = 2^3 = 8
f(2.001) = 2.001^3 ≈ 8.012006001
Plugging these values into the formula, we get:
slope = (8.012006001 - 8) / (2.001 - 2)
slope ≈ 1.006001
Therefore, the slope of the secant over the interval from x=2 to x=2.001 is approximately 1.006001. So the answer is B. slope = 1.006001.
To find the slope of the secant line for the function f(x) over the interval [2, 2.001], we will use the slope formula:
slope = (f(2.001) - f(2)) / (2.001 - 2)
First, find the values of f(2) and f(2.001) by plugging the values of x into the given function f(x) = x^3:
f(2) = 2^3 = 8
f(2.001) = (2.001)^3 ≈ 8.006012
Now, plug these values into the slope formula:
slope = (8.006012 - 8) / (2.001 - 2) = 0.006012 / 0.001 = 6.012
The slope of the secant line over the interval is approximately 6.012. The given options do not match this result, so it's possible there is an error in the provided choices.
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You are going to run at a constant speed of 7.5
miles per hour for 45
minutes. You calculate the distance you will run. What mistake did you make in your calculation? [Use the formula S=dt
.]
Answer: Did not convert the minutes to hours
Step-by-step explanation:
The most obvious mistake here would be to not convert the minutes into hours.
Remember, the speed given, (7.5), is in miles per HOUR. Your time is given in MINUTES. a conversion is required. 45 minutes are 45/60 = 0.75 hrs.
NOW you can use S = DT to find your distance:
7.5 = D/0.75
.: D = 5.625 miles
how many ways are there to distribute the comic books if there are no restrictions on how many go to each kid (other than the fact that all 20 will be given out)?
There are 15,504 ways to distribute 20 comic books among five kids if there are no restrictions on how many go to each kid.
To evaluate this expression, we can use the formula for combinations:
ⁿCₓ = n! / (x! (n-x)!)
where n is the total number of objects, x is the number of objects to be selected, and "!" denotes factorial
In this case, we have:
n = 20 and r = 5
so we can plug these values into the formula:
²⁰C₅ = 20! / (5! (20-5)!)
= (20 x 19 x 18 x 17 x 16) / (5 x 4 x 3 x 2 x 1)
= 15,504
Therefore, there are 15,504 ways to distribute the 20 comic books among the five kids if there are no restrictions on how many go to each kid.
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Complete Question:
20 different comic books will be distributed to five kids.
How many ways are there to distribute the comic books if there are no restrictions on how many go to each kid (other than the fact that all 20 will be given out)?
I need help. Assume the base is 2
a = 5
b = 4
c= 0
Therefore, the equation for graph C is Y = a ^b + c
Y = 5 ^4 + 0
What is a graph?A graph is described as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
Graphs are a popular tool for graphically illuminating data relationships.
A graph serves the purpose of presenting data that are either too numerous or complex to be properly described in the text while taking up less room.
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What type of triangle would be represented by the vertices (1, 3), (4, -1), and (5, 6)?
Can somebody please just give me an example problem for exponential decay? I will give brainliest, thanks!
Example problem:
A radioactive substance has a half-life of 10 years. If there are initially 100 grams of the substance, how much will be left after 30 years?Solution:
Using the formula for exponential decay:
[tex]\sf\qquad\dashrightarrow N(t) = N0 * e^{(-kt)}[/tex]
where:
N(t) is the amount of the substance at time tN0 is the initial amountk is the decay constante is the mathematical constant approximately equal to 2.718Since the half-life is 10 years, we know that:
[tex]\sf\qquad\dashrightarrow k = \dfrac{\ln(0.5)}{10} = -0.0693[/tex]
(where ln is the natural logarithm)Substituting the given values, we get:
[tex]\sf:\implies N(30) = 100 * e^{(-0.0693 * 30)}[/tex]
[tex]\sf:\implies N(30) = 100 * e^{(-2.079)}[/tex]
[tex]\sf:\implies N(30) = 100 * 0.126[/tex]
[tex]\sf:\implies \boxed{\bold{\:\:N(30) = 12.6\: grams\:\:}}\:\:\:\green{\checkmark}[/tex]
Therefore, after 30 years, only 12.6 grams of the radioactive substance will be left.
Find cot0, sin 0, and csc 0, where 0 is the angle shown in the figure.
Give exact values, not decimal approximations.
0
11
8
cot 0 = 0
sin 0 = 0
csc 0 = 0
Answer:
Step-by-step explanation:
sun cos
1. Sanchez deposited $3,000 with a bank in a 4-year certificate of deposit yielding 6% interest
compounded daily. Find the interest earned on the investment. (4pts)
The compound interest generated on the investment is roughly $813.67, which is the solution to the question based on compound interest.
What is Principal?The initial sum of money invested or borrowed, upon which interest is based, is referred to as the principle. The principal is then periodically increased by the interest, often monthly or annually, to create a new principal sum that will accrue interest in the ensuing period.
Using the compound interest calculation, we can determine the interest earned on Sanchez's investment:
[tex]A = P(1 + \frac{r}{n} )^{(n*t)}[/tex]
where A is the overall sum, P denotes the principal (the initial investment), r denotes the yearly interest rate in decimal form, n denotes the frequency of compounding interest annually, and t denotes the number of years.
In this case, P = $3,000, r = 0.06 (6%), n = 365 (compounded daily),
and t = 4.
Plugging in the values, we get:
[tex]A = 3000(1 + \frac{0.06}{365} )^{(365*4)}[/tex]
A= $3813.67
The difference between the final amount and the principal is the interest earned.
Interest = A - P
Interest = $3813.67 - $3000
Interest = $813.67
As a result, the investment's interest yield is roughly $813.67.
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Antonio, a professional wrestler, went on a very strict liquid diet for 26 weeks to lose weight. When he
began the diet, he weighed in at a healthy 235 pounds and during the diet, he consistently lost 1. 5% of his
body weight each week. His weight loss can be modeled by the function W (t) = 235(0. 985)' where Wis
his weight in pounds and t is the time in weeks that he has been on the diet.
What was his weight in pounds after 5 weeks?
How long did it take(in weeks) him to weigh in at 161. 05 pounds?
Antonio's weight after 5 weeks was 202.34 pounds, and it took him 19 weeks to weigh in at 161.05 pounds.
To find Antonio's weight after 5 weeks, we can simply substitute t = 5 into the given exponential function:
W(5) = 235(0.985)⁵
W(5) ≈ 209.88 pounds
So his weight after 5 weeks was approximately 209.88 pounds. To find how long it took him to weigh in at 161.05 pounds, we can set the function equal to 161.05 and solve for t:
161.05 = 235(0.985)ᵗ
0.685106383 ≈ 0.985ᵗ
t ≈ 25.5 weeks
So it took him approximately 25.5 weeks to weigh in at 161.05 pounds
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Complete question - Antonio, a professional wrestler, went on a very strict liquid diet for 26 weeks to lose weight. When he began the diet, he weighed in at a healthy 235 pounds and during the diet, he consistently lost 1. 5% of his body weight each week. His weight loss can be modeled by the function W (t) = 235(0. 985)ᵗ where W is his weight in pounds and t is the time in weeks that he has been on the diet. What was his weight in pounds after 5 weeks? How long did it take(in weeks) him to weigh in at 161. 05 pounds?
Ben is 140 cm tall. Fareed is 1090 mm tall. Who is taller? How much taller?
Answer:
Ben is 31 cm taller
Step-by-step explanation:
1090mm is 109 cm
Subtract Fareeds height from Bens:
140-109=31
Hope this helps!
Mariana tiene un peso de 175 libras y su nutrióloga le ha otorgado una nueva dieta y ella misma a creado una nueva rutina de ejercicio su comida semanal consiste en lo siguiente 3 libras de pollo, 9 libras de frutas, 15 libras de verduras cocinadas o crudas y solo 1 libra de tortilla o pollo
¿cual es el peso en kilogramos de mariana?
¿cuantos kilos debe conseguir de pollo a la semana?
¿cuantos de fruta?
¿cuantos kg de verduras deberá consumir?
plis es para hoy
El peso de Mariana en kilogramos es aproximadamente 79.378 kg. Debe conseguir 1.361 kg de pollo a la semana, 4.082 kg de frutas y 6.803 kg de verduras.
How to convert Mariana's weight from pounds to kilograms?Para convertir el peso de Mariana de libras a kilogramos, debemos recordar que 1 libra equivale a aproximadamente 0.4536 kilogramos. Por lo tanto:
Peso de Mariana en kilogramos = 175 libras * 0.4536 kg/libra ≈ 79.3792 kg
Entonces, el peso de Mariana es aproximadamente 79.3792 kilogramos.
En cuanto a la cantidad de pollo que Mariana debe conseguir a la semana, la dieta establece que debe consumir 3 libras de pollo. Para convertirlo a kilogramos:
Cantidad de pollo a la semana = 3 libras * 0.4536 kg/libra ≈ 1.3618 kg
Por lo tanto, Mariana debe conseguir aproximadamente 1.3618 kilogramos de pollo a la semana.
De manera similar, para las frutas, la dieta establece 9 libras. Convertimos a kilogramos:
Cantidad de frutas a la semana = 9 libras * 0.4536 kg/libra ≈ 4.0824 kg
Por lo tanto, Mariana debe conseguir aproximadamente 4.0824 kilogramos de frutas a la semana.
Para las verduras, la dieta establece 15 libras. Convertimos a kilogramos:
Cantidad de verduras a la semana = 15 libras * 0.4536 kg/libra ≈ 6.804 kg
Por lo tanto, Mariana debe consumir aproximadamente 6.804 kilogramos de verduras (cocinadas o crudas) a la semana.
En resumen, el peso de Mariana es de aproximadamente 79.3792 kilogramos. Debe conseguir alrededor de 1.3618 kilogramos de pollo, 4.0824 kilogramos de frutas y 6.804 kilogramos de verduras a la semana.
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Darren made a display board in the shape of a trapezoid.
Part A
The height of the trapezoid is half the length of the shorter base, and the longer base is twice the length
of the shorter base.
4 yd
2 yd
2 yd
b
What are the lengths of the height and the longer base? Enter your answers in the boxes.
h =
yd
b=
yd
Part B
Use the measurements from Part A to find the area of Darren's display board.
o 8 yd?
12 yd?
O 16 yd
24 yd2
Part A:
The height (h) of the trapezoid is half the length of the shorter base (b), so h = (1/2)b.
The longer base is twice the length of the shorter base, so the longer base is 2b.
Given: 4 yd + 2 yd + 2 yd + b = 8 yd (since the sum of all sides of the trapezoid is equal to the perimeter of the display board)
Solving for b, we get:
b = 2 yd
Substituting this value in the equation for h, we get:
h = (1/2)(2 yd) = 1 yd
Therefore, the length of the height is 1 yd and the length of the longer base is 4 yd.
Part B:
The formula for the area of a trapezoid is A = (1/2)(h)(b1 + b2), where h is the height and b1 and b2 are the lengths of the two bases.
Using the values from Part A, we have:
A = (1/2)(1 yd)(2 yd + 4 yd)
A = (1/2)(1 yd)(6 yd)
A = 3 yd^2
Therefore, the area of Darren's display board is 3 yd^2.
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Jules took the first piece of a pizza, and Margo noticed that, by doing so, Jules made an angle. Jules estimated he made a 20 degree angle and Margo estimated he made a 45 degree angle. Who is right? How did you determine your answer?
Margo is right; Jules made a 45 degree angle.
How can we determine who is right about the angle measurement?To determine who is right about the angle made by Jules while taking the first piece of pizza, we need to compare their estimates of 20 degrees and 45 degrees.
Since angles are measured using a protractor or other measuring tools, we rely on accurate measurement techniques to determine their values. If both Jules and Margo used appropriate measuring tools and techniques, we would expect their measurements to be close.
However, a 20-degree angle is significantly smaller than a 45-degree angle. Therefore, based on the provided information, Margo's estimate of a 45-degree angle seems more reasonable and likely to be correct.
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Last week, hayden rode his bike 5 times. each time, he biked a 3-mile path, a 2-mile path, and a 2 1 4 -mile path. which expression represents the total number of miles he biked? a. 5 × ( 3 2 2 1 4 ) b. 5 ( 3 × 2 × 2 1 4 ) c. 5 × ( 3 × 2 × 2 1 4 ) d. 5 ( 3 2 2 1 4 )
The correct expression to represent the total number of miles Hayden biked is A. 5 × (3 + 3 + 2 1/4)
This is because each time Hayden rode his bike, he biked a 3-mile path, a 2-mile path, and a 2 1/4 -mile path. To find the total number of miles he biked, we need to add up the distance he biked each time and then multiply by the number of times he biked.
Using the distributive property of multiplication over addition, we can rewrite the expression as:
= 5 × (3 + 3 + 2 1/4)
Therefore, Hayden biked a total of 41 1/4 miles. The correct answer is A
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1) A politician is about to give a campaign speech and is holding a 'stack of ten cue cards, of which the first 3 are the most important. Just before the speech, she drops all of the cards and picks them up in a random order. What is the probability that cards #1, #2, and #3 are still in order on the top of the stack? A) 0. 139% B) 3. 333% C) 0. 794% D) 0. 03%â
The probability that cards #1, #2, and #3 are still in order on the top of the stack is 0.03%. Therefore, the correct option is D.
To find the probability, we need to calculate the number of ways in which the first 3 cards can remain in order on the top of the stack, and divide it by the total number of ways the cards can be arranged.
The number of ways in which the first 3 cards can remain in order is 3! (3 factorial), because there are 3 cards and they can be arranged in 3! = 6 ways.
The total number of ways the cards can be arranged is 10!, because there are 10 cards and they can be arranged in 10! = 3,628,800 ways.
So, the probability is:
3! / 10! = 6 / 3,628,800 = 0.000166 = 0.0166%
We can convert it to a percentage by multiplying by 100:
0.0166 x 100 = 1.66%
However, this is the probability that the first 3 cards are in a specific order, not necessarily the original order. Since the question asks for the probability that the original order is maintained, we need to divide the probability by 3!, which gives:
0.0166 / 3! = 0.000277 = 0.0277%
This is closest to answer choice D) 0.03%.
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help I am not sure of the answer it asks for the domain and the range thank you
Answer:
480 - 96x = 0, so x = 5.
Domain: [0, 5]
Range: [0, 480]
only answer if you know! NO SPAM PLEASE. Must show all calculations and answer both questions!! Please make sure you double check your answer! Will mark brainliest!
Answer:
5. 0
6. a: π/3; b: 45π/2 m ≈ 70.69 m; c: 30/π min ≈ 9.549 min; d: π/900 rad/s; e: 0.2°/s
Step-by-step explanation:
You want the exact value of cos(-39π/6), and some angles, distances, and speeds related to the London Eye Ferris wheel.
5. Exact valueThe argument of the cosine function can be reduced:
[tex]\cos{\left(-\dfrac{39\pi}{6}\right)}=\cos{\left(\dfrac{13\pi}{2}\right)}\qquad\text{using cos(-x)=cos(x)}[/tex]
We notice this is an odd multiple of π/2, so its value is 0.
cos(-39π/6) = 0
6. London Eyea) Angle in 5 minutesThe rate of movement is given as 2π radians (one revolution) in 30 minutes. Then the angle in 5 minutes is ...
(5 min)(2π rad)/(30 min) = (2π/6) rad = π/3 rad
The passenger will travel π/3 radians in 5 minutes.
b) Distance in 5 minutesThe arc length is given by ...
s = rθ . . . . . . where r is the radius and θ is the central angle in radians
For a radius of (135/2 m) and an angle of π/3 radians, the distance traveled is ...
s = (135/2 m)(π/3) = 45π/2 m ≈ 70.69 m
c) Time for 2 radiansWe know that 2π radians takes 30 minutes, so the time for 2 radians is ...
t = (2 rad)·(30 min)/(2π rad)
t = 30/π min ≈ 9.549 min . . . . about 9:32.96 min
d) Radians per secondThe angular velocity is ...
(2π rad)/(30 min) = (2π rad)/(30 min) × (1 min)/(60 s) = 2π/1800 rad/s
= π/900 rad/s
e) Degrees per second360 degrees in 1800 seconds is ...
360°/(1800 s) = (1/5)°/s
The wheel turns at the rate of 1/5 degree per second.
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Additional comment
At one revolution per half hour, the wheel turns about twice as fast as the minute hand on a clock. This explains why the wheel never appears to be moving when observed from a distance, as when it appears briefly in a movie.
A bucket held 24 gallons of water. Water leaked out of a hole in the bucket at a rate of 3 gallons every 4 days. At this rate, how many days did it take for all 24 gallons to leak out?
It will take 32 days for all 24 gallons to leak out of the bucket at a rate of 3 gallons every 4 days.
If water is leaking out of a bucket at a rate of 3 gallons every 4 days, then the rate of leakage is 3/4 gallons per day.
Let x be the number of days it takes for all 24 gallons to leak out. To explain this situation, we can construct an equation.
24=3/4*x
To solve for x, we can cross-multiply.
24*4=3x
3x=96
x=96/3
x = 32
Therefore, it will take 32 days for all 24 gallons to leak out of the bucket at a rate of 3 gallons every 4 days.
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100 POINTS!!!! PLEASE HELP!! ITS DUE IN 1 HOUR!!!!!!!!!!!!!!