Answer:
7.834 × 10^-8
Step-by-step explanation:
= 7.834 × 10^-8
(scientific notation)
= 7.834e-8
(scientific e notation)
= 78.34 × 10^-9
(engineering notation)
(billionth; prefix nano- (n))
= 0.00000007834
(real number)
^ means the number after is exponent.
without actually calculating the cubes find the value of each of the following (-28)^3+(12)^3+(16)^3
Answer:
-16128
Step-by-step explanation:
This expression can be calculated by algebraic means, whose process is described below:
1) [tex](-28)^{3}+(12)^{3}+(16)^{3}[/tex] Given.
2) [tex](-12-16)^{3} + (12)^{3}+(16)^{3}[/tex] Definition of addition.
3) [tex](-12)^{3} + 3\cdot (-12)^{2}\cdot (-16)+3\cdot (-12)\cdot (-16)^{2}+(-16)^{3}+(12)^{3}+(16)^{3}[/tex] Cubic perfect binomial.
4) [tex](12)^{3}+[(-1)\cdot (12)]^{3}+(16)^{3} + [(-1)\cdot (16)]^{3}+3 \cdot (-12)^{2}\cdot (-16) + 3\cdot (-12)\cdot (-16)^{2}[/tex] Commutative property/[tex](-x)\cdot y = -x\cdot y[/tex]
5) [tex](12)^{3} + (-1)^{3}\cdot (12)^{3} + 16^{3} +(-1)^{3}\cdot (16)^{3} + (-3)\cdot [(-12)^{2}\cdot (16) +(-16)^{2}\cdot (12)][/tex] Distributive property/[tex](-x)\cdot y = -x\cdot y[/tex]/[tex]x^{n}\cdot y^{n} = (x\cdot y)^{n}[/tex]
6) [tex](12)^{3} + [-(12)^{3}]+(16)^{3} + [-(16)^{3}]+ (-3)\cdot [(-12)^{2}\cdot (16)+(-16)^{2}\cdot (12)][/tex] [tex](-x)\cdot y = -x\cdot y[/tex]
7) [tex](-3)\cdot [(-12)^{2}\cdot (16) + (-16)^{2}\cdot (12)][/tex] Existence of the additive inverse/Modulative property for addition.
8) [tex](-3) \cdot [(12)^{2}\cdot (16)+(16^{2})\cdot (12)][/tex] [tex]x^{n}\cdot y^{n} = (x\cdot y)^{n}[/tex]/[tex](-x)\cdot (-y) = x\cdot y[/tex]
9) [tex](-3)\cdot (12)\cdot (16)\cdot (12+16)[/tex] Distributive property.
10) [tex]-16128[/tex] [tex](-x)\cdot y = -x\cdot y[/tex]/Definition of sum/Definition of multiplication/Result
find the missing part of the proportion 12/x = 3/7 x= _
Answer:
x = 28
Step-by-step explanation:
12/x = 3/7
Using cross products
3x = 12*7
3x = 84
Divide by 3
x = 28
Please help, 50 points! :) Please do all parts
you WILL get brainiest
PDF attached below
1. The first step here is to arrange the data set's form least to greatest,
Sherelle: 26, 39, 56, 58, 60, 62, 65, 66, 66, 68, 71, 72, 72, 73, 74, 75, 81, 83, 84, 85
Venita: 44, 45, 51, 51, 53, 53, 55, 57, 58, 62, 65, 66, 69, 69, 70, 73, 75, 77, 78, 79
Now we can determine our 5 - number summary based on the numbers respective positions.
First Data Set,
(Five - Number Summary) - Minimum : 26, Quartile 1 : 60, Median : 69.5, Quartile 3 : 75, Maximum : 85
Second Data Set,
(Five - Number Summary) - Minimum : 44, Quartile 1 : 53, Median : 63.5, Quartile 3 : 73, Maximum : 79
2. This part is based on your drawings of the box and whisker plots, so you would have to figure that part out by yourself.
3. First off we know that our data set is composed of the years from 1900, so let's rewrite the set based off of the actual year -
Sherelle: 1926, 1939, 1956, 1958, 1960, 1962, 1965, 1966, 1966, 1968, 1971, 1972, 1972, 1973, 1974, 1975, 1981, 1983, 1984, 1985
Venita: 1944, 1945, 1951, 1951, 1953, 1953, 1955, 1957, 1958, 1962, 1965, 1966, 1969, 1969, 1970, 1973, 1975, 1977, 1978, 1979
( a ) Now in Sherelle's defence, she can say that the lowest coin date in her group is 1926, comparative to Venita's group - the lowest coin date in hers being 1944. Therefore, she is more likely to have the 1916 coin, after all that date is the lowest overall in both their data set.
( b ) In Venita defence, she can say that the mean of her data set is lower than the mean of Sherelle's data set. Take a look at the calculations below,
Sherella's Mean : [tex]\frac{39336}{20}[/tex] = [tex]\frac{9834}{5}[/tex] = 1966.8,
Venita's Mean : [tex]\frac{39250}{20}[/tex] = [tex]\frac{3925}{2}[/tex] = 1962.5
( c ) I would say Sherella's bag would most likely contain the 1916 coin. The mean is a prominent factor, but their mean(s) only differ by a very small quantity. That too, Sherella's bag contains the lowest coin in both their groups, and though that is not a prominent factor, it could be that she does have the 1916 coin.
Roberto is x years older than his only sister but 10 years ago he was twice her age. What are the current ages of the siblings?
Answer:
S = x + 10
R = 2x + 10
Step-by-step explanation:
If R is Roberto's age, and S is his sister's age, then:
R = S + x
R − 10 = 2 (S − 10)
Solve with substitution.
S + x − 10 = 2 (S − 10)
S + x − 10 = 2S − 20
S = x + 10
R = 2x + 10
Work out the mean for the data set below: 3, 5, 4, 3, 5, 6 Give your answer as a fraction. answer
Answer:
4 1/3
Step-by-step explanation:
3 + 5 + 4 + 3 + 5 + 6 = 26
26/6 = 4 2/6 (4 1/3)
Answer:
13/3
Step-by-step explanation:
To find the mean, add up all the numbers and divide by the number of terms
( 3+5+4+3+5+6) /6
26/6
Divide top and bottom by 2 to simplify the fraction
13/3
How many of the positive integer factors of 15552 are perfect squares?
There are 12 factors which are perfect squares is 1, 4, 9, 16, 36, 64, 81, 144, 324, 576, 1296, 5184.
What is factors?Factors can be define splitting the value in multipliable values.
Factorization of 15552
= 1 * 4 * 4 * 4* 9 * 9 * 3
Perfect squares can be formed by above factors are
= 1, 4, 9, 16, 36, 64, 81, 144, 324, 576, 1296, 5184.
Thus, there are 12 factors which are perfect squares is 1, 4, 9, 16, 36, 64, 81, 144, 324, 576, 1296, 5184.
Learn more about factors here:
https://brainly.com/question/24182713
#SPJ2
What is —4р + (- 6р) equals?
Answer
[tex] \boxed{10p}[/tex]
Step by step explanation
[tex] \mathsf{ - 4p + (- 6p)}[/tex]
When there is a ( + ) in front of an expression in parentheses, the expression remains the same
[tex] \mathsf{ - 4p - 6p}[/tex]
Collect like terms
[tex] \mathsf{ - 10p}[/tex]
Hope I helped!
Best regards!
To make a net from a container, you start by cutting one of the seams along the edge where the two sides meet. If you wanted to make a different net for the container, what would you do differently?
Answer:
I would not separate the same edges when making a second net. Also, I would make sure that the result cannot be rotated or flipped so that it is the same as the first.
Step-by-step explanation:
FWML is a parallelogram. Find the values of x and y. Solve for the value of z, if z=x−y.
Answer:
x = 5, y = 8, z = -3
Step-by-step explanation:
Opposite sides of a parallelogram are congruent so to find x:
x + 7 = 3x - 3
-2x = -10
x = 5
To find y:
y + 2 = 2y - 6
-y = -8
y = 8
Therefore, z = x - y = 5 - 8 = -3.
If a is an arbitrary nonzero constant, what happens to a/b as b approaches 0
It depends on how b approaches 0
If b is positive and gets closer to zero, then we say b is approaching 0 from the right, or from the positive side. Let's say a = 1. The equation a/b turns into 1/b. Looking at a table of values, 1/b will steadily increase without bound as positive b values get closer to 0.
On the other side, if b is negative and gets closer to zero, then 1/b will be negative and those negative values will decrease without bound. So 1/b approaches negative infinity if we approach 0 on the left (or negative) side.
The graph of y = 1/x shows this. See the diagram below. Note the vertical asymptote at x = 0. The portion to the right of it has the curve go upward to positive infinity as x approaches 0. The curve to the left goes down to negative infinity as x approaches 0.
A plane set off to Paris at a speed of 300mph. On the return flight of 12 hours, the plane cruised at 242mph. How many hours long was the flight to Paris
Answer:well the answer is 2 hours 16 minutes.
Step-by-step explanation:
To find your plane's rate of speed, you calculate the distance ... amount of time in the air (2 hours and 16 minutes) to.
8(4k - 4) = -5k - 32
Answer:
k=0
Step-by-step explanation:
8(4k-4)=5k-32
32k-32=-5k-32
32k-32+32=-5k-32+32
32k=-5k
32k+5k=-5k+5k
37k=0
37k/37=0/37
k=0
Answer:
k=0
Step-by-step explanation:
To solve for k, we need to first distribute the 8 through the parenthesis.
32k-32=-5k-32
Lets add 5k to both sides.
37k-32=-32
add 32 to both sides
37k=0
divide 37 from both sides
k=0
Type the correct answer in the box. Use numerals instead of words. The height of a baseball, in feet, is represented by this expression, where t is time in seconds. -16t squared+64t+3 The height of the baseball after 3.5 seconds is BLANK feet.
Answer:
31 Feets
Step-by-step explanation:
Given the expression for the height of a baseball:
Height(t) = -16t^2 +64t +3
Height in Feets ; time (t) in seconds
Height of baseball after 3.5 seconds :
Height(3.5) = -16(3.5)^2 + 64(3.5) + 3
Height = - 16(12.25) + 64(3.5) + 3
Height = - 196 + 224 + 3
Height = 31 Feets
Height after 3.5 seconds = 31 feets
What is the factorization of 2x^2 + 5x + 3?
A. (x+3)(x + 3)
B. (x+3)(x + 1)
C. (2x+3)(x + 1)
D. (2x + 3)(x + 3)
Answer:
( 2x +3) (x+1)
Step-by-step explanation:
2x^2 + 5x + 3
2 factors to 2 and 1
3 factors to 3 and 1
We need to get 5x in the middle
( 2x +3) (x+1)
Melissa put her $500 In a savings account that earns 4% interest compounded annually. How much will be in the account after 3 years? Round your answer to the nearest hundredth
Work Shown:
A = P*(1+r/n)^(nt)
A = 500*(1+0.04/1)^(1*3)
A = 562.432
A = 562.43
Answer: $562.43
Step-by-step explanation:
The initial start up amount is 500 and we want to expressed this as an exponential function. So since we know the initial value we need to find the rate of change. So if you earn 4% interest you are earning 4% percent more on top the actual 100%.
So 100% + 4 % = 104% = 1.04
The common difference is 1.04.
so 500 * 1.04^n= A where n is the number of years and A is the total amount.
A = 500 * [tex]1.04^{3}[/tex]
A= 562.43
Glass A measures 84 mm in diameter and 175 mm tall. Glass B measures 96 mm in diameter and 125 mm tall. Which glass holds more liquid? How much more?
Answer:
Glass A
Step-by-step explanation:
Volume = п r ² h
п = 3.14 aprox.
r = radius = diameter/2
h = tall
glass Avolume = 3.14 * (84/2)² * 175
volume = 3.14 * 42² * 175
volume = 3.14 * 1764 * 175
volume = 969318mm³
glass Bvolume = 3.14 * (96/2)² * 125
volume = 3.14* 48² * 125
volume = 3.14 * 2304 * 125
volume = 904320mm³
Answer:
969318 > 904320
then:
Glass A holds more liquid
How would you write Twice the difference of 9 and a number.
Answer:
Hey there!
You would write that as 2(9-n), where n is the number.
Hope this helps :)
PLEASE help me with this question! This is really urgent! No nonsense answers please.
Answer:
140°
Step-by-step explanation:
[tex] \because m\widehat{BG} = 360\degree - m\widehat{GCB} \\
\therefore m\widehat{BG} = 360\degree - 300\degree \\
\therefore m\widehat{BG} = 60\degree \\
\because m\widehat{BGD} = m\widehat{BG}
+m\widehat{GD}\\
\therefore m\widehat{BGD} = 80\degree+60\degree\\
\therefore m\widehat{BGD} = 140\degree\\
\because m\angle BAD = m\widehat{BGD} \\
\huge\purple {\boxed {\therefore m\angle BAD =140\degree}} [/tex]
A line that contains the points (5, −3) and (7, 3) has a slope, m, that equals
Answer:
m = 3
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (5, - 3) and (x₂, y₂ ) = (7, 3)
m = [tex]\frac{3+3}{7-5}[/tex] = [tex]\frac{6}{2}[/tex] = 3
A rectangle's length and width are in a ratio of 3:1. The perimeter is 72 inches. What are the length and width?
Answer:
Step-by-step explanation:
If the sides exist in a ratio to one another, then when you multiply some number x by both the length and the width, they still remain as a ratio. The length will be 3x and the width will be 1x. The perimeter formula is
P = 2L + 2W and since our perimeter is 72 and we have both the length and the width, we can fill in the formula and solve for x:
72 = 2(3x) + 2(1x) and
72 = 6x + 2x and
72 = 8x so
9 = x.
If x = 9, then 1x = 9 and 3x = 27. Let's check the perimeter against those side lengths.
P = 2(3x) + 2(1x) and
P = 2(27) + 2(9) and
P = 54 + 18 so
P = 72
and you're done! (The bold numbers above are the width and length, respectively.)
Simplify this equation -8a-5a
Answer:
-13a
Step-by-step explanation:
Since -8 and -5 have like variables, you can subtract them. -8-5 is -13, so the answer is -13a.
Answer:
-13a
Step-by-step explanation:
These two numbers are already like terms, so you can subtract it easily.
First, don't look at the a.
-8-5= -13 because if something is negative and gets subtracted, that means it'll still be negative.
Now that we now it equals -13, we can add the variable a back onto the answer. We get -13a.
What is -13/20 in decimal form
Answer:
-0.65
Step-by-step explanation:
Step 1: Write out fraction
-13/20
Step 2: Evaluate fraction
-13/20 = -0.65
ASAP i need to know the complete working
Answer:
a(1):30%
(2):2135.34
(3):15000
Step-by-step explanation:
a(1):the total is 18750 and 5625 was not taxed therefore 5625 of 18750 was not taxed so get the amount expressed as a percentage by multiplying by 100
{5625/18750}×100
(2):so get the tax from the taxable amount and the taxable amount is 13125 and the tax is 22% of it so (22/100)×13125=2887.5
she takes home the amount remaining after taxation so 18750-2887.5(tax)(don't subtract 5625)=15862.5
she receives the above amount in 52 equal amounts so divide 15862.5/52 to get one amount =305.048 (meaning that per week she receives one of the 52 equal amounts I guess)
(3):so the original salary before moving to A was 100% but after moving it increases by 25 so the salary is 125% =18750(don't deduct tax I guess) so it will be (100/125)×18750
If an arrow is shot upward on Mars with a speed of 62 m/s, its height in meters t seconds later is given by y = 62t − 1.86t². (Round your answers to two decimal places.) Estimate the speed when t = 1. Can you please show me the steps to solve this?
Answer:
Approximately [tex]58.28\; \rm m \cdot s^{-1}[/tex].
Step-by-step explanation:
The velocity of an object is the rate at which its position changes. In other words, the velocity of an object is equal to the first derivative of its position, with respect to time.
Note that the arrow here is launched upwards. (Assume that the effect of wind on Mars is negligible.) There would be motion in the horizontal direction. The horizontal position of this arrow will stays the same. On the other hand, the vertical position of this arrow is the same as its height: [tex]y = 62\, t - 1.86\, t^2[/tex].
Apply the power rule to find the first derivative of this [tex]y[/tex] with respect to time [tex]t[/tex].
By the power rule:
the first derivative of [tex]t[/tex] (same as the first derivative of [tex]t^2[/tex] (same as [tex]t[/tex] to the second power) with respect toTherefore:
[tex]\begin{aligned}\frac{dy}{d t} &= \frac{d}{d t}\left[62 \, t - 1.86\, t^2\right] \\ &= 62\,\left(\frac{d}{d t}\left[t\right]\right) - 1.86\, \left(\frac{d}{d t}\left[t^2\right]\right) \\ &= 62 \times 1 - 1.86\times\left(2\, t) = 62 - 3.72\, t\end{aligned}[/tex].
In other words, the (vertical) velocity of this arrow at time [tex]t[/tex] would be [tex](62 - 3.72\, t)[/tex] meters per second.
Evaluate this expression for [tex]t = 1[/tex] to find the (vertical) velocity of this arrow at that moment: [tex]62 - 3.72 \times 1 =58.28[/tex].
Answer:
58.28 m/s
Step-by-step explanation:
y = 62t - 1.86t²
Speed, S = dy/dt = 62 - 2(1.86)t
S = 62 - 3.72t
When t = 1
S = 62 - 3.72 = 58.28 m/s
What is the value of x?
7
7 square root 2
14
14 square root 2
Answer:
14
Step-by-step explanation:
Using the sine ratio in the right triangle and the exact value
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , thus
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7\sqrt{2} }{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
x = 7[tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex] = 7 × 2 = 14
Answer:
x = 14i hope it helps :)Step-by-step explanation:
[tex]Hypotenuse = x \\Opposite = 7\sqrt{2} \\\alpha = 45\\\\\Using \: SOHCAHTOA\\Sin \alpha = \frac{Opposite}{Hypotenuse}\\ \\Sin 45 = \frac{7\sqrt{2} }{x} \\\\\frac{\sqrt{2} }{2} = \frac{7\sqrt{2} }{x} \\\\\sqrt{2x} = 14\sqrt{2} \\\\\frac{\sqrt{2x} }{2} = \frac{14\sqrt{2} }{2} \\x = 14[/tex]
What is the recursive definition for 25,20,15,10?
Answer:
aₙ = 30 - 5n
Step-by-step explanation:
25,20,15,10, ...
We see from the given series that it is AP with:
First term = 25Common difference = -5 and it is decreasing seriesThen formula is:
aₙ= a₁ + (n-1)daₙ= 25 + (n-1)(-5) aₙ= 25 - 5n + 5aₙ = 30 - 5nA 2-column table with 8 rows. The first column is labeled x with entries negative 6, negative 5, negative 4, negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 34, 3, negative 10, negative 11, negative 6, negative 1, negative 2, negative 15. Using only the values given in the table for the function, f(x), what is the interval of x-values over which the function is increasing? (–6, –3) (–3, –1) (–3, 0) (–6, –5)
Answer:
Step-by-step explanation:
The only place that the function is increasing is [-3, -1] (learn your interval notation). At x = -3, y = -11; at x = -2, y = -6 (-6 is greater than -11); and at x = -1, y = -1 (-1 is greater than -6). The next x value, 0, returns a y value of -2. But -2 is less than -1, the value before it, so it begins deceasing again at x = 0.
Based on the values given in the table for f(x), the interval of x-values that show the function increasing is (-3, -1).
Which interval shows the function increasing?The value of f(x) was decreasing from 34 until it got to -11 where it then started to rise again. The relevant value of x here is -3.
The value then began to rise until it reached -1 where it then fell to -2. The x value here is -1.
The interval of x-values where the function is increasing is therefore (-3, -1).
Find out more on intervals of x-values at https://brainly.com/question/26680949.
#SPJ5
Variance 0.7775
Find the standard deviation (hint: the standard deviation is the square root of the variance)
Answer:
0.88175960442
Step-by-step explanation:
The square root of 0.7775 is 0.88175960442
The value of standard deviation will be;
⇒ 0.8803
What is mean by square root of a number?
A square root of a number is a value that multiplied by itself gives the same number.
Given that;
The value of Variance = 0.7775
Now,
Since, The standard deviation is the square root of the variance.
Hence, We can formulate;
The value of standard deviation = √0.7775
= 0.8803
Thus, The value of standard deviation will be;
⇒ 0.8803
Learn more about the standard deviation visit:
https://brainly.com/question/475676
#SPJ2
A car advertisement claims that a certain car can accelerate from rest to 70 km/hr in 7 seconds find the car acceleration
Answer:
acceleration [tex]\approx 2.78\,\,\frac{m}{s^2}[/tex]
Step-by-step explanation:
The acceleration is the change in velocity per unit of time.
Therefore to have this rate in appropriate units that can combine, we re-write the change from 0 to 70 km/h in meters per second using:
[tex]70 \frac{km}{h} = \frac{70000}{3600} \frac{m}{s}[/tex]
so in this case the acceleration becomes:
[tex]accel=\frac{change\,\,vel}{change\,\,time} =\frac{70000m}{3600\,*7\,s^2} \approx 2.78\,\,\frac{m}{s^2}[/tex]
the angle of elevation of the top of a tower from a point 42m away from the base on level ground is 36 find the height of the tower
Answer:
30.51 meters
Step-by-step explanation:
Given that:
The distance from the point to the base of the tower = 42 m, the angle of elevation = 36°.
According to sine rule if a,b,c are the sides of a triangle and its respective opposite angles are A, B, C. Therefore:
[tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]
Let the height of the tower be a and the angle opposite the height be A = angle of elevation = 36°
Also let the distance from the point to the base of the tower be b = 42 m, and the angle opposite the base of the tower be B
To find B, since the angle between the height of the tower and the base is 90°, we use:
B + 36° + 90° = 180° (sum of angles in a triangle)
B + 126 = 180
B = 180 - 126
B = 54°
Therefore using sine rule:
[tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}\\\\\frac{a}{sin(36)}=\frac{42}{sin(54)}\\\\ a=\frac{42*sin(36)}{sin(54)}\\ \\a=30.51\ meters[/tex]
The height of the tower is 30.51 meters
