9514 1404 393
Answer:
exact: 1.3924×10^-10rounded to 2 sf: 1.4×10^-10Step-by-step explanation:
The factor 10^-6 can be brought out:
((5.5 +6.3)×10^-6)^2 = (11.8^2)×10^-12 = 1.3924×10^-10
Often, a problem like this wants you to round to a precision appropriate to the given values. Here, that is 2 significant figures:
≈ 1.4×10^-10
_____
Additional comment
Your scientific or graphing calculator can do this nicely, even showing you the result in scientific notation. A spreadsheet can do the same.
The usual rules of exponents apply.
(a^b)(a^c) = a^(b+c)
(ab)^c = (a^c)(b^c)
(a^b)^c = a^(bc)
Find The Base Of Parallelogram Whose Area Is 80cm And Height Is 5cm
Answer:
16cm
Step-by-step explanation:
Area is A = bh
to find a base, b = A/h
A=80
h=5
so then we have b = 80/5 = 16
What is the slope of a roof on a house that has a vertical height of 2.4 feet from the ceiling of the top floor to the top of the pitch and a length of 8.2 feet from the center of the edge of the house?
Answer:
Step-by-step explanation:
It is unclear from the phrasing what dimension 8.2 ft represents.
If 8.2 ft is the direct distance from the edge of the roof to the top of the pitch, then the horizontal distance from the edge to the top is √(8.2²-2.4²) ≅ 7.84 ft, and the slope is 2.4/7.84 ≅ 0.31
If 8.2 ft is the horizontal distance from the edge of the root to the top of the pitch, then the slope is 2.4/8.2 ≅ 0.29
The slope of a roof on a house is 0.2926 and the angle of elevation is 16.31°.
What is slope of a line?
The slope or gradient of a line is a number that describes both the direction X and Y and the steepness of the line. It is the ratio of the vertical change to the horizontal change between any two distinct points on a line.
For the given situation,
The diagram below shows the house with the roof.
The vertical height of roof on a house, rise = 2.4 feet
The horizontal length of a roof on a house, run = 8.2 feet
The slope of a roof can be found as
[tex]Slope = \frac{rise}{run}[/tex]
⇒ [tex]slope = (\frac{2.4}{8.2} )[/tex]
⇒ [tex]slope = 0.2926[/tex]
The angle of the slope of a roof can be found as
[tex]tan \alpha =\frac{vertical height}{horizontal length}[/tex]
⇒ [tex]\alpha =tan^{-1} (\frac{2.4}{8.2} )[/tex]
⇒ [tex]\alpha =tan^{-1} (0.2926)[/tex]
⇒ [tex]\alpha =16.31[/tex]
Hence we can conclude that the slope of a roof on a house is 0.2926 and the angle of elevation is 16.31°.
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The sum of one and three times a number is -89. What is the number?
A) Translate the statement above into an equation that you can solve to answer this question. Do not solve it yet. Use
x
as your variable.
The equation is
B) Solve your equation in part [A] for
Answer:
A. 1 + 3x = -89
B. x = -30
Step-by-step explanation:
Let the unknown variable be x.
A. Translating the word problem into an algebraic expression, we have;
1 + 3x = -89
B. To solve for the unknown variable;
1 + 3x = -89
3x = -89 -1
3x = -90
x = -90/3
x = -30
Check:
1 + 3x = -89
Substituting the value of x;
1 + 3(-30) = -89
1 + (-90) = -89
1 - 90 = -89
-89 = -89
Find the missing side of the triangle.
Answer:
x = 2(sqrt26) or x = 10.1980390272...
Step-by-step explanation:
Right triangles can be solved using Pythagorean theorem, where the legs are squared and added together to get the hypotenuse's length squared.
If we set up the equation:
11^2 + x^2 = 15^2
which is
121 + x^2 = 225
subtract 121 from both sides
x^2 = 104
sqrt both sides
x = 2(sqrt26), or x = 10.1980390272...
Answer:
Using Pythagoras theorem
c²=a²+b²
(15)²=x² +(11)²
225=x²+ 121
-x²=121-225
-x²=-104
multiply both sides by (-1)
x²=104
x=✓104
x=10ft
From September 1991 to September 1994 the enrollment at a particular school declined by 20 percent. If the number of students enrolled at that school in September 1994 was 720, what was the enrollment in September 1991
Answer:
900
Step-by-step explanation:
Given that :
Enrollment declined by 20% from between September 1991 to September 1994
This means there was a reduction in enrollment ;
Enrollment in September 1994 = 720
Enrollment in September 1991 = x
Hence,
Enrollment in 1994 = (1 - decline rate ) * enrollment in 1991
720 = (1 - 20%) * x
720 = (1 - 0.2) * x
720 = 0.8x
720 / 0.8 = 0.8x/0.8
900 = x
Hence, Enrollment in September 1991 = 900 enrollments
please help me i have a couple mins
Answer:
x + 3
Step-by-step explanation:
Because he bought an unknown number of soccer balls that is where we use the variable, x. And we know that he bought 3 baseballs, and we add them both to get the total number of things bought. Hope this helped and you could give brainliest :)
Assuming boys and girls are equally likely, find the probability of a couple having a baby boy when their third child is born, given that the first two children were both boys
The required probability of a couple having a baby boy when their third child is born is 1/2.
What is probability?probability is the ratio of the number of favorable outcomes and the total number of possible outcomes. The chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%.
Given:
Assuming boys and girls are equally likely.
The first two children were both boys
According to given question we have
The probability of having a baby girl is an independent probability.
The first two children were both boys
So, it is not related to the previous child.
So required probability = 1/2
Therefore, the required probability of a couple having a baby boy when their third child is born is 1/2.
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Express as index form
log 2 64 = 6
Answer:
hsv s deutsche ki bhar ke dekhte hai mera gham na
A motorboat travels 104 kilometers in 4 hours going upstream. It travels 200 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
[tex] \Large \mathbb{SOLUTION:} [/tex]
[tex] \begin{array}{l} \text{Let }r\text{ be the rate of the boat in still water and} \\ c\text{ be the rate of the current.} \\ \\ \text{So } \\ \begin{aligned} \quad&\bullet\:\text{Rate Upstream}= r - c \\ &\bullet\:\text{Rate Downstream}= r - c\end{aligned} \\ \\ \text{We know that }\text{Rate} = \dfrac{\text{Distance}}{\text{Time}}. \end{array} [/tex]
[tex] \begin{array}{l} \bold{Equations:} \\ \\ \begin{aligned} &\quad\quad \quad r - c = \dfrac{104}{4} = 26\quad (1) \\ \\ & \quad \quad \quad r + c = \dfrac{200}{4} = 50\quad (2)\\ \\ & \text{Adding (1) and (2), we get} \\ \\ &\quad\quad 2r = 76 \implies \boxed{r = 38\ \text{kph}} \\ \\ &\text{Using (2), it follows that} \\ \\ & \quad \quad c = 50 - r \implies \boxed{c = 12\ \text{kph}} \end{aligned} \end{array} [/tex]
The graph of y=x√ is translated 5 units to the left and 7 units up. What is the equation of the graph that results from this translation?
Answer:
[tex]y = \sqrt{x - 5} + 7[/tex]
The graph of the function f(x)= x2 − 4x + 6 is shown here. What is its axis of symmetry? A. x = 0 B. x = 2 C. x = 6 D. x = -2
9514 1404 393
Answer:
B. x = 2
Step-by-step explanation:
The graph is symmetrical about the vertical line through its vertex. The x-value of that vertex is 2, so the line of symmetry is ...
x = 2
Which expressions are equivalent to 6 + 12x?
A.
5(1 + 2x) + 1 + 2x
B.
7(1 + 2x) + 2x - 1
C.
3(2 + 6x) + 2x
D.
7(1 + 2x) - 2x - 1
E.
3(2 + 4x)
Answer:
A. 5(1 + 2x) + 1 + 2x
D. 7(1 + 2x) - 2x - 1
E. 3(2 + 4x)
find all the missing measurement
Answer:
Hello,
|FD|=15
Step-by-step explanation:
Since the triangles are similar, the bissects are also.
k*35=21 ==> k=21/35
k*25=|FD|
|FD|=(21/35)*25=15
look at the image for the question
Answer:
112 ft^2
Step-by-step explanation:
The volume of the rectangular prism is
V = l*w*h where l is the length, w is the width and h is the height
V = 4*4*7
V = 112 ft^2
Which of the following functions best describes this graph? y=(x+2)(x+7)
Answer:
hope. It helps. What. I Understood
Simplify this expression.
6 + 8 ÷ 2
3
7
10
12
Megan and Suzanne each have a plant. They track the growth of their plants for four weeks.
Whose plant grew at a faster rate, and what was the rate?
Suzanne’s at 2 inches per week
Suzanne’s at 1.5 inches per week
Megan’s at 3 inches per week
Megan’s at 2.5 inches per week
Megan’s plant grew at a faster rate, Growing at a rate of 3 inches per week.
What is the slope?The y-rate axis of change with respect to the x-axis is known as the slope.
y = mx + b, where slope = m and y-intercept = b, is the slope-intercept form equation of a line.
We are aware that a slope's graph or rate of change will be steeper the higher its absolute value.
Given, Megan and Suzanne each have a plant. They track the growth of their plants for four weeks.
From the given options, Megan's plant which is growing at a rate of 3 inches per week has a faster growth rate.
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In this diagram,which equation could prove to be true in order to conclude that the lines are parallel?
Answer:
b/a = c/d (first option)
Step-by-step explanation:
Two lines:
f(x) = a*x +b
g(x) = m*x + s
are parallel if m = a, and s ≠ b.
So the lines must have the same slope and different y-intercept.
For the graphed lines is obvious that the y-intercepts are different, so let's look at the slopes.
Remember that if a line passes through the points (x₁, y₁) and (x₂, y₂), then the slope can be written as:
slope = (y₂ - y₁)/(x₂ - x₁)
So now let's look to our lines.
The top one, passes through (-a, 0) and (0, b)
Then its slope is:
a₁ = (b - 0)/(0 - (-a)) = b/a
The bottom line passes through the points (0, -c) and (d, 0)
Then the slope will be:
m₁ = (0 - (-c))/(d - 0) = c/d
Then the lines will be only parallel if the slopes are equal, which means that we must have
b/a = c/d
The correct option is the first one.
Can anyone help me?
Answer:
y is not a function of x
Step-by-step explanation:
This fails the vertical line test. This means that not all inputs have exactly one output. This makes this not a function.
Which key correctly represents the information below? A. 11 | 2 = 12 B. 1 | 2 = 12 C. 11 | 2 = 112 D. 11 | 2 = 13
Answer:
The answer is (B) 1/2=12
Compare and contrast measures of central tendency and measures of variability.
Answer:
While central tendency tells you where most of your data points lie, variability summarizes how far apart your points from each other. Data sets can have the same central tendency but different levels of variability or vice versa. Together, they give you a complete picture of your data.
Step-by-step explanation:
Venn diagrams: unions, intersections, and complements
Attached is the photo reference
Answer:
(a) {5}
(b) {1, 2, 5, 6}
(c) {1, 2, 5, 6}
An MP3 player costs $220, and sales tax is 73%. What will the total price be,
with tax?
Answer:
221.61
Step-by-step explanation:
First we need to put 73% into decimal form.
73%= 0.73.
0.73 * 220= 160.6
Sales tax is 0.161.
After rounding its $1 and 61 cents.
220 + 1.61 = 221.61.
Hope that helped.
a) Express the prime number 31 as the difference of two squares? 31 =
Answer:
31 = 16²-15²
Step-by-step explanation:
16² = 256
15² = 225
256 - 225 = 31
what is the probability that the 2 cards you will draw will be blackjacks?
Answer:
Need more explation of the question
Step-by-step explanation:
A sound technician analyzes the audio feedback by placing a microphone at certain distances from a speaker. If the microphone is connected to the speaker, then the microphone senses 606060 decibels (\text{dB})(dB)left parenthesis, start text, d, B, end text, right parenthesis at a distance of 000 meters (\text{m})(m)left parenthesis, start text, m, end text, right parenthesis from the speaker with the decibel level decreasing by half of itself for every additional meter from the speaker. If the microphone is not connected to the speaker, then the microphone senses 30 \, \text{dB}30dB30, start text, d, B, end text at a distance of 0 \, \text{m}0m0, start text, m, end text from the speaker with the decibel level decreasing by 888 for every additional meter from the speaker. Three meters from the speaker, what is the difference between the decibel level when it is connected to the speaker versus when it is not connected to the speaker?
At three meters, the difference in the decibel level if and if not connected to the speaker is 1.5 dB
The reason for arriving at the above value is as follows:
The known parameters:
The audio sensed by the microphone when connected to the speaker are;
0 meters = 60 decibels
The level of the decibel decrease by half for each additional meter;
Therefore, when the microphone is connected to the speaker, we have;
[tex]\begin{array}{|c|cc|}\mathbf{Distance \ (m)}&&\mathbf{Sound \ (dB)}\\0&&60\\1&&30\\2&&15\\3&&7.5\end{array}\right][/tex]
If the microphone is not connected to the speaker, we have;
0 meters = 30 decibels
The level of the decibel decreasing by 8 dB for every additional meter from the speaker, therefore, when the microphone is not connected to the speaker we have;
[tex]\begin{array}{|c|cc|}\mathbf{Distance \ (m)}&&\mathbf{Sound \ (dB)}\\0&&30\\1&&22\\2&&14\\3&&6\end{array}\right][/tex]
At three meters from the speaker, the difference in the decibel level when it is connected and when it is not connected to the speaker is therefore;
Decibel level at 3 meters when connected, s₁ = 7.5 dB
Decibel level at 3 meters when not connected, s₂ = 6 dB
The difference in the decibel level = s₂ - s₁ = 7.5 dB - 6 dB = 1.5 dB
The difference in the decibel level when connected to the speaker and when not connected to the speaker is 1.5 dB
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-3x^5y^7/6xy^8
PLEASE HELP
9514 1404 393
Answer:
-x^4/(2y)
Step-by-step explanation:
Perhaps you want to simplify ...
[tex]-\dfrac{3x^5y^7}{6xy^8}=-\dfrac{3}{6}x^{5-1}y^{7-8}=-\dfrac{x^4y^{-1}}{2}=\boxed{-\dfrac{x^4}{2y}}[/tex]
__
The applicable rules of exponents are ...
(a^b)/(a^c) = a^(b-c)
a^-b = 1/a^b
_____
Comment on notation
When writing a fraction in plain text, any denominator that includes an arithmetic operation must be enclosed in parentheses. Your given expression is properly written as ...
-3x^5y/(6xy^8)
Without the parentheses, the product xy^8 is in the numerator. This is demanded by the order of operations, which requires you evaluate your expression as (-3x^5y^7/6)·xy^8
A ball was bounced 3 times between 3:15p and 3:18p, thrown 10 times between 3:20p and 3:30p and bounced 7 times between 4:15p and 4:20p. What is the rate per hour of ball bouncing based on a 2 hour data collection time period.
Answer:
strange phrasing of a question
If one assumes that the "observation" was from 3:00 pm - 5:00 pm (2 hours)
and the ball was ONLY "bounced" 10 times (3+7)
we can can say that the rate was 10 bounces/2 hours or 5 b.p.h. (bounces per hour)
Step-by-step explanation:
Someone please help me with this
Answer:
Step-by-step explanation:
match the polynomial with its correct name
Answer
Attach a file for us to see the problem
Step-by-step explanation:
