Answer:
In scientific notation:
The first number in the mathematical equation is called the "coefficient." The coefficient must be greater than or equal to one and less than 10. For example to create the scientific notation for the number 256, the coefficient would be 2.56.
The second number in the equation is a power of 10, written as 10 with an exponent, like 102 which stands for 10 x 10.
Combining these two numbers would create this scientific notation equation for 256 - 2.56 x 102.
A negative exponent shows the decimal is moved that many places to the left and a positive exponent shows the decimal is moved that many places to the right.
Scientific Notation Examples
Here are examples of scientific notation:
1 = 100
10 = 1 x 10¹
100 = 1 x 10²
1000 = 1 x 10³
10000 = 1 x 104
100000 = 1 x 105
42,000,000 = 4.2 x 107
676,000,000,000 = 6.76 x 1011
0.1 = 1 x 10-1
0.01 = 1 x 10-2
0.001 = 1 x 10-3
0.0001 = 1 x 10-4
0.00001 = 1 x 10-5
0.00000078 = 7.8 x 10-7
0.000000000000000 = 3.56 x 10-13
Real Life Examples of Scientific Notation
Explore how scientific notation is used to express large numbers.
7 x 109 = Population of the world is around 7 billion written out as 7,000,000,000
1.08 x 109 = Approximate speed of light is 1080 million km per hour or 1,080,000,000 km per hour
2.4 x 105 = Distance from the Earth to the moon is 240 thousand miles or 240,000 miles
9.3 x 107 = Distance from the Earth to the sun is 93 million miles or 93,000,000 miles
3.99 x 1013 = Distance from the sun to the nearest star (Proxima Centauri) is 39,900,000,000,000 km
9.4605284 × 1015 = Distance light travels in a year is less than 9.5 trillion kilometers, or exactly 9,460,528,400,000,000 km
1.4 x 108 = Amount of water surface area on the Earth is 140 million square miles or 140,000,000 square miles
1.0 x 1014 = Approximate number of cells in the human body is 100 trillion or 100,000,000,000,000
1.332 x 10-3 = Density of oxygen is 1332 millionths g per cc or .001332 g per cc
2.4 x 10-3 = Diameter of a grain of sand is 24 ten-thousandths inch or .0024 inch
7.53 x 10-10 = Mass of a dust particle is 0.000000000753 kg
9.1093822 × 10-31 = Mass of an electron is 0.00000000000000000000000000000091093822 kg
4.0 x 10-7 = Length of the shortest wavelength of visible light (violet) is 0.0000004 meter
How many solutions exist for the given equation?
3x + 13 = 3(x + 6) + 1
Answer:
0
Step-by-step explanation:
3x+13 = 3(x+6)+1
3x+13=3x+19
13=19
This is never true so there are 0 solutions
If the x's didnt cancel out, you could use the fundemental theorom of algebra, which states that in the simplest form(nothing will cancel out anymore), the highest degree(highest power) on a variable is the number of solutions.
which compound inequality is equivalent to the absolute value inequality |b|>6?
The compound inequality equivalent to the absolute value inequality |b|>6 is b > 6, and b < -6
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the inequality:
|b| > 6
Hence:
b > 6 and -b > 6
b > 6, and b < -6
The compound inequality equivalent to the absolute value inequality |b|>6 is b > 6, and b < -6
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Answer:
Answer is A
Step-by-step explanation:
Got it right on the quiz
The table shows the weights (in pounds) and the prescribed dosages (in milligrams) of medicine for six patients.
Weight (lb), x Dosage (mg), y
94 72
119 90
135 103
150 115
185 140
202 156
a. Find an equation of the line of best fit. Round the slope and the y -intercept to the nearest tenth, if necessary.
y=
Question 2
Identify the correlation coefficient. Round your answer to the nearest thousandths.
Question 3
Interpret the correlation coefficient.
0 / 10000 Word Limit
Question 4
b. Interpret the slope of the line of best fit.
Question 5
c. A patient who weighs 140 pounds is prescribed 135 milligrams of medicine. How does this affect the line of best fit? Explain.
(A) Using calculator, the equation of the line of best fit is y=0.77x-1.1y=0.77x−1.1 and correlation coefficient is 0.9990.999
The relationship is strongly positive as correlation coefficient is very close to +1.
Step 2
(B) The slope of best fit gives the change in dosage for a unit (lb) increase in weight of patient. We find that the dosage increases by about 0.77 mg for a unit increase in weight of patient.
Step 3
(C) Adding observation (140, 135)(140,135) to the data set. the regression line changes to y=6.12+0.75xy=6.12+0.75x. It increases the intercept but decreases slope.
But the correlation falls to 0.9340.934, weakening the relationship. This happens as the observation is an outlier.
Result
a. y=0.77x-1.1y=0.77x−1.1, strong positive relationship
b. represents change in dosage for a unit increase in weight
c. regression line changes to y=6.12+0.75xy=6.12+0.75x.
(A) The line of best fit's equation is y=0.77x-1.1y=0.77x1.1, and the correlation coefficient is 0.9990.999. The correlation coefficient is near +1, indicating that the link is positive.
What is the equation?The definition of an equation in algebra is a mathematical statement demonstrating the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Step 2
(B) The change in dosage for a unit (lb) increase in patient weight is indicated by the best-fit slope. We discover that for every unit increase in patient weight, the dosage rises by around 0.77 mg.
Step 3
(C) Including observation (140, 135) in the data set. y=6.12+0.75xy=6.12+0.75x is the new value of the regression line. Although the slope is reduced, the intercept is increased.
However, the link is weakened when the correlation drops to 0.9340.934. This occurs because the observation is an anomaly.
Result
a. Strong positive association, y=0.77x-1.1y=0.77x1.1
B. indicates a dose modification for a unit weight increase
C. y=6.12+0.75xy=6.12+0.75x is the new value of the regression line.
Therefore, y=0.77x-1.1y=0.77x1.1 is the equation for the line of best fit, and the correlation coefficient is 0.9990.999.
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(18) (3, -2) lies on terminal side of angle (θ).
Find the EXACT value of sec (θ)
Show steps
By applying fundamental and derivate trigonometric expressions it is to be concluded that the secant of the line segment whose terminal side is (3, - 2) is approximately 1.202.
How to apply trigonometric expressions
Trigonometric expressions are trascendent expressions derived from relationships between sides of the triangle contained in a goniometrical diagram.
There are at least six trigonometric expressions: sine, cosine, tangent, cotangent, secant, cosecant. The first two expressions are fundamental, whereas the rest are derived from them.
We can derive an expression for the secant of the angle by applying trigonometric expressions:
[tex]\sec \theta = \frac{1}{\cos \theta} = \frac{\sqrt{x^{2}+y^{2}}}{x}[/tex] (1)
If we know that x = 3 and y = - 2, then the secant of the angle is:
[tex]\sec \theta = \frac{\sqrt{3^{2}+(-2)^{2}}}{3}[/tex]
sec θ ≈ 1.202
By applying fundamental and derivate trigonometric expressions it is to be concluded that the secant of the line segment whose terminal side is (3, - 2) is approximately 1.202.
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DE joins the midpoints of AB and AC. Find the value of x
and y.
Answer:
x = 6
y = 4
Step-by-step explanation:
2(4x + 1) = 11x - 16
8x + 2 = 11x - 16
8x + 2 + 16 = 11x - 16 + 16
8x + 18 = 11x
8x + 18 - 8x = 11x - 8x
18 = 3x
6 = x
5y + 4 = 8(y - 1)
5y + 4 = 8y - 8
5y + 4 + 8 = 8y - 8 + 8
5y + 12 = 8y
5y + 12 - 5y = 8y - 5y
12 = 3y
4 = y
If it take 8 cups of flour to make 4 Loaves of bread, how many loaves of bread can you make from 40 cups of flour
Answer:
20
Step-by-step explanation:
Since 8 x 5 is 40, we can multiply 4 x 5 to get 20.
How do you convert joules to kJ
Answer:
Divide by 1000.
Step-by-step explanation:
For example, 1 joule is 0.001 kilo joule.
1 divided by 1000 is 0.001.
If there were 30 joules, there would be 0.032 kilo joules.
Look at this function:
x y
−3 −8
−2 −6
−1 −4
0 0
Matt said that the function is linear.
Justine said that the function is nonlinear.
Which of the following explains who is correct?
Matt, because for every 1-unit increase in x, there is an increase in y by 2
Matt, because for every 2-unit increase in x, there is an increase in y by 1
Justine, because the point (−3, −8) does not lie on the straight line that contains the other points
Justine, because the point (0, 0) does not lie on the straight line that contains the other points
Justine, because the point (0, 0) does not lie on the straight line that contains the other points.
Explanation:
See the graph below. The following coordinates are not in a stright line.
Hence, it is a non linear function. Justine is right.
When drawn a straight line. the coordinates: (0,0) does not lie on the line.
What are the possible transformations that could have been used to create the red figure A'B'C'D' from the blue
figure ABCD?
A
D'
-5-4-3-2-1. B
3 A 5 x
-2
a reflection across
the y axis followed by a translation of 5 units up and 5 units left
O a reflection across the y axis followed by a 90-degree rotation counterclockwise about the origin
a rotation of 90 degrees counterclockwise about the origin followed by a reflection across the y axis
A
5
4
3
2
B
BB
Ni
& &
2
Answer:
Second option.
Step-by-step explanation:
A reflection across the y axis followed by a counterclockwise rotation around the origin.
The equation y - 1 =-7(x-3) is written in point-slope form. What is the y-intercept of the line?
O -4
O-2
O 20
O 22
Bob has $600 in a savings account that earns' 5% annually. The interest is not compounded
How much interest will he earn in 1 year?
Use the formula /= prt, where I is the interest earned, p is the principal (starting amount),
is the interest rate expressed as a decimal, and t is the time in years.
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$600\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (600)(0.05)(1)\implies I=30[/tex]
Answer:
30
Step-by-step explanation:
You would frist start by mutiplying 600 you principal by .05 your rate which equals 30. The you would multiply that by you time which is 1.
Ollie drank 1/2 of a 16 fluid ounce bottle of juice how many cups of juice are left in the bottle explain
Answer:
Step-by-step explanation:
1 cup is left because 16 ounces is 2 cups so half would be one
How much is a square mile
a square mile is equivalent to 27878400 square feet
Find the value of x.
Explain your answer.
Answer:
Step-by-step explanation:
The hypotenuse is 16 and the adjacent angle is x.
So using SohCahToh
O is opposite, H is the hypotenuse, and A is adjacent.
Soh: sin(theta)= O/H
Cah: cos(theta)= A/H
Toh: tan(theta)= O/A
Any side length that is next to degree 60° is adjacent so x is adjecent.
Using Cah.
cos(theta)= A/H
cos(60°)= x/16
x=16*cos(60°)
x=16*1/2
x=8
Performance Task A. Directions: Solve the problem and answer the following questions. Renz' family attended a pool party. The pool is circular in shape. He wants to find out the area of the pool. If the radius is six meter, what could be the area? Fill in the blanks. 1. The radius of the pool is m 2. The diameter of the pool is __m 3. The value of pi is 4. Formula in finding the area of a circle 5. Area of the swimming pool X m²
Answer: 144 meters
Step-by-step explanation: area of circle = r^2
6^2 = 36 = 144 Meters given = 4
radius of pool is 6 meters
diameter of pool is 12 meters
= 4
area of circle = r^2
area of swimming pool is 144 meters
"Place a number in each box so that each equation is true and each equation has at least one negative number."
Answer:
x=1, y=-1
Step-by-step explanation:
Given the equation:
where x and y are the blank boxes.
We want to find
A positive value of x
A negative value of y
That makes the equation true.
If x=1, y=-1
This can be confirmed using addition law of indices()
In general, any pair of a number and its negative value will satisfy the equality.
Step-by-step explanation:
Evaluate 3x+ y when x equals 1/3 and y equals -7/4. Write your answer as a fraction in simplest form.
Please help!! Thanks!!
Answer:
-3/4
Step-by-step explanation:
Put in the values for 'x' and 'y'
3 * (1/3) + (-7/4)
1 - 7/4
4/4 - 7/4
(4-7)/4 = -3/4
A bucket of water was 1/2 full, but it still had 3 and 3/5 gallons of water in it. How much water would be in one fully filled bucket?
Question:
A bucket of water was 1/2 full, but it still had 3 and 3/5 gallons of water in it. How much water would be in one fully filled bucket?
Answer:
7 1/5
Step-by-step explanation:
The bucket was halfway full. It still had 3 3/5 gallons in it. So all you'd have to do is multiply 3 3/5 by 2. Here is the actual work for proof:
3 3/5 × 2 =
18/5 × 2 =
18 × 2
5 × 1 =
36/5 = 7 1/5.
correct answer please!
Use the numbers from the item bank to write the value of each expression.
Photo down below!
Step-by-step explanation:
4347 ÷ 21 = 207
4715 ÷ 23 = 205
5200 ÷ 25 = 208
5356 ÷ 26 = 206
2 ≤ s-2 Find variable for s
Please show your work
Answer:
∂x. )2 + (. ∂z. ∂y. )2 = √1 +. 1. 9. +. 1. 4. = 7/6. Then the area of S is found by calculating the surface integral over S for the function f(x, y, z) =
hope this helps
Answer:
s <= 4
Step-by-step explanation:
First we re arrange
s - 2 >= 2
a-2+2>=2+2
a>=2+2
a>=4
22. A small-appliance manufacturer finds that it costs $9000 to produce 1000 toaster ovens a week and $12,000 to produce 1500 toaster ovens a week.
(b) What is the slope of the graph and what does it represent?
A small-appliance manufacturer finds that it costs $9000 to produce 1000 toaster ovens a week and $12,000 to produce 1500 toaster ovens a week.
solve for the value of k
pls help me asap
Answer:
k=13
Step-by-step explanation:
We know that
straight angle is equal to 180⁰
(4k-7)⁰+90⁰+(3k+6)⁰=180⁰
4k-7+3k+6=90
7k=91
k=13
I hope it helped you
Subtract 89.768 from 201.316
show your work
Answer:
111.548
-------------------------------
Subtract 201 from 89.
[tex]201 - 89 = 112[/tex]
we can estimate the answer will be close to 112
Next, work with the decimals. Note that the more you subtract, the bigger the decimal places get.
[tex]0.768 - 0.316 = 0.452[/tex]
Round 0.452 up from the hundredths place to nearest tenths place.
[tex]0.452 = 0.5[/tex]
Since the decimal place is bigger, estimate 0.55 instead.
Subtract 0.22
[tex]0.55 - 0.2 = 0.548[/tex]
Add this number to 112
[tex]112 + 0.548 = 112.548[/tex]
Subtract 1 because of the estimate.
[tex]112 - 1 = 111[/tex]
Therefore, we have 111.548 based off of subtracting and estimating in a specific method.
Easy math what one a b c d e
Answer:
problem 14 = E
Step-by-step explanation:
well that's all ther is to it, it's E because y or x being 0 would make the equation undefined
When designing a training plan, what do you need to think about?
A. Frequency, rest, progression
B. Moderation, progression and overtraining
C. Rest, goals, overload
D. Frequency, overtraining, time
Translate the following phrase into an algebraic expression. Do not simplify. Use the variable names "x" or "y" to describe the unknowns.
8 divided by the sum of 2 and a number
Answer:
8/x+2 or [tex]\frac{8}{2+x}[/tex]
Step-by-step explanation:
To answer, carefully read the question and pick up on key words like "sum." To begin, we know that "sum" means addition, therefore the sum of 2 and a number (which will be replaced by the variable x) is equivilent to 2 + x. Furthermore, we know that 8 is being divided by the sum. So, the final expression should be [tex]\frac{8}{2+x}[/tex] . Good luck!
Oil leaks from a tank. At hour t = 0 there are 360 gallons of oil in the tank. Each hour after that, 3% of the oil leaks out.
(a) What percent of the original 360 gallons has leaked out after 8 hours?
%
(b) if Q(t) = Q0e^kt the quantity of oil remaining after t hours, find the value of k.
k=
(c) What does k tell you about the leaking oil? Select all that apply if more than one statement is true
A. It tells what percent of oil remains after each hour.
B. It is the amount that the oil that leaks out each second.
C. Because it is less than one, we know the amount of oil in the tank is decreasing,
D. It tells by what percent of oil decays each hour.
E. Because it is negative, we know the amount of oil in the tank is decreasing.
F. It gives the continuous hourly rate at which oil is leaking.
G. None of the above
x+3=y
what is y?
GIVING BRANLIEST
Answer:
There isn't a way to solve for y but I can give you this
Step-by-step explanation:
Slope=1
x-intercept is -3/1
y-intercept is 3/1
How do you know if a net will fold into a pyramid?
Step-by-step explanation:
A pyramid is made when 4 triangle meet on square then mate on each together .
PLEASE HELP ASAP WILL MARK BRAINLIEST!
Solve and show your work for each question.
Note: Remember per the rule of 9s if you have a repeating and non-repeating component you need
to handle them separately.
(a) What is 0.47 expressed as a fraction in simplest form?
(b) What is 0.4-7 expressed as a fraction in simplest form?
(c) What is 0. -47 expressed as a fraction in simplest form?
There are lines above the seven in decimal B and the line in decimal C is above both numbers. pleaseeeee help me
Answer:
See below
Step-by-step explanation:
a) 47/100
b) .4777777..... =x
then 10x = 4.77777....
100x = 47.777777 .... now subtract 10x to get
90x = 43
x = 43/90
c) .4747474747...... = x
100x = 47.474747 now subtract x to get
99x = 47
x = 47/99