Find the sum. Express the answer in scientific notation.
(8.7 x 10°)+(4.58 x 10')
O 1.328x108
1.328 x 1010
13.28 x 10°
13.28 x 1018
Answer: A
Step-by-step explanation:
The sum of [tex]8.7 \times 10^9[/tex] and [tex]4.58 \times 10^9[/tex] in scientific notation is [tex]13.28 \times 10^9[/tex].
To find the sum of [tex](8.7 \times 10^9)[/tex] and [tex](4.58 \times 10^9)[/tex] and express it in scientific notation.
we need to add the coefficients and keep the same exponent.
[tex]8.7 \times 10^9 + 4.58 \times 10^9[/tex]
[tex]= (8.7+4.58)\times 10^9[/tex]
[tex]= 13.28 \times 10^9[/tex]
Therefore, the sum of [tex]8.7 \times 10^9[/tex] and [tex]4.58 \times 10^9[/tex] in scientific notation is [tex]13.28 \times 10^9[/tex].
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Complete question:
Find the sum. Express the answer in scientific notation.
(8.7 x 10⁹)+(4.58 x 10⁹)
1.328x10⁸
1.328 x 10¹⁰
13.28 x 10⁹
13.28 x 10¹⁸
Find the center (h, k), the radius r, and the intercepts, if any of each circle.
x2 + y2 - 6x + 2y + 6 = 0
a
(h, k) = (3, -1); r = 2; x-int: 3 ± √3 (x-intercept is three plus or minus the square root of three); y-int: none
b
(h, k) = (3, -1); r = 4; x-int: 3 ± √3 (x-intercept is three plus or minus the square root of three); y-int: none
c
(h, k) = (-3, 1); r = 4; x-int: 3 ± √3 (x-intercept is three plus or minus the square root of three); y-int: none
d
(h, k) = (-3, 1); r = 2; x-int: 3 ± √3 (x-intercept is three plus or minus the square root of three); y-int: none
e
none
Answer:
A. [tex]C(x,y) = (3,-1)[/tex], [tex]r = 2[/tex], x-Intercepts: [tex]x = 3\pm\sqrt{3}[/tex], y-Intercepts: none.
Step-by-step explanation:
Let [tex]x^{2}+y^{2}-6\cdot x + 2\cdot y + 6 = 0[/tex] be the general equation of the circle, we must transform the expression into standard form to determine its center, radius and intercepts. The procedure is shown below:
1) [tex]x^{2}+y^{2}-6\cdot x + 2\cdot y + 6 = 0[/tex] Given.
2) [tex](x^{2}-6\cdot x)+(y^{2}+2\cdot y) +6= 0[/tex] Commutative and associative properties.
3) [tex](x^{2}-6\cdot x)+(y^{2}+2\cdot y) + 6 + 3 + 1 = 3 + 1[/tex] Compatibility with addition.
4) [tex](x^{2}-6\cdot x +9)+(y^{2}+2\cdot y +1) = 4[/tex] Definition of addition/Commutative and associative properties.
5) [tex](x-3)^{2} + (y+1)^{2} = 4[/tex] Perfect square trinomial/Result.
The equation of the circle centered in (h, k) in standard form is defined as:
[tex](x -h)^{2} + (y-k)^{2} = r^{2}[/tex] (Eq. 1)
Where:
[tex]h[/tex], [tex]k[/tex] - Coordinate of the center of the circle, dimensionless.
[tex]r[/tex] - Radius of the circle, dimensionless.
By direct comparison we find that circle is centered in [tex]C(x, y) = (3, -1)[/tex] and has a radius of 2.
Finally, we obtain the intercepts of the given function:
x-Intercepts ([tex]y = 0[/tex])
[tex](x-3)^{2} + (0+1)^{2} = 4[/tex]
[tex]x^{2}-6\cdot x +9+1 = 4[/tex]
[tex]x^{2}-6\cdot x +6=0[/tex]
Roots are found analitically by Quadratic Formula:
[tex]x = 3\pm\sqrt{3}[/tex]
y-Intercepts ([tex]x=0[/tex])
[tex](0-3)^{2}+(y+1)^{2} = 4[/tex]
[tex]9+y^{2}+2\cdot y +1 = 4[/tex]
[tex]y^{2}+2\cdot y +6 = 0[/tex]
Roots are found analitically by Quadratic Formula:
[tex]y = -1\pm i\,\sqrt{5}[/tex]
In a nutshell, there are no y-Intercepts.
We include a graphic including circle, center and x-Intercepts.
Finally, we came to the conclusion that correct answer is A.
Round 9.96 to the nearest tenth
Answer:
10
I hope this helps!
Which of the following fractions has the same value as the decimal number 0.65?
Answer:
13/20
Step-by-step explanation:
Given that a=4,b=2 and c=-1, find the value of a-b+c
Answer:
1
General Formulas and Concepts:
Order of Operations: BPEMDAS
Step-by-step explanation:
Step 1: Define
a - b + c
a = 4
b = 2
c = -1
Step 2: Solve
Substitute: 4 - 2 - 1Subtract: 2 - 1Subtract: 1Need help can you help me
Answer:
Class width
Step-by-step explanation:
Class width is the difference between two consecutive lower limits (or two consecutive lower class boundaries) in a frequency distribution.
The histogram shows the distribution of hurricanes that have hit a country from 1851 through 2015, where 1 is the weakest level and 5 is the strongest level.
1= 0.411
2=0.278
3=0.221
4=0.080
5=0.010
(a) Find the mean, variance and standard deviation of the probability distribution.
(b) Interpret the results: A, B, C or D.
A. The average hurricane is aprox. category 1.
B. The average hurricane is aprox. category 2.*
C. Most of the hurricane sizes differ from the average by about 2 or 3.
D. Most of the hurricane sized differ from the average by about 1 or 2.*
Answer:
a) mean = 0.2
variance = 0.0391
standard deviation = 0.198
b) The average hurricane is aprox. category 2.* (B)
Step-by-step explanation:
In order to find the mean, variance, and standard deviation, let us for a table for the data:
level x
1 0.411
2 0.278
3 0.221
4 0.080
5 0.010
Calculating the mean ([tex]\bar{x}[/tex])
[tex]\bar{x} = \frac{x_1+x_2+x_3+x_4 + x_5}{n}\\\\\bar{x} = \frac{0.411 + 0.278 + 0.221 + 0.080 + 0.010}{5}\\\bar{x} = \frac{1}{5}\\ \bar{x} = 0.2[/tex]
∴Mean = 0.2
level x [tex]x- \bar{x}[/tex] [tex](x - \bar{x})^2[/tex]
1 0.411 0.211 0.0445
2 0.278 0.078 0.0608
3 0.221 0.021 0.000441
4 0.080 -0.12 0.0144
5 0.010 -0.19 0.0361
[tex]\sum(x - \bar{x})^2 = 0.1562[/tex]
[tex]variance = \frac{\sum(x - \bar{x})^2}{n-1} \\variance = \frac{0.1562}{4} \\variance = 0.0391[/tex]
standard deviation = √(variance)
Standard deviation = √(0.0391)
Standard deviation = 0.198
b) the average hurricane is aprox. category 2 (B)
Help please thanks :)
Answer:No Solution
Step-by-step explanation:
Consistent dependent like 0=0 or x=x
A journalist interviews 123 people after they leave a restaurant and asks them how confident they are that the food is safe.
Answer:
what do I need to do to answer
Step-by-step explanation:
Is 18.18 rational or irrational
Answer:
Rational
Step-by-step explanation:
You are able to put 18.18 in a fraction.
Hope this helped, Have an AMAZING day/night!
78 feet wide and 27 feet long what is the perimeter?
Answer:
105
Step-by-step explanation:
When finding the perimeter add them together
A farmer sold 54 pumpkins the first weekend of a fall festival and 42 pumpkins the second weekend.
Which expression uses the distributive property to show equivalent expressions for this situation?
54 + 42 = (3)(18) + (6)(7)
54 + 42 = (9)(10) + 6
54 + 42 = 90 + 6
54 + 42 = 6(9 + 7)
Answer:
54 + 42 = 6(9 + 7)
Step-by-step explanation:
Using distributive property on the right side of the equality, you multiply 6 and nine and 6 and 7 to get rid of the parenthesis.
Answer:
its the last one
Step-by-step explanation:
If the measure of 1 is 50 degrees what is the measure of 2 ?
Answer:
100
Step-by-step explanation:
if 1 is 50 then the measure of 2 would be 100
Answer:
The measure of angle 2 is
Step-by-step explanation:
angle 1 is 50 degrees and it creates a linear pair (adds up to 180) with the angle right under it.
so we can say that 50+x=180 (x represents angle 2)
subtract x from both sides , 50-50+x=180-50
x= 130
A marathon runner travels 9/2 miles in 1/2 hour what is the unit rate
Answer:
9/2:1/2
Step-by-step explanation:Here's the answer
What is 8.5+ 3.4 - 6.5 - (-1.6) = ?
A metal bar has the D of 7.9 g/mL. If the volume of the bar is 500mL, what is the mass in kg?
The density of a substance is the mass per unit volume. The mass of the metal bar is 3.95 kg.
What is density?The density of a substance is the mass per unit volume.
It can be given as,
[tex]\rho=\dfrac{m}{v}[/tex]
Here, [tex]m[/tex] is the mass of the substance and [tex]v[/tex] is the volume of hte substance.
Given information
A metal bar has the D of 7.9 g/mL .
Volume of the bar is 500 mili liter.
Suppose the mass of the metal bar is [tex]m[/tex] grams. Thus put the values in the above formula as,
[tex]\rho=\dfrac{m}{v}\\7.9=\dfrac{m}{500}\\[/tex]
Solve for m,
[tex]m=500\times7.9\\m=3950[/tex]
Thus the mass of the metal bar is 3950 grams. Convert it into the kg as divide by 1000. Thus,
[tex]m=\dfrac{3950}{1000}\\m=3.950[/tex]
Hence the mass of the metal bar is 3.95 kg.
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Given f(x) = -x - 2, find x when f(x) = 12.
es
A)
-14
B)
-12
C)
10
D)
14
Answer:
We substitute
12 = -x - 2
14 = -x or -x = 14
so the answer is -14!
I am in honors high school algebra and I am 11. Trust me bro.
Step-by-step explanation:
In a primary school class, the ratio of boys to girls is 3:4. If there are 12 girls in the class, what is the total number of students in the class? *
Answer:
21
Step-by-step explanation:
A ratio of 3:4 means that for every 3 boys there are 4 girls and vice versa.
12 girls / 4 girls = 3
3 boys * 3 = 9 boys
There are 9 boys in the class.
9 boys + 12 girls = 21 total students
What’s 6r+3=4r-11?????
Answer:
-7
Step-by-step explanation:
6r+3=4r-11
distributive property
6r-4r=-11-3
2r=-14
r=-7
The difference between two positive integers is 6. If the smaller is added to the square of the larger, the sum is 84. Find the integers.
Answer:
Step-by-step explanation:
B
Your favorite dog groomer charges according to your dog's weight. If your dog is 15 pounds and under, the groomer
charges $35. If your dog is between 15 and 40 pounds, she charges $40. If your dog is over 40 pounds, she charges $40,
plus an additional $2 for each pound.
a. Write a piecewise function that describes what your dog groomer charges.
b. Graph the function.
Answer:
hope the pics below helps!!
Plz mark brainliest :DD
The groomer charges is an illustration of a piece-wise function, where different functions are used to handle different inputs.
The piece-wise function is:
[tex]f(x) = \left[\begin{array}{ccc}35,&x \le 15\\40, &15 < x \le 40\\2x - 40,&x > 40\end{array}\right[/tex]
Let:
[tex]x \to[/tex] weight of dog
[tex]y \to[/tex] charges
Dogs that weigh 15 pounds or under
This means that: [tex]x \le 15[/tex]
And the charges is [tex]y = 35[/tex]
Dogs that weigh between 15 and 40 pounds
This means that: [tex]15 < x \le 40[/tex]
And the charges is [tex]y = 40[/tex]
Dogs that weigh over 40 pounds
This means that: [tex]x > 40[/tex]
And the charges is [tex]y = 40 + (x - 40) \times 2[/tex]
Simplify
[tex]y = 40 + 2x - 80[/tex]
Collect like terms
[tex]y = 2x +40- 80[/tex]
[tex]y = 2x - 40[/tex]
So, the piece-wise function is:
[tex]f(x) = \left[\begin{array}{ccc}35,&x \le 15\\40, &15 < x \le 40\\2x - 40,&x > 40\end{array}\right[/tex]
See attachment for the graph of the piece-wise function
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6. (02.01 MC)
The US Department of Health and Human Services wants to know whether the national healthcare system is achieving its goals in Florida. Much information about healthcare comes from
patient records, but that source doesn't allow us to compare people who use health services with those who don't. Therefore, the US Department of Health and Human Services conducted the
Florida Health Survey, which was used to interview a random sample of 62,348 people who live in the state of Florida.
Part A: What is the population for this sample survey? What is the sample? (4 points)
Part B: The survey found that 74% of males and 83% of females in the sample had visited a general practitioner at least once during the past year. Do you think these estimates are close to
the truth about the entire population? Explain. (6 points) (10 points)
Answer:
A)i) Population: Total number of people that reside in Florida..
II) Sample: 62348 people that took part in the random survey.
B) No, the estimates are not close to the truth of the entire population.
Step-by-step explanation:
A)i) The population is the total number of people that reside in Florida.
II) The sample is the 62348 people that took part in the random survey.
B) From the details given in the question, we will see that people who are not part of the healthcare system weren't included due to the fact that they used patients records to judge. This means that if they don't have healthcare, then they will have no patient records. Therefore, we can conclude that the estimates are not close to the truth of the entire population due to the fact that that those who weren't part of the Healthcare system were not considered.
PLEASE HELPPPPPP
the side length of the base of a rectangular prism with a height of 18 inches can be found with the equation b=(v/18)^1/2 v is the volume of the prism find the side length of the base of the volume of the prism is 4050 cubic meters
Answer:
15 if b is supposed to the side length, √15 if b is the base which is a square.
Step-by-step explanation:
Susan borrows $4500 from the bank to purchase new furniture. The bank finances for 5 years at 8% simple interest. How much will Susan pay for the furniture. (I = Prt) (A = I + P) PLS HELP ME I HAVE TO TURN THIS IN SOON!!!!!!!!!!!!!!!!!!!
Answer:
$6300
Step-by-step explanation:
A = P(1 + rt)
A = Total Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
r = Rate of Interest per year in decimal; r = R/100
t = Time Period involved in months or years
P = $4500
t = 5 years
r = 8% = .08
A = P(1 + rt)
A = 4500 ( 1 + (.08*5))
A = 4500 ( 1 + .4)
A = 4500 (1.4)
A = $6300
Susan will pay $6300 for the furniture
________________________________________________________
The equation I used is the same as what you were given:
I = Prt
A = I + P Re-write as I = A - P
So you plug in A - P for I:
A - P = Prt Add P to each side
A - P + P = Prt + P
A = Prt + P Pull P out
A = P(rt + 1) Re-arrange
A = P(1 + rt)
Same equation!
what is 12÷ 1 1/5 = nnnnnn
Rewrite 1 1/5 as 6/5
Now you have 12 / 6/5
When dividing by a fraction, flip the fraction over and multiply:
12 / 6/5 = (12 x 5) /6 = 60/6 = 10
The answer is 10
Answer:
8
Step-by-step explanation:
Rename 2 1/2 as an improper fraction
Answer:
5/2
Step-by-step explanation:
Because that is the answer
Answer:
5/2
Step-by-step explanation:
Because it is an improper fraction so you move it to the top.
Pls Brainliest! ;) It would mean a lot!
Find the value of the expression:
70–a2 for a=–25; 1; 10
Simple answer.
You will have to replace a, with the given numbers.
For the 1st one)
70-25² since a=25. 70-625=-55
2nd)
70-1²=70-1=69
3d)
70-10²=70-100=-30
Hope this helped.
can someone please help me :)
Answer:
30
Step-by-step explanation:
RST=RSV-TSV
2x+8=11x+10-101
2x-11x=10-8-101
-9x=-99
x=99/9
x=11
--->RST=2(11)+8
RST=30
Day 2- Real World- Midpoint
While planning the layout of her yard, Laura created a grid
system representing her backyard. On the grid, Laura placed
the center of a herb garden at the coordinates (3.14) and wants
to place a bird bath at the point (7,29). If Laura wants to
position the center of a flower garden so that the bird bath is
halfway between the herb and flower gardens, at what
coordinates should the center of the flower garden be placed?
(11, 150
O (11,44)
O (4,44)
O (4,15)
Help
Answer:
Point of the flower garden R ( 11, 44 )
Step-by-step explanation:
Let´s call P ( 3, 14 ) The center of the herb garden, and Q ( 7 , 29 ) the birdbath point
Differences in coordinates of these two points are:
x axis 7 - 3 = 4
y axis 29 - 14 = 15
Then the point Q ( x , y ) will be at: Q ( 11, 44)
x axis x = 11 because 7 + 4 = 11 means that the coordinate 7 is just halfway way between coordinates (x) 3 and 11 ( 4 above 3, and 4 below 11)
Reasoning the same way we conclude y = 44 in this case 29 is just halfway between coordinates (y) 14 and 44 ( 15 above 14 and 15 below 44)
We can probe getting distance d₁ between P and Q and d₂ distance between Q and R as:
d₁ = √ (7-3)² + ( 29-14)²
d₁ = √ 16 + 225
d₂ = √ (11 - 7)² + ( 44 - 29)²
d₂ = √ 16 + 225
Please help!!!!! Assume the blue lines are parallel. Based on the diagram, select all angles that are congruent to angle 3.
Answer:
Angle 7
Step-by-step explanation:
It is on the same side down from 3 so it would be congruent because they are lined up.
