The number 8.42 x 10³ lies in between pairs of numbers 8400 and 8500.
Option D is correct.
What is PEDMAS?The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations.
PEMDAS stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.
We have the number 8.42 x 10³.
Now, expanding the exponents we get
= 8.42 x 10³
= 8.42 x 1000
= 84.2 x 100
= 842 x 10
= 8420
Thus, the values lie between 8400 and 8500.
Learn more about PEDMAS here:
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Determine the equation of the graph and select the correct answer below.
y = (x + 3)^2 − 2y = (x − 3)^2 − 2y = (x + 3)^2 + 2y = (x − 3)^2 + 2
19. What is the sum of the measures of the exterior angles in a nonagon? Explain.
Answer:
360°
Step-by-step explanation:
I just took the test.
One Question Please Help
A customer who opens a savings account at a bank, in turn, becomes a(n) _____.
A. lender
B. investor
C. insurer
D. borrower
@lulu22,
You are scheduled to receive $38,000 in two years. when you receive it, you will invest it for 10 more years at 6.0 percent per year. how much will you have in 12 years?
The following set of numbers is going to be graphed on a histogram.
3, 19, 11, 29, 4, 6, 10, 16, 2, 21, 15, 22, 13, 9, 1, 17, 2, 26, 18, 7
If there are going to be six intervals in the display, what is the length of each interval?
1.) 5
2). 6
3.) 3
Answer:
The answer is 5.
Step-by-step explanation:
A group of art students are painting a mural on a wall. the rectangular wall has dimensions of (6x + 7) by (8x + 5) and they are planning the mural to be (x + 4) by (2x + 5). what is the area of the remaining wall after the mural has been painted?
The area of the remaining wall after the mural has been painted is 46x^2+73x+15. Hence, he correct answer is [tex]\(\boxed{\text{A. }46x^2+73x+15}\)[/tex]
To find the area of the remaining wall after the mural has been painted, we need to find the area of the entire wall and then subtract the area of the mural.
The area of the rectangular wall is given by the product of its dimensions:
[tex]\[ \text{Area of wall} = (6x+7)(8x+5) \][/tex]
Expanding this expression:
[tex]\[ \text{Area of wall} = 48x^2 + 30x + 56x + 35 \][/tex]
[tex]\[ \text{Area of wall} = 48x^2 + 86x + 35 \][/tex]
Now, the area of the mural is given by the product of its dimensions:
[tex]\[ \text{Area of mural} = (x+4)(2x+5) \][/tex]
Expanding this expression:
[tex]\[ \text{Area of mural} = 2x^2 + 5x + 8x + 20 \][/tex]
[tex]\[ \text{Area of mural} = 2x^2 + 13x + 20 \][/tex]
Now, to find the area of the remaining wall, we subtract the area of the mural from the area of the wall:
[tex]\[ \text{Area of remaining wall} = \text{Area of wall} - \text{Area of mural} \][/tex]
[tex]\[ \text{Area of remaining wall} = (48x^2 + 86x + 35) - (2x^2 + 13x + 20) \][/tex]
[tex]\[ \text{Area of remaining wall} = 48x^2 + 86x + 35 - 2x^2 - 13x - 20 \][/tex]
[tex]\[ \text{Area of remaining wall} = 46x^2 + 73x + 15 \][/tex]
So, the correct answer is [tex]\(\boxed{\text{A. }46x^2+73x+15}\)[/tex].
The complete question is:
A group of art students are painting a mural on a wall. The rectangular wall has dimensions of (6x+7) by (8x+5) and they are planning the mural to be (x+4) by (2x+5). What is the area of the remaining wall after the mural has been painted?
A. 46x^2+73x+15
B. 48x^2+86x+35
C. 2x^2+13x+20
D. 50x^2+99x+55
1.
(08.01 MC) Determine all zeros for the function f(x)=(x2−2−8)(x+6)
-48
-8
-6
-4
-2
0
2
4
6
8
48
An online company sells handmade samurai katana swords. The website costs $ 475 a month to maintain. Each katana costs $ 200 to make, and they sell each katana for $ 755. Create a linear model in the form y = m x + b where x is the number of swords sold per month and y is the net monthly profit. Using this model, find the number of swords that would need to be sold per month to have a monthly profit of $ 4370.,
A pilot approaching a 3000-meter runway finds that the angles of depression of the ends of the runway are 14° and 20°. How far is the plane from the closer end of the runway? Round to the nearest tenth place.
Final answer:
To find out how far the plane is from the closer end of the runway, we use the angles of depression and runway length to calculate the distance using trigonometric ratios. The distance is found to be approximately 26153 meters.
Explanation:
To determine the distance from the plane to the closer end of the runway, we use trigonometric ratios based on the angles of depression given. The angles of depression to the ends of the runway are 14° and 20°. Since the problem involves a horizontal surface (runway) and vertical angles (angles of depression), we can create two right triangles. One triangle has an angle of 14° between the plane's line of sight and the horizontal surface, and the other one has a 20° angle.
Let x be the distance from the plane to the point directly above the closer end of the runway and y be the distance from the plane to the point directly above the far end of the runway. We are looking for x, which can be found using the tangent of the 14° angle.
x = runway length / (tan(20°) - tan(14°))
Given the runway length as 3000 meters, we can calculate:
x = 3000 / (tan(20°) - tan(14°))
Crunching the numbers:
x ≈ 3000 / (0.3640 - 0.2493)
x ≈ 3000 / 0.1147
x ≈ 26153 meters (rounded to the nearest tenth)
Therefore, the distance from the plane to the closer end of the runway is approximately 26153 meters.
Really need some help understanding this problem?!?!
The temperature of a cup of coffee varies according to Newton's Law of Cooling: dT/dt = -k (T-A), where T is the water temperature, A is the room temperature, and k is a positive constant.
If the coffee cools from 180°F to 100°F in 10 minutes at a room temperature of 75°F, how long (to the nearest minute) will it take the water to cool to 80°F?,
The table shows the predicted growth of a particular bacterium after various numbers of hours.
Write an explicit formula for the sequence of the number of bacterium.
A) an=24n+1
B) an=24n
C) an=1/24n
D) an=n+24
The equation of a circle is (x + 12)2 + (y + 16)2 = (r1)2, and the circle passes through the origin. the equation of the circle then changes to (x – 30)2 + (y – 16)2 = (r2)2, and the circle still passes through the origin. what are the values of r1 and r2?
a.r1 = 10 and r2 = 17
b.r1 = 10 and r2 = 34
c.r1 = 20 and r2 = 17
d.r1 = 20 and r2 = 34
Answer:
Option D is correct
Step-by-step explanation:
Given Equations of Circles:
Circle 1 - [tex](x+12)^2+(y+16)^2=(r_1)^2[/tex]
Circle 2 - [tex](x-30)^2+(y-16)^2=(r_2)^2[/tex]
Both circles passes through origin.
To find: Values of [tex]r_1\:,\:r_2[/tex]
Coordinates of origin = ( 0 , 0 )
Circles passes through origin means x = 0 & y = 0 must satisfy the equation of circles.
So, Substituting x = 0 & y = 0 in Eqn of Circle 1
we get
[tex](0+12)^2+(0+16)^2=(r_1)^2[/tex]
[tex](r_1)^2=12^2+16^2[/tex]
[tex](r_1)^2=144+256[/tex]
[tex](r_1)^2=400[/tex]
[tex]r_1=\sqrt{400}[/tex]
[tex]r_1=20[/tex]
Now, Substituting x = 0 & y = 0 in Eqn of Circle 2
we get
[tex](0-30)^2+(0-16)^2=(r_2)^2[/tex]
[tex](r_2)^2=(-30)^2+(-16)^2[/tex]
[tex](r_2)^2=900+256[/tex]
[tex](r_2)^2=1156[/tex]
[tex]r_2=\sqrt{1156}[/tex]
[tex]r_2=34[/tex]
Therefore, Option D is correct .i.e., [tex]r_1=20\:\:,\:\:r_2=34[/tex]
Find tan U.
CR=6.3
UC=4.1
RU=7.7
For the parallelogram, find the value of the variables. Show your work
ok trying to figure out how to solve this problem
5x + 2
3y - 6 21
17
In circle O, AE and FC are diameters. Arc ED measures 17°
Answer:
c
Step-by-step explanation:
Find the length of the side of an isosceles triangle with perimeter of 12 and maximum area
In a 45-45-90 triangle, what is the length of the hypotenuse when the length of one of the legs is 5 in.? 25√ in. 52√ in. 5√ in. 55√ in.
Answer: [tex]5\sqrt{2}\ in[/tex]
Step-by-step explanation:
Given: In a 45-45-90 triangle, the length of one of the legs= 5 in.
Let H be the hypotenuse of the given right triangle.
Since the two angles are equal (45°) in the given right triangle,also in a triangle the side opposite to the equal angles are equal.
Therefore, the other leg of given right triangle = 5 in.
Now applying Pythagoras theorem, we get
[tex]H^2=5^2+5^2=25+25\\\\\Rightarrow\ H^2=50\\\\\Rightarrow H=\sqrt{50}\\\\\Rightarrow H=5\sqrt{2}\ in[/tex]
Hence, the length of the hypotenuse = [tex]5\sqrt{2}\ in[/tex]
Can someone help me with this one
Find the area of the following ellipse. (Round answer to the nearest tenth).
2a = 10 cm; 2b = 20 cm.
A = _____cm²,
Answer:
Approximately 157.08 sq. cm.
Step-by-step explanation:
The Area of an Ellipse is given by the formula [tex]A=\pi a b[/tex]
Here 2a = 10, so a = 5
Also, 2b = 20, b = 10
Substituting these into the area formula gives us:
[tex]A=\pi a b\\A=\pi (5)(10)\\A=50\pi\\A=157.08[/tex]
The Area is approximately 157.08 sq. cm.
Using 70 POINTS NEED YOUR HELP NOT SPAMMERS. To make an ice-cream cone, employees at an ice-cream shop completely fill the cone and then add one scoop of ice cream on top. The cone has a height of 6 inches and a diameter of 2 inches.
To the nearest cubic inch, how much ice cream is in the cone before the scoop is added on the top?
6 in³
19 in³
25 in³
75 in³
also
A candy machine contains 120 spherical candies. Each candy is solid and has a diameter of 0.25 inches.
What is the total volume of the candies in the machine?
Select from the drop-down menu to correctly complete the statement.
The total volume of the candies in the machine is about
Solution for Q1:
Given is the height of ice-cream cone, h = 6 inches.
Given is the diameter of ice-cream cone, d = 2 inches. Then radius of cone would be half of diameter, r = d/2 = 1 inch.
The ice-cream without scoop would be in the shape of cone only. So we need to find the volume of cone.
We know the formula for volume of cone is given as follows :-
[tex] Volume = \frac{1}{3} \pi r^{2} h \\\\Volume = \frac{1}{3} \pi (1)^{2} (6) \\\\Volume = \frac{6\pi}{3} = 2\pi = 2(3.14) = 6.28 \;cubic \;inches. [/tex]
So the volume is 6.28 ≈ 6 in³.
Hence, option A is correct i.e. 6 cubic inches.
Solution for Q2:
A candy is in shape of sphere with diameter, d = 0.25 inches.
Then radius of sphere, r = d/2 = 0.250/2 = 0.125 inches.
The formula for volume of sphere is given as follows :-
[tex] Volume = \frac{4}{3} \pi r^{3} \\\\Volume = \frac{4}{3} \pi (0.125)^{3} \\\\Volume = 0.00818123 \;cubic \;inches. [/tex]
So, volume of one candy = 0.00818123 cubic inches.
There are total 120 candies in the machine.
Total volume of all 120 candies = 120 x 0.00818123 = 0.981748 cubic inches.
Hence, the total volume of all candies in the machine is about 0.982 in³.
Answer:
This should definitely help for question 1 :)
What is the volume of a ball if its diameter is 6 inches? Leave your answer in terms of π.
A)V = 12 π cubic inches
B)V = 36 π cubic inches
C)V = 288 π cubic inches
D)V = 27.75 π cubic inches
Explanation:The volume of the ball above is V = 36 π cubic inches. Use the formula V = 4/3π 3. Just remember to cut the diameter in half to get the radius.
Step-by-step explanation:
Suppose x is any positive number. circle 1: center (5, 4) and radius 5x circle 2: center (5, 4) and radius 2x why is circle 1 similar to circle 2? circle 1 and circle 2 have the same radius. circle 1 is a dilation of circle 2 with a scale factor of 2.5. circle 1 is a dilation of circle 2 with a scale factor of 0.4. circle 1 is congruent to circle 2.
Answer:
circle 1 is a dilation of circle 2 with a scale factor of 2.5.
Step-by-step explanation:
The radius of circle 1 is 5x and the radius of circle 2 is 2x.
This means the scale factor of the dilation is 5x/2x = 2.5.
Circle 1 is a dilation of circle 2 with a scale factor of 0.4.
What are similar figures?Two figures are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion.
Given that circle 1 has radius of 5x and circle 2 has radius of 2x, hence:
Circle 1 scale factor = 2x / 5x = 0.4
Hence:
Circle 1 is a dilation of circle 2 with a scale factor of 0.4.
Find out more on similar figures at: https://brainly.com/question/14285697
which of the following statements is not always true ?
a. if a function contains the origin , then its inverse contains the origin.
b.if a function has 3 x-intercepts, then its inverse has 3 y-intercepts.
c.if a function contains no points in the fourth quadrant, then its inverse contains no points in the second quadrant.
d.if the slope of a linear function is less than 1, then the slope of its inverse is greater than 1.,
What is the larger figure?
Properties of Parallelograms
find x.
Order the steps to solve the equation
Log(x^2-15)=log(2x) form 1 to 5.
Answer:
x2 − 15 = 2xx2 − 2x − 15 = 0(x − 5)(x + 3) = 0x − 5 = 0 or x + 3 = 0Potential solutions are −3 and 5Answer:
The answers in order are 2,5,1,4,3
Step-by-step explanation:
Correct on edge
She bought 3 t shirt for 8$ each. she paid with a $50 bill how much change should she get
Answer:
26
Step-by-step explanation:
3 x 8 = 24
50-24=26
She will get $26 dollars back
Easy Step by Step explanation
Given an exponential function for compounding interest, A(x) = P(.91)^x, what is the rate of change?
A. −0.09%
B. −9%
C. 0.91%
D. 91%
The confirmed correct answer is -9%. Trust me.
Answer:
Option B = -9%
Step-by-step explanation:
Given : Given an exponential function for compounding interest, [tex]A(x) = P(.91)^x[/tex]
To find : What is the rate of change?
Solution :
The general form of the exponential function is [tex]f(x)=a(1+r)^x[/tex]
Where,
r is the rate of change
if r> 1 then it is growth rate
if r< 1 then it is decay rate.
Comparing given function with exponential function,
[tex]A(x) = P(.91)^x[/tex]
[tex]1+r=0.91[/tex]
[tex]r=0.91-1[/tex]
[tex]r=−0.09[/tex]
It is a decay rate.
Convert into percentage, multiply with 100
[tex]-0.09\times 100=-9\%[/tex]
Therefore, Option B is correct.
The rate of change is -9%.
Match the corresponding function formula with each function when h(x)=3x+2 and g(x)=2^x
1. K(x)=2^x+3x+2
2. K(x)=2^x-3x-2
3. K(x)=(3x)2^-x+2^-x+1
4. K(x)=2^3x+2
5.k(x)=2^x(3x+2)
6. K(x)=3(2^x)+2
————————————
A. K(x)=g(x)+h(x)
B. K(x)=h(x) divided g(x)
C.k(x)=g(x)-h(x)
D.k(x)=g(x)*h(x)
E. K(x)=g(x)•h(x)
F. K(x)=h(x)•g(x)
What is the slope of the line
The height in feet, h, of a model rocket t seconds after launch is given by the equation h(t) = 3+70t - 16t^2. The average rate of change in h(t) between t = 1 second and t = 3 second is 6. What does the average rate of change tell you about the rocket?
Answer:
The rocket is at a greater height when t = 3 than it is when t = 1.
Option B
Step-by-step explanation:
Just took the test
Answer:
B
Step-by-step explanation:
!