The number of times 5×10³ greater than 15×10⁹ is 3×10⁶.
What is scientific notation?Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.
Given that, 15×10⁹ and 5×10³.
Number of times 5×10³ greater than 15×10⁹ is
Now, 15×10⁹/5×10³
= 3×10⁶
Therefore, 3×10⁶ times 5×10³ greater than 15×10⁹.
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Which is 3 logx + 4 log(x-2) written as a single logarithm?
logx (x - 2)
logx(x-2)
b. 12 logx(x - 2)
d. 12 logx(x-2)
Answer:
The answer is [tex]12\log{(x(x-2))}[/tex]
Step-by-step explanation:
Exponential property of logarithm:
We have that:
[tex]a \log{x} = \log{x^{a}}[/tex]
Sum of logarithms:
We have that:
[tex]\log{a} + \log{b} = \log{ab}[/tex]
Applying the exponential property:
[tex]3\log{x} = \log{x^3}[/tex]
[tex]4\log{(x-2)} = \log{(x-2)^4}[/tex]
So
[tex]3\log{x} + 4\log{x-2} = \log{x^3} + \log{(x-2)^4}[/tex]
Additive property
[tex]\log{x^3} + \log{(x-2)^4} = \log{x^3(x-2)^4} = \log{(x(x-2))^12}[/tex]
Exponential property:
[tex]\log{(x(x-2))^12} = 12\log{(x(x-2))}[/tex]
The answer is [tex]12\log{(x(x-2))}[/tex]
What is the gravitational potential energy of a 55-kg person that has climber a 4,000 meter tall mountain?
Bonus: if one snickers bar is 1,100,000 joules of energy, how many snickers bars would provide enough fuel to climb the mountain ?
Answer:
2156000 J.
Bonus: 2 snickers bar
Step-by-step explanation:
Applying
P.E = mgh................. Equation 1
Where P.E = Gravitational potential energy, m = mass of the person, h = height of the mountain, g = acceleration due to gravity.
From the question,
Given: m = 55 kg, h = 4000 m
Constant: g = 9.8 m/s²
Substitute these values into equation 1
P.E = (55×4000×9.8)
P.E = 2156000 J.
If one snikers bar is 1100000 J of energy,
Then, (2156000/1100000) snickers bar would be enough to climb the mountain
Number of snickers bar = (2156000/1100000) = 1.96 ≈ 2
The length of a rectangle is twice its width. The perimeter is 30. Find it’s dimensions.
Answer:
Length = 10 Width = 5Step-by-step explanation:
Let's assume that,
→ Length = 2x
→ Width = x
→ Perimeter = 30
Perimeter of rectangle formula,
→ P = 2(L + W)
Now the value of x will be,
→ P = 2(L + W)
→ 2(2x + x) = 30
→ 2 × 3x = 30
→ 6x = 30
→ x = 30/6
→ [ x = 5 ]
Then required dimensions are,
→ Length = 2x = 2 × 5 = 10
→ Width = x = 5
Hence, these are the dimensions.
Length = 10
width = 5
Given-
Perimeter =30
l=2b........................................................ i
so
P =2(l+b)
here
30 = 2(2b +b)... ... .............. as l=2b from i
30 = 2*3b
30 = 6b
b= 5
which implies l= 2*5 --->10............................................ from i
so
Length = 10
width = 5
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A mother is now 2 and ahalf times old as her daughter Mary. Four years ago the ratio of their ages was 3:1. Find the present age of the mother.
Given:
A mother is now 2 and a half times old as her daughter Mary.
Four years ago the ratio of their ages was 3:1.
To find:
The present age of the mother.
Solution:
Let x be the present age Mary's mother and y be the present age of Mary.
A mother is now 2 and a half times old as her daughter Mary. So,
[tex]x=2\dfrac{1}{2}y[/tex]
[tex]\dfrac{x}{y}=\dfrac{2(2)+1}{2}[/tex]
[tex]\dfrac{x}{y}=\dfrac{5}{2}[/tex]
It means the ratio of their present age is 5:2. Let 5z be the present age of Mary's mother and 2z be the present age of Mary.
Four years ago the ratio of their ages was 3:1.
[tex]\dfrac{5z-4}{2z-4}=\dfrac{3}{1}[/tex]
[tex]1(5z-4)=3(2z-4)[/tex]
[tex]5z-4=6z-12[/tex]
[tex]-4+12=6z-5z[/tex]
[tex]8=z[/tex]
Now, the present age of the mother is:
[tex]5z=5(8)[/tex]
[tex]5z=40[/tex]
Therefore, the present age of the mother is 40 years.
Find the volume of the cone. Round your answer to the nearest tenth.
27 in.
16 in.
it is 17371.8 I put it into a calculator and got it haha
Someone please help with this!
Answer:
27/1
Step-by-step explanation:
3³=3·3·3=27
27=27/1
can someone please help me on this question?
Answer: D
Step-by-step explanation:
If the graph is shifted 5 units down, each output value should decrease by 5.
5 1/10-1 7/10=
A.3 3/5
B.6 4/5
C.3 2/5
D. 3 3/10
please help me to solve this
Answer:
Below in bold.
Step-by-step explanation:
First find the height by use Pythagoras theorem on the right triangle:
h = sqrt (5^2 - 4^2)
= sqrt 9
= 3.
Volume of the prism = area of the triangle * length
= 1/2 * 3 * 4 * 10
= 1/2 * 12 * 10
= 60 cm^3.
Total area = area of 2 triangles + area 0f 3 rectangles
= 2 * 1/2 * 3 * 4 + 3 * 10 + 4 * 10 + 5 * 10
= 12 + 30 + 40 + 50
= 132 cm^2.
Two methods were used to teach a high school algebra course. A sample of 75 scores was selected for method 1, and a sample of 60 scores was selected for method 2. The results are:
Method 1 Method 2
Sample mean 85 83
Sample s.d. 3 2
Required:
Test whether method 1 was more successful than method 2 at the 1% level.
Answer:
Since the calculated value of t =4.629 falls in the critical region t> 2.355 we reject the null hypothesis and conclude that method 1 was more successful than method 2 at the 1% level.
Step-by-step explanation:
Applying two sample t test as both methods are independent
The null and alternate hypotheses are
H0: u1= u2 against the claim Ha: u1> u2
The significance level is 0.01 and the critical region is t > t∝( n-1)
The degrees of freedom is calculated using the formula
υ = [s₁²/n1 + s₂²/n2]²/ (s₁²/n1 )²/ n1-1 + (s₂²/n2)²/n2-1
This formula is used when the the variances are unequal.
So as we do not know anything about variances we assume they are unequal.
The calculated degrees of freedom is 132
The critical region is t > 2.355 for one tailed test.
The test statistic is
t= x1`- x2`/ √s1²/n1 + s2²/n2
t= 85-83/ √3²/75+ 2²/60
t= 2/ 0.432
t= 4.629
Since the calculated value of t =4.629 falls in the critical region t> 2.355 we reject the null hypothesis and conclude that method 1 was more successful than method 2 at the 1% level.
What is the range of the function x is 0 and y is 40
Answer:
range is y-coordinates so it should be 40
Step-by-step explanation:
domain is x-coordinates
Please help giving brainliest please
find the area of right angle triangle whose base 9, Height 8?
Answer:38cm2
Step-by-step explanation:
The area of right angle triangle is 36 sq.cm. Whose base 9, Height 8 .
Base is 9 cm.
8 centimeters tall.
Triangle area equals 1/2 x base x height
Triangle's area is 1/2 x 9 x 8 = 36 square centimeters.
Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.
The surface inside a flat figure is measured by its area. Squares are used to measure area. To obtain the square units, multiply the length by the width.
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How many times less
is 0.054 than 54?
Answer: 1000 times less
Step-by-step explanation: multiply 0.054x1000
Answer:
1000 times
Step-by-step explanation:
To find how many times less 0.054 is than 54,
we can divide 54 by 0.054.
This gives us 54/0.054 = 1000
This means that 0.054 is 1000 times less than 54.
5 divided by G1 equals
Answer:
5/g
Step-by-step explanation:
plz helpppppppppppppppppppppppppppppppppppp quick
Answer:
B. 8
Step-by-step explanation:
6, 15, 7, 5, 11, 11, 8
5, 6, 7, 8, 11, 11, 15
The middle number is 8.
Answer:
8
Step-by-step explanation:
2 Images Below, PLEASE HELP! If I wanna go to Disneyland (I do) I gotta get this in! I MARK BRAINLIEST IF U R RIGHT!!!
Answer:
ITS B
Step-by-step explanation:
I hope im right srry if im not i hope you to disney and stay safe
Kenny loves to drink milk. He drinks 20 quarts of milk in 5 weeks. How many quarts of milk will Kenny drink in 12 weeks?
Answer:
32 mutipliy 20 and 5
Step-by-step explanation:
find the volume of each figure
Answer:
1) 17.5×14×64
→ 1568 in³2) volume= 0.5×3.6×10×5=
→ 903) d= 13, r=13/2= 6.5, h= 19
→ v= πr²h→ π(6.5)²×19→ 2521.91 mm³4) Base Area= a+b/2×h
→ (37+15)/2×25.7 cm²→26×25.7 cm²→ 668.2 cm²height= 20cmvoulme = 668.2×20→ 13364 cm²5) L×W×H
→ 25×7×18→ 175×18→ 3150 ft³6) v=πr²h
→ π(3.2²)(8)→ 81.92π→ 257.36 km²[tex]------------[/tex]
hope it helps...
have a great day!!
[tex] \huge \boxed{1}[/tex]
→17.5 × 14 × 6.4
→1568 in³
[tex] \huge \boxed{2}[/tex]
→0.5 × 3.6 × 10 × 5
→90 m³
[tex] \huge \boxed{3}[/tex]
→ Diameter = 13 mm
→ Radius = 13/2 = 6.5
→ Height = 19 mm
→Volume => πr²h
=> 22/7 × (6.5)² × 19
=> 2521.91 mm³
[tex] \huge \boxed{4}[/tex]
→ Base Area → a+b/2×h
→ (37+15)/2×25.7 cm²
→26×25.7 cm²
→ 668.2 cm²
(height= 20cm)
→volume => 668.2×20
→13364 cm²
[tex] \huge \boxed{5}[/tex]
→Area→ L × B × H
→ 25×7×18
→ 175×18
→ 3150 ft³
[tex] \huge \boxed{6}[/tex]
→Volume → πr²h
→ π(3.2²)(8)
→ 81.92π
→ 257.36 km²
[tex] \boxed{Extra-Information}[/tex]
Always divide the diameter with 2 to get the radius.Volume is expressed in cube³ unit.[tex] \bold \green{TheExtraterrestrial}[/tex]
Worked Example:
Select all the expressions that have the same value as 4 1/2% of 50.
A. 0.045x50
B. 4.5%x50
C. 43%x50
D. 4.5x50
E. 0.45x50
F. 412x50
Answer:
Options A and B------------------------------------------
4 1/2% of 50 is 4.5% of 50 which is same as:
4.5% × 50or substituting % with 1/100,
4.5/100 × 50 = 0.045 × 50The matching choices are A and B.
Write two numbers that are opposites and more than 6 units away from 0.
Answer:
-7, 7
Step-by-step explanation:
Opposites are basically two numbers that are at different sides of the number line. For example, -2 and 2 are opposites because they are the same distance away from 0 on a number line making them opposites. To make an opposite just take a positive number, and then add a negative to it. (8, -8) Hope that helps :)
Determine the value of x that make the equation true . 5 (x + 2) = 7 (4 - x)
Answer:
[tex]\huge \fbox \pink {A}\huge \fbox \green {n}\huge \fbox \blue {s}\huge \fbox \red {w}\huge \fbox \purple {e}\huge \fbox \orange {r}[/tex]
[tex]5(x + 2) = 7(4 - x) \\ 5x + 10 = 28 - 7x \\ 5x + 7x = 28 - 10 \\ 12x = 18 \\ x = \frac{18}{12} \\ x = \frac{3}{2} \\ x = 1.5[/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
[tex] \huge\blue{ \mid{ \underline{ \overline{ \tt ꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐ }} \mid}}[/tex]
Can someone please help asap need work to
In a 30-60 right triangle the side opposite the 30 degree angle is half the length of the hypotenuse.
so RT= 10
A box office sold 147,523 tickets for an auto race.
Of this number, 68,724 tickets were for adults.
The rest were children's tickets.
How many children's tickets were sold?
78,709
81,799
121,201
Answer:
78,799 children's tickets
Step-by-step explanation:
147,523 total tickets, 68,724 adult tickets
Subtract to find amount of children's tickets:
147,523-68,724 = 78,799
What is the distance, rounded to the nearest tenth, between the points (-2,4) and (6,-4)?
PLEASE HELP, ASAP. I WILL MARK YOU BRAINLIEST‼️
evaluate the following polynomial when x = - 3
+6x² – 3x+5
2x
Answer:
-93
Step-by-step explanation:
Substitute by - 3 instead of X
Graph the function n(x) = |x6|.
+Move Ray
-6
-4
-2
104
9
4
2
0
-2
Undo
2
4
Redo
6
x Reset
8
10
Answer:
x
)
=
2
x
4
−
3
x
+
3
f(x)=2x
4
−3x+3, then what is the remainder when
f
(
x
)
f(x) is divided by
x
−
1
x−1?
HELP ASAP!!! I’m very confused and need help. I WILL MARK BRAINLIST!!!!
Step-by-step explanation:
In ∆PQR and ∆TSU
[tex]\because\begin{cases}PQ\approx TS \\ QR\approx TU \angle \\ Q\approx \angle T\end{cases}[/tex]
[tex]\therefore{∆PQR\approx ∆TSU(\because SAS)}[/tex]
And
<Q is greater than <TSo SU will be less than PR(22cm)Use the figures to complete the statements proving the converse of the Pythagorean theorem.
Drag and drop a phrase, value, or equation into the box to correctly complete the proof.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
To prove the converse of the Pythagorean theorem, we can define a right triangle, Response area, with sides a, b, and x. Then, we will show that if △ABC is a triangle with sides a, b, and c where a² + b² = c², then it is congruent to △DEF and therefore a right triangle.
By the Pythagorean theorem, because △DEF is a right triangle, a² + b² = x².
If a² + b² = x² and a² + b² = c² , then c² = x². Further, since sides of triangles are positive, then we can conclude that c = x. Thus, the two triangles have congruent sides and are congruent.
If △ABC is congruent to a right triangle, then it must also be a right triangle.
To prove the converse of the Pythagorean theorem, we can define a right triangle Δ DEF with sides a, b, and x.
\What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We have,
ΔABC and ΔDEF
To prove the converse of the Pythagorean theorem, we can define a right triangle DEF with sides a, b, and x.
Thus,
ΔDEF is filled in the box.
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