The 108 decibel sound is 6.31 times more intense than a 100 decibel sound option (B) is correct.
What is a logarithm?It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.
[tex]\rm a^b = c\\log_ac =b[/tex]
We have:
The loudness L of sound in decibels is given by
[tex]\rm L=10log(\dfrac{I}{I_0})[/tex]
Here I is the intensity of the sound.
[tex]\rm I_0=10^{-12} \ W/m^2[/tex]
Loudness for 108 decibel sound:
[tex]\rm 108=10log(\dfrac{I}{10^-^1^2})[/tex]
I = 0.06309
Similarly, for:
100 decibel sound:
i = 0.01
I/i = 0.06309/0.01 = 6.31
I = 6.31i
Thus, the 108 decibel sound is 6.31 times more intense than a 100 decibel sound option (B) is correct.
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Use the following table of Registered Voters at Kensington College, Registered Voters at Kensington College 2009 2010 640 790 Democrats Republicans 960 410 Independents 320 300 11) What is the probability that a voter registered in Kensington College in 2009 was not a Republican?
Step-by-step explanation:
remember, a probability is ultimately always
desired cases / total possible cases
what are the total possible cases for our question here ?
all registered voters in 2009 :
640 + 960 + 320 = 1920
the desired cases (not republican) out of all these 1920 possibilities are
640 + 320 = 960
so, the probability for a registered voter to not be republican was
960 / 1920 = 1/2 = 0.5
Solve
x=4
-7x +y =-22
Answer:
y = 6
Step-by-step explanation:
-7 (4) + y = -22
-28 + y = - 22
+28 + 28
y = 6
Select the correct answer. If is modified as , what transformations will be seen in the graph? A. The graph will reflect across the x-axis and then shift units up. B. The graph will reflect across the y-axis and then shift units down. C. The graph will reflect across the x-axis and then shift units to left. D. The graph will reflect across the y-axis and then shift units to right.
The transformation is (b) The graph will reflect across the y-axis and then shift 5 units down.
How to determine the transformation?The missing phrase in the question is: "If f(x) = 2ˣ + 1 is modified as g(x) = 2⁻ˣ + 1 - 5"
The functions are given as:
f(x) = 2ˣ + 1
g(x) = 2⁻ˣ + 1 - 5
First, the function f(x) is reflected across the y-axis (this eliminates options a and c)
The rule of this transformation is
(x,y) ⇒ (-x,y)
So, we have:
f'(x) = 2⁻ˣ + 1
Next, the function f(x) is shifted down by 5 units (this eliminates options d)
The rule of this transformation is
(x,y) ⇒ (x,y - 5)
So, we have:
f''(x) = 2⁻ˣ + 1 - 5
By comparing the functions f"(x) and g(x), we have:
g(x) = f''(x) = 2⁻ˣ + 1 - 5
Hence, the transformation is (b) The graph will reflect across the y-axis and then shift 5 units down.
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-6>2x+6 ≤18
graph the inequality
Answer:
y= x + b
-6 > 2x+6- graph a doted line that crosses through -6, and 2 shade below the dotted line going to the negative
18 >< 2x+6 graph a solid line through 18 and 2 and shade everything above the line going positive
have a good day hope this helped
Step-by-step explanation:
The discussion in this lesson offers two tips for saving money. Write 1-2 paragraphs that describe the following: 1. state the two money saving tips 2. tell why these tips work
The first tip is to travel by public transport instead of using your own vehicle. The second tip would be to stop smoking and drinking it is a total waste of money and health.
What is saving?Saving is the method of saving your money for the future. We can not predict the future if anything bad happens and we need a large amount of money these savings will help us.
The first tip is to travel by public transport instead of using your own vehicle. The second tip would be to stop smoking and drinking it is a total waste of money and health.
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can someone help please
Answer:
2 good scoops
Step-by-step explanation:
I got you I think
Question 1 Complete the missing reasons for the proof. Given: 4(x - 2) = 6x + 18 Prove: x= -13 Statements Reasons 1.4(x - 2) = 6x +18 given 2. 4x8= 6x +18 distributive property 3.-2-8-18 4.-2x = 26 addition property of equality 5.x = -13 O 3. subtraction property of equality; 5. multiplication property of equality O 3. subtraction property of equality; 5. division property of equality 3. addition property of equality; 5. division property of equality O 3. addition property of equality; 5. multiplication property of equality
Looking at the problem statement, the question is asking us to determine what the missing reasons are. The information that is given to us is a step-by-step process of solving an expression for an unknown. There are also two blanks in the reasons column for steps 3 and 5 which we will need to determine.
For step #3, we can see that they subtracted 6x from both sides which means that options 3 and 4 are automatically out since they reference addition in the first part. The correct reasoning for this part would be Subtraction Property of Equality which states that we subtract the same item from both sides of the expression.
We can see this being done in the following actions
[tex]4x - 8 = 6x + 18[/tex][tex](4x - 6x) - 8 = (6x - 6x) + 18[/tex][tex](4x - 6x) - 8 = 18[/tex][tex]-2x - 8 = 18[/tex]For step #5, we can see that they divided both sides by -2 which means that option 1 is out since it references the multiplication property of equality. The correct reasoning for this part would be Division Property of Equality which states that we divide both sides by the same item.
We can see this being done in the following actions
[tex]-2x = 26[/tex][tex]\frac{-2x}{-2} = \frac{26}{-2}[/tex][tex]x= \frac{26}{-2}[/tex][tex]x= -13[/tex]Therefore, the option that would best fit the description that we provided during our work would be option 2 (3. subtraction property of equality; 5. division property of equality).
Answer:
b) 3. addition property of equality; 5. division property of equality.
Step-by-step explanation:
Given: 4(x - 2) = 6x + 18
Prove: x = -13
Algebraic Properties:
Addition: If a = b, then a + c = b + cSubtraction: If a = b, then a - c = b - cMultiplication: If a = b, then ac = bcDivision: If a = b, then a ÷ c = b ÷ cDistributive: a(b + c) = ab + acSteps:
1. Given:
⟹ 4(x - 2) = 6x + 18
2. Distribute property:
4(x) + 4(-2) = 6x + 18 [distribute 4]
⟹ 4x - 8 = 6x + 18
3. Subtraction property of equality:
4x - 6x - 8 = 6x - 6x + 18 [subtract 6x from both sides]
⟹ -2x - 8 = 18
4. Addition property of equality:
-2x - 8 + 8 = 18 + 8 [add 8 to both sides]
⟹ -2x = 26
5. Division property of equality:
-2x ÷ -2 = 26 ÷ -2 [divide both sides by -2]
⟹ x = -13
In conclusion, the missing reasons are the subtraction and division properties of equality.
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Evan picks up a cantaloupe that weighs 3.24 pounds. Suppose Evan
could buy 100 cantaloupes that are all this weight. Without using the
multiplication algorithm, explain how Evan could figure out the total
weight of all 100 cantaloupes.
The total weight of the 100 cantaloupe is 324 pounds
How to determine the total weight?The given parameters are:
Weight of each = 3.24 poundsNumber of cantaloupe = 100Since the number of zeros in 100 is 2;
All Evans needs to do is to move the decimal point in 3.24 two places forward.
i.e. 3.24 becomes 324 when the decimal point is moved
Hence, the total weight of the 100 cantaloupe is 324 pounds
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( brain + 95 points ) A triangular prism has a height of 10 cm and the triangle has a base of 4 cm and a height of 6 cm. Find the volume of the triangular prism.
Area of base
1/2BH1/2(4)(6)2(6)12cm²Volume
Area of base× height12(10)120cm³Triangle XYZ is rotated 90º clockwise about the origin to form triangle X'Y'Z', then reflected across the x-axis to form triangle X''Y''Z''. Which of the following statements is true for ΔXYZ and ΔX''Y''Z''? Question 25 options: ΔXYZ and ΔX''Y''Z'' are similar ΔXYZ and ΔX''Y''Z'' are congruent ΔXYZ and ΔX''Y''Z'' are neither congruent nor similar There isn't enough information given to identify whether ΔXYZ and ΔX''Y''Z'' are similar or congruent
1.ΔXYZ and ΔX''Y''Z'' are similar
2.ΔXYZ and ΔX''Y''Z'' are congruent
3.ΔXYZ and ΔX''Y''Z'' are neither congruent nor similar
4.There isn't enough information given to identify whether ΔXYZ and ΔX''Y''Z'' are similar or congruent
The statement that is true for ΔXYZ and ΔX''Y''Z'' is; 2: ΔXYZ and ΔX''Y''Z'' are congruent
How to identify coordinates of transformed triangles?We are told that;
- Triangle XYZ is rotated 90º clockwise about the origin to form triangle X'Y'Z'.
- Thereafter, reflected across the x-axis to form triangle X''Y''Z''
Now, in transformation, Reflection is flipping an object across a line without changing its size or shape while Rotation is rotating an object about a fixed point without changing its size or shape. Thus, it means that the size and shape of the triangle formed is not different from the original one.
Thus, we can say that both triangles are congruent because the shape and size didn't change.
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Two triangles are proportional, and the first triangle has a base of 10 cm and a height of 15 cm. If the base of the second triangle is 12 cm, what is the height of the second triangle?
Answer: b1/b1=h1/h2=10/12=15/h2 so use criss cross and equel to 15×12=10h2 both sides devide by 10 and equel 180/10=18
so h2=18
What is the measure of angle B in degrees
Angle C and the 112 degree angle are supplementary, so angle C measures 180-112=68 degrees.
This means that by the exterior angle theorem, [tex]m\angle B=51^{\circ}+68^{\circ}=\boxed{119^{\circ}}[/tex]
Find the missing side of this right triangle.
X
9
22
X = [?]
Enter the number that belongs in the green box.
Answer:
x = sqrt(403)
Step-by-step explanation:
Use Pythagorean Theorem for right triangles
x^2 + 9^2 = 22^2
x = sqrt 403
what is -23/6 - 7/3
A -37/6
B -30/9
C -16/6
D 37/6
Answer:A
Step-by-step explanation:
-23/6 - 7/3 =-6.16666666667
-37/6 = -6.16666666667
Answer:
[tex] \frac{ - 37}{6} [/tex]
Step-by-step explanation:
[tex] \frac{23}{6} - \frac{7}{3} \\ lcm = 6 \\ \frac{ - 23 - 14} {6} = - \frac{ - 37}{6} \\ final \: answer \\ = \frac{ - 37}{6} [/tex]
Estimate the product.
14×212
A circular garden has a circumference of 42.3 feet. Find the approximate diameter of the garden. Use 3.14 for π.
Answer:
13.5
Step-by-step explanation:
c = 2πr
42.3 = 2(3.14)r
42.3 = 6.28r
6.74 = r
d = r + r
d = 6.74 + 6.74
d = 13.5
According to the general equation for conditional probability, if P(A n B') = 2/9 and P(B) = 1/3, what is P( A I B')?
A. 5/6
B. 2/3
C. 1/6
D. 1/3
Answer:
B. 2/3Step-by-step explanation:
Formula:
[tex]p\left( A|B\right) =\frac{p\left( A\cap B\right) }{p\left( B\right) }[/tex]
Then
[tex]p\left( A|B\right) =\frac{\frac{2}{9} }{\frac{1}{3} } =\frac{2}{9} \times \frac{3}{1}=\frac{6}{9}=\frac{2}{3}[/tex]
PLEASE ILL GIVE 25 POINTS ANS MARK BRAINIEST IF SOMEONE GIVES ME THE RIGHT ANSWER PLEASE PLEASE PLWASE
Answer:
Radius:3.14
Circumference: 6.28
Step-by-step explanation:
C=2(pi)(r)
replace r with 1
and you get 6.28
R=(pi)(r)^2
Replace r with 1
multiply and you get 3.14
Fill in the blank.
5 × 5/2 = __ x 1/6
Answer:
25
Step-by-step explanation:
When multiplying a whole number by a fraction, the first step is to multiply the whole number by the numerator. Then, you divide by the denominator. For example, on the left side, 5 x 5 = 25. You are left with 25/6. Finally, when you divide by 6, you are left with 4.166.....
If the denominator is the same (6) on both sides, to get the same answer, you somehow need to get the numerator (25) the same. So, what whole number can be multiplied by 1 to get 25? This number is 25. Therefore, the missing number is 25. This answer is correct because 25 x 1 = 25. You would be left with 25/6 and get a final answer of 4.166....
choose the symbol for the line XY.
The mathematical symbol for the line XY is XY(a line on top it) . The first option
How to represent a line with a symbol?There are so many mathematical symbols use in geometry. They include ∠(angles), ⊥(perpendicular line), Δ(triangle), ≅(congruency) and many more.
Therefore, the symbol for the line XY is as follows;
XY(a line on top it)
It means line segment "XY"
In words, it is the line segment between X and Y
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If √ 24 + √ 96 7 √600 = y√ 6, find the value of y. -
How do I complete this?
Answer + Step-by-step explanation:
CE bisects AB
CE ⊥ AB
Then
CE is the perpendicular bisector of AB.
Therefore
CA = CB and DA = DB
…………………………………
we have :
CA = CB
DA = DB
CD is a common side of the two triangles ACD and BCD
Hence , ΔACD ≅ ΔBCD
⇒ ∠CAD ≅ ∠CBD.
What is the minimum value of the following function f(x)=(x-1)^2 +1
Answer:
1
Step-by-step explanation:
f(x)=(x-1)²+1
f(1)=(1-1)²+1
f(1)=0²+1
f(1)=0+1
f(1)=1
Find the quotient.
7/8 ÷ 2 1/4
WILL GIVE 30 POINTS
Step-by-step explanation:
Hello there!
This is how we solve this problem
7/8 ÷ 2 1/4
[tex] \frac{7}{8} \div 2 \frac{1}{4} \: conveting \: to \: improper \: faction\\ \\ = \frac{7}{8} \div \frac{9}{4} \\ = \frac{7}{8} \times \frac{4}{9} \: multiply \: through \\ = \frac{7}{18} [/tex]
= 7/18
I hope this helps.
Have a nice studies.
Which of the following produces an image that is not congruent to the pre-image?
A. translation
B. dilation
C. rotation
D. reflection
Answer:
Dilation
Step-by-step explanation:
it’s a dilation because the dilation changes how big the image is or what it looks like after the original image.
Which equation is the inverse of 5y+4= (x+3)² + 2?
y = 12•3x for x = -2
Answer:
y=12×3(-2)
y=-72
Step-by-step explanation:
please mark me as brainlest
The product of 80 and 5,000 is...
Answer: 400,000
Step-by-step explanation:
The product is the result of multiplication. In other words, you would multiply 80×5,000.
I hope this helps!! :)
Find the surface area of this cube 7m 7m 7m. Be sure to include the correct unit in your answer.
Answer:
294[tex]m^2[/tex]
Step-by-step explanation:
The area of one face of the cube would be 7 x 7 = 49 [tex]m^2[/tex]
Since there are 6 faces on a cube, the total surface area would therefore be 49 x 6 = [tex]294m^2[/tex]
Explain how you would use addition to find the product of -2 and 5