The life of the battery is about 36.5 years, if it requires 35 watts.
What is termed as logarithmic functions?A logarithmic term is a number expressed in logarithmic form. Some other name for it is a log term.
A number could also be the sum of two or more numbers. As a result, a term can be the product of two or even more quantities, at least one of which should be in logarithmic form. These same terms are recognised as log terms in such cases.A quantity can also be described as the variation between two quantities. However, if a term contains a quotient of quantities, or if at least one of the amounts can also be conveyed in log form, the term is referred to as a log term.Consider some formulas used in log.
Quotient Rule: ㏒(A/B) = ㏒A - ㏒BProduct Rule : ㏒A + ㏒B = ㏒(AB)Power Rule: n㏒A = ㏒AⁿBase Rule = ㏒ₐb = ㏒ₓb/㏒ₓaExponent Rule = e∧lnx = xNow, as per the given question,
The function is written as;
P = 42e∧(-0.005t).
The value of the power P is mentioned in the question; (P = 35 watt).
Thus, substitute the value of the P in teh equation;
35 = 42e∧(-0.005t).
Now, divide both sides by 42.
0.8333 = e∧(-0.005t)
Taking natural log on both side;
㏒0.8333 = ㏒e∧(-0.005t)
㏒0.8333 = -0.005t
Solve the value of the log by using calculator,
-0.182 = -0.005t
t = 36.5
Therefore, the the life for which the battery will run is 36.5 years.
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URGENT DUE TODAY PLEASE HELP
Lines k and p are parallel. If m<1 = 5x + 1 and m<2 = 8x - 20, find
the measure of angle 2.
Evaluate the expression for the given value of the variable
|x-19| ; x = 10
Answer:
|(10)-19| = |-9| = 9
Step-by-step explanation: Just plug it in. Oh btw the absolute value means distance from 0.
Copy trapezoid CDEF and point P . Then use a protractor and ruler to draw a 50° rotation of CDEF about point P .
Repeat steps 1-3 for vertices C,E and F to finish the trapezoid .
Describe the trapezoid shape.
A quadrilateral with one set of parallel opposite sides is referred to as a trapezoid. It can have congruent sides (isosceles) and right angles (a right trapezoid), but neither is necessary.
Step 1 - Draw line DP.
Step 2 - Use a protractor to create a 50° angle with DP'.
Step 3 - Use a ruler to draw D such that DP' = DP
Step 4 - Repeat steps 1-3 for vertices C,E and F to finish the trapezoid .
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The temperature of an object goes up by 1k. how much did it go up in degrees fahrenheit and how much in degrees celsius?
Given that the temperature of an object goes up by 1.0 Kelvin, the rise in degrees Fahrenheit and Celsius are -457.87°F and 272.15°C respectively.
What is the value of 1 Kelvin in in degrees Fahrenheit and Celsius?The formula used in converting temperature from Kelvin to Fahrenheit is expressed as;
(( x - 273.15 ) × 9/5 + 32)°F
Also, to convert temperature form Kelvin to Celsius, we use;
( x - 273.15)°C
Given that;
Temperature goes up by 1 Kelvin1 Kelvin in degrees Fahrenheit = ?1 Kelvin in degrees Celsius = ?Convert 1 Kelvin to degrees Fahrenheit.
(( x - 273.15 ) × 9/5 + 32)°F
(( 1 - 273.15 ) × 9/5 + 32)°F
( 272.15 × 9/5 + 32)°F
( -489.87 + 32)°F
-457.87°F
Convert 1 Kelvin to degrees Celsius.
( x - 273.15)°C
( 1 - 273.15)°C
272.15°C
Given that the temperature of an object goes up by 1.0 Kelvin, the rise in degrees Fahrenheit and Celsius are -457.87°F and 272.15°C respectively.
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what does SSA stand for? what does it have to do with similar triangles?
Answer:
SSA stands for side-side angles.
Step-by-step explanation:
SSA means there are two known sides of a triangle and one known angle that is not between the two sides and they are equal to two known sides and a angle of another triangle, the triangles are similar (that’s what SSA has to do with similar triangles)
Converting Units of Rates
Nina can ride her bike 63,360 feet in 3,400 seconds, and Sophia can ride her bike 10 miles in 1 hour. What is Nina's
rate in miles per hour if there are 5,280 feet in a mile?
Which girl bikes faster?
Nina's rate in miles per hour is 12.711 and Nina bikes faster than Sophia.
Nina's speed can also be defined as her Average Speed.
Similarly, Sophias's speed can also be defined as her Average Speed.
We have Sophia's speed = 10 miles in hour = 10 miles per hour
What is average speed and average?
Average speed is the total distance travelled by an object to the total time taken. means,
[tex]Average Speed = \frac{Total Distance}{Total Time }\\[/tex]
Total Distance covered by Nina = 63,360ft.
[tex]1 \ mile = 5280 \ feet\\[/tex]
So,Nina's Distance (in miles) [tex]\frac{63360}{5280}= 12 \ miles[/tex]
Nina's Time (in hour) [tex]\frac{3400}{60*60}= 0.944 \ hour[/tex]
Nina's Average Speed = [tex]\frac{12}{0.944}= 12.711 \ miles/hour[/tex]
So, Nina's Average Speed = 12.711 miles per hour
Since, Sophia's Average Speed = 10 miles per hour
Therefore, Nina bikes faster on a average speed of 12.711 miles per hour.
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Nina's rate in miles per hour is 12.711 and Nina bikes faster than Sophia.
Nina's speed can also be defined as her Average Speed.
Similarly, Sophias's speed can also be defined as her Average Speed.
We have Sophia's speed = 10 miles in hour = 10 miles per hour
What is average speed and average?
Average speed is the total distance travelled by an object to the total time taken. means,
[tex]Average Speed = \frac{Total Distance}{Total Time }\\[/tex]
Total Distance covered by Nina = 63,360ft
1 mile = 5280 feet
So,Nina's Distance (in miles) [tex]\frac{63360}{5280}= 12 \ miles[/tex]
Nina's Time (in hour) [tex]\frac{3400}{60*60}= 0.944 \ hour[/tex]
Nina's Average Speed = [tex]\frac{12}{0.944}= 12.711 \ miles \ / \ hour[/tex]
So, Nina's Average Speed = 12.711 miles per hour
Since, Sophia's Average Speed = 10 miles per hour
Therefore, Nina bikes faster on a average speed of 12.711 miles per hour.
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Calculate the probability of the spinner landing on a purple section of the board. what is the probability that the spinner will land on a purple section of the board? or or
The probability of purple section on spinning is 1/2.
As per the given image of question, we can see there six parts of board. Out of these, three parts of board are purple colored.
Now, the formula of probability is -
Probability = number of favorable outcomes÷total number of outcomes
Number of favorable outcomes = number of purple colored parts of board
Number of favorable outcomes = 3
Number of favorable outcomes = number of colored parts of board
Number of favorable outcomes = 6
Keep the value in formula to find the probability -
Probability = 3/6
Performing division
Probability = 1/2
Hence, the probability that the spinner will land on a purple section of the board is 1/2.
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The complete question is -
Calculate the probability of the spinner landing on a purple section of the board. What is the probability that the spinner will land on a purple section if the board.
A) 1/6
B) 2/6 or 1/3
C) 3/6 or 1/2
If you dig a 6ft hole, how deep is it?
Answer: 8 feet
Step-by-step explanation:
5 times the difference of a number and 3
number meaning x
The value of an unknown number x will be equal to ( 15 / 4).
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that 5 times, the difference between a number and 3 is x. The value of the unknown number will be calculated as:-
5 ( x - 3 ) = x
5x - 15 = x
4x = 15
x = 15 / 4
Therefore, the value of an unknown number x will be equal to ( 15 / 4).
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Find the center and the radius of each circle. x²+y²=14
The equation of the circle x^2 + y^2 = 14 has a radius of √14 and a center located at (0 , 0).
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle,x^2 + y^2 = 14, is in standard form, then
h = 0
k = 0
r = √14
Hence, the equation of the circle x^2 + y^2 = 14 has a radius of √14 and a center located at (0 , 0).
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(18, -7) and (18, 2) m =
Answer:
m = undefined
Step-by-step explanation:
I'm assuming it's "m" as in y=mx+b
(18, -7), (18, 2)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 2 - (-7) 9
m = ----------- = ------------ = ---------- = undefined
x₂ - x₁ 18 - 18 0
I hope this helps!
Determine the values of y in the equation y2 = 121.
whoever gets it right gets a crown pls help
Answer:
y = 11
Step-by-step explanation:
Let's solve your equation step-by-step.
[tex] \rightarrow \sf \: y {}^{2} =121[/tex]
Step 1: Take square root.
[tex] \sf \: y=± \sqrt{121} [/tex]
y=11 or y=−11
I need this answered answered please
One is a constant, as it has no variable besides it.
Given the following series of numbers, determine the mode.
a. 50, 45, 55, 55, 45, 50, 55, 45, 55
b. 89, 87, 88, 83, 86, 82, 84
c. 11, 17, 14, 12, 12, 14, 14, 15, 17, 17
The most frequent numerical value in a set of data exists named the mode.
The mode in 50, 45, 55, 55, 45, 50, 55, 45, 55 is 55.
There is no mode in 89, 87, 88, 83, 86, 82, 84.
The mode in 11, 17, 14, 12, 12, 14, 14, 15, 17, 17 is 14 and 17.
What is the mode?A data set's mode is its most prevalent value. It is the number that appears most frequently on a list. The number with the highest sum is referred to as the mode.
The most frequent numerical value in a set of data is called the mode. In other words, the number that appears the most times in a list is the mode.
Rearranging the list of integers from least to greatest and then counting the occurrences of each number in the new order will reveal the mode. The mode is the most frequent number.
The average value in a data set exists in the most popular statistical data analysis technique, named Mean.
The median exists the data set's midway.
Mode exists the value that dominates a data set.
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i'll give brainliest
Answer:
its d
Step-by-step explanation:
Choose the number sentence that illustrates the distributive property of multiplication over addition.
A. 5x (7+2) = (5+7) × (5+2)
B. 5x (7+2) = (5 × 7) +2
C. 5x (7+2) = (5 × 7) + (5 × 2)
Answer:its
a80
b16
c60
Step-by-step explanation:
Answer:
Step-by-step explanation:
C. 5 × (7 + 2) = (5 × 7) + (5 × 2)
Write each equation in slope-intercept form. Then find the slope and y -intercept of each line. -3 x+2 y=7
The slope-intercept form of the given equation of a line is: y = 3/2(x) + 7/2 The slope here, is 3/2 and y-intercept is 7/2.
What is the equation of a line to the curve?A line's equation has the standard form ax + by + c = 0. Here, the variables are x and y, the coefficients are a and b, and the constant term is c. It is a first-order equation with the variables x and y. The coordinates of the point on the line shown in the coordinate plane are represented by the values of x and y.Now,
The slope-intercept form of an equation of a line is given by: y = mx + c, where m = slope of the line and c = y-intercept of the line.
Transforming the given equation of the line: -3x + 2y = 7
=> 2y = 7 + 3x
=> y = 3/2(x) + 7/2
On comparing it with y = mx + c, we get that: m (slope) = 3/2 and c = 7/2 (y-intercept).
Hence, The slope-intercept form of the given equation of a line is: y = 3/2(x) + 7/2. The slope here, is 3/2 and y-intercept is 7/2.
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If g+9=4 and h-8--3, what is the
value of g + h?
Answer:
g + h = 6
Step-by-step explanation:
We are told that:
• [tex]g + 9 = 4[/tex]
• [tex]h- 8=3[/tex].
To calculate the value of g + h, we have to rearrange the above equations to make g and h their respective subjects:
• [tex]g + 9 = 4[/tex]
⇒ [tex]g + 9 - 9 = 4 - 9[/tex] [Subtracting 9 from both sides]
⇒ [tex]g = \bf -5[/tex]
• [tex]h- 8=3[/tex]
⇒ [tex]h - 8 + 8 = 3 + 8[/tex] [Adding 8 to both sides]
⇒ [tex]h = \bf 11[/tex]
Now that we know the values of g and h, we can find the value of g + h:
[tex]g + h[/tex]
[tex]= -5 + 11[/tex]
[tex]= \bf 6[/tex]
Therefore the value of g + h is 6.
evaluate the expression 13 divided by (2.5 - |-3 1/8|) times 3 to the third power
Answer: -561.6
Step-by-step explanation:
First, recall PEMDAS (Parenthesis, Exponents, Multiply, Divide, Add, Subtract)
In the equation, we need to work through (2.5 - |-3 1/8|) first.
The absolute value of |-3 1/8| is 3 1/8
We change 3 1/8 to a decimal
3 1/8 = 3.125
Now Subtract (2.5 - 3.125)
This equals -0.625
Next, divide 13 by -0.625
13 ÷ -0.625 = -20.8
Then, multiply -20.8 by 3³
3³ = 27
So -20.8 × 27 = -561.6
What is the average speed of an
automobile trip of 275 miles that
began at 7:30 in the morning and
ended at 12:30 in the afternoon
The average speed of an automobile is a 55 miles per hour.
According to the statement
We have to find that the value of the average speed of an automobile.
So, For this purpose, we know that the
The average speed is the total distance traveled by the object in a particular time interval.
From the given information:
automobile trip of 275 miles that began at 7:30 in the morning and ended at 12:30 in the afternoon
Then
The total distance covered = 275 miles
And
The total time taken = From 7:30 in the morning to 12:30 in the afternoon
Then
The total time taken = 5 hours,
Then
Average speed = total distance covered / total time taken
Average speed = 275 miles / 5 hours
Then
Average speed = 275 / 5
Average speed = 55 miles per hour.
So, The average speed of an automobile is a 55 miles per hour.
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Please help asap Geometry
Step-by-step explanation:
72+68=140°
180-140=40°
z=40°
How should the decimal point in 6.8 be moved to determine the product of 6.8 and 100
The decimal point should be moved two places to the right.
The number we have given is = 6.8
We have to find how many decimal point should be moved when 6.8 is multiplied by 100
We know that when we multiply a decimal number with 10, 100, 1000,…. and so on. We shift the decimal point to the right side according to the number of zeroes present.
According to the question, we have two zeroes therefore we will shift the decimal point to the rights side two times, that is,
6.8 * 100 = 680
Hence the decimal point should be moved two places to the right.
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Find the 17 th term of each sequence. a₁₈ = -5, d=12
The 17 th term of each sequence a₁₈ = -5, d=12 is [tex]a_{17}[/tex] = 187.
What is a sequence?
a₁₈ = -5, d=12
[tex]a_{17}[/tex] = a + (n-1)d
[tex]a_{17}[/tex] = -5 + (16)12
[tex]a_{17}[/tex] = 187
succession: the doing of one thing after another. A list of books is presented in alphabetical order. a succession of sonnets that is continuous or connected. a later event, outcome, or repercussion; something that happens after.
A series of numbers is an ordered list. The three dots signify moving forward in the set pattern. Each digit in the sequence is referred to as a word. The first term in the list is 1, followed by the second by 3, the third by 5, and so on.
Arithmetic sequences, geometric sequences, quadratic sequences, and special sequences are the four primary categories of distinct sequences you need to be familiar with.
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The mass of a paperclip is 8.0 × 10^−4 mg. If a box of paperclips has 7.68 × 10^4 paperclips, determine the total mass of the paperclips in the box. Write the final answer in scientific notation with the correct number of significant digits.
6.1 × 10^1mg
6 × 10^1 mg
6.144 × 10^1 mg
9.6 × 10^0 mg
The required mass of the paper clips in the box is = 61.44 mg.
Given that,
mass of a paperclip = 8.0 × 10⁻⁴
Number of paperclip in the box = 7.68 × 10⁴
The total mass of the paper clips is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Mass of paperclips = 8.0 × 10⁻⁴ x 7.68 × 10⁴
Mass of paperclips = 61.44 * 10 ⁻⁴⁺⁴
Mass of paperclips = 61.44 * 10 ⁰
Mass of paperclips = 61.44 * 1
Thus, the required mass of the paper clips in the box is = 61.44 mg.
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COORDINATE GEOMETRY Find the measures of the sides of ΔJ K L and classify each triangle by the measures of its sides. (Lesson 4-1)
J(9,9), K(12,14), L(14,6)
The measure of the sides of ΔJKL is 17.26 units.
What do we mean by a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.So,
The formula of perimeter: √√(x₂−x₁)²+(y₂−y₁)²
Filling the values in the formula, we obtain:
= √(12−9)²+(14−9)²= 17.26 unitsThen, each side of the triangle will be: 17.26 units
Therefore, a measure of the sides of ΔJKL is 17.26 units.
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Write each subtraction equation as an
addition equation.
a) - 9 = 6
p) - 20 =-30
z) - (-12) = 15
x) - (-7) = -10
WILL REWARD WITH BRAINLIEST + THANKS
Answer:
a) 6+9=15
p) -30+20= -10
m) 15-12=3
X) -10-7= -17
6 of 6
Triangles A and B are congruent.
Find the area of triangle A. Give your answer to 1 dp.
area =
17cm
108 cm²
area = cm²
A
Not drawn accurately.
B
12cm
O
F
You may use
Get help
Report a mista
On-screen keyp
Che
Ski
Area of triangle A is 72.2 cm square.
Here, we are given that triangles A and B, as shown in the figure are congruent to each other.
They are also both right angle triangles.
The length of the hypotenuse of A is 17cm
and the height of triangle be = 12cm
But as these two are congruent,
height of triangle A will also be 12cm.
Now, according to Pythagoras theorem,
[tex]hypotenuse^{2} = base^{2} +height^{2}[/tex]
[tex]17^{2}[/tex] = [tex]12^{2}[/tex] + [tex]base^{2}[/tex]
289 = 144 + [tex]base^{2}[/tex]
[tex]base^{2}[/tex] = 145
base = 12.04
Thus, the area of the triangles = 1/2 * base height
= 1/2 x 12 x 12.04
= 72.2
Thus the area of triangle A will be 72.2 cm square.
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Let f ( x ) = 1 x and g ( x ) = x 2 + 5 x . a. Find (f · g)(x). b. Find the domain and range of (f · g)(x).
The answer to all the subparts are given:
(f · g)(x) = [(f X g)(x) = x + 5]The domain of the given function: (-∞, 0) ∪ (0, ∞)The Range of the given function: (-6.25, 0) ∪ (0, ∞)(A) (f · g)(x):
So,
(f×g)(x)=f(x)*g(x)Plug in:
[tex](f X g)(x)=\frac{1}{x}\left(x^2+5 x\right)[/tex]Simplify as follows:
[tex]\begin{aligned}&(f X g)(x)=\frac{1}{x}(x(x+5)) \\&(f X g)(x)=x+5\end{aligned}[/tex]
(B) Domain:
First, we will determine the domain of f(x), g(x), and (fxg) (x).
Then we can look for a common domain.
The domain of f(x):
[tex]f(x)=\frac{1}{x}[/tex]At x=0, we know that f(x) is undefined.
As a result, the domain will be:
[tex](-\infty, 0)_{\cup}(0, \infty)[/tex]The domain of g(x):
[tex]g(x)=x^2+5 x[/tex]
Because it is polynomial.
As a result, it is defined for all real values of x.We can now find a common domain.As a result, the domain will be:
[tex](-\infty, 0) \cup(0, \infty)[/tex](C) Range:
First, we will determine the range of f(x), g(x), and (fxg) (x).
Then we can determine the common range.
f(x) range:
[tex]f(x)=\frac{1}{x}[/tex]We know that range refers to all possible y values for which x is defined.
Because the horizontal asymptote will be at y=0.
As a result, the range is:
[tex](-\infty, 0) \cup(0, \infty)[/tex]Range of g(x):
[tex]g(x)=x^2+5 x[/tex]Because it is a quadratic equation.
As a result, its range will be:
[tex][-6.25, \infty)[/tex]We can now find a common range.
As a result, the range will be:
[tex](-6.25,0) \cup(0, \infty)[/tex]
Therefore, the answer to all the subparts are given:
(f · g)(x) = [(f X g)(x) = x + 5]The domain of the given function: (-∞, 0) ∪ (0, ∞)The Range of the given function: (-6.25, 0) ∪ (0, ∞)Know more about domain range here:
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1) |x|-4 = 9
2) |x - 4| = 9
Solve the absolute value for each equation.
Answer:
13 & 5
Step-by-step explanation:
Absolute for x still gives a positive X value
So: X- 4 = 9
X = 9 + 4
X = 13
|x-4| = 9
Gives X + 4 = 9
x = 9 - 4
X = 5
Is the ordered pair (3/4, 0) a solution of 3x+y>3 ? Explain.
The Given expression in the question is this 3x+y>3; the answer to this expression is (3/4,0).
So, we need to find the solution to the given expression and then compare the answers to see if they match each other. If so, the ordered pair is the solution of the given word; if not, the ordered pair is not the solution of the given expression.
In this problem, you substitute ordered pairs of x and y values into the equation.
3(3/4) + (0) > 3
9/4 + 0 > 3
9/4 > 3 No, 9/4 is not greater than 3, so the ordered pair is (3/4,0). Not the solution to the equation
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