Log3(14)
= log(14) / log(3) (Change of base formula)
= 4 / 1.965 (log(3) = 1.965)
= 2.041 (rounded to 3 decimal places)
2.041
Answer:
Step-by-step explanation:
To emulate the logarithm using the change of base formula, we need to use a base that is more convenient to evaluate. Let's use base 10:
log3(14) = log10(14) / log10(3)
Using a calculator, we can evaluate the numerator and denominator:
log10(14) ≈ 1.146
log10(3) ≈ 0.477
Dividing the numerator by the denominator gives:
log3(14) ≈ 2.402
Rounding to three decimal places, the final result is:
log3(14) ≈ 2.402
Help now quickly will give brainlist
Answer:
x = - 12
Step-by-step explanation:
the central angle subtended by the arc with measure 45° are congruent, that is central angle is 45°
the 3 angles on the diameter then sum to 180° , that is
45 + 65 + x + 82 = 180
x + 192 = 180 ( subtract 192 from both sides )
x = - 12
Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Focus (0,1)
Precision manufacturing: A process manufactures ball
bearings with diameters that are normally distributed
with mean 25.1 millimeters and standard deviation
0.08 millimeter.
a. Find the 60th percentile of the diameters.
b. Find the 32nd percentile of the diameters.
c. A hole is to be designed so that 1% of the ball bearings will
fit through it. The bearings that fit through the hole will be
melted down and remade. What should the diameter of the
hole be?
To find the height of a pole, Elka lays a mirror on the level ground 20 feet from the base of the pole. She moves back away from the mirror until she can exactly see the top of the pole. If she backed way 5.5 feet and her eyes are 5 feet above the ground, how tall is the flag pole?
The height of the pole is 18.18 feet
Given data ,
Elka uses similar triangles to find the height of the pole. The situation forms two similar right triangles: one with the pole and the mirror, and another with Elka's eyes and the mirror.
Let's denote the height of the pole as "h" feet.
Distance from the base of the pole to the mirror = 20 feet
Distance Elka moves back away from the mirror = 5.5 feet
Height of Elka's eyes above the ground = 5 feet
Using the concept of similar triangles, we can set up the following proportion:
h / 20 = 5 / 5.5
Multiply by 20 on both sides , we get
h = 100 / 5.5
h = 18.18 feet
Hence , the height of the flagpole is approximately 18.18 feet
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Comparing Rates of Change Station Cards
(y=mx+b form)
Write a function rule that has a rate of change greater than the function
that passes through the points given in the table.
-2
-1
0
1
2
7
1
-2
-5
Answer: y = -4x + 1. Brainliest?
Step-by-step explanation:
To write a function rule that has a greater rate of change than the given function, we need to find the slope of the given function. We can use the two points (-2, 7) and (2, -5) from the table to calculate the slope as:
slope = (change in y) / (change in x) = (-5 - 7) / (2 - (-2)) = -3
So the slope of the given function is -3. To create a new function rule with a greater rate of change, we can choose a larger slope. Let's choose a slope of -4. We also need to find the y-intercept (b) of the new function, which we can do by plugging in one of the points from the table and solving for b. Let's use the point (0, 1):
y = mx + b
1 = (-4)(0) + b
b = 1
So the function rule with a greater rate of change and passing through the point (0, 1) is:
y = -4x + 1
The scale factor of figure STUV to figure WXYZ is 3:1. If ST = 39 mm and SV = 51 mm, what is the length of side WX?
The scale factor of figure STUV to figure WXYZ is 3:1. If ST = 39 mm and SV = 51 mm, the length of side WX is 13 mm.
If the scale factor of figure STUV to figure WXYZ is 3:1, it means that every length in figure STUV is three times longer than the corresponding length in figure WXYZ.
To find the length of side WX, we need to first identify the corresponding sides of the two figures. We know that ST is three times longer than W, and SV is three times longer than Y. So, we can set up the following proportion:
ST/WX = SV/YZ
Substituting the given values, we get:
39/WX = 51/YZ
We need to find the value of WX, so we can solve for it by cross-multiplying the proportion:
39 * YZ = 51 * WX
Since we don't know the value of YZ, we need to find it in terms of WX. We can use the scale factor of 3:1 to relate the lengths in the two figures:
ST = 3 * W
SV = 3 * Y
Substituting the first equation, we get:
W = ST/3 = 39/3 = 13 mm
Substituting the second equation, we get:
Y = SV/3 = 51/3 = 17 mm
Now we can substitute these values into the proportion:
39/WX = 51/17
Solving for WX, we get:
WX = (39 * 17) / 51 = 13 mm
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Complete question is:
The scale factor of figure STUV to figure WXYZ is 3:1. If ST = 39 mm and SV = 51 mm, what is the length of side WX?
Why do you think influences exchange rates?
(Subject: Economics)
Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The graph that shows a proportional relationship between x and y is given as follows:
Graph D.
What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.
The equation that defines the proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
From the equation y = kx we have that it is a linear function with intercept of zero, meaning that the graph D represents the proportional relationship for this problem.
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(42) Using a waste factor of 6 percent, determine the number of cubic yards of concrete needed to pour the foundation walls shown in Figure 11.4. The footing is 12 foot wide and 1 foot thick.
The 7.34 cubic yards of concrete needed to pour the foundation walls, which is calculate the volume of the walls and then add the waste factor of 6%.
To find the volume of the concrete needed to pour the foundation walls, we first need to find the total area of the walls. We can do this by breaking it down into three sections
The two 26 ft x 1 ft walls
Area = 2 x (26 ft x 1 ft) = 52 sq ft
The two 42 ft x 1 ft walls
Area = 2 x (42 ft x 1 ft) = 84 sq ft
The 12 in x 15 in x 12 ft wall
First, we need to convert the dimensions to feet:
Length = 12 in ÷ 12 = 1 ft
Breadth = 15 in ÷ 12 = 1.25 ft
Height = 12 ft
Area = (1 ft + 1.25 ft) x 2 x 12 ft = 51 ft²
Total area of the walls = 52 sq ft + 84 sq ft + 51 sq ft = 187 sq ft
Now, we need to add the waste factor of 6% to this to account for any material that may be lost or wasted during the pouring process
Total area with waste factor = 187 sq ft + 6% of 187 sq ft = 198.22 sq ft
Finally, we need to calculate the volume of concrete needed, assuming a thickness of 1 ft
Volume = area x thickness = 198.22 sq ft x 1 ft = 198.22 cubic ft
Since 1 cubic yard is equal to 27 cubic feet, we can convert the volume to cubic yards
Volume in cubic yards = 198.22 cubic ft ÷ 27 = 7.34 cubic yards
Therefore, we need 7.34 cubic yards of concrete to pour the foundation walls with a 6% waste factor.
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1. You go to the ice cream shop with your friends and you can choose an ice cream,
and sprinkles. How many different sundaes can you make when you order one flavor
cream, one topping and one color of sprinkles from the chart below? Show all possib
outcomes in a tree diagram.
10
Ice Cream
Chocolate
Vanilla
Strawberry
Topping
Fudge
Marshmallow
b. P (Chocolate, Fudge, Rainbow)
S
C
F
How many sample spaces are there? HINT: How many possible combination
There are 18 possible combinations of ice cream, topping, and sprinkles.
Probability P(Chocolate, Fudge, Rainbow) = 1/18
How to Solve the Probability?There are 18 different possible sundaes that can be made when choosing one flavor of ice cream, one topping, and one color of sprinkles.
To visualize all the possible outcomes, we can use a tree diagram:
Ice Cream
|
------------------------------
| | |
Chocolate Vanilla Strawberry
| | |
-------------- -------------- --------------
| | | | | |
Fudge Marshmallow Fudge Marshmallow Fudge Marshmallow
| | | |
-------------- -------------- --------------
| | | | | |
Rainbow Chocolate Rainbow Vanilla Rainbow Strawberry
So there are 18 possible combinations of ice cream, topping, and sprinkles.
To answer part b) which asks for the probability of choosing Chocolate ice cream with Fudge topping and Rainbow sprinkles, we need to know the total number of possible outcomes (which we just calculated as 18) and the number of outcomes that match the specific combination of Chocolate ice cream, Fudge topping, and Rainbow sprinkles. There is only one outcome that matches this combination, so the probability is:
P(Chocolate, Fudge, Rainbow) = 1/18
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20 students each rolled dice 5 times each to measure the median. Here is the data in the picture attached. What can we infer from this graph by looking at the median data?
A. when rolling a dice multiple times, the median is less likely to fall between numbers 1 and 6.
B. it's not possible to tell the likelihood of where the median is going to be when measuring probability since rolling dice is completely randomized, etc.
C. some other response
Considering the given graph, we infer that while rolling a dice is random, the median values do exhibit some patterns that can be analyzed and used to make predictions about the expected values.
What is the information from the graph?Looking at the median data from the graph, we can infer that option A is not true, as the median appears to be equally likely to fall between any two numbers from 1 to 6. However, we can also infer that option B is not entirely accurate.
While it is true that rolling a dice is random and each roll is independent, we can observe patterns in the median data.
For example, the median values are more likely to be closer to 3.5, which is the theoretical median value of a fair six-sided dice. This suggests that the more times the dice is rolled, the more likely the median value will approach the expected value.
We can also observe that the spread of the median values tends to decrease as the number of rolls increases, indicating that more rolls lead to more consistent results.
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1. a gallon of water weighs 8 1/3 lbs.
a. what is the weight of 25
gallons of water?
b. If the weight of an empty 25 gallon tank is 1/10 of the water it can hold, what is the weight of the tank?
c. what is the weight of a 25 gallon tank filled with water?
a. Weight of 25 gallons of water [tex]= (25 \times 25)/(3) = 625/3 lbs[/tex] B. Weight of the empty tank [tex]= (625 \times 1)/(3 \times 10) = 625/30 lbs[/tex] C. Weight of tank filled with water[tex]= 229 5/6 lbs[/tex]
What is the gallon of water?a. The weight of 25 gallons of water can be calculated by multiplying the weight of one gallon of water by 25.
Given:
Weight of 1 gallon of water = 8 1/3 lbs
Calculation:
Weight of 25 gallons of water = (Weight of 1 gallon of water) × 25
[tex]= 8 1/3 lbs \times 25[/tex]
To perform the multiplication, let's convert the mixed number 8 1/3 to an improper fraction:
[tex]8 1/3 = (8 \times 3 + 1)/3 = 25/3[/tex]
Substituting back into the equation:
Weight of 25 gallons of water [tex]= 25/3 \times 25[/tex]
Now, we can multiply the fractions:
Weight of 25 gallons of water [tex]= (25 \times 25)/(3)= 625/3 lbs[/tex]
b. The weight of the empty 25-gallon tank can be calculated as 1/10 of the weight of water it can hold.
Given:
Weight of 25 gallons of water = 625/3 lbs
Calculation:
Weight of the empty tank = (Weight of 25 gallons of water) × (1/10)
[tex]= (625/3 lbs) \times (1/10)[/tex]
We can simplify the fractions:
Weight of the empty tank [tex]= (625 \times 1)/(3 \times 10)[/tex]
[tex]= 625/30 lbs[/tex]
c. The weight of a 25-gallon tank filled with water would be the sum of the weight of the empty tank (calculated in part b) and the weight of 25 gallons of water (calculated in part a).
Given:
Weight of 25 gallons of water = 625/3 lbs
Weight of empty tank = 625/30 lbs
Calculation:
Weight of tank filled with water = Weight of 25 gallons of water + Weight of empty tank
[tex]= 625/3 lbs + 625/30 lbs[/tex]
We can find a common denominator for the fractions and add them:
Weight of tank filled with water [tex]r = (625 \times 10)/(3 \tiimes 10) + (625)/(30)[/tex]
[tex]= (6250/30) + (625/30)= 6875/30 lbs[/tex]
We can simplify the fraction:
Weight of tank filled with water [tex]= 229 5/6 lbs[/tex]
Therefore,a.Weight of 25 gallons of water [tex]= (25 \times 25)/(3) = 625/3 lbs[/tex] B. Weight of the empty tank [tex]= (625 \times 1)/(3 \times 10) = 625/30 lbs[/tex] C. Weight of tank filled with water[tex]= 229 5/6 lbs[/tex]
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a. Weight of 25 gallons of water [tex]= (25 \times 25)/(3) = 625/3 lbs[/tex] B. Weight of the empty tank [tex]= (625 \times 1)/(3 \times 10) = 625/30 lbs[/tex] C. Weight of tank filled with water[tex]= 229 5/6 lbs[/tex]
What is the gallon of water?a. The weight of 25 gallons of water can be calculated by multiplying the weight of one gallon of water by 25.
Given:
Weight of 1 gallon of water = 8 1/3 lbs
Calculation:
Weight of 25 gallons of water = (Weight of 1 gallon of water) × 25
[tex]= 8 1/3 lbs \times 25[/tex]
To perform the multiplication, let's convert the mixed number 8 1/3 to an improper fraction:
[tex]8 1/3 = (8 \times 3 + 1)/3 = 25/3[/tex]
Substituting back into the equation:
Weight of 25 gallons of water [tex]= 25/3 \times 25[/tex]
Now, we can multiply the fractions:
Weight of 25 gallons of water [tex]= (25 \times 25)/(3)= 625/3 lbs[/tex]
b. The weight of the empty 25-gallon tank can be calculated as 1/10 of the weight of water it can hold.
Given:
Weight of 25 gallons of water = 625/3 lbs
Calculation:
Weight of the empty tank = (Weight of 25 gallons of water) × (1/10)
[tex]= (625/3 lbs) \times (1/10)[/tex]
We can simplify the fractions:
Weight of the empty tank [tex]= (625 \times 1)/(3 \times 10)[/tex]
[tex]= 625/30 lbs[/tex]
c. The weight of a 25-gallon tank filled with water would be the sum of the weight of the empty tank (calculated in part b) and the weight of 25 gallons of water (calculated in part a).
Given:
Weight of 25 gallons of water = 625/3 lbs
Weight of empty tank = 625/30 lbs
Calculation:
Weight of tank filled with water = Weight of 25 gallons of water + Weight of empty tank
[tex]= 625/3 lbs + 625/30 lbs[/tex]
We can find a common denominator for the fractions and add them:
Weight of tank filled with water [tex]r = (625 \times 10)/(3 \tiimes 10) + (625)/(30)[/tex]
[tex]= (6250/30) + (625/30)= 6875/30 lbs[/tex]
We can simplify the fraction:
Weight of tank filled with water [tex]= 229 5/6 lbs[/tex]
Therefore,a.Weight of 25 gallons of water [tex]= (25 \times 25)/(3) = 625/3 lbs[/tex] B. Weight of the empty tank [tex]= (625 \times 1)/(3 \times 10) = 625/30 lbs[/tex] C. Weight of tank filled with water[tex]= 229 5/6 lbs[/tex]
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Find the volume of the right cone below. Round your answer to the nearest tenth if necessary.
16
7
The volume of the given right cone is approximately 597.9 cubic units.
In this problem, we are going to find the volume of a right cone. A cone is a three-dimensional object that has a circular base and tapers to a point. The term "right" means that the axis of the cone is perpendicular to its base. The formula for the volume of a right cone is V = (1/3)πr²h, where V is the volume, r is the radius of the circular base, and h is the height of the cone.
Now, let's apply this formula to the given cone. We are given that the radius of the circular base is 16 and the height of the cone is 7. So, we can substitute these values into the formula to get:
V = (1/3)π(16)²(7) V = (1/3)π(256)(7) V = (1/3)(1,792π) V ≈ 597.9
We round our answer to the nearest tenth as requested. So, the final answer is V ≈ 597.9.
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A recipe uses 3/4 teaspoon of cinnamon for every 4 cups of granola mix.
How many teaspoons are needed for 12 cups of granola mix?
Okay, here are the steps to solve this problem:
* The recipe calls for 3/4 teaspoon of cinnamon for every 4 cups of granola mix.
* So for 1 cup of granula mix, you need 3/4 / 4 = 3/12 teaspoon of cinnamon.
* For 12 cups of granula mix, you would need 12 * (3/12) = 3 teaspoons of cinnamon.
Therefore, for 12 cups of granola mix you would need 3 teaspoons of cinnamon.
Which angles are adjacent to AGC? Select all that apply.
A BOAT NEEDS TO TRAVEL NORTH AT 30 km/h AND A CONSTANT CURRENT OF 4km /h IS FLOWING IN NORTH-WEST DIRECTION WHAT IS THE EQUIVALENT SPEED IN STILL WATER TO ACHIEVE ACTUAL SPEED OF 30 km/h?
The equivalent speed in still water to achieve the actual speed is 27.172 km/h
Given data ,
The boat's velocity vector in still water will have two components: one along the north direction (opposite to the current) with magnitude "v" km/h, and one along the northwest direction (due to the current) with magnitude 4 km/h.
Since the boat is moving in a direction that is 45 degrees between north and northwest, we can use trigonometry to find the component of velocity in the northwest direction. By using the cosine of 45 degrees, we get:
Component of velocity in northwest direction = 4 km/h x cos(45 degrees) = 4 km/h x 0.707 = 2.828 km/h
Now , adding the components of velocity in the north and northwest directions should result in a speed of 30 km/h, which is the real speed needed to go through still water.
v + 2.828 = 30
v = 27.172 km/h
Hence , the equivalent speed of the boat in still water to achieve an actual speed of 30 km/h is approximately 27.172 km/h
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Juan deposited $7000 into an account with a 3.4% annual interest rate, compounded quarterly. Assuming that no withdrawals are made, how long will it take for the investment to grow to $9737?
Do not round any intermediate computations, and round your answer to the nearest hundredth.
Answer:
It will take approximately 6.89 years for the investment to grow to $9737.
Step-by-step explanation:
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the present value of the investment
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
We know that P = $7000, r = 0.034, n = 4 (since the interest is compounded quarterly), and we want to find t when A = $9737.
$9737 = $7000(1 + 0.034/4)^(4t)
Divide both sides by $7000:
1.391 = (1 + 0.034/4)^(4t)
Take the natural logarithm of both sides:
ln(1.391) = ln[(1 + 0.034/4)^(4t)]
Use the power rule of logarithms:
ln(1.391) = 4t * ln(1 + 0.034/4)
Divide both sides by 4 ln(1 + 0.034/4):
t = ln(1.391) / [4 * ln(1 + 0.034/4)]
Using a calculator, we find:
t ≈ 6.89 years
Therefore, it will take approximately 6.89 years for the investment to grow to $9737.
Can someone please explain this to me?
[tex]\textit{since we know that }\triangle FGH \cong \triangle CDE \\\\[-0.35em] ~\dotfill\\\\ HF=EC\implies -3s+44=-3t+50 \\\\\\ HG=ED\implies 6s=t+43\implies \boxed{6s-43=t} \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{-3s+44=-3(6s-43)+50}\implies -3s+44=-18s+129+50 \\\\\\ 15s+44=129+50\implies 15s+44=179\implies 15s=135 \\\\\\ s=\cfrac{135}{15}\implies \boxed{s=9}\hspace{9em}\stackrel{ 6(9)-43 }{\boxed{t=11}}[/tex]
4. The TAs repeat this process of tagging birds, except
this time they tag a population of 522 blue jays on the
fourth day of the survey. Over the course of the study they
calculate the per capita birth rate to be 0.10 and the per
capita death rate to be 0.07. With this information,
calculate the following:
a. How many blue jays were born during the study?
Round your answer to the nearest whole number.
b. How many blue jays died during the study? Round
your answer to the nearest whole number:
c. What is the per capita growth rate of the blue jay
population? Round your answer to the nearest
hundredth.
Show work here:
A.
Answer:
Step-by-step explanation:
A
B
D
31.
An expression is shown.
6(2+3)² - 1
What is the value of the expression?
A. 20
B. 59
C. 149
D. 899
Answer:
149
Step-by-step explanation:
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
The correct statement and value should be matched as follows;
The percent of time that customers at the old store bought milkshakes: 20%.
The percent of time that customers at the new store bought milkshakes: 26%.
The percent of total sales that were Ice Cream sales in both shops: 78%.
The percent of new store sales out of the total sales for both shops: 35%.
How to determine correct statement and value?First of all, we would have to determine the total number of sales for both the Old store with respect to the number of servings of ice cream and milk shakes that were sold;
Total sales = 52,100 + 13,400
Total sales = 65,500
Next, we would determine the percent of time that customers at the old store bought milk shakes;
Percent = 13,400/65,500 × 100
Percent = 20.46 ≈ 20%.
Similarly, we would determine the percent of time that customers at the new store bought milk shakes;
Total sales = 25,800 + 9,200
Total sales = 35,000
Percent = 9,200/35,000 × 100
Percent = 26.29 ≈ 26%.
Total sales in both stores = 52,100 + 13,400 + 25,800 + 9,200
Total sales in both stores = 100,500
Percent of ice cream in both stores = (52,100 + 25,800)/100,500 × 100
Percent of ice cream in both stores = 77.51 ≈ 78%.
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Write an equation for the polynomial graphed below
The polynomial function that best fits the graph is f(x) = 130(x+3)(x-2)²(x-5).
The given graph exhibits three x-intercepts at x = -3, 2, and 5, and the y-intercept is positioned at (0, 2). The graph passes through the x-axis linearly at x = -3 and x = 5, indicating that the corresponding factors of the polynomial will be linear. However, at x = 2, the graph bounces off the x-axis at the intercept, implying that the corresponding factor of the polynomial will be quadratic. Therefore, the polynomial function can be expressed as follows:
f(x) = a(x+3)(x-2)²(x-5)
To find the stretch factor 'a,' we can use another point on the graph, such as the y-intercept (0, 2). By plugging in the values, we obtain:
f(0) = a(0+3)(0-2)²(0-5)
-2 = a(0+3)(0-2)²(0-5)
-2 = -60a
a = 130
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Find what the value of x is please
The choices are...
1. 118
2. 108
3. 28
4. 58
Answer:
choice 1
Step-by-step explanation:
62 and x are a linear pair and sum to 180 , that is
62 + x = 180 ( subtract 62 from both sides )
x = 118
Answer:
1. 118
Step-by-step explanation:
Given the image provided:
Supplementary angles are where the two angles add up to 180°A straight line is equal to 180°Solve for x:
Since, the image is of a supplementary angle that adds up to 180° and one angle is 62°, then we take 180 minus 62.
180 - 62 = 118Answer:
Therefore, x = 118 and the answer is 1.
Base twelve needs twelve digits, so we use t for ten and e for eleven and our usual ten digits. What base ten number does 1t5e twelve represent?
Therefore, 1t5e twelve represents the number 3239 in base ten.
what is system of equations?
A system of equations is a set of two or more equations with the same variables. The solution to a system of equations is a set of values for the variables that satisfy all the equations in the system simultaneously.
For example, consider the following system of two equations:
x + y = 5
2x - y = 3
This is a system of two equations with two variables, x and y. The solution to this system is the values of x and y that make both equations true at the same time. In this case, the solution is x = 2 and y = 3, because when we substitute these values into the equations.
In base twelve, the place values increase by a factor of twelve at each position, starting from the rightmost position. The rightmost position has a place value of 1, the next position to the left has a place value of 12, the next position to the left has a place value of 12^2 = 144, and so on.
To convert the number 1t5e in base twelve to base ten, we need to multiply each digit by its corresponding place value, and then add up the results:
1t5e (base twelve) = 1 * 12^3 + 10 * 12^2 + 5 * 12^1 + 11 * 12^0
= 1 * 1728 + 10 * 144 + 5 * 12 + 11 * 1
= 1728 + 1440 + 60 + 11
= 3239
Therefore, 1t5e twelve represents the number 3239 in base ten.
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A 9v battery produces a current of 18 amps. What is the resistance
If a 9v battery produces a current of 18 amps then the resistance of the circuit element is 0.5 ohms.
We can use Ohm's law to determine the resistance (R) of a circuit element
Given the voltage (V) and current (I) through it:
R = V / I
In this case, the voltage (V) is 9 volts and the current (I) is 18 amps. Substituting these values into the formula, we get:
R = 9 V / 18 A
Simplifying the expression on the right-hand side, we get:
R = 0.5 Ω
Therefore, the resistance of the circuit element is 0.5 ohms.
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Help asap math homework
Help me please this is getting tricky!
1. The difference between the longest and shortest pencil is 4 5/12
2. The total length is 22 3/4 inches
3. The statement is false
4. There are 9 pencils that measure more than 5½ inches and less than 7 2/4 inches
What is word problem?A word problem is a math problem written out as a short story or scenario. This statements are interpreted into mathematical equation or expression.
1. The difference between longest and shortest pencil = 8⅔ - 4¼
= 26/3 - 17/4
= (104-51)/12
= 53/12 = 4 5/12
2. The total length of pencils less than 5 ½ inches = 5×2 + 17/4 × 3
= 10+ 51/4 = 40+51)/4
= 91/4 = 22 3/4 inches
3. The Statement is false because the pencils less than 6 inches is 8 and not upto half of the total pencil
4. There are 9 pencils that measure more than 5½ inches and less than 7 2/4 inches.
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The advertising fee for a 30-second spot on the TV show Deal or No Deal is $165,000. The show averages 16.1 million viewers. (Source: USA Today, December 18, 2006) What is the advertiser's cost per viewer for a 30-second ad? Round to the nearest cent.
Te advertiser's cost per viewer for a 30-second ad is $0.01025.
How do we get the cost per viewer?Cost per view means an ads model that charges the advertiser whenever a user watches an ad for a set duration.
To calculate the cost per viewer for the advert, we need to divide the advertising fee by the number of viewers which gives us:
Cost per viewer = Advertising fee / Number of viewers
Substituting the values, we get:
= $165,000 / 16.1 million viewers
= $165,000 / 16,100,000 viewers
= 0.0102484472 per viewer
= $0.01025 per viewer.
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Help on Part A and B
Answer:
The Correct answer is B
Step-by-step explanation:
Can you explain why you need to multiply x and y (and not add x and y) when you are adding
logarithms?
The exponent by which base b must be raised to get a positive real number an is the logarithm of a positive real number a with regard to base b, a positive actual number that is not exactly one.
What is a logarithm?A logarithm is the power to which a number must be raised in order to receive extra values. The simplest approach to express really large numbers is in this way. A number of important features of a logarithm demonstrate the fact that multiplication and division of logarithms can also be used to represent addition and subtraction logarithms.
The exponent by which base b must be raised to get a positive real number an is the logarithm of a positive real number a with regard to base b, a real number that is positive but not equal to one.
i.e., [tex]b^y=a[/tex] ⇔ [tex]log_b[/tex] a = y
In this case, "A" and "B" are two positive real numbers.
Y is an actual number.
Argument occurs inside the log as "a" by the name argument.
It is said that the base, or "b," is at the bottom of the log.
To put it another way, the logarithm provides a solution to the problem of "How many times is a number divided to get the other number?"
How numerous times must three be multiplied, for instance, to yield the number 27?
27 is the outcome of multiplying 3 times by 3.
Consequently, the logarithm is 3.
The logarithm form is written as follows:
[tex]log_3[/tex] (27) = 3 - equation 1
The base 3 logarithm of 27 is therefore 3.
It is also possible to write the above logarithm form as:
3x3x3 = 27
3³ = 27 - equation 2
Equations (1) and (2) are hence equivalent.
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