The calculated value of the area of the circle is 5544 square yards
What is the area of the given circle?From the question, we have the following parameters that can be used in our computation:
Radius, r = 42
Using the above as a guide, we have the following:
Area = π * r^2
Substitute the known values in the above equation, so, we have the following representation
Area = 22/7 * 42^2
Evaluate the products and exponents
Area = 5544
Approximate
Area = 5544
Hence, the value of the area is 5544 square yards
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graph the piecewise function. f(x)= {3x-5 if x is less than or equal to -1. -2x+3 if -1 is less than x is less than 4. 2 if x is greater than of equal to 4.
Answer:
Here's how to graph the piecewise function:
First, we graph the function for the first interval, which is f(x) = 3x - 5 when x ≤ -1. This is a straight line with a slope of 3 and a y-intercept of -5. Since this interval includes -1, we draw a closed circle at x = -1 to indicate that it is included in the interval. The line is decreasing as x increases.
Next, we graph the function for the second interval, which is f(x) = -2x + 3 when -1 < x < 4. This is also a straight line, but with a slope of -2 and a y-intercept of 3. Since this interval does not include -1, we draw an open circle at x = -1 to indicate that it is not included in the interval. We also draw an open circle at x = 4 to indicate that it is not included in the interval. The line is increasing as x increases.
Finally, we graph the function for the third interval, which is f(x) = 2 when x ≥ 4. This is a horizontal line at y = 2. Since this interval includes 4, we draw a closed circle at x = 4 to indicate that it is included in the interval.
When we put all three intervals together, we get a graph that looks like this:
```
| /
2 | /
| /
| /
| /
| /
| /
| /
| /
|/
_______|_____________
-1 4
```
The graph consists of a downward-sloping line from (-∞, -1], an upward-sloping line from (-1, 4), and a horizontal line from [4, ∞).
What is the Pythagorean theorem and how is it used?
The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
It is used to find the length of one of the sides of a right-angled triangle when the lengths of the other two sides are known. It is also used to determine if a triangle is a right-angled triangle or not, by checking if the lengths of the sides satisfy the theorem.
The Pythagorean Theorem has many practical applications, such as in construction, engineering, and physics. For example, it can be used to calculate the distance between two points in a two-dimensional plane, the height of a building or tower, or the force required to move an object up a ramp at a given angle.
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2 3/4=pints as a mixed numbers
2 3/4 cups is equivalent to 1 3/8 pints as a mixed number.
There are 2 cups in a pint. To convert 2 3/4 cups into pints, we can follow these steps:
Convert the whole number part of the mixed number to pints by dividing by 2.
Convert the fractional part of the mixed number to cups, then divide by 2 to get the corresponding pints.
Add the two results together to get the total in pints as a mixed number.
So, let's apply these steps to 2 3/4 cups:
The whole number part is 2, so 2 cups = 1 pint.
The fractional part is 3/4 cups, which is equivalent to 3/4 ÷ 2 = 3/8 pints.
Adding the two results, we get:
1 pint (from the whole number part) + 3/8 pint (from the fractional part) = 1 3/8 pints.
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The diameter of a bicycle wheel is 60 centimeters. How far does the wheel travel when it makes 35 revolutions? Give your answer in. meters( Math in focus singapore math course 1 B)
Answer:
The circumference of a circle is given by the formula "C = pi x d" where "d" is the diameter and "pi" is the mathematical constant with an approximate value of 3.14.
In this problem, the diameter of the bicycle wheel is 60 centimeters, so its circumference is:
C = pi x d = 3.14 x 60 = 188.4 centimeters
When the wheel makes one revolution, it travels one circumference distance. Therefore, when the wheel makes 35 revolutions, it will travel:
distance = 35 x circumference = 35 x 188.4 = 6584 centimeters
We can convert centimeters to meters by dividing the distance by 100:
distance = 6584 ÷ 100 = 65.84 meters
Therefore, the wheel travels 65.84 meters when it makes 35 revolutions.
ELECTRICAL POTENTIAL The electrical potential between two electrons is given by a formula has the form 1/r + 1/ 1-r
In a case whreby the electrical potential between two electrons is given by a formula has the form 1/r + 1/ 1-r the simpification of the expression is 1/r(1-r).
How can the expression be simplified?Looking at the expression we can see that it is adion of two expression which implies that we will need to perform an addition operation then later simplified the result, this is been done below
We can find the LCM as r(1-r)
(1-r +r)/ r(1-r)
=1/r(1-r)
Therfore, after performing the addition operation as well as the simplification, then the the simpification of the expression is 1/r(1-r).
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complete question;
The electrical potential between two electrons is given by a formula has the form 1/r + 1/ 1-r simplify the expression.
Choose the most reasonable unit of measure.
3) Area of a baseball infield: 925
A) mm² B) km² C) m² D) cm²
4) Area of a lake: 4
A) mm² B) km² C) m² D) cm²
5) Area of a door: 20
A) yd² B) in.² C) ft² D) mi²
The most reasonable unit of measurement for 3) is option (C): [tex]m^2[/tex], 4) is option (B): [tex]km^2[/tex], 5) is [tex]in^2[/tex].
3) The most reasonable unit for the measurement of the baseball field is [tex]m^2[/tex] because the baseball field covers a large distance which is not accurately measured by small units [tex]cm^2[/tex] or [tex]mm^2[/tex] where it is not that big to be measured in large units like [tex]km^2[/tex]. So option C is the correct option.
4) The most reasonable unit for the measurement of a lake is [tex]km^2[/tex] because lakes are generally very large water bodies that cover a large distance and are not accurately measured by small units like [tex]cm^2[/tex] , [tex]mm^2[/tex] , and [tex]m^2[/tex]. So option B is the correct option.
5) The most reasonable unit for the measurement of the area of a door is [tex]in^2[/tex] because doors are relatively small compared to the other options and are often measured in square inches or square feet. So option B is the correct option.
Therefore the correct answers question-wise are:
3) [tex]m^2[/tex]
4) [tex]km^2[/tex]
5) [tex]in^2[/tex]
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If the geometric series 54+36+…+128/27 has seven terms in its sum then the value of the sum is?
The sum of the geometric series is 306. We can start by finding the first term and the common ratio of the geometric series.
The first term is 54, and to find the common ratio we divide any term by its previous term:
36 / 54 = 2/3
(2/3) * 54 = 36
128/27 / 36 = 4/3
So the common ratio is 2/3.
S = a * (1 - r^n) / (1 - r)
where S the sum of a geometric series with first term a, common ratio r, and n terms is no. of terms.
We are given that there are seven terms in the sum, so n = 7.
Using the values we have:
S = 54 * (1 - (2/3)^7) / (1 - 2/3)
S = 54 * (1 - 128/2187) / (1/3)
S = 54 * (2059/2187) * 3
S = 306
Therefore, the sum of the geometric series is 306
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The box plot below represents some data set. What percentage of the data values are between 110 and 170?
The percentage of the data values are between 110 and 170 = 37.5%
We know that in the box plot, the first quartile is nothing but 25% from smallest to largest of data values.
The second quartile is nothing but between 25.1% and 50% (i.e., till median)
The third quartile: 51% to 75% (above the median)
And the fourth quartile: 25% of largest numbers.
In the attached box plot, we can observe that between two numbers on the number line there are 5 equal parts.
So, each unit length measures 10 units.
Also, the median of the data = 110
We need to find the percentage of the data values are between 110 and 170.
i.e., the percentage of the data values are in the third quartile.
The range of this box plot is: 190 - 30 = 160
The data values are between 110 and 170 = 60
Using percentage formula,
P = (60/160) × 100
P = 37.5%
This is the required percentage.
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Find the complete question below.
I need help with my math project so if anyone can do this for me real quick
I don't really know but try to read
the price stock A at 9 am was $13.92. since then the price has been increasing at the rate of $0.11 each hour. At noon the price of Stock B was 14.67. It begins to decrease at the rate of $0.14 each hour. if the two rates continue , in how many hours will the prices of the two stocks be the same
The number of hours when the two stocks would be the same is 1.68 hours.
In how many hours would the two stocks be the same?The first step is to determine the price of stock A at noon.
Price of stock A at noon = price at 9am + (rate of increase per hour x time difference)
Time difference = 12 - 9am = 3 hours
= $13.92 + (0.11 x 3)
= $13.92 + 0.33
= $14.25
Value of stock A t hours after noon = $14.25 + (0.11 x t)
= $14.25 + 0.11t
The equation that can be used to determine the price of stock B at time t is:
Price of stock B at time t = beginning price - (rate of decline x time)
= $14.67 - (0.14 x t)
= $14.67 - 0.14t
When the two stocks are the same, the two equations would be equal to each other:
$14.25 + 0.11t = $14.67 - 0.14t
solve for t:
0.11t + 0.14t = $14.67 - $14.25
0.25t = 0.42
t = 0.42 / 0.25
t = 1.68 hours
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If a fair coin is tossed twice the possible outcomes are HH, HT, TH or TT, where HH means both tosses are heads and HT means that the first toss is a head and the second toss is a tail, etc. Since the coin is fair, a 50-50 chance of getting a head or a tail, we assign a probability of 1/4 to each of the four outcomes. Assuming that a fair coin was tossed twice, find the probability that exactly one of the tosses is a head and the other toss is a tail.
Assuming that a fair coin was tossed twice, the probability that exactly one of the tosses is a head and the other toss is a tail is 1/2.
The probability of a certain event happening is the number of ways that event can occur, divided by the total number of possible outcomes. In this case, we are interested in finding the probability that exactly one of the two coin tosses results in a head and the other results in a tail.
There are two possible outcomes that satisfy this condition: HT and TH. Since the coin is fair, each of these outcomes has a probability of 1/4. Therefore, the total probability of getting exactly one head and one tail is:
P(HT or TH) = P(HT) + P(TH) = 1/4 + 1/4 = 1/2
In other words, there is a 50-50 chance of getting exactly one head and one tail when a fair coin is tossed twice.
To see why this is the case, we can think of each toss as an independent event with two possible outcomes (head or tail). There are four possible outcomes when we toss a coin twice, and two of these outcomes satisfy the condition of exactly one head and one tail. Therefore, the probability of getting exactly one head and one tail is 2/4, which simplifies to 1/2.
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The sales data for July and August of a frozen yogurt shop are approximately normal.
The mean daily sales for July was $270 with a standard deviation of $30. On the 15th of July, the shop sold $315 of yogurt.
The mean daily sales for August was $250 with a standard deviation of $25. On the 15th of August, the shop sold $300 of yogurt.
Which month had a higher z-score for sales on the 15th, and what is the value of that z-score?
a.)
August, with a z-score of 1.67.
b.)
July, with a z-score of 1.5.
c.)
July, with a z-score of 1.8.
d.)
August, with a z-score of 2.
Answer: D
Step-by-step explanation:
To determine which month had a higher z-score for sales on the 15th, we need to calculate the z-scores for each month's sales.
For July:
z-score = (x - μ) / σ
where x is the sales on the 15th, μ is the mean daily sales for July, and σ is the standard deviation of daily sales for July.
Plugging in the values, we get:
z-score for July = (315 - 270) / 30 = 1.5
For August:
z-score = (x - μ) / σ
where x is the sales on the 15th, μ is the mean daily sales for August, and σ is the standard deviation of daily sales for August.
Plugging in the values, we get:
z-score for August = (300 - 250) / 25 = 2
Since the z-score for August is higher than the z-score for July, August had a higher z-score for sales on the 15th.
The value of the z-score for August's sales on the 15th was 2.
Ethan's class is handing out balloon arrangements consisting of 4 balloons each. Each balloon has an equally likely chance of being red, blue, or yellow. Ethan created a spinner to simulate this probability. Here is Ethan's data from 30 trials of 4 spins on the spinner (r = red, b = blue, y = yellow):
ybrr bybb rbbb rrry rbbb rryy yybb ryry ryyr rbyr ryyr rryy rrrr yrby bbyy byyr byyr byyb rbby ybry rryy rbrr rybb bbbr rrbr ybry ryrr rryb rrrb rryr
According to this data, what is the experimental probability that an arrangement will contain at least one red balloon and at least one blue balloon?
0.67
0.53
0.5
0.47
The experimental probability that an arrangement will contain at least one red balloon and at least one blue balloon is 0.53. Therefore, option B is the correct answer.
The given sample space is {ybrr bybb rbbb rrry rbbb rryy yybb ryry ryyr rbyr ryyr rryy rrrr yrby bbyy byyr byyr byyb rbby ybry rryy rbrr rybb bbbr rrbr ybry ryrr rryb rrrb rryr}
We know that, probability of an event = Number of favorable outcomes/Total number of outcomes.
Here, total number of outcomes = 30
Number of favorable outcomes =16
Probability of an event 16/30
= 0.53
Therefore, option B is the correct answer.
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A contractor needed a small workshop. He found a preengineered steel building advertised for $12,099. If the building is a 36-ft by 36-ft square, what is the cost of the
building per square foot?
The cost of the building per square foot is $(Round to the nearest cent as needed.)
Answer:
$9.34 per square foot
Step-by-step explanation:
You want the cost per square foot of a 36 foot square building that costs $12,099.
Cost per square footThe cost per square foot is found by dividing the cost by the number of square feet. That area is found as the square of the side length:
A = s²
A = (36 ft)² = 1296 ft²
Then the cost is ...
cost per square foot = ($12099)/(1296 ft²) ≈ $9.34/ft²
The cost of the building is about $9.34 per square foot.
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y = 2x X 0 2 3 4 6 4 8 5 10 Click to select points on the graph. 10 9 8 0 7 5
Answer:
The points selected on the graph are:
(0, 0), (2, 4), (3, 6), (4, 8), (6, 12), (4, 8), (8, 16), (5, 10)
Here is a table showing the coordinates of the selected points:
x y
0 0
2 4
3 6
4 8
6 12
4 8
8 16
5 10
me no work math[tex]-3X+5y=-3\\y=-7+7[/tex]
The value of 'x' is 1 and value of y is '0'.
What is an equation?An equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
We have the equations are:
-3x + 5y = -3 ___eq.1
and, y = -7 + 7 ___eq.2
We have to find the value of 'x' and 'y'
Now, Firstly find the value of y
We know that :
Opposite sign with same digit is cancel to each other it is always zero.
y = -7 + 7
So, y = 0
Now, We have to put the value of y in eq. 1
-3x + 5(0) = -3
-3x + 0 = -3
x = -3/-3
x = 1
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I NEED HELP
Please!!!!!!!!!!!!!!!
The exponential function for the given data is y = 1.806(1.107)ˣ ,
Interpretation about parameters are,
a represents initial population and b increase in growth by 10.7%.
Population size during 35th year is 63.
The exponential function that best represents the population growth of the species of crocodiles.
Values for parameters a and b in equation y = abˣ that best fit given data.
Using the data in the table, set up a system of equations as follows,
2 = ab¹
5 = ab¹⁰
12 = ab²⁰
22 = ab³⁰
25 = ab⁴⁰
To solve for a and b, we can divide the equations to eliminate a.
5/2 = (ab¹⁰)/(ab¹)
⇒5/2 = b⁹
12/5 = (ab²⁰)/(ab¹⁰)
⇒ 12/5= b¹⁰
22/12 = (ab³⁰)/(ab²⁰)
⇒ 22/12= b³/²
25/22 = (ab⁴⁰)/(ab³⁰)
⇒25/22 = b⁴/³
Taking the ninth root of the first equation,
The tenth root of the second
b = 1.107
a = 1.806
Exponential function that best represents the population growth of species of crocodiles is y = 1.806(1.107)ˣ
Interpreting the parameters of the model in the context of the problem.
a represents the initial population when x = 0 which is not given in the table.
And b represents the growth factor or rate of increase.
The growth factor is approximately 1.107, meaning that the population is increasing by about 10.7% each year.
To predict the population size during their 35th year, we simply plug x = 35 into the equation.
y = 1.806(1.107)³⁵
= 63.4
= 63(whole number)
Predict that population size of species of crocodiles during their 35th year will be approximately 63 individuals.
Therefore, the exponential function is y = 1.806(1.107)ˣ ,
Interpretation of parameters are a is the initial population and b represents the growth increased by 10.7%.
During 35th year population is 63.
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Tony and Jim go on a hiking trip. They start from the same spot in the morning. Tony travels 5 miles due south and Jim travels 6 miles north east, by noon. To the nearest mile, how far apart are Tony and Jim?
Answer:
To the nearest mile, Tony and Jim are 9 miles apart.
To visualize this, imagine a right triangle where Jim's starting point is at the right angle. Tony travels 5 miles due south, which is the adjacent side of the triangle. Jim travels 6 miles north east, which is the hypotenuse of the triangle. The opposite side of the triangle is the distance between Tony and Jim.
Using the Pythagorean theorem, we can find the length of the opposite side:
opposite side = sqrt(hypotenuse^2 - adjacent side^2)
opposite side = sqrt(6^2 - 5^2)
opposite side = sqrt(11)
To the nearest mile, the distance between Tony and Jim is 9 miles.
a ball leaves a bat in a horizontal direction from a height of 0.39 m above the ground. the speed of the ball is 35ms-1. the ball takes 0.28 seconds to reach the ground again. what is the horizontal distance the ball has travelled?
The horizontal distance the ball travelled is 2.73 m.
What is a projectile?A projectile is any object that is moving in space under the influence of gravity and its momentum. The horizontal distance covered by a projectile from its point of projection is called range. It can be determined by;
R = U[tex]\sqrt{\frac{2H}{g} }[/tex]
where u is the initial speed of the object, H is the height of projection and g is the gravitational constant.
So that in the information given, we can determine the range as;
R = U[tex]\sqrt{\frac{2H}{g} }[/tex]
= 35[tex]\sqrt{\frac{2*0.39}{10} }[/tex]
= 35*0.078
= 2.73
R = 2.73 m
The horizontal distance the ball has travelled is 2.73 m.
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The linear growth equation and graph show a population
that is growing at a Constant rate
Given that the starting population, M(0), is 5 and has a growth rate, m, of 2
individuals per unit of time, what will the population be at 20 units of time?
O A 55
O B. 45
O c. 30
O D. 25
Answer:
B
Step-by-step explanation:
N(0) = 5
m = 2 individuals per unit time
t = 20 unit time
N(20) = 2*20+5 = 45 individuals
The linear growth equation, M(t) = M(0) + m*t, can be used to calculate population growth at a constant rate. By substituting in the given starting population of 5 and growth rate of 2, it is determined that the population at 20 units of time is 45.
Explanation:In the context of this question, we're dealing with a simple linear growth equation, which can be expressed algebraically as M(t) = m*t + M(0), where M(t) is the population at time t, m is the rate of growth, and M(0) is the starting population.
In this case, the starting population, M(0), is 5 and the growth rate, m, is 2 individuals per unit of time. So if we want to calculate the population at 20 units of time, we would substitute these values into the equation.
According to the equation, M(20) = M(0) + m*20 = 5 + 2*20 = 5 + 40 = 45. Therefore, the population at 20 units of time would be 45 individuals.
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Please help me with my question
Answer:
The length is 35 meters (m).
Step-by-step explanation:
182/2
91 = area of 1/5 of the field.
91 * 3
273 = area of cabbages.
182 + 273
455 = area of whole field.
a/w = l, because l * w = a
455/13
35
how do you find the domain of the resulting function?
To find the domain of a function, we need to determine all values of the independent variable (usually denoted as x) for which the function is defined and has a real output.
For example, if we have the function:
f(x) = 1/(x-3)
We need to exclude any values of x that would make the denominator zero, since division by zero is undefined. Therefore, the domain of this function would be all real numbers except x = 3. We could write this as:
Domain: x ∈ ℝ, x ≠ 3
If we have a more complex function, we need to consider any other restrictions on the independent variable that may be imposed by the function.
For instance, if we have the function:
g(x) = sqrt(x-2)/(x+3)
Here, the square root function is defined only for nonnegative values of its argument. Therefore, we need to ensure that x-2 ≥ 0, or equivalently, x ≥ 2. Additionally, the denominator of the fraction cannot be zero, so we need to exclude x = -3. Combining these two conditions, we get:
Domain: x ∈ [2, ∞), x ≠ -3
This means that the function g(x) is defined and has a real output for all values of x greater than or equal to 2, except x = -3.
In general, to find the domain of a function, we need to consider any restrictions on the independent variable imposed by the function itself (such as division by zero, taking the square root of a negative number, etc.), as well as any restrictions that may be imposed by the context in which the function is used (such as physical or mathematical constraints). We then express the domain as a set of values of x that satisfy all the relevant conditions.
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PLEASE HELP FAST.
Marie-Renee wants to hang 4 identical posters on her wall. The wall is 16 feet wide, and there must be at least 5 feet of space total between the posters and between the edges of the wall. How wide can the posters be?
Marie-Renee writes the inequality 4w + 5 ≤ 16 to help her plan. Complete each statement below to describe what w, 4w, 5, and 16 represent in this inequality.
w represents...
4w represents...
5 represents...
16 represents...
Marie-Renee knows to find the acceptable width of each poster, she must first solve the associated equation to find the boundary value for her inequality. Solve 4w + 5 = 16 and show your work.
Does the boundary value you found in part (b) make Marie-Renee’s inequality true or false? Show your work and explain your reasoning.
Write the solution to Marie-Renee’s inequality and interpret it within the context of the problem.
The width of each poster cannot be greater than 11/4 feet or 2.75 feet.
For given expression w represents the width, 4w represents the total width of four posters, 5 represents space between posters and edges of wall, and 16 represents width of the wall.
The boundary value satisfies the inequality.
In the given problem, Marie-Renee wants to hang 4 identical posters on her wall, and she needs to leave at least 5 feet of space total between the posters and between the edges of the wall. Let's assume that the width of each poster is w feet.
The inequality 4w + 5 ≤ 16 represents the maximum space the posters can take on the wall. In this inequality,
w represents the width of each poster,
4w represents the total width of four identical posters,
5 represents the total space between the posters and between the edges of the wall, and
16 represents the total width of the wall.
To find the acceptable width of each poster, we need to solve 4w + 5 = 16.
4w + 5 = 16
4w = 16 - 5
4w = 11
w = 11/4
So, the width of each poster cannot be greater than 11/4 feet or 2.75 feet.
Now, we need to check if the boundary value of w satisfies the original inequality or not.
4w + 5 ≤ 16
4(11/4) + 5 ≤ 16
11 + 5 ≤ 16
16 ≤ 16
Since the boundary value satisfies the inequality, the solution to Marie-Renee's inequality is w ≤ 11/4 or w ≤ 2.75 feet.
Therefore, the width of each poster cannot exceed 2.75 feet, and all four posters can be hung on the 16 feet wide wall with at least 5 feet of space total between them and the edges of the wall.
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you roll a die numbered from 1 to 6. What is the probability that the sum is not 6?
Answer:2/3 or approximately 0.667.
Step-by-step explanation:
total number of outcomes =6
We can obtain a sum of 6: rolling a 1 and a 5, or rolling a 2 and a 4.
Therefore, the number of outcomes that do not result in a sum of 6 is:
6 - 2 = 4
So the probability of getting a sum that is not 6 is:
P(sum is not 6) = number of outcomes that do not result in a sum of 6 / total number of possible outcomes
P(sum is not 6) = 4 / 6
P(sum is not 6) = 2 / 3
IN CASE YOU ARE LOOKING FOR THE ANSWER
A climber is standing at the top of Mount Kilimanjaro, approximately 3.7 mi above sea level. Earth has a radius of 3959 mi.
What is the climber's distance to the horizon?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Answer: The answer is 171.2 Miles
Step-by-step explanation: You can easily find a "Horizon finder" online. It helps for harder equations like this.
Also I just realized that you put 171.20. When a question asks for a nearest tenth, only put the first digit of the decimal.
A viral video had 100,000 views on the first day. Each day, the number of views is 70% of the previous day. How many views will the video receive on the fourth day?
O49,000
O 34,300
O 24,010
O 16,807
Answer:
[tex]100000( {.70}^{3} ) = 34300[/tex]
what is the angle of depression on top of a 15 foot tall tree to a lake exactly at 30 feet from the top of the tree? what is the angle of elevation for someone on a boat that is 35 feet from shore looking up at the top of the tree?
Answer: We can use basic trigonometry to solve both of these problems:
Angle of depression from the top of the tree to the lake:
Let's draw a diagram of the situation:
A (top of tree)
|\
| \
30 | \ 15 ft
| \
| \
| \
| \
| \
| \
| \
| \
|__________\
B (lake)
In this diagram, A represents the top of the tree, B represents the lake, and the lines connecting them form a right triangle. We want to find the angle of depression, which is the angle between the horizontal line (from the top of the tree to the lake) and the line of sight from the top of the tree to the lake. This is angle θ in the diagram.
We know that the opposite side of this right triangle is 30 feet (the horizontal distance from the top of the tree to the lake) and the adjacent side is 15 feet (the height of the tree). Therefore:
tan(θ) = opposite/adjacent = 30/15 = 2
Taking the arctangent of both sides gives us:
θ = arctan(2) ≈ 63.4 degrees
Therefore, the angle of depression from the top of the tree to the lake is approximately 63.4 degrees.
Angle of elevation from the boat to the top of the tree:
Let's draw a diagram of the situation:
C (person on boat)
|\
| \
35 | \
| \
| \
| \
| \
| \
| \
| \
| \
|__________\
A (top of tree)
In this diagram, C represents the person on the boat, A represents the top of the tree, and the lines connecting them form a right triangle. We want to find the angle of elevation, which is the angle between the horizontal line (from the person on the boat to the shore) and the line of sight from the person on the boat to the top of the tree. This is also angle θ in the diagram.
We know that the opposite side of this right triangle is 15 feet (the height of the tree) and the adjacent side is 35 feet (the horizontal distance from the person on the boat to the tree). Therefore:
tan(θ) = opposite/adjacent = 15/35
Taking the arctangent of both sides gives us:
θ = arctan(15/35) ≈ 23.1 degrees
Therefore, the angle of elevation from the boat to the top of the tree is approximately 23.1 degrees.
what is the area of the square if it’s 15 by 15
Answer:
225 is the answer
15 times 15
Step-by-step explanation:
how many positive integers with three digits have at least one digit divisible by 3?
Answer:
There are a total of 900 three-digit positive integers, from 100 to 999.
PLEASE HURRY!!!
Write the expression using only positive exponents. Assume no denominator equals zero.
(−3^4 ^−7)^−3
The given expression ((−3⁴)⁻⁷)⁻³ using only positive exponents is equal to (-3)⁻⁸⁴.
To write the expression ((−3⁴)⁻⁷)⁻³ using only positive exponents, we can apply the rule of exponentiation that states that a negative exponent can be converted to a positive exponent by moving the base to the denominator and changing the sign of the exponent.
In this case, we have a negative exponent raised to another negative exponent, so we need to apply this rule twice.
First, we can rewrite the expression as:
((-3⁴)⁻⁷)⁻³ = (-3⁴)⁷³
Next, we can apply the rule of negative exponent to obtain:
(-3⁴)⁷³ = (1/(-3⁴))⁻²¹
Finally, we can simplify the expression by moving the negative exponent to the numerator, changing the sign of the exponent and using the power rule of exponents to get:
(1/(-3⁴))⁻²¹ = (-3⁻⁴)²¹ = (-3)⁻⁸⁴
In conclusion, we can convert a negative exponent to a positive exponent by moving the base to the denominator and changing the sign of the exponent. We can use this rule multiple times to simplify expressions with negative exponents.
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