after 1000 years, there will be approximately 218.7 mg of Radium-226 remaining in the sample. use formula for radioactive decay to solve
what is radioactive decay ?
Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation, such as alpha particles, beta particles, and gamma rays. The decay occurs in order to achieve a more stable configuration of the nucleus.
In the given question,
The formula for radioactive decay is:
N(t) = N0 * (1/2)ᵃ⁾ᵇ
where:
N(t) is the amount of radioactive material at time t
N0 is the initial amount of radioactive material
t is the time elapsed since the initial measurement
T is the half-life of the radioactive material
We can use this formula to solve the problem as follows:
N0 = 500 mg (the initial amount)
T = 1590 years (the half-life)
t = 1000 years (the time elapsed)
N(t) = 500 * (1/2)¹⁰⁰⁰⁾ ¹⁵⁹⁰
N(t) = 500 * 0.4374
N(t) = 218.7 mg
Therefore, after 1000 years, there will be approximately 218.7 mg of Radium-226 remaining in the sample.
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Determine the line of Reflection. A(-3,3) B(-3,6) C(1,6) D(1,3) E(-1,1); A'(-5,3), B(-5,6), C(-9,6), D(-9,3) E(-7,1)
The line of reflection is the vertical line passing through (-5, 6), (-9, 6), (-9, 3), and (-7, 1).
What is line of reflection?A line of reflection is a line that acts as a mirror, reflecting a figure across it. Each point on the original figure is reflected over the line and the resulting image is the same size and shape as the original, but appears to be "flipped" or "mirrored" across the line of reflection. The line of reflection is the perpendicular bisector of the segment connecting each point on the original figure to its corresponding point on the reflected image.
In the given question,
To determine the line of reflection, we need to find the perpendicular bisector of each line segment between the point and its image.
First, we find the midpoint of the line segment between A and A': (A + A')/2 = (-3 + (-5))/2, (3 + 3)/2 = (-4, 3)
The perpendicular bisector of the line segment AA' is a vertical line passing through (-4, 3).
Similarly, we find the midpoints and perpendicular bisectors of the line segments BB', CC', DD', and EE'.
The perpendicular bisectors of the line segments BB', CC', DD', and EE' are also vertical lines passing through (-5, 6), (-9, 6), (-9, 3), and (-7, 1), respectively.
Therefore, the line of reflection is the vertical line passing through (-5, 6), (-9, 6), (-9, 3), and (-7, 1).
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Cheryl and her sister Diane walk to school along the same route. Cheryl walks at an average of
80 steps per min while Diane walks at an average of 90 steps per min. Cheryl takes steps
of 81 cm each. She takes 12 min to walk to school.
A) If each of Diane's steps in 72 cm, how long does Diane take to walk to school?
Answer: Let's first convert Cheryl's walking speed to meters per minute. Since she takes 80 steps per minute and each step is 81 cm, her walking speed is:
80 steps/min x 81 cm/step = 6480 cm/min
To convert this to meters per minute, we can divide by 100:
6480 cm/min ÷ 100 cm/m = 64.8 m/min
Now, let's find out the distance Cheryl walks to school. Since she walks for 12 minutes at a speed of 64.8 m/min, the distance she covers is:
distance = speed x time = 64.8 m/min x 12 min = 777.6 m
Next, let's find out how many steps Diane takes per minute on average:
90 steps/min
Since each of Diane's steps is 72 cm long, her walking speed is:
90 steps/min x 72 cm/step = 6480 cm/min
To convert this to meters per minute, we can divide by 100:
6480 cm/min ÷ 100 cm/m = 64.8 m/min
So Diane's walking speed is the same as Cheryl's. To find out how long it takes Diane to walk to school, we can use the formula:
distance = speed x time
Since Diane and Cheryl walked the same distance, we can use the distance we found for Cheryl:
777.6 m = 64.8 m/min x time
Simplifying this equation, we get:
time = 12 minutes
Therefore, Diane takes 12 minutes to walk to school.
Answer:
12 min
Step-by-step explanation:
You want to know how long it takes Diane to walk to school if she takes 90 steps of 72 cm per minute, while Cherly takes 80 steps of 81 cm per minute and traverses the distance in 12 minutes.
SpeedThe speed of each girl is the product of the number of steps per minute and the length of the step:
Cheryl: (80 step/min)(81 cm) = 6480 cm/min
Diane: (90 step/min)(72 cm) = 6480 cm/min
Both girls travel at the same speed, so will take the same amount of time to get to school. It takes Diane 12 minutes to walk to school.
Solve the given equations. Place the name of each equation in order by the least number of solutions to the greatest number of solutions.
The order of the equations from least number of solutions to greatest number of solutions is: C, B , and A.
What is equation and expression?In algebra, an expression is made up of several numbers, variables, and mathematical operations including addition, subtraction, multiplication, and division. One expression is, for instance, 3x + 2y - 5.
In algebra, an equation is a claim that two expressions are equal to one another. Often, it asks us to determine the value of a variable that would make the equation true.
Equation A:
4x + 12 = 2(2x + 3) + 6
4x + 12 = 4x + 12
This equation has infinitely many solutions, as 0 = 0 is always true.
Equation B:
5(x - 1) = 3(x + 7)
5x - 5 = 3x + 21
2x = 26
x = 13
This equation has one solution, which is x = 13.
Equation C:
2x - 4 = 2(x + 18)
2x - 4 = 2x + 36
-4 = 36
This equation has no solutions.
Hence, the order of the equations from least number of solutions to greatest number of solutions is: C, B , and A.
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The probability that Rosie goes to the beach after school is 6 11 If she does go to the beach, then the probability that she does her homework is ) If she does not go to the beach, then the probability that she does her homework is 3 4 Work out the probability that Rosie does her homework. Give your answer as a fraction in its simplest form.
The probability that Rosie does her homework is: 27/44
How to find the conditional probability?Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.
Thus, we can solve this probability as:
(6/11 * 1/2) + ((1 - (6/11) * 3/4)
= (3/11) + (5/11 * 3/4)
= (3/11) + 15/44
= 27/44
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CAN SOMEONE HELP WITH THIS QUESTION?
The total cost for the first 25 units is given as follows:
$140.
How to obtain the total cost?The marginal cost function is defined as follows:
[tex]c(x) = \frac{14}{\sqrt{x}} = 14x^{-\frac{1}{2}}[/tex]
The total cost function is the integral of the marginal cost function, hence it is given as follows:
[tex]t(x) = \int c(x) dx[/tex]
[tex]t(x) = 28\sqrt{x}[/tex]
Applying the Fundamental Theorem of Calculus, the total cost from x = 0 to x = 25 is given as follows:
t(25) - t(0).
Thus:
t(25) = 28 x 5 = 140.t(0) = 28 x 0 = 0.Hence:
140 - 0 = $140.
(Applying the Fundamental Theorem of Calculus, we subtract the numeric values at each endpoint of the integral).
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Please help me find the length of OP. (See attached picture)
The length of OP in the given circle figure is 2.
We know that the area of a sector which obtain 'A' degree at center in a circle with radius 'r' is given by,
A = (A/360)*πr²
Here length of OP represents the radius of the circle with center O.
Let OP = R.
The area of the whole circle will be = πR²
Given that the sector which intends an angle of 72 degrees in center has area 4π/5.
According to the condition,
(72/360)* πR² = 4π/5
R²/5 = 4/5
R² = 4
R = 2 [since length cannot be negative so the negative value of square root is ignored.]
Hence the length of OP is 2.
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The administrator of a county's museum is considering increasing the price of an annual pass by 1% from $25 to $25.25. At the current price, the museum sells 2500 annual passes and the point of elasticity is 0.73. What effect would the increase in price have on the museum's annual pass revenue?
Answer: the increase in price from $25 to $25.25 would result in a small increase in annual pass revenue of $178.50 or about 0.3%.
Step-by-step explanation: we can calculate the modern yearly pass income by increasing the modern amount requested by the unused cost of $25.25:
Unused yearly pass income = Modern cost x Modern amount requested
Unused yearly pass income = $25.25 x 2482 = $62,678.50
We as of now know that the ancient yearly pass income is $62,500 (since 2500 passes were sold at $25 each), so ready to calculate the alter in yearly pass income:
Alter in yearly pass income = Unused yearly pass income - Ancient yearly pass income
Alter in yearly pass income = $62,678.50 - $62,500 = $178.50
Given that f (x) = StartFraction 120 Over x squared EndFraction , What is the domain of the function f ? a. only positive integers c. only negative integers b. All non zero real numbers. d. All real numbers including zero
For the function "f (x) = 120/x²", the domain of the function "f" is (b) All non zero real numbers.
The "Domain" of a function is the set of all possible "input-values" for which the function is defined. In this case, the function is defined as:
f (x) = 120/x²
The only restriction on the input values is that the denominator cannot be equal to zero, because division by zero is undefined.
So, the domain of the function f is all non-zero real numbers.
Therefore, the correct option is (b): All non-zero real numbers.
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The given question is incomplete, the complete question is
Given that f (x) = 120/x², What is the domain of the function f ?
(a) only positive integers,
(b) All non zero real numbers,
(c) only negative integers,
(d) All real numbers including zero.
help pls i dont understand this
The equation that can be used to determine the cost of each admission ticket is 4x + $25.00 = $175.00.
The cost in dollars of the admission ticket is $ 37.50.
How to find the cost of the tickets ?Let x be the cost, in dollars, of each admission ticket, including tax.
The total cost of 4 admission tickets can be expressed as 4x, since the cost of each ticket is the same.
The total cost of 4 admission tickets and parking is given as $175.00, so we can write:
4x + $25.00 = $175.00
Simplifying the equation, we can solve for x:
4x = $175.00 - $25.00
4x = $150.00
x = $37.50
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wing Lines Parallel
Solve for x to make A||B.
B
3x
A
X = = [?]
7x
Enter
If line A is parallel to line B then the value of x is 18.
Given that a line A is parallel to line B
We have to find the value of x
3x+7x=180
Combine the like terms
10x=180
Divide both sides by 10
value x=18
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Log22/Log9 express log_9 22 in terms of common logarithms
What is common logarithms?Common logarithms, is commonly describd as base-10 logarithms.
It is a type of logarithm that involve taking the logarithm of a number with respect to the base of 10.
This means that common logarithms show how many powers of ten must be increased to get a particular number. The usual logarithm of 100, for example, is 2, because 10 raised to the power of 2 equals 100.
The answer provided is based on the full question below;
-------------express log_9 22 in terms of common logarithms
a. Log 22/9
b. Log 198
c. Log22/Log9
d. Log9/Log22
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The graph shows the area in square feet Sally has left to paint. The equation A=392-14x gives the square feet Lisa has left to paint as a function of time in minutes. Which statements are true?
The statements that are true include the following:
B. Lisa paints more square feet per minute than Sally.
C. Lisa will finish painting before Sally.
D. After 10 minutes of painting Sally will have less to paint than Lisa.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (0 - 360)/(30 - 0)
Slope (m) = -360/30
Slope (m) = -12
At data point (0, 360) and a slope of -12, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 360 = -12(x - 0)
y = -12x + 360
A = 360 - 12x
For Sally, the time to finish;
360 = 12x
x = 360/12 = 30 min.
For Lisa, the time to finish;
392 = 14x
x = 392/14 = 28 min (Lisa will finish painting before Sally)
For Sally, when x = 10;
A = 360 - 12(10)
A = 240 sq. feet.
For Lisa, when x = 10;
A = 392 - 14(10)
A = 252 sq. feet.
For Sally, when x = 20;
A = 360 - 12(20)
A = 120 sq. feet.
For Lisa, when x = 20;
A = 392 - 14(20)
A = 112 sq. feet.
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3. How many different numbers can be created by selecting 4 of the digits from the number 8712395?
840 different numbers can be created selecting 4 of the digits from the number
How many different numbers can be created selecting 4 of the digits from the numberFrom the question, we have the following parameters that can be used in our computation:
Number = 8712395
Digits = 4
The count of digits in the number is 7
Using the above as a guide, we have the following:
First digit = any of the 7second digit = any of the remaining 6Third digit = any of the remaining 5Fourth digit = any of the remaining 4So, we have
Numbers = 7 * 6 * 5 * 4
Evaluate
Numbers = 840
Hence, 840 numbers can be formed
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HELP PLEASE I REALLY NEED HELP ON THIS QUESTION HELP!
Answer:
No I don't. The editor will receive 360 undelivered mail.
Step-by-step explanation:
He sends 12000 emails, 3/100 of them come back undelivered.
Multiply to find the answer:
12000 x 3/100 = 36000/100 = 360
Simple as that; the editor will find that 360 of his sent emails will come back undelivered.
A researcher performs an experiment to test a hypothesis that involves the nutrients niacin and retinol. She feeds one group of laboratory rats a daily diet of precisely 28.4 units of niacin and 37,335 units of retinol. She uses two types of commercial pellet foods. Food A contains 0.11 unit of niacin and 190 units of retinol per gram. Food B contains 0.35 unit of niacin and 95 units of retinol per gram. How many grams of each food does she feed this group of rats each day?
The grams of each food she feeds this group of rats each day is 80 grams of food A and 100 grams of food B each day.
Let us consider that the researcher feeds x grams of food A and y grams of food B each day. Then we can restructure the two equations on the basis of the amount of niacin and retinol present in the food
0.11x + 0.35y = 28.4 (equation 1)
190x + 95y = 37,335 (equation 2)
We can evaluate this system of equations applying the substitution or elimination method.
Let us apply substitution method:
In case of equation 1, we can evaluate concerning x:
x = (28.4 - 0.35y) / 0.11
Staging this value for x in equation 2
190[(28.4 - 0.35y) / 0.11] + 95y
= 37,335
Applying simplification and evaluating for y
y = 100
Staging this value for y in equation 1 to evaluate x
x = 80
Then, the researcher feeds 80 grams of food A and 100 grams of food B each day.
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Researchers are analyzing the total annual cost for the top ranked universities. They need to display the data in a way that is helpful
for relaying information regarding the data.
Identify the advantage of using a dotplot (choose one) :
A- Easily identify outliers
B- Easily determine the total number of data points for larger data sets
C- Cannot determine the minimum or maximum
D-Cannot identify the exact median
One advantage of using a dot plot is that it makes it easy to identify outliers. Option A is correct.
An outlier is a data point that is significantly different from the others in the data set, either in terms of its value or its position within the range of values. In a dot plot, outliers are represented by individual dots that are far away from the other dots, either above or below them.
By looking at the dot plot, researchers can quickly identify any outliers and investigate them further to determine why they are different and whether they should be included or excluded from the analysis.
Hence, A. is the correct option.
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7. Find (i) the length of an arc and (ii) the area of a sector in a circle of radius 7 meters subtended by the central angle of 85°.
i) The length of the arc is approximately 73.148 meters.
ii) The area of the sector is approximately 85.584 square meters.
(i) The length of an arc can be calculated using the formula:
Arc Length = (θ/360) × 2πr
where;
θ = central angle in degrees
r = radius of the circle
π = mathematical constant approximately equal to 3.14159.
Given that the central angle is 85° and the radius is 7 meters, we can substitute these values into the formula:
Arc Length = (85/360) × 2π × 7
= (17/72) × 2 × 3.14159 × 7
≈ 1.7454 × 6.28318 × 7
≈ 73.148 meters (rounded to three decimal places.
(ii) The area of a sector can be calculated using the formula:
Sector Area = (θ/360) × πr²
Given that the central angle is 85° and the radius is 7 meters, we can substitute these values into the formula:
Sector Area = (85/360) × π × 7²
= (17/72) × 3.14159 × 7²
≈ 1.7454 × 3.14159 × 49
≈ 85.584 square meters (rounded to three decimal places)
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The correct question is:
Find:
(i) the length of an arc
(ii) the area of a sector in a circle of radius 7 meters subtended by the central angle of 85°.
Find the volume of the composite solid. Round your answer to the nearest hundredth.
To the nearest hundredth, the volume of composite solid, giving us 904.600 cubic metres.
specify the solid volume?How many areas of space are occupied by an object is determined by its volume. It is determined by counting how many unit cubes are required to completely fill the solid. Cubic units like cubic centimeters, cubic meters, cubic feet, etc. are used to measure the volume of solids.
For instance, the volume V of a rectangular prism with dimensions of l, w, and h can be calculated as follows:
V = l × w ×h
The composite solid has a length of 14 metres and a radius of 6 metres** and is made up of a cylinder and two hemispheres. The cylinder's volume plus twice the hemisphere's volume will add up to the entire volume.
Where r is the radius and h is the height, V = πr²h is the formula for a cylinder's volume3. Therefore, V = (6)²(14) = 504 cubic meters is the cylinder's volume.
V = (2/3)r³π where r is the radius gives the volume of a hemisphere. Therefore, V = 2(2/3)(6)³π = 2(2/3)216π = 904 cubic meters is the volume of two hemispheres.
We arrive at a total volume of 792 cubic meters by adding these volumes together.
To the nearest hundredth=904.600 cubic meters.
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How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 3%? a previous study indicates that the proportion is 21%
Using the data given such as the margin of error, sample size and z-score, the maximum sample size required is 499
How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 3%?To solve this problem, we need to know the minimum sample size required. The formula for this is given as;
n = (z² * p(1 - p))/ E²
n = sample sizeE = Maximum margin of errorp = estimated proportion from the given previous studyz = z-scoreSubstituting the values into the formula;
n = (1.645² * 0.21(1 - 0.21))/ 0.03²
n = 498.8
The sample size should be at least approximately 499
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I know how to use the explicit formula to find a_1, but having a_n-1 being multiplied by 2 has thrown me for a loop. I am not sure how to fit it into the formula.
The first four elements of the sequence are:
a11 = 5350
a12 = 10702
a13 = 21406
a14 = 42814
How to calculate the sequenceStarting with a11 = 5350, we can use the recursive formula to find a12:
a12 = 2a11 + 2 = 25350 + 2 = 10702
a13 = 2a12 + 2 = 210702 + 2 = 21406
a14 = 2a13 + 2 = 221406 + 2 = 42814
Therefore, the first four elements of the sequence are:
a11 = 5350
a12 = 10702
a13 = 21406
a14 = 42814
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The table below shows primary school enrollment for a certain country. Here, x represents the number of years after 1820, and y represents the enrollment percentage. Use Excel to find the best fit linear regression equation. Round the slope and intercept to two decimal places.
x y
0 0.1
5 0.1
10 0.1
15 0.2
20 0.2
25 0.3
30 0.4
35 0.5
40 0.6
45 1.1
50 1.5
55 3.0
60 4.5
65 5.5
70 6.1
75 6.8
80 7.0
85 8.0
90 9.3
95 10.7
100 12.4
105 14.1
110 16.6
115 17.5
120 19.7
125 19.4
130 32.7
135 40.9
140 47.6
145 57.8
150 57.0
155 61.7
160 63.2
165 75.0
170 76.5
175 96.0
180 92.0
185 100.0
190 100.0
The best-fit linear regression equation gives us the equation y = 0.0804x + 1.1794, where the slope is 0.0804 and the y-intercept is 1.1794.
The trendline equation will give us the equation for the linear regression line, which can be written in the form of y = mx + b, where m is the slope and b is the y-intercept.
Once we have the trendline equation, we can use it to make predictions about future enrollment percentages based on the number of years after 1820.
The slope of the line tells us the rate at which the enrollment percentage is increasing or decreasing over time, and the y-intercept tells us the enrollment percentage when x is equal to zero (i.e., in 1820).
Here we have find that the best-fit linear regression equation gives us the equation
=> y = 0.0804x + 1.1794,
where the slope is 0.0804 and the y-intercept is 1.1794.
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What are the domain and range of the function f(x) x^2 +8x+7 over x+1
Answer: The function given is f(x) = (x^2 + 8x + 7)/(x + 1).
The domain of a function is the set of all possible input values for which the function is defined. In this case, the function f(x) is defined for all real numbers except for x = -1, because division by zero is undefined in mathematics. Therefore, the domain of f(x) is all real numbers except x = -1, or in interval notation: (-∞, -1) ∪ (-1, ∞).
The range of a function is the set of all possible output values that the function can produce. For this rational function, the range depends on the behavior of the function as x approaches positive and negative infinity. As x approaches positive or negative infinity, the function f(x) approaches 0, because the highest power of x in the numerator (x^2) and the highest power of x in the denominator (x) have the same degree, and their coefficients (1 in the numerator and 1 in the denominator) are equal. Therefore, the range of f(x) is all real numbers except 0, or in interval notation: (-∞, 0) ∪ (0, ∞). Note that f(x) never actually equals 0, because the function is defined for all real numbers except x = -1. However, it can arbitrarily approach 0 as x approaches positive or negative infinity. So, 0 is excluded from the range. Therefore, the correct answer is: Range = (-∞, 0) ∪ (0, ∞). Note that the range is expressed in interval notation, which uses parentheses to indicate open intervals (excluding the endpoints) and the union symbol (∪) to indicate the combination of two or more sets. In this case, the range consists of all real numbers except 0, expressed as two separate open intervals. The domain is also expressed in interval notation, with the union symbol (∪) used to indicate the combination of two disjoint sets. In this case, the domain consists of all real numbers except -1, expressed as the union of two separate intervals. So, the final answer is: Domain = (-∞, -1) ∪ (-1, ∞) and Range = (-∞, 0) ∪ (0, ∞). I hope this helps! Let me know if you have any further questions. I am here to help! Keep in mind that if you need to use the function f(x) in a real-world context, you should also consider any additional restrictions or conditions that may apply. It's always important to carefully analyze the properties of a function in the context of the problem you are trying to solve.
Step-by-step explanation:
The hanger image below represents a balanced equation. Select an equation that represents the image. Choose 1 answer: (Choice A) 45 = 3 + � , equals, 3, plus, z A 45 = 3 + � , equals, 3, plus, z (Choice B, Checked) 45 = 3 � equals, 3, z B 45 = 3 � equals, 3, z Find the value of � z that makes the equation true. � z, equals
The balanced equation of the hanger is 3z = 45 and the solution is z = 15
Selecting an equation that represents the imageFrom the question, we have the following parameters that can be used in our computation:
The hanger image
On the hanger image, we have the following
One side = z + z + z
The other side = 45
The expressions on either sides must be equal to have a balanced equation
So, we have
z + z + z = 45
Evaluate the like terms
3z = 45
Divide both sides of the equation by 3
z = 15
Hence, the balanced equation is 3z = 45 and the solution is z = 15
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A Petri dish is filled with 250 bacterial cultures. The number of bacteria in the dish triples every hour.
a. Write a recursive and an explicit formula to represent the sequence that models the scenario.
Explicit formula:
Recursive formula:
b. Predict the number of bacterial cultures in the dish after 8 hours. Explain your reasoning.
c. Does this sequence represent a function? Explain your reasoning.
Answer:
a. Let's denote the number of bacterial cultures after n hours by B_n. We know that the number of bacteria triples every hour, so we can write:
- Recursive formula: B_n = 3*B_(n-1) with initial condition B_0 = 250.
- Explicit formula: B_n = 250 * 3^n.
b. To predict the number of bacterial cultures after 8 hours, we can use the explicit formula and substitute n=8:
B_8 = 250 * 3^8 = 250 * 6561 = 1,640,250
Therefore, there will be 1,640,250 bacterial cultures in the dish after 8 hours.
c. Yes, this sequence represents a function. For each input value (number of hours), there is a unique output value (number of bacterial cultures). The explicit formula gives a direct way of computing the output for any input, so it satisfies the definition of a function.
please answer the question in pic
Note that given the factors above, Orr should replace the above plant. This has to do with depreciation and book value.
Why is this so ?We need to first compute the current total cost of keeping the old plant.
Book value = $4,500,000 - $1,000,000/year x 4 years
= $500,000
Thi smean that the current total cost of keeping the old plan tfor the reamining 10 year is
Total cost of keeping old plant = $1,000,000/year x 10 years - $500,000 + $150,000
= $9 650 000
Now lets calculate the total cost of purchasing the new plant for 10 years.
$600,000 - $150,000
= $450,000 per year.
The salvage value after 10 years is $0.
Total cost of new plant = $3,500,000 + $450,000/year x 10 years = $8,000,000
Since the cost of keeping is higher than the new one, then Orr should get a new plant.
$9 650 000 > $8,000,000
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The equation y = 10x + 15 models the amount of money y, in dollars, that Jack earns shoveling snow for x hours. How many hours does Jack need to work to earn $55?
−9⋅(5j+k)
Apply the distributive property to create an equivalent expression.
Answer:
-45j - 9k
Step-by-step explanation:
-9(5j + k)
-9(5j) + -9(k)
-45j - 9k
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Can someone help me with this pls
In the diagram, AB, BC and CD are three sides of a regular polygon F
A
a) Work out the size of angle y.
square polygon P
B
D
square
regular 12-sided polygon
y z
b) Work out the size of angle z.
c) What is the name of polygon P?
Answer:
Step-by-step explanation:
The size of each interior angle of the polygon is 4x+28 °
The value of x is 34 degree and y is 56 degree.
What is a Tangent?Tangents to circles are lines that cross the circle at a single point. Point of tangency refers to the location where a tangent and a circle converge. The circle's radius, where the tangent intersects it, is perpendicular to the tangent. Any curved form can be considered a tangent.
here, we have,
We have, BOA is an isosceles triangle.
< CBO = 90°
So, < DBO = 90 - 56
<DBO = 34
and, <ODB = 34°
Now, let the angle ODB be x
As, from the figure < EBD is also 90°
So, <y = 180 - (90+34) (Angle sum property)
<y = 56
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complete question:
Work out the size of angle x and work out the size of angle y
Which of the following statements is true about the numbers below?
(i)
(the digits cycle through repeatedly)
(ii)
(the number of
inbetween the
increases by one each time)
The statement that is true about the numbers above include the following: C. (i) is rational and (ii) is rational.
What is a rational number?In Mathematics and Geometry, there are six (6) common types of numbers and these include the following:
Irrational numbersIntegersReal numbersRational numbersNatural (counting) numbersWhole numbersIn Mathematics and Geometry, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the 2/3, 0.12345678901234567890.
What is an irrational number?In Mathematics and Geometry, an irrational number can be defined a type of number which comprises non-terminating or non-repeating decimals such as the square root of 11 or √11.
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