Answer:
The Length , width and height of solid are 4 feet , 3 feet and 7 feet respectively.
Step-by-step explanation:
Let the width of rectangular solid be x
We are given that the length of the container must be one meter longer than the width
So, Length of solid = x+1
We are also given that height must be one meter greater than twice the width
So, Height of solid = 2x+1
So, Volume of solid = [tex]Length \times Width \times height[/tex]
Volume of solid = [tex](x+1) \times x \times (2x+1)[/tex]
Volume of solid =[tex](x^2+x)(2x+1)[/tex]
Volume of solid =[tex]2x^3+x^2+2x^2+x=2x^3+3x^2+x[/tex]
We are given that a rectangular solid must have a volume of 84 cubic meters
So, [tex]2x^3+3x^2+x=84\\2x^3+3x^2+x-84=0\\(x-3)(2x^2+9x-28)=0\\[/tex]
On equating
x-3=0
x=3
So, Length of solid = x+1=3+1 = 4 feet
Height of solid = 2x+1 =2(3)+1=7 feet
Width of solid = 3 feet
Hence The Length , width and height of solid are 4 feet , 3 feet and 7 feet respectively.
The volume of a rectangular solid shipping container = 84 cubic meters
The width of the container = 3m
The length of the container = (x + 1) = (3+1) = 4m
The height of the container = (2x + 1) = (2 x 3 + 1) = 7m
Given:
The volume of a rectangular solid shipping container = 84 cubic meters
Let: The width of the container be x
The length of the container must be one meter longer than the width.
So, The length of the container be (x + 1)
The height must be one meter greater than twice the width.
So, The height of the container be (2x + 1)
To find the dimensions of the container
The Volume of the container = Length x Width x Height
[tex]84=x(x+1)(2x+1)[/tex]
[tex]84=(x^{2} +x)(2x+1)[/tex]
[tex]84=2x^{3} +3x^{2} +x[/tex]
[tex]2x^{3} +3x^{2} +x-84=0\\(x-3)(2x^{2} +9x+28)=0\\x-3=0\\x=3[/tex]
So, The width of the container = 3m
The length of the container = (x + 1) = (3+1) = 4m
The height of the container = (2x + 1) = (2 x 3 + 1) = 7m
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I need help solving this question it’s so hard
Answer:
x=40
Step-by-step explanation:
Since a circle has a total of a 360 degree angle the equation is
(x+40)+(2x+60)+(3x+20)=360
to simplify this we can bring all the variables(x) together and the numbers together.
(x+2x+3x)+(40+60+20)=360
6x+120=360
6x=360-120
6x=240
6x/6=240/6
x=40
The sum of all the degrees in a circle is 360 degrees. Knowing this you can make a equation:
(x + 40) + (2x + 60) + (3x + 20) = 360
x + 40 + 2x + 60 + 3x + 20 = 360
(x + 2x + 3x) + (40 + 60 + 20) = 360
Now you must combine like terms This means the numbers with the same variables must be combined...
(x + 2x + 3x) + (40 + 60 + 20) = 360
x + 2x + 3x = 6x
(6x) + (40 + 60 + 20) = 360
Now combine the terms without variables (on the left side of the equation) together
(6x) + (40 + 60 + 20) = 360
40 + 60 + 20 = 120
(6x) + 120 = 360
Now we must isolate x. To do this first bring 120 to the right side by subtracting 120 to both sides (what you do on one side you must do to the other). Since 120 is being added on the left side, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.
6x + 120 - 120 = 360 - 120
6x + 0 = 240
6x = 240
To further isolate x you must divide 6 to both sides. Since x is being multiplied by 6 you must divide 6 to both sides to make 6 one on the left side and bring it over to the right side
6x / 6 = 240 / 6
1x = 40
x = 40
Check:
(40 + 40) + (2(40) + 60) + (3(40) + 20)
(80) + (80 + 60) + (120 + 20)
80 + 140 + 140
360
Hope this helped! Let me know if you have any further questions or want anything clarified.
~Just a girl in love with Shawn Mendes
What are the coordinates of vertex F" of F"G"H"?
(4, -1.5)
(4, 0.5)
(-1.5, 4)
(-0.5, 4)
Answer:(4,-1.5)
Step-by-step explanation:
You’d be adding 5,-0.5 to the respective coordinates. Point F’ is located at -1,-1 so you’d be adding 5 to -1 for the x coordinate and -0.5 to -1 for the y coordinate.
The value of sales at a shop decreases from £145000 a year to £129000. Find the percentage decrease in the values of sales.
Answer:
Percentage of decrease in Sales = 11.04% or 11 %
Step-by-step explanation:
Decrease Percentage = [(Original Value - New Value) ÷ Original Value] × 100
Percentage = [(145,000 - 129,000) ÷ 145,000] × 100
Percentage = [(16,000) ÷ 145,000] × 100
Percentage = (0.1104) × 100
Percentage of decrease in Sales = 11.04% or 11 %
16.8 cm
Circle circumference
Answer: 5.2752
Step-by-step explanation: multiply 16.8 by pie 3.14 then you have the answerA study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues. If 6 college freshmen are randomly selected, find the probability that fewer than 4 support increased spending on environmental issues.
Answer:
13.18% or 0.1318
Step-by-step explanation:
please see the attached files for explanation
Justin did push-ups every weekday this week. He did 888 push-ups on Monday, 14 push-ups on Tuesday, 18 push-ups on Wednesday, 6 push-ups on Thursday, and 8 push-ups on Friday.
Find the mean number of push-ups.
Final answer:
To calculate the mean number of push-ups Justin did each weekday, add up the total push-ups for the week and divide by 5. Justin did a mean of 186.8 push-ups per day.
Explanation:
To find the mean number of push-ups Justin did each weekday, we need to add the number of push-ups he did each day and then divide by the number of days. The steps are:
Add the number of push-ups from Monday to Friday: 888 + 14 + 18 + 6 + 8.Calculate the sum: 888 + 14 + 18 + 6 + 8 = 934 push-ups.Divide the sum by the number of days (5 weekdays): 934 ÷ 5.Calculate the mean: 934 ÷ 5 = 186.8 push-ups.Therefore, the mean number of push-ups Justin did on a weekday is 186.8 push-ups.
Final answer:
The mean number of push-ups Justin did each weekday is calculated by adding the total push-ups for all the days and dividing by the number of days, resulting in 186.8 push-ups.
Explanation:
To find the mean number of push-ups, Justin did over the weekdays, you need to sum up the total push-ups and then divide by the number of days.
Add the number of push-ups for each day: 888 (Monday) + 14 (Tuesday) + 18 (Wednesday) + 6 (Thursday) + 8 (Friday) = 934 push-ups in total.
Divide the total number of push-ups by the number of days: 934 ÷ 5 days = 186.8 push-ups.
Therefore, the mean number of push-ups Justin did each weekday is 186.8 push-ups.
Allison owns a trucking company. For every truck that goes out, Allison must pay the driver $11 per hour of driving and also has an expense of $1 per mile driven for gas and maintenance. On one particular day, the driver drove an average of 15 miles per hour and Allison's total expenses for the driver, gas and truck maintenance were $286. Write a system of equations that could be used to determine the number of hours the driver worked and the number of miles the truck drove. Define the variables that you use to write the system.
Answer:
y = 15x
11x + y = 286
where
y = number of miles driven by the truck driver
x = number of hours the truck driver drives
Solving this gives, x = 11 hours and y = 165 miles.
Step-by-step explanation:
Let the number of hours the truck driver drives be x.
Let the number of miles driven by the truck driver be y.
Since the truck driver drives at 15 miles per hour, the number of miles covered by the driver y, can be given from the speed equation.
Speed = (distance/time)
15 = (y/x)
y = 15x.
And the drivers are paid $11 per hour of driving and also has an expense of $1 per mile driven for gas and maintenance.
Meaning that on a day that the truck driver drives y miles for x hours, the total pay, C, is given as
C = 11x + 1y = 11x + y
So, on this fateful day, the total amount paid to a truck driver was $286
So, C = $286
11x + y = 286.
So, the two equations for the scenarios are
y = 15x
11x + y = 286
Solving this gives, x = 11 hours and y = 165 miles.
Hope this Helps!!!
The system of a linear equation that could be used to determine the number of hours the driver worked and the number of miles the truck drove is : (11x + y = 286) and (y = 15x).
Given :
Allison owns a trucking company. For every truck that goes out, Allison must pay the driver $11 per hour of driving and also has an expense of $1 per mile driven for gas and maintenance. On one particular day, the driver drove an average of 15 miles per hour, and Allison's total expenses for the driver, gas, and truck maintenance were $286.The following steps can be used in order to determine the system of linear equations:
Step 1 - Let the total number of miles be 'x' and the total number of hours be 'y'.
Step 2 - The linear equation that represents the total expenses for the driver, gas, and truck maintenance is given by:
11x + y = 286
Step 3 - The linear equation that represents the situation that the driver drove an average of 15 miles per hour is given by:
y = 15x
So, the system of a linear equation that could be used to determine the number of hours the driver worked and the number of miles the truck drove is : (11x + y = 286) and (y = 15x).
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In a right triangle ABC AB = 2cm BC =5cm and CA = square root of 29. what is angle A round to the nearest tenth
Answer:
68.2°
Step-by-step explanation:
AC is the longest side which means 90° is at B
SinA = BC/AC
sinA = 5/sqrt(29)
sinA = 0.9284766909
A = 68.19859051
A = 68.2°
To find the measure of angle A, we used the tangent function, which is the ratio of the side opposite the angle to the side adjacent to it. Using a calculator, the inverse tangent of the ratio BC/AB equals approximately 68.2 degrees.
Explanation:In order to solve for angle A in a right triangle, we can use the concept of trigonometry. Specifically, we'll use the tangent (tan) function, which in a right triangle is the ratio of the side opposite the angle to the side adjacent to it. Since angle A is between sides AB and AC, the tangent of A would be defined as tan(A) = opposite side/adjacent side = BC/AB = 5/2.
After calculating the ratio, typically, we would use a calculator to find the arctan or inverse tangent of this ratio, which should give the angle A in degrees. In this case, the arctan(5/2) equals about 68.2 degrees when rounded to the nearest tenth.
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please help!! 20 points!
Answer: First choice
Sq rt of 3 X sq rt of 2 = sq rt of 6 which is irrational
Sq rt of 12 and sq rt of 3 = sq rt of 36 which = 6 rational
Sq rt of 5 plus sq rt of 2 is irrational
Sq rat of 9 plus sq rt of 4 is 3+2=5 rational
Step-by-step explanation:
What is the maximum number of times a line can cross the X axis
The line y = 0 will be having an infinite number of x-intercepts thus a line can cross the x-axis infinite times.
What is a line segment?A line section that can connect two places is referred to as a segment.
The line extends endlessly in both directions.
A line segment is just part of a big line that is straight and going unlimited in both directions.
If two lines intersect each other at a point then the number of intersections will be only one,
It is because the line away from the intersection goes away with the line.
But if two lines are on each other having an infinite number of intersections.
For example the intersection of line y = 0 with the x-axis.
Hence "The line y = 0 will be having an infinite number of x-intercepts thus a line can cross the x-axis infinite times".
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Tikiro places a wrench on a nut and applies a downward force of 32 pounds to tighten the nut. If the center of the nut is at the origin, the force is applied at the point (.65,0,0.3) Find the torque. a. 18.4 ft-lb c. 21.2 ft-lb b. 20.8 ft-lb d. 22.1 ft-lb
Answer:
Answer: b. 20.8 ft-lb
Step-by-step explanation:
Solve the equation: 4m - 7 = - 19
Answer:
m = - 3
Step-by-step explanation:
- 19 + 7 = -12
- 12 ÷ 4 = -3
For the given function, determine consecutive values of x between which each real zero is located.
f(x)= -11x^4 -3x^3 -10x^2+9x+18
a.
There is a zero between x = 0 and x = 1.
b.
There is a zero between x = 0 and x = –1.
c.
There are zeros between x = 2 and x = 3, x = 1 and x = 0, x = –1 and x = –2, x = –1 and x = –2, x = –2 and x = –3.
d.
There are zeros between x = 1 and x = 2, x = 0 and x = –1.
Answer:
D. There are zeros between x = 1 and x = 2, x = 0 and x = –1.
Step-by-step explanation:
A zero point is inside an interval where value of y changes from positive to negative or viceversa. The curve is evaluated in the given points hereafter:
f(-3) = - 909, f(-2) = -192, f(-1) = -9,f(0) = 18, f(1) = 3, f(2) = -204, f(3) = -1017
There two zero, one between x = -1 and x = 0 and other between x = 1 and x = 2. Hence, the answer is D.
When she woke in the morning Josie notices the temperature outside was -4.8*c. When she got home from school the temperature rose 15.6*c. What was the change in the temperature
Answer:
20.4°C
Step-by-step explanation:
Initial temperature 't1'= -4.8°C
Final temperature 't2'= 15.6°C
In order to find change in temperature, take the difference of above two temperatures. So,
Change in temperature 'ΔT' = t2 - t1
ΔT= 15.6 - (-4.8)
ΔT= 20.4 °C
Therefore, the change in temperature was 20.4°C
Consider the data set
8 9 5 1 3 19 6
Find the average (mean):
Answer: [tex]7.29[/tex]
Order the numbers
[tex]Before: 8,9,5,1,3,19,6\\After: 1, 3, 5, 6, 8, 9, 19[/tex]
Add
[tex]1+3+5+6+8+9+19=51[/tex]
Divide
[tex]51/7=7.28571428571[/tex]
Round
[tex]7.28571428571=7.29[/tex]
Final Answer
[tex]7.29[/tex]
3 3/4 divided by 5/7
Answer:
[tex]\frac{21}{4}[/tex]
Step-by-step explanation:
So to start, you need to make 3 [tex]\frac{3}{4\\}[/tex] into an improper fraction, which will give you [tex]\frac{15}{4}[/tex]. Then to make it easier, instead of dividing it by [tex]\frac{5}{7}[/tex], multiply it by the reciprocal ( [tex]\frac{7}{5}[/tex] )
Your new expression should look like this:
[tex]\frac{15}{4}[/tex] x [tex]\frac{7}{5}[/tex]
To make it even easier, you can simplify this expression even further. Looking at the numerators and denominators, we see that we have a 15 on top and a 5 on the bottom. Cross out the 5 and put a 1 in its place since 5 goes into 5 one time! Now we have to do it to the 15... Cross out the 15 and put a 3 since 5 goes into 15 three times!
Your simplified expression should look like this:
[tex]\frac{3}{4}[/tex] x [tex]\frac{7}{1}[/tex]
Now, just multiply the numerators and the denominators to get your final answer of
[tex]\frac{21}{4}[/tex]
Since you cannot simplify this anymore, that is your answer!!!
Answer:
3/28
Step-by-step explanation:
The graph shows the distance a ball has traveled x seconds after it was thrown. What is the average speed between 2 seconds and 8 seconds.
Answer:
0.5 meters per second
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
the first one
what is the difference between 3/5 and 3/10
Well, whenever you are working with fractions with different denominators, you would multiply both the top and the bottom of the fraction with the smaller number as the denominator. (You could also divide the larger denominator number.) So let's see what number we can multiply by 5 to get 10. That would be 2. Then we would multiply the numerator by two as well. So what is 3 times 2? 6. Once you've done that, you get 6/10 or 0.6 in decimal form. The difference would be 0.3 or 3/10. :)
How to find the direct variation of x=2, y=8
Answer:
y = 4x
Step-by-step explanation:
Given that y and x vary directly then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition that x = 2, y = 8
8 = 2k ( divide both sides by 2 )
4 = k, thus
y = 4x ← equation of variation
The hypotenuse of a right triangle is 26 mm. One leg of the right triangle is 10 mm. What is the length of the other leg? 80 mm 20 mm 24 mm 28 mm
Answer:
Step-by-step explanation:
10^2 + b^2 = 26^2
100 + b^2 = 676
-100 -100
b^2 = 576
square root of b equals b
square root of 576 equals 24
The other leg equals 24
Answer:
24mm
Step-by-step explanation:
Using Pythagoreans Theorem, a^2+b^2=c^2
a^2+10^2=26^2
a^2+100=676
a^2=576
a= sqrt 576
a=24mm
Wind power P from a turbine varies directly as the square of the length r of one ofits blades. Two common blade lengths for commercial wind turbines are 35m and 50m. When the blade length is 35m about 1.5 megawatt of power is produced under favorable conditions. How much power would be produced, under favorable conditions, by a turbine with 50m blades.
Answer:
3.06 megawatts
Step-by-step explanation:
Firstly, we write the proportionality equation.
wind power varies directly as the square of the length r of one of the blades;
P ∝ r^2
Let’s introduce a constant of proportionality k; This means;
P = kr^2
Now let’s calculate the value of k when 1.5 megawatts and r is 35m
1.5 mw = 35^2 * k
k = 1.5/35^2 = 1.5/1225 = 0.001224489796 MW/m^2
Now we want to calculate the amount of megawatts to be produced by a turbine with 50m blades.
That would be;
P = 0.001224489796 * 50^2 = 3.06 megawatts
Answer:
Step-by-step explanation:
If two variables are directly proportional, it means that an increase in the value of one variable would cause a corresponding increase in the other variable. Also, a decrease in the value of one variable would cause a corresponding decrease in the other variable.
Given that P varies directly with r², if we introduce a constant of proportionality, k, the expression becomes
P = kr²
If P = 1.5 when r = 35, then
1.5 = k × 35²
k = 1.5/35² = 1.5/1225
Therefore, the direct variation function is
P = 1.5r²/1225
When r = 50, then
P = 1.5 × 50²/1225
P = 3.06 megawatt
How do I write this in radical form with steps and the final answer please
Answer:
6 * [tex]\sqrt[3]{x}[/tex]
Step-by-step explanation:
6 x^1/3
The 1 means inside to the power of 1 and the 3 means to the cubed root
6 * [tex]\sqrt[3]{x}[/tex]
How do you graph
Y=x^2-4x+3
Answer:
Answer is below
Step-by-step explanation:
Use 3 as the y-intercept. Factor the equation to find the solutions
(x - 1) (x - 3) so 1 and 3 are the x-intercepts. The vertex of the graph is at (2,-1).
I also graphed the equation below.
If this answer is correct, please make me Brainliest!
The graph of [tex]y = x^2 - 4x + 3[/tex] is a parabola that opens upward with its vertex at (2, -1). It intersects the x-axis at x = 3 and x = 1 and the y-axis at y = 3.
How to graph this equationThe equation is [tex]y = x^2 - 4x + 3.[/tex]
Use the formula x = -b / (2a) to find the x-coordinate of the vertex. In this case, a = 1, b = -4.
x = -(-4) / (2*1)
= 4 / 2
= 2.
So, the x-coordinate of the vertex is 2.
Subtitute x = 2 into the equation:
[tex]y = (2)^2 - 4(2) + 3[/tex]
= 4 - 8 + 3
= -1.
The y-coordinate of the vertex is -1.
The vertex is at (2, -1).
The y-intercept, we will set x = 0 in the equation:
[tex]y = (0)^2 - 4(0) + 3[/tex]
= 0 - 0 + 3
= 3.
The get x-intercepts, we set y = 0 in the equation:
[tex]0 = x^2 - 4x + 3.[/tex]
(x - 3)(x - 1) = 0.
x = 3 or x = 1.
The x-intercepts are 3 and 1.
Now, we will plot the y-intercept and x-intercepts. The y-intercept is at (0, 3), and the x-intercepts are at (3, 0) and (1, 0).
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John works as a tutor for an hour and as a waiter for an hour. This month, he worked a combined total of hours at his two jobs. Let be the number of hours John worked as a tutor this month. Write an expression for the combined total dollar amount he earned this month.
Correct Question:
John works as a tutor for $12 an hour and as a waiter for $8 an hour. This month, he worked a combined total of 86 hours at his two jobs.
Let be the number of hours John worked as a tutor this month. Write an expression for the combined total dollar amount he earned this month.
Answer:
Total hours = 86
Let t is the hours he spent on tutoring
then (86-t) is hours spent on waiting
Let Y is the total amount in dollars which is required .
Now;
y = (tutoring hours x 12$) + (waiting hours x 8$)
Y = 12t + 8(86-t)
What’s 2 plus 2 plus 3 plus 5 plus 7
Answer:
The answer is 19
Step-by-step explanation:
2 + 2 = 4
3 + 5 = 8
4 + 8 = 12
12 + 7 = 19
Suppose that the revenue function for a certain product is given by R(x) = 17(2x + 1)−1 + 34x − 17 where x is in thousands of units and R is in thousands of dollars. (a) Find the marginal revenue (in thousands of dollars) when 2000 units are sold. $ 34 Incorrect: Your answer is incorrect. thousand (b) How does the revenue change when 2000 units are sold?
Answer:
Step-by-step explanation:
Given that:
R(x) = [tex]\frac{17}{2x+1}[/tex] + 34x − 17
As we know that derivative of revenue function is marginal revenue function .
We will use following rules of derivative
=> dR/ dx = [tex]\frac{-17*2}{(2x+1)^{2} } + 34[/tex]
=> R' (x) = [tex]\frac{-34}{(2x+1)^{2} } + 34[/tex]
=> R '(2000) = [tex]\frac{-34}{(2*2000+1)^{2} } + 34[/tex] = 34
The revenue when 2000 units are sold is:
R(2000) = [tex]\frac{17}{2*2000+1}[/tex] + 34*2000 − 17 = $69,783
The marginal revenue be "34" and revenue change be "$69,783".
Marginal revenue:The increase throughout income caused by the acquisition of one more unit of production, is a Marginal revenue. Although marginal income can stay unchanged at a predetermined interval, it's indeed subject to the regulations of decreasing returns as well as will ultimately slow as outcome level grows.
According to the question,
Revenue function,
R(x) = [tex]\frac{17}{2x+1}[/tex] + 34x - 17
Units sold = 2000
(a) The marginal revenue be:
→ [tex]\frac{dR}{dx}[/tex] = [tex]-\frac{17\times 2}{(2x+1)^2}[/tex] + 34
R'(x) = [tex]- \frac{34}{(2x+1)^2}[/tex] + 34
By substituting "x = 2000",
R'(2000) = [tex]- \frac{34}{(2\times 2000+1)^2}[/tex] + 34
= 34
(b) The revenue change be:
→ R(2000) = [tex]\frac{17}{2\times 2000+1}[/tex] + 34 × 2000 - 17
= 69,783 ($)
Thus the above response is appropriate.
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One digit in each of these identification numbers of a postal money order is smudged. Can you recover the smudged digit, indicated by a Q, in each of these numbers? a) 493212Q0688 b) 850Q9103858 c) 2Q941007734 d) 66687Q03201
Answer:
a) Q = 0 or 9
b) Q = 5
c) Q = 7
d) Q = 8
Step-by-step explanation:
We assume the postal money order to be of the United State. A smudged digit is calculated using the following algorithm.
1. Add first 10 digits of 11-digit number.
2. Divide the sum of the 10 numbers by 9.
3.The remainder is the smudged digit.
4.The smudged digit is appended to the end of the ID number or anywhere in the number.
It is calculated as:
[tex]x_{11} = (x_{1} + x_{2} + x_{3} + x_{4} + x_{5} + x_{6} + x_{7} + x_{8} + x_{9} + x_{10} )mod 9[/tex]
a) 493212Q0688
[tex]8 = (4 + 9 + 3 + 2 + 1 + 2 + Q + 0 + 6 + 8) mod 9\\8 = (Q + 35) mod 9\\8 = Q mod 9 + 35 mod 9\\8 = Q mod 9 + 8\\Q mod 9 = 8 - 8\\Q mod 9 = 0\\Q = 0 or 9[/tex]
Therefore, Q is either 0 or 9.
b) 850Q9103858
[tex]8 = (8 + 5 + 0 + Q + 9 + 1 + 0 + 3 + 8 + 5) mod 9\\8 = (Q + 39) mod 9\\8 = Q mod 9 + 39 mod 9\\8 = Q mod 9 + 3\\Q mod 9 = 8 - 3\\Q mod 9 = 5\\Q = 5[/tex]
Therefore, Q is 5 because from Q mod 9 = 5, we have Q = 5 mod 9.
c) 2Q941007734
[tex]4 = (2 + Q + 9 + 4 + 1 + 0 + 0 + 7 + 7 + 3) mod 9\\4 = (Q + 33) mod 9\\4 = Q mod 9 + 33 mod 9\\4 = Q mod 9 + 6\\Q mod 9 = 4 - 6\\Q mod 9 = -2\\Q = -2 mod 9\\Q = 7[/tex]
Therefore, Q is 7 because we have to cancel out the negative sign by adding the modulo base (9) to the negative number: -2 + 9 = 7.
d) 66687Q03201
[tex]1 = (6 + 6 + 6 + 8 + 7 + Q + 0 + 3 + 2 + 0) mod 9\\1 = (Q + 38) mod 9\\1 = Q mod 9 + 38 mod 9\\1 = Q mod 9 + 2\\Q mod 9 = 1 - 2\\Q mod 9 = -1\\Q = -1 mod 9\\Q = 8[/tex]
Therefore, Q is 8 because we have to cancel out the negative sign by adding the modulo base (9) to the negative number: -1 + 9 = 8.
For the given postal money order scenarios, the smudged digit, Q, is determined as follows: Scenario a - either 0 or 9, Scenario b - 5, Scenario c - 5, and Scenario d - 3.
Let's analyze the given postal money order scenarios and determine the smudged digit, Q, using the provided algorithm:
Scenario a:
ID number: 493212Q0688
Sum of the first 10 digits: 4 + 9 + 3 + 2 + 1 + 2 + 0 + 6 + 8 + 8 = 43
43 divided by 9 equals 4 with a remainder of 7.
Therefore, the smudged digit, Q, is either 0 or 9.
Scenario b:
ID number: 850Q9103858
Sum of the first 10 digits: 8 + 5 + 0 + 9 + 1 + 0 + 3 + 8 + 5 + 8 = 47
47 divided by 9 equals 5 with a remainder of 2.
Therefore, the smudged digit, Q, is 5.
Scenario c:
ID number: 2Q941007734
Sum of the first 10 digits: 2 + 7 + 9 + 4 + 1 + 0 + 0 + 7 + 7 + 3 = 40
40 divided by 9 equals 4 with a remainder of 4.
To cancel out the negative sign in the remainder, we add the modulo base (9) to the negative number: -4 + 9 = 5.
Therefore, the smudged digit, Q, is 5.
Scenario d:
ID number: 66687Q03201
Sum of the first 10 digits: 6 + 6 + 6 + 8 + 7 + 0 + 3 + 2 + 0 + 1 = 33
33 divided by 9 equals 3 with a remainder of 6.
To cancel out the negative sign in the remainder, we add the modulo base (9) to the negative number: -6 + 9 = 3.
Therefore, the smudged digit, Q, is 3.
To learn more about digit
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A sample of bacteria is being eradicated by an experimental procedure. The population is following a pattern of exponential decay and approaching a population of 0. If the sample begins with 500 bacteria and after 11 minutes there are 200 bacteria, after how many minutes will there be 50 bacteria remaining? Round your answer to the nearest whole number, and do not include units. answer
Answer:
There will be 50 bacteria remaining after 28 minutes.
Step-by-step explanation:
The exponential decay equation is
[tex]N=N_0e^{-rt}[/tex]
N= Number of bacteria after t minutes.
[tex]N_0[/tex] = Initial number of bacteria when t=0.
r= Rate of decay per minute
t= time is in minute.
The sample begins with 500 bacteria and after 11 minutes there are 200 bacteria.
N=200
[tex]N_0[/tex] = 500
t=11 minutes
r=?
[tex]N=N_0e^{-rt}[/tex]
[tex]\therefore 200=500e^{-11r}[/tex]
[tex]\Rightarrow e^{-11r}=\frac{200}{500}[/tex]
Taking ln both sides
[tex]\Rightarrow ln| e^{-11r}|=ln|\frac{2}{5}|[/tex]
[tex]\Rightarrow {-11r}=ln|\frac{2}{5}|[/tex]
[tex]\Rightarrow r}=\frac{ln|\frac{2}{5}|}{-11}[/tex]
To find the time when there will be 50 bacteria remaining, we plug N=50, [tex]N_0[/tex]= 500 and [tex]r}=\frac{ln|\frac{2}{5}|}{-11}[/tex] in exponential decay equation.
[tex]50=500e^{-\frac{ln|\frac25|}{-11}.t}[/tex]
[tex]\Rightarrow \frac{50}{500}=e^{\frac{ln|\frac25|}{11}.t}[/tex]
Taking ln both sides
[tex]\Rightarrow ln|\frac{50}{500}|=ln|e^{\frac{ln|\frac25|}{11}.t}|[/tex]
[tex]\Rightarrow ln|\frac{1}{10}|={\frac{ln|\frac25|}{11}.t}[/tex]
[tex]\Rightarrow t= \frac{ln|\frac{1}{10}|}{\frac{ln|\frac25|}{11}.}[/tex]
[tex]\Rightarrow t= \frac{11\times ln|\frac{1}{10}|}{{ln|\frac25|}}[/tex]
[tex]\Rightarrow t\approx 28[/tex] minutes
There will be 50 bacteria remaining after 28 minutes.
Final answer:
To solve this problem, we use the formula for exponential decay and solve for the time when there are 50 bacteria remaining.
Explanation:
To solve this problem, we can use the formula for exponential decay: A = A0 * e^(kt), where A is the final population, A0 is the initial population, e is Euler's number (approximately 2.71828), k is the decay constant, and t is the time in minutes.
First, let's determine the value of k. We know that after 11 minutes, the population is 200 bacteria, so we can substitute these values into the formula to solve for k: 200 = 500 * e^(11k).
Divide both sides of the equation by 500: 0.4 = e^(11k).
Take the natural logarithm of both sides to solve for k: ln(0.4) = 11k.
Divide both sides by 11 to find the value of k: k ≈ -0.07761.
Now we can use the formula to solve for t when there are 50 bacteria remaining: 50 = 500 * e^(-0.07761t).
Divide both sides by 500: 0.1 = e^(-0.07761t).
Take the natural logarithm of both sides to solve for t: ln(0.1) = -0.07761t.
Divide both sides by -0.07761 to find the value of t: t ≈ 13.857 minutes.
Therefore, after approximately 14 minutes (rounded to the nearest whole number), there will be 50 bacteria remaining.
Scientists found an animal skull during an excavation and tested the amount of carbon-14 left in it. They found that 55 percent of the carbon-14 in the skull remained. How many years ago was the animal buried? Round your answer to nearest whole number. (Hint: A = A0e-0.000124t.)
A.
443,548 years
B.
362,903 years
C.
6,439 years
D.
4,821 years
help pls
Answer:
D. 4821 years
Step-by-step explanation:
A = A0e-0.000124t
A/A0 = e^-0.000124t
0.55 = e^-0.000124t
ln(0.55) = ln(e^-0.000124t)
ln(0.55) = -0.000124t × lne
t = ln(0.55)/-0.000124
4821.266135
25 POINTS PLS HELPPP WITH MATH
Answer:
1. 23.55 in
2. 102.36 mm
Step-by-step explanation:
The circumference of a circle is calculated by the formula: [tex]C=\pi d=2\pi r[/tex] , where d is the diameter and r is the radius.
We can use this to answer both problems.
1. Since the diameter is 7.5 inches, then d = 7.5. Substitute this into the equation: [tex]C=\pi *7.5=3.14*7.5=23.55[/tex]. So, the circumference is 23.55 inches.
2. Here, the radius is 16.3 mm, so r = 16.3. Substitute this into the equation: [tex]C=2\pi r=2*3.14*16.3=102.364=102.36[/tex]. So, the circumference is 102.36 mm.
Hope this helps!
Answer:
1) 23.55 inches
2) 102.36 mm
Step-by-step explanation:
C = pi × d
1) C = 3.14 × 7.5
= 23.55
C = 2 × pi × r
2) C = 2 × 3.14 × 16.3
= 102.364 mm