Hello its urgent i really need help its a math question! i will give brainlist thank you
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We know that we will eventually rotate it 180° about the origin due to the direction it’s facing. If we were to reflect it, the triangle would wind up either sideways or upside down unless we reflected it across both the x axis then the y axis. However, reflecting over both axises is the same as rotating 180° about the origin. Before we can rotate the triangle though, we need to translate it first. Let’s take point V at (2,2). If we first translate it up 1 and right 2, it maps to (4,3). If we then rotate it 180° about the origin, point V will map to (-4,-3), which is the correct point V”. Since we already determined that the orientation of the triangle is correct, we can assume the rest of the points will map correctly as well.
Related Questions
please help 14 points ASAP
Here are yesterday's high temperatures (in Fahrenheit) in 12 U.S. cities. 48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80 Notice that the temperatures are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median: Upper quartile:
Maximum:
Interquartile range:
Answers
The desired measures for the data-set is given by:
Minimum: 48Lower quartile: 54.Median: 63.5.Upper quartile: 74.Maximum: 80.IQR: 20How to find the five number summary and interquartile range of the data-set?The five number summary is composed by the measures explained below, except the IQR.
The minimum value is the smallest value from the data-set, as the maximum value is the greatest value of the data-set.The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.The interquartile range is the difference of the third quartile and the first quartile.In this problem, we have that:
The minimum value is the smallest value, of 48.The maximum value is the smallest value, of 80.The data-set has even cardinality, hence the median is the mean of the middle elements, which are 63 and 64, hence the median is of 63.5.The first quartile is the median of the five elements of the first half, hence it is of 54.The third quartile is the median of the five elements of the second half, hence it is of 74.The IQR is the difference between the quartiles, hence 74 - 54 = 20.More can be learned about five number summaries at brainly.com/question/17110151
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pls help me urgent pls help me
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The answers to the questions are:
43.22 minutes15 km/hr6 km0.37 = 37/1000.086 = 86/1000What is distance?This defined as the total number of points that a person has been able to cover at a given period. It is calculated by taking the time and the speed of takeoff into consideration. The speed that a person used and the time it took them to get to their destination is what is used to calculate distance
The time it takes for sunlight to reach is given as
distance/speed
778000000000/300000000
=2593.33 * 60
= 43.22 minutes
The formula for distance is given as speed * time
speed = 15km/hr
time = 1 hour
The distance = 15 * 1
= 15 km/hr
If the time is 2*1/2
the distance = 15 / 2.5
= 6 km
Expressed as a fraction we have the following
0.37 = 37/100
0.086 = 86/1000
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What is 6x^2 + 4(x^2 - 1)? Like terms.
Answers
The value of x for the given equation is 0.632 and -0.632.
According to the statement
We have given that the equation and we have to a find the value of the x.
So, The given quadratic equation are:
Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power solve for x in the quadratic equation
The given terms are
[tex]6x^2 + 4(x^2 - 1) = 0[/tex]
Solving the equation the the outcome equation is
[tex]6x^2 + 4x^2 - 4 = 0\\10x^2 - 4 = 0\\10x^2 = 4\\x^2 = 4/10[/tex]
The value of x is 0.632 and -0.632.
So, The value of x for the given equation is 0.632 and -0.632.
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i need the answer for number 13
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Answer:
The answer is 1. This table is an example of the principle of independence.
Step-by-step explanation:
This means any Trade activity is performed without reliance on another party.
He got the perfect answer to his question and he can get his answer without any other information.
What is the product?
StartFraction 4 n Over 4 n minus 4 EndFraction times StartFraction n minus 1 Over n + 1 EndFractiontartFraction 2 Over x EndFraction
Answers
Based on the given task content; the product of StartFraction 4 n Over 4 n minus 4 EndFraction times StartFraction n minus 1 Over n + 1 EndFractiontartFraction 2 Over x EndFraction is (4n² - 8n) / (4n²x - 5nx - x)
ProductProduct of numbers refers to the multiplication of two or more values to arrive at a single result.
4n / (4n - 1) × (n - 1) / (n + 1) 2/x
= 4n / (4n - 1) × 2(n - 1) / x(n + 1)
= 4n / (4n - 1) × (2n - 2) / (nx + x)
= 4n(2n - 2) / (4n - 1) (nx + x)
= 4n² - 8n / (4n²x - 4nx - nx - x)
= (4n² - 8n) / (4n²x - 5nx - x)
Therefore, the product of 4n / (4n - 1) × (n - 1) / (n + 1) 2/x is (4n² - 8n) / (4n²x - 5nx - x)
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Machine a can make 350 widgets in 1 hour, and machine b can make 250 widgets in 1 hour. if both machines work together, how much time will it take them to make a total of 1000 widgets?
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If machine a can make 350 widgets in 1 hour and machine b can make 250 widgets in 1 hour then by forming equation we will get that both machines have to work for one hour and 40 minutes to make 1000 widgets.
Given that machine a can make 350 widgets in 1 hour, and machine b can make 250 widgets in 1 hour.
How much time will both machines take to make 1000 widgets?
Suppose the time taken by both machines be x hours. Time is equal because both the machines need to work together.
According to the question the equation will be as under:
350x+250x=1000
600x=1000
x=1000/600
x=10/6
x=5/3
x=1.67
Converting 0.67 to minutes 0.67*60=40.2
Adding will result 1 hour and 40 minutes.
Hence if machine a can make 350 widgets in 1 hour and machine b can make 250 widgets in 1 hour then by forming equation we will get that both machines have to work for one hour and 40 minutes to make 1000 widgets.
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Consider this quadratic equation.
2x²2²-1=3x+4
Which equation correctly applies the quadratic formula?
COA
OB.
OC.
OD.
2=
H=
H=
-(-3) ± √(-3)²-4(2)(-5)
-(-3);
2
-(-3) ± √(-3)²-4(-5)
(2)
-(-3) ± √(-3)²(2)(-5)
(2)
-(-3) ± √(-3)²-4(2)(-5)
2(2)
Answers
Answer:
-(-3) ± √(-3)^2 - 4(2)(-5) / 2(2) (the last choice).
Step-by-step explanation:
Im ignoring the 2^2 in the equation
The equation transforms to
2x^2 - 3x - 5 = 0 (standard form)
So x = -(-3) ± √(-3)^2 - 4(2)(-5) / 2(2)
Evaluate the integral. 3 f(x) dx −4 where f(x) = 3 if −4 ≤ x ≤ 0 4 − x2 if 0 < x ≤ 3
Answers
It looks like you have
[tex]f(x) = \begin{cases} 3 & \text{if } -4 \le x \le 0 \\ 4 - x^2 & \text{if } 0 < x \le 3\end{cases}[/tex]
and the integral you want to compute is
[tex]\displaystyle \int_{-4}^3 f(x) \, dx[/tex]
Split the integral up at [tex]x=0[/tex]. Then
[tex]\displaystyle \int_{-4}^3 f(x) \, dx = \int_{-4}^0 f(x)\,dx + \int_0^3 f(x)\,dx \\\\ ~~~~~~~~~~~~ = \int_{-4}^0 3 \, dx + \int_0^3 (4 - x^2) \, dx \\\\ ~~~~~~~~~~~~ = 3(0 - (-4)) + \left(4\cdot3 - \frac{3^3}3\right) = \boxed{15}[/tex]
After evaluating the integral we get 15
Integral is the representation of the area of a region under a curve. We approximate the actual value of an integral by drawing rectangles. A definite integral of a function can be represented as the area of the region bounded by its graph of the given function between two points in the line.
Given,
f(x) = 3 if - 4 ≤ x ≤ 0
f(x) = 4 - [tex]x^{2}[/tex] if 0 < x ≤ 3
Then,
[tex]f(x) = \left \{ {{3} \atop {4-x^{2} }}[/tex]
We need to solve the integral -[tex]\int\limits^3_4 {f(x)} \, dx[/tex]
Elaborate the integral with x = 0
-[tex]\int\limits^3_4 {f(x)} \, dx[/tex]
= -[tex]\int\limits^0_4 {f(x)} \, dx + \int\limits^3_0 {f(x)} \, dx[/tex]
= -[tex]\int\limits^0_4 {3} \, dx + \int\limits^3_0 {4-x^{2} } \, dx[/tex]
= 3 ( 0 - (-4)) + (4.3 - [tex]\frac{3^{3} }{3}[/tex])
= 15
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Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle. y = 2 x , y = 2 x2 , x = 4
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The region enclosed by the given curves are integrated with respect to x and the area is 4.2724 square units.
In this question,
The curves are y = 2/x, y = 2/x^2, x = 4
The diagram below shows the region enclosed by the given curves.
From the diagram, the limit of x is from 1 to 4.
The given curves are integrated with respect to x and the area is calculated as
[tex]A=\int\limits^4_1 {\frac{2}{x} } \, dx -\int\limits^4_1 {\frac{2}{x^{2} } } \, dx[/tex]
⇒ [tex]A=2[\int\limits^4_1 {\frac{1}{x} } \, dx -\int\limits^4_1 {\frac{1}{x^{2} } } \, dx][/tex]
⇒ [tex]A=2[\int\limits^4_1( {\frac{1}{x} } - {\frac{1}{x^{2} } } )\, dx][/tex]
⇒ [tex]A=2[lnx-\frac{1}{x} ] \limits^4_1[/tex]
⇒ [tex]A=2[(ln4-\frac{1}{4} )-(ln1-\frac{1}{1} )][/tex]
⇒ A = 2[(1.3862-0.25) - (0-1)]
⇒ A = 2[1.1362 + 1]
⇒ A = 2[2.1362]
⇒ A = 4.2724 square units.
Hence we can conclude that the region enclosed by the given curves are integrated with respect to x and the area is 4.2724 square units.
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A positive five-digit integer is in the form ; where , and are each distinct digits. What is the greatest possible value of that is divisible by eleven
Answers
The the biggest 5 digit number based on the computation will be 87,978.
How to compute the value?The difference between the sum of the odd-numbered digits (1st, 3rd, 5th...) and the sum of the even-numbered digits (2nd, 4th...) is divisible by 11.
An example is that 34871903 is divisible by 11
3+8+1+0=12
4+7+9+3=23
23-12=11
Here, we want (b + b) - (a + c + a) to be divisible by 11.
2b - (2a + c) to be divisible by 11
ab,cba (using 7 and 8 and 9 since they biggest)
78 987 --> 2*8 - (2*7 + 9) = 16 - (14 + 9) = 16 - 23 = -7 NO
87 978 --> 2*7 - (2*8 + 9) = 14 - (16 + 9) = 14 - 25 = -11 YES
79 897 --> 2*9 - (2*7 + 8) = 18 - (14 + 8) = 18 - 22 = -4 NO
97 879 --> 2*7 - (2*9 + 8) = 14 - (18 + 8) = 14 - 26 = -12 NO
89 798 --> 2*9 - (2*8 + 7) = 18 - (16 + 7) = 18 - 23 = -5 NO
98 789 --> 2*8 - (2*9 + 7) = 16 - (18 + 7) = 16 - 25 = -9 NO
Therefore, the biggest 5 digit number is 87,978.
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Select the correct answer.
Find the inverse of function f.
f(c) = 9x + 7
Answers
Answer:
B.) f⁻¹(x) = (1/9)x - 7/9
Step-by-step explanation:
Remember, f(x) is another way of writing "y". The inverse can be found by swapping the positions if the "x" and "y" variables and then solving to isolate the "y" variable.
f(x) = 9x + 7 <----- Original function
y = 9x + 7 <----- Substitute f(x) for "y"
x = 9y + 7 <----- Swap variable positions
x - 7 = 9y <----- Subtract 7 from both sides
(x - 7) / 9 = y <----- Divide both sides by 9
(1/9)x - 7/9 = y <----- Divide each term individually by 9
The inverse function is represented by the symbol f⁻¹(x).
what do I check off
Answers
Reason.
364 ____ 225
A = not equal sign
E = greater than or equal to sign
F = greater than sign
The population of a certain city can be modeled by the exponential * 1 poi
function below, where x represents the number of years since 2010. The graph for the function is also shown below. Which of the following statements are true? SELECT ALL THAT APPLY. I need help now please
Answers
The true statements about the functions are:
b. The population of the city in 2010 is 25000c. The rate at which the population decreases every year is 4% f. The function value would approach 0 as it decreasesHow to determine the true statement?The function is given as:
f(x) = 25000 * 0.96^x
Set x = 0 to determine the initial value of the function
f(0) = 25000 * 0.96^0
Evaluate
f(0) = 25000
This means that the population of the city in 2010 is 25000 i.e. option (B) is correct
Also, we have:
f(x) = 25000 * 0.96^x
The rate at which the population decreases every year is calculated as:
r = 1 - 0.96
Evaluate the difference
r = 0.04
Express as percentage
r = 4%
This means that the rate at which the population decreases every year is 4% i.e. option (C) is correct
The population after 5 and 10 years are:
f(5) = 25000 * 0.96^5
f(5) = 20384
f(10) = 25000 * 0.96^10
f(10) = 16621
Divide these populations by the initial population in 2010
20384/25000 = 82%
16621/25000 = 66%
This means that the population decreased by 82% and 66% in 5 years and 10 years since 2010, respectively.
So, options (d) and (e) are false
Lastly, because the population function is an exponential decay function;
The function value would approach 0 as it decreases
This means that option (f) is correct
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A circle is shown. Angle Q R S is 84 degrees.
What is the measure of Arc Q S?
°
Answers
In the given diagram, the measure of arc QS is 168°
Calculating measure of an arcFrom the question, we are to determine the measure of arc QS
The measure of the arc is the angle subtended by the arc at the center of the circle.
From one of the circle theorems, we have that
The angle subtended by an arc of a circle at its center is twice the angle it subtends anywhere on the circle's circumference
In the given diagram,
The angle subtended by arc at the circumference of the circle = 84°
∴ The angle subtended by the arc QS at the center = 2 × 84°
The angle subtended by the arc QS at the center = 168°
Hence, in the given diagram, the measure of arc QS is 168°
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Answer: 168°
Step-by-step explanation: TRUST ME!!! Answer is correct in Edge! :)
PLS HELP, WLL GIVE BRAINLEST, AND DONATE POINTS, PLEASE HELP ASAP!!!!!! ALSO GIVING 30 POINTS
Answers
The answer is J.
The probability of spinning B on Spinner 1 is equal to the ratio of number of B to the total number of letter spaces.
2/81/4The probability of spinning 1 on Spinner 2 is equal to the ratio of number of 1 to the total number of number spaces.
2/61/3The probability is equal to :
1/4 × 1/31/12Answer:
J [tex]\frac{1}{12}[/tex]
Step-by-step explanation:
• First, let's find the probability of landing a letter B in Spinner 1.
We have a total of eight possibilities, and two of them are the letter B.
∴ [tex]P(B) = \frac{2}{8}[/tex]
= [tex]\bf \frac{1}{4}[/tex]
• Next, let's find the the probability of landing the number 1 on Spinner 2.
There are a total of six possibilities, and two of them are the number 1.
∴ [tex]P(1) = \frac{2}{6}[/tex]
= [tex]\bf \frac{1}{3}[/tex]
• Now we have to calculate the probability of spinning a letter B and the number 1:
[tex]P(B \space\ and\space\ 1) = \frac{1}{4} \times \frac{1}{3}[/tex]
= [tex]\bf \frac{1}{12}[/tex]
I will give you 10 pts if you teach me
Answers
Answer:
time required = 26 min
Step-by-step explanation:
To solve this, let's first list all the given information, and change the units to millimeters (mm) if required (because the discharge rate is given in mm/s):
○ diameter of pipe = 64 mm ⇒ radius = 32 mm
○ water discharge rate = 2.05 mm/s
○ diameter of tank = 7.6 cm = 76 mm ⇒ radius = 38 mm
○ height of tank = 2.3 m = 2300 mm.
Now, let's calculate the cross-sectional area of the pipe:
Area = πr²
⇒ π × (32 mm)²
⇒ 1024π mm²
Next, we have to calculate the volume of water transferred from the pipe to the tank per second. To do that, we have to multiply the pipe's cross-sectional area and the discharge rate of the water:
Volume transferred = 1024π mm² × 2.05 mm/s
⇒ 6594.83 mm³/s
Now. let's find the volume of the cylindrical tank using the formula:
Volume = π × r² × h
⇒ π × (38)² × 2300
⇒ 10433857 mm³
We know that 6594.83 mm³ of water is transferred to the tank every second, so to fill up 10433857 mm³ with water,
time required = [tex]\frac{10433857 \space\ mm^3}{6594.83\space\ mm^3/s}[/tex]
⇒ 1582.12 s
⇒ 1582.13 ÷ 60
≅ 26 min
Answer:
26 minutes
Step-by-step explanation:
The rate of filling the tank matches the rate of discharge from the pipe. Each rate is the ratio of volume to time. Volume is jointly proportional to the square of the diameter and the height.
VolumeFor some constant of proportionality k, the volume of discharge in 60 seconds from the pipe is ...
V = k·d²·h . . . . d = diameter; h = rate×time
V = k(0.64 dm)²(0.0205 dm/s × 60 s) = k·0.503808 dm³
For the tank, the height (h) is the actual height of the tank. The volume of the tank is ...
V = k(0.76 dm)²(23 dm) = k·13.2848 dm³
ProportionThen the proportion involving (inverse) rates is ...
time/volume = (fill time)/(k·13.2848 dm³) = (1 min)/(k·0.503808 dm³)
fill time = 13.2848/0.503808 min ≈ 26.369
__
Additional comments
1 dm = 100 mm = 10 cm = 0.1 m
1 dm³ = 1 liter, though we don't actually need to know that here.
We have used 1 decimeter (dm) as the length unit to keep the numbers in a reasonable range. We have worked out the rate numbers, but that isn't really necessary (see attached).
__
The value of k is π/4 ≈ 0.785398. We don't need to know that because the values of k cancel when we solve the proportion.
x-1/x-2+x+3/x-4=2/(x-2).(4-x)
Answers
The given equation x-1/x-2+x+3/x-4=2/(x-2).(4-x) is correct. the answer is proved.
According to the statement
we have given that the equation and we have to prove that the given answer is a correct answer for those equivalent equation.
So, The given expression are:
[tex]\frac{x-1}{x-2} +\frac{x+3}{x-4} = \frac{2}{(x-2).(4-x)}[/tex]
And we have to prove the answer.
So, For this
[tex]\frac{x-1}{x-2} +\frac{x+3}{x-4}[/tex]
[tex]\frac{({x-1}) ({x-4}) +({x+3})({x-2})} {(x-2) (x-4)}[/tex]
Then the equation become
[tex]\frac{x^{2} -4x -x +4 + x^{2} -2x + 3x -6 }{(x-2) (x-4)}[/tex]
Now solve it then
[tex]2x^{2} - 4x -2 / (x-2) (x-4)[/tex]
Now take 2 common from answer then equation become
[tex]\frac{x-1}{x-2} +\frac{x+3}{x-4} = \frac{2}{(x-2).(4-x)}[/tex]
Hence proved.
So, The given equation x-1/x-2+x+3/x-4=2/(x-2).(4-x) is correct. the answer is proved.
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If a2 = i, where i is the identity matrix, which matrix correctly represents matrix a?
Answers
[tex]A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]
We can find the A as shown below:
Given A^2=I
We know that A^2=A×A
And [tex]I=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]
So, [tex]A^2=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]
Let [tex]A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]
[tex]A^2=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right] \left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]
[tex]A^2=\left[\begin{array}{ccc}9-8&-6+6\\12-12&-8+9\end{array}\right][/tex]
[tex]A^2=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]
Hence, [tex]A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]
Hence, option C is correct
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Disclaimer: Given question is incomplete. Complete question is attached.
Consider the line y equals 2 over 5 x plus 4.
Find the equation of the line that is parallel to this line and passes through the point left parenthesis 5 comma negative 1 right parenthesis.
Answers
the parallel linear equation is:
y = (2/5)*x - 3
How to find the parallel line?Two lines are parallel if the lines have the same slope but different y-intercept.
Here we know the line equation:
y = (2/5)*x + 4
Then a parallel line is of the form:
y = (2/5)*x + c
Where c is different than 4.
We want this line to pass through (5, -1), then:
-1 = (2/5)*5 + c
-1 = 2 + c
-1 - 2 = -3 = c
Then the parallel linear equation is:
y = (2/5)*x - 3
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The second highest point measured above sea level is the summit of
Kangchenjunga which is 8,586m above sea level and the lowest point is
challenger deep at the bottom of Mariana Trench which is 10,911 m below
the sea level. What is the vertical distance between these two points? Collect
some more information about these two points and present them withimages.
Answers
Answer:
19497 m
Step-by-step explanation:
The vertical distance between the given points is:
10911 + 8586 = 19497 mAnswer:
19,497m
Step-by-step explanation:
8,856-(-10,911)
=8856+10,911
=19,497m
Which inequality is represented by the graph below? Check all that apply. A number line going from 4 to 14. An open circle is at 9. Everything to the left of the circle is shaded. x greater-than 9 x less-than 9 any rational number greater than or including 9 any rational number less than or including 9 any rational number greater than 9 any rational number less than 9
Answers
the correct inequality is"any rational number less than 9"
x < 9
Which inequality is represented by the graph?Remember that when we have a number line, an open circle means that we can use the symbols > or <.
While a closed circle uses the symbols ≤ or ≥.
Here we know that we have an open circle at 9, ant everything to the left of the circle is shaded.
To the left of 9 there are the numbers smaller than 9, then the inequality would be:
x < 9
Then the correct option is "any rational number less than 9"
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Answer: x<9
any rational number less than 9"
Step-by-step explanation:
Draw a diagram to show that the square root of 121 is 11.
Answers
Answer:
i think this may help you
The diagram to show that the square root of 121 is 11 attached below
What is a perfect square?A perfect square is a number system that can be expressed as the
square of a given number from the same system.
Assume that x-a be the closest perfect square less than x,let x+b be the closest perfect square more than x, then we get: x-a < x < x+b (no perfect square in between x-a and x+b, except possibly x itself).
Then, we get:
[tex]\sqrt{x-a} < \sqrt{x} < \sqrt{x+b}[/tex]
Thus, [tex]\sqrt{x-a} and \sqrt{x+b}[/tex] are the closest integers, less than and more than the value of {x}. (assuming x is non-negative value).
Herewe are given the number as 121
It is perfect root then ;
√121 = 11
The solution that show that the square root of 121 is 11 attached below
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Solve the inequality 6 > x² - 5x.
Answers
Answer:
Step-by-step explanation:
6 > x² - 5x.
The answer for the inequality is -1 the greater than sign x greater than 6
The interval notation is ( -1,6)
Answer:
[tex]-1 < x < 6[/tex]
Step-by-step explanation:
Moving all terms to one side, we get [tex]x^2-5x-6 < 0[/tex]. Notice that we can factor the left side. Doing so, we get [tex](x-6)(x+1) < 0[/tex]. The zeroes in this equation are [tex]x-6=0 \Rightarrow x=6[/tex] and [tex]x+1=0\Rightarrow x=-1[/tex]. Now, we must create test points in the intervals: [tex]x < -1, -1 < x < 6, x > 6[/tex]. For example, we can choose [tex]x=-2,x=0,x=7[/tex]. For [tex]x=-2[/tex], we get that [tex](-2-6)(-2+1) = 8 < 0[/tex] is false, since the expression is positive. Doing the same thing for [tex]x=0[/tex] and [tex]x=7[/tex], we get that only [tex]x=0[/tex] creates a negative value. This means that the values in the interval [tex]\boxed{-1 < x < 6}[/tex] all work.
The table shows the temperature of a cooling cup of coffee.
Minutes 1 2 3 4
Temperature (degrees C) 97 95.1 93.2 91.3
What is the common ratio of the sequence? Express your answer as a decimal rounded to the nearest hundredth.
Write an explicit formula for the nth term of the sequence where n represents the number of minutes and T(n) represents the temperature of the coffee.
If the pattern continues, what will be the temperature of the coffee after 15 minutes? Express your answer as a decimal rounded to the nearest tenth.
Answers
Based on the given table, the common ratio, explicit formula and temperature of the coffee after 15 minutes is 0.98, Tn = 97 × 0.98^(n-1) and 73.1°C
Geometric sequenceCommon ratio, r = second minutes / first minutes
= 95.1 / 97
= 0.98041237113402
Approximately,
r = 0.98
nth term of the sequence, Tn = ar^n -1
Tn = 97 × 0.98^(n-1)
Temperature of the coffee after 15 minutes, T15 = 97 × 0.98^(n-1)
= 97 × 0.98^(15-1)
= 97 × 0.98^14
= 97 × 0.7536419414749019520643907584
= 73.1032683230654893502459035648
Approximately,
T15 = 73.1°C
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algebra Expression •x minus x
Answers
The answer is 0.
The expression in algebraic form is :
x - x0We know subtracting a term from its equivalent term will be 0.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation: }[/tex]
“[tex]\textsf{x minus x}[/tex]”
[tex]\huge\textbf{Simplifying it: }[/tex]
[tex]\textsf{x minus x}[/tex]
[tex]\mathsf{= x - x}[/tex]
[tex]\mathsf{= 1x - 1x}[/tex]
[tex]\mathsf{= 0x}[/tex]
[tex]\mathsf{= 0}[/tex]
[tex]\huge\textbf{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\frak 0}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Out of the total respondents, the percentage of respondents from the 46–55 age group who rated the film excellent is %. write your answer up to two decimal places.
Answers
Missing data:
Viewer's Age Group Excellent Good Average Poor Marginal Total
16–25 52 42 12 7 113
26–35 33 50 5 9 97
36–45 58 12 28 34 132
46–55 25 17 22 12 76
56 + 12 5 3 8 28
Marginal Total 180 126 70 70 446
A rating of good or excellent indicates the audience liked the movie, while a rating of poor indicates the audience disliked the movie.
How to determine the rating of the film from the 46–55 age group?A movie producer accomplished a survey behind a preview screening of her latest movie to estimate how the film would be accepted by viewers from various age groups. The table displays the numbers of viewers in various age groups who ranked the film excellent, good, average, and poor.
25/446 = 0.05605
0.05605 [tex]*[/tex] 100% = 5.605%
Out of the entire respondents, the percentage of respondents from the 46–55 age group who ranked the film excellent exists at 5.605%.
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If the first and the last term of an arithmetic progression, with common difference
[tex]1 \times 1\frac{1}{2} [/tex]
, are
[tex]? \times 2\frac{1}{2} [/tex]
and 19 respectively, how many term has the sequence?
Answers
The number of terms in the given arithmetic sequence is n = 10. Using the given first, last term, and the common difference of the arithmetic sequence, the required value is calculated.
What is the nth term of an arithmetic sequence?The general form of the nth term of an arithmetic sequence is
an = a1 + (n - 1)d
Where,
a1 - first term
n - number of terms in the sequence
d - the common difference
Calculation:The given sequence is an arithmetic sequence.
First term a1 = [tex]1\frac{1}{2}[/tex] = 3/2
Last term an = [tex]2\frac{1}{2}[/tex] = 5/2
Common difference d = 1/9
From the general formula,
an = a1 + (n - 1)d
On substituting,
5/2 = 3/2 + (n - 1)1/9
⇒ (n - 1)1/9 = 5/2 - 3/2
⇒ (n - 1)1/9 = 1
⇒ n - 1 = 9
⇒ n = 9 + 1
∴ n = 10
Thus, there are 10 terms in the given arithmetic sequence.
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Disclaimer: The given question in the portal is incorrect. Here is the correct question.
Question: If the first and the last term of an arithmetic progression with a common difference are [tex]1\frac{1}{2}[/tex], [tex]2\frac{1}{2}[/tex] and 1/9 respectively, how many terms has the sequence?
A candlemaker uses 240 cubic centimeters of wax to create a scented candle using a cylindrical mold. he decides to offer a larger-sized candle, which uses twice as much wax as the smaller-sized candle. which mold can he use to make the larger-sized candle?
Answers
The mold the candlemaker can use to make the larger-sized candle is 480 cubic centimeters.
CylinderA cylinder is a surface created by projecting a closed two-dimensional curve along an axis intersecting the plane of the curve.
smaller-sized candle = 240 cubic centimeterslarger-sized candle = 2(smaller-sized candle)
= 2(240 cubic centimeters)
= 480 cubic centimeters
Therefore, the mold the candlemaker can use to make the larger-sized candle is 480 cubic centimeters.
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Answer:
A cylinder with a height that is double the height of the original mold, and a radius that is the same as the radius of the original mold.
Hope this helps!
Step-by-step explanation:
Chris buys 4 more shirts than p number of pants. Shirts cost $18 each and pants cost $25 each. What does each term in the expression 25p+18(p+4) represent? What does the entire expression represent?
Answers
The expression 25p+18(p+4) represents the total amount spent on shirts and pants
How to interpret the terms of the expression?The given parameters are:
Shirts = 4 more than pants (p)
Cost of shirt = $18
Cost of pant = $25
The above means that:
p + 4 represents the number of shirts Chris buys, while p represents the number of pants
The terms of the expression 25p + 18(p+4) are
25p and 18(p+4)
This means that:
25p = The total cost of pants
18(p+4) = The total cost of shirts
Hence, the expression 25p+18(p+4) represents the total amount spent on shirts and pants
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which function describes this table of value x -8, -4, 4, 8, y -2, 0, 4, 6
Answers
we conclude that the linear equation represented by the given table is:
y = (1/2)*x + 2
Which function is the one described by the table?A general linear equation is given by:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through (x₁, y₁) and (x₂, y₂), then the slope is given by:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we can use just the first two points on the given line:
(-8, -2) and (-4, 0)
Then the slope will be:
[tex]a = \frac{0 - (-2)}{-4 -(-8)} = \frac{2}{4} = \frac{1}{2}[/tex]
Then the linear equation is something like:
y = (1/2)*x + b
To find the value of b, we can use one of the two given points, I will use (-4, 0), then:
0 = (1/2)*(-4) + b
0 = -2 + b
2 = b
Then we conclude that the linear equation represented by the given table is:
y = (1/2)*x + 2
Then the correct option is the first one.
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