The given exponential function f(t) = 34000 (1/2)^ (t/12) can be written in the form f(t) = a b^(t) as f(t) = 34000 (0.94387)^t.
Given exponential function is,
f(t) = 34000 (1/2)^ (t/12)3
We have to write this function in the form f(t) = a b^(t).
The given function needs the variable t only in the exponent.
So f(t) can be written as,
f(t) = 34000 [(1/2)^(1/12)]^(t), which has only t in the exponent.
Comparing the given form and the given function, it is clear that,
a = 34,000
b = (1/2)^(1/12) = 0.94387
So the function can be written as,
f(t) = 34000 (0.94387)^t
Hence the function can be written as f(t) = 34000 (0.94387)^t.
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What is the volume of a sphere with a radius of 25.9 in, rounded to the nearest tenth of a cubic inch?
Please Help!!-Timed-50pts!
Answer each question individually please!
——————————————————
4. Researchers weighed a sample of river otters and a sample of sea otters. These
dot plots show the results (rounded to the nearest pound).
a) identify the shape of each dot plot
b)which dot plot has a larger center? What does this mean in terms of the otters?
c) identity any outliers. What do you think the outliers represent
d)which plot has a larger spread
e) how do the outliers affect the spread of the dot plot
The answers are:
(a). River otters: Symmetric Sea otters: Negative skewness(b). Sea otters' plot has a larger center, so sea otters are heavier than river otters.(c). There are three outliers in the sea otters' plot. They would represent the weight of baby otters.(d). Sea otters' plot has a larger spread(e). The outliers increase the spread of the dot plotfurthered explained below
What is a dot plot?A dot plot is a graphical display of data using dots. A good example would be the choice of foods that you and your friends ate for snacks. The illustration below shows a plot for a random sample of integers. Simple plot showing the types of foods a group of friends eats.
(a).
To know the shape of the plots, we will compare the plot with the following figures:
Therefore, for each group, we get:
River otters: Symmetric
Sea otters: Negative skewness
(b).
The river otters have weights that are around 10 and 26 lbs and the majority of the sea otters have weights around 38 and 64 lbs.
Therefore, the plot with the larger center is the plot for the sea otters and it means that the sea otters are heavier than the river otters.
(c).
The outliers are those dots that are too far from the majority of the data. In this case, there are outliers in the plot of the sea otters because we can consider the three dots located at 8, 10, and 12 lbs as outliers.
We can say that these outliers represent the weight of the baby otters. That's why they are smaller than the others.
(d).
We can see the spread as the extension of the dots in the number line. In the first case, the dots go from 10 to 26. However, in the second plot, the dots go from 8 to 64.
Since the difference of 64 and 8 is greater, we can say that the sea otters' plot has a larger spread.
(e).
Since there are outliers in the second plot, the spread is greater because they are too far from the other points. So, the outliers increase the spread of the data.
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I want to solve for x
Answer:
x = [tex]\frac{A*t^2}{800}[/tex]
Step-by-step explanation:
First move t² to the left side by multiplying it.
A×t² = 800x - to get rid of 800, we divide both sides by 800. This isolates x.
x = [tex]\frac{A*t^2}{800}[/tex]
Suppose $6000 is invested at 3% interest compounded continuously. How long will it take for the investment to grow to $12000?
The time it takes for the investment to grow to $12,000 if the interest is compounded continuously is 23.1 years.
Given that,
Principal amount invested, P = $6000
Rate of interest, r = 3% = 3/100 = 0.03
If the interest compounded continuously,
Final amount, A = P e^(rt)
12000 = 6000 e ^(0.03t)
2 = e ^(0.03t)
Taking logarithms on both sides,
ln (2) = 0.03t
t = 23.1 year.
Hence the time is 23.1 years.
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Determine the equation of the circle graph below
The equation of the circle graphed is (x + 6)² + y² = 4
How to determine the equation of the circle graphedFrom the question, we have the following parameters that can be used in our computation:
The circle
Where, we have
Center = (a, b) = (-6, 0)
Radius, r = 2 units
The equation of the circle graphed is represented as
(x - a)² + (y - b)² = r²
So, we have
(x + 6)² + y² = 2²
Evaluate
(x + 6)² + y² = 4
Hence, the equation is (x + 6)² + y² = 4
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Help what is the answer
Answer:
175 cm²
Step-by-step explanation:
Calculate each shape separately, then add them together.
Parallelogram: A = bh = (14)(5) = 70
Trapezium: A = ((a + b)/2)(h) = ((21 + 14)/2)(11-5) = 105
Total area = 70 + 105 = 175 cm²
Which ordered pair does NOT satisfy the relation 2 x - y = - 3
a ( -2 ,-1 )
b( -3, - 3)
c (0,- 3 )
d ( -1 , 1 )
Show that the path of a moving point parallel to the axes of x and y with velocitiesu +
ey andv + ex is a conic section
We have shown that the path of a moving point with velocities u + ey and v + ex, parallel to the axes of x and y, is either a line (when v - [tex]e^2[/tex] ≠ 0) or a horizontal line (when v - [tex]e^2[/tex] = 0), both of which are conic sections.
To show that the path of a moving point parallel to the axes of x and y with velocities u + ey and v + ex is a conic section, we can analyze the motion of the point using the principles of calculus and conic sections.
Let's denote the position of the point at any given time t as (x, y). We are given that the velocities along the x and y axes are u + ey and v + ex, respectively. This means that the derivatives of x and y with respect to time, dx/dt and dy/dt, can be expressed as:
dx/dt = u + ey
dy/dt = v + ex
Now, let's integrate these expressions to obtain x and y as functions of t. Integrating dx/dt with respect to t gives:
x = ut + eyt + C1
Similarly, integrating dy/dt with respect to t gives:
y = vt + ext + C2
Where C1 and C2 are constants of integration.
Now, we can eliminate the parameter t by expressing t in terms of x and y. From the equation y = vt + ext + C2, we can solve for t:
t = (y - ext - C2) / v
Substituting this value of t into the equation for x, we get:
x = u[(y - ext - C2) / v] + ey[(y - ext - C2) / v] + C1
Simplifying this equation, we obtain:
vx - u - evx + ue + vy - [tex]e^2[/tex]x - eyC2 = C1v
Rearranging the terms, we get:
vx - vy + ue + evx - [tex]e^2[/tex]x = C1v + eyC2 - u
Let's define new constants A = ue + ev and B = C1v + eyC2 - u. The equation then becomes:
(v - [tex]e^2[/tex])x + (u + ev)y = A + B
This equation is in the standard form of a conic section, specifically a line. However, we can manipulate this equation further to reveal other possible conic sections.
Let's consider the case when v - [tex]e^2[/tex] ≠ 0. In this case, we can divide both sides of the equation by v - [tex]e^2[/tex], yielding:
x + [(u + ev)/(v - [tex]e^2[/tex])]y = (A + B)/(v - [tex]e^2[/tex])
Now, let's define another constant C = (u + ev)/(v -[tex]e^2[/tex]) and rewrite the equation as:
x + Cy = D
Where D = (A + B)/(v - [tex]e^2[/tex]).
This equation represents a line in the x-y plane.
On the other hand, if v - [tex]e^2[/tex] = 0, the equation becomes:
0x + (u + ev)y = A + B
This simplifies to:
(u + ev)y = A + B
Which is a horizontal line parallel to the x-axis.
Therefore, we have shown that the path of a moving point with velocities u + ey and v + ex, parallel to the axes of x and y, is either a line (when v - [tex]e^2[/tex] ≠ 0) or a horizontal line (when v - [tex]e^2[/tex] = 0), both of which are conic sections.
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If we add the number 20 into the following list as a sixth value, then how much does the median increase by? 21, 2, 26, 10, 4
Answer:
Step-by-step explanation:
The median of the original list is 10. After adding 20, the new median is 15. Thus, the median has increased by 5.
Explanation:The subject of this question is Mathematics, specifically a concept within statistics known as the median. To find the median of a set of numbers, you first need to sort the numbers from smallest to largest. Once sorted, the median is the middle number. If there is an even number of observations, the median is then calculated as the average of the two middle numbers.
Let's first figure out the median of the original list, which when sorted is 2, 4, 10, 21, 26. The middle number here, the median, is 10.
Then we add 20 to the list, which then is 2, 4, 10, 20, 21, 26. For an even number of observations, we find the average of the two middle numbers, thus, (10+20)/2 = 15.
So, by adding 20 to this list, the median moves from 10 to 15, an increase of 5.
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Find the measure of each specified angle or arc
Arc JK
Angle JHI
Arc IJL
Arc JKL
H
30°
K
L
180
90
60
120
Answer:
the answer is 60
Step-by-step explanation:
Suppose y varies directly with x. When x is 5, y is 15. What is y when x is 12?
Answer:
y = 36
Step-by-step explanation:
given y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the condition when x = 5 , y = 15
15 = 5k ( divide both sides by 5 )
3 = k
y = 3x ← equation of variation
when x = 12 , then
y = 3 × 12 = 36
write and solve an euation to find the measure of angle x
Answer:
a= 65, b=75
Step-by-step explanation:
Angle a= 180-70-45
=65
Angle b= 180-60-45
=75
28. Which unit rate is equivalent to the ratio 12 to 3?
A. 12/1
B. 4/1
C. 9/1
D.3/1
Answer:
B. 4/1
Step-by-step explanation:
12/3 can be divided by 3.
Therefore 4/1.
Help pls What is the general solution to the trigonometric equation
The general solution to the differential equation -√3 cscθ = 2 is θ = 2π/3 + nπ.
To find the general solution to the trigonometric equation -√3 cscθ = 2, where n is an integer, we need to solve for θ.
Let's start by rewriting the equation:
-√3 cscθ = 2
Since cscθ is the reciprocal of sinθ, we can rewrite the equation as:
-√3 / sinθ = 2
To solve for θ, we can take the reciprocal of both sides:
sinθ / -√3 = 1/2
Next, we can take the reciprocal of both sides again:
-√3 / sinθ = 2
Now, we can find the values of θ that satisfy this equation. The general solution is given by:
θ = arcsin(-√3/2) + nπ
θ = 2π/3 + nπ
where n is an integer.
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Solve the system of equations below using substitution.
y= 6x - 11
2x + 3y = 7
What's the solution of the system?
O A.(-2.-1)
O B.(-1,-2)
O C. (2,1)
O D. (1.2)
The correct option is C. (2, 1).
Given equations:
y = 6x - 11
2x + 3y = 7
We'll start by solving equation 1) for y:
y = 6x - 11
Now, substitute this value of y into equation 2):
2x + 3(6x - 11) = 7
Simplify the equation:
2x + 18x - 33 = 7
20x - 33 = 7
Add 33 to both sides:
20x = 40
Divide both sides by 20:
x = 2
Now, substitute the value of x back into equation 1) to find y:
y = 6(2) - 11
y = 12 - 11
y = 1
Therefore, the solution to the system of equations is (x, y) = (2, 1).
Determine the values of max{3,π, √2}
The maximum value among 3, π, and √2 is π (approximately 3.14159).
To determine the maximum value among 3, π, and √2, we compare the numbers to find the largest one.
Comparing 3 and π:
Since π (approximately 3.14159) is greater than 3, we can eliminate 3 from consideration.
Comparing π and √2:
To compare these two numbers, we can square both of them. Squaring π yields approximately 9.8696, while squaring √2 gives us exactly 2. Since 9.8696 is greater than 2, we can eliminate √2 from consideration.
Thus, the maximum value among 3, π, and √2 is π (approximately 3.14159).
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find the exact value of Sin A
Step-by-step explanation:
sin A = opposite/ Hypotenuse
Sin A = 5/7
Hello !
sin(A) = opposite/hypotenuse = 5/7
arcsin(5/7) ≈ 45,58°
sin(A) = 5/7
the angle A ≈ 45,58°
[1] 2 (a) Using the information given in the advertisement shown, find the sale price of the table. Answer.... SALE All prices reduced by 30% Save $180 on this table
Based on the information given in the advertisement, we can conclude that the sale price of the table is $420.
Here's how we can arrive at this answer:
Let the original price of the table be represented by P.
We know that the sale price of the table is obtained by reducing the original price by 30%. Mathematically, this can be represented as:
Sale price = P - 0.3P
Simplifying this expression, we get:
Sale price = 0.7P
We are also given that the sale saves us $180 on this table. Mathematically, this can be represented as:
0.7P - P = -$180
Simplifying this expression, we get:
-0.3P = -$180
Dividing both sides by -0.3, we get:
P = $600
Therefore, the original price of the table was $600.
Using the equation for sale price that we derived earlier, we can now find the sale price of the table:
Sale price = 0.7P = 0.7 x $600 = $420
Hence, the sale price of the table is $420.
What is the area of a triangle
Answer:A=BxH divided by 2
_
Step-by-step explanation:
Evelyn's car costs her $151 per month plus $0.11 per mile. How many miles can Evelyn drive so that her monthly car expenses are no more than $260? Round your answer down, if necessary to ensure that the budget is not exceeded.
Answer:
Evelyn can drive 990 miles so her monthly car expenses are no more than $260
Step-by-step explanation:
Set up an equation:
151 + 0.11 ≤ 260
Subtract 151 from both sides.
0.11 ≤ 109
Divide both sides by 0.11.
x ≤ 990.909091
The question said to round your answer down so the budget doesn't exceed, therefore the answer would be 990 miles.
I don’t know what this is trying to tell can someone make it more easier to understand
Please find attached the graph of the straight line equation; y = -2·x + 3/2, which is the same as the graph of the equation; 4·x + 2·y = 3, created with MS Excel
What is an equation of a straight line graph?An equation of a straight line is an equation of the form; y = m·x + c
b. 1. The equation of the line is; 4·x + 2·y = 3
The above equation of the line can be expressed in slope-intercept form; y = m·x + c, where; m is the slope of the graph of the equation and c is the y-coordinate of the y-intercept, by making y the subject as follows;
2·y = 3 - 4·x
y = (3 - 4·x)/2
y = 3/2 - 2·x
Therefore; y = -2·x + 3/2
The above equation indicates;
The slope, m = -2
The y-intercept, c = 3/2
The coordinate of the y-intercept is therefore; (0, 3/2)
The point (0, 3/2) is to be plotted on the graph
2. In order to draw the graph, the coordinates of a second point can be found as follows;
The slope of the graph = The ratio of the rise to the run of the graph
Slope = Rise/Run = Δy/Δx
The rise = The number of units a point progresses vertically
The run = The number of units a point progresses horizontally
Therefore, a slope of -2, indicates;
Slope = Rise/run = Δy/Δx = -2 = -2/1
A rise of -2 units is accompanied by a run of 1 unit
In terms of x and y an increase of 1 unit in the x-value is accompanied in the y-value by a -2 units increase.
Therefore, a second point on the graph is; (0 + 1, ((3/2) - 2)) = (1, -1/2)
3. The line of the graph therefore passes through both (0, 3/2) and (1, -1/2)
Drawing a line through the above two points creates the graph of the equation, 4·x + 2·y = 3
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The diagram shows a scale drawing of the
side elevation of a building.
3 cm represents 1 m.
What is the width of the building in metres?
(Give your answer in meters).
Answer:
The answer for the width of the building is 5m
Step-by-step Explanation:
3cm=1m
15cm=x
cross multiply
x×3=15×1
3x=15
divide both sides by 3
3x/3=15/3
x=5m
In the following diagram,
What is the measure of
∠x
Answer:
Step-by-step explanation:
BAD = 42
x + 103 + 42 = 180
x = 180 - 145
x = 35
complete the fraction that is equivalent to 3/16.
Answer:
[tex]\frac{9}{48}[/tex]
Step-by-step explanation:
the 3 on the numerator has been multiplied by 3 to get the 9 on the numerator on the right.
the same operation must be applied to the 16 on the denominator of the fraction.
16 × 3 = 48
then
[tex]\frac{3}{16}[/tex] = [tex]\frac{3(3)}{16(3)}[/tex] = [tex]\frac{9}{48}[/tex]
The equation to the graph shown is y = ax + p, where a and p are real numbers. What
is true about a and p?
The true statement about a and p is a is positive and p is positive.
We have the equation
y= ax+ p
where a and p are real numbers.
In general, "a" represents the slope of the line (the rate of change of y with respect to x).
and, "p" represents the y-intercept (the value of y when x = 0).
The specific values of a and p can be determined by examining the graph or given data points.
By looking the graph, the slope is positive
b is the y intercept, where x = 0 and that is positive.
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Explain how you know that (3, 5) is not a solution to the given inequality by looking at the graph.
The reason that the point (3, 5) is not a solution to the given inequality is given below.
We are given that;
y > 2x + 1
Now,
The inequality y > 2x + 1 can be graphed by first graphing the boundary line y = 2x + 1. Since the inequality is strict (y >), we draw a dashed line to indicate that points on the line are not solutions to the inequality. Then, we shade the region above the line to indicate all points that satisfy the inequality.
If we have (3,5) as a point, we can see that it lies on the boundary line
y = 2x + 1.
Since the inequality is strict (y >), points on this line are not solutions to the inequality
Therefore, by the inequality the answer will be given above.
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Spiderman ascends a building to its peak The peak is 812ft above sea level. Spiderman then descends 30ft to face the Chameleon. Find the Spiderman's evevation above the sea level after meeting the Chameleon.
A. 812 ft above sea level
B. 30 ft below sea level
C. 782 ft above sea level
Spiderman's elevation above sea level after meeting the Chameleon is 782ft.
An elevation is the view of a 3D shape when it is looked at from the side or from the front.
Angle of elevation: Angle of elevation is the angle between the horizontal line and the line of sight. It is formed at the vertex of intersection of the horizontal line and line of sight. It is the same angle as used in trigonometry.
To calculate Spiderman's elevation above sea level after descending 30ft to meet the Chameleon, we need to subtract 30ft from the initial elevation of 812ft.
812ft - 30ft = 782ft
Therefore, Spiderman's elevation above sea level after meeting the Chameleon is 782ft.
So, the correct answer is C. 782ft above sea level.
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Simone has 16 square inch tiles she glues all of them on cardboard to make two different rectangles each with the same area what are the side lengths of the two rectangles she can make
Simone can make two different rectangles with the following side lengths:
Rectangle 1: Length = 16 inches, Width = 1 inch
Rectangle 2: Length = 8 inches, Width = 2 inches
To find the side lengths of the two rectangles that Simone can make using 16 square inch tiles, we need to consider the factors of 16 and check which pairs of factors can form rectangles with the same area.
The factors of 16 are 1, 2, 4, 8, and 16. We can pair these factors to form different rectangles and calculate their areas:
Pairing: 1 and 16
Length: 16
Width: 1
Area: 16 square inches
Pairing: 2 and 8
Length: 8
Width: 2
Area: 16 square inches
Pairing: 4 and 4
Length: 4
Width: 4
Area: 16 square inches
Therefore, Simone can make two different rectangles with the following side lengths:
Rectangle 1: Length = 16 inches, Width = 1 inch
Rectangle 2: Length = 8 inches, Width = 2 inches
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What is the rent of the apartment 3 in the table above?
Answer:
B. $750
Step-by-step explanation:
600÷100=6
720÷120=6
840÷140=6
so the difference between all of them is x6
this means we times 125 by 6
125×6=750
Answer: B. $750
Step-by-step explanation:
If all of the apartments are proportional by the dollar to the area, we will find the constant of proportionality by dividing.
$600 / 100 m² = 6 $/m²
Next, we will multiply the area of apartment 3 by this value to find the rent dollar amount.
125 m² * 6 $/m² = $750
The half life of Radium is 1620 years. When will 20 g sample ony have 15 g left?
Answer:
The formula for radioactive decay is:
N = N₀ * (1/2)^(t/T)
where:
N₀ = initial amount
N = remaining amount
t = time elapsed
T = half-life
Let's plug in the given values:
N₀ = 20 g
N = 15 g
T = 1620 years
15 = 20 * (1/2)^(t/1620)
Dividing both sides by 20:
0.75 = (1/2)^(t/1620)
Taking the logarithm base 1/2 of both sides:
log(0.75) = t/1620 * log(1/2)
Solving for t:
t = log(0.75) / log(1/2) * 1620
t ≈ 623 years
Therefore, it will take approximately 623 years for a 20 g sample of Radium to decay to 15 g.
Step-by-step explanation: