Answer:
a. Account 1: 1 year Account 2: 10 years
b. Account 1: 2 years Account 2: 30 years
c. The first account grows exponentially, while the second one grows at a linear rate. Therefore, over time the first account tends to surpass the second one in value.
Step-by-step explanation:
The first account can be modeled by using a compounded formula with 100% rating, since it doubles every year. The formula is shown below:
M = C*(1 + r)^t
Where M is the final amount, C is the initial amount, r is the interest rate and t is the elapsed time. If r = 1, then it doubles every year, so we have the following expression for the first account:
M = 200*(2)^t
While the second acount grows at a steady rate of $100, therefore it can be modeled by the initial amount added by the growth rate multiplied by the elapsed time as shown below:
M = 1000 + 100*t
a. The first acount take 1 year to double, since it doubles every year.
In order for the second acount to double it needs to reach M = 2000, so we have:
2000 = 1000 + 100*t
100* t = 2000 - 1000
100*t = 1000
t = 10
It will take 10 years to double.
b. The first account will double again in 1 more year, so 2 years total.
The second account will need to reach M = 4000, therefore:
4000 = 1000 + 100*t
100*t = 4000 - 1000
100*t = 3000
t = 30
It'll take 30 years total for the second account to double again.
c. Since the first account grows exponentially it grows at a faster rate in comparison to the second one that grows linearly over time. Therefore over time the first account tends to surpass the second one in value.
In this exercise we will have to use the knowledge of finance to calculate the income time in this way we can say that:
a. [tex]Account 1: 1 year \\Account 2: 10 years[/tex]
b. [tex]Account 1: 2 years\\ Account 2: 30 years[/tex]
c. The first account grows exponentially, while the second one grows at a linear rate.
Then writing the yield formula as:
[tex]M = C*(1 + r)^t[/tex]
Where:
M is the final amountC is the initial amountr is the interest ratet is the elapsed timeIf r = 1, then it doubles every year, so we have the following expression for the first account:
[tex]M = 200*(2)^tM = 1000 + 100*t[/tex]
a. In order for the second acount to double it needs to reach M = 2000, so we have:
[tex]2000 = 1000 + 100*t100* t = 2000 - 1000100*t = 1000t = 10[/tex]
b. The second account will need to reach M = 4000, therefore:
[tex]4000 = 1000 + 100*t100*t = 4000 - 1000100*t = 3000t = 30[/tex]
c. Since the first record of finances evolve exponentially it become larger at a faster rate distinguished to the second individual that evolve linearly over opportunity. Therefore over opportunity the first fees be apt to outdo something or someone the second individual fashionable advantage.
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The equation of a circle is x2+y2+10x−4y−20=0 .
What is the radius of the circle?
Enter your answer in the box.
Answer:
7
Step-by-step explanation:
Let's start by converting this to standard form.
[tex]x^2+10x+y^2-4y=20\\(x^2+10x+25)-25+(y^2-4y+4)-4=20\\(x+5)^2+(y-2)^2=49[/tex]
The center of the circle is at (-5,2), and the radius is [tex]\sqrt{49}=7[/tex] units. Hope this helps!
The radius of the circle is r = 7 units
What is a Circle?A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the radius of the circle be r
Now , the equation of circle is
x² + y² + 10x - 4y - 20 = 0
And , standard form of a circle is
( x - h )² + ( y - k )² = r²
We need to complete the square for both the x and y terms in the given equation:
x² + y² + 10x - 4y - 20 = 0
( x² + 10x + 25 ) + ( y² - 4y + 4 ) - 49 = 0
On Adding and subtracting constants to complete the square
( x + 5 )² + ( y - 2 )² = 49
Now we can see that the equation is in standard form.
The center of the circle is at (-5, 2), and the radius is the square root of 49, which is 7
Hence , the radius is 7 units
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How do lichens weather rock?
Answer:
Biological weathering is the actual molecular breakdown of minerals. There are things called lichens (combinations of fungi and algae) which live on rocks. Lichens slowly eat away at the surface of rocks. The amount of biological activity that breaks down minerals depends on how much life is in that area
Step-by-step explanation:
The length of the base of a square pyramid is 15 inches. The slant height is 10 inches. What is the surface area of the pyramid?
The surface area of a square pyramid is the sum of the area of the base and the area of the four side squares. The surface area of the square base pyramid is 525 in².
What is the surface area of a square pyramid?The surface area of a square pyramid is the sum of the area of the base and the area of the four side squares. It is given by the formula,
Surface Area of the Square pyramid = a² + 2al
where a is the length of the side of the base, and l is the length of the slant height of the pyramid.
The length of the base of the square pyramid is 15 inches, while the length of the slant height of the pyramid is 10 inches. Therefore, the surface area of the pyramid is,
[tex]\text{Surface Area of the Square pyramid} = a^2 + 2al[/tex]
[tex]\rm = (15)^2 + (2 \times 15 \times 10)\\\\= 225 + 300\\\\= 525\ in^2[/tex]
Hence, the surface area of the square base pyramid is 525 in².
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find the exact length of the third side
Answer: 30
Step-by-step explanation:
I’m big smart
Answer:
30
Step-by-step explanation:
24^2 + 18^2 = c^2
(576 + 324 = c)
900 = c^2
[tex]\sqrt{900}[/tex] = 30
c = 30
A1 B1 C1
A2 2 7 1
B2 2 10 3
C2 1 3 1
The table shows the number of students in a class that received letter grades on 2 recent exams. The first exam is shown across the top and is summarized as A1, B1, and C1, and the second exam is in the first column, A2, B2, and C2. Given that a student earns a B on the first exam, what is the probability the student earns a B on the second exam?
A) 25%
B) 33%
C) 50%
D) 67%
Answer:
C) 50%
Step-by-step explanation:
The probability the student earns a B on the second exam, given that a student earns a B on the first exam is 0.5 or 50%.
How to find the probability of an event?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
The below table shows the number of students in a class that received letter grades on 2 recent exams.
A1 B1 C1A2 2 7 1B2 2 10 3C2 1 3 1The first exam is shown across the top and is summarized as A1, B1, and C1, and the second exam is in the first column, A2, B2, and C2. In the given table, the student get B in first exam is,
[tex]X=(7+10+3)\\X=20[/tex]
The student get B in second exam is which got B in first exam are 10.
[tex]Y=10[/tex]
The total number of students are,
[tex]2+2+1+7+10+3+1+3+1=30[/tex]
The probability the student earns a B on the second exam, given that a student earns a B on the first exam, is,
[tex]P(Y|X)=\dfrac{P(Y\cap X)}{P(X)}\\P(Y|X)=\dfrac{\dfrac{10}{30}}{\dfrac{20}{30}}\\P(Y|X)=0.5[/tex]
Thus, the probability the student earns a B on the second exam, given that a student earns a B on the first exam, is 0.5 or 50%.
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17.0027992+z= 35.0780212 I need to solve for z
Answer:
z= 18.075222
Step-by-step explanation:
Z=35.0780212-17.0027992
so z= 18.075222
Answer:
18.075222
Step-by-step explanation:
17.0027992+z=35.0780212
leave z so that it's by itself by subtracting.
z=35.0780212-17.0027992
then solve
z=18.075222
What is the value of x? A) 6 B) 8 C) 10 D) 12
Pls help ?
I don’t know the answer, sorry. I made this post on accident.
A room contains 2 parrots, 2 dogs, 1 cat, and 3 turtles. One animal is chosen at random. What is the probability that the animal chosen is a bird?
30 %
25 %
20%
40%
Answer:
25%
Step-by-step explanation:
There are 2 parrots out of 8 animals. Probability is 2/8 or 1/4 or 25%
Simplify.
(4x3y−6)(2xy6)
A) 8x3
B) 8x3y−1
C) 8x4
D) 8x4y−1
Answer:
C
Step-by-step explanation:
Examine the diagram to answer the question.
A circle with its center at (negative 0, 0) and passing through point (negative 3, negative 4).
What is the equation of the circle?
x2+y2=5
x2+y2=5–√
x2+y2=25
x2+y2=10
Answer:
x^2 + y^2 = 25 (third one)
Step-by-step explanation:
formula is x^2 + y^2 = r^2 (r = the radius)
the radius is 5 so r^2 is 25.
The equation of the circle is x² + y² = 5², is x²+ y² = 25.
To determine the equation of the circle with its center at (-0, 0) and passing through the point (-3, -4), use the standard equation of a circle:
(x - h)² + (y - k)² = r²
Where (h, k) represents the center coordinates of the circle and r represents the radius.
In this case, the center of the circle is (-0, 0), so the equation becomes:
(x - 0)² + (y - 0)² = r²
Simplifying:
x² + y² = r²
to find the radius (r). Since the circle passes through the point (-3, -4), we can use the distance formula to find the radius:
r = √((x2 - x1)²+ (y2 - y1)²)
r = √((-3 - 0)² + (-4 - 0)²)
r = √(9 + 16)
r = √25
r = 5
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Which value is a solution for the equation cot x/2 =1
Step-by-step explanation:
cot(x/2) = 1
Take inverse of both sides.
tan(x/2) = 1
Solve for x/2.
x/2 = π/4 + kπ
Solve for x.
x = π/2 + 2kπ
Possible values for x are π/2, 5π/2, 9π/2, etc.
Answer:
it's 3pi
Step-by-step explanation:
Which function is graphed here?
Answer:
B
Step-by-step explanation:
Create your own equation chain using these numbers for the variables: a = 10, b = 6, c = 18, and d = 3.
Answer:
a + b + d - 1 = c
Step-by-step explanation:
a + b + d - 1 = c
10 + 6 + 3 - 1 = 18
please help!!!!!! A rectangle and a parallelogram have the same base and the same height. How does the area of the parallelogram compare to the area of the rectangle? Explain.
Answer:
Equal Areas
Step-by-step explanation:
Area of a Rectangle =Base X Height
Area of a Parallelogram =Base X Height
If the rectangle and a parallelogram have the same base and the same height, then their areas are equal.
Take for an example,
A rectangle with a base of 5 cm and a height of 6cm
Area of the Rectangle =5*6=30 Square Centimeters.For a parallelogram with same base and height
Area of the parallelogram =5*6=30 Square Centimeters,
Final answer:
A rectangle and a parallelogram with the same base and height have equal areas as both can be calculated using the formula Base x Height = Area, disregarding the shape's orientation.
Explanation:
A rectangle and a parallelogram with the same base and height will have the same area. This is because the area of both shapes can be calculated by multiplying their base by their height. For the rectangle, this is straightforward as the height is perpendicular to the base. In the case of a parallelogram, the height is also considered perpendicular to the base, but it might be oriented at an angle relative to the base's length. Despite these differences in shape orientation, the calculation Base x Height = Area still applies, resulting in equal areas if the base and height measurements are the same.
Which measurement is shorter?
6 kilometers or 5,500 meters?
The answer is 5500 meters.
i.e. 5500 meters is shorter than 6 km.
What is measurement?Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared to a basic reference quantity of the same kind.
Here, we have,
6 kilometers=6000m.
because, 1 kilometer=1000 meters
6000>5500
Hence, 5500 meters is shorter than 6 km.
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PLEASE HELPPPPPPPP ME
Answer:
12.87
Step-by-step explanation:
If the angle of depression is 25, then the angle of elevation is also 25.
You need to use tangent for this problem. (opposite and adjacent sides)
Use tan(25)= 6/x
Divide 6 by tan(25) = 12.87
Which expression shows 2x² + 18 factored completely
Answer:
2(x^2+9)
Step-by-step explanation:
2x^2 +18
Factor out a 2
2(x^2+9)
The systolic blood pressure readings of customers at a 24-hour gym franchise are normally distributed with a mean of 122 and a standard deviation of 15. Find the z-score corresponding to the following blood pressure reading.
A blood pressure score of 77 has a z-score of:
Answer:
the answer is -3
Step-by-step explanation:
To find the z-score corresponding to a blood pressure reading, you would use the formula:
[ z =fraction{(X -mu)}{sigma}]
where:
- \( X \) is the value for which you're calculating the z-score,
- \( \mu \) is the mean of the population, and
- \( \sigma \) is the standard deviation of the population.
Given the values from the question:
- \( X = 77 \) (the blood pressure score for which we're finding the z-score),
- \( \mu = 122 \) (the mean systolic blood pressure reading),
- \( \sigma = 15 \) (the standard deviation of the systolic blood pressure readings).
Now we can plug these values into the formula:
[ z = \fraction{(77 - 122)}{15} \]
[ z = \fraction{-45}{15} \]
[ z = -3 \]
So, the z-score corresponding to the blood pressure reading of 77 is -3. This means that a reading of 77 is 3 standard deviations below the mean systolic blood pressure reading for customers at the gym franchise.
What is the mean absolute deviation of Robin's
scores?
Robin's
Scores
99
108
102 107 119
MAD-8
8 + 1 + 5 + 0 + 12
Distance
from the 81 50 12
Mean
Answer:
5.2
Step-by-step explanation:
Answer:
5.2
Step-by-step explanation:
just did it
Mr.fox purchased 3,648 candies and divided them Into treat bags of 14 pieces, how many treat bags was he apple to make
Answer:
260
Step-by-step explanation:
divide 3,648 by 14
this equals 260.57
Because he is putting the same amount of candy in each bag, you would round down. He is not going to put a fraction of candy in a bag so he would be able to make 260 bags with some candy left over.
Therefore, Mr. Fox was able to make 260 treat bags with 14 pieces of candy in each.
To solve the problem, we need to determine how many treat bags of 14 pieces each can be made from 3,648 candies. This is a simple division problem where the total number of candies is divided by the number of candies per treat bag.
Here is the step-by-step solution:
1. Start with the total number of candies Mr. Fox has, which is 3,648.
2. Determine the number of candies per treat bag, which is given as 14.
3. Divide the total number of candies by the number of candies per treat bag to find out how many treat bags can be made.
4. Perform the division: [tex]\( \frac{3,648}{14} = 260 \)[/tex].
Mr. Fox was able to make 260 treat bags.
What is the slope intercept equation of this line
the answer is C
dont know if its to late to answer but here
Create the inequality that describes the scenario.
Answer:
y<.73x+2
Step-by-step explanation:
To create an inequality that describes a scenario, you need to identify the relationship between two metric measurements. You can represent this inequality using appropriate symbols and sketch a graph to visualize the scenario.
Explanation:To create an inequality that describes the scenario, you need to identify the relationship between two metric measurements.
For example, let's say we have two cars and we want to describe the age of one car relative to the other.
If Car A is at most 5 years old, we can represent this inequality as age of Car A ≤ 5.
To sketch the graph, you would plot the age of Car A on the x-axis and shade the area that represents Car A being at most 5 years old.
what is the area of the triangle in units
Answer:
14
Step-by-step explanation:
4 times 7 (28) divided by 2 (14)
The area of a triangle is base times height times 1/2
Hi! 6=3+b? please help me
Answer:
b = 3
Step-by-step explanation:
All you need to do is subtract 3 from both sides, like so:
6 = 3 + b
-3 -3
________
3 = b
Answer:
B = 3
Step-by-step explanation:
6 = 3 + b, subtract the 3 from 6
6 - 3 = b
3 = b
The mean height of a American males is 69.5 inches. The height of the 43 male presidents have a mean 70.78 inches and a standard deviation of 2.77 inches. Treating the 43 presidents as a simple random sample , determine if there is evidence to suggest that the us presidents are taller than the average American male .
Answer:
American presidents are taller than the average American man
Step-by-step explanation:
We have to:
H0: m = 69.5
Ha: m> 69.5
Since the population standard deviation is unknown and the hypothesis test of the population mean, the t-test should be used. Here the sample size is large, so we can assume that the sample distribution of the sample mean It is normal.
sd = 2.77, x = 70.78 and n = 43
Then the test statistics will be:
t = (x - m) / (s / n ^ (1/2))
replacing
t = (70.78 - 69.5) / (2.77 / 43 ^ (1/2))
t = 3.03
Here the test is correct and the degree of freedom of the test is df = n-1 = 43-1 = 42.
Critical approach:
So
alpha = 0.05, the critical value of the test is 1,682.
Rejection region:
If t> 1,682, reject the null hypothesis.
Since the value of the test statistics is greater than the critical value, we reject the null hypothesis.
P-value approach:
The p-value using the Excel function "= TDIST (3,030,42,1)" is:
p value = 0.0021
Since the p-value is less than α = 0.05, we reject the null hypothesis.
Which means that American presidents are taller than the average American man.
Answer:
American presidents are taller than the average American man
Step-by-step explanation:
Given Data :
sd = 2.77, x = 70.78 n = 43
Test statistics will be:
t = (x - m) / (s / n ^ (1/2))
t = (70.78 - 69.5) / (2.77 / 43 ^ (1/2))
t = 3.03
df = n-1 = 43-1 = 42.
Thus the American presidents are taller than the average American man
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If the vertex of a parabola is (2. - 4). what is the axis of symmetry?
Answer:
x = 2
Step-by-step explanation:
The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves.
The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.
You already know the vertex, so the axis of symmetry is the line, x = 2.
This is because the equation to graph a vertical line is x = a, where a is the x-value you want the line to intersect.
The axis of symmetry for a parabola with the vertex at (2, -4) is the vertical line x = 2.
If the vertex of a parabola is at the point (2, -4), then the axis of symmetry is a vertical line that passes through the x-coordinate of the vertex. Thus, the equation of the axis of symmetry would be x = 2. This is because, for a parabola, the axis of symmetry always passes through the vertex and is perpendicular to the directrix.
What is the mean absolute deviation of the data set? 8, 5, 12, 4, 5, 8, 7
a.1
b.2
c.5
d.7
Answer:
The MAD is: 2
Step-by-step explanation:
First, you add all the terms together. So we get 49.
Then, we divide 49 by the amount of terms. There are 7 terms, so we do 49/7.
We get 7. Now we have to find out the distance between each point and the mean, which is seven.
8-7= 17-5= 212-7=57-4=37-5=28-7=17-7=0Now, we add all the distances together. We get 14.
Now, we divide 14 by the amount of terms, which is 7. 14/7 is 2.
The answer is b.
The correct option is b. The mean absolute deviation of the data set is 2.
To find the mean absolute deviation (MAD) of the data set [tex]\(\{8, 5, 12, 4, 5, 8, 7\}\)[/tex], follow these steps:
1. Calculate the mean (average) of the data set.
[tex]\text{Mean} = \frac{\sum \text{data points}}{\text{number of data points}} \\\\\text{Mean} = \frac{8 + 5 + 12 + 4 + 5 + 8 + 7}{7} = \frac{49}{7} = 7[/tex]
2. Find the absolute deviations from the mean for each data point.
[tex]|8 - 7| &= 1 \\|5 - 7| &= 2 \\|12 - 7| &= 5 \\|4 - 7| &= 3 \\|5 - 7| &= 2 \\|8 - 7| &= 1 \\|7 - 7| &= 0 \\[/tex]
3. Calculate the mean of these absolute deviations.
[tex]\text{Mean Absolute Deviation} = \frac{\sum \text{absolute deviations}}{\text{number of data points}} \\\\\text{Mean Absolute Deviation} = \frac{1 + 2 + 5 + 3 + 2 + 1 + 0}{7} = \frac{14}{7} = 2[/tex]
So, the mean absolute deviation of the data set is: b. 2
The radius of a circle is 3 kilometers. What is the circle's circumference?
r=3 km
Use 3.14 for . helpp please!!!!
Answer:
18.84 km
Step-by-step explanation:
The formula for the circumference is 2πr. 6.28*3=18.84
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Have a nice day.
Final answer:
The circumference of the circle is approximately 18.84 kilometers.
Explanation:
The circumference of a circle is calculated using the formula C = 2πr, where r is the radius of the circle.
In this case, the radius of the circle is given as 3 kilometers.
So, the circumference of the circle is C = 2π(3) = 6π kilometers.
To find a numerical approximation for π, we can use the value 3.14.
Therefore, the circumference of the circle is approximately C = 6(3.14) = 18.84 kilometers. This calculation demonstrates a practical method to assess the distance around a circle based on its radius, providing a tangible measurement for the circle's outer boundary in a real-world context.
what kinds of arcs does the circle have
Answer:
You can divide a circle into smaller portions. A part of a circle is called an arc and an arc is named according to its angle. Arcs are divided into minor arcs (0° < v < 180°), major arcs (180° < v < 360°) and semicircles (v = 180°). When diameters intersect at the central of the circle they form central angles.
Step-by-step explanation:
Answer:
You can divide a circle into smaller portions. A part of a circle is called an arc and an arc is named according to its angle. Arcs are divided into minor arcs (0° < v < 180°), major arcs (180° < v < 360°) and semicircles (v = 180°). When diameters intersect at the central of the circle they form central angles.Arc Of A Circle. The arc of a circle is a portion of the circumference of a circle. Measure an arc by two methods: 1) the measure of the central angle or 2) the length of the arc itself.
Step-by-step explanation:
(happy to help)
Use the graph to complete the statement
The triangle at the top of the graph is a reflection of the
triangle at the bottom
Over what line is the triangle reflected?
The triangle is reflected over line
here is the graph for anyone needing it and the answer is C