By the principle of mathematical induction, we have shown that
M(2k) = k 2k for all k ∈ N.
The Principle of Mathematical Induction:The principle of mathematical induction is a proof technique used to prove a statement that holds for all positive integers.
It consists of two steps:
Base case: Show that the statement is true for the smallest possible value of the positive integer, usually n = 1.
Inductive step: Assume that the statement is true for an arbitrary positive integer k, and then use this assumption to show that the statement must also be true for k + 1.
Here we have
The following recursive function computes the number of comparisons used in the worst case of merge sort.
M (1) = 0
M (2k) = 2M (2k−1) + 2k for all k > 0
To prove that M(2k) = k × 2k for all k ∈ N using mathematical induction, we will first show that the base case holds:
Base case: When k = 1,
we have M(2) = 2M(1) + 2¹ = 2(0) + 2 = 2, and k × 2k = 1 × 2¹ = 2.
Therefore, the base case holds.
Inductive hypothesis:
Assume that M(2k) = k × 2k holds for some positive integer k.
Inductive step:
We need to show that M(2k+1) = (k+1) × 2k+1.
Using the recursive definition of M, we have:
M(2k+1) = 2M(2k) + 2(2k+1)
= 2(k × 2k) + 2(2k+1) (using the inductive hypothesis)
= 2k(2k+2) + 2(2k+1)
= 2k(2(k+1)) + 2(2k+1)
= 2(k+1) × 2k + 2(2k+1)
= (k+1) × 2(2k+1)
Therefore, the inductive step holds.
Hence,
By the principle of mathematical induction, we have shown that
M(2k) = k 2k for all k ∈ N.
Learn more about Mathematical Induction at
https://brainly.com/question/31244444
#SPJ1
Carlita surveyed all the students in her grade and reported the fraction of students who liked each type of pet.
Three-sevenths liked hamsters.
Five-sixths liked dogs.
One-half liked cats.
liked snakes.
Which list has the animals in order from least liked to most liked?
A. dogs, cats, snakes, hamsters
B. snakes, dogs, cats, hamsters
C. dogs, cats, hamsters, snakes
D. snakes, hamsters, cats, dogs
On the basis of data reported by Carlita in form of fractions , on comparing the given fractions order of animals from least liked to most liked is option-D:Snakes, hamsters, cats, dogs.
What are fractions?
A fraction represents a portion of a total. This entire may refer to a place or a group of places. The Latin word "fractio," which meaning "to break," is the source of the English term "fraction." It is simpler to identify the greater or smaller fraction when comparing fractions with the same or similar denominators. We must change fractions with dislike or different denominators to fractions with like or the same denominators in order to compare them. To do this, we must determine the denominators' Least Common Multiple (LCM). We can compare fractions simply when the denominators are made the same or similar.
Given data collected by Carlita:
Fraction of students who like hamsters= [tex]\frac{3}{7}[/tex]
Fraction of students who like dogs = [tex]\frac{5}{6}[/tex]
Fraction of students who like cats= [tex]\frac{1}{2}[/tex]
Fraction of students who like hamsters= [tex]\frac{1}{9}[/tex]
To compare all four fractions [tex]\frac{3}{7}[/tex] , [tex]\frac{5}{6}[/tex] , [tex]\frac{1}{2}[/tex] & [tex]\frac{1}{9}[/tex]
We find LCM of denominators 2,6,7 & 9
prime factors:
2=2
6=2 x 3
7=7
9= 3 x 3
LCM=2 x 3 x 3 x 7
=126
Equivalent fractions with denominator 126:
[tex]\frac{3}{7}[/tex] = [tex]\frac{3}{7}[/tex] × [tex]\frac{18}{18}[/tex] = [tex]\frac{54}{126}[/tex]
[tex]\frac{5}{6}[/tex] = [tex]\frac{5}{6}[/tex] × [tex]\frac{21}{21}[/tex] = [tex]\frac{105}{126}[/tex]
[tex]\frac{1}{2}[/tex] = [tex]\frac{1}{2}[/tex] × [tex]\frac{63}{63}[/tex] = [tex]\frac{63}{126}[/tex]
[tex]\frac{1}{9}[/tex] = [tex]\frac{1}{9}[/tex] × [tex]\frac{14}{14}[/tex] = [tex]\frac{14}{126}[/tex]
On arranging least to most [tex]\frac{54}{126}[/tex], [tex]\frac{105}{126}[/tex], [tex]\frac{63}{126}[/tex] & [tex]\frac{14}{126}[/tex] we get
[tex]\frac{14}{126}[/tex] < [tex]\frac{54}{126}[/tex] < [tex]\frac{63}{126}[/tex] < [tex]\frac{105}{126}[/tex]
snakes<hamsters<cats<dogs
To know more about fractions, visit:
https://brainly.com/question/10354322
#SPJ1
Refer to the attachment for the complete question.
Emma solved a problem on graphing linear inequalities as shown below. She made a mistake. What mistake did she make? What should she have done instead? Explain her error and explain how you would do the problem correctly. (Hint: solve the problem first and see what your graph looks like, then see if you can identify the error).
Graph the following linear inequality to show all possible solutions.
m= 1/4 b=(-2)
This is false, which means that the region below the line does not satisfy the inequality. So,we should shade the region above the line.
What is linear inequality?A linear inequality is a mathematical statement that compares two expressions using one of the inequality symbols: < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).
One can write a linear inequality in one variable as ax + b c, ax + b > c, ax + b c, or ax + b c.
The linear inequality given is:
m = 1/4, b = -2
To graph this inequality, we first need to plot the line with equation y = mx + b, where m = 1/4 and b = -2.
y = 1/4 x - 2
We can plot this line by finding two points on it. One way to do this is to set x to two different values and solve for y. For example, when x = 0, y = -2, and when x = 4, y = -1.
Next, we need to shade the region above or below the line to show all possible solutions.
We can determine which region to shade by choosing a test point that is not on the line and substituting its coordinates into the inequality
For example, the point (0,0) is not on the line, so we can substitute its coordinates into the inequality:
y < 1/4 x - 2
0 < 1/4 (0) - 2
0 < -2
Emma's mistake could be that she shaded the region below the line instead of above it. To do the problem correctly, we should shade the region above the line, as explained above.
To know more about expressions visit:
https://brainly.com/question/8774365
#SPJ1
Lines RS, TV, and SW are shown.
On a coordinate plane, 3 lines are shown. Line R S goes through (negative 8, 6) and (2, 6). Line T V goes through (negative 6, negative 4) and (8, negative 4). Line S W goes through (2, 6) and (2, negative 8).
Which statements are true about these lines? Select three options.
Line RS has a slope of 6.
Line SW has an undefined slope.
Line TV has a slope of 0.
Lines RS and TV are parallel.
Line SW is perpendicular to line RS, but not to line TV
4. Find the surface area of the triangular prism below
205.9 cm²
203.2 cm²
207.8 cm2
204.6 cm²
The formula for the surface area of a triangular prism is
Surface Area(SA) = (b*h) + [(a+b+c) * l]
Where, b = length of the base of the triangular face,
h = height of the triangular face,
a, b, c = length of the three sides of the triangular face respectively, and
l = length of the rectangular face.
Here, b = 7.2 cm, a = 7.1 cm, c = 7.1 cm, h = 6.9 cm and l = 7.3 cm
Therefore, SA = (7.2*6.9) + [(7.1 + 7.2 + 7.1) * 7.3]
= 49.68 + (21.4*7.3)
= 49.68 + 156.22
= 205.9 cm² (Answer)
To learn more about Triangular Prism:
https://brainly.com/question/29663752
If w = 10 units, x = 5 units, and y = 6 units, what is the surface area of the figure? Round your answer to the nearest tenth. (1 point) Figure is composed of a right square pyramid on top of a square prism. The sides of the square pyramid are equal to the sides of the square prism, the length and width of the square prism is w, the height of the square prism is x, and the height of the square pyramid, which forms a right angle with the center, is y.
The surface area of the figure is 456.2 units²,
How to determine the surface area?The area of the square base is:
base area = w² = (10 units)² = 100 units²
The lateral area is 4 times the area of one rectangular face:
lateral area = 4wx = 4(10 units)(5 units) = 200 units²
The area of one triangular face is half the product of its base length (w) and its slant height (h). The latter is found using the Pythagorean theorem:
h² = y² +(w/2)² = (6 units)² +((10 units)/2)² = 61 units²
h = √61 units
So, the area of 4 triangles is ...
area of triangular faces = 4(1/2)wh = 2(10 units)(√61 units) ≈ 156.2 units²
Now we have the areas of the parts, so we can add them together to get the total surface area:
surface area = base area + lateral area + area of triangular faces
= 100 units² + 200 units² + 156.2 units²
therefore, surface area = 456.2 units²
Learn more about surface area on https://brainly.com/question/29298005
#SPJ1
is trigonometry hard?
Answer:
yes it is pretty hard but I believe I. you
Circle B is shown, with GHJK inscribed in the circle. The mGHJ = (3x+50)°, and mzHJK = (4x)° and mLGK] = (4x-10)°.
Find HGK and JHG
The value of
m∠GHJ = (3(20°)+50)° = 110°.
m∠GkJ = (4(20°)-10)° = 70°
m∠HJK = (4(20°))° = 80°
What is an angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Here, we have
Given: Circle B is shown, with GHJK inscribed in the circle. The m∠GHJ = (3x+50)°, and m∠HJK = (4x)° and mLGK] = (4x-10)°.
we have to find the value of HJK and JHG.
We know that
m∠GHJ + m∠GkJ = 180°
(3x+50)° + (4x-10)° = 180°
7x + 40 = 180°
7x = 140°
x = 20°
Hence, the value of
m∠GHJ = (3(20°)+50)° = 110°.
m∠GkJ = (4(20°)-10)° = 70°
m∠HJK = (4(20°))° = 80°
To learn more about the angle from the given link
https://brainly.com/question/24999711
#SPJ1
Flying against the wind, an airplane travels 2370 kilometers in 3 hours. Flying with the wind, the same plane travels 10160 kilometers in 8 hours. What is the rate of the plane in still air and what is the rate of the wind?
In still air, the jet's speed is 1030 mph, while the wind's speed 240 miles per hour.
What is velocity?It is the rate of change of an object's position with regard to time and a frame of reference. Although it may appear difficult, velocity is essentially speeding in a particular direction. Due to the fact that it is a vector quantity, velocity must be defined in terms of both magnitude (speed) and direction. It has a metre per second SI unit (ms-1).
What is speed?The distance travelled in relation to the time it took to travel that distance is how speed is defined. As speed simply has a direction and no magnitude, it is a scalar quantity.
Jet's velocity against wind is 2370/3=790 mile per hour and flying with wind it is 10160/8= 1270 miles per hour.
According to question,
Let the velocity of jet in still air be x miles per hour and velocity of wind be y miles per hour.
As such its velocity against wind is x−y and with wind is x+y and therefore
x−y=790 and x+y=1270
Adding the two 2x= 2060 and x=1030
and y=240
Hence velocity of jet in still air is 1030 miles per hour and velocity of wind is 240 miles per hour.
To know more about velocity visit:
brainly.com/question/17127206
#SPJ1
For each right prism, find:
( a ) the lateral area,
( b ) the total area, and
( c ) the volume.
a) The lateral area of a rectangular prism is 360 square units. b) The total area of a rectangular prism is 6 square units. c) The volume of is 1200 cubic units.
What is a prism?A prism is a three-dimensional solid consisting of two bases that are parallel and congruent and are joined by a series of parallelograms. A prism's lateral faces are all parallelograms or rectangles. On the other hand, a pyramid is a three-dimensional solid with a polygonal base and an apex. A pyramid's lateral faces are triangles that converge at the top. The perpendicular distance between the bases of a prism determines its height, whereas the distance between the apex and base of a pyramid determines its height.
a) The lateral area of a rectangular prism is given by 2h(l+w):
Substituting the values we have:
2(6)(20+10) = 360 square units
b) The total area of a rectangular prism is given by 2lw + 2lh + 2wh:
Substituting the values we have:
2(20)(10) + 2(20)(6) + 2(10)(6) = 520 square units.
c) Volume is given as V = lwh substituting the values we have:
(20)(10)(6) = 1200 cubic units.
For Cube:
a) The lateral area is give as 4s(s)
Substituting the values:
LA = 4(1)(1) = 4
b) The total area is given as 6(s)(s):
Substituting the values:
TSA = 6(1)(1) = 6 square units.
c) The volume is given as s^3:
(1)^3 = 1 cubic unit.
For the triangular prism:
a) The lateral area is given as perimeter of base multiplied by height.
The perimeter of the base is (8 + 6 + 10) = 24, and h = 8.
LA = (24)(8) = 192 square units.
b) The total area is given by area of base + the lateral area:
Area of the base triangle is:
A = 1/2(6)(8) = 24
For two triangles at the base we have: 2(24) 48
Thus, total area of the prism is 176 + 48 = 224 square cm.
c) The volume of the triangular prism is given as:
1/2(base x height) x length = 1/2(6)(8)(8) = 192 cubic cm.
Learn more about volume here:
https://brainly.com/question/13338592
#SPJ1
Which missing x-value would make the table a function?
we can replace the second occurrence of x = -2 with x = 1:
What is function?
In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.
For the table to be a function, each x-value must correspond to a unique y-value. To determine the missing x-value, we need to find if there are any repeated x-values with different y-values.
The x-value 3 is paired with y-values -3 and -1, which means that the table is not a function. Therefore, we need to replace one of the x-values that appears twice with a different value.
Since x = 0 is already paired with y = 5, we cannot use 0 as the replacement. The only other x-value that appears more than once is x = -2. Therefore, we can replace one of the occurrences of x = -2 with a different value.
For example, we can replace the second occurrence of x = -2 with x = 1:
x y
3 -3
1 4
-2 -1
-2 -2
0 5
Now each x-value corresponds to a unique y-value, so the table represents a function.
To learn more about functions from the given link:
https://brainly.com/question/12431044
#SPJ1
Which angle is congruent to D?
Answer: Where is the picture?
Step-by-step explanation:
how did slugger mcfist get a black eye
PLEASE HELP ME WITH THIS!!!!! I NEED HELP! A backyard pool is in the shape of a rectangle. The pool has a perimeter of 90 feet and and area of 500ft^2. which of the following could he the pools length and width? 1) 15 feet and 30 feet 2)10 feet and 35 feet 3) 50 feet and 10 feet 4) 25 feet and 20 feet.
Answer:3) 50 feet and 10 feet
Step-by-step explanation: Multiply every single choice
Answer:
4)
Step-by-step explanation:
Let x1 = length; x2 = width
+) x1 × x2 = 500
+) 2(x1 + x2) = 90 => x1 + x2 = 45
=> x1 and x2 are the roots of equation: [tex]x^2-45x+500=0[/tex]
=> x1 = 25; x2 = 20
Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.
Answer: 0.6954
Step-by-step explanation:
To find the area between two z scores, in this case P(-0.82<z<1.29), we can either use a z score calculator or a standard normal distribution table, which I will use for this.
The probability of P(-0.82<z<1.29) = P(z<1.29)-(z<-0.82).
To find P(z<2.01), we use a positive z score standard normal distribution table and find that P(z<1.29)=0.9015
Using a negative z score standard normal distribution table, we can find that (z<-0.82)=0.2061.
So, P(-0.82<z<1.29) = P(z<1.29)-(z<-0.82)=0.6954.
Graph the function.
f(x)=√x-4
Plot four points on the graph of the function: the leftmost point and three additional points. Then click on the graph-a-function button.
The four points on the graph of f(x) = √x-4 including the left most point are: (4,0), (5,1), (8,2), and (20,4).
Finding four points on the graph of the functionTo find points on the graph of f(x) = √x-4, we can choose values of x and find the corresponding values of y.
The leftmost point on the graph is when x is the smallest possible value, which is x = 4 (since we can't take the square root of a negative number). At x = 4, f(x) = √0 = 0, so the leftmost point is (4,0).
To find three additional points, we can choose values of x that are greater than 4 and find the corresponding values of y:
When x = 5: f(5) = √1 = 1, so the point is (5,1)
When x = 8: f(8) = √4 = 2, so the point is (8,2)
When x = 20: f(20) = √16 = 4, so the point is approximately (20.4)
So, four points on the graph of f(x) = √x-4 are: (4,0), (5,1), (8,2), and (20,4).
Read more about functions at
https://brainly.com/question/28532394
#SPJ1
I attached the question
x = -3 is the vertical asymptote of the function.
What is vertical asymptote?A vertical asymptote of a function is a vertical line on the graph where the function approaches positive or negative infinity as the input (x-value) approaches a certain value.
According to question:To identify the vertical asymptote(s) of the rational function f(x) = (x + 4)/(2x + 6), we need to look for the values of x that make the denominator equal to zero.
So, we solve the equation 2x + 6 = 0 for x:
2x = -6
x = -3
Therefore, x = -3 is the vertical asymptote of the function.
The other answer choices (B) x = -4 and (C) y = 1/2 are not correct as they do not make the denominator of the function equal to zero. And (D) is also not correct as this function has a vertical asymptote at x = -3.
To know more about vertical asymptote visit:
https://brainly.com/question/4084552
#SPJ1
In 2012, the population of a city was 5.51 million. The exponential growth rate was 3.82% per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be 10 million?
d) Find the doubling time.
helppppppp
Answer:
a) To find the exponential growth function, we can use the formula:
P(t) = P0 * e^(rt)
Where:
P(t) = the population at time t
P0 = the initial population (in this case, 5.51 million)
e = the mathematical constant e (approximately 2.71828)
r = the annual growth rate (in decimal form)
t = the number of years
Substituting the given values, we have:
P(t) = 5.51 * e^(0.0382t)
b) To estimate the population of the city in 2018, we can substitute t = 6 (since 2018 is 6 years after 2012) into the exponential growth function:
P(6) = 5.51 * e^(0.0382*6) ≈ 6.93 million
Therefore, the estimated population of the city in 2018 is approximately 6.93 million.
c) To find when the population of the city will be 10 million, we can set P(t) = 10 and solve for t:
10 = 5.51 * e^(0.0382t)
e^(0.0382t) = 10/5.51
0.0382t = ln(10/5.51)
t ≈ 11.7 years
Therefore, the population of the city will be 10 million in approximately 11.7 years from 2012, or around the year 2023.
d) To find the doubling time, we can use the formula:
T = ln(2) / r
Where:
T = the doubling time
ln = the natural logarithm
2 = the factor by which the population grows (i.e., doubling)
r = the annual growth rate (in decimal form)
Substituting the given value of r, we have:
T = ln(2) / 0.0382 ≈ 18.1 years
Therefore, the doubling time for the population of the city is approximately 18.1 years.
It costs $350 to spend 4 nights at the Econo Motel. It costs $475 to spend 6 nights at the Bluebird Inn. Which of these statements is true?
Answer: A
Step-by-step explanation: The bluebird Inn is more expensive per night because 475 is greater than 350.
Find the Volume of 10 ⅕in 4 ¼in 2in
The volume of the rectangular prism is (867/20) cubic inches.
What is volume?A volume is just the amount of space taken up by any three-dimensional solid. A cube, a cuboid, a cone, a cylinder, or a sphere are examples of solids. Volumes differ depending on the shape.
To find the volume of a rectangular prism, we need to multiply its length, width, and height. In this case, the length is 10 1/5 inches, the width is 4 1/4 inches, and the height is 2 inches. We can convert the mixed numbers to improper fractions and then multiply:
length = 10 1/5 inches = (51/5) inches
width = 4 1/4 inches = (17/4) inches
height = 2 inches
Volume = length x width x height
= (51/5) inches x (17/4) inches x 2 inches
= (867/20) cubic inches
Therefore, the volume of the rectangular prism is (867/20) cubic inches.
Learn more about volume on:
https://brainly.com/question/6204273
#SPJ1
If you horizontally…
Check the picture below.
so following the template below, a shift 2 units to the left, means C=2
[tex]G(x)=\sqrt{x+2}[/tex]
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
Answer: option (a) and option (e).
Step-by-step explanation:
Answer:
(a) and (e) are correct
Step-by-step explanation:
(a) x² + (y - 3)² = 6²
(b) x² + (y - 5)² = (√6)²
(c) (x - 4)² + y² = 6²
(d) (x + 6)² + y² = 12²
(e) x² + (y + 8)² = 6²
The general equation of a circle is:
(x - a)² + (y - b)² = r², where (a, b) represents the x-y coordinates of the centre, and r represents the radius.
Hence, by process of elimination, the options that have a diameter of 12 units and therefore, a radius of 6 units, are (a), (c), and (e).
Therefore, the correct choices are (a), and (e), as (c) has a circle centre of (4,0) and does not lie on the y-axis.
write the data in eighths, by using equivalent fractions. 3, 1 3/4, 2 1/4 , 1 1/2, 2 1/4, 2 7/8
The data in eighths is: 24/8, 14/8, 18/8, 12/8, 18/8, 23/8.
What are equivalent fractions?
Equivalent fractions are different fractions that represent the same value. Two fractions are equivalent if they have the same overall value or magnitude, even though they may appear differently.
To write the data in eighths, we need to convert each fraction into an equivalent fraction with a denominator of 8. Here's how we can do it:
3 can be written as 24/8 (since 3 = 3 x 8/8 = 24/8)
1 3/4 can be written as 14/8 (since 1 3/4 = 4/4 + 3/4 = 8/8 + 3/4 = 14/8)
2 1/4 can be written as 18/8 (since 2 1/4 = 16/8 + 2/8 = 18/8)
1 1/2 can be written as 12/8 (since 1 1/2 = 8/8 + 4/8 = 12/8)
2 1/4 can be written as 18/8 (same as above)
2 7/8 can be written as 23/8 (since 2 7/8 = 16/8 + 7/8 = 23/8)
Therefore, the data in eighths is: 24/8, 14/8, 18/8, 12/8, 18/8, 23/8.
To learn more about equivalent fractions visit the link:
https://brainly.com/question/29796627
#SPJ1
What is the degree of -4x to the power of 3 + 6x to the power of 4 -1
what even is 2 + 2?
Answer:
Definitely 4 always 4!!!
A line has a slope of -4 and passes through the point (-1, 10). Write its equation in slope- intercept form.
Answer:
[tex]10 = -4( - 1) + b[/tex]
[tex]10 = 4 + b[/tex]
[tex]b = 6[/tex]
[tex]y = - 4x + 6[/tex]
The equation of the line in slope-intercept form is y = -4x + 6.
Explanation:The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.
Given that the slope is -4 and the line passes through the point (-1, 10), we can substitute these values into the equation.
Using the point-slope formula (y - y1) = m(x - x1), we can rewrite it as (y - 10) = -4(x - (-1)). Simplifying this equation, we get y - 10 = -4x - 4, and rearranging it, we have y = -4x + 6. Therefore, the equation of the line in slope-intercept form is y = -4x + 6.
Learn more about Equation of a line here:https://brainly.com/question/33578579
#SPJ3
How many 5 digit numbers can be formed?
Answer:
Step-by-step explanation:
a lot (90,000) (i think)
The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 60.1% of their carbon-14. How old were the bones at the time they were discovered?
please help me with this problem.....
Answer: To solve the problem, we can use the formula for exponential decay:
N(t) = N0 * (1/2)^(t/T)
where:
N(t) is the amount of the radioactive element at time t
N0 is the initial amount of the radioactive element
t is the time that has elapsed
T is the half-life of the radioactive element
Let's assume that the initial amount of carbon-14 in the bones was N0. After the bones were discovered, they had lost 60.1% of their carbon-14, which means that only 39.9% of the original carbon-14 remained. Therefore, we can write:
N(t) = 0.399 * N0
We want to find the time t that has elapsed since the mastodon died. We can rearrange the formula for exponential decay to solve for t:
t = T * log( N(t) / N0 ) / log(1/2)
Substituting the given values, we get:
t = 5750 * log( 0.399 ) / log(1/2)
Using a calculator, we find that t is approximately 16060 years. Therefore, the bones were approximately 16060 years old at the time they were discovered.
Step-by-step explanation:
for ouls salt 1/4 (8x+12) = 19
Answer:
x = 8
Step-by-step explanation:
1/4 (8x + 12) = 19
Distribution property
1/4 x 8= 2
1/4 x 12= 3
2x + 3 = 19
19 - 3= 16
2x= 16
16/2 = 8
X= 8
Choose scales for the coordinate plane shown so that you can graph the points J (5, 50), K(3, 50), L (4, -40), M (-2, 40), and N (-5, -10). on the x-axis use a scale of ____ units for each grid square. on the y-axis use a scale of ____ units of each grid square. complete the explanation for using these scales for each axis. the x-coordinates range from ____ to ____, and the y-coordinates range from ____ to ____.
On the x-axis use a scale of 2 units for each grid square. on the y-axis use a scale of 10 units of each grid square. The x-coordinates range from -5 to 5. y-coordinates range from -40 to 50.
What is coordinate plane?In mathematics, points and functions are represented and graphed on the coordinate plane, commonly known as the Cartesian plane. The x-axis and y-axis are two perpendicular number lines that meet at the origin to form the plane (0,0).
On the coordinate plane, points are denoted by ordered pairs (x, y), where x denotes the point's separation from the y-axis and y denotes its separation from the x-axis.
For the given coordinates the range of x and y coordinates are:
x-coordinates range from -5 to 5
y-coordinates range from -40 to 50.
Thus, we use a scale of 2 on the x-axis and 10 units on the y axis.
Learn more about coordinate plane here:
https://brainly.com/question/24134413
#SPJ1
A newscaster earns $25,100 and wants to invest 10% of his/her monthly salary to save for
retirement in 29 years. If he/she invests this money at 4.1% compounded monthly, how much
money will he/she have at retirement?
a) How much will be saved each year?
b) What will be the monthly deposit?
c) What will be the amount in the account after 29 years?
Answer:
A) $2510
B) $209.17
C) $128,273.36
Step-by-step explanation:
Let's break this problem down into three parts:
a) To find out how much will be saved each year, we first need to calculate the annual salary and then determine 10% of it. Since the newscaster earns $25,100, we can calculate the annual savings as follows:
Annual savings = Annual salary * 10%
Annual savings = $25,100 * 0.1
Annual savings = $2,510
So, the newscaster will save $2,510 each year.
b) To find the monthly deposit, we need to divide the annual savings by the number of months in a year:
Monthly deposit = Annual savings / 12
Monthly deposit = $2,510 / 12
Monthly deposit ≈ $209.17
The newscaster will deposit approximately $209.17 per month into the retirement account.
c) To find the amount in the account after 29 years, we will use the formula for the future value of an ordinary annuity, since the investment has a monthly deposit and a monthly compounding interest rate:
FV = P * [(1 + r)^nt - 1] / r
Where FV is the future value, P is the monthly deposit, r is the monthly interest rate (annual interest rate divided by 12), n is the number of times interest is compounded per year (monthly, so 12), and t is the number of years.
In this case, P = $209.17, r = 4.1%/12, n = 12, and t = 29 years.
First, convert the annual interest rate to a decimal and then find the monthly interest rate:
Monthly interest rate = (4.1%/12) / 100
Monthly interest rate = (0.041/12)
Now, plug the values into the formula:
FV = $209.17 * [(1 + 0.041/12)^(12*29) - 1] / (0.041/12)
Calculate the future value:
FV ≈ $209.17 * [(1.003417)^(348) - 1] / (0.003417)
FV ≈ $209.17 * (3.42307) / (0.003417)
FV ≈ $128,273.36
After 29 years, the newscaster will have approximately $128,273.36 in the retirement account.
