Answer:
The solutions for 1 + 3 + 5 +...+ (2n - 1), for the first 10 natural numbers are given in the explanation section below.
Step-by-step explanation:
To calculate 1 + 3 + 5 +...+ (2n - 1) for several natural numbers n, we will use several natural numbers to represent n.
For n= 1,
2n - 1 = 2(1) - 1 = 2 - 1 = 1
Hence, 1 = 1
For n = 2,
2n - 1 = 2(2) - 1 = 4 - 1 = 3
Hence, 1 + 3 = 4
For n = 3,
2n - 1 = 2(3) - 1 = 6 - 1 = 5
Hence, 1 + 3 + 5 = 9
For n = 4,
2n - 1 = 2(4) - 1 = 8 - 1 = 7
Hence, 1 + 3 + 5 + 7 = 16
For n = 5,
2n - 1 = 2(5) - 1 = 10 - 1 = 9
Hence, 1 + 3 + 5 + 7 + 9 = 25
For n = 6,
2n - 1 = 2(6) - 1 = 12 - 1 = 11
Hence, 1 + 3 + 5 + 7 + 9 + 11 = 36
For n = 7,
2n - 1 = 2(7) - 1 = 14 - 1 = 13
Hence, 1 + 3 + 5 + 7 + 9 + 11 + 13 = 49
For n = 8,
2n - 1 = 2(8) - 1 = 16 - 1 = 15
Hence, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64
For n = 9,
2n - 1 = 2(9) - 1 = 18 - 1 = 17
Hence, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81
For n = 10,
2n - 1 = 2(10) - 1 = 20 - 1 = 19
Hence, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100
Write an equation in point-slope form and slope-intercept form for the line.
passes through (6, -6), slope = 5
Answer:
y = 5- 36
Step-by-step explanation:
6 is the x
-6 is the y
y=mx+b
so m times x, m is the slope
5 times 6 is 30
-6=30+b
so -36
y=5x-36
SORRY IF IM WRONG I TRIED
The heights of women in the USA are normally distributed with a mean of 64 inches and a standard deviation of 3 inches.
Required:
a. A random sample of six women is selected. What is the probability that the sample mean is greater than 63 inches?
b. What is the probability that a randomly selected woman is taller than 66 inches?
c. What is the probability that the mean height of a random sample of 100 women is greater than 66 inches?
Answer:
(a) 0.2061
(b) 0.2514
(c) 0
Step-by-step explanation:
Let X denote the heights of women in the USA.
It is provided that X follows a normal distribution with a mean of 64 inches and a standard deviation of 3 inches.
(a)
Compute the probability that the sample mean is greater than 63 inches as follows:
[tex]P(\bar X>63)=P(\frac{\bar X-\mu}{\sigma/\sqrt{n}}>\frac{63-64}{3/\sqrt{6}})\\\\=P(Z>-0.82)\\\\=P(Z<0.82)\\\\=0.20611\\\\\approx 0.2061[/tex]
Thus, the probability that the sample mean is greater than 63 inches is 0.2061.
(b)
Compute the probability that a randomly selected woman is taller than 66 inches as follows:
[tex]P(X>66)=P(\frac{X-\mu}{\sigma}>\frac{66-64}{3})\\\\=P(Z>0.67)\\\\=1-P(Z<0.67)\\\\=1-0.74857\\\\=0.25143\\\\\approx 0.2514[/tex]
Thus, the probability that a randomly selected woman is taller than 66 inches is 0.2514.
(c)
Compute the probability that the mean height of a random sample of 100 women is greater than 66 inches as follows:
[tex]P(\bar X>66)=P(\frac{\bar X-\mu}{\sigma/\sqrt{n}}>\frac{66-64}{3/\sqrt{100}})\\\\=P(Z>6.67)\\\\\ =0[/tex]
Thus, the probability that the mean height of a random sample of 100 women is greater than 66 inches is 0.
What is the greatest common factor of 24 and 48?
Answer:
Greatest Common Factor: 24
Step-by-step explanation:
The greatest common factor is found by multiplying all the factors which appear in both lists: So the GCF of 24 (2x2x2x3) and 48 (2x2x2x2x3) is 2x2x2x3 which is 24.
The greatest common factor of 24 and 48 is 24.
Here, we have,
To find the greatest common factor (GCF) of 24 and 48,
we can use the prime factorization method:
Step 1: Find the prime factorization of each number.
Prime factorization of 24:
24 = 2 * 2 * 2 * 3
Prime factorization of 48:
48 = 2 * 2 * 2 * 2 * 3
Step 2: Identify the common prime factors and their lowest exponents.
Common prime factors: 2 * 2 * 2 * 3
Step 3: Multiply the common prime factors with their lowest exponents.
GCF(24, 48) = 2 * 2 * 2 * 3 = 24
So, the greatest common factor of 24 and 48 is 24.
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The land area of a country is about 3.5 million square miles and the population is about 200 million people. What is the average population density?
9514 1404 393
Answer:
about 57.1 persons per square mile
Step-by-step explanation:
To find persons per square mile, divide persons by square miles:
(200 million persons)/(3.5 million mi^2) = (200/3.5) persons/mi^2
≈ 57.1 persons/mi^2
Look at the picture please!!!!
Answer:
Angle 1: 131
Angle 6: 49
Answer:
m∠1 = 131º
m∠6 = 49º
Step-by-step explanation:
So we know that a straight line is equal to 180º and we already know the measure of angle 8 (49º) so to find the measure of angle 7, we just subtract 49 from 180.
180 - 49 = 131
So m∠7 = 131º
Now because of the alternate exterior angle rule, we can now find out that m∠7 is the same as m∠1
Now for the measurement of angle 6, we know that it's 49º because of the vertical angles rule.
An angle measures 14° less than the measure of its complementary angle. What is the measure of each angle?
Answer:
38 and 52
Step-by-step explanation:
x = small angle
Complementary angles add to 90 degrees
x + x+14 = 90
2x = 76
x= 38
90-38 = 52
52-14 = 38
38 +52 = 90
The equations y = tan^2 (x) and y = 1 are graphed below. According to the graphwhich of the following is part the solution to the trigonometric inequality tan^2 (x) < 1 over the interval 0 <= x <= 2pi radians?
Answer: a
Step-by-step explanation:
just took test edg2020
The part of the solution of the equation that lies in the solution region of the inequality is x = π/6, the correct option is A.
What is an Inequality?An Inequality is a statement that is formed when two expressions are joined using an inequality operator.
The equation is
y = tan²x
y = 1
the inequalities are
tan²x < 1 ( 0≤ x ≤ 2π)
The graph of the system of equations and the inequality is plotted, and attached with the answer.
The answer can be seen as x = π/6.
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Express the following
ratio in its simplest
terms: 4 weeks 6 days
Answer:
it would be 2/3............
Answer:
=4:6
4
6
=2
3
2:3
Step-by-step explanation:
Hope this helps
Pls mark me the brainliest
Find the value of y
pls let me know how u solve this
Answer:
X° = 45°
Y = 8√2
Step-by-step explanation:
Angle of this triangle 45°:45°:90° so ratio of the triangle = 1:1:√2
8:8:8√2
I hope you understand it and sorry if it is wrong
Salim walked113miles to school and then212miles to work after school. How far did he walk in all? 316 miles 325 miles 345 miles 356 miles
Answer:
Total distance traveled = 1/3 + 1/2 = 2+3/6 = 5/6 miles
Hope this helps!
Step-by-step explanation:
kaley and tom both work at publix
Answer:
Sorry, is there more to the question?
Step-by-step explanation:
Put it DB and I'll gladly answer!
question: what is the relationship between measures of angle 1 and angle 2
pls help need answer fast
Answer:
C.
Step-by-step explanation:
m1 is greater than m2 because the angle is larger
Which algebraic expression is equivalent to the expression below? 4/5x - 7/5y
A. 1/5(4x - 7y)
B. 5(7x - 7y)
C. 5(4x - 7y)
D. 1/5(7x + 4y)
Use this picture and help please
Answer:
This would be 55 degrees because the sum of angles A, B and C = 180 degrees
Convert the binary number 11011010 to decimal.
Answer:
218
Step-by-step explanation:
im not sure im sorry in advance if im not
128+64+0+16+8+0+2+0=218
The population f(x), in millions, of State A of a country after x years is represented by the function shown below: f(x) = 4(1.08)x The graph shows the population g(x), in millions, of State B of the country after x years: Graph of function g of x equals 2 multiplied by 1.08 to the power of x Which conclusion is correct about the population of State A and State B? The original population of State A was double of the original population of State B. The original population of State B was double of the original population of State A. The original population of State A was four times of the original population of State B. The original population of State A was equal to the original population of State B.
We want to compare the population equations for two given states.
The correct option is:
"The original population of State A was double of the original population of State B"
We know that the population of state A is given by:
f(x) = 4*(1.08)^x
While for state B, the population is given by:
g(x) = 2*(1.08)^x
We want to see which conclusion is correct about the population of state A and state B.
First, the general exponential growth equation is given by:
h(x) = A*(r)^x
Where A is the initial value and r is the rate of growth.
With this, we can see that f(x) and g(x) have the same rate, and f(x) has an initial value that is twice the one of g(x).
Then the correct option is "The original population of State A was double of the original population of State B"
Because the initial value represents the initial population.
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Units of Length
Write a conversion factor that you would use to convert
from feet to meters.
Customary System
Units
Metric System Units
new units of measure
original units of measure
1 inch
2.54 centimeters
numerator =
1 foot
0.3048 meters
denominator =
1 mile
1.61 kilometers
Intro
Done
Answer:
1 foot = 0.3048 meters
Step-by-step explanation:
1 foot = 12 inches
1 inch = 2.54 centimeters
1 foot = 12 * 2.54 = 30.48 centimeters
1 meter = 0.01 centimeters
1 foot = 0.3048 meters
Answer:
numerator =
✔ 0.3048 meters
denominator =
✔ 1 foot
Step-by-step explanation: I got it right
According to a disease control center, 26% of people in a certain country have high blood pressure. If a person in this country is selected at random, determine the odds in favor of this person having high blood pressure.
Answer:
Squirrel has High BLood pressure
Step-by-step explanation:
Squirrels
Last question Please I really need help ASAP! I WILL GIVE BRAINLIEST!!!!!
∠AOB is a right angle.
OC bisects ∠ AOB
D is on the interior of ∠ AOC
E is on the interior of ∠ COB
∠ AOD = 23 degrees
∠ DOC is congruent to ∠ EOB
∠ BAD = ∠ EAF = ∠ FAC
Draw this picture and then using that picture identify the true statements below.
a)
m∠ DOC = 23
b)
m∠ DOC = 22
c)
m∠ AOC = 90
d)
m∠ COE= 23
e)
m∠ AOC= 45
Step-by-step explanation:
a) is true
b) is true
c) is false
d) is false
e) is true
The volleyball team raised $350 from its fundraiser. It wants to buy jerseys and volleyballs. The jerseys cost $12 each, and the team needs 22 jerseys. Volleyballs cost $15 each. What is the maximum number of volleyballs the team can buy and still have money left? Write your answer and explain the steps you took. WILL GIVE BRAIKNLIEST IF RIGHT!!!!!!!!
Answer:
6
Step-by-step explanation:
Answer:
The team can buy 5 volleyballs at maximum with no money left over.
Step-by-step explanation:
First, you need to find the money that the jerseys used:
12 × 22 = $264
Next, you have to subtract that from the total amount:
350 - 264 = $86
Finally, you have to see how many volleyballs you can buy:
If volleyballs cost $15 each then, 86 ÷ 15 = 5.73333333(Infinite)
But you can not buy part of a volleyball so you would have to buy 5 volleyballs. Then you would only have .7333333(Infinite) money left over, but that wouldn't be good for anything.
Is this a good answer????
The sum of three consecutive numbers is 84. What is the largest of these numbers?
26
27
28
29
Step-by-step explanation:
set 3 no is ,x _ I ,x,x+1
X-1 + x + x + I = 84
3 X = 84
X= 84/ 3
X= 2 8
largest no is 29
A submarine started at the surface of the water and
was moving down at –15 kilometers per
minute
toward the ocean floor. The submarine traveled at
this rate for 52 minutes before coming to rest on the
ocean floor. What is the depth of the ocean floor?
Answer:
The depth of the Ocean Floor is -780 kilometers
Step-by-step explanation:
The answer is -780 because -15 multiplied by 52 equals -780.
HELP ILL GIVE BRAINLIEST!!!!
Answers:
A. 0 and 4
B. -4,-2 and 0
C. 0,2, abs 4
D. -4 and 0
Its A i had the same one. Hope it helps.
Agrocery store sells 4 avocados for $6.00. What is the unit cost of each avocado?
A) $2.40
B) $0.10
C $1.50
D
$0.60
Find the surface area of the square pyramid shown below.
9514 1404 393
Answer:
160 units^2
Step-by-step explanation:
Each of the four triangular faces has an area of ...
A = (1/2)bh = (1/2)(8)(6) = 24 . . . square units
The square base has an area of ...
A = s^2 = 8^2 = 64
Then the total surface area is ...
A = base area + 4 · triangle area
A = 64 + 4(24) = 160 . . . square units
What is the surface area of a rectangular prism that measures 10 in x 6 in x 4 in?
Answer: 240 in
Step-by-step explanation: 10 x 6 x 4 = 240 in
I hope that helps
A deep ocean trench is 30,000 feet deep How deep is that in miles? Round your answer to two decimal places. (There are 5,280 feet in a mile.)
If a mile =5,208 ft that means you need to divide 30,000÷5,280 to get your answer!
Step-by-step explanation:
30,000÷5,280= 5.68mil
2:3= 10:
12:15 = 4:
1:5= 5:
15:30 = 1 :
Answer:
I think this is the answer
Step-by-step explanation:
2:3=10:15
12:15=4:5
1:5=5:25
15:30=1:2
Find the area of the shaded region
Answer: To find the area of the shaded region :
Calculate the area of both shapes. The area of a rectangle is determined by multiplying its length times its width. The area of a circle is Pi (i.e., 3.14) times the square of the radius. Find the area of the shaded region by subtracting the area of the small shape from the area of the larger shape.
Step-by-step explanation: I cannot see the picture to answer your question but I hope this helps you find put your answer. :)
Answer:
13
Step-by-step explanation:
Start with the smaller sqaure without the x varible which is 7 x 3 = 21
Then the larger square without the varible, 8 x 4 = 32
Now we subtract 21 from 34 and get 13.
So the area for the shaded region should be 13
If AB = 2x – 5, BC = x – 2, and AC = 20,
find AB.
please help me out yall
Answer:
as the picture shown
Step-by-step explanation: