Answer: Archimedes
Step-by-step explanation:
Archimedes was considered the father of mathematics, simply because he made profound advancements in both science and math. His title is purely a nickname, and not because he actually created math.
Answer:
Archimedes is known as the Father Of Mathematics
Step-by-step explanation:
Which of the following expressions are equivalent to 6 + (-4) - 56+(−4)−56, plus, left parenthesis, minus, 4, right parenthesis, minus, 5?
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
-(-6+4)-5−(−6+4)−5minus left parenthesis, minus, 6, plus, 4, right parenthesis, minus, 5
(Choice B)
B
6-4-(-5)6−4−(−5)6, minus, 4, minus, left parenthesis, minus, 5, right parenthesis
(Choice C)
C
6-(4+5)6−(4+5)6, minus, left parenthesis, 4, plus, 5, right parenthesis
(Choice D)
D
6+4-56+4−56, plus, 4, minus, 5
(Choice E)
E
-(-6)+(-4)-(-5)−(−6)+(−4)−(−5)
Answer:
Step-by-step explanation:
−5+6−4
and
−4+(−5)+6
What is the value of log625^5
Answer:
13.979
Step-by-step explanation:
log 625^5 = 5 log 625 = 5*2.79588=
Answer:
Exact Form:
1/4
Decimal Form:
0.25
Step-by-step explanation:
According to the Knot, 22% of couples meet online. Assume the sampling distribution of p follows a normal distribution and answer the following questions.
a. Suppose a random sample of 150 couples is asked, "Did you meet online>" Describe the sampling distribution of p, the proportion of couples that met online.
b. What is the probability that in a random sample of 150 couples more than 25% met online?
c. What is the probability that in a random sample of 150 couples between 15% and 20% met online?
Using the normal distribution and the central limit theorem, we have that:
a) The sampling distribution is approximately normal, with mean 0.22 and standard error 0.0338.
b) There is a 0.1867 = 18.67% probability that in a random sample of 150 couples more than 25% met online.
c) There is a 0.2584 = 25.84% probability that in a random sample of 150 couples between 15% and 20% met online.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].In this problem:
22% of couples meet online, hence p = 0.22.A sample of 150 couples is taken, hence n = 150.Item a:
The mean and the standard error are given by:
[tex]\mu = p = 0.22[/tex]
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.22(0.78)}{150}} = 0.0338[/tex]
The sampling distribution is approximately normal, with mean 0.22 and standard error 0.0338.
Item b:
The probability is one subtracted by the p-value of Z when X = 0.25, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.25 - 0.22}{0.0338}[/tex]
Z = 0.89
Z = 0.89 has a p-value of 0.8133.
1 - 0.8133 = 0.1867.
There is a 0.1867 = 18.67% probability that in a random sample of 150 couples more than 25% met online.
Item c:
The probability is the p-value of Z when X = 0.2 subtracted by the p-value of Z when X = 0.15, hence:
X = 0.2:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.2 - 0.22}{0.0338}[/tex]
Z = -0.59
Z = -0.59 has a p-value of 0.2776.
X = 0.15:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.15 - 0.22}{0.0338}[/tex]
Z = -2.07
Z = -2.07 has a p-value of 0.0192.
0.2776 - 0.0192 = 0.2584.
There is a 0.2584 = 25.84% probability that in a random sample of 150 couples between 15% and 20% met online.
To learn more about the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213
Award: 1.00 point Exercise 6-10A (Static) Why is it important to prepare the benefit analysis report or the total compensation report? [You may select more than one answer. Single flick the box with the question mark to produceea check marka forma correct answer and doubye-click the both with the question mark to empty the box for a wrong answer. Any boxes left with a question mark will be automatically graded as incorrect.) The reports may be used to accompany benefits billing. The reports may be used as employee contracts. The reports promote employee education about the total value of their salary and benefits. The reports inform labor planning and employer cost strategies. References Check All That Apply Difficulty: 1 Easy Exercise 6-10A (Static) Learning Objective: 06-06 Complete Benefit Analysis as a Function of Payroll
Answer:
i think its option one
Step-by-step explanation:
The length of a rectangle is triple the width. If the area of the rectangle is 75 square inches, then find the length and width
Answer:
W = 5
L = 15
Step-by-step explanation:
Formula for Area of Rectangle is L × W
Since stated triple;
L = 3W
Area = L×W = 3W² = 75
It'll be:
3W² = 75
Divide both sides with 3:
3W² = 75
3 3
W² = 25
Then square root both sides:
w = 5
Again stated that length is triple the width:
L = 5 × 3
L = 15
Therefore;
W = 5
L = 15
Why would it
be better to measure the length of your classroom with
meterstick instead of a centimeter ruler?
Answer:
Meterstick
Step-by-step explanation: A standard classroom is basically just a large open room, no rooms. So it is more straight than it is curved, and if you can cover a larger area in a shorter time, it is more effecient.
Use the compound interest formulas A = P1+
and A = Pert to solve.
Suppose that you have $11,000 to invest. Which investment yields the greater return over 9 years: 7.5% compounded
continuously or 7.6% compounded semiannually?
Answer:
7.5% compounded continuously yields the greatest return after 9 years
Step-by-step explanation:
Compounded interest = P(1+r/n)^(nt), where P is the principle, r is the rate of interest, n is the number of times compounded annually, and t is the time of the investment.
7.6% compounded semiannually:
I = 11000(1+0.076/2)^(2*9) --> 11000(1.038)^18 ~ $21525.09
7.5% compounded continuously:
Since it is compounded continuously, we use the mathematical constant e.
I = 11000e = $29901.01
A triangular prism and its dimensions are shown in the diagram. What is the lateral surface area of this triangular prism in square feet?
Answer:
112 ft
Step-by-step explanation:
AL = (a+b+c)h
= (6+12+10) x 4
= 112 ft
The selling price for a classic speedboat is $20,000, which is $2000 less than two times its original price. What was the original price of the speedboat?
Answer:
$11,000
Step-by-step explanation:
let x = original price.
2x-2000=20000
2x=22000
x=11000
325.39 3.26.3 326.15 326.48 from greatest to least
Answer: 1)3.26.3
2)326.15
3)325.39
4)326.48
Step-by-step explanation: you want to start from the lowest number to get your answer
Calculus hw, need help asap with steps.
Answers are in bold
S1 = 1
S2 = 0.5
S3 = 0.6667
S4 = 0.625
S5 = 0.6333
=========================================================
Explanation:
Let [tex]f(n) = \frac{(-1)^{n+1}}{n!}[/tex]
The summation given to us represents the following
[tex]\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!}=\sum_{n=1}^{\infty} f(n)\\\\\\\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!}=f(1) + f(2)+f(3)+\ldots\\\\[/tex]
There are infinitely many terms to be added.
-------------------
The partial sums only care about adding a finite amount of terms.
The partial sum [tex]S_1[/tex] is the sum of the first term and nothing else. Technically it's not really a sum because it doesn't have any other thing to add to. So we simply say [tex]S_1 = f(1) = 1[/tex]
I'm skipping the steps to compute f(1) since you already have done so.
-------------------
The second partial sum is when things get a bit more interesting.
We add the first two terms.
[tex]S_2 = f(1)+f(2)\\\\S_2 = 1+(-\frac{1}{2})\\\\S_2 = \frac{1}{2}\\\\S_2 = 0.5\\\\\\[/tex]
The scratch work for computing f(2) is shown in the diagram below.
-------------------
We do the same type of steps for the third partial sum.
[tex]S_3 = f(1)+f(2)+f(3)\\\\S_3 = 1+(-\frac{1}{2})+\frac{1}{6}\\\\S_3 = \frac{2}{3}\\\\S_3 \approx 0.6667\\\\\\[/tex]
The scratch work for computing f(3) is shown in the diagram below.
-------------------
Now add the first four terms to get the fourth partial sum.
[tex]S_4 = f(1)+f(2)+f(3)+f(4)\\\\S_4 = 1+(-\frac{1}{2})+\frac{1}{6}-\frac{1}{24}\\\\S_4 = \frac{5}{8}\\\\S_4 \approx 0.625\\\\\\[/tex]
As before, the scratch work for f(4) is shown below.
I'm sure you can notice by now, but the partial sums are recursive. Each new partial sum builds upon what is already added up so far.
This means something like [tex]S_3 = S_2 + f(3)[/tex] and [tex]S_4 = S_3 + f(4)[/tex]
In general, [tex]S_{n+1} = S_{n} + f(n+1)[/tex] so you don't have to add up all the first n terms. Simply add the last term to the previous partial sum.
-------------------
Let's use that recursive trick to find [tex]S_5[/tex]
[tex]S_5 = [f(1)+f(2)+f(3)+f(4)]+f(5)\\\\S_5 = S_4 + f(5)\\\\S_5 = \frac{5}{8} + \frac{1}{120}\\\\S_5 = \frac{19}{30}\\\\S_5 \approx 0.6333[/tex]
The scratch work for f(5) is shown below.
find the product 4 (-9 1/8)
Answer:
4/8=2
-91/2=-45.5
by eliminate 4 by dividing by 8
The diameter of a circle is 8 miles. What is the angle measure of an arc 3 miles long?
Answer:
[tex]\sf \theta=\dfrac34 \ radians=42.97 \textdegree \ (nearest \ hundredth)[/tex]
Step-by-step explanation:
Formulae
[tex]\sf radius (r)=\dfrac12 d[/tex]
(where d is the diameter of a circle)
[tex]\sf arc \ length =r\theta[/tex]
(where r is the radius and [tex]\theta[/tex] is measured in radians)
Calculation
Given:
[tex]\sf radius (r)=\dfrac12 \cdot 8=4 \ mi[/tex]arc length = 3 miSubstituting these values into the formula for arc length:
[tex]\implies \sf 3 =4\theta[/tex]
[tex]\implies \sf \theta=\dfrac34 \ radians[/tex]
To convert radians to degrees use
[tex]\sf 1 \ rad \cdot \dfrac{180\texrdegree}{\pi}[/tex]
[tex]\implies \sf \dfrac34 \cdot \dfrac{180\texrdegree}{\pi}=42.97183463...\textdegree[/tex]
Now
[tex]\\ \rm\rightarrowtail \theta=\dfrac{l}{r}[/tex]
[tex]\\ \rm\rightarrowtail l=r\theta[/tex]
[tex]\\ \rm\rightarrowtail 3=4\theta[/tex]
[tex]\\ \rm\rightarrowtail \theta=\dfrac{3}{4}^c[/tex]
Which pair of segments must be parallel?
HELPP
Answer:
AB and GH
Step-by-step explanation:
Calculation of slope of each segment
AB = -1/4CD = -5/6EF = -5/5 = -1GH = -2/8 = -1/4Parallel lines have the same slope.
⇒ AB and GH are the pair of segments which are parallel
20 POINTS
Part E
How many of the 320 million Americans would you predict wear glasses?
If z varies directly with the square of x and inversely with the cube of y, when x = 8, y = 2, and z = 12, what is x when y = 1 and z = 24?
PLEASE HELP!!! :))))
Step-by-step explanation:
it just means
z = k×x²/y³
12 = k×8²/2³ = k×64/8 = k×8
k = 12/8 = 3/2
24 = k×x²/1³ = 3/2 × x²/1 = 3/2 × x²
24/(3/2) = x²
48/3 = x²
16 = x²
x = 4 or
x = -4
The _____ of two sets X and Y is denoted by X-Y
Answer:
Cartesian product
Step-by-step explanation:
The Cartesian product of two sets, X and Y, denoted by X × Y, is the set of all ordered pairs (x, y), where x is an element of X and y is an element of Y: 8 (2.4.1) X × Y = { (x, y) ∣ x ∈ X ∧ y ∈ Y } For example, if Children = { Peter, Mark, Mary }, and Parents = { Paul, Jane, Mark, Mary }, then
The length is :____ meters and the width is ____meters.
Answer:
Length= 8, Width= 4
Step-by-step explanation:
Say the length is l, and the width is w.
We can set l, the length as 2w, as it is double the length.
The perimeter= 2l + 2w= 24
Input l as 2w, get
4w+2w=24
6w=24, w=4.
Length is w*2, so length is 8.
Expand to write an equivalent expression…
1/2(-4x + 2y)
Help!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
53
Step-by-step explanation:
[tex] \frac{sin(56)}{78.6} = \frac{sin(90)}{ab} \\ \\ absin(56) = sin(90) \times 78.6 \\ \\ ab = \frac{sin(90) \times 78.6}{sin(56)} \\ ab = 94.8 \\ \\ {x}^{2} + {78.6}^{2} = {94.8}^{2} \\ {x}^{2} = {94.8}^{2} - {78.6}^{2} \\ {x}^{2} = 8987.04 - 6177.96 \\ {x}^{2} = 2809.08 \\ x = \sqrt{2809.08} \\ x = 53[/tex]
What is the area of this shape?
Answer:
Area is 80[tex]m^{2}[/tex]
Step-by-step explanation:
Since the shape is a triangle, then the formula for area is: a = bh/2
Given values:
b = 20m
h = 8m
Substitute the given values into the equation
a = 20 x 8 / 2
a = 160/2
a = 80 meters squared
hope this helps and is right!! p.s. i really need brainliest :)
the present ages of a father and his son are 40 years and 8 years respectively how many years ago the product of their ages was 105
Answer:
5 years ago
Step-by-step explanation:
5 years ago, they were 35 years old and 3 years old. 35*3=105.
I need help with this question
Answer:
301 feet
Step-by-step explanation:
plug in the known values
[tex]85=\sqrt{24d}[/tex]
square both sides to cancel the square root
[tex]7225=24d[/tex]
divide both sides by 24 to get d on its own
[tex]d=301.041[/tex] feet
to the nearest foot is 301 feet
I do not understand how they got this answer. I am stuck on the exponent party- Please see attached
Looking at the question, the answer gotten is:$4316.55. The question is related to compound interest.
What is compound interest?Compound interest is known to be the interest that is earned on a principal sum in addition to the accumulated interest previously. It is as a result of reinvesting interest.
To find the compound interest, the formula used is:
A= P(1+r/n)^nt.
Where
P is the principal sum= $3500
r is the rate = 0.035
n is the compounding period = 12 months.
t is the time = 6 years.
Substituting them in the equation, we have:
A = 3500 ( 1 + 0.035/12)^12×6
Working out the one in the bracket and multiplying the exponent, we have:
A = 3500 (1.00291667)^72
Note: We got 72 by multiplying 12 by 6.
1.00291667 raised to the power of 72 = 1.23330133
A = 3500× 1.23330133 = $4,316.55
Ans: $4,316.55
Learn more about compound interest on https://brainly.com/question/24274034
choco chip cookies cost $3.20 for the 15oz size . The 18oz size $3.75 Which is the better buy
Answer:
18 oz
Step-by-step explanation:
Choco Chip Cookies (15 oz): [tex]\frac{\$3.20}{15oz}=\frac{\$0.213}{oz}[/tex]
Choco Chip Cookies (18 oz): [tex]\frac{\$3.75}{18oz}=\frac{\$0.208}{oz}[/tex]
So, the 18oz package is the better buy by about [tex]\$0.005[/tex]
PLEASE HELP ME WITH THIS !!
Answer: C
Step-by-step explanation:
When Flipped Down A is on the same point as D
Answer:
c
Step-by-step explanation:
because they are mirrored the only one that is equivilent is c
b doesnt corrospond to f it corrosponds to e
bc corrosponds to ef
ab corrosponds to ed.
Find the missing numerator that will make the rational expressions equivalent.
82x+7=?6(2x+7)
The missing numerator that will make the rational expressions equivalent is (82x + 7) / (12x + 42)
What is an equation?
An equation is an expression that shows the relationship between two or more variables and numbers.
Let y represent the missing numerator, hence:
82x + 7 = y * 6(2x+7)
82x + 7 = y * (12x + 42)
y = (82x + 7) / (12x + 42)
Find out more on equation at: https://brainly.com/question/2972832
Help help help help
If f(x)=3x−1 and f(a)=−43, what is the value of a ??
Answer:
a = -14
Step-by-step explanation:
f(a) = -43
3a - 1 = -43
3a = -43 + 1
3a = -42
a = -42/3
a = -14
need help with geometry (number3)
Answer:
Step-by-step explanation:
If this is a parallelogram., this means that the opposite angles are congruent. Thus, the erasure of angle E is equal to the measure of angle G.
So, 10x-21=4x+27, meaning x=8.
Therefore, the measure of angle E is 10(8)-21=59 degrees