[tex]\left( \sqrt 3 + \sqrt 7\right) \left( \sqrt 3 - \sqrt 7\right)\\\\=\left(\sqrt 3 \right)^2 - \left(\sqrt 7 \right)^2\\ \\=3-7\\\\=-4[/tex]
Answer:
- 4
Step-by-step explanation:
([tex]\sqrt{3}[/tex] + [tex]\sqrt{7}[/tex] )([tex]\sqrt{3}[/tex] - [tex]\sqrt{7}[/tex] )
each term in the second factor is multiplied by each term in the first factor.
[tex]\sqrt{3}[/tex] ([tex]\sqrt{3}[/tex] - [tex]\sqrt{7}[/tex] ) + [tex]\sqrt{7}[/tex] ([tex]\sqrt{3}[/tex] - [tex]\sqrt{7}[/tex] ) ← distribute parenthesis
= 3 - [tex]\sqrt{21}[/tex] + [tex]\sqrt{21}[/tex] - 7 ← collect like terms
= - 4
In 2014 the population of Kenya was estimated to be 45,121,040 with a growth rate of 2.7%. Question 1 Use the exponential growth formula to write an equation that estimates the population y in terms of the time t. Enter your answer in the box. Then apply the exponential growth formula to estimate the population of Kenya in 2020. Round to the nearest whole number
Answer:
y = 45,121,040×1.027^t
Step-by-step explanation:
An exponential growth equation is generally of the form ...
value at time t = (initial value)(growth factor)^t
where the growth factor is the multiplier for a period equal to one time unit.
Here, the initial value (in 2014) is 45,121,040. The growth factor is given as 1.027 (2.7% added per year), and we can define t as the number of years after 2014. Then our equation is ...
y = 45,121,040×1.027^t . . . . where t = years after 2014
SOMEONE HELP ME PLEASEE
Answer:
area: 165yd^2 perimeter:26yd or 33yd
Step-by-step explanation:
11ydx15yd= 165yd^2
11yd+15yd=26yd
Answer:
56.1, 36.2
Step-by-step explanation:
For this we need to use the Pythagorean Theorem, which is a^2+b^2=c^2. We have our a and c values, so we can make the equation 11^2+b^2=15^2, or 121+b^2=225. Next, we isolate b.
121+b^2=225
-121 -121
___ ___
0 104
b^2=104
Now, we have to find the square roots of both sides. If we do this, we get b= 10.2.
Now, we can find our perimeter:
11+15+10.2= 36.2
For area, the formula is 1/2(b)h (1/2 times the base and height), so:
1/210.2=5.1
5.1*11=56.1
Hope this helps!
Factor completely 16x8 − 1.
Answer:
Step-by-step explanation:
(4x^4 - 1)(4x^4 + 1)
(2x^2 - 1)(2x^2 + 1)(4x^4 + 1)
what's the difference between dy/dx and d/dx?
Answer:
There is a slight difference but the result is the same.
In the notation ddx(y) the ddx part is an operator which says ‘the function which is the differential with respect to x of ⋯’ and y is the function being operated on. The ddx and y are two separate entities in this notation.
In the notation dydx we mean the function that is the result of differentiating the function y with respect to x. In this case, there is only a single entity: dydx.
Both notations mean ‘the function which is the differential of function y by x
Describe the transformations necessary to transform the graph of f(x) into that of g(x).
Using translation concepts, it is found that the necessary transformations are given as follows:
Reflection over the y-axis. Horizontal stretch by a factor of 2.Shift left 3 units.Reflection over the x-axis.Shift down 1 unit.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The original function f(x) is given by:
[tex]f(x) = \sqrt{x}[/tex]
The transformations are as follows:
For the values of x, the function was multiplied by -1/2 and then 3 was added. Thus it was reflected over the y-axis, horizontally stretched by a factor of 2 and shifted left 3 units.Outside the domain, in the values of y, the function was multiplied by -1 and then subtracted by 1, hence it was reflected over the x-axis and shifted down one unit.More can be learned about translation concepts at https://brainly.com/question/4521517
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What is the value of y?
a.) 17.25
b.) 33
c.) 37
d.) 39
Answer:
a
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
u know that the left triangle is not a right angles triangle so u cannot do Pythagoras and 27 is the other bottom side meaning that the length of the left triangle base is 20.25
A segment with endpoints at the center and on the circle.
Answer:
The set of points equidistant from a given point (the center). Radius : A segment with endpoints at the center and on the circle.
Step-by-step explanation:
Need help please answer ASAP!
Answer:
39. (4) 4 1/16
Step-by-step explanation:
Simplifying
f(x) = 4x⁰ + (4x)⁻¹Any term to the power is equal to 1f(x) = 4(1) + 1/4xSubstituting x = 4
f(4) = 4 + 1/4(4)f(4) = 4 + 1/16f(4) = 4 1/16(4) 4 1/16Please help l don’t understand
Based on the graph given, the two points that need to be plotted are (9, 4) and (7, 3).
How should a graph on Age v. Hours of TV watched be plotted?The points that are already plotted on the graph represent the results of the hours of television watched by children.
For instance, children of 6 years watched 2 hours of television. For that reason, the point where 6 (x axis) and 2 (y axis) meet on the graph is marked with an x.
The last two points would therefore be (9, 4) and (7, 3) to show that 9 year olds watch 4 hours of television and 7 year olds watch 3 hours of television.
Find out more on constructing graphs at https://brainly.com/question/1660438?referrer=searchResults.
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Express x^2-5x+8 in the form (x-a)^2+b where a and b are integers
Answer:
[tex]f(x)=(x-\frac{5}{2})^2+\frac{7}{4}[/tex]
Step-by-step explanation:
Complete the square
[tex]f(x)=x^2-5x+8\\\\f(x)-1.75=x^2-5x+8-1.75\\\\f(x)-1.75=x^2-5x+6.25\\\\f(x)-1.75=(x-2.5)^2\\\\f(x)=(x-2.5)^2+1.75\\\\f(x)=(x-\frac{5}{2})^2+\frac{7}{4}[/tex]
What ratio is equivalent to the rate 40 miles / 1 hour
Answer:
40:1
Step-by-step explanation:
hope this helps:)
PLEASE HELPPP!!!!
Which of the following is the best buy?
3 lb. for $5.13
2 lb. for $3.37
3.25 lb. for $5.53
1.5 lb. for $2.52
Answer:
3.25\
Step-by-step explanation:
Answer:
$2.52
Step-by-step explanation:
u have to at the lb. and the $ and which will give u more for a less price so we x out $5.53 and then 5.13.now all you have left is 2.52 and 3.37 and 3.37 is more than 2.52 and 2 lb. is more ik but u save more money by buying 1.5 lb.
hope this helps:)!!
Help me with this extremely hard differentiation question , [Scroll] >>
[tex]\huge\frac{d}{dx}[\sum_{n=0}^{∞}[(\frac{(-1) ^ {n}}{(2n+1)!})(\frac{1}{1+e^{x}})^{2n+1}] ][/tex]
Answer:
[tex]f'(x)=\displaystyle -\frac{e^x}{(1+e^x)^2}\cos\biggr(\frac{1}{1+e^x}\biggr)[/tex]
Step-by-step explanation:
Recall the power series [tex]\sin(x)=\displaystyle \sum\limits^\infty_{n=0}(-1)^n\frac{x^{2n+1}}{(2n+1)!}[/tex].
In this case, [tex]x[/tex] is replaced with [tex]\displaystyle \frac{1}{1+e^x}[/tex], so our power series actually works out to be [tex]\displaystyle \sin\biggr(\frac{1}{1+e^x}\biggr) =\sum\limits^\infty_{n=0}(-1)^n\frac{\bigr(\frac{1}{1+e^x}\bigr)^{2n+1}}{(2n+1)!}[/tex]! Amazing, huh?
Now, we find the derivative of the function by using the chain rule:
[tex]\displaystyle \frac{d}{dx}\sin\biggr(\frac{1}{1+e^x}\biggr)=\frac{d}{dx}\biggr(\frac{1}{1+e^x}\biggr)*\cos\biggr(\frac{1}{1+e^x}\biggr)=-\frac{e^x}{(1+e^x)^2}\cos\biggr(\frac{1}{1+e^x}\biggr)[/tex]
You didn't specify if you just wanted the derivative of the series to be a function or a series, so I'm going to assume you want the function. Let me know if there's more to your problem.
is −1.28 a rational number?
The number -1.28 is rational if it is an integer or decimal, so yes it is.
Answer:
we have 1.28 with bar above 28 signifying that the number can also be written as 1.28282828 The mixed number is then equal to,
1 and 28/99 or 1 and 28 over 99
Therefore, the answer to this item is the second choice.
Step-by-step explanation:
My brother helped me with this one
2(x + 3) = x - 4 solve
Answer:
x=-10
Step-by-step explanation:
2(x+3)=x-4
2x+6=x-4
-2x -2x
6=-x-4
+4 +4
10=-x
-1 -1
-10=x
[tex] \Large{\boxed{\sf x = 10}} [/tex]
[tex] \\ [/tex]
Explanation:Given equation:
[tex] \sf 2(x + 3) = x - 4 [/tex]
[tex] \\ [/tex]
Expand the left side using the following distributive property:
A(B + C) = AB + AC
[tex] \\ [/tex]
Here, A = 2, B = x, and C = 3.
We get:
[tex] \sf 2(x) + 2(3) = x - 4 \\ \\ \sf 2x + 6 = x - 4 [/tex]
[tex] \\ [/tex]
Now, subtract 6 from both sides:
[tex] \sf 2x + 6 - 6 = x - 4 - 6 \\ \\ \sf 2x = x - 10 [/tex]
[tex] \\ [/tex]
Subtract x from both sides :
[tex] \sf 2x - x = x - 10 - x \\ \\ \\ \boxed{\boxed{\sf x = -10}} [/tex]
[tex] \\ \\ [/tex]
▪️Learn more about first-degree equations here:
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How to do 2/5 = (x-3)/(7x+15)
Answer:
[tex]x = - 5 [/tex]
Step-by-step explanation:
To work out this question you have to first cross multiply.
[tex] \frac{2}{5} = \frac{(x - 3)} {(7x + 15)} \\ \\ 2(7x + 15) = 5(x - 3)[/tex]
When you cross multiply you will get the equation above. Therefore
[tex](2 \times 7x) + (2 \times 15) = (5 \times x) \\ - (5 \times 3) \\ \\ 14x + 30 = 5x - 15 \\ \\ 14x - 5x = - 30 - 15 \\ \\ 9x = - 45[/tex]
Therefore
[tex] \frac{9}{9} x = \frac{ - 45}{9} \\ \\ x = - 5[/tex]
Answer:
x = -5
Step by step:
multiply both side by 7x + 15.
2/5 (7x+15)= x − 3
Simplify 2)5 (7x+15) to 2(7x+15)/5.
2(7x+15)/5= x - 3
multiply both sides by 5.
2(7x+15)= 5x - 15
Expand.
14x+30= 5x - 15
subtract 5x from both sides.
14x+30−5x= − 15
Simplify 14x + 30 - 5x14x + 30−5x to 9x + 309x + 30.
9x+30= - 15
Subtract 30 from both sides.
simplify
x = -5
Mr smith has 28 children if he wants 2 give 2 sweets to his class how many sweets
Answer:
56
Step-by-step explanation:
If each child gets 2 sweets then we have to multiply the number of children by 2.
[tex]28 \times 2 = 56[/tex]
Answer:
30 sweets.
Add 28 and 2.
PLEASE HELP ANSWERING THE QUESTIONS ILL GIVE BRAINLIEST OR WHATEVER
Answer:answer to 9:$1,025.00 answer to 10:$243.90 answer to 11:$1,025.15
Step-by-step explanation:
explanation to 9:First, converting R percent to r a decimal
r = R/100 = 7%/100 = 0.07 per year.
Solving our equation:
A = 500(1 + (0.07 × 15)) = 1025
A = $1,025.00
The total amount accrued, principal plus interest, from simple interest on a principal of $500.00 at a rate of 7% per year for 15 years is $1,025.00.explanation to 10:First, converting R percent to r a decimal
r = R/100 = 7%/100 = 0.07 per year.
Solving our equation:
P = 500 / ( 1 + (0.07 × 15)) = 243.90243902439
P = $243.90
The principal investment required to get a total amount, principal plus interest, of $500.00 from simple interest at a rate of 7% per year for 15 years is $243.90. explantion to 11:First, converting R percent to r a decimal
r = R/100 = 7%/100 = 0.07 per year.
Solving our equation:
A = 500(1 + (0.07 × 15)) = 1025
A = $1,025.00
The total amount accrued, principal plus interest, from simple interest on a principal of $500.00 at a rate of 7% per year for 15 years is $1,025.25.
help me solve please!!!!!!!!!
The probability of drawing a number card and then number card without replacement is 105/221 option first is correct.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
The total number of cards = 52
Total number of cards printed number on it = 36
The probability of drawing a number card and then number card without replacement:
[tex]= \rm \dfrac{36}{52}\times \dfrac{35}{51}[/tex]
= 1260/2652
= 105/221
Thus, the probability of drawing a number card and then number card without replacement is 105/221 option first is correct.
Learn more about the probability here:
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which of the following numbers ae divisible by 3?
a. 534
b.2176
c.59742
d.45846
which of the following numbers are divisible by 4?
a.9698
b.98746
c.5620
d.56208
Answer:
1. A
2. C
Step-by-step explanation:
1. A
2. C
Jeremy finished 3/5 of his homework what percent of homework did he finish
Answer:
60%
Step-by-step explanation:
Percent means per hundred. Change to "per hundred"
3/5 = 6/10 = 60/100
3/5 is 60%
OR
Divide 3/5 means 3÷5...
3÷5 = .6
Change decimal to percent by multiplying by 100.
.6 × 100 = 60
60%
Answer:
60%
Step-by-step explanation:
well if they only finished 3/5 it’s going to be
60/100 = 60%
Please help me,Please I have a class in 2 hours Please help me
To find the perimeter of a shape you add all the side lengths together.
Perimeter of A is 20cm because 7+7+3+3=20
Perimeter of B is 27cm because 9+8+10=27
Perimeter of C is 17cm because 6+6+5=17
Perimeter of D is 34cm because 10+10+4+4+3+3=34
On shape E there is one side length that we do not know. To find that do 8-3=5 because 5+3 would be the opposite side of the 8. Now do 5+8+8+4+12+3=40 cm which is the perimeter of shape E.
I hope this helps you have a good day
WILL MARK BRAINLIEST . PLEASE HELP . Pigeons can fly at a rate of 168ft every 6 minutes, and ravens can fly at a rate of 472ft every 12.5 mins. Which unit rate, per hour, represents the speed of the faster bird?
Answer:
2,265.60 ft/hr
Step-by-step explanation:
168ft/6min = 28ft/min * 60min= 1,680ft/hr
472ft/12.5min= 37.76ft/min * 60min= 2,265.60ft/hr
This figure shows three identical spherical billiard balls of diameter 6 cm inside an equilateral triangular frame.
Work out the perimeter of the frame, leaving your answer
in surd form.
Answer:
Perimeter = 18(1 + √3 ) cm
Step-by-step explanation:
The radius of each ball = 1/2 * 6 = 3 cm.
Lines drawn from the 2 points of contact for one billiard ball to the center of the ball are at right angles to the sides of the triangle ( Tangent/radius theorem).
If we now draw a line from the vertex of the big triangle to the center of the ball we get 2 right triangles, and they are 30-60-90 triangles.
If the adjacent side of a triangle ( which is part of the side of the big triangle) = x:
tan 30 = 3 / x
x = 3 / tan 30
= 3 / 1/√3
= 3√3 cm.
There are 6 of these sides in the big triangle so their total length =
18√3 cm.
The three 'middle' sides joining 2 billiard balls each have a length of 2 radii = 6 cms ( as they form a rectangle with the radii of 2 billiard balls).
So the perimeter of the triangle = 18√3 + 3(6)
= 18(1 + √3 ) cm
I would have liked to transfer a diagram but I can't get to copy it to this site.
Calculating Binomial Probabilities - Suppose you work for an airline and you are taking reservations for a flight on an aircraft that has 152 seats. You know, based on historical flights trends, that if you sell a single ticket there is a 91% chance that the person with the ticket will actually show up for the flight. You decide to try to make a little extra money by overbooking your flight and you sell 160 tickets hoping that not more than 152 people will actually show up for the flight (note: this is a common business practice! Click here to watch a video that explains why)
Explain how this scenario meets the four requirements in the definition of a Binomial Distribution.
Identify what n and p are in this example
Use technology (StatCrunch, Statdisk, or Excel) to calculate the probability that if you sell 160 tickets for your flight, more passengers will show up than there are seats available (again, the plane has 152 seats total). Post an image of your technology output using the Insert/Edit Image feature in Blackboard (no attachments!)
Based on this probability, do you think it is a wise business practice to oversell your flight in this manner? Explain.
The probability that if you sell 160 tickets for your flight, more passengers will show up than there are seats available is 0.02
How the scenario meet the requirements?The scenario meets the following requirements
The value of n is fixed i.e. 160The outcome has two possible values i.e. seats available or notThe chance that a person shows up is the same for each outcome i.e. p = 91%Each observation is independent.Identify n and pThe given parameters are:
n = 160
p = 0.91 i.e. 91%
x = 152
How to determine the probability?The distribution is a binomial distribution, and it is calculated using:
[tex]P(x) = ^nC_x * p^x * (1 - p)^{n -x}[/tex]
The probability is represented as:
P(x > 152) = P(153) + ..... P(160)
Using a technology tool, we have:
P(x ≤ 152) = 0.02
Conclusion on the calculationProbability values less than 0.25 are unlikely probabilities.
Because the probability value 0.02 is less than 0.25, then we can conclude that it is a wise business practice to oversell your flight in this manner.
Read more about probability at:
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Round 7.09 to the nearest tenth
Answer:
7.1
Step-by-step explanation:
To round 7.09 to the nearest tenth, you must use the hundredths' place value of 7.09, which is 9 and equal or more than 5. Therefore, the tenths value of 7.09 increases by 1 to 7.1.
how do u find the surface area of all the prisms?
What is the radius of a hemisphere with a volume of 281,250 2.14 cm^3
Answer:
:
Answer:the radius would be 88cm
Step-by-step explanation:
radius. r = base circumference. C = volume. V = curved surface area.
Solve for d.
3(d + 2) = 12
d =
Answer:
d = 2
Step-by-step explanation:
3(d + 2) = 12 ( divide both sides by 3 )
d + 2 = 4 ( subtract 2 from both sides )
d = 2
Answer:
d=2
Step-by-step explanation:
3(d+2)=12
divide both side by 3
d+2 =4
substract 2 from both side
d=2
Graph (x - 2)2 + (y - 1)2 = 9 - Double tap to add text
Answer:
Step-by-step explanation:
(x−2)2+(y−1)2=9
This is the form of a circle. Use this form to determine the center and radius of the circle.
(x−h)2+(y−k)2=r2
Match the values in this circle to those of the standard form. The variable r
represents the radius of the circle, h represents the x-offset from the origin, and k
represents the y-offset from origin.
r=3
h=2
k=1
The center of the circle is found at (h,k)
.
Center: (2,1)
These values represent the important values for graphing and analyzing a circle.
Center: (2,1)
Radius: 3
