Answer:
See below. The result using the binomial theorem is 1049.8560 compared with 1049.8573 using a calculator.
Step-by-step explanation:
Binomial theorem:-
( a + x)^n = a^n + nC1 a^(n-1) x + nC2 a^(n - 2)x^2 + .......
(4 + 0.02)^5 = 4^5 + 5C1* 4^4 *0.02 + 5C2* 4^3* 0.02^2 + 5C3*4^2*0.02^3
+ 5C4 * 4 * 0.02^4 + 0.02^5
= 1024 + 5*4^4*0.02 + 10*4^3*0.02^2 + 10*4^2*0.02^3 + 5*4*0.02^4 + 0.02^5
= 1024 + 25.6 + 0.256 + 0.0000032
Answer:
Keisha's Response: The 4th term is almost 0, so the 5th and 6th terms are also close to 0. Add the terms shown to approximate 4.025: 1024 + 25.6 + 0.256 + 0.001 = 1049.857.
Step-by-step explanation:
EDGINUITY
Select Independent or Not independent for each pair of events.
Rolling a 1 on a number cube and then rolling a 6 on the same number cube
Flipping heads on a coin flip and then spinning an odd number on a spinner
Selecting a quarter from a bag of coins, putting it in a parking meter, and then selecting a dime from the same bag
Answer:
The first pair of events are independent, the second pair of events are independent and the third pair of events are dependent.
Step-by-step explanation:
Independent events are events that do NOT rely on previous events. So, the chances of each of event happening in a pair of events is independent, or has no effect, on the chances of the other event. In the case of rolling a number cube and then rolling it again, your chances would be the same each time you roll the number cube as to what number you would get. Just because you rolled a '1' on the first roll, doesn't mean you can't get the same number (or another number) on another roll. The same reasoning applies to the coin flip and the spinner. These two events are not related and in no way would rely on each other. A coin flip will not affect the chances of spinning an odd number. However, if we have several coins in a bag and select a quarter, but do not replace it, our chances of selecting another coin changes because there are not only less coins in the bag, but there are less quarters to choose from. In the case of events with NO replacement, these events are dependent.
convert improper fractions such as 29/6
Answer:
Step-by-step explanation: to covert improper fractions to normal fractions.
29/6 would be 4 wholes and 5/6
You count how much 6’s are in the 29 which is 4. And then the left over would be 5 so 5/6
Which of following statements are true? 1. -18>5 2. -5> 0.5 3. -5>. 0 4. -5 > 5squared 5. -5> -18
A negative number is always less than a positive number.
When comparing two negative numbers, the smaller negative number is the greater value.
The answer would be 5. -5 > -18
Answer:
5. -5 > -18
Step-by-step explanation:
Positive numbers are greater than negative ones. Also think of the numbers on a mercury thermometer :- -5 his greater ( and warmer!) than -18.
Which angle has a positive measure ?
The given angle is measured clockwise with respect to {+x} axis. So, it has negative measure.
What is angle?An angle is formed when two rays have the same end point. The common end point is called vertex.
Given is to identify the positive angle.
Any angle measured clockwise with respect to + x axis is negative. Similarly, any angle measured anti - clockwise with respect to + x axis is negative.
Since only one angle is shown in the image, we will describe about it. It can be seen that the angle is measured clockwise with respect to + x axis. Hence, it is negative.
Therefore, the given angle is measured clockwise with respect to {+x} axis. So, it has negative measure.
To solve more questions on angles, visit the link below-
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how would you graph 4x+2y=16
Answer:
Step-by-step explanation:
There are several ways in which you could do this.
One involves finding the x- and y-intercepts, plotting them and drawing a straight line through them. Starting with 4x + 2y = 16, let x = 0 to find the y-intercept: 2y = 16, or y = 8. The y-intercept is (0,8). Next, let y = 0 in 4x + 2y = 16 and solve for x; this leads to the x-intercept. 4x = 16, so x = 4. The x-intercept is then (4, 0). Plot (4,0) and (0, 8) and draw a straight line through these two points.
Another involves solving 4x+2y=16 for y, obtaining the equivalent in slope-intercept form of this equation. Subtracting 4x from both sides, we get 2y = 16 - 4x. Dividing all terms by 2 results in y = -2x + 8.
As before, the y-intercept is (0,8). Plot this point. Now use the slope, m = -2, to find another point on this line: Starting at (0,8), move 1 unit to the right (increasing x by 1) and then move 2 units down, arriving at (1, 6). Plot this point. Now draw a straight line through (1,6) and (0,8). Your result should look the same as the previous graph you drew.
When Tom purchased a new motorcycle, he paid a 5% sales tax. The amount of sales tax he paid was $265. What was the total cost of the motorcycle including the sales tax? Enter your answer in the box. $
What is the negative x-intercept of the graph of the quadratic function f(x) = 5x2 + 4x - 1? A) - 7 5 B) - 2 5 C) - 1 5 Eliminate D) -1
Answer:
D
Step-by-step explanation:
The quadratic formula is
[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex].
It is important because while some quadratics are factorable and can be solved not all are. The formula will solve all quadratic equations and can also give both real and imaginary solutions. Using the formula will require less work than finding the factors if factorable. We will substitute a=5, b=4 and c=-1.
[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}\\x=\frac{-4+/-\sqrt{(4)^2-4(5)(-1)} }{2(5)}\\x=\frac{-4+/-\sqrt{16+20} }{10}[/tex]
We will now simplify and solve.
[tex]x=\frac{-4+/-\sqrt{36}}{10}\\x=\frac{-4+/-6}{10}[/tex]
x=-1 and x=0.2
The location of four game stops are on a coordinate grid are as follows: Stop 1 at (−2,1) Stop 2 at (−2, −7) Stop 3 at (5,−7) Stop 4 at (5, 1) Paulo begins at Stop 1 and then walks to Stop 2, then Stop 3, and then Stop 4. Then he walks to Stop 1 again. The path between each stop is a straight line. One unit on the coordinate grid equals 125 feet. What is the total distance Paulo walked?
Answer:
3750 ft
Step-by-step explanation:
Denote Stops as points A(-2,1), B(-2,-7), C(5,-7) and D(5,1) and find all distances between two consecutive points:
[tex]AB=\sqrt{(-2-(-2))^2+(1-(-7))^2}=8\ units;[/tex][tex]BC=\sqrt{(-2-5)^2+(-7-(-7))^2}=7\ units;[/tex][tex]CD=\sqrt{(5-5)^2+(1-(-7))^2}=8\ units;[/tex][tex]DA=\sqrt{(5-(-2))^2+(1-1)^2}=7\ units.[/tex]The total distance Paolo walked is
[tex]8+7+8+7=30\ units.[/tex]
Since 1 unit on the coordinate grid equals 125 feet, then the total distance Paolo walked is
[tex]30\cdot 125=3750\ ft.[/tex]
Can someone pls help me solve this question!!!!!!!
Total of 90 fish:
c + p = 90
Charlie gave 1/4 c to Peter. Now
Charlie has c - (1/4) c
Peter has p + (1/4) c
Peter gave 2/5 of his to Charlie. Now
Peter has p + (1/4) c - 2/5( p + (1/4) c )
Charlie has c - (1/4) c + 2/5( p + (1/4) c )
And then they had equal number:
c - (1/4) c + 2/5( p + (1/4) c ) = p + (1/4) c - 2/5( p + (1/4) c )
Let's do the easy subtractions then multiply by 20 to clear the fractions,
(3/4) c + 2/5( p + (1/4) c ) = 3/5( p + (1/4) c )
15c + 8p + 2c = 12p + 3c
14c = 4p
7c = 2p
c + p = 90
2c + 2p = 180
2c + 7c = 180
9c = 180
c = 20
p = 70
Answer: Charlie started with 20, Peter with 70
Check:
Initially C:20, P:70
1/4(20)=5 to P
C:15, P:75
(2/5) 75 = 30 to C
C:45, P45
Good
Help me again, please. ;w;
5x - 7y =58
y =-x +2
Using the substitution method, replace y in the first equation with the second equation:
5x - 7(-x+2) = 58
Simplify by using the distribution property:
5x - (-7x) - 14 = 58
Simplify by combining like terms:
12x -14 = 58
Add 14 from each side of the equation:
12x = 72
Divide both sides by 12:
X = 72/12
x = 6
Now you have x, replace x in the second equation and solve for y:
y = -x +2
y = -6 +2
y = -4
X = 6, y = -4
What is the greatest number of pairs of shoes sold in 1 week?
Answer:
30
Step-by-step explanation:
Answer:
It is 50,000
Step-by-step explanation:
The Pythagorean theorem, a^2+b^2=c^2, is used to calculate the side length of a right triangle. Which equation can be used to calculate the missing side length, b, of a right triangle?
Answer:
D b = sqrt(c^2 -a^2)
Step-by-step explanation:
We are using the Pythagorean theorem,
a^2+b^2=c^2
We want to solve for b
Subtract a^2 from each side
a^2 -a^2+b^2=c^2-a^2
b^2 = c^2 -a^2
Take the square root of each side
sqrt(b^2) = sqrt(c^2 -a^2)
b = sqrt(c^2 -a^2)
Answer:
answer A : b=√(c-a)
Step-by-step explanation:
a²+b²=c²
subtract a² from both sides to isolate b²
b²=c²-a²
take the square root of both sides to get from what b² equals to what b equals
b=√(c-a)
you have a 20 ounce bottle of juice. you pour out 1/4 of the bottle to share with a friend. if your our out 3 ounces for yourself, what fraction of the 20 ounces will be left in the bottle?
To determine the remaining fraction of juice in the bottle, subtract the poured amount from the original 20 ounces. The fraction left in the bottle is 3/5 of the original 20 ounces.
To find the fraction of juice left in the bottle:
Start with 20 ounces.
Pour out 1/4 for a friend, which is 5 ounces (1/4 of 20).
Pour out 3 more ounces for yourself.
Subtract the total poured out (5 + 3 = 8) from the starting amount (20) to find what's left.
So, 20 - 8 = 12 ounces left in the bottle, which represents 3/5 of the original 20 ounces.
$1,400 ,3.8%, 1 year
Answer:
$1453.2
Step-by-step explanation:
I assume you mean the accumulated value on a principal of $1400 with 3.8% interest in 1 year.
1400 * (100%+3.8%) = 1400 * 1.038 = 1453.2
53° 78° x° find the value of x
Answer:
I would say 49 is your answer
Step-by-step explanation:
53 plus 78 qould equal 131
subtract 131 from 180 and you get 49
add up all your numbers including x then they should all equal 180
sin ( pi/4 - B) =
Please explain!
Answer:
sqrt2/2 ( cos b - sin b)
Step-by-step explanation:
I know thats the answer but I have no idea how you solve to get it. Im looking for help too.
Find the slope between the following 2 coordinate points. (-3,6) and (-1,-8)
Answer:
-7
Step-by-step explanation:
Use slope equation m=y2-y1/x2-x1 aka m=rise/run.
Insert in the correct values.
-1-(-3)=2=run
-8-6=-14=rise
SO, -14/2=m
Simplify:-14/2=-7
m=-7
Last week kellie ran 28 miles. This week she ran 32 miles. What is the perecent of change in the number she ran?
Answer:
60%
Step-by-step explanation:
first do 28+32.
Next it equals 60. So change 60 to percentage form. It would be 60%
Describe how you can use compatible numbers to estimate 17 x 27
Answer:
600
Step-by-step explanation:
Well, the closest number for 17 is 20, and for 27 is 30.
When we multiply those two numbers :
20*30=600
We got 600
To estimate 17 x 27 using compatible numbers, round 17 to 20 and 27 to 25, then multiply to get an estimated product of 500.
Using compatible numbers to estimate the product of 17 x 27 involves finding numbers close to 17 and 27 that are easier to multiply mentally, such as multiples of 10.
A good choice here would be to round 17 up to 20 and 27 down to 25 for the approximation.
By doing so, we simplify the multiplication to 20 x 25.
The estimated product using compatible numbers would be:
20 x 25 = 500
So, an estimated answer to 17 x 27 using compatible numbers would be 500.
This method provides a quick and easy way to estimate the result, which is particularly useful when exact calculations are not necessary, or you need a fast approximation.
It cost six dollars Per pound of peanuts at Blessed Food Market. Which of the following represents The range of the function in terms of cost per pound?
A. $6
B. Amount of peanuts
C. Cost of peanuts purchased
D. Peanuts purchased
Answer:
C. Cost of peanuts purchased
Step-by-step explanation:
The range is the values that the y variable, or the output can take.
The output is the cost of the peanuts
How much water should we add to 35 kg of sugar syrup to change its concentration from 30% to 25%?
35kg - a mass of sugar syrup
30% of 35kg it's a mass of sugar
30% = 30 : 100 = 0.3
30% of 35kg = 0.3 · 35kg = 10.5kg - a mass of sugar
Add xkg water. Then we have (35 + x)kg of sugar syrup and still 10.5kg of sugar.
10.5kg is 25% of (35 + x)kg .
(35 + x) -- 100%
10.5 -- 25% multiply both sides by 4
42 -- 100%
Therefore we have the equation:
35 + x = 42 subtract 35 from both sides
x = 7
Answer: We should add 7kg of water.Evaluate -tan²A + 1 + sec²A
Answer:
Step-by-step explanation: sec^2A-tan^2A+1
=1+1
=2
Answer:
Hello :
secA= 1/cosA
tanA = sinA / cosA
- tan²A + 1 + sec²A = - (sinA / cosA)² + 1 + ( 1/cosA)²
= - sin²A / cos²A + 1 + 1 /cos²A
= ( - sin²A + cos²A +1)/cos²A
= ( 1 - sin²A + cos²A ) / cos²A
but : 1 - sin²A = cos²A because : sin²A + cos²A = 1
so : - tan²A + 1 + sec²A = ( 2 cos²A) / (cos²A)
- tan²A + 1 + sec²A = 2
Maya wants to divide 3/4 pound box of trail into small bags. Each bag will hold 1/12 pound of trail mix. How many bags of trail mix can maya fill ?
Answer:
9 bags of trail mix
Step-by-step explanation:
I would take the fraction 3/4 and make it have a common denominator with 1/12. In order to do that, multiply each number in 3/4 by 3. It results in 9/12.
You can put 9 of 1/12 in 9/12
To find out the number of bags Maya can fill with 3/4 pound of trail mix, divide 3/4 by 1/12. The division equates to multiplication by the reciprocal, so (3/4) x (12/1) = 9. Therefore, Maya can fill 9 bags of trail mix.
Explanation:This problem can be solved by division. Maya has 3/4 pound of trail mix and each small bag holds 1/12 pound of trail mix. Therefore, divide 3/4 by 1/12 to find out exactly how many bags Maya can fill.
To perform this division, you could first convert the fractions to decimals or do it directly. But let's stick with fractions and apply the principle of multiplying by the reciprocal. Change the division to multiplication and multiply 3/4 by the reciprocal of 1/12.
(3/4) x (12/1) = 9
So, Maya can fill 9 bags of trail mix.
Learn more about Division of Fractions here:https://brainly.com/question/17205173
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choose the correct solution set for each graph
1. The range of the Domain: x I x ≤ -2
2. The range of the Domain: (-5, ∞)
3. The range of the Domain: (-2, 3)
Leftmost Graph:
Domain: x I x ≤ -2
Range: All real numbers (-∞, ∞)
Visual: A solid line extending infinitely to the left from a closed circle at -2, indicating all values less than or equal to -2.
Interpretation: Includes -2 and all numbers to its left (negative infinity).
Middle Graph:
Domain: (-5, ∞)
Range: All real numbers (-∞, ∞)
Visual: A solid line starting with an open circle at -5 and extending infinitely to the right, indicating all values greater than -5.
Interpretation: Includes all numbers greater than -5, but not -5 itself.
Rightmost Graph:
Domain: (-2, 3)
Range: All real numbers (-∞, ∞)
Visual: A solid line between open circles at -2 and 3, indicating values between those points but not including those endpoints.
Interpretation: Includes all numbers strictly between -2 and 3, but not -2 or 3 themselves.
Answer: attachment
Step-by-step explanation:
For the equation 2x^3 -11x^2 + 12x + 9 = 0 , the root 3 has a multiplicity of
A. 1
B. 2
C. 3
Please explain!
Answer:
B. 2
Step-by-step explanation:
The multiplicity of a root is the number of times it occurs as a root.
We must solve the equation to find the number of times 3 occurs as a root.
Since we know that 3 is a root, we can use synthetic division to find the other roots.
f(x) = 2x³ -11x² + 12x + 9
3|2 -11 12 9
| 6 -15 -9
2 -5 -3 0
So, (2x³ - 11x² + 12x +9)/(x - 3) = 2x² - 5x – 3
=====
Let’s use synthetic division again to see if 3 is a root of this quadratic
3|2 -5 -3
| 6 3
2 1 0
So, 2x² - 5x – 3 = (x - 3)(2x + 1), and
2x³ - 11x² + 12x +9 = (x - 3)(x - 3)²(2x+1)
The factor x – 3 appears twice, so the root 3 has a multiplicity of two.
In the number 668 the 6 in the hundreds place is _ the value of the 6 in the tens place
Meg deposited a $3,000 bonus check in a new savings account. The account has an interest rate of 3% for 5 years. The interest is compounded daily. How much money did Meg have at the end of the account term? (Round your answer to the nearest dollar.)
Answer:
The $3485.52 money did Meg have at the end of the account term.
Step-by-step explanation:
Formula for compounded monthly
[tex]Amount = P(1+\frac{r}{365})^{365n}[/tex]
Where P is the principle , r is the rate of interest in the decimal form and n is the number of years.
As given
Meg deposited a $3,000 bonus check in a new savings account. The account has an interest rate of 3% for 5 years.
Principle = $3000
3% is written in the decimal form
[tex]= \frac{3}{100}[/tex]
= 0.03
Time = 5 years
Put in the formula
[tex]Amount = 3000(1+\frac{0.03}{365})^{365\times 5}[/tex]
[tex]Amount = 3000(1+\frac{0.03}{365})^{1825}[/tex]
[tex]Amount = 3000(1+\frac{0.03}{365})^{1825}[/tex]
[tex]Amount = 3000(1+ 0.0000822)^{1825}[/tex]
[tex]Amount = 3000(1.0000822)^{1825}[/tex]
[tex]Amount = 3000\times 1.16184[/tex]
Amount = $ 3485.52
Therefore the $ 3485.52 money did Meg have at the end of the account term.
Answer:
The Answer is $3,485 btw
Step-by-step explanation:
Answer C
Simplify 8^10 ÷ 8^5.
8^15
8^5
8^2
8^50
Answer:
8^5
Step-by-step explanation:
When we divide exponents with the same base, we subtract the exponents
8^10 ÷ 8^5
8^ (10-5)
8^5
Answer:
8^5 Disclaimer this is not the complete simplification. (see below)
Step-by-step explanation:
Simplify the following:
8^10/8^5
Hint: | For all exponents, a^n/a^m = a^(n - m). Apply this to 8^10/8^5.
Combine powers. 8^10/8^5 = 8^(10 - 5):
8^(10 - 5)
Hint: | Subtract 5 from 10.
10 - 5 = 5:
8^5
Hint: | Compute 8^5 by repeated squaring. For example a^7 = a a^6 = a (a^3)^2 = a (a a^2)^2.
8^5 = 8×8^4 = 8 (8^2)^2:
8 (8^2)^2
Hint: | Evaluate 8^2.
8^2 = 64:
8×64^2
Hint: | Evaluate 64^2.
| | 6 | 4
× | | 6 | 4
| 2 | 5 | 6
3 | 8 | 4 | 0
4 | 0 | 9 | 6:
8×4096
Solve for the variable 2(3x+1)=3
Answer:
x = 1/6
Step-by-step explanation:
2(3x+1)=3
Distribute.
6x + 2 = 3
Subtract 2 from both sides.
6x = 1
Divide by 6 on both sides.
x = 1/6
Hello there!
Question:-
[tex]\sf \longmapsto2(3x+1)=3[/tex]
We need to find the value of x.
Solution:-
[tex]\sf \longmapsto2(3x+1)=3[/tex]
Distribute:-
[tex]\sf \longmapsto \: (2)(3x)+(2)(1)=3[/tex]
On Simplification:-
[tex]\sf \longmapsto \: 6x + 2 = 3[/tex]
Subtract 2 from both sides :-
[tex]\sf \longmapsto 6x+2 - 2=3 - 2[/tex]
On Simplification:-
[tex]\sf \longmapsto6x + 0 = 3 - 2[/tex]
[tex]\sf \longmapsto6x = 1[/tex]
Divide the two sides by 6:-
[tex]\sf \longmapsto \: \dfrac{6x}{6} = \dfrac{1}{6} [/tex]
Cancel 6/6, leave x, answer is 1x. 1/6 can't be cancelled.
[tex]\sf \longmapsto \: \dfrac{ \cancel6x}{ \cancel6} = \dfrac{1}{6} [/tex]
[tex]\sf \longmapsto \: x = \dfrac{1}{6} [/tex]
In Decimal:-
[tex]\sf \longmapsto \: x = 0.16[/tex]
______________________________________
Henceforth,the value of x is :-
[tex]\boxed{\huge\tt x = \dfrac{1}{6}} [/tex]
[tex] \bold{OR,}[/tex]
[tex]\boxed{\huge\tt x = 0.16}[/tex]
_____________________________________
Please let me know if you have any questions.
~MisterBrian
steve ran 15 miles in 2 hours what in his speed in miles per hour
Answer:
speed = 7.5 miles per hour
Step-by-step explanation:
To find the speed, we divide the distance by the time
speed = distance/time
speed = 15miles/2 hours
speed = 15/2 miles per hour
speed = 7.5 miles per hour