Answer:
63 dimes
Step-by-step explanation:
Set up a system of equations where d is the number of dimes and q is the number of quarters:
d + q = 106
0.1d + 0.25q = 17.05
Solve by elimination by multiplying the top equation by -0.25 to eliminate q:
-0.25d - 0.25q = -26.5
0.1d + 0.25q = 17.05
Add together and solve for d:
-0.15d = -9.45
d = 63
So, there were 63 dimes in the piggy bank
Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for each function. 5e^(-x)^2 cos(4x)
Answer:
The first three nonzero terms in the Maclaurin series is
[tex]\mathbf{ 5e^{-x^2} cos (4x) }= \mathbf{ 5 ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }[/tex]
Step-by-step explanation:
GIven that:
[tex]f(x) = 5e^{-x^2} cos (4x)[/tex]
The Maclaurin series of cos x can be expressed as :
[tex]\mathtt{cos \ x = \sum \limits ^{\infty}_{n =0} (-1)^n \dfrac{x^{2n}}{2!} = 1 - \dfrac{x^2}{2!}+\dfrac{x^4}{4!}-\dfrac{x^6}{6!}+... \ \ \ (1)}[/tex]
[tex]\mathtt{e^{-2^x} = \sum \limits^{\infty}_{n=0} \ \dfrac{(-x^2)^n}{n!} = \sum \limits ^{\infty}_{n=0} (-1)^n \ \dfrac{x^{2n} }{x!} = 1 -x^2+ \dfrac{x^4}{2!} -\dfrac{x^6}{3!}+... \ \ \ (2)}[/tex]
From equation(1), substituting x with (4x), Then:
[tex]\mathtt{cos (4x) = 1 - \dfrac{(4x)^2}{2!}+ \dfrac{(4x)^4}{4!}- \dfrac{(4x)^6}{6!}+...}[/tex]
The first three terms of cos (4x) is:
[tex]\mathtt{cos (4x) = 1 - \dfrac{(4x)^2}{2!}+ \dfrac{(4x)^4}{4!}-...}[/tex]
[tex]\mathtt{cos (4x) = 1 - \dfrac{16x^2}{2}+ \dfrac{256x^4}{24}-...}[/tex]
[tex]\mathtt{cos (4x) = 1 - 8x^2+ \dfrac{32x^4}{3}-... \ \ \ (3)}[/tex]
Multiplying equation (2) with (3); we have :
[tex]\mathtt{ e^{-x^2} cos (4x) = ( 1- x^2 + \dfrac{x^4}{2!} ) \times ( 1 - 8x^2 + \dfrac{32 \ x^4}{3} ) }[/tex]
[tex]\mathtt{ e^{-x^2} cos (4x) = ( 1+ (-8-1)x^2 + (\dfrac{32}{3} + \dfrac{1}{2}+8)x^4 + ...) }[/tex]
[tex]\mathtt{ e^{-x^2} cos (4x) = ( 1 -9x^2 + (\dfrac{64+3+48}{6})x^4+ ...) }[/tex]
[tex]\mathtt{ e^{-x^2} cos (4x) = ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }[/tex]
Finally , multiplying 5 with [tex]\mathtt{ e^{-x^2} cos (4x) }[/tex] ; we have:
The first three nonzero terms in the Maclaurin series is
[tex]\mathbf{ 5e^{-x^2} cos (4x) }= \mathbf{ 5 ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }[/tex]
examples of parallel lines and interesting lines
Answer:
when the lines are opposite and doesnot intersect at any point then the lines are parallel
for example the opposite lines of parallelogram are parallel
when the lines cut each other at one point then we can say that lines are intersecting
hope it helps u
Answer:
Parallel lines :When thè lines are parellel and opposte to each other then it is called parellel lines.
Intersecting lines :When thè lines intersect each other and meet at a point then it is called intersecting lines.
Sandra calculated the height of a cylinder that has a volume of 576 pi cubic centimeters and a radius of 8 centimeters. Her work is shown below. V = B h Step 1: 576 pi = pi 8 squared h Step 2: 576 pi = 64 pi h Step 3: StartFraction 576 pi Over 64 pi EndFraction = StartFraction 64 pi Over 64 pi EndFraction h Step 4: h = 9 pi cm What error did Sandra make when calculating the height of the cylinder? In step 1, she substituted into the volume formula incorrectly. In step 2, she calculated 8 squared incorrectly. It should be 16 rather than 64. In step 4, the pi should have canceled, making the correct answer 9 cm. Sandra calculated the height of the cylinder correctly.
Answer:
C. In step 4, the (pie) should have canceled, making the correct answer 9 cm.
Step-by-step explanation:
Volume=576π cubic centimeters
Radius=8 cm
h=?
Her work:
Volume of a cyclinder=πr^2h
Step 1:
576π= π8^2h
Step 2:
576π = 64πh
Step 3:
576π / 64π = 64πh / 64π
Step 4:
h=9π cm
Correct workings:
Step 1:
576π= π8^2h
Step 2:
576π = 64πh
Step 3:
576π / 64π = 64πh / 64π
Step 4:
h= 9 centimeters
Her error is in step 4
C. In step 4, the (pie) should have canceled, making the correct answer 9 cm.
Answer:
the error was made in step 4, should have also been cancelled making the correct answer as 9 cm.
Step-by-step explanation:
someone please help me with this question
Answer:
3rd and 4th option
Answer: Option 3. [tex]\sqrt[c]{a^b}[/tex] Option 4. [tex](\sqrt[c]{a} )^b[/tex]
Step-by-step explanation:
concept to know: when the exponent is a fraction, the numerator will be the real exponent with the base (i.e 7^5), while the denominator will be the root
----------------------------------
[tex]a^{\frac{b}{c}[/tex]
b is the numerator which means it will result in [tex]a^b[/tex]
c is the denominator which means it will result in [tex]\sqrt[c]{a}[/tex]
The combination of this two will be [tex]\sqrt[c]{a^b}[/tex]
This will also be presented as [tex](\sqrt[c]{a} )^b[/tex]
Hope this helps!! :)
Please let me know if you have any question
what is standered form of 6,600,000,000,000,000,000,000
Answer:
6.6×10²¹
Step-by-step explanation:
6,600,000,000,000,000,000,000 → there are 21 place values after the first non-zero number ''6''
to convert to standard form, we move the decimal point after the first non-zero number.
6,600,000,000,000,000,000,000.0 ← decimal in the end
the decimal will be moved, all the digits after the decimal are counted and they will resemble the index.
6.6×10²¹
paper plus sells reams ofpaper of $5.25 each discount paper sells the same reams of paper for $3.99 each, how much would you save by purchasing 15 reams of paper at discount paper instead of at paper plus?
Answer: $18.90
Step-by-step explanation:
multiply both by 15
subtract from each other
A group of students conducted several trials of an experiment to study Newton’s second law of motion. They concluded that tripling the mass required tripling the net force applied. What quantity were the students holding constant?
net force
acceleration <-- MY ANSWER
number of trials
mass
Answer:
Acceleration
Step-by-step explanation:
The Newton's second law of motion can be expressed as;
F = ma
Where F is the force acting on an object, m is the mass of the object and a is the acceleration of the object.
For an object of mass 2kg and acceleration of 5 m/[tex]s^{2}[/tex], we have;
[tex]F_{1}[/tex] = 2 × 5 = 10 N
If we triple the mass,
m = 2 × 3 = 6 kg
Therefore,
[tex]F_{2}[/tex] = 6 × 5 = 30 N
Thus, at constant acceleration, [tex]F_{2}[/tex] = 3 × [tex]F_{1}[/tex]
The first term in the sequence is 1, and each other term is 5 more than three times the previous term.
[tex]a_1=1, a_n=a_{n-1}+5[/tex] ([tex]n>1[/tex]).
Hope this helps.
PLEASE HELP!!
express as a trinomial
(x-6) (2x-7)
Answer:
2x² - 19x + 42
Step-by-step explanation:
We want to expand (x - 6)(2x - 7) into a trinomial.
We use the FOIL (first, outer, inner, last) method.
First, multiply the first terms of each parenthetical expression; in the first one, that's x, and in the second, that's 2x:
x * 2x = 2x²
Next, multiply the outer terms; in the first one, that's x, and in the second, that's -7:
x * (-7) = -7x
After that, multiply the inner terms; in the first one, that's -6 and in the second, that's 2x:
(-6) * 2x = -12x
Finally, multiply the last terms; in the first one, that's -6 and in the second, that's -7:
(-6) * (-7) = 42
Now, add all these results together:
2x² + (-7x) + (-12x) + 42
2x² - 19x + 42
The answer is thus 2x² - 19x + 42.
~ an aesthetics lover
Answer:
2x²-19x+42
Step-by-step explanation:
x·2x-x·7-6·2x+6·7
2xx-7x-12x+42
2x²-7x-12x
2x²-7x-12+42
Where do the lines y=2x+1 and y=-5x-6 intersect?
Answer:
(-1, -1)
Step-by-step explanation:
To find where two lines in slope-intercept form intersect, set them equal to each other.
2x + 1 = -5x - 6
7x = -7
x = -1
Knowing they intersect at x = -1, substitute -1 into either of the two equations to find the y-value of their intersection.
y = 2(-1) + 1
y = -2 + 1
y = -1
So the intersection point of the two lines is (-1, -1).
The value 346.7812 rounded to the nearest hundredth is
346.7800
QQI 300
346.781
346.78
Answer:
346.78
Step-by-step explanation:
Rounding a number to hundredth means approximating or making the number after the second position of the decimal to either a 10 or zero.
Thanks for the number after the second is greater or equal to 5, it is rounded up to ten where the 1 is added to the second position if not it turns 0.
So 346.7812 to hundredth
= 346.78
A car travels 50 mph for 10 minutes. How many miles per minute is the car travoling? Round to the
nearest tenth
To the nearest tenth of a mile, how far doos the car travel in 1 minuto?
0 0.12 miles per minute
o 0.83 miles per minute
1.2 miles per minute
8.3 miles per minute
Answer:
8.3
Step-by-step explanation:
10 minutes is 1/6th of an hour so divide 50 by 6 to find the answer.
50/6= 8.3333333 so rounded to the nearest tenth is 8.3
a man dropped his keys into the sea, and watched them fall to a depth of -8 meters before landing on a rock. how far are the keys from the surface of the sea?
Please help. Calculate the loading dose, in mg of heparin for a 5-year-old with a total body weight of 40 lbs., with 10% body fat (that is, 90% of that 40 lbs. is lean body mass). You may also be interested to know that 1 kg = 2.20 lbs. Think about the steps you need to go through to find the correct dose. Remember, first you need to find the dosing mass.
Answer:
≈ 3 mg
Step-by-step explanation:
Dose rate of heparin is 0.16 mg per kg of DMDosing mass calculation formula is:
DM = LBM + (TBM - LBM)/3, where LBM = lean body mass, TBM = total body massTBM = 40 lbsBody fat = 10%LBM = 90% of TBM = 0.9*TBMDosing mass
DM = 40 *0.9 + ( 40 - 40*0.9)/3 = 37.33 lbsConverting to kg
1 kg = 2.2 lbsDM = 37.33 lbs /2.2 = 16.97 kgLoading dose
dose = DM * dose rate per kgdose = 16.97 kg *0.16 mg/kg = 2.7152 mg ≈ 3 mgA man walks along a straight path at a speed of 3 ft/s. A searchlight is located on the ground 4 ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 3 ft from the point on the path closest to the searchlight
Answer:
0.48 rad/sec
Step-by-step explanation:
From the diagram:
We can find 'x' using trigonometry :
Tanθ = opposite / Adjacent
Opposite = x ; adjacent = 4
Tanθ = x / 4
x = 4tanθ
Let u = 4 and v = tanθ
If dx/dt = 3ft/s ;
dθ/dt when x = 3ft
Differentiate x with respect to t
dx/dt (4tanθ)
Let d/dθ tanθ = sec^2θ
Sec^2θ = 1 / cos^2θ
dθ/dt = 1/4cos^2θdx/dt
dθ/dt = 1/4cos^2θ(3)
dθ/dt = 3/4cos^2θ
When x = 3ft
Cosθ = Adjacent / Hypotenus
Hypotenus = √(4^2 + 3^2
Hypotenuse = √16 + 9 = √25 = 5
Cosθ = 4/5
dθ/dt = 3/4(4/5)^2
dθ/dt = 3/4(16/25)
dθ/dt = 48/100 = 12/25 = 0.48 rad/sec
If you get this, you are a critical thinker.
I enter the bedroom.
There are 34 people. You kill 30. How many people are in the bedroom?
Good Luck!
If you get it correct your answer will be deleted and I’ll message you to continue the game. Don’t bother playing if you’re not going to continue, party poopers!
Answer:
The correct answer is 34 people
Step-by-step explanation:
Killing 3 people does not change the number of people in the bedroom, it only means that there are 30 dead people and 4 living people, but overall, here are 34 people in the room.
There are 35 people in the room.
Killing 30 people does not exclude them from the room.
Similarly I entered the room when there were 34 people adding 1 more to 34 gives 35 people.
35= 34+1
There are 35 people in the room.
https://brainly.com/question/20700704
Alastair drives 18.2 miles in 14 minutes.
He passes a sign which gives the speed limit as 50 mph.
By how much, in mph, did Alastair's average speed exceed the speed limit?
Answer:
28 mph
Step-by-step explanation:
Distance
18.2 milesTime
14 min = 14/60 hrAverage speed
d/t = 18.2 ÷ 14/60 = 182/10 × 60/14 = 78 mphThe difference with allowed speed
78 - 50 = 28 mphAnswer:
28mph
Step-by-step explanation:
Round 467 to the nearest 10
Answer:
470.
Step-by-step explanation:
The units digit 7.
As this is greater than 4 we add 1 to the tens digit. ( 6 + 1 = 7), and the units digit becomes 0.
Multiply.
(-7x - 2) (5x+3)
Simplify your answer.
Answer:
= -35x² - 31x - 6
Step-by-step explanation:
(-7x -2)(5x+3) = -7x*5x -7x*3 -2*5x -2*3 = -35x² - 21x - 10x - 6
= -35x² - 31x - 6
Evacuation and emergency procedures should be displayed in the classroom lab/office. * 4 points True False
Answer:
The answer is true. I hope this helps
Answer:
yes. If there will be Evacuation and emergency procedures then the students can learn about that and can use that when there is an emergency case.
Was it evaluated correctly?
explain your reasoning.
Answer:
It's not evaluated correctly
Step-by-step explanation:
in the problem 6 × 5 + 30 ÷ 30 we first need to multiply 6 and 5 then divide the 30 by 10 and finally add them up
6×5 = 30
30 ÷ 10 = 3
30 + 3 = 33
(-w^3+8w^2-3w)-(4w^2+5w-7)
Answer:
[tex] \boxed{ \bold{ { \boxed{ \sf{ - {w}^{3} + 4 {w}^{2} - 8w + 7}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{( - {w}^{3} + 8 {w}^{2} - 3w) - (4 {w}^{2} + 5w - 7)}[/tex]
Remove the unnecessary Parentheses
⇒[tex] \sf{ - {w}^{3} + 8 {w}^{2} - 3w - (4 {w}^{2} + 5w - 7)}[/tex]
When there is a ( - ) in front of a parentheses, change the signs of each term in the expression
⇒[tex] \sf{ - {w}^{3} + 8 {w}^{2} - 3w - 4 {w}^{2} - 5w + 7}[/tex]
Collect like terms
⇒[tex] \sf{ - {w}^{3} + 8 {w}^{2} - 4 {w}^{2} - 3w - 5w + 7}[/tex]
⇒[tex] \sf{ - {w}^{3 } + 4 {w}^{2} - 8w + 7 }[/tex]
Hope I helped!
Best regards!!
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Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
[tex]\boxed{-w^3 + 4w^2 + -8w + 7}[/tex]
Let's simplify step-by-step.
[tex](-w^3+8w^2-3w)-(4w^2+5w-7)[/tex]
Distribute the Negative Sign:
[tex]= -w^3 + 8w^2 - 3w + -1( 4w^2 + 5w - 7 ) \\= - w^3 + 8w^2 + 3w + -1(4w^2) + -1 (5w)+(-1 )(-7)\\= -w^3 + 8w^2 + -3w + -4w^2 + 5w + 7[/tex]
Combine Like Terms:
[tex]= -w^3 + 8w^2 + -3w + -4w^2 + -5w + 7 \\= (-w^3) + ( 8w^3 + -3w + -4w^2) + ( -3w + -5w) + 7 \\= -w^3 + 4w^2 + -8w + 7[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
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Have a great day/night!
❀*May*❀
6.2×10 +6×10³ Brainiest if right
Answer: 6062
Add Parentheses
[tex](6.2*10)+(6*10^3)[/tex]
Note: Always Multiply the Parentheses first!
Multiply
[tex]6.2*10=62[/tex]
[tex]6*10^3=6000[/tex]
How is 6×10^3 6000?
Before you multiply the whole equation you first Multiply 10 3 times. This is called an Exponent. In my own words, an exponent is a number that tells you how many times to multiply that number. So if we had 6^2 I will multiply 6×6 2 times. So we multiply 10×10×10 and get 1000. Then we multiply 6×1000 and get 6000.
Add
Since the final step is to add we Add the answer we got for 6.2×10 and 6×10^3.
Therefore we are adding 62*6000 and we get 6062.
i need help with this
Answer:
1a. either AC ≅ DF or AB ≅ DE
1b. <A ≅ <D
2a. B
2b. D
Step-by-step explanation:
Gunnar’s car gets 22.4 miles per gallon, and his gas tank can hold 17.82 gallons of gas. PART B: Gunnar’s car is close to empty and only has 0.98 gallon of gas left. He stops at a gas station that charges $2.05 per gallon of gas. How much does it cost for Gunnar to refill his tank? Round your answer to the nearest penny.
Answer:
399.17 miles
Step-by-step explanation:
Gunnar's car gets 22.4 miles per gallon. His gas tank can hold 17.82 gallons of gas.
Gunnar's car travels with one gallon of gas = 22.4 miles
He can travel with 17.82 gallon of gas = 17.82 × 22.4
= 399.168 ≈ 399.17 miles
Gunnar can travel 399.17 miles if he uses all of the gas in the gas tank.
Choose the best answer from the four choices given. You may use scratch
paper.
(3x2y3 )3 =
3x5y6
O 9x6yº
O 27x5y6
O 27x6y
Answer:
27x^6y^9
Step-by-step explanation:
(3x^2y^3)^3 = 3^3 * (x^2)^3 * (y^3)^3 =
= 27x^6y^9
Hi I am a teacher or 52 years old and I am wondering how I can become an online tutor?
Answer:
Go online and do research, I'm pretty sure you have websites around your area that is looking for tutors
Step-by-step explanation:
Will Give Brainliest! (And 25 Points) Easy Algebra Question! Please show all steps! Solve for x [tex]b+3/x=f/2[/tex]
Answer:
Step-by-step explanation:
Hello, we assume that x is different from 0 and f different from 2b
[tex]b+\dfrac{3}{x}=\dfrac{f}{2}\\\\\text{Subtract b}\\\\+\dfrac{3}{x}=\dfrac{f}{2}-b\\\\\text{Mulitply by 2x}\\\\+\dfrac{3*2*x}{x}=6=\dfrac{2xf}{2}-2bx=(f-2b)x\\\\\text{Divide by f-2b}\\\\\Large \boxed{\sf \bf x=\dfrac{6}{f-2b}}[/tex]
Thanks
what is LCM of 2 4 8
Answer:
the LCM would be 8 based on the following set of multiples: Multiples of 2: 2, 4, 6, 8, 10, 12, 14, ... Multiples of 8: 8, 16, 24, 32, 40, 48, 56, ...
Step-by-step explanation:
add 5 to me then you divide by 7 if you add 12 then subtract 7 you get 10 what number am i
Answer:
x+5=x÷7+12=x-7=10 it is 30
Answer:
30
Step-by-step explanation:
Given number is x, then:
(x + 5) ÷ 7 + 12 - 7 = 10(x + 5) ÷ 7 + 5= 10(x + 5) ÷ 7 = 5x + 5 = 5*7x + 5 = 35x = 35 - 5x = 30The number is 30