Please help me and this is very hard for me

Answers

Answer 1

Answer: I'm assuming you want help with numbers 7 and 8 because multiplication should be easy

so
7. rico average=15.5mph or 15.5/h
in 2.5 hours how far travel
15.5 in 1 hour
in 2 hours he will travel 2 times 15.5 miles
so in 2.5 hours he will travel 15.5 times 2.5 miles or 38.75

8. use estimation to show reasonable
15.5 can be rounded to 16
16 times 2 is 32
16 times 3 is 48
0.5 is half of 1 so the average is about the answer
(32+48)/2=80/2=40
he will travel about 40 miles (less since you rounded 15.5 up to 16)
so it is reasonable

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a jar contains 65 pennies 27 nickels 30 dimes and 18 quarters a coin is randomly selected from the jar find each probability

Answers

The required probabilities are $P(\text{pennies})=(13)/(28),P(\text{nickels})=(27)/(140),P(\text{dimes})=(3)/(14),P(\text{quarters})=(9)/(70)$ .

Given:

Pennies = 65

Nickels = 27

Dimes = 30

Quarters = 18

To find:

The probability of each.

Solution:

The probability formula:

$\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total outcomes}}$

Total number of coins:

$65+27+30+18=140$

The probability of selecting Pennies is:

$P(\text{pennies})=(65)/(140)$

$P(\text{pennies})=(13)/(28)$

The probability of selecting nickels is:

$P(\text{nickels})=(27)/(140)$

The probability of selecting dimes is:

$P(\text{dimes})=(30)/(140)$

$P(\text{dimes})=(3)/(14)$

The probability of selecting quarters is:

$P(\text{quarters})=(18)/(140)$

$P(\text{quarters})=(9)/(70)$

Therefore, the required probabilities are $P(\text{pennies})=(13)/(28),P(\text{nickels})=(27)/(140),P(\text{dimes})=(3)/(14),P(\text{quarters})=(9)/(70)$ .

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Use the Laplace transform to solve the given initial value problem. y' + 6y = e^4t ; y(0)=2 ...?

Answers

Performing laplace transform of the equation.

sY(s) - y(0) + 6Y(s) = 1/(s-4)
(s+6)Y(s) - 2 = 1/(s-4)
Y(s) = 2/(s+6) + 1/(s-4)(s+6), by partial fraction decomposition
Y(s) = 2/(s+6) + 1/10 * (1/(s-4) + 1/(s+6))
Y(s) = 0.1/(s-4) + 2.1/(s+6)

Performing inverse laplace transform,
y(t) = 0.1e^4t + 2.1e^(-6t)

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

Final answer:

The Laplace transform method is applied to solve the differential equation y' + 6y = e^4t with the initial condition y(0)=2. After transforming, simplifying, and solving for Y(s), we use inverse Laplace transform to find the solution y(t) in the time domain.

Explanation:

Laplace transform is a powerful tool in the field of mathematics used for solving differential equations. To solve the given initial value problem y' + 6y = e^4t ; y(0)=2, we can start by taking the Laplace transform of both sides of the equation.

The Laplace transform of y' is sY(s) - y(0) and the Laplace transform of y is Y(s). Therefore, the Laplace transform of y' + 6y gives sY(s) - y(0) + 6Y(s). Given that y(0)=2, this simplifies to sY(s) + 6Y(s) - 2.

On the right-hand side, the Laplace transform of e^4t is 1/(s-4). Thus, we have the equation sY(s) + 6Y(s) - 2 = 1/(s-4).

By solving for Y(s), we can find the inverse Laplace transform to get the solution y(t) in the time domain.

Learn more about Laplace Transform here:

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The value of the 2in 204.75 is how many times the value of the 2 in 103.52

Answers

Answer:

10000

Step-by-step explanation:

Given : Number :204.75

Number :103.52

To Find:The value of the 2 in 204.75 is how many times the value of the 2 in 103.52?

Solution:

Number :204.75

Value of 2 is 200

Number :103.52

Value of 2 = $(2)/(100)=0.02$

So, $10000 * 0.02 = 200$

Thus 10000 times of 0.02 is 200.

So, the value of the 2 in 204.75 is 10000 times the value of the 2 in 103.52.

I made it into an equation and took out all the other numbers so the equation would be 000.02x=200 and your trying to find x so you divide 200 by 000.02 equals 10000 and if you put it back in the equation 000.02(10000)=200 it comes out 200 so the answer is 10000

Which expression is a difference of cubes? 9w^33-y^12 18p^15-q^21 36a^22-b^16 64c^15- a^26

Answers

we know that

A polynomial in the form $a^(3)-b^(3)$ is called adifference of cubes. Both terms must be a perfect cubes

Let's verify each case to determine the solution to the problem

case A) $9w^(33) -y^(12)$

we know that

$9=3^(2)$ ------> the term is not a perfect cube

$w^(33)=(w^(11))^(3)$ ------> the term is a perfect cube

$y^(12)=(y^(4))^(3)$ ------> the term is a perfect cube

therefore

The expression $9w^(33) -y^(12)$ is not a difference of cubes because the term $9$ is not a perfect cube

case B) $18p^(15) -q^(21)$

we know that

$18=2*3^(2)$ ------> the term is not a perfect cube

$p^(15)=(p^(5))^(3)$ ------> the term is a perfect cube

$q^(21)=(q^(7))^(3)$ ------> the term is a perfect cube

therefore

The expression $18p^(15) -q^(21)$ is not a difference of cubes because the term $18$ is not a perfect cube

case C) $36a^(22) -b^(16)$

we know that

$36=2^(2)*3^(2)$ ------> the term is not a perfect cube

$a^(22)$ ------> the term is not a perfect cube

$b^(16)$ ------> the term is not a perfect cube

therefore

The expression $36a^(22) -b^(16)$ is not a difference of cubes because all terms are not perfect cubes

case D) $64c^(15) -a^(26)$

we know that

$64=2^(6)=(2^(2))^(3)$ ------> the term is a perfect cube

$c^(15)=(c^(5))^(3)$ ------> the term is a perfect cube

$a^(26)$ ------> the term is not a perfect cube

therefore

The expression $64c^(15) -a^(26)$ is not a difference of cubes because the term $a^(26)$ is not a perfect cube

I'm adding a new case so I can better explain the problem

case E) $64c^(15) -d^(27)$

we know that

$64=2^(6)=(2^(2))^(3)$ ------> the term is a perfect cube

$c^(15)=(c^(5))^(3)$ ------> the term is a perfect cube

$d^(27)=(d^(9))^(3)$ ------> the term is a perfect cube

Substitute

$64c^(15) -d^(27)=((2^(2))(c^(5)))^(3)-(d^(9))^(3)$

therefore

The expression $64c^(15) -d^(27)$ is a difference of cubes because all terms are perfect cubes

The expression $\boxed{64{c^(15)} - {d^(27)}}$ is a difference of cubes.

Further Explanation:

Given:

The options are as follows,

(a). $9{w^(33)} - {y^(12)}$

(b). $18{p^(15)} - {q^(21)}$

(c). $36{a^(22)} - {b^(16)}$

(d). $64{c^(15)} - {a^(26)}$

(e). $64{c^(15)} - {d^(27)}$

Calculation:

The cubic formula can be expressed as follows,

$\boxed{{a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right)}$

The expression is $9{w^(33)} - {y^(12)}.$

9 is not a perfect cube of any number, ${w^(33)}$ can be written as ${\left( {{w^(11)}} \right)^3}$ and ${y^(12)}$ can be represents as ${\left( {{y^4}} \right)^3}.$

$9{w^(33)} - {y^(12)}$ cannot be written as the difference of cube. Option (a) is not correct.

The expression is $18{p^(15)} - {q^(21)}.$

18 is not a perfect cube of any number, ${p^(15)}$ can be written as ${\left( {{p^5}} \right)^3}$ and ${q^(21)}$ can be written as ${\left( {{q^7}} \right)^3}.$

$18{p^(15)} - {q^(21)}$ cannot be written as the difference of cube. Option (b) is not correct.

The expression is $36{a^(22)} - {b^(16)}.$

36 is not a perfect cube of any number, ${a^(22)}$ is not perfect cube and ${b^(16)}$ is not a perfect cube.

$36{a^(22)} - {b^(16)}$ cannot be written as the difference of cube. Option (c) is not correct.

The expression is $64{c^(15)} - {a^(26)}.$

64 can be written as ${\left( {{2^2}} \right)^3}, {a^(26)}$ is not perfect cube and ${c^(15)}$ can be written as ${\left( {{c^5}} \right)^3}.$

$64{c^(15)} - {a^(26)}$ cannot be written as the difference of cube. Option (d) is not correct.

The expression is $64{c^(15)} - {d^(27)}.$

64 can be written as ${\left( {{2^2}} \right)^3}, {d^(27)}$ can be written as ${\left( {{d^9}} \right)^3}$ and ${c^(15)}$ can be written as ${\left( {{c^5}} \right)^3}.$

$\boxed{64{c^(15)} - {d^(27)} = {{\left( {{2^2}{c^5}} \right)}^3} - {{\left( {{d^9}} \right)}^3}}$

$64{c^(15)} - {d^(27)}$ can be written as the difference of cube. Option (e) is correct.

The expression $\boxed{64{c^(15)} - {d^(27)}}$ is a difference of cubes.

Learn more:

1. Learn more about unit conversion brainly.com/question/4837736

2. Learn more about non-collinear brainly.com/question/4165000

3. Learn more aboutbinomial and trinomial brainly.com/question/1394854

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Exponents and Powers

Keywords: Solution, factorized form, expression, difference of cubes, exponents, power, equation, power rule, exponent rule.

A ball is dropped from a certain height. The function below represents the height f(n), in feet, to which the ball bounces at the nth bounce:f(n) = 9(0.7)n

What does the number 0.7 represent?

The ball bounces to 30% of its previous height with each bounce.
The height at which the ball bounces at the nth bounce is 0.3 feet.
The ball bounces to 70% of its previous height with each bounce.
The height from which the ball was dropped at the nth bounce is 0.7 feet.

Answers

Answer:

The ball bounces to 70% of its previous height with each bounce.

Step-by-step explanation:

In physics terminology, the number 0.7 is the coefficient of restitution. It is the ratio of the height of bounce (n+1) to the height of bounce (n).

The meaning of the number is that the ball bounces to 70% of the height of the previous bounce.

Answer:

The ball bounces to 70% of its previous height with each bounce.

Step-by-step explanation:

A ball is dropped from a certain height. The function below represents the height f(n), in feet, to which the ball bounces at the nth bounce:

f(n) = 9(0.7)n

The number 0.7 represents that the ball bounces to 70% of its previous height with each bounce.

Ii dont understand how to solve a system of linear equations using the substitution method

Answers

so 8x-7y=-7
-16+12x=14
you can simplify the sceon equation
-8+6x=7
add 8 to both sides
6x=15
divide by 6
x=15/6
subssitute
8(15/6)-7y=-7
120/6-7y=-7
20-7y=-7
subtract 20
-7y=-27
divide by -7
y=27/7

x=15/6
y=27/7

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