All students in peters class have $1.05, consisting of nickels and or dimes and or quarters. each student has a different combination of coins. what is the probability peter is unable to give his friend jenny change for $1.00

A number system is defined as the representation of numbers by using digits or other symbols. It is possible for a number to be both a whole number and an integer.

A number system is defined as the representation of numbers by using digits or other symbols in a consistent manner.

The given question is Is it possible for a number to be both a whole number and an integer why and why not.

The answer is yes because every whole number is an integer but not every integer to be a whole number.

For example 5 is both a whole number and integer but -5 is a integer but ot a whole number because in whole numbers we do not have negative numbers.

Therefore it is possible for a number to be both whole number and integer.

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The coupon gives Shanice 40% off the original price, based on the coupon of $20 on an original price of $50

What is the price after having considered the coupon?

The price of the pair of jeans after having considered the coupon is the original price of $50 minus the $20 coupon

price after the coupon=$50-$20

price after the coupon=$30

However, the task at hand is to determine the coupon as a percentage of the original price

coupon as % of original price=$20/$50

coupon as % of original price=40.00%

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The simplified form of the given expression [tex]7^{\frac{5}{6} }[/tex] × [tex]7^{\frac{7}{6} }[/tex] is option d 49.

Given,

The expression = [tex]7^{\frac{5}{6} }[/tex] × [tex]7^{\frac{7}{6} }[/tex]

We can simplify this expression by using Laws of Indices;

The first rule: [tex]a^{n}[/tex] × [tex]a^{m}[/tex] = [tex]a^{m+n}[/tex]

The second rule: [tex](a^{n}) ^{m}[/tex] = [tex]a^{mn}[/tex]

The third rule: [tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{m-n}[/tex]

The fourth rule: [tex]a^{0}[/tex] = 1

The fifth rule: [tex]a^{-1}[/tex] = [tex]\frac{1}{a}[/tex]  ; [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

The sixth rule: [tex]a^{\frac{1}{2} }[/tex] = [tex]\sqrt{a}[/tex]  ; [tex]a^{\frac{1}{m} }[/tex] = [tex]\sqrt[m]{a}[/tex]  ; [tex]a^{\frac{n}{m} }[/tex] = [tex](a^{\frac{1}{m} } )^{n}[/tex] = [tex](\sqrt[m]{a} )^{n}[/tex]

Here we can use First, Second, Fifth and Sixth rule:

[tex]7^{\frac{5}{6} }[/tex] × [tex]7^{\frac{7}{6} }[/tex]

= [tex](7^{5} )^{\frac{1}{6} }[/tex] ×[tex](7^{7} )^{\frac{1}{6} }[/tex]

= [tex]16807^{\frac{1}{6} }[/tex] × [tex]823543^{\frac{1}{6} }[/tex]

= 5.061140185 × 9.68161288

= 49

That is, the simplified form of the expression [tex]7^{\frac{5}{6} }[/tex] × [tex]7^{\frac{7}{6} }[/tex] is 49.

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The average change in speed each second is 0.0583 miles per squared second

The given parameters are:

Speed = 3.5 miles per second

Time = 60 seconds

The average change in speed each second is calculated as

Average change = Speed/Time

This gives

Average change = (3.5 miles per second)/60 seconds

Evaluate the quotient

Average change = 0.0583 miles per squared second

Hence, the average change in speed each second is 0.0583 miles per squared second

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The temperature of the liquid at 3PM will be -7.5 °C

The initial temperature of the liquid at 9 AM  = 0°C

Given that the temperature changes by -5/4 °C each hour.

That is the rate of change of temperature = -5/4 °C

We have to find the temperature of the liquid at 3 PM.

Let x denote the number of hours.

Then the temperature after x hours, t = 0 + ( -5/4)x = -(5/4)x is the linear equation modelling this set up.

So from 9 AM to 3PM, the number of hours =  6 hours

Put x = 6 .

Then, t = (-5/4) x 6

            = -7.5

Therefore, the temperature of the liquid at 3 PM = -7.5°C

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Answer:

2.5£ =25tacos

1£ =?

=1*25/2.5

=10 tacos:

The Quatric polynomial is x⁴ + 11x³ + 20x² - 44x - 96

Given,

Zeros are: x = 2, x = -3, x = 8, and x = 2

That is: x + 2 = 0, x - 3 = 0, x + 8 = 0, and x + 2 = 0

So the factors are: (x + 2) (x - 3) (x + 8) (x + 2) = 0

Multiply two at a time:

   (x + 2)(x - 3) = x² - x - 6

   (x + 8)(x + 2) = x² + 10x + 16

Now multiply those polynomials together using distributive method:

x² (x² + 10x + 16)  - x(x² + 10x + 16)  - 6(x² + 10x + 16)

= x⁴ + 10x³ + 16x² + x³ + 10x² + 16x - 6x² - 60x - 96

= x⁴ + 11x³ + 20x² - 44x - 96

The Quatric polynomial is x⁴ + 11x³ + 20x² - 44x - 96

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Answer:

7.9

Step-by-step explanation:

yep

Answer:

-2

Step-by-step explanation:

Integer math!

Answer: Part to whole is 1:2

Answer:

h = -9

Step-by-step explanation:

Open the parentheses:

2(h+3.5) = -11

2h+7 = -11

Subtract 7 both sides

2h = -11 - 7

2h = -18

h = -9

Step-by-step explanation:

14a)

the 4th term = 4² + 3×4 - 2 = 16 + 12 - 2 = 26

b)

1, 7, 17, 31, 49

s1 = 1

s2 = s1 + 6

s3 = s2 + 10

s4 = s3 + 14

s5 = s4 + 18

the added term d grows with every step by 4. starting with a constant "+ 2" on top of -1 to create s1.

d1 = 2

d2 = d1 + 4

d3 = d2 + 4

dn = dn-1 + 4 = d1 + 4(n-1)

s1 = -1 + d1

s2 = s1 + d2 = -1 + d1 + d1 + 4

s3 = s2 + d3 = -1 + d1 + d1 + 4 + d1 + 4 + 4

s4 = s3 + d4 = -1 + d1 + d1 + 4 + d1 + 4 + 4 + d1 + 4 + 4 + 4

sn = -1 + n×d1 + sum(4(n - 1)) = -1 + 2n + 4n(n - 1)/2 =

= -1 + 2n + 2n(n - 1) = -1 + 2n(1 + n - 1) = -1 + 2n² =

= 2n² - 1

The number that is closest to the square root of 161 is 13.

In mathematics, the square root is a factor that, when multiplied by itself, equals the original integer.

A number y such that y² = x, or a number y whose square is x, is referred to as the square root of a number x in mathematics. For instance, -4 and 4 are the square roots of 16.

It should be noted that the square root of 161 is 12.689. Therefore, the number that is closest to the square root of 161 is 13.

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Which number is closest to the square root of 161 ?

The area of this rectangular object is equal to 12 × 10⁹ square microns.

Given the following data:

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

Substituting the given parameters into the formula, we have;

Area of a rectangle = 6,000 microns × 2,000,000 microns

Area of a rectangle = 12 × 10⁹ square microns.

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The slopes are:

A general linear equation in the slope-intercept form is written as:

y = m*x + k

Where m is the slope and k is the y-intercept.

Particularly, if the slope is positive, we will see that the line goes upwards when read from left to right, while if it is negative, it goes downwards.

First the top graphs, we have (from left to right)

Negative, positive, positive, positive.

Now the bottom ones:

Negative, positive, negative, positive.

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Answer:

63

Step-by-step explanation:

Numbers divisible by 9:

18, 27, 36, 45, 63, 72, 81, 90 and 99.

Numbers divisible by 7:

7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98.

Least common multiple=63

Using the graph of solubility, D. Ce₂(SO₄)₃ is a gas

A gas is a state of matter with no fixed shape or volume.

Solubility of a substance is the amount of solute that can dissolve in unit volume of solvent at a given temperature.

Note that the solubility of a substance depends on the temperature

From the graph above, we see that the compound with the least solubility is Ce₂(SO₄)₃. Since the solubility of gases derease with increasing temperature, thus Ce₂(SO₄)₃ is a gas

So, using the graph of solubility, D. Ce₂(SO₄)₃ is a gas

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Answer: 3.4/8 or 0.425

Step-by-step explanation:

Use this Rule: a/b * c/d = ac/bd

Simplify numerator (top): 1 * 3.4 = 3.4

Than Simplify denominator (bottom): 2 * 4 = 8

Finally: 3.4/8 or 0.425 (decimal)

This is my answer and I know this is correct because of using the Rule which demostrates that you should multiply top and bottom

Answer:

12

Step-by-step explanation:

See attachment for step-by-step instructions

The methods used to analyze data produced by scientific studies are called statistics. Option (c) is correct.

What are experiments and how do we analyze them using statistics?

Experiments are procedures or methods carried out under controlled conditions to discover a new fact or to test or  establish a hypothesis  that already exists.

From experiments we generate certain scientific data but to analyze data we need statistics.

Statistics is a process of collecting and analyzing and interpreting data.

Therefore the methods used to analyze data produced by scientific studies will be done by statistics.

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Answer:

Step-by-step explanation: Hello,

the answer

a) Jeremy get to keep 85%

b) $6.273 is Jeremy's hourly take home wage.

Given,

Jeremy has a job at the movie theatre.

Hourly wage of Jeremy = $7.38

The % of income withheld for taxes and social security = 15%

7.38 × (15/100) = 1.107

That is, $1.107 from Jeremy's income is withheld for taxes and social security.

a) Percentage of income Jeremy get to keep:

= 100% - Withheld percentage

= 100 - 15

= 85

So, Jeremy gets 85% of his income to keep with him.

b) Jeremy's hourly take home wage:

Total income - Withheld amount

7.38 - 1.107 = 6.273

That is, Jeremy's hourly take home wage is $6.273.

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The solution of the expression 1/4 + 1/2 ÷ 2/3 ÷ 3/5 is 1 1/2

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

1/4 + 1/2 ÷ 2/3 ÷ 3/5

Express the quotient as a product

So, we have

1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 1/4 + 1/2 x 3/2 ÷ 3/5

Evaluate the product

So, we have

1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 1/4 + 3/4 ÷ 3/5

Express the quotient as a product

So, we have

1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 1/4 + 3/4 x 5/3

Evaluate the product

So, we have

1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 1/4 + 5/4

Evaluate the sum

So, we have

1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 6/4

Simplify

1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 1 1/2

Hence, the solution of the expression 1/4 + 1/2 ÷ 2/3 ÷ 3/5 is 1 1/2

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The amount a customer will save if she buys 5 CDs will be equal to $ 30.25

We are given that:

Rebate a customer receives if he buys a regular priced CD at $ 13 each = $ 5.

If a customer registers for the store member, he get a discount = 15 %.

Now, let the regular priced CD purchased be x and the application for store member be y.

So, the functions will become:

For rebate:

R (x) = 5 x

For discount:

M (y) = 15 % of x

M (y) = 0.15 x

Now, the amount a customer has to pay if she takes the membership and then takes the rebate =(1 − 0.15) (13 x) − 5 x = 6.05 x

If x = 5 ( number of CD)

= 6.05 ( 5)

= $ 30.25

Therefore, we get that, the amount a customer will save if she buys 5 CDs will be equal to $ 30.25

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Answer:

y=-x+3

Step-by-step explanation:

the gradient of the equation is -1

and the y intercept is 3

[tex]125. 125^{\frac{1}{3} }[/tex] can be simplified into 625.

Prime factorization is the process of breaking down a number into its prime factors. Multiplying these prime numbers gives back the original number.

Prime factorization of 125 = 5 x 5 x 5 = [tex]5^{3}[/tex]

According to the law of indices, if a term with a power is raised to a power, then the powers are multiplied together.

i.e., [tex](x^{m})^{n} = x^{mn}[/tex]

Another law of indices says that if two terms having same base are multiplied together, then their indices are added.

i.e., [tex]a^{m} X a^{n} = a^{m+n}[/tex]

According to the given condition,

[tex]125. 125^{\frac{1}{3} }[/tex] = [tex]5^{3} .( 5^{3} )^{\frac{1}{3} }[/tex]

Applying the laws of indices mentioned above,

[tex]125. 125^{\frac{1}{3} }[/tex] = [tex]5^{3} .( 5^{3 X} ^{\frac{1}{3} })[/tex]

= [tex]5^{3} .( 5 )[/tex]  = [tex]5^{3 + 1}[/tex]

= [tex]5^{4} = 625.[/tex]

Thus,  [tex]125. 125^{\frac{1}{3} }[/tex] can be simplified into 625.

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Answer:

Step-by-step explanation:

If the diameter is 8 cm, and the formula is A=pie*radius^2, the radius is 4.

The area would be 16*pie

The formula for finding the circumference 2*pie*radius, so the circumference is 8*pie.

According to linear equation, Renting from Company A will always be cheaper. Thus option A is correct option.

According to the statement

We have to find that the correct statement.

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

Samir can rent a moving truck from Company A for $135 plus $0.50 per mile or from Company B for $125 plus $0.70 per mile.

Then

The equation is given as,

y = mx + c

Where m is that the slope of the road and c is that the y-intercept of the line.

Let y be the whole amount and x be the amount of miles.

Samir can rent a moving truck from Company A for $135 plus $0.50 per mile. Then the equation are going to be

y = 0.5x + 135 ....1

Company B for $125 plus $0.70 per mile. then the equation are going to be

y = 0.7x + 125 ....2

For the identical rent, the amount of miles are going to be

0.7x + 125 = 0.5x + 135

0.2x = 100

x = 500 miles

Renting from Company A are going to be cheaper if Samir drives the truck 500 miles. Then the right option is A .

So, According to linear equation, Renting from Company A will always be cheaper. Thus option A is correct option.

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Answer:

3/7y= -8/7

Step-by-step explanation:

reduce the greatest common factor on both sides of th equation

The inequality expression is 8.8t < 55 + 6.6t and your friend will be ahead for at most 25 seconds

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The given parameters are

Your rate, r1 = 6 miles per hour

Your friend's rate, r2 = 6.6 feet per second

Distance apart = 55 feet

Convert your rate to feet per second, we have

Your rate, r1 = 6 * 1.47 feet per second

Evaluate

Your rate, r1 = 8.8 feet per second

To calculate the time that your friend is ahead of you, we use the following expression

r1 * t < distance apart + r2 * t

So, we have

8.8t < 55 + 6.6t

Collect the like terms

So, we have

8.8t - 6.6t < 55

Evaluate the like terms

So, we have

2.2t < 55

Divide both sides by 2.2

So, we have

t < 25

Hence, the inequality expression is 8.8t < 55 + 6.6t and your friend will be ahead for at most 25 seconds

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