All men are mortal. Joe is a man. Therefore Joe is mortal. If the first two statementsare true, then the conclusion must be true.

There will be 15724800 computer passwords possible with 1 letter followed by 7 digits without any repetition of letters or digits.

It is given to us that -

A computer password is required to be 8 characters long

The computer password requires 1 letter(s) followed by 7 digits

The 7 digits are from numbers 0-9.

It is also mentioned that there will be no repetition of any letter or digit

We know that,

The total number of English alphabets = 26 (from a-z)

The total number of digits = 10 (from 0-9)

Since it is given that the computer password has

1 letter followed by 7 digits without any repetition of any letters or digits

So, the number of computer passwords that are possible can be -

[tex]26*10*9*8*7*6*5*4\\= 15724800[/tex]  (1 letter and 7 digits with no repetition)

Thus, 15724800 computer passwords are possible that contains 1 letter followed by 7 digits where no repetition of any letter or digit is allowed.

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ANSWER:

  4x-1=27

or,4x=27+1

or, x=28/4

or, x=7

3. 300

4. $180

5. $23.75

6. $102.6

Answer: 1 is 300 2 is 180 3 is 23.75 and the fourth one is 102.6

Step-by-step explanation: dont forget to add your $ signsss

Answer:+0.82 and -0.8

Step-by-step explanation:

Using combination, there are 1932 arrangments possible.

A combination is a mathematical approach that counts the number of potential configurations in a box containing objects, regardless of their order.

In combinations, we can select items in any order. In combinations, the order doesn’t matter.

The combination formula of given as: n! / r!(n-r)!

Each candy would be distributed in three different ways if there were no limits on how many candies might fit in a bag. 3⁷ different ways to distribute the sweets in this scenario. However, only empty blue and red bags count in this scenario.

There are 2⁷ methods to distribute candy if the red bag is left empty.

Similarly, for the blue bag.

Hence there are 2⁷ +2⁷ – 1 ways to distribute candy such that either blue or red bag is empty.

The total amount of circumstances and ways to deliver the sweets

= 3⁷ – (2⁷ + 2⁷ -1)

= 1932

Therefore, there are a total of 1932 arrangements possible.

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The probability that a day requires more water than is stored in city reservoirs will be; 0.965

The z-score is a numerical measurement used in statistics to refer to how much a given value differs from the standard deviation.

Given that Water use in the summer is normally distributed with a mean of 310 million gallons and a standard deviation of 45 million gallons.

Let X be the random variable that shows the quantity of water required on a particular day.

Z-score :

[tex]Z = \dfrac{X - \mu}{\sigma},[/tex]

Now, the probability that a day requires more water than is stored in city reservoirs will be;

[tex]Z = \dfrac{350 -310}{45},[/tex]

Z = 0.965

We can see that the above value to the given P(X > 350)= 1 - P(Z < b), we get the value of b is; 0.965.

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The piece of carpet on each side of the floor will be 10.8 feet.

From the information, Amber wants to put a carpet on the floor of her bedroom and the floor is a square with an area of 7.29 square feet.

It should be noted that the side will be

= ✓7.29

= 2.7 feet.

Therefore, the perimeter will be found and this will be:

= 4 × side

= 4 × 2.7

= 10.8 feet

This illustrates the length.

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The range of values that a bottle could contain to pass inspection will be 7.840 - 8.160 ounces.

It was stated that the toy company that makes bubbles fills its 8-ounce bottles using a machine.

The bottle passes inspection if the percent error of the amount is 2% or less. The minimum range will be:

= 8 ounces - (2% × 8 ounces)

= 8 ounces - 0.16 ounces

= 7.84 ounces

The maximum range will be:.

= 8 ounces + (2% × 8 ounces)

= 8 ounces + 0.16 ounces

= 8.16 ounces.

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The allowable range for the toy company is [7.84, 8.16].

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, the allowable percentage error is 2% or less.

Now, 2% of 8 ounces is,

= (2/100)×8.

= 0.16 ounces.

So, the allowable range is from (8 - 0.16) = 7.84 ounces to

(8 + 0.16) = 8.16 ounces.

As it is being given that it is 2% or less we'll use include the least value too.

So, the allowable range of the bottles is [7.84, 8.16].

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Write an equation of the line in slope- point form

[tex]y- 6 = \frac{4}{5} (x+2)[/tex]

How to write the point- slope form of the equation?

We know, the point- slope formula is given by,

[tex]y-y_1=m(x-x_1)[/tex]

Given:

m= 4/5

[tex](x_1,y_1)= (-2,6)[/tex]

So, the equation of the line is,

[tex]y-y_1=m(x-x_1)\\\\y- 6 = \frac{4}{5} (x+2)[/tex]

It can also be written as ,

y- 6 = 0.8 (x+2)

What is point- slope form?

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Answer:

(3, - 4 )

Step-by-step explanation:

under a reflection in the line y = x

a point (x, y ) → (y, x ) , then

(- 4, 3 ) → (3, - 4 )

The fraction expression given as  -1/3-4/5  is a negative number

The fraction expression is given as

-1/3 - 4/5

From the above expression, we observe that:

The sum of two negative numbers will result in another negative number

This means that the value of -1/3 - 4/5 is a negative expression

Solving further, we have:

-1/3 - 4/5

Evaluate the expression

-1/3 - 4/5 = -17/15

See that 17/15 is negative

Hence, -1/3 - 4/5 is negative

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The possible coordinates of the point C are : (-6,-2) and (2,-2).

A stiff transition called a rotation involves turning the item around a center point. The direction is changed, but the shape is still oriented in the same way. You can spin a form in any direction. A 180 degree rotation of the triangle is made around point C. A rigorous transition like this one may be seen here.

Rotation and translation are the only two elements of a rigid transformation. It does not alter the size or shape of an input object, nor does it involve reflection.

Hence as the graph shows, the coordinates of C' could be:

(-6,-2) and (2,-2)

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The required allowance that Dan has prior is given as $11.6.

Given that,
Dan spent half of his weekly allowance. He then earned $8.90 by completing some chores. What is his weekly allowance if he currently has $14.70 (prior to getting his weekly allowance he had $0) is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Let the allowance Dan has be x,
According to the question,
x/2 + 8.90 = 14.70
x = 29.40 - 17.80
x = $11.6

Thus, the required allowance that Dan has prior is given as $11.6.

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If Danielle sold $4500 in electronics merchandise last week then she earn a total of $1073.75 .

In the question ,

it is given that

Commission of Danielle on everything she sells at electronic store = 7.75%

Base salary of Danielle = $725

amount of electronics merchandise sold by Danielle last week = $4500

So according to question

money earn = base salary + 7.75% of 4500

substituting the value of base salary as $725

= 725 + 0.0775*4500

= 725 + 348.75

= 1073.75

So, Danielle earns $1073.75 .

Therefore , If Danielle sold $4500 in electronics merchandise last week then she earn a total of $1073.75 .

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Answer:

Step-by-step explanation:

You want to know how many adults and children were admitted if there were twice as many children who paid $5.25 for admission as there were adults who paid $7.50, and total admission revenue was $378.

Let 'a' represent the number of adults admitted. Then 2a is the number of children. The total revenue is ...

  7.50a +5.25(2a) = 378

Collecting terms, we have ...

  18a = 378

  a = 21 . . . . . . . divide by 18

  2a = 2·21 = 42 . . . . . find the number of children admitted

21 adults and 42 children were admitted.

21 adults were admitted.

42 children were admitted.

Algebra is one of the numerous subfields of mathematics. The study of mathematical symbols and the rules for employing them in formulas is commonly referred to as algebra, which runs across almost all of mathematics.

Due to that,

Carnival earns a total of $378 in one hour.

Adult fees are $7.50.

Children's fees equal $5.25

Suppose that the carnival allows twice as many youngsters as adults.

If there are x adult, then

Children will thereafter be twice as many.

Since,

$378 is the total amount from both adults and children.

Then,

7.50x + 5.25(2x) = 378

7.50x + 10.50x = 378

18x = 378

x = 378 / 18

x = 21

As x was the total number of adults

Then, in an hour, 21 adults were admitted.

Since there were a total of two children,

Next, there were

42 kids were admitted in an hour (2(21)).

As a result, 42 kids and 21 adults were admitted in one hour.

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Answer:

100.00

Step-by-step explanation:

it's 100.00 because the roof is being repaired and the person will have to pay after

Answer: Choice A.  [tex](5\text{x}^2+2)(3\text{x}-1)[/tex]

==================================================

Work Shown:

[tex]15\text{x}^3-5\text{x}^2+6\text{x}-2\\\\(15\text{x}^3-5\text{x}^2)+(6\text{x}-2)\\\\5\text{x}^2(3\text{x}-1)+2(3\text{x}-1)\\\\(5\text{x}^2+2)(3\text{x}-1)\\\\[/tex]

Explanation:

The idea is to pair up the terms into two groups. Factor each group separately. Then we pull out the overall GCF (3x-1) to finish up the factorization. You can use the FOIL rule to expand out the answer to get the original expression again, which helps confirm the answer.

Answer: 129

Step-by-step explanation: 180-51

Answer:

129.

Step-by-step explanation:

it's 129 believe me

The factorized polynomial 6x² + 15xy -14x -35y is given as (2x + 5y) (3x - 7)

A polynomial is an expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power.

To solve this problem, we simply need to factorize the polynomial given.

[tex]6x^2 + 15xy - 14x - 35y[/tex]

[tex]6x^2 + 15xy - 14x - 35y\\(2x + 5y) (3x - 7)[/tex]

This is the the reduced or factorized form of the given polynomial.

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The value of x after solving the expression is 3.

What is an expression?

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. To assist identify the sequence of operations and other features of logical syntax, mathematical symbols can denote numerals (constants), variable, operations, equations, brackets, punctuation, and grouping. Many writers differentiate between an expression and a formula, with the former referring to a mathematical item and the latter referring to a statement about mathematical things. However, in modern mathematics, and particularly in computer algebra, formulae are considered as expressions that may be evaluated as true or false based on the values assigned to the variables in the expressions.

Given expression 6x-7 = 4x-1

   or, 6x-4x = -1+7

   or, 2x = 6

   or, x = 6/2 = 3

Hence, the value of x after solving the expression is 3.

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The length of the legs of the sun shade is 8√2 feet.

The equation used is option b , y = 1/2x² and y = 64

Isosceles triangle: What is it?

A triangle with two sides that have the same length is said to be isosceles.

Given,

Area of triangle = 64 sq.ft

Here, an isosceles triangle has two equal sides 

Let

x is equal to the length side of a right isosceles triangle's leg.

y is the area of a right isosceles triangle at position

Currently, the legs of a right isosceles triangle are equal.

Area of triangle = 1/2 ×  base × height

y = 1/2 × (x) × (x)

y = x²/2

64 = x²/2

128 = x²

x = √128

x = 8√2

The length of the legs of the sun shade is 8√2 feet.

The equation used is option b , y = 1/2x² and y = 64

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Answer:

Step-by-step explanation:

first part: B.

second part: -11.3 or 11.3, 11.3

The value of the expression will be;

⇒ log₅ (1/25) = - 2

Option D is true.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ log₅ (1/25)

Now,

Solve the expression as;

⇒ log₅ (1/25)

Since, log (a/b) = log a - log b

Hence,

⇒ log₅ (1/25) = log₅ 1 - log₅ 25

Since, log 1 = 0

⇒ log₅ (1/25) = 0 - log₅ 25

⇒ log₅ (1/25) = - log₅ 5²

Since, log a² = 2 log a

⇒ log₅ (1/25) = - 2 log₅ 5

Since,  log₅ 5 = 1

⇒ log₅ (1/25) = - 2 x 1

⇒ log₅ (1/25) = - 2

Thus, The value of the expression will be;

⇒ log₅ (1/25) = - 2

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Step-by-step explanation:

the 2 triangles are similar.

that means their corresponding angles are equal, and their side lengths (and heights and so on) have all the same constant scaling factor.

so, we see that the side with the length 6 must corresponds to the side with the length 3 (factor 1/2).

as then the side with the length 5 corresponds to the side with the length 2.5, and the side with the length 4 corresponds to the side with the length 2 (all have the same factor 1/2).

a is the angle between 6 and 5 (the 2 longest sides).

the angle between the 2 longest sides in the smaller triangle (3 and 2.5) is d.

so, a and d correspond.

b is the angle between 6 and 4 (the longest and the shortest side).

the angle between the corresponding sides 3 and 2 is c.

so, b and c correspond.

therefore, the 4th and last answer choice is correct.

Answer: I think it’s t{(-3,2).(5.5).(3.3).(3.-2)}

Step-by-step explanation:

Eyesight is key m’lady

The first graph represents the same relation as the set {(-3,2).(5.5).(3.3).(3.-2)}

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The given relation is {(-3,2).(5.5).(3.3).(3.-2)}

We have to find the graph which represents the relation of the set

A binary relation on a set may, or may not, hold between two given set members.

The first number in the ordered pair represents the x coordiantes

The second number in the ordered pair represents the y coordiantes

When we match the ordered pairs with the given graphs

The first graph matches with the given relation

Hence, the first graph represents the same relation as the set {(-3,2).(5.5).(3.3).(3.-2)}

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Approximately, the unit cost of the plastic cups is $0.25

Here, we want to get the unit rate of the plastic cups

By unit rate, we mean the price of 1

From the question, the total 72 costs $17.99

The cost of one is thus;

Answer:

always

never

always

always (not 100% sure)

sometimes

sometimes (not 100% sure)

Step-by-step explanation:

this is what I got, hope it helps

How many pounds of walnuts that cost $.80 per pound must be mixed with 8 pounds of cashews that cost $1.25 per pound to make a mixture of nuts that cost $1.00 per pound?​

Let

x ------> pounds of walnuts

we have that

0.80x+

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

The value of t exists [tex]$t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$$[/tex].

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Expressions have the following structure: (Number/variable, Math Operator, Number/variable).

Given: [tex]$275000=\frac{3001-\left(1+\frac{0.038}{12}\right)^{(-12 t)}}{\left(\frac{0.038}{12}\right)}$$[/tex]

Multiply both sides by 0.038 / 12, we get

[tex]$275000 \cdot \frac{0.038}{12}=\frac{3001-\left(1+\frac{0.038}{12}\right)^{-12 t}}{\frac{0.038}{12}} \cdot \frac{0.038}{12}$$[/tex]

Simplifying the above equation, we get

[tex]$\frac{5225}{6}=3001-\left(1+\frac{0.038}{12}\right)^{-12 t}$$[/tex]

Add [tex]$\left(1+\frac{0.038}{12}\right)^{-12 t}$[/tex] to both sides

[tex]$\frac{5225}{6}+\left(1+\frac{0.038}{12}\right)^{-12 t}=3001-\left(1+\frac{0.038}{12}\right)^{-12 t}+\left(1+\frac{0.038}{12}\right)^{-12 t}$$[/tex]

Simplifying the above equation, we get

[tex]$\frac{5225}{6}+\left(1+\frac{0.038}{12}\right)^{-12 t}=3001$$[/tex]

Subtract 5225 / 6 from both sides

[tex]$\frac{5225}{6}+\left(1+\frac{0.038}{12}\right)^{-12 t}-\frac{5225}{6}=3001-\frac{5225}{6}$$[/tex]

Simplify

[tex]$\left(1+\frac{0.038}{12}\right)^{-12 t}=\frac{12781}{6}$$[/tex]

By using exponent rules, we get

[tex]$-12 t \ln \left(1+\frac{0.038}{12}\right)=\ln \left(\frac{12781}{6}\right)$$[/tex]

Solve [tex]$-12 t \ln \left(1+\frac{0.038}{12}\right)=\ln \left(\frac{12781}{6}\right): \quad t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$[/tex]

[tex]$t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$$[/tex]

Therefore, the value of t exists [tex]$t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$$[/tex].

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The Area of a Rectangle as a Sum and as a Product are as follows:

21. Area as sum = 12x + 60

Area as Product = 12(x + 5)

22. Area as sum = 5x + 20

Area as Product = 5(x + 4)

As a product, we can multiply the height and the base of the rectangle.

As a sum, we can estimate the area finding the sum of the areas of each piece of the rectangle.

The missing pieces that will fill into the circles exists shown in the diagram attached below. The Area of a Rectangle as a Sum and as a Product are as follows:

21. Area as sum = 12x + 60

Area as Product = 12(x + 5)

22. Area as sum = 5x + 20

Area as Product = 5(x + 4)

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ok

Slope = (y2 - y1) / (x2 - x1)

P1 = (12, -4)

P2 = (14, 8)

Substitution

Slope = (8 - - 4) / (14 - 12)

= (8 + 4) / 2

= 12/2

= 6

Result

Slope = 6