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In a set of eight consecutive integers, the smallest integer is more than $\frac35$ of the largest integer. What is the smallest possible value of the sum of the eight integers?

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

(- 1, 3 )

Step-by-step explanation:

2x + 3y = 7 → (1)

- 2x + 4y = 14 → (2)

add (1) and (2) term by term to eliminate x

(2x - 2x) + (3y + 4y) = (7 + 14)

0 + 7y = 21

7y = 21 ( divide both sides by 7 )

y = 3

substitute y = 3 into either of the 2 equations and solve for x

substituting into (1)

2x + 3(3) = 7

2x + 9 = 7 ( subtract 9 from both sides )

2x = - 2 ( divide both sides by 2 )

x = - 1

As a check

substitute the values of x and y into the left side of both equations and if equal to the right side in both equations then the values of x and y are true.

(1) 2(- 1) + 3(3) = - 2 + 9 = 7 ← true

(2) - 2(- 1) + 4(3) = 2 + 12 = 14 ← true

then (- 1, 3 ) is the solution to the system

Answer:(- 1, 3 )

Step-by-step explanation:

Answer:

b) [-11, 3]

Step-by-step explanation:

Given equation,

→ 3 + |t + 4| = 10

Now the value of t will be,

→ 3 + |t + 4| = 10

→ 3 + t + 4 = 10 || → 3 -(t + 4) = 10

→ t + 7 = 10 || → -t - 1 = 10

→ t = 10 - 7 || → -t = 10 + 1

→ [ t = 3 ] || → [ t = -11 ]

Hence, value of t is 3 (or) -11.

Answer:

Answer: 2x-12

Step-by-step explanation:

First, you distribute and then combine like terms. :)

Answer:

Step-by-step explanation:

Step 1 : Distribute

The distributive property is a rule in mathematics that is used to help simplify equations by using brackets

-3(x+4) + 5x

-3x - 12 + 5x

Step 2 : combine similar tribes

Similar terms are terms in algebra that have the same variables or constants in algebra. Similar terms of the algebraic form above are. Similar terms are terms in algebra that have the same variables or constants in algebra.

-3x - 12 + 5x

2x - 12

Step 3 : common factor

Common factor is the same factor of two or more numbers. For example, the factors of the numbers 18 and 12 can be determined in the following way. So, the common factors of these two numbers are 2, 3, and 6.

2x - 12

2 (x-6)

Completion

2(x-6)

The inequality will be 3.70x ≤ 145 and the number of items that you can by is  x ≤ 39

Total budget that you have = $145

The price of each item = $3.70

Consider the number of items = x

The inequality will be

3.70x ≤ 145

We have to solve the inequality to find the number of items

3.70x ≤ 145

Divide 3.70 on the both side of the inequality

3.70x / 3.70 ≤ 145 / 3.70

x ≤ 39.18

x ≤ 39

The number of items that you can buy is x ≤ 39

Hence, the inequality will be 3.70x ≤ 145 and the number of items that you can by is  x ≤ 39

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For the given triangle MNO, as per the given measurements the smallest angle among all the three angles is ∠M.

As given in the question,

In the given triangle MNO,

Measure of the sides of the triangle are as follow:

MN = 18 yd

NO = 17 yd

MO = 19 yd

Arrange them in ascending order we have,

17 < 18 < 19

NO < MN < MO

From the given measurement of the sides of the triangle , smallest side is NO.

Angle opposite to side MN = ∠O

Angle opposite to side NO = ∠M

Angle opposite to side MO = ∠N

Angle opposite to the smallest side is the smallest angle.

∠M is the smallest angle.

Therefore, for the given triangle MNO, as per the given measurements the smallest angle among all the three angles is ∠M.

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Answer:

no chart

Step-by-step explanation:

show chart let us see what to use

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

you multiply the denominator with the denominator and the numerator with the numerator

[tex]\frac{5}{6}x\frac{2}{5}[/tex]

[tex]\frac{5x2}{6x5}[/tex]

[tex]\frac{10}{30}[/tex]

[tex]\frac{1}{3}[/tex]

Hopes this helps please mark brainliest

The error made in the calculation was improper use of quotient rule of logarithm

The problem will be solved by using the rules of logarithm as done below

logₐ 2x + 2 ( logₐ x - logₐ y )

expanding the parenthesis

logₐ 2x + 2logₐ x - 2logₐ y

applying exponential rule of logarithm

logₐ 2x + logₐ x² - logₐ y²

applying product rule of logarithm

logₐ (2x * x²) - logₐ y²

logₐ (2x³)  - logₐ y²

applying quotient rule of logarithm

logₐ (2x³/ y²)

The error was that the quotient rule of logarithm was not properly applied

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The probability that the representation in base-9 and the representation in base-11 are both three-digit numbers is 0.6753 which is approximately 0.7 option E.

Given,

We require the following inputs to determine the probability that both the base-9 representation and the base-11 representation are three-digit numbers:

The base-11's lowest 3-digit number is 100.

The comparable number is 121 when expressed in base 10.

888 is the biggest 3-digit base-9 number.

The corresponding number is 728 when expressed in base 10.

As a result, there are the following possibilities:

Possibilities = 728 - 121 + 1

Possibilities = 608

The total number of 3-digit base-10 numbers is

Count = 999 - 100 + 1

Count = 900

The necessary probability is:

P = 608/900

Evaluate

P = 0.6753 ≈ 0.7

Therefore,

The probability that the representation in base-9 and the representation in base-11 are both three-digit numbers is 0.6753 which is approximately 0.7 option E.

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Answer:

-6

Step-by-step explanation:

to solve you need to substitute the value of x in the equation which is given as 2so if you rewrite the equation it will be

-2(2)+10

=(-2*2)+10

=-4+10

=6

Volume of the rectangular solid in cubic inches for the given measures of edges 1. 5 feet by 1½ feet by 3 inches is equal to 972 cubic inches.

As given in the question,

Given measures of edges of the rectangular solid is equal to :

1. 5 feet by 1½ feet by 3 inches

Length = 1.5 feet

Conversion 1 feet = 12 inches

1.5 feet = 1.5 × 12

            = 18 inches

Width = 1½ feet

          = 3/2 feet

          = ( 3/2 ) × 12

          = 18 inches

height = 3 inches

Volume of the rectangular solid = length × width × height

                                                     = 18 × 18 × 3

                                                     = 972 cubic inches

Therefore, volume of the rectangular solid in cubic inches for the given measures of edges 1. 5 feet by 1½ feet by 3 inches is equal to 972 cubic inches.

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Answer:

sin(79°) - cos(11°) = 0

Step-by-step explanation:

Based on the rule sin(90-x) = cos(x), we can transform the expression. See the attached for more details

Answer:

x = 0.08

Step-by-step explanation:

2x²+ 8x - 1 = 0

4x + 8x - 1 = 0

12x - 1 = 0

Add 1 to the -1 and to the 0 too

12x = 1

Divide both side

x = 0.08

Functional dependency SSN --> Name exists in the table STUDENT is TRUE, The correct option is (A)

due to the fact that a student ID is a primary key in a table and that (StudentID, SSN) can also combine to form a composite key that can be used to identify a record in a table in a unique way. The augmented functional dependency between the StudentID and SSN enables you to locate additional data in the table. However, using only StudentID will also assist you in finding data in the table.

Since it could be a candidate key, this is true because it can be used in part of augmented functional dependency.

Thus, the SSN matches the name in the STUDENT table.

So, SSN ----> Name holds in STUDENT table.

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(complete question)

Observe the table STUDENT:

STUDENT

StudentID SSN Name Class

D111 111-11-1111 Connor Freshman

D222 222-22-2222 Trevor Freshman

D333 333-33-3333 Connor Sophomore

D444 444-44-4444 Parker Sophomore

D555 555-55-5555 Connor Sophomore

Functional dependency SSN --> Name exists in the table STUDENT.

True

False

A graph which represents the linear function y = -2x is: graph B.

In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.

Generally speaking, the graph of any proportional relationship is characterized by a straight line with the data points passing through the origin (0, 0) because as the values on the x-axis (x-coordinate) either increases or decreases, the values on the y-axis (y-coordinate) increases or decreases simultaneously.

In this context, we can reasonably infer and logically deduce that the relationship between x-values and y-values in the graph of y = -2x is proportional as it passes through the origin (0, 0).

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Answer:

4 Hot dogs packages and 5 hot dog buns packages.

Step-by-step explanation:

This question seems to be regarding the LCM or the least common multiple. Least common multiple is found by figuring out the first time when both numbers, in this case 10 and 8 have the multiple. You can do this by setting up a table with the multiples of each number.

8  | 16 | 24 | 32 | 40

10 | 20| 30 | 40

We can see that the LCM is 40 so we can see that we need 4 Hot Dog packets and 5 buns packets.

Answer:

Step-by-step explanation:

$603.5

Answer:39.65

Step-by-step explanation:

turn 6.5% to 0.065

610 x 0.065=39.65

Answer:

1. Y = 2x

2. 2

3.

Step-by-step explanation:

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

(8-4)/(4-2)

4/2

2

3.

The amount of tax that Walmart pay annually in FUTA is  $630 million .

In the question ,

it is given that ,

the amount that an employee earns in 1 year(E) = $7000

the tax rate (r) = 6%

number of employees in Walmart = 1.5 million = 1.5 × 10⁶

So , the amount of tax paid by Walmart in Federal Unemployment Tax Act(FUTA) can be calculated using the formula

Amount = r × n × E

Substituting the values of r , n , E in the amount formula ,

we get ,

Amount = 0.06 × 1.5 × 10⁶ × 7000

= 630,000,000

= 630 million .

Therefore , The amount of tax that Walmart pay annually in FUTA is  $630 million .

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The integers in the set S:{-24, -6, 12, 24) that will make the inequality 1/3(m - 3) ≤ 1/6(m - 12) false are: S:{12, 24}​.

In order to determine which integers are true and false with respect to a solution of the given inequality, we would have to test the given integers by substituting their values into the inequality as follows;

For integers (-24, 24), we have:

1/3(m - 3) ≤ 1/6(m - 12)

1/3(-24 - 3) ≤ 1/6(-24 - 12)

1/3(-27) ≤ 1/6(-36)

-9 ≤ -6 (True).

For integers (-24, 24), we have:

1/3(m - 3) ≤ 1/6(m - 12)

1/3(24 - 3) ≤ 1/6(24 - 12)

1/3(27) ≤ 1/6(36)

9 ≤ 6 (False).

For integers (-24, -6), we have:

1/3(m - 3) ≤ 1/6(m - 12)

1/3(-6 - 3) ≤ 1/6(-6 - 12)

1/3(-9) ≤ 1/6(-18)

-3 ≤ -3 (True).

For integers (-6, 12), we have:

1/3(m - 3) ≤ 1/6(m - 12)

1/3(12 - 3) ≤ 1/6(12 - 12)

1/3(9) ≤ 1/6(0)

3 ≤ 0 (False).

For integers (12, 24), we have:

1/3(m - 3) ≤ 1/6(m - 12)

1/3(12 - 3) ≤ 1/6(12 - 12)

1/3(9) ≤ 1/6(0)

3 ≤ 0 (False).

1/3(m - 3) ≤ 1/6(m - 12)

1/3(24 - 3) ≤ 1/6(24 - 12)

1/3(27) ≤ 1/6(36)

9 ≤ 6 (False).

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The cost of each bag of flour is $ 18.85 and the cost of each bag of $ 25.7 which a wholesale food supplier charges for each bag of flour and for each bag of sugar.

Given that:

The cost of each bag of flour = x dollars

The cost of each bag of sugar = y dollars

Bakery A purchases seven bags of flour and five bags of sugar for a total cost of $260.45.

Bakery B purchases five bags of flour and three bags of sugar for a total cost of $171.35.

Making equation from both the above statements. We get,

7x + 5y = 260.45 ...... (1)

5x + 3 y = 171.35 ....... (2)

Multiplying equation (1) by 5 and equation (2) by 7. We get the value,

35x + 25y = 1302.25 ....... (3)

35x + 21y = 1199.45 ........ (4)

Subtracting equation (4) from (3). We get,

4y = 102.80

=> y = $ 25.70

Putting the value of y in equation (1). We get,

7x + 25.70 x 5 = 260.45

7x = 260.45 - 128.5

7x = 131.95/7

=> x = $ 18.85

Hence, we can say that a wholesale food supplier charges 18.85 dollars for each bag of flour and 25.7 dollars for each bag of sugar.

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The monthly bill for 20 gallons of water is $88.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

A water bottling company charges $8 per month for their water dispenser and $4 for each gallon of water delivered.

If you have g gallons of water delivered in a month.

Then, the equation to represent the  amount of your bill for that month.

8+ 4g

Now, for g=20 the amount of bill would be

= 8 +4(20)

= 8+ 80

= $88

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The percent increase between the total without Daya's employer contribution and the total with is A. 94%.

From the information, Daya contributes a set percentage of her gross pay towards a 401k account and will have a total of $172,486.00 by retirement and her employer also contributes a set percentage, which will increase her total by $161,531.00.

Therefore, the percentage increase will be:

= Increase in amount / Original amount × 100

= 161,531/172486 × 100

= 94%

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The value of x is 17, y is 2 and length of DF is 20.

Basic Proportionality Theorem (can be abbreviated as BPT) states that, if a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.

For x

DG = GE ( Given )

DG + GE = DE

DE = 2(DG)

DG/DE = 1/2

hence GH/EF = 1/2

By Basic Proportionality Theorem ( BPT )

(x – 3) / 28 = 1/2

after cross multiplication

2(x – 3) = 28

2x – 6 = 28

2x = 34

x = 17

For y

By Basic Proportionality Theorem (BPT) to side DF

DF = 2(DH)

DH/DF = 1/2

(y + 8) / (y + 8 + x – 7) = 1/2

after cross multiplication

2(y + 8) = y + 8 + x – 7

put x = 17

2(y + 8) = y + 8 + 17 – 7

2(y + 8) = y + 18

2y + 16 = y + 18

2y = y + 2

2y – y = 2

y = 2

DF = 2(2+8)

     = 2(10)

     = 20

Hence, x is 17, y is 2 and DF is 20.

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Answer:

The correct answer is B

Step-by-step explanation:

I went a weird way to get this.  I wrot the line in the slope intercept form and  then converted it to the standare form.

For the slope intercept form I need a slope and a y interctp.  I used the two points given to find the slope.  The slope is the change in y over the change in x.  From the points the y values are 3 and -1.  The x values are 1.2 and -4

[tex]\frac{3 - -1}{\frac{1}{2}- - 4 }[/tex] = [tex]\frac{3+1}{\frac{1}{4}+4 }[/tex] = [tex]\frac{4}{\frac{9}{2} }[/tex]

4 ÷[tex]\frac{9}{2}[/tex] = [tex]\frac{4}{1}[/tex] x [tex]\frac{2}{9}[/tex] = [tex]\frac{8}{9}[/tex]

[tex]\frac{8}{9}[/tex] is the slope

Now to find the y intercept

I will use

slope [tex]\frac{8}{9}[/tex] (m)

y = -1            from the point (-4,-1) given

x = -4            from the point (-4,-1) given

y=mx + b

-1 = [tex]\frac{8}{9}[/tex](-4) + b

-1 = [tex]\frac{-32}{9}[/tex]x + b       Add [tex]\frac{32}{9}[/tex] to both sides

[tex]\frac{23}{9}[/tex] = b

y = [tex]\frac{8}{9}[/tex]x + [tex]\frac{23}{9}[/tex]  Multiply all the way thorugh by 9

9y = 8x + 23  Subtract 9y from both sides

0 = 8x -9y + 23  Subtract 23 from both sides

-23 = 8x -9y

or

8x -9y = -23

Answer:

7

Step-by-step explanation: