Jane and Jill collect yo-yos. The ratio of the number of Janes yo-yos to the number of JIlls yo-yos is 5:4. If jane will give 15 of her yo-yos to her little brother, Jane and Jill will have the same number of yo-yos in their collections. How many yo-yos do both girls have together?

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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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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The simplification of the given expression will be 54.

A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.

Given that the expression is 2 x 4 + 6 + 5  thex 8

To solve the given expression we have to first solve the multiplication operation.

2 x 4 + 6 + 5 x 8

8 + 6 + 40

Now add the terms;

8 + 6 + 40

= 54

Hence, the simplification of the given expression will be 54.

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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 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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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

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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The area of the rectangle with one dimension sizes three more than twice the other dimension is A= x(2x+3)

We assume that there is rectangle ABCD with lines AB and CD are parallel with each other. Meanwhile lines BC and DA are parallel with each other. We could ssume that lines BC and DA are the shortest lines.

Please take a look at the picture below.

Based on the formula of rectangle, the area of rectangle could be calculated using the multiple between the longest line and the shortest line.

It could be written based on the rectangle we have into such formula:

A = AB × BC

A = CD × DA

A = AB × DA

A = CD × BC

If we input the rules from the question, then we could find the relationship between the shortest and the longest lines. Hence:

AB = CD = 2(BC) + 3

AB = CD = 2(DA) +3

if we assume that the shortest line is x, then we will get the formula:

BC = DA = x ...(1)

AB = CD = 2x+3 ...(2)

If we input equation (1) and (2) into the rectangle area formula, we will get the result:

A = AB × BC

A = (2x+3)

A = x(2x+3)

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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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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.

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

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

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

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:

-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

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.

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

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:

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.

The solution for f ( x ) = 72 is x = -3 ; which is not a viable solution in this scenario.

It follows from the task content that the solution for the function instance, f(x) = 72 is to be determined according to the given function.

Since the given function is; f ( x ) = − 4 x + 60;

The solution for f (x) = 72 can be determined as follows;

72 = - 4 x + 60

- 4x = 72 - 60

- 4x = 12

x = 12/-4

x = - 3

On this note, since x = -3 which is negative; it follows that it is not a a viable solution in this regard.

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The function is odd because f(-x) = -f(x)

What is a Function?

A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).

Solution:

For a function to be even it must satisfy the condition that,

f(-x) = f(x)

else,

if f(-x) = -f(x), then the function is odd

we are given with the function f(x) = [tex]4x^{3}[/tex]

replacing x by (-x)

f(-x) = 4(-x)^3

f(-x) = -4x^3

this implies that, f(-x) = -f(x)

Therefore, the function is an odd function

So, option D is correct

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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:

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:

7

Step-by-step explanation:

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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Answer:

Step-by-step explanation:

General equation of circle:

Comparing with the general equation we see that the circle x² + y² = 36 has:

The circle radius of 6 units, so y = - 6 has only one common point.

Since there is only one common point of the circle and line, the line is tangent to the circle.

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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