Evaluate each logarithm.
log₇49

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

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.

Learn more about wages here:

https://brainly.com/question/7159569

#SPJ1

[tex]27x^{12}[/tex] smaller cubes will fit in the larger cube.

Given,

Side length of the smaller cube = [tex]x^{2}[/tex] units.

Side length of the larger cube = [tex]3x^{6}[/tex] units.

We have to find the number of smaller cubes that can be fitted in the larger cube.

Volume of cube is given by the formula,

Volume = (side)³

Volume of the larger cube = [tex](3x^{6} )^{3}[/tex]   =  [tex]27x^{18}[/tex]units³

Volume of the smaller cube = [tex](x^{2} )^{3}[/tex] = [tex]x^{6}[/tex] units³

Let the number of smaller cube that can be fitted in the larger cube = n

Volume of  n cubes = [tex]nx^{6}[/tex] units³

If space inside the larger cube will be occupied by 'n' smaller cubes,

  volume of n smaller cubes = Volume of a larger cube

                                      [tex]nx^{6}[/tex]           =  [tex]27x^{18}[/tex]

                                       n             = [tex]27x^{12}[/tex]

Therefore, [tex]27x^{12}[/tex] smaller cubes can be fitted in the larger cube.

Learn more about cubes here: https://brainly.com/question/18789836

#SPJ1

Based on the attached graph, the point that is located at (5,-2) is point F

The graph that completes the question is added as an attachment

The point located at (5,-2) implies that the coordinates of the point are

x-coordinate = 5

y-coordinate = -2

From the attached graph, we can see that the point F has the following properties

x-coordinate = 5

y-coordinate = -2

This means that the point F is located at (5,-2)

Hence, the point that is located at (5,-2) is point F

Read more about coordinates at

https://brainly.com/question/11337174

#SPJ1

No valid conclusion drawn from the statements.

You can "detach" the hypothesis from the conclusion using the law of detachment. More specifically, if p and p -q are known to be true, we can infer that q is true. On the other hand, we can cram conditional statements together using the law of syllogism. When p-q and q-r are known to be true, they can be combined to form p-r. After all, it would be silly-gism to go through q when we can just go from p to r.

P = quadrilateral has diagonals

Q = quadrilateral diagonals bisect each other

R= the quadrilateral is a parallelogram

Statement P is true because all quadrilaterals have 2 diagonals that runs from one edge to another eg square, rectangle, parallelogram, kite etc

Statement Q is False because not all quadrilateral's diagonals bisect each other as in the case of trapezium, likewise quadrilateral whose diagonals bisects each other are not only parallelogram, kite, square and rectangle diagonals bisect each other.

Statement R is False because a quadrilateral whose diagonals bisect each other is not only parallelogram. Square, rectangle and Kite diagonals also bisect each other, and they are also parallelogram.

Therefore, no valid conclusion made from the statements because parallelogram is not the only quadrilateral whose diagonals bisect each other and not all quadrilateral's diagonals bisect each other.

To learn more about using Law of Syllogism to draw conclusions. Click, https://brainly.com/question/28560801

#SPJ4

Answer: Part to whole is 1:2

Answer:

12

Step-by-step explanation:

See attachment for step-by-step instructions

Answer:

y=-x+3

Step-by-step explanation:

the gradient of the equation is -1

and the y intercept is 3

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.

Learn more about linear equation here

https://brainly.com/question/4074386

#SPJ9

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

Learn more about solubility of gas here:

https://brainly.com/question/27294956

#SPJ1

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.

Learn more about statistics at

https://brainly.com/question/8058700

#SPJ1

Answer:

Step-by-step explanation: Hello,

the answer

Answer: |81 - (-29)|==> C

Step-by-step explanation:

h=high temperature

h=81

l=low temperature

l=-29

d=difference in high and low temperature

h-l=d

81-(-29)=d

81+29=d

d=110 ==> |81 - (-29)|=|81 +29|=|110|=110

|81 - (-29)|==> C

|81 -29|=|52|=52

-29 + 81=81-29=52

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

Read more about expressions at

https://brainly.com/question/723406

#SPJ1

Answer:

2.5£ =25tacos

1£ =?

=1*25/2.5

=10 tacos:

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.

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.

Learn more about simplification here:

https://brainly.com/question/71406

#SPJ1

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.

Learn more about square root on:

https://brainly.com/question/3617398

#SPJ1

Which number is closest to the square root of 161 ?

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.

To learn more on number system click:

https://brainly.com/question/14272440

#SPJ1

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

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

Learn more about linear equations at https://brainly.com/question/25677592

#SPJ4

The transformation is rotation 90° clockwise followed by a reflection over the y-axis

The question is given as

Which of the following BEST represents this transformation?

From the question, we have the figure shown to be

A transformation of a figure from Quadrant II to Quadrant IV

From the figure, we can see that the shapes in both quadrants have the same dimensions

This means that the shapes are not dilated

However, the orientation of the figures are difference

Because of the positioning of the shapes, we can conclude that the transformaton is rotation 90° clockwise followed by a reflection over the y-axis

Hence, the transformation is rotation 90° clockwise followed by a reflection over the y-axis

Read more about transformation at

https://brainly.com/question/4289712

#SPJ1

Answer:

3/7y= -8/7

Step-by-step explanation:

reduce the greatest common factor on both sides of th equation

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

Learn more about function here:

https://brainly.com/question/25638609

#SPJ4

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.

If you want to learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1

Answer:

Seems correct. I would never use pen for a math assignment though ;-;

Here’s the answer sheet lol.

Step-by-step explanation:

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

Read more about speed at

https://brainly.com/question/14335655

#SPJ1

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

Learn more about Quartic polynomial here:

https://brainly.com/question/11865916

#SPJ1

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:

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