Use the change of base rule to find the logarithm to four decimal places. (2 points) log base nine of 0.877.

Answer:

For a, the machine depreciates 20% of its current value each year.  So, It will lose 20% of its value in the first year.  Then in the second year, it will lose 20% of THAT value (not of the original value) and so on.

b) Since the machine loses 20% of its value each year, it retains 80% of its value each

Answer:  0.0386

Step-by-step explanation:

Given: The population of 400 tall women has a mean height[tex](\mu)[/tex] of 179.832 cm and a standard deviation[tex](\sigma)[/tex] of 12.192 cm.

Let X be a random variable that represents the height of woman.

Sample size : n= 50

The probability that the mean for this sample group is above 182.88 will be :

[tex]P(\overline{X}>182.88)\\\\=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{182.88-179.832}{\dfrac{12.192}{\sqrt{50}}})\\\\ =P(Z>1.7678)\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-P(Z<1.7678)\\\\=1-0.9614\ \ \ [\text{By p-value table}]\\\\= 0.0386[/tex]

Hence, Required probability =  0.0386

Answer:

No, he won't

Step-by-step explanation:

Given

Target = 480 pages in 28 days

Rate = 60 pages in 4 days

Required:

Determine if he'll reach his target

The rate can be expressed using:

[tex]Rate = \frac{Pages}{Days}[/tex]

So, we have:

[tex]Rate = \frac{60\ pages}{4\ days}[/tex]

Multiply the fraction by [tex]\frac{7}{7}[/tex]

[tex]Rate = \frac{60\ pages}{4\ days} * \frac{7}{7}[/tex]

[tex]Rate = \frac{60\ pages * 7}{4\ days * 7}[/tex]

[tex]Rate = \frac{420\ pages}{28\ days}[/tex]

This can be interpreted as: 420 pages in 28 days

And his target is 480 pages in 28 days

Hence, he wont finish the book at that rate

Answer:

Step-by-step explanation:

One zettabyte is equal to 1, 000 exabytes or 1021 or 1, 000, 000, 000, 000, 000, 000, 000 bytes. A zettabyte is a little bit smaller than zebibyte that contains 1, 180, 591, 620, 717, 411, 303, 424 (2^70) bytes, and is abbreviated as “ZB”.

Answer:

B. -2 *4

Step-by-step explanation:

Answer:

4602

Step-by-step explanation:

Answer:75 × 62 - 58 + 68 - 58 = 4602

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step one:

given data

charged = $40 call fee

additional charges= $15 per mile

let the number of miles be m

and let the total charges be c

Required, the linear function which represents the total charges

Step two:

the equation for the charges in slope-intercept form is

c=15m+40

Your answer should be:

The three significant figures would be the 9, 0, then 1.

The result of 392,196 divided by 87 is 4,508.

Long division is a mathematical process to divide numbers by using multiple steps. This process is applied to big numbers because it facilitates the process of dividing without using a calculator.

Here are the steps you need to follow:

1. Identify the divident and the divisor.

Divident: 392,196

Divisor: 87 (number that divides)

2. Start dividing using one number at a time.

Learn more about division in: https://brainly.com/question/369266

Answer: 6

Step-by-step explanation: The y-intercept is 6 and the slope is -2.

First, we subtract 10x.

5y = -10x+30

Then we divide by 5.

y = -2x + 6

Now we have everything we need!

So the y-intercept is 6.

Hope this helps! :)

The y-intercept is "6".

Given:

[tex]10x+5y=30[/tex]

y-intercept

[tex]10x+5y=30[/tex] y-intercepts

When y-intercepts the value it indicates that x=0 then

[tex]\to 10x+5y=30\\\\\to 10(0)+5y=30\\\\\to 5y=30\\\\\to y=\frac{30}{5}\\\\\to y=6[/tex]

When the y-intercept is value will be "6".

Find out more information about intercept here:

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Answer:

Wouldn't it be just 2 since it's already solved

Answer:

For a line:

y = a*x + b

where a is the slope, and b is the y-intercept.

Any other line with the same slope but different y-intercept will be parallel to this line.

Then if we have two lines like:

y1 = a*x + c

and

y2 = a*x + k

Both of them are parallel to our first line, and as you can see, both of them have the same slope and different y-intercept, then these lines are also parallel.

Now, the statement says that:

"If two lines are parallel to the same line..."

Then we can have the lines:

y1 = a*x + k

y2 = a*x + k

Both of them are parallel to our first line (same slope)

Buth these lines are the same line, then these lines are not parallel to each other (a line is not parallel to itself, because it intersects itself in infinity points), then the actual statement should be:

"If two different lines are parallel to the same line, then they are parallel to each other".

Now, this theorem does not have a particular name, just call it as the above statement.

Answer:

A.) 6

B.) 24

C.) $60

Step-by-step explanation:

Given that :

Cost of Mango = $2

Purchase of 6 mangoes earns 2 free mangoes

(a) Robin purchased $36.00 worth of mangoes.

How many free mangoes did Robin get?

$36 / price per Mango

$36 / $2 = 18 mangoes

18 / 6 = 3

Hence, free mangoes (3 * 2) = 6 free mangoes

(b) How many mangoes did he get all together?

18 mangoes + 6 mangoes = 24 mangoes

(c) Peter also bought mangoes. He received 40 mangoes. How much did Peter pay?

Set of mangoes purchased:

40/ (6 + 2) = 40/8 = 5 sets of mangoes

Hence, amount paid :

2 * 6 * 5 sets

$60

Answer:

9x^2-3x - 12

Step-by-step explanation:

(9x^2 + 6x - 7) + (-9x -5)

Simplify the expression:

9x^2 - 3x - 12

Factor:

Add and subtract the second term to the expression and factor by grouping.

3( x + 1 ) ( 3x - 4 )

Standard form:

9x^2 - 3x - 12

I hope this helps :)

Answer:

504 m³

Step-by-step explanation:

The volume of the rectangular prism is V = 504 m³

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

The volume of a prism is the product of its base area and height

Volume of Prism = B x h

where B = base area of prism

h = height of prism

Given data ,

Let the volume of the prism be represented as V

Now , the value of V is

Let the height of the rectangular prism be H = 9 m

Let the length of the rectangular prism be L = 7 m

Let the width of the rectangular prism B = 8 m

where the base area of prism B = L x W = 7 x 8 = 56 m²

Now , the volume of the prism V = B x H

The volume of prism V = 56 x 9 = 504 m³

Hence , the volume of the rectangular prism V = 504 m³

To learn more about volume of prism click :

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#SPJ3

Answer:

3

Step-by-step explanation:

Given that:

Weight of shipment = 40 1/2 kg

Weight per bag = 13 1/2 kg

The value of 40 1/2 divided by 13 1/2 will be ;

40 1/2 ÷ 13 1/2

81 /2 ÷ 27 /2

81/2 * 2/27

= 162 /54

= 3

Answer:I believe the answer is 12

Step-by-step explanation: if you split the triangle into 2 then you can do 1/2bh then add them. (1/2)(2)(3)+(1/2)(6)(3)=12

Answer:

y = x + 4

Step-by-step explanation:

For a line to be Parallel it has to have the same slope but different y intercept

Answer:

1

Step-by-step explanation:

This equation is written in the

y = mx + b,

where "m" is the slope, and "b" is the y-intercept.

In this case, m=1, hence the "x" has no coefficient; therefore, the slope of the given line is 1.

When 2 lines are parallel, they run next to each other, for infinitely long, yet they never touch. This means that 2 parallel lines have the same slope. Hence a line running parallel to the given one will also have a slope of 1.

5000

Step-by-step explanation:

because u have to add

Answer: You need to buy about 10 cans of paint.

Step-by-step explanation:

Given : Diameter of round swimming pool = 59 ft

Radius = half of diameter

= [tex]\dfrac{59}{2}[/tex] ft

Area of circle = [tex]\pi r^2[/tex] , where r= radius

Area of bottom of pool = [tex]\dfrac{22}{7}\times\dfrac{59}{2}\times\dfrac{59}{2}[/tex]

[tex]=\dfrac{38291}{14}\ ft^2[/tex]

Each can of paint cover 300 ft².

So , Number of cans required to cover 1 ft² = [tex]\dfrac1{300}[/tex]

Number of cans required to cover[tex]\dfrac{38291}{14}\ ft^2[/tex] = [tex]\dfrac{38291}{14}\times\dfrac{1}{300}=9.1169047619\approx10[/tex]

Hence, you need to buy about 10 cans of paint.

Answer:

infinite number of solutions

Step-by-step explanation:

Given the 2 equations

y = 2x + 3 → (1)

3y = 6x + 9 → (2)

Divide the terms in (2) by 3

y = 2x + 3 → (3)

Since the equations are the same in (1) and (3) , then

The system has an infinite number of solutions

Answer:

1 2/4

Step-by-step explanation:

Answer:

no, it won't be enough because you would need $80.06

Step-by-step explanation:

I just found 6.75% of 75 and added it on

Answer: 0.27

Step-by-step explanation:

Given that :

Probability of being a strike ; p(strike) = 0.3

Note : the probability of each pitch Beau is independent :

Probability that next three will be a strike :

p(strike) * p(strike) * p(strike)

= 0.3 * 0.3 * 0.3

= 0.27

Answer:

x = 24

Step-by-step explanation:

Here, The Right angled triangle is given

So, The sum of angles of right angled triangle is 180

Now,

2x + 42 + 90 = 180

2x + 132 = 180

2x = 180 - 132

2x = 48

x = 48/2

x = 24

2x + 42 + 90 = 180

2(24) + 42 + 90 = 180

48 + 42 + 90 = 180

180 = 180

Hence, L.H.S = R.H.S

-TheUnknownScientist

Answer:

A) The standard form of a linear equation is given as follows;

Ax + By = C

In order to change the above linear equation from standard form to slope and intercept form which is the form y = mx + c, we have;

1) Move the x-variable (and its coefficient) to the right side of the equation as follows;

By = C - Ax

2) Divide both sides of the equation above equation, by the coefficient of y as follows;

By/B = C/B - Ax/B

y = C/B - A/B·x

3) Rearrange the right hand side of the above equation

y = -A/B·x + C/B

The equation given above is in the slope and intercept form, y = m·x + c, where;

m = -A/B

c = C/B

B) Two reasons why it is important to have a slope and intercept form of a linear equation are;

1) The slope and intercept for shows the initial value of the dependent variable, y, when the dependent variable, x is 0 which is the constant term, c, in the equation

2) The slope coefficient term, m, in the slope and intercept form of a linear equation shows the rate of increase of the y-coordinate value with a unit increase in x-coordinate value.

Step-by-step explanation: