The table below shows how the age of a certain tree is related to the
diameter (width) of its trunk. How old (in years) is a tree whose trunk is 12
inches in diameter?
Trunk diameter
(inches)
4
5
6
7
8
69
Age
(years)
10
20
30
40
50
60
Answer here
years old

The standard deviation is 6.09

The variance is 37.04.

Standard deviation is used to determine how the values in a group differs from the mean of the values in the group. It is a measure of variation.

In order to determine the standard deviation, take the following steps:

(162 - 170.40)² + (166-  170.40)² + (179 -  170.40)² + (170 -  170.40)² + (175 -  170.40)²

70.56 + 19.36 + 73.96 + 0.16 + 21.16 = 185.20

√185.20 / 5 = 6.09

Variance measures the rate of dispersion of a data point around the dataset. It can be calculated by finding the square of the standard deviation of a dataset.

6.09² = 37.04

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Since f(x) appears to admit a local minimum at the point of abscissa zero, then the tangent drawn at that point must admit a slope equal to zero.

Answer:04,6and 12

Explation:factors are numbers which divide the original number without leaving a remainder.The factors are:1,2,3,4,6,8,12,16,32,48and 96

The percentage of matter in the ore that is neither gold nor diamond is 99.9388%.

In the question, we are given that a sample of ore is found to be 0.0022% gold and 0.059% diamond.

We are asked for the percentage of matter in the ore that is neither gold nor diamond.

We know that in any quantity, the total is shown as 100%.

If we assume the percentage of matter in the ore that is neither gold nor diamond to be x%, then using the above theory, we can say that;

x% + 0.0022% + 0.059% = 100%.

This can also be shown as:

x + 0.0022 + 0.059 = 100, which can be simplified as:

x + 0.0612 = 100, which can be solved by subtracting 0.0612 from both sides to get:

x = 100 - 0.0612 = 99.9388‬.

Thus, the percentage of matter in the ore that is neither gold nor diamond is 99.9388%.

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Answer:

5-4=12x+x

1=13x

1/13=×

Answer: False, not a solution because 1 is not greater than 1.

Step-by-step explanation:

Original Equation: b + 6 > 1

[plug in -5 for b] -5 + 6 > 1

[reduce]                1 > 1

One is not greater than one, therefore, it is false.

The probability that the customer is at least 30 but no older than 60 is o.45, that the customer is either older than 60 or younger than 40 is 0.68 and that the customer is at least 60 is 0.22.

We have the data:

  Age                 Number of Customers

 < 20                                78

20 - 30                             58

30 - 40                             53

40 - 50                             77

50 - 60                             52

 > 60                                91

The probability that the customer is at least 30 but no older than 60 will be:

P = 182 / 409

P = 0.45

The probability that the customer is either older than 60 or younger than 40 will be:

P = 280 / 409

P = 0.68

The probability that the customer is at least 60 will be:

P = 91 / 409

P = 0.22

Therefore we get the probability that the customer is at least 30 but no older than 60 is o.45, that the customer is either older than 60 or younger than 40 is 0.68 and that the customer is at least 60 is 0.22.

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Answer:

For the function f(x) = 9x f(x + h) - f(x) construct and simplify the difference quotient h 3 1 The difference quotient for f(x) = is 9x

Step-by-step explanation:

Answer:

x = -4

Step-by-step explanation:

A perpendicular bisector is a line that divides the existing line or shape evenly and at 90° angles. First, we want to find the center point of our existing line. In this case, the center sits right at x = -4. Since the existing line is y = 3 and it is perfectly horizontal, we don’t need to do anything further. Our perpendicular bisector is x = -4.

*** When the existing line is y = [singular number], the perpendicular bisector will always be x = [midpoint of existing line], and vice versa.

Hope this helps!

The coordinate points on the line plotted satisfy the equation -

y + 1/3x = 4.

We have the equation of a straight line.

We have to find the coordinates that satisfy this equation.

The general equation of straight line is -

y = mx + c

According to the question -

y + 1/3x=4

y = - (1/3)x + 4

Comparing it with general equation of line, we get -

m = - 1/3  and  c = 4

Now, we will plot the line on graph -

All the coordinate points that are present on this line satisfy the equation of line. The graph extends in both the direction along the x - axis.

Hence, the coordinate points on the line plotted satisfy the equation

y + 1/3x = 4.

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Answer: 160 ounces

Step-by-step explanation:

1 pint=16 ounces

10 pints * 16 ounces/1 pint=

10*16/1=

10*16=160 ounces

Answer:

192.152

Step-by-step explanation:

there in us ounces

The hospital needs to employ 21 nurses, 7 for each shift.

So, there are 3 shifts in a day and 7 nurses are needed for each shift.

Then,

Therefore, 21 nurses are needed, 7 for each shift.

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The complete question is given below:
During each shift, there are 7 nurses needed at each ward. If there are three shifts in a day, each nurse only can be on duty for one shift each day. How many more nurses does the hospital need to employ?

The wavelength  λ , of a photon that has an energy of E = 4.26×10^−19 J is 21504.29 meter.

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now, the given equation for photon energy, E , is

E = hcλ

Here, h = 6.626×10^−34 J⋅s (Planck's constant) and

c = 2.99×10^8 m/s (the speed of light)

Therefore, we have

E = hcλ

⇒ λ = E/hc

Put the values of E, h and c we get,

λ = 4.26×10^−19 / (6.626×10^−34*2.99×10^8)

Solving we get,

λ = 4.26×10^−19 / 19.81×10^(−34+8)

⇒ λ = 4.26×10^−19 / 19.81×10^-26

⇒ λ = (4.26/19.81)*10^(-19+26)

⇒ λ = 0.215042×10^5 meter

⇒ λ = 21504.29 meter

Thus, the wavelength  λ , of a photon that has an energy of E = 4.26×10^−19 J is 21504.29 meter.

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The value of m would be 7 if XZ is the angle bisector of the angle ∠WXY which are the angles ∠WXM and ∠YXZ would be 42°.

An angle bisector is defined as a line that divides an angle into two equal angles. Draw the given angle first, then cut it in half, and then draw the angle's bisector.

We have been given that XZ is the angle bisector of angle WXY.

⇒ ∠WXM = ∠YXZ

Solve for m

⇒ 10m -28 = 5m + 7

⇒ 10m - 5m = 28  + 7

⇒ 5m = 35

⇒ m = 35/5

⇒ m = 7

So ∠WXM = 10(7) -28 = 42

And ∠YXZ = 5(7) + 7 = 42

Therefore, the value of m would be 7.

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The required probability is given by  P(E') =4/35  .

Probability is the study of chance. It can also be defined as the ratio of the favorable outcomes to an event to the total number of outcomes of the event.

Given the total number of people in the USA = 273000000

Let E be the number of people who speak English at home.

Therefore the number of people who don't speak English at home is E'.

∴ E' = 31200000

S speak Spanish in their homes.

∴ S = 50% of 31200000 = 15600000

Now let us find the required probabilities.

We know that probability = favorable outcome ÷ total outcome

total outcome = 273000000

a) favorable outcome(E') = 31200000

P(E')=31200000/273000000

P(E') =4/35

b)favorable outcome(E) = 273000000 - 31200000 = 241800000

P(E) = 241800000/273000000

P(E)={31}/{35}

c)favorable outcome = 15600000

P(S)={15600000}/{273000000}

P(S)={2}/{35}

Therefore the required probability is given by P(E') =4/35 , [tex]P(E)=\frac{31}{35}[/tex] P(E)=31/35 and P(E)=2/35and .

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Answer:

y = -3x -34

Step-by-step explanation:

m= -3

plug the point in to find b

slope intercept form: y=mx+b

-7 = -3(-9) +b

-7 = 27 = b

-7 -27 = b

b= -34

plug in the m and b you found into the final equation:

y = -3x -34

Answer:

y = -3x -34

Step-by-step explanation:

Answer:

160

Step-by-step explanation:

1 is in 10s place 16x10=160

The scale factor used to draw is 7.2

The size by which the shape is enlarged or reduced is called as its scale factor.

Given:

5 inches = 1 yard

Now, we know that

1 yd = 3 ft

now, to  Convert yards to inches

1 yd = 3 x 12

i yards = 36 inches

and, the scale factor is

=36 ÷ 5

= 7 1/5

= 7.2

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Answer:39

Step-by-step explanation:

njhhvhj

Answer: 11

2x^3 + 5 - 10 =

2(2)^3 + 5 - 10 =

2(8) - 5=

16-5=11

Step-by-step explanation:

The number of videos will be 3 and the number of CDs will be 2.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Christine went shopping and bought each of her five nephews a gift, either a video costing $14.95 or a CD costing $16.88. She spent $78.61 on the gifts.

The number of the videos and CD will be calculated by forming an equation:-

14.95x + 16.88y = 78.61

From heat and trial, we put x = 3 and y = 2 then calculate.

14.95 x ( 3 )  + 16.88 x ( 2 ) = 78.61

44.85 + 33.76 = 78.61

78.61 = 78.61

Therefore, the number of videos will be 3 and the number of CDs will be 2.

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Answer:

[tex]x=\frac{3\left(-y+6\right)}{7}[/tex]

Step-by-step explanation:

[tex]14x+6y-6y=36-6y\\14x=36-6y\\Divide\\\frac{14x}{14}=\frac{36}{14}-\frac{6y}{14}\\\frac{14x}{14}\\\frac{14}{14}= 1\\\frac{36}{14}-\frac{6y}{14}\\\frac{36-6y}{14}\\36-6y\\6\cdot \:6-6y\\=6\left(6-y\right)\\=\frac{6\left(6-y\right)}{14}\\=\frac{3\left(-y+6\right)}{7}[/tex]

Hope this helps you, and I hope that you get un-stuck! Have a good day.

i hope this helps you

have a nice day

The correct option  D. x = 9, y = 7; obtained by the elimination method.

Now, as per the given question;

The equations are-

0.12x − 0.09y = 0.45 (multiply both side with 100)

12x - 9y = 45 ......equation 1

and,

-0.3x + 1.6y = 8.5 (multiply both side with 40)

-12x + 64y = 340 .......equation 2

Add equation 1 and 2;

55y = 385

y = 5

Put y = 5 in equation 1

12x = 45 + 45

x = 9

Thus, the values of the variables are obtained as (x = 9) and ( y = 7).

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The correct question is-

Use the elimination method to solve the system of equations below.

0.12x − 0.09y = 0.45

-0.3x + 1.6y = 8.5

Choose one • 4 points

A. x = −15, y = 7

B. x = 5, y = 7

C. x = 9, y = 5

D. x = 9, y = 7

The reasonable estimate of the probability that the next dad to join Dads Club has fewer than 333 children is 50%.

Number of children for 333 = 111 members

It should be noted that the total members is illustrated as:

= 666 + 111 + 111 + 888

= 1776

Therefore, the reasonable estimate of the probability that the next dad to join Dads Club has fewer than 333 children:

= 888 / 1776

= 50%.

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The slope of the tangent is equal to zero when the derivative is equal to zero, in other words when the function attains a local extremum (maximum or minimum)

So we have to ask ourselves, at which "x" value does f(x) admit a maximum or minimum.

From the graph we can tell that it is at the point of abscissa 2

The slope of the line having the points ( -1 , 8 ) and ( 8 , 9 ) is 1 / 9.

We are given the two points:

( -1 , 8 ) and ( 8 , 9 )

We need to find the slope of the line that contains these two points.

We know that the formula for calculating the slope of the line is given by:

m = y₂ - y₁ / x₂ - x₁

Here, we have:

x₁ = - 1                     y₁ = 8

x₂ =  8                     y₂ = 9

Substituting the values in the formula, we get that:

m = 9 - 8 / 8 + 1

m = 1 / 9

Therefore, the slope of the line having the points ( -1 , 8 ) and ( 8 , 9 ) is 1 / 9.

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Total cost is $ 11,369.45

Rental truck costs $53.45 for a day $69 per mile.

a) If x is the number of miles driven

So, c(x)=53.45+69(x)

          c=53.45+69x

b) If x=164 miles

      c=53.45+164

      c=53.45+11,316

      c=$11369.45

∴Total cost is $11,369.45

What does number of miles mean?

the aggregate number of miles traveled over in a given time. length, extent, or distance in miles. the number of miles or the average distance that a vehicle can travel on a specified quantity of fuel: the car gets good mileage.

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(D) V512 is not a rational number.

Since, numbers in options (A), (B), and (C) can be written in fractions, then these numbers are rational numbers.

Therefore, (D) V512 is not a rational number.

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The new balance in Jimmy's account is 324.

An account is a record that records financial transactions concerning a specific asset, liability, equity, revenue, or expense in an accounting system. As the business events take place throughout the course of the accounting period, these records grow and shrink. The general ledger stores each individual account and is used to create financial statements at the end of an accounting period.

ACCORDING TO GIVEN STATEMENT;

Jimmy had a deposited amount of $500

minus $176, per the information provided;

his new balance is $500 minus $176,

= $324.

The new balance in Jimmy's account is 324.

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