Winter temperatures tend to be cold in the city of johnstown. the table of values represents the temperature of johnstown during one winter week. use the table to approximate the key features of the function. find the extrema, zeros, end behavior, increasing and decreasing intervals, and positive and negative intervals.

a. The growth rate of zt in terms of gx and gy is given by gz = α × gx + (1-α) × gy.

b. The growth rate of zt in terms of gx and gy is given by gz = β × gx - gy.

To solve for the growth rate of zt in terms of gx and gy for the equation zt = xt²α × yt²(1-α):

Taking the natural logarithm of both sides:

ln(zt) = ln(xt²α × yt²(1-α))

Using the logarithmic property ln(a×b) = ln(a) + ln(b):

ln(zt) = ln(xt²α) + ln(yt²(1-α))

Applying the power rule of logarithms ln(a²b) = b × ln(a):

ln(zt) = α ×ln(xt) + (1-α) × ln(yt)

Differentiating both sides with respect to t:

d/dt ln(zt) = α ×d/dt ln(xt) + (1-α) × d/dt ln(yt)

The left-hand side represents the growth rate of zt (denoted as gz). Similarly, the right-hand side represents the growth rates of xt (gx) and yt (gy):

gz = α × gx + (1-α) × gy

(b) To solve for the growth rate of zt in terms of gx and gy for the equation zt = α × xt²β / yt:

Taking the natural logarithm of both sides:

ln(zt) = ln(α × xt²β / yt)

Using the logarithmic properties ln(a/b) = ln(a) - ln(b) and ln(ac) = c ×ln(a):

ln(zt) = ln(α) + ln(xt²β) - ln(yt)

Applying the power rule of logarithms ln(a²b) = b × ln(a):

ln(zt) = ln(α) + β × ln(xt) - ln(yt)

Differentiating both sides with respect to t:

d/dt ln(zt) = β ×d/dt ln(xt) - d/dt ln(yt)

The left-hand side represents the growth rate of zt (denoted as gz). Similarly, the right-hand side represents the growth rates of xt (gx) and yt (gy):

gz = β × gx - gy

To know more about rate here

https://brainly.com/question/28287556

#SPJ4

Answer:

5/12

Step-by-step explanation:

Answer:

is this answer correct?

let me know in comment section below!

Step-by-step explanation:

hope you liked it!

Answer:

b

Step-by-step explanation:

Answer:

4 miles west

Step-by-step explanation:

Answer:

I would say PB=40% D

Step-by-step explanation:

thier 4 blue balls and 20% is low for 5 and 40% is low for 9

Answer:

12

Step-by-step explanation:

12*6.5=78

44-12=32

32*4=128

128+78=206

In linear equation, $54.3  is  the original price of the jumper.

Which equation is linear equation ?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                        Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

17% of 319.41

17/100 * 319.41

= 54.2997

Learn more about linear equation

brainly.com/question/11897796

#SPJ1

In a case whereby An article reports "attendance dropped 6% this year, to 1150."  the attendance before the drop was 4,130.

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means.

Given 8% = 8/100 = 0.08

x (1-0.08)= 3800

x (0.92) =3800

Solving for x

x = 3800/0.92

x= 4,130

Learn more about  percentage at;

https://brainly.com/question/12395177

#SPJ4

71.2 was the mean of dr. ringo star's biology final exam when z-score of 1.5 .

What does "z-score" mean?

X - μ/σ = Z

85 - μ/9.2 = 1.5

μ = 85 - ( 1.5 * 9.2 )

μ = 71.2

Learn more about Z-score

brainly.com/question/15016913

#SPJ4

Step-by-step explanation:

here is your answer bro..just use the formula and keep the value

Store B sells 12591 products.

An equation is a mathematical statement that demonstrates the equality of two mathematical expressions.

Let the number of products Store A sells be x, the number of products store B sells be y, and the number of products store C be z.

Now,

Store C sells 125910 products.

z = 125910 products

Store A sells one-half as many as store C.

x = ( 1/2 )z

x = ( 1/2) × 125910

x = 62955 products

Store A sells five times as many products as store B can be expressed as the equation,

x = 5y

62955 = 5y

Dividing each side by 5,

y = 62955 / 5

y = 12591 products

Store A, B, and C sell 62955, 12591, and 125910 products.

Learn more about equations here:

brainly.com/question/2972832

#SPJ4

Answer:

Step-by-step explanation:

\(\frac{1.107}{123} \times \frac{1.998}{333} = \)

\( = > 9 \times 6\)

\( = 45\)

Answer:

Step-by-step explanation:

\(\frac{1.107}{123}*\frac{1.998}{333}= 0.009 * 0.006 = 0.000054\)

1107÷ 123 = 9

The dividend has 3 decimal places. So, take 3 decimal places from the right towards left in the result  0.009

1.107 ÷ 123 = 0.0009

0.009 * 0.006

First multiply 9 * 6 = 54

Now, count the number of decimal place in the multiplicands. 0.009 has 3 decimal places and 0.006 has 3 decimal places. So totally, 3+ 3 = 6 decimal places in the result

0.009 * 0.006 = 0.000054

The car gets 214.3 miles per gallon of gasoline in the city and 27.8 miles per gallon of gasoline on the highway.

Let the number of miles per gallon that the car gets in the city be x. Hence, the number of miles per gallon that the car gets on the highway would be 3x.

A salesperson purchased a car that is advertised as getting 3 times as many miles per gallon of gasoline on the highway than it does in the city. On a recent sales trip that covered 1500 miles in total, the car used up 18 gallons on the highway and 7 gallons in the city.

Calculation of miles per gallon of gasoline in the city:7 gallons of gasoline cover city distance: x miles is covered by 1 gallon of gasoline.

Thus, 7 gallons will cover 7x miles. Hence, we can equate: 7x = 1500 ....(1)

Calculation of miles per gallon of gasoline on the highway:18 gallons of gasoline cover the highway distance.3x miles is covered by 1 gallon of gasoline.

Thus, 18 gallons will cover 54x miles.

Hence, we can equate: 54x = 1500 ....(2)

Dividing equation (1) by 7:7x/7 = 1500/7x

= 214.3 miles per gallon of gasoline in the city.

Dividing equation (2) by 54:54x/54

= 1500/54x

= 27.8 miles per gallon of gasoline on the highway.

Therefore, the car gets 214.3 miles per gallon of gasoline in the city and 27.8 miles per gallon of gasoline on the highway.

To learn more about gasoline visit;

https://brainly.com/question/14588017

#SPJ11

Answer:

20

Step-by-step explanation:

2(12) - 4.  24 - 4= 20

Answer:

x = 8

Step-by-step explanation:

12 = 2x - 4

16 = 2x

8 = x

Check by plugging in:

12 = 2(8) - 4

12 = 16 -4

12 = 12

The length of the stick was 7.55 cm.

Given that,

initial speed of bug is given by, v=0.65 m/s

m refers to the mass of bug.

Mass of stick is given by, M= 10m

I refers to the moment of inertia of bug and stick together about the end of the stick.

ω refers to the angular velocity of the bug and stick immediately after collision.

L refers to length of stick

Stick can be considered rod.

Now, moment of inertia about end of a rod is given by = 1/3 ML²

From angular momentum conservation theory we can get,

total initial angular momentum = total final angular momentum

mvL = Iω

mvL = [mL² + 1/3 ML²] ω

mvL = [mL² + 1/3 (10m) L²] ω

0.65 L = 4.333 L²ω

L = 0.15/ω

ω = 0.15/L

Change in vertical position center of mass of rod is given by,

H = L/2 [1 - cos θ]

Change in vertical position of bug after reaching max height is given by,

h = L [1 - cos θ]

From energy conservation law we can conclude that,

Rotational kinetic energy immediately after collision = Potential energy of bug and stick system at max height .

(1/2) [mL² + 1/3 ML²] ω² = mgh + MgH

(1/2) [mL² + 1/3 (10m) L²] ω² = m(gh + 10gH)

2.167 L²ω² = g (h + 10H)

2.167 L² (0.15/L)² = g [L [1 - cos θ] + 5L [1 - cos θ]] (Substituting the relations from previous)

(2.167) (0.15)² = 6 (9.8) L (1 - cos 8.5)

L = 0.0755 m (Rounding off to nearest fourth decimal places)

L = 7.55 cm

Hence the length of the stick was 7.55 cm.

To know more about angular momentum here

https://brainly.com/question/30656024

#SPJ4

The question is incomplete. The complete question will be -

The simplification of the given expression (1/3)(b + 12) - (1/4)(b + 12)  is (b + 12)/12.

According to the given question.

We have an expression

(1/3)(b + 12) - (1/4)(b + 12)

As we know that, simplification of an expression means to write an equivalent expression which contains no similar terms.

Therefore, the simplification of the given expression (1/3)(b + 12) - (1/4)(b + 12)  is given by

(1/3)(b + 12) - (1/4)(b + 12)

= (b + 12)[(1/3) -(1/4)]             (taking (b + 12) common from each expression)

= (b + 12)[ (4-3)/12 ]

= (b + 12)[1/12]

= (b + 12)/12

Hence,the simplification of the given expression (1/3)(b + 12) - (1/4)(b + 12)  is (b + 12)/12.

Find out more information about expression here:

https://brainly.com/question/25201049

#SPJ4

The planning value for the population standard deviation is estimated to be $3,350, and sample sizes of approximately 46, 566, and 2,262 would be needed to achieve desired margins of error of $500, $200, and $100, respectively.

(a) Desired margin of error = $500

The formula for the sample size required to estimate the population mean with a desired margin of error is:

n = (Z * σ / E)²

Where:

n = sample size

Z = Z-score corresponding to the desired confidence level (95% confidence level corresponds to a Z-score of 1.96)

σ = population standard deviation

E = desired margin of error

Since we don't have the actual population standard deviation, we can estimate it using the planning value.

Range of expected salaries = $55,400 - $42,000 = $13,400

Planning value for standard deviation = Range / 4 = $13,400 / 4 = $3,350

Substituting the values into the formula:

n = (1.96 * $3,350 / $500)² ≈ 45.96

Since we can't have a fraction of a sample, we need to round up to the nearest whole number.

Therefore, the sample size needed for a desired margin of error of $500 is 46.

(b) Desired margin of error = $200

Using the same formula:

n = (1.96 * $3,350 / $200)² ≈ 565.44

Rounding up to the nearest whole number, the sample size needed for a desired margin of error of $200 is 566.

(c) Desired margin of error = $100

Using the same formula:

n = (1.96 * $3,350 / $100)² ≈ 2,261.76

Rounding up to the nearest whole number, the sample size needed for a desired margin of error of $100 is 2,262.

(d) Would you recommend trying to obtain the $100 margin of error? Explain.

Obtaining a margin of error as low as $100 would require a sample size of 2,262. While this larger sample size may provide a more precise estimate, it also increases the cost and time required for data collection and analysis. Therefore, the decision to obtain such a small margin of error should be based on the practicality and resources available. It is important to consider the trade-off between the desired level of precision and the associated costs and efforts.

Therefore, the planning value for the population standard deviation is estimated to be $3,350, and sample sizes of approximately 46, 566, and 2,262 would be needed to achieve desired margins of error of $500, $200, and $100, respectively.

To know more about margin of error check the below link:

https://brainly.com/question/15691460

#SPJ4

Answer:

y=−8x+53

Step-by-step explanation:

I think... I'm not sure so I'm sorry if its wrong

Answer: Here is an explanation of how to get the answer.

Step-by-step explanation:

It tells you the slope is -8, so you know your equation will look like this:

y = -8x + b,

where b is the intercept. You also are given a point that is on the line, so that is an x and a y value that are a solution to the equation. You can plug those in and solve for b.

5 = -8(6) + b

53 = b

So, your equation is y = -8x + 53

Answer:

36 units

Step-by-step explanation:

One leg of the triangle is 9 and the other is 12.  Now you use the pythagorean theorem to solve for the last side of the the triangle.  The pythagorean theorem is a^2+b^2=c^2.  a and b are 9 and 12.  It doesn't matter which order because of the commutative property.  You know which ones are a and b because they are the shorter sides.

Now you plug it into the equation.  9^2+12^2=c^2.  this simplifies to 81+144=c^2.  Now you combine like terms and get c^2=225.  You square root both sides now and get c=15.  The longest side is 15.  Now you add all of them together to find the perimeter.  9+12+15= 36

The zeros of the polynomial f(x) are the values of x that make f(x) equal to zero. We can find the zeros of f(x) by setting the polynomial equal to zero and solving for x:

f(x) = (x-5)²6 (x²-25)²7 = 0

The polynomial f(x) has two factors, each of which contributes to the zeros of the polynomial:

Factor 1: (x-5)²6

This factor is equal to zero when x-5=0, or x=5. Therefore, the polynomial f(x) has a zero of multiplicity 6 at x=5.

Factor 2: (x²-25)²7

This factor is equal to zero when x²-25=0, or x=±5. Therefore, the polynomial f(x) has two more zeros at x=±5. Each of these zeros has a multiplicity of 7, since the factor (x²-25) is raised to the 7th power.

Therefore, the zeros of f(x) are x=5 and x=±5, with multiplicities of 6 and 7, respectively.In summary

To know more about polynomial f(x)

https://brainly.com/question/29199219?

#SPJ4

Answer:

1. x = 21

2. x = 19

Step-by-step explanation:

Since the interior angles of all quadrilaterals add up to 360, all we have to do is add them up and set them equal to 360. Combine like terms and we get

7x + 213 = 360

Which further turns to 7x = 147

So x = 21

For the second problem, it's the same thing

By the end we get 2x + 8 = 46

2x = 38

x = 19

Hope this helps

To estimate the population mean using pooling, we can combine the two samples and calculate the mean of the combined data.

Sample 1: (0.5, 0.2, 0.4, 0.4, 0.3, 0.5, 0.3)

Sample 2: (0.2, 0.4, 0.3, 0.1, 0.4, 0.2, 0.3, 0.3, 0.2)

Combining the samples, we have:

Combined data: (0.5, 0.2, 0.4, 0.4, 0.3, 0.5, 0.3, 0.2, 0.4, 0.3, 0.1, 0.4, 0.2, 0.3, 0.3, 0.2)

To estimate the population mean, we calculate the mean of the combined data:

Mean = (0.5 + 0.2 + 0.4 + 0.4 + 0.3 + 0.5 + 0.3 + 0.2 + 0.4 + 0.3 + 0.1 + 0.4 + 0.2 + 0.3 + 0.3 + 0.2) / 16

Mean = 5.6 / 16

Mean = 0.35

Therefore, the best unbiased estimate of the population mean using pooling is 0.35.

Learn more about pooling and population mean estimation here:

https://brainly.com/question/3536442

#SPJ11

The actual area of the closet's floor is 3.52 square meters.

To find the actual area of the closet's floor, we first need to convert the dimensions from the scale drawing to their actual dimensions.

According to the given scale, 2 cm on the scale drawing represents 1 meter in reality. Thus, to convert the dimensions from the scale drawing to actual dimensions, we need to multiply each dimension by the conversion factor:

Actual length = 4.4 cm × (1 m / 2 cm) = 2.2 m

Actual width = 3.2 cm × (1 m / 2 cm) = 1.6 m

Now that we have the actual dimensions, we can calculate the actual area of the closet's floor:

Actual area = Actual length × Actual width

= 2.2 m × 1.6 m

= 3.52 square meters

Therefore, the actual area of the closet's floor is 3.52 square meters.

Learn more about area from

https://brainly.com/question/25292087

#SPJ11

The height of the prism shaped storage container that Jose is using is found to be 2.585 meters,

We can use the formula for the volume of a rectangular prism to find the height of Jose's storage container.

Volume of a rectangular prism = length x width x height

It is given that the volume is 39.442 cubic meters and the length and width is 4.1 meters and 3.7 meters. Putting the values and solve for the height:

39.442 = 4.1 x 3.7 x height

Simplifying this equation, we get:

39.442 = 15.27 x height

Dividing both sides by 15.27, we get:

height = 2.585 meters

Therefore, the height of storage container is 2.585 meters.

To know more about volume of prism, visit,

https://brainly.com/question/23766958

#SPJ4

It will take a minimum of 10 clock hours (not driving hours) for the truck driver to travel 450 miles from Charlotte, NC to Pittsburgh, PA.

The current Hours of Service (HOS) rules for truck drivers stipulate that a truck driver cannot drive for more than 11 hours after 10 consecutive hours off duty.

Additionally, the driver is not allowed to drive beyond 14 hours after coming on duty.

The driver's shift includes both driving and non-driving time.

Therefore, it is necessary to consider the total amount of time spent on the job.

The truck driver will have to stop for rest breaks, refueling, or other reasons during the 450-mile journey to Pittsburgh, Pennsylvania. The driver is required to take a 30-minute break after eight hours of driving.

Therefore, the minimum number of clock hours (not driving hours) it will take the truck driver to travel the 450-mile distance from Charlotte, NC to Pittsburgh, PA is calculated as follows:

Time for the trip = (Distance ÷ Average Speed) + Breaks

Time for the trip = (450 ÷ 50) + (30 ÷ 60) × 2

Time for the trip = 9 + 1

Time for the trip = 10 clock hours

Therefore, it will take a minimum of 10 clock hours (not driving hours) for the truck driver to travel 450 miles from Charlotte, NC to Pittsburgh, PA.

Know more about Hours of Service (HOS) here:

https://brainly.com/question/32726922

#SPJ11

The total number of hands with a full house of aces and fives is 36 * 10 = 360.

(a) To find the number of hands with only black cards:
Step 1: There are 26 black cards in a standard 52-card deck (13 spades and 13 clubs).
Step 2: We need to choose 5 black cards from the 26 available.
Step 3: Use the combination formula: C(n, k) = n! / (k!(n-k)!) where n is the total number of items and k is the number of items we want to choose.
Step 4: Calculate C(26, 5) = 26! / (5!(26-5)!) = 26! / (5!21!) = 65,780.

Answer (a): There are 65,780 hands with only black cards.

(b) To find the number of hands with a full house of aces and fives:
Step 1: There are 4 aces and 4 fives in a standard 52-card deck.
Step 2: Choose 3 aces from the 4 available (C(4, 3)).
Step 3: Choose 2 fives from the 4 available (C(4, 2)).
Step 4: Multiply the combinations from steps 2 and 3: C(4, 3) * C(4, 2).
Step 5: Calculate C(4, 3) = 4! / (3!(4-3)!) = 4.
Step 6: Calculate C(4, 2) = 4! / (2!(4-2)!) = 6.
Step 7: Multiply the results from steps 5 and 6: 4 * 6 = 24.

Answer (b): There are 24 hands with a full house of aces and fives.

to learn more about number click here:

brainly.com/question/30752681

#SPJ11