A student in botany researches the growth of certain plants. She observes that the plant grows to 80mm in the first year. In the second year the height increases with 30mm. From the third year onwards the annual growth of the plant is 4÷5 of its growth of the previous year. 2. 1 Determine the height to which the plant grew during the third year

2. 2Calculate the maximum height that the plant will reach

Without additional information about the specific location and angle of the slice, we cannot determine the exact dimensions of the resulting triangle slice.

We have,

To determine the dimensions of the triangle sliced vertically and intersecting the 9 mm edge, we need to consider the given dimensions of the triangle:

9 mm, 10 mm, and 3 mm.

Assuming that the 9 mm edge is the base of the triangle, the vertical slice would intersect the triangle along its base.

The dimensions of the resulting slice would depend on the location and angle of the slice.

Without additional information about the specific location and angle of the slice, we cannot determine the exact dimensions of the resulting triangle slice.

The dimensions would vary depending on the position and angle at which the slice is made.

Thus,

Without additional information about the specific location and angle of the slice, we cannot determine the exact dimensions of the resulting triangle slice.

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Answer: A.culture within the city-state

C.loyalty to the polis

E.different languages

Step-by-step explanation:

The options include:

A.culture within the city-state

B.trips to the agora

C.loyalty to the polis

D.separation by land and sea

E.different languages

The characteristics that pulled the Greek city apart were:

• culture within the city-state

• loyalty to the polis

• different languages

Due to the fact that every oolis possessed their own culture, there was loyalty to the polis. While Spartans focused on war and competition, Athens focus was on culture and democracy. Also, the different languages was a distraction as it didn't help in uniting the people.

Answer:

m∆IED= 83°

m∆JFG= 87°

Step by step

m∆IED is 97° so if you subtract 97 from 180(a straight line) you would get 83°

and the same for m∆JFG if you subtract 93 from 180 you get 87°

hope this helps

Answer: 7x^2+3y^2-4x

Choose the first option

Step-by-step explanation:

Ok, so let me show you how to do this.

First, distrubute the negative sign

12x^2-11y^2-13x-(5x^2-14y^2-9x)=

12x^2-11y^2-13x-5x^2+14y^2+9x

Now combine like terms

(12x^2-5x^2)=7x^2

(-11y^2+14y^2)=3y^2

(-13x+9x)=-4x

7x^2+3y^2-4x is the answer.

There are 17,280 distinguishable orderings of the letters of millimicron that contain the letters "cr" next to each other in order and also the letters "on" next to each other in order.

To solve this problem, we can treat the letters "cr" as a single letter. This reduces the number of letters to 8: {m, i, l, l, i, m, i, cron}.

Now, we need to count the number of distinguishable orderings of these 8 letters such that the letters "cr" and "on" are next to each other in order.

First, consider the letters "cr" as a single letter. Then, we have 7 letters: {m, i, l, l, i, m, cron}. The number of ways to arrange these 7 letters is 7!. However, we need to account for the fact that the letters "cr" must be next to each other in order. So we can think of "cr" as a "super-letter" and permute the 6 remaining letters along with the "super-letter". This gives us a total of 6! arrangements.

Next, we need to ensure that the letters "on" are also next to each other in order. We can treat the letters "on" as a single letter. Then, we have 6 letters: {m, i, l, l, i, mcron}. We can think of "on" as another "super-letter" and permute the 5 remaining letters along with the "super-letters". This gives us a total of 5! arrangements.

Finally, we need to account for the fact that "cr" and "on" must be next to each other in order. There are two ways this can happen: "cron" or "oncr". So, we multiply the number of arrangements in the previous step by 2.

Putting it all together, the number of distinguishable orderings of the letters of millimicron that satisfy the given conditions is:

6! * 5! * 2 = 17,280

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Answer:

a) growth

b) 3%

c) 6 years (since the beginning of the decade)

Step-by-step explanation:

Given:

The population P (in thousands) of Austin, Texas during a recent decade can be approximated by \(y=494.29(1.03)^t\) when t is the number of years since the beginning of the decade.

General form of an exponential function: \(y=ab^x\)

where:

If \(b > 1\) then it is an increasing function

If \(0 < b < 1\) then it is a decreasing function

a) The model represents exponential growth as 1.03 > 1

b) The annual percent increase of the population is 3%

1.03 - 1 = 0.03

0.03 x 100 = 3%

c) To estimate when was population about 590,000 set y = 590 and solve for t:

\(\implies 590=494.29(1.03)^t\)

\(\implies \dfrac{590}{494.29}=(1.03)^t\)

Take natural logs of both sides:

\(\implies \ln\left(\dfrac{590}{494.29}\right)=\ln (1.03)^t\)

\(\implies \ln\left(\dfrac{590}{494.29}\right)=t\ln (1.03)\)

\(\implies t=\dfrac{\ln\left(\dfrac{590}{494.29}\right)}{\ln (1.03)}\)

\(\implies t=5.988069001...\)

Therefore the population was about 590,000 6 years since the beginning of the decade.

The probability that he draws a pair of tens is  1/2652 or approximately 0.000378 which is approx 0.04%

The probability of drawing a pair of tens from a standard deck of cards is (number of ways to get a pair of tens) / (total number of possible outcomes).

In this case there are 4 tens (2 of hearts, 2 of diamonds, 2 of spades, 2 of clubs) and he is drawing 2 cards from the deck, so there is only 1 way to get a pair of tens. There are 52 cards in a standard deck, so the total number of possible outcomes is 52 * 51 = 2652.

So the probability of drawing a pair of tens is 1/2652 or approximately 0.000378 which is approx 0.04%

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Answer: 5w plus 23 equals 98

Step-by-step explanation:

This answer is more reasonable because Paula already has $23 and she can save $5 per week.  She only needs 75 dollars more to get the records. So it will take her 17 weeks to get $75.

The probability that the professor ends up riding the bus is approximately 0.777.

The professor's chances of riding in a car into town are: P(waiting time > t) = e(-6t)

The probability that the professor will catch a ride in a passing car rather than taking the bus is: P(car ride only) = (0 to 1) (1/3) * e(-6t) dt

This integral is evaluated as follows: P(car ride only) = 1/2 - e(-6/3)/6 0.223

We need to calculate the likelihood that the professor does not receive a ride with a car and instead waits for the bus:

P(only bus journey) = (0 to 1) (2/3) * e(-6t) dt

When this integral is evaluated, we get:

P(only bus journey) = 1/2 + e(-6/3)/6 0.777

Therefore, the probability that the professor ends up riding the bus is approximately 0.777.

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Answer:

5 r o 2 t

Step-by-step explanation:

(√3+√7)²

We know ,[(a+b)²=a²+2ab+b²]

=>(√3+√7)²=(√3)²+2(√3)(√7)+(√7)²

=>(√3+√7)²=3+2√21+7

=>(√3+√7)²=10+2√21

Answer:

did not get the point of the sum

Answer:

D - 353.7

Step-by-step explanation:

Edge 2020

Step-by-step explanation:

Red=4

Blue=3

Yellow=3

Total=10

Pr(BY) without replacement= 3/10 *3/9

=6/90

=1/15

Answer: y = -1 and x = 3

Step-by-step explanation:

x=-2y+6

3x-4y = 28

There are two ways to solve this:  1) solve directly with the equations, and 2) graph the line and look for the intersection.

---

Use the definition of x from the first equation and substitute it in the second:

3x-4y = 28

3(-2y+6)-4y = 28

-6y + 18 -4y = 28

-10y = 10

y = - 1

---

Graph the two lines and find the value of y at the point they intersect.  See the attachment.

y = -1 at x= 8

=======================

For the second question:

y=3x-10

4x+5y=7

---

4x+5y=7

4x+5(3x-10)=7

4x+15x-50=7

19x = 57

x = 3

----

Answer: x=4+2i , x=4-2i hope this helps tho :>

Step-by-step explanation

The solutions to the equation x 2 −8x+20=0 are x= 10,-2.

The equation  x 2 −8x+20=0  can be written as (x-10) (x+2) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x-10=0

x+2=0

so, the solution to the equation x 2 −8x+20=0 are x=10 and x=-2.

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The inflation rate between 2017 and 2018 is 2.86%.

Inflation rate is used to determine the rate at which the general price levels in an economy is increasing with the passage of time.

The inflation rate = (2018 CPI / 2017 CPI) - 1

(180 / 175) - 1 = 0.0286 = 2.86%

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The correct answer is B. No, because there is at least one number in the intersection of the specified sets.

To determine whether the sets H' and E' are disjoint, we need to understand the definitions of the sets H, E, H', and E'.

Given:

N = set of positive integers (universal set)

H = {x | x ∈ N, x > 100}

T = {n | n ∈ N, n < 1,000}

E = {n | n ∈ N, n is even}

P = {n | n ∈ N, n is prime}

Now, let's define H' and E':

H' = complement of set H (elements in N that are not in H)

E' = complement of set E (elements in N that are not in E)

To determine if H' and E' are disjoint, we need to check if they have any common elements or if their intersection is empty.

H' contains all the elements in N that are not in H, which means it includes all positive integers less than or equal to 100.

E' contains all the elements in N that are not in E, which means it includes all positive integers that are odd or not divisible by 2.

Since the set of positive integers less than or equal to 100 (which is included in H') has odd numbers and numbers not divisible by 2, it intersects with E' (which also includes odd numbers and numbers not divisible by 2).

Therefore, the correct answer is B. No, because there is at least one number in the intersection of the specified sets.

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Answer:

D(-4, -3), E(-7, 4), and F(-7, -3).

Step-by-step explanation:

The current coordinates are A(4, 2), B(7, 9), and C(7, 2).

If you reflect the coordinates over the y-axis, the y-values will not be changing, but the signs of the x-values will flip. So, you will have A'(-4, 2), B'(-7, 9), and C'(-7, 2).

When you translate the resulting triangle down 5 units, the y-values will decrease by 5 units. So, the coordinates of triangle DEF will be D(-4, -3), E(-7, 4), and F(-7, -3).

Hope this helps!

Answer:

D (-4, -3)

E (-7, 4)

F (-7,-3)

Step-by-step explanation:

Well triangle ABC reflected over the y-axis to make triangle DEF looks like the image below. ↓

Then we have to translate triangle DEF 5 units down.

With the coordinates D, E, F,

D (-4,2)

E (-7,9)

F (-7,2)

To translate it 5 units down we just subtract the y coordinates by 5.

D (-4, -3)

E (-7, 4)

F (-7,-3)

Thus,

the coordinates for triangle DEF are (-4, -3) , (-7, 4) , (-7,-3).

Hope this helps :)

Answer:

x=1

Step-by-step explanation:

-16+x=-15

-16+x+16=-15+16   Add the terms to both sides of the equation.

After that you simplify.

Answer:

2^5 *3

Step-by-step explanation:

You can solve this multiple ways but should get 2^5*3

Answer:

\(2^5*3\)

Step-by-step explanation:

\(96\\\\=2*48\\\\=2*2*24\\\\=2*2*2*12\\\\=2*2*2*2*6\\\\=2*2*2*2*2*3\\\\=2^{5}*3\)

a. Multi-factor productivity in November: 0.231 b. Multi-factor productivity in December: 0.203 c. Percentage of productivity change: -12.12% d. Predicted impact on profits: It experience reduced profitability.

a. To calculate the multi-factor productivity in November, we use the formula:Multi-factor productivity = Output / (Labor cost + Material cost + Overhead costs). In November:

Output = Orders fulfilled = 3537

Labor cost = $9800

Material cost = $3500

Overhead costs = $2000

Multi-factor productivity = 3537 / (9800 + 3500 + 2000) = 3537 / 15300 ≈ 0.231

b. To calculate the multi-factor productivity in December, we use the same formula:In December:

Output = Orders fulfilled = 2945

Labor cost = $9000

Material cost = $3500

Overhead costs = $2000

Multi-factor productivity = 2945 / (9000 + 3500 + 2000) = 2945 / 14500 ≈ 0.203. The productivity has decreased from November to December.

c. The percentage of productivity change can be calculated using the formula: Percentage of productivity change = ((New productivity - Old productivity) / Old productivity) * 100

Percentage of productivity change = ((0.203 - 0.231) / 0.231) * 100 ≈ -12.12%. The productivity has decreased by approximately 12.12%.

d. Since the productivity has decreased and the price of the food remains unchanged, it suggests that the costs have increased relative to the output. This can have a negative impact on the profits of Hotdog Palace. With higher labor costs and potentially lower productivity, the company may experience reduced profitability unless it takes measures to address the labor shortage and improve productivity.

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Answer:

I think its A

hope this helps

have a good day :)

Step-by-step explanation:

The change in the advertising budget necessary to maintain a monthly profit of $93,500 if the insurance company hires 5 new sales associates is estimated to be an increase of $2,308.

To estimate the change in advertising budget necessary to maintain a monthly profit of $93,500 with the addition of 5 new sales associates, we need to consider the potential impact of these new hires on the company's revenue and expenses.

Assuming that each new sales associate is expected to generate $10,000 in revenue per month, the total increase in revenue would be $50,000 (5 sales associates x $10,000).

However, there may also be additional expenses associated with the new hires, such as salaries and benefits. Let's assume that the total cost of adding 5 new sales associates is $30,000 per month.

Therefore, the net increase in monthly profit due to the new hires would be $20,000 ($50,000 in revenue - $30,000 in expenses).

To maintain a monthly profit of $93,500, the company would need to increase its advertising budget by an amount that would generate an additional $20,000 in profit. Assuming that the company's profit margin on its products is 20%, this would require an additional $100,000 in revenue per month ($20,000 / 0.20).

Based on the historical data and market conditions, the company could estimate the additional advertising budget required to generate this amount of revenue.

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Here, 1 is only the factor because there is no other numeral in the equation.

\(ab - a - b + 1\)

Answer:

y=4 because 8x4=32

32-2 =30

30+60=90

Answer:

the value of y is 4, so 8(4)-2 are 30 , then 30 degrees are the angle

answer:

this is the solution

The mode is 18.5.

What is mode?

In statistics, there  are most repeated value among the given set of data. Those are called mode. Among the given set of data, mode is the value which has the maximum frequency. Sometimes, it may be possible to have more than one value which has the equal maximum frequency.

Formula for mode for grouped data is given by:

Mode = l + [(f₁-f₀)/(2f₁-f₀-f₂)]×h.-------------------(1)

Where, l = lower class limit of modal class, h = class size, f₁ = frequency of modal class, f₀ = frequency of class preceding to modal class, f₂ = frequency of class succeeding to modal class.

In the given problem l= 15.5

                                   f₀= 8

                                  f₁= 10

                                  f₂= 8

                                  h= 6

Putting all the values in equation (1) we obtain mode

                     mode= 15.5 +{(10-8)/(2×10-8-8)} ×6

                              = 15.5+(2/4)×6

                              = 15.5+ 3

                               = 18.5

Hence, the mode is 18.5.

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Which of the following is an accurate definition for the power of a statistical test is C. The power of a statistical test refers to the probability of rejecting a false null hypothesis. This means that the test is able to correctly identify when there is a significant difference between two groups or conditions.

statistical tests are used to determine whether the results of an experiment are likely due to chance or whether there is a real effect. The null hypothesis states that there is no significant difference, while the alternative hypothesis states that there is. The power of a statistical test refers to the ability of the test to correctly reject the null hypothesis when it is false, and thus support the alternative hypothesis.

, the power of a statistical test is the probability of correctly rejecting a false null hypothesis, which indicates that there is a significant difference between two groups or conditions.

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Answer:

If the equation is in the form, ax + b = c, where x is the variable, you can solve the equation as before. First “undo” the addition and subtraction, and then “undo” the multiplication and division. Solve 3y + 2 = 11. Subtract 2 from both sides of the equation to get the term with the variable by itself.

Step-by-step explanation:

hope this helps, sorry if late

A correlation coefficient is consistently a number between 1 and - 1 .

The correlation coefficient is a factual measure that demonstrates the strength and heading of the straight connection between two factors. It goes from - 1 to 1, where - 1 addresses a completely bad correlation (i.e., as one variable expands, different declines), 0 addresses no correlation, and 1 addresses an entirely sure correlation (i.e., as one variable builds, the other likewise increments).

The indication of the correlation coefficient demonstrates the heading of the relationship, while the extent of the coefficient shows the strength of the relationship. A correlation coefficient of 0 shows no straight connection between the factors, while values nearer to - 1 or 1 demonstrate a more grounded direct relationship.

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