On the first day of spring, an entire field of flowering trees blossoms. The population of locusts consuming these
flowers rapidly increases as the trees blossom.
The relationship between the elapsed time, t, in days, since the beginning of spring, and the total number of
locusts, L(t), is modeled by the following function:
t
L(t) = 750 - (1.85)^t
Complete the following sentence about the daily rate of change of the locust population.
Every day, the locust population
grows/shrinks
by a factor of______?

Answer:B

Step-by-step explanation:

Step-by-step explanation:

This is a circle with center, h,k = 3,2 and radius = 2

   circle equation is   ( x-h)^2 + (y-k)^2 = r^2

so:

(x-3)^2 + (y-2)^2 = 4

Answer:

C

Step-by-step explanation:

All sides make a cube

Answer:

D

Step-by-step explanation:

The weekly cost per worker is: $800

Unit rate can be used for calculating expenses, calculating cost of multiple units, or calculating expenses.

Recall:

Unit rate is calculated using: \(\mathbf{\frac{y_2 - y_1}{x_2 - x_1} }\)

Unit rate represents the amount of a quantity compared to its unit of measure.

Unit rate can be used for calculating expenses, calculating cost of multiple units, or calculating expenses.

Since the relationship between number of workers and weekly cost is proportional, we would apply \(\mathbf{\frac{y_2 - y_1}{x_2 - x_1} }\) in determining the weekly cost per worker using the points, ​(6​, 4800​) and ​(15​, 12000​):

Unit rate/weekly cost per worker = \(\frac{12,000 - 4,800}{15 - 6} = \frac{7,200}{9} = 800\)

Unit rate/weekly cost per worker = $800

In summary, the weekly cost per worker is: $800

Unit rate can be used for calculating expenses, calculating cost of multiple units, or calculating expenses.

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Answer:

21829787.23 joules

Step-by-step explanation:

The recycling will require 6%energy if initial energy, let's say x.

94% of x will be used to power a 100W TV for 3 hours

X = (100*3*60*60)/0.94

X = 1148936.17 joules.

To make 19 aluminum cans ,

It will take 1148936.17*19

= 21829787.23 joules

Answer:

Step-by-step explanation:

m(x) =2^x+1 increases / positive infinity

n(x) =10^x^-2+5 decreases / the line y=5

p(x) =-e^x-2 increases / the line y=-2

Answer:

n = 12

Step-by-step explanation:

\(\frac{3}{13}\) = \(\frac{n}{52}\) ( cross- multiplying )

13n = 3 × 52 = 156 ( divide both sides by 13 )

n = 12

The value of the underlined digit in the number 27,416,385.( 4 is the underlined number.) is the hundred thousandths place.

The symbols, from 0 to 9 can be described as a digit. For instance, the numbers 2 and 3 are used to represent the number 23.  however amount is represented by a number.

It should be noted that It may be expressed using one, two, three, or even more digits however only single symbol used to represent a number is a digit in the case above we can see that 4 is the hundred thousandths place.

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We are asked to write the appropriate number of decimal places in each sum, difference, product, or quotient.

Problem 1:

As you can see, the result of the above difference has only 1 decimal number.

Problem 2:

As you can see, the result of the above product has 3 decimal numbers.

Problem 3:

As you can see, the result of the above quotient has 0 decimal numbers.

Problem 4:

As you can see, the result of the above sum has 2 decimal numbers.

Problem 5:

As you can see, the result of the above product has 3 decimal numbers. (3,9

Answer:

1) 113.0 m^2

2) 12.6 ft^2

3) 50.2 in^2

4) 153.9 m^2

5) 254.3 yd^2

Step-by-step explanation:

pi (3.14) times radius squared

1) 3.14 times 6^2 (36)

113.04

2) diameter is given, divide by 2 to find radius

3.14 times 4^2

12.56

Answer:

1.2

Step-by-step explanation:

9+10y=21

Subtract 9 from both sides:

10y=21-9=12

Divide both sides by 10 to isolate y:

y=1.2

Hope this helps!

Answer:

y = 6/5 = 1 1/5 = 1.2

Step-by-step explanation:

9 + 10y = 21

Subtract 9 from each side

9-9 + 10y = 21-9

10 y = 12

Divide each side by 10

10y/10 = 12/10

y = 6/5

y = 1.2

Answer:

y = -x + 2

Step-by-step explanation:

The slope intercept form equation of this line can be written like this :

y = my + p ; where m is the slope and p is the y intercept.

\(m = \frac{-1-4}{3-(-2)} = \frac{-5}{5} =-1\)

then the equation becomes y = -x + p

(-2,4) is a point of the line means 4 = -(-2) + p

then p = 4 - 2 = 2

finally, y = -x + 2

If the triple point of iodine is at 90 torr and 115°C , then the true statement about liquid I₂(l) is (d)I₂(l) cannot have a vapor pressure greater than 90 torr.

In the question ,

it is given that ,

Iodine substance exhibits three phases , solid , liquid and gases .

The iodine gas over solid l₂ is the molecule of iodine that has evaporated

, If the iodine pressure is low enough , it will resublime on cooling without going through the liquid phase .

So , the point in the gas phase that has temperature > 115°C ,

So , the curve move horizontally right ,

we can see that the pressure can be > 90 torr .

hence the statement (d) concerning liquid I₂(l) is True .

Therefore , the correct option is (d) .

The given question is incomplete , the complete question is

Iodine, like most substances, exhibits only three phases: solid, liquid, and vapor. The triple point of iodine is at 90 torr and 115 °C. Which of the following statements concerning liquid I₂(l) must be true?

a. I₂(l) is more dense than I₂(g).

b. I₂(l) cannot exist above 115°C.

c. I₂(l) cannot exist at 1 atmosphere pressure.

d. I₂(l) cannot have a vapor pressure greater than 90 torr.

e. I₂(l) cannot exist at a pressure of 10 torr.

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After calculating we found that: a) 95% of widget weights lie between 42 and 54 ounces.b) 97.35% of widget weights lie between 39 and 54 ounces and c) 0.3% of widget weights lie above 45 ounces.

a) Since the distribution is bell-shaped and the mean is 48 ounces with a standard deviation of 3 ounces, we can use the 68-95-99.7 Rule to determine that 68% of the widget weights lie within one standard deviation of the mean, 95% lie within two standard deviations of the mean, and 99.7% lie within three standard deviations of the mean. Thus, we know that 95% of the widget weights lie between:

48 - 2(3) = 42 ounces and 48 + 2(3) = 54 ounces.

b) To find the percentage of widget weights that lie between 39 and 54 ounces, we need to determine how many standard deviations away from the mean these values are.

39 ounces is 9 ounces below the mean, so it is (9/3) = 3 standard deviations below the mean.

54 ounces is 6 ounces above the mean, so it is (6/3) = 2 standard deviations above the mean.

Using the 68-95-99.7 Rule, we know that 99.7% of the widget weights lie within three standard deviations of the mean. Since 39 ounces is three standard deviations below the mean, we can conclude that 0.15% (or 0.003 x 100) of the widget weights lie below 39 ounces.

Likewise, since 54 ounces is two standard deviations above the mean, we know that 2.5% of the widget weights lie above 54 ounces. Thus, the percentage of widget weights that lie between 39 and 54 ounces is:

100% - 0.15% - 2.5% = 97.35%

c) We need to find the percentage of widget weights that lie above 45 ounces. Since 45 ounces is three standard deviations below the mean, we know that 99.7% of the widget weights lie above 45 ounces. Therefore, the percentage of widget weights that lie above 45 ounces is:

100% - 99.7% = 0.3%.

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The expression calculates the population x years from now will be given as y = 1024 (0.75)ˣ.

Consider the function:

y = a (1 ± r) ˣ

Where x is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.

If there is a plus sign, then there is exponential growth happening by r fraction or 100r %

If there is a minus sign, then there is exponential decay happening by r fraction or 100r %

The population of sea turtles decreases by 25% per year. The population size is currently 1,024.

Let y be the population of sea turtles and x be the number of years.

Then we have

y = 1024 (1 - 0.25) ˣ

y = 1024 (0.75) ˣ

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The two diameters that separate the top 35 from the bottom 35 in the normal distribution are 5.35 mm and 5.61 mm .

Normal distributions are crucial to statistics because they are widely used in the natural and social sciences to represent real-valued covariates whose distributions are unknown.

First we will find the bottom 3% such that P(X ≤ x) = 0.03

⇒ \(P(\frac{X-5.48}{0.07}\leq \frac{x-5.48}{0.07} )=0.03\)

⇒\(P(Z\leq \frac{x-5.48}{0.07} )=0.03\)

Now we will use the normal table to calculate the corresponding z-score.

\(\frac{x-5.48}{0.07} =-1.88\\\\\implies x = 5.348\)

Now we will find the same for the top part of the distribution.

\(P(\frac{X-5.48}{0.07}\leq \frac{x-5.48}{0.07} )=0.97\\\\\implies P(Z\leq \frac{x-5.48}{0.07} )=0.97\)

Now we will use the normal table to calculate the corresponding z-score.

\(\frac{x-5.48}{0.07} =1.88\\\\\implies x = 5.612\)

The two diameters that separate the top 35 from the bottom 35 in the normal distribution are 5.35 mm and 5.61 mm .

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Answer:

I think the answer is 75.

Step-by-step explanation:

because 35 + 70 is equal to 105. So now we will just subtract 105 by 180. which will give us 75.

Answer:

4/15

Step-by-step explanation:

2/5 drive

1/3 bus

and rest walk

fraction of those who walk is 1-(2/5+1/3)

2/5+1/3=(6+5)/15=11/15

15/15-11/15=4/15

If the sequence be 2, 9, 22, 45, 82, 137, 214 then the pattern be 6, 13, 23, 37, 55, 77.

The term "patterns" describes common, repeatable sorts of practices or regulations. To forecast what has happened or what might happen, patterns are helpful. come following a group of integers that are ordered specifically. Sequence describes this grouping of numbers.

Putting events or information in a precise order is referred to as sequencing. Higher-order thinking abilities—such as those for detecting patterns, figuring out causes and effects, and more—are necessary for sequencing. Sequencing aids students in both understanding and organizing the material they have learnt and in problem-solving.

Let the given sequence be 2, 9, 22, 45, 82, 137, 214

The differences to a pattern in the sequence be

= 9 - 2, 22 - 9, 45 - 22, 82 - 45, 137 - 82, 214 - 137

= 6, 13, 23, 37, 55, 77

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Answer: D. 15 square root with 3 inside

Step-by-step explanation:

Just try it

Answer:

c

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

Step 1:

4 ( 3x - 2 ) - x = 3x - 4x

Step 2:

12x - 8 - x = - x

Step 3:

11x - 8 = - x

Step 4:

11x = - x + 8

Step 5:

12x = 8

Answer:

x = 2/3

Hope This Helps :)

Answer:

\(\displaystyle{x=\frac{2}{3}}\)

Step-by-step explanation:

\(4(3x-2)-x=3x-4x\\(12x-8)-x=3x-4x\\12x-x-8=3x-4x\\11x-8=3x-4x\\11x-8=-x\\11x=-x+8\\12x=8\)

\(\displaystyle{x=\frac{8}{12}}\)

\(\displaystyle{x=\frac{2}{3}}\)

The probability that 2 of the 9 voters will prefer Candidate A is 0.30033

Given that 25 % of voters prefer candidate A

Total number of voters = 9

Do we have to calculate the probability that 2 of the 9 voters will prefer Candidate A =?

In this question, we used binomial distribution to find the probability that 2 of the 9 voters will prefer candidate A.

The binomial distribution follows the probability  mass function of:

⁹C₂ * (0.25) ² *  (0.75)⁷ =>

⁹C₂  = (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)/ (7 * 6 * 5 * 4 * 3 * 2 * 1) (2 * 1) =>

⁹C₂  = 9 * 8/2 = 36

Now, 36 * (1/4)² * (3/4)⁷ = 0.30033

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Answer:

Answer is c. I, II and II

Step-by-step explanation:

Solution:

Answer is c. I, II and II

It will be increase by 10 points and it will be 10 points higher than the median for the noncurved data. and it will be halfway between Q1 and Q3 for the curved data.

Median for noncurved data = Q2 = 80

Median for curved data = 90

It will increase by 10 points = 90  

It will be 10 points higher than the noncurved data = 90-80 = 10 points

if the set contains 20 values then, noncurved data will be:

60 _ _ _ _ 70 _ _ _ _ 80 _ _ _ _ 87 _ _ _ _ 95

Curved data will be: (all grades increased by 10 points)

70 _ _ _ _ 80 _ _ _ _ 90 _ _ _ _ 97 _ _ _ _ 105

Here, we can see median = Q2 = 90, exactly, halfway between Q1 =80 and Q3 = 97

Hence, C is the right answer

Answer:

It cannot

Step-by-step explanation:

The hypotenuse is always the longest side, which in this instance of the left triangle, it is 14

If x were to be 10, this would make line KM to be 15 units long,  (10 + 5)

Despite line LM being unknown, x must have a number below 10 (, and 9) to make it possible

The linear equation that passes through points (-2,7) and (6,-9) is given by:

y = -2x + 3

A linear function is modeled by:

y = mx + b

In which:

The line passes through points (-2,7) and (6,-9), hence the slope is given by:

m = (-9 - 7)/(6 - (-2)) = -2.

Hence, since when x = -2, y = 7, when x = 0, y = 7 - 2 x (0 - (-2)) = 3, which means that the y-intercept is of b = 3, and the equation is given by:

y = -2x + 3.

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The correct two - way frequency table for the data on High School Students, and the kind of band they want to play at the school dance, is:

                                                     Rap          Rock           Country      Total

Grades 9 - 10                                40              30                55              125

Grades 11 - 12                                60              25                35              120

Total                                              100              55                90             245

Option A is therefore correct.

In a two-way frequency table, there will be totals for both the rows and the columns.

The totals for the rows in this instance are:

Grade 9 - 10 totals :

= 40 + 30 + 55

= 125

Grade 11 - 12 :

= 60 + 25 + 35

= 120

The totals for the columns are:

Rap totals :

= 40 + 60

= 100

Rock :

= 30 + 25

= 55

Country :
= 55 + 35

= 90

Two-way frequency tables allow for us to be able to conclude on the event described by looking at totals from both the columns and the rows. This gives a clearly understanding on preferences and categories.

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Answer:

1.97 day; 1 day.

Step-by-step explanation:

0.07*100 = 7

31.91x - 7 = 70

70 - 7 = 63

31.91x = 63

63 / 31.91 = 1.97