Which numbers have line symmetry?
2, 3, 4 7,8,9​

The product of 13.5 and 12.1 using a regrouping strategy is 163.35.

To begin with, we can start by breaking down each number into its place value components, which are the ones, tenths, and hundredths places. We can represent 13.5 as 13 + 0.5 and 12.1 as 12 + 0.1.

So, we can rewrite 13.5 as (10 + 3) + 0.5 and 12.1 as (10 + 2) + 0.1. Now, we can use the distributive property of multiplication to multiply 13.5 by 12.1 as follows:

13.5 x 12.1 = (10 + 3 + 0.5) x (10 + 2 + 0.1)

= 10 x 10 + 10 x 2 + 10 x 0.1

+ 3 x 10 + 3 x 2 + 3 x 0.1

+ 0.5 x 10 + 0.5 x 2 + 0.5 x 0.1

Next, we can simplify each of these products by multiplying the numbers in the ones and tenths places separately, and then adding the results. For example, 10 x 10 = 100, 10 x 2 = 20, 10 x 0.1 = 1, 3 x 10 = 30, and so on.

So, continuing from the previous step, we get:

13.5 x 12.1 = 100 + 20 + 1

+ 30 + 6 + 0.3

+ 5 + 1 + 0.05

Finally, we can add up all these products to get the final answer:

13.5 x 12.1 = 163.35

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The volume of the prism is 87 and 1/2 cubic yards or 87.5 [tex]yd^{3}[/tex]

The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.

In this case, the length is 5 yards, the width is 5 yards, and the height is 3 and 1/2 yards. We can convert the height to a mixed number fraction of 7/2 yards.

Therefore, the volume of the prism is:

V = lwh = 5 yards × 5 yards × 7/2 yards = 87.5 cubic yards

So, the volume of the prism is 87 and 1/2 cubic yards or 87.5 [tex]yd^{3}[/tex]

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Answer:

Whether it is possible or likely that the mean time for all patients is 2 hours depends on the context of the situation and the characteristics of the data.

If the data on patient wait times is very tightly clustered around the 2-hour mark, such that there is very little variation or dispersion in the data, then it is possible that the mean time for all patients is 2 hours. However, in most real-world situations, it is unlikely that all patients would have exactly the same wait time, so it is unlikely that the mean time for all patients would be exactly 2 hours.

Furthermore, the statement that the mean time for all patients is 2 hours may be misleading or inaccurate if it does not take into account other factors that may affect wait times, such as the time of day, the day of the week, the severity of patients' conditions, and the efficiency of the hospital's operations. Therefore, it is important to consider not only the mean time but also other measures of central tendency and dispersion, as well as other factors that may impact patient wait times, in order to fully understand and interpret the data.

Answer:

$5.39 × 5 = $26.95

5 books about airplanes would cost $26.95.

The lake activity with a central angle of  [tex]39.6^\circ[/tex] is Wakeboarding.

11. the number of tortilla sandwich wraps falling into each interval can be represented by the height or area of the bars. This allows for an easy visualization of the distribution of the data.

12. To determine which bus typically has the faster travel time, we need to compare the measures of center for each data set. Since there are outliers in both data sets, the median would be a more appropriate measure of center than the mean.

For Bus 14, the median is (10 + 12)/2 = 11.

For Bus 18, the median is (10 + 14)/2 = 12.

Therefore, Bus 18 typically has the faster travel time, with a median of 12 minutes.

13. The IQR (interquartile range) is the best measure of variability for the data because it is less sensitive to outliers than the range, and it gives us an idea of how spread out the middle 50% of the data is.

To find Q1, we need to find the median of the lower half of the data: (1+2)/2 = 1.5.

To find Q3, we need to find the median of the upper half of the data: (8+8+8)/3 = 8.

Therefore, the IQR = Q3 - Q1 = 8 - 1.5 = 6.5.

14. To determine the central angle of each lake activity, we need to calculate the percentage of campers who chose each activity and then multiply that percentage by 360 (the total degrees in a circle).

The percentage of campers who chose Kayaking is 15%, so the central angle would be 0.15 x 360 = 54°.

The percentage of campers who chose Wakeboarding is 11%, so the central angle would be 0.11 x 360 = 39.6°.

The percentage of campers who chose Windsurfing is 7%, so the central angle would be 0.07 x 360 = 25.2°.

The percentage of campers who chose Waterskiing is 13%, so the central angle would be 0.13 x 360 = 46.8°.

The percentage of campers who chose Paddleboarding is 54%, so the central angle would be [tex]0.54 x 360 = 194.4^\circ.[/tex]

Therefore, The lake activity with a central angle of  [tex]39.6^\circ[/tex] is Wakeboarding.

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Answer:

the answer is 0.77 yes that is the answer

Answer:

C. 0.64

Step-by-step explanation:

the answer is on the picture

Hence, The theoretical probability of selecting a "O", returning it to the bag, and then selecting a "A" from the collection is 2/21.

The probability  of an occurrence is a number used in mathematics to describe how likely it is that the event will take  place. In terms of percentage  notation, it is expressed as a number  between 0 and 1, or between 0% and 100%. The higher the likelihood, the more  likely it is that the event will take place.

In probability theory,  an event is a set of outcomes  of an experiment to which a probability is assigned. A single outcome may be  an element of many different events, and different events  in an experiment are usually not equally likely, since they may include  very different groups of outcomes.

The  word  "ORLANDO"  consists of 7 letters,

in this word  "ORLANDO"  the  O letter is 2 times  and A is one times

probability  of "O" letters  is 2/7  before  there are two "O"s in  total out of the  seven letters because we are putting the first letter back before drawing the second.

After  that, there are  still 2 "O"s and 1 "A" in the bag for  the  second draw because  we placed the first "O" back. Because there is only one "A" out of a  possible three letters,  the probability  of drawing one on the second draw is one in three.

We multiply the   probabilities of each occurrence  to determine the probability that both will occur:

P("O" on the first draw)* P("A" on the second draw) = (2/7) * (1/3) = 2/21

The theoretical probability of selecting a "O", returning it to the bag, and then selecting a "A" from the collection is therefore 2/21, or roughly 0.095, or 9.5%.

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No. of individuals Suspected drug and didn't give birth to in infants malformed is 10.

Number of individuals who did not take the drug and did not give birth to malformed infants.

subtract the number of individuals who took the drug and gave birth to malformed infants.

The total number of mothers, and then subtract the number of infants born with malfunctions.

Total number of mothers = 40

Number of mothers who gave birth to malformed infants after taking the drug = 35

Number of infants born with malfunctions = 10

the number of mothers who did not take the

drug = 40 - 35 = 5

The number of infants born without malfunctions = Total number of infants - Number of infants born with

malfunctions = (40 - 35) + 5 = 10

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Thus, coach Sanchez can only create a side length of 8 for one side of the court, which is the longest side length.

The factor of a number that, when multiplied by itself, equals the original number is known as the square root of the number. Practically speaking, determining a number's square root is the reverse of doing so to find its square.

Properties

You only need to find that square root of the area to determine the length of a side because we know that a square already has equal sides so the area is determined by two sides.

√64 = 8

Thus, coach Sanchez can only create a side length of 8 for one side of the court, which is the longest side length.

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The value of AC to the nearest tenth is 29.5

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

Angle B = 180-(33+58)

= 180-91 = 89°

using sine rule

represent AC by x

x/ sin89 = 25/sin 58

xsin58 = 25sin89

0.848x = 0.9998×25

0.848x = 24.995

x = 24.995/0.848

x = 29.5( nearest tenth)

therefore the value of AC is 29.5.

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Therefore, the time in minutes when the trough is empty is approximately 0.313 minutes.

To find the time in minutes when the trough is empty, we need to solve the equation f(x) = 0, since f(x) represents the volume of water in the trough.

So, we need to solve the quadratic equation:

[tex]10x^2 - 19x + 6 = 0[/tex]

To solve this equation, we can use the quadratic formula:

[tex]x = (-b ± \sqrt(b^2 - 4ac)) / 2a[/tex]

where a = 10, b = -19, and c = 6.

Plugging in these values, we get:

[tex]x = (-(-19) ± \sqrt((-19)^2 - 4(10)(6))) / 2(10)[/tex]

[tex]x = (19 ± sqrt(241)) / 20[/tex]

So, the two solutions are:

[tex]x = (19 + \sqrt(241)) / 20 \approx1.807 minutes[/tex]

[tex]x = (19 - \sqrt(241)) / 20 \approx0.313 minutes[/tex]

However, only the second solution makes sense in this context, since the trough cannot be empty before we start draining the water. Therefore, the time in minutes when the trough is empty is approximately 0.313 minutes.

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Answers are ,Right triangle with legs 3 meters and 33 meters, Right triangle with legs 1 meter and 15 meters, Right triangle with legs 12 meters and 140 meters, Right triangle with legs 12 meters and 150

what is Right triangle ?

A right triangle is a triangle that has one angle equal to 90 degrees (a right angle). The other two angles are acute angles (less than 90 degrees). The side opposite to the right angle is called the hypotenuse, and the other two sides are called legs.

In the given question,

The ratio of the legs of the right triangle for a ramp should be 1:12, which means that for every 1 inch of rise, there should be 12 inches of ramp length. To calculate the angle of inclination, we can use the inverse tangent function, which gives us the angle whose tangent is equal to the ratio of the legs. The angle of inclination should be less than or equal to 4.8 degrees.

Let's calculate the angle of inclination for each ramp design:

Right triangle with legs 3 meters and 33 meters:

The ratio of the legs is 3:33, which simplifies to 1:11. The length of the ramp is 11 times the height of the rise. The angle of inclination is:

arctan(1/11) ≈ 4.76 degrees

The angle of inclination is less than or equal to 4.8 degrees, so this ramp design meets the requirements of the Americans with Disabilities Act.

Right triangle with legs 1 meter and 15 meters:

The ratio of the legs is 1:15. The length of the ramp is 15 times the height of the rise. The angle of inclination is:

arctan(1/15) ≈ 3.81 degrees

The angle of inclination is less than or equal to 4.8 degrees, so this ramp design also meets the requirements of the Americans with Disabilities Act.

Right triangle with legs 12 meters and 140 meters:

The ratio of the legs is 12:140, which simplifies to 3:35. The length of the ramp is 35 times the height of the rise. The angle of inclination is:

arctan(3/35) ≈ 4.56 degrees

The angle of inclination is less than or equal to 4.8 degrees, so this ramp design meets the requirements of the Americans with Disabilities Act.

Right triangle with legs 12 meters and 150 meters:

The ratio of the legs is 12:150, which simplifies to 2:25. The length of the ramp is 25 times the height of the rise. The angle of inclination is:

arctan(2/25) ≈ 4.62 degrees

The angle of inclination is less than or equal to 4.8 degrees, so this ramp design meets the requirements of the Americans with Disabilities Act.

Right triangle with legs 24 meters and 240 meters:

The ratio of the legs is 24:240, which simplifies to 1:10. The length of the ramp is 10 times the height of the rise. The angle of inclination is:

arctan(1/10) ≈ 5.71 degrees

The angle of inclination is greater than 4.8 degrees, so this ramp design does not meet the requirements of the Americans with Disabilities Act.

Therefore, the ramp designs that meet the requirements of the Americans with Disabilities Act are:

Right triangle with legs 3 meters and 33 meters.

Right triangle with legs 1 meter and 15 meters.

Right triangle with legs 12 meters and 140 meters.

Right triangle with legs 12 meters and 150 meters.

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Answer:

The rewritten function by completing the square is:

[tex]f(x)=(x-4)^2-18[/tex]

The solutions of the function are:

[tex]x=4+3\sqrt{2},\;x=4-3\sqrt{2}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=x^2-8x-2[/tex]

To rewrite the function by completing the square, begin by adding and subtracting the square of half the coefficient of the term in x. (Place these between the term in x and the constant).

[tex]f(x)=x^2-8x+\left(\dfrac{-8}{2}\right)^2-\left(\dfrac{-8}{2}\right)^2-2[/tex]

Simplify:

[tex]f(x)=x^2-8x+\left(-4\right)^2-\left(-4\right)^2-2[/tex]

[tex]f(x)=x^2-8x+16-16-2[/tex]

We have now created a perfect square trinomial from the first three terms: x² - 8x + 16.

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{\sf \large Perfect Square Trinomial}\\\\\sf A perfect square trinomial is a polynomial of the form $a^2 + 2ab + b^2$ or $a^2 - 2ab + b^2$, where $a$ and $b$ are constants. \\\\When factored, a perfect square trinomial becomes the square of a binomial: $(a + b)^2$ or $(a - b)^2$. \\\end{minipage}}[/tex]

Factor the perfect square trinomial x² - 8x + 16.

[tex]f(x)=(x-4)^2-16-2[/tex]

Simplify by subtracting the numbers outside the parentheses:

[tex]f(x)=(x-4)^2-18[/tex]

Therefore, the given function rewritten by completing the square is:

The solutions to a quadratic function are the x-values which satisfy the equation f(x) = 0. Therefore, to find the solutions, set the function equal to zero and solve for x.

[tex]\begin{aligned}f(x)&=0\\\implies (x-4)^2-18&=0\\(x-4)^2-18+18&=0+18\\(x-4)^2&=18\\\sqrt{(x-4)^2}&=\sqrt{18}\\x-4&=\pm\sqrt{18}\\x-4+4&=\pm\sqrt{18}+4\\x&=4\pm\sqrt{18}\\x&=4\pm\sqrt{3^2 \cdot 2}\\x&=4\pm\sqrt{3^2} \sqrt{2}\\x&=4\pm3 \sqrt{2}\end{aligned}[/tex]

Therefore, the solutions of the function are:

[tex]x=4+3\sqrt{2},\;x=4-3\sqrt{2}[/tex]

Answer:7/20

Step-by-step explanation:

35% [tex]= 0.35 = \frac{35}{100} = \frac{35/5}{100/5} = \frac{7}{20}[/tex]

Step-by-step explanation:

From 4:26 to 6:50  is   2 hr and 24 in = 2  24/60  hrs =  2.4 hours

2.4 hrs is what percent of 15 hrs ?

2.4  /  15  * 100% = 16%

The distance between building B and C is 10√2 meters, or 9.38 meters, rounded to two decimal places.

Triangle is a three-sided geometric shape. It has three vertices which join together to form three sides. The sum of the three angles in a triangle is always equal to 180°. It can be classified into three types, namely equilateral, isosceles, and scalene based on the length of the sides. Triangles can also be classified as right, obtuse, or acute depending on the angles. Triangles are one of the most basic shapes in geometry and are used in many real-world applications such as architecture and engineering.

To answer this question, we need to use the Pythagorean theorem, which states that the sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse.

Using the given information, we can set up the equation:

10² + x² = (x√2)²

Where x is the distance between building B and C.

We can solve this equation with algebra to find x:

100 + x² = 2x²

x² = 100

x = 10√2

Therefore, the distance between building B and C is 10√2 meters, or 9.38 meters, rounded to two decimal places.

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Answer: It should be the same?

(edit) Answer: The direct answer is 6:2 or 6 (cups) flour 2 (cups) milk

Step-by-step explanation: I'm Confused, the ratio is 3:1 or 1:0/3 even if you double the ratio it would be 6:2 the portions of flour will always 3 times the amount (measurement) of the milk. Correct me if i'm wrong, a bit perplexed why this question is asked.

The correct option is C, the skews are different.

We have two dot plots and we want to see which statement is the best suported by these.

The right one is better distributed, so we can conclude that the correct statement is that the data have different skews.

The ranges may seem also to be different, but are the same ones, in the first one is:

20 - 12 = 8

In the second it is:

19 - 11 = 8

so the correct option is C.

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Answer:

Remember SOHCAHTOA  

SOH- Sin= Opposite/Hypotenuse

CAH- Cosine= Adjacent/Hypotenuse

TOA- Tangent= Opposite/Adjacent

sin Θ is 24/25

cos Θ is 7/25

tan Θ is 24/7

Step-by-step explanation:

If using the SOHCAHTOA method all you have to do is memorize your Pythagorean triples

Ex: 3,4,5

7,24,25

5,12,13

The margin of error for the school's claim  is 0.055 or approximately 5.5%.

To find the margin of error, we need to use the formula:

Margin of error = Critical value x Standard error

For a sample size of 500, the critical value can be found by:

critical value = 1.96

Next, we need to find the standard error. The formula for the standard error is:

standard error = sqrt(p_hat * (1 - p_hat) / n)

In this case, the sample proportion is 150/500 = 0.3.

standard error = sqrt(0.3 * (1 - 0.3) / 500) = 0.028

Finally, we can calculate the margin of error:

Margin of error = 1.96 x 0.028 = 0.055

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--The complete Question is, What is the margin of error for the school's claim that 30% of grade 3 pupils stay in the playground after their classes, given the results of the survey of 500 grade 3 pupils, which revealed that 150 of them stay in the playground after their classes? Assume a confidence level of 95%.--

Part A: A reasonable domain to plot the growth function would be from d = 0 to d = 11.

Part B: The y-intercept of the graph of the function f(d) is 7

Part C: The average rate of change of the function f(d) from d = 4 to d = 11 is approximately 0.64 mm/day.

The domain of a function represents the set of input values for which the function is defined and can produce a meaningful output.

The y-intercept of a function represents the value of the function when the input is equal to zero.

The average rate of change of a function from x = a to x = b is given by the slope of the secant line passing through the points (a, f(a)) and (b, f(b)).

Here we have

A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:

=> f(d) = 7(1.06)^d

Since it is given that the radius of the algae was approximately 13.29 mm when the biologist concluded her study, we can set f(d) = 13.29  

=> 13.29 = [tex]7(1.06)^{d}[/tex]

=> ln(13.29/7) = d ln(1.06)

=> d = ln(13.29/7)/ln(1.06) ≈ 11  

Therefore, A reasonable domain to plot the growth function would be from d = 0 to d = 11.

Part B: The y-intercept of the graph of the function f(d) represents the value of the function when d = 0.

Substituting d = 0 into the given equation, we get:

f(0) = 7(1.06)⁰ = 7

Therefore, The y-intercept of the graph of the function f(d) is 7

Part C: The average rate of change of the function f(d) from d = 4 to d = 11 is given by the slope of the secant line passing through the points (4, f(4)) and (11, f(11)). Using the given equation, we can evaluate f(4) and f(11):

f(4) = 7(1.06)⁴ ≈ 8.84

f(11) = 7(1.06)¹¹ ≈ 13.29

The slope of the second line passing through these two points is:

Slope = (f(11) - f(4))/(11 - 4) = [ 13.29 - 8.84]/7 = 0.64

Therefore,

The average rate of change of the function f(d) from d = 4 to d = 11 is approximately 0.64 mm/day.

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Stop using brainly. This whole website has became a big money grab over the last few months and they will remove all your posts and answers unless you pay them money. I've had it happen several times now.

We need to integrate the function

y = 2x - x² with respect to x, from x = 0 to x = 2.

The graph of the function intersects the x-axis at x = 0 and x = 2.

So,

Area of region R = ∫[0,2] (2x - x²) dx

= [x² - (1/3)x³] from 0 to 2

= [2² - (1/3)(2)³] - [0² - (1/3)(0)³]

= 4/3

Now, let's find the equation of the line y = cx. Since the line passes through the origin (0,0), we have y = cx.

To find the value of c that divides the region R into two equal subregions, we need to find the value of x where the

area under the curve y = 2x - x² is equal to the area under the line y = cx.

∫[0,a] (2x - x²) dx = ∫[0,a] cx dx

[2x²/2 - x³/3] from 0 to a = [c/2 x²] from 0 to a

2a²/2 - a³/3 = c/2 a²

We multiply both sides by 6, we get:

12a² - 2a³ = 3ac

2a² - (1/3)a³ = (1/2)ac

2a - (1/3)a² = (1/2)c

c = (4a - (2/3)a²)/2

We know that the area under the line is equal to the area under the curve up to the point of intersection, we have:

∫[0,a] (2x - x²) dx = ∫[0,a] (cx) dx - ∫[a,2] (2x - x²) dx

2a²/2 - a³/3 = c/2 a² - 2a² + (8/3)a³ - 4a + (4/3)a²

10a³/3 - 7a² + 4a = 0

a = 0, 1.4105, -0.6172

The only value of a that is within the range 0 to 2 is a = 1.4105. Substituting this value into the equation for c, we get:

c = (4a - (2/3)a²)/2 = 1.636

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While hiring change managers, businesses should take into account their nonconformist, risk-taking nature.

To successfully implement organizational change efforts, change managers must question the status quo, take measured risks, and foster creativity. Organizational stability and routine tasks may be maintained more successfully with a large number of conformists, but change managers need a distinct skill set. They must be able to think creatively, try out novel concepts, and deal with ambiguity and uncertainty.

Option 3: Being seen as a rule-following peacemaker may be an asset in some situations, but it is not always necessary for a change manager. Similarly, having a lot of radical innovators (option 4) could backfire if there isn't a balance with other qualities and abilities crucial for effective change management.

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The complete question is:

identify a characteristic of change managers that an organization should consider when employing people.

→ Change managers are nonconformists who take risks.

→ Having a large number of conformist is effective for an organization.

→ Change managers are usually regarded as peacemakers who follow rules.

→ Having a large number of radical innovators is effective for an organization.

While hiring change managers, businesses should take into account their nonconformist, risk-taking nature.

To successfully implement organizational change efforts, change managers must question the status quo, take measured risks, and foster creativity. Organizational stability and routine tasks may be maintained more successfully with a large number of conformists, but change managers need a distinct skill set. They must be able to think creatively, try out novel concepts, and deal with ambiguity and uncertainty.

Option 3: Being seen as a rule-following peacemaker may be an asset in some situations, but it is not always necessary for a change manager. Similarly, having a lot of radical innovators (option 4) could backfire if there isn't a balance with other qualities and abilities crucial for effective change management.

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Here is the tree diagram to represent the sample space of spinning the spinner twice:

sp1 - Possible outcomes of the first spin:

Red, Blue, Green

sp1 - Red

sp2 - Red Red, Red

sp2 - Blue Red, Blue

sp2 - Green Red, Green

sp1 - Blue

sp2 - Red Blue, Red

sp2 - Blue Blue, Blue

sp2 - Green Blue, Green

sp1 - Green

sp2 - Red Green, Red

sp2 - Blue Green, Blue

sp2 - Green Green, Green

So the full sample space would be:

{(Red, Red), (Red, Blue), (Red, Green),

(Blue, Red), (Blue, Blue), (Blue, Green),

(Green, Red), (Green, Blue), (Green, Green)}

Does this capture the correct sample space for spinning the spinner twice? Let me know if you need any clarification.

The standard format of the polynomial given in the image is given as follows:

0.5x^5 - x^4 - 5x² - 6.

The standard format of a polynomial is to write it in descending order of the exponents of the variable, with each term separated by a plus or minus sign. For example, the standard format of a polynomial with one variable (x) is:

a_nx^n + a_{n-1}x^{n-1} + ... + a_2x^2 + a_1x + a_0

The exponents of the polynomial in this problem are given as follows:

5, 0, 4, 2.

Hence the descending order is:

5, 4, 2, 0.

And the standard format of the polynomial is of:

0.5x^5 - x^4 - 5x² - 6.

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Answer:

The first, third, fifth and 6th statements are true.

Step-by-step explanation:

Answer:

Here are the ones you should select:

Step-by-step explanation:

1) The slope of AB is equal to slope of AC

Rise over run for AB =2/4=1/2

Rise over run for AC=3/6=1/2

so they are equal

2) Slope of AB is not equal to BE because of visual reasons but if you need an explanation I can provide it

3) AB is a segment on the line, so the slopes are equal as you can see in the illustration provided in the question

4/5) Slope=[tex]\frac{rise}{run}[/tex], but AE/AB is not that, BE/AB is rise/run, so it's correct

6) CD/AD=rise/run, so it's correct

sorry if i got anything wrong!

For the given integer, the maximum starting population size that will eventually lead to extinction is 98, since any larger value will result in the population either stabilizing at a positive value or growing indefinitely.

The equation in question is:

dN/dt = -0.001N(N - 110)(N - 99)

Here, N represents the population size, and dN/dt represents the rate of change of the population with respect to time. The right-hand side of the equation tells us how the population size changes over time, and it's determined by the current population size N, as well as the two constants 110 and 99.

We can do this by setting dN/dt equal to zero and solving for N:

dN/dt = -0.001N(N - 110)(N - 99) = 0

=> N = 0, N = 99, N = 110

We can then plot the direction field (i.e., arrows indicating the direction of change) on each interval, and use this to determine the behavior of the solution curve. In this case, we can see that the direction of the arrows changes at each critical point, indicating that the population behavior switches between growing and declining as we move from one interval to the next.

Specifically, we can see that if the initial population size A is less than 99, the population will decline to extinction. If the initial population size is between 99 and 110, the population will initially decline but then grow and eventually stabilize at N = 110. If the initial population size is greater than 110, the population will grow exponentially and tend towards infinity.

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The fraction of the year representing the Christian celebration of Easter on April 16 is equal to 0.3.

In 2017, there were 365 days in the year.

It was not a leap year.

Easter Sunday occurred on April 16th.

Number of days in months before Easter,

January = 31

February = 28

March = 31

April = 16

Total days in Easter = 31 + 28 + 31 +16

                                  =  106th day of the year

January 1 is the first day of the year.

Total number of days in a year = 365

Fraction of the year

= the number of days up to and including April 16th / the total number of days in the year

= 106 / 365

= 0.2904

= 0.3 (rounded to 1 decimal place)

Therefore, Easter Sunday in 2017 represented as 0.3 fraction of the year.

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The above question is incomplete , the complete question is:

In 2017, the Christian celebration of Easter occurred on Sunday, 16 April. What fraction of the year was this? (to 1 decimal place).