the population in Knox is 42000 and it is declining at a rate of 3.2% per year predict the population to the nearest whole number after 8 years

Answers

Answer 1

The predicted population of Knox, rounded to the nearest whole number, after 8 years is 32,599.

To predict the population of Knox after 8 years, we can use the given information that the population is currently 42,000 and it is declining at a rate of 3.2% per year.

To calculate the population after 8 years, we need to apply the rate of decline for each year. Let's break down the calculation step by step:

Calculate the population after the first year:

Population after 1 year = 42,000 - (3.2% of 42,000)

= 42,000 - (0.032 * 42,000)

= 42,000 - 1,344

= 40,656

Calculate the population after the second year:

Population after 2 years = 40,656 - (3.2% of 40,656)

= 40,656 - (0.032 * 40,656)

= 40,656 - 1,299.71

= 39,356.29

Continue this process for each year up to 8 years, applying the 3.2% rate of decline each time.

After performing these calculations for each year, we arrive at the population after 8 years:

Population after 8 years ≈ 32,599

Therefore, the predicted population of Knox, rounded to the nearest whole number, after 8 years is 32,599.

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Related Questions

Which is the best deal over 5 years? Investing at 7.87% compounded semi annually, 7.8% compounded quarterly, or 7.72% compounded every minute?

Answers

The best deal over 5 years would be investing at 7.8% compounded quarterly.

Although the interest rates of 7.87% compounded semi-annually and 7.72% compounded every minute may appear slightly higher, the frequency of compounding plays a significant role in determining the overall return.

Compounding more frequently leads to a higher effective annual rate. In this case, compounding quarterly provides a greater compounding frequency than semi-annual or minute-by-minute compounding, resulting in higher returns over time.

When interest is compounded quarterly, the compounding occurs four times a year, whereas semi-annual compounding only occurs twice a year. Compounding every minute may seem more frequent, but the actual effect on the return is minimal since there are a large number of minutes in a year.

Therefore, the 7.8% compounded quarterly is the best deal over 5 years as it offers a higher effective annual rate compared to the other options.

In summary, investing at 7.8% compounded quarterly is the most advantageous choice over a 5-year period. The frequency of compounding plays a crucial role in determining the overall return, and compounding quarterly provides a greater compounding frequency compared to semi-annual or minute-by-minute compounding.

It is essential to consider both the interest rate and the compounding frequency when evaluating investment options to make an informed decision.

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An architect is designing a swimming pool with a base in the shape of a right triangle according to the architect the pools depth should be 6 feet less than It’s length x and it’s width should be 8 feet less than it’s length the volume of water in the pool cannot exceed 1680 cubic feet which statement

Answers

Let's use the formula for the volume of a right triangular prism to find the length of the pool:
Volume = (1/2) x base x height x depth
We know that the base of the pool is a right triangle, so we can use the Pythagorean theorem to find the base:
a^2 + b^2 = c^2
where a and b are the legs of the right triangle and c is the hypotenuse, which is the length of the pool.
We also know that the width of the pool is 8 feet less than its length, so we can write:
b = c - 8
We are given that the depth of the pool is 6 feet less than its length x, so we can write:
depth = x - 6
Substituting the values of b and depth in the formula for the volume of a right triangular prism, we get:
Volume = (1/2) x (c - 8) x c x (x - 6)
Simplifying the equation, we get:
Volume = (1/2) x (c^2 - 8c) x (x - 6)
Multiplying both sides by 2 and expanding, we get:
2 x Volume = (c^2 - 8c) x (x - 6)
2 x 1680 = (c^2 - 8c) x (x - 6)
3360 = (c^2 - 8c) x (x - 6)
We can solve this quadratic equation for c using the quadratic formula:
c = [8 ± sqrt(64 + 4 x 3360 x (x - 6))] / 2
c = 4 ± sqrt(16 + 3360 x (x - 6))
We know that the length of the pool cannot be negative, so we can eliminate the negative root:
c = 4 + sqrt(16 + 3360 x (x - 6))
Now we can substitute this value of c in the equation for b:
b = c - 8
b = 4 + sqrt(16 + 3360 x (x - 6)) - 8
b = sqrt(16 + 3360 x (x - 6)) - 4
Therefore, the length, width, and depth of the pool are:
Length = c = 4 + sqrt(16 + 3360 x (x - 6))
Width = b = sqrt(16 + 3360 x (x - 6)) - 4
Depth = x - 6
We are given that the volume of water in the pool cannot exceed 1680 cubic feet, so we can write:
Volume = Length x Width x Depth
1680 = (4 + sqrt(16 + 3360 x (x - 6))) x (sqrt(16 + 3360 x (x - 6)) - 4) x (x - 6)
We can solve this equation for x using numerical methods or a graphing calculator. The solution is approximately x = 12.5 feet.
Therefore, the statement that is true is: The length of the pool cannot exceed 4 + sqrt(16 + 3360 x (x - 6)) feet, the width of the pool cannot exceed sqrt(16 + 3360 x (x - 6)) - 4 feet, and the depth of the pool cannot exceed 6.5 feet, in order to ensure that the volume of water in the pool does not exceed 1680 cubic feet.

TIME REMAINING
01:48:30
On a coordinate plane, 2 lines are shown. Line H J has points (negative 4, negative 2) and (0, 4). Line F G has points (negative 4, 1) and (0, negative 2).

Which statement best explains the relationship between lines FG and HJ?

They are perpendicular because their slopes are equal.
They are perpendicular because their slopes are negative reciprocals.
They are not perpendicular because their slopes are equal.
They are not perpendicular because their slopes are not negative reciprocals.

Answers

Answer:

Its b i bealive

Step-by-step explanation:

Need help solving the problem, please.

Answers

The equation y = -6x + 2 (option c) is parallel to the graph of y = -6x + 3.

Which of the given lines is parallel to y = -6x + 3?

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the graph in the question:

y = -6x + 3

To determine which of the given options:

a) y = (1/6)x + 3

b) y = -(1/6) + 3

c) y = -6x + 2

d) y = 3x - 6

is parallel to the graph of y = -6x + 3, we need to compare their slopes.

The given equation of the graph is y = -6x + 3:

Slope of the graph is -6.

Now, lets check each option:

a) y = (1/6)x + 3

This equation has a slope of 1/6, which is not equal to -6.

Therefore, it is not parallel to y = -6x + 3.

b) y = -(1/6) + 3

This equation also has a slope of 1/6 (the negative sign doesn't affect the slope), it is not parallel to y = -6x + 3.

c) y = -6x + 2

This equation has a slope of -6, which is the same as the slope of y = -6x + 3. Therefore, it is parallel to the given graph.

d) y = 3x - 6

This equation has a slope of 3, which is not equal to -6. Thus, it is not parallel to y = -6x + 3.

Therefore option C) y = -6x + 2 is the correct answer.

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NO LINKS!! URGENT HELP PLEASE!!

Find the value of x ​

Answers

Answer:

  x = 4

Step-by-step explanation:

You want the value of x in the figure of a circle with intersecting secants.

Secant relation

The product of lengths from the near and far circle intercepts to the point where the secants intersect is the same for both secants:

  6(6+10) = 8(8+x)

  6·16 = 8·(8+x)

  12 = 8 +x . . . . . . . divide by 8

  4 = x . . . . . . . . . . subtract 8

The length x is 4 units.

<95141404393>

9
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
A system of linear equations is given by the tables. One of the tables is represented by the equation y = -x + 7
y
9
8
X
0
3
6
9
y
5
6
7
8
X
-6
-3
0
3
7
6
The equation that represents the other equation is y= 1/3
The solution of the system is (
)
X+
Reset
5
Next I

Answers

The solution of the system of linear equations can be found by determining the values of x and y that satisfy both equations simultaneously. From the given information, one equation is y = -x + 7, and the other equation is y = 1/3.

To find the solution, we need to find the point where the two equations intersect. By setting the right sides of the equations equal to each other, we can solve for x:

-x + 7 = 1/3

Adding x to both sides:

7 = 1/3 + x

To simplify, we convert 7 to its fraction form:

7 = 21/3

Now, we can combine the fractions on the right side:

21/3 = 1/3 + x

21/3 - 1/3 = x

20/3 = x

So, x = 20/3.

To find the corresponding value of y, we substitute this value of x into either of the equations. Let's use the equation y = -x + 7:

y = -(20/3) + 7

To simplify, we can convert 7 to its fraction form:

y = -(20/3) + 21/3

y = (21 - 20) / 3

y = 1/3

Therefore, the solution of the system of linear equations is (x, y) = (20/3, 1/3).

Roger can run one mile in 9 minutes. Jeff can run one mile in 6 minutes. If Jeff gives Roger a 1 minute head start, how
long will it take before Jeff catches up to Roger? How far will each have run?
Not including the head start, it will take
-

--
minutes for Jeff to catch up to Roger.

Answers

Answer:  2 minutes

Each person runs 1/3 of a mile when Jeff catches up to Roger.

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

Explanation

x = number of minutes that Jeff runs

x+1 = number of minutes Roger runs

Roger has the head start of 1 minute, so he has been running for 1 minute longer compared to Jeff.

Roger runs 1 mile in 9 minutes. His unit rate is 1/9 of a mile per minute.

Jeff's unit rate is 1/6 of a mile per minute.

Let's set up a table with what we have so far

[tex]\begin{array}{|c|c|c|c|} \cline{1-4} & \text{Distance} & \text{rate} & \text{time}\\\cline{1-4}\text{Jeff} & d & 1/6 & \text{x}\\\cline{1-4}\text{Roger} & d & 1/9 & \text{x}+1\\\cline{1-4}\end{array}[/tex]

The distance equation for Jeff is d = (1/6)x

The distance equation for Roger is d = (1/9)(x+1)

note: distance = rate*time

Both runners travel the same distance when Jeff catches up to Roger, so both "d"s are the same value at this specific moment. Set the right hand sides equal to each other and solve for x.

(1/6)x = (1/9)(x+1)

18*(1/6)x = 18*(1/9)(x+1)

3x = 2(x+1)

3x = 2x+2

3x-2x = 2

x = 2

Jeff runs for 2 minutes when he catches up to Roger.

----------

Check:

Jeff runs for 2 minutes, at 1/6 of a mile per minute, so he runs 2*(1/6) = 2/6 = 1/3 of a mile.

Roger runs for 2+1 = 3 minutes (remember he gets the head start) at 1/9 of a mile per minute, so he has run 3*(1/9) = 3/9 = 1/3 of a mile as well.

Both men have run the same distance which confirms Jeff catches up to Roger at this point. The answer is confirmed.

Solve - the mean age of a family of seven is 23 years the median is 16 years the modes are 12 years and 45 years and the range is 35 years. Find the ages of the seven family members.

Answers

The ages of the seven family members are 12, 16, 16, 45, 45, 45, and 80 years.

To solve this problem, let's break it down step by step:

1. We are given that the mean age of the family is 23 years. The mean is calculated by summing up all the ages and dividing by the number of family members. Since there are seven family members, the total sum of their ages is 7 * 23 = 161 years.

2. The median age is 16 years. This means that when the ages are arranged in ascending order, the fourth age is 16. Since there are seven family members, the fourth age is the middle age. Therefore, the ages in ascending order are: _ _ 12 16 _ 45 _.

3. The modes are 12 years and 45 years, which means these two ages occur more frequently than any other age. Since the median is 16, it can't be one of the modes. Hence, we can conclude that the family members' ages are: _ _ 12 16 16 45 _.

4. The range is 35 years, which is the difference between the highest and lowest ages. Since the ages are arranged in ascending order, the highest age must be 45 + 35 = 80 years. Therefore, the ages of the family members are: _ _ 12 16 16 45 80.

In summary, the ages of the seven family members are 12, 16, 16, 45, 45, 45, and 80 years.

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What is the graph of the solution to the following compound inequality?
3-x22 or 4x+2210
O A.
B.
O c.
O D.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
H
He
+++
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4
5 6 7 8 9 10
1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3
4
€1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2
5 6 7 8 9 10
3 4 5 6 7 8 9 10

Answers

Answer:

Step-by-step explanation:

To graph the solution to the compound inequality 3 - x < 22 or 4x + 2 > 10, we need to graph the individual inequalities and find the overlapping region.

First, let's graph the inequality 3 - x < 22:

Subtract 3 from both sides to isolate x:

-x < 19

Multiply both sides by -1, which reverses the inequality direction:

x > -19

This means that x is greater than -19, but not including -19. So, we will have an open circle at -19 and shade everything to the right of it.

Next, let's graph the inequality 4x + 2 > 10:

Subtract 2 from both sides to isolate 4x:

4x > 8

Divide both sides by 4:

x > 2

This means that x is greater than 2, but not including 2. So, we will have an open circle at 2 and shade everything to the right of it.

Combining the two inequalities, we need to find the overlapping region. Since both inequalities have an open circle at their endpoint, we will use a dashed line to represent them.

The graph should look like this:

markdown

Copy code

 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

  +                                                     +

  |                                                     |

  |                                                     |

  +---------------------------------|-------------------->

                                      -19       2

The shaded region will be to the right of -19 and to the right of 2, including all numbers greater than those values.

Therefore, the correct answer is:

O A. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

The graph below shows the solution to which system of inequalities?
O A. x< 1 and yz x
OB. ys 1 and y> x
O C. x≤ 1 and y> x
OD. y< 1 and yz x
6

Answers

The system of inequalities shown in this problem is defined as follows:

d) y < 1 and y ≥ x.

How to obtain the system of inequalities?

The line in the image has an intercept of zero and slope of 1, hence it is given as follows:

y = x.

Points above the solid line are plotted, hence the first condition is:

y ≥ x.

The upper bound, represented by the dashed horizontal line, is y = 1, hence the second condition is:

y < 1.

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A particular type of vaccine comes in a Brand-1 and a Brand-2. Sixty-five percent
of all patients at a certain vaccination centre want the Brand-2.
i) Among ten randomly selected patients who want this type of vaccine, what
is the probability that at least six want the Brand-2?
ii) Among ten randomly selected patients, what is the probability that the
number who want the Brand-2 vaccine is within 1 standard deviation of
the mean value?
iii) The store currently has seven vaccines of each brand. What is the probability that all of the next ten patients who want this vaccine can get the brand
of vaccine they want from current stock?

Answers

i) Probability of at least six patients wanting Brand-2: P(X ≥ 6)

ii) Probability of number of patients within 1 standard deviation of mean: P(μ - σ ≤ X ≤ μ + σ)

iii) Probability that all ten patients get their desired brand from current stock: (7/14) * (6/13) * ... * (1/5)

i) The probability of at least six patients wanting Brand-2 out of ten randomly selected patients can be calculated using the binomial distribution. We need to sum the probabilities of six, seven, eight, nine, and ten patients wanting Brand-2.

The probability can be calculated as P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10), where X follows a binomial distribution with n = 10 and p = 0.65. The answer is the sum of these individual probabilities.

ii) To calculate the probability of the number of patients who want the Brand-2 vaccine being within 1 standard deviation of the mean value, we need to find the range of values that fall within one standard deviation of the mean.

We can use the normal approximation to the binomial distribution since n = 10 is reasonably large. We calculate the mean (μ) and standard deviation (σ) using μ = n * p and σ = √(n * p * (1 - p)), where p = 0.65. Then we calculate the probability of the number of patients falling within the range μ - σ to μ + σ.

iii) Since there are seven vaccines of each brand in stock, the probability that all ten patients who want the vaccine can get the brand they want from the current stock is equal to the probability of the first patient getting their desired brand (7/14) multiplied by the probability of the second patient getting their desired brand (6/13), and so on until the tenth patient (1/5). The final probability is the product of these individual probabilities.

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y'=y +8z +e^x
x'=2y+z+e^-3x

Answers

Answer:

I have not comed across this question before

Determine the percentile of 6.2 using the following data set.
4.2 4.6 5.1 6.2 6.3 6.6 6.7 6.8 7.1 7.2
Your answer should be an exact numerical value.
The percentile of 6.2 is
%.

Answers

The percentile of 6.2 in the given dataset is 30%. This means that 30% of the values in the dataset are lower than or equal to 6.2.

To determine the percentile of 6.2 in the given dataset, we need to calculate the percentage of values in the dataset that are lower than or equal to 6.2.

First, we arrange the dataset in ascending order: 4.2, 4.6, 5.1, 6.2, 6.3, 6.6, 6.7, 6.8, 7.1, 7.2.

Next, we count the number of values that are lower than or equal to 6.2. In this case, there are three values: 4.2, 4.6, and 5.1.

The next step is to calculate the percentage. We divide the count (3) by the total number of values in the dataset (10) and multiply by 100.

(3/10) * 100 = 0.3 * 100 = 30%

Percentiles are used to understand the relative position of a particular value within a dataset. In this case, 6.2 is higher than 30% of the values in the dataset and lower than the remaining 70%.

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NO LINKS!! URGENT HELP PLEASE!!!

4. What is a regular polygon?

5. For a regular pentagon, (NOT MULTIPLE CHOICE),
a. Find the measure of a single interior angle.
b. Find the measure of a single exterior angle.

6. The measure of the interior angle of a regular polygon is 162°. How many sides does it have?

Answers

4. A regular polygon is a polygon that has all sides of equal length and all angles of equal measure. In other words, it is a polygon with both equal sides and equal angles.

5. For a regular pentagon:
a. The measure of a single interior angle can be found using the formula: (n - 2) * 180° / n, where n represents the number of sides of the polygon. For a pentagon, n = 5. Plugging the values into the formula:
Single interior angle = (5 - 2) * 180° / 5 = 3 * 180° / 5 = 540° / 5 = 108°

b. The measure of a single exterior angle in a regular polygon can be found by subtracting the measure of the corresponding interior angle from 180°.
Single exterior angle = 180° - Single interior angle = 180° - 108° = 72°

6. If the measure of the interior angle of a regular polygon is 162°, we can use the formula for the measure of a single interior angle: (n - 2) * 180° / n = 162°, where n represents the number of sides of the polygon.

Solving for n:
(n - 2) * 180° / n = 162°
Multiplying both sides by n:
(n - 2) * 180° = 162° * n
Distributing:
180°n - 360° = 162°n
Subtracting 180°n from both sides:
-360° = -18°n
Dividing both sides by -18°:
n = 20

Therefore, the regular polygon with an interior angle of 162° has 20 sides.



Star answer please ?

Answer:

4.
A regular polygon is a polygon in which all sides are equal in length and all angles are equal in measure.

5.

a. The measure of a single interior angle in a regular pentagon is:
[(n – 2)*180°]/n = 540°/5 = 108°.

b. The measure of a single exterior angle in a regular pentagon is:
360°/n = 360°/5 = 72°.

6.
This can be found using the following formula:

[(n – 2)*180°]/n = Interior angle

(n-2)*180=162°*n

180n-360=162n

180n-162n=360

18n=360

n=360/18

n=20

where n is the number of sides in the regular polygon.

A regular polygon with an interior angle of 162° has 20 sides.

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?

y < 3x + 2
y > 3x + 2
y < One-thirdx + 2
y > One-thirdx + 2

Answers

The linear inequality represented by the graph is y < 3x + 2. Option A.

To determine the linear inequality represented by the graph, let's analyze the given information and the slope-intercept form of a linear equation (y = mx + b), where m represents the slope and b represents the y-intercept.

We are given two points on the line: (-3, -7) and (0, 2). Using these points, we can calculate the slope (m) as follows:

m = (y2 - y1) / (x2 - x1)

= (2 - (-7)) / (0 - (-3))

= 9 / 3

= 3

Therefore, the slope of the line is 3.

Next, we can substitute the slope and one of the given points into the slope-intercept form to find the y-intercept (b). Let's use the point (0, 2):

y = mx + b

2 = 3(0) + b

2 = b

So, the y-intercept (b) is 2.

Now we have the equation of the line: y = 3x + 2.

The shaded region is to the left of the line. To express this region as an inequality, we need to find the inequality symbol. Since everything to the left of the line is shaded, we need the inequality to represent values less than the line.

Therefore, the correct inequality is y < 3x + 2.

Hence, the linear inequality represented by the graph is y < 3x + 2. So Option A is correct.

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Note the complete question is

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.

Which linear inequality is represented by the graph?

A.) y < 3x + 2

B.) y > 3x + 2

C.) y < 1/3x + 2

D.) y > 1/3x + 2

AB=BC
A
60°
ODC
D
AB
374
B
The longest segment shown is
BC
C

Answers

Note that the longest segment in the shapes shown is DC (Option B).

How is this so?

The longest side of a triangle is opposite to greatest angle.

To determine the longest side in a triangle, compare the lengths of all three sides. The side with the greatest length is the longest side.

You can use a ruler or a measuring tool to measure the lengths of the sides or compare the numerical values if they are provided.

In this case,

∠A = ∠DBA = 60°

So ∠ ABD is an equilateral triangle.

So, AB = BD = AD

Since

AB = BC

Then

∠BDC = ∠C ∠ 38°

so ∠DBC > 90°

This means that DC is the longest side.

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anwser it pls aaaaaaaassaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Answers

Answer:

Step-by-step explanation:

Volume = Bh

Turn the shape so the trapezoid is on the bottom/base

h=18   for overall shape

B = area of base, trapezoid

B = 1/2 (b₁ + b₂) h  

b₁ = 11

b₂ = 25

h = 24   for trapezoid

B = 1/2 (11 + 25)(24)

B = 432

V = Bh

V = (432)(18)

V= 7776 in³

4
Number of Years
m
N
1
16
18
18°
19°
22°
30°
20
Mark this and return
28
22
24
26
Average Daily Temperature
30
The mean of the temperatures in the chart is 24° with a standard deviation of 4°. Which temperature is within one
standard deviation of the mean?
32
Save and Exit
Next
Submit

Answers

The temperature of 30° is within one standard deviation of the mean.

To determine which temperature is within one standard deviation of the mean, we need to consider the range that falls within one standard deviation above and below the mean.

Given that the mean temperature is 24° with a standard deviation of 4°, one standard deviation above the mean would be 24° + 4° = 28°, and one standard deviation below the mean would be 24° - 4° = 20°.

Looking at the temperatures in the chart, we can see that the temperature of 30° is within one standard deviation of the mean. It falls within the range of 28° (one standard deviation above the mean) and 20° (one standard deviation below the mean).

Therefore, the temperature of 30° is within one standard deviation of the mean.

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taber invested money in an account where interest is compounded every year. he made no withdrawals or deposits. the function A(t) = 525(1+0.05) represents the amount of money in the account after t years. how much money did taber originally invest?

Answers

hujc woudnakrifnsdjfowbdjdd

A requested task is subject to be reported when:

Answers

Answer:

A requested task is subject to be reported when it has been completed according to the instructions provided.

To demonstrate this with chain of thought reasoning:

1. The task requested will have details outlining what needs to be done.

2. To fulfill the request of the task, the instructions outlined must be followed.

3. Once all instructions are met, the task is complete.

4. Completion of the task means it is subject to be reported.

Step-by-step explanation:

. Initially 100 milligrams of a radioactive substance was present.
After 6 hours the mass had decreased by 3%. If the rate of
decay is proportional to the amount of the substance present at
time t, nd the amount remaining after 24 hours.

Answers

Answer:

Incomplete Question

how many pattern block rhombuses would 4 triangles create?

Answers

With 4 triangles, you can create a total of 3 pattern block rhombuses, depending on their arrangement.

To determine the number of pattern block rhombuses that can be created using 4 triangles, let's start by understanding the properties and arrangement of these shapes.

Pattern block rhombuses are a type of geometric shape commonly used in mathematics education. Each rhombus is made up of 2 triangles, specifically two congruent (equal) acute triangles. The triangles are placed together in a specific way to form the rhombus shape.

When 4 triangles are used, they can be arranged in different configurations to create different numbers of pattern block rhombuses. Let's explore the possibilities:

Arrangement 1:

In this arrangement, you can create 2 pattern block rhombuses. The triangles are placed side by side, with two triangles forming one rhombus, and the other two triangles forming another rhombus.

Arrangement 2:

In this arrangement, you can create 1 pattern block rhombus. The triangles are placed on top of each other, forming a larger triangle. Since a pattern block rhombus requires two acute triangles, only one rhombus can be formed in this case.

So, with 4 triangles, you can create a total of 3 pattern block rhombuses, depending on how the triangles are arranged.

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Select the correct answer.
Which expression is equivalent to
OA. 5 (¹
OB.
5 (x¹ - 4x² + 3)
2¹-4²+3
O c. 24
O D. 2¹-2²+3
4x² + 3
1
+3²? Assume that the denominator does not equal zero.

Answers

Answer:

B

Step-by-step explanation:

[tex]\frac{x^6-4x^4+3x^2}{5x^2}[/tex]

factor out the common factor of x² from each term on the numerator

= [tex]\frac{x^2(x^4-4x^2+3)}{5x^2}[/tex] ( cancel x² on numerator/ denominator )

= [tex]\frac{x^4-4x^2+3}{5}[/tex]

the image is the question
a) c = 22 feet
b) c = 23
c) c = 24
d) c = 30

Answers

The length of the triangle's hypotenuse (c) is approximately 22 feet. The closest option provided is "a) c = 22 feet."

The Pythagorean theorem, which asserts that given a right triangle, the sum of the squares of the two shorter sides (a and b), is equal to the square of the hypotenuse (c), can be used to determine the length of the triangle's hypotenuse (c).

a = 10 feet

b = 20 feet

Using the Pythagorean theorem, we can calculate c as follows:

c^2 = a^2 + b^2

c^2 = 10^2 + 20^2

c^2 = 100 + 400

c^2 = 500

To find c, we take the square root of both sides:

c = √500

c ≈ 22.36

Rounding the answer to the nearest whole number, we get c ≈ 22.

Therefore, the length of the triangle's hypotenuse (c) is approximately 22 feet. The closest option provided is "a) c = 22 feet."

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Evaluate. -15 +7-(-8)

The answer options are

16

0

-16

-3

Answers

Answer:

To evaluate -15 + 7 - (-8), we can simplify the expression by first removing the double negative.

-15 + 7 + 8 = 0

Therefore, the answer is 0.

Step-by-step explanation:

The answer is:

0

Work/explanation:

Remember the integer rule,

[tex]\bullet\phantom{4444}\sf{a-(-b)=a+b}[/tex]

Similarly

[tex]\sf{-15+7-(-8)}[/tex]

[tex]\sf{-15+15}[/tex]

Simplify fully.

[tex]\sf{0}[/tex]

Therefore, the answer is 0.

write 718000 in standard form

Answers

Answer:

718000

Step-by-step explanation:

718000 is already in standard form

7. What is the slope of a line that is perpendicular to the line represented by the equation y=-2/5x+4/5

5

5/4

2/5

5/2​

Answers

Answer:  the correct answer is 5/2

Step-by-step explanation:

To find the slope of a line perpendicular to a given line, we can use the property that the product of the slopes of two perpendicular lines is equal to -1.

The given line has an equation of y = -2/5x + 4/5.

The slope of this line can be determined by comparing it to the slope-intercept form (y = mx + b), where "m" represents the slope. In this case, the slope of the given line is -2/5.

To find the slope of the line perpendicular to this line, we take the negative reciprocal of the given slope. The negative reciprocal of -2/5 is 5/2.

The table shows the daily high temperature (°F) and the number of hot chocolates sold at a coffee shop for eight randomly selected days.

Answers

The line of best fit for the data in this problem is given as follows:

y = -0.5x + 60.

How to define a linear function?

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

m is the slope.b is the intercept.

Two points on the scatter plot are given as follows:

(30, 45) and (60, 30).

When x increases by 30, y decays by 15, hence the slope m is given as follows:

m = -15/30

m = -0.5.

Hence:

y = -0.5x + b.

When x = 30, y = 45, hence the intercept b is obtained as follows:

45 = -15 + b

b = 60.

Thus the function is given as follows:

y = -0.5x + 60.

Missing Information

The data is given by the image presented at the end of the answer, and the problem asks for the line of best fit for the data.

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Solve for x leave your answer in simplest radical form​

Answers

Answer:

X=11 trust me on my mom

What is the value of the expression (-2)(3)º(4)-2 ?
A. -3/2
B. -1/2
C. -3/4
D. 0

Answers

The value of the expression (-2)(3)º(4) - 2 is -164.

Based on the answer choices provided, none of the options matc.

To solve the expression (-2)(3)º(4)-2, we need to follow the order of operations, which is parentheses, exponents, multiplication, and subtraction.

Let's break down the expression :

(-2)(3)º(4) -2

First, we calculate the exponent:

(-2)(81) - 2

Next, we perform the multiplication:

-162 - 2

Finally, we subtract:

-164

Therefore, the value of the expression (-2)(3)º(4) - 2 is -164.

Based on the answer choices provided, none of the options match the value of -164.

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