70 points! Complete each proof using the most appropriate method.

Answer:

34

Step-by-step explanation:

34 trees will be left after 11 years

The probability that the standard normal deviation variable z is greater than 2.13 is approximately 0.017.

What is standard normal deviation?

The standard normal deviation is a normal distribution with a mean of 0 and a standard deviation of 1. It is also referred to as the standard normal distribution or the z-distribution.

Standardizing a normally distributed variable involves transforming it into a standard normal variable by subtracting the mean of the original distribution from each value and dividing the result by the standard deviation. This transformation is known as standardization or normalization.

According to the question:

Yes, you can use the "normcdf" function on a TI-84 calculator to find the probability that the standard normal deviation variable z is greater than 2.13. Here's how:

Press the "2nd" button, then the "Vars" button to access the DISTR menu.

Scroll down to "2: normalcdf(" and press ENTER.

Enter the lower limit as -9999 (or any number much smaller than -2.13) since we want to find the probability to the right of 2.13.

Enter the upper limit as 2.13.

Enter the mean as 0 and the standard deviation as 1 since we are working with a standard normal distribution.

Press ENTER to get the probability.

The result should be approximately 0.01744. Rounding to three decimal places, we get:

P(z > 2.13) ≈ 0.017.

Therefore, the probability that the standard normal deviation variable z is greater than 2.13 is approximately 0.017.

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Using null hypothesis, we can find that the researcher has done type II error in this case.

Hypothesis testing uses sample data from the population and draws conclusions about the population's probability distribution. It looks at a data assumption and uses a variety of methods for testing assumptions. The null hypothesis is rejected or not according to the results of the hypothesis test.

The chance of rejecting the null hypothesis when it is true is what is meant by type I error.

Probability of adopting the null hypothesis when it is untrue is the definition of type II error.

Here, CAPSULES is not actually 100 Mg and you have taken the decision of fail to reject the null hypothesis, (which means that accepting the null hypothesis) so, this is a type II error.

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The equation of the straight line is 4x -y = 13. It is general form of equation of a line.

What is a line?

A line has length but no width, making it a one-dimensional figure. A line is made up of several points that are endlessly extended in opposite directions. Two points in a two-dimensional plane determine it. Collinear points are described as two points that are on the same line.

The equation of a line that passes through the points (x₁, y₁) and (x₂, y₂) is

y - y₁ = [(y₂ - y₁)/(x₂ - x₁)](x - x₁).

The coordinates of the points are (4, 3) and (2, -5).

The slope of the line is (-5-3)/(2-4)

=-8/-2

= 4

The equation of line is

y - 3 = 4(x - 4)

→ y - 3 = 4x - 16

→ 4x -y = 13

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Answer:

Your answer is about t = 621.5 days the population of insect will equal to 1000.

Step-by-step explanation:

Given:

[tex]P(t)=200e^{0.01t}[/tex] and population equal to 1000?

You are trying to find t in number of days when the insect population reaches equal to 1000 so.

[tex]1000=200e^{0.01t}\\\\\frac{1000}{200}=e^{0.01t} \\\\500=e^{0.01t}\\\\ln(500)=0.01t\\\\t=\frac{ln(500)}{0.01} \\\\t=621.4608098[/tex]

Answer

109.861 days

Step-by-step explanation:

a) initial population means  when t=0, p(0)=500

b) dP/dt=5e^.01t

c)500e.01t =1000 (divide both sides of eq by 500)

  e.01t =2  (take natural log of both sides)

ln( e.01t)=ln(2)

.01t= ln(2) (divide both sides of the eq by .01)

t= ln(2)/.01

t=69.315 days

d) 500e.01t=1500

(repeat steps in (c) above and you will get)

t=ln(3)/.01

t=109.861 days

Each of these vertices, which together make up a full graph with five equation vertices, can be seen to be linked to the other four vertices in the subgraph.

A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A formal statement that proves the equality of two calculations is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two phrases that are inscribed on opposite sides of a letter. Frequently, the logo and indeed the particular software are identical. like in 2x - 4 = 2, for example.

This graph is not planar because it has a subgraph that is isomorphic to the whole, non-planar graph with five vertices (K5).

K5 is a non-planar graph as it cannot be represented in a planar manner on a 2D plane without at least five crossing edges. This graph is also non-planar since K5 is a subgraph of it.

We may determine five vertices that make up a whole subgraph, for instance, vertices 1, 2, 3, 5, and 6, to demonstrate that this graph has K5 as a subgraph. Each of these vertices, which together make up a full graph with five vertices, can be seen to be linked to the other four vertices in the subgraph.

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1. The fencing and grass for this playground cost $16,360.

2. Springfield's playground can hold approximately 800 kids at a density of 25 square feet per child.

3. We can recommend a rectangular playground measuring approximately 166 yards by 40 yards, with a total area of 6,666.67 square yards. This playground should cost $49,200 for the fencing and grass.

1. To calculate the cost of the fencing and grass, we first need to know the dimensions of the playground. Let's assume that the playground is a rectangular shape measuring 100 feet by 200 feet, for a total area of 20,000 square feet.

To determine the cost of the fence, we need to know how many rolls of fencing are required. Each roll is 50 feet long, so we need four rolls to fence the perimeter of the playground (100 + 100 + 200 + 200 = 600 feet / 50 = 12 rolls, but we can't buy half a roll, so we round up to four rolls). Therefore, the cost of the fence is:

4 rolls x $90/roll = $360

To determine the cost of the grass, we need to know how many square feet of grass we need to cover the playground. Since each roll of grass covers 500 square feet, we need:

20,000 sq ft / 500 sq ft per roll = 40 rolls of grass

Therefore, the cost of the grass is:

40 rolls x $400/roll = $16,000

Adding the cost of the fence and the grass, we get the total cost:

$360 + $16,000 = $16,360

So the fencing and grass for this playground cost $16,360.

2. To calculate how many kids per square yard the playground can hold, we need to know the area of the playground in square yards. There are 9 square feet in a square yard, so the playground measures:

20,000 sq ft / 9 sq ft per sq yd = 2,222.22 sq yds

Assuming that each child requires 25 square feet of space to play, we can calculate how many kids can fit on the playground:

2,222.22 sq yds x (9 sq ft per sq yd / 25 sq ft per child) = 800 kids

Therefore, Springfield's playground can hold approximately 800 kids at a density of 25 square feet per child.

3. To recommend a playground shape and size that would fit Wintermeadow's budget and hold at least 3 times as many kids as Springfield's playground at the same density of kids per square yard, we first need to know Wintermeadow's budget.

Let's assume that Springfield's budget is $50,000, so Wintermeadow's budget is $150,000.

To determine the size of the new playground, we can start by calculating the cost of the fencing and grass for Springfield's playground per square yard:

$16,360 / 2,222.22 sq yds = $7.38 per sq yd

We can then use this cost to estimate the size of the new playground. Let's assume that the new playground will also be rectangular, and that we want it to hold at least 3 times as many kids as Springfield's playground, or 2,400 kids. Using the same density of 25 square feet per child, we need:

2,400 kids x 25 sq ft per child = 60,000 sq ft

Since there are 9 square feet in a square yard, this is:

60,000 sq ft / 9 sq ft per sq yd = 6,666.67 sq yds

Multiplying this area by the cost per square yard, we get the cost of the fencing and grass for the new playground:

6,666.67 sq yds x $7.38 per sq yd = $49,200

Therefore, we can recommend a rectangular playground measuring approximately 166 yards by 40 yards, with a total area of 6,666.67 square yards. This playground should cost $49,200 for the fencing and grass.

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About 420 visitors might go to the food pantry on an extremely cold day

What is the percentage?

Percentage refers to a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%". For example, if 30 out of 100 students in a class are girls, the percentage of girls in the class is 30%. Percentages are commonly used in many fields, such as finance, statistics, and science, to express proportions, rates, and changes over time.

The problem states that on average, about 240 people visit the food pantry every day in search of groceries. To find out how many visitors might go to the food pantry on an extremely cold day, we need to use the given percentage increase.

The phrase "175% of the average amount" means that we need to find 175% of 240, which is the same as multiplying 240 by 1.75 (since 175% is the same as 1.75 as a decimal). Using the multiplication, we get:

175% of 240 = (175/100) * 240 = 420

So, on an extremely cold day, the number of visitors to the food pantry might be around 420.

Therefore, about 420 visitors might go to the food pantry on an extremely cold day.

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The values that make the inequality m + 4 > -6 true are -4, 0, and 5.

The values that make the inequality n - 3n ≤ 8 true are -4, 0, and 5.

The values that make the inequality -5 < 5f true are 0 and 5.

The values that make the inequality 7 ≤ -y + 7 true are -10, -4, 0, and 5.

An inequality for the statement "Hank's height (h) is less than or equal to 6 feet." is h ≤ 6.

An inequality for the statement "A magazine (m) cost more than $3.50" is m > $3.50.

An inequality for the statement "The temperature (t) is at least -5 degrees" is t ≥ -5.

In this exercise, we would evaluate the given inequalities as follows;

-4 + 4 > -6

0 > - 6 (True).

0 + 4 > -6

4 > - 6 (True).

5 + 4 > -6

9 > - 6 (True).

n - 3n ≤ 8

-4 - 3(-4) ≤ 8

8 ≤ 8 (True).

0 - 3(0) ≤ 8

0 ≤ 8 (True).

5 - 3(5) ≤ 8

-10 ≤ 8 (True).

Generally speaking, the phrase "at least" simply means or represents greater than or equal to and it can be denoted by this inequality symbol (≥).

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One major weakness of the constitution was that it failed to provide for the elective principle. In other words, no member of the Legislative Council was elected by Africans through the ballot box.

Tact is a term that B.F. Skinner used to describe a verbal operant which is controlled by a nonverbal stimulus and is maintained by nonspecific social reinforcement. Less technically, a tact is a label. Chapter five of Skinner's Verbal Behavior discusses the tact in depth.

here, we have,

Tameka's company is introducing a new invoicing and billing system as tameka is presenting the new system to the accounting team, she is careful to explain why the changes are important by the time she is done, the accounting team has shown their acceptance of the new procedures. this is likely because Tameka has used tact.

Tact is the ability to avoid upsetting or offending people by being careful not to say or do things that would hurt their feelings. implies the skill in dealing with persons or difficult situations of one who has a quick and delicate sense of what is fitting and thus avoids giving offense.

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The area of the image is 56ft²

A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object. If the scale factor is a whole number, the copy will be larger. If the scale factor is a fraction, the copy will be smaller.

The area scale factor is the square of the linear scale factor.

Therefore area scale factor = 2² = 4

Therefore the area of the image of the triangle = 14× 4

= 56ft²

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In a round-robin chess tournament with 4 players, a total of 6 games were played.

What is function ?

In mathematics, a function is a relation between a set of inputs (also called the domain) and a set of possible outputs (also called the range) with the property that each input is related to exactly one output.

The formula for the number of chess games, N, in a round-robin tournament with n players is:

N = (n(n-1))/2

When n = 4, the number of games played is:

N = (4(4-1))/2 = 6

So, in a round-robin chess tournament with 4 players, a total of 6 games were played.

To identify a point on the graph, we need to plot the values of n and N on a graph with n as the x-axis and N as the y-axis. We can then plot the point (4,6) on the graph, where 4 represents the number of players and 6 represents the number of games played in the tournament. This point corresponds to the intersection of the horizontal line n=4 and the vertical line N=6. The graph is shown below:

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Thus, using the matrix technique, the solutions to the simultaneous equations are x = -1 and y = 1.

A rectangular array of numbers or even other mathematical objects that can perform actions like addition and multiplication is known as a matrix. Matrices are widely used to describe systems of equations, transformations, and data in mathematics, physics, engineering, computer science, and many other disciplines. The individual matrix components are frequently identified by their row and column positions, and matrices have a predetermined number of rows and columns. There are numerous actions that can be carried out on matrices, including addition, subtraction, and multiplication by other matrices.

given

We can write the equations in matrix form as follows to answer the simultaneous equations 1x + 4y = 9 and 2x - 3y = 7 using the matrix method:

Then, on the left side of the equation, we can locate the inverse of the coefficient matrix:

| 1 4 |^-1 = 1/(-11) | -3 -4 |

|-2 -1 |

When we multiply both sides of the equation by the coefficient matrix's inverse, we obtain:

| x | | 1 4 |^-1 | 9 |

| x | | -3/11 -4/11 | | 9 |

| y | = | -2/11 -1/11 | x | 7 |

If we simplify, we get:

x = (-3/11)*9 + (-4/11)*7 = -1

y = (-2/11)

*9 + (-1/11)

*7 = 1

Thus, using the matrix technique, the solutions to the simultaneous equations are x = -1 and y = 1.

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Answer:

Below

Step-by-step explanation:

A) this one is easy....twice the manpower would take 1/2 the time = 1 hr

B) this requires a bit of calculation    find man-hrs required per lorry

    (3 men x 2 hr )/1 lorry = 6 man hours per lorry

              then:         5 men * x hr = 6 man hours

                    x =  6/5 hr    ( 1 hr 12 min)

C)  similar to B       2 men * x hr = 6 man hrs

                                         x = 6/2 hrs = 3 hrs

Answer:

see below

Step-by-step explanation:

more men = more hands = more help = less hrs cos faster

so your ans must be..

more men = less hrs

less men = more hrs

if...

3 men = 2hrs

1 man = 2hrs x 3 = 6hrs

so...

6 men = 6hrs ÷ 6 = 1 hr

5 men = 6hrs ÷ 5 = 6/5hr = 1 1/5hrs

2 men = 6hrs ÷ 2 = 3hrs

A plot of the given complex numbers is shown in the Argand diagram attached below.

In Mathematics, a complex number can be defined as any numerical quantity that comprises two main parts, which include a real number and an imaginary number.

In this exercise, you are required to plot the given complex numbers on an Argand diagram. Additionally, the sum and difference of the complex numbers z₁ and z₂ can be calculated as follows;

z₁ + z₂ = 5 + 2i + 1 + 3i

z₁ + z₂ = 6 + 5i

z₁ - z₂ = 5 + 2i - (1 + 3i)

z₁ - z₂ = 5 + 2i - 1 - 3i

z₁ - z₂ = 4 - i

In conclusion, we would use an online graphing calculator to plot all of the complex numbers as shown in the image attached below.

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Answer:

The graph will shift 5 units to the left

The correct answer is (b) Ratings with a high mean and a low mean absolute deviation.

What is the mean absolute deviation?

Mean absolute deviation (MAD) is a statistical measure of how much the data values in a set deviate from the mean of the set.

Given options are

a. Ratings with a high mean and a high mean absolute deviation

b. Ratings with a high mean and a low mean absolute deviation

c. Ratings with a low mean and a high mean absolute deviation

d. Ratings with a low mean and a low mean absolute deviation

The manager at Frydays wants to receive consistent, positive ratings by customers on social media over the next month. Consistency means that the ratings are close to each other, and positive ratings mean that they are higher than average. Therefore, the goal is to have ratings with a high mean and a low mean absolute deviation.

The mean is a measure of central tendency that represents the average rating of customers, and a high mean indicates that the ratings are positive. The mean absolute deviation (MAD) is a measure of dispersion that represents how spread out the ratings are from the mean. A low MAD indicates that the ratings are close to each other and consistent.

Hence, The correct answer is (b) Ratings with a high mean and a low mean absolute deviation.

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The surface area of right rectangular prism is equal to 150 square centimeter

The surface area of a right rectangular prism can be found by finding the sum of the area of each of the faces of the prism.

A = 2(lw + hl + hw)

Where, "l" is the length and "h" is the height and "w" is the width

To determine the surface area of right rectangular prism.

Given the paramters as;

length = 4 cm

width = 9 cm

height = 3 cm

Substituting the given values, we get;

A = 2(lw + hl + hw)

A = 2 (36 + 27 + 12)

A = 150

Thus,  surface area of right rectangular prism is 150 square centimeter

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Answer:

x = -5 and x =5

Step-by-step explanation:

However, we notice that the solutions -5 and 5 satisfy the original equation in case 2, because |-6(-5)| = 30 and |-6(5)| = 30 is true. Therefore, the two solutions that satisfy the original equation in both cases are x = 5 and x = -5.

Hence, the solution to the equation |-6x| = 30 is x = 5 and x = -5.

Answer: b + p ≤ 7

Step-by-step explanation:

Let's use b to represent the number of bags of popcorn purchased and p to represent the number of bags of pretzels purchased.

Since Cai can buy a maximum of 7 bags of popcorn and pretzels altogether, we know that:

b + p ≤ 7

This is the inequality that represents the possible values for the number of bags of popcorn purchased (b) and the number of bags of pretzels purchased (p).

Answer:

Yes, it will fit.

Step-by-step explanation:

To determine whether 375 cubic inches of sand will fit into the given rectangular prism, we need to calculate the volume of the prism and compare it to the amount of sand.

The formula for the volume of a rectangular prism is:

Volume = Base x Height x Width

In this case, the base of the prism is 5 by 7 inches, so the area of the base is:

Area of Base = 5 inches x 7 inches = 35 square inches

The height of the prism is 9 inches. Therefore, the volume of the prism is:

Volume = Base x Height = 35 square inches x 9 inches = 315 cubic inches

So, the volume of the prism is 315 cubic inches, which is less than the amount of sand Jack has (375 cubic inches). Therefore, all of the sand will fit inside the rectangular prism with room to spare.

In summary, the sand will fit inside the rectangular prism because the volume of the prism is greater than the amount of sand Jack has.

So, by resolving the given, we obtain the result: Hence, the two angles angles  have respective measurements of 18 degrees and 54 degrees.

An angle is a form in Euclidean geometry made composed of two rays, referred to as the angle's sides, that converge at a centre point known as the angle's vertex. In the plane where they are positioned, two rays may come together to make an angle. A planar collision produces an angle as well. Dihedral angles are what these are known as. A potential arrangement of two rays or lines that share a termination is called an angle in plane geometry. The Latin word "angulus," which means "horn," is where the English word "angle" originates. The intersection of the two rays, often referred to as the angles' sides, is known as the vertex.

Let's designate "x" for the smaller angle and "y" for the greater angle.

We understand the following from the problem:

x + y = 72 (the total of the measurements of two neighbouring angles equals 72) (the sum of the measures of two adjacent angles is 72)

x/y = 1/3 (the ratio of the smaller angle to the bigger angle is 1:3) (the ratio of the smaller angle to the larger angle is 1:3)

x/y = 1/3

x = (1/3)y

x + y = 72

(1/3)y + y = 72

(4/3)y = 72

y = (3/4) * 72

y = 54

Hence, 54 degrees is the greater angle.

We can now utilise the second equation once more to get the value of x:

x/y = 1/3

x/54 = 1/3

x = (1/3) * 54

x = 18

The smaller angle is 18 degrees as a result.

Hence, the two angles have respective measurements of 18 degrees and 54 degrees.

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Answer:

the answer is 28
4+62 = 66
66x2 = 132
132-20 = 112
112 divided by 4 = 28

hope this helps <3

Answer:

28

Step-by-step explanation:

i hope this helps

Answer:

[tex]\frac{49}{45}[/tex] OR [tex]1\frac{4}{45}[/tex]

Step-by-step explanation:

The area of the image of AQRS after dilation with scale factor 2 is 56 square feet.

Given the data in the question;

If we dilate a figure with a scale factor of 2, the area of the dilated figure will be 2² = 4 times the area of the original figure.

So, to find the area of the image of AQRS after dilation with scale factor 2, we just need to multiply the area of AQRS by 4:

Area of dilated image = 4 × Area of AQRS

Area of dilated image = 4 × 14

Area of dilated image = 56 square feet

Therefore, the area of the image of AQRS is 56 square feet.

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A = 4 ft × 3ft = 12 ft²

∴ The area of the base of the prism is 12 ft².

Answer:

Kara has 67 in total

Tyrone has 82 in total

and together they have 149

im not to sure what your asking but heres what i got...

Answer: P = 15N - 2t

Step-by-step explanation:

To find "P", we get rid of the last thing done to the subject (P).

Here it is "/15"

So we get rid of it by doing the opposite, remember, we do this to both sides.

Step 1:

             N = P - 2t/ 15

      x15 ↓                 ↓ ×15

              15N = P - 2t

Step 2:

Now, the last thing done to the "P" is "-2t". So we get rid of it by adding 2t to both sides.

                 15N = P - 2t

             +2t ↓             ↓ +2t

                  15N + 2t = P

So, we got P by its own, so we have made P the subject of the formula!

              N = P - 2t/ 15

      x15 ↓                 ↓ ×15

               15N = P - 2t  

           +2t ↓            ↓ +2t

               15N + 2t = P

               P = 15N - 2t

According to the information in the graph, the majority of women had children by the age of 20, while the majority of men had children by the age of 24.

The most important data of the age of women to have children according to the survey is that the majority of women had children at the age of 20 years. Additionally, that women began to have children from the age of fifteen to 40 years.

Based on the data in the graph, it can be inferred that most of the men had children by the age of 24. Additionally, these cover a range from 15 years to 41 years.

According to the survey data, we can establish that women had children at younger ages than men because women who had children are concentrated between the ages of 18 and 24, while men are more evenly distributed. between the ages of fifteen and 32.

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