Will 5 divided by 0.4 be rational or irrational and why

The altitude of the triangle ΔABC, can be constructed using a compass and a straight edge, using the method of constructing the perpendicular line segment from a point to a line.

The steps to construct the altitude to a line segment AB from the point C are as follows;

The line segment CG is the altitude from C to AB

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Answer:

x = 26

Step-by-step explanation:

sum of consecutive interior angles is 180

2(x + 15) + (3x + 20) = 180

2x + 30 + 3x = 160

5x = 130

x = 26

Answer:

value of x is 26.

Step-by-step explanation:

Given:

2(x+15)°+(3x+20)°=180°

Since the sum of angle of co interior angle is supplementary.

Solving for x.

2(x+15)°+(3x+20)°=180°

2x+30+3x+20=180

5x+50 =180

5x=180-50

5x=130

x=130/5

x=26

Therefore value of x is 26.

Alright, let's take this for a spin! We're gonna be using the binomial probability formula, which is kind of like a recipe to calculate the likelihood of something happening a specific number of times. The formula looks like this:

P(x; n, p) = C(n, x) * (p^x) * ((1 - p)^(n-x))

Where:

- P(x; n, p) is the probability of getting x successes in n trials,

- C(n, x) is the combination of n items taken x at a time (how many different ways we can get x successes),

- p is the probability of success on an individual trial (in this case, the chance a random student plans to go to college),

- x is the number of successes we want,

- n is the total number of trials (students),

- and (1 - p) is the probability of failure (a student not planning to go to college).

For all these problems, n = 19 (our number of students), and p = 0.72 (the percentage of students planning to go to college).

a.) To find the probability that all 19 students plan to attend college, we'd set x = 19. We plug in these values:

P(19; 19, 0.72) = C(19, 19) * (0.72^19) * ((1 - 0.72)^(19-19))

= 1 * (0.72^19) * (0.28^0)

= 0.72^19

= 0.0001 (rounded to four decimal places)

b.) Now, for the probability that exactly eleven of them plan to attend college, we set x = 11:

P(11; 19, 0.72) = C(19, 11) * (0.72^11) * ((1 - 0.72)^(19-11))

= 75582 * (0.72^11) * (0.28^8)

= 0.1013 (rounded to four decimal places)

c.) For the probability that at most fourteen of them plan to attend college, we need to add up the probabilities for x = 0 through 14:

P(x ≤ 14; 19, 0.72) = ∑ P(i; 19, 0.72) for i = 0 to 14

Calculating this might take a while by hand, so I'd recommend using a binomial distribution calculator. Doing so gives us approximately 0.5745.

d.) Finally, for the probability that at least seventeen of them plan to attend college, we add up the probabilities for x = 17, 18, and 19:

P(x ≥ 17; 19, 0.72) = P(17; 19, 0.72) + P(18; 19, 0.72) + P(19; 19, 0.72)

Again, I'd suggest a binomial distribution calculator for this. The result should be around 0.0258.

So, yeah, that's the way the cookie crumbles! Hope this helps you out, fam!

The standard deviation of the possible outcomes is approximately 3.46.

To calculate the standard deviation of the possible outcomes in a binomial trial, we use the formula:

σ = sqrt(n * p * (1 - p))

where σ is the standard deviation, n is the number of trials, and p is the probability of success.

In this case, the probability of success is 0.2, and the number of trials is 75. Plugging these values into the formula, we have:

σ = sqrt(75 * 0.2 * (1 - 0.2))

= sqrt(75 * 0.2 * 0.8)

= sqrt(12)

Evaluating the square root of 12, we find:

σ ≈ 3.464

Rounding to two decimal places, the standard deviation of the possible outcomes in this binomial trial is approximately 3.46.

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By using the graph the estimates for the solutions of each equation are as follows;

i) (-1, 5) and (2, 5).

ii) (-0.554, 2.446) and (1.804, 4.804).

In Mathematics and Geometry, a point of intersection is the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair with a point that corresponds to the x-coordinate and y-coordinate on a cartesian coordinate.

By critically observing the graph of the lines representing the given system of equations 4x² - 4x -3 = 5 and 4x² - 4x - 1 = x + 3, the solution is denoted by the point of intersection of both the x-coordinate and y-coordinate as shown in the image attached below.

4x² - 4x -3 = 5 are (-1, 5) and (2, 5).

4x² - 4x - 1 = x + 3 are (-0.554, 2.446) and (1.804, 4.804).

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Chronological order of transactions:

Accommodation at a rate of $100.00 CAD per night for May 12 & 13.

$15.00 movie rental charge for the afternoon of the 13th.

$40.00 room service charge for dinner on the evening of the 13th.

Mr. Ritz settling his account with his Visa card.

Hotel Guest Folio

Guest Name: Mr. Caesar Ritz

Room Number: 1010

Check-Out Date: May 14, 2023

Telephone: 905-575-1212

Fax: 905-575-2319

Guest Room Rate: $100.00 CAD per night

Chronological Order of Transactions:

May 12-13, 2023:

Accommodation at a rate of $100.00 CAD per night for May 12 & 13.

Debit: $200.00 CAD

May 13, 2023:

Afternoon movie rental charge of $15.00.

Debit: $15.00 CAD

May 13, 2023:

Room service charge for dinner of $40.00.

Debit: $40.00 CAD

May 14, 2023:

Settlement of the account with a Visa card.

Credit: $-255.00 CAD (Total charges: $200.00 + $15.00 + $40.00 = $255.00)

Balance Outstanding: $0.00 CAD

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Answer:

(X-5)

Step-by-step explanation:

tHANKS

(a) The average cost in 2011 is  

(b) A graph of the function g for the period 2006 to 2015 is shown below.

(c) Assuming that the graph remains accurate, its shape suggest that the average cost increases at a slower rate as time goes on.

Based on the information provided, we can logically deduce that the average annual cost (in dollars) for health insurance in this country can be approximately represented by the following function:

g(x) = -1736.7 + 1661.6Inx

where:

x = 6 corresponds to the year 2006.

For the year 2011, the average cost (in dollars) is given by;

x = (2011 - 2006) + 6

x = 5 + 6

x = 11 years.

Next, we would substitute 11 for x in the function:

g(11) = -1736.7 + 1661.6In(11)

g(11) = $2247.64

Part b.

In order to plot the graph of this function, we would make use of an online graphing tool. Additionally, the years would be plotted on the x-axis while the average annual cost would be plotted on the x-axis of the cartesian coordinate as shown below.

Part c.

Assuming the graph remains accurate, the shape of the graph suggest that the average cost of health insurance increases at a slower rate as time goes on.

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Complete Question:

The average annual cost (in dollars) for health insurance in a country can be approximated by the function g(x) = -1736.7 + 1661.6Inx, where x = 6 corresponds to the year 2006.

(a) Estimate the average cost in 2011.

(b) Graph the function g for the period 2006 to 2015

(c) Assuming that the graph remains accurate, what does the shape of the graph suggest regarding the average cost of health insurance?

The correct statements about the figure are:

(B) In the two similar triangles, Angle 1 and Angle 4 are alternate interior angles.

(C) Vertical angles prove that Angle 3 is congruent to Angle 6.

(D) The triangles are similar because alternate interior angles are congruent.

Vertical angles are formed when two lines intersect, and they are always congruent.In the two similar triangles, Angle 1 and Angle 4 are alternate interior angles.

Similarly, vertical angles are formed when two lines intersect, and they are always congruent. Here, vertical angles are Angle 3 and Angle 6, which means they are equal.

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The length of fencing that must be purchased to enclose the entire field is 459.7 feet.

To find the length of fencing required to enclose the entire field, we need to calculate the perimeter of the parallelogram.

Length of one side of the parallelogram = 208.8 feet

Length of another side of the parallelogram = 21.05 feet

Altitude to the longer side = 14.66 feet

The perimeter of a parallelogram can be calculated by adding the lengths of all four sides.

In this case, we have two pairs of congruent sides.

First, let's calculate the length of the longer side using the altitude:

Area of the parallelogram = base [tex]\times[/tex] altitude

Area = 208.8 feet [tex]\times[/tex] 14.66 feet

Area = 3057.408 square feet

Since the length of one side is 208.8 feet, the length of the other congruent side is also 208.8 feet.

Next, let's calculate the length of the shorter side:

Area = base [tex]\times[/tex] altitude

3057.408 square feet = 21.05 feet [tex]\times[/tex] altitude.

altitude = 145.38 feet

Now we have all the side lengths:

Side 1: 208.8 feet

Side 2: 21.05 feet

Side 3: 208.8 feet

Side 4: 21.05 feet.

To find the perimeter, we add all four sides:

Perimeter = 208.8 feet + 21.05 feet + 208.8 feet + 21.05 feet

Perimeter = 459.7 feet

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Therefore, 2 mL of the medication should be given if the patient is prescribed 500 mg.

To determine the volume of the medication to be given, we can set up a proportion using the concentration provided.

Given:

Reconstituted concentration: 250 mg/mL

Prescribed dosage: 500 mg

Let's assume the volume to be given is "x" mL.

We can set up the following proportion

250 mg/1 mL = 500 mg/x mL

To solve for "x," we can cross-multiply and solve the equation:

250x = 500 * 1

250x = 500

x = 500/250

x = 2

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Answer:

Last option (4th option)

Step-by-step explanation:

Parallel lines have the same slope and the only choice that has the same slope of 3/4 is the last option

The probability that either four students out of the 10   students are females or four students outof the 10 students would like to take Math for Business next semester is approximately 0.206 or 20.6%.

The probability of Event A (Four students are females) can be calculated as follows  -

P(A) = (0.2)⁴ * (0.8)⁶ * (10 C 4)

    = 0.0016 * 0.4096 * 210

    ≈ 0.135

The probability of Event B (Four students would like to take Math for Business) can be calculated as follows:

P(B) = (0.6)⁴ * (0.4)⁶ * (10 C 4)

    = 0.1296 * 0.0256 * 210

    ≈ 0.071

To calculate   the probability of either Event A OR Event B occurring,we sum the probabilities:

P(A or B) = P(A) + P(B)

         ≈ 0.135 + 0.071

         ≈ 0.206

Hence,  the probability that either four students out of the 10 students are females or 4students out of the 10 students would like to take Math for Business next semester is approximately 0.206 or 20.6%.

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Ray uses 1/4 of a gallon of gasoline to drive a distance of 5 1/2 miles. At this rate, Ray can drive 22 miles on 1 gallon of gas.

Let's analyze the given information:

Ray uses 1/4 of a gallon of gasoline to drive a distance of 5 1/2 miles.

We need to determine how many miles Ray can drive on 1 gallon of gas. To do this, we'll calculate the rate of gas consumption in terms of miles per gallon.

Rate of gas consumption = Distance traveled / Gas used

Gas used = 1/4 gallon

Distance traveled = 5 1/2 miles = 5 + 1/2 = 11/2 miles

Now, let's substitute the values into the formula:

Rate of gas consumption = (11/2) miles / (1/4) gallon

To divide by a fraction, we can multiply by its reciprocal:

Rate of gas consumption = (11/2) miles * (4/1) gallon

Simplifying:

Rate of gas consumption = (11 * 4) miles / (2 * 1) gallon

Rate of gas consumption = 44 miles / 2 gallon

Rate of gas consumption = 22 miles per gallon

Therefore, based on the given information, Ray can drive 22 miles on 1 gallon of gas.

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Question

Ray uses 1/4 of a gallon of gasoline to drive a distance of 5 1/2 miles. At this rate, how many miles can he drive on 1 gallon of gas?

Ray can drive ???? miles on 1 gallon of gas.

The correct answer is: The median stays 6.5.

The median is the middle value in a set of data. First, organize and order the data from smallest to largest. To find the midpoint value, divide the number of observations by two. If there are an odd number of observations, round that number up, and the value in that position is the median.

The median is the value in the middle of a data set, meaning that 50% of data points have a value smaller or equal to the median and 50% of data points have a value higher or equal to the median.

To determine how the median changes when a shoe size of 4 is added to the data, we need to arrange the shoe sizes in ascending order:

4, 5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8.5

The median is the middle value in a sorted list. In this case, since there are 10 values, the median is the average of the two middle values: 6.5 and 6.5. So, the median is 6.5.

Adding a shoe size of 4 to the data does not affect the median because the new value is lower than all the other values in the list. Therefore, the median stays the same at 6.5.

So, the correct answer is: The median stays 6.5.

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To find the combined rate of all the individuals working together, you must add the individual rates.

When calculating the combined rate of individuals working together, you need to add up the individual rates. Each worker contributes their own rate of work or productivity, and by adding these rates together, you can determine the combined rate at which they are working collectively.

This allows you to assess the overall efficiency and output of the team or group. By summing up the individual rates, we have better understanding of the overall productivity and performance of the group.

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To pay off the balance of $7000 on a credit card with an APR of 16.99% in 2 years, the monthly payment to be made is $349.11. So, the correct option is (a) $349.11.

What is APR?

APR stands for Annual Percentage Rate, which is the rate at which credit is issued and expressed as a yearly rate. Interest and fees are included in the APR, which makes it the most precise way to determine the actual expense of borrowing.

What is monthly payment?

A monthly payment is an amount of money that is paid to a creditor or lender every month as part of a loan or debt repayment plan. The monthly payment must be sufficient to pay off the interest accrued during the month and a portion of the principal balance to make a dent in the outstanding debt owed.

What is the formula for calculating monthly payments?

The formula for calculating monthly payments is: Monthly Payment = [APR/12 × (Present balance)] / [1 - (1 + APR/12)-n], Where APR is the Annual Percentage Rate, Present balance is the amount owed, n is the number of payments to be made. To pay off the balance of $7000 on a credit card with an APR of 16.99% in 2 years, the monthly payment to be made is $349.11. Therefore, the correct option is (a) $349.11.

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The coordinates of the triangle after the translation are given as follows:

R'(0, 5), S'(7, 8), T'(0, -1).

The four translation rules are defined as follows:

The figure is translated 4 units right and 3 units up, hence the rule is given as follows:

(x, y) -> (x + 4, y + 3).

The original coordinates are given as follows:

R(-4,2), S(3,5) and T(-4,-4).

Hence the translated coordinates are given as follows:

R'(0, 5), S'(7, 8), T'(0, -1).

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For 37 students, the cost will be the same, and the cost will be $37 (option b).

To find the number of students for which the total cost of each field trip is the same, we need to equate the two cost equations and solve for x.

Equating the cost equations:

25 + 3x = 33 + x

Simplifying the equation:

3x - x = 33 - 25

2x = 8

Dividing both sides by 2:

x = 4

Therefore, for 4 students, the cost will be the same. To find the cost, we substitute this value of x into either of the cost equations. Let's use the second equation:

y = 33 + x

y = 33 + 4

y = 37

Hence, for 4 students, the cost will be the same, and the cost will be $37.

However, it seems there was an error in the given options. The correct answer is not provided. Let's continue solving for the correct answer.

To find the correct number of students and the corresponding cost, we can substitute different values of x into the cost equations and see where the costs are the same.

Substituting x = 1 into the cost equations:

Cost (S) = 25 + 3(1) = 28

Cost (S) = 33 + 1 = 34

Substituting x = 2 into the cost equations:

Cost (S) = 25 + 3(2) = 31

Cost (S) = 33 + 2 = 35

Substituting x = 3 into the cost equations:

Cost (S) = 25 + 3(3) = 34

Cost (S) = 33 + 3 = 36

Substituting x = 4 into the cost equations:

Cost (S) = 25 + 3(4) = 37

Cost (S) = 33 + 4 = 37

As we can see, for x = 4, the costs are the same at $37. Therefore, the correct answer is: For 4 students, the cost will be the same, and the cost will be $37.

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The solutions to the two inequalities is (-0.5, 2.5) as shown in the attached graph.

The inequalities we have are given as:

y ≤ −3x + 1

y ≤ x + 3

Step1 :  Remove the inequalities

This gives us:

y = −3x + 1

y = x + 3

Step2 :  Finding intersection points of equations

x + 3 = -3x + 1

4x = -2

x = -0.5

Plug in -0.5 for x in the second equation to get:

y = -0.5 + 3

y = 2.5

Thus, intersection point is: (-0.5, 2.5)

Step 3: Test of origin (0,0)

If inequalities holds true for origin then, shades the graph towards the origin.

For equation 1.

y = −3(0) + 1

y = 1

0 ≤ 1

True, Shade graph towards origin.

For equation 2.

y = x + 3

y = 0 + 3

y = 3

0 ≤ 3

True, Shade graph towards origin.

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Complete question is:

Choose the graph that represents the following system of inequalities:

y ≤ −3x + 1

y ≤ x + 3

In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB.

Answer:

Step-by-step explanation:

Let 's x the length of the pyramid:

V=x²*h/3

V=1024 and h=12

So x²*12/3=1024

==>x²=1024*3/12

==>x²=256

==>x²=16²

==> x=16 for (x=-16 must be exclude <0)

......brainpower pts pls

Mrs. Tan poured in approximately 31.04 liters of water.

To find the volume of water poured by Mrs. Tan, we need to calculate the difference between the initial volume of water poured by Mr. Tan and the final volume of water in the tank.

The initial volume of water poured by Mr. Tan is given as 8000 cm³.

The dimensions of the tank are given as 48 cm (length) and 24 cm (width). The depth to which Mrs. Tan poured the water is given as 20 cm.

To calculate the final volume of water, we need to consider the additional volume poured by Mrs. Tan. This additional volume can be calculated by multiplying the area of the base (length × width) by the depth.

The area of the base = 48 cm × 24 cm = 1152 cm².

The additional volume poured by Mrs. Tan = 1152 cm² × 20 cm = 23,040 cm³.

Now, to find the total volume of water in the tank after Mrs. Tan poured the water, we add the initial volume (8000 cm³) to the additional volume (23,040 cm³):

Total volume = 8000 cm³ + 23,040 cm³ = 31,040 cm³.

Finally, to convert the volume from cm³ to liters, we divide by 1000 (since 1 liter = 1000 cm³):

Total volume in liters = 31,040 cm³ / 1000 = 31.04 liters.

Therefore, Mrs. Tan poured in approximately 31.04 liters of water.

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i. The first two terms of the series are 50/3 and 100/9, and the fifth term is 800/243.

ii. the first two terms of the series are 0 and 3, and the fifth term is 48.

(i) The formula for the nth term of the series is given by:

nothing term = 25(2/3[tex])^n[/tex]

first two terms,  substitute n=1 and n=2 into the formula

1st term = [tex]25(2/3)^1 = 25(2/3) = 50/3[/tex]

2nd term = [tex]25(2/3)^2 = 25(4/9) = 100/9[/tex]

To find the fifth term,  substitute n=5 into the formula

Fifth term: nothing term = 25(2/3[tex])^5[/tex] = 25(32/243) = 800/243

Hence, the first two terms of the series are 50/3 and 100/9, and the fifth term is 800/243.

(ii) The formula for the nth term of the series is given by:

nth term = [tex]3(n-1)^2[/tex]

To find the first two terms, we can substitute n=1 and n=2 into the formula

First term= [tex]3(1-1)^2 = 3(0)^2 = 0[/tex]

Second term= [tex]3(2-1)^2 = 3(1)^2 = 3[/tex]

To find the fifth term, we can substitute n=5 into the formula:

Fifth term: nth term = 3(5-[tex]1)^2[/tex] = 3(16) = 48

Thus, the first two terms of the series are 0 and 3, and the fifth term is 48.

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Answer:

I think it is √(79) + √(63)  is last, √(143). 2nd , 4π 1st

I could be very wrong... Forgive me if im wrong.

Step-by-step explanation:

Answer:

the answer is 150 degrees because it is the biggest

The value of angle x is 149°

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

Since MN and OP are parallel lines, we can introduce a transverse that will cut through Q and extend the parallel lines of MN and OP

Therefore;

The adjascent angle of N will be

180-138 = 42°

This means that angle Q is divided into 42° and 31° i.e 42+31 = 73°

This means the adjascent angle of P is 31°( alternate angles)

Therefore x = 180-31

x = 149°

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Answer:

We have parallelogram ABCD, with BC as the diagonal, so alternate interior angles are congruent.

100° + 30° + x = 180°, so x = 50°

The value of the missing leg from the triangle that has been shown is 8 mi .

The Pythagorean theorem provides a way to find the length of one side of a right-angled triangle if the lengths of the other two sides are known. It is widely used in various fields, such as engineering, architecture, physics, and trigonometry, to solve problems involving right triangles and calculate distances, angles, or other related quantities.

We know that;

[tex]c^2 = a^2 + b^2\\b^2 = 10^2 - 6^2[/tex]

b = 8 mi

The Pythagorean theorem is named after the ancient Greek mathematician Pythagoras

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The equation of the possible way to begin solving for x is 2/5x - 7/20x = 3/4 - 1/2

From the question, we have the following parameters that can be used in our computation:

-3/4 + 2/5x = 7/20x -1/2

The first step is to collect the like terms

So, we have

2/5x - 7/20x = 3/4 - 1/2

This represents an equation of the possible way to begin solving for x

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