4.
[2020/Canberra Sec]
The numbers 1450 and 2400, written as a product of its prime factors are
2x5²x29 and 25×3×52 respectively. Find
(a) the largest integer which is a factor of both 1450 and 2400,

the perimeter of the figure is approximately 48.56 cm.

The perimeter of a shape in geometry refers to its whole boundaries. The lengths of a shape's edges and sides are added to find its perimeter.

from the question:

The lengths of all the figure's sides must be added up in order to determine their perimeter.

The rectangle has two sides that are 10 cm long and two that are 8 cm long, making its perimeter:

P_rect = 2(10 cm) + 2(8 cm) = 36 cm

Since it shares a side with the rectangle, the quarter circle has a radius of 8 cm and an arc length that is one-fourth of the circle's diameter, which is:

L_circle = (1/4)(2πr) = (1/4)(2π)(8 cm) = 4π cm

Therefore, the perimeter of the figure is:

P = P_rect + L_circle = 36 cm + 4π cm ≈ 48.56 cm

The figure's perimeter, when rounded to two decimal places, is roughly 48.56 cm.

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Hence the product of the slope of RT and SU is -1, so the lines are perpendicular

RS=ST, Hence RS, and ST are congruent to each other, which is why it is a rhombus.

A particular type of rhombus is a parallelogram. In a rhombus, the opposing sides and angles are parallel and equal. The diagonals of a rhombus meet at right angles to form its shape, and it also has equal-length sides on each side. Another name for the rhombus is a diamond or rhombus. The plural of a rhombus is a rhombus or rhombuses.

Quadrilateral RSTU has vertices at T(1,11), S(9,12), T(13,5) and U(2,-2).

The slope RT is k[tex]=-\frac{1}{2}[/tex] and the slope SU is [tex]l=2[/tex]

[tex]kl=-1\\\\RS=\sqrt{8^2+1}=\sqrt65\\and ST=\sqrt(65)\\\\[/tex]

RS=ST ,

hence RS is congurent to ST

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The sum of the measures of the interior angles of an 11-sided polygon is 1620 degrees.

The formula to find the sum of the measures of the interior angles of a polygon is:

Sum of interior angles = (n - 2) × 180 degrees

Where n: number of sides of the polygon.

Using this formula, we can find the sum of the measures of the interior angles of a polygon with 11 sides:

Sum of interior angles = (11 - 2) × 180 degrees

Sum of interior angles = 9 × 180 degrees

Sum of interior angles = 1620 degrees

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The area of the circle given a diameter of 24 inches is 452 square centimeters

To calculate the area of a circle with a diameter of 24cm, we first need to find the radius.

The radius is half the diameter, so it would be 12cm.

Once we have the radius, we can use the formula for the area of a circle, which is A = πr².

Substituting the value of the radius into the formula gives us:

A = π(12)² = 144π

Evaluate

A = 452cm²

Hence, the area of the circle is 144π square centimeters or 452cm²

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1, 3, -4

Second-degree functions are known as quadratics.

Quadratic Functions

Quadratic functions are second-degree. This means that the highest exponent of any term is 2. When graphed, quadratic functions form parabolas, which look like U-shape.

To find the a, b, and c values of a quadratic, the function must be set equal to zero and in standard form. Remember that standard form is when the terms are written in descending order of degree (exponent). This equation given is already set equal to zero and in standard form.

Standard Form

When in standard form, quadratics are written like ax^2+bx+c. The coefficients go in alphabetic order.

This means that for the given equation: a = 1, b = 3, c = -4. These values can be used in different ways, mainly the quadratic equation.

Answer:

The number of rooms he can wire with 3/4 of a roll of wire is 1/4.

What are proportions?

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Given that, an electrician needs 3 rolls of electrical wire to wire each room in a house.

Let the number of rooms he can wire with 3/4 of a roll of wire be x.

Now, the proportion is

3/1 = 3/4/x

3x=3/4

x=1/4

Therefore , the solution of the given problem of probability comes out to be a random result will be produced with a success probability equal to the specified success rate of 0.702.

Finding the likelihood that a claim is true or that a specific event will occur is the primary objective of the branch of mathematics known as parameter estimation. Any number between range 0 but rather 1, where 1 is usually used to symbolise certainty and 0 is typically used to represent possibility, may be utilized to represent chance. A probability diagram shows the chance that a specific event will occur. .

Here,

Here is a potential Python method for modelling the subsequent pass:

Python: import the random package.

import arbitrary

0.702 is the desired performance rate:

makefile

success rate for copying is 0.702

The random.random() function can be used to produce a random integer between 0 and 1:

random.random rand num ()

Simulate the pass being caught if the random number is less than or equivalent to the success rate. If not, pretend that the throw was not caught:

python

output if rand num = success rate ("The pass is caught.")

if not: output ("The pass is not caught.")

Every time this process is executed, a random result will be produced with a success probability equal to the specified success rate of 0.702.

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A group of penguins swam 4/5 mile in 1/3 hour, [tex]\frac{4*3}{5}=\frac{12}{5}[/tex]  miles did the penguins swim in one hour.

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

We frequently employ these fundamental mathematical operations in our daily lives: +, -,, and. We employ mathematical operations for every situation when we must determine the annual budget or distribute things equitably to a lot of people.

[tex]\frac{4}{5}[/tex] miles swim in [tex]\frac{1}{3}[/tex] hour

swim in one hour = [tex]\frac{4*3}{5}=\frac{12}{5}[/tex] mile

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Answer: To prove the relationship between segments AB and CD, we need to determine if they are parallel, perpendicular, or neither.

First, let's find the slope of line AB:

y − 9 = −4(x + 1)

y − 9 = −4x − 4

y = −4x + 5

So the slope of line AB is -4.

Now let's find the slope of line CD:

y − 6 = one fourth(x − 3)

y − 6 = (1/4)x − (3/4)

y = (1/4)x + (21/4)

So the slope of line CD is 1/4.

Since the slopes of the two lines are not equal and not negative reciprocals, they are neither parallel nor perpendicular. Therefore, we cannot determine the relationship between segments AB and CD based on the given information.

Step-by-step explanation:

To simplify 3(w+11) /6w, we can first simplify the numerator by distributing the 3:

3(w+11) = 3w + 33

Now we have:

(3w + 33) / 6w

We can further simplify by factoring out a 3 from the numerator:

3(w + 11) = 3 * 1(w + 11)

So we have:

(3 * 1(w + 11)) / 6w

The 3's cancel out, leaving:

(w + 11) / 2w

Therefore, the fully simplified expression is (w + 11) / 2w.

The original price of the car is 85,000. b. The car loses 3,400 in value per year. c. The car will totally depreciate after 25 years. This is because 85,000 divided by 3,400 equals 25.

Value in math is the result of a mathematical operation or equation. It is a number or quantity assigned to a mathematical expression. Value can also refer to the worth of an object or activity, such as the value of a specific type of currency or the value of a certain action. Value can refer to the magnitude of a number or a quantity relative to other numbers or quantities, such as the value of a particular number on a scale.

a.  The original price of the car can be calculated by setting x=0 in the equation, which gives 85,000. This means that the original price of the car is 85,000.

b. The value of the car decreases by 3,400 per year. This is calculated by looking at the coefficient of x in the equation, which is −3,400. This means that for every year that passes, the value of the car decreases by 3,400.

c. The car will take 25 years to totally depreciate. This is calculated by setting the equation equal to 0 and solving for x. The equation 0 = −3,400x + 85,000 can be rearranged to x = 25. This means that the car will take 25 years to totally depreciate.

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Answer: 592

Step-by-step explanation:

A=2(wl+hl+hw)

A=2(8*10+12*10+12*8)=592

Answer[tex]n^{2} -4n+4[/tex]

Step-by-step explanation:

had to keep the minus than add a plus sign

Answer:

im sure this isnt much help but i  used desmos and i  got the answer 0.5 w

Step-by-step explanation:

heres what i did on the calculator. i did what the screen shows it shows an adjacent(4) and the opposite(2) so therefor i  did the obvious evaluation and thought oppostie over adjacent which is tangent formula by the way. so then i  did tan(2/4) and got 0.008726867791 and then did what a video that i  watched to refresh myself on this topic. so the video said that after that your supposed to do tan-1(0.00872687791) and then i  got 0.5... not sure if that makes sense. i  typed alot so ill just link the video for you to watch.

https://youtu.be/Rbxb6DOjarI

(a) The probability that at least half the patients are under 15 years old is  0.01562.

(b)  The probability that from 2 to 5 patients are 65 years old or older is, 0.92179.

(c) The probability that from 2 to 5 patients are 45 years old or older is, 0.9216.
(d) The probability that all the patients are under 25 years of age is  0.00065.

(e) The probability that all the patients are 15 years old or older is 0.16777.

(a) We can model this situation as a binomial distribution with 8 trials, where success is a visitor age being under 15 years old and the probability of success is unknown.

To find the probability that at least half the patients are under 15 years old, we can use the binomial cumulative distribution function.

Assume that the probability of success (visitor age under 15) is 0.5,

The probability of at least half of the patients being under 15 is,

⇒ P(X ≥ 4) = 1 - P(X < 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3))

                   = 1 - (0.03125 + 0.21875 + 0.42188 + 0.3125)

                    = 0.01562

Therefore,

The probability that at least half the patients are under 15 years old is  0.01562.

(b) To find the probability that from 2 to 5 patients are 65 years old or older,

First find the probability of each individual case and then add them up. The probability of success (visitor age being 65 or older) on a single trial is unknown.

Assume it is 0.2. Then,

⇒ P(X = 2) = 0.29376 P(X = 3)

                 = 0.32496 P(X = 4)

                 = 0.21499 P(X = 5)

                 = 0.08808

Therefore, the probability that from 2 to 5 patients are 65 years old or older is,

⇒ P(2 ≤ X ≤ 5) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

                           = 0.29376 + 0.32496 + 0.21499 + 0.08808

                           = 0.92179

(c) To find the probability that from 2 to 5 patients are 45 years old or older,

We need to use a different probability of success for each individual case, depending on the age of the patients scheduled for the day.

Assume that the probability of success (visitor age being 45 or older) is 0.6. Then,

⇒ P(X = 2) = 0.2304 P(X = 3)

                 = 0.3456 P(X = 4)

                 = 0.2592 P(X = 5)

                 = 0.0864

Therefore, the probability that from 2 to 5 patients are 45 years old or older is,

⇒ P(2 ≤ X ≤ 5)  = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

                            = 0.2304 + 0.3456 + 0.2592 + 0.0864

                            = 0.9216

(d) To find the probability that all the patients are under 25 years of age, we can assume that the probability of success (visitor age under 25) is unknown.

Assume it is 0.3. Then,

⇒ P(X = 8) = [tex]0.3^8[/tex]

                 = 0.00065

Therefore, the probability that all the patients are under 25 years of age 0.00065.

(e) To find the probability that all the patients are 15 years old or older, we can assume that the probability of success (visitor age being 15 or older) is unknown.

Assume it is 0.8. Then,

⇒ P(X = 8) = [tex]0.8^8[/tex]

                 = 0.16777

Therefore, the probability that all the patients are 15 years old or older is approximately 0.16777.

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The angles are classified as follows

angle 1 angle of elevation

angle 2 angle of depression

angle 3 angle of elevation

angle 4 angle of depression

The angle of elevation is the angle between the horizontal plane and the line of sight or upward direction to an object or point that is above the observer. It is usually measured from the observer's eye to the object or point of interest, and is expressed in degrees or radians.

The angle of elevation is commonly used in trigonometry to solve problems involving right triangles and heights of objects.

The angle of depression is the angle between the horizontal plane and the line of sight or downward direction to an object or point that is below the observer. It is measured from the observer's eye to the object or point of interest, and is also expressed in degrees or radians.

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Answer:

2000 pounds

Step-by-step explanation:

Let's start with the initial amount of gravel in the mound, which is g pounds.

After 300 pounds are added, the total amount of gravel in the mound becomes:

g + 300

Then, two orders of 600 pounds are sold and removed from the mound. So, the total amount of gravel in the mound after these two orders are sold becomes:

g + 300 - 2(600) = g + 300 - 1200 = g - 900

Finally, we know that at the end of the day, the mound has 1400 pounds of gravel. So, we can set up an equation:

g - 900 + 300 = 1400

Simplifying this equation, we get:

g - 600 = 1400

Adding 600 to both sides, we get:

g = 2000

Therefore, the initial amount of gravel in the mound was 2000 pounds.

Answer:

2000 pounds

Step-by-step explanation:

sorry it took a while;)

The answer of the given question based on the exponential random variable with mean  i.e. [tex]\mu o \leq \bar x + \frac{z \alpha \sigma}{\sqrt{n} }[/tex].

The null hypothesis is  statement or assumption about population parameter that is tested for its validity using statistical methods. It is  statement of no effect, no difference, or no relationship between the variables of interest,

(a) To test the null hypothesis  [tex]H$ o: \mu =\mu o[/tex], we can use a one-sided test with rejection region R =  [tex]\bar x \geq \mu o + \frac{z \alpha \sigma}{\sqrt{n} }[/tex], is the critical value from the Standard Normal distribution that corresponds to a significance level of α = 0.10 (since we want a 90% confidence interval). If the observed sample mean  falls in the rejection region R, we reject the null hypothesis and conclude that the true mean μ is greater than μ0 with 90% confidence.

To find the confidence interval of the form [∗,[infinity]), we can solve the inequality   [tex]\bar x \geq \mu o + \frac{z \alpha \sigma}{\sqrt{n} }[/tex]  for [tex]\mu[/tex] which gives:

[tex]\mu o \leq \bar x - \frac{z \alpha \sigma}{\sqrt{n} }[/tex]

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Research scenariο wοuld mοst likely be biased against nοn-vοters are :

Bias in research refers tο a systematic deviatiοn frοm the truth in the results οf a study, usually due tο factοrs that affect the sampling, measurement, οr analysis οf data. A research scenariο is biased against nοn-vοters if it systematically under-represents οr misrepresents the views, οpiniοns, οr behaviοrs οf peοple whο dοn't vοte in the sample οr pοpulatiοn under study.

In the given οptiοns, the scenariοs that are biased against nοn-vοters are:

Therefοre, research scenariο wοuld mοst likely be biased against nοn-vοters are :

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Answer:

Step-by-step explanation:

[tex]\frac{3x+9}{12x} \\we \ can \ write \ 3x+9 \ as 3(x+3)\\\frac{3x+9}{12x}=\frac{3(x+3)}{3*4x}=\frac{x+3}{4x}[/tex]

Answer:

[tex]\frac{x+3}{4x}[/tex]

Step-by-step explanation:

[tex]\frac{3(x)+9}{12x}[/tex]

[tex]\frac{3(x+3)}{12x}[/tex]

The simplification of the following equations will be:[tex]4\sqrt{3}\ \ 6\sqrt{2}\ \ 20\sqrt{3}\ \ 5\sqrt{5}\ \ 50\sqrt{3}\ \ 24\sqrt{2}\ \ 20\sqrt{7}\ \ 6\sqrt{15}\ \ 40\ \ 21\sqrt{2}\ \ 10\sqrt{11907}[/tex].

Prime factorization is the process of transforming a number into a prime product. A prime number simply has the number itself and the number itself as its two components. The prime numbers, for instance, are 2, 3, 5, 7, 11, 13, and 19. Any integer can be expressed as the sum of prime integers thanks to prime factorization.

[tex]$\sqrt{48} = \sqrt{16 \cdot 3} = \sqrt{16} \cdot \sqrt{3} = 4 \sqrt{3}$[/tex]

[tex]$\sqrt{72} = \sqrt{36 \cdot 2} = \sqrt{36} \cdot \sqrt{2} = 6 \sqrt{2}$[/tex]

[tex]$\sqrt{1200} = \sqrt{400 \cdot 3} = \sqrt{400} \cdot \sqrt{3} = 20 \sqrt{3}$[/tex]

[tex]$\sqrt{125} = \sqrt{25 \cdot 5} = \sqrt{25} \cdot \sqrt{5} = 5 \sqrt{5}$[/tex]

[tex]$\sqrt{98}$[/tex] 98 already has the simplest root form, since it does not have a perfect square factor.

[tex]$\sqrt{7500} = \sqrt{25 \cdot 300} = \sqrt{25} \cdot \sqrt{300} = 5 \sqrt{300} = 5 \sqrt{100 \cdot 3} = 5 \cdot 10 \sqrt{3} = 50 \sqrt{3}$[/tex]

[tex]$6 \sqrt{32} = 6 \sqrt{16 \cdot 2} = 6 \sqrt{16} \cdot \sqrt{2} = 6 \cdot 4 \sqrt{2} = 24 \sqrt{2}$[/tex]

[tex]$10 \sqrt{28} = 10 \sqrt{4 \cdot 7} = 10 \sqrt{4} \cdot \sqrt{7} = 20 \sqrt{7}$[/tex]

[tex]$3 \sqrt{60} = 3 \sqrt{4 \cdot 15} = 3 \sqrt{4} \cdot \sqrt{15} = 6 \sqrt{15}$[/tex]

[tex]$5 \sqrt{64} = 5 \cdot 8 = 40$[/tex]

[tex]$7 \sqrt{18} = 7 \sqrt{9 \cdot 2} = 7 \sqrt{9} \cdot \sqrt{2} = 21 \sqrt{2}$[/tex]

[tex]$\sqrt{1190700} = \sqrt{100 \cdot 11907} = \sqrt{100} \cdot \sqrt{11907} = 10 \sqrt{11907}$[/tex]

So the above are the prime factors of the given equation. Among them, the square root is not exact. 

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Answer:

A triangular prism.

Step-by-step explanation:

Answer: Triangular prism

Step-by-step explanation:

A triangular prism is a three dimensional shape, consisting of two triangular and three rectangular faces. Based on the image provided, and the description of a triangular prism, we can deduct this three dimensional shape is a triangular prism.

Answer:

Below in bold.

Step-by-step explanation:

The median will be the average of the 2 middle numbers

so it is:

(x + x + 2)/2 and this equal 53,

(2x + 2)/2 = 53

x + 1 = 53

x = 52.

So, the list is

45, 47, 50, 52, 54, 60, 62, 63

Mean = (45 + 47+ 50+ 52 +54+ 60+ 62+ 63)/ 8

          = 54.125

There is no Mode.

The domain of the function is y = -1/2(x-5)^2 + 4, for 3 ≤ x ≤ 9.

To transform the function y=x^2 according to the given specifications, we can use the following steps:

Domain: Finally, the domain of the transformed function is given as [3, 9], which means that the function is only defined for x-values between 3 and 9. Therefore, we need to restrict the domain of the function to this interval. Therefore, the final transformed function is:

Therefore the transformation is y = -1/2(x-5)^2 + 4, for 3 ≤ x ≤ 9.

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Accοrding tο the given infοrmatiοn the measure οf arc PQR is 170 degrees.

A quadrilateral is a fοur-sided pοlygοn, which is a twο-dimensiοnal geοmetric figure with straight sides. Quadrilaterals can have a variety οf shapes, sizes, and angles, but they all have fοur sides and fοur vertices (cοrners).

Since the quadrilateral PQRS is inscribed in a circle, we knοw that angle PQR is an inscribed angle οf arc PR. By the Inscribed Angle Theοrem, the measure οf an inscribed angle is equal tο half the measure οf its intercepted arc. Therefοre, the measure οf arc PQR is twice the measure οf angle PQR, which is:

2 * 85 = 170 degrees.

Therefοre, accοrding tο the given infοrmatiοn the measure οf arc PQR is 170 degrees.

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The experimental probability that the next customer will want mustard on their hot dog is 2/3.

The ratio of the number of times an event has occurred to the total number of trials or observations is the experimental probability that the event will occur.

We are told that 10 out of the previous 15 customers at Downtown Dogs requested mustard on their hot dogs in this instance. Hence, the following is the experimental likelihood that a client will request mustard on their hot dog:

Number of consumers who requested mustard divided by the total number of customers is the experimental probability.

10/15 is the experimental probability.

By dividing the numerator and denominator of the fraction by 5, we may simplify it to:

2/3 is the experimental probability.

The experimental likelihood that the following consumer will request mustard on their hot dog is therefore 2/3.

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Answer:

5

Step-by-step explanation:

First, we can add the whole numbers together.

1 + 3 = 4

Next, we know that the denominators (base/bottom of fraction) of the fractions are the same, meaning we simply add the numerators (top of fraction).

1/3 + 2/3 = 3/3

3/3 is equal to 1.

Now, we add the 4 from above to this 1 to get our answer, 5.

Feel free to comment down if this doesn't make sense, and I can explain it in a different way.

Answer:

Let's call the number of hours before 8 P.M. that Meghan babysat "x", and the number of hours after 8 P.M. "y". We can set up two equations based on the information given:

5x + 8y = 26 (this is the total amount she earned)

x + y = total number of hours she babysat

We can solve for one of the variables in terms of the other and substitute it into the first equation:

y = total number of hours - x

5x + 8(total number of hours - x) = 26

5x + 8total number of hours - 8x = 26

3x = 26 - 8total number of hours

x = (26 - 8total number of hours)/3

Now we can try different values for the total number of hours she babysat to see if we get a whole number for x:

If she babysat for 1 hour, x = (26 - 8)/3 = 6, which is not a whole number.

If she babysat for 2 hours, x = (26 - 16)/3 = 3, which is a whole number.

If she babysat for 3 hours, x = (26 - 24)/3 = 0.67, which is not a whole number.

So we know she babysat for 2 hours before 8 P.M. and 1 hour after 8 P.M.:

5(2) + 8(1) = 18

2 + 1 = 3 total hours babysat

Therefore, Meghan babysat between 6 P.M. and 9 P.M.

Step-by-step explanation: