Express in simplest radical form

Answer:

3cm or 1.5

Step-by-step explanation:

Long leg = radical of 3

Short leg = 1

Hypotenuse= 2

Step-by-step explanation:

Let the two numbers be x and y.

We know that:

HCF(x,y) × LCM(x,y) = x × y

Substituting the given values:

4 × 288 = x × y

Simplifying:

x × y = 1152

Now we need to find two numbers whose product is 1152 and HCF is 4. One way to do this is to list all the factors of 1152 and find a pair of factors whose HCF is 4. However, we can also solve this problem by prime factorization.

Prime factorization of 1152:

1152 = 2^7 × 3^2

To find the two numbers, we need to divide these factors into two groups, one group for x and the other group for y. We can choose any combination of factors, as long as their product is 1152. However, we also need to ensure that the HCF of x and y is 4.

One possible way to do this is to choose one factor of 2 from the prime factorization of 1152 for x and the remaining factors for y:

x = 2^1 × 3^a

y = 2^6 × 3^b

where a and b are non-negative integers.

Multiplying x and y and equating to 1152, we get:

2^1 × 3^a × 2^6 × 3^b = 1152

Simplifying:

2^7 × 3^(a+b) = 1152

Since 1152 = 2^7 × 3^2, we have:

2^7 × 3^(a+b) = 2^7 × 3^2

Equating the exponents of 2, we get:

7 + 0 = 7

a + b = 2

Since the HCF of x and y is 4, we need to ensure that both x and y have a factor of 2^2 = 4. Thus, we choose a = 2 and b = 0:

x = 2^1 × 3^2 = 12

y = 2^6 × 3^0 = 64

Therefore, the two numbers are 12 and 64.

Answer: The formula for the circumference of a circle is C = πd, where d is the diameter of the circle.

If the diameter of the circle is 8 inches, then:

C = πd

C = π(8)

C = 8π

Using an approximation of π as 3.14, we can estimate the circumference:

C ≈ 8 × 3.14

C ≈ 25.12

Therefore, the answer closest to the circumference of the circle is 25.12 inches.

Step-by-step explanation:

It is a true statement that tangent segment is a line segment that has a point on the tangent line and on the center of the circle.

In geometry, a tangent segment is a line segment that intersects a circle at exactly one point, known as the point of tangency. This line segment is called a tangent because it touches the circle at a single point and does not cross through the circle.

The tangent segment's length is determined by the distance between the point of tangency and a point on the line that is outside the circle, known as the external point. This distance is equal to the radius of the circle, as the radius is the distance between the center of the circle and any point on the circle's circumference.

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Answer:

- 1/2

Step-by-step explanation:

We can use the slope formula to find the slope.

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

    = ( -40 - -75)/(-15 - 55)

   = (-40+75)/( -15-55)

   =35/-70

  =- 1/2

Answer:

m = -0.5

Step-by-step explanation:

Given that, ( Coordinates of a line )

( 55, - 75 ) ⇒ ( x₁ , y₁ )

( - 15 , - 40 ) ⇒ ( x₂ , y₂ )

The formula to find the slope of a line is:

[tex]\sf m =\frac{y_1-y_2}{x_1-x_2}[/tex]

Let us find it now.

[tex]\sf m =\frac{y_1-y_2}{x_1-x_2} \\\\\sf m =\frac{-75-(-40)}{55-(-15)} \\\\\sf m =\frac{-75+40}{55+15} \\\\\sf m =\frac{-35}{70} \\\\m = -0.5[/tex]

Answer:

c 136 degrees

Step-by-step explanation:

After answering the provided question, we can state that As a result, the equation shortcut is approximately 72.1 metres long. The length is 72.1 metres, rounded to the nearest tenth.

To calculate the length of the shortcut, we must apply the Pythagorean theorem, which states that the square of the hypotenuse (the longest side) in a right triangle is equal to the sum of the squares of the other two sides. The hypotenuse in this case is the shortcut PQ, and the other two sides are the distances from P to the park's corner (which we'll call A) and from Q to A.

shortcut length2 = 402 + 602

shortcut length2 = 1600 + 3600

shortcut length2 = 5200 = 72.1 metres

As a result, the shortcut is approximately 72.1 metres long. The length is 72.1 metres, rounded to the nearest tenth.

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Answer:

the height is 6 meters

Step-by-step explanation:

v = [tex]\pi r^{2} h[/tex]

471 = 3.14(25)h

471 = 78.5h  Divide both sides by 78.5

[tex]\frac{471}{78.5}[/tex] = [tex]\frac{78.5h}{78.5}[/tex]

6 = h

Helping in the name of Jesus.

Each values of the function are;

[tex]F(3) = \frac{9}{2} , F(-12) = -\frac{1}{2} , F(\frac{1}{3}) = \frac{73}{2} , F(\frac{3}{4}) =\frac{33}{2}[/tex]

A function is a relationship between two sets of numbers, called the domain and the range, such that each input value from the domain corresponds to exactly one output value from the range. A function can be thought of as a rule that assigns to each input value a unique output value. The most common way to represent a function is by using an equation or formula that defines the relationship between the input values and the output values. The variable in a function represents the input values from the domain.

Given function;

[tex]F(x) = \frac{12}{x} + \frac{1}{2}[/tex]

We need to find the values of function [tex]F(3) , F(-12) , F(\frac{1}{3}) , F(\frac{3}{4})[/tex]

Put the values of x = 3, -12, 1/3, 3/4 one by one in the given function of      [tex]F(x) = \frac{12}{x} + \frac{1}{2}[/tex]

1.  If x= 3;        [tex]F(3) = \frac{12}{3} + \frac{1}{2} = \frac{9}{2}[/tex]

2. If x= -12;      [tex]F(-12) = \frac{12}{(-12)} + \frac{1}{2} = -1 + \frac{1}{2}[/tex]  [tex]= -\frac{1}{2}[/tex]

3.  If [tex]x=\frac{1}{3}[/tex];      [tex]F(\frac{1}{3} ) = \frac{12}{(\frac{1}{3}) } + \frac{1}{2} = 36+\frac{1}{2}[/tex] [tex]= \frac{73}{2}[/tex]

4.  If [tex]x=\frac{3}{4}[/tex];      [tex]F(\frac{3}{4} ) = \frac{12}{(\frac{3}{4}) } + \frac{1}{2} = 16 +\frac{1}{2}[/tex] [tex]= \frac{33}{2}[/tex]

Therefore the values are;  [tex]F(3) = \frac{9}{2} , F(-12) = -\frac{1}{2} , F(\frac{1}{3}) = \frac{73}{2} , F(\frac{3}{4}) =\frac{33}{2}[/tex]

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Complete question-

the equation to represent the number of hours, t, the bird will take to fly d kilometers at this rate is t = 2d / 71.2

We can use the formula for distance, rate, and time:

distance = rate x time

We can rearrange this formula to solve for time:

time = distance / rate

If we substitute the given distance of 71.2 km and rate of (71.2 km / 2 hours) into this formula, we can find the time it took the bird to fly 71.2 km:

time = 71.2 km / (71.2 km / 2 hours) = 2 hours

Now, we can use the same formula to find the time it will take the bird to fly d kilometers:

time = d km / (71.2 km / 2 hours) = 2d / 71.2 hours

Therefore, the equation to represent the number of hours, t, the bird will take to fly d kilometers at this rate is t = 2d / 71.2

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The length of the base of the given parallelogram is 2 feet.

The area of ​​a parallelogram is all the square units that fit inside, measured in square units (cm2, m2, in2, etc.). It is the area surrounded or enclosed by parallelograms in two places. The elements of a parallelogram. Since a rectangle and a parallelogram have the same properties, the area of ​​the rectangle is the same as that of the parallelogram.

Given us the area in sq. feet but height in yards, So let's convert the height in feet instead.

We know, 1 yard = 3 feet

∴ Height = 5 feet.

Now, We know

⇒ Area = Base × Height

⇒ 10 = Base × 5

⇒ Base = 2 feet

Hence, The length of the base of the given parallelogram is 2 feet.

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We cannot claim that the newsletter publisher's statement is incorrect. Hence, the conclusion is uncertain.

The newsletter publisher's claim is uncertain after performing a test at the 0.02 level of significance as the testing firm fails to reject the null hypothesis.

In this case, we cannot claim that the publisher's statement is incorrect without additional tests and proof. Here is an explanation of the above statement.

A hypothesis test is conducted to find out whether or not there is sufficient evidence to contradict a hypothesis. In this case, the hypothesis test's null hypothesis claims that the newsletter publisher's statement is correct.

The alternate hypothesis claims that the newsletter publisher's claim is incorrect. As a result, the null hypothesis is represented by [tex]H_0[/tex]:

p = 0.71 (71%) and

the alternate hypothesis is represented by [tex]H_a[/tex]:

p ≠ 0.71 (71%).

Where 'p' denotes the percentage of newsletter readers who own a Rolls Royce.

The test statistic for a sample proportion can be calculated by

z = (p - P) / √(P(1 - P) / n)

Where 'p' denotes the sample proportion,

P denotes the population proportion, and

n denotes the sample size.

A two-tailed test is used because the alternate hypothesis is written as [tex]H_a[/tex]:

p ≠ 0.71 (71%).

At a 0.02 significance level, the test statistic's critical value is ±2.58 (round off) Because the test statistic does not fall in the rejection region, we fail to reject the null hypothesis.

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The standard error of the average sample weight when 15 participants are randomly selected for the sample is 9.05 (rounded to two decimal places).

The standard error of the average sample weight when 15 participants are randomly selected for the sample can be calculated using the formula given below:SE = σ/√nWhere,σ = standard deviation of the populationn = sample sizeSE = standard error of the meansubstituting the given values,SE = 35/√15 = 9.05

Note:When using the given formula, it is important to note that it assumes a normal distribution of sample means. The standard error is used to estimate the true value of the mean from the sample data. The larger the sample size, the smaller the standard error. The smaller the standard error, the more precise the estimate of the true value of the mean.

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Answer:

6

Step-by-step explanation:

The constant of proportionality for the work done when lifting an object is given as follows:

k = 14.78.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other. This means that if one quantity is multiplied by a certain factor, the other quantity will also be multiplied by the same factor.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

The work, W (in joules), done when lifting an object is jointly proportional to the product of the mass, m (in kilograms), of the object and the height, h (in meters), that the object is lifted, hence the equation is given as follows:

W = khm.

The work done when a 100-kilogram object is lifted 1.5 meters above the ground is 2116.8 joules, the the constant is given as follows:

150k = 2216.8

k = 2216.8/150

k = 14.78.

The problem asks for the constant of the proportional relationship.

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The expressions are matched as;

5³· 5³    add the exponents

(4x³)⁵.  write as the product of the powers

6⁹ ÷ 6⁵.  subtract the exponents

(7²)³. multiply the exponents

Index forms are described as those mathematical models that are used to represent numbers too small or large in more convenient forms.

They are represented as variables or numbers that are being raised to an exponent.

Other names for index forms are;

The rules of the index forms are;

From the information given, we have that;

5³· 5³    multiply the exponents

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In Linear equation, 121 the number of people per square mile.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                                   Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

A = (12 + 21) * 14 * 1/2

    = 33 * 14 * 1/2

     = 231 mi²

 28000 ÷ 231  = 121 people

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Items: 1 Pen: 1.50

     3 DVDS: ???

Total : 22.50

It is A, 1.5+3d=22.5.

Hope this helps!!!

It is not B because you are not multiplying the number and cost of 3 DVDS by the cost of one pen.

It is not C because you are not subtracting to find the total cost. You are adding.

It is not D because 3d is part of the total cost so that option just doesn't make sense.

Answer:2

Step-by-step explanation:bc

The probability that the jury makes the correct decision is 0.9999

This is a binomial distribution problem where the event of interest is a juror making a correct decision (voting guilty) and the number of trials is 12 (the number of jurors).

The probability of a single juror making the correct decision is 0.80. Therefore, the probability of a single juror making the incorrect decision (voting not guilty) is 1 - 0.80 = 0.20.

To calculate the probability that at least 10 out of 12 jurors make the correct decision (voting guilty) if the defendant is guilty, we can use the binomial distribution formula:

P(X ≥ 10) = 1 - P(X < 10)

where X is the number of jurors who make the correct decision.

Since the probability of a single juror making the correct decision is 0.80, we can use the binomial probability formula to calculate the probability of X jurors making the correct decision

P(X = x) = (12 choose x) * 0.80^x * 0.20^(12-x)

where (12 choose x) is the number of ways to choose x jurors out of 12.

Using this formula, we can calculate the probability of fewer than 10 jurors making the correct decision:

P(X < 10) = P(X = 0) + P(X = 1) + ... + P(X = 9)

We can use a calculator or software to calculate this probability:

P(X < 10) = 0.00000436

Therefore, the probability of at least 10 out of 12 jurors making the correct decision if the defendant is guilty is:

P(X ≥ 10) = 1 - P(X < 10) = 1 - 0.00000436 = 0.99999564

Rounding to four decimal places, the probability is 0.9999.

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The perimeter of the shaded region is 22.58 units.

What is perimeter of rectangle?

Perimeter of a rectangle is 2×(Length+Breadth).

Here in this figure we have three part. They are a rectangle and two semicircles.

Length of the rectangle is 13 unit and breadth is 6 unit

So, perimeter of the rectangle part = 2×(length+breadth) = 2×(13+6) = 38 unit

Again, diameter of two semicircles is 6 unit

So, radius of two semicircles will be [tex] \frac{6}{2} = 3 \: unit[/tex]

So, perimeter of one semicircle

[tex] = \pi \: r + 2r \\ = \pi \times 3 + 2 \times 3 \\ = 3\pi + 6[/tex]

Now, perimeter of two semicircles will be

[tex]2 \times (3\pi + 6) = 3(\pi + 2) \: unit[/tex]

If we subtract perimeter of two semicircles from the perimeter of rectangle then we will get perimeter of the shaded portion.

So, required perimeter of shaded region

[tex] = 38 - 3(\pi + 2) = (32 - 3\pi) = 22.58 \: unit[/tex]

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Answer:

Steps:

1. Draw a 3 x 3 table

2. Place the titles on the left and top of the table (play sports and don't play sports on left for example and instruments on top)

3. Place the numbers inside accordingly

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The function is not a polynomial function,

Leading coefficient, Constant, Highest degree, is not possible with a rational function, Type of function: Rational function

An expression is a mathematical equation that combines variables, numbers, and other mathematical operations to represent a value or a set of values. It can be simple or complex, and it is often used in algebra to solve problems and represent mathematical relationships.

We have the given function is, [tex]f(x)= 5x - 12 + x^3 + 9x^{-4} + x^2[/tex]

The standard form, means arranging the terms in descending order of degree; So,

[tex]f'(x) = x^3 + x^2 + 5x - 12 + 9x^{-4}[/tex]

No, the function f'(x) is not a polynomial function because it contains a term with a negative exponent, which makes it a rational function rather than a polynomial function.

To find the leading coefficient, constant, highest degree, and type of function of a polynomial function, we would put it in standard form, but this is not possible with a rational function.

Instead, we can identify that the term 9[tex]x^{-4}[/tex] is a rational term, which means it contains a variable raised to a negative exponent. Polynomial functions, by definition, cannot have terms with negative exponents, so f(x) is not a polynomial function.

In summary, the function [tex]f'(x) = x^3 + x^2 + 5x - 12 + 9x^{-4}[/tex] is a rational function, not a polynomial function, because it contains a term with a negative exponent.

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The area of the given shape is 73.5 ft squared

The question content area indicates that we need to find the area of a shape with dimensions of 10 ft, 7 ft, and 11 ft. However, the units are not specified, so it is assumed that we are dealing with a two-dimensional shape and the units are in feet.
To find the area of this shape, we need to use the appropriate formula for the shape.

Since the question does not provide any further information about the shape, we cannot determine the formula for certain. However, based on the dimensions given, we can assume that this is a trapezoid.
The shape can be divided into a rectangle and a triangle.

Calculate the area of the rectangle.

The dimensions of the rectangle are 7 ft by 10 ft.

To find the area, multiply the length by the width:

Area of rectangle = length × width = 7 ft × 10 ft = 70 ft²

Calculate the area of the triangle.

The base of the triangle is 10 ft, and its height is the difference between the 11 ft and 7 ft sides of the shape, which is 4 ft.

Multiply the base by the height and then divide by 2:

Area of triangle = (base × height) / 2 = (10 ft × 4 ft) / 2 = 20 ft²

Total area = area of rectangle + area of triangle = 70 ft² + 20 ft² = 90 ft²

The formula for the area of a trapezoid is:
Area = ((b1 + b2) / 2) * h
where b1 and b2 are the lengths of the two parallel sides, and h is the height (or perpendicular distance between the parallel sides).
Using the given dimensions, we can plug them into the formula:
Area = ((10 + 11) / 2) * 7
Area = (21 / 2) * 7
Area = 147 / 2
Area = 73.5 ft squared
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Answer:

Britney will run approximately 9,090 meters in total.

Step-by-step explanation:

To solve the problem, we can use the Law of Cosines to find the distance of the final straight line back to her starting position.

Let A be the starting position, B be the end of the first leg, and C be the end of the second leg. Then, we have:

AB = 2.1 km BC = 3.3 km ∠ABC = 180° - 105° = 75°

Using the Law of Cosines, we have:

AC² = AB² + BC² - 2(AB)(BC)cos(∠ABC)

AC² = (2.1)² + (3.3)² - 2(2.1)(3.3)cos(75°) AC ≈ 3.69 km

Therefore, Britney will run a total distance of approximately:

2.1 km + 3.3 km + 3.69 km ≈ 9.09 km

So, Britney will run approximately 9,090 meters in total.

The equivalent decimal of a fraction of 6/11 is given as follows:

0.5454.

To obtain the equivalent decimal of a fraction, divide the numerator (the top number) by the denominator (the bottom number) using a calculator or long division.

The fraction for this problem is given as follows:

6/11.

The numerator and the denominator of the fraction are given as follows:

The division of 6 by 11 has a result of 0.5454, hence the equivalent decimal of the fraction is given as follows:

0.5454.

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Answer:

messageAdam, Ben and Carly work out the mean of their ages.Adam is 4 years older than the mean. Ben is 1 year younger than the mean.Is Carly older or younger than the mean?By how many years?Let's start by finding the mean of their ages. We can do this by adding their ages and dividing by the number of people: Mean = (Adam's age + Ben's age + Carly's age) / 3 Let's call the mean "M" for now. We can use this to create two equations based on the information given: Adam = M + 4 Ben = M - 1 We can substitute these equations into the mean equation to get: M = (M + 4 + M - 1 + Carly's age) / 3 Simplifying this equation gives us: 3M = 2M + 3 + Carly's age Carly's age = M - 3 So Carly's age is younger than the mean by 3 years

A graph of the equation y = 2x - 3 is shown in the image attached below.

In order to to graph the solution to the given linear equation on a coordinate plane, we would use an online graphing calculator to plot the given linear equation and then take note of the point that lie on it;

y = 2x - 3

In this scenario and exercise, we would use an online graphing calculator to plot the given linear equation as shown in the graph attached below.

Based on the graph shown in the image attached below, we can reasonably infer and logically deduce that the domain for this linear equation is -2 < x < 4.

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Answer:

The function h(x) = -log(x + 5) has a vertical asymptote at x = -5, since the logarithm of a non-positive number is undefined. To find the intercepts of this function, we can set h(x) equal to zero and solve for x:

h(x) = 0

-log(x + 5) = 0

x + 5 = 1

x = -4

So the function has an x-intercept at (-4, 0). To find the y-intercept, we can set x equal to zero and evaluate h(x):

h(0) = -log(0 + 5) = -log(5)

So the function has a y-intercept at (0, -log(5)).

To verify these intercepts using the graph, we can look for the points where the graph intersects the x and y axes. The x intercept is where the graph crosses the x-axis, which in this case is at x = -4. The y-intercept is where the graph crosses the y-axis, which is at y = -log(5) or approximately -1.609. The vertical asymptote is the vertical line where the graph approaches but never touches. From the graph, we can see that this occurs at x = -5.

It is important to note that when graphing logarithmic functions, it is recommended to plot a few points, including the intercepts and vertical asymptote, to help visualize the graph accurately.