Find the range for the measure of the third side of a triangle given the measures of two sides.

5 ft, 10 ft

Answer:

I think its "he had no idea it was a precious jewel"

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Mean is all of your numbers added up and then divided by the amount of numbers in total there are. So 2+4+6+9+14 = 35 35÷5 = 7

Hope this helped <3

The prime factorization of the radicand 2 is 9√15.

A number can be expressed as the product of its prime components through the process of prime factorization. A number with precisely two elements, 1 and the number itself, is said to be a prime number.

As an illustration, let's use the number 30. We know that 30 = 5 × 6, but 6 is not a prime number. The number 6 can further be factorized as 2 × 3, where 2 and 3 are prime numbers. Therefore, the prime factorization of 30 = 2 × 3 × 5, where all the factors are prime numbers.

Given that,

x= 3√135

Solving the equation further using the rule √A*B = √A*√B

x= 3√9*15

x= 3√9*√15

x=3*3*√15

x= 9√15

Therefore, the prime factorization of the radicand 2 is 9√15.

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The equation for the line in point-(1, 1) is y = -0.5x + 0.5.

Given that the slope of the line below is -0.5. We are to enter the equation for the line in point-(1, 1).The equation for the slope-intercept form of the line is y = mx + c where m is the slope and c is the y-intercept.

Now, the slope of the line is given as -0.5.Therefore, the equation for the slope-intercept form of the line is y = -0.5x + c. Now we need to find the value of c for the equation of the line.

To find the value of c, substitute the values of x and y in the equation of the slope-intercept form of the line.

Given that the point is (-1,1), x=-1 and y=1y = -0.5x + c⇒ 1 = (-0.5) (-1) + c⇒ 1 = 0.5 + c⇒ c = 1 - 0.5⇒ c = 0.5

Therefore, the equation for the line in point-(1, 1) is y = -0.5x + 0.5.The slope of a line refers to how steep the line is and is used to describe its direction. Slope is defined as the vertical change between two points divided by the horizontal change between them.A positive slope moves up and to the right, while a negative slope moves down and to the right. If a line has a slope of zero, it is said to be a horizontal line.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept, or the point at which the line crosses the y-axis. To find the equation of a line with a given slope and a point, we can use the point-slope form of a linear equation.

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By using the volume of a cube formula, The length of one side of the shipping box is 12.5 cm.

To find the length of one side of the box, we can use the formula for the volume of a cube, which is V = s^3, where s is the length of one side. Given that the volume of the box is 1525 cubic centimeters, we can solve for s:

V = 1525

s^3 = 1525

s = cubic root of 1525

s = 12.5 cm

So, the length of one side of the box is 12.5 cm.

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With that information we can create the equation

10x + 5000 = 20x

where x is the number of earphones produced

10x is the cost to make each earphone, 5000 being the fixed costs of manufacturing, and 20x being the total revenue of selling each earphone for $20

Now to solve the equation:

subtract both sides by 10x

10x - 10x + 5000 = 20x - 10x

5000 = 10x

Now divide both sides by 10

5000/10 = 10/10 x

500 = x

Answer: D

Hope it helps :)

500 earphones must be produced to get the cost price of one ear phone of $20.

The linear equations in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.

According to the given question

The start-up costs for manufacturing earphones is $5,000.

Also, the cost to make earphones is $10.

Let x number of  earphones will produced to get a cost per unit of $20.

From the given conditions, we will get a linear equation in one variable

10x + 5000 = 20x

⇒ 5000 = 20x -10x

⇒ 5000 = 10x

⇒ x = 500

Hence, 500 earphones must be produced to get the cost of earphone of $20.

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Answer:

m+m×0.15

because it increased by 15%

you get m's 15% if you multiply it with 0.15

Answer:

B

Step-by-step explanation:

Answer:

0.15866

Step-by-step explanation:

First, we calculate z-score

Mathematically;

z-score = value-mean/SD

here, mean = 47 , SD = 5 and value = 52

z-score = (52-47)/5 = 5/5 = 1

The probability we want to calculate is;

P(z<1) and we can access this from the standard score table

P(Z<1) =0.15866

Answer:

\(x=-\frac{2}{3}+\frac{\sqrt{2}}{3}i\\\\x=-\frac{2}{3}-\frac{\sqrt{2}}{3}i\)

Step-by-step explanation:

The Quadratic Formula gives us the roots of a quadratic and is defined as: \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

The discriminant is the part in the square root which is: \(b^2-4ac\)

if the discriminant of the quadratic is zero, then the quadratic only has one distinct zero with a multiplicity of 2.

To see why, let's plug in zero for the discriminant: \(x=\frac{-b\pm\sqrt{0}}{2a}\)

The square root of zero is just going to be zero: \(x=\frac{-b\pm0}{2a}\)

Adding or subtracting zero doesn't change the value: \(x=\frac{-b}{2a}\)

As you can see here it doesn't matter if we take the positive or negative solution, we'll get one value.

If the discriminant of the quadratic is positive, then the quadratic will have two distinct real solutions.

Well the solutions are real because the square root has real solutions for positive numbers. The reason we have two distinct solutions is because the square root of a positive number will have a positive and negative solution. These square roots will have a non-zero value and will affect the value of the numerator based on whether you take the negative or positive solution giving you two distinct solutions.

If the discriminant of the quadratic is negative, then the quadratic will have two distinct complex solutions.

To clarify, real numbers are technically complex numbers, since complex numbers are just: \(a+bi\), where a=real part, and b=imaginary part. We could use this to represent any real number where b=0.

So when I'm saying "complex solution" I mean a complex solution where b does not equal zero, so there is a non-zero imaginary component to the complex solution.

The reason we have a complex solution in the first place is because we have a negative number in the square root. The square root only has real solutions for positive numbers, since any real number squared will give you a positive number regardless of the sign (positive or negative). The only number that is negative when squared is an imaginary number.

The reason we have two distinct solutions is actually the same reason we have two distinct solutions when the discriminant is positive. Since the square root will yield a non-zero number, so when we add it or subtract it to b, we will get to different values for the numerator, giving us two different values, or two different solutions.

So now let's solve the equation: \(3x^2+4x+2=0\)

We have it in standard form where: \(ax^2+bx+c=0\)

we want to use the Quadratic Formula: \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

Plugging in values we get:

\(a=3,\ b=4,\ c=2\\\\x=\frac{-4\pm\sqrt{4^2-4(3)(2)}}{2(3)}\\\\x=\frac{-4\pm\sqrt{16-24}}{6}\\\\x=\frac{-4\pm\sqrt{-8}}{6}\)

From here you'll notice the discriminant is -8, and thus we complex solutions since it's negative. We can first break up this square root into multiple square roots using the fact that: \(\sqrt{ab}=\sqrt{a}*\sqrt{b}\)

and since -8 can be defined as: -1 * 8, we can split it up like this

\(x=\frac{-4\pm\sqrt{-1}*\sqrt{8}}{6}\\\\x=\frac{-4\pm i\sqrt{8}}{6}\)

We can actually simplify the square root a bit more, since we can once more use the identity: \(\sqrt{ab}=\sqrt{a}*\sqrt{b}\), to simplify the radical. The number 8 can be represented as 4 * 2, and sqrt(4) can be simplified easily.

\(x=\frac{-4\pm i *\sqrt{4}*\sqrt{2}}{6}\\\\x=\frac{-4\pm 2i\sqrt{2}}{6}\\\\x=\frac{(-2 * 2)\pm2i\sqrt{2}}{(3*2)}\\\\x=\frac{-2\pm i\sqrt{2}}{3}\)

Now let's take the positive and negative solution to get the two distinct complex solutions. You can start with either but I'll just do the positive first.

Positive Solution:

\(x=\frac{-2+ i\sqrt{2}}{3}\)

You could leave it like this, but generally whenever we have a complex number we want it in the form: \(a+bi\) where the real and imaginary part are separate, so we can just distribute the division of 3

Positive Solution Continued:

\(x=\frac{-2+ i\sqrt{2}}{3}\\\\x=\frac{-2}{3}+\frac{\sqrt{2}}{3}i\)

I also moved the "i" outside the fraction, so it's a bit easier to see the value of "b"

Negative Solution:

\(x=\frac{-2-i\sqrt{2}}{3}\\\\x=\frac{-2}{3}-\frac{\sqrt{2}}{3}i\)

Answer:

not exactly sure what is being asked butttt i think it's 90

Step-by-step explanation:

Answer:

17 feet

Step-by-step explanation:

We have to use the pythagorean theorem, this is actually a bit more complicated than it seems at a first glance.

If Tony is 8 feet to Lexi's right, then we can form a triangle as such

I can't paste it (sorry)

but we can use the formula a^2+b^2=c^2, so 15^2=225, and 8^2=64, and 225+64=289, and \(\sqrt289=17\)

so they're 17 feet apart!

Answer:

x-int=(2,0)

y-int=(0,4)

Step-by-step explanation:

Answer:

I think it might be the last answer

Step-by-step explanation:

sorry just tryna help ok dokie

Answer:

yaaa last one

Step-by-step explanation:

Answer:

y = -2x - 2

Step-by-step explanation:

Given:

m = -2

Slope-intercept:

y - y1 = m(x - x1)

y + 8 = -2(x - 3)

y + 8 = -2x + 6

y = -2x - 2

The probability that two randomly chosen individuals in the United States both wear a seat belt while driving is approximately 18.49%.

To calculate the probability that both randomly chosen individuals are wearing a seat belt, we can multiply the individual probabilities together.

The probability of the first person wearing a seat belt is 43%, which can be expressed as 0.43 or 43/100. Since the first person's choice does not affect the second person's probability, the probability of the second person wearing a seat belt is also 43%.

To find the probability of both events occurring, we multiply the two probabilities together:

0.43 * 0.43 = 0.1849 or 18.49%

Therefore, the probability that both randomly chosen individuals are wearing a seat belt is approximately 18.49%.

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Answer: B

Step-by-step explanation:

Reflection does preserve side length and dilation preserves angles.

The solution is Option B.

The reflection preserves the side lengths of the triangle ABC and the dilation preserves angles but not side lengths

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given data ,

Let the triangle be represented as ΔABC

Now , Triangle ABC is reflected across the y-axis and then dilated by a factor of 2 centered at the origin

And , when you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

So , only the x coordinate of the point changes and there is no change in the angles or the side lengths

Now , dilation changes the side lengths of the triangle by a factor of 2

But there is no change in the angles of the triangle after a dilation

Hence , reflection preserves the angles and side lengths of a triangle

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Using implicit differentiation dz/dt = -34

Differentiation is the process of finding the derivative of a function.

Since x² + y² + z² = 9, dx/dt = 8, and dy/dt = 9, we need to find dz/dt when (x, y, z) = (2, 2, 1).

So, differentiating implicitly and also applying the chain rule, we have that

x² + y² + z² = 9

d(x² + y² + z²)/dt = d9/dt

dx²/dx × dx/dt  + dy²/dy × dy/dt + dz²/dz × dz/dt = d9/dt

2xdx/dt  + 2ydy/dt + 2zdz/dt = 0

xdx/dt  + ydy/dt + zdz/dt = 0

Making dz/dt subject of the formula, we have that

zdz/dt = -(xdx/dt  + ydy/dt)

dz/dt =  -(xdx/dt  + ydy/dt)/z

Given that

Substituting the values of the variables into the equation, we have that

dz/dt =  -(xdx/dt  + ydy/dt)/z

dz/dt =  -(2 × 8  + 2 × 9)/1

= -(16 + 18)/1

= - 34

So, dz/dt = -34

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The question is incomplete. Here is the complete question

If  x² + y² + z²  = 9, dx/dt = 5, and dy/dt = 4, find dz/dt when (x, y, z) = (2, 2, 1).

The two intrinsic parameters associated with Cepheid variables are their period (the time it takes for one pulsation cycle) and their luminosity (the total amount of energy emitted).

Cepheid variables are a type of pulsating stars that exhibit regular variations in their brightness. The two intrinsic parameters associated with Cepheid variables are their period (the time it takes for one pulsation cycle) and their luminosity (the total amount of energy emitted).

The significant feature lies in the relationship between these two parameters. By measuring the period, which can be done relatively easily from observational data, it becomes possible to determine the luminosity of the Cepheid variable.

This relationship, known as the period-luminosity relationship, allows astronomers to estimate the absolute luminosity of Cepheid variables based on their observed periods. This information is crucial for determining distances to celestial objects and studying the properties of the universe.

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Max heaps that follow the binary tree structure are popularly utilized in sorting methods such as heap sort and priority queues.

The correct answer is B.

A complete binary tree-based data structure known as a binary max heap exists.

The following attributes can be attributed to it:

The binary max heap is a complete binary tree that's completely filled at all levels except for the last level, which may not be completely filled and is filled from left to right.

The Heap Property is defined as follows: the value of any node must be equal to or greater than that of its children. Simply put, the highest value is stored in the root node of the heap.

Max heaps that follow the binary tree structure are popularly utilized in sorting methods such as heap sort and priority queues.

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Answer:

37

Step-by-step explanation:

50*26%

50-(50*26%)

Answer: The answer would be D.

Step-by-step explanation: (4x+3)(2x−1)

the probability that at most 40 will get less than 40 seconds and at most 40 will get more than 40 seconds to solve the puzzle.

less than 40 seconds -  Event A

more than 40 sec  - A ' ( A bar / A compliment)

not

maximum number of people in Event A = 40

maximum number of people in A' = 40

total number of maximum people in A or A'  = 40 +40 = 80

but here there are 100 people > 80

hence

this is not possible

Required probability = 0

Probability is a branch of mathematics that quantifies the likelihood of an event occurring or the likelihood of a statement being true. The probability of an event is a number between 0 and 1, with approximately 0 indicating the improbability of the event and 1 indicating certainty.

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The marked price of the television is Rs. 20,000.

The market price is the current price at which a good or service can be purchased or sold.

Here, let the marked price of the television be Rs. x

          Discount = 16% on MP

          VAT = 13% additional on MP

          Total paid amount = Rs. 18984

Now, according to question;

     MP X (1 - Discount) X (1 + VAT) = 18984

              x (1 - 0.16)(1+0.13) = 18984

              x = 18984/(0.84 X 1.13)

              x = 18984 / 0.9492

              x = 20,000

Thus, the marked price of the television is Rs. 20,000.

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Answer:

It's A. 11.12 gallons. I'm sure

Step-by-step explanation:

The question asks for the maximum amount a firm should pay for a project that will generate $1 million annually for 5 years, given an opportunity cost of 10%.

The opportunity cost represents the return the firm could earn on an alternative investment. We need to calculate the present value of the cash flows to determine the maximum amount the firm should pay.

To calculate the maximum amount a firm should pay for a project, we need to find the present value (PV) of the future cash flows. The PV represents the current value of the expected future cash flows, taking into account the opportunity cost. Using the formula for calculating the present value of an annuity, we can determine the maximum amount the firm should pay. The formula is:

PV = CF x (1 - (1 + r)^(-n)) / r,

where PV is the present value, CF is the cash flow per period, r is the discount rate (opportunity cost), and n is the number of periods. In this case, the cash flow is $1 million per year for 5 years, and the discount rate is 10% (0.10). Plugging these values into the formula, we get:

PV = $1 million x (1 - (1 + 0.10)^(-5)) / 0.10 = $3.7908 million.

Therefore, the maximum amount the firm should pay for the project is approximately $3.7908 million. This amount represents the present value of the expected future cash flows, taking into account the opportunity cost of 10%.

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Answer:

it is 8cm

Step-by-step explanation:

i forgot how to do the explanation but I know the answer is 8cm

Answer:

The answer is 9.0909

Step-by-step explanation:

n=1  p=.11

mean = 1/0.11 = 9.0909

The mean of X, the number of patients seen until an injection-site reaction occurs is 9.0909.

The mean refers to "the average set of values".

According to the question,

The percentage of patients experiencing injection- site reactions with the current needle is 11%.

Mean = \(\frac{sum of the all values}{Total number of values}\)

Total number of values = 11% = 0.11 and  n = 1.

Mean = \(\frac{1}{0.11}\)

=9.0909.

Hence, the mean of X, the number of patients seen until an injection-site reaction occurs is 9.0909.

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