Three numbers in the interval $\left[0,1\right]$ are chosen independently and at random. What is the probability that the chosen numbers are the side lengths of a triangle with positive area

Answer:

[tex]39 yd^2[/tex]

Step-by-step explanation:

So, let's start by calculating the surface area of the base, which in this case is a square. The area of a square can be calculating by taking any of the lengths and squaring it, since all the sides should be equal if it's a square. Since one of the sides of the square is 3 yd, you have the equation: [tex](3 yd)^2 = 9yd^2[/tex]. Now to calculate the area of the four triangles. The area of a triangle can be calculating by using the formula: [tex]\frac{1}{2}bh[/tex], and in this case the base is 3 yd, and the height is 5 yd (lengths can be determined by looking at the given values in the diagram). But there's 4 of the triangles so we multiply it all by 4, and this gives you the equation: [tex]4(\frac{1}{2}(5 yd)(3 yd)) = 4(\frac{15 yd^2}{2}) = 4(7.5 yd^2)=30yd^2[/tex]. So now all that's left is to add this to the area of the square which gives you the equation: [tex]30yd^2+9yd^2=39yd^2[/tex] which is the surface area

we conclude that at 5:00 p.m. there are 8 more inches of snow than at 8:00 a.m.

We know that at 8:00 a.m. there were t inches of snow in the ground.

At 5:00 p.m. there were 3t inches of snow in the ground.

Then the difference between the heights of the snow is:

3t- t = 2t

And we know that at 5:00 p.m. there were 12 inches of snow then we can solve the linear equation for t:

3t = 12in

t = (12in)/3 = 4 in

Replacing that in the difference of heights:

2t = 2*4in = 8in

From this, we conclude that at 5:00 p.m. there are 8 more inches of snow than at 8:00 a.m.

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For the given linear equation:

We know that Sarah buys one pair of sneakers and several pairs of laces.

We know that the amount that she spends is:

$35 + $3*l

The first term, the constant one, represents the cost of the pair of sneakers.

The linear term:

$3*l

Represents the cost of buying l pairs of laces, assuming that each pair costs $3.

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Answer:

Function 1 has the larger maximum at (4, 1)

Explanation:

After observation, graph of function 1 has vertex at Maximum (4, 1)

In order to find vertex of function 2, complete square the equation.

f(x) = -x² + 2x - 3

f(x) = -(x² - 2x) - 3

f(x) = -(x - 1)² - 3 + (-1)²

f(x) = -(x - 1)² - 2

Vertex form: y = a(x - h)² + k where (h, k) is the vertex

So, here for function 2 vertex: Maximum (1, -2)

Function 1 = Maximum (4, 1), Function 2 = Maximum (1, -2)

Function 1 has greater maximum value of (4, 1) as "1 is greater than -2"

The number of Red supporters are 345

From the given information, we have that

Red supporters = 1/3 x

Let the total number of supporter be x

1/3 x + blues = x

1/3x + 1/3x + 345 = x

2/3x + 345 = x

Collect like terms

[tex]x - \frac{2x}{3} = 345[/tex]

[tex]\frac{1}{3} x = 345[/tex]

Cross multiply

[tex]x = 3[/tex] × [tex]345[/tex]

[tex]x = 1035[/tex]

We have red supporters = 1/3x

⇒ [tex]\frac{1}{3}[/tex] × [tex]1035[/tex]

⇒ [tex]345[/tex]

Thus, the number of Red supporters are 345

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By evaluating in x = 25 we get:

Here we know that the measure of angle 1 is given by:

∠1 = 5x - 5

And the given value of x is 25, then if we just evaluate the above expression, then we get:

∠1 = 5*25 - 5 = 120

And for angle 2 we will have:

∠2 = 2*25 - 10 = 60

Notice that the sum of these two angles is equal to 180°, which is what we should get when adding two supplementary angles.

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The office concluded that the driver exceeded the speed limit by 64.3mi/h.

Given that the second cop, who arrived 28 minutes later, was recorded traveling at 60 mph while the patrol officer was traveling 30 miles along the roadway.

According to the mean value theorem, There exists a value of x = c such that f'(c) = [f(b)-f(a)][b-a] if f(x) is continuous on the closed interval [a,b] and differentiable on the open interval (a,b).

This implies the following in "lay man's" terms:

the instantaneous speed (the speed at any given time) must be equal to his average speed

Since the driver is driving along the highway, we can assume his position to be continuous and differentiable

his average speed is defined as:

average speed=[x(b)-x(a)]÷[b-a] where x represents his position

average speed=[30 - 0]÷[(28÷60) - 0]

average speed=30÷0.466

average speed=64.3mi/hr

Since the time is given in minutes, we convert it in hours by dividing it by 60.

Therefore, by the MVT the police officers can determine that at some point in time (even though he was only driving 60mph at the second patrol officer's location) since his average speed was approximately 64.3 mi/hr there was a point in time during the 28 minutes that his speed exceeded 60 mph.

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The answer to the Diophantine equation (x³+y³+z³=k) is given below. First lets us see the definition of the same.

A Diophantine equation in mathematics is a polynomial equation with two or more unknowns, where the only solutions of interest are integer ones.

A linear Diophantine equation is equal to the sum of two or more monomials of degree one.

Unknowns can emerge in exponents in an exponential Diophantine equation.

Recall that this problem is called the "summing of three cubes." Thus, from the values given, the minimum value of K can be 1.

To arrive at that, we can do

x = 0, y = 0, z = 1

so  0³+0³+1³; hence

k = 1

and maximum value  of k can be 99

with that we work with x=2,y=3, z=4

2³+3³+4³=99

Hence, so x can be 0, or 2

y can be 0 or 3; and

z can be 1 or 4.

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Answer:

The function of j(t) is decreasing.

Step-by-step explanation:

In the question two functions are given as h(t)=3t-4 and j(t)=5-t.

It is required to find whether j(t) is an increasing/decreasing or neither function.

To solve this question, first find the slope of the function. If, the slope is positive the function is increasing and if the slope is negative the function is decreasing.

Step 1 of 1

Find the slope of the function j(t) by comparing these to the standard form.

y=mx+b

Then, m=-1

Since the slope is negative.

Therefore, the function is decreasing.

Assuming you drove the car 78 miles than driving it 77 miles, the total rental cost would be equal to $0.40.

Assuming you drove the car 78 miles than driving it 77 miles, the total rental cost would be calculated by determining the slope of the line for Quick Car Rental (Q) and for Speedy Car Rental.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Substituting the given points into the formula, we have;

[tex]Slope = \frac{55\;-\;15}{100\;-\;0}\\\\Slope = \frac{40}{100}[/tex]

Slope = 0.40.

Therefore, the total rental cost would be equal to $0.40.

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Complete Question:

At both Quick Car Rental and Speedy Car Rental, the cost, in dollars, of renting a full - size car depends on a fixed daily rental fee and a fixed charge per mile that the car is driven. However, the daily rental fee and the charge per mile are not the same for the 2 companies. In the graph below, line Q represents the total cost for Quick Car Rental and line S represents the total cost for Speedy Car Rental. If you rent a full-size car from Quick Car Rental for 1 day how much would the total rental cost be if you drove the car 78 miles than if you drove it 77?

Answer:

10.04°F

Step-by-step explanation:

(12.8°C × 9/5) + 32 = 55.04 - 45 = 10.04

Answer:

D) 72°

Step-by-step explanation:

Tangent:

[tex]\sf \boxed{\angle PQR =\dfrac{Difference \ between \ major \ arc \ and \ minor \ arc }{2}}[/tex]

       ∠PQR = 2x + 252 - (2x + 108)

      2x +72 = (2x + 252 - 2x - 108) ÷ 2

      2x + 72 = (2x - 2x + 252 - 108) ÷ 2  

     2x + 72 = 144 ÷ 2

      2x + 72 = 72

2x + 72-72 = 72 - 72

              2x = 0

             [tex]\sf \boxed{\bf x = 0}[/tex]

m∠PQR = 2x + 72

             = 2*0 + 72

             = 72°

By the quotient and product rules,

[tex]\left(\dfrac fg\right)'(0) = \dfrac{g(0) f'(0) - f(0) g'(0)}{g(0)^2} = 1[/tex]

[tex](f\times g)'(0) = f(0) g'(0) + f'(0) g(0) = 21[/tex]

Given that [tex]f'(0)=5[/tex] and [tex]g'(0)=3[/tex], we have the system of equations

[tex]\dfrac{5g(0) - 3f(0)}{g(0)^2} = 1 \implies 5g(0) - 3f(0) = g(0)^2[/tex]

[tex]3f(0) + 5g(0) = 21[/tex]

Eliminating [tex]f(0)[/tex] gives

[tex]\bigg(5g(0) - 3f(0)\bigg) + \bigg(3f(0) + 5g(0)\bigg) = g(0)^2 + 21[/tex]

[tex]10g(0) = g(0)^2 + 21[/tex]

[tex]g(0)^2 - 10g(0) + 21 = 0[/tex]

[tex]\bigg(g(0) - 7\bigg) \bigg(g(0) - 3\bigg) = 0[/tex]

[tex]\implies \boxed{g(0) = 7 \text{ or } g(0) = 3}[/tex]

Solve for [tex]f(0)[/tex].

[tex]3f(0) + 5g(0) = 21[/tex]

[tex]3f(0) + 35 = 21 \text{ or } 3f(0) + 15 = 21[/tex]

[tex]3f(0) = -14 \text{ or } 3f(0) = 6[/tex]

[tex]\implies \boxed{f(0) = -\dfrac{14}3 \text{ or } 3f(0) = 2}[/tex]

Answer:

2x^2+56x

Step-by-step explanation:

Answer:

y + 2 = 5/3(x - 4)

Step-by-step explanation:

Point-slope form of the equation of a line is a shortcut, fill-in-the-blank formula. You can write an equation just by filling in the slope and a point (hence the name, point-slope)

It looks like this:

y - Y = m(x - X)

The point given is (4,-2) fill in the -2 for the Y. Leave the first y just like it is, it stays a y. Fill in the 4 for X. Leave the first little x in the parenthesis alone Leave it an x.

y - -2 = m(x - 4)

Fill in the slope for the m.

y - -2 = 5/3(x - 4)

Simplify if possible.

y + 2 = 5/3 (x - 4)

Answer:

2(-5 - 7j) = -10 - 14j

Step-by-step explanation:

Using the distributive property means that we have to multiply both -5 and -7j by 2:

2(-5 - 7j)

⇒ 2 × -5  +  2 × -7j

⇒ -10 - 14j

The solution for the system of equations: y = 3 - 2x and y = 8 - 7x, is x = 1, y = 1.

In the question, we are given a system of equations,

y = 3 -2x ... (i), and

y = 8 - 7x ... (ii).

We have been asked to solve the given system of equations.

To solve the system of equations, we do as follows:

Substitute the value of y = 3 - 2x, from (i) in (ii), to get:

y = 8 - 7x,

or, 3 - 2x = 8 - 7x, which is a linear equation in one variable.

To solve this, we follow these steps:

3 - 2x = 8 - 7x,

or, 3 - 2x + 7x = 8 - 7x + 7x {Adding 7x to both side of the equation},

or, 3 + 5x = 8 {Simplifying},

or, 3 + 5x - 3 = 8 - 3 {Subtracting 3 from both sides of the equation},

or, 5x = 5 {Simplifying},

or, 5x/5 = 5/5 {Dividing both sides of the equation by 5},

or, x = 1.

Substituting x = 1, in (i), we get:

y = 3 - 2x,

or, y = 3 - 2(1),

or, y = 3 - 2 = 1.

Thus, the solution for the system of equations: y = 3 - 2x and y = 8 - 7x, is x = 1, y = 1.

Note: The language seemed not gettable.

The question has been done assuming the question asking to solve the system of equations:

y = 3 - 2x, y = 8 - 7x.

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Answer:

(f+g)(x)=f(x)+g(x)

=(-3x-5)+(4x-2)

= -3x-5+4x-2. collect like term

= -3x+4x-5-2

= x-7. the final answer

The computation shows that the value of the length of ZY will be B. 24.

Let the assumed figures be:

BZ = 48

BA = 12

WV = 24

ZY = Unknown

Let's assume that the opposite sides in the quadrilateral are the same, the value of ZY will be:

ZY = (48 × 12)/24

ZY = 24

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Answer:

C.12

Step-by-step explanation:

Trust

Answer: Option (4)

Step-by-step explanation:

We need factors of [tex](x+2), (x+1), (x-4)[/tex]

The balanced equation for the given reaction [tex]\mathbf{AgNO_3+NaCl \to AgCl_{(s)} + NaNO_3}[/tex]

A double replacement is a chemical reaction that takes place in which two reactants swap cations or anions to produce two distinct products.

Whenever the cations representing one of the reactants interact with the anions from another reactant to produce an insoluble ionic compound, a precipitate occurs.

The balanced equation for the given reaction:

[tex]\mathbf{AgNO_3+NaCl \to AgCl_{(s)} + NaNO_3}[/tex]

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Answer:

Around 12.25

Step-by-step explanation:

There are around 2205 (2204.62) lbs  per metric tonnes.

So 27000/2204.62  or 27000/2205 gives you between 12.24-12.25

Then, the elevation of Mount Everest's peak as a rational number is[tex]\frac{8,848}{1}[/tex] meters. The elevation of Kanchenjunga's peak as a rational number is  [tex]\frac{8,586}{1}[/tex] meters.

1. The number 8,848 is an integer and the number 8,586 is also an integer.

2. Therefore, to solve this problem you must convert the integers shown above to fractions (Because a rational number is that one that can be written as a fraction), as you can see below:

Write each integer as the numerator of the fraction a write 1 as the denominator. This will not change the value.

A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.

Then you obtain the following fractions:

[tex]\frac{ 8,848}{1}[/tex]

[tex]\frac{8,586}{1}[/tex]

3. Then, the elevation of Mount Everest's peak as a rational number is[tex]\frac{8,848}{1}[/tex] meters. The elevation of Kanchenjunga's peak as a rational number is  [tex]\frac{8,586}{1}[/tex] meters.

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The value of b is [tex]1 \cdot02[/tex].

What is compound interest?

Compound interest is when you earn interest on both the money you have saved and the interest you earn.

Formula for compound interest is

[tex]A= P(1+\frac{r}{100})^n[/tex] ...................(1)

where, A = total amount( principal + interest )

r = rate of interest in compound interest

n = number of years

Given,

For [tex]n=1[/tex]

Principal amount [tex]p=\$ 1000[/tex]

Total amount [tex]A=\$ 1020[/tex]

For [tex]n=2[/tex]

Principal amount [tex]p=\$ 1000[/tex]

Total amount [tex]A=\$ 1040[/tex]

This scenario can be represented by an exponential function of the form of [tex]f(x)=1000(b)^x[/tex]

Comparing the above function with equation (1), we get

[tex]A=f(x)\\P=1000\\b=(1+\frac{r}{100})[/tex]

For 1st year

[tex]f(x)=1000(b)^1\\\Rightarrow 1020=1000(b)\\\Rightarrow b=\frac{1020}{1000}\\\Rightarrow b= \frac{102}{100}\\\Rightarrow b= 1\cdot02[/tex]

now, check the amount for 2nd year

[tex]f(x)=1000 \times (1 \cdot01}^2\\\Rightarrow f(x)=1000 \times \frac{102}{100}\times \frac{102}{100}\\\Rightarrow f(x)=1040[/tex]

Hence, the value of b is [tex]1 \cdot02[/tex] .

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Answer:

[tex](x+1)(x-3)[/tex]

Step-by-step explanation:

A quadratic in factored form is usually expressed as: [tex]a(x\pm a)(x \pm b)[/tex] where the sign of a and b depends on the sign of the zero. And I said "usually" since sometimes the x will have a coefficient. Anyways in the quadratic there are two zeroes at x=-1 and x=3. This can be written as: [tex]a(x+1)(x-3)[/tex]. Notice how the signs are different? This is because when you plug in -1 as x you get a factor of (-1+1) which becomes 0 and it makes the entire thing zero since when you multiply by 0, you get 0. Same thing for the x-3 if you plug in x=3. Now a is in front and it can influence the stretch/compression. To find the value of a, you can take any point (except for the zeroes, because it will make the entire thing zero, and you can technically input anything in as a)

I'll use the point (1, -4) the vertex

-4 = a(1+1)(1-3)

-4 = a(2)(-2)

-4 = -4a

1 = a. So yeah the value of a is 1

So the equation is just: [tex](x+1)(x-3)[/tex]

By applying the concept of finite sum and the properties of the series, we conclude that the finite sum [tex]p = \sum \limit_{x=1}^{3} 2^{x}+ 2[/tex] is equal to the value of 34.

Let be a sum of the form [tex]p = \sum\limits_{i= 1}^{n} a_{i}[/tex], where n represents an integer. This kind of sum represents a finite sum, whose expanded form is presented below:

p = a₁ + (a₁ + a₂) + (a₁ + a₂ + a₃) + ... + (a₁ + a₂ + a₃ + ... + aₙ₋₁ + aₙ)     (1)

If we know that [tex]p = \sum \limit_{x=1}^{3} 2^{x}+ 2[/tex], then the result of the finite sum is:

p = (2 + 2¹) + (2 · 2 + 2¹ + 2²) + (3 · 2 + 2¹ + 2² + 2³)

p = 4 + (4 + 6) + (6 + 14)

p = 4 + 10 + 20

p = 34

By applying the concept of finite sum and the properties of the series, we conclude that the finite sum [tex]p = \sum \limit_{x=1}^{3} 2^{x}+ 2[/tex] is equal to the value of 34.

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Answer: [tex]f^{-1} (x)=\frac{4x-5}{2}[/tex]

Step-by-step explanation:

Let [tex]f(y)=x\\[/tex].

[tex]\implies x=\frac{2y+5}{4}\\\\4x=2y+5\\\\4x-5=2y\\\\y=\frac{4x-5}{2}\\\\\therefore f^{-1} (x)=\frac{4x-5}{2}[/tex]