Find the slope using the following two points:
(2,-7) and (-1,6)

Answer:

12

Step-by-step explanation:

because you can see that in the first column, the y value is 4 times the x value

and in the third column, the y value is still 4 times greater than the x value

meaning that you need to find a number that is 4 times the value of 3 (because that is the x value)

3 times 4 is 12

Answer:

16

Step-by-step explanation:

22-6=16

Option C. which corresponds to the probability of approximately 0.0771 that there will be 8 occurrences within a period of ten minutes.

This problem follows a Poisson distribution, where the mean and variance of the distribution are equal to λ. Here, λ = 5, and we need to find the probability of having 8 occurrences in 10 minutes. The probability mass function of Poisson distribution is:

P(X = k) = (e⁽⁻λ⁾ * λᵏ) / k!

Substituting the given values, we get:

P(X = 8) = (e⁽⁻⁵⁾ * 5⁸) / 8!

P(X = 8) ≈ 0.0771

Therefore, the probability that there are 8 occurrences in ten minutes is approximately 0.0771, which corresponds to option C.

This problem follows a Poisson distribution, where the mean and variance of the distribution are equal to λ. Here, λ = 5, and we need to find the probability of having 8 occurrences in 10 minutes. The probability mass function of Poisson distribution is:

P(X = k) = (e⁽⁻λ⁾ * λᵏ) / k!

Substituting the given values, we get:

P(X = 8) = (e⁽⁻⁵⁾ * 5⁸) / 8!

P(X = 8) ≈ 0.0771

Therefore, the probability that there are 8 occurrences in ten minutes is approximately 0.0771, which corresponds to option C.

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The value of given differential equation \(y' = y - x\) with the initial condition \(y(0) = 1.5\), on the interval \(0 \leq x \leq 1.5\), is \(y(1.5) = y_4 = 5.4296875\).

The differential equation we are given is \(y' = y - x\), with the initial condition \(y(0) = 1.5\). We are asked to approximate the solution on the interval \(0 \leq x \leq 1.5\) with a step size of \(h = 0.5\), and we want to achieve an accuracy of \(e = 0.0001\).

We start by calculating the first two values, \(y_0\) and \(y_1\), using the formula:

\(y_1 = y_0 + h \cdot f(x_0, y_0)\)

Here, \(h\) represents the step size, \(f(x, y)\) represents the derivative \(y'\) in terms of \(x\) and \(y\), and \((x_0, y_0)\) is the initial condition.

Using the given values, we can calculate \(y_1\) as:

\(y_1 = 1.5 + 0.5 \cdot (1.5 - 0) = 2.25\)

Next, we calculate \(y_2\) using the same formula:

\(y_2 = y_1 + h \cdot f(x_1, y_1)\)

Substituting the values \(x_1 = 0.5\) and \(y_1 = 2.25\), we get:

\(y_2 = 2.25 + 0.5 \cdot (2.25 - 0.5) = 3.375\)

Similarly, we can calculate \(y_3\) and \(y_4\) as:

\(y_3 = 3.375 + 0.5 \cdot (3.375 - 1) = 4.3125\)

\(y_4 = 4.3125 + 0.5 \cdot (4.3125 - 1.5) = 5.4296875\)

So, the value of \(y\) at \(x = 1.5\) is \(y(1.5) = y_4 = 5.4296875\).

Using Euler's method with a step size of \(h = 0.5\) and an accuracy of \(e = 0.0001\), the solution to the given differential equation \(y' = y - x\) with the initial condition \(y(0) = 1.5\), on the interval \(0 \leq x \leq 1.5\), is \(y(1.5) = y_4 = 5.4296875\).

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Answer:

Step-by-step explanation:

If you mean 3x^3 - 42x^2 - 4x + 5 = 0 you can graph it manually or with technology

The roots are 14.09, 0.30 and -0.39 to nearest hundredth.

Answer:

10

Step-by-step explanation:

\(x+70=16(5)\\\\x+70=80\\\\x=10\)

Therefore, the number is 10

Answer:

all real numbers greater than or equal to 2

Step-by-step explanation:

the range of a function is the values that y can have.

the minimum value of y is at y = 2

the solid blue circle indicates that y can equal 2.

above y = 2 the values of y keep increasing

range is y ≥ 2 , y ∈ R

Answer:f(n)=259

Step-by-step explanation:

F(n)=75+25(n-1)

F(n)= 75+25(7)

F(n)=75+175

F(n)=250

The area and circumference of the circle will be 28.26 square units and 18.84 units, respectively.

Let r be the radius of the circle. Then the area of the circle will be

A = πr² square units

The circumference of the circle will be

C = 2πr units

From the diagram, the radius of the circle is 3 units. Then the area of the circle will be

A = πr²

A = 3.14 x 3²

A = 3.14 x 9

A = 28.26 square units

Then the circumference of the circle will be

C = 2πr

C = 2 x 3.14 x 3

C = 18.84 units

The area and circumference of the circle will be 28.26 square units and 18.84 units, respectively.

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Given:

The quadratic equation is:

\(10m^2-7m+3=0\)

To find:

The solutions for the given equation by using the quadratic formula.

Solution:

If a quadratic equation is \(ax^2+bx+c=0\), then the quadratic formula is:

\(x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\)

We have,

\(10m^2-7m+3=0\)

Here, \(a=10,b=-7,c=3\). Using the quadratic formula, we get

\(m=\dfrac{-(-7)\pm \sqrt{(-7)^2-4(10)(3)}}{2(10)}\)

\(m=\dfrac{7\pm \sqrt{49-120}}{20}\)

\(m=\dfrac{7\pm \sqrt{-71}}{20}\)

\(m=\dfrac{7\pm i\sqrt{71}}{20}\)             \([\because \sqrt{-a}=i\sqrt{a},a>0]\)

Therefore, the solution set of the given equation is \(\left\{\dfrac{7- i\sqrt{71}}{20},\dfrac{7+ i\sqrt{71}}{20}\right\}\). Hence, the correct option is D.

The system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped are:

50x+80y=1750

y = x+4 ,

where x represent the number of small boxes of paper and y represent the number of large boxes of paper.

We have:

Weight of small box of paper = 50 pounds

Weight of large box of paper = 80 pounds

Total weight of boxes = 1750 pounds

Let us consider that  the number of small boxes of papers be x.

The number of large boxes of papers be y.

Then, according to question

50x+80y=1750

y = x+4  

Therefore, the equations 50x+80y=1750 and y = x+4 can be used to determine the number of small boxes and large boxes of paper shipped.

where, x represent the number of small boxes of paper and y represent the number of large boxes of paper.

Answer:

Statement 1 is true; Statement 2 is false.

Step-by-step explanation:

Statement 1:

√12 - √8 = a

Let's use the given value of √12 + √8 ,that is, 4/ a.

If we multiply both the expressions such that their Left Hand Sides get multiplies together and Right Hand Sides together:

=> (√12- √8)(√12 + √8) = a × 4/a

On the LHS,

identity used:

(a-b)(a+b) = a²-b²

On the RHS:

a gets canceled due to its presence in both the numerator as well as the denominator.

=> 12 - 8 = 4

=> 4 = 4

That's it!

We got LHS = RHS, that approves the existence of the given statement.

___________________

Statement 2:

"a + √b is called the rationalizing factor of c + √d if their product is 1"

That's not entirely right!

The correct statement would be:

" a + √b is called the rationalizing factor of c + √d if their product is a rational number ."

Since, rationalizing has got nothing to do with 1, (1 is just another rational number), even if we get 2 by their multiplication, it will be called rationalizing as long as we're getting a rational number.

___________________

Answer:

Hence, I'd say:

Statement 1 is correct but Statement 2 isn't.

That's the third option.

Answer:i think it is 5

Step-by-step explanation:

A shifted ramp signal is a type of analog signal that starts from a specific value and gradually increases in a linear manner until it reaches another value, at which point it remains constant.

The "shifted" part refers to the starting value, which is not necessarily zero but can be any arbitrary value. This type of signal is commonly used in electronics and signal processing applications, such as in voltage-controlled oscillators and analog-to-digital converters. In essence, a shifted ramp signal is a linearly increasing signal that has been shifted up or down to start from a non-zero value.

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The probability that the randomly selected sample will have less than 97.5% of the units that can hold at least 400 lbs of weight before breaking is 2.4249.

What is the binomial distribution?

In probability theory and statistics, the discrete probability distribution of the number of successes in a series of n separate experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success or failure, is known as the binomial distribution with parameters n and p.

Here, we have

Given: For one product, 98% of all the units made at a particular factory can hold at least 400 lbs. of weight before breaking to check the product, quality control selects a random sample of 300 units made at the factory and determines whether or not the product can hold at least 400 lbs.

p = 0.98

q = 1 - p = 1 - 0.98 = 0.02

n = 300

Using the binomial distribution,

Standard deviation = σ = √npq = √300 × 0.98 × 0.02 = 2.4249

Standard deviation = σ = 2.4249

Hence, the probability that the randomly selected sample will have less than 97.5% of the units that can hold at least 400 lbs of weight before breaking is 2.4249.

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Answer: (d)- 1.76 kg

Step-by-step explanation:

Given

The first laptop mass was 11 kg

The rate of mass decreases by 4.7% per year

In 1982, it was

\(\Rightarrow 11-11\times 4.7\%=11-11\times 0.047\\\Rightarrow 11(1-0.047)\ kg\)

In 1983, it was

\(\Rightarrow 11(1-0.047)-11(1-0.047)\times 0.047=11(1-0.047)^2\)

In 2019 i.e. after 38 years, it is

\(\Rightarrow 11(1-0.047)^38=11\times 0.953^{38}=1.76\ kg\)

The answer is 2 1/4 cupcakes

Answer:

2 1/4 cupcakes

Step-by-step explanation:

Step 1: State what is know

There are 3 people Jake, Brother 1, and Brother 2.  They all ate 3/4 of a cup cake each

Step 2: Solve

Multiple 3 by 3/4

3 x 3/4 = \(C_{Total}\)

2.25 = \(C_{Total}\\\)

0.25=1/4

2 1/4 cupcakes

Step 3: Therefore Statement

Therefore the 3 brothers ate 2 1/4 cupcakes

Answer:

60.000 x 10 to the power of 3

Step-by-step explanation:

The probability that the three segments can be arranged to form a triangle is 1 - 1/6 = 5/6. Answer: 5/6

Let's consider a unit segment that is 1 unit in length. Assume two points A and B are chosen arbitrarily on the segment. Now, we need to determine the probability that the three segments formed by these two points can be arranged to form a triangle. Let these segments be AB, AC, and BC,

where C is any point that lies between A and B.There are several techniques for solving this problem. We'll use the geometric probability approach.

First, we'll draw a diagram of the segment AB and then a point C between A and B. Let the lengths of segments AB, AC, and BC be represented by x, y, and z, respectively, as shown in the figure below.  \(\overline{AB}\) is a unit segment and C lies between A and B.

The lengths of \(\overline{AC}\) and \(\overline{BC}\) are x and y units respectively.Let's use the Triangle Inequality theorem to see if these segments can form a triangle.

According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, or a + b > c, where a, b, and c are the lengths of the sides.

Using this theorem, we can write the following inequalities:x + y > zx + z > yz + y > xAdding these three inequalities together, we get:2x + 2y + 2z > x + y + z, orx + y + z > 1.  

Hence, the probability that the three segments can be arranged to form a triangle is 1 - P(x + y + z ≤ 1). Let's compute P(x + y + z ≤ 1) by determining the area of the region where x + y + z ≤ 1. This area is a tetrahedron with a base of area 1/2 and a height of 1/3, giving a volume of 1/6.  

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n = -16 - √336÷2=-8-2√21= 17•165

n=-16+√336

_______

2. = -8+2√21 = 1•165

The maximum volume square candy box to be cut out is 2.88 inches.

If the size of the squares to also be cut out is x, then

A rectangular box's volume is provided by length x width x height.

V = (25 - 2x)(14 - 2x)x = x(350 - 78x + 4x²)

V = 350x - 78x² + 4x³

For the maximum volume of the candy box.

dV/ dt = 0

Differentiate the volume with respect to time.

dV/ dt = 350 - 156x + 12x².

Then,

350 - 156x + 12x² = 0

Solve the above quadratic equation by the quadratic formula and find the roots as-

x = 10.12  and 2.88

However, the size of a square cut out cannot be 10.12 because 10.12 inches cannot be cut from both sides of a 14-inch width.

As a result, the maximum volume square to be cut out is 2.88 inches.

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Answer:

\(n^6\).

Step-by-step explanation:

\(n^4 * \frac{n^7}{n^5}\)

= \(n^4 * n^{7 - 5}\)

= \(n^4 * n^2\)

= \(n^{4 + 2}\)

= \(n^6\).

Hope this helps!

The geometrical representation of y=3 as an equation in

a) one variable is y = 3

b) in two variables is 0x + y = 3.

Based on the information illustrated, the geometrical representation of y=3 as an equation in one variable is y = 3.

Also, the geometrical representation of y=3 as an equation in two variables is:

y = 3.

0x + y = 3

0x + y - 3 = 0

Therefore, y = 3.

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Answer:

1/3 is the correct answer...

Hope it helps!!!!

The probability that the exam scores are at least 37 is 0.4013 or 40.13%

The probability that the exam scores are at least 37 can be calculated using the normal distribution function. To calculate the probability, we first need to standardize the variable using the formula z = (x - μ) / σ, where x is the value of interest (in this case, x = 37), μ is the mean, and σ is the standard deviation.

z = (37 - 36.12) / 3.53 = 0.25

Using a standard normal distribution table or a calculator, we can find the probability that a standard normal random variable is greater than or equal to 0.25, which is approximately 0.4013.

Therefore, the probability that the exam scores are at least 37 is 0.4013 or 40.13%

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The estimate of the mean length of the insects Ciara found is 17 millimeters (mm).

To calculate an estimate of the mean length of the insects Ciara found, we need to find the weighted average of the lengths using the given frequencies.

Let's denote the lower limits of the length intervals as L1 = 0, L2 = 10, and L3 = 20.

Similarly, denote the upper limits as U1 = 10, U2 = 20, and U3 = 30.

Next, we calculate the midpoints of each interval by taking the average of the lower and upper limits.

The midpoints are M1 = (L1 + U1) / 2 = 5, M2 = (L2 + U2) / 2 = 15, and M3 = (L3 + U3) / 2 = 25.

Now, we can calculate the sum of the products of the frequencies and the corresponding midpoints.

This gives us (5 \(\times\) 5) + (6 \(\times\) 15) + (9 \(\times\) 25) = 25 + 90 + 225 = 340.

Next, we calculate the sum of the frequencies, which is 5 + 6 + 9 = 20.

Finally, we divide the sum of the products by the sum of the frequencies to find the weighted average, which is 340 / 20 = 17.

Therefore, the estimate of the mean length of the insects Ciara found is 17 millimeters (mm).

Thus, the mean length of the insects Ciara found is approximately 17 millimeters (mm).

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