Consider the quadratic equation y^2-y=6. What is the error with the solution below?

Answer:

13.2 cm

Step-by-step explanation:

b = [tex]\sqrt{c^{2} - a\\^{2} }[/tex]

b = [tex]\sqrt{20^{2} - 15\\^{2} }[/tex]

b = [tex]\sqrt{400-225\\} \\[/tex]

b = [tex]\sqrt{175}[/tex]

b = 13.228

b= 13.2 cm

:) good luck on the rest!

The probability of exactly 6 radioactive particles passing through a counter in 1 millisecond, with an average rate of 4, is approximately 0.1041 or 10.41%.

To find the probability of a specific number of events occurring in a Poisson distribution, use the formula:

P(X = k) = [tex](e^{(-\lambda)} \times \lambda^k) / k![/tex]

Where:

P(X = k) is the probability of observing k events.

e is the base of the natural logarithm, approximately equal to 2.71828.

λ (lambda) is the average rate of events occurring in a given time period.

k is the number of events you want to find the probability for.

k! is the factorial of k.

λ is the average number of radioactive particles passing through the counter in 1 millisecond, which is 4.

So, to find the probability of 6 particles entering the counter in a given millisecond:

P(X = 6) = (e⁻⁴) × 4⁶) / 6!

Let's calculate it step by step:

Calculate 6! (6 factorial):

6! = 6 x 5 x 4 x 3 x 2 x 1

    = 720

Calculate e⁻⁴:

e⁻⁴ ≈ 0.01832 (rounded to five decimal places)

Calculate 4⁶:

4⁶ = 4 x 4 x 4 x 4 x 4 x 4

    = 4,096

Now, plug these values into the formula:

P(X = 6) = (0.01832 × 4,096) / 720

P(X = 6) ≈ 0.1041

Therefore, the probability that exactly 6 radioactive particles enter the counter in a given millisecond is approximately 0.1041, or about 10.41%.

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It is the bottom left.

76 is the correct answer

The price of the jersey before the mark-up = $76

"A number that can be expressed as a fraction of 100."

"It is a mathematical statement which consists of equal symbol between two algebraic expressions."

For given question,

A basketball jersey has been marked up by 25% and is now selling for $95.00

Let 'm' be the price of the jersey before the mark-up.

So, we get an equation,

⇒ m + (25 percent of m) = 95

25 percent of m

= [tex]\frac{25}{100}\times m[/tex]

= 0.25 m

so, the equation becomes,

⇒ m + 0.25 m = 95

⇒ 1.25 m = 95

⇒ m = 76

Therefore, the price of the jersey before the mark-up = $76

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The first three iterates of the function f(z) = 2z + (3 - 2i) with z0 = 5i are 3 + 8i, 9 + 14i, and 21 + 26i after consecutive substitutions. The first three iterates of the function are 3 + 8i, 9 + 14i, and 21 + 26i.

To find the first three iterates of the function f(z) = 2z + (3 - 2i) with the initial value z0 = 5i, we perform successive substitutions into the function.

Thus, the first three iterates of the function are 3 + 8i, 9 + 14i, and 21 + 26i.

Final answer:

To find the first three iterates of the function f(z) = 2z + (3 - 2i) with an initial value of z0 = 5i, substitute the initial value into the function to get the first iterate. Then, substitute the first result back into the function to find the second iterate. Finally, substitute the second result back into the function to find the third iterate.

Explanation:

To find the first three iterates of the function f(z) = 2z + (3 - 2i) with an initial value of z0 = 5i, we substitute the initial value into the function:

f(z0) = 2(5i) + (3 - 2i) = 10i + 3 - 2i = 3 + 8i.

Then, we substitute the result back into the function to find the second iterate:

f(3 + 8i) = 2(3 + 8i) + (3 - 2i) = 6 + 16i + 3 - 2i = 9 + 14i.

Finally, we substitute the second result back into the function to find the third iterate:

f(9 + 14i) = 2(9 + 14i) + (3 - 2i) = 18 + 28i + 3 - 2i = 21 + 26i.

24 is the  largest number of identical sets can be made of these crayons and pictures

A number system is defined as a system of writing to express numbers.

To find out the largest number of identical sets that can be made, we need to determine the common factors of the total number of crayons and pictures.

The prime factorization of 48 is 2 x 2 x 2 x 2 x 3, and since all three colors have the same number of crayons, we can say that there are 48 x 3 = 144 crayons in total.

The prime factorization of 72 is 2 x 2 x 2 x 3 x 3, and the prime factorization of 120 is 2 x 2 x 2 x 3 x 5.

The common factors of 144, 72, and 120 are 2 x 2 x 2 x 3 = 24. This means that we can make 24 identical sets.

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Answer:

  7.25%

Step-by-step explanation:

You want the effective rate of interest on a $12,000 Treasury bill with a nominal interest rate of 7% and maturity in 15 weeks.

The Treasury computes the selling price of the bill by subtracting the interest from the face value. The interest is computed as "ordinary interest" using a 360-day year. 15 weeks is 105 days.

  I = Prt

  I = $12000·0.07·(105/360) = $245

Then the cost of the bill is $12,000 -245 = $11,755.

Using the formula for the maturity value with a 365-day year, we have ...

  A = P(1 +rt)

  12000 = 11755(1 +r(105/365))

Solving for r gives ...

  [tex]r=\left(\dfrac{12000}{11755}-1\right)\cdot\left(\dfrac{365}{105}\right)\approx0.0724514\approx\boxed{7.25\%}[/tex]

The effective rate of interest is about 7.25%.

Grass can grow up to six inches in a week depending on temperature, humidity, and time of year

We have to calculate how tall will grass grow in 24 days

we know there are seven days in a week

so in one day grass can grow up to 6/7 inches

therefore we could say that grass can grow up to 24*6/7 inches

so the answer is 20.57 inches

so in 24 days grass can grow up to 20.57 inches

Grass can grow approximately 20.58 inches in 24 days.

To calculate the height that grass will grow in 24 days, we need to find out how much it grows in 1 week, and then multiply that by the number of weeks in 24 days. If grass can grow up to six inches in a week, we can calculate the height it will grow in 24 days as follows:

Therefore, grass will grow approximately 20.58 inches in 24 days.

The roots of the Given quadratic equation are x₁ = -2 and x₂ = -12.

ax²+bx+c=0, with a not, equal to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given a quadratic equation, x² + 24 = 14 x

Simplifying the equation using the factorization method,

=> x² + 24 = 14 x

=> x² +14 x +24 = 0

factorize the "x term"

=> x² +12x + 2x +24 = 0

=> x(x +12)+2(x + 12) = 0

=>(x + 2)(x + 12) = 0

x = -2, -12

thus,

the value of x will be either -12 or -2

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Final answer:

The secant of an angle is the reciprocal of its cosine. Given cos θ = 2/3 for an acute angle in a right triangle, the sec θ equals 3/2.

Explanation:

In the context of trigonometry, the secant (sec) of an angle is the reciprocal of the cosine (cos) of that angle.

Given that cos θ = 2/3 for an acute angle in a right triangle, we can find the value of sec θ by taking the reciprocal of the cosine value. Hence, the value of sec θ is simply the reciprocal of 2/3, which is 3/2.

Answer: Each piece is 2.6 long

Step-by-step explanation: All you have to do is divide 8 and 3 and you will get 2.6

(sorry if i'm wrong)

Final answer:

A real-world problem involving the calculation of a triangle's area could include finding the area of a triangular plot of land to determine how much grass seed is needed for landscaping. By using the formula for the area of a right-angled triangle, we can calculate the area in square meters and subsequently determine the required quantity of grass seed.

Explanation:

Real World Triangle Area Problem

Calculating the area of a triangle is a common problem in real-world applications. For instance, consider a scenario where you need to find the area of a triangular plot of land to determine how much grass seed to purchase for landscaping. If the plot is a right-angled triangle with one leg measuring 50 meters and the other leg measuring 40 meters, you can use the formula for the area of a right-angled triangle, which is ½ × base × height.

In this case, the base would be one leg of the triangle (50 meters), and the height would be the other leg (40 meters). Therefore, the area would be:

Area = ½ × 50 m × 40 m

Area = 25 m × 40 m

Area = 1000 square meters

Knowing the area of the triangular plot, you can then calculate the amount of grass seed needed, based on the recommended seeding rate per square meter. This practical example demonstrates how mathematics, specifically triangular area calculation, is applied in landscaping projects.

The two numbers will be 21.5 and -14.5. Addition, subtraction, multiplication, and division are the four basic math operations.

Arithmetic is an area of mathematics involving the study of numbers and the different operations that can be performed on them.

Let the two numbers will be x and y

The sum of the two numbers is 7

x+y=7 ------ 1

The difference between the two numbers is 36

x-y=36 -------2

On subtracting the equation 2 by equation 1 we get;

x-y-x-y=36-7

-2y=29

y= -14.5

From equation 1

x+y=7

x-14.5=7

x=7+14.5

x=-21.5

Hence the two numbers will be 21.5 and -14.5.

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When the height of a triangle is 4 cm and the area is 12 square cm, with the height increasing at 2 cm/min and the area increasing at 12 square cm/min, then the base of the triangle is changing at a rate of 5 cm/min.

The subject of this question is Mathematics and is at the High School level. This question deals with the concept of related rates in calculus. First and foremost, remember the formula for the area of a triangle, which is A = 1/2bh, where A is the area, b is the base, and h is the height. Since we're given the rate of change of the height (dh/dt=2 cm/min) and the area (dA/dt=12 square cm/min), we can use this information in combination with the formula for the area of a triangle to derive an implicit function representing the rate of change of the base. By differentiating with respect to time t, we get dA/dt = 1/2b dh/dt + 1/2h db/dt. Plugging in the given values and solving for db/dt (the rate of change of the base length), we get db/dt = (2*dA/dt/h) - dh/dt. Then input the specific values at the given point, h = 4 cm and dA/dt = 12 square cm/min, dh/dt = 2 cm/min. The calculation results in db/dt = 5 cm/min. Therefore, the base of the triangle changes at a rate of 5 cm/min when the height is 4 cm and the area is 12 square cm.

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