The two tables below show the success rates of several groups of businesses in a certain city. The first shows the number of businesses of several types started in Sharon’s city over the course of two years, and the number of those businesses which did not succeed and were forced to shut down within two years of opening. The second deals with separate records of successful new businesses, showing how much profit those new businesses turned over two years. Businesses on the boundary lines fall in the lower category. Type Food Retail Financial Service Opened 3,193 2,280 1,898 5,045 Closed 1,977 1,626 1,443 3,548 Up to $25k $25-50k $50-75k $75-100k Over $100k Food 945 623 601 258 114 Retail 813 548 347 188 63 Financial 316 244 195 86 51 Service 979 739 432 174 124 Using the tables as experimental data, determine which of the following situations have a probability of at least 15.00%. I. a food establishment succeeding and earning $50,000 or more II. a service establishment succeeding and earning between $25,000 and $75,000 III. a retail establishment succeeding and earning no more than $50,000 a. I only b. I and II c. II and III d. III only

It is the bottom left.

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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Rhono earns a net monthly pay of $560.00 after taxes, with monthly expenses totaling $113.75. This leaves him with $446.25 per month, resulting in a total savings of $5,355.00 at the end of 12 months.

Rhono works:

- 3 hours each night after school

- 5 hours on Saturdays

His gross hourly pay is $8.75.

In a week, he works 3 hours × 5 days from Monday to Friday and 5 hours on Saturday,

which totals 15 hours + 5 hours

= 20 hours per week.

In a month (considering approximately 4 weeks per month), he works 20 hours × 4 weeks

= 80 hours per month.

Gross monthly income = hourly wage × total hours worked per month

Gross monthly income = 8.75 × 80

Gross monthly income = $700

Rhono's gross monthly income is $700, and 20% of this will be deducted.

Tax deduction = 0.20 × 700

Tax deduction = 140

Total monthly expenses = 35.00 + 21.00 + 18.00 + 24.00 + 15.75

Total monthly expenses = $113.75

Net monthly income = Gross monthly income - Tax deduction - Total monthly expenses

Net monthly income = 700 - 140 - 113.75

Net monthly income = $446.25

This is the amount Rhono has left over at the end of each month.

Total savings after 12 months = 446.25 × 12

Total savings after 12 months = $5,355

So, Rhono would have saved $5,355 at the end of 12 months.

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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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)

Answer: C: 9.26

Step-by-step explanation:

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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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.

m<1 +m<2 = 180° is the answer

Answer:

Third option is the right choice.

Step by step explanation:

We have been given an diagram and we are asked to choose the true statement about the diagram.

Let us see our all choices one by one.

1. [tex]m\angle5+m\angle6=m\angle1[/tex]

We can see that [tex]\angle5[/tex] and [tex]\angle6[/tex] are supplementary and there measure should be equal to 180 degrees. [tex]\angle1[/tex] is exterior angle of our triangle and its measure must be equal to sum of measures of [tex]\angle5[/tex] and [tex]\angle3[/tex].

Therefore, 1st option is incorrect.  

2. [tex]m\angle3+m\angle4+m\angle5=180^{o}[/tex]

We can see that [tex]\angle3[/tex] and [tex]\angle4[/tex] are supplementary and they must be equal to 180 degrees.  Therefore, 2nd option is also incorrect.

3. [tex]m\angle1+m\angle2=180^{o}[/tex]

We can see from our diagram that [tex]\angle1[/tex] and [tex]\angle2[/tex] are supplementary. Therefore, 3rd option is the correct choice.

4. [tex]m\angle2+m\angle3=m\angle5[/tex]

We can see that [tex]\angle2[/tex], [tex]\angle3[/tex] and [tex]\angle5[/tex] are interior angles of our triangle and their measure should be equal to 180 degrees. By exterior angle theorem sum of measures of [tex]\angle2[/tex] and [tex]\angle3[/tex] will be equal to measure of [tex]\angle6[/tex] instead of [tex]\angle5[/tex].

Therefore, our 4th option is also incorrect.