EASY GEOMETRY**
IDENTIFY THE angle shown​

5 feet is the greatest distance that a person could be from the lamp and be detected.

A circle is defined as round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center).

Since we have given that

The equation is :

\((x+15)^2+(y-12)^2=25\)

It is the equation of circle in which center is (h,k) i.e. ( 15,12)

The general equation of circle is given by

\((x-h)^2+(y-k)^2=r^2\)

Here, the radius 'r' is given by

\(r^2=25\)

\(r=\sqrt{25\)

\(r=5\)

Here, the greatest distance a person could be from the lamp and be detected is represented by radius i.e. r = 5 feet.

Hence, 5 feet is the greatest distance that a person could be from the lamp and be detected.

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To determine the number of lawns Carlos and Jack need to mow in order to have enough money for the school trip, an inequality is established based on their current savings and the cost of the trip. The inequality is solved to find the minimum number of lawns they need to mow individually.  

Part A: To find the number of lawns each boy needs to mow individually, we can set up an inequality based on their current savings and the cost of the trip. Carlos has $42 and Jack has $51. Let's assume Carlos needs to mow 'x' lawns, and Jack needs to mow 'y' lawns. The inequality can be written as:

42 + 30x ≥ 156

51 + 30y ≥ 156

Solving these inequalities will give us the minimum number of lawns each boy needs to mow to have enough money for the trip.

Part B: Now, if Carlos and Jack want to earn an additional $75 each for spending money, they plan to work together mowing lawns. Let 'z' represent the number of lawns they mow together. The new inequality can be written as:

30z ≥ 75

To find the number of lawns they need to mow together to earn the extra money, we can solve this inequality. By solving the inequalities, you will obtain the specific values for 'x' and 'y' in Part A and 'z' in Part B, which represent the minimum number of lawns each boy needs to mow individually or together to have enough money for the trip and earn additional spending money.

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Answer:

-2

Step-by-step explanation:

f(x)=-3x+3

substitute value of f(x) with 9.

9=-3x+3

9-3=-3x

6/-3=x

-2=x

Given:

f(x)=-3x+3

When,

★Substituting the values in the above equation

f ( 9 ) = - 3 × 9 + 3

= -18 + 3

= -15

The two squares and the shaded region of square A is in the attachment.

Answer: The shaded region of A is 12.5% of the area of B.

Step-by-step explanation: Assume that the length of side of square A is a and the length of side of square B is b.

Length a is half (50%) of length b:

a = \(\frac{b}{2}\)

The shaded region is a triangle. The area of a triangle is: A = \(\frac{b.h}{2}\)

b and h are the sides of the square A, so:

\(A_{1}\) = \(\frac{\frac{b}{2}.\frac{b}{2}}{2}\)

\(A_{1} = \frac{b}{2}.\frac{b}{2}.\frac{1}{2}\)

\(A_{1} = \frac{b^{2}}{8}\)

Area of square B is:

\(A_{2}\) = b.b

\(A_{2} = b^{2}\)

Comparing areas:

\(\frac{\frac{b^{2}}{8} }{b^{2}}\) = \(\frac{b^{2}}{8}.\frac{1}{b^{2}}\) = \(\frac{1}{8}\)

As percentage:

\(\frac{1}{8}\) × 100 = 0.125 × 100 = 12.5%

Comparing the shaded region of A to square B, the area of the first is 12.5% smaller than the second.

At least 5 expected observations in each cell in order to apply the chi-square test of independence, we prefer to have at least 5 expected observations in each cell. The correct answer is c.

The chi-square test of independence is a statistical method used to determine whether two categorical variables are independent or associated with each other.

To apply this test, it is preferred to have at least 5 expected observations in each cell of the contingency table. The expected frequency is calculated based on the assumption of independence between the two variables.

If the expected frequency is less than 5 in any cell, the chi-square test may not be valid and alternative methods, such as Fisher's exact test, should be considered. Having a sufficient sample size can also improve the accuracy and reliability of the test results.

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150.72

...............

13.2

Step-by-step explanation:

r = 2.1

circumference of circle = 2πr

=2 × 22/7 × 2.1

= 13.2

Aksa is correct, that each layer has 24 cubes in it, as each layer is composed of four lines, and each line is composed by six cubes.

The number of cubes in each layer is obtained applying the proportions in the context of the problem.

For each layer, we have that:

Then the number of cubes in each layer is given as follows:

6 x 4 = 24 cubes.

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The correct answer is:

c. $2,485

Explanation: After considering the salary, RPP deduction, and other adjustments, the taxable income is determined. Applying the federal tax rate of 15% to the taxable income gives us the federal tax owed, which amounts to $2,485.

The probability that a randomly selected automobile worker works less than 41 hours per week is 0.0383 (or 3.83% when expressed as a percentage).

The given information can be represented by the following formulas:

Mean μ = 44.2

Standard deviation σ = 1.8

Now, for the probability that the randomly selected automobile worker works less than 41 hours per week.

P(X < 41) = ?

The formula for calculating Z-score is given by

Z = (X - μ) / σ

Where,

X = 41

μ = 44.2

σ = 1.8

Substituting the values in the formula, we get,

Z = (41 - 44.2) / 1.8 = -1.777778

Now, we need to find out the probability of a Z-score of -1.78 from the normal distribution table.

The probability can be calculated by subtracting the value of the Z-score from 0.5 and looking up the remaining value in the standard normal table.

P(Z < -1.78) = 0.0384

Therefore, the probability that a randomly selected automobile worker works less than 41 hours per week is 0.0384.

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Answer:

\( \frac{1}{3} \times 12 \times area = 90 \\ area = 90 \div 4 = 22.5\)

We have that The  inequality that will represent how many  laps Lucy must swim in order for her to spend the same number or more minutes exercising than Dan.

\(20*3\frac{1}{2}a \geq 30+2 \frac{3}{4}a\)

From the question we are told

Generally the Inequality equation for the Statement  is mathematically given as

\(20*3\frac{1}{2}a \geq 30+2 \frac{3}{4}a\)

Therefore

The  inequality that will represent how many  laps Lucy must swim in order for her to spend the same number or more minutes exercising than Dan.

\(20*3\frac{1}{2}a \geq 30+2 \frac{3}{4}a\)

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\(\frac{237}{100}\)

Hi there !

2.37 = 237/100

Good luck !

Answer:

no

Step-by-step explanation:

False. The box plot of a perfectly symmetrical distribution does not necessarily have the box at the center of the range, nor does it guarantee that the median will be in the center of the box.

The box plot is a graphical representation of the distribution of a dataset. It consists of a box that represents the interquartile range (IQR) and a line inside the box that denotes the median. The whiskers extend from the box to the minimum and maximum values, or to a certain range depending on the specific plot.

While a perfectly symmetrical distribution would have the median at the center, it does not guarantee that the box will be centered within the range. The position of the box is determined by the quartiles, which are affected by the spread of the data. Therefore, in cases where the data is skewed or has outliers, the box might not be centered within the range.

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Answer:

1 1/2 + 1 1/2

Step-by-step explanation:

1 1/2 (or 1.5) plus 1 1/2 equals 3

Answer: You and Sarah went to the gas station to get sodas. Sarah got a Dr. Pepper and it cost $2.50. You got a Sprite and it cost $3.00. You notice Sarah is short on change and want to help her. You have a $10 Bill and are going to pay for it. How much change will you get back?

Step-by-step explanation:

False. If two lines are perpendicular, they do not have the same slope. When two lines are perpendicular, they intersect at a right angle, and their slopes are negative reciprocals of each other.

This implies that when one slope is a, the other slope is -1/a. We can define perpendicular lines using the following theorem.

The two lines in a plane are perpendicular if and only if the product of their slopes is -1. If line 1 has slope m1 and line 2 has slope m2, then the product of their slopes is m1*m2 = -1, which means m2 = -1/m1 and vice versa. The converse is also true, which means if m1*m2 = -1, then line 1 and line 2 are perpendicular.

Hence, the statement, "If two lines are perpendicular, they have the same slope" is false because the slopes of perpendicular lines are negative reciprocals of each other, not equal. Therefore, the answer is False.

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With all of the edges 6 feet long, the total surface area of the greenhouse including the floor is approximately 98.39 ft².

To find the total surface area of Reina's greenhouse, we'll need to calculate the area of the equilateral triangular sides and the square base.

1. Equilateral triangular sides:
There are four congruent equilateral triangles with edges of 6 feet each. To find the area of one triangle, we can use the formula A = (s² * √3) / 4, where A is the area and s is the side length.

A = (6² * √3) / 4 = (36 * √3) / 4 = 9√3 square feet

Since there are four triangles, the total area of the triangular sides is 4 * 9√3 = 36√3 square feet.

2. Square base:
The base is a square with side lengths of 6 feet. To find the area, we can use the formula A = s².

A = 6² = 36 square feet

Now, let's add the area of the triangular sides and the square base

Total surface area = 36√3 + 36 ≈ 98.39 ft² (rounded to the nearest hundredth)

So, the total surface area of the greenhouse including the floor is approximately 98.39 ft².

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To decrease the width of the confidence interval, the researcher can take the following steps:

1. Decrease the confidence level: The confidence interval width is inversely proportional to the confidence level. By decreasing the confidence level, the researcher can have a narrower interval. However, it is important to note that decreasing the confidence level also increases the chance of the interval not capturing the true population mean.

2. Increase the sample size: The sample size affects the precision of the estimate. Increasing the sample size reduces the standard error, which leads to a narrower confidence interval. This is because a larger sample provides more information about the population.

Therefore, the researcher can decrease the width of the confidence interval by either decreasing the confidence level or increasing the sample size. Both approaches will result in a narrower interval, providing a more precise estimate of the mean fat content of hen's eggs.

The researcher can decrease the width of the confidence interval by either decreasing the confidence level or increasing the sample size. Both approaches will result in a more precise estimate of the mean fat content of hen's eggs.

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The arrival rate is found to be 30 emails per hour and the service rate is calculated to be 45 emails per hour.

It has been mentioned in the question that in every 2 minutes, customers send emails to a help desk of an online retailer, on an average, and the standard deviation of the inter-arrival time is also given to be 2 minutes. The online retailer has three employees for answering those emails.

It takes almost 4 minutes to write a response email to the customer, on average. The standard deviation (SD) of the service times is 2 minutes. This is a g/g/k type queue.

Therefore the arrival rate per hour is given by the following relation:

Arrival rate in 1 hr = No. of minutes in an hr / inter arrival time of email taken in minutes

Given here,

No. of minutes in an hour = 60 minutes

Inter arrival time of the email taken in minutes = 2 minutes

∴ Arrival rate in 1 hr = 60 / 2

                                = 30 emails / hr

Hence the arrival rate is 30 emails per hour.

Now for finding out the service rate we have the following formula:

Service rate = No. of minutes in an hr x No. of employes answering/ average time that is required to write response email

Given here,

No. of minutes in an hr = 60 minutes

No. of employes answering = 3

Average time that for writing response email = 2 minutes

∴ Service rate = 60 * 3 / 4

                       = 45 emails / hr

Hence the service rate is 45 emails per hour.

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Answer:

7.35 pints

Step-by-step explanation:

If we use 1/4 of the 9.8 pints for blue, then the remaining white paint takes up 3/4 of the 9.8 pints of paint. To find how many pints of paint is equal to 3/4 of it, you must multiply that fraction by the amount (9.8).

\(\frac{3}{4}\) * 9.8 (or 0.75 * 9.8) = 7.35

Therefore, 7.35 pints of the total paint used is white.

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The present ages of the father and son are 36 and 9, respectively.

The sum of the ages of a father and son is 45 years. Five years ago, the product of their ages was four times the father's age at that time. To find the present ages of the father and son, we can set up a system of equations.

Let's denote the present ages of the father as "F" and the present age of the son as "S".

From the information given, we have two equations:

Equation 1: F + S = 45 (The sum of their ages is 45)
Equation 2: (F - 5)(S - 5) = 4(F - 5) (Five years ago, the product of their ages was four times the father's age at that time)

To solve this system of equations, we can use substitution or elimination method.

Let's solve it using the substitution method:

From Equation 1, we can express F in terms of S: F = 45 - S

Now, substitute F in Equation 2 with 45 - S:

(45 - S - 5)(S - 5) = 4(45 - S - 5)

Simplify the equation:

(40 - S)(S - 5) = 4(40 - S)

Expand and simplify:

40S - 5S - 200 + 25 = 160 - 4S

Combine like terms:

35S - 175 = 160 - 4S

Add 4S to both sides:

35S + 4S - 175 = 160

Combine like terms:

39S - 175 = 160

Add 175 to both sides:

39S = 335

Divide both sides by 39:

S = 335/39

Simplify:

S ≈ 8.59

Since age cannot be in decimal places, we can approximate the son's age to the nearest whole number:

S ≈ 9

Now, substitute S = 9 into Equation 1 to find the father's age:

F + 9 = 45

Subtract 9 from both sides:

F = 45 - 9

F = 36

Therefore, the present ages of the father and son are 36 and 9, respectively.

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Answer:

i dont know just trying to get pionts haha sorry rihana

Step-by-step explanation:

It takes 35 years for the population of West Fremont to double. We have the following condition;

West Fremont is a tiny town with 50,000 residents. If West Fremont experiences 2% growth. To solve the given case to get how long it takes for the population of West Fremont to double.

Here, we use the rule of 70 case. The rule of 70: By dividing the number 70 by the growth rate of the variable, the rule of 70 may be used to calculate how many years it will take for a variable to double.

According to the yearly rate of return, the rule of 70 is typically used to calculate how long it would take for an investment to double.

Doubling time = 70 / Growth rate                

= 70 / 2                        

= 35 years

So, it takes 35 years for the population of West Fremont to double.

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Answer:

1. 170.083 in³

2. 126π in³

3. 92.106 m³

4. 2412.74 in³

5. 612π m³ and 1922 m³

Step-by-step explanation:

1.

Cylinder:

\(V = \pi r^{2}h\)               *Plug in numbers*

\((3.14)(2.5)^{2}(7)\)         *Square 2.5*

\((3.14)(6.25)(7)\)        *Solve*

≈ \(137.375in^{3}\)

Sphere:

\(V = \frac{4}{3}\pi r^{3}\)              *Plug in numbers*

\(\frac{4}{3} (3.14)(2.5)^{3}\)         *Cube 2.5*

\(\frac{\frac{4}{3}(3.14)(15.625)}{2}\)         *Divide by 2 and Solve*

≈ \(32.7083 in^{3}\)

Add both volumes

\(137.375 + 32.7083\) ≈ \(170.083in^{3}\)

2.

Cylinder:

\(V = \pi r^{2}h\)         *Plug in numbers*

\(\pi (3)^{2}(10)\)            *Square 3*

\(\pi (9)(10)\)             *Multiply*

\(90\pi\)

Sphere:

\(V = \frac{4}{3}\) π \(r^{3}\)            *Plug in numbers*

\(\frac{4}{3}\pi (3)^{3}\)                   *Cube 3*

\(\frac{4}{3} \pi (27)\)                   *Multiply*

\(36\pi\)

Add both Volumes to get total

\(90\pi + 36\pi = 126in^{3}\)

3.

Sphere:

\(V = \frac{4}{3}\pi r^{3}\)              *Plug in numbers*

\(\frac{4}{3} (3.14)(3)^{3}\)            *Cube 3*

\(\frac{4}{3} (3.14)(27)\)            *Multiply*

\(113.04m^{3}\)

Cone:

\(V = \frac{\pi r^{2}h}{3}\)             *Plug in numbers*

\(\frac{(3.14)(2)^{2}(5)}{3}\)           *Square 2*

\(\frac{(3.14)(4)(5)}{3}\)             *Solve*

\(20.93m^{3}\)

Subtract the volumes to get the volume of the blue area

\(113.04 - 20.93 = 92.106m^{3}\)

4.

Sphere:

\(V = \frac{4}{3} \pi r^{3}\)            *Plug in numbers*

\(\frac{4}{3}\pi (8)^{3}\)                 *Cube 8*

\(\\\frac{4}{3}\pi (512)\)               *Multiply*

\(\\\\\pi (682.6)\)              *Solve*

\(2133.66in^{3}\)           *Divide by 2 since it's a hemisphere*

Cone:

\(V = \frac{\pi r^{2}h}{3}\)            *Plug in numbers*

\(\frac{\pi (8)^{2}(20)}{3}\)              *Square 8*

\(\frac{\pi (64)(20)}{3}\)              *Multiply and Divide*

\(1340.41 in^{3}\)

Add both volumes

\(1072.33 + 1340.41 = 2412.74in^{3}\)

5.

Cylinder:

\(V = \pi r^{2}h\)            *Plug in numbers*

\(\pi (6)^{2}(16)\)              *Square 6*

\(\pi (36)(16)\)             *Multiply*

\(576\pi\)

Cone:

\(V = \frac{\pi r^{2}h}{3}\)            *Plug in numbers*

\(\frac{\pi (6)^{2}3}{3}\)                  *Square 6*

\(36\pi\)

Add both volumes

\(576\pi + 36\pi = 612\pi m^{3}\)

Alternative: *Multiply π*

\(1922m^{3}\)

Answer:

1) 175 \(in^2\)

2) 1st option

3) 92 \(m^2\)

4) 2412 \(in^3\\\)

5) 2nd option

Step-by-step explanation:

\(1)\ A = D * Pi = 5 * 3.14 = 15.7\\\)

\(2)\ V_{1} = 15.7 * 7 = 109.9\)

\(3)\ V_{2} = 4Pi*\frac{R^3}{3} = 12.56*\frac{15.625}{3} = 65.41(6)\)

\(4)\ V_1 + V_2 = 65.4 + 109.9 = 175.3\) which is close to 175

\(1)\ A = Pi * R^2 = 3.14 * (\frac{6}{2})^2 = 3.14 * 3^2 = 28.26\\\)

\(2)\ V_1 = A * h = 28.26 * 10 = 282.6\)

\(3)\ V_2 = \frac{4}{3} * Pi * R^3 = \frac{4}{3} * 3.14 * (\frac{6}{2})^3 = 113.04\)

\(4)\ V_1 + V_2 = 282.6 + 113 = 395.6\) which is very close to 396

\(5)\ 396 = 126 * pi\)

\(1) V_1 = \frac{1}{3} * Pi * R^2 * h = \frac{1}{3} * 3.14 * 2^2 * 5 = 20.9(3)\) =

\(2)\ V_2 = \frac{4}{3} * Pi * R^3 = \frac{4}{3} * 3.14 * 3^3 = 113.04\\\)

\(3)\ V_2 - V_1 = 113.04 - 20.93 = 92.14\) which is very close to 92

\(1)\ V_1 = \frac{\frac{4}{3} * Pi * R^3}{2} = \frac{\frac{4}{3} * 3.14 * 512}{2} = 1,071.786\\\)

\(2)\ V_2 = \frac{1}{3} * Pi * R^2 * h = \frac{1}{3} * 3.14 * 64 * 20 = 1,339.733\)

\(3)\ V_1 + V_2 = 1072 + 1340 = 2,411 = 2412\)

\(1)\ A = Pi * R^2 = 36*Pi\\\)

\(2)\ V_1 = 36*Pi * 16 = 576 * Pi\\\)

\(3)\ V_2 = \frac{1}{3} * Pi * R^2 * h = \frac{1}{3} * Pi * 36 * 3 = 36 * Pi\)

\(4) V_1 + V_2 = 576Pi + 36Pi = 612Pi\)

A team that controls decisions about and execution of a complete range of tasks, including acquisitions, operations, quality control, maintenance, and shipping, is known as a cross-functional team. This type of team consists of individuals from different functional areas or departments within an organization who come together to work collaboratively on specific projects or goals.

Cross-functional teams are designed to break down silos and foster cooperation and communication between different departments or functions. By including representatives from various areas, such as finance, marketing, operations, and logistics, cross-functional teams bring together diverse perspectives, expertise, and skills to address complex issues and achieve common objectives.

These teams are responsible for making decisions related to their assigned tasks, executing plans, and ensuring the successful completion of the project or initiative. Their comprehensive range of responsibilities allows for greater efficiency, coordination, and integration across different functions, leading to improved outcomes and performance.

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wAnswer:

e

Step-by-step explanation:

Step-by-step explanation: The square root of 12 is represented in the radical form as √12 which is equal to 2√3. Since, 2√3 cannot be further simplified, hence such roots are called surds.