A fire engine takes the shortest possible route when it drives from the firehouse to one of the schools. The route can go only horizontally and vertically on the grid. Each unit on the grid represents 1-half mile. What is the maximum distance, in miles, the fire engine travels to reach one of the schools?

Answer:

r = 7

Step-by-step explanation:

equation of circle is (x - a)² + (y - b)² = r²

where a is x-coordinate of centre of circle, b is y-coordinate of centre of circle, r is the radius. radius = half of diameter.

x² - 8x + y² - 10y = 8

we need to complete the sqaure for both x and y

x² - 8x = (x - 4)² = x² - 8x + 16, which is 16 more than x² - 8x. so we need to subtract that 16.

we now have (x - 4)² - 16.

now do the same with y

(y - 5)² = y² - 10y + 25, which is 25 more than y² - 10y. so we need to subtract 25.

we now have (y - 5)² - 25.

back to our full equation.

(x - 4)² -16 + (y - 5)² - 25 = 8

(x - 4)² + (y - 5)² - 41 = 8

(x - 4)² + (y + 5)² = 49 = r²

radius r = √49 = 7

There are a total of 15 good students, 35 weak and 40 in bad shape if number of good students are fraction of 1/6th of total students.

As we know that the total number of students are 90.

Good students are fraction of 1/6th of total students.

Good students= 1/6x90

Good students=15

There are 40 good students in a whole block, so X = 40.

In the whole grade, average number of students is 1/3 of students in whole grade.

Students in each class = 1/3x90

Students in each class = 30

Students who are not good in economics and government = 90-40

Students who are not good in economics and government = 50

As the total number of students is sum of good students and weak students.

15+Weak students =90-40

15+Weak students=50

Weak students=50-15

Weak students=35    

So, total of 15 good students, 35 weak and 40 in bad shape.

Read more about fractions at-

https://brainly.com/question/10354322

The volume of the prism is 195 cubic meters.

To find the volume of the prism, we need to multiply the length, width, and height of the prism.

Length = 13 m

Width = 3 m

Height = 5 m

Volume = Length x Width x Height

Volume = 13 m x 3 m x 5 m

Volume = 195 cubic meters

Answer:

Perdón no te puedo ayudar no entiendo

Step-by-step explanation:

To find the average velocity of the particle over the interval [1, e], we need to calculate the net displacement divided by the time interval.

Given the position function x(t) = ln(t), let's find the displacement by evaluating x(e) and x(1):

x(e) = ln(e) = 1

x(1) = ln(1) = 0

So, the net displacement is 1 - 0 = 1.

The time interval is e - 1.

Therefore, the average velocity is:

average velocity = (net displacement) / (time interval)

average velocity = 1 / (e - 1)

The correct answer is B. 1/(e - 1).

A construction of the box-and-whisker plot based on the data is shown below.

In Mathematics and Statistics, a box plot is also known as a box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the data (information) provided above, the five-number summary for the given data set include the following:

In conclusion, we can reasonably infer and logically deduce that the maximum number is 10 while the minimum number is 2, and the median is equal to 5.

Read more on boxplot here: brainly.com/question/29648407

#SPJ1

The test statistic is 14.5 and the P-value is less than 0.05. Therefore, we have evidence to suggest that the distribution of days of the week of the appointments disagrees with an Even distribution.

To carry out the chi-squared goodness-of-fit test, we need to calculate the expected number of appointments for each day if there were an even distribution. Since there are 5 days of the week, each day would have an expected value of 100 (i.e., 500 appointments / 5 days = 100 appointments per day).

Day | Monday | Tuesday | Wednesday | Thursday | Friday

Observed | 115 | 100 | 115 | 100 | 70

Expected | 100 | 100 | 100 | 100 | 100

To calculate the chi-squared test statistic, we use the formula:

χ2= ∑ (observed − expected)^2 / expected

Plugging in the observed and expected values, we get:

χ2= [(115 - 100)^2/100] + [(100 - 100)^2/100] + [(115 - 100)^2/100] + [(100 - 100)^2/100] + [(70 - 100)^2/100]

  = 2.75 + 0 + 2.75 + 0 + 9

  = 14.5

To find the P-value, we need to use the chi-squared distribution table with 4 degrees of freedom (5 days of the week minus 1 for the expected value). Using the table, we find that the P-value for a chi-squared statistic of 14.5 with 4 degrees of freedom is less than 0.05. Therefore, we reject the null hypothesis that the appointments have an even distribution from Monday through Friday.the test statistic is 14.5 and the P-value is less than 0.05. Therefore, we have evidence to suggest that the distribution of days of the week of the appointments disagrees with an even distribution.

To know more about Even distribution.

https://brainly.com/question/23286309

#SPJ11

The number of multiples of both 2 and 5 that are there between 34 and 417 is given as follows:

39.

The rules for the multiples of 2 and 5 are given as follows:

Hence the numbers that are multiples of both 2 and 5 finish in zero, which are the multiples of 10.

Then the divisions are given as follows:

Hence the number of multiples is given as follows:

41 - 3 + 1 = 39.

More can be learned about multiples at https://brainly.com/question/26856218

#SPJ1

The amount of volume of 1 coin in the stack underneath is 0.433 cm³. The distance between the coins is 1 in, and each coin having a radius approximately 0.5 in. 7 inches make up the tilt.

Any three-dimensional solid's volume is the area it takes up. The volume of these solids include cubes, cuboids, cones, cylinders, and spheres. Different shapes have different volumes. We have looked at a variety of three-dimensional solids and shapes, including cubes, cuboids, cylindrical objects, cones, and and more.

V= πD²×h/4

  =π0.5²×7/4

   = 0.433 cm³

To know more about volume, here:

https://brainly.com/question/28058531

#SPJ1

Inverse variation is a relationship between two variables where one variable increases as the other variable decreases, and vice versa.

This means that as one variable doubles, the other variable will decrease by half, or vice versa.

The following are situations that depict inverse variation:

1. When you are traveling at a constant speed, the time it takes to cover a given distance is inversely proportional to the distance. This is because the distance will decrease as the speed increases.

2. If you have a light source, the intensity of the light decreases as you move further away from the source. This is because the distance between the source and the object increases as the intensity of the light decreases.

3. The force of gravity between two objects is inversely proportional to the square of the distance between them. This is because the force of gravity will decrease as the distance between the objects increases.

4. When the temperature of a gas decreases, its pressure increases. This is because the volume of the gas remains constant as the temperature decreases, which causes the pressure to increase according to the gas laws.

5. The period of a pendulum is inversely proportional to the square root of its length. This is because the length of the pendulum will decrease as the period increases.

To learn more about : Inverse variation

https://brainly.com/question/13998680

#SPJ8

Answer:

The polygons are similar. They are similar in the way that the larger polygon is 3 times the size of the smaller one.

The expression with the greatest value when a = 5 is:

a + 9 × 8 ÷ 7, with 9 in the first box, 8 in the second box, and 7 in the third box.

To create the expression with the greatest value when a = 5, we want to choose the largest possible numbers to fill in the missing parts.

Since each whole number can only be used once, we should choose the three largest numbers from 1 to 9.

The three largest numbers from 1 to 9 are 9, 8, and 7. So we can fill in the expression as follows:

a + 9 × 8 ÷ 7

When a = 5, this expression evaluates to:

5 + 9 × 8 ÷ 7 = 5 + 72 ÷ 7 = 15.2857...

To learn more about the expression;

brainly.com/question/24242989  

#SPJ1

Answer:

B) strong

Step-by-step explanation:

The correlation coefficient is close to 1, meaning it is both a strong correlation and a positive correlation.

The equation that represents the direct variation between a and b in the given problem is: b = -a. So, option is correct.

The statement "a number, b, is located the same distance from 0 as another number, a, but in the opposite direction" means that b = -a. The statement "The number b varies directly with the number a" means that b is proportional to a, or mathematically, b = k*a, where k is the constant of proportionality.

Substituting b = -a into the equation b = ka, we get -a = ka. Solving for k, we get k = -1. Therefore, the equation that represents the direct variation between a and b is b = -a which is option B, "-b = -a".

To know more about linear equation, visit,

https://brainly.com/question/2030026

#SPJ1

Complete question - On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction. The number b varies directly with the number a. For example b = 22 when a =  -2 Which equation represents this direct variation between a and b?

A. a = -1

B. -b = -a

C. b-a = 0

D. b(-a) = 0.

Answer:

----------------

The line that is perpendicular to x = 8 has a form of:

Since it has a point (-3, - 2), the value of a is the y-coordinate of this point. Therefore the line is:

1. Using mathematical operations, the cost of three 5kg bags of rice at ¢2 per kg is ¢30.

2. From the 2km piece, you can cut 2,000 pieces with each one meter long.

3. The fraction of a liter that is 259 ml can be written as ²⁵⁹/₁₀₀₀.

4. 60ps expressed as a decimal of ¢240 is 0.25.

5. The groups of 4 marks in 20, based on a division operation, is 5.

6. If an orange costs ¢150, by multiplication, 9 oranges will cost ¢1,350.

7. The product of 35 and 12, which is a multiplication operation, is 420.

8. Using division operation, from 1 kg, one could obtain 5.55 units of 180g each.

The four basic mathematical operations are addition, subtraction, division, and multiplication.

In this situation, the mathematical operations involved are division and multiplication.

1) The cost of price per kg = ¢2

The number of bags bought = 3

The weight per bag = 5kg

The total weight of 3 bags = 15kg (5 x 3)

The total cost = ¢30 (¢2 x 15)

2) The total length of the piece = 2km

1 km = 1,000 meters

2km = 2,000 meters

The length of each string = 1 meter

The number of strings = 2,000 (2,000 ÷ 1)

3) 1 liter = 1,000 ml

259 ml/1,000 ml = 259/1,000

= ²⁵⁹/₁₀₀₀

4) 60p as a decimal of ¢240

= 0.25 (60 ÷ 240)

5) 20 ÷ 4 = 5

4 x 5 = 20

6) The cost per orange =  ¢150

The number of oranges bought = 9

The total cost of 9 oranges = ¢1,350 (¢150 x 9)

7) The product of 35 and 12 = 420 (35 x 12)

8) The quantity of each unit = 180g

The total quantity = 1 kg

1 kg = 1,000 g

5.55 (1,000 ÷ 180)

Learn more about mathematical operations at https://brainly.com/question/4721701.

#SPJ1

The combined length of the two pieces of wire is 3/2 inches or 1 and 1/2 inches.

To find the combined length of the pieces of wire, we need to add the lengths of the two pieces of wire together.

The first piece of wire is 7/8 of an inch long.

The second piece of wire is 5/8 of an inch long.

To add the two fractions, we need to find a common denominator. The smallest number that both 8 and 5 will divide into is 40.

7/8 can be rewritten as 35/40 (multiply the numerator and denominator by 5)

5/8 can be rewritten as 25/40 (multiply the numerator and denominator by 5)

Now we can add the two fractions:

35/40 + 25/40 = 60/40

Simplifying the fraction:

60/40 = 3/2

Therefore, the combined length of the two pieces of wire is 3/2 inches or 1 and 1/2 inches.

Know more about  fractions   here:

https://brainly.com/question/78672

#SPJ11

According to the figure the required lengths are

BD = 7 units

BC = 9.9 units

The required lengths is solved knowing that in a right triangle having angle 45 degrees, the lengths of the legs of the right triangle are equal.

Also,  the perpendicular bisector creates another angle 45 degrees at angle B.

hence we another right triangle with a leg as 7 units hence BD is 7 units

solving for BC

BC = BA

BC² + BA² = CA²

BC² + BC² = 14²

2 x BC² = 196

BC² = 98

BC = √(98)

BC = 9.9 units

Learn more about right triangle at

https://brainly.com/question/2217700

#SPJ1

The median score, considering the frequency distribution in this problem, is given as follows:

334.5.

The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.

The total number of observations in the data-set is given as follows:

189.

Hence the position in the cumulative frequency table of the median element is given as follows:

0.5 x (189 + 1) = 95.

Which is in the following interval:

330-339.

Hence the median is of 334.5, as it is the middle value of the interval.

More can be learned about the median of a data-set at brainly.com/question/3514929

#SPJ1

The amount of water that flows into the tank each minute is given as follows:

0.56 cm.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The dimensions for this problem are given as follows:

45 cm, 50 cm and 38 cm.

Hence the volume of the tank is given as follows:

V = 45 x 50 x 38

V = 85,500 cm³.

Three-fifths of the volume is given as follows:

3 x 85500/5 = 51300 cm³.

The height associated with 3/5 of the volume is given as follows:

50 x 38 x h = 51300

h = 51300/(50 x 38)

h = 27 cm.

This means that 27 - 13 = 14 cm flew into the tank in 25 minutes, hence the minute rate is given as follows:

14/25 = 0.56 cm.

More can be learned about the volume of a rectangular prism at brainly.com/question/22070273

#SPJ1

Option D is the correct answer.

From the graph, we can conclude that,

1. The two lines are continuous lines and not broken lines. So, the inequality sign should be either ≤ or ≥.

2. The points on the lines of the shaded region are also included in the solution.

The only option that matches with the above conditions is option D. So, option D is the correct answer.

Let us verify it.

Now, let us consider a point that is inside the shaded region and also on any one line.

Let us take (0, 2).

Plug in 0 for x and 2 for y in each of the options and check which inequality holds true.

Considering the inequalities,

y ≥ 3x - 2

x + 2y ≤ 4

Solving we get,

2 ≥ 3(0) - 2

2 ≥ -2

x + 2y ≤ 4

0 + 2(2) ≤ 4

4 ≤ 4

Here, both inequalities are correct.

So, option D is the correct answer.

Learn more about inequality click

https://brainly.com/question/20383699

#SPJ1

The complete question is =

Which system of linear inequalities is graphed?

A. y < 3x-2

x + 2y ≥ 4

B. y < 3x - 2

x + 2y > 4

C. y > 3x - 2

x + 2y < 4

D. y ≥ 3x - 2

x + 2y ≤ 4

Answer:

-235+84i

Step-by-step explanation:

I hope this is what you were looking for.

The solution is: the period for the graph of y = cos (0) is:

c.360

We have the following equation:

y = cos (0)

The first thing you should know is that the period of a function is that value for which the function repeats itself.

We have then:

y = cos (0) = 1

y = cos (360) = 1

Therefore, the period is 360.

Answer:

the period for the graph of y = cos (0) is:

c.360

To learn more on function click:

brainly.com/question/21145944

#SPJ1

complete question:

What is the period for the graph of y=cos(0)? (Sketch a graph to help determine the answer.)

a.180

b.90

c.360

d.270

All points that lie on the line that passes through point `P` and is perpendicular to line ' t' are: (4, -1) and (6, -5)

The equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

Using two coordinates on line t as: (-4, 1) and (2, 4), the slope of the line t is:

Slope = (4 - 1)/(2 + 4)

Slope = 3/6

Slope = 1/2

Equation of line t is:

(y - 1)/(x + 4) = 1/2

y - 1 = x/2 + 2

y = ¹/₂x + 3

Thus, slope of line passing through P and perpendicular to t is: -1/(1/2) = -2

Now, coordinates of point P is (3, 1). Thus:

Equation passing through point P and perpendicular to line t is:

(y - 1)/(x - 3) = -2

y - 1 = -2x + 6

y = -2x + 7

The only coordinates that fits into this are (4, -1) and (6, -5)

Read more about Equation of Line at: https://brainly.com/question/18831322

#SPJ1

The three accurate statements concerning the new prism are as follows:

The volume will experience a growth of 6 units, as each of the three dimensions is increased by 2.

This can be calculated by multiplying 2 by 3, resulting in an increase of 6.

Learn more about Prism here:

https://brainly.com/question/12649592

#SPJ1

A positive value for n that makes the statement true is n = 1.5.

We need to find a positive value for n that satisfies the given inequality: 1 < 1 x n < 2.
Step 1: Choose a value of n such that it's greater than 1 when multiplied by 1.
Step 2: Ensure the chosen value also makes the product less than 2 when multiplied by 1.
Let's try n = 1.5:
1 x 1.5 = 1.5
Now, let's check if it satisfies the inequality:
1 < 1.5 < 2
Yes, it does. So, a positive value for n that makes the statement true is n = 1.5.

For more questions on positive value

https://brainly.com/question/30845581

#SPJ11

Answer: 3r

Step-by-step explanation: because 2r+1r=3r

Answer:

exact form : 2√3

decimal form : 3.46410161… or 3.46

hope this helps you!

Answer:

The value of the function is [tex]\sqrt{12}[/tex]. Rounded to the nearest hundredth, the answer is 3.46

Step-by-step explanation:

We are given the value of x, so we simply have to evaluate the function:

[tex]f(x)=\sqrt{x+4}[/tex]

Substitute 8

[tex]f(8)=\sqrt{8+4}[/tex]

Add in the radical

[tex]\sqrt{12}[/tex]

The value of the function is sqrt(12).

Rounded to the nearest hundredth: [tex]3.46[/tex]

Answer:

34 units²

Step-by-step explanation:

triangle=1/2×5×2=5

other triangle at the right=5

square 6 ×5= 30

unshaded square= 3×2=6

30-6=24

total=5+5+24=34units²

We cannot conclude that 95% of the population agrees that there is no difference in Taste between Coke and Pepsi.

To calculate the probability that 95% of the population agrees that there is no difference in taste between Coke and Pepsi, we can use the binomial distribution formula.

Let X be the number of students who say there is no difference in taste, and n be the total number of students in the sample. Then, X follows a binomial distribution with parameters n and p, where p is the true proportion of students who say there is no difference in taste.

The point estimate of p is 7/10 = 0.7. The standard error of the proportion can be calculated as the square root of p(1-p)/n = sqrt(0.7*0.3/10) = 0.23.

Using a normal approximation to the binomial distribution, the 95% confidence interval for p is given by:

0.7 +/- 1.96*0.23 = (0.24, 1.16)

Since the interval includes 0.5, which represents the point where the proportion of agreement and disagreement is equal, we cannot conclude that 95% of the population agrees that there is no difference in taste between Coke and Pepsi.

To know more about Taste .

https://brainly.com/question/23851293

#SPJ11