The diameter of a circle divides the circle into two equal sectors true or false

The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.

To create a box and whisker plot for the given dataset {69, 88, 94, 73, 78, 90, 68}, follow these steps:

Step 1: Arrange the data in ascending order:

68, 69, 73, 78, 88, 90, 94

Step 2: Find the five-number summary:

Minimum: The smallest value in the dataset, which is 68.

First quartile (Q1): The median of the lower half of the dataset. In this case, it's the median of {68, 69, 73}, which is 69.

Median (Q2): The middle value of the dataset. In this case, it's 78.

Third quartile (Q3): The median of the upper half of the dataset. In this case, it's the median of {88, 90, 94}, which is 90.

Maximum: The largest value in the dataset, which is 94.

Step 3: Create the box and whisker plot:

Draw a number line with a range from the minimum (68) to the maximum (94).

Mark the first quartile (Q1) at 69.

Mark the median (Q2) at 78.

Mark the third quartile (Q3) at 90.

Draw a box from Q1 to Q3.

Draw a vertical line (whisker) from the box to the minimum (68) and another vertical line from the box to the maximum (94).

The resulting box and whisker plot for the given dataset would look like this:

  |

 94|                 ▄

  |                ╱ ╲

 90|              ╱   ╲

  |             ╱     ╲

 88|            ▇       ▂

  |            ▇       ▂

 78|            ▇       ▂

  |            ▇       ▂

 73|          ╱         ╲

  |         ╱           ╲

 69|        ▃             ▃

  |       ╱               ╲

 68|      ╱                 ╲

  |_________________________________

    68     73     78     88     94

This plot represents the distribution of the given dataset, showing the minimum, maximum, first quartile (Q1), median (Q2), and third quartile (Q3).

The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.

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Considering it's asymptotes, the rational function shown in the graph is:

C. \(F(x) = \frac{1}{(x + 2)(x - 1)}\)

In this graph, there are vertical asymptotes at x = -2 and x = 1, hence the denominator of the function is:

(x + 2)(x - 1).

The horizontal asymptote is of y = 0, hence the function can be given by:

C. \(F(x) = \frac{1}{(x + 2)(x - 1)}\)

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Step-by-step explanation:

similar means they have the same angles, and there is one common scaling factor for all pairs of corresponding sides. we need to find it for one pair, and we then have it also for the x pair and can calculate x.

comparing the sides in relation to each other we find that F corresponds to L, H to J and G to K.

so, the scaling factor of LK/FG is then also the scaling factor of JK/HG.

LK × f = FG

45 × f = 27

f = 27/45 = 3/5

JK × 3/5 = 3x + 6

65 × 3/5 = 3x + 6

13 × 3 = 3x + 6

39 = 3x + 6

33 = 3x

x = 11

Answer:  25º

 Explanation :  Since a triangle always add up to 180 degrees, add the 155 and 40. Then subtract what you get from 180, and that’ll be the last angle.

Answer:

75 degrees

Step-by-step explanation:

Let's label the angles:

The one near 115 degrees is A.

The ? is B.

The one near 40 is C.

(All of them are interior.)

To find A:

180 - 115 = 65

A = 65 degrees

To find C (this one's a bit hard to explain):

The cross made by two lines near the 40 degrees makes vertical angles.

So, C = 40 degrees

All angles in a triangle add up to 180 degrees so:

65 + 40 = 105

180 - 105 = 75

So:

Angle B = 75 degrees

Hope this helps!

(please let me know if you need further clarification)

To calculate the product \(\( zw \),\) we multiply the real parts and imaginary parts separately and combine them to obtain the final result.

Using the distributive property, we have:

\(( zw = (4 + 3i)(5 - 2i) \)\)

Expanding this expression, we get:

\(( zw = 4 \cdot 5 + 4 \cdot (-2i) + 3i \cdot 5 + 3i \cdot (-2i) \)\)

Simplifying further, we have:

\(zw = 20 - 8i + 15i - 6i^2 \)\)

Since \(\( i^2 \)\) is equal to -1, we can replace \(\( i^2 \)\)  with -1:

\(\( zw = 20 - 8i + 15i - 6(-1) \)\)

Continuing to simplify:

\(\( zw = 20 - 8i + 15i + 6 \)\)

Combining like terms, we get:

\(\( zw = 26 + 7i \)\)

Therefore, the product of \(\( z = 4 + 3i \) and \( w = 5 - 2i \)\) is \(\( 26 + 7i \)\).

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Answer:

The first column would be (x,y)---> (x,-y)

The second column would be (x,y)---> (x+3, y-8)

The third column would be (x,y)----> (-x,-y)

Then the last column would be (x,y)---> (x-8, y-3)

Answer:

Step-by-step explanation:

\(A_{trapezoid}\) = \(\frac{b_{1} +b_{2} }{2}\) × h

\(A_{rectangle}\) = lw

~~~~~~~~~~~~~~

\(A_{1}\) = \(\frac{12+3}{2}\) × 4 = 30 m²

\(A_{2}\) = 10 × ( 10 - 4 ) = 60 m²

\(A_{total}\) = \(A_{1}\) + \(A_{2}\) = 30 + 60 = 90 m²

Probability of two black Erminette chickens crossed is equal to 1/4.

As given in the question,

Erminette chickens are basically a chicken with a gene of black and white feathers.

There are two groups of chicken black feather chicken and white feather chicken.

All possible outcomes when Erminette chicken crossed each other are:

= { BB , BW, WB, WW}

Total number of outcomes are = 4

Favourable outcomes are ={ BB }

Number of favourable outcomes = 1

Probability of two black Erminette chickens crossed each other

= ( Favourable outcomes) / ( Total number of outcomes )

= 1 / 4

Therefore, probability of two black Erminette chickens crossed each other with the given condition is equal to 1/ 4.

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Answer:

\((x+5)^2+(y-6)^2=41\)

Step-by-step explanation:

Hi there!

Equation of a circle: \((x-h)^2+(y-k)^2=r^2\) where the circle is centered at \((h,k)\) and r is the radius

1) Plug in the center (-5,6)

\((x-(-5))^2+(y-6)^2=r^2\\(x+5)^2+(y-6)^2=r^2\)

2) Plug in the given point (-1,1) and solve for r²

\((-1+5)^2+(1-6)^2=r^2\\(4)^2+(-5)^2=r^2\\16+25=r^2\\41=r^2\)

Therefore, r² is 41. Plug this back into \((x+5)^2+(y-6)^2=r^2\):

\((x+5)^2+(y-6)^2=41\)

I hope this helps!

Manny must save for at least 50 months to have enough money to buy the car. this can be solved by setting up an inequality expression for the condition.

Let's set up an inequality to represent Manny's saving situation.

Manny saves $300.00 per month, so the total amount he will save in m months is 300m. The cost of the used car is $15,000.

To buy the car, Manny needs to save enough money, which can be represented by the inequality: 300m ≥ 15000

This inequality states that the total amount Manny saves, 300m, must be greater than or equal to $15,000, the cost of the car. To solve this inequality for m, we can divide both sides of the inequality by 300: m ≥ 15000/300

Simplifying this expression, we get: m ≥ 50

Therefore, Manny must save for at least 50 months to have enough money to buy the car.

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We need first to change the speed of miles per hour to meter per min, then compare both speeds

Since 1 mile = 1.61 km

Since 1 km = 1000 m, then

1 mile = 1 x 1.61 x 1000

1 mile = 1610 meters

Since 1 hour = 60 min, then

50 miles per hour = 50 miles / 1 hour

Multiply 50 by 1610

Multiply 1 h by 60

Simplify it

Since the other speed is 1250 meters per min

Since 1341 2/3 > 1250

Then you have to drive at 50 miles per hour

This question is about ratios. Initially, 8 people have enough water for 9 days. When 4 more people join, the water supply will now last for 6 days.

This question involves a concept of Mathematics, specifically in the area of ratios or proportions. The initial premise is that 8 people on a trek have enough water to last them for 9 days. We can express this ratio as 8:9, which means for every 8 persons, the group can sustain its water supply for 9 days.

Now, we must calculate what would happen if 4 more people join the trek. Since now there are 12 people (8 original + 4 new), the new ratio becomes 12:9. However, the amount of water remains fixed. We can find the number of days the water will now last by dividing the quantity of water by the increased number of people, i.e., 9 days * (8 people/12 people) = 6 days.

So, when 4 more people join the group, the water supply will last the whole group for 6 days.

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To determine the line symmetry of your figure (C), examine the shape and try to identify if it can be divided into mirror-image halves using any of these lines. If so, that will be the type of line symmetry it has. If not, choose "none of the above."

1. Vertical line symmetry: A figure has vertical line symmetry when it can be divided into two equal halves by a vertical line, and the halves are mirror images of each other.

2. Horizontal line symmetry: A figure has horizontal line symmetry when it can be divided into two equal halves by a horizontal line, and the halves are mirror images of each other.

3. Diagonal line symmetry: A figure has diagonal line symmetry when it can be divided into two equal halves by a diagonal line, and the halves are mirror images of each other.

4. None of the above: If the figure cannot be divided into equal halves by any line (vertical, horizontal, or diagonal) and have mirror-image halves, then it does not have any line symmetry.

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Answer:

the answer would be

0.0256

Answer: Yes, it does. It must bounce of a low of 4.08 feet and a high of 4.5 feet

Step-by-step explanation:

Answer:

Step-by-step explanation:

There is only one intercepting point, it means one solution.

a. Pair 2 is selected.

b. Respiratory system, its function is to breathe. Digestive system, its function is to break down food into nutrients.

c. The two systems work together by sharing the region of the mouth and upper throat.

First picture in Pair 2 is Respiratory system, which its function is to breathe. Second picture in Pair 2 is Digestive system, which its function is to break down food into nutrients such as carbohydrates, fats and proteins. The respiratory system takes in oxygen from the air, and also gets rid of carbon dioxide. The digestive system absorbs water and nutrients from the food we consume.

The respiratory system is mainly used to transport air, whilst the digestive system is used to transport fluids and solids, from water and food we eat. The respiratory and the digestive systems share the area of the mouth and upper throat, in which air, fluids, and solids can be mixed.

The digestive system does homeostasis by ensuring that the stomach area has the right pH balance. The body uses both positive and negative mechanisms to perform homeostasis. If the body detects an imbalance, the other systems work together to counterbalance and restore the right equilibrium.

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The reasonable domain for this function is 0 < x < 50

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

Given;

A = 50W - W2

The area of a rectangle cannot be negative;

The practical domain of A is determined when;

50W-W^2>0

Taking common factor W

W(50-W)>0

Since W must be positive W>0

50-W>0

Or equivalently

50>w

W<50

The total interval is

0<W<50

Therefore, the domain of the function will be 0 < x < 50

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The number of hours Jackson worked washing cars is 8 hours and the number of hours he worked landscaping is 6 hours

The payment of car washing per hour = $10

The payment for landscaping = $12

Total number of hours worked = 14  hours

Number of hours worked in car washing = x

Number of hours worked in landscaping = y

Then the first equation will be

x + y = 14

x = 14 - y

Total amount he earned = $152

Next equation will be

10x + 12y = 152
Here we have to use substitution method

10(14-y) + 12y = 152

140 - 10y +12y = 152

140 + 2y = 152

2y = 152 - 140

2y = 12

y = 12/2

y = 6 hours

Then

x = 14 - y

x = 14 -6

x = 8  hours

Hence, the number of hours Jackson worked washing cars is 8 hours and the number of hours he worked landscaping is 6 hours

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Answer:

-12

Step-by-step explanation:

Substitute x for 3

6(3-5)

Simplify in the parenthesis

6(-2)

multiply

-12

Answer:

(-5 , 1)

Step-by-step explanation:

If you are reflecting over the x-axis, you are changing the sign of the y.

If you are reflecting over the y-axis, you are changing the sign of the x.

In this case, you have the point (5 , 1). You are reflecting over the y-axis, which means that you are flipping the sign of the x value.

(5 , 1) reflected over the y-axis is (-5 , 1)

(-5 , 1)

~

Answer:

5 is how many units on the x axis (the horizontal one) and 1 is how many units on the y axis (the vertical one). So, the correct answer is 1.

The Logarithmic function is a mathematical operation that is used to determine the logarithm of a number.

The logarithm of a number x is the exponent to which a fixed number, the base, must be raised to produce x. The most common bases used are 10 and e. The formula for determining the logarithm of a number x base d is: log base d of x = (log base d of x)/(log base d of b).

For example, if we want to calculate the log base 10 of a number x, we would use the formula: log base 10 of x = (log base 10 of x)/(log base 10 of b). We can calculate the log base 10 of a number x by taking the logarithm of x and dividing it by the logarithm of the base, 10. The result will be the log base 10 of x.

For example, if we want to calculate the log base 10 of 25, we would calculate the logarithm of 25 and divide it by the logarithm of 10. The calculation would be: log base 10 of 25 = (log base 10 of 25)/(log base 10 of 10) = (1.3979)/(1) = 1.3979. This means that the log base 10 of 25 is 1.3979.

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The given statement "For any sampled population, the population of all sample means is approximately normally distributed" is true. This is a result of the Central Limit Theorem, which states that when sample sizes are large enough, the means of all samples will be approximately normally distributed.

A sample is a smaller portion of the population that has been taken to draw conclusions about the characteristics of the population as a whole. The sample needs to be representative of the population for the data analysis to be valid.

A sample mean is a statistical analysis in which the sum of all data points in a sample is divided by the number of observations. It gives an idea of the average value of the data points in the sample population.

For any sampled population, the population of all sample means is approximately normally distributed. The central limit theorem states that when the sample size is sufficiently large, the distribution of the sample means will be approximately normal, regardless of the underlying distribution of the population.

The central limit theorem is an important concept in inferential statistics because it provides a theoretical foundation for the use of statistical inference methods to draw conclusions about population parameters based on sample statistics.

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There are approximately 2.97 billion droplets per acre being sprayed.

To calculate the number of droplets per acre, we need to first convert the diameter of the droplets from microns to inches (since we are using acres as our unit of area). There are 25,400 microns in one inch, so the diameter of the droplets in inches is 250/25,400 = 0.0098 inches.

Next, we need to calculate the area of one droplet. The formula for the area of a circle is A = πr², so the area of one droplet is A = π(0.0049)² = 0.0000754 square inches.

Finally, we can calculate the number of droplets per acre by dividing the total area of one acre (43,560 square feet) by the area of one droplet: 43,560 / 0.0000754 = 2.97 billion droplets per acre.

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Answer:

Step-by-step explanation:

A-domain (-∞,∞)

B- Range(0,∞)  the range is the set of values tat correspond with the domain

C- the y intercept (0,1) , y intercept is when x =0 (2/3)^0=1

D-the horizontal asymptote is x-axis y=0

E- the graph is always decreasing

F-it depend on the base

Answer:

774 km

Step-by-step explanation:

Actual distance

\( =\frac{4.3}{100000} \times 18000000 \\ \\ = 4.3 \times 180 \\ = 774 \: km\)

1)

4136 mm = 4136/1000 = 4.136 m = 4.14 m

2)

Since 1 yard = 91.44 cm

Hence, 14.7 yard = 14.7*

91.44 = 1,344.168 cm = 1344 cm

3)

342 inches = 9 yards, 1 ft, 6 inches.

Given:

The point is located at (-1,-4).

Point T is reflected over the x-axis to create point T′.

Point T′ is then reflected over the y-axis to create point T′′.

To find:

The ordered pair describes the location of T''.

Solution:

We have, the given point T(-1,-4).

Point T is reflected over the x-axis to create point T′. So, the rule of reflection is

\((x,y)\to (x,-y)\)

\(T(-1,-4)\to T'(-1,4)\)

Point T′ is then reflected over the y-axis to create point T′′. So, the rule of reflection is

\((x,y)\to (-x,y)\)

\(T'(-1,4)\to T''(1,4)\)

Therefore, the ordered pair (1,4) escribes the location of T′′.

The source, format, assumptions and constraints, and other facts concerning certain data are collectively called 'metadata'.

Metadata provides information about data that helps users understand and use it effectively.

Some examples of metadata include,

The date and time the data was collected.

The file format of the data.

The units of measurement used.

And any assumptions or limitations that were made during the collection or analysis of the data.

By providing metadata along with the data, users can better understand the context and quality of the data.

This can help them make more accurate and informed decisions.

Metadata is classified into three types which are known as descriptive, administrative, and structural.

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The missing number in the unit conversion problem is composed as follows:

9 ft = 108 inches.

The missing number is obtained applying the proportions in the context of the problem.

The unit conversion rate between ft and inches is given as follows:

1 feet = 12 inches.

Hence the number of inches in 9 feet is obtained multiplying 9 by 12, as follows:

9 x 12 = 108 inches.

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