The following are the ages of 13 history teachers in a school district. 24, 27, 29, 29, 35, 39, 43, 45, 46, 49, 51, 51, 56 Notice that the ages are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum: Interquartile range:

Answer:

-10, -4

Step-by-step explanation:

Answer:

590

Step-by-step explanation:

2360_

_8+12

=2360_

_4

590

Answer:

area: 576 cm ^2

perimeter: (48 + 24π) cm

Step-by-step explanation:

the semicircle taken out of the square (the white area) is equal to the semicircle added to the left of it. thus, we just have the area of a square. we know this because both have the same diameter and are semicircles. thus, our area is 24^2 = 576 cm ^2

for perimeter:

top: 24 cm

bottom: 24 cm

right: this is equal to half the circumference of a circle. this is because we know it's a semicircle taken out. circumference = πd = 24 * π. divide this by 2 to get 12π.

left: this is also equal to half the circumference of a circle = 12π

sum = 48cm + 24π

Answer:

275 miles

Step-by-step explanation:

Answer:

4.5

Step-by-step explanation:

Step 1. Turn the second fraction (the one you want to divide by) upside down

(this is now a reciprocal).

Step 2. Multiply the first fraction by that reciprocal

Step 3. Simplify the fraction (if needed)

1.) D.

2.) D.

3.) B.

4.) A.

5.) A.

Hope it helps :)

Answer:

ED = AB = 25√3

Step-by-step explanation:

Let ED = AB = X

DC = 100 - BC

Tan 60 = \(\frac{\sqrt{3} }{1} = \frac{ED}{DC}\) = \(\frac{X}{100-BC}\)

\(\sqrt{3} (100-BC) = X\)

Tan 30 = \(\frac{1}{\sqrt{3} } = \frac{AB}{BC} = \frac{X}{BC}\)

\(\frac{BC}{\sqrt{3} } = X\)

\(\sqrt{3} (100-BC) = \frac{BC}{\sqrt{3} } \\3(100-BC) = BC\\300 - 3BC = BC\\300 = BC + 3BC\\300 = 4BC \\75 = BC\)

X = \(\frac{BC}{\sqrt{3} } = \frac{75}{\sqrt{3} }\\\)

X = 25√3

Based on this data, for every inch in height, the arm span increases by 1.1 inches.

Here, we have,

I put the height of people on the x-axis because this is what I am trying to correlate the arm span to. I put the arm span on the y-axis because it is dependent on height.

I used point (60,61) and (70,72) to draw the line of best fit and to get the equation. First, to get the slope I would use the slope formula of m = 72-61/70-60 or 11/10 to get a slope of approximately 1.1. Then I used (60,61) to get the rest of the equation by plugging it in: y-61 = 1.1(x -60). This becomes y-61 = 1.1x - 66. Add 61 to both sides and the final equation is y = 1.1x – 5.

The slope represents the rate of change arm span based on height. The y intercept is the arm span.

Using points (66,68) and points (70,72) I plug each into the equation y=1.1x-5 to figure each out based on the difference from the actual points and get .4 for (66,68) and 0 for point (70,72) so I would say, based on .4 and 0 for these two points that this is a good line of best fit.

Based on this data, for every inch in height, the arm span increases by 1.1 inches.

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complete question:

There are many measurements of the human body that are positively correlated. For example, the length of one's forearm (measured from elbow to wrist) is approximately the same length as the foot (measured from heel to toe). They are positively correlated because, as one measurement increases, so does the other measurement.

The length of arc HK is 30.8 units

The length of the arc is defined as the distance between two points on the arc on the circumference.

Length of arc = θ/360 x 2πr

where, r is the radius of arc and θ is the angle formed by the arc at the center.

Given, circle J with ∠HJK = 126° and HJ = 14 units'

Plug, the values, we get

length of arc = 126°/360° x 2π x 14 units

length of arc = 30.8 units

Thus, the length of arc HK is 30.8 units.

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They will be exactly 124 miles apart 40 minutes before they meet.

First, we can find the combined speed of Car A and Car B by adding their individual speeds:

68 mph + 76 mph = 144 mph

This means that they will be covering a total distance of 144 miles every hour.

To find out how far apart they will be after 40 minutes, we need to calculate how much distance they will cover in that time.

We know that 60 minutes = 1 hour, so 40 minutes = 40/60 = 2/3 hour.

So, in 40 minutes, Car A will cover a distance of:

68 mph × 2/3 hour = 45.33 miles

And Car B will cover a distance of:

76 mph × 2/3 hour = 50.67 miles

Therefore, the total distance they will cover together in 40 minutes is:

45.33 miles + 50.67 miles = 96 miles

Subtracting this distance from their initial distance of 220 miles, we get:

220 miles - 96 miles = 124 miles

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Answer:

x=5 or x=-5

Step-by-step explanation:

(x+5)=0 (x-5)=0

The air speed of a small airplane during the first 25 seconds of takeoff and flight can be modeled by Newton's Second Law of Motion.

According to Newton's Second Law of Motion, the rate of change of the airplane's momentum is equal to the sum of all the forces acting on the airplane. As the plane takes off and accelerates, the thrust of the engines acting in the forward direction causes the plane's momentum to increase. This increase in momentum results in an increase in air speed. The air resistance acting against the motion of the plane is another force that affects the plane's speed. As the plane accelerates, the air resistance increases, and the plane's speed decreases.

In summary, the air speed of a small airplane during the first 25 seconds of takeoff and flight can be modeled by Newton's Second Law of Motion, where the thrust of the engines and air resistance act as forces that influence the plane's air speed.

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Answer:

Sometimes

Step-by-step explanation:

A linear pair are angles that are adjacent to each other, with one shared side.

Complementary angles can be anywhere but they have to be coplanar(have to share the same plane)

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

Option (C)

Step-by-step explanation:

Formula to get the scale factor of any image from it's preimage,

Scale factor of an image = \(\frac{\text{Dimension of the image}}{\text{Dimension of the preimage}}\)

From the figure attached,

F' is the image of preimage F after dilation.

Scale factor = \(\frac{\text{Length of A'B'}}{\text{Length of AB}}\)

                    = \(\frac{4}{6}\)

                    = \(\frac{2}{3}\)

Therefore, Figure F has been dilated by a scale factor of \(\frac{2}{3}\) to form F'.

Option (C). will be the answer.

Answer:

SAS, ASA, SSS, ASA, Yes

Step-by-step explanation:

\(\tan 60^{\circ}~\text{equals y coordinate divided by x coordinate, where }(x,y) = \left(\dfrac 12, \dfrac{\sqrt 3}2 \right)\)

\(\tan 60^{\circ}\\\\= \dfrac yx \\\\\\=\dfrac{\sin 60^\circ}{\cos 60^\circ}\\\\\\=\dfrac{\tfrac{\sqrt 3}2}{\tfrac 12}\\\\\\=\dfrac{\sqrt 3}2 \times 2\\\\\\=\sqrt 3\)

This rule is enough

Now

Here A=60°

By using power properties, the expression y⁸ · y³ · x⁰ · x⁻² is equivalent to the expressions 1 / (x² · y⁵) and x⁻² · y⁻⁵. (Correct choices: C, D)

In this question we have a power function with two variables and which has to be simplified by using power properties. The detailed procedure is shown below:

By using power properties, the expression y⁸ · y³ · x⁰ · x⁻² is equivalent to the expressions 1 / (x² · y⁵) and x⁻² · y⁻⁵. (Correct choices: C, D)

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Answer:

2 does not belong

Step-by-step explanation:

We know that 2 cups of orange juice make 3 cups of fruit punch. So 2/3 cups of orange juice makes 1 cup of fruit punch. Due to this, you know that 2/3 belongs.

When rolling a number cube one time, there are several things that are true. Here are three options:

1. The outcome will be a whole number between 1 and 6: Since the number cube has faces numbered from 1 to 6, rolling it one time will result in one of these whole numbers.

2. Each face has an equal chance of landing face-up: The number cube is designed in such a way that each face has an equal probability of landing face-up when rolled. This means that the chances of rolling a 1, 2, 3, 4, 5, or 6 are all the same.

3. The outcome is independent of previous rolls: Rolling the number cube one time does not depend on or affect any previous rolls. Each roll is considered an independent event, so the previous outcome does not influence the next roll.

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For the expression to have a true value for x, the limit of k must lie within the range of 4 and 6, inclusive.

The value of x in the formula kx2-6x+4/4x2-6x+x must exist within the range of 4 and 6, inclusive, for k to have a genuine value. Thus, k must be more than or equal to 4 and less than or equal to 6, respectively. When x is real, the expression cannot take on a real value if k is outside of this range. This is because division by zero is illogical because the denominator will be equal to zero. Therefore, x is real for the expression to be capable of the value, k must be between 4 and 6.

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Answer:

D) 98/280 = p/100

Step-by-step explanation:

Since p is the missing percentage, it has to be OVER 100, so C is eliminated.

Total:

182 + 98 = 280

Spotted sheep probability:

98/280 = 0.35 or 35%

To check:

\(\frac{98}{280} =\frac{p}{100} \\\\280p=9800\\x=35\)

The answer is:

5/4

Work/explanation:

Let's work out the slope of the line.

The equation is in y = mx + b form where m = slope; b = y intercept.

Similarly, in y=5/4x - 7/4, the slope is 5/4.

According to the question, the four consecutive numbers can be written as :

First = \(x\); Second = \(x+2\);  Third = \(x+4\); Fourth = \(x+6\)

As per the question, the final expression is :

\(2((x+2)+(x+4)) = 3(x)+32\)

\(4x+12 = 3x+32\)

\(x = 20\)

Therefore, the four values can be calculated by substituting the above value:

\(x=20; x+2=22; x+4=24; x+6=26\)

The four consecutive numbers are: \(20,22,24,26\)

Substitute the calculated values in the final expression, to check whether the answer is correct or not.

\(2(22+24) = 3(20)+32\)

\(92=92\)

Therefore, the calculated values are correct.

What are consecutive terms?

Consecutive terms are those terms which follow one sequential order.

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Answer:

2x^3-6x^2-14x+24

Step-by-step explanation:

Answer: x would be 6

Step-by-step explanation: x is a variable, its being used as multiplication here and u need to find the number x is representing

with 2x = 12

divide both sides by 2

2x divided by 2, 12 divided by 2

ur left with

x = 6

The fraction pairs that are equivalent are 16/20 and 9/12, 6/21 and 14/35, and 2/8 and 7/28.

To determine if two fractions are equivalent, we need to check if they reduce to the same simplified form.

For the given fraction pairs:

Therefore, the fraction pairs that are equivalent are 16/20 and 9/12, 6/21 and 14/35, and 2/8 and 7/28.

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The equivalent fractions are 2/8 and 7/28 as they both simplify to 1/4, whereas the other fractions do not simplify to the same value.

To determine if two fractions are equivalent, one can either simplify both fractions to their lowest terms and compare, or cross-multiply and see if the products are equal.

Now let's examine your given pairs:

Therefore, only the third pair (2/8 and 7/28) are equivalent fractions.

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Answer: -2/11

Step-by-step explanation:

All of the following statements are true:

a. Effective listening is vital to success in selling.

b. visual aids play a part in the listening process.

c. people can talk approximately twice as fast as they can listen.

d. you should listen closely to everything you hear.

e. listening refers to the process of trying to detect sounds.

Listening is the act of paying attention to sounds that are happening around you. It involves both hearing the sounds and interpreting what they mean. Good listening skills are important for many reasons, including being able to communicate effectively with others and understand instructions. To listen effectively, you need to be able to focus on the speaker and try to understand their perspective, rather than just waiting for your turn to talk.

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