What is the value of the expression shown below?

3 + (2 + 8)^2 ÷ 4 × 1 over 2 to the power of 4 (4 points)


4 and 1 over 32

4 and 9 over 16

6 and 1 over 8

6 and 1 over 32

Answer:

Both the median and the range changed.

Step-by-step explanation:

We first ensure this data set is from least to greatest.  This one is.

Next we find the median.  This is the middle value; in this set, it is 16.

Next we find Q1, the lower quartile.  This is the middle of the lower set of data (once the data is "split" by the median).  This is 15.

Next we find Q3, the upper quartile.  This is the middle of the upper set of data (once the data is "split" by the median).  This is 20.

The IQR is Q3-Q1, or 20-15 = 5.

The range is the max subtracted by the min, or 21-4 = 17.

Any outlier will be 1.5 times the IQR below Q1 or 1.5 times the IQR above Q3.

1.5(5) = 7.5; 15-7.5 = 7.5.  Any lower outlier would be below this value; this makes 4 an outlier.

20+7.5 = 27.5.  Any upper outlier would be above this value; this means there are no outliers on the upper end.

Taking the data value 4 out, the median is now 17.  Q1 would still be 15 and Q3 would still be 20; this means the IQR would still be 5.

The range would now be 21-14 = 7.

This means the median and the range have changed.

The true statement comparing the box plots is that Both the median and the range changed.

When we get data that can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.

Quartiles are then selected as 3 points such that they create four groups in the data, each group approximately possessing 25% of the data.

The box plots display the same data for the number of crackers in each snack bag, but one includes the outlier in the data and the other excludes it.

4, 14, 15, 15, 16, 16, 18, 19, 20, 20, 21 Number of Crackers in Each Bag, with Outlier Number of Crackers in Each Bag, without Outlier

The median in this set is 16.

Q1, the lower quartile. This is the middle of the lower set of data.

This is 15.

Q3, the upper quartile. This is the middle of the upper set of data. This is 20.

The IQR is Q3-Q1

20-15 = 5.

The range will be

21-4 = 17.

Any outlier will be 1.5 times the IQR below Q1 or 1.5 times the IQR above Q3.

1.5(5) = 7.5

15-7.5 = 7.5.  

Any lower outlier would be below this value, this makes 4 an outlier.

20+7.5 = 27.5.  

Any upper outlier would be above this value, this means there are no outliers on the upper end.

Taking the data value 4 out, the median is now 17.  

Q1 would still be 15 and Q3 would still be 20; this means the IQR would still be 5.

The range would now be 21-14 = 7.

Thus, This means the median and the range have changed.

Learn more about quartiles here:

brainly.com/question/9260741

#SPJ3

To determine the value of ↑ which the equation ax²-3x-5=0 has 1 as a root, we substitute x=1 into the equation and solve for a, yielding the result that a=8.

To find the value of a for which the equation ax² - 3x-5=0 has 1 as one of its roots, we can substitute x=1 into the equation and solve for a. When x=1, the equation simplifies to:

a(1)² - 3(1) - 5 = 0

a - 3 - 5 = 0

a - 8 = 0

Therefore, a = 8.

This means that the value of a is 8 for the equation to have 1 as one of its roots. This is a direct application of the fact that if a polynomial has a certain number as a root, then by substituting that number in place of the variable, the equation should result in zero.

Answer:

the answer is 9 hours

Step-by-step explanation:

I got it right on the test

The time taken by Jan and Jo with constant rate of 70 mph and 60 mph respectively, will meet in 9 hours while driving towards each other along a 1,170-mile road.

To find out how long it will take Jan and Jo to meet, you can use the formula:

Time = Distance / Speed

Since they are driving toward each other, their combined speed is the sum of their individual speeds:

Combined Speed = Jan's Speed + Jo's Speed

Combined Speed = 70 mph + 60 mph

Combined Speed = 130 mph

Now, you can use this combined speed to calculate the time it will take for them to meet:

Time = Distance / Combined Speed

Time = 1,170 miles / 130 mph

Time = 9 hours

Therefore, time taken by Jan and Jo is 9 hours to meet while driving toward each other on the same road.

Learn more about time here

brainly.com/question/24560894

#SPJ3

Answer:

3 miles per hour

Step-by-step explanation:

Using speed formula:

[tex]\text{Speed} = \frac{\text{Distance}}{\text{Time}}[/tex]

As per the statement:

Team tool Bella canoed 15 3/4 miles in 5 1/4 hours.

⇒[tex]\text{Distance} = 15\frac{3}{4} = \frac{63}{4}[/tex] miles and

[tex]\tetx{Time} = 5\frac{1}{4} = \frac{21}{4}[/tex] hours

Using speed formula we have;

[tex]\text{Speed}= \frac{\frac{63}{4} }{\frac{21}{4}} = \frac{63}{4} \cdot \frac{4}{21} = \frac{63}{21}[/tex]

Simplify:

[tex]\text{Speed} =3[/tex] miles per hour

Therefore, their average rates of speed in miles per hour is, 3 miles per hour

They do not occur more frequently than any other value in the distribution, the values 220, 260, 250, and 270 are not modes.

Distributed mode is the most common value. From the given frequency distribution we can see that both the values ​​220 and 230 occur with the highest frequencies of 6 and 7 respectively. Therefore, both 220 and 230 are modes of this distribution.

that the values ​​260, 250, and 270 are not modes, as they all have frequencies of 0 or 1. Also, the No Mode value is not a valid value in the distribution, indicating that there is no single mode value.

The values 220, 230, 240, 250, 260, and 270 all appear six times in this distribution, seven times each for values 230, seven times for values 240, one for value 250, zero for values 260, and one for value 270.

As a result, the value with the highest frequency—230—is the mode. Therefore, 230 is the mode for this distribution.

Due to the fact that they do not occur more frequently than any other value in the distribution, the values 220, 260, 250, and 270 are not modes.

To know more about distribution visit:-

https://brainly.com/question/31197941

#SPJ1

The problem involves the concept of related rates in Calculus. By using the relationship between the height and radius of the cone and the rate of change of the volume, we set up a differential equation. Upon solving, we find the rate at which the height of the pile changes is 5/(18π) feet per minute when the pile is 12 feet high.

The subject matter of this question is related to Calculus, specifically the concept of related rates. In this scenario, sand is falling off a conveyor and onto a conical pile at a rate of 10 cubic feet per minute. Here, the given rate is the rate of change of the volume of the sand pile. The diameter of the base of the cone is approximately three times the altitude, which gives the relationship between the height and the radius of the cone: r=h/3. The student is asked to find at what rate the height of the pile is changing when the pile is 12 feet high.

First, let's recall the formula for the volume of a cone, which is V=(1/3)*π*r²*h. Based on the relationship between the radius and the height, we can substitute r with h/3. Therefore, the volume V=(1/3)*π*(h/3)²*h = (1/27)*π*h³. By differentiating this equation with respect to time t, we get dV/dt = (1/9)*π*h²*dh/dt.

We are given that dV/dt is 10 cubic feet per minute, and we want to find dh/dt when h = 12 feet. Substituting these values into the differentiated equation, we get 10 = (1/9)*π*(12²)*dh/dt. Solving this for dh/dt, we find that dh/dt = 10 / [(1/9)*π*(12²)] = 5/(18π) feet per minute.

https://brainly.com/question/29898746

#SPJ11

Final answer:

To calculate the total length of the boards, the first board at 47/100 meters (0.47 meters) is added to the second board at 5/10 meters (0.5 meters), resulting in a total length of 0.97 meters.

Explanation:

To find the total length of the two boards placed end to end, we simply add the lengths of the individual boards. The first board is 47/100 meters long, and the second board is 5/10 meters long.

The second board's length can be simplified as 5/10 is equivalent to 1/2, which is 0.5 in decimal form. Adding the lengths together, we get:

Length of board 1: 47/100 meters (or 0.47 meters)
Length of board 2: 5/10 meters (or 0.5 meters)

Total length = 0.47 meters + 0.5 meters
Total length = 0.97 meters

Therefore, the total length of the two boards when placed end to end is 0.97 meters.

The perimeter of a rectangle is 35.

So the function that represents the length of the flower bed in terms of its width is:

l(w) = (35 - 2w) / 2.

The whole distance that a rectangle's borders, or its sides, cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the total of its four sides.

To write a function that represents the length of the flower bed in terms of its width, we can use the equation for the perimeter of a rectangle:

2l + 2w = p

where l is the length, w is the width, and p is the perimeter. We know that the perimeter is 35 feet, so we can substitute that into the equation:

2l + 2w = 35

We want to solve this equation for l, so we can isolate the variable on one side of the equation:

2l = 35 - 2w

Dividing both sides by 2 gives:

l = (35 - 2w) / 2

So the function that represents the length of the flower bed in terms of its width is:

l(w) = (35 - 2w) / 2

where l(w) is the length of the flower bed for a given width w.

To learn more about the rectangular perimeter;

https://brainly.com/question/22109593

#SPJ3

The 22nd term of the arithmetic progression in the series 161, 147, 133, 119.... is -133.

This question involves finding the 22nd term in a series of numbers where each term is 14 less than the preceding term. This is an arithmetic progression where the first term, 'a' is 161 and the common difference, 'd' is -14.

The formula for the nth term in an arithmetic progression is: a + (n - 1)*d.

Substituting the given values into the formula, we get:

'a' + (22 - 1)*'d' = 161 + (21)*(-14) = 161 - 294 = -133

So, S22 for 161+147+133+119+... = -133.

https://brainly.com/question/30364336

#SPJ12

To find y'' by implicit differentiation, differentiate the equation 5x^2 + y^2 = 3 twice with respect to x. Simplify and isolate y'' to find the second derivative of y.

To find y'' by implicit differentiation, we differentiate the equation 5x^2 + y^2 = 3 with respect to x twice.

Step 1: Differentiate both sides of the equation with respect to x using the chain rule.

Step 2: Simplify the equation and isolate y'' to find the second derivative of y.

Step 3: Rewrite the equation with the second derivative of y isolated on one side.

https://brainly.com/question/11887805

#SPJ12

Answer: The value of BP is 5.25.

Step-by-step explanation:

Here's why:

Find the ratio between the two different groups of line segments. If you do it in decimal or fraction, it's the same. So, 4/6 = 0.666666667. Then you must find the number that when 3.5 is divided by it, gives you 0.666666667. So that number is 5.25.