A collection of five positive integers has a mean of 4.4, a unique mode of 3, and a median 4. If an 8 is added to the collection, what is the new median? Express your answer as a decimal to the nearest tenth.

Answer:

Solution given:

(x1,y1)=(-4,-5)

(x2,y2)=(0,-8)

distance=?

we have

distance=\( \sqrt{(x2-x1) ²+(y2-y1) ²}\)

d=\( \sqrt{(0+4)²+(-8+5) ²}\)

d=\( \sqrt{25}\)

d=\( 5\)units

\( 5\)units I travelled.

Answer: 2.35%

Step-by-step explanation:

Answer:

~10.8 (ft)

Step-by-step explanation:

Apply the Pythagorean theorem, you can work out the measure of diagonal.

\(Diagonal = \sqrt{9^{2}+6^{2} } =\sqrt{81 + 36} =\sqrt{117} =~10.8(ft)\)

The measure of the diagonal of a rectangle is 10.8 feet.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Given that, a rectangle measures 9 feet by 6 feet.

Let the length of diagonal be x.

x²=9²+6²

x²=81+36

x²=117

x=√117

x=10.8 feet

Therefore, the measure of the diagonal of a rectangle is 10.8 feet.

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The probability that a randomly selected person from this sample was a friend of the bride OR of the groom is 0.9875.

Given that, at a wedding each guest asked the 80 guests whether they were a friend of the bride or of the groom.

What is the probability?

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Total Number of Guests which forms the Sample Space, n(S)=80

Let the event (a friend of the bride) =A

Let the event (a friend of the groom) =B

n(A) =59

n(B)=50

Friends of both bride and groom,

So,

n(A∪B)=n(A)+n(B)-n(A∩B)

n(A∪B)=59+50-30

n(A∪B)=79

The number of Guests who was a friend of the bride OR of the groom = 79

Thus,

P(A∪B)=n(A∩B)/n(S)

= 79/80

= 0.9875

Hence, the probability that a randomly selected person from this sample was a friend of the bride OR of the groom is 0.9875.

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By using the concept of internal angles of a triangle, the solution of the system of linear equations related to the geometrical system is (x, y) = (40, 40).

In this system we have a geometrical system formed by two right triangles with a common hypotenuse. Right triangles are triangles where one of its internal angles are right angles and the sum of the measures of the internal angles within a triangle equals 180°. Then, this geometrical system can be modelled by using the following linear equations:

(x + 20) + 90 + 30 = 180         (1)

20 + 90 + (y + 30) = 180         (2)

By using the concept of internal angles of a triangle, the solution of the system of linear equations related to the geometrical system is (x, y) = (40, 40).

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u=-54

you have -54 because

-54(-2)=108/9=12

Answer:

u =-54

Step-by-step explanation:

-2/9u=12

To solve for u multiply each side by -9/2 to isolate u

-9/2 * -2/9 u= 12 * -9/2

u =-54

5th term of the sequence is -4

To find the 5th term in the sequence, we need to substitute n =  5 into the expression given

 \(a_5\) =  26- 6( 5)  

\(a_5\) =  26- 30

\(a_5\) = -4  

The formula given, an =  26- 6n, represents an  computation sequence with a common difference of-6.

This means that each term in the sequence is  attained by obtain 6 from the  former term.  

It's important to note that the formula is written in general form, meaning that it can be used to find any term in the sequence by simply plugging in the  matching value of  n.

 In this case, we were asked to find the 5th term, so we substituted n =  5 into the formula to get a5 = -4.

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Answer:

No

Step-by-step explanation:

Scaling is the procedure for either increasing or decreasing the size of a given object. While a scale is the representative fraction used for the purpose.

scale = \(\frac{length on drawing}{original length}\)

For triangle B to be a scaled copy of triangle A,

scale = \(\frac{5}{1}\)

         = 5:1

This is an enlarged scale, therefore each side of triangle A should be multiplied by 5 not increased by 5.

Triangle B is not a scaled copy of triangle A.

The approximate difference in the circumferences of the two circles is: C. 61 cm.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = 2πr or C = πD

Where:

Substituting the given parameters into the circumference of a circle formula, the circumference of the small circle is;

Circumference of circle, C = πD

Circumference of circle, C = 3.14 × 4.5

Circumference of circle, C = 14.13 cm.

For the larger circle, we have:

Circumference of circle, C = 3.14 × 24

Circumference of circle, C = 75.36 cm.

Difference = 75.36 cm - 14.13 cm.

Difference = 61.23 ≈ 61 cm.

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According to the given function, it is found that fewer than 38.1% of U.S. voters will use punch cards or lever machines starting from the year of 2004.

\(P(t) = -2.5t + 63.1\)

It will be fewer than 38.1% when:

\(P(t) < 38.1\)

Hence:

\(-2.5t + 63.1 < 38.1\)

\(-2.5t < -25\)

\(2.5t > 25\)

\(t > 10\)

Fewer than 38.1% of U.S. voters will use punch cards or lever machines starting from the year of 2004.

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Answer:

A.

Step-by-step explanation:

Let's think of this as a clock.  We can see that the 2 lines start in the same place, around 3 o'clock.  Next, one of the line segments shifts down to around 6 o'clock.  Next, it shifts to about 9 o'clock.  Logically, the next step (in a clock) would be 12 o'clock, making A the correct choice.

We can also just use a regular circle, with one of the line segments moving 90 degrees each time.

Hope this helps! :)

Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

Answer:

Step-by-step explanation:

point m

Answer:

Like the ellipse, the hyperbola can also be defined as a set of points in the coordinate plane. A hyperbola is the set of all points

(

x

,

y

)

in a plane such that the difference of the distances between

(

x

,

y

)

and the foci is a positive constant.

Notice that the definition of a hyperbola is very similar to that of an ellipse. The distinction is that the hyperbola is defined in terms of the difference of two distances, whereas the ellipse is defined in terms of the sum of two distances.

Answer:

10

Step-by-step explanation:

it is one of the properties and derived "abilities" of a hyperbola that the distance of a point on one branch to the focal point of the other branch is the sum of the minimum distance of both branches (in our case 4) and the distance to its "own" focal point (in our case 6).

so, the length of the dotted line is

4 + 6 = 10

to extend and clarify the information from the other answer :

there are 3 different curves when slicing a double-cone (2 cones standing straight on top of each other with their tips touching - in other words, each cone is the mirrored upside-down version of the other).

1. ellipse

a plane is slicing through one of the cones, so that it never touches the other cone.

the ellipse is the outline of that cut around the cone.

a circle is an extreme case, where the plane cuts perpendicular to the central axis of the cone.

2. parabola

an infinite ellipse (another extreme case of ellipse). the slicing plane is parallel to the outline of the cone(s).

but still, only one of the 2 cones is touched.

3. hyperbola

the slicing plane is so inclined that it cuts through both cones. the 2 branches of a hyperbola are the outlines of the cuts through both cones.

usually shown as example is the extreme case, where the slicing plane is parallel to the central axis of the double-cone.

all 3 forms are therefore related.

The common difference of the sequence is 70, the slope of the 1st and 2nd lines is 70, the slope of the 3rd and 4th points is 70, and the slope is constant.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. Y and x are the net changes in the y and x coordinates, respectively.

Given:

Time in minutes and jumping jack table, coordinates of lines (1, 70) and (2, 140)

(a)

Consider 70, 140, 210, and 280 as an arithmetic sequence then the common difference will be,

Common difference = 140 - 70 = 70

(b)

Calculate the slope of the line as shown below,

\(m = (y_2-y_1) / (x_2 - x_1)\)

m = (140 - 70) / (2 - 1)

m = 70 / 1

m = 70

(c)

Calculate the slope for 3rd and 4th points,

m = (280 - 210) / (4 - 3)

m = 70 / 1

m = 70

(d)

As you can, the slope is constant, and the common difference is also constant.

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The partial products of 3706 × 4 is ( 3000 × 4 ) + ( 706 × 4 ).

Calculating the product of two or more numbers is the procedure known as multiplication in mathematics. When two integers are multiplied together in mathematics, the result is a product or an expression that describes the factors to be multiplied.

The decimal numeral system is widely used to express both integer and non-integer numbers. The way of representing numbers in the decimal system is known as decimal notation.

The given product is 3706 × 4 and can be written as:-

3706 × 4 = [ 3000 + 706 ] × 4

3706 × 4 = ( 3000 × 4 ) + ( 706 × 4 )

Therefore, the partial products of the given expression is ( 3000 x 4 ) + ( 706 x 4 ).

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Answer:

x-4+(20)/(x+4)

Answer: 18.78 cubic feet

Step-by-step explanation:

The detailed analysis is attached below.

The mode will not change.

Given data,

58,60,53,54,60,35,58,60

Outlier is the value in a set of data that much higher or lower than other values in data.

from given data, outlier is 35.

Mode is the value in a set of data that occurs more frequently in set of data.

from given data, 60 occurs more frequently.

Hence, 60 is the mode of data.

If outlier is removed from the data set then it will not affect the mode of the data

Thus, the mode will not change.

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where is m?

if it was asking for angle A the answer would be D.

Answer:

D. 70

Step-by-step explanation:

because the D side is the same line as A and the D side is also 70

Answer:

The  number is  \(N =1147\) students

Step-by-step explanation:

From the question we are told that

    The population mean is  \(\mu = 281\)

     The standard deviation is  \(\sigma = 34.4\)

    The sample size is  n = 2000

percentage of the would you expect to have a score between 250 and 305 is mathematically represented as

      \(P(250 < X < 305 ) = P(\frac{ 250 - 281}{34.4 } < \frac{X - \mu }{\sigma } < \frac{ 305 - 281}{34.4 } )\)

Generally  

             \(\frac{X - \mu }{\sigma } = Z (Standardized \ value \ of \ X )\)

So  

         \(P(250 < X < 305 ) = P(-0.9012< Z<0.698 )\)

       \(P(250 < X < 305 ) = P(z_2 < 0.698 ) - P(z_1 < -0.9012)\)

From the z table  the value of  \(P( z_2 < 0.698) = 0.75741\)

                                         and  \(P(z_1 < -0.9012) = 0.18374\)

     \(P(250 < X < 305 ) = 0.75741 - 0.18374\)

      \(P(250 < X < 305 ) = 0.57\)

The  percentage is  \(P(250 < X < 305 ) = 57\%\)

The  number of students that will get this score is

           \(N = 2000 * 0.57\)

           \(N =1147\)

The shaded region of the rectangle is 242.9 cm² and the shaded region of the sector is 7.1 square units.

Question 17) is a figure of a rectangle and two inscribed circles.

The area of a rectangle is expressed as: A = length × width

The area of a circle is expressed as: A = πr²

Where r is the radius.

To determine the area of the shaded region, we simply subtract the areas of the two circles from the area of the rectangle.

Area = ( Length × width ) - 2( πr² )

Area = ( 40 × 10 ) - 2( π × 5² )

Area = ( 400 ) - 2( 25π )

Area = 400- 50π

Area = 242.9 cm²

Area of the shaded region is 242.9 squared centimeters.

Question 18) is the a figure a sector of a circle and a right triangle.

The area of a sector is expressed as: A = (θ/360º) × πr²

The area of a triangle  is expressed as: A = 1/2 × base × height

To determine the area of the shaded region, we simply subtract the areas of the triangle from the area of the sector.

Hence:

Area = ( (θ/360º) × πr² ) - ( 1/2 × base × height )

Plug in the values:

Area = ( (90/360º) × π × 5² ) - ( 1/2 × 5 × 5 )

Area = 25π/4 - 12.5

Area = 7.1

Therefore, the area of the shaded region is 7.1 square units.

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Answer:

cars weighed the most per item and desks the least

The probability of selecting a girl and a boy for the class committee can be calculated by considering the total number of outcomes and the number of favorable outcomes.

Identify the number of girls and boys in the class. In this case, there are 5 girls and 7 boys.

Determine the total number of students in the class. That is 5 + 7 = 12.

Determine the number of ways to select two students from the class.

Here we can use the combination formula, which is written as C(n, r), where n is the total number of items and r is the number of items to be chosen.

In our case, n = 12 (total number of students) and r = 2 (number of students to be selected).

C(12, 2) = 12! / (2!(12-2)!) = 66.

Determine the number of favorable outcomes.

In this case, we want to select one girl and one boy. We multiply the number of girls by the number of boys: 5 x 7 = 35.

To find the probability, we divide the number of favorable outcomes (35) by the total number of outcomes (66):

Probability = Number of favorable outcomes / Total number of outcomes = 35 / 66 = 5/6.

So, the probability of selecting a girl and a boy for the class committee is 5/6.

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Answer: 2 meters

Step-by-step explanation:

The length of one train car is 80 millimeters. Therefore, the length of the entire train is:

25 cars × 80 mm per car = 2000 mm

To convert millimeters to meters, we need to divide by 1000:

2000 mm ÷ 1000 = 2 meters

Therefore, Venell's model train is 2 meters long.

Answer:

A) D) F)

Step-by-step explanation:

\(y=x^2\)

\(y=x^2+3\)