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2 years ago

Create a set of 5 positive numbers (repeats allowed) that have median 7 and mean 10.

Mathematics

1 answer:

damaskus [11]2 years ago

6 0

Answer:

Step-by-step explanation:

Two cases arise to obtain the median.

Case (1): Sample size (n) is odd

First, arrange the data in ascending order. Then, the median is the middle value and lies at the ${\left( {\frac{{n + 1}}{2}} \right)^{{\rm{th}}}}$ position.

Case (2): Sample size (n) is even

First, arrange the data in ascending order. Then, the median is the mean of the two data values that lie on and positions.

Formula for mean is, where is the sum of all observations and n is the total number of observations.

(1)

Use the below process to create a set of 5 positive numbers (repeats allowed) that have median 7 and mean 10.

1.Select the 5 ordered numbers with middle value 7.

2.Adjust the remaining 4 numbers other than 7 to get mean 10 without changing the order of the numbers.

Based on the process to select the 5 ordered numbers with middle value 7 and change the other ordered numbers to get the mean value 10.

(2)

The product of the mean and the total number of observations is obtained. Then, the sum of four observations is subtracted from the product.

Here, the first four numbers are (5, 6, 7, 8).

The last number by using mean 10 is,

$\begin{array}{c}\\\bar x = \frac{{5 + 6 + 7 + 8 + a}}{5}\\\\10 = \frac{{5 + 6 + 7 + 8 + a}}{5}\\\\50 = 26 + a\\\\a = 50 - 26\\=24\end{array}$

The last number is 24.

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Kate writes an algebraic expression using each of the variables x and y only once. they first expression she writes uses x and y

kotykmax [81]

Answer:

B: Using x and y factor results in an expression of greater value than using x and y as terms.

Step-by-step explanation:

For her first expression, x and y are factors;

For her second expression, x and y are written as terms;

x + y

For x and y are both negative integers, then;

-x * -y = xy ............... 1

-x + (-y) = - x - y

= - (x + y) .............. 2

Therefore, the value of x and y factors is greater than that when x and y are as terms. Thus the correct option is B.

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2 years ago

An isosceles triangle ABC with the base BC is inscribed in a circle. Find the measure of angles of it, if measure of arc BC = 10

Usimov [2.4K]

Answer:

The measures of the angles of the triangle are 51° , 64.5° , 64.5°

The measures of the angles of the triangle are 129° , 25.5° , 25.5°

Step-by-step explanation:

* Lets explain the meaning of the inscribed triangle in a circle

- If a triangle inscribed in a circle, then the vertices of the triangle lie

on the circumference of the circle and each vertex is an inscribed

angle in the circle subtended by the opposite arc

- Fact in the circle the measure of the inscribed angle is 1/2 the

measure of its subtended arc

* Now lets solve the problem

- Δ ABC is an isosceles with the base BC

∴ AB = AC

∴ m∠B = m∠C

- Δ ABC is inscribed in a circle

∴ ∠A is inscribed angle subtended by arc BC (minor or major)

# The measure of the minor arc is less than 180° and the measure of

the major arc is greater then 180° and the sum of the two arcs

equals the measure of the circle which is 360°

∴ ∠B subtended by arc AC

∴ ∠C subtended by arc AB

∵ The measure of the arc BC = 102°

- There is two cases in this question

(1) If the angle A subtended by the minor arc BC

(2) If the angle A subtended by the major arc BC

- Lets solve case (1)

∵ ∠A is an inscribed angle subtended by the minor arc BC

∴ m∠A = 1/2 the measure of the arc BC

∵ The measure of the arc BC is 102°

∴ m∠A = 1/2 × 102 = 51°

∵ The sum of the measures of the interior angles of a triangle is 180°

∴ m∠A + m∠B + m∠C = 180°

∴ 51 + m∠B + m∠C = 180° ⇒ subtract 51 from both sides

∴ m∠B + m∠C = 129°

∵ m∠B = m∠C ⇒ isosceles Δ

∴ m∠B = m∠C = 129/2 = 64.5°

* The measures of the angles of the triangle are 51° , 64.5° , 64.5°

- Lets solve case (2)

∵ ∠A is an inscribed angle subtended by the major arc BC

∴ m∠A = 1/2 the measure of the arc BC

∵ The measure of the minor arc BC is 102°

∵ The measure of the circle is 360°

∴ The measure of the major arc = 360 - 102 = 258°

∴ m∠A = 1/2 × 258 = 129°

∵ The sum of the measures of the interior angles of a triangle is 180°

∴ m∠A + m∠B + m∠C = 180°

∴ 129 + m∠B + m∠C = 180° ⇒ subtract 129 from both sides

∴ m∠B + m∠C = 51°

∵ m∠B = m∠C ⇒ isosceles Δ

∴ m∠B = m∠C = 51/2 = 25.5°

* The measures of the angles of the triangle are 129° , 25.5° , 25.5°

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2 years ago

Chandresh is helping his father paint the fence in their back yard. The fence is represented by the shaded part of the diagram b

Lyrx [107]

B. The total area painted is 864; they must buy two cans of paint.

Step-by-step explanation:

Step 1:

A rectangle's area can be calculated by multiplying its length and its width. The wall is made up of 5 different types of rectangular walls. All walls are 8 feet tall but the length varies.

Step 2:

The area of the 20 feet long wall = $(length)(width)= (20)(8) =160,$

The area of the 10 feet long wall = $(length)(width)= (10)(8) =80,$

The area of the 5 feet long wall = $(length)(width)= (5)(8) =40,$

The area of the 4 feet long wall = $(length)(width)= (4)(8) =32,$

The area of the 15 feet long wall = $(length)(width)= (15)(8) =120.$

The area of all the walls = 432 square feet.

Since there are two sides for every wall, total area = $432(2)=864$ square feet.

Step 3:

If one paint can covers 500 square feet,

the number of cans required to paint 864 square feet = $\frac{864}{500} = 1.728$ cans.

so 2 paint cans are needed to paint 864 square feet which is option B.

7 0

2 years ago

Marty is asked to draw triangles with side lengths of 4 units and 2 units, and a non-included angle of 30°. Select all the trian

777dan777 [17]

Answer:

The drawn in the attached figure

see the explanation

Step-by-step explanation:

First case

In the triangle ABC

Let

$a=4\ units\\b=2/ units\\B=30^o$

Applying the law of sines

Find the measure of angle A

$\frac{a}{sin(A)}=\frac{b}{sin(B)}$

substitute the given values

$\frac{4}{sin(A)}=\frac{2}{sin(30^o)}$

$sin(A)=1$

$A=90^o$

Find the measure of angle C

In a right triangle

we know that

$B+C=90^o$ ----> by complementary angles

$B=30^o$

therefore

$C=60^o$

Find the length side c

Applying the law of sines

$\frac{c}{sin(C)}=\frac{b}{sin(B)}$

substitute the given values

$\frac{c}{sin(60^o)}=\frac{2}{sin(30^o)}$

$c=2\sqrt{3}\ units$

therefore

The dimensions of the triangle are

$A=90^o$

$B=30^o$

$C=60^o$

$a=4\ units\\b=2\ units\\c=2\sqrt{3}=3.46\ units$

Second case

In the triangle ABC

Let

$a=4\ units\\b=2/ units\\A=30^o$

Applying the law of sines

Find the measure of angle B

$\frac{a}{sin(A)}=\frac{b}{sin(B)}$

substitute the given values

$\frac{4}{sin(30^o)}=\frac{2}{sin(B)}$

$sin(B)=0.25$

using a calculator

$B=14.48^o$

Find the measure of angle C

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

$A+B+C=180^o$

$A=30^o\\B=14.48^o$

therefore

$30^o+14.48^o+C=180^o$

$C=135.52^o$

Find the length side c

Applying the law of sines

$\frac{c}{sin(C)}=\frac{a}{sin(A)}$

substitute the given values

$\frac{c}{sin(135.52^o)}=\frac{4}{sin(30^o)}$

$c=5.61\ units$

therefore

The dimensions of the triangle are

$A=30^o$

$B=14.48^o$

$C=135.52^o$

$a=4\ units\\b=2\ units\\c=5.61\ units$

see the attached figure to better understand the problem

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Kobotan [32]

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2 years ago

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