The median of the values in a data set is x. If 32 were subtracted from each
of the values in the data set, what would be the median of the resulting data?
A. X+32
B. X-32
C. X
D. 32 - x

Answer:

A 5% raise can be written as 1.05 so the new salary is 25100 * 1.05 = $26355.

The correct answer is $307.5

Explanation:

The total of the bond after 20 years is $150 plus the interests during this time (105% of $150). This last value can be calculated by multiplying the percentage (105) by the total ($150) and dividing it into 100% (total percent represented by $150. The process is shown below:

[tex]150 = 100[/tex]%

[tex]x = 105[/tex]%

[tex]x = \frac{150 x 105}{100}[/tex]

[tex]x = 157.5[/tex]

This means the total money in interest is $157.5 and this added to $150 is equivalent to $307.5

Answer:

x≤2−√6 or 0<x≤2+√6

Answer:

AB ║ CD, reason If two lines (AB and CD) and a transversal AD, form alternate interior angles, (∠1 and ∠4) that are congruent, then the two lines are parallel

Step-by-step explanation:

Statement,                                      Reason

Triangle ACD is isosceles,             Given

∠1 ≅ ∠3,                                           Given

∠3 ≅ ∠4,                                          Base angles of isosceles triangle

∠1 ≅ ∠4,                                           Substitution

∠1 and ∠4, are alt int. ∠s,                Definition

AB ║ CD,                                          Have congruent alternate interior angles

If two lines (AB and CD) and a transversal AD, form alternate interior angles, (∠1 and ∠4) that are congruent, then the two lines are parallel

The two-column proof that shows that Segment AB║Segment CD is shown in the image attached below (See attachment).

Given the image showing an isosceles triangle, ΔACD.

The two-column proof that shows segment AB || Segment CD has been provided in the table shown in the image attached below.

We know already that:

ΔACD is isosceles

∠1 ≅ ∠3

∠3 and ∠4 base angles of the isosceles triangle, therefore, ∠3 ≅ ∠4.

By substitution, ∠1 ≅ ∠4

∠1 and ∠4 are alternate interior angles, therefore, based on the Converse of Alternate Interior Angles Theorem: AB║CD

The complete two-column proof is in the image attached below.

Learn more about Alternate Interior Angles Theorem on:

https://brainly.com/question/19486848

Answer:

Domain: (−∞,∞)

Range: (−∞,∞)

Step-by-step explanation:

trust me

Answer:

A =  0    -7                             b=   0     -7

      3     2d                                   3      2d    

Let's calculate A and B:

Calculte (AB)^(-1):

Calculte B^(-1) and A^(-1):

so:

(AB)^(-1) = B^(-1) * A^(-1)

Answer:

The domain is -418 < a < 8848 where a is an integer.

Step-by-step explanation:

We see from the data given that the  domain of T(a) takes both positive and negative integer values ( 8848 meters and  -418 meters); T(a) never gets decimal values (and in real life thy won't be of much use because we are not looking for that much accuracy).

So the appropriate number type for the domain of T(a) would be integers. And if you are interested, the domain is -418 < a < 8848.

Answer:

first term a=4

Step-by-step explanation:

Sum of the first 6 terms S6 = 15624

common ratio r= 5

n= 6

first term a=?

Formula: S6= a(r^n-1)/r-1

15624 = a( 5^6-1)/5-1

15624 = a(15625-1)/4

15624= a( 15624)÷4

15624= 15624a÷4

Cross multiply

15624×4 = 15624a

62496 = 15624a

divide both sides by 15624

62496÷15624 = 15624a÷15624

4 = a

a= 4

Tenemos que sean x e y los lados de la huerta entonces el perímetro sería:

P = 2*x + 2*y

Sabemos que el perimetro es 140, reemplazando:

140 = 2*x + 2*y

x + y = 70

despejamos y, nos queda:

y = 70 - x

Ahora tenemos que el área sería:

A = x*y

reemplazamos y:

A = x*(70 - x)

A = 70*x - x^2

Esta sería la ecuación que modela el área de la huerta.

Derivamos e igualamos a 0:

0 = 70 - 2*x

x = 70/2

x = 35

ahora calculamos y:

y = 70 - 35

y = 35

El área máxima sería:

A = 35*35

A = 1225 m^2

Answer:

The answer is option D

Step-by-step explanation:

Circumference of a circle is πd

where d is the diameter

From the question

d = 6½ feet = 13/2 feet

Circumference is

π × 13/2

= 22/7 × 13/2

= 143/7

[tex] = 20 \frac{3}{7} [/tex]

Hope this helps you

Answer:

d

Step-by-step explanation:

/its wat he sed

Answer:

Step-by-step explanation:

[tex]sin \: 54 = \frac{opposite \: side}{hypotenuse} [/tex]

[tex]sin \: 54 = \frac{h}{10} [/tex]

[tex]0.8090 = \frac{h}{10} [/tex]

[tex]h = 10 \times 0.8090[/tex]

[tex]h = 8.09[/tex]

[tex]h = 8.1[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

h = 8.1 m

Step-by-step explanation:

Sin 54 = [tex]\frac{opposite }{hypotenuse}[/tex]

Where opposite = h, hypotenuse = 10 m

0.809 * 10 = h

=> h = 8.1 m

Answer:

given,

base= 10

height= 8

now, area of triangle =

[tex] \frac{1}{2} \times b \times h[/tex]

or, area =

[tex] \frac{1}{2} \times 10 \times 8[/tex]

therefore the area of a triangle is 40 sq units.

hope its helpful..

Answer:

A, 40 sq.units

Step-by-step explanation:

Area of Triangle:   1/2·b·h

Substitute:  h= 8, b= 10

                  A = 1/2 (10)(8)

Simplify:   A = 1/2(80) = 40

Area= 40 sq. units

Answer: D.) Cultural knowledge

Step-by-step explanation:

Answer:

solution,

Sum of exterior angles=360°

[tex]3x + 2x + 40 + 4x + x + 50 = 360 \\ or \: 3x + 2x + 4x + x + 40 + 50 = 360 \\ or \: 10x + 90 = 360 \\ or \: 10x = 360 - 90 \\ or \: 10x = 270 \\ or \: x = \frac{270}{10} \\ x = 27[/tex]

Hope this helps..

Good luck on your assignment...

Answer:

see explanation

Step-by-step explanation:

The statements tells us that w is inversely proportional to v and the equation relating them is

v = [tex]\frac{k}{w}[/tex] ← k is the constant of proportion

To find k use the condition v = 9, w = 5, that is

9 = [tex]\frac{k}{5}[/tex] ( multiply both sides by 5 )

45 = k

v = [tex]\frac{45}{w}[/tex] ← equation of proportion

When w = 4 , then

v = [tex]\frac{45}{4}[/tex] = 11.25

Answer: 168 hours

Step-by-step explanation:

There are 24 hours in a day.  Thus, simply multiply 7*24 to get 168.

Hi there! Hopefully this helps!

-------------------------------------------------------------------------------------------------------------

Answer: There are 168 hours in 7 days.

Since there 24 hours in a day, Multiply 24 times 7 and you get 168.

Example : 24 x 7 = 168.

Answer:

B

Step-by-step explanation:

Since the diagonals of a rhombus bisect each other, that means P is the midpoint of LN. Therefore, LP = 1/2 * LN = 1/2 * 30 = 15.

Answer:

15

Step-by-step explanation:

4x=60

60 divided by 4 = 15

Answer:

Required angle measures 39°

Step-by-step explanation:

Let's say, x measures the angle between the hypotenuse and the common base of two triangles.

Sin(x) = 5/8

x = 39°

This angle is complementary to the angle other than theta (let's say y) in the required triangle.

90 - x = y and 90 - theta = y

>>> Theta = x

Best Regards!

Answer:

y - 1 = (3/5)x

Step-by-step explanation:

First find the slope of this line.  As we move from (0, -2) to (5, 1), x (the 'run') increases by 5 and y (the 'rise') increases by 3.  Thus, the slope of this line is m = rise / run = 3/5.

Using the point-slope formula for the equation of a straight line:

y - 1 = (3/5)(x - 5), or

y - 1 = (3/5)x                This can also be written as 5y - 5 = 3x, or

y = (3/5)x + 1

Answer:

A and e

Step-by-step explanation:

Answer:

x = 6/5

y = 8/5

Step-by-step explanation:

3x - y = 2

2x + y = 4

Add the equations, cancelling y.

5x = 6

x = 6/5

Put x as 6/5 in the second equation and solve for y.

2(6/5) + y = 4

12/5 + y = 4

y = 4 - 12/5

y = 8/5

━━━━━━━☆☆━━━━━━━

▹ Answer

3x + 5

▹ Step-by-Step Explanation

8x - 2 - 5x + 7

= 3x - 2 + 7

= 3x + 5

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer: For the equation to have one solution, use any number that does not contain 3x.

Step-by-step explanation:

8x - 2 - 5x + 7

Combine like terms

3x + 5

Answer:

[tex]B.\ x^3 - 2x^2 - 4x + 1[/tex]

Step-by-step explanation:

Given

Polynomials A to D

Divisor: x - 2

Required

Which of polynomial A - D has a remainder of -7

We start by equating the divisor to 0

[tex]x - 2 = 0[/tex]

Make x the subject of formula

[tex]x = 2[/tex]

Next is to substitute 2 for x in the polynomials to get the remainder;

[tex]A.\ 4x^3 + 2x^2 + 5[/tex]

[tex]4(2)^3 + 2(2)^2 + 5[/tex]

Open Brackets

[tex]4 * 8 + 2 * 4 + 5[/tex]

[tex]32 + 8 + 5[/tex]

[tex]Remainder = 45[/tex]

[tex]B.\ x^3 - 2x^2 - 4x + 1[/tex]

[tex](2)^3 - 2(2)^2 - 4(2) + 1[/tex]

Open Brackets

[tex]8 - 2 * 4 - 4 * 2 + 1[/tex]

[tex]8 - 8 - 8 + 1[/tex]

[tex]Remainder = -7[/tex]

[tex]C.\ 3x^2 + 6x - 2[/tex]

[tex]3(2)^2 + 6(2) - 2[/tex]

Open Brackets

[tex]3 * 4 + 6 * 2 - 2[/tex]

[tex]12 + 12 - 2[/tex]

[tex]Remainder = -2[/tex]

[tex]D.\ -2x^3 + 4x^2 + 3x - 2[/tex]

[tex]-2(2)^3 + 4(2)^2 + 3(2) - 2[/tex]

Open Brackets

[tex]-2 * 8 + 4 * 4 + 3 * 2 - 2[/tex]

[tex]-16 + 16 + 6 - 2[/tex]

[tex]Remainder = 4[/tex]

From the calculations above, the polynomial with a remainder of -7 when divided by [tex]x - 2[/tex] is [tex]B.\ x^3 - 2x^2 - 4x + 1[/tex]

The value of the polynomial [tex]x^3-2x^2-4x+1[/tex] is -7 at x = 2. So, option B is correct.

Important information:

According to the Remainder Theorem, if a polynomial is p(x) is divided by (x-c), then the remainder is p(c).

If polynomials have a remainder of -7 when divided by x – 2. So, the value of the polynomial must be -7 at x = 2.

Substitute x = 2 in the first polynomial.

[tex]4(2)^3+2(2)^2+5=45\neq -7[/tex]

Substitute x = 2 in the second polynomial.

[tex](2)^3-2(2)^2-4(2)+1=-7[/tex]

Substitute x = 2 in the third polynomial.

[tex]3(2)^2+6(2)-2=22\neq -7[/tex]

Substitute x = 2 in the fourth polynomial.

[tex]-2(2)^3+4(2)^2+3(2)-2=4\neq -7[/tex]

Only the value of the second polynomial is -7 at x = 2. Therefore, the correct option is B.

Find out more about 'Remainder Theorem' here:

https://brainly.com/question/4515216

Answer: The bottom option, the graph.

Step-by-step explanation:

A relation is something that gets input from a set, called domain (usually the x) and "transforms" them into an output, from a set called the range.

Now, a relation is only a function if, for all the elements x in the domain, each one of them has only one element y in the range associated to it.

For example, in the first set we can see that the value x = 1 appears two times, it is related to different values in the range, then this is not a function.

The second relation is not a function.

the third relation is:

x = 3*y^2 - 7

This is a function, but in this relation x is the output and y the input, so this is a function of y.

In the fourth relation we can see a graph, this is a function (each value in the domain is related to only one in the range), and in the horizontal axis we can see a x, so this is a function of x.

Answer:

D

Step-by-step explanation:

Answer:

B.No. The input is not possible.

Step-by-step explanation:

According to the given scenario, as we know that f(x) indicates that the baskets number and x the number of players at the practice.

Therefore, if we are having the point (12, 36) we can conclude that during practice there were 36 baskets and 12 players.

Hence, it does not make any sense which results that input is not possible

Answer:

13

Step-by-step explanation:

There are 6 ways to choose the first number and 5 ways to choose the second number to paint so the total number of ways is 6 * 5 = 30 but we are over counting by a factor of 2 since 1 and 6 is the same as 6 and 1 so it's 30/2 = 15, not 30. The only choices that have a product of 6 are 2 and 3 or 1 and 6 so the answer is 15 - 2 = 13.

Answer:

13 ways

Step-by-step explanation:

Total number of distinct ways to pair two faces

= C(6,2) = 6! / (2!4!) = 15

Total number of ways to pair two faces so that the product equals six

=cardinality {1*6, 2*3} = 2

Therefore

number of ways to paint two faces such that the product is not six

= 15 - 2

=13

Answer:

a) x = 10

Step-by-step explanation:

En este romboide, el angulo A es igual a el angulo C, y el angulo ABC es igual a el angulo CDA.

Entonces, el angulo C es 7x.

En un triangulo, los angulos se suman para ser 180 degrados. En el triangulo BCE, hay un angulo recto.

7x + 2x + 90 = 180

7x + 2x = 90

9x = 90

x = 10

Espero que este te ayude!

Answer:

in 1st sequence put 1 instead of n

i.e

a1=3×1+2

=3+2

=5

Step-by-step explanation:

now do all the 50 terms by placing 1 to 50 instead of n

Answer:

<B = 47°

<C = 28°

b = AC = 28.0

Step-by-step explanation:

Given:

∆ABC

AB = c = 18

BC = a = 37

<A = 105°

Required:

Length of AC = b

measure of angle B and angle C

SOLUTION:

==>Use the sine rule, sin A/a = sinC/c to find the angle of C:

SinA = sin(105) = 0.9659

a = 37

sinC = ?

c = 18

0.9659/37 = sinC/18

Cross multiply

0.9659*18 = 37*sinC

17.3862 = 37*sinC

Divide both sides by 37

17.3862/37 = sinC

0.4699 = sinC

sinC = 0.4699

C = Sin-¹(0.4699)

C = 28.0° (nearest tenth)

==>Find angle B using sum of angles in a triangle:

Angle B = 180 - (105+28)

Angle B = 180 - 133

Angle B = 47°

==>Find length of b using sine rule, b/sinB = c/sinC:

SinC = sin(28) = 0.4695

SinB = sin(47) = 0.7314

c = 18

b = ?

b/0.7314 = 18/0.4695

Cross multiply

b*0.4695 = 18*0.7314

b*0.4695 = 13.1652

Divide both sides by 0.4695

b = 13.1652/0.4695

b = 28.0 (nearest tenth)

Answer:

A ≈ 3215.36

Step-by-step explanation:

A = πr²

Radius - D/2

Radius - 64/2 → 32

A = 3.14(32)²

A = 3215.36

Hope this helps! :)

Answer:

3215.36 um²

Step-by-step explanation:

d = 2r => r = d/2 = 64/2 = 32 um

A = π·r²

= 3.14·32²

= 3.14·1024

≈ 3215.36 um²