I have $5$ different mathematics textbooks and $4$ different psychology textbooks. In how many ways can I place the $9$ textbooks on a bookshelf, in a row, if there must be a psychology textbook exactly in the middle, and there must be a mathematics textbook at each end?

Answer:

[tex] \gamma = 125.00 \: degrees \\ a = 2.18 \\ b = 3.59[/tex]

Step-by-step explanation:

[tex] \gamma = 180 - 20 - 35 \\ = 125 \: degrees[/tex]

[tex]using \: sine \: rule \\ \frac{a}{sin20} = \frac{b}{sin35} = \frac{5.122}{sin125} \\ a = 2.1386 \\ b = 3.5865[/tex]

Answer:

y = 4x+ 5 is the equation that describes the data...

that is a linear equation ... the slope is 4 thus "the y value increases 4 for every 1 unit increase in x"

Step-by-step explanation:

Answer:

65 + 30x.

Step-by-step explanation:

The $65 is a one-time fee for when you first purchase the instrument. The $30 is every month you rent it, and x = the months you rent it.

Therefore, to find the whole cost over time, you would do

65 (first month) + 30x (how much you'll spend over the time you rent the instrument).

Answer:

10 years

Step-by-step explanation:

Given :

Population of Canyon falls = 22500

Rate of decrease = 740 per year

Population after x years :

f(x) = 22500 - 740x ; x = number of years

Population of Swift Creek = 15200

Rate of Increase = 1500 per year

Population after x years :

f(x) = 15200 + 1500x ; x = number of years

Number of years when, population of swift creek will be twice that of Canyon falls

15200 + 1500x = 2(22500 - 740x)

15200 + 1500x = 45000 - 1480x

15200 - 45000 = - 1480x - 1500x

-29800 = - 2980x

x = 29800 / 2980

x = 10

After 10 years

The x-intercept is when y=0. It is the point on the x-axis. Solve for x when y=0 in the first equation.

2x + 3(0) + 6 = 0

2x = -6

x = -3

x-intercept is (-3, 0).

The line we want has the same slope as the second equation because it is parallel. From the second equation,

-5y = -2x + 7

y = (2/5)x - (7/5)

The slope is 2/5.

Using the x-intercept and slope, along with the general form of the line y = mx + b , we can solve for b.

y = mx + b

0 = (2/5)(-3) + b

0 = (-6/5) + b

(6/5) = b

The equation we want is

y = (2/5)x + (6/5)

Step-by-step explanation:

drop some thanks plss ✌

follow too

Step-by-step explanation:

Consecutive odd integers are integers that take on the form n, n + 2, n +4, n + 6, and so on, where n is odd.

Now, Product of two consecutive positive odd integers = 2499

=>n*(n+2) = 2499

=>n^2+2^n-2499=0

=>n^2+51^n-49^n-2499=0 =>n(n+51)-49(x+51)=0

=>(n+51)(n-49)=0

=>n=49 (n is not equal to -51 which is negative integer).

So,bigger integer =(n+2)=49+2=51.

Answer:

6

Step-by-step explanation:

======================================================

Explanation:

Exponents of 1/2 are the same as square roots

[tex]36^{1/2} = \sqrt{36} = 6[/tex]

If the exponent was say 1/3, then we'd be taking a cube root

[tex]36^{1/3} = \sqrt[3]{36}[/tex]

and this is what a fourth root would look like

[tex]36^{1/4} = \sqrt[4]{36}[/tex]

and so on

Answer: $ 91.50.

Step-by-step explanation:

Let x be the original price.

Since discount is applied before tax.

New price = (Original price - Discount)-Tax rate (Original price - Discount)

, where Discount = Discount rate x Original price.

Substituting values, we get

[tex]62.28=(x-0.25x)-0.0925(x-0.25x)[/tex]

[tex]62.28=(0.75x)-0.0925(0.75x)[/tex]

[tex]62.28=0.75x-0.069375x[/tex]

[tex]62.28=0.680625x[/tex]

[tex]x=\frac{62.28}{0.680625}[/tex]

[tex]x=91.50[/tex]

Hence, the original price was  $ 91.50.

Answer:

6

Step-by-step explanation:

(whole secant) * (external part) = (tangent)^2

(KL) * (KM) = KJ^2

(KM+ ML) * KM = KJ^2

(2+ ML) * 2 = 4^2

(2+ ML) * 2 =16

Divide each side by 2

(2+ ML)  = 8

Subtract 2 from each side

ML = 6

9514 1404 393

Answer:

  27

Step-by-step explanation:

For point (x, y) and slope m, the y-intercept can be found from the equation ...

  b = y -mx

  b = 0 -(-3)(9) = 27

The y-intercept is +27. The corresponding ordered pair is (0, 27).

Answer:

The answer is below

Step-by-step explanation:

Let x represent the length of the rectangular pen and y represent the width of the rectangular pen. Since the total area of the pen is 169 ft², hence:

Area = length * width

169 = xy

y = 169/x

Also the perimeter of the rectangular pen is:

Perimeter (P) = 2(length + width)

P = 2(x + y)

P = 2x + 2y

P = 2x + 2(169/x)

P = 2x + 338/x

The least amount of fencing is at dP/dx = 0, hence:

dP/dx = 2 - 338/x² = 0

338/x² = 2

2x² = 338

x² = 169

x = 13 feet

y = 169 / x = 169/13 = 13 feet

The least amount of fencing = P = 2(x + y) =  2(13 + 13) = 52 feet

Answer:

since angle x and y are the same the answer will be

A: x=y

Answer:

15x^2 + 23x = 4

Step-by-step explanation:

NOT BOX METHOD :

(-5x-1)(-3x-4)

=15x^2+20x+3x+4

=15x^2+23x+4

Answer: 2.81 s

Step-by-step explanation:

Given

Ball is kicked upward with velocity [tex]u=90\ ft/s[/tex]

Height of the ball is given by the function [tex]h(t)=-16t^2+90t[/tex]

Derivative of a function gives the maxima or minima at certain point

[tex]\Rightarrow \dfrac{dh}{dt}=-32t+90\\\\\Rightarrow \dfrac{dh}{dt}=0\\\\\Rightarrow -32t+90=0\\\\\Rightarrow t=\dfrac{90}{32}\\\\\Rightarrow t=2.81\ s[/tex]

Thus, it takes ball 2.81 s to reach the top.

Answer:

40 cm

Step-by-step explanation:

volume = length x width x height

10,000 = 25 x 10 x h

h = 10,000/ (25 x 10)

h = 10,000 / 250

h = 40 cm

Answer:

perimeter

Step-by-step explanation:  If she walks around its perimeter.  If she covers every inch of ground covered by the field its area.

Perimeter would be like an outline.  And area would be the whole thing shaded.  

Answer:

8,24 metros cuadrados de vidrio

Step-by-step explanation:

Área de un rectángulo = Largo × Ancho

De la pregunta anterior

Longitud = 3,23 m

Ancho = 2,55 m

Área del rectángulo = 3,23 m × 2,55 m

= 8.2365 m²

Aproximadamente = 8,24 m²

Por tanto, Ramiro tiene que comprar 8,24 metros cuadrados de vidrio

Answer:

27.2 ft

Step-by-step explanation:

We solve using the Trigonometric function of tan

tan θ = Opposite/Adjacent

θ = 66°

Opposite = Height of the building = 61 ft

Adjacent = Length of the shadow = ? = x

tan 66 = 61/x

Cross Multiply

tan 66 × x = 61

x = 61 ft/tan 66

x = 27.158949804 ft

Approximately = 27.2 ft

The length of the shadow = 27.2 ft

Answer:

.5 or (1/2)

.5  or (1/2)

2.5 or (5/2)

Step-by-step explanation:

all you really have to do is mulitply the numbers by .5

1*.5= .5

5*.5= 2.5

Answer:

x=4

Step-by-step explanation:

(whole secant) x (external part) = (tangent)^2

(x+5) *x = 6^2

x^2 +5x = 36

Subtract 36 from each side

x^2 +5x - 36 = 0

Factor

( x-4) (x+9) = 0

Using the zero product property

x-4 = 0  x+9 =0

x = 4  x=-9

Cannot be negative since that is negative length

x=4

Answer:

Given a line segment AB

open the compass more than half of the distance between A and B, and scribe arcs of the same radius centered at A and B.

Call the two points where these two arcs meet C and D. Draw the line between C and D.

CD is the perpendicular bisector of the line segment AB. Call the point where CD intersects AB E.

Step-by-step explanation:

for more help please follow

Answer:

Follow the steps below to construct a perpendicular bisector of a line segment.

Step 1: Draw a line segment XY of any suitable length.

Step 2: Take a compass, and with X as the center and with more than half of the line segment XY as width, draw arcs above and below the line segment.

Step 3: Repeat the same step with Y as the center.

Step 4: Label the points of intersection as 'P' and 'Q'.

Step 5: Join the points 'P' and 'Q'. The point at which the perpendicular bisector PQ intersects the line segment XY is its midpoint. Label it as 'O'.

Step-by-step explanation:

Answer:

 6 just 6 Your welcome !!

Step-by-step explanation:  

Answer:

No way its too blur XD

Step-by-step explanation:

sports

watching tv

reading books

surfing

and sleeping maybe

Answer:

Sports - 25%

Surfing - 25%

Reading Books - 20%

Watching TV - 25%

Malling - 5%

Step-by-step explanation:

Answer:

510 divided by 380 is 1.34210526316 so multiple by 10 to get 134.210526316

rounding to the tenth we get 134.2

Answer: proportionate

Step-by-step explanation:

Proportional quota sampling is when the total number of people that are to be surveyed are decided in advance. This form of sampling is usually used in opinion polls and surveys.

Since due to the fact that there are many more women in teaching jobs than men, the researcher selected more women than men for her study to ensure that it represented the actual distribution of men and women teachers in the job, then this was decided in advance and indicates the proportionate quota sampling.

Answer:

87.9°

Step-by-step explanation:

arctan(50/40)=87.9°