A.85
B.98
C.102
D.34

Answer:

-√3/2

Step-by-step explanation:

Given the expression:

Cos(7π/6)

Conver to degrees

=  Cos(7(180)/6)

= cos 210

= -√3/2

Hence the value of cos(7π/6) is -√3/2

Answer:

We can conclude that her walking speed is 2.1 miles per hour.

Step-by-step explanation:

We have the relation:

Speed = distance/time.

Here we know:

She walked for 44 miles.

And she ran along the same route, so she ran for 44 miles.

The total time of travel is 22 hours, so if she ran for a time T, and she walked for a time T', we must have:

T + T' = 22 hours.

If we define: S = speed runing

                     S' = speed walking

Then we know that:

"and she ran 33 miles per hour faster than she walked."

Then:

S = S' + 33mi/h

Then we have four equations:

S'*T' = 44 mi

S*T = 44 mi

S = S' + 33mi/h

T + T' = 22 h

We want to find the value of S', the speed walking.

To solve this we should start by isolating one of the variables in one of the equations.

We can see that S is already isoalted in the third equation, so we can replace that in the other equations where we have the variable S, so now we will get:

S'*T' = 44mi

(S' + 33mi/H)*T = 44mi

T + T' = 22h

Now let's isolate another variable in one of the equations, for example we can isolate T in the third equation to get:

T = 22h - T'

if we replace that in the other equations we get:

S'*T' = 44mi

(S' + 33mi/h)*(  22h - T') = 44 mi

Now we can isolate T' in the first equation to get:

T' = 44mi/S'

And replace that in the other equation so we get:

(S' + 33mi/h)*(  22h -44mi/S' ) = 44 mi

Now we can solve this for S'

22h*S' + (33mi/h)*22h + S'*(-44mi/S')  + 33mi/h*(-44mi/S') = 44mi

22h*S' + 726mi - 44mi - (1,452 mi^2/h)/S' = 44mi

If we multiply both sides by S' we get:

22h*S'^2 + (726mi - 44mi)*S' - (1,425 mi^2/h) = 44mi*S'

We can simplify this to get:

22h*S'^2 + (726mi - 44mi - 44mi)*S' - (1,425 mi^2/h) = 0

22h*S'^2 + (628mi)*S' - ( 1,425 mi^2/h) = 0

This is just a quadratic equation, the solutions for S' are given by the Bhaskara's equation:

[tex]S' = \frac{-628mi \pm \sqrt{(628mi)^2 - 4*(22h)*(1,425 mi^2/h)} }{2*22h} \\S' = \frac{-628mi \pm 721 mi }{44h}[/tex]

Then the two solutions are:

S' = (-628mi - 721mi)/44h = -30.66 mi/h

But this is a negative speed, so this has no real meaning, and we can discard this solution.

The other solution is:

S' = (-628mi + 721mi)/44h = 2.1 mi/h

We can conclude that her walking speed is 2.1 miles per hour.

Anwer:$285

Explaination: Division method

$1995.00÷7=$285

Answer:

Step-by-step explanation:

Sinθ = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

If, sinθ = -[tex]\frac{1}{2}[/tex] and π < θ < [tex]\frac{3\pi }{2}[/tex]

Since, sinθ is negative, angle θ will be in IIIrd quadrant.

And the measure of angle θ will be (180° + 30°)

θ = 210°

It's necessary to remember that tangent and cotangent of angle θ in quadrant III are positive.

Therefore, cos(210°) = [tex]-\frac{\sqrt{3} }{2}[/tex]

tan(210°) = [tex]\frac{1}{\sqrt{3} }[/tex]

csc(210°) = [tex]-\frac{1}{2}[/tex]

sec(210°) = [tex]-\frac{2}{\sqrt{3} }[/tex]

cot(210°) = √3

Answer:

x ≤ 11.20

Step-by-step explanation:

solve it like a regular equation

5x ≤ 67 - 11

5x ≤ 56

x ≤ 11 1/5

x ≤ 11.20

Answer:

105 in³

Step-by-step explanation:

Volume of triangular prism = base area * height

here

base area =  (10*7)/2 = 35

height = 3

Volume = 35* 3 = 105

Answer:

4

Step-by-step explanation:

Use the direct variation equation, y = kx.

Replace y with t, and replace x with s:

y = kx

t = ks

Plug in 260 as k and 65 as s, then solve for k (the constant of variation):

t = ks

260 = k(65)

4 = k

So, the constant of variation is 4.

Answer:

A. 25

Step-by-step explanation:

From the diagram given, we can deduce that <D EG = <F EG

Therefore:

3y + 4 = 5y - 10

Collect like terms and solve for y

3y - 5y = -4 - 10

-2y = -14

Divide both sides by -2

y = -14/-2

y = 7

✔️m<D EG = 3y + 4

Plug in the value of y

m<D EG = 3(7) + 4

m<D EG = 25°

Given:

The distance between the two buildings on a map = 14 cm

The scale is 1:35000.

To find:

The actual distance in km.

Solution:

The scale is 1:35000.

It means 1 cm on map = 35000 cm in actual.

Using this conversion, we get

14 cm on map = [tex]14\times 35000[/tex] cm in actual.

                       = [tex]490000[/tex] cm in actual.

                       = [tex]4.9\times 1000o0[/tex] cm in actual.

                       = [tex]4.9[/tex] km in actual.          [tex][1\text{ km}=100000\text{ cm}][/tex]

Therefore, the actual distance between two buildings is 4.9 km.        

[tex]\huge\bold{Given:}[/tex]

Length of the base = 8

Length of the hypotenuse = 17

[tex]\huge\bold{To\:find:}[/tex]

The length of the third side ''[tex]x[/tex]".

[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]

[tex]\longrightarrow{\purple{x\:=\: 15}}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

Using Pythagoras theorem, we have

(Perpendicular)² + (Base)² = (Hypotenuse)²

[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] + (8)² = (17)²

[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] + 64 = 289

[tex]\longrightarrow{\blue{}}[/tex]  [tex]{x}^{2}[/tex] = 289 - 64

[tex]\longrightarrow{\blue{}}[/tex]  [tex]{x}^{2}[/tex] = 225

[tex]\longrightarrow{\blue{}}[/tex]  [tex]x[/tex] = [tex]\sqrt{225}[/tex]

[tex]\longrightarrow{\blue{}}[/tex]  [tex]x[/tex] = [tex]15[/tex]

Therefore, the length of the missing side [tex]x[/tex] is [tex]15[/tex].

[tex]\huge\bold{To\:verify :}[/tex]

[tex]\longrightarrow{\green{}}[/tex] (15)² + (8)² = (17)²

[tex]\longrightarrow{\green{}}[/tex] 225 + 64 = 289

[tex]\longrightarrow{\green{}}[/tex] 289 = 289

[tex]\longrightarrow{\green{}}[/tex] L.H.S. = R. H. S.

Hence verified.

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♨}}}}}[/tex]

Answer: I don't know the exact details but Egypt is home to some of the world's most famous tombs, among them the monumental pyramids. Egyptians built rectangular benches over graves during the fourth dynasty, which was known as the Masabas period. During this time period, pyramids were constructed by stacking square or rectangular tombs on top of one another.

Step-by-step explanation:

Answer:

-4 , -1 , -2 , 0 , +1 , +3

Step-by-step explanation:

Answer:

the integers -4,-2,-1,0, +1, +3

Step-by-step explanation:

because when you put them in order  you find which pairs are located between -5 and +5

-8,-4,-2,-1,0,+3,+8,+9

which tells you that

-4,-2,-1,0, +1, +3 are between -5 and +5

Answer:

Radius = 41

Step-by-step explanation:

Diameter/2=radius

82/2 =41

Answer:

Radius=41

Step-by-step explanation:

Preamble

Diameter=82

Radius=?

Formula

Radius=diameter/2

Radius=82/2

reduce the fraction

82/2=82÷2/2÷2=41/1

therefore radius=41

Answer:

Option C

Step-by-step explanation:

In the given triangles ΔRSW and ΔWXY,

m(∠S) = m(∠X) = 60° [Given]

Properties of congruence of two triangles applicable in this question,

SAS or ASA

For the congruence of two triangles by the property SAS,

"Two corresponding sides and the included angle should be congruent"

RS ≅ WX, ST ≅ XY and ∠S ≅ ∠X

Which is not given in any option.

For the congruence of two triangles by the property ASA,

"Two consecutive angles and the side having these angles should be congruent"

∠R ≅ ∠W, ∠S ≅ ∠X and RS ≅ XY

Option C will be the correct option.

Answer:

The quadrilateral is Rhombus

B=70°

Step-by-step explanation:

110+110+z+z=360

220+2z=360

2z=360-220

2z=140

z=140/2

Therefore, z=70

So Angle B=70

Since z= Angle B=Angle D

9514 1404 393

Answer:

  it depends on the accuracy and resolution required of the answer

Step-by-step explanation:

The shaded portion appears to be about half the length of the unshaded portion, suggesting the shaded amount is 1/3.

__

Using a pair of dividers, one could determine the number of times the shaded portion fits into the whole bar. Depending on how much is left over, the process could repeat to determine the approximate size of the remaining fraction relative to the bar or to the shaded portion. (Alternatively, one could replicate the length of the bar to see what integer number of shaded lengths fit into what integer number of whole lengths.)

One could measure the shaded part and the whole bar with a ruler, then determine the relative size of the shaded part by dividing the first measurement by the second. The finer the divisions on the ruler, the better the approximation will be.

Answer:

bbbbbhbbvcgccfggfgggggggggihh

Answer:

H0 : μ = 1220

H1 : μ > 1220

Test statistic = 1.30

Step-by-step explanation:

Sample mean, x = 1235.91

Standard deviation, σ = 211.67

Sample size, n = 300

The hypothesis :

Null ; H0 : μ = 1220

Alternative ; H1 : μ > 1220

Tbe test statistic :

(x - μ) ÷ (σ/√(n))

(1235.91 - 1220) ÷ (211.67/√(300))

15.91 / 12.220773

= 1.3018

= 1.30

Answer:

3

Step-by-step explanation:

Numbers between 21 and 30 divisible by 3 are 24 and 27. so you get the HCF of the two.

Answer:

99.7% of IQ scores are between 46 and 148.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 97, standard deviation of 17.

What percentage of IQ scores are between 46 and 148?

97 - 3*17 = 46

97 + 3*17 = 148

Within 3 standard deviations of the mean, so:

99.7% of IQ scores are between 46 and 148.

Given:

The system of inequalities is:

[tex]y>-\dfrac{1}{3}x+1[/tex]

[tex]y>2x-3[/tex]

To find:

The graph of the given system of inequalities.

Solution:

We have,

[tex]y>-\dfrac{1}{3}x+1[/tex]

[tex]y>2x-3[/tex]

The related equations are:

[tex]y=-\dfrac{1}{3}x+1[/tex]

[tex]y=2x-3[/tex]

Table of values for the given equations is:

    [tex]x[/tex]                   [tex]y=-\dfrac{1}{3}x+1[/tex]             [tex]y=2x-3[/tex]

   0                             1                              -3

   3                             0                              3

Plot (0,1) and (3,0) and connect them by a straight line to get the graph of [tex]y=-\dfrac{1}{3}x+1[/tex].

Similarly, plot (0,-3) and (3,3) and connect them by a straight line to get the graph of [tex]y=2x-3[/tex].

The signs of both inequalities are ">". So, the boundary line is a dotted line and the shaded region or each inequality lie above the boundary line.

Therefore, the graph of the given system of inequalities is shown below.

Answer:

C(min)  =  277.95 $

Container dimensions:

x = 2.822 m

y = 1.411 m

h = 3.52 m

Step-by-step explanation:

Let´s call x  and  y the sides of the rectangular base.

The surface area for  a rectangular container is:

S = Area of the base (A₁) +  2 * area of a lateral side x (A₂) + 2 * area lateral y (A₃)

Area of the base is :

A₁ =  x*y       we assume, according to problem statement that

x  =  2*y      y  = x/2

A₁  =  x²/2

Area lateral on side x

A₂  = x*h           ( h  is the height of the box )

Area lateral on side y

A₃ = y*h        ( h  is the height of the box )

s = x²/2  + 2*x*h + 2*y*h

Cost  =  Cost of the base + cost of area lateral on x + cost of area lateral on y

C = 10*x²/2  + 8* 2*x*h  + 8*2*y*h

C as function of x is:

The volume of the box is:

V(b) = 14 m³  = (x²/2)*h       28 = x²h      h = 28/x²

C(x) = 10*x²/2  + 16*x*28/x² + 16*(x/2)*28/x²

C(x)  =  5*x²  +  448/x  + 224/x

Taking derivatives on both sides of the equation we get:

C´(x)  =  10*x  -  448/x² - 224/x²

C´(x)  =  0             10x  -  448/x² - 224/x² = 0     ( 10*x³ - 448 - 224 )/x² = 0

10*x³ - 448 - 224 = 0       10*x³ = 224

x³  =22.4

x = ∛ 22.4

x = 2.822 m

y = x/2  =  1.411 m

h = 28/x²  =  28 /7.96

h =  3.52 m

To find out if the container of such dimension is the cheapest container we look to the second derivative of C

C´´(x) = 10 + 224*2*x/x⁴

C´´(x)  =  10 + 448/x³    is positive then C has a minimum for x = 2.82

And the cost of the container is:

C = 10*(x²/2) +  16*x*h + 16*y*h

C = 39.82 +  158.75  + 79.38

C =  277.95 $

Answer:

se supone que debes usar el SINE RATIO ya que se trata del lado opuesto y la hipotenusa.

Answer:

x = 30

F = 130

G =  50

Step-by-step explanation:

f and g are supplementary which means they add to 180

5x-20 + 3x - 40 = 180

Combine like terms

8x - 60 = 180

Add 60 to each side

8x-60+60 = 180+60

8x = 240

Divide by 8

8x/8 = 240/8

x = 30

F = 5x -20 = 5*30 -20 = 150 -20 = 130

G = 3x-40 = 3*30 -40 = 90-40 = 50

Answer:

Because a straight line = 180, we can find x like this :

(5x - 20) + (3x - 40) = 180

Step 1 - collect like terms

8x - 60 = 180

Step 2 - Move terms around to isolate x

8x = 180 + 60

Step 3 - Divide both sides by 8

x = 30

Now you can find the value of the angles by plugging in x

∠f = (5 x 30) - 20

     = 130 degrees

∠g = (3 x 30) - 40

      = 50 degrees

We can check to see if this works by adding them up

130 + 50 = 180, so this is correct

Hope this helps! I would really appreciate a brainliest if possible :)

(√3 - i ) / (√3 + i ) × (√3 - i ) / (√3 - i ) = (√3 - i )² / ((√3)² - i ²)

… = ((√3)² - 2√3 i + i ²) / (3 - i ²)

… = (3 - 2√3 i - 1) / (3 - (-1))

… = (2 - 2√3 i ) / 4

… = 1/2 - √3/2 i

… = √((1/2)² + (-√3/2)²) exp(i arctan((-√3/2)/(1/2))

… = exp(i arctan(-√3))

… = exp(-i arctan(√3))

… = exp(-iπ/3)

By DeMoivre's theorem,

[(√3 - i ) / (√3 + i )]⁶ = exp(-6iπ/3) = exp(-2iπ) = 1

Answer:

0.1111

Step-by-step explanation:

From the given information;

Number of staffs in the actuary = 80

Out of the 80, 10 are students.

i.e.

P(student actuary) = 10/80 = 0.125

number of weeks in a year = 52

off time per year = 10/52 = 0.1923

P(at work || student actuary) = (50 -10/52)

= 42/52

= 0.8077

P(non student actuary) = (80 -10)/80

= 70 / 80

= 0.875

For a non-student, they are only eligible to 4 weeks off in a year

i.e.

P(at work | non student) = (52-4)/52

= 48/52

= 0.9231

∴

P(at work) = P(student actuary) × P(at work || student actuary) + P(non student actuary) × P(at work || non studnet actuary)

P(at work) =  (0.125 × 0.8077) + ( 0.875 × 0.9231)

P(at work) = 0.1009625 + 0.8077125

P(at work) = 0.90868

Finally, the P(he is a student) = (P(student actuary) × P(at work || student actuary) ) ÷ P(at work)

P(he is a student) = (0.125 × 0.8077) ÷ 0.90868

P(he is a student) = 0.1009625 ÷ 0.90868

P(he is a student) = 0.1111

Answer:

The probability of obtaining a sample mean less than or equal to $8.85 per hour=0.0082

Step-by-step explanation:

We are given that

Average wage, [tex]\mu=[/tex]$9.00/hour

Standard deviation,[tex]\sigma=[/tex]$0.50

n=64

We have to find the  probability of obtaining a sample mean less than or equal to $8.85 per hour.

[tex]P(\bar{x} \leq 8.85)=P(Z\leq \frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}})[/tex]

Using the values

[tex]P(\bar{x}\leq 8.85)=P(Z\leq \frac{8.85-9}{\frac{0.50}{\sqrt{64}}})[/tex]

[tex]P(\bar{x}\leq 8.85)=P(Z\leq \frac{-0.15}{\frac{0.50}{8}})[/tex]

[tex]P(\bar{x}\leq 8.85)=P(Z\leq -2.4)[/tex]

[tex]P(\bar{x}\leq 8.85)=0.0082[/tex]

Hence, the probability of obtaining a sample mean less than or equal to $8.85 per hour=0.0082

Answer:

Below in bold.

Step-by-step explanation:

x + y = 33      where x = 10 cent coin and y = 20 cent coin

10x + 20y = 460

Multiply first equation by 10:

10x + 10y = 330

Subtract this from the second equation:

10y = 130

y = 13

So there are 13 20c coins

and 33 - 13 = 20 10c coins.