Find the sine and the cosine of 30°.
A. sin 30° =1/2, cos 30°= √3
B. sin 30°=1/2, cos 30° = √3/2
C. sin 30° = √3/3, cos 30°= √3/4
D. sin 30° = √3/3, cos 30° = √3/2

b. Total fixed cost are $49885

Sometimes production of a product may increase or decrease, but the cost which do not change with the change of output is called fixed cost of the product.

Highest monthly total cost = $83800

Highest monthly production units = 3500 desks

Lowest monthly total cost = $61900

Lowset monthly production units = 1240 desks

So, variable cost per unit = (Highest cost-lower cost)/(highest production units-lowest production units)

= ($83800-$61900)/(3500-1240)

= $21900/2260

= $9.7

∴ Total fixed costs=Highest monthly total cost-(highest production units×variable cost per unit)

= $83800-(3500×$9.7)

= $83800-$33950

= $49850

Nearest value is $49885, whch is the correct one.

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Step-by-step explanation:

please attach a picture for us to see the choices

Answer:

angle 1 is 105degrees and angle 2 is 75degrees

Step-by-step explanation:

The angle below angle 2, presumably angle 6, is also 75 degrees since line c and line d are parallel. If angle 2 is 75 degrees then we know that angle 1 is 105 degrees since both angles equal a straight line and a straight line has 180 degrees.

Answer: (1+2a)^2 or (1+2a)(1+2a)

Step-by-step explanation:

Answer:

[tex](2a +1)( 2a + 1)[/tex]

Step-by-step explanation:

Answer:

ANSWER IS B

Step-by-step explanation:

NEXT TIME USE any graph website online

Answer:

25%

Step-by-step explanation:

In the sentence "15 is 25% of 60.", 25% is the percentage.

15 is the partial amount and 60 is the total amount.

15/60 = .25

convert a decimal to a percentage by multiplying by 100

.25 × 100 = 25

Some people use a shortcut of moving the decimal two places to the right. This is the same as multiplying by 100.

15/60 is 25%

Answer:

sure how can I help you? please tell me

Answer:

[tex]a = 7[/tex]

Step-by-step explanation:

[tex]1. \: 7a - 70 = 13 - 4a - 6 \\ 2. \: 7a - 70 = - 4a + 7 \\ 3. \: 7a = - 4a + 7 + 70 \\ 4. \: 7a = - 4a + 77 \\ 5. \: 7a + 4a = 77 \\ 6. \: 11a = 77 \\ 7. \: a = \frac{77}{11} \\ 8. \: a = 7[/tex]

Answer:

1491 girls (99.4 percent)

Step-by-step explanation:

explanation is in the attached picture

Answer:

10

Step-by-step explanation:

24/30 = 0.8

24+x/30+x =0.85

10=x

If you want more clarification just ask

Total games Chase has to win in a row to achieve an 85% win percentage would be 10.

We can write the total number game won by Chase as -

w = 80% of 30

w = 80/100 x 30

w = 4/5 x 30

w = 24

Assume that he wins {x} games after winning 24 games to achieve 85% win percentage. Now, we can write that out of (30 + x) number of games played, Chase won (24 + x) games to achieve 85% win percentage. So, we can write that -

(24 + x)/(30 + x) = 85/100

(24 + x)/(30 + x) = 0.85

(24 + x) = 0.85(30 + x)

24 + x = 25.5 + 0.85x

0.15x = 1.5

x = 10

Total games Chase has to win in a row to achieve an 85% win percentage would be 10.

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Answer: B. (2,2)

Step-by-step explanation:

The vertex of the parabola in the form [tex](x-h)^2 = 4p(y-k)[/tex] is (h, k).

The value of m∠G = 48.6° .

A triangle is a polygon with three sides , angles and vertices.

It is given that

In ΔFGH, FH = 9 ft, FG = 11 ft, and m∠F = 65°

m∠G = ?

well, using the law of cosines,

GH ² = 9² + 11² - 2(9)(11) cos65°

f = 10.88 ft

now, using the law of sines,

sinG/9 = sin65°/10.88

m∠G = 48.6°

Therefore the value of m∠G = 48.6° .

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Answer:

u = -18

Step-by-step explanation:

[tex]\frac{-5u}{6} =15[/tex]

Multiply both sides by 6.

-5u = 15 × 6

-5u = 90

Divide both sides by -5.

u = -18

Answer:

Solution:

Here,

[tex]\begin{array}{ | c| c c | } \hline\ \ \text{length \: of \: iron \: rod}& \text{weight} \\ \hline 13 \rm{m}& \rm{23.4kg} \\ \hline \rm{6m}&?\\ \hline\end{array}[/tex]

Weight of 13 m of rod=23.4 kg

Weight of 1 m of rod=23.4/13 kg

[less length,less weight]

Weight of 6 m of rod=23.4/13 ×6 kg=10.8 kg

[more length,more weight]

Thus,the weight of 6 m of rod is 10.8 kg.

Alternative method:

Let,the required weight be x kg.

Then,

[tex]\begin{array}{ | c| c c | } \hline\ \ \text{length \: of \: iron \: rod}& \text{weight} \\ \hline \rm{13m}& \rm{23.4 \: kg }\\ \hline \rm{6m}& \rm{x =? } \\ \hline\end{array}[/tex]

We know that,

More length of iron rod([tex]\red{\uparrow}[/tex]) will have the more weight([tex]\red{\uparrow}[/tex]).

So,using the rule of direct proportion;

i.e. Ratio of length=Ratio of weight

[tex] \displaystyle{ \frac{13}{6} = \rm\frac{23.4}{x} }[/tex]

[tex] \rm{13x = 6 \times 23.4}[/tex]

[tex] \rm{x = \displaystyle{ \frac{6 \times 23.4}{13} }}[/tex]

[tex] \therefore{x = 10.8}[/tex]

Thus,the weight of 6 m long iron rod is 10.8 kg.

Answer:

True, True, False

Step-by-step explanation:

Answer:

(x-5)²+(y+2)²=200.

Step-by-step explanation:

1) using the given coordinates it is possible to calculate

- the centre of the given circle:

[tex]x_0=\frac{10+0}{2}=5; \ y_0=\frac{2-8}{2}=-2;[/tex]

- the radius of the given circle:

[tex]r=\sqrt{(10-0)^2+(2+8)^2} =\sqrt{200} ;[/tex]

2) finally, the required equation (common form is (x-x₀)²+(y-y₀)²=r²):

(x-5)²+(y+2)²=200.

Answer:

I think it's 80%

Step-by-step explanation:

Method 1: (40/50)*100 = 80%

Method 2: [tex]\frac{40*2}{50*2} = \frac{80}{100}[/tex] = 80%

The values of x and y at t=3 are -4.95 and 0.423 respectively.

The value of dx/dt and dy/dt are 0.71 and -2.97 respectively.

The value of the tangent slope at t=3 is 4.21.

The speed at t=3 is 3.05 units/sec.

Given the equation of x as the function of t is

x= 5 cos t

similarly, the equation of y as the function of t is

y= 3 sin t

At t=3 the value of x will be

x (at t=3) = 5 cos 3= 5(-0.989)= -4.95

At t=3 the value of y will be

y (at t=3) = 3 sin 3= 3(0.141)= 0.423

The derivative of the function of x with respect to t will be

dx/dt= d(5 cos t)/dt= 5d(cos t)/dt= -5 sin t

at t=3 the value of dx/dt will be

dx/dt (at t=3) = -5 sin 3= -5(0.141)= 0.71

The derivative of the function of y with respect to t will be

dy/dt= d(3 sin t)/dt= 3d(sin t)/dt= 3 cos t

at t=3 the value of dy/dt will be

dy/dt (at t=3) = 3 cos t= 3(-0.989)= -2.97

The tangent slope is dy/dx which can be calculated by

dy/dx= (dy/dt)(dt/dx)= (dy/dt)/(dx/dt)= 3 cos t/ -5 sin t=  (-3/5) cot t

at t=3 the value of tangent slope will be

dy/dx (at t=3) = (-3/5) cot 3= 4.21

The speed at t=3 will be

speed v= [tex]\sqrt{v_{x} ^{2} + v_{y} ^{2} }[/tex]

= √(dx/dt)²+(dy/dt)²

at t=3

= √(0.71)²+(-2.97)²

= √9.325

= 3.05 unit/sec

Therefore the values of x and y at t=3 are -4.95 and 0.423 respectively.

The value of dx/dt and dy/dt are 0.71 and -2.97 respectively.

The value of the tangent slope at t=3 is 4.21.

The speed at t=3 is 3.05 units/sec.

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Answer:

$800

Step-by-step explanation:

per hour $40×10hours=$400

$400÷$50=8 times initial fee

8×$50=$400 total initial fee

$400hours fee+$400 initial fee=$800 total payment

Answer:

Step-by-step explanation:

It represents a linear function because there is a constant rate of change.

Step-by-step explanation:

Since, if the rate of change for y ( output value ) with respect to x ( input value ) remains constant for a function then it is called linear function.

Here, number of hours represents input value and minutes represents the output value,

Now, By the given table,

The function is passing through the points (1,60), (2,120), (3,180), (4,240) and (5,300),

Also,

⇒  The rate of change output value with respect to input value remains constant,

Hence, It represents a linear function because there is a constant rate of change.

The function has a local minima at  ( 20 , -7 )

Function is a mathematical statement formed when two algebraic expression are equated by an equal sign.

The expression given is

y = -2 +5sin ( (π/12) (x-2))

the minima of the given expression will be when

the sine term = -1

as the lowest value sin can have is -1

y = -2 +5 * (-1)

y = -7

The sin ( (π/12) (x-2)) = -1

(π/12) (x-2) = 3π /2

On solving this

x = 20

Therefore the function has a local minima at  ( 20 , -7 )

It can also be confirmed form the graph attached with the answer.

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Step-by-step explanation:

{-1,2,3,4,5,6,8} is the answer

Answer:

21

Step-by-step explanation:

[tex]3t-7=5t[/tex]

subtract 3t from both sides

[tex]-7 = 2t[/tex]

multiply both sides by 3

[tex]-21 = 6t[/tex]

so 6t = -21

Answer:

slant length (l) = 7.5 m

perimeter of base P = 40 m

area of base B = 100 m^2

Surface Area = 250 m^2

Step-by-step explanation:

Surface area of a pyramid formula

1/2Pl + B

1/2 (40)(7.5) + 100

150 + 100 = 250 square meters

Jaira is completing the construction of a regular hexagon inscribed in a circle, as shown below: The next step in her construction should be:

A closed polygon with six equal sides and six equal angles is called a regular hexagon.

Thus, the steps highlighted above will help Jaira complete her construction.

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Another way to write the equation is 7x + 54 = 0

Given the equation;

[tex]\frac{7}{8}x + \frac{3}{4} = -6[/tex]

Find the LCM on the left side, which is 8

[tex]\frac{7x + 6}{8} = -6[/tex]

Cross multiply

[tex]7x + 6 = -6[/tex] × [tex]8[/tex]

[tex]7x + 6 = -48[/tex]

Collect like terms

[tex]7x = -48 - 6[/tex]

[tex]7x = -54[/tex]

Take all to one side

[tex]7x + 54 = 0[/tex]

Thus, another way to write the equation is 7x + 54 = 0

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The triangle ABC and triangle CDA are congruent by AAS [Angle - Angle-Side] property.

If two triangles are congruent, this means they are the same shape and the same size. By definition, all corresponding angles of two congruent triangles are congruent. Additionally, all corresponding sides of two congruent triangles are congruent.

In the given triangles we can see that:-

Therefore we can see that the triangle ABC and triangle CDA are congruent by AAS [Angle - Angle-Side] property.

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Answer: A. -3.65

Step-by-step explanation: The best way to figure this out is by using a calculator. One specific rule to remember is the positive/negative rule. When it applies to multiplication, it also applies to division.

[tex](+)*(+)=+\\(+)*(-)=-\\(-)*(+)=-\\(-)*(-)=+\\[/tex]

Knowing this, we can input it into the calculator and find the answer's sign.

[tex]-27.375/7.5=-3.65[/tex]

Therefore, the answer is A. -3.65.

I hope this helps! Pls mark brainliest!! :)