Given that log 2= 0.30103 and log 3= 0.47712. Evaluate log 12​

We can use sine ratio in given right angled triangle.

The sine of ∠Q is represented by ratio 48/73.

Given data:

∠R=90°,

QP = 73,

PR = 48,

RQ = 55

We know that;

The sine of a given angle in a right angle triangle is the ratio of perpendicular and hypotenuse seen from the viewpoint of that angle.

Since, against ∠Q lies the side PR, thus, PR is perpendicular. The side PQ is hypotenuse.

Thus, we have:

sin Q = PR/PQ

        = 48/73

Thus, the sine of ∠Q is represented by ratio,

48/73.

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Answer:

option c (19.2, -6.7) is correct

Step-by-step explanation:

Mid point - it is the middle point of a line segment. It is equidistant from both endpoints and it is the centroid both of the segment and of the endpoints.

if ([tex]x,y[/tex]) and ([tex]x_{1},y_1[/tex]) are the end points of a line segment then mid point is

given by :- [tex](x+x1)/2 , (y+y1)/2[/tex]

according to question :

given : end point T(-16.8, 31.7)  and mid point M(1.2, 12.5)

let coordinates of another end point S (a, b)

therefore, using mid point formula

1.2 = (-16.8 + a)/2

2.4= (-16.8 + a)

19.2 = a

and,

12.5 = (31.7 + b)/2

25 = 31.7 + b

-6.7 = b

so the option c (19.2, -6.7) is the correct answer

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Answer:

√96

Step-by-step explanation:

halve the diameter to set up the pythagorean theorem

2²+b²=10²

4+b²=100

-4 on each side

b²=96

square root each side

b=√96

it could the be further simplified to 4√6

Answer: x-1

Step-by-step explanation:

Answer:

L is not valid.

Step-by-step explanation:

For any triangle, the sum of the two legs must be greater than the hypotenuse. Otherwise the two legs would not be long enough to touch.

Answer:

L

Step-by-step explanation:

to add to the previous basically correct answer :

for a triangle the sum of any 2 sides must be greater than the third side (not just legs and Hypotenuse).

for all other options any combination of sum of 2 sides being bigger than the third side works.

but for L

2 + 5 = 7, which is smaller than the third side (8). so, this cannot be a triangle.

The cost of one ft² of sod is $2 and the cost of one geranium is $9.

9s + 2g = 36 equation 1

9s + 5g = 63 equation 2

Subtract equation 1 from equation 2:

3g = 27

g = 27 / 3

g = $9

Substitute for g in equation 1

9s + (2 x 9) = 36

9s + 18 = 36

9s = 36 - 18

9s = 18

s = 18 / 9

s = $2

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Answer:

-4 x³+2x²-5x+3x²

combine like terms

-4x³ +5x²-5x

common factors

-1(4x³-5x²+5x)

find one factors

Ans: -x (4x²-5x+5)

Answer: -20

Step-by-step explanation: i hope its right

The function represents the weekly weed growth f(x) = 86(1.01)^7x; They grow at approximately the rate of 1% per day.

The function is a type of relation, or rule, that maps one input to specific single output.

The following function represents the weekly weed growth:

f(x) = 86(1.08)x.

we'll represent the growth function by day g(x). If x is to represent days, then x/7 represents weeks.

We can write,

 g(x) = f(x/7) = 86·1.08^(x/7)

 g(x) = 86·(1.08^(1/7))^x

 g(x) = 86·1.011055^x

The function represents the weekly weed growth f(x) = 86(1.01)^7x; They grow at approximately the rate of 1% per day.

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The amount of water will remain in the bottle after Cory rides for 2 1/2 hours will be;

⇒ y = 12 ounces

What is Equation of line?

The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The average amount of water, in ounces, in his water bottle can be represented by the equation,

⇒ y = - 8x + 32

Where, y is the amount of water remaining after x hours.

Now,

Since, The average amount of water, in ounces, in his water bottle can be represented by the equation,

⇒ y = - 8x + 32

Hence, The amount of water will remain in the bottle after Cory rides for 2 1/2 hours is,

Substitute x = 2 1/2 in above equation,

⇒ y = - 8 × 2 1/2 + 32

⇒ y = - 8 × 5/2 + 32

⇒ y = - 20 + 32

⇒ y = 12 ounces

Thus, The amount of water will remain in the bottle after Cory rides for 2 1/2 hours is,

⇒ y = 12 ounces

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Answer:

  8 hours 32 minutes

Step-by-step explanation:

Working together, the construction rates add. We can use the given relation to write an equation for the total time when the pair work together.

__

Let k represent Kirk's time (in hours) to build the wall by himself. Then (k-1) is the time it takes for Jeff to build it. Their working-together rate in "walls per hour" is ...

  1/k +1/(k -1) = 1/4

__

Multiplying by 4k(k-1), we have ...

  4(k-1) +4k = k(k -1)

  k² -9k = -4 . . . . . . . . subtract 8k and simplify

  k² -9k +20.25 = 16.25 . . . . . add (9/2)² to complete the square

  k -4.5 = √16.25 . . . . . . . . . take the square root

  k = 4.5 +√16.25 ≈ 8.531129 . . . hours

The fractional hour is ...

  0.531129 × 60 min ≈ 31.9 min ≈ 32 min

It would take Kirk about 8 hours 32 minutes to build the wall by himself.

_____

Additional comment

For most "working together" problems the rates of completing work need to be expressed in jobs per unit time. Usually, the rates are given in terms of time per job, as they are here. That is why reciprocals get involved.

It will take Kirk about 8 hours 32 minutes to build the wall by himself.

Quadratic equations are second-degree algebraic expressions and are of the form ax² + bx + c = 0.

Here, Let k represent Kirk's time (in hours) to build the wall by himself. Then (k-1) is the time it takes for Jeff to build it. Their working-together rate in "walls per hour" is ...

 1/k +1/(k -1) = 1/4

Multiplying by 4k(k-1), we have ...

 4(k-1) +4k = k(k -1)

 k² -9k = -4 . . . . . . . . subtract 8k and simplify

 k² -9k +20.25 = 16.25 . . . . . add (9/2)² to complete the square

 k -4.5 = √16.25 . . . . . . . . . take the square root

 k = 4.5 +√16.25 ≈ 8.531129 . . . hours

The fractional hour is ...

 0.531129 × 60 min ≈ 31.9 min ≈ 32 min

Thus, It will take Kirk about 8 hours 32 minutes to build the wall by himself.

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Answer:

center (0, 3) and radius 2√2

Step-by-step explanation:

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

where:

Given equation:

[tex]x^2+y^2-6y+1=0[/tex]

Subtract 1 from both sides:

[tex]\implies x^2+y^2-6y=-1[/tex]

To create a trinomial with variable y, add the square of half the coefficient of the y term to both sides:

[tex]\implies x^2+y^2-6y+\left(\dfrac{-6}{2}\right)^2=-1+\left(\dfrac{-6}{2}\right)^2[/tex]

[tex]\implies x^2+y^2-6y+9=8[/tex]

Factor the trinomial with variable y:

[tex]\implies x^2+(y^2-6y+9)=8[/tex]

[tex]\implies x^2+(y-3)^2=8[/tex]

Factor [tex]x^2[/tex] to match the general form for the equation of a circle:

[tex]\implies (x-0)^2+(y-3)^2=8[/tex]

Compare with the general form of the equation for a circle:

[tex]\implies a=0[/tex]

[tex]\implies b=3[/tex]

[tex]\implies r^2=8 \implies r=2\sqrt{2}{[/tex]

Therefore, the center is (0, 3) and the radius is 2√2

Step-by-step explanation:

option 2 is correct

here the question ask for value of X

to find it we multiple the matrix X with the given matrix in question and equate the answer.

Answer:

1. santina drove 14 more miles than carole

2. the owner will need to buy 8 bags this week

Step-by-step explanation:

1. 203-189= 14

2. if they use 80 pounds a week and can only buy 10 pounds in one bag, they'll need 8 bags to equal 80 pounds since each bag is 10 pounds

1. 14

2. 8

3. 48

4. 318

5. 23

6. 4

7. a) 10 b) 60 c) 8 d) 107

8. $1,532

9. 1

10. $15.50

11. .95

Step-by-step explanation:

The preparation of the journal entry to record the accounting transaction can be seen in the table below.

Initially, when preparing a journal, you have to read the transaction carefully and comprehend it. Discover which accounts need to be credited and debited before entering a journal entry.

From the given information:

The common stock par value = no of shares × par value of shares

The common stock par value = 4000 shares × $5/ share

The common stock par value = $20000

However, the amount paid in capital excess of the par value for the common stock is:

= $35000 - $20000

= $15000

Therefore, the Journal entry can be computed as follows:

Date        Account Title                          Post Ref     Debit ($)    Credit ($)

             Cash                                                            35,000

        Paid-in capital in excess of par

       value, common stock                                                         20,000

       (To record the insurance of common stock)    

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A translation 2 units to the left followed by dilation by 1/2.

The correct option is (B).

It states that that two triangles are said to be congruent if they are copies of each other and when superposed, they cover each other exactly.

The complete question is:

Which of the following composition of transformations would create an

image that is not congruent to its original image?

A rotation of 45° followed by a reflection across the x-axis

A translation 2 units to the left followed by dilation by 1/2

A reflection across the y-axis followed by a rotation of 60°

A rotation of 135º followed by a translation of 4 units to the right.

After a translation of 2 units to the left followed by dilation by 1/2 the image will not be congruent to its original image.

All other options are reflection and rotation, which not fit into the situation.

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The vertex form of the quadratic function f(x) = x² + 2x + 3 is given as follows:

f(x) = (x + 1)² + 2

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In this problem, the function is:

f(x) = x² + 2x + 3

Completing the squares, we find the equation in vertex form, as follows:

f(x) = (x + 1)² + 2

As (x + 1)² = x² + 2x + 1, hence 2 has to be added to find the equivalent function.

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Since the product of variables in inverse proportion is constant, the equation is [tex]\boxed{xy=-1300}[/tex]

E. y = -3x

I can give you an explanation in the comments if you'd like

[tex]\left(\frac{-3+1}{2}, \frac{-3+2}{2} \right)=\boxed{\left(-1, -\frac{1}{2} \right)}[/tex]

The Function models Jay's total monthly salary s(x) in dollars would be s(x) = 0.03s - 1060.

A function is a type of relation, or rule, that maps one input to a specific single output.

Given

Base salary = $2500 per month

Commision = 3% on Sales over 48000

Determine the function s(x) for sales over $48000

Let's Represent the total sales in a month with s.

So, the function s(x) is:

s(x)  = Base Amount + Commission x Sales over $48000

s(x) = 2500  + 3% (s - 48000)

s(x) = 2500  + 0.03(s - 48000)

s(x) = 2500  + 0.03s - 1440

s(x) = 0.03s - 1060

Hence, the Function models Jay's total monthly salary s(x) in dollars would be s(x) = 0.03s - 1060.

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Answer:

66

Step-by-step explanation:

The sequence you provided seems to be arithmetic as it increases as 4 each term. Assuming 1 is the first term the equation would be [tex]a_{n}=1 + 4(n-1)[/tex]. You could just take the first 6 terms and add them together since you already have 4 values calculated and you could calculate the other 2 by adding 4. This would give you

(1 + 5 + 9 + 13 + 17 + 21) = 66

But there's an easier way to do it. You could use the formula [tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]. You can calculate [tex]S_6[/tex] by plugging in those values. You would need to calculate [tex]a_6[/tex] before hand, but you can calculate that using the formula I defined above. Which in general is [tex]a_n = a_1 + d(n-1)[/tex] where d is like the slope, or how much it changes each term. So if you calculate [tex]a_6[/tex] you'll get [tex]1+4(6-1) = 1+4(5) = 21[/tex]. Now plug this into the series formula above and you get [tex]S_6 = \frac{6(1+21)}{2}=\frac{6(22)}{2}=\frac{132}{2}=66[/tex] which is exactly what you get if you add the first 6 terms as shown above when you do it manually.

[tex]\text{First let's find two more terms, because we have only six. We can do that by}\\\text{adding 4:: 13+4=17; 17+4=21}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{Now we just add the terms: 1+5+9+13+17+21}[/tex]

[tex]\rule{300}{1.7}\\\text{66}[/tex]

Answer:

Answer: 0.628 radian

Step-by-step explanation:

how to convert from degrees to radians?

Answer:To convert the value of the angle in degree, to its equivalent radians, we need to multiply the given value with π/180. For example, the value of 180 degrees is π in radians.

Answer:

See below

Step-by-step explanation:

- 36  *  PI / 180 = -pi/5 radians  = -  .6283 R

The distribution of X is X ~ N (20 , 6) and the probability that this American will receive no more than 24 Christmas cards this year is 0.7486.

a. Distribution

X ~ N (20 , 6)

b. P(x ≤24)

= P[(x - μ ) / σ  (24 - 20) / 6]

= P(z  ≤0.67)

=  0.74857

=0.7486

Hence:

Probability = 0.7486

c. P(21 < x < 26)

= P[(21 - 26)/ 6) < (x - μ  ) / σ   < (24 - 20) / 6) ]

= P(-0.83 < z < 0.67)

= P(z < 0.67) - P(z < -0.)

=  0.74857- 0.2033

= 0.54527

Hence:

Probability =0.54527

d. Using standard normal table ,

P(Z < z) = 66%

P(Z < 0.50) = 0.66

z = 0.50

Using z-score formula,

x = z×  σ +  μ

x = 0.50 × 6 + 20 = 23

23 Christmas cards

Therefore the distribution of X is X ~ N (20 , 6) and the probability that this American will receive no more than 24 Christmas cards this year is 0.7486.

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Answer:

average of the no. = sum of all no. / no. of terms

= 2 + 5 + 8 + 1 / 4

= 16/4

= 4

4 is the answer

D. 9.5 cm

To find the perimeter you need to add all the sides.

2.1 + 2.1 + 1 + 3.3 + 1 = 9.5

Answer:

It is 98. Just look down for the explanation↓:

Step-by-step explanation:

Log 10 (x + 2) = 2

So, the Inverse log is:

10^2 = x + 2

100 = x + 2

98 = x