If ∠G measures 40°, ∠F measures 49°, and f is 7 feet, then find g using the Law of Sines. Round your answer to the nearest foot.

triangle EFG with side e across from angle E, side f across from angle F, and side g across from angle g


4 feet

5 feet

6 feet

7 feet

Answer:

0.7.

Step-by-step explanation:

x^2 = 0.7x

x^2 - 0.7x = 0

x(x - 0.7) = 0

x = 0, 0.7.

After solving the quadratic equation x² = 0.7x , we get that the original number is 0.7

Quadratic equation is an equation which contains one unknown variable and the highest power of this unknown variable is 2. Let x be the unknown variable then the standard quadratic equation in x is given by

ax²+bx+c =0, where a, b, c are constants and a≠0

We can  solve this equation by factorizing ax²+bx+c and  putting those factors equal to zero to solve for x.

Let a non zero number be x, x≠0 and given that the square of a non zero number is equal to the 70% of the original number.

As 70 % of the original number = 70/100(x) = 0.7 x

⇒ x² = 0.7 x

⇒x²-0.7 x = 0

⇒ x(x -0.7)= 0

⇒ x =0 and x - 0.7 = 0

⇒  x = 0.7, as we have given that x is a non zero number

Therefore, the original number is 0.7

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Answer:

13

Step-by-step explanation:

First you would create a ratio.

Convert 3 1/4 gallons in a decimal -> 3.25 gallons

If 1 gallon = 4 quarts, then

[tex]\frac{3.25}{1} =\frac{x}{4}[/tex]

Now, solve for x via cross multiplying

[tex]x=13[/tex]

and sidenote ripp iready i feel your pain

Answer: A) -0.5 and -0.5

Step-by-step explanation:

Answer:

it is w45 y 10

Step-by-step explanation:

Answer:

20 cm²

Step-by-step explanation:

Look at the diagram attached.

If the height is 4cm, we will have two sides that are 4cm for our rectangle.

We can label the other sides as x.

They are both x since opposite sides of a rectangle are equal in length.

We can make an equation with our perimeter:

[tex]2(4) + 2(x) = 18\\8 + 2x = 18\\2x = 10\\x = 5[/tex]

Now that we know the length & height, we can calculate the area:

4 × 5 = 20 cm²

The probability that a person has a positive rh factor given that he/she has type O blood is approximately 82.2 %

For two events A and B:

The chain rule states that the probability that A and B both occur is given by:

[tex]P(A \cap B) = P(A)P(B|A) = P(B)P( A|B)[/tex]

Suppose two dimensions are there, viz X and Y. Some values of X are there as [tex]X_1, X_2, ... , X_n[/tex] and some values of Y are there as [tex]Y_1, Y_2, ... , Y_n[/tex]

List them in title of the rows and left to the columns. There will be n \times k table of values will be formed(excluding titles and totals), such that:

Value(ith row, jth column) = Frequency for intersection of  [tex]X_i[/tex] and [tex]Y_j[/tex] (assuming X values are going in rows, and Y values are listed in columns).

Then totals for rows, columns, and whole table are written on bottom and right margin of the final table.

For n = 2, and k = 2, the table would look like:

[tex]\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}[/tex]

where S denotes total of totals, also called total frequency.

n is showing the frequency of the bracketed quantity, and intersection sign in between is showing occurrence of both the categories together.

The missing two-way table for this problem is given below:

[tex]\begin{array}{cccccc}&A&B&AB&O&\rm Total\\\text{Negative}&0.07&0.02&0.01&0.08&0.18\\\text{Positive}{&0.33&0.09&0.03&0.37&0.82\\\rm Total & 0.40&0.11&0.04&0.45&1 \end{array}[/tex]

Instead of frequencies, it contains ratio of frequency to total count of people surveyed (thus, relative frequency).

We want the probability that a person has a positive rh factor given that he/she has type O blood.

If we take:

E = event that a random person chosen has a positive rh factor

and F = event that a random person chosen has type O blood

Then, the needed probability is written symbolically as:

P(E|F).

Using the considered two-way table and the chain rule, we get this probability as:

[tex]P(E|F) = \dfrac{P(E \cap F)}{P(F)} = \dfrac{n(E \cap F)/ n(Total)}{n(F)/n(Total)}[/tex]

Since the two way table consists relative frequency with total count, so, we get:

[tex]n(E \cap F)/n(Total) = 0.37\\n(F)/n(Total) = 0.45[/tex]

[tex]P(E|F) = \dfrac{n(E \cap F)/ n(Total)}{n(F)/n(Total)} = \dfrac{0.37}{0.45} \approx 0.822 = 82.2\%[/tex]

Thus, the probability that a person has a positive rh factor given that he/she has type O blood is approximately 82.2 %

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Answer:

The answers will be

The probability that a person has a positive Rh factor given that he/she has type O blood is 82 percent.There is a greater probability for a person to have a positive Rh factor given type A blood than a person to have a positive Rh factor given type O blood.

Step-by-step explanation:

Hope this help!

Answer:

z×(-5+3)then you complete the sum and that is your answer

Step-by-step explanation:

hope it helps you

Answer:

A

Step-by-step explanation:

Because A small parallelogram has a left side length of 10 centimeters and a top side length of 15 centimeters. A larger parallelogram has a left side length of x centimeters and the top side length of y centimeters.

Answer:The length of the third side is a-2.

Step-by-step explanation:

Answer:

Below in bold.

Step-by-step explanation:

a) The volumes will be in the ratio of the cubes  of the edges.

So volume of A / volume B = 20^3 / 5^3

Volume A / 25 = 8000/125

Volume a = (25* 8000) / 125

= 8000/ 5

= 1600 cm^3.

b) ratio of the surface area of A to surface area of B

=  20^2 : 5^2

= 400:25

= 16:1.

c. The volume of pyramid B is 25 cm*3 so it' height is  25 / area of its base = 25/5^2

= 1 cm.

Now its slant height = √(1^2 + (2.5)^2)

= √7.25

= 2.6926 cm

So surface area = 25 + 4 * 1/2 * 5 * 2.6926

= 51.926

= 51.93 cm^2 to nearest hundredth.

and the surface area of pyramid B = 51.926 * 16

= 830.82 cm^2 to nearest hundredth.

Answer:

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

Step-by-step explanation:

the angles 5 and 8 are also congruent to A.

Answer:

1. 9 6/12

2. 4 3/12

Step-by-step explanation:

I did the math on it.

Answer:

3. 9 (6/12)

4. 4 (3/12)

Step-by-step explanation:

Question 3:

6 (2/6) × 1 (1/2)

multiply the whole number by the denominator

6 x 6 = 36 + 2 (numerator) = 38/6

2 x 1 = 2 + 1 = 3/2

(38/6) x (3/2)

multiply (3/2) by 3

3 x 3 = 9

2 x 3 = 6

38/6 x 9/6

38 x 9 = 342

6 x 6 =  36

19/2 = 9 (1/2) or 9 (6/12)

Question 4:

5 (2/3) × (3/4)

15 + 2 = 17

17/3 x 3/4

17 x 4 = 68

3 x 4 = 12

3 x 3 = 9

4 x 3 = 12

(68/12) x (9/12)

68 x 9 = 612

12 x 12 = 144

612/144 = 4 (1/4) or 4 (3/12)

I hope this helps! I'm sorry if this is confusing.

Answer:

he will have 29 nickles

Step-by-step explanation:

I just solved it on paper, hope it helps and if it's right

When the bill came, she would need to pay Millersburg sales tax of 8% and would want to leave a 15% tip on the original $300. Including tax and tip, Camilla's meal cost $369.

Given that,

Original Meal Cost: $300

Sales Tax: 8% of the original meal cost

Tip: 15% of the original meal cost

Total Cost: Sum of the original meal cost, sales tax, and tip

Original Meal Cost = $300

Sales Tax = 8% of $300 = 0.08 * $300 = $24

Tip = 15% of $300 = 0.15 * $300 = $45

Total Cost = Original Meal Cost + Sales Tax + Tip

Total Cost = $300 + $24 + $45 = $369

Including tax and tip, Camilla's meal cost $369.

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Using the Factor Theorem, it is found that yes, it is possible for a sixth degree polynomial function with integer coefficients to have no real zeroes, as they can have three complex-conjugate pairs.

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

If a complex number is a root of a function, it's conjugate will also be a root. Thus, with three pairs of complex-conjugate roots, for example, [tex]\pm i, \pm 2i, \pm 3i[/tex], a sixth degree function with no real zeros is formed, so the answer is Yes.

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The distance between you and train 1 at time t is

20.6 km + (0.2 km/h) t

and the distance between you and train 2 at time t is

59.7 km - (2.1 km/h) t

The trains are an equal distance away from you when

20.6 km + (0.2 km/h) t = 59.7 km - (2.1 km/h) t

Solve for t :

(2.3 km/h) t = 39.1 km

t = 17 h

at which point they are

20.6 km + (0.2 km/h) (17 h) = 24 km

away from you.

Using it's concept, it is found that there is a [tex]\frac{3}{16}[/tex] probability that George will choose a white pair of shoes and a pair of socks that are not white.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem:

Since the events are independent:

[tex]p = \frac{1}{4} \times \frac{3}{4} = \frac{3}{16}[/tex]

[tex]\frac{3}{16}[/tex] probability that George will choose a white pair of shoes and a pair of socks that are not white.

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I assume the limit you're asked to copmute is supposed to be

[tex]\displaystyle \lim_{x\to5} \frac{\sqrt{x+4}-3}{x-5}[/tex]

Rationalize the numerator by multiplying it by its conjugate:

[tex]\dfrac{\sqrt{x+4}-3}{x-5} \times \dfrac{\sqrt{x+4}+3}{\sqrt{x+4}+3} = \dfrac{\left(\sqrt{x+4}\right)^2-3^2}{(x-5) \left(\sqrt{x+4}+3\right)} = \dfrac{x-5}{(x-5) \left(\sqrt{x+4}+3\right)}[/tex]

Since x is approaching 5, we have x ≠ 5 and can cancel the factors of x - 5 to remove the discontinuity.

Then

[tex]\displaystyle \lim_{x\to5} \frac{\sqrt{x+4}-3}{x-5} = \lim_{x\to5} \frac1{\sqrt{x+4}+3} = \frac1{\sqrt9+3} = \boxed{\frac16}[/tex]

because the simplified limand is continuous at x = 5.

Answer:

it is C. 1/6th

Step-by-step explanation:

Answer:

(2 x 3 x [tex]13x^6[/tex][tex]Y^{4[/tex])

Step-by-step explanation:

Answer:

a₃₀ = 201

Step-by-step explanation:

there is a common difference between consecutive terms , that is

453 - 462 = 444 - 453 = - 9

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 462 and d = - 9 , then

a₃₀ = 462 + (29 × - 9 ) = 462 - 261 = 201

Lets see

ATQ

Answer:

a = 3 cm

Step-by-step explanation:

The length of each side of a cube is 3 cm.

(Refer to the attachment)

Step-by-step explanation:

I guess you mean it is

12 cm long, 4cm wide and 5 cm high.

and the fabric goes outside on the box ? strange, but ok.

a box (like a die) has 6 sides in the form of 3 pairs of equal rectangles :

top-bottom, left-right, front-back

the surface area is the sum of all 6 rectangles.

top-bottom :

2 × 12×4 = 2 × 48 = 96 cm²

left-right :

2 × 4×5 = 2 × 20 = 40 cm²

front-back :

2 × 12×5 = 2 × 60 = 120 cm²

in total

120 + 40 + 96 = 256 cm²

The statistical test at the 5% significance level shows that we fail to reject the null hypothesis.

From the information given, the level of significance is 0.05 and n is 600. The degree of freedom will be:

= 4 - 1 = 3

The test statistic will be:

= ∑(O - E)²/E

= 6.92

The critical value is also given as 7.815 from the table. Since the test statistic is lesser than the critical value, we fail to reject the null hypothesis.

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Answer:

25 and 49

Step-by-step explanation:

25 = 1, 5, 25

49 = 1, 7, 49

Hope this helps!

Answer:

312 divided by 24 = 13.

So the hourly rate is 13/hour

Answer:

$13.00. To find the hourly rate you need to divide the total amount Jackie earned by the amount of hours she worked in total. When you divide 312 by 24 you will get 13, therefore Jackie makes a total of $13.00 per hour.

Answer:

297.99

Step-by-step explanation:

367.99-45-25=297.99