Select the angle that correctly completes the law of cosines for this triangle.
82 +1722(8) (17)cos ____ = 15²
-
28°
17
15
62°
90°
8

Answer:

x = 4

Step-by-step explanation:

Move the x to the left-hand side and change its sign

2x - x = 9 - 5

x = 9 - 5

Answer:

x=4

Step-by-step explanation:

Subtract 1x from both sides

Subtract 5 from both sides to isolate the variable

x=4

The 35.99-carat diamond weighs approximately 7.198 grams (0.254 ounces).

We can use the conversion factor of 1 carat = 0.2 g to convert carats to grams.

Diamond weight in grams: 35.99 carats x 0.2 g/carat = 7.198 g (rounded to three decimal places)

We can use the conversion factor of 1 ounce = 28.3495 g to convert the weight in grams to ounces.

Diamond weight in ounces: 7.198 g / 28.3495 g/o z = 0.254 o z (rounded to three decimal places)

Carats are now commonly used to measure the weight of gemstones, including diamonds, and are abbreviated as "ct." A 1-carat diamond, for example, weighs 0.2 grams while a 2-carat diamond weighs 0.4 grams.

As a result, the 35.99-carat diamond weighs approximately 7.198 grams (0.254 ounces).

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The value of csc(3π/2) is -1.

What is a trigonometric function?

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Numerous trigonometric identities and formulas indicate the relationship between the functions and aid in determining the triangle's angles.

The given trigonometry function is csc(3π/2)

Assume that y = csc(3π/2)

Break the angle:

y = csc(π + π/2)

Applying the formula csc(π + θ) = -csc θ:

y = - csc(π/2)

y = -1 [since csc(π/2) = 1]

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As a rule of thumb, altitude corrections of less than 100 feet for determining the pressure at a given altitude should be corrected using the standard pressure-altitude correction tables.

These tables provide the correction factor for the difference between the actual and standard atmospheric pressure at a given altitude. The correction factor can then be applied to the standard pressure value to obtain the actual pressure value at that altitude. Note that the standard atmospheric pressure is defined as 29.92 inches of mercury (in Hg) at sea level. The pressure decreases with increasing altitude in the lower atmosphere. The pressure-altitude correction tables provide a convenient and accurate way of determining the atmospheric pressure at different altitudes.

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We need  9 sophomore girls to make sex and class independent when a student is selected at random.

No. of freshman boys     (fb) = 4

No. of freshman girls      (fg) = 6

No. of sophomore boys (sb) = 6

Let, the no. of sophomore girls = sg

The total number of students in the class T = fb + fg + sb +sg

                                                                     T = 4+6+6+sg

                                                                     T = 16 + sg

The probability of selecting a girl is  P(G) = (fg + sg) / T

                                                                    = (6+sg)/(16+sg)

The probability of selecting a sophomore is  P(S) = (sb + sg)/T

                                                                                  = (6+sg)/(16+sg)

As the events are independent, the probability of selecting a sophomore girl is                       P(sg) = P(G)*P(S)

                       sg/(16+sg) = (6+sg)*(6+sg)/(16+sg)(16+sg)

                       sg(16+sg)  = (6+sg)(6+sg)

                       16sg + [tex]sg^{2}[/tex] = 36 + 6sg + 6sg + [tex]sg^{2}[/tex]

                                 4sg = 36

                                   sg = 9

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Answer:

A. First, outer, inner, last.

Step-by-step explanation:

Answer:

4cm

Step-by-step explanation:

∵∆DEF ~ ∆ABC，AB/AC =2/3，

∴DE/DF=2/3.

∵DF=6cm，

∴DE=6*2/3=4cm.

Answer:

Step-by-step explanation:

14 doughnuts in total

We can draw the conclusion that Sadio and Amir's methods for solving the equation are both valid.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

As in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, and others.

Equation: A declaration that two expressions with variables or integers are equal.

In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

So, as we have the equation:

12x + 3 = 3(5x + 9)

Now, as we can see, Sadio took out 3 as common from LHS and RHS and solved the equation.

Which gave her the value of x as -8.

Amir, on the other hand, did not take out anything as common and directly multiply 3 with other terms in the brackets to solve the equation.

He also got -8 as the value of x.

Hence, we can conclude that yes both the ways of solving the equation is correct which is done by Sadio and Amir.

Therefore, we can draw the conclusion that Sadio and Amir's methods for solving the equation are both valid.

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Answer: Frank is going to plant "b" vegetables in one garden and "2b + 1" vegetables in another garden. So, the total number of seeds he is going to plant is b + (2b + 1) = 3b + 1.

Step-by-step explanation:

ABCD is a rectangle, and P, Q, R, and S are mid points of the sides AB, BC, CD, and DA, respectively. show that the quadrilateral PQRS is a rhombus

Answer:

Step-by-step explanation:

Let's say Trace's age is "x".

Then, Hunter's age would be (x+3)

And Jacob's will be 2*(x+3)

The Total of three ages would be

x+(x+3)+2*(x+3)=49

4x+9=49

4x=40    

x=10

So Trace is 10 years old

     Hunter is 13 years old

     Jacob is 26 years old.

The probability that the line pressure will surpass 13.0 bars during any measurement is P [Z > 13] = 0,1587, or 15.87%.

If the line pressure exceeds 13.0 bars, there is a chance that:

P [ Z > 13 ] = 1 - P [ Z ≤ 13]

P [Z 13] will be located in the z table when z (score) =

Z (score) equals (Z - 0) /

Z = (13 - 12)/1 (score).

the z-table, we then discover

P [ Z ≤ 13] = 0,8413

Finally . P [ Z > 13 ] = 1 - P [ Z ≤ 13]

P [ Z > 13 ] = 1 - 0,8413

P [Z > 13] = 0,1587, which is equal to 15,87%.One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. It is essential to appreciate the most basic definitions of this branch, such as the formula for computing probabilities in equiprovable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc., in order to properly understand it.

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Answer:

Hello if you are solving for x the for the equation -4x+4y=-4

your answer is x=y+1

Step-by-step explanation:

4y -4x= -4

subtract 4y from both sides

-4x = -4y- 4

divide both sides by -4

x= y+1

I HOPE THIS HELPS!

The expression 4^n+3 x 16^n - 8^3n cannot be solved for n

from the question, we have the following parameters that can be used in our computation:

4^n+3 x 16^n - 8^3n

The question implies that we solve for n

This in other words mean that we determine the solution for n

The given parameter is an expression (not an equation or an inequality)

To solve for a variable, the given parameter must be an equation or an inequality

Hence, the value of n cannot be determined or it has infinite many solutions

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If Zach moved the existing sand from the old terrarium into the new terrarium , then the sand in the new terrarium will be  5cm deep .

The dimensions of the old terrarium is = 20 by 50   cm  ;

The dimensions of the new terrarium is = 25 by 64 cm ;

So , amount of sand that Zach has is =  Volume of sand in the old terrarium, that is ( Area of base of the old terrarium) × (height of sand) ;

Volume of Sand = 20 × 50 × 8 = 8000 cm³  ;

When Zach moves the sand to the new terrarium, volume of sand will be same, so we can write the equation ;

⇒ 20 × 50 × 8 = 25 × 64 × h  ;

where h is = height of sand in new terrarium.

Now solving for h, we get ;

⇒ h = (20 × 50 × 8 cm)/(25 × 64 )

⇒h = 8000/1600  ;

⇒ h = 5 cm  ;

Therefore, the sand will be 5 centimeters deep in the new terrarium.

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The given question is incomplete , the complete question is

Zach keeps his pet chameleon pinky in a terrarium with the dimensions 20 by 50 cm . there's sand in the bottom of the terrarium that reaches a height of 8 88 centimeters.

Zach gets a new terrarium for pinky that is larger. the base of the new terrarium is 25 by 64 centimeters. Zach moved the existing sand to the new terrarium. how deep will the sand be in the new terrarium ?

Answer:

Step-by-step explanation:

Given the volume of a cylinder, V = πr^2h, where r is the radius, h is the height, and π is Pi, we can find the radius by rearranging the equation and solving for r.

V = πr^2h, so r^2 = V / (πh)

Taking the square root of both sides, we have:

r = √(V / (πh))

Substituting the given values:

r = √(950 / (π * 10))

Since Pi is approximately equal to 3.14, we can calculate the approximate value of r:

r = √(950 / (3.14 * 10))

r ≈ 7.46

Therefore, the radius of the cylinder with a volume of 950 cubic inches and a height of 10 inches is approximately 7.46 inches.

The man can wear 15 different outfit combinations by mixing and matching his six different sport shirts and four different pairs of slacks.

Combination is a way of counting the number of different groups of items that can be selected from a larger set without regard to the order in which they are selected.

In this case, the man has six different sport shirts and four different pairs of slacks, and he wants to know how many different outfit combinations he can wear. We can use the formula for combinations to calculate the number of possibilities.

The formula for combinations is:

ⁿCₓ = n! / (x! * (n - x)!)

Where n is the total number of items, x is the number of items being selected, and the exclamation mark (!) represents the factorial of a number (i.e., the product of all positive integers up to that number).

Using this formula, we can calculate the number of different combinations the man can wear as follows:

Number of sport shirts (n) = 6

Number of slacks (x) = 4

Number of combinations = ⁶C₄ = 6! / (4! * (6 - 4)!)

= (6 * 5 * 4 * 3 * 2 * 1) / [(4 * 3 * 2 * 1) * (2 * 1)]

= 15

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D. The length is 18 inches and the width is 9 inch

What is a scale factor?

A scale factor resembles a unit scale in several ways. It is a ratio that assesses the relationship between scale and real dimensions. Because it doesn't provide any specified units, it differs.

It is given that the scale factor of the gardener is 1:15.

The dimensions of his drawing are 6 inches long by 3 inches wide.

Therefore the original dimensions are 6*15= 90 inches.

3*15= 45 inches.

The scale of his partner is 1:5.

So, we have to divide the original dimensions by 5.

The dimensions of the scale drawing are 90/5= 18 inches long

45/5=9 inches wide.

Therefore length is 18 inches and the width is 9 inches.

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Answer: The total amount paid for shoes = $63.75

Step-by-step explanation:

The original price of the shoes = $ 80

Sale Discount = 25 %

So, the discount offered = 25 % of 80 = 20

So, the Discounted Price  = Marked price - discount

= $ 80 -$ 20 = $ 60

Now, we need to calculate the sale tax of 6.25 % on $ 60.

Also, we know that  Sales Tax = Sales Tax rate x Sale Price

= $ 60 x 0.0625  = $ 3.75

Total Cost = Sale Price + Sales Tax

=  $ 60 + $ 3.75  = $63.75

Hence, the total amount paid for shoes = $63.75 included sales tax

Answer:

A van can carry 18 students; a bus can carry 41 students.

Step-by-step explanation:

Let v = capacity of van.

Let b = capacity of bus.

School A:

3v + 12b = 546

School B:

13v + 6b = 480

Our system of equation is:

3v + 12b = 546

13v + 6b = 480

      3v + 12b = 546

+  -26v - 12b = -960

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

    -23v         = -414

v = 18

3v + 12b = 546

3(18) + 12b = 546

54 + 12b = 546

12b = 492

b = 41

Answer: A van can carry 18 students; a bus can carry 41 students.

The probability that one card is a spade and the other is a king when two cards are drawn at random from a deck of 52 cards is 0.0196.

To calculate the probability that one card is a spade and the other is a king when two cards are drawn at random from a deck of 52 cards, we need to first determine the total number of possible outcomes, which is the number of ways to select two cards from a deck of 52. This can be calculated using the formula for combinations, which is:

nCr = n! / r!(n-r)!

where n is the total number of objects (52 cards in this case), r is the number of objects to be selected (2 cards), and ! denotes the factorial operation.

So, the total number of possible outcomes is:

52C2 = 52! / 2!(52-2)! = 1326

Next, we need to determine the number of favorable outcomes, which is the number of ways to select one spade and one king from the deck. Since there are 13 spades and 4 kings in a deck, there are 13 x 4 = 52 ways to select one spade and one king.

However, we need to divide this number by 2 to avoid double counting the two possible orders (king-spade or spade-king), which gives us 26 favorable outcomes.

P = favorable outcomes / total outcomes = 26 / 1326 = 0.0196 or about 1.96%

So, there is a very low probability of selecting one spade and one king when two cards are drawn at random from a deck of 52 cards.

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Explanation:

The left-most digits are more significant than digits on the right.

For example, in the very large number 1,234,567 the "1" and "2" are more important than the "6" and "7". We focus on the more important digits when rounding. This would mean 1,234,567 rounds to 1,200,000 = 1.2 million = 1.2*10^6

Going back to 3.162, we have "3" and "1" as the left-most digits. We'll bump 3.1 up to 3.2 because of the digit 6 fits the criteria of "5 or larger".

Put another way: 3.162 is closer to 3.2 than it is to 3.1

This is why 3.2 is the final answer.

B, 222 units, is the correct answer.

The profit is £1,370. Then the percentage profit of the company will be 124.54%.

A monetary profit, particularly the distinction between the amount gained and the actual cost of purchasing, running, or creating anything.

The profit is given as,

Profit = Selling price - Cost price

The number of pins left after the donation to charity is given as,

⇒ (1 - 0.35) x 1,000

⇒ 0.65 x 1,000

⇒ 650 pins

The selling price when 60% are sold for £3 and 40% are sold for £5 is given as,

Selling price = 0.60 x 650 x £3 + 0.40 x 650 x £5

Selling price = £1,170 + £1,300

Selling price = £2,470

The cost price is given as,

Cost price = £1.10 x 1,000

Cost price = £1,100

The profit is given as,

P = £2,470 - £1,100

P = £1,370

Then the percent of profit is given as,

P = [(£1,370) / £1,100] x 100

P = 124.54%

The profit is £1,370. Then the percentage profit of the company will be 124.54%.

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The solution of the expression at x = 2 is 53 and at x = 7 is 33.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that the expression is h(x) = −4x + 61. The value of the expression at x = 2 and x = -7 will be calculated as:-

At x = 2,

h(x) = −4x + 61

h(2) = -4 x 2 + 61

h(2) = -8 + 61

h(2) = 53

At x =7

h(x) = −4x + 61

h(2) = -4 x 7 + 61

h(2) = -28 + 61

h(2) = 33

Therefore, the values are 53 and 33.

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