_____+29 ÷4 = 16
Fill in the blank, Please

The possible solutions using the Sine Law are given as follows:

Triangle A:
B = 50.26°

C = 79.74°

Triangle B:

B = 62.79°

C = 70.21°

The sine law asserts that the ratio of a triangle's side length to the sine of the opposing angle is the same for all three sides. The sine rule is another name for it.

Triangle A

Given the sine law:
a/SinA = b/SinB

Hence

Sin B = (b/a) SinA

Sin B = 15/10 (Sin 50)

Sn B = (15/10) * 0.766

Sin B = 1.5 * 0.766

B = Sin⁻1 (1.14)

B = 50.26°

Hence, C =

180 - B - A

= 180 - 50.26 - 50

C = 79.74°

Solution B

Given the sine law:

a/SinA = b/SinB

Hence

Sin B = (b/a) SinA

Sin B = 2/1.6 (Sin 47)

Sn B = 1.25 * 0.73

Sin B = 0.9125

B = Sin⁻1 (0.9125)

B = 62.79°

Hence,

C = 180 - 62.79 - 47

C = 70.21°

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Answer:

VY = 28 units

Step-by-step explanation:

the perimeter (P) of a rectangle is calculated as

P = 2 ( length + breadth )

given P = 130 , then

2(5y + 2 + 4y) = 130 ( divide both sides by 2 )

9y + 2 = 65 ( subtract 2 from both sides )

9y = 63 ( divide both sides by 9 )

y = 7

Then

VY = 4y = 4 × 7 = 28

Answer: 36

Step-by-step explanation:

[tex]\overline{AB} \cong \overline{BC}[/tex] (Triangle ABC is isosceles)

[tex]m\angle CAB=m\angle CBA=30^{\circ}[/tex] (base angles of an isosceles triangle are congruent)

[tex]\angle MCB=90^{\circ}[/tex] (In triangle CMB, angles in a triangle add to 180 degrees)

[tex]\angle ACM=30^{\circ}[/tex] (triangle sum theorem)

[tex]MB=24[/tex] (30-60-90 triangle CMB)

[tex]AB=12[/tex] (sides opposite congruent angles in a triangle are congruent)

[tex]AB=36[/tex] (segment addition postulate)

Answer:

3:7

Step-by-step explanation:

So to solve this problem, you have to understand what the ratio 1:4 and 2:3 means. The 1:4 ratio in the first equation means that for "each unit of alcohol" there is 4 of those units of water. So let's say I had 2 gallons of alcohol and mixed it with 8 gallons of water. This means for each gallon of alcohol, there is 4 gallons of water, or in other words a 1:4 ratio. This can be described as a percentage as well. For each 5 gallons there are 4 gallons of water, and 1 gallon of alcohol or 20% is alcohol. So let's just say that x=alcohol and y=water, this means that: [tex]x+y=c[/tex]  where c is the total amount in the glass. This means that: [tex]x=0.20c[/tex]

Let's do the same thing to the second equation. the ratio means that for every 2 units of alcohol there are 3 units of water. This means for every 5 gallons of the mixture there is 2 units of alcohol which is 40%. In this case let's also say that j=alcohol and k=water. This means that: [tex]j+k=c[/tex] and that: [tex]j=0.40c[/tex].

So if we're going to add the two glasses, we simply add the two sides, and get: [tex]j+x+k+y=2c[/tex]. Now remember how can can express j and x in terms of c, since it's a certain percentage of c (the entire thing). This means that we get: [tex](0.4c+0.2c)+x+k=2c[/tex] Now we can add like terms to get the equation: [tex]0.6c+y+k=2c[/tex]. We can find how much 0.6c is to 2c by dividing the 2, in doing so we get that 0.6c/2c = 0.3, or in other words the 0.6c is only 30% of the final mixture, and since the 0.6c represents the alcohol in this mixture, that means that's the percentage of alcohol. To write this as a ratio, this means for every 3 units of alcohol, there is 7 units of water, because 3/10 = 30%.

Answer:

3 : 7

Step-by-step explanation:

We can do this question using a easier way.

For example, A glass contains sugar and water, the ratio to sugar to water is 2 : 5. And the second glass's sugar to water is 2 : 3. The mixture of the first glass is 200 mL. The mixture of the second glass is the same as the first glass.

This kind of glass question, is very important to Math.

Try using this to solve this question.

Answer:

A. 19

Step-by-step explanation:

Slove this expression using the order of operation PEMDAS.

12 + 2x -5

Replace x with 6

12 + 2(6) - 5

12 + 12 - 5

24 -5

19

Therefore the answer is the first option A.19 .

Answer: 4/3

Step-by-step explanation:

[tex]\tan \theta=\frac{20}{15}=\boxed{\frac{4}{3}}[/tex]

Answer:

Hence the expression  [tex]$$(10a-b)(3a-4)=30a^2-3ab-40a+4b$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{matrix}{} & {} & {} & {} & 10a & - & b \\ \times & {} & {} & {} & 3a & - & 4 \\ \end{matrix}$$[/tex]

___________________

[tex]$$\begin{matrix}{} & {} & {} & - & 40a & + & 4b \\ 30{{a}^2} & - & 3ab & {} & {} & {} & {} \\ \end{matrix}$$[/tex]

___________________

[tex]$$\begin{matrix}30{{a}^2} & - & 3ab & - & 40a & + & 4b \\ \end{matrix}$$[/tex]

Answer: d. 6.

Step-by-step explanation:

AD=3      DC=27       BD=x+3      x>0     x=?

1. Consider triangle ABD:

It's rectangular (∡ADB=90°).       ⇒

AB²=(x+3)²+3²=(x+3)²+9.

2. Consider triangle BDC:

It's rectangular (∡BDC=90°).       ⇒

BC²=(x+3)²+27²=(x+3)²+729.

3. Consider triangle ABC:

It's rectangular (∡ABC=90°).      

AC=AD+CD=3+27=30.      ⇒

AC²=AB²+BC²

(x+3)²+9+(x+3)²+729=30²

2*(x+3)²+738=900

2*(x²+6x+9)+738=900

2x²+12x+18+738=900

2x²+12x-144=0 |:2

x²+6x-72=0

D=324   √D=18

x₁=-12 ∉ 'cause x>0

x₂=6.

Answer:

Step-by-step explanation:

its A i just did it lol

The probability that he will use both bus and the train among bus, cab, train is 0.11.

Given There are 3 choices to people each among bus, cab, train for his trip home.

Probability is the likeliness of happening an event among all the events possible. The value of probability lies between 0 and 1. The formula to calculate probability is as under:

Probability= number of things/ total things.

The value of probability cannot be negative.

Number of buses=3

Number of cab=3

Number of train=3

Probability that he will go through train and bus is 3/9*3/9

=9/81

=1/9

=0.11

Hence the probability that he will travel with bus and train is 0.11.

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Question is incomplete as it includes:

What is the probability that he will use both train and bus?

Possible values of x is -4 or -16

[tex]{x}^2[/tex] + 20x +100 = 36

[tex]\\{x}^2[/tex] + 20x + 100-36 = 0

[tex]\\{x}^2[/tex] + 20x + 64 = 0

Using middle term split

In this method splitting of middle term in to two factors, In Quadratic Factorization using Splitting of Middle Term which is x term is the sum of two factors and product equal to last term.

[tex]{x}^2[/tex] + 4x + 16x + 64 = 0

x(x+4) + 16(x+4) = 0

taking common (x+4)

(x+4)(x+16) = 0

Either

x+4 = 0

⇒ x = -4

or (x+16) = 0

⇒ x = -16

Thus possible values of x is -4 or -16

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Answer: A

Step-by-step explanation:

Using the combination formula, it is found that the probability that you and your 3 friends will get to sit together in the same row is given by:

[tex]p = \frac{1}{17550}[/tex].

We do not consider the order, hence the combination formula is used to solve this question.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

4 students will be taken from a set of 27, hence the number of ways they can sit is given by:

[tex]C_{27,4} = \frac{27!}{4!23!} = 17550[/tex]

Only one outcome is desired, hence the probability is given by:

[tex]p = \frac{1}{17550}[/tex].

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The probability that the operator is busy is 33.33% if the call rate is 2 per minute and average time to handle is 10 seconds.

Given rate of calls 2 per minute and average time to handle a call is 10 seconds.

We have to find the probability that the operator is busy.

Probability is the chance of happening an event among all the events possible. The value of probability lies between 0 and 1.

Probability= number of items/ total items

If rate is 2 per minute then the customers handled in 1 hour=2*60=120

The average time to handle a call=10 seconds.

Therefore customers to be handled in 1 hour=360 (10*6*60)

Probability that the operator is busy is as under:

Probability=λ/μ

=120/360

=1/3

=1/3*100

=33.33%

Hence the probability that the operator is busy is 33.33%.

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The statement which must be true are Options B, C and D

which are the triangles have the same size and shape, the corresponding sides of the triangles are congruent and the corresponding angles of the triangles are congruent.

Congruent triangles are triangles that have corresponding sides, angles which are all equal in measure.

They can be rotated and turned to be look be identical.

Thus, the statement which must be true are Options B, C and D

which are the triangles have the same size and shape, the corresponding sides of the triangles are congruent and the corresponding angles of the triangles are congruent.

The complete question is

If two triangles are congruent which of the following statements must be true? CHECK ALL THAT APPLY

A. The triangles have the same size but not the same shape.

B. The triangles have the same size and shape

C. The corresponding sides of the triangles are congruent.

D. The corresponding angles of the triangles are congruent.

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The distance of Miles' destination is 225 miles.

A scale drawing is a reduced form in terms of dimensions of an original image / building / object. The map is a scale drawing of a larger town. The scale drawing is reduced by constant dimensions.

Actual distance = (15 x 15) / 1 = 225 miles

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The number of those who attended the picnic was 8.

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = [tex]ax^{2} + bx + c[/tex] = 0 where a, b, c, ∈ R and a ≠ 0.

Such questions are best examples of quadratic equations where  the unknown is simply assumed to be a variable which when substituted according to the conditions yield a quadratic equation which can easily be solved.

Let x represent the whole population.

Total Spending = Rs. 96

Thus, each individual's contribution is equal to 96/x.

Four people did not show up causing

others to contribute Rs. 4 extra.

So the given condition can be written as

96/(x-4) – 96/x = 4

=>96x – 96(x-4) = 4x(x-4)

=> 96x -96x + 384 = 4x2 – 16x

=> 4x2 – 16x – 384 = 0

=> x2 – 4x – 96 = 0

=> (x – 12)(x + 8) = 0

=> x = 12 or x = -8 (neglect)

So x = 12

x-4 = 8  ( because  four of them did not turn up)

∴ The number of those who attended the picnic was 8.

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Answer: $233

Step-by-step explanation:

- A flat fee is an amount that is charged or paid that doesn’t account for hourly use or work

- Then, you must pay by the hour for use

- So you would use the equation:

(22 • 9) + 35

- 22 is the maximum hours and 9 is the hourly rate

- 35 is your flat fee

- So, (22 • 9) + 35 = $233

hope this helps :)

Answer:

$233

Step-by-step explanation:

We can make up a linear equation. We already know that it costs $35 to rent a small auger.

Every hour there is a extra fee of 9$.

So, 9 can be the slope, while 35 can be the x intercept.

y=9x+35

x=22; maximum hours

y=9(22)+35

y=198+35

y=$233

Here is a more simple way

multiply 22 hours with 9 dollars, =$198

then add the 35 dollars; 198+35=$233

Answer:

x = 34 degrees

Step-by-step explanation:

Corresponding Angles Theorem: If 2 parallel lines are cut by a transversal, their corresponding angles are congruent.

Angle RNM = 78 degrees

Triangle RMN = 180 degrees

180 = 78 + 2x + x

102 = 3x

x = 34

[tex]x + 4x + 4x + 135 + 135 = 540[/tex]

[tex]9x + 270 = 540[/tex]

[tex]9x = 540 - 270 \\ 9x = 270[/tex]

[tex]x = \frac{270}{9} = 30[/tex]

Answer:

D 15

Step-by-step explanation:

Count all of the x's less than 1 1/2  =  15

Answer:

I don't know the answer

Step-by-step explanation:

it's hard solve it for me

Answer:

let why is equal to FX b and function with an independent variable X and dependent variable y if a function of f provide a way to successfully produced the single value using for the prepos a value of x then the chosen X value is called belong to domain f

Answer:

2/3

Step-by-step explanation:

that the ratio of that number

[tex]\frac{FI}{IG}=\frac{14}{28}=\frac{1}{2}\\\\\frac{FE}{EH}=\frac{12}{26}=\frac{6}{13}[/tex]

So, IE is not parallel to GH.

The statements hold the contradiction, just by confusion in keep meaning of statements and get confused with "12" which is string in quotes

Let  be “the smallest integer not describable in fewer than  English words.” (Note that the total number of strings consisting of  or fewer English words is finite.)

What do you mean by contradiction?
Contradiction means that couple of statements that opposes each other.

Here,
The statement says let n be  “the smallest integer not describable in fewer than  English words.” which implies that n is connected with string mentioned in "" quotes, which is not a definition but contain 11 words in the quotes.
and another statement -  Note that the total number of strings consisting 11  or fewer English words is finite which implies that:
the limit of words inside the quotes ≤ 11 words

Thus, strings implies in quotes is simple meaning with 11 word in it
While in statement in brackets implies the limit of words as a string should be ≤ 11. the string "12" create the contradiction in minds.

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The range of the function across the domain is {18, 2, -6}

The function is given as:

f(x) = -2x + 12

The domain is given as:

{-3, 5, 9}

So, we have:

f(-3) = -2*-3 + 12 = 18

f(5) = -2*5 + 12 = 2

f(9) = -2*9 + 12 = -6

Hence, the range of the function across the domain is {18, 2, -6}

The function is

f(x) = 3x - 11

To calculate f(4), we have:

f(4) = 3 * 4 - 11

Evaluate

f(4) = 1

Hence, the value of f(4) is 1

The function of the graph is given as:

w(x)

To calculate w(2), we check the corresponding point on the graph where x = 2

From the graph, we have:

w(2) = 5

Hence, the value of w(2) is 5

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Answer:

1.  f(4) = 1

2.  range: {18, 2, -6}

3.  w(2) = 5

Step-by-step explanation:

Question 1

[tex]\textsf{Given}: \quad f(x)=3x-11[/tex]

To find f(4) substitute x = 4 into the given function:

[tex]\begin{aligned}\implies f(4) & = 3(4)-11\\& = 12-11\\& = 1\end{aligned}[/tex]

Question 2

Domain: set of all possible input values (x-values)

Range: set of all possible output values (y-values)

[tex]\textsf{Given}: \quad b(x)=-2x+12[/tex]

To find the range of the given function for the domain {-3, 5, 9} simply input these values of x into the function:

[tex]\implies b(-3)=-2(-3)+12=18[/tex]

[tex]\implies b(5)=-2(5)+12=2[/tex]

[tex]\implies b(9)=-2(9)+12=-6[/tex]

Therefore, the range of the given function is {18, 2, -6}.

Question 3

Given:  The graph of function w(x)

To find w(2) simply find the y-value of the point on the graph where x = 2:

Therefore, w(2) = 5

The interval around the mean that contains 95% of the airfare is (250.2,524.2).

Normal Distribution is bell shaped and symmetrical in nature.

We use standard normal to find probabilities of normal distribution

Normal distributions have key characteristics that are easy to spot in graphs: The mean, median and mode are exactly the same. The distribution is symmetric about the mean—half the values fall below the mean and half above the mean. Diagram below shows standard normal figure.

In a normal distribution, 95% of the values fall between mean±2*sd

Give:  mean=387.20

          sd=68.50

So the interval around the mean that contains 95% of the airfare is (250.2,524.2).

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The value of a is  0.10.

The value of b is 20.78.

The value of c is 0.02.

When two variables have inverse variation, the two variables move in opposite directions. If one variable increases, the other decreases.

p = 8.31 / V

V = 8.31 / p

a = 8.31 / 83.1 = 0.10

b = 8.31 / 0.4 = 20.78

c = 8.31 / 415.5 = 0.02

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Answer:

a= 0.1

b=20.775

c=0.10

Step-by-step explanation:

edge 2023