74 - 21 x 6 + 329 / 2

The value of sin θ of the given right angle triangle using trigonometric ratios is; A: 5/13

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). They are based on the angles formed from the ratio of sides of a right angle triangle. Thus;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

From the given image, we see that;

Hypotenuse = 13

Adjacent = 12

Opposite = 5

Thus;

tan θ = 5/12

θ = tan⁻¹(5/12)

sin θ = 5/13

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The following are the answers:

23. The cost for 7 lessons is $82, and the cost of 11 lessons is $122, we have;

The total cost of lessons is;  f(x) = y = 10·x + 12 and one lesson costs $22

24. The equation of population of Laredo, Texas is :

p = 92500t/17 + 123000

25. The linear equation to represent the temperature T at an elevation of x, where x is in thousands of feet is T = -(2000/3)x + (4228/3).

26. The equation to represent the amount 'R' Natalia and her friends raised after selling 'c' cakes will be;

⇒ R = 4c

Given:

23. Lydia wants  to purchase guitar lessons.

7 lessons = $82

11 lessons = $122

we are asked to determine the linear equation which finds the total cost C for d lessons.

The general equation for the total cost of lessons is;

Let a represent the cost of 7 guitar lessons, and let b represent the cost of 9 guitar lessons, given that the cost increases linearly with the number of lessons, we have;

The cost increase per lesson = The slope of the linear function representing the total cost of a guitar lesson

Therefore,

slope = b-a/11-7 = b-a/4

Expressing the equation in slope and intercept form, we get:

(y-a) = b-a/4 . (x-7)

y = b-a/4 . x-7 × b-a/4 + a = b-a/4 . x + 11.a-7.b/4

y = b-a/4 . x + 11.a-7.b/4 = 1/4.((b-a).x+11.a-7.b

where a=$82 and b=$122 we ahve:

y = 1/4 . (122-82) . x+1/4 . (11×82-7×122) = 10x+12

The total cost of a lesson is:

y = 10×1+12

= 22

24. Given:

t = the number of years after 1990.

So, for 1990, t = 0. So the coordinate is (0, 123000).

For 2007, t = 17. So the coordinate is (17, 215500).

using point slope formula:

m = 215500-123000/17-0

m = 92500/17

⇒ p = 92500t/17 + 213000

25. The equation of a line in slope-intercept form is y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at

x = 0.

We know the slope is (y₂ - y₁)/(x₂ - x₁).

∴ Here the temperature is y and the height is x.

And the points are (6000, 76) and (12000, 49)

So, slope =(12000 - 6000)/(49 - 76).

Slope = (6000/-27).

Slope = -(2000/9).

Now we have to determine the y-intercept by putting any of the points in y = mx + b.

So, 76 = -(2000/9)×6000 + b.

76 = -(12000/9) + b.

76 = -(4000/3) + b.

b = 4000/3 + 76.

b = 4228/3.

∴ y = -(2000/3)x + (4228/3) or T = -(2000/3)x + (4228/3).

26. The equation of line 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;

he friends sold 15 cakes on the first day and 22 cakes on the second day of the bake sale.

On first day, they collect = $60

On second day, they collect = $88

Now,

We have to find the equation as;

⇒ R = mc + b

We need to find the value of m and b.

Since, The first point = (15, 60)

The second point = (22, 88)

Hence, Slope (m) = (88 - 60) / (22 - 15)

m = 28 / 7

m = 4

And, To find b substitute R = 60 , c = 15 and m = 4 in above equation,

⇒ R = mc + b

⇒ 60 = 4 x 15 + b

⇒ b = 0

Thus, Substitute m = 4 and b = 0 in equation (i) we get;

⇒ R = mc + b

⇒ R = 4c + 0

⇒ R = 4c

Therefore, The equation to represent the amount 'R' Natalia and her friends raised after selling 'c' cakes will be;

⇒ R = 4c

Hence we get the required answers.

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Answer:

26

Step-by-step explanation:

you are given 45° and 90° so you know the third angle will also be 45° because the sum of all angles always is 180°
with all 3 angles you apply the sine law
a / sin( α ) = b / sin( β ) = c / sin( γ )
then you'll see that a = 26

Answer:

11-k

Step-by-step explanation:

if you are asking what is as a equation its 11-7 because decreased means minus

The required mathematical expression for the given statement is 11-k.

A mathematical statement containing variables, numbers and related by at least one mathematical operator is considered as an expression.

Given that, a statement, what's eleven decreased by k,

Converting it into a mathematical expression,

Here, a value k is being extracted or subtracted by 11, that mean, the expression should be like k is being subtracted by 11.

That is = 11-k

Hence, the required mathematical expression for the given statement is 11-k.

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The expression that represents the total number of illustrations in Julio's sketch pad after his museum visit is given as follows:

Total number = 20 + x.

The expression that represents the total number of illustrations in Julio's sketch pad after his museum visit is obtained adding the previous amount of illustrations to the number of illustrations that were added during the visit to the museum, hence:

Total number of illustrations = Previous number of illustrations + number of illustrations added during the visit.

In the context of this problem, the values of these parameters are given as follows:

Hence the expression is defined as follows:

Total = 20 + x.

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8.1^4 x 8.1^8 will be equal to 8.1^12. But, 8.1^12 will not be equal to 8.1^6.

Some laws of exponents are:

We are given:

8.1^4 x 8.1^8

We need to check if 8.1^4 x 8.1^8 be equal to 8.1^12 and if 8.1^12 be equal to 8.1^6.

We will use laws of exponents to solve the given expression:

8.1^4 x 8.1^8 = 8.1^(4 + 8) = 8.1^12

So, 8.1^4 x 8.1^8 = 8.1^12

Also,

8.1^12 = 8.1^(2 * 6) = (8.1^2)^6

So, 8.1^12 ≠ 8.1^6.

Thus, 8.1^4 x 8.1^8 will be equal to 8.1^12. But, 8.1^12 will not be equal to 8.1^6.

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Answer:

X = -4

Step-by-step explanation:

25^(x+3) = 1/5

5^2^(x+3) = 5^(-2)

5^(2x+6) = 5^(-2)

2x+6 = -2

2x = -8

x = -4

Answer:

x = -7/2

or can be written,

x = -3.5

Step-by-step explanation:

25 is a power if 5 and so is 1/5. If you can write both sides as 5 to "some" power. Then the equation is just getting those two exponents equal. See image.

 Using logarithms is a nice shortcut. But then you need need a calculator. See image.

Answer:

Urban

Step-by-step explanation:

According to the distance-speed-time formula, the equation that could be used to solve this formula is 60/x+10 - 60/x = 1/2

Distance-speed-time

Basically, the formula for speed is speed = distance ÷ time.

In order to work out what the units are for speed, you need to know the units for distance and time.

Given,

Jackie travels 60 km to work. Since she began taking a new route (still 60 km to work) she gets there 30 minutes sooner because she can drive 10 km/hour faster.

Here we need to find the equations could you use to solve the problem.

Let us consider x be the speed of Jackie.

Therefore, the time has been calculated as,

Time1 = 60/ x

Now, the speed is increased as 10, then it can be written as,

=> x + 10

Therefore, the new time Time2 is calculated as,

=> Time2 = 60 / x + 10

So, the equation is obtained by calculating the difference of the times,

So, the equation is,

=> Time 2 - Time1

=> 60/x+10 - 60/x

Now, we know in this one she gets there 30 minutes sooner,

So, it can be written as,

=> 60/x+10 - 60/x = 30/60

=> 60/x+10 - 60/x = 1/2

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Answer:Total time minute Casey can talk= 689 Minute

Step-by-step explanation:Total charges of flat rate per month= $3. 99

Total Additional charge per minute = $0.05

Total monthly bill = $38. 44

Total additional charge=Total monthly bill - Total charge of flat rate

=$38.44-$3.99

=$34.45

Total time minute Casey cann talk=Total additional charge÷Total additional charge per minute

=$34.45÷$0.05

=689 Minute

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689 minutes long If Casey's monthly bill was $38.44, she would talk on her cell phone.

Given;

A cell phone provider charges a set monthly fee of $3. 99 plus an extra $0.05 per minute.

If Casey's monthly phone bill was $38.44, how many minutes did she use? 

The total charges of the flat rate per month = $3.99

The total additional charge per minute = $0.05

Total monthly bill = $38.44

Total additional charge = Total monthly bill - Total charge of flat rate

                                       = $38.44 - $3.99

                                       = $34.45

Total time per minute Casey can talk = Total additional charge/Total additional charge per minute

                                                       = $34.45 / $0.05

                                                       = 689 Minutes

Therefore, for 689 minutes Casey talk on her cell phone if her monthly bill was $38.44

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The missing number so that the equation has no solution is -3 5/6.

A linear equation is an equation that has a single variable that is raised to the power of one. When shown on a graph, a linear equation is a straight line that slopes either upwards or downwards.

If the equation has no solution, it means that the value of the left hand equation and the value of the right hand equation are equal.

In order to determine the solution, take the following steps:

x + 19 = 2x - 4 - 7x

Combine similar terms together: 19 + 4 = 2x - 7x - x

Add similar terms together: 23 = -6x

Divide both sides of the equation by -6: x = 23 / - 6

x = -3 5/6

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Regarding the objective function C = 3x + 4y, the minimum and the maximum value are given as follows:

The objective function is defined as follows:

C = 3x + 4y.

The extremas of the function, that is, the minimum and the maximum values, can be obtained at either of these following points:

These extreme values are the numeric values at these points.

In this problem, there is only a single curve, hence the vertices are given as follows:

(0,0), (0,4) and (4,0).

Then the numeric values of the objective function are these points are given as follows:

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Answer:

8 hours

Step-by-step explanation:

2 cars will be $400 since 2x200=400

500-400=120

He made $120 from hours alone so now we divide by 15

120/15=8

He worked 8 hours

Hopes this helps please mark brainliest

The value of y coordinate of the unit circle is given by [tex]\sqrt{7}/4[/tex]

Given that,

x - coordinate of p =-3/4 . Let the co-ordinate of point P = (-3/4 , y).

To find : The y coordinate in Quadrant IV

By using the formula for unit circle,

Unit circle means a circle whose radius is one or 1

x²+ y² = 1

y²+ (-3/4)² = 1

y²+ (9/16) = 1

y² = 1 -9/16

y² = 7/16

y= [tex]\sqrt{7/16}[/tex]

y =  ± [tex]\sqrt{7}/4[/tex]

It is given that point P is in quadrant IV so in IV quadrant y is positive.

Therefore, y =  [tex]\sqrt{7}/4[/tex]

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Answer:

A square number is always nonnegative. So a quantity squared must be nonnegative.

The largest integer value of x in the solution of the following inequality is 7/4.

We have given equation is 4x+6 ≥13

In the question we have to determine the largest integer value of a in the solution of the following inequality.

So first we have to solve this inequality equation:

4x+6 ≥13

4x≥13-6

4x≥7

x≥7/4

So the largest value of x is 7/4

Hence, the largest integer value of a in the solution of the following inequality is 7/4.

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The right answer is

Determine the largest integer value of x in the solution of the following inequality.

4x+6≥13

First number 79 about friction is correct statement with initial velocity .

What is friction?

Friction is a force that opposes motion between any surfaces that are touching. Friction can work for us yet against of us .

It is the action of one surface or object rubbing against another .

According to the given question in this case force of friction has a tendency to rotate the cube in anticlock wise direction. So normal reaction will shift in forword direction to balance the force due to torque of friction.

Thus, During motion the normal reaction shift towards posetive x- axis from the centre of mass is correct.

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The total Cost of the equipment is $2,27,700. In which the following included, excluded and expensed as incurred are

Invoicing costs - included in the price

Electrical work required for installation - Included in the price

Delivery costs - included in the price

Sales tax - included in the price

Repair costs - not included or excluded

A machine used by a company to produce products and services is known as a machine tool. It is a vital long-term asset as it speeds up the production process such as transportation, computers and other equipment. These costs will include the costs that were necessary to start opening the plant property. There are equipment costs.

We have given the following details ,

Total Cost DR Machinary DR Expense

Invoice cost $190,000 $190,000

electric work

and $20,000 $20,000

installation cost

delivery cost। $4,000 $4,000

sales tax $13,700 $13,700

repair cost $1,850 $1,850

total $22,9550 $22,7700 $ 1,850

Accordingly, all the mentioned costs except for the repair of the part will be included in the cost of the machinery.

Included in price Excluded

invoice repair cost

electric and installation

delivery

sales tax

Hence , the total equipment cost is $22,7700.

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The coefficient would be 3.6

The confidence interval estimate is (6.41, 7.11) of the population mean rating for Miami

The question includes a sample of the data.

The sample size, n = 50

The sample mean:

x= ∑X /n

= 6.76

The sample standard deviation;

s= √∑(X-x)²/(n-1)

=2.55

The confidence level =0.95

The significance level , α = 0.05

The sample mean, X

= 6.76

The sample standard deviation, s = 2.55

The sample size , n= 50

Degree of freedoms :

Df = n-1

=49

Using the t-distribution table, the critical value of t is:

t critical = t α/2, df

= t 0.025,49

= 0.098

95% confidence interval :

μ =  X ± t.s/√n

 t.s /

= 6.76  2.01  2.55 / √50

= 6.76  0.7249

Therefore, The confidence interval is ( 6.41, 7.11)

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The interpolations;

(a) 81st

= NORM.INV(0.81;0;1)

0.878

(b) 19th

=NORM.INV(0.19;0;1)

-0.878

(c) 76th

=NORM.INV(0.76;0;1)

0.706

(d) 24th

=NORM.INV(0.24;0;1)

-0.706

(e) 11th

=NORM.INV(0.11;0;1)

-1.227

Given,

Data near the mean are more likely to occur than data distant from the mean, according to the normal distribution, which is a probability distribution that is symmetric around the mean.

"A numerical measurement used in statistics of a value's relationship to the mean (average) of a set of values, assessed in terms of standard deviations from the mean," according to Wikipedia, is the Z-score.

For this case we can find the percentiles with the Norm.inv function in Excel and we got:

(a) 81st

= NORM.INV(0.81;0;1)

0.878

(b) 19th

=NORM.INV(0.19;0;1)

-0.878

(c) 76th

=NORM.INV(0.76;0;1)

0.706

(d) 24th

=NORM.INV(0.24;0;1)

-0.706

(e) 11th

=NORM.INV(0.11;0;1)

-1.227

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Answer:

Step-by-step explanation:

3 because at the bottem it is 3 away and top three away.

Answer: x+x+y.y.y = 2x+y^3 ( y cube)

Step-by-step explanation:

Answer:

2x+y^3

Step-by-step explanation:

x's are added while y's are multiplied

The set of probabilities for the number of eaglets is the

probabilities for how many eaglets will survive.

The table that shows the probability distribution is the option C;

X      0         1         2

p(x)   0.35   0.60   0.05

  P(O) = 0.5 is the likelihood that the elder eaglet will live.

  Therefore;

   P(O') = 1 - 0.5 = 0.5 is the probability that the older eaglet won't survive.

  The likelihood that the younger eaglet will survive if the older eaglet              does not P(Y|O) = 10%

Therefore;

The likelihood that the elder eaglet will live while the younger eaglet does not survive is P(Y'|O) = 1 - 10% = 90%.

When the older eaglet does not survive, the younger eaglet has a 30% survival chance (P(Y|O')).

Therefore;

The likelihood that the younger eaglet will not survive, compared to the elder eaglet, is P(Y'|O') = 1 - 30% = 70%

The collection of potential probabilities for the number of eaglets that survive is expressed as the probability distribution, or P(X)

The range of potential results includes:

Never survives:

The likelihood that no eaglets survive is equal to P(O') × P(Y'|O') = 0.5 × 0.7 = 0.35.

The only survivor is:

The likelihood that only one eaglet survives is determined by P(O) = P(Y'|O) × P(O') = P(Y|O'), which results in P = 0.5 × 0.9 + 0.5 × 0.3 = 0.6 Both survive:

The odds of both eaglets surviving are P(O) ×P(Y|O) = 0.5 × 0.1 = 0.05.

The table of the probability distribution is therefore;

X      0         1         2

p(x)   0.35   0.60   0.05

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Percentage change expresses the ratio of the change in the amount of an initial quantity to the initial quantity as a percentage.

Mathematically, the formula for percentage change, C, can be presented as follows;

[tex]C = \dfrac{x_{2} - x_{1} }{ x_{1} } \times 100[/tex]

Where:C = The percentage change

[tex]x_{1} [/tex] = The original value

[tex]x_{2} [/tex] =The new value

Graphically, percentage change can be presented as follows;

When the number of fruits that drops from a three each month, changes from 10 to 8, the percentage change is therefore;

[tex] C = \dfrac{10-8}{10} = 20\% [/tex]The percentage change is 20%

Initial number of fruits that drops monthly from the tree;

##########

The new number of fruits that drops from the tree on the specified month;

########

The difference in the number of fruits that drops from the tree is 2, which corresponds to the 20 % calculated for the percentage change.

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Answer:

3x7

Step-by-step explanation:

product is multiplication so 3x7 is only correct answer

Hopes this helps please mark brainliest

Answer:

Your answer should be x = 2

Step-by-step explanation:

149 + 13(2) + 5 = 180.

Hope this helps.

Answer:

x=2

Step-by-step explanation:

You add 149 and 5, which is 154. Then you take the total which is 180, and subtract it by 154. So 180-154=26 Then you take and do 26/13 which is 2.

149+13(2)+5=180

149+26+5=180

Definitely 2.

Hope this helps!!!

Answer:

it needs to be written step by step