Find the tangent of angle Θ in the triangle below.
A. 7/7
B. 0
C. sqroot2
D. 1
E. 7/sqroot98

The probability that a randomly selected cable repair visit will take at least 43 minutes will be 88%.

Given: The times required for a cable company to fix cable problems in its customers' homes are uniformly distributed between 40 minutes and 65 minutes.

It can be deduced that the probability that a randomly selected cable repair visit will take at least 43 minutes will be calculated thus:

= 1 - [(43 - 40)/(65 - 40)

= 1 - 0.12

= 0.88

Hence, The probability that a randomly selected cable repair visit will take at least 43 minutes will be 88%.

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Answer:

C

Step-by-step explanation:

let f(x)=y and g(x)=x

so y=x²

if y-2=(x-2)

y=x

Answer:

C

Step-by-step explanation:

Given y = amount of money spend for the long distance plan per month

and x = minutes used each month

Note these 2 plans are in per month basis.

Plan A: Flat $5 + $0.99 Per min used (variable cost)

transform into an equation:

y = 0.99x + 5

Plan B: Flat $10 + $0.79 per min used (variable cost)

transform into equation:

y = 0.79x + 10

Put these 2 equations together, will give you the answer as C.

The nearest tenth of how fast a rover will hit Mars' surface after a bounce of 15 ft in height is 20.7ft/s.

From the question:

Mars: F(x) = 2/3[tex]\sqrt{64x}[/tex]

Therefore, If x = 15

Then:

f (15) =  2/3 [tex]\sqrt[8]{15}[/tex]

= 16/3[tex]\sqrt{15}[/tex]

= 20.7ft/s

Hence, The nearest tenth of how fast a rover will hit Mars' surface after a bounce of 15 ft in height is 20.7ft/s.

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Answer:

The initial value in the word problem is the output value when input value is set to zero.

Step-by-step explanation:

Answer:

Step-by-step explanation:

2. Given a point with integral coordinates (a, b):

   Vertical line that contains (a, b):

       So here it's not to hard, all you have to understand, is what a vertical line is. If you were to draw a vertical line, you would notice that the x-values remain constant, and the only thing that changes is the y-value. So you're going to have an equation as such: x=a, where a is some constant value, and y is literally anything. So in this case b doesn't matter. The only thing that matters is that x=a. Which is the equation. As long as x is equal to a, it should pass through (a, b)

   Horizontal line that contains (a, b):

       So this is very similar to the vertical line, as one of the values is constant, although the variable that's constant is different. If you were to draw a horizontal line, you would notice the x is changing, but the y-value isn't. This means the y is going to equal to constant value, which may look something like: y=b, which is the equation in this case, since as long as y=b, then the x should at some point equal a on the horizontal line

Why is it impossible to write the equation of a vertical line in slope-intercept form:

   As mentioned before, in a vertical line, the only thing that varies is the y-value, so if you wrote a vertical line as such: y=mx+b, then the x-value would have to vary. But if we were to put restrictions on the equation so that x can only equal some constant value, that means y would only be one point, but if you draw a vertical line, you would know that the y-value is all real numbers (unless of course you put some range restriction), but even then it's going to be more than one number. The other thing is to write an equation in slope-intercept form, you need to know the slope. which is defined as [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. and by definition a vertical line only varies in y-values and not x. The value of x is defined in the constant equation: x=a. So the slope would be defined as: [tex]\frac{y_2-y_1}{a-a} = \frac{y_2-y_1}{0} = \text{undeefined}[/tex] ("I typed undefined wrong intentionally since it won't let me type it for some reason"). anyways the point is you can divide by 0. So main takeaways: the x-value can't vary, the formula has to output all real numbers for the y-value (unless some range restriction), the slope will have 0 as the denominator since x doesn't vary meaning x_2 - x_1 will = 0, because x_2 = x_1 (because x doesn't vary)

Given an equation in point slope form, explain how to determine the coordinate of the y-intercept:

   There are two ways to do this. The point slope form is expressed as such: y-a = m(x-b). But the m can be distributed so the equation becomes y-a = mx-mb and then add "a" to both equations to get y=mx -mb+a, in this case (0, -mb+a) will be the y-intercept, because if you plug in x as 0, mx will become 0 and it will leave these two values. You could also just of course plug in 0 as x in the point slope intercept form: y-a = m(x-b) and then solve for y. This gives the same result as it simplified to y-a = m(-b) which becomes y-a=-mb which then becomes y=-mb+a.

Answer:

Step-by-step explanation:

Note : I am assuming that the question is asking for all no. of total pens.

If 5 red pens were 25% of the total quantity, we can say that 1/4th of the pens were red.

If 5 pens = 1/4, we multiply 5 * 4 to find the total quantity. 5*4 = 20

So, Ms. Sullivan bought 20 pens.

Hope this helps!

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. An isosceles triangle is one with two equal-length sides.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angle of a triangle is always equal to 180°.

In ΔBAD and ΔBDC,

m∠ADB = m∠CDB {Given}

BD = BD {Common side in two triangles}

AD ≅ DC {Given}

Using the ASA postulate the two triangles are congruent. Therefore,

m∠BAD= m∠BCD.........equation 1

m∠ABD= m∠CBD

In ΔADC, AD ≅ DC {Given}, therefore, the triangle is an isosceles triangle. Thus,

m∠DAE = m∠DCE.......equation 2

Adding two of the equation 1 and 2,

m∠BAD + m∠DAE = m∠DCE + m∠BCD

∠BAC = ∠BCA

Since in ΔABC, ∠BAC = ∠BCA therefore, the triangle is an isosceles triangle, thus, AB = BC,

BE is the common side between ΔAEB and ΔCEB

Also, m∠ABD= m∠CBD

Therefore, ΔAEB ≅ ΔCEB

Now as ΔAEB ≅ ΔCEB, therefore, AE=EC,

Thus, BE is the median of the isosceles triangle ABC, and for an isosceles triangle, the median opposite to the non-common sides is the perpendicular bisector to the opposite side.

Hence, BD⊥AC.

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The First graph does not have an initial Value

The second graph's solution is (3, -4)

A quadratic graph is a pictorial representation of quadratic functions.

It shows the relationship between a variable on the x-axis and a variable on the y-axis.

Analysis:

The First graph did not either start from the x or y-axis so it does not have an initial value.

The second graph each mark is 0.5 on both axes so the point of intersection of the two graphs is the solution of the graphs which the x- value is 3 and the y-value is -4.

Therefore (3, -4) is the solution of the graph.

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Answer:

D: 4(2a+3)=8a+3

Step-by-step explanation:

4x2a = 8a and 4x3 = 12

Answer:

just saying this so other can get brainliest

Step-by-step explanation:

d

The inverse of the given function is y = (12-x)/6

Given the following function expressed as:

f(x) = -6x +1/2

Replace y with x

x = -6y + 1/2

Make y the subject of the formula

6y = -x + 12

y = (12-x)/6

Hence the inverse of the given function is y = (12-x)/6

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LM=XY, then LM-GH= XY - GH and this illustrates the subtraction property of equality.

It should be noted that the subtraction property of equality simply implies that when the same number is subtracted form both sides, then the two sides will still remain equal.

In this case, when LM=XY, then LM-GH= XY - GH. This illustrates the subtraction property.

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Answer: 60°

Step-by-step explanation:

- the two angles created by CD and EF are vertical angles so they are equal

- one angle is 30° so the other one is 30° and it splits an existing 90° angle so 90-30 = 60 so x is 60°

hope this helps :)

Answer:

∠x=60°

Step-by-step explanation:

Add 90° and 30° then subtract by 180 to find ∠x.

How I got 30 degrees is because of the vertical angle. Vertical angles are always equal.

I got the 90 degrees from the left top side.

180 degrees is the degrees of a straight angle.

90+30=120

180-120=60

Hope this helps!

If not, I am sorry.

Answer:

yes , y = - 3.3x

Step-by-step explanation:

if y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation , then

k = [tex]\frac{y}{x}[/tex]

checking k for each ordered pair in the table

[tex]\frac{-6.6}{2}[/tex] = - 3.3

[tex]\frac{-9.9}{3}[/tex] = - 3.3

[tex]\frac{-13.2}{4}[/tex] = - 3.3

[tex]\frac{-16.5}{5}[/tex] = - 3.3

thus k = - 3.3

so y varies directly with x and the equation of direct variation is

y = - 3.3x

Answer:

24 km/h and 17 km/h

Step-by-step explanation:

We know that when two cyclists are traveling together, they will meet in the same time as if one cyclist with the combined speed of the two cyclists travelled the whole length. We don't know the speeds of the cyclists, so let's assign the one with the slower speed "x", and the one with the faster speed "x+7" the combined speeds is "2x+7"

Since the speed = distance / time, we can plug in the values

2x+7=205/5
2x+7=41
2x=34
x=17
We substitute x into the equation for the speed of the cyclists

Cyclist 1's speed: x, so their speed is 17 km/h
Cyclist 2's speed: x+7, so their speed is 17 + 7, or 24 km/h

Based on the number of coins in the jar, the probability that Nina would not pick a penny or dime is a. 0.36.

The cost of the entire trip to the Cross family should they use the two cars is c. $107.07.

This can be found as:

= Number of quarters, and nickels) / (Number of quarters, nickels, dimes, and pennies)

= (13 + 18) / (13 + 25 + 18 + 30)

= 0.36

= Cost of gas to first car + Cost of gas to second car

= (450/18 x 2.49) + (450 / 25 x 2.49)

= 62.25 + 44.82

= $107.07

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The number of cube that can be packed in the rectangular prism is 30 cubes

Volume of the rectangular prism in terms of small cube and unit cube = 30(1 / 8) ft³

volume of rectangular prism = lwh

where

Therefore,

volume of rectangular prism = 3 / 2 × 1 × 5 / 2  = 15 / 4 ft³

volume of cube = 1 / 2 × 1 / 2 × 1 / 2  = 1 / 8 ft³

number of cube that can be packed in the rectangular prism = 15 / 4 × 8 =  30 cubes

Volume of the rectangular prism in terms of small cube and unit cube = 30(1 / 8) ft³

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The solution of the equation is given by (-2,-1), This is represented by option C.

A system of equations is a set of equation that have a common solution.

The solution of the equations can be determined by using the Elimination and Substitution method

3x-5y = -1

2x-y = -3

-7x = 14

x = -2

Substituting this value in the equation

3 * (-2) -5y = -1

-6 -5y = -1

-5y = 5

y = -1

Therefore, the solution of the equation is given by (-2,-1), This is represented by option C.

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Answer: 50,001²-49,999²=0,2.

Step-by-step explanation:

[tex]50,001^2-49,999^2=(50,001+49,999)*(50,001-49,999)=100*0,002=0,2.[/tex]

Answer:

The area of the shape is 68 cm².

Step-by-step explanation:

We have to calculate the areas of the rectangle and triangle separately, and then add them together.

• Area of rectangle = length × breadth

                                = 30 cm × 2 cm

                                = 60 cm²

• Area of triangle = [tex]\frac{1}{2}[/tex] × base × perpendicular height

                             = [tex]\frac{1}{2}[/tex] × 2 cm × 8 cm

                             = 8 cm²

Adding the areas together = 60 cm² + 8 cm²

                                             = 68 cm²

See below for the description of changes when the dependent and the independent variables are switched

The table of values

When the dependent and the independent variables are switched, the values also become switched on the table.

This means that the table becomes an inverse table of the function

The scatter plot

Switching the variables implies that the original function is being reflected across the line y = x

The description in words

This description is an inverse relation of the original function

The equation

This description is an inverse equation of the original function.

If the initial equation is y = ax + c, the new equation becomes x = ay + c

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There is a significant value in the difference in the value of the car after nine years

The table of values is given as:

Years     1     2     3

Car 1 17,390 16,346.60 15,365.80

Car 2 17,500 16,500 15,500

The values of car 1 have a common ratio of 0.94; this is calculated by dividing the terms of the function

The common ratio implies that the function of car 1 is a geometric function.

The values of car 2 have a common difference of -1000.

The common difference implies that the function of car 2 is a linear function.

Car 1

In (a), we have:

Common ratio, r = 0.94

The initial value is given as:

a = 18,500

So, the function of car 1 is

f(x) = 18500 * 0.94^x

Car 2

In (a), we have:

Common difference, d = -1000

The initial value is given as:

a = 18,500

So, the function of car 2 is

f(x) = 18500 - 1000x

This means that

x = 9

So, we have:

Car 1

f(9) = 18500 * 0.94^9

f(9) = 10600

Car 2

f(9) = 18500 - 1000 *9

f(9) = 9500

10600 is greater than 9500

Hence, there is a significant value in the difference in the value of the car after nine years

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This shows that if s is doubled and h tripled, then V multiplied by 12

Given the formula below expressed as:

V = s²h

If s is doubled and h tripled, the new volume will ne:

V1 = (2s)² * 3h

V2 = 4s² * 3h

V2 = 12s²h

V2 = 12V

This shows that if s is doubled and h tripled, then V multiplied by 12

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The probability that a customer spends 10+ hours or have below $40,000 is 0.6034

Let A represent spending 10+ hours, and B represent having below $40,000

The probability is then calculated using:

P(A or B) = P(A) + P(B) = P(A and B)

This gives

P(A or B)= (476 + 621 - 131)/1601

Evaluate the sum and difference

P(A or B)= 966/1601

Divide

P(A or B)= 0.6034

Hence, the probability is 0.6034

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It is to be noted that the flow rate is 50mL/h for the first instance, and;

100mL/h for the second instance.

Flow rate (Fr) is computed with the following formula:
Fr (mL/h) = Volume (mL)/ Time (Hours)

Time = 1 hour

Volume = 50 mL

It is to be noted that we don't need 500mg because it is already infused into the 50mL solution) hence,

Hourly flow rate = unknown

To compute for Flow Rate (Fr)

Recall that:

Fr (mL/h) = Volume (mL)/ Time (Hours)

Inserting the values we have
Fr = 50/1

Fr = 50mL/h

We have been given the following:
Time = 0.5 hours (30 minutes = 0.5 hours)

Volume = 50mL

It is to be noted that we don't need 500mg because it is already infused into the 50mL solution) hence

Fr = 50/0.5

Fr = 100 mL/h

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Answer:

all real numbers or [tex](-\infty, \infty)[/tex]

Step-by-step explanation:

since both f(x) and g(x) are polynomials, neither of them have restrictions on their domains. Since they can be defined for all real numbers. It's not like the square root which has a domain of (0, infinity), or log x which is defined only from (0, infinity). So adding these two polynomials would result in a domain of all real numbers.

Nicolai would get worth of 13958.62 in five years for an 8% rate of return.

The net gain or loss of an investment over a given period stated as a percentage of the investment's starting cost is known as a rate of return (RoR).

Any type of investment instrument, including real estate, bonds, equities, and fine art, can be subject to a rate of return.

You determine the percentage change from the start of the period to the end when computing the rate of return.

Initial amount=9500

Rate of return=8%

Amount after 5 years=[tex]9500*(1+\frac{8}{100}) ^{5}[/tex]

                                    [tex]=9500*(\frac{108}{100} )^{5}[/tex]

                                   [tex]\\=13958.62[/tex]

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Answer:

[tex]\textsf{C)} \quad 11-60i[/tex]

Step-by-step explanation:

[tex]\textsf{Multiply }\: (6-5i)^2[/tex]

[tex]\implies (6-5i)(6-5i)[/tex]

[tex]\implies 6(6-5i)-5i(6-5i)[/tex]

[tex]\implies 36-30i-30i+25i^2[/tex]

[tex]\implies 36-60i+25i^2[/tex]

[tex]\textsf{Remember that }i^2=-1:[/tex]

[tex]\implies 36-60i+25(-1)[/tex]

[tex]\implies 36-60i-25[/tex]

[tex]\implies 36-25-60i[/tex]

[tex]\implies 11-60i[/tex]

The two general approaches are qualitative and quantitative.

Forecasting is a technique that uses past data as inputs to make future predictions by determining the direction of trends in the future.

It is an estimation methodology that uses judgment, other than numerical analysis. This type of forecasting depends upon the knowledge of most experienced employees and consultants to provide predictions for future outcomes.

It is a data-based math process that teams use to understand performance and predict future based revenue on the data and the patterns. Forecasting results gives businesses the ability to make informed decisions on strategies and processes to ensure continuous success

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Answer: