if f(5) = 14, f ' is continuous, and 6 f '(x) dx 5 = 19, what is the value of f(6)? f(6) =

The inequality graph is interpreted to have the equation as;

y  > ⁻³/₄x - 3

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

From the given graph, the y-intercept is seen to be -3.

The slope is gotten by using two coordinates from the formula;

m = (y₂ - y₁)/(x₂ - x₁)

(0, -3) and (-4,0)

m = (0 - (-3))/(-4 - 0)

m = -3/4

Thus, equation of line is;

y = ⁻³/₄x - 3

Since the upper part of the inequality is shaded and the line is a dashed line, then the symbol is greater than and it is expressed as;

y  > ⁻³/₄x - 3

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The total amount of time Michelle's family spends at Mount Rushmore is 93.38 minutes, which is equivalent to 1 hour and 33.38 minutes.

The time Michelle and her family spend watching the movie in the visitor center is 14/60 of an hour or 14 minutes. We are told that this accounts for 15% of the total time they spend at Mount Rushmore, so to find the total amount of time they spent at Mount Rushmore, we need to divide the time spent watching the movie (14 minutes) by the percentage of the total time this accounts for (15%). This gives us the equation:

time = 14 / (15/100)

time = 14 × (100/15)

time = 14 × (6.67)

time = 93.38 minutes or 1 hour and 33.38 minutes.

So the total amount of time Michelle's family spends at Mount Rushmore is 93.38 minutes, which is equivalent to 1 hour and 33.38 minutes.

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The equation used to determine the value of the car ,v, after 5 years is V= 12500*4.5*5/100-D.

An equation represents equality of two or more mathematical expression.

When someone asks you to solve an equation, then they usually mean to find the values of the unknowns for which that equation would be true (the equality between expressions should hold true for those values).

Solutions to an equation are those values of the variables involved in that equation for which the equation is true.

Given;

A car depreciates ( loses value ) at a rate of 4.5% annually

Greg purchased a car for 12,500

Time= 5years

Here, the depreciation is equal to the simple interest but in depreciation

So, Let the depreciation be D

D=P*R*T/100

D=12500*4.5*5/100

=2812.5

Now, value of car v;

V= 12500*4.5*5/100-D

Therefore, the equation will be V= 12500*4.5*5/100-D

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The measure of angle R is 16.1°

Law of Sines In trigonometry, an equation relating the lengths of the sides of any triangle to the sines of its angles.

Given that, a triangle RST, with one angle S = 39° and RT = 25, ST = 11

We need to measure the angle R,

Using law of sine,

Sin R / TS = Sin T / RS = Sin S / RT

Sin R / 11 = sin 39° / 25

Sin R = 11 × sin 39° / 25

Sin R = 0.2769

R = sin⁻¹(0.2769)

R = 16.1

Hence, the measure of angle R is 16.1°

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The surface area of the right triangular prism is 108 ft²

An equation is an expression that shows the relationship between two or more numbers and variables.

The surface area of a three dimensional figure is gotten by individually adding each of their respective areas of the surfaces.

From the net and the diagram shown:

A = 5 feet, B = 4 feet, D = 3 feet and C = 8 feet

Surface area = area of triangle 1 + area of triangle 2 + area of rectangle 1 + area of rectangle 2 + area of rectangle 3

Surface area = (0.5 * B * D) + (0.5 * B * D) + (A * C) + (C * B) + (D * C)

Substituting:

Surface area = (0.5 * 4 * 3) + (0.5 * 4 * 3) + (5 * 8) + (4 * 8) + (3 * 8) = 108 ft²

The surface area is 108 ft²

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If BC = 8 cm, ∠B = 60°and ∠C = 70° then the triangle is an acute triangle and the value of ∠A is 50.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

BC = 8 cm

∠B = 60° and ∠C = 70°.

Now,

The sum of all the angles is 180.

This means,

∠A + ∠B + ∠C = 180

∠A = 180 - 130

∠A = 50

Now,

The triangle is an acute triangle since all the angles are acute.

i.e less than 90.

Thus,

The triangle is an acute triangle.

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There are 4 steps to build a VI to compute the variance of an array x.

Here is a VI in LabVIEW to compute the variance of an array x:

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The  temperature when the plane reaches an altitude of ​3000ft is 51.8 F

Temperature is the degree of hotness or coldness of an object.

Given here: the temperature drops every 1.2 F for every thousand feet ascend.

Thus if the temperature on the ground is 55.4 F

When the plane ascends to 3000 feet the number of temperature drops would be 3 .

Thus drop in temperature is 1.2×3=3.6 F

Therefore the temperature at an altitude at an altitude of 3000 ft. is

55.4-3.6=51.8 F

Hence, The  temperature when the plane reaches an altitude of ​3000ft is 51.8 F

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Answer:

Below

Step-by-step explanation:

Domain is the 'x' values a function can have   for this one  {1,3,4,5}

Range is the 'y' values a function has   {6,8,10}

When determining sample size for the first test, it is most important to Weigh the potential consequences of a test that does not lead to improvement against the belief in success.

When evaluating a patient, a patient assessment form is used to evaluate the patient's potential diagnosis and the appropriate course of therapy. To prevent misdiagnosis and ensure that the right therapy is given, it is crucial to gather relevant data. In order to register patients for operations provided by medical institutions, patient registration forms are utilised. Our free patient registration forms will efficiently capture patient information online, streamlining the registration and onboarding process whether you need to register new patients for your hospital, clinic, health centre, or private practise. Usability testing may find and support data-driven design decisions that have been drawn from practitioner usage of the system in a hectic office setting. Health care safety may be improved by using human factors understanding of HCI design and its effects on human performance.

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Answer: It will take 63 minutes for the group to make a wood pile of 45 sticks

Step-by-step explanation:

i hope this helps if so pls mark brainliest !!

It has n-k basic variables. The basic variables are the variables that are not free variables, and they are the ones that can be solved for as part of the general solution.

The general solution of a system of m linear equations in n variables contains k free variables. This means that there are k variables that have no restrictions and can take on any value. The remaining n-k variables are the basic variables, which are the ones that can be solved for as part of the general solution. The basic variables are the ones that have restrictions and need to be solved for in order to determine the solution of the system. In other words, the number of basic variables is equal to the number of variables minus the number of free variables. Thus, the general solution of the system has n-k basic variables.

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They sold 400 student tickets and 200 student tickets.

And at a certain performance, they sold 100 adult tickets and 200 student tickets.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

Given, Let 'x' represents the number of adult tickets and 'y' represent the number of student tickets.

So, The two equations can be formed as,

x + y = 600 and 7.5x + 4.5y = 3300.

Multiplying equation 1 by 7.5x we have 7.5x + 7.5y = 4500 and subtracting it from equation 2 we have,

- 3y = - 1200.

y = 400 and hence x = 200.

At a certain performance, they sold twice as many student tickets as adult tickets.

y = 2x.

x + y = 300.

x + 2x = 300.

3x = 300

x = 100 and hence y = 200.

100×7.5 + 200×4.5 = 750 + 900 = 1650.

So, they were 3300 - 1650 = $1650 short.

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Answer:2 45833333333/50000000000

If the price paid for a certain item is $40 and the consumer surplus is $4, then the maximum buying price for that item is $44 .

The Consumer's Surplus is defined as the difference between the maximum price a consumer is willing to pay for an item and the actual price paid for the item.

If the price paid for the item is $40 and the consumer's surplus is $4, then the maximum buying price for that item can be calculated as :

⇒ Maximum buying price = Price paid + Consumer's surplus

Substituting the values of Price paid and consumer surplus ,

we get ;

⇒ $40 + $4

⇒ $44

Therefore , the maximum buying price for that item is $44 .

The given question is incomplete , the complete question is

If the price paid for a certain item is $40 and the consumer surplus is $4, then what is the maximum buying price for that item ?

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Aaron should answer 3 open-ended questions and 0 multiple-choice questions to get a maximum of 3 * 20 points/question = 60 points

Aaron has 45 minutes to answer the questions, so he has 45 minutes / 15 minutes/question = 3 open-ended questions that he can answer.

For the remaining questions, he has 45 minutes - (3 * 15 minutes) = 45 minutes - 45 minutes = 0 minutes.

So he cannot answer any more open-ended questions.

He can answer 0 minutes / 1 minute/question = 0 multiple-choice questions.

Therefore, Aaron should answer 3 open-ended questions and 0 multiple-choice questions to get a maximum of 3 * 20 points/question = 60 points.

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Considering the Question G(x) = -x + 5 is the equation for such reflections at f(x) = x + 5 from across y-axis.

Similar to a vertical ruler is the y-axis. It displays the location of an object on a two-dimensional Cartesian graph with in y (vertical) plane. On a graph, it serves as the starting point, or "zero," from which to calculate how far a tip is from right or left (horizontally).

The sign of the x-coordinate is altered by reflection across the y-axis, while the y-coordinate remains constant. By changing the sign of x, we may represent f(x) = x + 5 from across y-axis as g(x) = -x + 5. G(x) = -x + 5 is the equation for the reflections for f(x) = x + 5 from across y-axis.

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Answer: See below

Step-by-step explanation:

A) The best way to estimate average speed is to make sure that each number is a whole number (with no decimals). This will make division much easier. The number of meters is already a whole number, but to make the number of minutes a whole number, we must round. Because the number after the decimal is greater than 5, that means we will round up, making the value of minutes 5. Now we can estimate 1500 metres/5 minutes = 300 metres/minute

As a little rounding tip, you can use this mnemonic: 4 and below, let it go (round down). 5 and above, give it a shove (round up)!

B) To do this part, we can simply plug the following into the calculator:

1500 metres/4.67 minutes = 321.2 metres per minute

Hope this helps!

At the point of tangency, a tangent to a circle is perpendicular to the radius.

A tangent is a line that extends from a point on the circle to two points that are eternally close to one another. To put it another way, we can say that tangents are lines that precisely cross a circle at a certain location. Where the tangent touches the circle is known as the point of tangency. An angle is tangent to the radius at the point of tangency. This is a key component of geometric constructions and proofs, and as such, it is related to a number of theorems. One by one, we will examine them.

Theorem: 1

By connecting the center with the point of tangency, a radius is produced. A circle's tangent at a given location is perpendicular to its radius. Simply adhere to the diagram below: Here AB⊥OP

Theorem:2  

According to this theorem, two tangents traced to a circle from a single exterior point have equal numbers of tangent segments. Line connecting the exterior point and the point of tangency is referred to as a tangent segment.

Hence the theorem of the tangent of circle mentioned above.

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Complete question:

At the point of tangency, a tangent to a circle is ______ to the radius.

Answer:

Step-by-step explanation:

P = k/Q where k is a constant.

P is 6 when Q is 24, so:

6 = k / 24

k = 6*24 = 144

so, the relation is P = 144/Q.

a. When P = 8,

8 = 144/Q

8Q = 144

Q = 144/8 = 18

b. When Q = 16

P = 144/16

  = 9.

Shapes A and B are enlargements of x by a scale factor of -1 because they are mirror images of x. Shape C is not an enlargement of x by scale factor -1 because it is not a mirror image of x. Therefore, the option is A and B.

An enlargement by a scale factor of -1 means that the image is flipped and has the same size as the original.

Therefore, any shape that is a mirror image of x is an enlargement of x by scale factor -1. Looking at the shapes, we can see that shapes A and B are mirror images of x, so they are enlargements of x by scale factor -1.

Shape C is not a mirror image of x, so it is not an enlargement of x by scale factor -1. Therefore, the answer is A and B.

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Answer:

  Sn = (7 -(6n +7)3^-n)/4

Step-by-step explanation:

You want the sum of n terms of the series 2/3 +5/9 +8/27 +11/81 +....

The sums of n terms for n = 1 .. 5 are ...

  2/3, 11/9, 41/27, 134/81, 416/243

We recognize the denominators as powers of 3. The numerator sequence is ...

  2, 11, 41, 134, 416, ...

Differences are ...

  9, 30, 93, 282

And second differences are ...

  21, 63, 189

We note that these have a common ratio of 3, leading us to speculate that the numerator sequence can be written as the sum of a linear expression and a power of 3.

Assuming the sequence of numerator terms is of the form ...

  a·3^n +bn +c

We can write equations for a, b, c:

  a·3 +b·1 +c = 2 . . . . . . for n = 1

  a·9 +b·2 +c = 11 . . . . . .for n = 2

  a·27 +b·3 +c = 41 . . . . for n = 3

These equations can be solved for a, b, c using any of your favorite techniques. The attached calculator output shows the values to be ...

  a = 1.75 = 7/4

  b = -1.5 = -6/4

  c = -1.75 = -7/4

Then the sum of n terms can be written as ...

  [tex]\boxed{S_n=\dfrac{7\cdot3^n -6n-7}{4\cdot3^n}}[/tex]  

__

Additional comment

The n-th term of the series is (3n-1)/3^n. This can be decomposed into two sums: 3(n/3^n) -1/3^n. The latter is the well-known sum of a geometric series. The sum of the first term is less well-known: ∑(k/3^k) = (3(3^n-1)-2n)/(4·3^n).

The complementary angle is 19 degrees and the supplementary angle is 109 degrees.

Complementary angles can be defined as the angles whose sum is 90 degrees.

The ‘c’ in complementary angle can be used to form 9 in 90 degrees. Supplementary angles are angles whose sum is 180 degrees. The ‘s’ in supplementary angle can be used to form 8 in 180 degrees

If the intersection of P and Q creates a 71 degree angle,

then 90 – 71 = 19 degrees is its complementary angle. Its supplementary angle is 180 – 71 = 109 degrees.

Therefore, The complementary angle is 19 degrees and the supplementary angle is 109 degrees.

So, The answer is D)

The complementary angle is 19 degrees and the supplementary angle is 109 degrees.

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Answer:

:)

Step-by-step explanation:

Just divide 1,004.7 by 59.1

Step-by-step explanation: To find the values of l and m, we need to solve the equation 15 - 28i = 3l + (4m)i for l and m.

First, we can move all the terms with i to one side of the equation:

15 = 3l + 4mi

-28i = 4mi

To solve for m, we can divide both sides by 4i:

-28i/4i = m

m = -7

Now that we know the value of m, we can substitute it back into the equation to solve for l:

15 = 3l + 4(-7)i

15 = 3l - 28i

3l = 15 + 28i

To solve for l, we can divide both sides by 3:

l = (15 + 28i)/3

So the values of l and m are l = (15 + 28i)/3 and m = -7

Answer:15

Step-by-step explanation:

Step-by-step explanation:

it is a arithematuc sequence because it has a common difference of 5

so the general term is Tn = 1 + (n-1)5

also the 5th term is T(5) = 1 + (5-1)5 = 21

The distance that Ann travelled is; 3.61 ft

Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.

Ann and Elena form the vertical leg of a right angle triangle of length = 3ft. Elena and Rob form the opposite side of the right angle triangle of length = 2 ft.

Using the Pythagorean theorem to find the distance that Anna traveled which is the length of the hypotenuse of the right angle triangle; let that length be x. Then:

x = √(3² + 2²)

x = √ 13

x = 3.61 ft

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At the haunted mansion, 6114 people were  scared by a group of 135 ghosts and 273 witches.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

According to the question each ghost must scare 19 people that means 135 ghost will scare:

135 ghosts x 19 people = 2,565 people......................(i)

And each witch must scare 13 people-no more and no less i.e 273 witches will scare:

273 witches x 13 people = 3,549 people.....................(ii)

Adding (i) and (ii) we get;

2,565 + 3,549 = 6114 people

Therefore, 6114 people were scared by a group of 135 ghosts and 273 witches.

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Answer:

Step-by-step explanation:

y=mx+c

7=2*-4+c

7=-8+c

7+8=c

15=c