Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(-13) = 20 B. g(0) = 2 C. g(7) = -1 D. g(-4) = -11

Answer:

46.21%

Step-by-step explanation:

The area of the table top is 1.3 x 1.3 = 1.69 m²

The area of the circular tablecloth is given by πr² where r is the radius of the table cloth

Give diameter of tablecloth is 2m, radius r = 2/2 = 1 m

Area of tablecloth = π · 1² = π

So the excess area of the tablecloth which overhangs

= π - 1.69 = 1.45 m²  (taking π = 3.14)

So the fraction of the tablecloth that overhangs
= Excess area of tablecloth ÷ total area of tablecloth
= 1.45 /π

= 0.4621

As a percentage this would be
0.4621 x 100

= 46.21%

The circumference of the circle is 110 m.

Let us assume that the wire has been cut into two equal halves thus the radius of the circle would be 35 m/2 = 17.5 m

Then;

C = 2πr

C = circumference

r = radius

"pi" is a mathematical constant approximately equal to 3.14 and "r" is the radius of the circle. If the diameter of the circle is known, the radius can be calculated by dividing the diameter by 2.

C = 2 * 3.142 * 17.5

C = 110 m as we can see here

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a) The expression showing the amount of money in the savings accounts compounded at 5% per annum after one year is 600 (1 + 0.05), which equals £630.

b) The expression showing the amount of money in the savings accounts compounded at 5% per annum after one year is 600 (1 + 0.05)^2, which equals £661.50.

A mathematical expression combines constants, numbers, variables, and values with mathematical operations without adding the equation symbol (=).

When the equation symbol is added to mathematical expressions, they become an equation.

In this situation, the compound interest final amount is depicted like an exponential growth function as follows:

f(x) = a(1+r)ˣ

f(x) = exponential growth function

a = initial amount

r = growth rate

x = number of time intervals

Initial amount = £600

Growth rate = 5% or 0.05

x = 1 or 2 years.

f(x) = 600 (1.05)^x

Thus, if $600 is compounded at 5% yearly for 1 or 2 years, the mathematical expressions showing the value of the account are 600 (1 + 0.05) and 600 (1 + 0.05)^2, respectively.

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Answer:

x = 5/2

y = 1/2

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 4x - 6y = 7x + 2y[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4x - 7x = 2y + 6y[/tex]

[tex]\qquad \sf  \dashrightarrow \: 8y = - 3x[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = - \dfrac{3}{8} x[/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{y}{x} = - \dfrac{3}{8} [/tex]

[tex]\qquad \sf  \dashrightarrow \: {y}:{x} = - {3}:{8} [/tex]

That's our required ratio ~

The sample standard deviation weight of the 50 candies is, 0.07 grams.

The amount of variation or dispersion in a set of data values is measured by standard deviation. A statistical calculation is used to determine how far the values vary from the mean (average) value. While a high standard deviation suggests that the data values are more dispersed, a low standard deviation suggests that the data values tend to be close to the mean.

To find the sample standard deviation weight,

we can use the formula:

[tex]s = \sqrt{((1/(n-1))} \sum((x - \bar x)^{2} ))[/tex]

where n is the sample size, x is the weight of each candy, [tex]\bar x[/tex] is the sample mean weight, and sum() means to add up the values.

We can first find the sample mean weight:

[tex]\bar x[/tex]= (0.98 + 0.85 + 0.92 + 0.98 + 0.71 + 0.88 + 0.86 + 0.75 + 0.85 + 0.85 + 0.86 + 0.78 + 0.75 + 0.75 + 0.74 + 0.82 + 0.85 + 0.91 + 0.78 + 0.72 + 0.81 + 0.81 + 0.81 + 0.84 + 0.87 + 0.85 + 0.89 + 0.77 + 0.85 + 0.97 + 0.74 + 0.89 + 0.82 + 0.86 + 0.82 + 0.84 + 0.91 + 0.87 + 0.94 + 0.85 + 0.71 + 0.83 + 0.87 + 0.94 + 0.81 + 0.81 + 0.78 + 0.77 + 0.85) / 50

[tex]\bar x[/tex] = 0.8456

Next, we can calculate the sample standard deviation:

s = √((1/(50-1)) x ((0.98-0.8456)² + (0.85-0.8456)² + ... + (0.77-0.8456)² + (0.85-0.8456)²))

s = sqrt(0.0045916)

s = 0.0678

Rounding to two decimal places, the sample standard deviation weight is 0.07 grams.

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The triangle inequality states that the sum of any two sides of a triangle must be greater than the third side.

Using this principle, we can calculate the range of possible distances between each of the following cities:

Minneapolis and San Francisco: The sum of the distances from Minneapolis to Chicago and from Chicago to San Francisco is 1584 + 355 = 1939. Therefore, the minimum distance between Minneapolis and San Francisco is 1939 - 1584 = 355. The maximum distance between Minneapolis and San Francisco is 1939.

Minneapolis and Houston: The sum of the distances from Minneapolis to Chicago and from Chicago to Houston is 1584 + 1056 = 2640. Therefore, the minimum distance between Minneapolis and Houston is 2640 - 1584 = 1056. The maximum distance between Minneapolis and Houston is 2640.

Minneapolis and New York: The sum of the distances from Minneapolis to Chicago and from Chicago to New York is 1584 + 1018 = 2602. Therefore, the minimum distance between Minneapolis and New York is 2602 - 1584 = 1018. The maximum distance between Minneapolis and New York is 2602.

Chicago and Houston: The sum of the distances from Chicago to Minneapolis and from Minneapolis to Houston is 1584 + 1056 = 2640. Therefore, the minimum distance between Chicago and Houston is 2640 - 1056 = 1584. The maximum distance between Chicago and Houston is 2640.

San Francisco and Chicago: The sum of the distances from San Francisco to Minneapolis and from Minneapolis to Chicago is 355 + 1584 = 1939. Therefore, the minimum distance between San Francisco and Chicago is 1939 - 355 = 1584. The maximum distance between San Francisco and Chicago is 1939.

New York and San Francisco: The sum of the distances from New York to Minneapolis and from Minneapolis to San Francisco is 1018 + 355 = 1373. Therefore, the minimum distance between New York and San Francisco is 1373 - 1018 = 355. The maximum distance between New York and San Francisco is 1373.

Houston and New York: The sum of the distances from Houston to Minneapolis and from Minneapolis to New York is 1056 + 1018 = 2074. Therefore, the minimum distance between Houston and New York is 2074 - 1056 = 1018. The maximum distance between Houston and New York is 2074.

A. Obtuse Triangle

B. Acute Triangle

C. Right Triangle

D. Right Triangle

What is meant by an obtuse triangle?

Obtuse-angled triangles or obtuse triangles are triangles with any one of its angles being an obtuse angle or greater than 90°. Only 180° is equal to the internal angles of an acute triangle.

Given triangles are A. 15,16,17. B 20,18,7. C 17,144,145. D 24,32,40.

If the sum of squares of least two sides is greater than the square of the largest side then it is an obtuse triangle.

If the sum of squares of least two sides is less than the square of the largest side then it is an acute triangle.

If the sum of squares of least two sides is equal to the square of the largest side then it is a right triangle.

A. side lengths are 15,16,17

[tex]15^{2}+16^{2} =481\\17^{2} =289\\481 > 289[/tex]

Therefore this triangle is an obtuse triangle.

B. side lengths are 7,18,20

[tex]7^{2} +18^{2} =373\\20^{2}=400 \\373 < 400[/tex]

Therefore this triangle is an acute triangle.

C. side lengths are  17,144,145

[tex]17^{2} +144^{2} =21025\\145^{2}=21025 \\21025=21025[/tex]

Therefore this triangle is a right triangle.

D. side lengths are  24,32,40

[tex]24^{2} +32^{2} =1600\\40^{2}=1600 \\1600=1600[/tex]

Therefore this triangle is a right triangle.

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The sector angle are 140.4° for bus, 43.2° for bike, 90° for walk and 86.4° for car.

A pie chart is a type of graph where a circle is divided into certain sectors where each sector shows a proportion of the whole.

We have to show the given data in a pie chart where each sector represents a proportion of a type of transportation.

39 students uses bus for transportation.

12 students uses bike for transportation.

25 students walk for transportation.

24 students uses car for transportation.

Total number of students = 39 + 12 + 25 + 24 = 100

Total sector angle of a circle = 360°

Sector angle for bus = (39 / 100) × 360 = 140.4°

Sector angle for bike = (12 / 100) × 360 = 43.2°

Sector angle for walk = (25 / 100) × 360 = 90°

Sector angle for car = (24 / 100) × 360 = 86.4°

Hence the sector angle for each mode of transportation is 140.4° for bus, 43.2° for bike, 90° for walk and 86.4° for car.

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On solving the provided question we can say that the net change will be 17 and average rate of change = 17/1 = 17.

The subject οf mathematics includes quantities and their variatiοns, equations and related structures, shapes and their locations, and places where they can be fοund.

The term "functiοn" refers to the relationship between a set of inputs, each of which has an associated output. A cοnnection between inputs and outputs in which each input leads to a single, distinct result is known as a functiοn.

Each function is given a dοmain and a codomain, or scope. Usually, f is used to denote functiοns (x). input is an x. There are fοur main types of functions accessible. based οn the following factors: οn functions, one-to-one functions, many-tο-one functions, inside functiοns, and on functions.

The functiοn will be

h(4)=2(4²)-4

=32-4

=28

h(5)=2(5²)-5

=50-5

=45

Net change is 45-28 = 17

average rate of change = 17/1 = 17

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Answer:

Step-by-step explanation:

To find the distance between a line and a point, we need to find the perpendicular distance from the point to the line. Here's the step-by-step process:

Find the equation of the line perpendicular to ℓ that passes through point F(-1, 7): Since the slope of line ℓ is -1, the slope of the perpendicular line will be the negative reciprocal of -1, which is 1. To find the equation of the line, we need a point and the slope. Point F(-1, 7) will be used, and the slope is 1.

Using the point-slope form of a line, we can write the equation of the perpendicular line passing through point F as: y - 7 = 1(x + 1). Simplifying, we get: y = x + 8.

To find the point of intersection between the two lines, we can substitute the equation of line ℓ into the equation of the perpendicular line:

-x + 4 = x + 8

Solving for x, we get x = 6. Substituting x = 6 into the equation of line ℓ, we get:

y = -6 + 4 = -2

So, the point of intersection between the two lines is (6, -2).

To find the distance between the point F and the line ℓ, we can use the distance formula:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) is the point F(-1, 7) and (x2, y2) is the point of intersection (6, -2).

So, substituting the values into the formula:

distance = √((6 - (-1))^2 + ((-2) - 7)^2) = √((7)^2 + (9)^2) = √(49 + 81) = √(130) = approximately 11.3

Therefore, the distance between the line ℓ and point F is approximately 11.3 units.

The required piecewise linear relations are f(x) = 4 if [0, 2), and f(x) = -2x + 8 if [2, 4).

A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).

The graph is given in the question, as shown

f(x) = 2x + 4 if [-2, 0]

This the sub-function define between the interval [-2, 0].

f(x) = 4 if [0, 2)

This the sub-function define between the interval [0, 2).

f(x) = -2x + 8 if [2, 4)

This the sub-function define between the interval [2, 4).

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The given triangles can be classified based on their sides and angles as:

1. Isosceles, acute triangle

2. Scalene, right triangle

3. Scalene, obtuse triangle

4 Equilateral

5. Isosceles, right triangle

6. Scalene, acute triangle

7. Equilateral, acute triangle

8. Isosceles, obtuse triangle

Triangles can be classified by both their sides and their angles.

Classification by sides:

Classification by angles:

Thus, using the sides or angles of the given triangles, they are classified as follows:

1. Isosceles, acute triangle

2. Scalene, right triangle

3. Scalene, obtuse triangle

4 Equilateral

5. Isosceles, right triangle

6. Scalene, acute triangle

7. Equilateral, acute triangle

8. Isosceles, obtuse triangle

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The amount of natural oil needed to make 869 liters of Petrolyn oil is given as follows:

1520.75 liters.

The necessary amount of natural oil is obtained applying the proportions in the context of this problem.

Considering the ratio given in the problem, a rule of three is established, as follows:

7 liters of natural oil - 4 liters of Petrolyn oil.

n liters of natural oil - 869 liters of Petrolyn oil.

Applying cross multiplication, the desired amount is obtained as follows:

4n = 7 x 869

n = 7 x 869/4

n = 1520.75 liters.

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Answer:

  see attached

Step-by-step explanation:

You want the difference between horizontal shrink and vertical stretch.

A horizontal shrink compresses a graph horizontally. In the attached figure, the original graph is the red circle. The blue ellipse is that circle shrunk horizontally by a factor of 3. It retains the same height, but is compressed sideways.

A vertical stretch expands the graph vertically. The green ellipse in the attached figure is the original circle stretched vertically by a factor of 3. The horizontal dimension remains unchanged.

You will notice that replacing a variable x by x/k effectively accomplishes a stretch by a factor of k in that variable's direction. Similarly, replacing a variable x by kx accomplishes a compression by a factor of k.

Your question suggests that you have noticed the similarities between vertical stretch and horizontal compression. For some figures, there is basically no difference.

Here are a couple of examples of that:

  line y = x. Vertical stretch by 2: y/2 = x, or y = 2x. Horizontal compression by 2: y = 2x. These equations are identical.

  parabola y = x². Vertical stretch by 4: y/4 = x² or y = 4x². Horizontal compression by 2: y = (2x)² = 4x². These equations are identical.

The differences between stretch in one direction and compression in the other direction are more apparent for figures with multiple reversals of direction. The second attachment shows the sine function (red) vertically stretched (blue) and horizontally compressed (green).

Step-by-step explanation:

you have to be careful when typing questions and particularly formulae and expressions here. automatic text conversion has the habit of transforming e.g. fractions into one line divisions without any brackets.

what your wrote here :

575,000/1 + 4000e^-T = 575,000 + 4000e^-T

that cannot be the function.

I am sure it must be

F(T) = 575,000/(1 + 4000e^-T)

right ?

I am basing the rest of my answer on that assumption.

how many people became ill, when the outbreak began ? that means T = 0.

F(0) = 575,000/(1 + 4000e^-0) =

= 575,000/(1 + 4000×1) =

= 575,000/(4001) = 143.7140715... ≈ 144 people

6 weeks after the outbreak

F(6) = 575,000/(1 + 4000e^-6) =

= 575,000/(1 + 4000/(e^6)) =

= 575,000/(1 + 9.915008707...) =

= 575,000/10.915008707... =

= 52,679.75642... ≈ 52,680 people

limit t -> infinity

F(infinity) = 575,000/(1 + 4000e^-infinity) =

= 575,000/(1 + 4000/(e^infinity)) =

= 575,000/(1 + 0) = 575,000 people

The two pieces relate to the number of minutes used, since there's the 400-minute limit.

Piece #1: When you use less than or equal to 400 minutes:

Cost calculation: $47.35 + $13.94 = $61.29

Piece #2: When you use more than 400 minutes:

Cost calculation: $47.35 + $13.94 + $0.60(x-400)

The x-400 piece is because you're only charged the $0.60/minute beyond the 400 minutes, so 401 minutes needs just 1 minute of extra charge

Cost calculation cleaned up: 61.29 + 0.60x - 240 = 0.6x - 178.71

Now it looks weird to have that -178.71, but keep in mind that this is only used if x > 400.

[tex]C(x) = \left \{ {{61.29 ~~~~~~~~~~~~~~ \text{ if } ~0 \leq x\leq 400} \atop {0.6x - 178.71~~~~ \text{ if } x > 400} \right.[/tex]

Your system might not require the "0≤x", but it technically should be there.

The measure of the angle m∠AEB, found using the angle of intersecting secant theorem, where the measure of the arcs intercepted by the secants are m[tex]\widehat{AB}[/tex] = 54°, and m[tex]\widehat{CD}[/tex] = 66° is; m∠AEB = 6°

The angle of intersecting secant theorem states that the measure of the angle formed by the intersection of two secant is half the positive difference of the arcs intercepted by the secants.

Please find attached the possible drawing in the question, obtained based on the specified parameters and on similar questions on the internet, created with MS Word.

The parameters indicates that we get;

m[tex]\widehat{AB}[/tex] = 54°

m[tex]\widehat{CD}[/tex] = 66°

The angle of intersecting secants theorem indicates that we get;

m∠AEB = (1/2) × (m[tex]\widehat{CD}[/tex] - m[tex]\widehat{AB}[/tex])

Therefore;

m∠AEB = (1/2) × (66° - 54°) = 6°

m∠AEB = 6°

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The end behavior of the given fucntion is [tex]x\rightarrow \infty , y\rightarrow-\infty\\x\rightarrow-\infty, y\rightarrow\infty[/tex].

End behavior of a equation is defined as behavior of graph of the function at the ends of the x-axis.

Given, [tex]4x^{5} +1[/tex].

We have to find the end behavior of the graph.

The corresponding graphical representation is given below:

From the graph it is clearly known that as,

Value of x increases ⇒Value of y decreases.

That is x approaches positive infinity and y approaches negative infinity.

i.e., [tex]x\rightarrow \infty , y\rightarrow-\infty\\x\rightarrow-\infty, y\rightarrow\infty[/tex]

Hence, the end behavior of the given equation is [tex]x\rightarrow \infty , y\rightarrow-\infty\\x\rightarrow-\infty, y\rightarrow\infty[/tex].

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Distance of the house from the base of the cliff is 282.27 m.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

From the figure attached,

AB = Height of the cliff = 60 m

Let the distance between the base of the cliff and the house 'C' = x m

If the angle of depression = 12°

Then angle of elevation of the top of the cliff from the house = 12°

Now from right triangle ABC,

tan12=60/x

x=60/tan 12

x=60/0.21256

x = 282.27 m

Therefore, distance of the house from the base of the cliff is 282.27 m.

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Answer:s

Step-by-step explanation:

There will be about 95 counselors there with the help of expression 2375/50.

What are expressions exactly?

In mathematics, expressions are mathematical claims that consist of at least two sentences that contain numbers, variables, or both, and are linked by an operator in between. Mathematical operations include addition, subtraction, multiplication, and division. For instance, x + y is an equation in which the words x and y are separated by an addition operator. In mathematics, there are two types of expressions: numerical expressions, which include only numbers, and algebraic expressions, which contain both numbers and variables.

e.g. A number is 6 more than half of another number, x. This proposition can be stated mathematically as x/2 + 6. Mathematical expressions are used to answer complex problems.

Now,

Given that Total campers = 2375

and for each cabin there are 2 counselors and 50 campers

then no. of cabins = 2375/50

No. of counselors= 2*no. of cabins

=2*2375/50

=95

Hence,

            There will be about 95 counselors there with the help of expression 2375/50.

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Example: Add 1/4 + 2/4

Solution: Let us add these fractions using the following steps.

Step 1: Check if the denominators are the same. (Here, the denominators are the same, so we move to the next step)

Step 2: Add the numerators and place the sum over the common denominator. This means (1 + 2)/4 = 3/4

Step 3: Simplify the fraction to its lowest form, if needed. Here, it is not needed. So, the sum of the given fractions is, 1/4 + 2/4 = 3/4

The height of the plane to the nearest metres is 1023 metres. Therefore, the answer is A.

A pilot flying over the gulf of Mexico sees an island at an angle of depression of 12 degrees. At this time the horizontal distance from the plane to the island is 4812 metres .

Therefore, the height of the plane can be found as follows:

The situation forms a right angle triangle.

Using trigonometric ratios,

tan 12 = opposite / adjacent

tan 12° = x /  4812

cross multiply

x =  4812 tan 12°

x =  4812 × 0.21255656167

Therefore,

x = 1022.82217476

x = 1023 metres.

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The number of guests that shared one platter is 10.

A. Since 3 people bring a total of 4 platters each, there are a total of 3 x 4 = 12 platters.

If the 120 guests share the platters equally, then each platter is shared by 120/12 = 10 guests. Therefore, 10 guests share 1 platter.

B. Landon's reasoning is incorrect.

While it is true that 3 people bring 4 platters each, the total number of platters is 3 x 4 = 12, not 7.

Therefore, 7 guests cannot be the correct answer. The correct answer is 10 guests share 1 platter, as explained in part A.

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Three people each bring 4 platters of food to a family reunion. The 120 guests all share the platters equally. A. How many guests share 1 platter? Explain your answer. 3.AR.1.2 B. Landon thinks that the answer is 7 guests. He says, " 3+4=7, and 7 rounds to 10 . Then 10×12=120." Do you agree with his reasoning

The correct answer for given dilation will be A and D i.e. Point P is midpoint of AA' and XY⊥AA'.

What precisely is dilation?

Dilation is the process of changing the size of an object or form by shrinking or extending its dimensions based on certain scale variables. For example, a circle with radius 10 unit is decreased to a circle with radius 5 unit. This method is used in photography, arts and crafts, and logo design, among other things. In geometry, there are four basic types of transformations. These are their names:

Properties of Rotation, Translation, Reflection, and Resizing

Dilation properties

The following are some features of shapes that remain constant with dilation changes:

Now,

As The image of A is made on line XY and the image will be A'

then XY⊥AA' because line formed between images is always perpendicular to the plane it is formed on and

P is the midpoint of AA' because we know that AP and A'P are same in a image formation.

Hence,

           Point P is midpoint of AA' and XY⊥AA'.

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The positive coterminal angle less than 360° is, 55°

Angles with the same initial and terminal sides but a multiple of 360° degree difference are known as coterminal angles (or a full rotation). In other words, you can create an angle that is coterminal with the original angle by taking it and adding or subtracting 360 degrees (or any multiple of 360 degrees).

To find a positive angle that is coterminal with -1025°,

we can add or subtract any multiple of 360° until we get an angle between 0° and 360°.

Adding 1080° (which is 3 revolutions of 360°) to -1,025° gives us:

= -1,025° + 1080°

=   55°

Since this angle is less than 360°,

Therefore, a positive angle less than 360° that is coterminal with -1025° is 55°.

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answer c)

cross x  at x = -2, x = 3, and x = 1

the square root tells us that it bounces off that location rather than intercepting

The value equivalent to the expression is (2)√6 and option B is the correct answer.

Finding the prime factors of a given number, such as a composite number, is done through the process of prime factorization. The prime numbers are the only components in these factors. A number with just the number itself and factor 1 is said to be a prime number.

the quantities that are multiplied to produce new quantities. For instance, the factors of 15 are 3 and 5, or 3 + 5 = 15.

The given expression is √24.

Find the prime factorization of 24:

2 | 24

2 | 12

2 | 6

3 | 3

  | 1

Thus, √24 can be written as:

√24 = √(2)²(2)3

√24 = (2)√6

Hence, the value equivalent to the expression is (2)√6 and option B is the correct answer.

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The equation which correctly represents the sentence in discuss as required is; n + 328 = 13.

It follows from the task content that the equation which correctly represents the sentence given in the task content is to be determined.

The word phrase; n and 328 more can be represented as; n + 328.

Therefore, n and 328 more is the same as 13 can be represented as; n + 328 = 13.

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