For each value of y , determine whether it is a solution to 10 < y

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:

5.15%

Step-by-step explanation:

Difference between estimated throw and actual throw

= estimated - actual

= 22.52 - 21.36

= 1.16 m

As a fraction of estimated throw:
1.16/22.52

As a percentage:
1.16/22.52  x 100 =  5.15%

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).

For product=6 and sum=7, the numbers or integers  are 1 and 6.

What exactly are integers?

In mathematics, integers are the collection of positive and negative numbers. Integers, like whole numbers, do not include the fractional element. Thus, integers are numbers that can be positive, negative, or zero, but not fractions. On integers, we can do all arithmetic operations such as addition, subtraction, multiplication, and division. Integers include numbers such as 1, 2, 5, 8, -9, -12, and so on. "Z" is the symbol for integers.

now,

As given product=6 and sum=7  

make factors for 6 i.e 1,2,3,6

from these choose the numbers whose sum=7

and they are 1,6.

Hence,

           For product=6 and sum=7, the numbers are 1 and 6.

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Answer:

He will need 64 ft of fencing

Step-by-step explanation:

To determine the amount of fencing, we need to find the perimeter.

P = 2 (l+w)  where l is the length and w is the width

P = 2(22+10)

P = 2(32)

P = 64

He will need 64 ft of fencing

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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Answer:

[tex]\boxed{\mathrm\bold {4\dfrac{43}{72}}}[/tex]

Step-by-step explanation:

Let the unknown fraction be x

We are given sum of the fractions = 5 3/8 and one of the fractions is 7/9

First convert 5 3/8 to an improper fraction for easier calculation

[tex]5 \dfrac{3}{8} = \dfrac{5\times 8 + 3}{8} = \dfrac{43}{8}[/tex]

Therefore we get:
[tex]\dfrac{7}{9} + x = 5\dfrac{3}{8}\\\\\dfrac{7}{9} + x = \dfrac{43}{8}\\\\[/tex]

Subtract  [tex]\dfrac{7}{9}[/tex]  on both sides to isolate x:

[tex]\dfrac{7}{9} - \dfrac{7}{9} + x = \dfrac{43}{8} - \dfrac{7}{9}[/tex]

[tex]x = \dfrac{43}{8} - \dfrac{7}{9}[/tex]

To compute the right side

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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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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Answer:

350

Step-by-step explanation:

∑ (xy) means the sum of the products of x and y , that is

∑ (xy)

= (7 × 2) + (2 × 5) + (5 × 7) + (9 × 4) + (6 × 2) + (10 × 9) + (9 × 9) + (8 × 4) + (4 × 10)

= 14 + 10 + 35 + 36 + 12 + 90 + 81 + 32 + 40

= 350

Answer:

[tex]x=-2(y+3)^2-4:[/tex]

Vertex: (-4, -3)

Focus: (-33/8, -3)

[tex]x=2(y-3)^2+4:[/tex]

Vertex: (4, 3)

Directrix: (x=31/8)

Step-by-step explanation:

Due to the formula being squared, you know it's going to be a parabola. The 4 at the end is to shift the parabola (-4 = left 4, 4 = right 4). From there you can deduce the vertex and from there the focus and directrix.

Answer:

3

Step-by-step explanation:

BT ≅ TD

[tex]19=5x+4\\15=5x\\3=x[/tex]

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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The answers include the following:

This is referred to as a mathematical operation in which two or more numbers or quantities are added together to form a sum.

3x = 18

x = 18/3 = 6

x+9 =22

x = 22-9 = 13

x/4 = 6

x = 6 × 4 = 24

x-12 =19

x = 19+12 =31

2x + 9 = 25

2x = 25-9 =16

x=16/2 = 8

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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 linear functions for this problem are classified as follows:

a. Parallel.

b. Neither parallel nor perpendicular.

c. Perpendicular.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

They are classified as parallel, perpendicular or neither according to their slopes as follows:

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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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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:

-------------------------------

Definition:

Substitute for cos α:

Answer:e

Step-by-step explanation:t

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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No, since interval contains 0, thus the difference between boys and girls is not significant.

This can be solved using the concept of standard deviation.

Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

Because it makes measures easier to comprehend when the data is spread, standard deviation is significant. The data's standard deviation will increase as the data's distribution becomes more widely scattered.

We have given,

n₁ = 200,    n₂ = 150

x₁ = 48.4     x₂ = 48.9

s₁ = 12.96    s₂ = 11.85

95% confidence interval for difference of mean scores of boys and girls

since, n₁ and n₂ are very large therefore we may use standard normal variate , thus 95% CI is given by:

x₁ - x₂ ± 2μ₂ √(s₁²/n₁ + s₂²/n₂)

now, 2μ₂ = 1.96

∴ CI = (48.4 - 48.9) ± 1.96 √(12.96)²/ 200 + (11.85)²/150

or, CI = (-3.119, 2.1119)

no, since interval contains 0, thus the difference between boys and girls is not significant.

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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 following that are possible units for measuring mass in the metric system include the following below:

B. Kilogram

D. Gram.

This is a quantitative measure of inertia and it is referred to as the amount of matter which is present in a given body.

Options B and D both have the suffix "gram" which represents a metric system and are used in measuring mass unlike anagram which isn't a form of measurement which was why they were chosen as the correct set of options.

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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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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

Step-by-step explanation:

The total distance biked by Yasmin on the first four days can be calculated as follows:

45 + 60 + 68 + 52 = 225 km

To find out how many kilometers she needs to bike on the last day to achieve an average of 58 km per day over the 5 days, we can set up an equation based on the formula for the mean:

(45 + 60 + 68 + 52 + x) / 5 = 58

Where x is the number of kilometers Yasmin needs to bike on the last day. Expanding the equation:

225 + x = 5 * 58

225 + x = 290

Subtracting 225 from both sides:

x = 65

So Yasmin needs to bike 65 kilometers on the last day to achieve an average of 58 kilometers per day over the 5 days

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

Answer: The simple interest on 16000 at 5% per annum for 1.5 years is calculated as:

I = P * r * t

I = 16000 * 0.05 * 1.5

I = 1200

The compound interest on 16000 at 5% per annum compounded half yearly for 1.5 years is calculated as:

A = P * (1 + r/n)^(nt)

A = 16000 * (1 + 0.05/2)^(2 * 1.5)

A = 16000 * (1.0253)^3

A = 16000 * 1.07897

A = 17253.576

The difference between the compound interest and simple interest is:

17253.576 - 1200 = 16053.576

So the difference between the simple interest and compound interest is 16053.576.

Step-by-step explanation:

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.