In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common is labeled AB.The graph represents which system of inequalities?

The expression for the cost is cost = 0.35x + 7.5 and the total cost for a small yogurt with no toppings and a large yogurt with 3 toppings is $8.55

To write an expression to show how much it costs to buy a small yogurt with no toppings,
The expression for the costs of a small yogurt with no toppings and a large yogurt with x toppings will be:

Cost = 2.85 + (4.65 + 0.35x)

Cost = 2.85 + 4.65 + 0.35x

Cost = 0.35x + 7.5

To find the total cost for a small yogurt with no toppings and a large yogurt with 3 toppings, substitute x = 3 into the above expression. That is:

Cost = 0.35x + 7.5

Cost = 0.35(3) + 7.5

Cost = $8.55

Thus, the total cost is $8.55

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Step-by-step explanation:

triangle BOY is congruent with triangle MAN by ASA (angle-side-angle) : 2 angles are the same and the side between them has the same length.

that is sufficient to declare the triangles congruent.

Take the PSI value and divide it by 14.696 or 14.7 to convert PSI to atm.

What is atmospheric pressure?

The force per unit area that an atmospheric column exerts is known as atmospheric pressure, also known as barometric pressure (that is, the entire body of air above the specified area). A mercury barometer (hence the commonly used synonym barometric pressure) can be used to measure atmospheric pressure because it displays the height of a mercury column that precisely balances the weight of the atmosphere over the barometer. An aneroid barometer, which uses one or more hollow, partially evacuated, corrugated metal discs supported against collapse by an inside or outside spring, can also be used to measure atmospheric pressure. The change in the disk's shape with changing atmospheric pressure can be recorded using a pen arm and a clock-driven revolving drum.

The Imperial system of measurement measures pressures in pounds per square inch (PSI). PSI is frequently used to calculate the pressure of liquids or gases (hydraulic pressure).

The model equation is ATM = PSI/14.7

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The given sequence is convergent and the limit is 1.

What is a sequence?

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members. The number of elements is called the length of the sequence.

Here, we have

Given: aₙ = (n/2) sin(2/n)

First, we will find the limit of a given sequence.

aₙ = [tex]\lim_{n \to \infty} (n/2)sin(2/n)[/tex]

We apply L'hospital's rule here and we get

aₙ = [tex]\lim_{n \to \infty} {cos(2/n)(-2/n^2)}/(-2/n^2)[/tex]

aₙ = [tex]\lim_{n \to \infty} cos(2/n)[/tex]

aₙ = 1

We concluded that the given series is convergent.

Hence, the given sequence is convergent and the limit is 1.

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The solution of the expression ( 10z - 3 ) is equal to 37.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the expression is 10z - 3. The value of the expression at z = 4 will  be calculated below,

Evaluate for z = 4,

E = 10x - 3

E = (10)(4)−3

E = (10)(4)−3

E = 37

Therefore, the solution for the expression is 37.

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Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips.

In Sandy's experiment, she used a virtual coin toss app to simulate the results of flipping a coin 100 times, 500 times, and 1,000 times. The experimental probability is the probability obtained from the observed outcomes of the experiment, while the theoretical probability is the probability calculated based on mathematical principles and assumptions.

Based on the information given, it is stated that Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips. This suggests that the observed outcomes of the 100 flips aligned more closely with the expected outcomes based on the theoretical probability.

It is important to note that experimental probability tends to converge towards theoretical probability as the number of trials increases. Therefore, it is expected that the experimental probability would be closer to the theoretical probability in the experiment with 1,000 flips compared to the experiment with 500 flips.

Without further information, it is not possible to determine whether Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments. However, based on the given statement, it can be concluded that Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips.

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In Sandy's experiment, the experimental probability was closest to the theoretical probability in the experiment with 100 flips.

In Sandy's experiment, she used a virtual coin toss app to simulate the results of flipping a coin 100 times, 500 times, and 1,000 times. The experimental probability is the probability obtained from the observed outcomes of the experiment, while the theoretical probability is the probability calculated based on mathematical principles and assumptions.

Based on the information given, it is stated that Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips. This suggests that the observed outcomes of the 100 flips aligned more closely with the expected outcomes based on the theoretical probability.

It is important to note that experimental probability tends to converge towards theoretical probability as the number of trials increases. Therefore, it is expected that the experimental probability would be closer to the theoretical probability in the experiment with 1,000 flips compared to the experiment with 500 flips.

Without further information, it is not possible to determine whether Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments. However, based on the given statement, it can be inferred that the experimental probability was closest to the theoretical probability in the experiment with 100 flips.

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9 m, 23 m, and 23 m are the triangle's measurements.

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Answer:

A

Step-by-step explanation:

Surface area of sphere is 4 pi r^2

                     144 pi   = 4 pi r^2

                          144 pi / (4 pi) = r^2

                             36 = r^2

                               r = 6 ft

The ratios of  the areas in the following sets or similar triangles are:

1. 9:1,         2. 4:1,         3. 25:9,

4. 46:9,     5. 9:4,        6. 4:1,

7. 25:4,      8.9:4,         9. 9:1.

Having three edges and three vertices, a triangle is a three-sided polygon. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.

Given a set of triangles is similar,

for similar triangles the ratio of their corresponding sides is equal,

so A/a = B/b = C/c

where A, B, and C are sides of larger triangles and a, b, and c are sides of small triangles.

area of small triangle = 1/2*b*h

here b =base and h = height

area of large  triangle = 1/2*B*H

here B =base and H = height

the ratio of areas = area of the large  triangle/area of the small triangle

the ratio of areas = [1/2*B*H]/[1/2*b*h]

the ratio of areas = BH/bh

since the triangles are similar, B/b = H/h

the ratio of areas = B²/b²

or the ratio of areas = (SIDE)²/(side)²

1. given side of large triangle = 3

side of small triangle = 1

ratio of areas = 3²/1²

ratio of areas = 9/1 = 9:1

2.  given side of large triangle = 4

side of small triangle = 2

ratio of areas = 4²/2²

ratio of areas = 16/4 = 4:1

3. given side of large triangle = 5

side of small triangle = 3

ratio of areas = 5²/3²

ratio of areas = 25/9 = 25:9

similarly for other questions,

4.ratio of areas = 16/9 = 16:9

5. ratio of areas = 9/4 = 9:4

6. ratio of areas = 64/16 = 4:1

7. ratio of areas = 25/4 = 25:4

8. ratio of areas = 36/16 = 9:4

9. ratio of areas = 4/1 = 4:1

Hence the ratios are as possible.

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The volume of cone B is calculated as: 384 cm³.

If the ratio of the surface area of cone A to the surface area of cone B is 25:4, then the ratio of the radii of the cones is 5:2 (since the surface area of a cone is proportional to the square of the radius).

Since the cones are similar, the ratio of their volumes is also the ratio of the cubes of their radii, which is 125:8.

So, if the volume of cone A is 6000 cm³, then the volume of cone B is (6000 * 8) / 125 = 384 cm³.

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Applying inequality, the minimum height of her brother is: 26 inches.

An inequality is a mathematical statement that shows the relationship between two values or expressions, where one value is either greater than, less than, greater than or equal to, or less than or equal to the other value. It is represented using symbols such as ">", "<", "≥", or "≤".

Let's call the height of Adriana's little brother "x".

So Adriana's height is 2x + 8 inches.

And because Adriana is at least 60 inches tall, we can write the following inequality:

2x + 8 ≥ 60

Subtracting 8 from both sides:

2x ≥ 52

Dividing both sides by 2:

x ≥ 26

So the minimum height of Adriana's little brother is 26 inches.

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The solution to the initial value problem is y(t) = 5e^8t.

y(t) = 5e^8t

This is a separable differential equation. Separating the variables, we have

dy/dt = 8y

dy = 8y dt

Integrating both sides, we have

∫dy = ∫8ydt

y = 4e^8t + C

To find C, we use the initial condition, y(1) = 5

5 = 4e^8(1) + C

C = 5e^-8

Substituting C into the equation, we have

y(t) = 5e^8t

The solution to the initial value problem is y(t) = 5e^8t.

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Answer:

is equal to the number minus six.

This strategy works for all cases with 40 or fewer total tiles. The pattern observed here is that XORing pattern.

If there are 5 red tiles and 7 blue tiles, the binary representation of these numbers is 101 and 111, respectively. Taking the bitwise XOR of these numbers gives 010, which is 2. Hence, the player should take 2 tiles of either color, leaving 3 tiles of one color and 5 tiles of the other color. This leaves the other player in a losing position.

The pattern observed here is that XORing all the numbers together effectively cancels out all the common bits, leaving only the unique bits. The player should then take a number of tiles such that the unique bits become 0.

Unique bits refer to the concept of binary representation of numbers in mathematics. The binary system is a base-2 numeral system where each digit can either be 0 or 1. Unique bits refers to the distinct and non-repeating number of binary digits used to represent a number. It is a measure of the number of bits needed to represent a unique number.

The unique bits in mathematics is a concept that is widely used in computer science, information theory and cryptography. The more unique bits used, the greater the number of unique combinations that can be produced and hence, the greater the accuracy in representation. For example, using 8 unique bits in binary representation can result in up to 256 unique combinations, compared to using only 7 unique bits, which can only result in 128 unique combinations. Unique bits plays a crucial role in ensuring the accuracy and efficiency of information representation and transmission.

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Hooke's Law states that when a spring is extended, the force is proportional to how much longer it is than its equilibrium length. The spring constant can be calculated using the formula k = -F/x.

Hooke aimed to show how a spring's elasticity and the forces acting on it are related.

According to Hooke's Law, a spring's extension is proportional to the load placed on it.

As long as the load does not exceed the material's elastic limit, a variety of materials will adhere to this rule.

F = k(x - x0), where x represents the spring's displacement from equilibrium and k is the spring constant.

The negative sign indicates that the force represented by the spring is a restorative force and operates in the opposite direction.

According to Hooke's Law, when a spring is stretched, the force applied is proportional to the lengthening from the equilibrium length.

The formula k = -F/x, where k is the spring constant, can be used to get the spring constant. F stands for force, and x is for the variation in spring length.

Therefore, Hooke's Law states that when a spring is extended, the force is proportional to how much longer it is than its equilibrium length. The spring constant can be calculated using the formula k = -F/x.

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The option that will give you the most money after 2 years is option (a)

Option (a)

Here, we have

Principal, P = $1000

Rate, r = 12% = 0.12

Number of times, n = 4

Time, t = 2

The formula of amount is

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

So, we have

A = 1000 * (1 + (0.12/4))^(4 *2)

A = 1266.77

Option (b)

Here, we have

Principal, P = $1000

Rate, r = 6% = 0.06

Time, t = 2

The formula of amount is

A = P * e^(rt)

So, we have

A = 1000 * e^(0.06 * 2)

A = 1127.50

1266.77 is greater than 1127.50

Hence, the option is option (a)

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Answer:

The equation is y = 1,460e^(2%)x, and the balance will be $2,067.54 in 8 years

An increase in consumer incomes would lead to a decrease in the demand and price of potatoes, and an increase in supply and quantity.

When consumer incomes increase, the demand for inferior goods such as potatoes usually decreases. This is because as people's incomes rise, they tend to switch to buying more superior goods, which are generally more expensive than inferior goods.

At the same time, the supply of potatoes may also increase as farmers respond to the potential for higher prices by growing more potatoes.

With both a decrease in demand and an increase in supply, the market price for potatoes is likely to fall. The quantity of potatoes supplied will likely increase as well, as the lower price attracts both consumers and producers.

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The function is continuous on [−2,2], and its derivative is f′(x)=4 x 3−9 x 2. Because x=9/4 is not in the interval [−2,2], the only critical point occurs at   x = 0 which is (0,−1).

What is meant by function ?

To the complete questions is;    

Find the maximum and minimum values of f(x)= x 4−3 x 3−1 on [−2,2].

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The parabola function has a minimum value of -4.

The given parameters are:

Declines through (-5,-2), (-3,-4)

Rises through  (-2, -3), (-1, -2), (0, 0), (0, 2) and (1, 4)

Because the parabola declines before it rises, it means that the function has a minimum

From the point of decline;

-4 is less than -2

Hence, the parabola function has a minimum value of -4.

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Answer:14 meters

Step-by-step explanation:

The value of the limit for the given function [tex]\lim_{x \to 5} \frac{x^2 - 5x}{x^2 - 25}[/tex] = 1/2.

A general technique for assessing indeterminate forms like 0/0 or / is the L'Hospital rule. L'Hospital's rule is applied to calculate the limits of indeterminate forms for calculus derivatives. It is possible to use the L Hospital rule many times. This rule is still valid after being applied, and it will take any indefinite form. L'Hospital's Rule cannot be applied if the issue is not of the indeterminate types.

The given function is:

[tex]\lim_{x \to 5} \frac{x^2 - 5x}{x^2 - 25}[/tex]

Substituting the value of limit we can see that the function is of the indeterminate form 0/0.

Using the L'Hospital rule we have:

[tex]\lim_{x \to 5} \frac{x^2 - 5x}{x^2 - 25}\\\\\lim_{x \to 5} \frac{2x - 5}{2x}\\[/tex]

Substitute the value of limits:

[tex]=\frac{2(5) - 5}{2(5)}\\ \\=\frac{1}{2}[/tex]

Hence, the value of the limit for the given function [tex]\lim_{x \to 5} \frac{x^2 - 5x}{x^2 - 25}[/tex] = 1/2.

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Answer:

Step-by-step explanation:

Given the function f(x) = 4 - 9x, the indicated values are:

(a) f(-8) = 4 - 9(-8) = 4 + 72 = 76

(b) f(0) = 4 - 9(0) = 4

(c) f(9) = 4 - 9(9) = 4 - 81 = -77

So, the values of f(-8), f(0), and f(9) are 76, 4, and -77, respectively.

Answer:

A) <5 and <6 are commentary

B) 72

C < 4 = 22

<3 = 68

Step-by-step explanation:

A) The square drawn over the 2 angles shows that the angles together measure 90 degrees

B) 90 - 18 = 72

C) 4x -10 + 5x + 28 = 90  Combine like terms

9x + 18 = 90  Subtract 18 from both sides

9x = 72   Divide both sides by 9

x = 8

<4

4x - 10

4(8) - 10

32 - 10

<4 = 22

<3

5x + 28

5(8) + 28

40 + 28

68

<3 = 68

Answer:

Part A: Yes, ∠5 and ∠6 are complementary angles because they add up to 90°.

Part B: If the measure of ∠6 is 18°, then the measure of ∠5 is 72° because ∠6+∠5=90° so 90°-18°=72°.

Part C: ∠4+∠3=90°

(4x-10)°+(5x+28)°=90°

add 10 to both sides

4x+5x+28=100

subtract 28 from both sides

4x+5x=72

combine like terms

9x=72

divide both sides by 9

x=8

now plug 8 in for x

∠4=(4(8)-10)°

∠4=22°

∠3=(5(8)+28)

∠3=68°

22°+68°=90°

The required inequality that shows the possible value of x is x < 404/3

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Let's call the number we're trying to find "x". Then, the inequality can be written as:

11 + (3/4)x < 112

To solve for x, we'll isolate x on one side of the inequality. First, we'll subtract 11 from both sides.

(3/4)x < 101

Next, we'll divide both sides by (3/4).

x < (4/3) * 101 = 404/3

So, all values of x that are less than 404/3 satisfy the inequality. The possible values of x are all numbers less than 404/3.

x < 404/3

or written as an interval:

x ∈ (-∞, 404/3)

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Atomic vectors typically come in four different types: logical, integer, double, and character. Complex and raw are the two less common varieties.

An atomic vector can have any properties, with the exception of a dimension attribute, and is either logical, integer, numeric, complex, character, or raw (like matrices). For example, a matrix or NULL are not atomic vectors, but a factor is. This is, in essence, the same as is. atomic. Using the built-in int function, one can transform texts in Python into integers. Any Python data type can be sent to the int() function to be transformed into an integer.

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The exact surface area of the cone having height 3 unit and radius 4 unit,  113.09734 unit²

An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².

Given that,

A Cone having,

Radius  r = 4 unit

Height  h = 3 unit

Surface Area = ?

Formula for the Cone,

Surface Area of Cone = πrl  + πr²

where, l = [tex]\sqrt{h^{2}+r^{2} }[/tex]

Surface Area of Cone = πr([tex]\sqrt{h^{2}+r^{2} }[/tex]) + πr²

                                     =  πr([tex]\sqrt{h^{2}+r^{2} }[/tex]  + r)

                                     =  4π([tex]\sqrt{3^{2}+4^{2} }[/tex]  + 4)

                                     =  4π(5 + 4)

                                     =   20π

                                     ≈   113.09734

Thus, the surface area of cone is  113.09734 unit²

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Teresa would need to work 10 weeks in order to earn the same total amount as the second job.

Assuming Teresa takes the first job, she would need to work for 10 weeks in order to earn the same total amount as the alternate job. The total amount earned from the first job can be calculated by (400 x 10) + 200 = 6000. The total amount earned from the second job can be calculated by (420 x 10) = 4200. Thus, in order to earn the same amount from the total of both jobs, Teresa would need to work 10 weeks at the first job. This can be expressed by the following formula: (400 x n) + 200 = 420 x n, working for n is the number of weeks. Solving for n gives n = 10.

Thus, Teresa would need to work 10 weeks in order to earn the same total amount as the second job.

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The surface area of a cone is given by the formula:

S = πl + πr^2

Solving for l, we can start by isolating l on one side of the equation:

S - πr^2 = πl

Dividing both sides by π:

(S - πr^2) / π = l

Therefore, the length l can be found by subtracting the product of π and r^2 from the surface area S, and dividing the result by π.

The white paint did she use to paint her bedroom walls will be 6.975 pints.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Molly uses 9.3 pints of blue paint and white paint to paint her bedroom walls 25% of this amount is blue paint.

The amount of white paint will be calculated as:-

Amount = [ 9.3 x ( 100 - 25 )%]

Amount = [ ( 9.3 x 0.75 ) ]

Amount = 6.975 pints.

Hence, the amount of white paint used for painting is 6.975 pints.

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