Sebastian has
x nickels and
y pennies. He has at least 20 coins worth at most $0.65 combined. Solve this system of inequalities graphically and determine one possible solution.

Answer:

674

Step-by-step explanation:

The maximum volume of the box is approximately 128.0in³.

Since the cardboard has dimensions of 8 inches by 12 inches, the largest possible length and width of the box are both 8 inches (since 8 is the smaller of the two dimensions).

Then we can cut two 8-inch by 8-inch squares from the cardboard to make the top and bottom of the box, and then cut out four 8-inch by 2-inch rectangles from the remaining cardboard to make the sides of the box.

The height of the box will be the same as the width of the 8-inch by 2-inch rectangles, which is 2 inches. Therefore, the maximum volume of the box is:

V = l × w × h = 8 in × 8 in × 2 in = 128 in³

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According to the given data,the equation y = 0.5x is correctly represented by the graph.

Graphs are visual representations of data or mathematical functions. They are useful tools for displaying and analyzing information in a clear and concise way. Graphs can be used to show trends, patterns, and relationships between different variables.

The statement "The equation y = 0.5x is correctly represented by the graph" is true.

The given equation y = 0.5x represents a proportional relationship between the variables x and y, where y is half of x. This means that as x increases, y increases in proportion to x.

The graph shown is a straight line that passes through the points (0,0) and (9,3), and this line represents the proportional relationship between x and y described by the equation y = 0.5x.

Therefore, the equation y = 0.5x is correctly represented by the graph.

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Answer:

3(x - 4) + 5x can be simplified to 8x - 12.

Answer: 8x - 12

Step-by-step explanation:

3(x - 4) + 5x

distribute = 3x - 12 + 5x

simplify = 8x - 12

The area of ​​the triangular pyramid is 787.27 mm²

The volume of a right-angled triangular pyramid  is given by the formula V = 1 3 × B × h, where B is the area of ​​the base of the triangle and h is the height (the distance from the apex to the base).

 To calculate the  area of ​​a triangular pyramid, we need to find the area and base of the four triangles.

First, we find the area of ​​the base of an equilateral triangle. The formula for the area of ​​an equilateral triangle is (sqrt(3)/4)*a², where a is the side length. Substituting a=19, we get:

Area of ​​base = (√(3)/4)*19²

= 207.39 mm²

Then we find the area of ​​one triangular surface. We can use the formula for the area of ​​a triangle, which is (1/2) the height of the base. The base of the triangle is the other side of an equilateral triangle with a length of 19 mm. The height of the triangle is the  height of the diagonal of the pyramid, which is 17 mm. Using the Pythagorean theorem, we can find the length of the height of the triangle:

h = √ (slope² - (1/2 base)²)

= √(17² - (1/219)²)

= 15.27 mm

Thus, the area of ​​one triangular surface is:

Area of ​​triangle = (1/2)1915.27

= 144.97 mm²

Since there are four triangular faces, the total area of ​​the triangular faces is:

Total area of ​​triangular surfaces = 4 × 144.97

= 579.88 mm²

Finally, the  area of ​​the pyramid is the sum of the area of ​​the base and the area of ​​the four triangular sides:

Area = area  of ​​base Total area of ​​triangular surfaces

= 207.39 + 579.88

= 787.27 mm²

Therefore the  area of ​​the triangular pyramid is 787.27 square millimeters.

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The correct postulate that states a line is determined by two points is:

• Postulate 2: Through any two different points, exactly one line exists.

Postulate 2 states that if you have two distinct points, you can uniquely determine a line that passes through both of them. In other words, any two points in space define a line, and there is only one line that can pass through those two points.

This postulate is a fundamental concept in Euclidean geometry, which is the study of geometry based on the work of the ancient Greek mathematician Euclid.

This postulate is often used as a basic assumption or starting point in geometric proofs and constructions. It implies that a line is uniquely defined by just two points, and any additional points on that line can be determined by extending it infinitely in both directions.

It also implies that two distinct points always lie on exactly one line, and no more than one line can pass through them.

Postulate 2 is a fundamental principle in geometry and serves as the basis for many geometric theorems and proofs.

It helps establish the relationship between points and lines in Euclidean space, and it is used to reason about the properties and behavior of lines and points in geometric constructions, proofs, and demonstrations.

therefore, The correct postulate that states a line is determined by two points is:

• Postulate 2: Through any two different points, exactly one line exists.

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Answer:

Step-by-step explanation:

point m

Required value of angle CMG is 53°.

What is supplementary angle?

Supplementary angles are angles whose sum is 180 degrees. For example, an angle of 130° and an angle of 50° are cause the sum of 130° and 50° equals 180°. Similarly, complementary angles add up to 90 degrees. Two supplementary angles, when joined together, form a right and a right angle.

But it should be noted that two complementary angles do not have to be adjacent. Thus, any two angles can be supplementary angles if their sum is 180°.

Geometry is one of the important branches of mathematics that deals with the study of different shapes. This will trigger the exploration of lines and angles. A straight line is a line without curves and is defined as the shortest distance between two points. An angle is formed when line segments meet at a point.

From the figure, it is clear that value of angle DMF is 180°.

Now angle DMF = angle CMD + angle CMG + angle GMF

So, 180° = 63° + angle CMG + 64°

Angle CMG = 180° - 64° - 63° = 180° - 127° = 53°.

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Correct question is "Find the angle CMG from the given picture".

Answer:

g(-5) = 8(-5) - 24 = -40 - 24 = -64

g(5) = 8(5) - 24 = 40 - 24 = 16

y = 8x - 24

8x = y + 24

x = (1/8)(y + 24) = (1/8)y + 3

g^-1(x) = (1/8)x + 3, -64 < x < 16

Answer:

The range is the difference between the greatest and least values in a set of data.

For Contest 1, the greatest kite height is 170 feet and the least kite height is 112 feet, so the range is:

170 - 112 = 58 feet

For Contest 2, the greatest kite height is 160 feet and the least kite height is 85 feet, so the range is:

160 - 85 = 75 feet

The difference between the ranges is:

75 - 58 = 17 feet

Therefore, the answer is B. 17.

The area of the shape ABCD and EFGH are 64cm² and 25cm²

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

Since the sides of a square are equal. The area of a square is given as;

A = l²

For square ABCD,

one grid square represents 1 square cm

Therefore ,ABCD represents 8 square centimeters.

This means the area of square ABCD is given as;

A = 8²

= 64cm²

For square EFGH,

EFGH has 5 grid squares, therefore the area of the square is given as;

A = 5²

A = 25cm²

therefore the area of squares ABCD and EFGH are 64cm² and 25cm²

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Answer:-39

Step-by-step explanation:

The first thing is to open the bracket.

By doing that, the question becomes -37-2.

note that plus×minus=minus.

Hence,-39 as the final answer

Answer:

C

Step-by-step explanation:

f(x) = 2 + x - x²

to obtain f(- 3) substitute x = - 3 into f(x)

f(- 3) = 2 + (- 3) - (- 3)²

        = 2 - 3 - 9

      = - 10

Answer:

Substituting -3 in the expression for f(x), we get:

f(-3) = 2 + (-3) - (-3)^2 = 2 - 3 - 9 = -10

Step-by-step explanation:

Therefore, the value of f(-3) is -10.

Option C is the correct answer.

Upon answering the query we can say that  As a result, in rectangle  AC is 75 units long.

A rectangle is a quadrilateral with four right angles in the Euclidean plane. It is also known as an equiangular quadrilateral since each of its angles is equal. A straight angle is an additional alternative for the parallelogram. A square has four sides that are the same length. A quadrilateral with a rectangle-like form has equal parallel sides and four 90-degree vertices. Due of this, it is occasionally referred to as a "equirectangular rectangle". Due to its opposing sides' equal and parallel lengths, a rectangle is occasionally referred to as a parallelogram.

The diagonals of a rectangle are of equal length. As a result, we have:

[tex]AC = BD\\3x + 15 = 4x - 5\\15 = x - 5\\x = 20\\[/tex]

Now, we can change the equation for AC to use this value of x:

[tex]AC = 3x + 15\\AC = 3(20) + 15\\AC = 60 + 15\\AC = 75\\[/tex]

As a result, AC is 75 units long.

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The first student didn't like the salad, there is a 0.2 chance that the second student won't either. The probability that neither of the first two students would choose a salad was 0.64.

The idea of probability is used to calculate the possibility or probability of a specific occurrence.

It is a number between 0 and 1, where 0 indicates that the event is inconceivable and 1 indicates that it is guaranteed to happen.

Probabilities can be expressed using fractions, decimals, or percentages.

There is a 0.2 likelihood that any student will choose a salad if their lunch tastes are assumed to be independent of one another's.

If you ask the principal understudy, there is a 0.2 chance that they will answer they prefer a dish of mixed greens. You move on to the next youngster if they don't want a salad.

Because the first student didn't like the salad, there is a 0.2 chance that the second student won't either. The probability that neither of the first two students would prefer a salad was (1-0.2) (1-0.2) = 0.64.

Since none of the n-1 understudies who came before them did, the likelihood that the nth understudy would like a platter of mixed greens is only 0.2. 1-0.2n-1 is the likelihood that none of the first n-1 students will choose a salad.

Therefore, in order to identify a student who prefers salad, you must ask an expected number of students the following questions:

E(x) = 1(0.2) + 2(1-0.2)(0.2) + 3(1-0.2)2(0.2) +...

Even though this is an infinite series, by truncating it after a predetermined amount of words, we can approximate it. Let's imagine we decide to quit after ten terms:

E(x) ≈ 1×(0.2) + 2×(1-0.2)(0.2) + 3(1-0.2)²×(0.2) + ... + 10×(1-0.2)⁹ × (0.2) E(x) ≈ 2.48

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Answer:

y = 4x + 11

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 4x + 9 ← is in slope- intercept form

with slope m = 4

• Parallel line have equal slopes , then

y = 4x + c ← is the partial equation of line A

to find c substitute (- 2, 3 ) into the partial equation

3 = 4(- 2) + c = - 8 + c ( add 8 to both sides )

11 = c

y = 4x + 11 ← equation of line A

Based on the angle of two-tangent theorem, the value of x in the image is: x ≈ 4.

The angle of two-tangent theorem states that when two tangent lines intersect outside of a circle, the angle that they form has a measure equal to half the positive difference between the measures of the arcs intercepted by the angle.

Applying the theorem, we have:

70 = 1/2[(360 - 27x + 2) - (27x + 2)]

140 = 360 - 27x + 2 - 27x - 2

140 = 360 - 54x

140 - 360 = -54x

-220 = -54x

-220/-54 = x

x ≈ 4

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Janet has 630 options to customize a car based on the given features.

How to solve the question?

To determine the number of ways Janet can customize a car, we need to multiply the number of choices she has for each feature. Therefore, the total number of ways Janet can customize a car can be calculated as:

10 car models x 7 exterior colors x 9 interior colors = 630

Thus, Janet has 630 options to customize a car based on the given features.

It's worth noting that this calculation assumes that each feature (car model, exterior color, and interior color) can be combined with any other feature, without any restrictions or dependencies. However, in reality, certain car models may not be available in certain exterior or interior colors, or there may be other restrictions on the customization options.

Additionally, there may be other features that Janet can customize, such as the type of engine, transmission, or other options. Therefore, the total number of customization options may be even greater than what we have calculated here.

In summary, based on the given information, Janet has 630 ways to customize a car, but in reality, the actual number of options may be more limited or varied depending on other factors.

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50 miles would make the two choices equivalent in cost.

The following formula is used to determine a line's slope:

slope is equal to y2 - y1 / x2 - x1.

where the two points on the line are (x1, y1) and (x2, y2). The steepness or rate of change of the line is indicated by the slope. A line with a positive slope is increasing from left to right, whereas a line with a negative slope is dropping from left to right. An undefined slope denotes a vertical line, while a slope of zero denotes a horizontal line.

To determine the choice where the two miles are equivalent we take x as the number of miles:

For the first company:

Total cost = 25 + 0.8x

For the second company:

Total cost = 35 + 0.6x

Setting the equations as equal:

25 + 0.8x = 35 + 0.6x

0.2x = 10

x = 50

Hence, 50 miles would make the two choices equivalent in cost.

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Here is the code that can be used to find the MLE of M allele in the 206th row of Mourant dataset using the HardyWeinberg package in R:

# Load HardyWeinberg package

library(HardyWeinberg)

# Load Mourant dataset

data(Mourant)

# Extract the genotype counts for the 206th row

counts <- Mourant[206, 2:4]

# Calculate the MLE of M allele frequency

mle <- hw_mle(counts)

# Extract the MLE of M allele frequency

mle_M <- mle$p[2]

Note that the code assumes that the Mourant dataset is already installed and loaded in R. If the dataset is not installed, you can install it by running install.packages("HardyWeinberg") in R.

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Answer:

m = 7√2/2

n = 7√2/2

Step-by-step explanation:

sin45 = m/7

√2/2 = m/7

m = 7√2/2

cos45 = m/7

√2/2 = m/7

m = 7√2/2

Answer:To determine the possible scales of the map, we need to calculate the ratio of the distance on the map to the corresponding distance on the ground in the actual state. We can do this using the following formula:scale = distance on map ÷ distance on groundFirst, we need to convert the dimensions of Kansas from miles to inches using a common scale factor. Since 1 mile is equal to 63,360 inches, we have:Length of Kansas: 410 miles × 63,360 inches/mile = 25,984,600 inchesWidth of Kansas: 210 miles × 63,360 inches/mile = 13,315,200 inchesNow we can calculate the possible scales of the map based on the dimensions of the page in Jada's book, which is 5 inches by 8 inches:For the length of Kansas:scale = 5 inches ÷ (25,984,600 inches ÷ 2.54 cm/in) = 0.0000484scale = 8 inches ÷ (25,984,600 inches ÷ 2.54 cm/in) = 0.0000774For the width of Kansas:scale = 5 inches ÷ (13,315,200 inches ÷ 2.54 cm/in) = 0.0000962scale = 8 inches ÷ (13,315,200 inches ÷ 2.54 cm/in) = 0.0001539Therefore, the possible scales of the map are 1:20,655, and 1:10,326.

We have the reasons given as;

<4 + <3 = 180 degrees; supplementary angles

m<1 + m<2 + m<3 = 180; sum of angles in a triangle

m<1 + m<2 = m<4; substitution of equality

Angle n and n are corresponding angles

angle n + <3 are supplementary angles

First, we need to know the following deductions;

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Hence, after finding the solution, Jimmy discovered 16 dimes and 15 nickels. By assuming variables, this problem can be resolved.

In mathematics, a variable is a symbol or letter that designates a value of the variable or amount. Variables are fundamental to many fields of science, technology, and mathematics and are used to formulate and solve equations.

Let's use constants to depict Jimmy's discovery of nickels and dimes.

Let x be the quantity of nickels and y be the quantity of dimes.

We may create the following pair of equations using the data:

Formula 1: x + y = 31 

Equation 2 reads: 0.05x + 0.10y = 2.35, which equals the total worth of the coins at $2.35.

The methods of substitution and elimination can be used to calculate the characteristics of x and y. Substitutions made

Equation 1 might be used to convert this x into units of y: x = 31 - y

In Equation 2, replace x with the following expression: 0.05(31 - y) + 0.10y = 2.35

Simplify the equation and find y as follows: 1.55 - 0.05y + 0.10y = 2.35 0.05y = 0.80 y = 16

Jimmy therefore found 16 pennies.

Equation 1 can be changed to y = 16 to determine the amount of nickels: x + 16 = 31 x = 15

Jimmy therefore discovered 15 nickels.

Jimmy discovered 16 dimes and 15 nickels as a result.

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If all nickels and dimes and came out to a total amount of $2.35. Jimmy found 15 nickels and 16 dimes.

What is linear equation?

A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:

y = mx + b

Let's assume that Jimmy found x number of nickels and y number of dimes. Then we can write two equations based on the given information:

The total number of coins is 31:

x + y = 31

The total value of the coins is $2.35:

0.05x + 0.10y = 2.35

To solve for x and y, we can use the first equation to solve for x in terms of y:

x = 31 - y

Then we can substitute this expression for x into the second equation:

0.05(31 - y) + 0.10y = 2.35

1.55 - 0.05y + 0.10y = 2.35

0.05y = 0.80

y = 16

So Jimmy found 16 dimes. To find the number of nickels, we can substitute this value of y into either of the two equations we started with. Let's use the first equation:

x + y = 31

x + 16 = 31

x = 15

Therefore, Jimmy found 15 nickels and 16 dimes.

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The magnitude of the car's acceleration when s=100m and x=0 is 3.49 [tex]m/s^2[/tex] evaluated using the kinematic equation of motion.

We can use the kinematic equation of motion to determine the acceleration of the car at the given distance:

[tex]s = ut + (1/2)at^2[/tex]

where s=distance traveled, u = initial velocity, a =acceleration, and t =

time taken.

We can rewrite this equation as:

[tex]t = (2s/u)^(1/2)[/tex]

Substituting the given values, we get:

[tex]t = (2(100)/20)^(1/2)[/tex] = 2.236 seconds

Now, we can use the kinematic equation:

v = u + at

where v is the final velocity.

We know the initial velocity u is 20 m/s, and the car's acceleration At=0.5 [tex]m/s^2[/tex]. To find the final velocity, we can use the kinematic equation again:

[tex]s = ut + (1/2)at^2 + vt[/tex]

Rearranging and substituting the given values, we get:

[tex]v = (s - ut - (1/2)at^2) / t[/tex]

v = (100 - (20)(2.236) - (1/2)(0.5)(2.236)^2) / 2.236

v = 27.839 m/s

Now we can evaluate the acceleration using the equation:

a = (v-u) / t

Substituting the given values, we get:

a = (27.839 - 20) / 2.236

a = 3.49[tex]m/s^2[/tex] (rounded to two decimal places)

Therefore, the magnitude of the car's acceleration when s=100m and x=0 is 3.49 [tex]m/s^2.[/tex]

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The quotient number is 1.

What is Quotient?

When two quantities are divided by one another, the result is a quotient. The number of times a quantity (the divisor) may be divided into a second amount (the dividend) without a remainder is known as the quotient in the division.

In order to express the given data, let's first set up the equation as follows:

(number/8) + 1/2 = 5/8

(x/8) + 1/2 = 5/8

We need to isolate the number as a variable on one side of the equation so that we can solve it.

Let's start by adding the fractions to simplify the left side of the equation:

(x/8) + 4/8 = 5/8

Next, we can combine the fractions further:

x/8 = 1/8

We can multiply both sides of the equation by 8 to find the number as follows:

number = 1

Therefore, the number is 1.

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To evaluate x=50+0.35m to find the amount Mr. Parker will pay if he drives 80 miles, we substitute m with 80 and simplify the expression as follows:

[tex]x = 50 + 0.35m[/tex]

[tex]x = 50 + 0.35(80)[/tex]

[tex]x = 50 + 28[/tex]

[tex]x = 78[/tex]

Therefore, Mr. Parker will pay $78 if he drives 80 miles.

I'm sorry to bother you but can you please mark me BRAINLEIST if this ans is helpfull

The given diagram implies that the triangle $ABC$ is an isosceles triangle with angles of $24^\circ$. This can be verified by computing the length of the hypotenuse and using the Pythagorean Theorem.

Equation is a mathematical expression that consists of variables, symbols, and numbers, and shows the relationship between different quantities. An equation can involve one or more unknowns, and can be represented as an equality or as an inequality. Solving an equation requires understanding the relationship between the different elements in the equation, and manipulating the equation to isolate the unknowns. Common types of equations include linear equations, quadratic equations, and polynomial equations.

From this diagram, we can conclude that $\angle ABC$ is an isosceles triangle. This is because the angles opposite equal sides of a triangle must be equal. Since $\angle BAC=24^\circ$, $\angle ABC$ must be $24^\circ$. Furthermore, the sides $AB$ and $AC$ are equal, so $ABC$ is an isosceles triangle.

This conclusion can be verified by using the Pythagorean Theorem. If $AB=AC$, then it follows that $BC = \sqrt{AB^2 + AC^2} = \sqrt{2AB^2}$. Since $AB=3$, it follows that $BC=\sqrt{2*3^2}=6$. Therefore, the triangle $ABC$ is a right triangle with legs of length 3 and hypotenuse of length 6. Since $\angle BAC = 24^\circ$, it follows that $\angle ABC = 24^\circ$, verifying that the triangle is isosceles.

In conclusion, the given diagram implies that the triangle $ABC$ is an isosceles triangle with angles of $24^\circ$. This can be verified by computing the length of the hypotenuse and using the Pythagorean Theorem.

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Answer:

78

Step-by-step explanation:

The break-even points in terms of customers served = 14 customers

Charge per customer = 120

Let the Number of customers= n

So,

Income from serving n customers = 120n

Expenditure from serving n customers = Fixed cost + cost of preparation of meal per customer

= 1400 + 20n

For beak-even:

Income = Expenditure

Substituting values, we get:

120n = 1400 + 20n

So, we get:

100 n = 1400

So, we get:

n =1400/100

= 14

So,

The break-even points in terms of customers served = 14 customers

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