The price of an airline ticket from New Orleans to Boston increased to $550. This is a 30% increase.

To the nearest cent, what is the old fare?

A $397.67
B $423.08
C $412.14
D $501.40

Answer:

b=6.5

Step-by-step explanation:

a²+b²=c²

7.4²+b²=3.6²

b²=3.6²-7.4²

b²=12.96-54.76

b²= -41.8

√b²=√-41.8

b=6.465

b=6.5

The dimensions of the box that will have the greatest volume are:

Length and width of the base: 2√3 feet

Height: h = (36 - x^2) / 8x = (√3)/2 feet

Let the length and width of the base be x, and let the height be h.

The surface area of the top is x^2, and the surface area of the remaining four sides is \(2(xh + xh) = 4xh\).

The cost of the top is \(x^2\), and the cost of the remaining four sides is \(2(4xh) = 8xh\). Therefore, the total cost is:

\(C(x,h) = x^2 + 8xh\)

We know that the total cost is $36, so we have:

\(x^2 + 8xh = 36\)

Solving for h, we get:

\(h = (36 - x^2) / 8x\)

The volume of the box is given by:

\(V(x,h) = x^2h\)

Substituting h in terms of x, we get:

\(V(x) = x^2 ((36 - x^2) / 8x)\)

Simplifying, we get:

\(V(x) = (1/8) x (36x - x^3)\)

To find the dimensions of the box that will have the greatest volume, we need to find the value of x that maximizes V(x). We can do this by taking the derivative of V(x) with respect to x, setting it equal to 0, and solving for x:

\(V'(x) = (1/8) (36 - 3x^2) = 0\)

Solving for x, we get:

x = 2√3

Therefore, the dimensions of the box that will have the greatest volume are:

Length and width of the base: 2√3 feet

Height: \(h = (36 - x^2) / 8x\) = (√3)/2 feet

The volume of the box is:

\(V = x^2h\)= (2√3)^2 ((√3)/2) = 9√3 cubic feet

Note: To confirm that this value represents the maximum volume, we can check that V''(x) < 0, which indicates a maximum point. We have:

\(V''(x) = (1/8) (-6x) = -3x/4\)

At x = 2√3, V''(x) = -3(2√3)/4 = -3√3/2 < 0, so this is indeed a maximum point.

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Using the formula of area of a circle, about 226.08in² has been eaten

The diameter of the pizza is given as 24 inches. To calculate the area of the entire pizza, we need to use the formula for the area of a circle:

Area = π * r²

where π is approximately 3.14 and r is the radius of the circle.

Given that the diameter is 24 inches, the radius (r) would be half of the diameter, which is 12 inches.

Let's calculate the area of the entire pizza first:

Area = 3.14 * 12²

Area = 3.14 * 144

Area ≈ 452.16 square inches

Now, if half of the pizza is consumed, we need to calculate the area of half of the pizza. To do that, we divide the area of the entire pizza by 2:

Area of half of the pizza = 452.16 / 2

Area of half of the pizza ≈ 226.08 square inches

Therefore, if half of the pizza is consumed, approximately 226.08 square inches of pizza would be eaten.

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There are 62,352 five-digit numbers that have at least one digit occurring more than once.

To determine the number of five-digit numbers that have at least one digit occurring more than once, we can use the principle of inclusion-exclusion.

Step 1: Calculate the total number of five-digit numbers.

Since the first digit cannot be zero, we have 9 choices (1-9) for the first digit. The remaining four digits can be any of the ten digits (0-9). Therefore, the total number of five-digit numbers is 9 * 10^4 = 90,000.

Step 2: Calculate the number of five-digit numbers with no repeated digits.

For the first digit, we have 9 choices (1-9). For the second digit, we have 9 choices (excluding the digit chosen for the first digit). For the third, fourth, and fifth digits, we have 8, 7, and 6 choices, respectively. Therefore, the number of five-digit numbers with no repeated digits is 9 * 9 * 8 * 7 * 6 = 27,648.

Step 3: Calculate the number of five-digit numbers with at least one repeated digit.

Using the principle of inclusion-exclusion, we can subtract the number of five-digit numbers with no repeated digits from the total number of five-digit numbers:

Number of five-digit numbers with at least one repeated digit = Total number of five-digit numbers - Number of five-digit numbers with no repeated digits

                                                              = 90,000 - 27,648

                                                              = 62,352

Therefore, there are 62,352 five-digit numbers that have at least one digit occurring more than once.

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The slope of a line shows the distance of that line. This means it tells us how far the line moves each time you move over one unit on the x-axis for that line.

The slope of a line can be defined a number that describes the direction and steepness of the line.

It is also known as gradient

It is denoted by the letter 'm'

Thus, the slope of a line shows the distance of that line. This means it tells us how far the line moves each time you move over one unit on the x-axis for that line.

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The point of intersection of the two lines is (9/7,18/7)

The equation of line m is given as:

\(y = 2x\)

The second equation is given as:

\(y = -\frac 13x + 3\)

Substitute 2x for y in the above equation

\(2x = -\frac 13x + 3\)

Collect like terms

\(2x +\frac 13x = 3\)

Multiply through by 3

\(6x +x = 9\)

\(7x = 9\)

Solve for x

\(x = \frac 97\)

Substitute 9/7 for x in \(y = 2x\)

\(y = 2\times \frac 97\)

\(y = \frac {18}7\)

Hence, the point of intersection of the two lines is (9/7,18/7)

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Answer:

\(f^{-1}(x)=\sqrt[3]{x}-6\)

Step-by-step explanation:

\(f(x)=(x+6)^3\)

\(y=(x+6)^3\)

\(x=(y+6)^3\)

\(\sqrt[3]{x}=y+6\)

\(\sqrt[3]{x}-6=y\)

ok

Dimensions = 5 ft x 7 ft

Brick = 4 in x 12 in

1.- Convert ft to in

1 ft -------------------- 12 in

5 ft ------------------- x

x = (5 x 12) / 1

x = 60 in

1 ft -------------------- 12 in

7 ft -------------------- x

x = (7 x 12) / 1

x = 84 in

2.- Calculate the area of the wall

Area = 60 x 84

= 5040 in^2

3.- Calculate the area of a brick

Area = 4 x 12 = 48 in^2

4.- Divide the area of the wall by the area of the brick

Number of bricks = 5040 / 48

= 105

There will be 105 brick on the wall.

Answer:what

Step-by-step explanation:what does this mean

To find the probability of saving a total of $20, we need to calculate the probability of both scenarios happening and add them together.

Scenario 1: Camera gets a 10% discount and game gets no discount.
The probability of the camera getting a 10% discount is 0.2 (or 20%) since there is a 20% chance of getting a discount on any item.
The probability of the game getting no discount is 0.8 (or 80%) since there is an 80% chance of not getting a discount on any item.
So, the probability of this scenario happening is 0.2 * 0.8 = 0.16 (or 16%).

Scenario 2: Game gets a 25% discount and camera gets no discount.
The probability of the game getting a 25% discount is 0.25 (or 25%) since there is a 25% chance of getting a discount on any item.
The probability of the camera getting no discount is 0.8 (or 80%) since there is an 80% chance of not getting a discount on any item.
So, the probability of this scenario happening is 0.25 * 0.8 = 0.2 (or 20%).

Therefore, the probability of saving a total of $20 is the sum of the probabilities of both scenarios: 0.16 + 0.2 = 0.36 (or 36%).

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The function y = x³ + 6x² + 9x + 2 is increasing in the intervals (-3, -1) and (-1, ∞) decreasing in the interval (-∞, -3).

To determine the intervals on which the function y = x³ + 6x² + 9x + 2 is increasing, we need to analyze the sign of the derivative.

First, let's find the derivative of y with respect to x:

y' = 3x² + 12x + 9

To determine the intervals of increase, we need to find where the derivative is positive.

To find the values of a and b, we set the derivative equal to zero and solve for x:

3x² + 12x + 9 = 0

Simplifying the equation, we get:

x² + 4x + 3 = 0

Factoring the quadratic equation, we have:

(x + 1)(x + 3) = 0

So the solutions are x = -1 and x = -3.

Now let's test the intervals (-∞, -3), (-3, -1), and (-1, ∞) by choosing test points within each interval.

Choose x = -4 for the interval (-∞, -3):

Substituting x = -4 into y', we get:

y' = 3(-4)² + 12(-4) + 9 = 12 - 48 + 9 = -27

Since the derivative is negative, the function is decreasing in the interval (-∞, -3).

Choose x = 0 for the interval (-3, -1):

Substituting x = 0 into y', we get:

y' = 3(0)² + 12(0) + 9 = 9

Since the derivative is positive, the function is increasing in the interval (-3, -1).

Choose x = 1 for the interval (-1, ∞):

Substituting x = 1 into y', we get:

y' = 3(1)² + 12(1) + 9 = 24

Since the derivative is positive, the function is increasing in the interval (-1, ∞).

Based on the analysis above, we can conclude the following:

The function y = x³ + 6x² + 9x + 2 is increasing in the intervals (-3, -1) and (-1, ∞).

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Answer:

x = 43

Step-by-step explanation:

Find out the length of the other side.

48 + 25 = 73

Use that to find x.

x + 30 = 73

- 30        -30

x = 43

Answer:

x = 4

Step-by-step explanation:

We have the algebraic expression 3x + 16 = 7x and are asked to solve.

When we need to solve for x, we need to get x alone always.

So 3x + 16 = 7x.

Subtract 3x from both sides :

16 = 4x

Divide 4 from both sides :

x = 4

Answer:

\( \large \boxed{x = 4}\)

Step-by-step explanation:

Goal

Given

\(3x + 16 = 7x\)

Step 1

\(16 = 7x - 3x \\ 16 = 4x\)

Step 2

\( \frac{16}{4} = x \\ 4 = x\)

Step 3

\(3x + 16 = 7x \longrightarrow 3(4) + 16 = 7(4) \\ 12 + 16 = 28 \\ 28 = 28\)

The equation is true for x = 4. Hence, the solution is x = 4

If a cuboid weighs 100N and has sides 5cm by 10cm, then the area of cuboid is 0.005m².

Weight of the cuboid = 100N

Sides of the cuboid = 5cm by 10cm

A solid structure or a three-dimensional shape in geometry is called a cuboid. It is similar to a cube in that a cuboid can become a cube by changing the angles between faces or the lengths of the edges. A convex polyhedron with the same polyhedral graph as a cube is referred to as a cuboid in mathematics.

Calculating the area of the Cuboid -

= 5cm × 10cm

= 50cm²

Converting -

Area of Cuboid

= 50/10000 m²

= 0.005 m²

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The fraction and equivalent decimals are 348/990 = 0.3515151 ,316/900 = 0.3511111 , 351/999 = 0.351351351 ,16/90 = 0.1777 and 17/99 = 0.171717.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

If we divide the fraction given in the table then the corresponding decimal obtained are ;

348/990 = 0.3515151

316/900 = 0.3511111

351/999 = 0.351351351

16/90 = 0.1777

17/99 = 0.171717

Hence "The fraction and equivalent decimals are 348/990 = 0.3515151 ,316/900 = 0.3511111 , 351/999 = 0.351351351 ,16/90 = 0.1777 and 17/99 = 0.171717".

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Answer:

\(\qquad\quad {:}\longrightarrow\sf {\mid} \dfrac {1}{\cancel3}}(\bcancel {3}x-6p)+4x-p{\mid}\)

\(\qquad\quad {:}\longrightarrow\sf {\mid}(x-6p)+4x-p {\mid}\)

\(\qquad\quad {:}\longrightarrow\sf x-6p+4x-p \)

\(\qquad\quad {:}\longrightarrow\sf x-4x-6p-p \)

\(\qquad\quad {:}\longrightarrow\sf -3x-5p \)

The option that best explains the relationship between altitude and the boiling point is; A. There is a strong negative correlation between altitude and water's boiling point.​

In correlation coefficient, we know that a positive correlation occurs when both x and y values increase at the same time while negative correlation occurs when y value decreases as x value increases.

Now, we see from the given graph that y-values are decreasing with increasing x-values and as such this is a negative correlation.

Now, we want to determine whether it is a strong or weak correlation.

The scatterplot is close to being a straight line and as such the correlation coefficient will be close to - 1 which makes it a strong negative correlation.

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Answer: A is correct

Step-by-step explanation:

took the test

Answer: They call it the “21” century because you have to count the first 100 years too, And do you mean 2021?

Step-by-step explanation:

Answer:

If you're talking about how it starts with 20 but its the 21st century, that's because the first 100 years were called the 1st century even though only the 2nd century actually started with 1.

Step-by-step explanation:

Answer:

isosceles trapezoid

Step-by-step explanation:

isosceles trapezoid

Answer:

2^(3/7)

Step-by-step explanation:

For these types of questions, what is inside the root is the numerator, and what is on top is the denominator.

3 is in the root, so it is the numerator

7 is outside the root, so it is the denominator

Therefore, The answer is 2^(3/7)

Answer:

136.17059542672028

Step-by-step explanation:

just divide my friend

The expectation value of the position squared when the particle in the box is in its third excited state is equal to \(\frac{9l^2}{8}\), where l is the length of the box. This is equal to nine-eighths of the length of the box squared.

The expectation value of the position squared when the particle in the box is in its third excited state can be calculated using the formula\(\langle x^2 \rangle = \frac{l^2}{8} \left( 2n^2 + 6n + 3 \right)\),

where n is the quantum number of the state and l is the length of the box. Here, n is 3, so the expectation value is equal to

\(\frac{l^2}{8} \left( 2 \times 3^2 + 6 \times 3 + 3 \right) = \frac{9l^2}{8}\).

This can be written as nine-eighths of the length of the box squared.

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Answer:

The answer is 2.55

Step-by-step explanation:

As, the original price = $17

So, 85% of it have been reduced from it so

85% of 17

= 85/100 x 17 = 14.45

So it have reduced by $14.45

So, $17 - $14.45= $2.55

Answer: No, the triangle sum theorem is not true for a sphere surface.

Explanation:

Consider 3 cities A,B,C at the following locations

The placement of C is important because this then allows angle ABC to be 90 degrees. Angles BAC and BCA are also 90 degrees each because B is directly north of both A and C (all northerly roads lead to the north pole at point B). This bizarre triangle has all three angles of 90 degrees. The angles here sum to 90+90+90 = 270 degrees.

No, the triangle sum theorem is not true on the surface sphere.

The triangle sum theorem states that, the sum of the three interior angles of any triangle is always 180°.

Given that, is the triangle sum theorem true on the surface sphere or not, so in relation to Euclid's geometry,

A statement that is equivalent to the parallel postulate is that there exists a triangle whose angles add up to 180°. Since spherical geometry violates the parallel postulate, there exists no such triangle on the surface of a sphere. The sum of the angles of a triangle on a sphere is 180°(1 + 4f), where f is the fraction of the sphere's surface that is enclosed by the triangle. For any positive value of f, this exceeds 180°.

Hence, there exists no such triangle on the surface of a sphere.

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The height of the 7.1 m tree in Miguel backyard in centimeters is 710 cm

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

An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

1 m = 100 cm

Hence:

7.1 m = 7.1 m * 100 cm per 1 m = 710 cm

The height of the 7.1 m tree in Miguel backyard in centimeters is 710 cm

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Answer:

Factoring Expressions With Exponents - Video & Lesson ...

To do this, take the greatest common factor of the numbers and the smallest exponent of each variable. 2. Divide the original expression by the greatest common factor. To do this, divide the coefficients, and subtract the exponents of the variables

Pls give brainliest

The greatest common factor (GCF) with variables and exponents is found by identifying the highest power of each variable that appears in the given expressions and choosing the one with the highest power. If a variable or exponent is not common to all the terms, it is not included in the GCF.

When finding the greatest common factor (GCF) with variables and exponents, we need to consider the highest power of each variable that appears in the given expressions. To find the GCF, we identify the common factors and choose the one with the highest power. If a variable or exponent is not common to all the terms, it is not included in the GCF.

Let's consider an example to illustrate this:

Given expressions: 2x^3y^2 and 4x^2y^3

To find the GCF, we look at the variables and exponents:

Therefore, the GCF is 2xy^2, as it is the highest power common to both expressions.

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The percent decrease in the price of the headphones is 26.32%.

Explanation:

To find the percent change in price, we can use the following formula:

percent change = (new value - old value) / old value * 100%

     
In this case, the old value is the original price of the headphones, which is $95.
   

The new value is the sale price, which is $70. Plugging these values into the formula, we get:percent change = (70 - 95) / 95 * 100%

percent change = -25 / 95 * 100%

percent change = -0.2632 * 100%

percent change = -26.32%

   
The negative sign indicates that the price has decreased, and the magnitude of the percent change is 26.32%, which means that the sale price is 26.32% lower than the original price.

Answer:

10000 meters = 6.214 miles

About 6 miles

Step-by-step explanation:

Soultion: How many meters are in a mile?

1600 meters: roughly 1 mile or 4 laps around the track.

Answer: 6.214

The final cost of the item after a 35% discount and 9.8% sales tax is $53.54.

The given problem is related to percentage discounts and sales tax and can be solved using the following steps:

Step 1: Firstly, we need to determine the discount amount, which is 35% of the original price. Let's calculate it. Discount = 35% of the original price = 0.35 x $75 = $26.25

Step 2: Now, we will calculate the new price after the discount by subtracting the discount amount from the original price.New Price = Original Price - Discount AmountNew Price = $75 - $26.25 = $48.75

Step 3: Next, we need to calculate the amount of sales tax. Sales Tax = 9.8% of New Price Sales Tax = 0.098 x $48.75 = $4.79

Step 4: Finally, we will calculate the final cost of the item by adding the new price and the sales tax.

Final Cost = New Price + Sales Tax Final Cost = $48.75 + $4.79 = $53.54

Therefore, the final cost of the item after a 35% discount and 9.8% sales tax is $53.54.I hope this helps!

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