A pilot flies in a straight path for 1.5 hrs. She then makes a course correction, heading 20 degrees to the right of her original course, and flies 2 hrs in the new direction. If she maintains a constant speed of 685 mi/h, how far is she from her starting position?

Answer:

C is your answer

Step-by-step explanation:

The inequalities that represent the regular price of eyeglass frames will be 0.4r ≤ 120 and r ≥ 4(360/5).

If we let r represent the regular price of the eyeglass frames, then we can write the following two inequalities based on the given information:

0.4r ≤ 120

This inequality represents the fact that the lowest regular price for the eyeglass frames is $120. We use 0.4 because a 60% discount means that the price paid is 40% of the regular price.

Also, r ≥ 4(360/5) as this inequality represents the fact that the highest regular price for the eyeglass frames is $360. We use 4(360/5) because a 75% discount means that the price paid is 25% of the regular price, which is equivalent to multiplying the regular price by 0.25. Then, 4 times that amount gives us the regular price, which is $360 in this case.

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The blueprint dimensions of a building that is 70 feet × 90 feet is: 4.375 inches X 5.625 inches.

Scale refers to the ratio or proportion between the dimensions of an object or a system in the real world and its representation in a model, drawing, or map. A scale is typically expressed as a ratio or a fraction, such as 1:100 or 1/4, which indicates the relationship between the size of the object in the real world and the size of its representation in the model or drawing.

Using a scale of 1 inch : 16 feet means that every inch on the blueprint represents 16 feet in the actual building. To find the blueprint dimensions of a building that is 70 feet x 90 feet, we need to divide each dimension by 16.

The blueprint dimensions are:

70 feet ÷ 16 = 4.375 inches

90 feet ÷ 16 = 5.625 inches

Therefore, the blueprint dimensions of the building are approximately 4.375 inches by 5.625 inches.

The answer is: 4.375 inches X 5.625 inches.

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The graph of 2x + 3y < 9 and y≥ - 2/3x-4 is given in the attachment.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

For the first inequality, 2x + 3y < 9, we will start by graphing the line 2x + 3y = 9, which is the boundary line of the inequality.

To do this, we will solve for y:

2x + 3y = 9

3y = -2x + 9

Divide both sides by 3

y = (-2/3)x + 3

For the second inequality, Y≥ - 2/3x-4

Hence, the graph of 2x + 3y < 9 and y≥ - 2/3x-4 is given in the attachment.

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The expression that represents the number of almonds in the bag is (6x+13) - (3x-7)

What is Linear Equation?

A linear equation is a mathematical equation that represents a straight line on a graph. It is an equation in which the highest power of the variable is one. A general linear equation can be represented as y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.

Linear equations can be solved algebraically using techniques like substitution or elimination, and they can be used to model real-world situations involving linear relationships.

The expression that represents the number of almonds in the bag is (6x+13) - (3x-7) which simplifies to 3x + 20.

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The classification of the variables in the question above is  as follows:

Discrete quantitative data refers to data that can be counted in whole numbers and is often used to describe things that can be categorized into groups. like the number of people in a room or the number of cars in a parking lot.

Quantitative continuous data refers to data that can be measured on a continuous scale, such as time, temperature, or weight, like the temperature of a room or the weight of a person.

Qualitative nominal data refers to data that can be categorized into groups but cannot be measured or ranked, like the type of car someone drives or the color of someone's eyes.

Qualitative ordinal data refers to data that can be categorized into groups and can be ranked or ordered, like the level of education someone has achieved or the ranking of a sports team.

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Answer:

The outputs are in order:

5

2

1

2

5

Answer:

5.2.1.2.5

Step-by-step explanation:

The solution of the given expression is y = -12 and there are no extraneous solutions.

A solution to an equation that appears during the solving process but does not fulfil the original problem is known as an extraneous solution. In other words, it is a solution that, when inserted back into the original equation, yields an untrue assertion. Extraneous solutions typically result from certain algebraic operations, such squaring an equation's two sides, which might introduce new solutions that don't truly satisfy the original problem.

The given expression is:

7y+3−6y+9=0

y = -12

Substitute y = -12 back into the original equation:

7y + 3 - 6y + 9 = 0

7(-12) + 3 - 6(-12) + 9 = 0

-84 + 3 + 72 + 9 = 0

The left-hand side simplifies to:

0 = 0

Hence, the solution of the given expression is y = -12 and there are no extraneous solutions.

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Terms: -5s^(7), -8s^(4), 6s^(3), 4s, and -6

Degree of each term: 7, 4, 3, 1, and 0

Degree of the polynomial: 7

Leading term: -5s^(7)

Leading coefficient: -5

Constant term: -6

The terms of the polynomial are -5s^(7), -8s^(4), 6s^(3), 4s, and -6. The degree of each term is 7, 4, 3, 1, and 0, respectively. The degree of the polynomial is the highest degree of any of its terms, which is 7.

The leading term is the term with the highest degree, which is -5s^(7). The leading coefficient is the coefficient of the leading term, which is -5. The constant term is the term with a degree of 0, which is -6.

So, the terms are -5s^(7), -8s^(4), 6s^(3), 4s, and -6; the degree of each term is 7, 4, 3, 1, and 0; the degree of the polynomial is 7; the leading term is -5s^(7); the leading coefficient is -5; and the constant term is -6.

Terms: -5s^(7), -8s^(4), 6s^(3), 4s, and -6

Degree of each term: 7, 4, 3, 1, and 0

Degree of the polynomial: 7

Leading term: -5s^(7)

Leading coefficient: -5

Constant term: -6

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When f(x) = 4, then, the value of x = 2 (domain = 2, range = 4).

According to the mapping above, the given relationship is bijective (one-to-one and onto or one-to-one correspondence) because each element of the range is mapped to by exactly one element of the domain.

When we say a relationship is bijective, it means the satisfies both the injective (one-to-one function) and surjective function (onto function) properties. Therefore, as a result, f(x)=4 implies f(2)=4 or simply x=2.

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The length and width of the toolbox are 8 feet and 5 feet respectively.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length.

Given that the volume of the toolbox is 80 cubic feet, so we can write:

V = w × h × l = 80ft³

Next, we know that the width is 3 feet less than the length, so we can write:

w = l - 3

Now we can substitute the second equation into the first equation to get an equation with just one variable:

V =  w × h × l = l(l - 3)(2) = 80

Simplifying this equation, we get:

2l² - 6l - 80 = 0

We can solve this quadratic equation using the quadratic formula:

l = (-b ± √(b² - 4ac)) / 2a

where a = 2, b = -6, and c = -80. Plugging in these values, we get:

l = (6 ± √(6² - 4(2)(-80))) / 4

l = (6 ± √(676)) / 4

We take the positive value of l since the length must be positive, so we get:

l = (6 + 26) / 4

l = 8

Now we can use the second equation (w = l - 3) to find the width:

w = l - 3

w = 8 - 3

w = 5

Therefore, the length of the toolbox is 8 feet and the width is 5 feet.

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Answer:0.15 miles a minute

Step-by-step explanation:

Her pace is 6 minutes and 40 seconds a mile, she is going 0.15 miles per minute and will go 9 miles an hour

15 - 60%

x - 100%

1500 = 60x

x = 25

∴ There are 25 students in the class in all.

Answer:

The answer is B

Step-by-step explanation:

To solve this, we need to combine like terms.
(9c-8d) + (2c-6) + (-d+3)
9c + 2c - 8d - d - 6 + 3
11c - 8d - d - 6 + 3
11c - 9d - 6 + 3
11c - 9d - 3

To show that the system AX = B is equivalent to the upper-triangular system UX = Y and find the solution, we need to use the Gaussian elimination method. The Gaussian elimination method is a process of reducing a system of linear equations to an equivalent upper-triangular system.

Step 1: Write the given system of equations in matrix form:
```
| 2 -2  5 |   | x1 |   |  6  |
| 2  3  1 | * | x2 | = | 13  |
|-1  4 -4 |   | x3 |   |  3  |
```
Step 2: Use the Gaussian elimination method to reduce the matrix to an upper-triangular form:
```
| 2 -2  5 |   |  6  |
| 0  7 -9 | = |  7  |
| 0  0 9/7|   | 18/7|
```
Step 3: Write the upper-triangular system in equation form:
```
2x1 - 2x2 + 5x3 = 6
0x1 + 7x2 - 9x3 = 7
0x1 + 0x2 + 9/7x3 = 18/7
```
Step 4: Solve the system using back substitution:
```
x3 = 18/7 * 7/9 = 2
x2 = (7 + 9*2)/7 = 4
x1 = (6 + 2*2 - 5*2)/2 = 1
```
Step 5: Write the solution in vector form:
```
| x1 |   | 1 |
| x2 | = | 4 |
| x3 |   | 2 |
```
Therefore, the solution to the system AX = B is x1 = 1, x2 = 4, and x3 = 2.

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Answer:

C

Step-by-step explanation:

I think its c because it said x = 3 less than 6, what is three less than 6? 3 so if you were to plug in 3 for x so bc = 3 and ab = 6 you multiply those two together but when you are doing area for a triangle its 1/2 bh so how i do this is i multiply 6 and 3 and get 18 and divide that by 2 and my final answer is 9. Hope this works, let me know if it doesnt!

1. To solve 3^(2x-1)=27, we first need to simplify 27 to  power of 3: 27=3^3
3^(2x-1)=3^3
Next, we can use the property that if the bases are the same, the exponents must be equal:
2x-1=3
Solving for x, we get:
2x=4
x=2

2. To solve 3^(x^2-3x)=81, we first need to simplify 81 to the power of 3: 81=3^4
3^(x^2-3x)=3^4
Next, we can use the property that if the bases are the same, the exponents must be equal:
x^2-3x=4
Solving for x, we can use the quadratic formula:
x=(-b±√(b^2-4ac))/(2a)
x=(-(-3)±√((-3)^2-4(1)(-4)))/(2(1))
x=(3±√(9+16))/2
x=(3±5)/2
x=4 or x=-1

3. To solve 4^(x+1)=64, we first need to simplify 64 to the power of 4: 64=4^3
4^(x+1)=4^3
Next, we can use the property that if the bases are the same, the exponents must be equal:
x+1=3
Solving for x, we get:
x=2

4. To solve 4^(x+1)=1/64, we first need to simplify 1/64 to the power of 4: 1/64=4^(-3)
4^(x+1)=4^(-3)
Next, we can use the property that if the bases are the same, the exponents must be equal:
x+1=-3
Solving for x, we get:
x=-4

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Answer:

a) The digit in the hundredths place in 0.453 is 3. Therefore, the value of the digit in color is 3/100.

b) The digit in the tenths place in 43.1 is 1. Therefore, the value of the digit in color is 1/10.

c) The digit in the thousandths place in 92.303 is 3. Therefore, the value of the digit in color is 3/1000.

d) The digit in the ten-thousandths place in 2.3214 is 1. Therefore, the value of the digit in color is 1/10,000.

radius of the circle is sqrt(3)x.

The radius of the circle can be found by using the Pythagorean Theorem. The side lengths of each equilateral triangle created by the diagonals is 2x, so the hypotenuse of the triangle is sqrt(3)x. Since the hypotenuse of each triangle is the same as the radius of the circle, the radius of the circle is sqrt(3)x.

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Answer:

No solution

Step-by-step explanation:

Use the given functions to set up and simplify f(9)

Given- A sequence as -6,-9,-12,-15

To find- The equation for the nth term of the arithmetic sequence and to find the value of [tex]a_{10}[/tex].

Explanation- The common difference is [tex]-9-(-6)=-3[/tex]

We know the arithmetic sequence formula is

[tex]a_n=a_1+(n-1)d\\a_n=-6+(n-1)(-3)[/tex]

When n=10

[tex]a_{10}=-6+(10-1)(-3)\\a_{10}=-6+9(-3)\\a_{10}=-6-27\\a_{10}=-33[/tex]

Final answer- The value of 10th term is -33.

Answer:

A

[tex]2y {}^{4} \div x {}^{4} [/tex]

Step-by-step explanation:

Divide 14 by 7 it will be 2.

Now divide the variables.

X variable will give you X{}^{-4} and y{}^{4}.

So bring X variable in the denominator to make it positive.

So your answer will be option A.

Answer:

A

Step-by-step explanation:

It was right for me

Yes, H is a subgroup. We can prove this by using the subgroup criterion, which states that a subset H of a group G is a subgroup if and only if it satisfies the following three conditions:

1. The identity element of G is in H.

2. If h1 and h2 are in H, then h1*h2 is in H.

3. If h is in H, then h^(-1) is in H.

Let's check if these conditions are satisfied for H:

1. The identity element of ???? is the zero function, f(x) = 0, which is differentiable. Therefore, the identity element is in H.

2. If h1 and h2 are in H, then they are both differentiable functions. The sum of two differentiable functions is also differentiable, so h1 + h2 is in H.

3. If h is in H, then it is a differentiable function. The inverse of a differentiable function under addition is its negative, which is also differentiable. Therefore,[tex]h^{-1} = -h[/tex] is in H.Since all three conditions are satisfied, H is a subgroup.

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Yes, this word problem is solvable using exponential functions.

To solve this problem, we need to use the formula for exponential growth:

P(t) = P0 * e^(rt)

where P(t) is the population after t hours, P0 is the initial population, r is the growth rate, and e is the mathematical constant approximately equal to 2.71828.

In this problem, we are given that the population doubles in size every 25 hours. This means that the growth rate is 1/25, since the population is multiplying by 2 each time.

We are also given that there are about 1.35 million infections every year. Since there are 365 days in a year, this means there are about 1.35 million/365 = 3699.18 infections per day.

We can now use this information to find the initial population:

P0 = 3699.18 / e^(1/25 * 24 * 365)

P0 ≈ 2135.05

So the initial population is about 2135.05 bacteria.

To find the population after one year, we can use the formula again:

P(365 * 24) = 2135.05 * e^(1/25 * 24 * 365)

P(365 * 24) ≈ 3.89 x 10^18

Therefore, there are approximately 3.89 x 10^18 bacteria present after one year.

The complex solutions to the given equation are -1 + i√2 and -1 - i√2.

To determine the complex solutions to the equation, we can first simplify the quadratic equation by dividing each term by 2. This gives x² + 2x + 3 = 0.

The discriminant (b² - 4ac) can be calculated to find the nature of roots.

b² - 4ac = 2² - 4(1)(3) = 4 - 12 = -8

As the discriminant is less than 0, the roots are imaginary roots. That is, the roots are complex numbers.

To find the roots of this quadratic equation, the following steps can be followed.

Since the coefficient of x² is 1, the quadratic formula can be used to solve the given quadratic equation. The quadratic formula is given by

x = [-b ± √(b² - 4ac)] / 2a

Substitute the given values into the formula.

x = [-2 ± √(-8)] / 2

On simplifying the above expression,

x = [-2 ± 2i√2] / 2= -1 ± i√2

Therefore, -1 + i√2 and -1 - i√2 are the complex roots or solutions of the given quadratic equation.

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Answer: C

Step-by-step explanation:

replace n=1 with f(n)= 5n-2 we have

f(1)=3 => remove answers B and D

f(n)= 5n-2 so f(n-1)= 5(n-1) -2=5n-7

Try with answers C and D to see if it satisfies this

f(n)= f(n-1)+5= 5n - 7+5=5n-2 => C is correct

E1 x E2 x E4 = (2 0) (0 1) (1 0) (3 1)

(a) A-1 can be expressed as a product of elementary matrices by following these steps:
1. Create a matrix A' = A (2 0)
                        (0 1)
2. Create an elementary matrix E1 = (1 -2)
                                            (0  1)
3. Multiply A' and E1 to get matrix E2 = (2 -4)
                                                            (0  1)
4. Create an elementary matrix E3 = (1  0)
                                            (-3 1)
5. Multiply E2 and E3 to get matrix E4 = (2  0)
                                                                        (-6 1)
6. Create an elementary matrix E5 = (1  0)
                                            (0  2)
7. Multiply E4 and E5 to get A-1 = (2  0)
                                                                  (-3 2)
Therefore, A-1 can be expressed as a product of elementary matrices, E1 x E3 x E5 = (2 0) (-6 1) (1 0) (0 2).

(b) A can be expressed as a product of elementary matrices by following these steps:
1. Create an elementary matrix E1 = (2  0)
                                            (0  1)
2. Create an elementary matrix E2 = (1  1)
                                            (0  1)
3. Multiply E1 and E2 to get matrix E3 = (2 1)
                                                                        (0 1)
4. Create an elementary matrix E4 = (1  0)
                                            (3  1)
5. Multiply E3 and E4 to get A = (2 1) (6 4)
Therefore, A can be expressed as a product of elementary matrices, E1 x E2 x E4 = (2 0) (0 1) (1 0) (3 1).

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The measure of the height of the tin in mm can be found using the steps below.

What are Measurements?

Measurement is the method of comparing the properties of a quantity or object using a standard quantity.

Measurement is essential to determine the quantity of any object.

Here, the activity is to measure the height of a tin.

Height of the tin is the vertical distance from the base of the tin to the top of the tin.

The height of the tin is the exact straight line measurement when the tin is placed upright on a flat surface.

The measurement has to be in millimeters.

So the best tool is the ruler.

Place the ruler vertically with point 0 at the baseline of the tin.

Mark the point in millimeters that the ruler coincides with the top of the tin.

Read the height to the nearest millimeter.

Hence, the height of the tin can be measured as above.

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The complete Question:

Measure the height of the tin in the mm and write down the real height in mm

Easton needs to complete 3 more jumps to reach his goal of completing 70% of the jumps on the skateboard course.

Easton's goal is to complete 70% of the jumps on the skateboard course. This means he needs to complete 70% of the total number of jumps.

We know that Easton has already completed 18 jumps out of 30, which is equivalent to completing 60% of the jumps.

The total number of jumps on the skateboard course is 30.

Easton's goal is to complete 70% of the jumps, which is:

0.7 x 30 = 21 jumps

Easton has already completed 18 jumps, so he needs to complete:

21 - 18 = 3 more jumps

So, he needs 3 more jumps

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After calculating the probability we get, there is a 7.20 percent chance that the first candidate will be identified during the fifth interview and it should take 3.33 interviews to discover the first candidate.

The quantity X of repeated trials needed to obtain r successes with p probability in a binomial experiment is known as the negative binomial distribution.

When x succeeds after n tries, the probability is given by:

P(X-x) = Cn-1, x-1*p(power x) * (1 - p)power (n-x)

The number of unique combinations of x items from a set of n elements, Cn,x, is determined by the formula below.

Cn,x = n! / x! ( n! - x! )

This problem involves that:

Let's say that 30 percent of those who apply for a certain industrial position have advanced expertise in computer programming. That follows that.

(a) We need to determine the probability that the first applicant with advanced programming training will be discovered during the fifth interview.

This is the likelihood that it will take 5 attempts to get 1 success.

So, n=5, x=1

P(X-x) = Cn-1, x-1*p(power x) * (1 - p)power (n-x)

P(X-5) = C 4,0* (0.30)(power 1) * (0.70)power (4)

= 0.0720.

During the sixth interview, there is a 7.20% chance that the first candidate with advanced programming training will be discovered.

(b) To find how many applicants should be expected to be interviewed in order to select the first candidate with advanced training, calculate

It is stated by how many trials are anticipated to result in r success:

E = r/p

Thus with the value r=1

E = r/p

= 1/0.3

= 3.33.

For the first candidate with advanced training, it will take an average of 3.33 interviews.

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