What are the next four numbers in the pattern below? ¼, ¾, 1 ¼, 1 ¾...

The airplane is approximately 1.7 miles from the runway at the start of the approach.

What is trigonometry?

Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry

To solve this problem, we need to use trigonometry. The angle of descent is 7 degrees, which means that the angle between the horizontal ground and the plane's flight path is 7 degrees. We can use the tangent function to find the distance from the runway:

tangent (7 degrees) = opposite / adjacent

The opposite side is the height of the plane above the ground, which is 1069 feet. The adjacent side is the distance from the plane to the runway, which we need to find.

tangent (7 degrees) = 1069 / adjacent

We can solve for the adjacent side by multiplying both sides by the denominator:

adjacent = 1069 / tangent(7 degrees)

Using a calculator, we get:

adjacent = 1069 / 0.122173048

adjacent = 8743.3 feet

To convert this to miles, we divide by the number of feet in a mile:

adjacent = 8743.3 / 5280

adjacent = 1.655 miles

Rounding to the nearest tenth of a mile, we get:

The airplane is approximately 1.7 miles from the runway at the start of the approach.

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Answer:

because 7*3*4 is 88 ft^3

Answer:

No , they are not

Step-by-step explanation:

Checking the ratios:

32/48 = 0.67

48/80 = 0.6

80/150 = 0.53

Since the values are not equal, they are not in proportion.

Answer:

32, 48, 80, and 150 are not in proportion.

Step-by-step explanation:

To determine if 32, 48, 80, and 150 are in proportion, we need to check if the ratio of any two numbers is equal to the ratio of any other two numbers in the set.

Let's check:

Ratio of 32 to 48: 32/48 = 2/3

Ratio of 48 to 80: 48/80 = 3/5

Ratio of 80 to 150: 80/150 = 8/15

Since the ratios are not equal, 32, 48, 80, and 150 are not in proportion.

To find the product of the face values (the values of the digits as they appear in the number) of all digits in 91250, we can simply multiply the face values of each digit together.

The face value of a digit is simply the value of the digit itself, regardless of its position in the number.

So, we have:

9 * 1 * 2 * 5 * 0 = 0

Note that the face value of the digit 0 is 0, so any product that includes a 0 will also be 0.

Therefore, the product of the face values of all digits in 91250 is 0.

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Answer:

The median of the data set is 18.5

Step-by-step explanation:

To find the median of this set of data values, we need to first arrange them in numerical order:

10, 14, 15, 17, 20, 21, 22, 25

The middle value is the median. If there is an odd number of values, there will be exactly one middle value, and if there is an even number of values, the median will be the average of the two middle values.

In this case, there are 8 values, which is an even number. So, we take the average of the sum of the 2 middle numbers:

Median of Data Set = (17 + 20)/2 = 18.5

Therefore, the median of the data set is 18.5.

By using a counting method, the driver can keep track of how many passengers have boarded the van, and by measuring the distance driven, they can update the odometer.

The formula for calculating the total number of passengers that can board a shuttle van is:

Total Passengers = Number of Seats in the Van - 1 (Driver)

For example, if the van has 10 seats, the total number of passengers that can board the van is 9 (10 - 1).

To keep track of how many passengers have boarded the van, we can use a simple counting method. Each time a passenger boards the van, the counter should be increased by 1. When the counter reaches the maximum number of passengers the van can hold, the driver should not allow any more passengers to board.

To update the odometer, the driver can measure the distance the van has driven since the last update. This can be done by using a GPS device or by measuring the distance between two points on a map. The total number of miles driven since the last update can then be added to the previous odometer reading to find the new odometer reading.

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Answer:

1st=3/50

2nd=2/50

3rd=1/50

thats is if the only possible number you can roll are only from 2,6 not 1,6

To the nearest degree, the angle of the incline was approximately 39°.

What is an angle?

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

We can use the inverse tangent function to calculate the angle of the incline. The angle θ is given by:

θ = tan⁻¹(opposite/adjacent)

where opposite is the vertical distance (the height Nick hiked) and adjacent is the horizontal distance (the distance he traveled eastward).

Using the Pythagorean theorem, we can find the height Nick hiked:

height = [tex]\sqrt{(10)^{2} - (8)^2}[/tex]≈ 6

So, the opposite is approximately 6 miles.

Now we can plug in the values to find the angle:

θ = tan⁻¹(6/8)

θ ≈ 38.66°

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In a case whereby concrete sidewalk is being put around a square park. If the diagonal line across the center of a square park is 24 feet, the exact length of each side is 12 feet.

Based on the given condition from the question, We know that A diagonal is a line segment that joins two opposing polygonal vertices (or corners). In other terms, a diagonal is a line segment that joins two polygonal vertices that are not next to one another. One type of straight line is the diagonal. There is no straight up, down, or across in a diagonal line. It is a line that joins two shape's corners.

Then we can formulate as 24/2

= 12 feet.

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Answer: 64 Rs

Step-by-step explanation:

Let x be the number of tables

4 x 48 = 3x

192 = 3x

x = 64

Yeah, it seems fine so you're doing great so far! ^^

The point [-8,-6] would be graphed 8 units left and 6 units down from the origin (0,0) on a coordinate grid.

A coordinate grid, also called a Cartesian plane, is a two-dimensional plane formed by a horizontal x-axis and a vertical y-axis that intersect at the origin (0,0). It is used to graph and locate points in a two-dimensional space by their x- and y-coordinates.

The coordinate grid is formed by two perpendicular lines, the horizontal x-axis and the vertical y-axis.

The point [-8,-6] represents an ordered pair where -8 is the x-coordinate and -6 is the y-coordinate.

To graph this point on a coordinate grid, start at the origin (0,0), which is where the x-axis and y-axis intersect. Then, move 8 units to the left along the x-axis since the x-coordinate is negative.

After that, move 6 units down along the y-axis since the y-coordinate is negative. The point where you end up after moving left 8 units and down 6 units is the point (-8,-6).

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The only common factor is [tex]b^{2}[/tex] so the GCF is [tex]14b^{3}[/tex] and [tex]5b^{2}[/tex] is [tex]b^{2}[/tex]

The term "common" means "same for both." The two numbers' common factor is one that applies to both numbers.

The common factor between [tex]6[/tex] and [tex]10[/tex] is [tex]2[/tex], for instance. Although it is not the sole quality shared by each number, it is a trait that they both have in common.

To find the GCF of [tex]14b^{3}[/tex] and [tex]5b^{2}[/tex] we need to find the largest factor for both

[tex]14b^{3}[/tex] = 2*7*[tex]b^{2}[/tex]*[tex]b[/tex]

[tex]5b^{2}[/tex] = [tex]5*b^{2}[/tex]

Therefore the only common factor is [tex]b^{2}[/tex] so the GCF is [tex]14b^{3}[/tex] and [tex]5b^{2}[/tex] is [tex]b^{2}[/tex]

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Answer:Factorise. 15(k+g)² - 20 (k+g)​

Step-by-step explanation:=[15(k+g)-20] (k+g)

                                            =15 k²+15kg-20k+15kg+15g²-20g                                                  

                                            =15k²+15g²+30kg-20k-20g

Answer:

600ft²

Step-by-step explanation:

Volume of a cube V = a³

a³ = 1000

Cube root of both sides

a = 10ft

Surface area A =6a²

A = 6 x 10 x10 ft²

Answer:

600 feet²

Step-by-step explanation:

1) Break down the info

To answer this question we have to figure out the values of the sides. As it is a cube all sides should have the same area and length!

We know that the equation for volume is...

This means that to simply find the sides, we can cube root 1000

Let's check...

2) Find the surface area

We now know that the sides are 10 feet each so to find the surface area is [tex]6a^2[/tex] where a is the length of one side!

We can solve the question by plugging our numbers into the equation...

Our surface area is 600 feet!

Hope this helps, have a lovely day! :)

The correct decision rule for a test hypothesis with a significance level of 0.02, with two tails, is given as follows:

C. Reject H0 if Zstat< -2.33 or Zstat > +2.33.

The decision regarding the null hypothesis depends on if the p-value is less or more than the significance level:

For a two-tailed test with a significance level of 0.02, the critical value is given as follows:

z = 2.33.

Hence the decision rule is given as follows:

Hence option C is the correct option for this problem.

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Mike cannot attain a mean grade of 85% for every one of his studies since a grade higher than 100% is not feasible.

The sum of all numbers divided by the entire number of values determines the mean (also known as the arithmetic mean, which differs from of the median) of a dataset. This central tendency is usually referred to as the "average".

Just dividing the total amount of information in a data collection even by sum of all of the values yields it. Both raw data and data that have been compiled into a frequency distribution table can be used for the computation.

mean = (sum of all numbers) / (number of numbers)

80% = (82% + 75% + 78% + 80% + m) / 5

85% = m

The another equation is,

85% = (82% + 75% + 78% + 80% + m) / 5

425% = 315% + m

110% = m

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Answer: 12=7

Step-by-step explanation: add one side ten add the other

Yes, this is a solution because the point(s) at which all the lines intersect are the solutions to the system.

Answer:

Step-by-step explanation:

I think to get the height is length x width

for distance you need to so SOH CAH TOA

The retail price of each art supply bundle, including the markup, would be $127.50.

The gross or whole profit on a certain item or service is what is meant by markup. Moreover, it can be shown as a % of the cost price. For instance, if a product costs Rs. 100 and is sold for Rs. 150, the markup in this case will be 50%.

In studying the fundamentals of business, students come across the words selling price and cost price. A commodity's cost price is the amount paid when buying it from a retailer. The selling price, however, is the cost at which it is offered for sale.

Given that, the products were marked them up by 70%, then the selling price would be:

Selling price = $75 + 70% of $75

Selling price = $75 + $52.50

Selling price = $127.50

Therefore, the retail price of each art supply bundle, including the markup, would be $127.50.

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Answer:

the a give the x value twords the b and adds up the equation

Assuming the family size selected is 6 persons,

Assuming the family size selected is 6 persons, the minimum diameter of a circular table to seat all members would be:

Minimum diameter = (Number of persons x Minimum distance between two persons) / π

= (6 x 24) / 3.14

= 45.86 inches (rounded up to 46 inches)

The minimum length of the side of a square table to seat all members would be:

Minimum length of side = (Number of persons x Minimum distance between two persons) / √2

= (6 x 24) / 1.41

= 101.41 inches

The area of the top of the circular table would be:

Area = π x (Diameter / 2)²

= π x (46 / 2)²

= 1,660.51 In²

The area of the top of the square table would be:

Area = (Length of side)²

= 102²

= 10,404 In²

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a. the factors of equation is [tex]f(x)=(x-1)(x-10)(2x-3)[/tex]

b. the factors of equation is [tex]f(x)=(x-1)(x^2+x+4)[/tex]

A polynomial is an expression consisting of variables and coefficients that involves only the operations of addition, subtraction, and multiplication, with non-negative integer exponents.

a. Given function,

[tex]f(x)=2x^3 -25x^2 + 53x - 30[/tex]

By using trial and error method, put values of x =1, x= 10, and x= 3/2 are satisfied values for above function,

[tex]f(x)=(x-1)(x-10)(2x-3)[/tex]

therefore, the factors of equation is (x-1) (x-10) (2x-3)

b. Given function,

[tex]f(x)=x^3 +3x - 4[/tex]

Similarly using trial and error method,

[tex]f(x)=(x-1)(x^2+x+4)[/tex]

therefore, the factors of equation is (x-1) (x² + x + 4)

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Factor of given polynomials are a. (x-1)(x-10)(2x-3), b. (x-1)(x² + x + 4) .

In mathematics, a polynomial is an expression that consists of variables and coefficients, combined using the operations of addition, subtraction, and multiplication, but not division by a variable. The variables in a polynomial can only have non-negative integer exponents.

Polynomials can have different degrees, which is the highest power of the variable in the expression. For example, the polynomial 3x² - 5x + 2 is a quadratic polynomial, since its highest power of x is 2. If the degree of a polynomial is n, then it has at most n roots, which are the values of x that make the polynomial equal to zero.

Polynomials are used in many areas of mathematics and science, including algebra, calculus, physics, and engineering. They are used to model and analyze many different types of phenomena, such as motion, population growth, and electrical circuits.

Polynomials can also be added, subtracted, and multiplied together to form new polynomials. Additionally, polynomials can be factored, which involves breaking them down into simpler polynomials that multiply together to give the original polynomial.

a) f(x)= 2x³ - 25x² + 53x - 30
⇒(x-1)(x-10)(2x-3)

b) f(x)= x³ + 3x - 4
⇒(x-1)(x² + x + 4)

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The complete question is:

The length of the rectangular prism is 1 inch.

The volume of a rectangular prism can be calculated using the formula V = lwh, where l is the length, w is the width, and h is the height. In this case, the volume of the prism is given as 1 cubic inch and the width and height are given as 1 inch and 1 inch, respectively. To solve for the length of the prism, we can rearrange the equation to l = V/wh. Plugging in our given values, we can calculate the length of the prism as l = 1/1 x 1 = 1 inch. Thus, the length of the rectangular prism is 1 inch.Therefore, the length of the rectangular prism is 1 inch.

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Answer:

its a negative slope because the battery is going down, not staying the same, or going up

Step-by-step explanation:

If the perimeter is 27 yards, then the length of the other side of the rectangle is 3.5 yards.

Let's start by defining our variables. Let x be the length of one side of the rectangle (in yards), and let y be the length of the other side. We know from the problem statement that one side is three yards longer than twice the length of the other side, so we can express this algebraically as:

x = 2y + 3

The perimeter of a rectangle is given by the formula P = 2(x + y), so we can substitute our expression for x into this formula:

P = 2(2y + 3 + y) = 2(3y + 3) = 6y + 6

We are given that the perimeter of the rectangle is 27 yards, so we can set up an equation:

6y + 6 = 27

Solving for y, we can subtract 6 from both sides and then divide by 6:

6y = 21

y = 3.5

To check our answer, we can plug it back into our equation for x:

x = 2y + 3 = 2(3.5) + 3 = 7 + 3 = 10

So the other side of the rectangle is 10 yards long. We can verify that the perimeter is indeed 27 yards:

P = 2(x + y) = 2(10 + 3.5) = 2(13.5) = 27

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Complete question is:

One side of a rectangle is three yards longer than twice the length of the other side. If the perimeter is 27 yards, what is the length of the other side?

A serving of skinny popcorn has 4 grams of fiber, which is about 16% of the recommended daily amount of fiber. The recommended daily amount of fiber is 25 grams.

If a serving of skinny popcorn has 4 grams of fibre and provides 16% of the necessary daily fibre intake, we can apply a proportion to calculate the entire recommended daily fibre intake:

If x is the required daily fibre intake in grams, we may calculate the following proportion:

4 / x = 16 / 100

We may cross-multiply and simplify to find x:

4 × 100 = 16 × x

400 = 16x

x = 25

As a result, the daily fibre recommendation is 25 grams.

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The equation that shows the relation ship between t and p is 0 ≤ t < 270.

A linear equation is an algebraic equation where the highest power of the variable is 1, and the equation represents a straight line when graphed.

Break down the information given in the problem to form an equation that relates the time t and the number of yards of painted fence p:

Tom painted 8 yards before running away, so Sid had to paint the remaining length of the fence, which is L - 8 yards, where L is the total length of the fence.

From noon to 12:30 p.m., Sid painted 14 - 8 = 6 yards.

From 12:30 p.m. to 2:00 p.m., Sid painted 32 - 14 = 18 yards.

From 2:00 p.m. to 2:30 p.m., Sid painted 38 - 32 = 6 yards.

We want to find an equation that relates the time t (in minutes) to the number of yards of painted fence p.

Based on the information above, we can create a piecewise equation that relates t and p:

p = { 8 + 0.2t, 0 ≤ t < 30

14 + 0.6(t - 30), 30 ≤ t < 90

32 + 0.4(t - 90), 90 ≤ t < 150

38 + 0.2(t - 150), 150 ≤ t < 210 }

Explanation of the equation:

The first segment of the piecewise equation, 8 + 0.2t, represents the yards of fence painted by Tom (8) plus the yards painted by Sid in the first 30 minutes (0.2t), where 0 ≤ t < 30.

The second segment, 14 + 0.6 (t - 30), represents the additional yards painted by Sid between 12:30 p.m. and 2:00 p.m., where 30 ≤ t < 90. The expression (t - 30) represents the time elapsed since 12:30 p.m., and the coefficient 0.6 represents the rate at which Sid is painting the fence in yards per minute during this period.

The third segment, 32 + 0.4 (t - 90), represents the additional yards painted by Sid between 2:00 p.m. and 2:30 p.m., where 90 ≤ t < 150. The expression (t - 90) represents the time elapsed since 2:00 p.m., and the coefficient 0.4 represents the rate at which Sid is painting the fence in yards per minute during this period.

The fourth segment, 38 + 0.2 (t - 150), represents the additional yards painted by Sid between 2:30 p.m. and 4:30 p.m., where 150 ≤ t < 210. The expression (t - 150) represents the time elapsed since 2:30 p.m., and the coefficient 0.2 represents the rate at which Sid is painting the fence in yards per minute during this period.

Note that we have limited the time t to be between noon and 4:30 p.m., which corresponds to 0 ≤ t < 270.

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The statement: If ∠F is a 60° angle, then cos (F) = sin (F), is never true.

Two of the six trigonometric functions used to connect angles to the sides of a right triangle are sine and cosine. The length of the opposite side of an angle divided by the length of the hypotenuse of a right triangle is known as the sine function. The length of the adjacent side of an angle divided by the length of the hypotenuse of a right triangle is known as the cosine function.

We know that,

If angle F is 60 degrees, then the value of cos F = 1/2 and sin F = sqrt(3)/2.

Therefore, cos F is not equal to sin F and the statement is never true.

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Answer:

A answer that is not yet known.

Step-by-step  

For example x is to sub in 21 but you do not know that yet

until you solve the question.