suppose that two people standing 2 miles apart both see the burst from a fireworks display. after a period of time, the first person standing at point a hears the burst. one second later, the second person standing at point b hears the burst. if the person at point b is due west of the person at point a and if the display is known to occur due north of the person at point a , where did the fireworks display occur?

The distance between the third traffic light from the second traffic light is 35 yards.

Three traffic lights on a street span 120 yards.

If the second traffic light is 85 yards away from the first.

Therefore, the third traffic light is 120 - 85 =35 yards away from the second traffic light.

This means that the third traffic light is directly adjacent to the first traffic light. The third traffic light from the second traffic light is at the same location as the first traffic light.

Thus, the distance between the third traffic light from the second traffic light is 35 yards.

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Answer:

We can use similar triangles to solve this problem. Let's call the length of the kite's line "x". Then, we can set up a proportion:

(length of kite) / (length of shadow) = (height of kite) / (length of shadow)

x / 9 = 10 / 9

To solve for x, we can cross-multiply and simplify:

x = 90 / 9

x = 10

Therefore, the length of the kite's line is 10 feet.

Step-by-step explanation:

Accοrding tο the fοrmula fοr the quadratic equatiοn, the maximum height is 98 ft.

A quadratic equatiοn is a secοnd-degree pοlynοmial equatiοn οf the fοrm:

[tex]ax^2 + bx + c = 0[/tex]

where a, b, and c are cοnstants, and x is the variable. The term "quadratic" cοmes frοm the Latin wοrd "quadratus," meaning square, because the variable is squared in this type οf equatiοn.

Quadratic equatiοns can have οne, twο, οr zerο real sοlutiοns, depending οn the values οf the cοnstants a, b, and c. The sοlutiοns can be fοund using the quadratic fοrmula:

[tex]x = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex] οr by factοring the quadratic expressiοn intο twο linear factοrs.

The quadratic functiοn tο mοdel the vertical mοtiοn is:

[tex]h(t) = -16t^2 + v0t + h0[/tex]

where:

h(t) is the height at time t

t is the time in secοnds

v0 is the initial vertical velοcity in ft/s

h0 is the initial height in ft

Given v0 = 32 ft/s and h0 = 82 ft, the functiοn becοmes:

[tex]h(t) = -16t^2 + 32t + 82[/tex]

Tο find the maximum height, we can use the vertex fοrm οf a quadratic equatiοn:

[tex]h(t) = a(t - t0)^2 + h0[/tex]

where:

a is the cοefficient οf the quadratic term

t0 is the time at which the maximum height is achieved

h0 is the initial height

Cοmparing the twο fοrms, we see that a = -16 and t0 = -b/2a, where b is the cοefficient οf the linear term. In this case, b = 32, sο:

t0 = -32 / (2(-16)) = 1

Therefοre, the maximum height is achieved at t = 1 secοnd. Substituting intο the οriginal equatiοn, we get:

[tex]h(1) = -16(1)^2 + 32(1) + 82 = 98 ft[/tex]

Sο the maximum height is 98 ft.

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The number of litres (Volume) of oil that is present in the tank of given dimension is calculated to be 806 litres (approximately).

The volume of any cylinder can be calculated using the formula,

V = πr²h

(Here V is the volume, r is the radius of the base, and h is the height of the cylinder)

As, the cylinder is one-fifth full of oil, which means that it is four-fifths empty. Therefore, the volume of oil in the tank is:

Volume of oil = (1/5) x Total Volume

Substituting the given values, we have:

Total Volume =  π(80cm)²(200cm) = 4,031,240 cm³

Volume of oil = (1/5) x 4,031,240 cm³ = 806,248 cm³

Converting cm³ to litres, we have:

1 litre = 1000 cm³

Volume of oil = 806,248 cm³ ÷ 1000 = 806.248 litres

Therefore, after rounding of the final volume (806.248 litres) to the nearest litre, the final answer is found to be 806 litres of oil.

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The product of (4x + 7) and (3x - 8) is 12x² + 7x - 56.

WHAT IS BOX METHOD ?

The box method, also known as the grid method, is a visual method used to multiply two numbers or two binomials. It involves creating a grid or box and filling it in with the products of the digits in each row and column. The method works for both single-digit and multi-digit numbers.

To use the box method for multiplying two numbers, we draw a box with two rows and two columns. We write one number along the top row and the other number along the left column. Then, we multiply the digits in each row and column and write the products in the corresponding cell of the box. Finally, we add the numbers in each cell of the box to get the product of the two numbers.

The box method can be used to multiply two binomials, such as (4x + 7) and (3x - 8). To use the box method, we draw a box with four cells, and we write the two binomials along the top and left sides of the box, like this:

     |  4x  |  7

-------------------

 3x  |      |

-------------------

    |      |

Then, we fill in the four cells of the box by multiplying the corresponding terms. For example, the top-left cell is filled by multiplying 4x and 3x, which gives 12x². The other cells are filled in a similar way:

     |  4x  |  7

-------------------

 3x  | 12x² | 28x

-------------------

    | -21x | -56

Next, we combine the terms in each row and column of the box, and write the final answer as the sum of these terms:

12x² + 28x - 21x - 56

Simplifying this expression gives:

12x² + 7x - 56

Therefore, the product of (4x + 7) and (3x - 8) is 12x² + 7x - 56.

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The solution of system of inequalities solved graphically is (18,6).

A group of two or more linear inequalities are graphed together on a coordinate plane to discover the solution that concurrently satisfies all the inequalities. This is known as a system of linear inequalities. The location where all the half-planes overlap is where the system is solved. Each inequality defines a half-plane on the coordinate plane. Every point in this area, which is referred to as the feasible region, fulfils all of the system's inequalities. To identify the optimum solution for an optimization problem given a set of constraints, systems of linear inequalities are frequently utilised.

Let us suppose the number of dimes = a.

Let us suppose the number of nickels = y.

According to the problem we have the following conditions:

a + y ≤ 28 (at most 28 coins)

0.10a + 0.05y ≥ 2 (worth at least $2)

a ≥ 18 (at least 18 dimes)

y ≤ 6 (no more than 6 nickels)

Using different values of a and y plot the points.

The solution of this system of inequality is any point that lies in the feasible region.

One such point is (18, 6).

Hence, the solution of system of inequalities solved graphically is (18,6).

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The division problem provided by the model shown here is [tex]3[/tex] ÷  [tex]\frac{1}{4}[/tex].

The first step of dividing fractions is to get the reciprocal of a second fraction, which involves flipping its numerator and denominator. Multiply all two numerators after that. Multiply the 2 denominators after that. Then finish, if required, simplify the fractions.

Simple Division: Little numbers can be divided into groups and pieces using the simple division method in mathematics. Divide easy and basic division problems into terms that can be divided using simple division sums. Arithmetic, subtraction, multiplying, & division are the four fundamental mathematical operations.

Given:

We have three section [tex]1+ 1 + 1= 3[/tex]

[tex]= \frac{4}{12}[/tex]

[tex]= \frac{1}{3}[/tex]

In this case, the model yields the division issue.

[tex]3[/tex] ÷ [tex]\frac{1}{4}[/tex]

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The surface area of the triangular prism is 2016 [tex]feet ^2[/tex], we get to the answer by adding area of all faces in this prism.

What is surface area ?

Surface area is the sum of the areas of all the faces or surfaces of a 3D object, measured in square units.

To find the surface area of the triangular prism, we need to calculate the area of each of its faces and then add them up.

First, let's find the area of the triangular base.

Area of triangle = (1/2) x base x height

Area of triangle = (1/2) x 18 x 24

Area of triangle = 216 [tex]feet ^2[/tex]

Next, let's find the area of each rectangular face.

Area of rectangle = length x width

Area of rectangle 1 = 24 x 22 = 528 [tex]feet ^2[/tex]

Area of rectangle 2 = 18 x 22 = 396 [tex]feet ^2[/tex]

Area of rectangle 3 =  22 x 30 = 660 [tex]feet ^2[/tex]

Now, we can add up the areas of all three faces to get the total surface area of the prism:

Surface area = area of rectangle (1+2+3) + 2 x area of triangle

Surface area = 528 + 396 + 660 + 2(216)

Surface area = 2016 [tex]feet ^2[/tex]

Therefore, the surface area of the triangular prism is 2016 [tex]feet ^2[/tex].

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Angles AOB and BOC are complimentary angles if AOC is a right angle. Let's use x to represent the angle BOC's size. Next, we have: Angle AOB plus Angle BOC equals 90° (definition of complementary angles).

BOC/AOB angle equals 2/3 (given) Angle AOB may be expressed in terms of angle BOC using the second equation: (3/2) × angle BOC, where angle AOB (multiplying both sides by angle AOB)    Angle BOC plus angle (3/2) equals 90 degrees. When we simplify this equation, we obtain: BOC angle (5/2) times equals 90 degrees. By multiplying both sides by 5, we obtain: BOC angle = (2/5) x 90 degrees BOC angle is 36 degrees. Hence, the angle's size Substituting this expression into the first equation, we get: (3/2) x angle BOC + angle BOC = 90 degrees Simplifying this equation, we get: (5/2) x angle BOC = 90 degrees.

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a) If the number 646 from the ordered list changes to 639, c) the median stays the same.

b) a) If the number 646 from the ordered list changes to 639, a) the mean decreases by 1.

The median is the middle value in an ordered list (descending or ascending).

The mean refers to the average value.

The mean or average is computed as the quotient of the division of the total data value by the total number of items in the data set.

The ordered numbers of trading cards owned by 7 middle-school students = 360, 373, 402, 499, 548, 644, 646

The total value (sum) = 3,472

The number of cards = 7

The median = 499

The mean = 496 (3,472/7)

If the number 646 changes too 639:

The total value (sum) = 3,465

The median = 499

The mean = 495 (3,465/7)

Difference in mean = 1 (496 - 495)

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Answer:

Were sorry! Answer is not available right now check in later.

Step-by-step explanation:

It would make it easier for the cafe to adjust prices if necessary, as they would only need to modify the cost per ounce for each size.

Cost is the amount of money or resources required to purchase or produce something. It can be the total expenditure on a product, service, or activity. It can also refer to the amount of money or resources consumed in order to maintain or achieve something. Cost can also be the value of a resource lost or sacrificed in order to obtain something.

To make the price of smoothies a function of the size, the sign should be modified to include the following additional information:

8 ounce       $2.29/ounce
12 ounce      $2.79/ounce
12 ounce.     $3.09/ounce
16 ounce       $3.69/ounce
20 ounce        $4.09/ounce
22 ounce
( Bonus size).  $4.09/ounce

This change would make the price of smoothies a function of the size, as each smoothie size would then have its own associated cost per ounce. This would make it easier for customers to compare the cost of different sizes and make an informed decision. Furthermore, it would make it easier for the cafe to adjust prices if necessary, as they would only need to modify the cost per ounce for each size.

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1. The retail prices are: $44.36, $34.10 and $67.57

2. The sales prices are: $263.20 and $65.59

Retail price refers to the price at which a product or service is sold to the final consumer by a retailer. This price includes the cost of production, transportation, marketing, and other related expenses, as well as a markup to generate profit for the retailer.

1. New Items - Calculate Retail Prices

  Item                    Wholesale        Mark Up       Calculation              Retail

                              Cost ($)            Percent%                                      Price ($)

a. Louisville             $22.75             95%          22.75+(95%×22.75)  =$44.36

Slugger bat and

batting glove set

b. Wilson                 $11.00                210%         11+(210%×11)              =$34.10

Basketball

c. Element               $26.50              155%      26.50+(155%×26.50) =$67.57

Skateboard

2. Items on sale - Calculate Sale Prices

    Item                 Retail             Discount           Calculation            Sales

                           price ($)          Percent %                                       Price ($)

a. Head              $329.00              20%          329-(20%×329)         $263.20

Snowboard

b. Kelly                $79.99                18%           79.99-(18%×79.99)     $65.59

Ski poles

All data is filled in below table.

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Step-by-step explanation:

20% off means you pay 80 % of the original price for two books

80% * ( 2 x 19.95 ) = .8 ( 39.90) = $ 31.92

If there are 500 students in total, the number of students who made the honor roll is 10 students, given that the ratio of students who made the honor roll to the total number of students is 1:50.

The number of students who made the honor roll can be found using proportions. Here's how to do it:

Let X be the number of students who made the honor roll.

The proportion can be set up using the given ratio as follows:

1:50 = X:500

Cross-multiplying this equation and solving for X gives:

50X = 500

X = 10

Therefore, 10 students made the honor roll.

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The cost of the notebook is $4.50

Let's call the cost of the necklace "N" and the cost of the scarf "S". We know that Elise spent a total of $184 on the scarf, necklace, and notebook, so we can write:

S + N + NB = 184

We also know that after making her purchases, Elise had $89.50 left, so we can write:

89.5 = 184 - (S + N + NB)

Simplifying this equation, we get:

S + N + NB = 94.5

We're also given that the scarf cost three-fifths the cost of the necklace, so we can write

S = (3/5)N

Finally, we're told that the notebook cost one-sixth as much as the scarf, so we can write:

NB = (1/6)S

Now we can the substitution method here

(3/5)N + N + (1/6)(3/5)N = 184 - 89.5

Simplifying the right-hand side

(3/5)N + N + (1/6)(3/5)N = 94.5

Combining like terms on the left-hand side

(21/10)N = 94.5

Multiplying both sides by 10/21

N = 45

So the necklace cost $45. We can use this to find the cost of the scarf

S = (3/5)N = (3/5)($45) = $27

And we can use the cost of the scarf to find the cost of the notebook

NB = (1/6)S = (1/6)($27) = $4.50

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Answer:392

Step-by-step explanation:

a) It would take one machine 392 minutes.

b) It would take one machine 49 minutes.

Two ratios are said to be equal when a proportion is stated. When comparing two quantities, ratios are used to divide one quantity by the other.

a) Here given that, to produce a batch of newspaper 7 printing machines needed 56 minutes.

Using this relationship, we can set up a proportion:

as given, 7 printing machine needed = 56 minutes

So, 1 printing machine needed = 7 × 56 minutes = 392 minutes

Therefore, it would take one machine 392 minutes to produce the same batch of newspapers.

b) Similarly, to find out for 8 machines to produce the same batch of newspapers, we can use the same relationship:

1 printing machine needed = 392 minutes

So, 8 printing machine needed = (392 / 8) minutes = 49 minutes

Therefore, it would take one machine 49 minutes to produce the same batch of newspapers.

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The equation that is equivalent to 2x + 6 = 30 - x - 3 is option (a): 2x + 6 = 30 - x - 3.

What is equation?

In mathematics, an equation is a statement that two expressions are equal, usually written with an equal sign (=) between them. Equations can contain variables, which are symbols that represent unknown or unspecified values.

We can simplify and solve the equation 2x + 6 = 30 - x - 3 as follows:

2x + 6 = 30 - x - 3

Adding x and adding 3 to both sides, we get:

3x + 9 = 30

Subtracting 9 from both sides, we get:

3x = 21

Dividing both sides by 3, we get:

x = 7

So the given equation simplifies to x = 7.

We can now substitute this value of x into each of the answer choices to see which one is equivalent to the given equation:

a) 2x + 6 = 30 - x - 3

Substituting x = 7, we get:

2(7) + 6 = 30 - 7 - 3

14 + 6 = 20

20 = 20

b) 2x + 6 = 10 - x - 3

Substituting x = 7, we get:

2(7) + 6 = 10 - 7 - 3

14 + 6 = 0

20 ≠ 0

Therefore, this equation is not equivalent to the given equation.

c) 2x + 6 = 30 - x + 3

Substituting x = 7, we get:

2(7) + 6 = 30 - 7 + 3

14 + 6 = 26

20 ≠ 26

Therefore, this equation is not equivalent to the given equation.

Therefore, the equation that is equivalent to 2x + 6 = 30 - x - 3 is option (a): 2x + 6 = 30 - x - 3.

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Answer:

6x + 7

Step-by-step explanation:

triangle has 3 sides right, which is 2x, 3x+5 and x+2

so basically you just have to add everything up since perimeter is just the total number of each sides combined

2x + (3x+5) + (x+2)

expand from the brackets

2x + 3x + 5 + x + 2

rearrange the numbers to avoid confusion

2x + 3x + x + 5 + 2

add everything up

6x + 7

Answer:

2/9 + 5/36 = 17/36

So the probability of getting 2 marbles of the same color is 17/36 or 0.472.

Answer:

17/36

Step-by-step explanation:

Answer: The smallest integer value of x that satisfies the inequality -2x+1<-9 is x=5.

Step-by-step explanation:

Answer: The smallest integer value of x that satisfies the inequality -2x+1<-9 is x=5.

Explanation:

To solve the inequality, we need to isolate the variable x on one side of the inequality symbol. Here are the steps:

   Subtract 1 from both sides of the inequality:

   -2x < -10

   Divide both sides of the inequality by -2, remembering to reverse the direction of the inequality symbol:

   x > 5

Therefore, the smallest integer value of x that satisfies the inequality is x = 5, since any value less than 5 would make the inequality false.

Answer:

x = 6

Step-by-step explanation:

- 2x + 1 < - 9 ( subtract 1 from both sides )

- 2x < - 10

divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity.

x > 5

since x must be greater than 5, it cannot equal 5

then the smallest integer value of x is x = 6

The required value of the base of the triangle is   [tex]\frac{7\sqrt{3} }{3}[/tex].

Right-angle triangles are formed when the angle formed by two of their edges is exactly 90 degrees. Obtuse angle triangle: An obtuse angle triangle is one in which the angle formed by two sides is larger than 90 degrees.

In the given triangle, we will use tangent function to find the value of x.

tan(∅) = Perpendicular/ base

tan(60°) = 7/x

x = 7/tan(60°)

x = 7/√3                         ∴ (tan(60°) =√3  )

On rationalizing

x = [tex]\frac{7\sqrt{3} }{3}[/tex]

Thus, required value of x is [tex]\frac{7\sqrt{3} }{3}[/tex].

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Elise walked a distance of 9.2 kilometers on Tuesday.

To solve the problem, we need to first understand the information provided.

On Monday, Elise walked a distance of 9.9 kilometers.

On Tuesday, she walked a distance that was 0.7 kilometers less than what she walked on Monday.

This means that we need to subtract 0.7 kilometers from the distance that she walked on Monday to find the distance she walked on Tuesday.

To do this, we can use subtraction. We start by writing down the distance Elise walked on Monday, which is 9.9 kilometers, and then subtract 0.7 kilometers from it.

9.9 km - 0.7 km = 9.2 km

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The equation to show the relationship between x and y is y = 0.08x, where y is the amount of sales tax in dollars for the item and x is the cost of the item in dollars before tax.

Tax is a compulsory financial charge or some other type of levy imposed upon a taxpayer by a governmental organization in order to fund various public expenditures. A failure to pay, along with evasion of or resistance to taxation, is punishable by law. Taxes consist of direct or indirect taxes and may be paid in money or as its labour equivalent. Most countries have a tax system in place to pay for public, common or agreed national needs and government functions. Some levy a flat percentage rate of taxation on personal annual income, but most scale taxes based on annual income amounts.

This equation reflects the fact that the amount of sales tax for an item is 8% of its cost before tax.

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Sales tax: The equation to show the relationship between x and y is x + y = C,

An equation is a mathematical statement that expresses two mathematical expressions to be equal. It usually consists of two numbers, variables, or a combination of the two. An equation may be used to calculate a desired result, or to determine the relationship between two variables. Equations can also be used to test whether a statement is true or false. Most equations are written in the form of "a = b," where a and b are two numbers or variables.

where C is the cost of the item plus the sales tax. This equation can be explained mathematically as follows: the cost of the item (x) is added to the amount of sales tax (y) to give the total cost of the item with tax (C).

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1/6 + 1/4= 10/24 (5/12 simplified)

2.50× 12= 30

This is the total sum of money shared.

7/12 is given to Farooq

7/12 of 30 is 17.5

answer= £17.5

The new ordered pairs of points A', B', and C' after the reflection over the y-axis are (1,-2.5), (0,1.5), and (-3,-1.5), respectively.

WHAT IS AXIS ?

An axis is a straight line around which an object rotates or is symmetrical. In geometry, it is a reference line that is used to measure distances, angles, and other geometric properties of objects. In a two-dimensional plane, there are two axes: the x-axis and the y-axis. The x-axis is the horizontal line that runs from left to right, while the y-axis is the vertical line that runs from bottom to top. Together, the x-axis and y-axis form a coordinate system that is used to plot points and graph functions. In three-dimensional space, there is also a z-axis that runs perpendicular to the x-axis and y-axis

To perform a dilation with a scale factor of 1/2 around the origin, we need to multiply the coordinates of each point by 1/2. This gives us:

A' = (1/2)A = (1/2)(-2,-5) = (-1,-2.5)

B' = (1/2)B = (1/2)(0,3) = (0,1.5)

C' = (1/2)C = (1/2)(6,-3) = (3,-1.5)

The new coordinates of points A, B, and C after the dilation are (-1,-2.5), (0,1.5), and (3,-1.5), respectively.

To reflect each point over the y-axis, we need to change the sign of its x-coordinate, while leaving the y-coordinate unchanged. This gives us:

A" = (-x,y) = (-(-1),-2.5) = (1,-2.5)

B" = (-x,y) = (-0,1.5) = (0,1.5)

C" = (-x,y) = (-3,-1.5) = (-3,-1.5)

The new ordered pairs of points A', B', and C' after the reflection over the y-axis are (1,-2.5), (0,1.5), and (-3,-1.5), respectively.

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As a result, utilizing the graph of the growth function is preferable for describing the growth of the mosquito population .

A vector is a mathematical concept that possesses both magnitude (or length) and direction. In physics, engineering, and other sciences, physical quantities with both a size and a direction, such as velocity, force, and acceleration, are frequently represented by vectors. In geometry, vectors can be represented as arrows, with the direction of the arrow indicating the vector's magnitude and the length of the arrow indicating its magnitude. In addition to being able to represent points in space and describe curves and surfaces, vectors may also be added, subtracted, and multiplied by scalars to create new vectors.

given

Based on the provided table and the growth function graph, I would argue that the report on the growth of the mosquito population is better supported by the graph.

On the other hand, there is no visual representation of the growth of the mosquito population in the table; it merely displays the data in a tabular format.

Although the table contains the same data as the graph, it is more difficult to understand and evaluate.

As a result, utilizing the graph of the growth function is preferable for describing the growth of the mosquito population .

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Answer:

y = 1/7x + 29/7

Step-by-step explanation:

Slope intercept form is y = mx + b

m = the slope

b = y-intercept

m = 1/7

Y-intercept is located at (0, 29/7)

So, the equation is y = 1/7x + 29/7

Function P represents the perimeter, in inches, of a square with the side length x inches. So, the perimeter of a square can be represented as P = x + x + x + x, which simplifies to P = 4x. This way is more efficient to write than the former.

Complete the table provided: x 0 1 2 3 4 5 6 P(x) 0 4 8 12 16 20 24. When x = 0, the perimeter of the square is 0.When x = 1, the perimeter of the square is P = 4(1) = 4. When x = 2, the perimeter of the square is P = 4(2) = 8. When x = 3, the perimeter of the square is P = 4(3) = 12. When x = 4, the perimeter of the square is P = 4(4) = 16. When x = 5, the perimeter of the square is P = 4(5) = 20. When x = 6, the perimeter of the square is P = 4(6) = 24.

Function P represents the perimeter, in inches : https://brainly.com/question/19110581

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Assuming a 0.05 significance level, both hypothesis tests would reject the null hypothesis. This means that there is enough evidence to suggest that the shopping cart icon's design affects the users' behavior. Therefore, the design should be changed to improve the user's experience.

Step by step explanation:

The problem is not stated, so we need to make some assumptions. We will assume that the hypothesis tests were done to determine whether a change in the shopping cart icon design would affect the users' behavior.

The null hypothesis (H0) is that the design of the shopping cart icon does not affect the users' behavior, while the alternative hypothesis (Ha) is that the design of the shopping cart icon affects the users' behavior.

The significance level is 0.05, which means that we are willing to accept a 5% chance of making a type I error (rejecting the null hypothesis when it is actually true).

If both hypothesis tests reject the null hypothesis, it means that the p-values were less than 0.05, and there is enough evidence to suggest that the design of the shopping cart icon affects the users' behavior.

Therefore, it is recommended to proceed with changing the design of the shopping cart icon to improve the user's experience.

See more about null hypothesis at: https://brainly.com/question/4436370

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