The top four winners in a golf tournament share the prize money in the ratio 9:5:2:1. If the top prize winner receives $45,00, then how much prize money is awarded in total?
(explanation would be appreciated I have to write it down)

The hypotenuse of the 45-45-90 triangle measures x / √2 units.Identify the given information. The given information is that the legs of a 45-45-90 triangle each measure x units. The question can be solved by following the steps :

1. Use the Pythagorean Theorem to solve for the hypotenuse. The Pythagorean Theorem states that a2 + b2 = c2 where a and b are the legs of the triangle and c is the hypotenuse. In this case, x2 + x2 = c2.

2. Simplify the equation. When two of the same numbers are added together, the sum is twice that number. Therefore, 2x2 = c2.

3. Solve for c. To solve for c, divide both sides of the equation by 2. This yields x2 = c2 / 2.

4. Take the square root of both sides. Taking the square root of both sides yields x = c / √2.

5.The answer to the question is that the hypotenuse of the 45-45-90 triangle measures x / √2 units.

To know more about Theorem here

https://brainly.com/question/30066983

#SPJ4

If A1 and A2, are mutually exclusive and exhaustive with P(A1)>0 and P(A2) >0, and B is an event in S. then P(B) = P(A1 ∩B) + P(A2∩ B). [TRUE]

The sets A and B are the sets of all objects that are members of set A and members of set B. In written notation form:

A ∩ B = {x | x ∈ A and x ∈ B}

Here's how to determine the separation of two sets:

One set which is another subset if A ⊆ B then A ∩ B = A and vice versa.

The sets are equal if A = B, then A ∩ B = (A = B).

Sets are mutually exclusive if A // B, then A ∩ B = … and vice versa.

The sets are not mutually exclusive.

The union of sets A and B is the set of all objects that are members of set A or members of set B. In written notation form:

A ∪ B = {x | x ∈ A or x ∈ B}

Here's how to determine the union of two sets:

A set that is a set in other parts if A ⊆ B, then A ∪ B = B and vice versa.

The set is equal if A = B then A ∪ B = (A = B).

Sets are mutually exclusive if A // B, then A ∪ B = {x | x ∈ A or x ∈ B} and vice versa.

The sets are not mutually exclusive if A ⊃⊂ B, then A ∪ B = {x | x ∈ A, x ∈ B or x ∈ (A ∩ B)}.

Your question is incomplete but most probably your full question was:

If A, and A, are mutually exclusive and exhaustive with P(A)>and P(A2) >0, and B is an event in s. then P(B) = P(ALB) + P(ANB). True False

Learn more about intersection at https://brainly.com/question/29055360.

#SPJ4

The height of the cube brick is 7 units and the volume is equal to 343 unit³

The volume of a cube is defined as the total number of cubic units occupied by the cube. The formula is given as V = a³ where "a" is the length of edge or sides.

The length of an edge for the cube brick is 7 units which implies the height represented by h is also 7 units and the volume is calculated as follows:

volume of cube brick = 7 units × 7 units × 7 units

volume of cube brick = 343 units ³

Therefore, the height of the cube brick is 7 units and the volume is equal to 343 unit³

Learn more about volume of cube here: https://brainly.com/question/1972490

#SPJ1

The two trapezoids below are similar. The value of Ef will be 6.

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

Given that there are two trapezoids ABCD and GHEF. The length of EF = x will be calculated as:-

Apply the similarity property in the two trapezoids.

AB / FE = DC / GH

24 / x = 30 / 7.5

x = ( 24 x 7.5 ) / 30

x = ( 1800 / 300 )

x = 6

Hence, the value of the side x = EF = 6.

To know more about similarities follow

https://brainly.com/question/14422880

#SPJ1

Mean with frequency represented by the number of times people visits the shop is equal to 1.9.

Let 'v' represents the visits of the people.

'f' represents the frequency that is number of times group of people visits the shop.

To calculate mean results of the table are as follow:

Visits ( v)       frequency ( f)         fv

0                            5                     0

1                             14                   14

2                            18                   36

3                            7                     21

4                            6                     24

Mean of the number of visits

= ( Sum of all the fv ) / ( Sum of all the frequency)

= ( 0 + 14 + 36 + 21 + 24 ) / ( 5 + 14 + 18 + 7 + 6 )

= 95 / 50

= 1.9

Therefore, the mean of the number of visits with the given frequency is equal to 1.9.

The above question is incomplete, the complete question is :

A group of people answer the question:

How many times did you shop at Ascobury's last week?

Here are the results:

Visits ( v)       frequency ( f)         fv

0                           5

1                             14

2                            18

3                            7  

4                             6

Find the mean number of visits.?

learn more about frequency here

brainly.com/question/5102661

#SPJ4

The graph of the polynomial function g(x) = -2x² - 5x³ + 2x² + 7x + 1 is plotted and attached

The zeros are (-1.10, 0), (-0.15, 0) and (1.25, 0) to the nearest hundredth)

Using a graph is potted by written the equation on the plotter , the plotter interprets the equation and presents the graph

Zero of polynomial equation is the point where the y is zero this is solved by equating the polynomial function to zero

From the graph, the zeros are identified by the points where the graph cuts the the x axis.

Examining the graph of the function g(x) = -2x² - 5x³ + 2x² + 7x + 1 the zeros are

(-1.104, 0), (-0.145, 0) and (1.249, 0)

Learn more about polynomial graphs at:

https://brainly.com/question/9696642

#SPJ1

The price of the delivery is $15 and the mileage is 40.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Given that the rosebud flower shop has a basic delivery charge of 5$ plus a rate of 25 cents per mile.

Total cost = basic delivery fee + (rate per mile x number of miles)

=$5 + (0.25 x m)

= $5 + 0.25m

The linear expression that represents the total delivery cost from Rosebud Flower Shop ;

Total cost = basic delivery fee + (rate per mile x number of miles)

=$7 + (0.2 x m)

$7 + 0.2m

When the costs are the same, the two expressions would be;

$7 + 0.2m = $5 + 0.25m

$7 - $5 = 0.25m - 0.20

$2 = 0.05m

m = 2 / 0.05

m = 40

Price = $7 + 0.2(40)

$7 + 8 = $15

Learn more about the unitary method, please visit the link given below;

https://brainly.com/question/23423168

#SPJ1

-37. 44 / 4. 8 gives  -7.8 when dividing -37.44 by 4.8 by simple dividing rule whereas after rounding off -37.44 and 4.8 that will be -37 and 5 will be 7.4.

In the given problem Division is = 4. 8 and dividend is = -37. 44, And as per law Division is divided by dividend  (Division/dividend), and the result produced, is called quotient In this case in this case, Quotient is -7.8.

And -37.44 is approximately -37 As .44 is rounded off to .00 (As per law 0-4 is 0 and 5-9 is rounded up to the next digit. And 4.8 could be around off to 5. And now if -37 is divided by 5 estimated will be 7.4.

Learn More about division: https://brainly.com/question/25289437

#SPJ4

Average rate of change of the function F (x ) = 9/ -2 (x)-7. Average rate is -3, 9

The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function. A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.

Divide the change in y-values by the change in x-values to determine the average rate of change. In order to determine changes in measurable parameters like average speed or average velocity, finding the average rate of change is extremely helpful.

f (x ) = -2

f (x) = 9/ -2 (-2)-7

      = 9 / 4 - 7

      =9 / -3

      = -3

f (x ) = -4

f (x) = 9/ -2 (4)-7

      = 9 / 8 - 7

      =9 / 1

      = 9

Average rate is -3, 9

To learn more about Average rate refer to :

https://brainly.com/question/24313700

#SPJ1

Step-by-step explanation:

To find the factor by which the dimensions of cylinder A were multiplied to produce the corresponding dimensions of cylinder B, we can use the fact that they are similar solids. This means that the ratio of corresponding dimensions is the same for both cylinders.

Since the base of cylinder A has a circumference of 4π units and the base of cylinder B has an area of 9π units, we can use these measurements to find the ratio of the radii of the two cylinders.

The circumference of a circle is given by 2πr, where r is the radius, so the radius of cylinder A is 4π/2π = 2 units.

The area of a circle is given by πr^2, so the radius of cylinder B is sqrt(9π/π) = sqrt(9) = 3 units.

The ratio of the radius of cylinder A to cylinder B is 2/3. Since similar solids have the same ratio for all dimensions, this means that the dimensions of cylinder A were multiplied by a factor of 2/3 to produce the corresponding dimensions of cylinder B.

Answer: The answer is 5

Step-by-step explanation:

-3-(-8)

-3+8

5

Answer: 5

Step-by-step explanation:

First the negative 3 adds to 8. Because if you see “- -“ it will be +. So we just have -3 + 8 = 5

The equation of the graphed function for this problem is given as follows:

y = x³ - 6x² - 7x - 6.

The function for this problem is obtained using the Factor Theorem, as a product of the linear factors of the function.

The zeros of the function are given as follows:

Hence the linear factors are given as follows:

Then the function is given as follows:

y = a(x - 1)(x - 2)(x - 3).

In which a is the leading coefficient.

The y-intercept is at y = -6, hence the leading coefficient is given as follows:

-6a = -6

a = 1.

Hence the function is:

y = (x² - 3x + 2)(x - 3)

y = x³ - 6x² - 7x - 6.

More can be learned about functions at https://brainly.com/question/24808124

#SPJ1

Answer:

N(-21,-20)

Step-by-step explanation:

We can apply midpoint formula to solve for endpoint (N):

[tex]\displaystyle{\text{Midpoint}= \left(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\right)}[/tex]

Let [tex]\displaystyle{x_1 = 1}[/tex], [tex]\displaystyle{y_1 = 12}[/tex] and Midpoint = (-10,-4). Therefore:

[tex]\displaystyle{\left(-10,-4\right)= \left(\dfrac{1+x_2}{2}, \dfrac{12+y_2}{2}\right)}[/tex]

Solve x with -10 and y with -4:

[tex]\displaystyle{\text{N}\left(x_2,y_2\right) = \left(\dfrac{1+x_2}{2}=-10, \dfrac{12+y_2}{2}=-4\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right) = \left(1+x_2=-20, 12+y_2=-8\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right) = \left(x_2=-20-1, y_2=-8-12\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right) = \left(x_2=-21, y_2=-20\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right)=\left(-21,-20\right)}[/tex]

Therefore, the coordinate of N is (-21,-20)

In the essay “A Modest Proposal”, The author includes the quote to give the reader an objective summary of how dangerous the conditions were at Mauna Loa.

Jonathan Swift, a satirist, suggested jokingly in an essay titled "A Modest Proposal" from 1729 that the people of Ireland sell their children as food. A radical or shocking notion is frequently introduced in an ironic way using the term a modest suggestion.

Swift's essay, which is hailed as a masterwork of irony, is officially titled "A Modest Proposal for Preventing the Children of the Poor People in Ireland from Being a Burden to Their Parents or Country, and for Making Them Beneficial to Their Public."

When a proposal takes the form of an essay, it typically proposes a fix for a social or political issue. The adjective "modest" denotes reason or modesty. Because the idea is genuinely absurd, it is humorously used in the title of "A Modest Proposal."

A modest proposal is frequently used in jest to make a point by taking something to its logical conclusion, which highlights a problem. Swift's article, which at the time caused controversy, has since become a satirical mainstay and has influenced a lot of authors.

To Learn more About A Modest Proposal Refer To:

brainly.com/question/9066127

#SPJ1

Answer:

first hand account

Step-by-step explanation:

I got a 100 on the test

Answer:

the twelve value will produce -3

Step-by-step explanation:

T(12) = 45 - 4(12)

T(12) = 45 - 48

T(12) = -3

The center of dilation if Quadrilateral N' is the image of quadrilateral N under a dilation is; Point C

The center of dilation is defined as a reference point that is used to appropriately scale the dilation of a figure.

Now, if we imagine that the corresponding vertices of the two quadrilaterals are extended, then it will be clear that the extensions intersect at a point C.

Therefore we can conclude that point C is the center of dilation by the fact that corresponding parts of a paragraphic intersect at a point.

Read more about center of dilatio at; https://brainly.com/question/3457976

#SPJ1

Answer:

b/w 19 & 55

Step-by-step explanation:

average of four equally weighted 100-point tests,

mark has scored 90, 86, and 85 on the first three.

C average = 70 and 79

90+86+85+x = 4*70 = 280, so x=19

90+86+85+x = 4*79 = 316, so x=55

Answer:

Step-by-step explanation:

To find the probability that exactly 35 vehicles pass through the drive-thru during the lunch hour rush on a given day, we can use the probability density function of the normal distribution. In this case, the mean is 38 and the standard deviation is 5.7.

The probability of a specific value x in a normal distribution is given by the formula:

P(x) = (1/(σ * √(2π)) * e^((-1/2) * ((x - μ)^2 / σ^2))

Where x is the specific value we are trying to find the probability of, μ is the mean, and σ is the standard deviation.

plugging in the given values, we get:

P(35) = (1/(5.7 * √(2π)) * e^((-1/2) * ((35 - 38)^2 / 5.7^2))

The result is very close to zero, the probability of exactly 35 vehicles passing through the drive-thru during the lunch hour rush is very low, almost impossible.

By applying the Golden Ratio rule, the width of the painting is equal to 12.5 inches.

In Mathematics, a proportion simply refers to an equation which is typically used to represent the equality of two (2) ratios.

This ultimately implies that, proportions is a mathematical operation which can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

By applying the Golden Ratio rule, the width of the painting can be calculated as follows;

20/x = 8/5

Cross-multiplying, we have the following:

8x = 20 × 5

8x = 100

x = 100/8

x = 12.5 inches.

Read more on ratio here: brainly.com/question/27817533

#SPJ1

The slope of a line perpendicular to the line is 5/4

A straight line of the form

y = mx + c

has its slope as 'm'

It is constant for a line. The more the slope is, the steeper the line is.

Sign convention takes bottom left to top right going line as positive sloped. And that line which goes from bottom right to top left is taken to have negative slope. Horizontal line has 0 slope and vertical line has infinite slope, as it is now at maximum steepness.

If two lines are perpendicular, their slopes are negative reciprocals, which means that their product is -1

Given;

4x+5y=35

We can write the equation as;

4*x + 5*y - 35  = 0

5*y  = - 4*x  + 35     or    

y  = -(4/5)*x  + 35    

m= -4/5

So, now the slope of this line is -4/5 and line perpendicular slope will be 5/4

Learn more about slope here:

https://brainly.com/question/2503591

#SPJ1

There are two phrases for how many sweet Sue and Tony have: 13-x and

Equivalent refers to the mathematical notion of equality between several terms and expressions with a comparable value.

Equivalent vs. Equal. Equivalent and equal are distinct terms in mathematics.

Equal means identical in every respect, as opposed to equivalent, which is similar but not the same.

18 + x/ 2 is the equivalent.

Sue has 18 delicious.

Tony has 18 delicious.

Sue gives Tony some candy. Sue Sweet is going to

18 - x Sue consumes 5 candies, thus his sweet will be

18 - 5 - x = 13 - x

Sue gave Tony x candy to take. His sweetness will

18 + x

Tony consumed half of his candy. His final treat will be

18 + x / 2

The phrase for Sue candies is 13 - x.

18 + x / 2 is the equation for Tony Sweets.

To Learn more About   sweet Sue and Tony  refer To:

https://brainly.com/question/5563028

#SPJ1

Graphs (C) and (D) having median value larger than the mean value.

What Is a Histogram?

A histogram is a graphical representation of data points organized into user-specified ranges.

In graphs (C) and (D), the median value is larger than the mean value as the distribution is skewed to the left which means most values are large but there are few exceptionally small values because of which means shift towards the left and thus the mean is less than the median, or we can say that the median value is larger that the mean value.

So, graphs (C) and (D) having median value larger than the mean value.

To learn more about histogram visit : brainly.com/question/16819077

#SPJ4

The price per ounce is given as follows:

$0.15 = 15/100.

The price per ounce is obtained applying the proportions in the context of this problem, dividing the total price by the number of ounces.

The parameters for this problem are given as follows:

Hence the price per ounce is calculated as follows:

2.25/15 = $0.15.

The total price was of $2.25 for 15 ounces, and the problem asks for the price per ounce.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:

No, they are not proportional

Step-by-step explanation

50*2=100

32*2=64, not 60

Answer:

32 & 12

Step-by-step explanation:

let age of andy = x

let age of brett = y

x + y = 44        (eq 1)

x= 8 + 2y         (eq 2)

putting the value of x from 2 in 1

8 + 2y + y = 44

3y = 36

y = 12

x = 8 + 2(12)

x = 32

Jetlag is a condition associated with crossing multiple time zones is experienced by sports tourists from Argentina travelling to Japan.

People who travel quickly between different time zones may experience jet lag, a sleep disorder.

Jet lag causes sporadic sleep problems. It occurs when signals from a new time zone cause the body's biological clock to become out of sync. Feeding times and light exposure are two examples of cues.

The term "jet lag" originated from the fact that it was uncommon to travel far and quickly enough to cause desynchronosis prior to the development of passenger jet aircraft. Propeller-driven travel was slower and covered less ground than jet flights, so it had a negligible impact on the issue.

To learn more about jet lag: https://brainly.com/question/7336967

#SPJ4

hmmm proofs like these can be a bit circular kinda, let's do some rigamarole on the equations and we'll see if that works for a definition

[tex]\stackrel{\theta \textit{ is always in radian unit}~\hfill }{s=r\theta\implies \cfrac{s}{\theta }=r \hspace{5em}v=\cfrac{s}{t}\implies t=\cfrac{s}{v}\hspace{5em}\omega=\frac{\theta }{t}} \\\\[-0.35em] ~\dotfill\\\\ \omega=\cfrac{\theta }{t}\implies \omega=\cfrac{\theta }{~~ \frac{ s}{v } ~~}\implies \omega=\cfrac{\theta }{1}\cdot \cfrac{v}{s}\implies \omega=\cfrac{\theta v}{s}\implies s\omega=\theta v \\\\\\ \cfrac{s\omega}{\theta }=v\implies \cfrac{s}{\theta }\cdot \omega=v\implies \boxed{r\cdot \omega=v}[/tex]

The function is d(t) = 6cos(πt/6 + π/4) + 6. It models the water depth in meters as a cosine function of time after midnight.

The cosine function models the water depth d(t) in meters as a function of time t (in hours after midnight) on a particular day. The amplitude of the cosine curve is the difference between the high and low tide water depths, which is 6 m. The period of the cosine curve is the same as the natural oscillation period, which is 12 hours. The phase shift is π/4, as the high tide occurred at 4:45 a.m. Therefore, the function is d(t) = 6cos(πt/6 + π/4) + 6.

Learn more about function here

https://brainly.com/question/29633660

#SPJ4