Question 1 (essay worth 4 points) (h2.02 mc) the cost of attending an amusement park is $15 for children and $40 for adults. on a particular day, the attendance at the amusement park is 5,000 attendees, and the total money earned by the park is $100,000. use the given matrix equation to solve for the number of children’s tickets sold. explain the steps that you took to solve this problem. a matrix with 2 rows and 2 columns, where row 1 is 1 and 1 and row 2 is 15 and 40, is multiplied by matrix with 2 rows and 1 column, where row 1 is c and row 2 is a, equals a matrix with 2 rows and 1 column, where row 1 is 5,000 and row 2 is 100,000.

Answer:

  t = 7

Step-by-step explanation:

You can use your knowledge of powers of 2, or you can use logarithms to find the value of t.

  2^1 = 2

  2^2 = 4

  2^4 = 16

  128 = 16×4×2 = (2^4)(2^2)(2^1) = 2^(4+2+1) = 2^7

Now, the equation is ...

  f(t) = 2^t = 2^7

Equating exponents, we have ...

  t = 7

Taking the log of both sides of the equation ...

  2^t = 128

we have ...

  t×log(2) = log(128)

  t = log(128)/log(2) = 7 . . . . . divide by the coefficient of t

The value of t is 7.

__

Additional comment

The relevant rule of exponents is ...

  (a^b)(a^c) = a^(b+c)

The relevant rule of logarithms is ...

  log(a^b) = b×log(a)

The number of $1, $5 and $10 are 49, 44 and 22 respectively.

There are 3 denominations of bills in a wallet: $1, $5, and $10.

There are 5 fewer $5-bills than $1-bills.

let

x = number of $1 bills

Hence,

number of $5 bills = x - 5

There are half as many $10-bills as $5-bills.

number of $10 bills = 1 / 2 (x - 5)

Therefore,

x + x - 5 + 1 / 2 (x - 5) = 115

2x - 5  + 1 / 2 x - 5 / 2 = 115

2x + 1 / 2 x - 5 - 5 / 2 = 115

5 / 2 x  - 7.5 = 115

2.5x  = 115 + 7.5

x = 122.5 / 2.5

x = 49

Number of $1 bills = 49

Number of $5 bills = 49 - 5 = 44

Number of $10 bills = 1 / 2 (49 - 5) = 22

learn more on equation here: brainly.com/question/13992796

#SPJ1

Answer: 420 minutes in 7 hours. 2 minutes in 120 seconds.

Step-by-step explanation: Multiply 7x60, as there are 60 minutes per hour. Divide 120/60 to find how many minutes are within those many seconds.

The given case of Gallup asking the same 50 people how many hours had they worked at a job in the past 7 days. is an example of dependent sample.

The measured values in relation in a dependent sample (also called a paired sample).

Some characteristics of dependent sample are-

To know more about dependent sample, here

https://brainly.com/question/20349318

#SPJ4

The exponential function illustrated as f(x)=50(1.02)^x has a growth rate of 2%.

The exponential function is a mathematical function that is represented by e^x. Unless otherwise specified, the term refers to a positive-valued function of a real variable, though it can be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras.

In this case, the function is given as:

f(x)=50(1.02)^x

It should be noted 1 + 2% = 1.02 which us the value in the parentheses.

In conclusion, the growth rate is 2%.

Learn more about functions on:

https://brainly.com/question/12940982

#SPJ1

The discrete probability distribution that finds  the probability that x exceeds 5 is  0.38

Opportunity provides records approximately the likelihood that something will manifest. Meteorologists, for instance, use weather patterns to are expecting the chance of rain. In epidemiology, the probability idea is used to recognize the connection between exposures and the risk of fitness consequences.

Finding the possibility of a simple event happening is fairly straightforward: upload the changes collectively. For example, if you have a 10% chance of triumphing $10 and a 25% threat of triumphing $20 then your normal odds of prevailing something is 10% + 25% = 35%.

If there is no ambiguity within the occurrence of an occasion, then the chance of such an occasion is equal to 1. In other phrases, the chance of a sure occasion is 1. If an occasion has no probability of taking place, then its chance is zero.

We want to find the probability for x exceeding 5 means for x>5

Consider,

           P(X>5)=P(x=6)+P(X=8)

              =0.18+0.2

               =0.38

Hence, the probability is  0.38

Learn  more about probability here https://brainly.com/question/24756209

#SPJ4

Answer:

y^2 = -8x  for example.

Step-by-step explanation:

General form is y^2 = -4ax

The focus of this parabola will be at (-a , 0) on the x axis.

So the parabola might be:

y^2 = -4x

y^2 = -12x

y^2 = -0.9x  and so on......

Answer:

Yes, they are proportional.

Step-by-step explanation:

The ratio for Veronica's trail mix is 3:7

The ratio for Casey's trail mix is 27:63 <--- Simplify this number

27:63 simplified is 3:7, which means these ratios are proportional.

hope this helps :)

Answer:

none

Step-by-step explanation:

From the markings in the diagram above, we know that corresponding angles of the two triangles are congruent, but since we can make infinite number of triangles with same angle measures as triangle RIE by changing the side lengths, we cannot conclude that the triangles are congruent.

Answer:

This the only one I know for sure right

I think the second one mn/on=qn/pn

I think the last one and the first one too but let me know which was right!

Step-by-step explanation:

Hi what unit of algebra or geometry is this because I did this before, and I can help you.

The value of s for the given conditions is 9/2.

Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. As there is no ax2 term when a = 0, the equation is linear rather than quadratic.

r = k*s*t

k = constant of proportionality

r = 8

s = 6

t = 5

Putting the value in the equation:

8 = k x (6) x (4)

8 = 24k

k = 8 /24

k = 1/3

Now,

t = 16

r = 24

Putting the value in the equation:

r = k*s*t

24 = 1/3( x (s) x (16))

((24) x (3) )/ 16  = s

((3) x (3))/2 = s

s = 9/2

The value of s for the given conditions is 9/2.

To know more about quadratic equation visit:

https://brainly.com/question/17177510

#SPJ4

Answer:

josh has the fastest average speed of 0.03 km/h

Step-by-step explanation:

shown my working in the image linked . i hope it is helpful how i have worked it out .

I hope its helpful . if you need any more help pls let me know if you can't read it pls let me know . I have tried explaining as much as I can.

pls give brainliest if you found my answer useful :)

The required radius of the cylinder that can be covered by the paint exists at 3.8 feet.

Franco has enough paint to protect an area of about 226 square feet. He must paint a cylinder that exists 5 feet, and the maximum possible radius of the cylinder that can be covered by the paint exists to be determined.

The cylinder exists described as a 3D solid that holds two identical bases joined by a curved surface, at a particular distance.

Here, Franco keeps sufficiently paint to cover an area of about 226 square feet.

Area of the cylinder = 226

Area of the cylinder = πr²h = 226

h = 5 feet and π = 3.14

3.14 [tex]*[/tex] 5 [tex]*[/tex] r² = 226

r² = 226/15.70

[tex]$r = \sqrt{14.70}[/tex]

r = 3.80

Therefore, the required radius of the cylinder that can be covered by the paint exists at 3.8 feet.

To learn more about cylinders refer to:

https://brainly.in/question/11560872

#SPJ4

Answer: 4

Step-by-step explanation: I got the answer 4 right on the test

Option A AY || XV given that A, Y, Z are midpoints of sides XW, VW, XV respectively. This can be obtained by knowing what similar triangles are and finding which sides are proportional.

Similar triangles: If two triangles have proportional sides the are similar.

For example, if ΔABC and ΔDEF are similar then

[tex]\frac{AB}{DE}= \frac{BC}{EF} =\frac{AC}{DF}[/tex]

∠ABC = ∠DEF and ∠ACB = ∠DFE

Then we can write that, ΔABC ~ ΔDEF

Here in this question,

Since A, Y, Z are midpoints of sides XW, VW, XV

XA = AW

WY = VY

XZ = VZ

To consider sides AY and XV we should take triangles ΔWAY and ΔWXV

[tex]\frac{WX}{WA} =\frac{2WA}{WA} = 2[/tex]  (since A is the midpoint of WX)

[tex]\frac{WV}{WY} =\frac{2WY}{WY} = 2[/tex]  (since Y is the midpoint of WV)  

∠AWY = ∠XWV (reflexive property)

Therefore ΔWAY and ΔWXV are similar triangles

[tex]\frac{WX}{WA}= \frac{XV}{AY} =\frac{WV}{WY}[/tex] = 2

∠WAY = ∠WXV and ∠AYW = ∠XVW

Hence,

AY || XV option A AY || XV given that A, Y, Z are midpoints of sides XW, VW, XV respectively.

Learn more about similar triangle here:

brainly.com/question/25882965

#SPJ1

Disclaimer: The question was given incomplete on the portal. Here is the complete question.  

Question: Analyze the diagram below and answer the question that follows. If Z, Y and A are midpoints of ΔVWX what is true about AY and XY?

A. AY || XV

B. 1/2 AY = XV

C. AY = XV

D. AY ≅ XV

Answer:

A

Step-by-step explanation:

Answer:

11.25

77.85

Step-by-step explanation:

1.6x + 3 = 21

use inverse operation (+ = -, x = ÷) by taking 3 to the opposite side and changing it's integer to negative

1.6x = 21 - 3

divide 2 sides by 1.6

1.6x = 18

1.6x/1.6 = 18/1.6

x = 11.25//

2.15(x-5)=75

inverse operation

x= 75 - 2.15 + 5

x= 77.85//

Answer:

Step-by-step explanation:

A function is even when f(-x) = f(x) for all x in the domain of f. We can say that the function is simetrical over x axis.

That's all i know, Hope it helps!

There will be 60 residuals for simple bivariate regression's  60 observations.

According to the statement

We have given that the there is 60 observations and we have to find the number of simple bivariate regression for these observations.

So, For the solution of this problem,

We know that the

A simple linear regression (also known as a bivariate regression) is a linear equation describing the relationship between an explanatory variable and an outcome variable, specifically with the assumption that the explanatory variable influences the outcome variable, and not vice-versa.

And we know that the it is always same for the number as the number of given observations.

That's why there is 60 residuals.

So, There will be 60 residuals for simple bivariate regression's  60 observations.

Learn more about simple linear regression here

https://brainly.com/question/26755306

#SPJ4

The surface area of the composite figure is: 300 cm².

Surface area of a triangular prism = (P)L + bh, where we have the following:

P = perimeter of the base

L = length of the triangular prism

h = height of the triangular base

b = base of the triangular base

Surface area = 2(wl + hl + hw), where:

h = height of prism

w = width of prism

l = length of prism.

The surface area of the composite figure = surface area of triangular prism + surface area of rectangular prism - 2(the area where both figures are joined at).

Surface area of the triangular prism = (5 + 12 + 13)4 + (5)(12)

Surface area of the triangular prism = 180 cm²

Surface area of rectangular prism = 2(wl + hl + hw) = 2·(4·12+3·12+3·4) = 192 cm²

The area where both figures are joined at = (l)(w) = (3)(12) = 36 cm².

The surface area of the composite figure = 180 + 192 - 2(36)

The surface area of the composite figure = 180 + 192 - 72

The surface area of the composite figure = 300 cm².

Learn more about surface area of composite figure on:

https://brainly.com/question/12205542

#SPJ1

Answer:

11

Step-by-step explanation:

for this question we can look at the whole answer for the square root of 120 which equals 10.9544511501

[tex]\sqrt{120} = 10.9544511501[/tex]

now looking at our answer (10.9544511501) we want to find the nearest WHOLE NUMBER. in the current answer the whole number is 10, followed by many decimals.

10.9544511501

but to find the nearest whole number we have to round the place value BEFORE our whole number. (in this case the 9)

10.9544511501

we can now look at this highlighted section of our equation and think... is 10.9  closer to 11 or 10. well logically, to get to 11 from 10.9 we only have to go up by 0.1, rather than to get to 10, where you have to subtract 0.9.

10.9 + 0.1 = 11

10.9 - 0.9 = 10

But to make it easier, remember the rule:

the place value one place to the RIGHT of what you're rounding to, is what determines the new number. (in this case the .9)

and as any number 5 or above rounds up, we can say that our new number, rounded to the nearest whole number equals 11

10.9 rounded to the nearest whole number = 11

Answer:

76

Step-by-step explanation:

In order for John's average to be 80, the sum of all of his test scores must be 4*80 = 320. We can add 84, 78, and 82 to get 244, and then we subtract 244 from 320 to obtain the answer 76.

Answer:

Step-by-step explanation:

80 * 4 = 320

84 + 78 + 82 + x = 244

244 + x = 320

x = 320 - 244

x = 76

Answer:

-1

Step-by-step explanation:

Since we have the linear equation, 2x-5, and it's increasing since the slope is positive, that means we want the maximum x-value, to find the maximum y-value, or possible value.

This means, we want to find the maximum x-value of 2x+5 that is less than or equal to 9, and since we want the maximum x-value, we want the right side to also be the maximum, and since we have a less than or equal to symbol, we can have the equation equal to 9, which is the make value. So we get the following equation

[tex]2x+5=9\\[/tex]

Subtract 9 from both sides

[tex]2x=4[/tex]

Divide both sides by 2

[tex]x=2[/tex]

This is the maximum x-value we can get from the inequality, and now we plug this into the equation 2x-5

[tex]2(2)-5[/tex]

4-1

-1

So the maximum value is -1

❄ Hi there,

let us first figure out what we need to do to find x in this equation.

Since x is

we will

In other words we'll do just the opposite.

[tex]\sf{3x=2}\\\sf{x=\dfrac{2}{3}}[/tex]

That's it!

❄

Answer:[tex]\Large\boxed{x=12~;~y=18}[/tex]

Step-by-step explanation:

Given a system of equations

[tex]1)~\frac{x}{y} =\frac{2}{3}[/tex]

[tex]2)~\frac{y}{24} =\frac{3}{4}[/tex]

Multiply 24 on both sides of 2) equation to isolate y-value

[tex]\frac{y}{24}\times24 =\frac{3}{4}\times24[/tex]

[tex]\Large\boxed{y=18}[/tex]

Substitute the y-value into the 1) equation

[tex]\frac{x}{18} =\frac{2}{3}[/tex]

Multiply 18 on both sides of 1) equation to isolate y-value

[tex]\frac{x}{18}\times18 =\frac{2}{3}\times18[/tex]

[tex]\Large\boxed{x=12}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The slope of the linear function described in this problem is:

m = -3.

A linear function is modeled by:

y = mx + b

In which:

In this problem, the line goes through points (5,3) and (8,-6). Considering that the slope is given by change in y divided by change in x, for this function, it is given by:

m = (-6 - 3)/(8 - 5) = -9/3 = -3

The slope of the linear function described in this problem is:

m = -3.

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

#SPJ1

The trendline has a positive slope and 3-day moving average is the trendline that is more sensitive to this change.

In this question,

Trendlines are used to give traders a good idea of the direction an investment's value might move. In a healthy trend, it's ideal to enter your trades on a pullback (towards the moving average).

Understanding the direction of an underlying trend is one of the most basic ways to increase the probability of making a successful trade because it ensures that the general market forces are working in your favor.

A moving average is a technical indicator that investors and traders use to determine the trend direction of securities. It is one of the commonly used technical tools best known as trend following or lagging indicator, because it is based on past prices.

The sales have been quite stable in the month, but the sales was exceptionally better in the past two days. If the analyst draws a line between these price points, they have an upward trend and 3-day moving average is the trendline that is more sensitive to this change.

The options for this question are a) 3 days moving average, b) 7 days moving average, c) They are both equally sensitive, d) None of them is sensitive to this change.

Hence we can conclude that the trendline has a positive slope and option (A) 3-days moving average is the trendline that is more sensitive to this change is the correct answer.

Learn more about trendlines and moving averages here

https://brainly.com/question/14254610

#SPJ4

Answer:

-456 I think but I could be wrong though

See below for the solution to the systems of equations

System of equations 1

Here, we have

3x - 4y = -16

3x + 4y = 8

We start by plotting the graph of both equations

Next, we write out the point of intersection of the equations

See attachment for the equation of the system

From the attached graph, the point of intersection of the equations is (-4/3, 3)

Hence, the solution to the system is (-4/3, 3)

System of equations 2

Here, we have

-x  = - 6 + 2y

-18 + 6y = -3x

We start by plotting the graph of both equations

Next, we write out the point of intersection of the equations

See attachment for the equation of the system

From the attached graph, both lines are on each other

This means that the system of equations have infinite many solutions

Read more about system of equations at:

https://brainly.com/question/14323743

#SPJ1

If the side are increased by 45% then the area of green part will be 26.6955 [tex]mm^{2}[/tex].

Given that area of a shape of 37 [tex]mm^{2}[/tex] in which 60% is green.

We are required to find the area of green region if the side is increased by 45%.

Area is basically part of a surface covered by a shape.

When the side is increased by 45% then the area will increase by 45%*45%=20.25%.

Increased area =37*20.25%=7.4925

New area=37+7.4925

=44.4925

We have been given that 60% is the area of green.

Area of green region=44.4925*60/100

=26.6955 [tex]mm^{2}[/tex]

Hence if the sides are increased by 45% then the area of green part will be 26.6955 [tex]mm^{2}[/tex].

Learn more about area at https://brainly.com/question/25965491

#SPJ1

The given function s/(s^2 +3s -4) is proved with the help of inverse Laplace theorem.

According to the statement

we have to find the inverse of the Laplace theorem with the help pf the given theorem in the statement.

So, For this purpose, we know that the

Laplace transformation is a transformation of a function f(x) into the function g(t) that is useful especially in reducing the solution of an ordinary linear differential equation with constant coefficients to the solution of a polynomial equation.

Now, We assume you want to find the inverse transform of [tex]s/(s^2 +3s -4).[/tex]

This can be written in partial fraction form as

[tex]\frac{(4/5)}{(s+4)} + \frac{(1/5)}{(s-1)}[/tex]

which can be found in a table of transforms to be the transform of

[tex]\frac{4}{5} e^{-4t} + \frac{1}{5} e^t[/tex]

There are a number of ways to determine the partial fractions. They all start with factoring the denominator.

[tex]s^2 +3x -4 = (s+4)(s-1)[/tex]

After that, you can postulate the final form and determine the values of the coefficients that make it so.

For example:

[tex]\frac{A}{(s+4)} + \frac{B}{s-1} = (A+B)s + \frac{(4B-A)}{(s^2 +3x -4)}[/tex]

This gives rise to two equations:

(A+B) = 1

(4B-A) = 0.

So, The given function s/(s^2 +3s -4) is proved with the help of inverse Laplace theorem.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

Use appropriate algebra and theorem 7.2.1 to find the given inverse laplace transform. (write your answer as a function of t.) ℒ−1 s s2 + 3s − 4.

Learn more about Laplace here

https://brainly.com/question/11630973

#SPJ4