According to a 2009 Reader's Digest article, people throw away approximately 10% of what they buy at the grocery store. Assume this is the true proportion and you plan to randomly survey 100 grocery shoppers to investigate their behavior. What is the probability that the sample proportion exceeds 0.02?

Answer:

  [1] = 6

  x = -3/2 is the root

Step-by-step explanation:

A perfect square trinomial is of the form ...

  (a + b)² = a² +2ab +b²

You have ...

Then the factorization is ...

  16w² +48w +36 = (4w +6)²

This will be zero when x = -6/4 = -3/2.

Answer:

Step-by-step explanation:

1. The magnitude of the multiplier is 6, so the magnitude of the new vector is 6×(15 m) = 90 m. The sign on the multiplier is negative, so the new vector will be in the opposite direction of East. It will be 90 m West.

__

2. The components can be found from ...

  (8.9 m/s)(cos(-40°), sin(-40°)) ≈ (6.82, -5.72) m/s

__

One or both of the components will usually be irrational if the angle is a rational number of degrees not a multiple of 90°. Here, we have rounded to 2 decimal places.

Answer:

  91.8 ft

Step-by-step explanation:

So we can talk about the diagram, let's name a couple of points. The base of the tree is point T, and the top of the tree is point H. We want to find the length of TH given the length AB and the angles HAT and ABT.

The tangent function is useful here. By its definition, we know that ...

  TA/BA = tan(∠ABT)

and

  TH/TA = tan(∠HAT)

Then we can solve for TH by substituting for TA. From the first equation, ...

  TA = BA·tan(∠ABT)

From the second equation, ...

  TH = TA·tan(∠HAT) = (BA·tan(∠ABT))·tan(∠HAT)

Filling in the values, we get ...

  TH = (24.8 ft)tan(87.3°)tan(9.9°) ≈ 91.8 ft

The height h of the tree is about 91.8 ft.

Answer:

23

Step-by-step explanation:

or 2.8 but try 23 frist

The percentage of increase of total number of students on the honor roll is obtained as 22.97%.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

And to convert a fraction or a decimal into percentage, they are multiplied by 100.

The number of boys and girls on the honor code last year is given as 132 and 90.

Then, the total number is 132 + 90 = 222.

When, the number of boys increased by 25%, it can be obtained as,

⇒ 132 + 25% × 132 = 165

And, the number of girls increased by 20% can be obtained as,

⇒ 90 + 20% × 90 = 108

Now, the total number of students is 165 + 108 = 273.

The percent increase can be obtained as follows,

Change in the total number ÷ Initial number × 100

⇒ (273 - 222) ÷ 222 × 100 = 22.97%

Hence, the percent value of the increase in the number is 22.97%.

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the result of subtracting[tex]\( (4x^2 - x) \)[/tex]  from [tex]\( -3x^2 \) is \( \boxed{-7x^2 + x} \).[/tex]

To subtract [tex]\( (4x^2 - x) \) from \( -3x^2 \)[/tex], we need to distribute the negative sign to each term inside the parentheses and then perform the subtraction.

Given:

[tex]\( -3x^2 - (4x^2 - x) \)[/tex]

Step 1: Distribute the negative sign inside the parentheses:

[tex]\( -3x^2 - 4x^2 + x \)[/tex]

Step 2: Combine like terms:

[tex]\( (-3x^2 - 4x^2) + x \)[/tex]

[tex]\( = -7x^2 + x \)[/tex]

Therefore, the result of subtracting[tex]\( (4x^2 - x) \)[/tex]  from [tex]\( -3x^2 \) is \( \boxed{-7x^2 + x} \).[/tex]

Answer:

  74 days

Step-by-step explanation:

The proportion left after d days is ...

  p = (1/2)^(d/100)

When that proportion is 60%, we have ...

  .60 = .50^(d/100)

  log(.60) = (d/100)log(.50) . . . . . take logarithms

  100·log(.60)/log(.50) = d ≈ 73.697 ≈ 74 . . . days

Answer:

Step-by-step explanation:One of the things you can use for that is RAP so here's how this goes:

R:A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs ​$61. A season ski pass costs ​$400. The skier would have to rent skis with either pass for ​$25 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily​ passes?

A:what do we want to know?(Understand the problem)

How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes

What do we already know?

A daily pass costs $61,A season ski pass costs $400,The skier would have to rent skis with either pass for ​$25 per day.

what is the plan??

Carry out the plan.Show work for your solution

Hopefully I helped a little

                                       blessings,lilabear

The correct answer is:

Option C: 5(2x^5+x^2−3)

A Quick Check:

5*2x^5 is 10x^5

5*x^2 is 5x^2

and 5*-3 is -15

making the equations match

The factored form of the expression 10x⁵ + 5x² - 15 is 5(x⁵ + x² - 3).

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

Given, A polynomial of degree five which is 10x⁵ + 5x² - 15.

Now, The HCF of 10, 15, and 5 is 5, and the HCF of x⁵, x², and x⁰ is x⁰ = 1.

Therefore,

10x⁵ + 5x² - 15.

= 5x⁰(x⁵ + x² - 3).

= 5(x⁵ + x² - 3).

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Answer:

-1, 2, 5, 8, 11

Step-by-step explanation:

There is an easy and fast way to solve this. A linear function means that the steps on y and x are constant.

On the x axis you are walking 5 steps each column, so you start from 5, plus 5 steps is 10, plus 5 steps is 15, plus 5 steps is 20, plus 5 steps is 25.

Now you have to do the same for the y axis, but you have to use your brain.

You start from -1, and you have to reach 11, using the same number of steps for each column, just like before the necessarily with the same number.

You start from -1, plus 3 steps is 2, plus 3 steps is 5, plus 3 steps is 8, plus 3 steps is 11. Done.

You can use maths also, but it will take time.

You need to find that function. A linear function can be written as:

[tex]y = mx + q[/tex]

You have two points of the line, (5, -1) and (25, 11), but you need to find the y coordinate of other three points.

Let's find the line by substituting those points in the general function of the line:

[tex] - 1 = 5m + q \\ 11 = 25m + q[/tex]

This is a system of two equations with two variables, m and q. You can solve it. From the first equation you have that:

[tex]q = - 1 - 5m[/tex]

Put this in the second equation to know the value of m:

[tex]11 = 25m + ( - 1 - 5m)[/tex]

[tex]11 = 25m - 1 - 5m \\ 20m = 12 \\ m = \frac{12}{20} = \frac{3}{5} [/tex]

Now you can use this in the first equation to know the value of q:

[tex]q = - 1 - 5( \frac{3}{5} ) \\ q = - 1 - 3 \\ q = - 4[/tex]

So your line is:

[tex]y = \frac{3}{5} x - 4[/tex]

If you want to know the y coordinates that you are missing, you just need to put the corresponding x coordinate in this function and you will find the same results as before.

To fill in a table for a linear function, you need to understand the relationship between x and y in a linear function (y = mx + b), calculate y values for given x values using this relationship, and arrange these pairs in the table.

To fill in a table that represents a linear function, we need to understand that in a linear function, the change in the output (y) is constant for every unit change in the input (x). The relationship between x and y can be written as y = mx + b, where m is the slope and b is the y-intercept.

Here's a simple example. For a linear function y = 2x + 1, if your x values are 1, 2, and 3, the y values would be y(1) = 2*1+1 = 3, y(2) = 2*2+1 = 5, y(3) = 2*3+1 = 7. So the table would look like:

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The answer will be 13

since he give you the C and X

you just need to add them and then subtract them from 90 degree

51+26-90=13

I hope this will helps you.

Answer:

[tex]y = - 2000x + 14000[/tex]

Answer:

Option A - 342 feet

Step-by-step explanation:

Given : Janice puts a fence around her rectangular garden. The garden has a length that is 9 feet less than 3 times its width.

To find : What is the perimeter of Janice fence if the area of her garden is 5,670 square feet?

Solution :

Let the width of the garden be w=x feet.

The garden has a length that is 9 feet less than 3 times its width.

The length of the garden be l=3x-9 feet

The area of the garden is A=5670 square feet.

The formula of area of garden is [tex]A=l\times w[/tex]

[tex]5670=(3x-9)\times x[/tex]

[tex]5670=3x^2-9x[/tex]

[tex]3x^2-9x-5670=0[/tex]

[tex]x^2-3x-1890=0[/tex]

[tex]x^2-45x+42x-1890=0[/tex]

[tex]x(x-45)+42(x-45)=0[/tex]

[tex](x-45)(x+42)=0[/tex]

[tex]x=45,-42[/tex]

Reject x=-42 as measurement cannot be negative.

The width of the garden is w=45 feet.

The length of the garden is l=3(45)-9=135-9=126 feet.

The perimeter of the garden is [tex]P=2(l+w)[/tex]

[tex]P=2(126+45)[/tex]

[tex]P=2(171)[/tex]

[tex]P=342[/tex]

The perimeter of Janice fence is 342 feet.

Therefore, Option A is correct.

The perimeter of Janice's fence is: [tex]\[ {342 \text{ feet}} \][/tex]

To determine the perimeter of Janice's garden, let's follow these steps:

Step 1: Define Variables

Let ( w ) be the width of the garden in feet.

The length ( l ) of the garden is given by: [tex]\[ l = 3w - 9 \][/tex]

Step 2: Set Up the Area Equation

The area of the rectangular garden is given as 5,670 square feet:

[tex]\[ \text{Area} = l \times w \][/tex]

[tex]\[ 5670 = (3w - 9) \times w \][/tex]

Step 3: Solve the Quadratic Equation

Expand and simplify the equation:

[tex]\[ 5670 = 3w^2 - 9w \][/tex]

Rearrange it to standard quadratic form:

[tex]\[ 3w^2 - 9w - 5670 = 0 \][/tex]

Step 4: Factor or Use the Quadratic Formula

Divide through by 3 to simplify:

[tex]\[ w^2 - 3w - 1890 = 0 \][/tex]

Solve using the quadratic formula [tex]\( w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)[/tex]:

[tex]\[ a = 1, \, b = -3, \, c = -1890 \][/tex]

[tex]\[ w = \frac{-(-3) \pm \sqrt{(-3)^2 - 4 \cdot 1 \cdot (-1890)}}{2 \cdot 1} \][/tex]

[tex]\[ w = \frac{3 \pm \sqrt{9 + 7560}}{2} \][/tex]

[tex]\[ w = \frac{3 \pm \sqrt{7569}}{2} \][/tex]

[tex]\[ w = \frac{3 \pm 87}{2} \][/tex]

This gives two potential solutions:

[tex]\[ w = \frac{90}{2} = 45 \][/tex]

[tex]\[ w = \frac{-84}{2} = -42 \][/tex]

Since width cannot be negative:

[tex]\[ w = 45 \][/tex]

Step 5: Find the Length

Substitute ( w = 45 ) into the length equation:

[tex]\[ l = 3(45) - 9 \][/tex]

[tex]\[ l = 135 - 9 \][/tex]

[tex]\[ l = 126 \][/tex]

Step 6: Calculate the Perimeter

[tex]\[ P = 2l + 2w \][/tex]

[tex]\[ P = 2(126) + 2(45) \][/tex]

[tex]\[ P = 252 + 90 \][/tex]

[tex]\[ P = 342 \][/tex]

Thus, the perimeter of Janice's fence is: [tex]\[ {342 \text{ feet}} \][/tex]

Answer:

(3,7) for the first line, and (12,0) for the second one.

Step-by-step explanation:

Hi Isabella,

1) The Midpoint of a line, when it comes to Analytical Geometry, is calculated as Mean of two points it follows:

[tex]x_{m}=\frac{x_{1} +x_{2} } {2}, y_{m} =\frac{y_{1}+ y_{2} }{2}[/tex]

2) Each segment has two endpoints, and their midpoints, namely:

a) (1,-9) and its midpoint (2,-1)

b) (-2,18) and its midpoint (5,9)

3) Calculating. You need to be careful to not sum the wrong coordinates.

So be attentive!

The first line a

[tex]2=\frac{1+x_{2} }{2}\\  4=1+x_{2}\\  4-1=-1+1+x_{2} \\ x_{2}=3\\-1=\frac{y_{2}-9}{2}\\-2=y_{2}-9\\+2-2=y_{2}-9+2\\ y_{2}=-7[/tex]

So (3,7) is the other endpoint whose segment starts at (1,-9)

The second line b endpoint at (-2,18) and its midpoint (5,9)

[tex]5=\frac{-2+x_{2} }{2} \\ 10=-2+x_{2} \\ +2+10=+2-2+x_{2}\\ x_{2}=12 \\ \\ 9=\frac{18+y_{2} }{2} \\ 18=18+y_{2} \\ -18+18=-18+18+y_{2}\\ y_{2} =0[/tex]

So (12,0) it is the other endpoint.

Take a look at the graph below:

Answer:(3,7) for the first line, and (12,0) for the second one.

Step-by-step explanation:

Hi Isabella,

1) The Midpoint of a line, when it comes to Analytical Geometry, is calculated as Mean of two points it follows:

Step-by-step explanation:

Answer:

The answer to your question is: 4.2 x 10⁻²

Step-by-step explanation:

Information: (3 x 10⁶) x (1.4 x 10⁻⁸)

                    3 x 1.4 = 4.2                                   we just multiply the integers

                   10⁶ + 10⁻⁸ = -2                                then we add 6 and -8

                   4.2 x 10⁻²                                   now join the results and -2 will be a power of ten.

Answer: 4,85 meters

Step-by-step explanation:

Using energy we get the velocity when the man gets to the bottom of the hill

mgh=1/2 m v^2

Then the velocity is the squareroot of two times the mass times the gravity constant =9,598 m/s2

Using energy again, we can get the velocity on the edge of the ledge (using the second mass, the one of the man plus the backpack)

1/2 M1 V1^2=1/2 M2 V2^2

We get V2=8,24 m/s2

Then we have to analyze the jump, horizontally, with constant velocity, and vertically, with constant acceleration equals to the gravity constant.

To get the time we analyze the vertical move

Y=1/2 g t^2

t=59 seconds

To get the horizontal distance we use

X= v t

X=4,85 meters.

[tex]\bf \sqrt{5x-9}+1=x\implies \sqrt{5x-9}=x-1\implies 5x-9 = (x-1)^2 \\\\\\ 5x-9=\stackrel{\mathbb{FOIL}}{x^2-2x+1}\implies 5x=x^2-2x+10\implies 0=x^2-7x+10 \\\\\\ 0=(x-5)(x-2)\implies x= \begin{cases} 5\\ 2 \end{cases}[/tex]

Answer:

The Andrew equitation is 4 times more bigger than Peter equation.

Step-by-step explanation:

(16x-8x=40) is:

4*(4x-2=10)=(16x-8=40)

Answer:

k=3

I mean the third choice

Step-by-step explanation:

f(x) = x-1

The required value of k is 3. Option C is correct.

Given that,
To find the value of k in the data set such that the data set represents a linear function.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
The slope of the function,
x, f(x) = (7,6) and (9,8)
Slope = 8 - 6 / 9 - 7
Slope = 2 / 2 = 1

Equation,
y + 3 = 1 (x + 2)
y = x - 1
Now at x = 4 : f(x) = k
k = 4 - 1
k = 3

Thus, the required value of k is 3. Option C is correct.

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Answer:

The functions are inverses; f(g(x)) = x ⇒ answer D

[tex]h^{-1}(x)=\sqrt{\frac{x+1}{3}}[/tex] ⇒ answer D

Step-by-step explanation:

* Lets explain how to find the inverse of a function

- Let f(x) = y

- Exchange x and y

- Solve to find the new y

- The new y = [tex]f^{-1}(x)[/tex]

* Lets use these steps to solve the problems

∵ [tex]f(x)=\sqrt{x-3}[/tex]

∵ f(x) = y

∴ [tex]y=\sqrt{x-3}[/tex]

- Exchange x and y

∴ [tex]x=\sqrt{y-3}[/tex]

- Square the two sides

∴ x² = y - 3

- Add 3 to both sides

∴ x² + 3 = y

- Change y by [tex]f^{-1}(x)[/tex]

∴ [tex]f^{-1}(x)=x^{2}+3[/tex]

∵ g(x) = x² + 3

∴ [tex]f^{-1}(x)=g(x)[/tex]

∴ The functions are inverses to each other

* Now lets find f(g(x))

- To find f(g(x)) substitute x in f(x) by g(x)

∵ [tex]f(x)=\sqrt{x-3}[/tex]

∵ g(x) = x² + 3

∴ [tex]f(g(x))=\sqrt{(x^{2}+3)-3}=\sqrt{x^{2}+3-3}=\sqrt{x^{2}}=x[/tex]

∴ f(g(x)) = x

∴ The functions are inverses; f(g(x)) = x

* Lets find the inverse of h(x)

∵ h(x) = 3x² - 1 where x ≥ 0

- Let h(x) = y

∴ y = 3x² - 1

- Exchange x and y

∴ x = 3y² - 1

- Add 1 to both sides

∴ x + 1 = 3y²

- Divide both sides by 3

∴ [tex]\frac{x + 1}{3}=y^{2}[/tex]

- Take √ for both sides

∴ ± [tex]\sqrt{\frac{x+1}{3}}=y[/tex]

∵ x ≥ 0

∴ We will chose the positive value of the square root

∴ [tex]\sqrt{\frac{x+1}{3}}=y[/tex]

- replace y by [tex]h^{-1}(x)[/tex]

∴ [tex]h^{-1}(x)=\sqrt{\frac{x+1}{3}}[/tex]

Answer:

D

Step-by-step explanation:

There are 1.61 km in 1 mi.

10 mi × (1.61 km/mi) = 16.1 km

Answer:

Let the number of hours traveled by train be "x".

The x = the number of hours traveled by plane.

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

Equation:

train distance + plane distance = 1300 miles

50x + 275x = 1300

x(325) = 1300

x = 4 hours

---

The trip took 8 hrs.

Step-by-step explanation:

Trust me

Answer:

The answer to your question is: time = 4 hours

Step-by-step explanation:

Data

Total distance = 1300 miles

train v = 50 mi/h      time is the same        distance = x

plane v = 275 mi/h                                      distance = 1300 - x

t = ?

Formula

v = d/t

Process

Train  t = d/v           t = x / 50

Plane  t = d/ v         t = (1300 - x) / 275

                   x / 50   =  (1300 - x) / 275

                  275 x  = 50 (1300 - x)

                  275 x = 65000 - 50x                   solve for x

                  275x + 50x = 65000

                  325x = 65000

                  x = 65000/325

                  x = 200

   Time with train

                                t = 200 / 50 = 4 hours

Time with plane

                               t = (1300 - 200) / 275

                               t = 1100 / 275 = 4 hours

Answer:

C - 4x4+14x2y+49y2

Step-by-step explanation:

Just took the test

To determine which option is a factor of the given expression, we need to check each option individually. After checking, we find that option 2, 2x^2 + 7y, is a factor.

To determine which of the given options is a factor of the expression 24x^6 - 1029y^3, we need to check each option individually.

Option 1: 24 - We can verify if 24 is a factor by dividing 24x^6 - 1029y^3 by 24 and checking if there is no remainder.

Option 2: 2x^2 + 7y - We can substitute values for x and y and simplify the expression to see if it equals zero for any values.

Option 3: 4x^4 + 14x^2y + 49y^2 - We can substitute values for x and y and simplify the expression to see if it equals zero for any values.

After checking each option, we can determine that option 2, 2x^2 + 7y, is a factor of the expression 24x^6 - 1029y^3.

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Answer: Hi, first lets give our variables some names.

Lets call Ks to Karen's salary and Js to Jason's salary.

then, in 1995:

Ks₁ - Js₁ = 2000$

in 1998:

Ks₂ - Js₂ = 2440$

now, we know that  Ks₂ = (1 +p)*Ks₁ and   Js₂ = (1+p)*Js₁

so we can write the second equation as:

p*(Ks₁ - Js₁ ) = 2440$

replacing the parentesis with the first equiation

(1+p)*(2000$) = 2440$

(1+p)= 2440/2000 = 1.22

so p = 0.22, or a 22%

Answer:

One ml is equal to a cm3, then

m=2.67g/cm3*30.5cm3

m=81.435g

If we divide this quantity by 1000 to pass this to Kg we get:

m=81.435/1000=0.081435kg

Step-by-step explanation:

Remember the formula of density is density=mass/volume, if we solve for mass we get:

mass=density*volume

I think it 8 I think this is the right answer

Answer:

g(3) = 34

Step-by-step explanation:

To evaluate g(3) substitute x = 3 into g(x), that is

g(3) = 4(3)² - 3(3) + 7 = (4 × 9) - 9 + 7 = 36 - 9 + 7 = 34

Answer:

4660194 metric ton

126802560 gallon

Step-by-step explanation:

1 cm = 0.01 m

6 km = 6000 m

8 km = 8000 m

Volume = 0.01 m x 6000 m x 8000 m =  480000 m³

480000 m³ = 480000000 kg of water (density of water = 1000kg/m³)

103 kg = 1 metric ton

480000000 kg = 480000000 / 103 = 4660194 metric ton

1 m³ = 264.17 gallon

480000 m³ = 480000 x 264.172 = 126802560 gallon

A total of 480,000 metric tons of water fell on the city, which is equivalent to approximately 126,802,560 gallons of water.

To calculate the amount of water in metric tons that fell on the city, we need to first determine the volume of the rainfall which can be calculated by taking the product of the rainfall's depth (1.0 cm), and the area of the city (6 km x 8 km).

Firstly, convert all dimensions into the same unit. Let's use meters: 1.0 cm = 0.01 m, 6 km = 6000 m, 8 km = 8000 m. Therefore, the volume equals 0.01 m x 6000 m x 8000 m = 480,000 m³.

The mass of the water is then found by multiplying the volume by the density of water. Given that the density of water is 1 g/cm³ (or 1000 kg/m³, which is more useful here, as mass needs to be in kg), this calculation gives us a mass of 480,000,000 kg = 480,000 metric tons.

To convert this to gallons, we use the fact that 1 m³ = 264.172 gallons. Therefore, 480,000 m³ = 480,000 x 264.172 = 126,802,560 gallons.

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Answer:

Step-by-step explanation:

You may recognize that you are given two relationships between two unknowns. You can write equations for that.

You are asked for numbers of adult tickets and of student tickets. It often works well to let the values you're asked for be represented by variables. We can choose "a" for the number of adult tickets, and "s" for the number of student tickets. Then the problem statement tells us the relationships ...

  a + s = 800 . . . . . . 800 tickets were sold

  12.50a + 7.50s = 8600 . . . . . . . revenue from sales was 8600

(You are supposed to know that the revenue from selling "a" adult tickets is found by multiplying the ticket price by the number of tickets: 12.50a.)

___

You can solve these two equations any number of ways. One way is to do it by elimination. We can multiply the first equation by 12.50 and subtract the second equation:

  12.50(a +s) -(12.50a +7.50s) = 12.50(800) -(8600)

  5s = 1400 . . . . simplify. (The "a" variable has been eliminated.)

  s = 280 . . . . . . divide by 5

Then the number of adult tickets can be found from the first equation:

  a + 280 = 800

  a = 520

280 student tickets and 520 adult tickets were sold.

520 adult tickets and 280 student tickets were sold.

To solve this problem, we need to set up a system of two linear equations using the given information and then solve for the number of adult and student tickets sold.

Let x be the number of adult tickets sold, and y be the number of student tickets sold.

Given information:

- Total number of tickets sold: [tex]x + y = 800[/tex]

- Total receipts: [tex]12.50x + 7.50y = 8600[/tex]

We have a system of two equations with two unknowns:

[tex]x + y = 800[/tex]

[tex]12.50x + 7.50y = 8600[/tex]

We can solve this system using the substitution method or the elimination method.

Using the substitution method:

From the first equation, [tex]y = 800 - x[/tex]

Substituting this into the second equation:

[tex]12.50x + 7.50(800 - x) = 8600[/tex]

[tex]12.50x + 6000 - 7.50x = 8600[/tex]

[tex]5x = 2600[/tex]

[tex]x = 520[/tex]

Substituting [tex]x = 520[/tex] into the first equation:

[tex]y = 800 - 520 = 280[/tex]

Therefore, 520 adult tickets and 280 student tickets were sold.

By setting up a system of linear equations based on the given information and solving them using algebraic methods, we can find the number of adult and student tickets sold that satisfy the conditions of the total number of tickets and the total receipts.

Answer:

The answer to your question is:   x > - 32/9

Step-by-step explanation:

                                            -5/2(3x+4)<6-3x

Multiply by 2                      -5(3x + 4) < 12 - 6x

Simplify                             -15x - 20 < 12 - 6x

Add +6x                            -15x + 6x -20 < 12 - 6x + 6x

Simplify                            - 9x - 20 < 12

Add + 20                          -9x -20 + 20 < 12 + 20

Simplify                            -9x  <  32

Divide by -9                     -9/-9 x > 32/-9

Simplify                             x > - 32/9

Answer:

  ray

Step-by-step explanation:

A ray is a line that extends in one direction from its end point.

Answer:

18 quarters

30 pennies

15 dimes

Step-by-step explanation:

Let number of quarters be q, number of pennies be p, number of dimes be d

The value of pennies is 0.01, the value of quarters is 0.25 and value of dimes is 0.10.

Jack has 63 pennies, dimes, and quarters worth $6.30:

We can write:

p + q + d = 63

0.01p + 0.25q + 0.10d = 6.30

Also, the number of dimes is three less than the number of quarters:

We can write:

d = q - 3

Now we have written 3 equations. Replacing 3rd equation in 1st gives us:

p + q + (q-3) = 63

p + 2q -3 = 63

p + 2q = 66

Solving for p:

p = 66 - 2q

Now we can use this and the 3rd equation and replace p and d with q:

0.01p + 0.25q + 0.10d = 6.30

0.01(66-2q) + 0.25q + 0.10(q-3) = 6.30

Solving for q, gives us:

[tex]0.01(66-2q) + 0.25q + 0.10(q-3) = 6.30\\0.66-0.02q+0.25q+0.10q-0.3=6.30\\0.36+0.33q=6.30\\0.33q=5.94\\q=18[/tex]

There are 18 quarters

Since, p = 66 - 2q, there are:

p = 66 - 2 (18) = 30 pennies

Also,

d = q - 3, so d = 18 - 3 = 15 dimes

Hence, there are:

18 quarters

30 pennies

15 dimes