At the ritz concert tickets for adults cost $6 and tickets for students cost $4. How many of each ticket were purchased if 480 tickets were bought for $2340?

Answer:

propability is the low of chance

Answer:

The probability of tail occurs =  [tex]\frac{1}{4}[/tex] = 0.25

and

The probability of heads occurs = [tex]\frac{3}{4}[/tex] = 0.75

Step-by-step explanation:

Given:

Let P be the tail as outcome in a toss.

Heads is three times as likely to come up as tails.

So, Probability of getting heads = 3P

The total probability is 1

So, P + 3P = 1

4P = 1

P = [tex]\frac{1}{4}[/tex] = 0.25

We denoted P as the probability of getting tail in a toss.

So probability of getting heads = 1 -  [tex]\frac{1}{4}[/tex] =  [tex]\frac{3}{4}[/tex]

Therefore, the probability of tail occurs =  [tex]\frac{1}{4}[/tex] = 0.25

and

The probability of heads occurs = [tex]\frac{3}{4}[/tex] = 0.75

There will be 1.078x students next year and equation is number of students in next year = x + 7.8% of x

Given, There are "x" number of students at helms.  

The number of students increases by 7.8% each year which means if there "x" number of students in present year, then the number of students in next year will be x + 7.8% of x

Number of students in next year = number of students in present year + increased number of students.

[tex]\begin{array}{l}{\text { Number of students in next year }=x+7.8 \% \text { of } x} \\\\ {\text { Number of students in next year }=x\left(1+\frac{7.8}{100}\right)} \\\\ {\text { Number of students in next year }=x(1+0.078)=1.078 x}\end{array}[/tex]

Thus there will be 1.078x students in next year

Answer:   d = 94.87 ft

Step-by-step explanation:

In a baseball game distances between bases is equal to 90 feet

Then if a shortstop get the ball one third of second base ( in the way from second base to third base) shortstop got the ball at 30 ft from second base

Now between the above mentioned point, first base and second base, we  have a right triangle. In which distance between shortstop and first base is the hypotenuse. Then

d²  =  (90)² + (30)²       d   = √ 8100 + 900       d = 94.87 ft

Final answer:

Using the Pythagorean theorem, the exact distance a shortstop must throw to make an out at first base is the square root of 11700 feet, approximately 108.17 feet.

Explanation:

The question pertains to the distance a shortstop must throw a baseball to make an out at first base. To answer this question, we need to use the geometry of a baseball diamond, which is a square with 90 feet between each base. The Pythagorean theorem can be applied to find the distance from the shortstop to first base. Specifically, when the shortstop is one-third of the way from second to third base, we treat the path from the shortstop to first base as the hypotenuse of a right-angled triangle, with the two sides being from the shortstop to second base and from second base to first base. A full side is 90 feet, so one-third of the way is 30 feet (one-third of 90), making the side from the shortstop to second base 60 feet (90 - 30). The other side is a full 90 feet.

We then calculate the hypotenuse (the throw distance) using the Pythagorean theorem (a² + b² = c²), where a is 60 feet and b is 90 feet:

The exact distance the shortstop must throw the ball is the square root of 11700, which is an irrational number, and an approximation to two decimal places is 108.17 feet.

Answer:

The answer to your question is 18m + 2

Step-by-step explanation:

                                            5(3m - 2) + 3(m + 4)

Multiply 5 by 3m and -2 and 3 by m and 4

                                           15m - 10 + 3m + 12

Simplify like terms

                                          15m +3m - 10 + 12

Result                                 18m + 2

Answer:

The percentage of boys students in Jamie's class is 20 %

Step-by-step explanation:

Given as :

The total number of boys in the Jamie's class = [tex]\frac{1}{5}[/tex] of the total student

Let the total number of student's in the class = x

So, The number of boys =  [tex]\frac{1}{5}[/tex] × x

I.e The number of boys =  [tex]\dfrac{x}{5}[/tex]

So , in percentage the number of boys students in class = [tex]\dfrac{\textrm Total number of boy student}{\textrm Total number of students}[/tex] × 100

OR, % boys students = [tex]\dfrac{\dfrac{x}{5}}{x}[/tex] × 100

or, % boys students = [tex]\frac{100}{5}[/tex]

∴ % boys students = 20

Hence The percentage of boys students in Jamie's class is 20 %  . Answer

Answer:

Step-by-stejfnqe ruhrhe ye\

Answer:

  a_n = 2^n + 3

Step-by-step explanation:

The first differences have a geometric progression, so the explicit definition will be an exponential function. (It cannot be modeled by a linear or quadratic function.) The above answer is the only choice that is an exponential function.

__

First differences are ...

  (7-5=)2, 4, 8, 16

Answer: [tex]a_n = 2^n + 3\ \ \ \, n=1,2,3,4,5...[/tex]

Step-by-step explanation:

The given sequence = 5, 7, 11, 19, 35,....

[tex]7-5=2\\11-7=4=2^2\\19-11=8=2^3\\35-19=16=2^4[/tex]

Here , it cam be observe that the difference between the terms is not common but can be expressed as power of 2.

We can write the terms of the sequence as

[tex]2^1+3=5\\2^2+3=4+3=7\\2^3+3=8+3=11\\2^4+3=16+3=19\\2^5+3=32+3=35[/tex]

Then , the required explicit definition that defines the sequence will be

[tex]a_n = 2^n + 3\ \ \ \, n=1,2,3,4,5...[/tex]

Answer

The sum of the possible numbers are {(1,2), (2,1)}

Step-by-step explanation:

Probability for rolling two dice with the eight sided dots are 1, 2, 3, 4, 5, 6, 7 and 8 dots in each die.  

When two dice are rolled or thrown simultaneously, thus number of event can be [tex]8^{2}[/tex]= 64 because each die has 1 to 8 numbers on its faces. Then the possible outcomes of the sample space are shown in the pdf document below .  

As Don rolls the dice and sums the number that appear on the top face, he gets a sum from 2 to 16.

Assuming; getting sum of 2  

Let E[tex]_{1}[/tex] = event of getting sum of 2

E[tex]_{1}[/tex] = { (1 , 1 ) }

Therefore, Probability of getting sum of 2 will be;  

P ( E[tex]_{1}[/tex] ) = [tex]\frac{Number of favorable outcome}{Total number of possible outcome}[/tex]

= [tex]\frac{1}{64}[/tex]

GETTING SUM OF TWO ( i.e  { (1 , 1 ) }  ) will give the probability of 1/64 of appearing. But we are looking for the probability of 1/32 of appearing. Let look at the possibility of getting sum of 3.

Assuming; getting sum of 3

Let E[tex]_{2}[/tex] = event of getting sum of 3

E[tex]_{2}[/tex] = { (1 , 2 ) (2 , 1) }

Therefore, Probability of getting sum of 3 will be;  

P ( E[tex]_{2}[/tex] ) = [tex]\frac{Number of favorable outcome}{Total number of possible outcome}[/tex]

= [tex]\frac{2}{64}[/tex]

= [tex]\frac{1}{32}[/tex]

For all probability of getting the sum greater than 3 to 16 will be void because there wont be a chance for 1/32 to appear. Therefore, the sum of the possible numbers are: {(1,2), (2,1)}  which have a probability of 1/32 of appearing.

I hope this comes in handy at the rightful time!

Answer:

at y-intercept: (0,2) is the correct

Step-by-step explanation:

We have equation 1  

9x-6=3y

to find the x-intercept, substitute in 0 for y and solve for x

3(0)=9x+6

3(0)=9x+6

9x+6=0

Subtract 6 from both sides  

9x=−6

So x = -6/9 = -2/3

Now to find for y-intercept, substitute in 0 for x and solve for y

3y=9(0)+6

3y=0+6

3y=6

These are the x and y intercepts of the equation 3y=9x+6

x-intercept: (−2/3,0)

y-intercept: (0,2)

Answer:

Correct.

Step-by-step explanation:

Check if x = 0 and y = -2 fits the equation:

9(0) - 6 = -6

3(-2) = -6.

They do so the student is correct.

Answer:

5

Step-by-step explanation:

First, notice that these two triangles are similar using AA.

Because sides BC and EC are corresponding, you can divide 24 by 8, to determine that the ratio of similitude is 3.

That means that because sides AC and DC are corresponding, 25 - 2x divided by x is 3.

25 - 2x / x = 3

25 - 2x = 3x

25 = 5x

x = 5

x is the same as side CD, so CD = 5.

Using similar triangles and proportions, we can determine that the length of CD in the figure is 10/3 units.

In order to determine the length of CD in the figure, we can use the properties of similar triangles. Since triangles ABC and CDE are similar, we can set up a proportion using their corresponding side lengths:

δ CD / δ AB = CD / AB

Then, we can substitute the given values:

4 / 12 = CD / 20

Next, we can cross multiply and solve for CD:

12 * CD = 4 * 20

CD = (4 * 20) / 12

CD = 40 / 12

CD = 10 / 3

Therefore, the length of CD is 10/3 units.

Learn more about Length of CD here:

https://brainly.com/question/32683994

#SPJ2

Answer:

P(-3)=-4

P(7) = 9

Step-by-step explanation:

Consider P(x) is a polynomial.

According to the remainder theorem, if a polynomial, P(x), is divided by a linear polynomial (x - c), then the remainder of that division will be equivalent to f(c).

Using the given information and remainder theorem we conclude,

If P(x) is divided by  (x+7), then remainder is 5.

⇒ P(-7)=5

If P(x) is divided by  (x+3), then remainder is -4.

⇒ P(-3)=-4

If P(x) is divided by  (x-3), then remainder is 6.

⇒ P(3)=6

If P(x) is divided by  (x-7), then remainder is 9.

⇒ P(7)=9

Therefore, the required values are P(-3)=-4 and P(7) = 9.

Answer:

[tex]-1.78>x\leq -1.46[/tex]

Step-by-step explanation:

1. Understanding the type of statement

We are given an OR statement. A certain x-value is a set of solution of the statement if it satisfies both of the inequalities.

Therefore, the solution of this statement is the Union of set of the solutions of both inequalities.

2. Finding the solutions to the two inequalities

[tex]-9x+2>18\\-9x>18-2\\-9x>16\\x<-\frac{16}{9}\\ \\x<-1.78[/tex]

Now Solving for other equation we get,

[tex]13x+15\leq-4\\13x\leq -4-15\\13x\leq -19\\x\leq -\frac{19}{13}\\ \\x\leq -1.46[/tex]

3. The solution is:

[tex]-1.78>x\leq -1.46[/tex]

Answer:

[tex]x \leq - 1.462[/tex]

Step-by-step explanation:

Let solve each inequation:

[tex]-9\cdot x + 2 > 18[/tex]

[tex]-16 > 9\cdot x[/tex]

[tex]9\cdot x < - 16[/tex]

[tex]x < - \frac{16}{9}[/tex]

[tex]x < -1.778[/tex]

[tex]13\cdot x + 15 \leq -4[/tex]

[tex]13\cdot x \leq -19[/tex]

[tex]x \leq -\frac{19}{13}[/tex]

[tex]x \leq -1.462[/tex]

The boolean operator OR means that proposition is true if at least one equation is true. Then, the domain that fulfill the proposition is:

[tex]x \leq - 1.462[/tex]

Answer:

Fraction of cake that was left for Amber = [tex]\frac{1}{8}[/tex]

Step-by-step explanation:

Given:

Amber had [tex]\frac{3}{8}[/tex] of a cake left after her party.

Amber wrapped a piece of cake for her friend that was [tex]\frac{1}{4}[/tex] of the original cake.

To find the fractional part of cake that was left for Amber.

Solution:

Fraction of cake left Amber had after party = [tex]\frac{3}{8}[/tex]

Fraction of cake she wrapped for her friend = [tex]\frac{1}{4}[/tex]

To find the fractional part of cake that was left for Amber we will subtract [tex]\frac{1}{4}[/tex] of the cake from  [tex]\frac{3}{8}[/tex] of the cake.

∴ Fraction of cake that was left for Amber = [tex]\frac{3}{8}-\frac{1}{4}[/tex]

To subtract fractions we need to take LCD

⇒  [tex]\frac{3}{8}-\frac{1}{4}[/tex]

LCD  will be =8 as its the least common multiple of 4 and 8.

To write [tex]\frac{1}{4}[/tex] as a fraction with common denominator 8 we multiply numerator and denominator with 2.

So, we have

⇒  [tex]\frac{3}{8}-\frac{1\times 2}{4\times 2}[/tex]

⇒  [tex]\frac{3}{8}-\frac{ 2}{8}[/tex]

Then we simply subtract the numerators.

⇒  [tex]\frac{3-2}{8}[/tex]

⇒  [tex]\frac{1}{8}[/tex]

∴ Fraction of cake that was left for Amber = [tex]\frac{1}{8}[/tex]

Answer:

20 peices

Step-by-step explanation:

The radius of the bowl R as a function of the angle theta is [tex]\mathrm{R}=\frac{3}{1-\sin \theta}[/tex]

Solution:

The figure is attached below

If we consider the centre of hemisphere be A

The radius be AC and AD

According to question,  

A bowl in the shape of a hemispere is filled with water to a depth h=3 inches .i.e. BC = h = 3 inches

And radius of the bowl is R inches .i.e. R = AD =AC

Now , using  trigonometric identities in triangle ABD we get

[tex]\sin \theta=\frac{\text { Perpendicular }}{\text { Hypotenuse }}=\frac{A B}{A D}[/tex]

[tex]\begin{array}{l}{\sin \theta=\frac{A B}{R}} \\\\ {A B=R \sin \theta}\end{array}[/tex]

Since , AC = AB + BC

R = R Sinθ + 3

R - R Sinθ = 3

R (1 – Sinθ ) = 3

[tex]\mathrm{R}=\frac{3}{1-\sin \theta}[/tex]

Which is the required expression for the radius of the bowl R as a function of the angle theta

Answer:

0.33

Step-by-step explanation:

Two fair number cubes can be thought as dice with sides numbered from 1 to 6. The throw of two dice may result in one of the following combinations in which (d1,d2) are the results of die 1 and 2 respectively:

Ω={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

There are 36 as many possible combinations

The sum of both quantities will produce 11 possible results

S={2,3,4,5,6,7,8,9,10,11,12}

The combinations which produce a sum of 4 are (1,3)(2,2),(3,1), 3 in total

The combinations which produce a sum of 5 are (1,4)(2,3),(3,2),(4,1) 4 in total

The combinations which produce a sum of 6 are (1,5)(2,4),(3,3),(4,2),(5,1) 5 in total

If we want to know the probability that the sum of the results of the throw is 4,5, or 6, we compute the total ways to produce them

T=3+4+5=12 combinations

The probability is finally computed as

[tex]P=\frac{T}{36}=\frac{12}{36}=\frac{1}{3}=0.33[/tex]

Final answer:

To find the probability of getting a sum of 4, 5, or 6 when two dice are rolled, all possible combinations are listed, resulting in 12 favorable outcomes. Those outcomes are then divided by the total number of possible outcomes, 36, resulting in a probability of 1/3.

Explanation:

The question asks about the probability of getting a sum of 4, 5, or 6 when throwing two fair number cubes (dice). Each die has six faces, with numbers ranging from 1 to 6. When rolling two dice, there are 36 possible outcomes (6 outcomes from the first die multiplied by 6 outcomes from the second die).

To find the probability of obtaining a sum of 4, 5, or 6, we first want to identify all the possible combinations that lead to these sums:

Altogether, there are 3 + 4 + 5 = 12 outcomes that result in either a 4, 5, or 6 as the sum. Therefore, the probability is the number of favorable outcomes (12) divided by the total number of outcomes (36), which simplifies to 1/3. Hence, the probability is 1/3.

Answer:

The correct answers are: Part A. A/π^1/2 = r and Part B. 4.15 centimeters.

Step-by-step explanation:

1. Let's review all the information provided for solving this question:

Area of the circle = π*r² where r is the circle's radius

2. Let's find the solution for r for part A and for part B:

Part A:

A = π*r²

A/π = r²

√A/π = r

A/π^1/2 = r

Part B:

If A = 54 centimeters² and π  = 22/7, what is the value of r in centimeters?

Using the result of part A and replacing with the real values, we have:

√A/π = r

√54/(22/7) = r

√54 * 7/22 = r

√378/22 = r

√17.1818 = r

4.1451 = r

4.15 = r (Rounding to two decimal places)

Answer:

a) 0.30

b) 0.90

c)   0.15

Step-by-step explanation:

When two events are independent then conditional probability take place.

Answer:

No

Step-by-step explanation:

N = 10,000

n= 800

p = .28

Sampling distribution drawn from specific population. So it is not safe to assume that sampling proportion of customers is approximately normal.

Final answer:

The sampling distribution of the sample proportion of customers planting a vegetable garden may not be approximately normal due to insufficient sample size, according to the central limit theorem.

Explanation:

No, it is not safe to assume the sampling distribution of the sample proportion of customers that plant a vegetable garden is approximately normal.

This situation involves calculating the normality of a sample proportion. The **central limit theorem** states that the sampling distribution of a sample proportion will be approximately normal if the sample size is large enough, specifically n * p >= 10 and n * (1-p) >= 10, where n is the sample size and p is the probability of success.

In this case, the sample size is 800 and the probability of success (customers planting a garden) is 28%, so 800 * 0.28 = 224, which is less than 10. Thus, the sampling distribution may not be normal.

Answer:

1, 3, and 5

Step-by-step explanation:

Answer:

Option b

Step-by-step explanation:

Given that a  researcher measures IQ and weight for a group of college students.

In general, we think that the weight has nothing to do with IQ of a person and hence not correlated.

But if we go deep, we find that after a certain weight, the person becomes lazy and inactive with a chance to have reduced IQ

Weight gain causes also health problems including less activity of both brain and body and hence there is a chance for less IQ

So we find that as weight increases iq decreases and when weight decreases, IQ increases.

Thus we can say that there is a negative correlation but not necessarily near to one.

Hence option b is right

The most likely correlation between IQ and weight among college students is near zero, indicating no meaningful relationship between these variables.

When it comes to the likelihood of obtaining a correlation between IQ and weight among college students, the correlation is expected to be c) a correlation near zero. This is because there is no theoretical basis or empirical evidence to suggest that these two variables are related in any systematic way. A correlation coefficient is a statistical measure that describes the strength and direction of a relationship between two variables. A coefficient close to 0 indicates a very weak or no correlation, whereas one closer to +1 or -1 indicates a strong positive or negative correlation, respectively. In our scenario, since weight and IQ are not assumed to be related, the correlation would likely be close to 0, suggesting no meaningful relationship.

Answer:

[tex]y=-30x+2380[/tex]

Step-by-step explanation:

[tex]x\rightarrow[/tex] represent price per video game.

[tex]y\rightarrow[/tex] represent demand.

The linear equation in slope intercept form can be represented as:

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

where [tex]m[/tex] is slope of line or rate of change of demand of game per dollar change in price and [tex]b[/tex] is the y-intercept or initial price of game.

We can construct two points using the data given.

When price was $66 each demand was 400. [tex](66,400)[/tex]

When price was $36 each demand was 1300. [tex](36,1300)[/tex]

Using the points we can find slope [tex]m[/tex] of line.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{1300-400}{36-66)}[/tex]

[tex]m=\frac{900}{-30}[/tex]

[tex]m=-30[/tex]

Using point slope form of linear equation to write the equation using a given point.

[tex]y-y_1=m(x-x_1)[/tex]

Using point [tex](66,400)[/tex].

[tex]y-400=-30(x-66)[/tex]

⇒ [tex]y-400=-30x+1980[/tex]    [Using distribution]

Adding 400 to both sides:

⇒ [tex]y-400+400=-30x+1980+400[/tex]

⇒[tex]y=-30x+2380[/tex]

The linear relationship between price and demand can be written as:

[tex]y=-30x+2380[/tex]

Answer:

The greatest number of baskets can be 81 and the least number of baskets can be 9.

Step-by-step explanation:

We have a constraint on our actions, that every basket should have the same number of fruits in each basket.

To find the highest number of fruits in each basket we have to find the Highest Common Factor( HCF) of the number of apples , bananas and oranges.

HCF of 36, 27 and 18 is 9.

Therefore the number of fruits in each basket is 9.

Apples will require 4 baskets, bananas will require 3 baskets and oranges will require 2 baskets. Thus Nina is right and total 9 baskets will be required.

9 is the least of number of baskets required

If we have to maximize the number of baskets, then we have to place the least number of same fruits in a basket ie. 1.

Therefore, he maximum number of baskets required is 36+27+18=81 baskets.

Answer:

16008

Step-by-step explanation:

Sum of an arithmetic sequence is:

S = (n/2) (2a₁ + (n−1) d)

or

S = (n/2) (a₁ + a)

To use either equation, we need to find the number of terms n.  We know the common difference d is 1 − (-9) = 10.  Using the definition of the nth term of an arithmetic sequence:

a = a₁ + (n−1) d

561 = -9 + (n−1) (10)

570 = 10n − 10

580 = 10n

n = 58

Using the first equation to find the sum:

S = (n/2) (2a₁ + (n−1) d)

S = (58/2) (2(-9) + (58−1) 10)

S = 29 (-18 + 570)

S = 16008

Using the second equation to find the sum:

S = (n/2) (a₁ + a)

S = (58/2) (-9 + 561)

S = 16008

Answer:

16008

Step-by-step explanation:

Answer:

620 minutes

Step-by-step explanation

In one day,Mata exercise 20minutes more than Greg

31 days so we have 20 *31=620

Answer:

A. It is an equivalence relation on R

B. In fact, the set [0,1) is a set of representatives

Step-by-step explanation:

A. The definition of an equivalence relation demands 3 things:

And the relation ∼ fills every condition.

∼ is Reflexive:

Let a ∈ R

it´s known that a-a=0 and because 0 is an integer

a∼a, ∀a ∈ R.

∼ is Reflexive by definition

∼ is Symmetric:

Let a,b ∈ R and suppose a∼b

a∼b ⇒ a-b=k, k ∈ Z

b-a=-k, -k ∈ Z

b∼a, ∀a,b ∈ R

∼ is Symmetric by definition

∼ is Transitive:

Let a,b,c ∈ R and suppose a∼b and b∼c

a-b=k and b-c=l, with k,l ∈ Z

(a-b)+(b-c)=k+l

a-c=k+l with k+l ∈ Z

a∼c, ∀a,b,c ∈ R

∼ is Transitive by definition

We´ve shown that ∼ is an equivalence relation on R.

B. Now we have to show that there´s a bijection from [0,1) to the set of all equivalence classes (C) in the relation ∼.

Let F: [0,1) ⇒ C a function that goes as follows: F(x)=[x] where [x] is the class of x.

Now we have to prove that this function F is injective (∀x,y∈[0,1), F(x)=F(y) ⇒ x=y) and surjective (∀b∈C, Exist x such that F(x)=b):

F is injective:

let x,y ∈ [0,1) and suppose F(x)=F(y)

[x]=[y]

x ∈ [y]

x-y=k, k ∈ Z

x=k+y

because x,y ∈ [0,1), then k must be 0. If it isn´t, then x ∉ [0,1) and then we would have a contradiction

x=y, ∀x,y ∈ [0,1)

F is injective by definition

F is surjective:

Let b ∈ R, let´s find x such as x ∈ [0,1) and F(x)=[b]

Let c=║b║, in other words the whole part of b (c ∈ Z)

Set r as b-c (let r be the decimal part of b)

r=b-c and r ∈ [0,1)

Let´s show that r∼b

r=b-c ⇒ c=b-r and because c ∈ Z

r∼b

[r]=[b]

F(r)=[b]

∼ is surjective

Then F maps [0,1) into C, i.e [0,1) is a set of representatives for the set of the equivalence classes.

Answer:

Step-by-step explanation:

inside the castle

Answer: length = 8 units

Width = 2 units

Step-by-step explanation:

Let the length of the rectangle be represented by L

Let the width of the rectangle be represented by W

The sum of 5 times the width of a rectangle and twice its length is 26 units. This means that

5W + 2L = 26 - - - - - - - - 1

The difference of 15 times the width and three times the length is 6 units. It means that

15W - 3L = 6 - - - - - - - - 2

The system equations are equation 1 and equation 2.

Multiplying equation 1 by 3 and equation 2 by 2, it becomes

15W + 6L = 78

30W - 6L = 12

Adding both equations,

45W = 90

W = 90/45 = 2

15W - 3L = 6

15×2 - 3L = 6

-3L = 6 - 30 = - 24

L = - 24/ -3 = 8

The length of the rectangle is 8 units, and the width is 2 units. This solution satisfies both equations given.

Let's denote the width of the rectangle as ( w ) units and the length as ( l ) units.

According to the given information, we have two equations:

1. ( 5w + 2l = 26 )  (sum of 5 times the width and twice the length is 26 units)

2. ( 15w - 3l = 6 )  (difference of 15 times the width and three times the length is 6 units)

We can set up a system of equations using these two equations.

To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method.

First, we'll multiply the second equation by 2 to eliminate the ( l ) term:

( 2 x (15w - 3l) = 2 x 6 )

This gives us:

( 30w - 6l = 12 )

Now, we have the system of equations:

1. ( 5w + 2l = 26 )

2. ( 30w - 6l = 12 )

We can now eliminate the ( l ) term by adding these equations together.

( (5w + 2l) + (30w - 6l) = 26 + 12 )

This simplifies to:

( 35w - 4l = 38 )

Now, we have one equation with only ( w ) as a variable.

Now, we can solve for ( w ):

( 35w - 4l = 38 )

( 35w = 38 + 4l )

[tex]\( w = \frac{38 + 4l}{35} \)[/tex]

Now, we can substitute this value of ( w ) into one of the original equations to solve for ( l ).

Let's use the first equation:

( 5w + 2l = 26 )

Substituting[tex]\( w = \frac{38 + 4l}{35} \)[/tex], we get:

[tex]\( 5\left(\frac{38 + 4l}{35}\right) + 2l = 26 \)[/tex]

Now, we can solve this equation for ( l ).

[tex]\( \frac{190 + 20l}{35} + 2l = 26 \)[/tex]

Multiply both sides by 35 to clear the fraction:

( 190 + 20l + 70l = 910 )

Combine like terms:

( 90l + 190 = 910 )

Subtract 190 from both sides:

( 90l = 720 )

Now, divide both sides by 90 to solve for ( l ):

[tex]\( l = \frac{720}{90} \)[/tex]

( l = 8 )

Now that we have the value of ( l ), we can substitute it back into one of the original equations to solve for ( w ). Let's use the first equation:

( 5w + 2(8) = 26 )

( 5w + 16 = 26 )

Subtract 16 from both sides:

5w = 10

Now, divide both sides by 5 to solve for ( w ):

[tex]\( w = \frac{10}{5} \)[/tex]

w = 2

So, the length of the rectangle is 8 units and the width is 2 units.

Answer: Time it took her to get to the school is 0.6 hours

The distance of the school from their home is 27 miles

Step-by-step explanation:

Mrs Dang drove her daughter to school at the average speed of 45 miles per hour.

Let x miles = distance from the school to their home.

Distance = speed × time

Time = distance / speed

Time used in going to school will be

x/45

She returned home by the same route. This means that distance back home is also x miles.

She returned at an average speed of 30 miles per hour.

Time used in returning home from school will be x/30

x/45

If the trip took one half hour, then the time spent in going to school and the time spent in returning is 1 1/2 hours = 1.5 hours. Therefore

x/30 + x/45 = 1.5

(15x + 10x) /450 = 1.5

15x + 10x = 450 × 1.5 = 675

25x = 675

x = 675/25 = 27

Time it took her to get to the school will be x/45

= 27/45 = 0.6 hours

Answer:

Step-by-step explanation:

A knitter wants to make a rug for a dollhouse. The length of the rug will be 2 inches more than it's width. Let the width of the rug be represented by w. This means that the length of the rug will be w + 2

The total area of the rug (in square inches ) based on the width W of the rug (in inches ) is given by

A(w) = w (2+w)

If the desired area of the rug is 15 square inches,,the width will be determined by substituting 15 for A(w). It becomes

15 = w^2 + 2w

w^2 + 2w - 15 = 0

w^2 + 5w - 3w - 15 = 0

w(w+5) -3(w+5)

w - 3 = 0 or w+ 5 = 0

w = 3 or w = -5

w cannot be negative. So w = 3 inches