A tailor charge $560 for a suit of clothes and gives a discount of 12% for cash. Calculate the discounted price for a suit of clothes.​

These two equations form a system that can be solved to find the values of x and y, representing the number of children and adults, respectively, who played on that day.

The correct system of equations to model this scenario is:

x + y = 414 (Equation 1)

9x + 12y = 3780 (Equation 2)

In this system, x represents the number of children and y represents the number of adults who played that day.

Equation 1 represents the total number of customers, which is 414. It states that the sum of the number of children (x) and the number of adults (y) is equal to 414.

Equation 2 represents the total cost of the games played. Since the cost for a child's game is $9 and the cost for an adult's game is $12, we multiply the number of children (x) by $9 and the number of adults (y) by $12. The equation states that the total cost, which is $3780, is equal to the sum of these individual costs.

Together, these two equations form a system that can be solved to find the values of x and y, representing the number of children and adults, respectively, who played on that day.

For more questions on equations

https://brainly.com/question/17145398

#SPJ8

(a) Given \(f(x) = x^3\), the derivative is

\(f'(x)=3x^2\)

which is exists for all \(x\) in the domain of \(f\), so \(]f\) is differentiable everywhere and satisfies the mean value theorem. There is some number \(c\) in the open interval (0, 2) such that

\(f'(c) = \dfrac{f(2) - f(0)}{2-0} \iff 3c^2 = \dfrac{8-0}2 = 4\)

Solve for \(c\) :

\(3c^2 = 4 \implies c^2 = \dfrac43 \implies \boxed{c = \dfrac2{\sqrt3}}\)

We omit the negative square root since it doesn't belong to (0, 2). Graphically, the MVT tells us the tangent line to the curve \(f(x)=x^3\) at \(x=\frac2{\sqrt3}\) is parallel to the secant line through the endpoints of the given interval.

(b) \(f(x)=1+x+x^2\) has derivative

\(f'(x)=1+2x\)

By the MVT,

\(f'(c) = \dfrac{f(2)-f(0)}{2-0} \iff 1+2c = \dfrac{7-1}2 \implies \boxed{c = 1}\)

(c) \(f(x) = \cos(2\pi x)\) has derivative

\(f'(x) = -2\pi \sin(2\pi x)\)

By the MVT,

\(f'(c) = \dfrac{f(2)-f(0)}{2-0} \iff -2\pi \sin(2\pi c) = \dfrac{0-0}2 \implies \sin(2\pi c) = 0 \\\\ \implies 2\pi c = n\pi \implies c = \dfrac n2\)

where \(n\) is any integer. There are 3 solutions in the interval (0, 2),

\(\boxed{c = \dfrac12, c = 1, c = \dfrac32}\)

(Pictured is the situation with \(c=\frac12\))

Answer:

50

Step-by-step explanation:

0.8 * x = 40

40/0.8=50

\(x-9z^5+4z+11+2z^5+14=-5z^5-3z+25\\x=2z^5-7z\)

Therefore, it's \(2z^5-7z\).

10-10=69.420!!!!!!!!!!

The equation of the tangent to the given curve x = t⁴ + 3 , y = t³ + t at the corresponding point is y = x - 2   .

In the question ,

it is given that ,

the parametric equation is x = t⁴ + 3 , y = t³ + t ,

differentiating with respect to t ,

we get ,

dx/dt = 4t³  and   dy/dt = 3t² + 1

On dividing dx/dt by dy/dt to get the slope ,

we get

dy/dx = (3t² + 1)/ (4t³)

Substituting in t=1

dy/dx = (3 + 1)/4 = 1

Slope (m) = 1 ;

Substituting t = 1 , in the parametric equation ,

we have , x = 4 and y = 2 .

So , (y - 2) = 1(x - 4)

y - 2 = x - 4

y = x - 2

Therefore , the equation of the tangent is  y = x - 2  .

The given question is incomplete , the complete question is

Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x = t⁴ + 3 , y = t³ + 3 ; t = 4 ?

Learn more about Tangent here

https://brainly.com/question/7252502

#SPJ4

If the sales amount doubles, the commission amount must also double.

The commission rate is 6%, which means that the salesperson earns 6 cents on every dollar of sales.

Therefore, for a sale of $44,000 worth of furnaces, the commission would be:

Commission = 0.06 * $44,000 = $2,640

If sales were to double, the commission would also double. This is because the commission is directly proportional to the amount of sales.

If the salesperson sells twice as many furnaces, they will earn twice the commission as they did before, assuming the commission rate remains the same.

This is true without using any calculations because the commission rate is a fixed percentage of the sales amount, regardless of the actual dollar value of the sales.

Read more about commission at

https://brainly.com/question/26283663

#SPJ1

Answer:

b^2

Step-by-step explanation:

You're going to add the exponents from b x b, both carry a 1 in their powers (or exponents)

so b^1 + b^1 = b^2

Answer:

b^2

Step-by-step explanation:

b*b = b^2

Answer:

The correct equation that initially models the value of Rob's boat is option A, y = 40,000(0.93)*.

Since the value of the boat decreased by 7% each year, the value of the boat after three years can be represented by:

y = 40,000(0.93)^3

where y is the value of the boat after three years, and 40,000 is the initial value of the boat.

Simplifying this equation, we get:

y = 40,000(0.7951)

y = 31,804

However, we know that the actual value of the boat after three years was $32,174.28. This means that our initial assumption that the boat decreased by 7% each year is incorrect and we need to adjust the equation accordingly.

To find the correct equation, we can use the formula for exponential decay:

y = a(1 - r)^t

where y is the final value, a is the initial value, r is the rate of decay (expressed as a decimal), and t is the time in years.

In this case, we know that the final value of the boat is $32,174.28, and that the boat was owned for three years. We also know that the value of the boat decreased by 7% each year.

So we can set up an equation:

32,174.28 = 40,000(0.93)^3

Simplifying this equation, we get:

32,174.28 = 31,804.00

This equation is approximately true, which means that the initial value of the boat was $40,000 and the correct equation that initially models the value of Rob's boat is:

y = 40,000(0.93)^t

where t is the time in years.

(a) To meet the desired 20g protein and 80g carbohydrate intake, prepare 4 servings of Pork & Beans and combine with 15 slices of "lite" rye bread.

(b) Bread: A/4 slices, Beans: B/21 - (A/4) * (12/21) servings.

(a) To prepare a meal of "beans-on-toast" that supplies 20 grams of protein and 80 grams of carbohydrates, you can use the following combination:

- Servings of Campbell's Pork & Beans: 4 servings.

- Slices of "lite" rye bread: 15 slices.

By using 4 servings of Campbell's Pork & Beans, you will obtain a total of 20 grams of protein (5 grams per serving) and 84 grams of carbohydrates (21 grams per serving).

Combining this with 15 slices of "lite" rye bread will contribute an additional 60 grams of carbohydrates (12 grams per slice) and 4 grams of protein (4 grams per slice). Thus, your meal will meet the desired nutritional requirements of 20 grams of protein and 80 grams of carbohydrates.

(b) The formula to determine the number of slices of bread and servings of Pork & Beans needed to meet specific protein and carbohydrate requirements is as follows:

- Number of slices of bread (Bread): A divided by 4.

- Number of servings of Pork & Beans (Beans): (B divided by 21) minus ((A divided by 4) multiplied by (12 divided by 21)).

Using this formula, you can calculate the appropriate quantities of bread and beans based on the desired protein (A) and carbohydrate (B) values.

For more such questions on carbohydrate, click on:

https://brainly.com/question/29917711

#SPJ8

Answer:

me too (help)

Step-by-step explanation:

Answer:

6 hours

Step-by-step explanation:

Since there are 60 minutes in one hour, you can ski 3 * 2 = 6 miles per hour. Therefore, it will take you 36 / 6 = 6 hours to ski that distance.

-

Answer : There are roughly 4 - 5 birds at the pet store

Step - by - step explanation :

Since there are 48 dogs, and 39 cats . . . in - order to find out how many birds there are we need to do . . .

48 + 39 = 87 <-- This is the total of cats and dogs combined

Now, because we know the remainder of animals at the store is birds we do . . .

99 <-- The total number of pets at the store - 87 = 12

There are 12 birds at the store

To find the remainder . . .

40/40 - 26/40 = 14/40 <-- The remaining amount of animals

I forgot how I got this but there are roughly 4 - 5 birds at the pet store

-

Answer:

width = 5k²

length = 3k² + 7k + 4

Step-by-step explanation:

(see attached)

Answer:

is it just that one graph

Step-by-step explanation:

Answer:hmm

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

x is higher than -2 so the colored line is an estimation of where x is

Answer:

Slope = y2 - y1/x2 - x1

Slope = 6-4 / 1--2

Slope = 2/3

Step-by-step explanation:

hope that will help you

The slope of the line will be 2/3.

The formula for the slope will be:

= (y2 - y1) / (x2 - x1)

where,

y2 = 6

y1 = 4

x2 = 1

x1 = -2

We will slot the values into the equation which will be:

= (y2 - y1) / (x2 - x1)

= (6-4) / (1- -2)

= 2/(1+2)

= 2/3

Therefore, the slope is 2/3.

Read related link on:

https://brainly.com/question/24645618

Answer:

Hope you understand not to sure but that's what I got

Answer:

x=-pie/12

sinxcosx=-1/4

multiply both sides by 2

sin2x = 2sinxcosx we know

now equation will be

sin2x = -1/2

2x=-pie/6

x=-pie/12

Step-by-step explanation:

It is important to know that the diagonals of a rhombus are PERPINDICUALR bisectors of each other .   Opposite angles are equal and adjacen angles sum to 180 degrees .

Then remember alternate angles are equal  and there are 180 degrees inside of a triangle .....then you should be able to solve these...here is the first one

Answer: q=13

Step-by-step explanation:

add the separate the q, add 4 to the 9= 13

13=q

The result of the addition operation of 1204.2 + 4.72613 is approximately 1208.93.

An addition operation involves two addends added together to result in a number called the sum.

The addition operation is one of the four basic mathematical operations, including subtraction, division, and multiplication.

Mathematical operations combine numbers, variables, and values with mathematical operands to solve mathematical questions.

1204.2 + 4.72613

= 1208.92613

= 1208.93

Thus, the addition of 1204 and 4.72613 yields a total of 1208.93 approximately.

Learn more about mathematical operations at brainly.com/question/20628271

#SPJ1

Answer:

321.25 per year

Step-by-step explanation:

In 2004 they had 5,545

In 2008 they had 6,830

Subtract them both and you get 4 years, 1285 people

Divide 1285 by 4 and get 321.25 per year.

Answer:

9 7/8

Step-by-step explanation:

1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.

2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.

3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.

Answer: x=8

for every 5 there is 2

so for x=8

there are four 5's in 20

I hope this is good enough:

Answer:

x = 8

Step-by-step explanation:

I can confirm this is right I took test

Solution;

To determine Proportion;

To determine the standard error;

To determine 90% confidence interval;

Lower bound is 12.3962

Upper bound is 13.6038

Answer:

C.  5x(-x + 2)

Step-by-step explanation:

To factor the expression -5x² + 10x, we need to look for a common factor that can be factored out.

Finding a common factor involves identifying a term or expression that can be factored out from each term of a given expression.

Both terms have the common factor of 5x, so we can factor out 5x:

5x(-x + 2)

Therefore, the factored form of -5x² + 10x is -5x(x - 2).

\(\hrulefill\)

Additional notes:

If we expand the expressions in the given answer options, we get:

  A.  −5x(x + 2) = -5x² - 10x

  B.  5(−x² + 10x) = -5x² + 50x

  C.  5x(−x + 2) = -5x² + 10x

  D.  x(5x + 10) = 5x² + 10x

Hence confirming that the correct answer is option C.

To factor \(-5x^2+10x\), we can begin by factoring out the greatest common factor, which is \(-5x\):

We can check our answer by distributing \(-5x\) to the expression inside the parentheses:

\(\therefore\) The answer is \(-5x(x-2)\).

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

Answer:

Step-by-step explanation:

Base on the given condition, formulate:

0.6+0.3-0.2

0.9-0.2 equals 0.7percent.and turn it into a percentage,which will give you 70 percent

Answer:

the answer is d

Step-by-step explanation: