A constant is a value in a formula that doesn't change. _______________

Answer: There are 875 fans the bus deliver to the concert in total.

Step-by-step explanation:

Since we have given that

On the first trip, the bus dropped off = 30

Here a = first term = 30

On the 14 trip, the last trip, the bus dropped off = 95

i.e. [tex]a_{14}=95[/tex]

So, the total number of fans the bus deliver to the concert is given by

[tex]S_{14}=\frac{n}{2}(a+a_n)\\\\S_{14}=\frac{14}{2}(30+95)\\\\S_{14}=7(30+95)\\\\S_{14}=125\times 7\\\\S_{14}=875[/tex]

Hence, there are 875 fans the bus deliver to the concert in total.

Answer:

The Algebraic expression that correctly represents the phrase 'the difference between 7 and a number squared' is

= 7 - x²

Step-by-step explanation:

Let's represent the unknown number be represented as x

The unknown number is also squared = x²

Therefore, the Algebraic Equation correctly representing the phrase 'difference of 7 and a number squared' is

= 7 - x²

The median of a data set with an even number of values is calculated by taking the average of the two middle values. For a data set with an odd number of values, the median is simply the middle value.

The median of a data set with an even number of values is calculated by taking the average of the two middle values. For example, if the data set is 6.8, 7.2, the median would be (6.8 + 7.2) / 2 = 7.

However, if the data set has an odd number of values, the median would simply be the middle value. For example, if the data set is 3, 5, 8, the median is 5.

It's important to note that the median is used to find the middle value of a data set and is often preferred over the mean when there are outliers in the data.

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Answer:

13.0

Step-by-step explanation:

The other leg of the right triangle will be 16.5cm.

The side which shares the common/neighboring border to the right angle in a triangle is called legs.

It states that the sum of the areas of the two squares on the legs equals the area of the of the square on the hypotenuse.

According to the given question, we have

length of one leg of the right triangle is 13cm.

hypotenuse of the right triangle is 21 cm .

Let x be the length of the other leg.

Now, according to the Pythagoras theorem

We can write as

[tex](21)^{2} = x^{2} +(13)^{2}[/tex]

⇒ 441 = [tex]x^{2} +169[/tex]

⇒[tex]441-169 =x^{2}[/tex]

⇒ [tex]272 =x^{2}[/tex]

⇒ [tex]x = \sqrt{272}[/tex]

⇒[tex]x = 16.49[/tex] ≈ 16.5cm

Hence, the other leg of the right triangle will be 16.5cm.

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Answer:

[tex]y=3x[/tex]

when Richard has 30 CDs, Benny has 10 CDs.

Step-by-step explanation:

Richard has 3 times as many music CDs as Benny does.

Let Benny has 'x' CD's.

If Richard has 'y' CDs, the number of CDs Benny has is given by the expression :

[tex]y=3x[/tex]

If Richard has 30 CDs, means y = 30

So, x will be => [tex]30=3x[/tex]

[tex]x=30/3=10[/tex]

So, when Richard has 30 CDs, Benny has 10 CDs.

subtract r from c to get 8x+10

 replace x with 3

8(3) +10 = 34 which in hundreds is 3400 dollars

the answer is C

Answer:

Write a proportion using the ratios. Find the cross products. If the cross products are equal, then the ratios form a proportion.

Step-by-step explanation:

The required, there were 25 chickens and 12 pigs on Old MacDonald's farm.

To solve this problem, we can use a system of equations to represent the number of chickens and pigs on Old MacDonald's farm. Let x be the number of chickens and y be the number of pigs. Then we have:

x + y = 37 (equation 1)

2x + 4y = 98 (equation 2)

Equation 1 represents the total number of animals, and Equation 2 represents the total number of legs. We can simplify equation 2 by dividing both sides by 2:

x + 2y = 49 (equation 3)

Now we have two equations with two variables. We can solve for x and y by using substitution or elimination. Let's use elimination by multiplying equation 1 by 2 and subtracting it from equation 3:

x + 2y = 49

-2x - 2y = -74

x = -25

Solving for x, we get:

x = 25

Substituting x = 25 into equation 1, we get:

25 + y = 37

Solving for y, we get:

y = 12

Therefore, there were 25 chickens and 12 pigs on Old MacDonald's farm.

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The equations are c + p = 37 and 2c + 4p = 98. Solving the system of equations the numbers are 26 and 11, respectively.

To solve this problem, we can use a system of equations.

Let's assume that the number of chickens is represented by 'c' and the number of pigs is represented by 'p'. Based on the given information, we can create two equations:

1. c + p = 37 (equation 1)

2. 2c + 4p = 98 (equation 2)

We have two equations with two variables, so we can solve this system of equations to find the values of 'c' and 'p'.

Using equation 1, we can express 'c' in terms of 'p': c = 37 - p.

Substituting this into equation 2, we get: 2(37 - p) + 4p = 98. Solving this equation, we find: p = 11.

Substituting the value of 'p' back into equation 1, we find: c = 26.

Therefore, Old MacDonald had 26 chickens and 11 pigs on his farm.

Answer:

Oliver and Peter both uses same length string.

Explanation:

Suppose length of rope or string = x meters

Oliver divide his rope into four equal parts

[tex] \frac{1}{4}, \frac{1}{4}, \frac{1}{4}, \frac{1}{4} [/tex]

Each part length is [tex] \frac{1}{4} [/tex]

NOw Oliver used 3 part of the string out of four parts

that means total used string is 3/4

Now peter also have same length of string = x meter

He divides the string eight equal parts and use the 6 parts out of 8

each part length is :[tex] \frac{x}{8} , \frac{x}{8} , \frac{x}{8} , \frac{x}{8} , \frac{x}{8} , \frac{x}{8} , \frac{x}{8} , \frac{x}{8} [/tex]

Use 6x/8

simplify the fraction 6x/8

divide by 2 both numerator and denominator

6x/8 = 3x / 4

So both uses same part of string.

A used book store buys a hardback book for $1.50 and then sells it for $5. Over time, the store sells the same number of books it buys. The store manager can use the equation P(x)=5x−1.5x to determine the store's profit, P(x), where x is the number of books that the store sells. Which statement about the book store is true based on the profit equation?

Cost Price of book, C.P.=$1.50

Selling Price of book, S.P.=$5

PROFIT=S.P. -C.P.

So, Profit=$5-$1.50=$3.50

So, Profit=$3.50 on each book

Or, we are given P(x)= 5x-1.50x

Or, P(x)=3.50x

For each book, we must divide the profit P(x) by x, that is, number of books

[tex] \frac{P(x)}{x}=\frac{3.5x}{x} [/tex]

[tex] \frac{P(x)}{x}=\frac{3.5*1}{1} [/tex]

[tex] \frac{P(x)}{x}=3.5 [/tex]

So, Profit for each book sold is $3.50

Answer:Option C

Answer:

C

Step-by-step explanation:

im too smort

The average sale per customer for Carla is $4.50.

To find Carla's average sale per customer, we need to determine the total revenue and the total number of customers.

The average sale per customer is calculated by dividing the total revenue by the total number of customers.

Given:

- Total revenue for the month: $4,500

- Total number of customers for the month: 1,000

The average sale per customer is calculated as:

[tex]\[ \text{Average sale per customer} = \frac{{\text{Total revenue}}}{{\text{Total number of customers}}}. \][/tex]

Plugging in the given values:

[tex]\[ \text{Average sale per customer} = \frac{{4,500}}{{1,000}} = 4.5. \][/tex]

Thus, the average sale per customer for Carla is $4.50.  

Question :

Carla sells hot coffee, cider and tea from a sidewalk cart near wall street in new york city. last month she sold $4,500 worth of product to 1,000 customers. she spent $800 on buying her beverages in bulk. her monthly costs are: utilities = $100, salary = $2,000, advertising = $0, insurance = $0, interest = $0, rent (cart) = $600, depreciation = $0. calculate carla's average sale per customer.

Answer:

1130.973355 is the answer

Step-by-step explanation:

pi10(10+sqrrt((24^2)+(10^2)))

31.416(10+sqrrt(576+100))

31.416(10+sqrrt(676))

31.416(10+26)

31.416(36)

1130.976

[tex] \text{Consider the quadratic function}\\ \\ f(x)=-5x^2-2\\ \\ \text{For a quadratic equation, }f(x)=ax^2+bx+c, \text{ we know that the x-coordinate}\\ \text{of the vertex (h,k) is given by}\\ \\ h=\frac{-b}{2a}\\ \\ \text{on comparing the given equation with standard equation, we have} [/tex]

[tex] a=-5, b=0, c=-2\\ \\ \text{so the x-coordinate of the vertex is }\\ \\ h=-\frac{b}{2a}=-\frac{0}{2(-5)}=0\\ \\ \text{so plug this vlaue of the h in the given function to get the y-coordinate}\\ \text{of the vertex. so}\\ \\ f(x)=-5(0)^2-2=0-2=-2\\ \\ \text{hence the vertex of the parabola is: }(h,k)=(0,\ -2)\\ \\ \text{A second point on the graph can be found by putting x=1, so }\\ \\ f(1)=-5(1)^2-2=-5-2=-7\\ \\ \text{so one other point on the parabola is }(1,-7) [/tex]

The grpah of the quadratic function is shown below:

Answer:(0,-2) (1,-7)

Step-by-step explanation:

Markup is the amount added to the cost price of goods to cover overhead and profit.

Sue’s Corner Market has a markup of 60% on bottled water.

Let us say original price was $x.

Now price after markup is $2.

So we can make an equation like:

original price + markup price = price after markup

x + 60% of x =2

[tex] x + 0.6x =2 [/tex]

[tex] 1.6x =2 [/tex]

dividing both sides by 1.6

x= 1.25

So original price was 1.25 dollars.

Answer:

1.25 dollars.

Step-by-step explanation:

The inequality [tex]\(-6x \geq 30\)[/tex] is equivalent to [tex]\(x \leq -5\)[/tex]. Therefore, the correct answer is option d: [tex]\(x \leq -5\)[/tex].

To solve the inequality [tex]\(-6x \geq 30\)[/tex] and find its equivalent form, follow these steps:

1. Write down the original inequality:

  [tex]\[ -6x \geq 30 \][/tex]

2. Isolate [tex]\(x\)[/tex] by dividing both sides of the inequality by [tex]\(-6\)[/tex]:

  - Note that when dividing both sides of an inequality by a negative number, the direction of the inequality sign must be reversed.

  [tex]\[ \frac{-6x}{-6} \leq \frac{30}{-6} \][/tex]

3. Simplify both sides:

  [tex]\[ x \leq -5 \][/tex]

So, the equivalent inequality to [tex]\(-6x \geq 30\)[/tex] is [tex]\(x \leq -5\)[/tex].

Therefore, the correct answer is:

[tex]\[\boxed{\text{d: } x \leq -5}\][/tex]

subtraction property of equality (i just took that test and got it right)