A triangular bandana has an area of 78 square inches. The height of the triangle is 9 3
4
inches. Enter and solve an equation to find the length of the base of the triangle. Use b to represent the length of the base.

An equation to find the length of the base of the triangle is 78=
The length of the base of the triangle is inches.

Answers

Answer 1

Answer: Area of a triangle = 1/2 × base × height

Plug in what we know.

78 = 1/2 × b × 9¾

Multilply each side by 2 to get rid of the 1/2...

156 = b × 9¾

Write 9¾ as an improper fraction.
(9¾ = 9 + 3/4 = (9×4)/4 + 3/4 = 36/4 + 3/4 = 39/4)

156 = b × 39/4

Multiply each side by 4...

624 = b × 39

Divide each side by 39...

16 = b

Done! The length of the base of the triangle is 16 inches.

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You and your friends pick up seven movies to watch over a holiday. You have time to watch only two. In how many ways can you select the two to watch?

Answers

Answer:

There are 21 ways to select the two movies to watch.

Step-by-step explanation:

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

${n\choose k}=(n!)/(k!(n-k)!)$

It is provided that there are n = 7 movies to watch.

But we only have time for k = 2.

Compute the total number of ways in which we can select 2 movies from 7 as follows:

${7\choose 2}=(7!)/(2!(7-2)!)$

$=(7!)/(2!* 5!)\n\n=(7* 6* 5!)/(2!* 5!)\n\n=(7*6)/(2* 1)\n\n=21$

Thus, there are 21 ways to select the two movies to watch.

The surface area of a cube is 294 cm2. Which statements are true about the same cube measured in square millimeters? Choose all answers that are correct. A. The number representing the surface area would decrease. B. The number representing the surface area would increase. C. The actual surface area would decrease. D. The actual surface area would increase. E. The actual surface area would stay the same.

Answers

The answer to the question that is being presented above would be letter E. The actual surface area would stay the same. This statement is true because although the unit of measurement is different, the actual surface area remains the same and unchanged.

The correct statements are B and E. Converting the value to millimeters, we have 29,400 mm^2. We see that the number which represents the surface area increased. However, since we still have the same cube and same dimensions, the actual surface area is still stay same.

Population of a city is 36000 in 2005 by 2010 it has grown to 43800. If the city has grown linearly since 2005 and grows at the same rate what will the population be in 2015

Answers

The population of the city in the year 2015 will be 51,600.

What is the rate of change?

The rate of change is the speed at which variable changes over a specific period of time.

The population of the city in the year 2005 = 36,000

The population of the city in the year 2010 = 43,800

The change in population in 5 years is given by;

= Population in the year 2010 - Population in the year 2005

= 43,800 - 36,000

= 7800

The change in population in 5 years = 7800

Let us assume the number population in the year 2015 = x

Here, according to the question:

Since the change of rate is a linear growth since 2005.

The change in population every 5 years = 7800

The change in population in the next 5 years is;

Rate of change = Population in year 2015 - Population in the year 2010

7800 = x - 43,800

x = 7800 + 43800

x = 51,600

Hence, the population of the city in the year 2015 will be 51,600.

Learn more about the rate of change here;

brainly.com/question/1296474

#SPJ2

36000 : 2005 = 43800 : 2010
Every five years it increases by 7800, so by 2015 it will be
43800 + 7800
= 51600

What is 8P3?A.
6720

B.
120

C.
336

D.
24

Answers

The value of 8P3 is 336, so the correct option is option C. 336

How did we get the value?

To find the value of 8P3, we use the permutationformula, which is calculated as:

nPk = n! / (n - k)!

In this case, n is 8 and k is 3. So, we can substitute these values into the formula:

8P3 = 8! / (8 - 3)!

= 8! / 5!

= (8 × 7 × 6 × 5!) / 5!

Simplifying further:

8P3 = 8 × 7 × 6

= 336

Therefore, the value of 8P3 is 336, so the correct option is C.

learn more about permutation formula: brainly.com/question/1216161

#SPJ6

8p3 = 336 hope this helps

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar. y=−5x^2+263x−1844

Answers

Answer: The maximum amount of profit the company can make is $1604.

Step-by-step explanation:

To find the maximum amount of profit the company can make, we need to determine the vertex of the quadratic equation y = -5x^2 + 263x - 1844. The x-coordinate of the vertex represents the selling price that will yield the maximum profit, and the y-coordinate represents the maximum profit itself.

The x-coordinate of the vertex can be found using the formula: x = -b / (2a), where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c.

In this case, a = -5 and b = 263. Let's substitute these values into the formula:

x = -263 / (2 * -5)

Now, let's simplify the expression:

x = -263 / -10

x = 26.3

To find the maximum profit, we substitute the x-coordinate of the vertex into the equation:

y = -5(26.3)^2 + 263(26.3) - 1844

Now, perform the calculations:

y = -5(691.69) + 6906.9 - 1844

y = -3458.45 + 6906.9 - 1844

y = 1604.45

Therefore, to the nearest dollar, the maximum amount of profit the company can make is $1604.

Final answer:

Profit is a financial gain that occurs when the revenue from a company activity is more than the costs, costs, and taxes required to support the activity. To put it another way, profit is what is left over after all costs have been subtracted from revenue