Angles in a Triangle

The value of quantity after 0.2 hours is, 960

Given that;

A quantity with an initial value of 480 grows exponentially at a rate such that the quantity doubles every 6 minutes.

We know that;

The exponential growth function is

A = A₀ (1 + r)ⁿ

Where, A= The number of quantity after t days

A₀ = initial number of quantity

r = rate of growth

n = time in minutes

A quantity with an initial value of 830 grows at a rate such that the quantity doubles in 0.2 hours = 12 minutes

And, A = 2 x 480 = 960

A₀ = 480

n = 12 minutes

r = ?

⇒ A = A₀ (1 + r)ⁿ

⇒ 960 = 480 (1 + r)¹²

⇒ 2 = (1 + r)¹²

⇒ [tex]r = \sqrt[12]{2} - 1[/tex]

Now, to find the quantity after 12 minutes, we plug A = 830, t = 12 minutes in exponential function;

⇒ A = A₀ (1 + r)ⁿ

⇒ [tex]A = 480 (1 + \sqrt[12]{2} - 1)^{12}[/tex]

⇒ A = 480 (2)

⇒ A = 960

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Answer:

 39 1/3 = 118/3 square units

Step-by-step explanation:

You want the area under the curve y = -x² +9x on the interval [3, 5].

The fundamental theorem of calculus tells us the integral of the function will be its anti-derivative. That is, for f(x) = -x² +9x, we want the function F(x) whose derivative is f(x). The reverse of the power rule for derivatives can be used:

  [tex]F(x)=-\dfrac{x^3}{3}+9\dfrac{x^2}{2}[/tex]

The area of interest is ...

  F(5) -F(3) = -1/3(5³ -3³) +9/2(5² -3²) = -98/3 +72

  F(5) -F(3) = 39 1/3

The area under the curve between x=3 and x=5 is 39 1/3 square units.

(1. 5,0 ) , (1 , 0 ) are the values of x in linear equation.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                        Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

2x² -5x + 5 = 3

2x² -5x + 5 - 3 = 0

2x² -5x + 3 = 0

2X² - (2+ 3)X + 3 = 0

 2X² -2X - 3X + 3 = 0

  2x(x - 1 )-3(x - 1 ) = 0

  (2x - 3) (x - 1 )

    x = 3/2 , 1

    x = 1. 5 , 1

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The equation that represent the graph is C) y=3x.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here let us take the two points [tex](x_1,y_1)=(1,3) , (x_2,y_2)=(3,9)[/tex].

Now using slope formula then,

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

=> m = [tex]\frac{9-3}{3-1}=\frac{6}{2}=3[/tex].

Now using equation formula then,

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

=> y-3=3(x-1)

=> y-3 = 3x-3

=> y=3x.

Hence the equation that represent the graph is C) y=3x.

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The chef makes 11 batches of dumpling wrappers.

What is dumpling wrapper?

Dumpling wrappers are thin pieces of dough that are used to wrap around fillings to make dumplings. They are a staple in many Asian cuisines, including Chinese, Japanese, Korean, and Thai. The dough is typically made with flour, water, and salt, and is rolled out into thin circles or squares. The size and thickness of the wrappers can vary depending on the type of dumpling being made and the regional cuisine. Dumpling wrappers can be used to make a variety of dumplings, such as pork and cabbage dumplings, shrimp dumplings, potstickers, and gyoza.

Let's assume that the chef makes "n" batches of dumpling wrappers.

For each batch of dumpling wrappers, the chef uses 2 cups of flour.

So, the total amount of flour used for making "n" batches of dumpling wrappers is 2n cups of flour.

In addition to the 2 cups of flour for each batch, the chef also uses an additional § cup of flour to keep the dough from sticking. So, the total amount of flour used for "n" batches is 2n + § cups of flour.

According to the problem statement, the chef uses a total of 21 cups of flour to make "n" batches of dumpling wrappers. So, we can set up the following equation 2n + § = 21

To solve for "n," we need to first convert the § cup of flour to a decimal. § is equivalent to 0.25 cups of flour.

So, the equation becomes 2n + 0.25 = 21

Subtracting 0.25 from both sides,

2n = 20.75

Dividing both sides by 2,

n = 10.375

Since we can't have a fraction of a batch, we can round up to the nearest whole number. Therefore, the chef makes 11 batches of dumpling wrappers.

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The chef makes 11 batches of dumpling wrappers.

What is dumpling wrapper?

Dumpling wrappers are thin pieces of dough that are used to wrap around fillings to make dumplings. They are a staple in many Asian cuisines, including Chinese, Japanese, Korean, and Thai. The dough is typically made with flour, water, and salt, and is rolled out into thin circles or squares. The size and thickness of the wrappers can vary depending on the type of dumpling being made and the regional cuisine. Dumpling wrappers can be used to make a variety of dumplings, such as pork and cabbage dumplings, shrimp dumplings, potstickers, and gyoza.

Let's assume that the chef makes "n" batches of dumpling wrappers.

For each batch of dumpling wrappers, the chef uses 2 cups of flour.

So, the total amount of flour used for making "n" batches of dumpling wrappers is 2n cups of flour.

In addition to the 2 cups of flour for each batch, the chef also uses an additional § cup of flour to keep the dough from sticking. So, the total amount of flour used for "n" batches is 2n + § cups of flour.

According to the problem statement, the chef uses a total of 21 cups of flour to make "n" batches of dumpling wrappers. So, we can set up the following equation 2n + § = 21

To solve for "n," we need to first convert the § cup of flour to a decimal. § is equivalent to 0.25 cups of flour.

So, the equation becomes 2n + 0.25 = 21

Subtracting 0.25 from both sides,

2n = 20.75

Dividing both sides by 2,

n = 10.375

Since we can't have a fraction of a batch, we can round up to the nearest whole number. Therefore, the chef makes 11 batches of dumpling wrappers.

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Answer:

C $540

Step-by-step explanation:

Food: .30 × $1,200 = $360

Drinks: .15 × $1,200 = $180

-------

$540

The value of (f∘g)(x) is 3x² - 2.

What is a function?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Here, we have

Given: f(x) = √x²-4 and g(x) = 3x²

We have to find the value of (f∘g)(x).

(f∘g)(x) = f(g(x))

(f∘g)(x) = f(3x²)

f(3x²) = √9x⁴- 4

f(3x²) = 3x² - 2

Hence, the value of (f∘g)(x) is 3x² - 2.

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The percentage of men who meet the height requirement is 19.09%. This result suggests that a relatively small proportion of men meet the height requirements for the characters at the amusement park.

To find the percentage of men who meet the height requirement, we need to calculate the probability that a randomly selected man has a height between 56 and 64 inches.

Using the z-score formula, we can standardize the height range as follows:

z = (64 - 67.3) / 3.8 = -0.87

z = (56 - 67.3) / 3.8 = -3.00

Using a standard normal distribution table, we can find that the area to the left of z = -0.87 is 0.1922 and the area to the left of z = -3.00 is 0.0013.

Therefore, the percentage of men meeting the height requirement is:

P(-0.87 < Z < -3.00) = P(Z < -0.87) - P(Z < -3.00) = 0.1922 - 0.0013 = 0.1909 or 19.09%.

It suggests that the park may be employing more women than men as characters, as the mean height for women is below the maximum height requirement.

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The average rate of change of the given function between the two given values is: 0.82

The Average Rate of Change of a function is one that is defined as the average rate at which one quantity is changing with respect to another thing changing. Thus, an average rate of change function is basically a process that helps to calculate the amount of change in one item divided by the corresponding amount of change in another.

It is given by the formula:

f'(x) = [f(b) - f(a)]/(b - a)

We are given the function:

f(x) = √(3x - 11)

Thus from x1 = 4 to x2 = 6, we will have:

f(4) = √(3*4 - 11) = 1

f(6) = √(3*6 - 11) = √7

Thus:

f'(x) = ((√7) - 1)/(6 - 4)

f'(x) = 0.82

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Answer: d) the amount of clay for each student. 8

Step-by-step explanation: For the sketch, draw 8 pieces of paper being divided evenly. For the expression write 2 divided by 1/4 = 8.

Step-by-step explanation:

See image

The odds of the next match from the probability of 11/23 is 11 : 12

From the question, we have the following parameters that can be used in our computation:

Probability = 11/23

For a probability represented as a/b, the odds is

Odds = a : b - a

In this case

a = 11 and b = 23

Using the above as a guide, we have the following:

Odds = 11 : 23 - 11

Evaluate the difference

So, we have

Odds = 11 : 12

Hence, the value of the odds is 11 : 12

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The 7th term of the binomial expression given can be found to be 8.136 × 10^7 × x^(-4)

To find the 7th term of (3x - 4/x²)¹⁴, we can use the binomial theorem, which states that for any positive integer n and any real numbers a and b:

(a + b)ⁿ = ∑(C(n, k) x a^(n-k) x b^k)

Using the binomial theorem formula, the 7th term can be calculated as follows:

Term_7 = C(14, 6) x (3x)^(14-6) x (-4/x²)^6

First, let's find C(14, 6):

C(14, 6) = 14! / (6! x (14-6)!)

C(14, 6) = 14! / (6! x 8!)

C(14, 6) = 3003

Now, we can put everything together:

Term 7 = 3003 x (3x)^8 x (4096 / x¹²)

Term 7 = 8.136 × 10^7 × x^(-4)

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The diameter of the lead in a pencil p must be within 0.01 millimetre of 1 millimeter. In the form of inequality, this can be expressed as 0.01<p<1.

A mathematical expression with values that on the left and right are not equal is referred to as having an inequality. In essence, an inequality examines any two values as well as demonstrates whether one is bigger than, less than, or neither greater nor less than the comparable quantity. Numbers are compared using inequalities to determine the range of quantities that fall inside the parameters of a variable. The diameter of the lead in a pencil p must be within 0.01 millimetre of 1 millimeter. This can be expressed as 0.01<p<1 inequality.

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Your question is incomplete but most probably your full question was,

The diameter of the lead in a pencil p must be within 0.01 millimetre of 1 millimeter. Express this statement of an inequality.

The frequency table that summarizes the data by the biologist and the additional plants is c. third table.

From the data by the biologist and the additional plants, we see that there are 11 plants with flowers and 7 with caterpillars.

The number of flowering plants with caterpillars is 6 plants. Those without flowers would then be:

= 11 - 6

= 5 plants

This is shown by the second frequency table.

In conclusion, the correct frequency table showing the data by the biologist is the second frequency table.

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Answer:

3hours 237 minutes 5700 seconds

Answer:B

Step-by-step explanation:the triangle has 3 sides

In the first hour of their run, Jenna ran 1 mile more than George.

Given graph shows the data on Jenna's running status.

It shows that Jenna ran 12 miles in 2 hours of time.

Jenna's running status in the first one hour = 12/2 = 6 miles.

Given that George ran at a constant of 5 miles per hour.

To find out how many miles will Jenna ran more than George in the first one hour = 6 -5 = 1 mile.

From the above analysis, we can conclude that the Jenna will run 6 miles in the first one hour and George will run 5 miles in the first one hour. So, Jenna will run 1 mile more than George.

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Given question is not having enough information, the complete question is attached below,

The values of x , y and z in the parallelogram are 12, -20 and -33 respectively

A parallelogram is a quadrilateral with opposite side equal to each other and opposite sides parallel to each other.

The opposite angles of parallelogram are equal . Consecutive angles in a parallelogram are supplementary .

Therefore,

-4y + 5 = 85

-4y = 85 - 5

-4y = 80

divide both sides by -4

y = 80 / -4

y = - 20

Therefore, let's find x and z as follows:

8x - 1 + 85 = 180

8x = 180 - 84

8x = 96

divide both sides by 8

x = 96 / 8

x = 12

Let's find z

- 3z - 4 + 85 = 180

-3z = 180 - 81

-3z = 99

divide both sides by -3

z = 99 / -3

z = -33

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The perimeter of the paperboard that remains after the semicircle is removed is 93.12 inches

Information given in the problem includes:

A rectangular paperboard measuring 26in long and 16in wide

information for the semicircle are

Width = 16 inches

Radius = 16 / 2 = 8 inches

Length = 26 inches

Circumference of the semi circle is calculated using the formula

= π * radius

Where the radius is 8 inches and π = 3.14.

Substituting in to the formula and solving for the circumference of the semicircle which same as perimeter of the semicircle gives:

= 8 x 3.14

= 25.12

The perimeter would be

26 inches + 26 inches + 25.12 inches + 16 inches

= 93.12 inches

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a) The number of possible area code numbers is: 69,299. b) the number of possible social security numbers is: 68,665,031,401

a. The first three digits can be any number from 001 to 999, except for 666. Since X can be any number from 1 to 7, there are 7 choices for X. For Y and Z, there are 10 choices each (0-9). Therefore, the number of possible area code numbers is:

(7 choices for X) x (10 choices for Y) x (10 choices for Z) - 1 (for 666) = 69,299

b. The middle two digits can be any number from 01 to 99, which gives 99 choices. The last 4 digits can be any number from 0001 to 9999, which gives 9999 - 1 (for 0000) = 9998 choices. Therefore, the number of possible social security numbers is:

(69,299 choices for the area number) x (99 choices for the group number) x (9998 choices for the serial number) - 1 (for 123-45-6789) = 68,665,031,401

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Answer:

Step-by-step explanation:

ok, so for the -1 1/2 your going to find the -1 point on the left of 0. Then from there you will count to the second small point (or small line intersecting through the number line) to the right of -1. It will be this one right here

Now for the second number 2 3/4 you will find the 2 point, to the right from 0. Now count three small points to the left to get the 3/4 part. It will be right here.

Hope this helps!!

a) To find the total sales in units by product and customer type, we need to multiply the number of bags sold by the selling price per bag. The table below shows the calculations:

Town Product Consumers Retailers Wholesalers

Huye Maize 800 600 800

Potatoes 6,000 2,000 3,000

Carrots 3,500 500 2,500

Tomatoes 2,800 4,200 2,100

Muhanga Maize 800 1,000 0

Potatoes 5,000 8,000 4,000

Carrots 1,500 2,000 0

Tomatoes 4,200 2,800 700

b) To determine the difference between the two towns in sales (in Units) by product and customer type, we subtract the sales in Muhanga from the sales in Huye. The table below shows the calculations:

Town Product Consumers Retailers Wholesalers

Maize 0 -400 800

Huye Potatoes 0 -1,000 0

Carrots 2,000 0 2,500

Tomatoes -1,400 1,000 1,400

Total 600 -400 4,700

Product Consumers Retailers Wholesalers

Maize 0 400 0

Muhanga Potatoes 0 6,000 1,000

Carrots -2,000 -500 0

Tomatoes 1,400 -1,400 -700

Total -600 4,500 300

c) To calculate the total sales in Rwf by each town, we need to add up the sales in units for each town and product and then multiply by the selling price per bag. The table below shows the calculations:

Town Total sales in Rwf

Huye 24,400

Muhanga 23,700

d) To find the sales in Rwf by customer type for each town, we need to multiply the number of bags sold by the selling price per bag and then add up the sales for each customer type. The table below shows the calculations:

Town Customer Maize Potatoes Carrots Tomatoes

Huye Consumers 800 6,000 3,500 2,800

Retailers   600 2  

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Answer:

lesser x = 9

greater x = 11

Step-by-step explanation:

(x-10)² - 1 = 0

(x-10)² = 1

(x-10) = +- root1 (positive and negative root1)

So (x-10) = +1 and (x-10) = -1

Firstly

X - 10 = 1

X = 11

Secondly

X - 10 = -1

X = 9

So you have x = 9, and x = 11

The smaller one is the lesser x (9)

The larger one is the greater x (11)