1. (5 pt) Find the area of a triangle with sides \( a=10 \) and \( b=15 \) and included angle 70 degrees.

In this case, the mean of the data set is 67, the sum of all the data values is 2291, the sum of all the squared data values is 182,361, the sample standard deviation is 8, the population standard deviation is 8.024961059, and the sample size is 29.

The TI-84 Plus display presents sample statistics for a set of data. The "x" symbol represents the mean, or average, of the data set. The "Σx" symbol represents the sum of all the data values, and the "Σx2" symbol represents the sum of all the squared data values.

These statistics can be used to analyze and interpret the data set. For example, the mean can be used to determine the central tendency of the data, and the standard deviation can be used to measure the spread of the data.

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x1 = -2, x2 = 1, and x3 = 5.5

This system of equations can be solved by first combining the equations and then isolating one of the variables. To combine the equations, subtract the first equation from the second equation:

4x1 + 5x2 + 5x3 = 9

- (x1 + x2 + 3x3 = -4)

3x1 + 4x2 + 2x3 = 13

Next, isolate one of the variables. In this case, let's isolate x3:

3x1 + 4x2 + 2x3 = 13

- (2x3) - (-2x3) = 0

3x1 + 4x2 = 13

x3 = \frac{13 - (3x1 + 4x2)}{2}

Now that x3 has been isolated, substitute it into one of the original equations and solve for the remaining two variables:

x3 = \frac{13 - (3x1 + 4x2)}{2}

x1 + x2 + 3\left(\frac{13 - (3x1 + 4x2)}{2}\right) = -4

Solve for x2:

x2 = \frac{-4 - x1 - 3\left(\frac{13 - (3x1 + 4x2)}{2}\right)}{4}

Substitute this expression for x2 into one of the original equations and solve for x1:

x1 + \frac{-4 - x1 - 3\left(\frac{13 - (3x1 + 4x2)}{2}\right)}{4} + 3\left(\frac{13 - (3x1 + 4x2)}{2}\right) = -4

Solve for x1 and then plug this value back into the expression for x2 to find x2:

x1 = -2

x2 = 1

x3 = \frac{13 - (-2 + 4x2)}{2}

x3 = \frac{13 - (-2 + 4 \cdot 1)}{2}

x3 = \frac{13 - 2}{2}

x3 = 5.5

Therefore, the solution to the system of equations is x1 = -2, x2 = 1, and x3 = 5.5.

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Answer:

[tex] = 3kd + 2d + 5r + 6kr[/tex]

Step-by-step explanation:

[tex]7dk + 6kr + 4d + 8r - 4 kd - 2 d - 3r \\ = 3kd + 2d + 5r + 6kr[/tex]

Answer:

1)  12<x<15 is:   f(x) = -5(x-12)^2 + 80

2) 15<x<17 is:    f(x) = 35

3) 27<x<30 is:  f(x) = 2.5x-22.5

Step-by-step explanation:

See the attached image.

1)  Plot all the lines as shown

2)  Add the inequalities, which will produce the colored regions on DESMOS.

3)  Assume that the function having the greatest value in each region is the function that determines the roller coaster's height  (My assumption - it is not clear in the problem which function should dominate)

4) for the three regions listed with no corresponding function, identify the line having the greatest value.  Thiose are the functions that are noted on the graph and in the answer box above.

5) Take a break

Answer:

fraction 3/9

percentage is 90%

Answer:

To solve for f in the equation:

f/3 + 22 = 17

We need to isolate f on one side of the equation. We can start by subtracting 22 from both sides:

f/3 = 17 - 22

Simplifying the right-hand side:

f/3 = -5

To isolate f, we can multiply both sides by 3:

f = -5 * 3

Simplifying:

f = -15

Therefore, the solution to the equation f/3 + 22 = 17 is f = -15.

The absolute deviation for 612 in the given data set is 14.8.

The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data set.

A measure of variance in a data set is the mean absolute deviation.

We may determine how "spread out" the values in a data collection are by looking at the mean absolute deviation.

So, get the mean as follows:
80+75+25+62+68)/5

310/5

62

Now, get the distance of each number as follows:
-----------------

| 80     |  18  |

|   75   |   13 |

|+   25   |   37 |

|    62  |    0  |

|   68   |   6   |

-----------------

Now, get the distance:

18+13+37+0+6/5

14.8

Therefore, the absolute deviation for 612 in the given data set is 14.8.

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What is the absolute deviation for 62 in the data set?

{80, 75, 25, 62, 68}

Yes, these expressions are equivalent expressions.

A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, or variables. Let's examine the writing style of expressions. A number is 6 times larger than the other number, x, by a factor of 2. The mathematical phrase x/2 + 6 represents this claim. Complex riddles are solved using mathematical expressions.

In the given question,

Expressions are as follows:

(9g-11+10g) - (12-11g+13)

Simplifying it, we get:

30g -36

In the 2nd expression given,

-3(-10g+12) and after simplifying:

30g-36

As the expressions after simplifying are equal to each other, we can say that these are equivalent expressions.

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Jolina paid 33.33% more than Kendall paid for the coat, as she paid the full price while Kendall received a 25% discount.

To calculate this, first find out how much Kendall paid after the discount. If the original price of the coat was X, then Kendall paid 0.75X, since the discount was 25%. We know that Kendall paid $100 for the coat, so we can set up the equation 0.75X = 100 and solve for X. X turns out to be $133.33.

Since Jolina paid the full price of $133.33 for the coat, the ratio of what Jolina paid to what Kendall paid is:

133.33 / 100 = 4/3 or 1.33:1

Therefore, Jolina paid 33.33% more than Kendall paid for the same coat.

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Two ratios that describe the collection of baseballs to gloves are

8:4 and 2:1 .

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio.

Given,

Number of gloves = 16

Number of baseballs = 8

Ratio of gloves to baseballs

= 16/8

= 8/4 = 8:4

= 2/1 = 2:1

Hence, 8:4 and 2:1 are two ratios that describe the collection of baseballs to gloves.

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Complete question is:

There are 16 baseballs and 8 gloves,

Choose two ratios that describe the collection of baseballs to gloves.

8:4, 6:4, 2:1, 2:4, 10:4

Answer:

We can use a recursive approach to solve this problem. Let's define a function $f(n)$ as the number of ways to ascend a flight of $n$ steps, where the priestess can only take one or two steps at a time.

To ascend a flight of 1 step, there is only one way to do it (take one step). Therefore, $f(1) = 1$.

To ascend a flight of 2 steps, there are two ways to do it (take two steps at once or take one step twice). Therefore, $f(2) = 2$.

For a flight of $n$ steps, the priestess can either take one step and ascend the remaining $n-1$ steps in $f(n-1)$ ways, or take two steps and ascend the remaining $n-2$ steps in $f(n-2)$ ways. Therefore, we have the recursive formula:

$$f(n) = f(n-1) + f(n-2)$$

Using this formula, we can calculate the number of ways to ascend a flight of 5 steps:

$$f(1) = 1$$

$$f(2) = 2$$

$$f(3) = f(2) + f(1) = 3$$

$$f(4) = f(3) + f(2) = 5$$

$$f(5) = f(4) + f(3) = 8$$

Therefore, there are 8 different ways for the priestess to ascend the steps. To find out if she can do this a different way each day for a week, we need to make sure that there are at least 7 different ways. Since there are 8 ways, it is possible for the priestess to ascend the steps in a different way each day for a week.

The value of x is 45 in the provided assertion, and the cointerior angles do sum up to 180°, indicating that AD and BC are parallel.

Parallel in mathematics refers to two lines which never cross one another; picture an equal symbol. Three close pals' parallel lives could be depicted in a tale.

(a)

3x + x + 2x + 90 = 360

6x = 360 - 90

6x = 270

x = 45

(b) The answer will be yes, they would be parallel.

We can justify this using co-interior angles, which state that 2 angles subtended by parallel lines add up to 180°

We can check this with both angles 3x & x, or 2x & 90°.

If AD and BC are parallel, then 3x + x = 180, and since you already found the value of x we can substitute this in:

3(45) + (45) = 180

135 + 45 = 180

180 = 180

So the co-interior angles do add up to 180°, which means that AD and BC are parallel.

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Answer:

30 baskets per minute

Step-by-step explanation:

We know

Shaq shot 420 baskets in 14 minutes.

Find his basket rate in baskets per minute.

We take

420 / 14 = 30 baskets per minute

So, the answer is 30 baskets per minute.

Answer:

8358 cubic ft

Step-by-step explanation:

If a regular pentagon and a regular hexagon have the same area, then the regular pentagon will have a smaller perimeter than the regular hexagon.

This is because a regular pentagon has less sides than a regular hexagon, which means that the length of each side of the pentagon will be shorter than the length of each side of the hexagon.

The hexagon would therefore have more distance to cover and more sides to be add up before one can get to the perimeter. The pentagon has three less sides than the hexagon and so would have a smaller perimeter.

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The real yeild is 0.65%.

The Estimated 10-year Treasury bond yield is 3.65%.

The 10-year Treasury bond yield can be estimated using the 5-year Treasury bond yield and the expected inflation rate of 3%.

This is done by calculating the real yield, which is the difference between the nominal yield and the expected inflation rate.

The 10-year Treasury bond yield can be estimated by adding the real yield of the 5-year Treasury bond to the expected inflation rate of 3%.

Real yield = Nominal yield - Expected inflation rate

Real yield (5-year Treasury bond) = 3.65% - 3% = 0.65%

Estimated 10-year Treasury bond yield = 0.65% + 3% = 3.65%

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The equation can be written as: x + 24° = 90°.

The measure of the unknown angle is 66°.

An algebraic equation is an equation that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

Let the measure of the unknown angle be x.

Since the angle in the corner measures 90° and one piece of the tile will have a measure of 24°. We can write the equation as:

x + 24° = 90°

The measure of the unknown angle can be determined as follow:

​x + 24° = 90°

x = 90° - 24°

x = 66°

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The inequality for this statement is "x - 5 > 22". So, the solution to this inequality is "x > 27".

To translate the given statement into an inequality, we need to identify the variable, the constant, and the inequality sign. The variable is the unknown number, which we can represent with x. The constant is the number 22, and the inequality sign is greater than (>).

So, the inequality can be written as:
x - 5 > 22

To solve for x, we need to isolate the variable on one side of the inequality. We can do this by adding 5 to both sides of the inequality:
x - 5 + 5 > 22 + 5

Simplifying gives:
x > 27

So, the solution to the inequality is x > 27. This means that any number greater than 27 will make the inequality true.

In conclusion, the inequality that represents the statement "Five subtracted from a number is greater than twenty-two" is x > 27.

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The number of comic books is given as follows:

P/100 x 560.

In which P is the percentage equivalent to comic books on the circle graph.

The number comic books sold at the book fair is given by the proportions in the context of the problem.

The circle graph gives the percentage out of each type of book, hence the percentage of comic books is given as follows:

P/100.

Then the amount of comic books is obtained multiplying the percentage by the total amount of 560 as follows:

P/100 x 560.

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Answer:

b.  6

Step-by-step explanation:

The equation x - 4 = 2 tells us that if we subtract 4 from a number (x), we'll have 2.  Let's add 4 to both sides of the equation:

x - 4 = 2

  +4   +4

    x  = 6

X is 6

The first step in finding the given operations for the functions is to substitute the expressions for f(x) and g(x) into the operations.

For the first set of functions, f(x) = x2 and g(x) = 4x − 3, we have:
(f + g)(x) = f(x) + g(x) = x2 + (4x - 3) = x2 + 4x - 3
(f - g)(x) = f(x) - g(x) = x2 - (4x - 3) = x2 - 4x + 3
(fg)(x) = f(x)g(x) = x2(4x - 3) = 4x3 - 3x2
(f/g)(x) = f(x)/g(x) = x2/(4x - 3)

For the second set of functions, f(x) = x2 + 5 and g(x) = 7 - x, we have:
(f + g)(x) = f(x) + g(x) = x2 + 5 + (7 - x) = x2 - x + 12
(f - g)(x) = f(x) - g(x) = x2 + 5 - (7 - x) = x2 + x - 2
(fg)(x) = f(x)g(x) = (x2 + 5)(7 - x) = 7x2 - x3 + 35 - 5x
(f/g)(x) = f(x)/g(x) = (x2 + 5)/(7 - x)

The given operations are:
1.) (f + g)(x) = x2 + 4x - 3, (f - g)(x) = x2 - 4x + 3, (fg)(x) = 4x3 - 3x2, (f/g)(x) = x2/(4x - 3)
2.) (f + g)(x) = x2 - x + 12, (f - g)(x) = x2 + x - 2, (fg)(x) = 7x2 - x3 + 35 - 5x, (f/g)(x) = (x2 + 5)/(7 - x)

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Answer:

y(x)=2*(x+-2)^2+5

Step-by-step explanation:

The solution set of the inequality x-15≤6/9 is  x≤47/3.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is x-15≤6/9

x minus fifteen lesser than or equal to six by nine.

x is the variable and minus is the operator,

x-15≤6/9

On the right side the numerator and denominator is divided by 3

x-15≤2/3

Add 15 on both sides

x≤2/3+15

x less than or equal to two by three plus fifteen.

x≤2+3(15)/3

When three is multiplied with fifteen we get 45.

x≤45+2/3

So when forty five and two are added we get 47.

x≤47/3

Hence, the solution set of the inequality x-15≤6/9 is  x≤47/3.

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Complete quesstion,

Find the solution set of the  inequality x-15≤6/9

Answer: θ=0.75448...πn

The given function is a piecewise function and we are asked to evaluate f(0). To do this, we need to find the expression that corresponds to x = 0. We can see that x < 2, so the expression we need to use is 1 + x.

Plugging in x = 0 into this expression gives us:

f(0) = 1 + 0 = 1

Therefore, the answer is 1.

In HTML format, the answer would be:

The given function is a piecewise function and we are asked to evaluate f(0). To do this, we need to find the expression that corresponds to x = 0. We can see that x < 2, so the expression we need to use is 1 + x.

Plugging in x = 0 into this expression gives us:

f(0) = 1 + 0 = 1

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The correct option regarding the amount of coins is given as follows:

c 4 nickels, 10 dimes, 4 quarters

The amounts are obtained by a system of equations, for which the variables are given as follows:

Amy has 18 coins consisting of nickels, dimes, and quarters, hence:

x + y + z = 18.

She has the same amount of nickels as quarters, hence:

x = z.

Thus:

2x + y = 18

y = 18 - 2x.

She has a total of $2.20 worth of coins, hence:

0.05x + 0.1y + 0.25z = 2.2

0.3x + 0.1y = 2.2

Since y = 18 - 2x, the value of x is obtained as follows:

0.3x + 0.1(18 - 2x) = 2.2

0.1x = 0.4

x = 0.4/0.1

x = 4.

Hence the remaining values are given as follows:

Meaning that option c is correct.

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Cost of 75 pound of candy = 75×6 = $450

Additional fee for each bulk = $250

Total = $700

Therefore, $700 is the correct answer.