Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options.

The value of f(–10) = 82
The graph of the function is a parabola.
The graph of the function opens down.
The graph contains the point (20, –8).
The graph contains the point (0, 0).

The relation is a function only if for element x in Set X, there is only one element in Set Y so, the choice B shows the relation.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable).

When a relation will be called as a function .

Consider there be a relation R from a set X to a set Y .

Since the relation will be called a function if each element of set X is related to exactly one element in set Y.

which is, an element x in X, there is only one element in Y that x is related to.

Therefore , the correct option is B.

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Joan completed the race 1.66 standard deviations faster than the typical female of her age group. The standard deviation will be denoted by the symbol “” and the women's average finish time by the symbol “”. Then, Joan's remaining time was plus 1.66.

The proportion of women who finished the race sooner than Joan. In this case, it is possible to apply the normal distribution.

The percentage of values to the left of z = 1.66 can then be calculated or found using a standard normal distribution table. The number of women who finished the race ahead of Joan is represented by the percentage in the table below.

According to a normal distribution table or calculator, there are approximately 0.9525 numbers to the left of the value z = 1.66.

Therefore, This means that out of the 410 female runners in Joan's age group, about 0.9525 × 410 = 391.23 of them beat her. The final count is 391 women, rounded to the next whole number.

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Answer:the answer is -69/8

Step-by-step explanation:

first you plug -9 into 3/8 and it gives you -72/8+3/8 if you add those together you get -69/8

Answer:

The correct answer is D. Step 4 is incorrect and should be 10x = 24.

Answer:

33.6-(-6.4)=40

Step-by-step explanation:

1. 8.4×4

2. 3.2x-2

3. 33.6-(-6.4)

4. 40

the two negatives become positive

Answer: Balu originally had 40 sweets.

Step-by-step explanation:

Let x be the number of sweets Balu originally had.

After Amal gives one third of his sweets to Balu, Balu's number of sweets becomes x + (1/3)x = (4/3)x.

After Balu gives one third of his sweets to Chandran, Chandran's number of sweets becomes 40 + (1/3)(4/3)x = 40 + (1/3)x.

After Chandran gives one third of his sweets to Amal, Amal's number of sweets becomes (2/3)x + (1/3)(40 +(1/3)x) = (2/3)x + (1/3)x + 40/3 = (5/3)x + 40/3.

Since all three of them now have the same number of sweets, we can set the number of sweets each of them has equal:

(4/3)x = (5/3)x + 40/3.

Now, we will isolate x by rearranging the equation. Subtracting (5/3)x from both sides, we get:

(4/3)x - (5/3)x = 40/3

Simplifying the left side:

-x/3 = 40/3

Dividing both sides by -1/3:

x = 40

Thus, Balu originally had 40 sweets.

The probability that a customer selected randomly would only like Carmel apple is 23/76

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Probability = sample space/ total outcome

sample space is the number of customers that like caramel apple latte only = 46

The total number of customers = 46+61+27+18 = 152

Therefore The probability that a customer selected randomly would only like Carmel apple = 46/152 = 23/76

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The time JBLM will you be the closest to Mt. Rainier will be 5.12 minutes.

A measurement of the distance between two places along a line or line segment.

The plane's flight route follows the line.

y = -125/135x = -25/27x

The direction of the perpendicular line passing across Mt. Rainier is,

y = 27/25(x -56) -40

In standard form, these two equations are,

25x +27y = 0

27x -25y = 2512

The coordinates at the closest approach are the answers to these two equations:

(x, y) = (33912/677, 31400/677)

The Pythagorean theorem (distance formula) states that the distance d from the origin to this point is as follows:-

d = 1256√(2/677) km

The airplane's speed can be used to convert this distance to time:

1256√(2/677) X 60/800 =  94.2√(2/677) ≈ 5.120019 mins

So, 5.12 minutes after leaving JBLM, Mt. Rainier will be the nearest.

The attached graph shows the geometry of the problem.

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The number of ways for which he can choose 7 lures if more than 5 must be jigs is of:

372 ways.

The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The possible combinations are given as follows:

Hence the number of ways is given as follows:

n = 9!/(6! x 3!) x 4!/(1! x 3!) + 9!/(7! x 2!)

n = 372 ways.

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a ) Construction of stem and leaf display of the data is:

For n = 129 and with splint unit = 0.1, the stem and splint map of the given data on Shower- inflow rate( L/ min) is as follows

a stem-and-leaf display of the data.

   Stems                                                Leaves

       2                                                       28

       3                                                1344567789

       4                                                 01356889

       5                                          00001114455666789

       6                              0000122223344456667789999

       7                                     00012233455555668

       8                                                02233448

       9                                         012233335666788

      10                                             2344455688

      11                                                2335999

      12                                                     17

      13                                                      9

      14                                                     36

      15                                                  0035

      16                                                  None

      17                                                  None

      18                                                     3

b) From brume and splint map we note that minimal Shower inflow rate is2.2 whereas outside is18.3 L/ mim. farther typical or representative rate is7.0 L/min.

c) The display of data on steam and leaf chart shows that data is positively skewed means concentration of data on left side or lower value side is high as compared to other side.

d) Distribution is not symmetric rather very clear positive skew ness is observed through steam and leaf chart. Even distribution is Unimodal.

e) From steam and leaf chart is indicative to conclude that the highest observation 18.3 is outlier.

A stem and splint plot, also known as a stem and splint illustration, is a way to arrange data so that it's simple to see how constantly colorful feathers of values do. It's a graph that displays ordered numerical data. A stem and a splint are divided into each piece of data.

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Complete question:

The accompanying data set consists of observations on shower-flow rate (L/min) for a sample of n = 129 houses:

4.6 12.1 7.1 7.0 4.0 9.2 6.7 6.9 11.5 5.1

11.2 10.5 14.3 8.0 8.8 6.4 5.1 5.6 9.6 7.5

7.5 6.2 5.8 2.8 3.4 10.4 9.8 6.6 3.7 6.4

8.3 6.5 7.6 9.3 9.2 7.3 5.0 6.3 13.9 6.2

5.4 4.8 7.5 6.0 6.9 10.8 7.5 6.6 5.0 3.3

7.6 3.9 11.9 2.2 15.0 7.2 6.1 15.3 18.3 7.2

5.4 5.5 4.3 9.0 12.7 11.3 7.4 5.0 3.5 8.2

8.4 7.3 10.3 11.9 6.0 5.6 9.5 9.3 10.4 9.7

5.1 6.7 10.2 6.2 8.4 7.0 4.8 5.6 10.5 14.6

10.8 15.5 7.5 6.4 3.4 5.5 6.6 5.9 15.0 9.6

7.8 7.0 6.9 4.1 3.6 11.9 3.7 5.7 6.8 11.3

9.3 9.6 10.4 9.3 6.9 9.8 9.1 10.6 4.5 6.2

8.3 3.1 4.9 5.0 6.0 8.2 6.3 3.8 6.0

(a) Construct a stem-and-leaf display of the data. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)

Stems Leaves

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

(b) What is a typical, or representative, flow rate?

L/min

(c) Does the display appear to be highly concentrated or spread out?

highly concentrated, except for a few values on the positive sidehighly concentrated in the middle highly concentrated, except for a few values on the negative sidespread out

(d) Does the distribution of values appear to be reasonably symmetric? If not, how would you describe the departure from symmetry?

Yes, the distribution appears to be reasonably symmetric.No, the data are skewed to the right, or positively skewed. No, the data are skewed to the left, or negatively skewed.No, the distribution of the values appears to be bimodal.

(e) Would you describe any observation as being far from the rest of the data (an outlier)?

Yes, the value 2.2 appears to be an outlier.Yes, the value 15.5 appears to be an outlier. Yes, the value 18.3 appears to be an outlier.No, none of the observations appear to be an outlier.

For the function f(x) = -tan 4x,

Given the function

f(x) = -tan 4x

The domain of the function is the set of all possible inputs of the function

The range is set of all possible outputs of the function

Here the function is

f(x) = -tan 4x

Domain of the function will be

π[(2n+1)/8] < x < π[(2n+3)/8]

The range of the given function is set of all real numbers

The period = π /4

Two vertical asymptotes are π/8 and -π/8

Therefore, the domain, range period and the two vertical asymptotes of the function has been found

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Answer: [tex]f^{-1} (x) = \sqrt{x} +1[/tex]

Step-by-step explanation:

[tex]y = x^2 - 2x + 1[/tex]

We know straight away the inverse will be a square root function. We also know that this inverse will have a restriction on the domain, (because you can only take the square root of a positive number).

So, to find the inverse, first we'll switch the x and y and solve for y:

[tex]x = y^2 - 2y +1[/tex]

[tex]x = (y-1)^2[/tex], (factor!)

±[tex]\sqrt{x} = y - 1[/tex]

So, the inverse "function" is:

[tex]f^-1(x)[/tex] = ±[tex]\sqrt{x} +1[/tex]

But theres an issue here!

If we tried graphing this, this "function" would not pass the vertical line test, so its not really a function at all!

We need to restrict the domain to only include the values that are above the x axis.

So our final inverse function is:

[tex]f^{-1} (x) = \sqrt{x} +1[/tex]

Answer:

[tex]10\sqrt{7}+8\sqrt{2}[/tex]

Step-by-step explanation:

Lets simplify.

[tex]3\sqrt{28}+4\sqrt{7} +2\sqrt{32}[/tex]

Rewrite [tex]28[/tex] as [tex]2^2*7[/tex]

[tex]3\sqrt{2^2*7}+4\sqrt{7} +2\sqrt{32}[/tex]

Pull terms out from under the radical.

[tex]3\left(2\sqrt{7} \right)+4\sqrt{7} +2\sqrt{32}[/tex]

[tex]6\sqrt{7} \right)+4\sqrt{7} +2\sqrt{32}[/tex]

Add [tex]6\sqrt{7}[/tex] and [tex]4\sqrt{7}[/tex].

[tex]10\sqrt{7} +2\sqrt{32}[/tex]

Rewrite [tex]32[/tex] as [tex]4^2*2[/tex].

[tex]10\sqrt{7} +2\sqrt{4^2*2}[/tex]

Pull terms out from under the radical.

[tex]10\sqrt{7}+2\left(4\sqrt{2}\right)[/tex]

[tex]10\sqrt{7}+8\sqrt{2}[/tex]

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Therefore, the area of the triangle ABC is approximately 18096.3 square units.

What is the area of the triangle?

To calculate the area of a triangle, use the formula area = 1/2 * base * height.

We can use Heron's formula to find the area of the triangle ABC when the lengths of its three sides are known:

[tex]Area = {\sqrt{(s(s-a)(s-b)(s-c))}[/tex]

where "s" is the semiperimeter of the triangle, which is half the sum of the lengths of its three sides:

s = (a + b + c)/2

In this case, we have:

a = AB = 154

b = BC = 346

c = AC = 349

So the semiperimeter is:

s = (a + b + c)/2 = (154 + 346 + 349)/2 = 424.5

Now we can use Heron's formula to find the area of the triangle

[tex]Area = \sqrt{(s(s-a)(s-b)(s-c))}\\\\Area = \sqrt{(424.5(424.5-154)(424.5-346)(424.5-349))}\\\\Area= 18096.3[/tex]

Therefore, the area of the triangle ABC is approximately 18096.3 square units.

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The estimate of the number 7th grader who play in the school band will be 120.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. The estimate of the number 7th grader who play in the school band will be:

= 60 / 200 × 400

= 120

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By using the continuous interest formula, we get 8.54 years that the amount will take to double itself.

The continuous interest formula is used to calculate the future value of a compound interest investment. It is written as follows:

Future Value = Principal × [tex](1 + r)^{n}[/tex]

where Principal is the original investment, r denotes the yearly interest rate, and n denotes the number of compounding periods.

The continuous interest formula is used to compute the future worth of an investment given its current value, yearly interest rate, number of times the interest is compounded each year, and number of years held.

In the given question,

A = A_0[tex]e^{rt}[/tex]

2A_0 = A_0[tex]e^{rt}[/tex]

2 = [tex]e^{rt}[/tex]

ln(2) = rt

t = [tex]\frac{2}{r}[/tex]

t = [tex]\frac{2}{0.08}[/tex]

t = 8.54 years

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The first mistake in Ismail's proof is that (3) cos(90 - Ф) = AC/BC

The complete question is added as an attachment

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

The two column proof

In the two column proof, we have

cos(90 - Ф) = AC/BC

This equation is incorrect because by the definition of cosine, we have

cos(90 - Ф) = AB/BC

i.e. cos(x) = adjacent/hypotenuse

Hence, the mistake in his proof is cos(90 - Ф) = AC/BC

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The dual problem of the primal problem "Maximize Z = 7X1 + 5X2, Subject to X1 + 2X2 ≤ 6, 4X1 + 3X2 ≤ 12, X1, X2 ≥ 0" is:

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Greater than (or greater than or equal to), less than (or less than or equal to), or not equal to signs are used in place of the equal sign.

Minimize Z = 6Y1 + 12Y2

Here

Y1 + 4Y2 ≥ 7

2Y1 + 3Y2 ≥ 5

Y1, Y2 ≥ 0

(b) The dual problem of the primal problem "Maximize Z = 3X1 + 4X2, Subject to 5X1 + 4X2 ≤ 200, 3X1 + 5X2 ≤ 150, 8X1 + 4X2 ≥ 80, X1, X2 ≥ 0" is:

Minimize Z = 200Y1 + 150Y2

Subject to:

4Y1 + 5Y2 ≥ 3

5Y1 + 3Y2 ≥ 4

4Y1 + 8Y2 ≤ -80

Y1, Y2 ≥ 0

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"Your question is incomplete, probably the complete question/missing part is:"

Write the dual of following problems:

(a) Maximize Z = 7X1 + 5X2

Subject to:

X1 + 2X2 ≤ 6

4X1 + 3X2 ≤ 12

X1, X2 ≥ 0

(b) Maximize Z= 3X1 + 4X2

Subject to:

5X1 + 4X2 ≤ 200

3X1 + 5X2 ≤ 150

8X1 + 4X2 ≥ 80

X1, X2 ≥ 0

Answer:

Step-by-step explanation:

area of pole=75×8=600 square inch

area if sign=12×12+1/2×12×4

=144+24

=168 square inches

total area=600+168

=768 square inches

Answer:

Step-by-step explanation:

A because the gcf of 20 is 4 and the gcf of 4 is 4

Answer:

b

..,..............................................is my answer

Answer:

1/5

Step-by-step explanation:

Answer:

The solution is 1/5 or 0,2

Step-by-step explanation:

[tex] \displaystyle \sf\lim_{x \to 3} \frac{ {x}^{2} - 5x + 6 }{2 {x}^{2} - 7x + 3} \: \: \: \: \: \: \: \: \: \\\\ = \displaystyle \sf\lim_{x \to 3} \frac{(x - 2)(x - 3)}{(2x - 1)(x - 3)} \\\\ = \displaystyle \sf\lim_{x \to 3} \frac{(x - 2)\cancel{(x - 3)}}{(2x - 1)\cancel{(x - 3)}} \\\\ = \displaystyle \sf \lim_{x \to 3} \frac{(x - 2)}{(2x - 1)} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\\\ \sf x = 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\\\ \sf = \frac{(3 - 2)}{(2(3) - 1)} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\\\ = \boxed{\sf \frac{1}{5} \: or \: 0.2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

There are 33% of the total is made up of Planes.

The percentage is defined as a ratio expressed as a fraction of 100.

The table is given in the question, as follows:

               Car       Plane      Train      Total

Green:     120       250        500       870

Blue:       150        350        750       1250

Yellow:   170         200      450        820

Red:       200        300      300       800

Brown:   220        450       320        990

Total:     860       1550    2320        4730

Total number of planes = 1550

The total number of all vehicles = 4730

The percent of planes = (number of planes/number of all vehicles) x 100

The percent of planes = (1550/4730) x 100

The percent of planes = 0.3276 x 100

The percent of planes = 32.76

Round to the nearest percent, and we get

The percent of planes = 33%

Thus, 33% of the total is made up of Planes.

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B) h = 38p

An equation represents a proportional relationship if the ratio of the dependent variable to the independent variable is constant. In this equation, h is directly proportional to p, meaning that if p increases, h increases, and if p decreases, h decreases. The constant of proportionality is 38.

In other words, the equation h = 38p can be written as h/p = 38, which shows that the ratio of h to p is always equal to 38. This means that the equation represents a proportional relationship.

The other equations listed do not represent a proportional relationship because the ratio of the dependent variable to the independent variable is not constant. For example, in equation A, h is not directly proportional to p because the constant of proportionality changes as p changes. In equation C, h and p are inversely proportional because h decreases as p increases, and h increases as p decrease. And in equation D, the equation is not in the form of a proportion because there is an additional constant term on the right-hand side.

Answer:

D. 0.79

Step-by-step explanation:

To find the probability that a Hospitality Management student has visited 21 or more states, we need to sum up the probabilities of the categories that represent students who have visited 21 states or more.

The probabilities of the categories are as follows:

Visited 21–30 states: 45% = 0.45

Visited 31–40 states: 19% = 0.19

Visited 41–50 states: 15% = 0.15

So, the total probability of a student having visited 21 or more states is:

0.45 + 0.19 + 0.15 = 0.79.

Therefore, the probability that a Hospitality Management student has visited 21 or more states is 0.79 or 79%.

Answer:

Step-by-step explanation:

To find the inverse of a function, we need to switch the x and y values and solve for y (or x, depending on how the original function is written). The inverse of the function f(x) = 3x + 7 is written as f^-1(x). To find f^-1(x), we can follow these steps:

Replace the function f(x) with y to make it easier to manipulate: y = 3x + 7.

Swap the x and y variables: x = 3y + 7.

Solve for y:

Subtract 7 from both sides to get x - 7 = 3y.

Divide both sides by 3 to get (x - 7) / 3 = y.

Write the inverse function using f^-1(x) instead of y:

f^-1(x) = (x - 7) / 3

So, the inverse of the function f(x) = 3x + 7 is f^-1(x) = (x - 7) / 3.

The answer is (a) MX + MY. Whether or not X and Y are independent, we cannot simplify (a) or (b) further.

The mean of X + Y is:

E(X + Y) = E(X) + E(Y)

So the answer is not (a) or (b).

(c) is incorrect because the formula given is only true if X and Y are independent, but no such assumption is given in the problem.

(d) is also incorrect because we cannot simply divide the means by the standard deviations to get the standard normal variables, especially when the variables X and Y have different means.

Therefore, the answer is (a) MX + MY.

Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.

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