Domain and function
Function or not a function

Answer:

Area of  square = 100 square cm

Step-by-step explanation:

Let the sides of a square be = a

Perimeter of a square = 4a

Let area of square = [tex]a^2[/tex]

Let the Length of rectangle be = [tex]l[/tex]

Given: width of the rectangle = 6 cm

Area of rectangle = length x breadth

          Perimeter of rectangle and square is equal.

          That is,

                     [tex]2(length + width) = 4a\\\\2(l + 6) = 4a\\\\l + 6 = 2a\\\\l = 2a - 6[/tex]

Therefore ,

    Area of rectangle

                              [tex]= Length \times width \\\\= (2a - 6) \times 6\\\\=6(2a - 6)[/tex]

Given area of rectangle is 16 less than area of square.

That is ,

         [tex]( 6(2a- 6) ) = a^2 - 16\\\\12a - 36 = a^2 - 16\\\\a^2 - 12a +20= 0\\\\a^2 - 2a -10a + 20 = 0\\\\a(a - 2) - 10(a - 2) = 0\\\\(a -10) ( a-2) = 0\\\\a = 10 , \ a = 2[/tex]

Check which value of 'a ' satisfies the equation:

[tex]\underline {when \ a = 2 }\\\\Length\ of \ rectangle \ l = 2a - 6 = 2 ( 2 ) - 6 = 4 - 6 = - 2. \\\\Length \ cannot \ be \ negative \ number. \\\\ \underline{ when \ a = 10 }\\\\Length \ of \ rectangle \ , l = 2a - 6 = 2 (10) - 6 = 20 - 6 = 14\\\\satisfies \ the \ conditions. \\\\Therefore , a = 10[/tex]

That is , side of the sqaure = 10

Therefore , area  of the square = 10 x 10 = 100 square cm.

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Answer:

  a) yes

  b) see attached

  c) see discussion

  d) neither

  e) increasing (2,5); decreasing (-2, 2)

Step-by-step explanation:

a) The graph passes the vertical line test, so is the graph of a function.

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b) A table of values is attached

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c) Generally, this sort of function would be defined piecewise:

  [tex]\displaystyle f(x)=\begin{cases}-\dfrac{1}{2}x+1&\text{for }-2\le x<2\\2x-4&\text{for }2\le x \le5\end{cases}[/tex]

In the attachment, we have shown the use of the "maximum" function to define it. The effect is the same.

__

d) The function has no symmetry about the origin or the y-axis, so is neither odd nor even.

__

e) The function is increasing where the line has positive slope, on the interval (2, 5). The function is decreasing where the line has negative slope, on the interval (-2, 2).

Answer:

Rs. 100 and Rs. 150

Step-by-step explanation:

the ratio = 2:3 => the sum = 2+3=5

Sita gets = 2/5 × 250 = 100

Ram gets = 3/5 × 250 = 150

Answer:

[tex]P(<47\%)=0.1468[/tex]

Step-by-step explanation:

From the question we are told that:

Percentage of Dentist Doctors P(D)=49\%

Sample size n=689

Generally the equation for  probability that the proportion of doctors who are dentists will be less than [tex]P(<47\%)[/tex] is mathematically given by

 [tex]P(<47\%)=Z>(\frac{\=x-P(D)}{\sqrt{\frac{P(D)*1-P(D)}{n}}})[/tex]

 [tex]P(<47\%)=Z>(\frac{0.47-0.49}{\sqrt{\frac{0.49*0.51}{689}}})[/tex]

 [tex]P(<47\%)=Z>(1.05)[/tex]

Therefore from table

 [tex]P(<47\%)=0.1468[/tex]

Answer:

[tex]\frac{8}{45}[/tex]

Step-by-step explanation:

'of' means 'multiply'

4/5 × 2/9 = 8/45

Answer:

B. <4

D. <5

Step-by-step explanation:

Exterior angle is the angle found outside the triangle. In the diagram given, angle 5 and angle 4 are located outside of the triangle, therefore, the exterior angles in the diagram given are <4 and <5.

Answer:

[tex]z = 1.6[/tex]

Step-by-step explanation:

Given

[tex]Pr = 0.05[/tex]

Required

The z value to the right

The z value to the right is represented as:

[tex]P(Z > z)[/tex]

So, the probability is represented as:

[tex]P(Z > z) = 0.05[/tex]

From z table, the z value that satisfies the above probability is:

[tex]z = 1.645[/tex]

[tex]z = 1.6[/tex] --- approximated

Answer:

<A ≈ 45 degrees

<B ≈ 57 degrees

<C ≈ 78 degrees

Step-by-step explanation:

Hi there!

1) Find <C with the law of cosines

Typically, we want to solve for the angle opposite the largest side first.

Law of cosines: [tex]cosC=\frac{a^2+b^2-c^2}{2(a)(b)}[/tex]

Plug in given values

[tex]cosC=\frac{5^2+6^2-7^2}{2(5)(6)}\\cosC=\frac{1}{5}\\C=cos^-^1(\frac{1}{5} )\\C=78[/tex]

Therefore, <C is approximately 78 degrees.

2) Find <B with the law of cosines

[tex]cosB=\frac{a^2+c^2-b^2}{2(a)(c)}[/tex]

Plug in given values

[tex]cosB=\frac{5^2+7^2-6^2}{2(5)(7)}\\cosB=\frac{19}{35}\\B=cos^-^1(\frac{19}{35})\\B=57[/tex]

Therefore, <B is approximately 57 degrees.

3) Find <A

The sum of the interior angles of a triangle is 180 degrees. To solve for <A, subtract <B and <C from 180:

180-57-78

= 45

Therefore, <A is 45 degrees.

I hope this helps!

Answer:

310/[tex]3^{3}[/tex] = 310/27 =11.48

Step-by-step explanation:

Answer:

310/ = 310/27 =11.48

Step-by-step explanation:

The sample statistic that must have changed after the correction was made is mean. Because mean is based on all the observation in the data. So changing any value in the data will impact mean.

Changing the highest salary in the data will have no impact on median because median lies at the center of data.

Changing the highest salary in the data will have no impact on mode because mode is the most frequently occurring value in the data.

Changing the highest salary in the data will have no impact on minimum because minimum is the smallest value in the data.

Hence the only statistic which will change is mean.

Answer: A-Mean

Step-by-step explanation:

A.) Mean

B.) Median

C.)  Mode

D.)  Minimum

Answer:

2+(-8)

Step-by-step explanation:

Answer:

Please find the complete question in the attached file.

Step-by-step explanation:

Total quantities of plant-produced pollutants:

[tex]=(10.88+15.82+0.92) \ L\\\\=27.62\ L[/tex]

We are three medicinal plants here, Pinecrest, Macon, and Ogala. The average number of contaminants produced by plants would be

[tex]\to 27.62\div 3 \\\\\to \frac{27.62}{3} \\\\ \to 9.206 \ L[/tex]

Answer:

(-4, -1)

Step-by-step explanation:

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Answer:

  23.4 ft³

Step-by-step explanation:

In terms of the perimeter of the square base, the volume of a pyramid can be found using the formula ...

  V = (1/48)P²h . . . . . where P is the base perimeter and h is the height

  V = (1/48)(10.7 ft)²(9.8 ft) ≈ 23.4 ft³

_____

Additional comment

The relevant formulas usually used are ...

  P = 4s . . . . perimeter of a square with side length s

  A = s² . . . . area of a square with side length s

  V = (1/3)Bh . . . . . volume of a pyramid with base area B and height h

Solving the perimeter equation for s, and using that result in the other formulas, we get ...

  s = P/4

  B = (P/4)² = P²/16

  V = 1/3(P²/16)h = (1/48)P²h . . . . the formula used above

Using this result saves the effort of computing the intermediate values of side length and base area.

Answer:

By similar triangles:    BE/20 = 18/25    BE 14.4

Also, (ED + 26) / 26 = 18/14.4

ED = 6.5   and AD = 32.5

Answer:

Parallelogram.

Step-by-step explanation:

Because parallelogram has its opposite sites equal.

Hello,

2 points of the line: (2,0) and (0,3)

[tex]\Delta\ y=3-0=3\\\Delta\ x=0-2=-2\\\dfrac{\Delta\ y}{\Delta\ x} =\dfrac{-3}{2} \\\\y-0=\dfrac{-3}{2}*(x-2)\\\\\boxed{y=-\dfrac{3x}{2}+3}\\[/tex]

Answer:

The p-value of the test is 0.0066 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean salary differs from $39,385

Step-by-step explanation:

The average salary for public school teachers for a specific year was reported to be $39,385. Test if the mean salary differs from $39,385

At the null hypothesis, we test if the mean is of $39,385, that is:

[tex]H_0: \mu = 39385[/tex]

At the alternative hypothesis, we test if the mean differs from this, that is:

[tex]H_1: \mu \neq 39385[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

39385 is tested at the null hypothesis:

This means that [tex]\mu = 39385[/tex]

A random sample of 50 public school teachers in a particular state had a mean of $41,680, and the population standard deviation is $5975.

This means that [tex]n = 50, X = 41680, \sigma = 5975[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{41680 - 39385}{\frac{5975}{\sqrt{50}}}[/tex]

[tex]z = 2.72[/tex]

P-value of the test and decision:

The p-value of the test is the probability that the sample mean differs from 39385 by at least 2295, which is P(|Z| > 2.72), which is 2 multiplied by the p-value of Z = -2.72.

Looking at the z-table, Z = -2.72 has a p-value of 0.0033

2*0.0033 = 0.0066

The p-value of the test is 0.0066 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean salary differs from $39,385

Answer:

D. 4x² + 3x/2 - 7

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

f(x) = x/2 - 3

g(x) = 4x² + x - 4

(f + g)(x) is f(x) + g(x)

Step 2: Find

Answer:

The answer is C.

Step-by-step explanation:

(f+g)(x)= f(x)+g(x).

So that would be x/2-3 + 4x^2+x-4.

If you combine like terms that would be:

4x^2+x/2+x-4-3=

4x^2+3/2x-7

Answer:

[tex] \large{ \tt{❃ \: S \: O \: L \: U \: T \: I \: O \: N : }}[/tex]

[tex] \large{ \tt{❉ \: m \: \angle \:SRQ = m \: \angle \: SRJ\: + \: m \: \angle \:JRQ}}[/tex]

[tex] \large{ \tt{⟼ \: 166 \degree = 110 \degree + m \: \angle \: JRQ}}[/tex]

[tex] \large{ \tt{⟼ \: 166 \degree - 110 \degree = m \: \angle \: JRQ}}[/tex]

[tex] \boxed{ \large{ \tt{⟼ \: 56 \degree = m \: \angle \: JRQ}}}[/tex]

*see attachment for missing diagram

Answer:

AC = 5 and BC = 5√3

Step-by-step explanation:

Given:

m<A = 60°

m<B = 30°

AB = 10

Required:

AC and BC

Solution:

Recall, SOH CAH TOA

✔️Find AC:

Reference angle (θ) = 30°

Hypotenuse = 10

Opposite = AC

Apply SOH:

Sin θ = Opp/Hyp

Substitute

Sin 30° = AC/10

10*Sin 30° = AC

10*½ = AC (sin 30° = ½)

5 = AC

AC = 5

✔️Find BC:

Reference angle (θ) = 60°

Hypotenuse = 10

Opposite = BC

Apply SOH:

Sin θ = Opp/Hyp

Substitute

Sin 60° = BC/10

10*Sin 60° = BC

10*√3/2 = BC (sin 60° = √3/2)

5*√3 = BC

BC = 5√3

Answer:

36281629273781646181993836619946527189119292937467482919198$7473828191927364732818919283838292927383883829118661552621718919191019284746617171819001187373765252728

Step-by-step explanation:

173899918377+28910873638282

The question is incomplete. The complete question is :

Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision.

[tex]$\{ x^5, x^5-1,3 \} \text{ on } (- \infty, \infty)$[/tex]

Solution :

Given :

Function : [tex]$\{ x^5, x^5-1,3 \} \text{ on } (- \infty, \infty)$[/tex]

We have to determine whether the given function is linear dependent or linearly independent for the interval [tex]$(-\infty, \infty)$[/tex].

The given function are linearly dependent because for the constants, [tex]c_1[/tex] and [tex]c_2[/tex], the equation is :

[tex]$c_1x^5 + c_23 = x^5-1$[/tex]  has the solution [tex]$c_1 = 1$[/tex] and [tex]$c_2 = -\frac{1}{3}$[/tex]

Therefore,

[tex]$1x^5 + \left(-\frac{1}{3}\right)3 = x^5-1$[/tex]

Answer:

104

Step-by-step explanation:

180-76=104

Answer:

104

Step-by-step explanation:

heres my proof. have a nice day :)

Answer:

x = 22

Step-by-step explanation:

In order to solve this, we need to understand that in an isosceles triangle the two angles that are located at its base are equal to each other.

base - (the side that is not one of the two sides that are equivalent to each other)

Knowing this we can see that ∠ACB will equal ∠BAC, therefore ∠ACB will be equal to x°. Since the sum of all inner angles of a triangle is equal to 180°, we can make the following equation...

x° + x° + (3x + 70)° = 180°

2x° + 3x° + 70° = 180°

5x° = 180° - 70°

5x° = 110°

x° = 110° / 5

x° = 22°

x = 22

Therefore, x = 22.

Answer:

Find the definitions and points below.

Step-by-step explanation:

1. Food Handling refers to any of the stages in the preparation, storage, transportation, packaging, and delivery of food.

2. Utensils are those vessels and tools that are used to carry, cut, stir, and store items and ingredients required in food preparation.

3.  Three quality points for dairy and eggs which indicate quality and freshness are;

a. Smell: A decaying and pungent smell indicates a lack of quality.

b. Color: An abnormal color with physical signs of rottenness shows a lack of quality.

c. The sinking test is used to check for the freshness of eggs. If an egg sinks when put in a glass of water, it is a sign of freshness. If it floats, it is an indication of decay.

4. Three quality points for dry goods that indicate quality and freshness:

Moisture: The presence of moisture in dry food shows a lack of quality.

Weight: Heaviness might be an indication that one coconut is better than another.

Texture: A dry food that is sticky might indicate a lack of freshness. Smoothness, crunchiness, hardness, and toughness are other qualities to look out for.

5. Five ways I could increase the nutritional value of pastries include

1. Using fresh ingredients: Fresh ingredients free from contamination will guarantee that foods with good nutritional values are produced.

2. Preparing them in a hygienic environment: A hygienic environment will prevent food poisoning by bacteria and other contaminants.

3. Using proper measurements: When the right measurements are used in the preparation of pastries a balanced snack is produced.

4. Good preservation techniques: The right preservation techniques will prevent food spoilage.

5. Good packaging and wrapping: These will prevent exposure of the food to moisture, rodents, and other unwanted factors. Thus, the nutritional value is preserved.

Answer:

c

Step-by-step explanation:

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Answer:

  1604 m

Step-by-step explanation:

The relevant trig relation is ...

  Sin = Opposite/Hypotenuse

Here, the "opposite" is the elevation of point B above point A, and the "hypotenuse" is the length of the railway. Then the total height of point B is ...

  B = 856 + 864·sin(120°)

  B = 856 +864(√3)/2 = 856 +432√3 ≈ 1604.246

The height of the train at point B is about 1604 m above sea level.

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Answer:

  1/3

Step-by-step explanation:

The slope of a line is the ratio of its "rise" to its "run." The "rise" is the change in vertical distance, and the "run" is the corresponding change in horizontal distance between two points on the line. The formula for the slope is ...

  [tex]m=\dfrac{y_2-y_1}{x_2-x_1}\qquad\text{where $(x_1,y_1)$ and $(x_2,y_2)$ are points on the line}[/tex]

In this problem, you are told the line passes through the origin, which is point (x, y) = (0, 0), and through point (6, 2). Using these coordinates in the slope formula gives ...

  [tex]m=\dfrac{2-0}{6-0}=\dfrac{2}{6}=\boxed{\dfrac{1}{3}}[/tex]

__

You may notice that when the line passes through the origin, the slope is simply the ratio y/x of any point on the line. Here, that ratio is 2/6 = 1/3.

_____

Additional comment

A line through the origin is the graph of a proportional relationship. That is, y is proportional to x. The slope of the line is the constant of proportionality. The equation of the line is ...

  y = kx . . . . . . where k is the constant of proportionality.

The line in this problem statement will have the equation ...

  y = (1/3)x

Answer:

(f • g) (x) = [tex]x^{3}[/tex] - 3[tex]x^{2}[/tex] - 16x - 12

Step-by-step explanation:

(x-6)([tex]x^{2}[/tex] + 3x + 2)

[tex]x^{3}[/tex] + 3[tex]x^{2}[/tex] + 2x - 6[tex]x^{2}[/tex] - 18x -12

[tex]x^{3}[/tex] - 3[tex]x^{2}[/tex] - 16x - 12