Which of the following are identities?

Answer:

t=150

Step-by-step explanation:

50+100=150

50×12=600

Answer:

15

Step-by-step explanation:

cost of 20 mobile set=300

cost of 1 mobile set

=cost of mobile set/number of mobile set

=300/20

=15

The cost of each mobile set is ₹1,50,000.

Unit rate can be defined as the ratio between two measurements with the second term as 1. It is considered to be different from a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity.

Given that, a shopkeeper sold 20 mobile sets of same brand for ₹3,000,000.

The selling price of each mobile set​ = Total cost of mobile sets/Number of mobile sets

= 3,000,000/20

= ₹1,50,000

Therefore, the cost of each mobile set is ₹1,50,000.

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Using the normal distribution, the z-scores are given as follows:

a) Z = 2.8.

b) Z = 2.8.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Item a:

The parameters are:

[tex]\mu = 15, \sigma = 2.5[/tex]

Hence the z-score is:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{22 - 15}{2.5}[/tex]

Z = 2.8.

Item b:

The parameters are:

[tex]\mu = 38.1, \sigma = 6.35[/tex]

Hence the z-score is:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{55.88 - 38.1}{6.35}[/tex]

Z = 2.8.

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Answer: 22

Step-by-step explanation:

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

If each collection consists of at most 3 books on each subject, the number of collection that can be made of 3 English, 4 Economics, and 5 Business Mathematics books are 40.

A combination, as a mathematical technique, determines the number of possible arrangements in a collection of items.

In the combination, the order of the selection does not matter.

The implication is that in combinations, one can select the items in any order, unlike permutations, where the order of selection matters.

English books on shelf = 3

Economics books on shelf = 4

Business Mathematics books on shelf = 5

Collections to be made = 3 books on each subject

The solution can be set up as a combination problem, as follows:

3 C 3 x 4 C 3 x 5 C 3

3! / 3! (3 – 3)! The solution is 1.

4! / 3! (4 – 3)! The solution is 4.

5! / 3! (5 – 3)! The solution is 10.

1 x 4 x 10

= 40

Thus, if each collection consists of at most 3 books on each subject, the number of collections that can be made of 3 English, 4 Economics, and 5 Business Mathematics books is 40.

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The first table with the following values of x and y, shows a linear function.

x = -4, y = 8

x = -1, y = 2

x = 1, y = 2

x = 2, y = 4

x = 3, y = 6

Definition of a Linear Function:

A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

For the above chosen option, the value of y corresponding to a value of x is twice that of its x value. This linear function can be represented as follows,

y = | 2x | .......... (1)

In this linear function, mod represents, that y is always maintained positive. Besides, the value of y is always twice that of the x. Hence, the linear function can also be written as, y ± 2x = 0.

Since, equation (1) is of the form, y = mx + c, it produces a straight line. Here, m = 2 and c = 0. Thus, it is a linear function.

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For the number line, an open circle will be drawn on the value of 6 and the arrow pointing to the right side.

Given the inequality expression as shown

-2x + 9 < x − 9

Collect the like terms

-2x - x < -9 - 9

-3x < -18

Divide through by -3

x > -18/-3

x > 6

For the number line, an open circle will be drawn on the value of 6 and the arrow pointing to the right side.

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Answer:

13200 needs to be less than 78*60+8840,

which is false because 13200 < 13520

Step-by-step explanation:

The truck cannot load 60 boxes as it exceeds the weight limit.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

W=78b+8840

So, b= 60

W= 78 x 66 + 8840

W = 5148 +8840

W = 13988 > 13200 ( limit for the weight)

Hence, the truck cannot load 60 boxes as it exceeds the weight limit.

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Using an exponential function, it is found that f(7.5) = 45.5.

An exponential function is modeled by:

[tex]y = ab^x[/tex].

In which:

For this problem, we have that f(3.5) = 12, then:

[tex]y = ab^x[/tex]

[tex]12 = ab^{3.5}[/tex]

[tex]a = \frac{12}{b^{3.5}}[/tex]

We also have that f(9) = 75, then:

[tex]y = ab^x[/tex]

[tex]75 = ab^9[/tex]

Since [tex]a = \frac{12}{b^{3.5}}[/tex]:

[tex]75 = \frac{12}{b^{3.5}} \times b^9[/tex]

[tex]b^{5.5} = \frac{75}{12}[/tex]

[tex]\sqrt[5.5]{b^{5.5}} = \sqrt[5.5]{\frac{75}{12}}[/tex]

[tex]b = \left(\frac{75}{12}\right)^{\frac{1}{5.5}[/tex]

b = 1.39542165

Then:

[tex]75 = ab^9[/tex]

[tex]a = \frac{75}{1.39542165^9}[/tex]

a = 3.7386

Hence:

[tex]y = 3.7386(1.39542165)^x[/tex]

When x = 7.5, we have that:

[tex]y = 3.7386(1.39542165)^{7.5} = 45.5[/tex]

Hence f(7.5) = 45.5.

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well, when it comes to fractions or rationals, they can never have a denominator that's 0, because if that ever happens, the fraction becomes undefined, so the values of "x" or namely the domain values, that we cannot have because they make the fraction undefined are those values that make the denominator 0, we can simply get them by setting the denominator to 0 and check what's "x".

[tex]x^2-9=0\implies x^2=9\implies x=\pm\sqrt{9}\implies x=\pm 3 \\\\[-0.35em] ~\dotfill\\\\ g(x)=\cfrac{x+6}{x^2-9}\hspace{5em} x\ne \begin{cases} 3\\ -3 \end{cases}[/tex]

We are looking for the graph of [tex]y=\sqrt{-x}[/tex]. which is shown in the attached image.

The underlined sentence in the text simply functions as; the conclusion of the text and connects ideas in the text, by making the main claim of the text describing why the information provided matters to readers.

The underlined text in the passage functions as the conclusion to the passage in which case, the information intended to be conveyed is that on the occasion that, regular feeding, good housing, occasional gentle corrections and kindness are in place, there'd be no need for such a cat to steal.

Therefore, the structural element of the paragraph in the underlined sentence, and how it connect ideas in the text is; by making the main claim of the text

describing why the information provided matters to readers.

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Answer:

Answer:

Step-by-step explanation:

Comment

You must solve x and then y in that order. The reason for that is there are 2 x values and they can be equated to each other. The you can go after the y value, since they are supplement with the value you get from the first operation.

Equations

x + 45 = 2x+ 8

<3 + y + 30 = 180

Solution

<1 and <3 are equal             Two vertically opposite angles are always =.

x  +  45 = 2x + 8                    Subtract x from both sides

x-x + 45 = 2x - x + 8              Combine

45 = x + 8                              Subtract 8 from both sides

45 - 8 = x + 8 - 8                   Combine

37 = x

<1 + <2 = 180                        These two angles sit on the same straight line and have a side in common

x + 45 + y + 30 = 180           Substitute for x

37 + 45 + y + 30 = 180         Combine

112 + y = 180                         Subtract 112 from both sides

112-112 + y = 180 - 112           Combine

y = 68

Answer:

f(x + 3) = 2(x + 7)

Step-by-step explanation:

Now lets find out what does f(x + 3) means.

f(x + 3) means shifting the entire function 3 units to the left. Which also means, all x values will be shifted to the left by that number of units. (Excluding the constant that is multiplied or divided by x, eg. 5x + 6 shifted by 7 units to the left is 5(x + 7) + 6 and not 5x + 7 + 6.)

From the above,

f(x + 3) = 4(x + 3) + 2 = 4x + 12 + 2 = 4x + 14 = 2(x + 7)

The interior angles of the triangle of 61°, 73°, and 46°, and the distance from James to Hadley of 15 meters gives;

The given angles are;

At James's location; 61°

At Hadley's location; 73°

At Gwen's location; 46°

The distance between James and Hadley = 15 meters

The angle facing the distance between James and Hadley is the angle at Gwen, 46°

The angle facing the distance between Gwen and James is the angle at Hadley, 73°

The angle facing the distance between Gwen and Hadley is the angle at James, 61°

The angle that faces the 15 meter length is the angle at Gwen, which is 46°

By the rule of sines, the distance from Gwen to Hadley is therefore;

[tex] \frac{15}{sin( 46 ^ \circ)} = \frac{Gwen \: to \: Hadley}{sin( 61 ^ \circ)} [/tex]

Which gives;

[tex] Gwen \: to \: Hadley= \frac{15 \times sin( 61 ^ \circ) }{sin( 46 ^ \circ)} \approx 18.24[/tex]

Similarly, we have;

[tex] \frac{15}{sin( 46 ^ \circ} = \frac{Gwen \: to \: James}{sin( 73 ^ \circ)} [/tex]

Therefore;

[tex] Gwen \: to \: James = \frac{15 \times sin( 73 ^ \circ) }{sin(46 ^ \circ)} \approx 19.94 [/tex]

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By eliminating exponents, the logarithmic expression [tex]\log_{c} x\cdot y^{6}\cdot z^{-4}[/tex] is equivalent to the logarithmic expression [tex]\log_{c} x + 6\cdot \log_{c} y - 4\cdot \log_{c} z[/tex].

In this problem we are supposed to eliminate all exponents of a logarithmic function by applying any of the following properties:

Now, we proceed to simplify the function:

[tex]\log_{c} x\cdot y^{6}\cdot z^{-4}[/tex]

[tex]\log_{c} x + \log_{c} y^{6} + \log_{c} z^{-4}[/tex]

[tex]\log_{c} x + 6\cdot \log_{c} y - 4\cdot \log_{c} z[/tex]

By eliminating exponents, the logarithmic expression [tex]\log_{c} x\cdot y^{6}\cdot z^{-4}[/tex] is equivalent to the logarithmic expression [tex]\log_{c} x + 6\cdot \log_{c} y - 4\cdot \log_{c} z[/tex].

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The area of a parallelogram is 20 inches square

The area of a parallelogram is the base of the shape multiplied by the height

Area of parallelogram = b × h

Where h = height = 2 In

base = 10 in

Area = 2 × 10

Area = 20 Inches square

Thus, the area of a parallelogram is 20 inches square

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The amount of money that you would pay less for basic contact is $15 while the amount you will pay more for premium =$465.

From the given table in the diagram, the cost of calls made for 10 hours at Standard time=

$6 × 10 = $60

The amount of calls done for basic contact is 3 hours per month for $15 . Total cost per month = 3×15= $45

The amount of calls done for premium contact is 15 hours per month for $35 . Total cost per month = 15× 35=$525

Ordinarily, you per $60 for standard call hours. This means that,

$60 - 45 = $15 less for basic contact and

$525 - $60 = $465 more for premium.

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The simplifications of all the given ratios are as detailed below.

The simplification of each of the given ratios are;

1) 56 : 49

The highest common multiple is 7 and so we divide by 7 to get;

56 : 49 = 8:7

2) 36:48

The highest common multiple is 12 and so we divide by 12 to get;

36 : 48 = 3:4

3) 48:42

The highest common multiple is 6 and so we divide by 6 to get;

48 : 42 = 8:7

4) 24:36

The highest common multiple is 12 and so we divide by 12 to get;

24 : 36 = 2:3

5) 20:30

The highest common multiple is 10 and so we divide by 12 to get;

20 : 30 = 2:3

6) 24:32

The highest common multiple is 8 and so we divide by 8 to get;

24 : 32 = 3:4

7) 18:27

The highest common multiple is 9 and so we divide by 9 to get;

18 : 27 = 2:3

8) 16:14

The highest common multiple is 2 and so we divide by 2 to get;

16 : 14 = 8:7

9) 9:12

The highest common multiple is 3 and so we divide by 3 to get;

9 : 12 = 3:4

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Considering the Central Limit Theorem, we have that:

a) The probability cannot be calculated, as the underlying distribution is not normal and the sample size is less than 30.

b) The probability can be calculated, as the sample size is greater than 30.

It states that the sampling distribution of sample means of size n is approximately normal has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], as long as the underlying distribution is normal or the sample size is greater than 30.

In this problem, the underlying distribution is skewed right, that is, not normal, hence:

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An expression which shows the length of this rope is: 10/cos35 ≈ 12.2 feet.

In order to determine the length of this rope, we would apply the law of cosine because both the rope and apple formed an angle that are adjacent in a right triangle:

cos(θ) = Adj/Hyp

Where:

Substituting the given parameters into the formula, we have;

cos(35) = 10/Hyp

Hyp = 10/cos35

Hyp = 12.2 feet.

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The volume of the shape will be 5652cm³.

The given values are:

Height = 30cm

Large diameter = 16cm: Radius = 16/2 = 8cm

Small diameter = 4cm; Radius = 4/2 = 2cm

The volume will be:

= (3.14 × 8² × 30) - (3.14 × 2² × 30)

= 6028.8 - 376.8

= 5652cm³

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Answer:

80 square units

Step-by-step explanation:

These are rectangles and triangles.

The formula to get the area of a rectangle is its length multiplied by its width.

The formula to get the area triangle is its base multiplied by its height, then divided by 2.

The 3 rectangles all share the width of 6 units, so we can combine the 3 rectangles and consider it as 1 large rectangle.

The lengths of the rectangles are 2, 8, and 2 units.

We can add them together to get a total height of 12 units.

So, the formula to get the area of this rectangle is:
[tex]6\times12= A[/tex]

By solving this, we get:
A = 72 square units

There are 4 triangles remaining.

The base and height of all the triangles are 2 units.

So, by plugging these values into the triangle area formula, as mentioned from the beginning, we get:

[tex](2\times2)\div2=A[/tex]

So, the area of 1 triangle is 2 square units.

But since there are 4 triangles with the same bases and heights, we will multiply the area of 1 triangle by 4.

So, [tex]4 \times 2 = A[/tex]

This means the area of all the triangles together is 8 square units.

By adding the area of the triangles and rectangles together, we will get the answer.

[tex]72+8 = A[/tex]

So, the total area of this box is 80 square units.

{(2,0),(-5,-2),(10,8),(6,0),(-9,-2)} is the correct answer (D)

Answer:

  (d)  {(2, 0), (-5, -2), (10, 8), (6, 0), (-9, -2)}

Step-by-step explanation:

The domain is the list of x-values. The range is the list of y-values. You are looking for the set that matches the given lists.

The list of x-values is {-9, -2}. The list is too short.

The list of x-values is {-9, -5, 2, 6, 10}. This matches the required domain.

The list of y-values is {-2, 0, 8, 5, 9}. The list is too long.

The list of x-values is {-2, 8, 0, -2, 0}. The list does not match the given domain list.

The list of x-values is {2, -5, 10, 6, -9}. This matches the given domain.

The list of y-values is {0, -2, 8, 0, -2}. This matches the given range.

The function of interest is ...

   {(2, 0), (-5, -2), (10, 8), (6, 0), (-9, -2)}

Answer:

x = [tex]6\sqrt{3}[/tex] i

Step-by-step explanation:

We can write the following equation according to Euclidian Theorem to find the value of x:

[tex]x^{2}[/tex] = 12*9 multiply 9 and 12

[tex]x^{2}[/tex] = 108 find the root of both sides

x = [tex]6\sqrt{3}[/tex] is the value of x

Answer:

A) 6.0

Step-by-step explanation:

First, total amount of hours, since average is sum of the numbers by how many numbers there is.

Day 1=8x2 hr

Day 2=6x1 hr

Day 3=4x2 hr

which is, 16+6+8=30

then divide 30 by how many days there is, which is 5 days.

30/5=6

The parametrization for the tangent line at time [tex]t_{0}[/tex] is (41 + 3t, -4/3 + 4t/3, 4/3 + 4t/3)

The point of intersection is (40, -4, 0)

The given curve is defined parametrically by the equations

x = 3t + 2

y = 4 cos t

z = 4 sin t

To find the parametrization for the tangent line at time t0 = 13, we need to find the point of tangency and the direction vector of the tangent line.

The point of tangency is the position of the curve at time t0, which is

(3 * 13 + 2, 4 cos 13, 4 sin 13) = (41, -4/3, 4/3)

The direction vector of the tangent line is the derivative of the curve at time t0, which is

(3, -4 sin 13, 4 cos 13) = (3, -4/3, 4/3)

Therefore, the parametrization for the tangent line is

(41 + 3t, -4/3 + 4t/3, 4/3 + 4t/3)

b. To find the point where this line intersects the -plane, we set z = 0 and solve for t. This gives us

4/3 + 4t/3 = 0

t = -1/2

Therefore, the point of intersection is

(41 - 3/2, -2, 0) = (40, -4, 0).

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The values of f⁻¹(f(6.022)) is 6.022 and f⁻¹(10) + f(-6) is 4

As  a general rule;

f⁻¹(f(x)) = x

This means that:

f⁻¹(f(6.022)) = 6.022

Also, we have:

f⁻¹(10) + f(-6)

From the table of values, we have:

f⁻¹(10) = -6 and f(-6) =10

So, we have:

f⁻¹(10) + f(-6) = -6 + 10

Evaluate

f⁻¹(10) + f(-6) = 4

Hence, the values of f⁻¹(f(6.022)) is 6.022 and f⁻¹(10) + f(-6) is 4

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