Which relation is a function?

Answer:

see explanation

Step-by-step explanation:

using the cofunction identities

cos x = sin(90 - x)

sin x = cos(90 - x)

then

cos76° = sin(90 - 76)° = sin14°

sin66° = cos(90 - 66)° = cos24°

sin53° = cos(90 - 53)° = cos37°

cos49° = sin(90 - 49)° = sin41°

The  Matched values are

cos(76) —> sin (14)

sin(66)—> cos (24)

sin(53)—> cos (37)

cos(49)—> sin (41)

One area of mathematics known as trigonometry examines the relationship between the sides and angles of a right triangle. The relationship between sides and angles is defined for 6 trigonometric functions.

For complementary angle,

a+ b= 90

So, sin (14)

= cos (90 - 76)

= cos 76

and, cos (37)

=sin (90 - 53)

= sin (53)

and, sin (49)

= cos (90- 41)

= cos 41

and, cos (66)

= sin (90 - 24)

= sin 24

Then, the Matched values are

cos(76) —> sin (14)

sin(66)—> cos (24)

sin(53)—> cos (37)

cos(49)—> sin (41)

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Sophie's favorite number is 83

We have that;

A two-digit number is Sophie's preferred number. Her favorite number is 45 less when the digits are in reverse. Her favorite number has digits that add out to 11 in total.

To get Sophie's favorite number, we need to assume the case as;

Let,

⇒10x + y = 10y + x + 45

   x + y = 11

   y = 11-x

⇒10x + 11 - x = 10(11 - x) + x + 45

  10x + 11 - x = 110 - 10x + x + 45

  9x + 11 = 155 - 9x

  18x + 11 = 155

  18x = 144

  x = 8

Therefore, y = 11 - 8

                  y = 3

Sum = x + y = 8 + 3 = 11

Hence, the given condition is satisfied.

Sophie's favorite number is 83.

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Answer:

~62.35°

Step-by-step explanation:

To find the degree of an angle from side lengths, use reverse trigonometric function.

arcsin, arccos, arctan / [tex]sin^-1, cos^-1, tan^-1[/tex]

Because we have adjacent and opposite, lets use arctan.

Set up the equation.

[tex]x = arctan\frac{21}{11}[/tex]

Use a calculator to solve.

Answer: f(4) = -171

Step-by-step explanation:

      To answer this question, we will solve the function for 4. In other words, we will input 4 into the function and simplify. Don't forget the order of PEMDAS when simplifying.

Given:

     f(x) = -11x² + 5

Input of 4:

     f(4) = -11(4)² + 5

Raise to the power of 2:

     f(4) = -11(16) + 5

Multiply:

     f(4) = -176 + 5

Add:

     f(4) = -171

The scale on the map is of 1 mile: 0.477 inches.

From the question, we have

65 miles - 31 inches

1 mile - x inches

Applying cross multiplication:

65x = 31

x = 31/65

x=0.477

The ratio of inches on a map to feet, miles, or another unit of measurement on the ground is known as the scale.

Scale (map):

The ratio between a distance on a map and its actual distance on the ground is known as the map's scale. Since scale must vary across a map due to the curvature of the Earth's surface, this straightforward idea is made more difficult. This change makes the idea of scale significant in two different ways.

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The probability that the component requires both painting and galvanizing is 0.06.

Considering the values provided in the question,

P(Painted) = 0.20

P(Galvanized) = 0.30

Both the events are independent of each other.

The probability of the part needs both painted and galvanized is

= P(Painted and Galvanized)

= P(Painted) × P(Galvanized)

= 0.20 × 0.30

= 0.06

Therefore, The probability of the part needs both painted and galvanized is 0.06.

The possibility of an event happening is determined by probability. We may need to forecast an event's result in a variety of real-world circumstances. The outcomes of an event may be certain or uncertain to us. In these circumstances, we say if there is a chance the event will happen or not.

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Prior to cellular radio, mobile radio and telephone services required

a. high-power transmitter/receiver.

A radio transmitter, also known as a transmitter, is an electronic device that generates radio waves using an antenna in electronics and telecommunications. The transmitter generates alternating current with a radio frequency that is applied to the antenna. The antenna emits radio waves when it is excited by this alternating current.

Typically, the term transmitter refers to equipment that generates radio waves for communication or radiolocation, such as radar and navigational transmitters. Even though they frequently use similar circuits, radio wave generators for heating or industrial purposes, such as microwave ovens or diathermy equipment, are not typically referred to as transmitters.

Transmitters are required components of all radio-communication devices, including radio and television broadcasting stations, cell phones, walkie-talkies, wireless computer networks, and Bluetooth-enabled devices.

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Answer:I am not fully going to do it for you, but here is the best way i can explain, it if not i am sorry.

Step-by-step explanation: Simply take the sales price minus the unit cost, and divide that number by the unit cost. Then, multiply by 100 to determine the markup percentage. For example, if your product costs $50 to make and the selling price is $75, then the markup percentage would be 50%: ( $75 – $50) / $50 = . 50 x 100 = 50%.

Answer:

y=2·6^2

Step-by-step explanation:

Use formula y=a[tex]b^x[/tex], plug in two different points.

72=ab^2

12=ab^1

isolate one so that a is on one side

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

plug in a into the other equation

72=[tex]\frac{12}{b}[/tex][tex]b^2[/tex]

72=[tex]\frac{12b^2}{b}[/tex]

72=12b

b=6

complete solving for a now

a=2

now put it back into [tex]y=ab^x[/tex]

y=2·6^2

The solution to the expression is given as 3 exponent 4 x (20.3 - 9) + 14.5 is 929.8

From the question, the expression is given as

3 exponent 4 x (20.3 - 9) + 14.5

When the expression is rewritten, we have the following representation

3⁴ x (20.3 - 9) + 14.5

Evaluate the exponent

So, we have

3⁴ x (20.3 - 9) + 14.5 = 81 x (20.3 - 9) + 14.5

Evaluate the expression in the bracket

3⁴ x (20.3 - 9) + 14.5 = 81 x 11.3 + 14.5

Solving further, we have

3⁴ x (20.3 - 9) + 14.5 = 915.3 + 14.5

Lastly, we have

3⁴ x (20.3 - 9) + 14.5 = 929.8

Hence, the solution is 929.8

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The only correct option that is minimized by the least squares regression line is. Option B the sum of the squared residuals.

lets check all the option -

Option A - This claim is untrue because the residuals' summation would provide a value of 0.

Option B - Because error must be kept to a minimum, the residuals must sum to zero and the line must be as close to the points as possible. Prior to summing them, we must first square the residuals, which will always result in a positive value. This option is accurate since the Least Square Regression Line minimizes the total of residuals.

Option C - This choice is incorrect because the least squares regression line cannot be created by adding the absolute values of the residuals.

Option D - This alternative is incorrect since the influence of outliers has nothing to do with the subject at hand.

Option E - Due to slope's lack of relevance to the subject at hand, this choice is also incorrect.

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Main Answer:

The constant term of h(x) is 4x^3 - 16x^2 - 75x - 63\

Supportive Question and Answer:

What is an Algebraic Expression?

An expression that includes variables, constants, and algebraic operations is an algebraic expression in mathematics (addition, subtraction, etc.). Terms combine to form expressions.

Solution Explained:
Given,
h(x) = f(x).g(x)

h(x) = (x-7)(2x+3)^2

now, simplify,

(x-7)(2x +3)                                                    Expand the expression
           

(x-7)((2x)^2+2 X 2x X 3+3^2)                        Simplify the expression

(x-7)(2^2 X x^2 +2 X 2x X 3+3^2)                Calculate

(x-7)(4x^2+2 X 2x X 3 + 9)                            Mutiply

(x-7)(4x^2 + 12x + 9)                                       Expand the expression

x X 4x^2 + x X 12x + x X 9 - 7 X 4x^2 - 7 X 12x -7 X 9       Mutiply

4x^3 + 12x^2 + 9x - 28x^2 84x - 7 X 9           Calculate

4x^3 + 12x^2 + 9x - 28x^2 - 84x - 63                    Combine like terms

Hence, the constant term for h(x) is 4x-16x-75x 63.

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The unit of price per oz = 114.2

According to our question-

the price of a 2 liter bottle of sprite holds 67.6 oz

and costs $3.38.

2 = 67.6

67.6/2= 33.8

33.8*3.38= 114.24

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The probability of an event is given by dividing the favorable outcomes by total number of outcomes. The sum of all the probabilities of events is always 1.

The probability that 2 red cards and 11 black cards are dealt is .

The probability of an event is given by dividing the favorable outcomes by total number of outcomes. The sum of all the probabilities of events is always 1. If for finding probability we have to select r out of n. Combination is used to select r items out of n, the formula is as follows,

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Finding the probability that 2 red cards and 11 black cards are dealt,

Number of favorable outcomes will be [tex]^{26}C_2\times^{26}C_{11}[/tex].

Total number of outcomes will be [tex]^{52}C_{13}[/tex]

Now, the probability will be,

[tex]P()=\frac{^{26}C_2\times^{26}C_{11}}{^{52}C_{13}} \\\\=\frac{325\times7726160}{635013559600} \\\\=0.00395[/tex]

Therefore, the probability that 2 red cards and 11 black cards are dealt is 0.00395.

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9% of the volume of the original volume is removed.

Given that the dimensions of solid box is 15 cm by 10 cm by 8 cm.

So the volume of solid box = 15*10*8 cubic cm = 1200 cubic centimeter

The volume of the cube with side 3 cm = 3*3*3 = 27 cubic centimeter

For each corner one cube so the number of cube is 4

So total volume removed = 4*27 = 108 cubic centimeters

The percent of volume is removed = (108/1200)*100% = 9%

Hence the percentage of volume removed is 9%.

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Answer: K 35

Step-by-step explanation:

We're given the inequality : 15n < 580.5

Divide both sides by 15.

-> 15n : 15 < 580.5 : 15
-> n < 38.7

Therefore, the final inequality is : n < 38.7

The person from the 4 people that will reach his or her goal is Friend C.

Friend A: Works 6 hours per week at $13.90 per hour. The amount in 8 weeks will be:

= 6 × $13.90 × 8

= $667.2

b) Friend B: Works 7.5 hours per week at $11.70 per hour. The amount in 8 weeks will be:

= 7.5 × 11.70 × 8

= $702

c) Friend C: Works 9 hours per week at $10.50 per hour. The amount in 8 weeks will be:

= 9 × $10.50 × 8

= $756

d) Friend D: Works 5.5 hours per week at $15.60 per hour. The amount in 8 weeks will be:

= 5.5 × $15.60 × 8

= $686.40

In this case, C had $756 which is above the amount needed.

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[tex]\fbox{1.333333}[/tex]

[tex]4\frac{2}{15} \div3.1[/tex]

Simplify:

[tex]4\frac{2}{15} \div3.1[/tex]

[tex]=1.333333[/tex]

let's firstly convert the  mixed fraction to improper fraction and the decimal one to a fraction.

[tex]\stackrel{mixed}{4\frac{2}{15}}\implies \cfrac{4\cdot 15+2}{15}\implies \stackrel{improper}{\cfrac{62}{15}}\hspace{10em} 3.\underline{1}\implies \cfrac{31}{1\underline{0}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{62}{15}\div \cfrac{31}{10}\implies \cfrac{62}{15}\cdot \cfrac{10}{31}\implies \cfrac{62}{31}\cdot \cfrac{10}{15}\implies \cfrac{2}{1}\cdot \cfrac{2}{3}\implies \cfrac{4}{3}\implies 1\frac{1}{3}[/tex]

The half-life of this sample is 535.1 days.

Half-life is defined as the time it will took a substance to reduce to half of its initial amount. The half-life of a substance is determined with respect to the rate of the reaction. It can be calculated using the formula below.

N(t) = N₀(1/2)^(t/T)

where N(t) = amount of substance remaining after time t

N₀ = initial amount of substance

t = time

T = half-life

If a sample of a certain substance decayed to 67.8% of its original amount after 300 days, then N(300) = 0.678N₀.

Plug in the given values to the equation.

N(t) = N₀(1/2)^(t/T)

0.678N₀ = N₀(1/2)^(300/T)

0.678 = (1/2)^(300/T)

T = 535.1 days

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Answer:

x=5

Step-by-step explanation:

Follow the steps in the image.

-Hope this helped

Answer:

26x-56y

Step-by-step explanation:

First you open the bracket and collect like terms

55x-29x-46y-10y

26x-56y

The number of soda bottles the machine can make each minute = 40

In this question, we have been given the graph shows the relationship between time and the number of soda bottles a machine can make.

Also, we have been given two points ​(​4,160​) and ​(6​,​240)

We need to find the number of soda bottles the machine can make each minute.

i.e., we need to find the slope of line passing through points  ​(​4,160​) and ​(6​,​240)

Using the formula of slope,

m = (240 - 160) / (6 - 4)

m = 80/2

m = 40

Therefore, the number of soda bottles the machine can make each minute = 40

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Answer:

Step-by-step explanation:

Thevalueof theAC segmentknown asthe AB and BC segmentsis:

AC = 12x + 2y + 18

What is a segment?

It is the distance or vector obtained from the sum of the differences of the coordinates of the ends of that segment.

AB = B - A

What are mathematical operations?

They are those such as addition, subtraction, multiplication and division, being the most basic and also have the roots, exponents, among others ...

Thesumis addition to one number to another.

Subtraction is subtractingone number from another.

Multiplicationis adding the same number as many times as the multiplier indicates.

Divisionis the decomposition or separation of one number from another.

What is the value of AC?

Assume that AC is the length of the segment containing AB and BC.

AC = AB + BC

Being;

AB= 8x + 2y

BC = 4x + 18

Replace

AC = 8x +2y + 4x + 18

AC = 12x + 2y + 18

Answer:Use the slope-intercept form to find the slope.

m=4

The equation of a perpendicular line to

y

=

4

x

−

9

must have a slope that is the negative reciprocal of the original slope.

m

perpendicular

=

-1/4

Step-by-step explanation:

hii lily how are u

( 0 , -1 , 5) point lies on xyz plane .

The xy-plane is the plane that houses the x- and y-axes, while the yz-plane and the xz-plane house the y- and z-axes, respectively. Space is divided into eight sections known as octants by these three coordinate planes. The positive axes determine the first octant, which is in the front.

To be expressed, everything needs a perspective and a point of view. The three spatial dimensions are represented by the X, Y, and Z coordinates. These stand for length, width, and depth. We employ the same X, Y, and Z denotations when referring to machines, but we assign them different values or meanings. Even more intriguingly, there are no clear laws defining the meaning, which makes it difficult to converse on these levels.

this given point lies on xyz plane bcz the point itself shows coordinates which is only possible in xyz plane .

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The solution to the expression given as 5x + 3y > 12 has the ordered pair of (3, 0)

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

5x + 3y > 12

Solving further, we need to collect the like terms

So, the expression becomes

3y > 12 - 5x

Next, we divide through the inequality by 3

So, we have the following representation

y > 12/3 - 5/3x

Evaluate

The equation becomes

y > 4 - 5/3x

At this point, we assume any value for x and then solve for y

Assume that the value of x is 3

So, we have the following representation

y > 4 - 5/3 * 3

Evaluate the products

y > -1

A value greater than -1 is 0

So, we have

x = 3 and y = 0

Express as ordered pairs

(x, y) = (3, 0)

Hence, the ordered pair of the solution is (3, 0)

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Answer:

-0.67

Step-by-step explanation:

What is the slope of the line created by this equation? Round your answer out to the two nearest decimal places. 6x + 9y = 1

_____________________________________________

Slope intercept form solves for y:

y = mx + b when m = slope and b = y-intercept

First, solve for y:

6x + 9y = 1

subtract 6x from both sides:

6x + 9y - 6x = 1 - 6x

9y = 1 - 6x

divide both sides by 9:

9y/9 = (1 - 6x)/9

y = 1/9 - 6/9x

reduce right side:

y = 1/9 - 2/3x

rearrange right side:

y =  - 2/3x + 1/9

Back to the equation: y = mx + b when m = slope and b = y-intercept

your slope is -2/3

in decimal form, rounded to two digits: -0.67

The area of the parallelogram shown is 6.6 square inches.

According to the question,

We have the following information:

We have a parallelogram with base 2.2 inches and height 3 inches.

We know that the following formula is used to find the area of parallelogram:

Area of parallelogram = Base*height

Area of parallelogram = 2.2*3

Area of parallelogram = 6.6 square inches

(Please note that area of any object or figure is always given in square units. For example, it may be square meters, square inches, square feet, etc.)

Hence, the area of the parallelogram shown is 6.6 square inches.

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