Which of the following types of functions have inverse functions?
A.May-to-one
B.One-to-many
C.One-to-one
D.Many-to-many​

Answer:

No

Step-by-step explanation:

To prove 2 triangles an congruent we need three pieces of information

SSS or SAS or ASA or RHS

S - Side

A - Angle

R - Right angle

H - Hypotenuse

We have an angle side and another side

So these two triangles can be proved congruent by SAS

Hope this helped and have a good day

If R is (7,5), i. find the coordinates of Q and S​ are (-2, 3) if the are adjacent

You should understand that two adjacent sides can intersect if they continue to be drawn

The two given equations are

5x-y=-7 and

3x-8y=18

Using elimination method to solve for x and y we have

3(5x-y=-7) = 15x -3y = -21

Also, 5(3x-8y=18) = 15x-40y=90

Solving the two equations simultaneously we have

(15x-40y=90)-(15x-3y=-21)

Subtracting to have

-37y = 101

Making y the subject we have y≅3

Putting y≅3 in equation 1

5x-y=-7

5x+3=-7

5x=-10

x=-2

Therefore the coordinates of Q and S are (-2, 3)

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Answer:

7^6

Step-by-step explanation:

7 to the power of 6

Answer: [tex]7^{6}[/tex]

Step-by-step explanation:

Exponential form denotes how many times a value is multiplied by itself.

This is 7 times itself 6 times, so it is written as 7 with a 6 in the top right corner.

Answer:

Angle = 71.08°

Step-by-step explanation:

Since we're given all of the sides, we're able to use any one of the trigonometric proportions.  I can go through all three to show how they all yield the same answer.

The sine proportion is [tex]\frac{opposite}{hypotenuse}[/tex]

Using the ? angle as our reference angle (which we can refer to as "a" for the sake of the math), the side measuring 70 units is the opposite side and the side measuring 74 units is the hypotenuse:

[tex]sin (a)=\frac{70}{74}\\ sin^{-1}=\frac{70}{74}=a = 71.07535558=71.08[/tex]

The cosine proportion is [tex]\frac{adjacent}{hypotenuse}[/tex]

Using a as our reference angle still, the side measuring 24 units is the adjacent side and the side measuring 74 units is the hypotenuse:

[tex]cos (a)=\frac{24}{74}\\ cos^-^1=\frac{24}{74}=71.07535558=71.08[/tex]

The tangent proportion is [tex]\frac{opposite}{adjacent}[/tex]

Using a as our reference angle still, the side measuring 70 units is the opposite side and the side measuring 24 units is the adjacent side:

[tex]tan(a)=\frac{70}{24}\\ tan^-^1=\frac{70}{24}=a=71.07535558=71.08[/tex]

Again, just use the steps for either one of the three trigonometric proportions

The probability that a person selected at random will live on campus OR have a low intention of attending the Fair is 0.584.

The data of Intention of Attending the Fall Career Fair is given below:

                           High                Medium                 Low               TOTAL

On Campus         99                       102                     22                   223

Off Campus         78                        80                      43                   201

>20 mi. Away      18                         32                      26                    76

TOTAL                 195                      214                     91                     500

We have to find the probability that a person selected at random will live on campus OR have a low intention of attending the Fair.

Probability that a person selected at random will live on campus OR have a low intention of attending the Fair = P(on campus) + P(low) - P(on campus and low)

Probability that a person selected at random will live on campus OR have a low intention of attending the Fair = 223/500 + 91/500 - 22/500

Probability that a person selected at random will live on campus OR have a low intention of attending the Fair = 292/500

Probability that a person selected at random will live on campus OR have a low intention of attending the Fair = 0.584

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The right question is:

The data shown below is for a sample of LSU students to evaluate their intention of attending the Fall 2023 Career Fair based on where they live.

                         Intention of Attending the Fall Career Fair

                           High                Medium                 Low               TOTAL

On Campus         99                       102                     22                   223

Off Campus         78                        80                      43                   201

>20 mi. Away      18                         32                      26                    76

TOTAL                 195                      214                     91                     500

What is the probability that a person selected at random will live on campus OR have a low intention of attending the Fair?

Answer: 34.51 dollars

Step-by-step explanation:

19 percent is the same as 0.19

Multiply the percent by the amount to find the percent of that number

29*0.19=5.51

Add the tip to the original amount

5.51+29=34.51

The distances between the points are given as follows:

As these two distances are equal, point A is equidistant from the endpoints of segment BC.

The distance between points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by the equation presented as follows:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Hence the distance of point A to the endpoint B is calculated as follows:

[tex]D = \sqrt{(7 - (-7))^2 + (0 - 8)^2} = \sqrt{260}[/tex]

The distance of point A to the endpoint C is calculated as follows:

[tex]D = \sqrt{(-5 - (-7))^2 + (-8 - 8)^2} = \sqrt{260}[/tex]

As the distance from point A to point B is equals to the distance from point A to point C, the point A is equidistant from the endpoints of segment BC.

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The area of the new rectangular bedroom represented by A'B'C'D 330.75 square feet.

We have that the dimensions of the bedroom on the drawing represented by ABCD are 4.5 inches by 6 inches, using a scale factor of 1 inch = 3.5 feet, we will have the dimensions of the new rectangular bedroom A'B'C'D as;

4.5 × 3.5 feet = 15.75 feet by

6 × 3.5 feet = 21 feet

area the new rectangular bedroom A'B'C'D = 15.75 × 21 square feet

area the new rectangular bedroom A'B'C'D = 330.75 square feet.

Therefore, 330.75 square feet is the area of the new rectangular bedroom represented by A'B'C'D.

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The probability of odds as a decimal rounded to the nearest hundredth is 0.398.

The probability of odds is given by the formula -

Probability of odds = probability odds ÷ probability (1 + odds)

Probability odds = 0.66

Probability (1 + odds) = 1 + 0.66

Performing addition on Right Hand Side of the equation

Probability (1 + odds) = 1.66

Keep the values in formula to find the probability of odds

Probability of odds = 0.66/1.66

Performing division on Right Hand Side of the equation

Probability of odds = 0.398

Hence, the probability of odds is 0.398.

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1. Move 12 to the right side.

2. Divide both sides by -7.

3. Simplify.

4. Square both sides.

5. Solve [tex]x-5=\frac{64}{49}[/tex]

Hence, our solution.

_______________________

Hope this helps!

The trigonometric equation be tan(-x)cos(-x) then we get -sin (x).

A function of an angle is a trigonometric function. They are utilized to connect the triangle's angles and sides' lengths.

Trigonometry is the study of angles and the angular connections between figures in two and three dimensions. The trigonometric functions that make up trigonometry are cosecant, cosine, cotangent, secant, sine, and tangent. These are also known as the circle functions.

Trigonometry is used to define directions such as the north, south, east, and west. It also tells you the direction to point the compass in order to travel straight forward. It helps to locate a certain location during navigation. The shore's separation from a certain place in the sea can likewise be determined using this method.

Let the given function be tan (-x) cos (-x)

Use the negative angle identity: tan (-x) = -tan (x)

= cos (x) (-tan (x))

Remove parentheses: (-a)= -a

= -cos (x) tan (x)

Express with sin, cos

= -sin (x)

Therefore, simplifying the equation, tan(-x)cos(-x) we get -sin (x).

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tan(-x).cos(-x) = -sin(x)

What are trigonometric ratios?

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle. Trig ratios are therefore assessed in relation to sides and angles.are therefore assessed in relation to sides and angles.

We know that, tan(x) = sin(x)/cos(x)

Now, calculating tan(-x).cos(-x)

⇒ [tex]\frac{sin (-x).cos (-x)}{cos (-x)}[/tex]

⇒ sin(-x)

Since, sin function is an odd function, it can be expressed as below.

sin(-x) = -sin(x)

Thus, tan(-x).cos(-x) = -sin(x)

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The rate of change of the volume when radius of sphere is 11 inch is 2904π inch³/minutes

According to the question,

The radius r of a sphere is increasing at a rate of 6 inches per minutes

Volume of sphere is 4/3 πr³

We have to find Rate of change of volume when r = 11 inch

Differentiating volume of sphere w.r.t time

V = 4/3 πr³

=> dV/dt = 4 πr² . dr/dt ---------(1)

As it is given that ,

dr/dt = 6

Substituting the value in equation (1)

=>  dV/dt = 4 πr² . 6

=> dV /dt = 24 πr²

r = 11

=> dV /dt = 24 π(11)²

=> 2904 π inch³/minutes is rate of change of volume

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For the given algebaric expression, 1.4f+1.1=8.3−f where "f " is variable the solved value of "f" is 3..

We have an algebraic expression of one variable say f ,

1.4 f + 1.1 = 8.3 - f --(1)

we have to solve it

Step 1 : Multiply both sides by 10

1.4 f ×10 + 1.1 ×10 = 8.3×10 - f ×10

=> 14/10(10f) + 11/10(10) = 83/10(10) - 10f

=> 14f + 11 = 83 - 10f

Step 2 : Subtract 11 from both sides

=> 14f + 11 - 11 = 83 - 10f -11

=> 14f = 72 - 10f

Step 3 : Add 10f both sides

=> 14f + 10f = 72 - 10f + 10f

=> 24f = 72

Step 4 : Divide both sides by 24

=> 24f/24 = 72/24

=> f = 3

Hemce,the solved value of "f" is 3 ..

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There are 195 natural numbers from 1 to 600

The term integer is referred as the combination of zero, natural numbers and their additive inverse

Here we need to find how many of the natural numbers from 1 to 600, inclusive, contain the digit 5 at least once.

While we looking, into the given range of numbers 100 integers from 500 - 599 contain at least one 5

And here we know that in each of the 499 integers

=> _5, _15, _25, _35, _ 45, _55 , _65, _ 75, _ 85 , _ 95

And we also know that in each hundred  from 1 to 499 contain at least one 5

Therefore, there are 5 sets of these = 5 * 10  =  50

So, in each hundred from 1 to 499 we have the  integers

Therefore, _5_   where the last digit is not a 5

So, we have 9 of these in every hundred

Then here we have  5 * 9  = 45 of these

=> 100 + 50 + 45  = 195

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As per the normal distribution, the probability that x is less than or equal to 38 is 0.9861.

Probability:

In math, probability denotes a  branch of mathematics concerning numerical descriptions of how likely an event is to occur.

Given,

Here let x be a normally distributed random variable with mean 5 and standard deviation 15. please express your answer as a number between 0 and 100. if you want to write 52%, please enter 52.

Here we need to find the probability that x is less than or equal to 28.

According to a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

Here first, we have to solve for the z-score using the formula below.

=> z-score = (x – μ) / σ

Here x refers the individual data value = 38

μ refers mean = 5

σ refers standard deviation = 15

Then when we apply the values on it, then we get,

=> z-score = (38 - 5) / 15

=> z-score = 33 / 15

=> z-score = 2.2

Then the probability that corresponds to the z-score in the z-table.

=> probability = 0.9861

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The 95% confidence interval for the variance in the pounds of impurities would be (3.829, 14.121).

In the given question, the quality-control manager of a chemical company randomly sampled twenty 100-pound bags of fertilizer to estimate the variance in the pounds of impurities.

The sample variance was found to be 6.62.

We have to find a 95% confidence interval for the population variance in the pounds of impurities.

From the question,

N=20,

s^2=6.62

So, the Standard Deviation(SD) = √s^2

SD = √6.62

SD = 2.573

The confidence interval for the population variance is given by the following formula:

[tex]\frac{(n-1)s^2}{ \chi_{\alpha/2}} \leq\sigma^2\leq \frac{(n-1)s^2}{ \chi_{1-\alpha/2}}[/tex]

On this case the sample variance is given and for the sample deviation is just the square root of the sample variance.

The next step would be calculating the critical values. First we need to calculate the degrees of freedom given by:

df = n-1

df = 20-1

df = 19

Since the Confidence is 0.95 or 95%, the value of α=0.05 and α/2=0.025, and we can use excel, a calculator or a table to find the critical values.  

The excel commands would be: "=CHISQ.INV(0.025,19)" "=CHISQ.INV(0.975,19)".

So for this case the critical values are:

[tex]\chi_{\alpha/2}[/tex] = 32.852

[tex]\chi_{1-\alpha/2}[/tex] = 8.907

Now putting the value in the formula:

[tex]\frac{19\times6.62}{32.852}\leq\sigma^2\leq\frac{19\times6.62}{8.907}[/tex]

3.829≤σ^2≤14.121

So the 95% confidence interval for the variance in the pounds of impurities would be (3.829, 14.121).

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The length of the Hypotenuse for the given right angle triangle, is 10√5.

What is Hypotenuse?

A right-angled triangle's longest side, or the side opposite the right angle, is known as the hypotenuse in geometry. The Pythagorean theorem states that the hypotenuse's square length equals the sum of the squares of the lengths of the other two sides, and this can be used to determine the hypotenuse's length.

Let the two sides of right angle triangle are, a = 20 and b = 10.

We have to find the length of Hypotenuse.

Let x be the length of Hypotenuse.

So, by using the Pythagoras theorem,

[tex]a^2 + b^2 = x^2[/tex]

Plug a = 20, b = 10

[tex](20)^2 + (10)^2 = x^2\\400 + 100 = x^2\\500 = x^2\\x^2 = 500\\x = 10\sqrt{5}[/tex]

hence, the length of the Hypotenuse for the given right angle triangle, is 10√5.

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Monomial has a degree of 4 in linear equation.

What in mathematics is a linear equation?

The algebraic equation y=mx+b is known as a linear equation. with m the slope and b the y-intercept as the single constant and a first-order (linear) term.

                       Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let's define some of the vocabulary words so we can understand what is being asked.

trinomial: 3 terms   → each term is separated by a plus or minus sign

                              Example: 5x² + 3x + 2

monomial: 1 term   →  no plus or minus sign exists in the term.

                              Example: 5x²

degree: the largest exponent → it can be in any of the terms.

                              Example: 5x² has a degree of 2

It is possible that a monomial has an exponent greater than that of a trinomial so the answer is NO!

trinomial:   5x² + 3x + 2      has a degree of 2

monomial: 5x⁴                    has a degree of 4

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the formula for y after a 15 percentage of increase will be y=1.15x

What is the Percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term per cent signifies. The letter "%" stands for it.

Example percentages include:

There is no dimension to percentages. As a result, it is known as a dimensionless number. When we say a number is 50% of anything, we imply that it is 50% of everything.

As in 0.6%, 0.25%, etc., percentages can also be expressed as decimals or fractions. The grades earned in any topic are calculated in terms of percentages in academics.

if there is a 15 percent increase in the initial value then the value will be y = 1.15x

y is the price after the  increase

x is the price before the increase

so the increase in the price will be x+ 15 percentage  of x

y= x+15/100 x

y=x+0.15x

y=1.15x

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Answer:

Step-by-step explanation:

ans will be (c) 11 cm, 7 cm, 2 cm

Step-by-step explanation:

Though the sum of any two sides of a triangle should be always greater than the third side i.e.,

11 + 7 > 2

7 + 2 = 9 < 11

so, no triangle can be formed of such sides.

The solution to the equation in surd form is x = 5 ± √41/2

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

2/x + 5/(x+2) = 1

Take the LCM

So, we have the following equation

(2(x + 2) + 5x)/x(x + 2) = 1

So, we have

(2(x + 2) + 5x) = x(x + 2)

Open the brackets

2x + 4 + 5x = x² + 2x

Evaluate the like terms

x² - 5x - 4 = 0

Using a quadratic formula, we have

x = 5 ± √[(-5)² - 4 * 1 * -4]/2 * 1

So, we have

x = 5 ± √41/2

Hence, the solution is x = 5 ± √41/2

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The expression to determine the number of bags is 2/3 x = 2 1/2 and the number of bags requited is 3 3/4 bags

Information from the problem

Maya rakes up the leaves and wants to put them into bags that hold 2\3 of a cubic yard

she rakes 2 1\2 cubic yards of leaves

one bag = 2/3 cubic yard

total leaves raked = 2 1/2 cubic yard

the number of bags required is how many 2/3 cubic yards are there in 2 1/2 cubic yard. this is solved by division

let the number of bags be x

2/3 cubic yard * x = 2 1/2 cubic yard

2/3 x = 2 1/2

x = (2 1/2) / (2/3)

x = 15/4

x = 3 3/4 bags

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The volume of an object is  length × width × height.

What is three dimension geometrical shape?

3D forms are three-dimensional solid shapes or figures in geometry. Typically, the dimensions of 3D objects are length, breadth, and height. These shapes are known by the common names cube, cuboid, cone, cylinder, and sphere. The characteristics of 3D shapes, such as their edges, faces, vertices, curved surfaces, lateral surfaces, and volumes, determine what they are.

In our daily lives, we encounter many items of all sizes and shapes. Golf balls, doormats, ice cream cones, Coke cans, and other items are available. The various 3D shapes, surface area, and volumes, as well as the method of creating 3D shapes utilizing nets with the aid of 2D Shapes, will all be covered in this article.

A rectangular prism's volume can be calculated by multiplying its base area by its height. A rectangular prism's area will be l × w since its base is also a rectangle. The volume of the prism is then calculated by multiplying this area by the prism's height. As a result, another method to construct this formula is to multiply the prism's length, breadth, and height and then convert the result to cubic units.

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Answer:

1/2

Step-by-step explanation:

Find the following limit:

lim_(x->∞) (x + 1)/(1 x + sqrt(x)^2 + 1)

(x + 1)/(1 x + sqrt(x)^2 + 1) = (x + 1)/(2 x + 1):

lim_(x->∞) (x + 1)/(2 x + 1)

The leading term in the denominator of (x + 1)/(2 x + 1) is x. Divide the numerator and denominator by this:

lim_(x->∞) (1 + 1/x)/(2 + 1/x)

The expressions 1/x and 1/x both tend to zero as x approaches ∞:

Answer: 1/2

Answer:

1) y = -x -1

2) y + 4 = 3( x -2)

3) y = x + 1

Step-by-step explanation:

1)

The slope is the change in y over the change in x.  The y values from the points given is 0 and -1.  The x values from the points given is -1 and o

Slope: [tex]\frac{o - -1}{-1 - o}[/tex] = [tex]\frac{1}{-1}[/tex] = -1

y -intercept

y = mx + b  Use the point (0,-1) and the slope to solve for b

y = -1

m = -1

x = 0

y = mx + b

-1 = -1(0) + b

-1 = 0 + b

-1 = b  This is the y intercept.

y = mx + b

y = =x -1

2)

point-gradient form is

y -y = m (x-x)

y - -4 = 3 (x -2)

y + 4 = 3( x - 2)

3)

Parallel lines have the same slope.

slope is 1.  Use this and the point (0,1) to solve for b

y = mx + b

1 = 1(0) + b

1 = 0 + b

1 = b

y = x + 1

Based on the information provided, the archaeological sample's estimated age is = 0.214136  years

Half life given is 5730

t₆.₅ = Ln2/k

k= ln 2/ 5730

The rate constant ,

k = 0.00012 year⁻¹

Given that 23 % of the 14C remains

then |A1|/|A2|  = 0.23

As we know ,

|A1|/|A2| = e ⁻₍kt₎

Hence, on solving the equation we get ,

ln(0.23)= -1.46967

t = -0.31471/ --1.46967

= 0.214136 years

The amount of time needed for a quantity (of substance) to decrease to half of its initial value is known as the half-life (symbol t12). In nuclear physics, the phrase is frequently used to indicate how rapidly unstable atoms decay radioactively or how long stable atoms last. The phrase is also used more broadly to describe any kind of exponential decay (or, very infrequently, nonexponential decay).

The biological half-life of medications and other compounds in the human body, for instance, is a term used in the medical sciences. Half-opposite life's in exponential growth is time's doubling.

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Answer:4.50t + 6.75b = 576

Step-by-step explanation:

Answer:

Check below/above

Step-by-step explanation:

A) The graph passes through the point (0,1).

The domain is all real numbers.

The range is y>0.

B) it would be a linear equation that shifts the graph vertically.

C) the slope of an exponential function continues to increase, while the slope of a linear function stays the same.