Identify the domain and range of the relation, and determine whether the relation is a function.
{(0, 3),(-1/3,0),(-5, 2),(1/3,4)}

6 is the intersection point mean in the given situation.

Two or more expressions with an Equal sign is called as Equation.

Given that Andre started with $15 and deposits $5 per week.

Noah started with $2.50 and deposits $7.50 per week.

Noah's Savings is given and his equation is y = 7.5x + 2.5, where x represents the number of weeks and y represents his savings.

The equations for Andre's savings is y = 5x + 15

The intersection point of the two equations is the point at which both Andre and Noah have the same amount in their savings.

5x+15=7.5x + 2.5

Subtract 7.5x on both sides

-2.5x + 15 = 2.5

Add 2.5x to both sides

Divide both sides by 2.5

x = 6

Hence, 6 is the  intersection point mean in this situation.

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Answer:

15t-94=103

Step-by-step explanation:

hav a nice day

Answer:

You already wrote the sentence, so im guessing that you want the equation...

(15)(t) - 94 = 103

Answer: f(x) has an axis of symmetry at x = 4 and h(x) has an axis of symmetry at x = -2

Step-by-step explanation:

You can easily find the axis of symmetry by investigating around which line the functions are symmetrical about

for instance, in h(x), the graph is symmetrical on either side of x = -2, meaning that the line x = -2 cuts the parabola in 'half'

in f(x), this is a little harder to think about, but if you know how the graph will be shifted on the x-axis you can figure it out! In this case (x-4)^2 means that the graph will be shifted on the x-axis 4 units to the right (or from the origin to +4 on the X axis)

as such the line x = 4 will cut the function f(x) in 'half'

The money was invested for 8.60 years

Given:

Amount in the savings account = $2750

Amount invested = $2000

rate = 4.36% = 0.0436

To find:

the time it took to invest the money to obtain the amount in the account

The investment was done using simple interest. So to get the time, we will apply simple interest formula

Answer:

7

Step-by-step explanation:

pretty sure its seven

Step-by-step explanation:

2x-1 - (4/(2x-1)) + 5

2x^2 -4x -2 -4 + 10x - 5

2x^2 +6x -11

The point of intersection is (3,3)

What is meant by intersection?

The intersection points show where both equations have their answers. To put it another way, the intersection point is the answer to both equations. There are multiple intersecting points if there are multiple solutions that satisfy both equations.

If we plot a function, y = f(x), and its inverse, y = f1(x), we can see that the inverse function is the exact opposite of the original function with regard to y = x.

Consequently, only when y = x can both intersect as show in the fig.

Therefore A place where the lines y and x cross must be there.

Find the spot that the line y = x meets at this time.

Of course, the line y = x is satisfied at only one point, which is (3,3).

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Answer:

yes

Step-by-step explanation:

12+3=5x-3+3

15=5x

15=5(3)

15=15

Answer:

\(P(z<\frac{a-\mu}{\sigma})=0.10\)

and we can set up the following equation

tex]z=-1.282<\frac{a-104.5}{23.62}\)

And if we solve for a we got

\(a=104.5 -1.282*23.62=74.22\)

And the best answer for this case would be:

b) $74.23

Step-by-step explanation:

Let X the random variable that represent the stocks price of a population, and for this case we know the distribution for X is given by:

\(X \sim N(104.5,23.62)\)  

Where \(\mu=104.5\) and \(\sigma=23.62\)

For this part we want to find a value a, such that we satisfy this condition:

\(P(X>a)=0.90\)   (a)

\(P(X<a)=0.10\)   (b)

As we can see on the figure attached the z value that satisfy the condition with 0.10 of the area on the left and 0.90 of the area on the right it's z=-1.282. On this case P(Z<-1.282)=0.10 and P(z>-1.282)=0.90

If we use condition (b) from previous we have this:

\(P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.10\)  

\(P(z<\frac{a-\mu}{\sigma})=0.10\)

and we can set up the following equation

tex]z=-1.282<\frac{a-104.5}{23.62}\)

And if we solve for a we got

\(a=104.5 -1.282*23.62=74.22\)

And the best answer for this case would be:

b) $74.23

Answer:

  C  2.35 x 10¹¹

Step-by-step explanation:

You want the number 235,000,000,000 written in scientific notation.

The exponent of 10 when a number is written in scientific notation is the same as the exponent of 10 for the most significant digit when the number is written in expanded form using exponents.

  235,000,000,000 = 2×10¹¹ +3×10¹⁰ +5×10⁹ +0×10⁸ +... +0

The place value multiplier for the most-significant digit is 10¹¹, so this is the multiplier when the number is written in scientific notation.

  2.35×10¹¹

As a first step we are going to fill the empty blanks with zeros, and then since the number that we are trying to subtract is greater than the digit that is on the bottom, we can ''borrow'' one digit from the number on the left, like this:

As we can see, we borrow one to 7, then remaining is 6:

Answer:

Yes

Step-by-step explanation:

Yes.  They did exponents and grouping symbols first, then multiplication and division left to right.  Addition came before multiplication and division because it was inside a grouping symbol.

Part A:

The required graph of the function is described.

The vertex of the function is (7,0)

The domain is : (-∝ , ∝) and

The range is : [0,∝), {yIy ≥ 0}

Part B:

The transformation which occurs from f(x) to h(x) is a vertical shift up to 2 units.

Expressions separated by an equal sign are functions. Both dependent and independent variables are present.

Given Part A:

given the function is g(x) = I x - 7 I

hence from the function, vertex = (h,k)

h = 7 and k = 0

(h,k) = (7,0)

Find the domain by finding where the function is defined.

therefore, domain =  (-∝ , ∝) , where {xIx ∈ R}

The range is the set of values that corresponds with the domain.

therefore, range =  [0,∝), {yIy ≥ 0}

Part B:

given the parent function is:  f(x) = |x|

which is transformed to h(x) = |x| + 2

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x axis or y axis, and if there is a vertical stretch.

Parent function = f(x) = |x|

Horizontal shift = none

Vertical shift = up 2 units.

Reflection about the x axis = none

hence from the function we can determine the vertex (h,k)

= (0,2)

Find the domain by finding where the function is defined.

therefore, domain =  (-∝ , ∝) , where {xIx ∈ R}

The range is the set of values that corresponds with the domain.

therefore, range = [2,∝) ,  {yIy ≥ 2}

Hence, we get the required answers.

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The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.

We have,

To evaluate the limit of the expression as x approaches 0, we can simplify the expression first.

The expression is given as lim(x approaches 0) (cosec(2x) - x cosec³(x)).

Using trigonometric identities, we can rewrite cosec(2x) as 1/sin(2x) and cosec³(x) as 1/(sin(x))³.

Substituting these into the expression,

We get lim(x approaches 0) (1/sin(2x) - x (1/(sin(x))³)).

Now, let's evaluate the limit term by term:

lim(x approaches 0) (1/sin(2x)) = 1/sin(0) = 1/0 (which is undefined).

lim(x approaches 0) (x (1/(sin(x))³))

= 0 (1/(sin(0))³)

= 0 x 1/0 (which is also undefined).

Since both terms of the expression are undefined as x approaches 0, we cannot determine the limit of the expression.

Therefore,

The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.

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Answer:

Step-by-step explanation:

(c) The number of gadgets the company must produce and sell in order to incur the least cost = 40 gadget.

We experienced a few technical difficulties when trying to submit the answers for (a) and (b) questions, but we made it much easier because we have the screenshots and we have attached it in the diagram below.

Thanks

If the reading on a mercury manometer at 25 C is 56.38 cm the local acceleration of gravity is 9.832m.s^-2 atmospheric pressure is 101.78kpa The absolute pressure in kpa being measured is: 176.803kPa.

Using this formula

Pabs=Pg+Patm

Where:

Pabs= Absolute pressure.

Patm=Atmospheric pressure

ρm=Density of mercury

g=Acceleration of gravity

h=Reading on a mercury manometer

Let plug in  the formula

Pabs=101.78×10³Pa+( 13.534×10³kg/m×9.832 m/s²×0.5638 m.

Pabs=101.78×10³Pa+75.023×10³kg/m.s²

Pabs=101.78×10³Pa+75.023×10³Pa

Pabs=176.803×10³Pa

Pabs=176.803kPa

Therefore If the reading on a mercury manometer at 25 C is 56.38 cm the local acceleration of gravity is 9.832m.s^-2 atmospheric pressure is 101.78kpa The absolute pressure in kpa being measured is: 176.803kPa.

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Answer:

The  decision rule is  

Reject the null hypothesis  

The conclusion is  

There is sufficient evidence to conclude that the population proportion of people who can correctly match a dog to their owner (out of two options) is better than just guessing

Step-by-step explanation:

From the question we are told that

   The sample size is n =  16  

   The population proportion =  0.5

     The number that of students that picked out the teachers dog is k  =  14

Generally the sample proportion is mathematically represented as

       \(\^ p  =\frac{k}{n}\)

=>     \(\^ p  =\frac{14}{16}\)

=>     \(\^ p  = 0.875 \)

The null hypothesis is  \(H_o :  p = 0.5\)

The null hypothesis is  \(H_o :  p >  0.5\)

Generally the test statistics is mathematically represented as

   \(z  =  \frac{\^  p  -  p }{\sqrt{ \frac{p(1- p )}{n} }  }\)

    \(z  =  \frac{0.875   -  0.50 }{\sqrt{ \frac{0.50 (1- 0.50 )}{16} }  }\)

    \(z  = 3\)

Generally the p-value is mathematically represented as

    \(p-value  =  P(Z > 3)\)

From the z table the probability of  Z>3  is mathematically represented as

      \(P(Z > 3) =  0.0013499\)

So

   \(p-value  =  0.0013499 \)

Let  assume the level of significance is  \(\alpha = 0. 05\)

Generally from the value  obtained we see that \(p-value  <  \alpha\) Hence  

The  decision rule is  

Reject the null hypothesis  

The conclusion is  

There is sufficient evidence to conclude that the population proportion of people who can correctly match a dog to their owner (out of two options) is better than just guessing

Answer:

x= 30

Step-by-step explanation:

angle AOB= 180- 4x

angle AOC is a right angle because OA is perpendicular to OC

180- 4x + x = 90 degrees

180- 3x = 90 degree

180- 90 = 3x

90= 3x

therefore x= 90/3= 30

Answer:

it is 16

Step-by-step explanation:

do 2x2x2x2 which will give you 16

Vertical lines have the form x = a, where a stands for the common x-coordinate of all points, while horizontal lines have the form y = b, where b denotes the y-intercept. Horizontal lines run left to right.

The link between two expressions on either side of the sign is represented by a mathematical equation. One variable and an equal sign are typically present. For instance, 2x – 4 = 2.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

Expressions that equal one another are the building blocks of an equation. The equation 4x2+3x = 22. A formula is an equation that has at least two variables and depicts the relationship between them.

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The volume of the sphere is approximately 3431.82 cubic miles.

To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.

In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.

C = 2πr

60 = 2πr

Divide both sides of the equation by 2π:

r = 60 / (2π)

r = 30 / π

Now that we have the radius, we can use the formula for the volume of a sphere:

V = (4/3)πr³

V = (4/3)π(30/π)³

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)(27000/π²)

V = (4/3)(27000/9.87) (approximating π to 3.14)

V ≈ 3431.82 cubic miles

Therefore, the volume of the sphere is approximately 3431.82 cubic miles.

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Question

You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?

Answer:

Explanation:

Let's go ahead and find the product as shown below;

Note that i^2 = -1, so we'll have;

Answer:

For 49 photos it takes 14 minutes.

Step-by-step explanation:

28 photos take 8 minutes

(21 + 28) 49 photos take x minutes

x = (49 * 8)/28

x = 14

Answer: $19.10

Step-by-step explanation:

To be honestly im not sure if this is 100% correct but, i did the work so it should be. So what i did was move the decimal from $27.50 one place to the left which is= 2.750. i then rounded the easiest number which then gave me the answer $2.80. Now the percentage, its 30% so you then change it to .30

then you multiply that number (.30 which is basically 3) with $2.80.

$2.80

x   .30

--------

you then get $8.40

which is the total cost of tax AND tip.

you subtract that with the cost of the dinner. ( $27.50 - $8.40 ) and you get the answer $19.10! I hope this helps! :))

Step-by-step explanation:

Define the problem and write what you know

a square has 4 sides that are all equal

the perimeter is the sum of all sidelengths

to find the side lengths: 23.8 / 4 sides

Answer:

one side =5.95

Step-by-step explanation:

perimeter =l+l+l+l

=l4

23.8÷4

=5.95

Answer:

1575

Step-by-step explanation:

3/8 as a decimal is .375. Multiply 4200 by .375 to get your answer.

Answer:

40°

Step-by-step explanation:

x +2x+50=180 [sum of interior angles of a triangle]

or,3x=180-50

or,x=130/3

x=130/3

2x=2×130/3