Is the following relation a function? Justify your answer.

No, because there is an input value with more than one output value
No, because there is an output value with more than one input value
Yes, because each input value has only one output value
Yes, because each output value has only one input value

Answer:

4x + 4y ≤ 80

6x + 8y ≤ 100

Explanation:

Let's define x as the number of children and y as the number of adults.

For Matinee tickets, they spend $4 per child and $4 per adult, so if the total is no more than 80, we get:

4x + 4y ≤ 80

In the same way, they spend $6 per child and $8 per adult on the evening tickets, so

6x + 8y ≤ 100

Therefore, the system is

4x + 4y ≤ 80

6x + 8y ≤ 100

The volume of a cone is given by the formula:

From the question, we are provided with following:

We have to use the given parameters to obtain the radius of the cone.

Thus, we have:

Therefore, the volume of the cone is:

Hence, the correct option is option BH

Step-by-step explanation:

right, M = ((xa + xb)/2, (ya + yb)/2) = (3.5, 3.5)

the line through O and M (I assume we need the slope-intercept form) is in general

y = ax + b

"a" is the slope, "b" is the y-intercept (the y-value when x = 0).

the slope is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.

so, our 2 points : (0, 0) and (3.5, 3.5).

x changes by +3.5 (from 0 to 3.5).

y changes by +3.5 (from 0 to 3.5).

so, the slope "a" is +3.5/+3.5 = 1.

the point (0, 0) gives us "b" (the y-value when x = 0) directly : 0.

so, the line equation is

y = x

We need 3 cups of spinach for each 1/2 cup of pecans.

Then we have:

Answer: It will be needed 1/3 cup of pecans

Given: A circle has a center point at the coordinates P(3,0) with a diameter line RT where R has the coordinates (-47,25).

Required: To determine the coordinates of T.

Explanation: The given circle is-

Let the coordinates of T be (x,y). Then the center of a circle is divided by the diameter in the ratio of 1:1. The section formula for a point (x,y) dividing a line segment in the ratio of 1:1 is-

Hence, for the given line RT, point P divided RT in 1:1. Thus-

Further solving for x and y as-

Final Answer: The coordinates of T are (53,-25).

Question:

Solution:

A quadratic Equation in Standard Form is given by the following formula:

now, the given equation is

this is equivalent to:

According to the Quadratic Equation in Standard Form, we can conclude that

and

The sampling distribution can be approximated to follow the normal distribution if the sample size is large, and the values of 'np' and 'n(1-p)' are much greater than 10.

Consider option A,

Consider option B,

Consider option C,

Consider option D,

It is observed that only the values in option D, give that 'np' and 'n(1-p)' are greater than 10. Therefore, option D will be the correct choice.

since the student do 32 questions in a time of 28 minutes, then the rate of response is 32/28=8/7 questions/minute ,then the students will be able to complete 160 questions in 20(7)= 140 minutes

Line equation: y = 5

Slope: 0

Intercept: 5

Formule:

. Equation : y = mx + b

. Slope: m = () / ()

Jane, Chau, and Deshaun have $22, $16 and $44 respectively in their wallets.

let x represent represent the amount of Jane.

let Y represent represent the amount of chau.

let z represent represent the amount of Deshaun.

Jane, Chau, and Deshaun have a total of $82"  can be represented as

x + y + z = $82 .......(1)

Deshaun has 4 times what Jane has. It  can be represented mathematically as

y = 2x     .......(2)

Chau has $6 less than Jane. It can be represented mathematically as

z= x- 6   .......(3)

we can now solve the equations using the substitution method

substitute equation (2)  and (3)  into equation (1)

x + y + z = $82

x + 2x + x-6 = $82

4x -6 = $82

4x - 6  = $82

4x = $82 + 6

4x = 88

x = $22

from equation 2

y = 2x

y = 2 x 22 = $44

z = x- 6

z = 22 - 6

z=$16

Jane, Chau, and Deshaun have $22, $16 and $44 respectively in their wallets.

To know more about equation

https://brainly.com/question/16644061

#SPJ1

SOLUTION

We want to solve the expression

Now, use the minus sign to multiply the other part

That is

We have

Hence the answer is 2y - 5

Consider that the experimental probability of an event is based upon the previous trials and observations of the experiment.

The experimental probability of occurrence of an event is given by,

As per the problem, there are a total of 1230 trials of rolling a dice.

And the favourable event is getting a 2.

The corresponding experimental probability is calculated as,

Thus, the required probability is 13.98% approximately.

Theref

In this question, we are given two lines.

1) y = 0.5*2^x

2) y = 2x + 25

The standard equation of a line is y = mx + b, where m is the slope and b is the y-intercept.

The positive slope moves the line upwards and the negative slope moves the line downwards.

If we compare both the equations, we see the 2nd equation maps with the standard line form. Hence, the second equation is a line with the slope equals to 2 and y-intercept equals 25. As the slope is positive, the line is moving upwards.

The standard equation of an exponential function is y = a*b^x, where b is the base, x is the exponent and a is the y-intercept.

The positive value of the base moves the function upwards and the negative value moves it downwards.

If we compare both the equations, we see the 1st equation maps with the standard exponential form. Hence, the 1st equation is an exponent form with the base to 2 and y-intercept equals 0.5. As the base is positive, the line is moving upwards.

Answer:

Graph A

Step-by-step explanation:

It is a function of f(x) = 2

Answer:  B) 46.67% approximately

=================================================

Work Shown:

A = it will be cloudy tomorrow

B = it will be rainy tomorrow

P(A) = 0.30

P(B) = 0.15

P(A and B) = 0.14

Apply the conditional probability formula.

P(B given A) = P(A and B)/P(A)

P(B given A) = 0.14/0.30

P(B given A) = 0.4667 approximately

P(B given A) = 46.67% approximately

Answer:

b)  About 46.67%.

Step-by-step explanation:

Let event A = being cloudy.

Let even B = being rainy.

Given probabilities:

Therefore:

Conditional Probability Formula

[tex]\sf P(B|A)=\dfrac{P(A \cap B)}{P(A)}[/tex]

The probability of being rainy given it is cloudy = P(B | A).

Substitute the given values into the formula:

[tex]\implies \sf P(B|A)=\dfrac{0.14}{0.3}=0.46666...=46.67\%\;(2\;d.p.)[/tex]

Therefore, the probability of it being rainy if you know it will be cloudy is about 46.67%.

It is a cylinder.

1.- Calculate the area of the base and the top

Area = 2*pi*r^2

Area = 2*3.14*5^2

Area = 157 cm^2

Total area of the base and top = 2 x 157 = 314 cm^2

2.- Calculate the perimeter of the circle.

Perimeter = 2*pi*r

Perimeter = 2*3.14*5

Perimeter = 31.4 cm

3.- Calculate the lateral area

Lateral area = 5 x 31.4

Lateral area = 157 cm^2

4.- Calculate the total area = 157 + 314

= 471 cm^2

5.- Result

D. None of the above

The systems of equations which correctly models the situation as described is;

It follows from the task content that the system of equations which models the production process of caffe mocha be determined.

As given in the task content;

Hence, since For each ounce of chocolate syrup, she uses 5 ounces of coffee, the situation can be represented algebraically as;

Also, since she wants to make 48 ounces of caffe mocha; we have;

Therefore, the required system of equations is;

Read more on system of equations;

https://brainly.com/question/13729904

#SPJ1

Explanation

The information given directly by the picture is that:

This means we have a pair of congruent sides and a pair of congruent angles.

We need one more information to prove congruency. There is no way of getting side information, by if we see the vertex C, the angles make a pair of vertical angles. Vertical angles are congruent, so:

This means now that we have 2 pairs of congruent angles and one pair of congruent sides, so we will use either AAS or ASA.

To determine which is the case, we can visualize the order in which the angles and side appear going around the triangle.

We can see that we have an Angle then the side then the other Angle, so the order is Angle-Side -Angle, so the rule we need to use is ASA.

Answer

Angle-Side-Anlge, that is ASA.

Answer:

The design fee is $40.

Step-by-step explanation:

The y intercept means the cost when the number of shirts ordered is 0. This means that in the context of this problem the y intercept is the design fee.

total square feet:

square feet 1:

x > -8

Let the number be represented by x:

Three times the number = 3x

Six minus three times the number = 6 - 3x

Six minus three times the number is less than 30:

That can be interpreted mathematically as:

6 - 3x < 30

To find the value of x:

Step 1: Collect like terms

- 3x < 30 - 6

-3x < 24

Step 2: Divide both sides by 3:

-x < 8

Multiply both sides by (-1) and change the < sign to >

(-1) (-x) > 8 x(-1)

x > -8

By the concept of set builder notification

(b) 4

(c) 6

(d) -6

In mathematics, the set-builder notation is used to express a set's elements or specify the conditions that each member of the set must meet. for instance The notation for the set builder is A = x Z | x 4 for the supplied set A =..., -3, -2, -1, 0, 1, 2, 3, 4. Sets can also be expressed using an interval or an equation by using the set-builder notation. In many cases, sets with an infinite number of elements have their elements written and represented in this way. These include integers, real numbers, and natural numbers, among other popular forms of numbers. One (or more) variables from these categories are utilized in this.

To know more about the set builder ,visit:

brainly.com/question/521552

#SPJ13

To find 27% of 16 using multiplication by a decimal, we can proceed as follows:

First, convert the number 27 in decimal:

A way to estimate the possible value, we can multiply the number 16 by the nearest tenth, that is, 0.3. We know that the possible value is a little greater than the actual value.

We can do this in the following way:

Then, after the estimation, we can say that the value must be less than 4.8. Multiplying by 3 or 30 is easier than by 27. This is a way to check the answer.

We can also say that if we multiply 16 by 3 is 48 (equivalently to 4.8, after doing the correct operations), and this is a quick value to know, that, approximately 4.32 is 27% of 16.

According to the basic definition of probability,

Given that the bin contains total 90 batteries, out of which 24 are duracell.

So the probability that a randomly selected battery is Duracell, is calculated as,

Thus, the probability that a randomly selected battery is Duracell, is 26.7% approximately.

Given the system of equations:

we will find the solution to the system by graphing

To draw the lines, we need to know two points on each line

so, substitute with two values of x and calculate the corresponding value of y

For line (1): y = -2x - 7

so, line (1) passes through the points ( 0, -7) and ( 1, -9)

For line (2): x - y = -8

y = x + 8

So, line 2 passes through the points ( 0, 8) and ( 1, 9)

The graph of the line will be as shown in the following picture

As shown in the figure:

Line (1) is the blue line

Line (2) is the red line

The point of intersection = ( -5, 3)

So, the solution is point ( -5, 3)

Arjun applied the wrong laws of logarithms.

The question can be solved as shown below:

Step 1: Apply the addition rule of logarithm given as

Thus, we have:

Step 2: Apply the subtraction rule of logarithm given as

Thus, we have:

Therefore, the correct answer is:

we can do a subtraction to calculate the savings

will save 3.46 buying store-brand laundry detergent

and your savings from using the coupon are 1.95

We make a subtraction between the savings to know how much you save more with one method than with the other

she save $1.51 more buying store-brand

Given that

The cost per ton f(x) to build an oil platform of x thousand tons is approximated by

The cost per ton for x = 30, i.e f(30) will be

Hence, the answer is 403.226 (3 d.p)

Answer:

20% means divide by 5 so 100 * 5 = 500

Step-by-step explanation:

because 20% of 500 is 100

Hello!

Original Question: 20% of blank = 100

 ⇒ 20% = [tex]\dfrac{20}{100} =0.2[/tex]

    ⇒ 0.2 of blank ⇒ 0.2 * blank = 100

Let's solve:

   [tex]0.2 *\text{blank}=100\\\\blank = \dfrac{100}{0.2} = 500[/tex]

Thus blank is 500!

Answer: 500

Hope that helps!