What is the value of 4p − 2, when p = 8

Final answer:

The direct variation equation relating Lee's pay (x) to the hours worked (y) is y = 7.60x. Lee's pay for working 25 hours in a week is $190.

Explanation:

Let's define the direct variation equation:

y = kx

We can substitute the information given in the question:
When x = 6.5, y = 49.40
49.40 = 6.5k
k = 49.40 / 6.5
k = 7.60

Therefore, the direct variation equation relating Lee's pay (x) to the hours worked (y) is y = 7.60x.

To find Lee's pay if she works 25 hours, we can substitute x = 25 into the equation:
y = 7.60(25)
y = 190

Lee's pay for working 25 hours in a week is $190.

Answer:

D. ; each drink cost $3

Step-by-step explanation:

Given that Elizabeth bought 4 drinks and some nachos.

Total amount spent = [tex]18[/tex]$

She can buy only in integers the drinks i.e.1,2,or 3

Nachos also she can buy 1,2...

If x is the no of nachos and d the cost of drink, we get

[tex]6x+4d=18[/tex]

If x=1, d =3

x=2, d = 1.50

d=3, d=0 (which is not possible)

Hence d can take values either as 3 or 1.50

Out of the options given 3 is only there.

D. ; each drink cost $3

12 times 9 = 108, 18 times 6 = 108, 27 times 4 = 108 and 36 times 3 = 108.

Multiplication is an operation that represents the basic idea of repeated addition of the same number.

Given that, what times what equals 108,

Below is a list of all the different ways that what times what equals 108.

12 times 9 equals 108

18 times 6 equals 108

27 times 4 equals 108

36 times 3 equals 108

54 times 2 equals 108

108 times 1 equal 108

Hence, 12 x 9 = 108. 18 x 6 = 108. 27 x 4 = 108. 36 x 3 = 108.

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There are multiple pairs of numbers that multiply to 108, such as 1 × 108, 2 × 54, 3 × 36, 4 × 27, 6 × 18, and 9 × 12. Therefore, any pair of these factors will correctly answer the question.

To determine what times what equals 108, we need to identify the factors of 108.

1 × 108 = 108

2 × 54 = 108

3 × 36 = 108

4 × 27 = 108

6 × 18 = 108

9 × 12 = 108

There are multiple pairs of numbers that, when multiplied together, equal 108. Therefore, any of these factor pairs are valid answers to the question.

For example, 9 times 12 or 6 times 18 are pairs that satisfy this condition.

A. how many minutes will it take the machine to use all the dough?

We are given the formula:

d (m) = - 5 m + 320

To find for the value of m when all dough is used, we set d (m) = 0:

0 = - 5  m + 320

m = 320 / 5

m = 64 minutes

B. The domain is time and time can never be negative so it always starts at zero, so at time = 0, the range d (m) is:

d (m) = - 5 (0) + 320

d (m) = 320

The other domain and range is already described in (A.), when all dough is used up.

So the pair of reasonable domain and range is:

(0, 320), (64, 0)

The volume of the cone is one-third of the volume of the cylinder which is equal to the product of area of the base and the height. The equation is,

    V = (1/3)(pi)(r^2)h         

Dividing both sides of the equation by (1/3)(pi)(h) will give us,

  3V/(pi)(h) = r^2

Taking the square-root of both sides,

  r = sqrt(3V/(pi)(h))

Answer:

[tex]r = \sqrt{\displaystyle\frac{3V}{h\pi}}[/tex]

Step-by-step explanation:

We are given the following information in the question.

Using the formula for volume of cone, we have to express r in terms of V, h and pi.

Formula:

[tex]\text{Volume of cone, V} = \displaystyle\frac{1}{3}\pi r^2 h\\\\\text{where r is the radius of cone, h is the height of radius}[/tex]

Now, we have to evaluate r, the radius of cone.

Rearranging the terms, we have,

Working:

[tex]V = \displaystyle\frac{1}{3}\pi r^2 h\\\\r^2 = \frac{3\times V}{\pi\times h}\\\\r^2 = \frac{3V}{h\pi}\\\\r = \sqrt{\frac{3V}{h\pi}}[/tex].

Thus, r in form of V, h and pi can be written as:

[tex]r = \sqrt{\displaystyle\frac{3V}{h\pi}}[/tex]

Answer:  The correct option is (B). Its image is attached below.

Step-by-step explanation:  We are given to select the graph that represents the circle with equation as follows:

[tex]x^2+y^2=9~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that the standard equation of a circle with center at the point (h, k) and radius r units is given by

[tex](x-h)^2+(y-k)^2=r^2.[/tex]

From equation (i), we have

[tex]x^2+y^2=9\\\\\Rightarrow(x-0)^2+(y-0)^2=3^2.[/tex]

Comparing the above equation with the standard equation of a circle, we get

Center, (h, k) = (0, 0) and radius, r = 3 units.

We draw the graph of the circle with center at the origin (0, 0) and radius 3 units in the attached figure below.

We see that the graph of the circle is same as the one provided in option (B).

Thus, option (B) is CORRECT.

Answer:

24 unit

Step-by-step explanation:

Given,

The vertices of the triangle ABC are,

A (1,1), B (7,1), and C (1,9),

By the distance formula,

[tex]AB=\sqrt{(7-1)^2+(1-1)^2}=\sqrt{6^2}=6\text{ unit}[/tex]

[tex]BC=\sqrt{(1-7)^2+(9-1)^2}=\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10\text{ unit}[/tex]

[tex]CA=\sqrt{(1-1)^2+(1-9)^2}=\sqrt{8^2}=8\text{ unit}[/tex]

Thus, the perimeter of the triangle ABC = AB + BC + CA = 6 + 10 + 8 = 24 unit

Answer:

Landon makes $10.5 per hour at babysitting and $7.75 per hour at water park.

Step-by-step explanation:

Let the amount made per hour in dollars for babysitting be = x

Let the amount made per hour in dollars at water park be = y

As per the condition, the equations form:

[tex]3x+10y=109[/tex]     .......(1)

[tex]8x+12y=177[/tex]     ......(2)

Multiplying (1) by 8 and (2) by 3, and subtracting (2) from (1), we get

[tex]44y=341[/tex]

=> y = 7.75

And [tex]3x+10(7.75)=109[/tex]

=> [tex]3x+77.5=109[/tex]

=> [tex]3x=109-77.5[/tex]

=> [tex]3x=31.5[/tex]

x = 10.5

Therefore, Landon makes $10.5 per hour at babysitting and $7.75 per hour at water park.

Since ∠E and ∠F are vertical angles, they are congruent, meaning that m∠E = m∠F

Plugging in the equations that were originally given, we can form the equation 9x + 12 = 3x + 24

Subtract both sides of the equation by 3x

6x + 12 = 24

Subtract 12 from both sides

6x = 12

Divide both sides by 6

x = 2

This should be your answer. Have an awesome day! :)

Probability measures to determine the possibility of an event. In this case, the events are cars with no 4 wheels and cars with third row seats.

The probability that a randomly selected car with no 4-wheel drive has third row seats is 0.3

Let:

[tex]A \to[/tex] A car with no 4-wheel drive

[tex]B \to[/tex] A car that has third row seats

The probability that a randomly selected car with no 4-wheel drive has third row seats is represented as:

[tex]P(B|A)= \frac{n(A\ n\ B)}{n(A)}[/tex]

From the 2-way table, we have the following parameters:

[tex]n(A\ n\ B) = 12[/tex]

[tex]n(A) = 40[/tex]

So, the probability is:

[tex]P(B|A)= \frac{n(A\ n\ B)}{n(A)}[/tex]

[tex]P(B|A)= \frac{12}{40}[/tex]

[tex]P(B|A)= 0.3[/tex]

Hence, the probability that a randomly selected car with no 4-wheel drive has third row seats is 0.3

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For the given equation 6eˣ-4e⁻ˣ=5 the value obtained after solving the equation will be x =0.29.

It is defined as a function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x, where a is a constant and a>1

It is given that,

6eˣ-4e⁻ˣ=5

Multiplying complete equation by eˣ

eˣ(6eˣ-4e⁻ˣ)=5(eˣ)

6(eˣ)(eˣ) - 4(e⁻ˣ)(eˣ) =5(eˣ)

6e²ˣ-4 = 5(eˣ)

6e²ˣ-5eˣ -4 = 0

Suppose y = eˣ

6y² - 5y -4 = 0

After solving the equation we get y = 4/3 and y = -1 / 2.As a result,

eˣ = 4/3  

x = log(4/3)

x = 0.29

Thus, for the given equation 6eˣ-4e⁻ˣ=5 the value obtained after solving the equation will be x =0.29.

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A. Let us say that:

s = number of small containers

m = number of medium containers

From the given data, the total volume of soup is:

total soup = 4 ounces * 6 + 6 ounces * 10 = 84 ounces

So the equation is:

4s + 6m = 84

B. We rewrite the equation explicit to one variable, here we choose s:

4s = 84 – 6m

s = 21 – 1.5m

Then we assign several values for m starting at 0 to get the corresponding value of s then plot the graph. See the graph attached.

C. From the graph, we choose the pair of s and m that are whole numbers. The four possible combinations are:

21 small containers, 0 medium containers

15 small containers, 4 medium containers

9 small containers, 8 medium containers

3 small containers, 12 medium containers

The statement fourth "You have at least $1000" is correct if you have a ruby, then it you have at least $1000.

Legal syllogism is a legitimate concept that deals with the law and how it is applied, specifically a type of argument that uses deductive reasoning to determine whether a given act is legal.

We have:

Assume that you own a ruby. Apply the law of detachment to the following conditional statement:

The statement is:

If you have a ruby, then it you have at least $1000.

As we know, the law of detachment, we must let go of attachment to both the desired end and all possible routes to get there in order to actualize our wants.

Thus, the statement fourth "You have at least $1000" is correct if you have a ruby, then it you have at least $1000.

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Given the statement 'If you have a ruby, then you have at least $1000.' and the fact that you have a ruby, the Law of Detachment leads to the conclusion 'You have at least $1000.'

The Law of Detachment (also known as Modus Ponens) in logic says that if a conditional statement ('if p then q') is true and the first part of the statement (p) is true, then the second part of the statement (q) is true. Let's apply it to your statement.

The original statement is 'If you have a ruby, then you have at least $1000.' You confirmed the first part 'You have a ruby.' So, according to the Law of Detachment, the resulting correct statement would be 'You have at least $1000.' The other statements about selling or someone buying the ruby are irrelevant to the Law of Detachment.

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