Show your work and explain how you can determine which is a better deal:
10 ounces of orange juice for $2.40 or 8 ounces for $2.08?

Answer:

c

Step-by-step explanation:

I think

The points that could be on the line

y = 7x - 16 are (-2, -30)

-30 = 7 X -2 - 16

-30 = -14 - 16

-30 = -30

Option B is the correct answer.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

A line has a slope = 7 and passes through the point (3, 5).

Now,

The equation of a line can be written as,

y = mx + c

m = 7

y = 3x + c

Now,

(3, 5) = (x, y)

5 = 7 x 3 + c

5 = 21 + x

5 - 21 = c

c = -16

The equation of the line.

y = 7x - 16

The points that could be on the line have to satisfy the equation.

y = 7x - 16

A.

(-1, -24)

y = 7 x -1 - 16 = -7 - 16 = -23

This is not true

B.

(-2, -30)

y = 7 x -2 - 16 = -14 - 16 = -30

This is true.

C.

(6, 24)

y = 7 x 6 - 16 = 42 - 16 = 26

This is not true.

D.

(10,55)

y = 7 x 10 - 16 = 70 - 16 = 54

This is not true.

Thus,

The points that could be on the line

y = 7x - 16 are (-2, -30)

-30 = 7 X -2 - 16

-30 = -14 - 16

-30 = -30

Option B is the correct answer.

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Step-by-step explanation:

Initial velocity ,u= 14 m/s

a =_g

= 9.8 m/s

velocity at highest point,v=30 m/ s

=2as=v sqare _u square

=s= 35.99 m

Answer:

A) Gradient = -3

B) 3y - x = 7

Step-by-step explanation:

The curve has the equation;

y = x³ - 6x² + 9x + 1

We are given the pints it passes through as;

A(2,3) and P(3, 1)

A) to find the gradient, we will find the derivative of the given equation.

Thus;

Gradient = y' = 3x² - 12x + 9

At point A, x = 2. Thus;

Gradient = 3(2²) - 12(2) + 9

Gradient = 12 - 24 + 9

Gradient = -3

B) since the gradient of the tangent = -3, it means the gradient of the normal will be; -1/-3 = 1/3

Thus, equation of the normal to the curve at point A will be;

(y - 3) = ⅓(x - 2)

Multiply both sides by 3 to get;

3y - 9 = x - 2

3y - x = 9 - 2

3y - x = 7

Answer in fraction form = 33/2

Answer in decimal form = 16.5

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Work Shown:

n = some number

2n = twice that number

2n+3 = "sum of twice a number and 3"

[tex]\sqrt{2n+3}[/tex] = square root of the previous expression

The equation we need to solve is [tex]\sqrt{2n+3} = 6[/tex]

We'll follow PEMDAS in reverse, undoing each operation, to isolate n

[tex]\sqrt{2n+3} = 6\\\\\left(\sqrt{2n+3}\right)^2 = 6^2 \ \ \text{ ... square both sides}\\\\2n+3 = 36\\\\2n+3-3 = 36-3 \ \ \text{ ... subtract 3 from both sides}\\\\2n = 33\\\\\frac{2n}{2}=\frac{33}{2} \ \ \text{ ... divide both sides by 2}\\\\n = \frac{33}{2}\\\\n = 16.5[/tex]

Answer:

[tex]\frac{33}{2}[/tex]

Step-by-step explanation:

 In the problem, "The square root of the sum of twice a number and 3 is 6" can be converted to an equation that looks like this:

Let x be the number:

[tex]\sqrt{2x+3 = 6 }[/tex]

In order to solve the problem:

[tex]\sqrt{2x+3}^2=6^2[/tex]

By squaring both sides to remove the exponent:

[tex]{2x + 3 = 36}[/tex]

Simplify:

[tex]{2x+3-3=36-3}[/tex]

Subtract 3 from both sides:

[tex]{2x = 33 }[/tex]

Then Simplifying further:

[tex]\frac{2x}{2} = \frac{33}{2}[/tex]

Divide both sides by 2 to remove 2 from the x.

[tex]{x = \frac{33}{2} }[/tex]

Thus, meaning the answer is [tex]\frac{33}{2}[/tex]

Hope this helps you.

Answer:

30

Step-by-step explanation:

Since this is a right angle, we can use trig functions

Cos theta = adjacent side/ hypotenuse

cos ? = 20/23

Take the inverse cos of each side

cos ^-1 (cos ?) = cos ^-1(20/23)

? =29.59184579

To the nearest degree

? = 30

Answer:

17. x=25

18. x=72

19. x=151

20. x=28

Step-by-step explanation:

Answer:

Hi

Step-by-step explanation:

Answer:

Adult Tickets 3a

Student Tickets = a

Senior Tickets a+8

Step-by-step explanation:

Answer:

a=students

3a=adults

3a+8=senior

Step-by-step explanation:

Answer:

i think its 64.3

Answer:

b = -9

Step-by-step explanation:

Answer:

-9

Step-by-step explanation:

-12 = 24 + 4b

-12 -24 = 4b

-36 / 4 = b

b = -9

Answer:

-9

Step-by-step explanation:

(7)(-3)+12

-21+12

-9

Answer:

-9

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

pg + 12

p = 7

g = -3

Step 2: Evaluate

Answer:

42

Step-by-step explanation:

It changes 42 cents each year

Answer:

Square

Step-by-step explanation:

Probably square

Answer:

104, 105, 106

Step-by-step explanation:

Consider three consecutive integers.  If the first is x then the second is 1 more than x (or x+1) and the third is x+2

The sum of these three integers is x + x+1 + x+2 and is known to be 312, so

x + x+1 + x+2 = 312, gather like terms

3x + 3 = 312, subtract 3 from both sides

3x = 309, divide both sides by 3

x = 104, so the integers are

104, 105, 106

Answer:

C

Step-by-step explanation:

Answer:

4:9

Step-by-step explanation:

12 red apples and 27 apples in total so it would be 12:27. Just divided it by 3

I think that's what the question is asking...

Answer:

three million

Step-by-step explanation:

Step-by-step explanation:

step 1. what is the question? solve for k? okay.

step 2. 4(k - 6) = 6(-4 - 5k)

step 3. 4k - 24 = -24 - 30k

step 4. 34k = 0

step 5. k = 0.

Answer:

15x+30<10x-45

Step-by-step explanation:

Answer:

0.3413 = 34.13% probability that the crew member earns between $20.50 and $24.00 per hour

Step-by-step explanation:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

A recent study of the hourly wages of maintenance crew members for major airlines showed that the mean hourly salary was $20.50, with a standard deviation of $3.50.

This means that [tex]\mu = 20.5, \sigma = 3.5[/tex]

a. Between $20.50 and $24.00 per hour

This is the pvalue of Z when X = 24 subtracted by the pvalue of Z when X = 20.5. So

X = 24

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{24 - 20.5}{3.5}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8413

X = 20.5

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{20.5 - 20.5}{3.5}[/tex]

[tex]Z = 0[/tex]

[tex]Z = 0[/tex] has a pvalue of 0.5

0.8413 - 0.5 = 0.3413

0.3413 = 34.13% probability that the crew member earns between $20.50 and $24.00 per hour

Answer:

3.6 more miles

Step-by-step explanation:

10.4 - 6.8 = 3.6

Using the law of total probability, the probability that the system will function is 0.86.

Let,

the probability of rainy day is= p(r),

probability of non-rainy day =  p(nr),

probability that system will function = p(f),

probability that system will function if it is a rainy day = p(f|r)

probability that system will function in non-rainy day = p(f|nr)

Then the following information is given in the question:

p(r) = 0.20

then, p(nr) = 1-0.20 = 0.80

p(f|r) = 0.7 (4 out of 6 components function with 0.7 probability each)

p(f|nr) = 0.9 (4 out of 6 components function with 0.9 probability each)

We have to find the probability that the system will function tomorrow.

According to the total probability law:

Probability that function will function tomorrow = p(r)p(f|r) + p(nr)p(f|nr)

Substitute the given probabilities:

P(f) = 0.20 x 0.7 + 0.80 x 0.9

P(f) = 0.14 + .72

P(f) = 0.86

Hence, the probability that the system will function tomorrow is 0.86.

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Step-by-step explanation:

To find the volume of a rectangular prism, we multiply the length of the prism by the width of the prism by the height of the prism.

Answer:iscusses the domain and range of a function, and how to find the domain ... {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)} ... If you find any duplicate x-values, then the different y-values mean that you do not have a function. ... I'll just list the x-values for the domain and the y-values for the range: domain: {–3, –2, –1, 0, 1, 2}. range: {5}.

Step-by-step explanation:

Step-by-step explanation:

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