3 Dylan needs to buy new contact lenses. His ophthalmologist sells 8-lens boxes in
packs of 2 for $52 and 10-lens boxes in packs of 4 for $120. Which option is the
better deal?

Answer:

The 90% confidence interval for (u1 - u2) is the range from; ( 0.50 - 2.06 )

Step-by-step explanation:

Given the data in the question;  

Adult with No children under 18                    Adult with children under 18

x"₁ = 5.65                                                             x"₂ = 4.37

s₁ = 2.43                                                               s₂ = 1.73

n₁ = 40                                                                  n₂ = 40

with 90% confidence

significance level ∝ = 1 - 90% = 1 - 0.9 = 0.1    

Degree of freedom df = 39

Now, since variance are not equal and are also unknown, we will use 2 sample t-distribution method;

Standard Error: σx"₁ - x"₂ = [tex]\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} }[/tex]

Critical value = [tex]t_{\alpha /2, df[/tex] = [tex]t_{0.05, df=39[/tex] = 1.645   { from standard normal table }

Now,

Margin of Error = E = [tex]t_{\alpha /2, df[/tex] × [tex]\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} }[/tex]

we substitute

E = 1.645 × [tex]\sqrt{\frac{2.43^2}{40} + \frac{1.73^2}{40} }[/tex]      

E = 1.645  × √( 0.1476225 + 0.0748225 )

E = 0.7758478

Now, our point difference will be; x"₁ - x"₂ = 5.65 - 4.37 = 1.28

So Limit at 90% confidence interval will be;

x"₁ - x"₂ ±  E

Lower Limit = x"₁ - x"₂ - E = 1.28 - 0.7758478 = 0.50415 ≈ 0.50

Upper Limit = x"₁ - x"₂ + E = 1.28 + 0.7758478 = 2.05584 ≈ 2.06

Therefore, The 90% confidence interval for (u1 - u2) is the range from; ( 0.50 - 2.06 )

Answer:

A= BH

A=8cm ×2.2 cm

A= 17.6cm²

Answer:

Mrs. Perry

Step-by-step explanation:

find the ratio by dividing the petunias by the daffodils

Ms. H =3

Mr. M = 3.5

mrs. P= 3.75

Answer:

your answer is right

Step-by-step explanation:

adjacent angles = angles with a common side and corner point

Answer:

u are correct bc adjacent means: next to or adjoining something else.

hope u get a good mark gl

Step-by-step explanation:

Answer:

The answer is -1

Step-by-step explanation:

Answer:

56.55 in is the answer

Hope this helps

Have a good day :)

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

i did 4x6

4x6=24

the reason i did this is because that is how i do this the rest of the class has their fancy diagrams and are being hyponthageese and not listening to me to find that it is the easiest way to find the answer

After simplification we got the above expression in the form 3f + 16m -56

The word "simplify" implies to turn something in a simpler form.

In mathematics, simplify an expression means write an expression in such a way that is comparatively less complicated than before. The main purpose of simplify an expression is to make it easy to solve as well as calculation.

3f + 8(2m-7)

we rearrange the expression by removing the parenthesis.

we remove the parenthesis by multiplying the factors.

3f + 8 × 2m - 8 × 7

3f + 16m -56

the above expression has no like terms to add or subtract so it is kept in this form.

Hence, 3f + 16m -56 is the simpler form.

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The unit rate is 18 commercials per hour.

A division is a process of splitting a specific amount into equal parts.

On Saturday morning, Wendy watched one and a half hours of her favorite shows on television.

During the shows there were 27 commercials.

We need to find the unit rate of commercials per hour.

To find this we have to divide 27 by number of hours

27/[tex]1\frac{1}{2}[/tex]

Convert [tex]1\frac{1}{2}[/tex] to improper fraction

27/(3/2)

When whole number is divided by fraction, the denominator is multiplied with whole number

27×2/3

54/3

18

Hence, the unit rate is 18 commercials per hour.

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Answer:18 commercials per hour

Step-by-step explanation:

Answer:

center (2, -3)

radius r = 3

Graph c

Step-by-step explanation:

Answer:

Graph A on edge

Step-by-step explanation:

On solving the provided question, we can say that -  f(x) = 3x2 - 6x + 2, and the value of the equation f(x) = +2

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

f(x) = 3x2 - 6x + 2

x = 1

f(x) = +2

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Answer:

Step-by-step explanation:

(2x – 3)(5x + 6)

10x2 + 12x - 15x - 18

10x2 - 3x - 18

The product of the given polynomials is 10x² - 3x - 18

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

The given polynomials are:

(2x – 3)(5x + 6)

By multiplying the two polynomials, we get

10x² + 12x - 15x - 18

10x²- 3x - 18

Hence, 10x²- 3x - 18 is the product of the given polynomials.

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Answer:

Step-by-step explanation:

Steps to find the equation of a line from two points:

   1) Find the slope using the slope formula. ...

   2) Use the slope and one of the points to solve for the y-intercept (b). ...

   3) Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = MX + b) to get the equation for the line.

Answer:

C. iv

Step-by-step explanation:

I calculated it logically

The numeric value of the expression ((2.1)² + 5.2 - 7.2) x 7.1 is given as follows:

17.1.

The expression for this problem is defined as follows:

((2.1)² + 5.2 - 7.2) x 7.1

The precedence of operators follows the PEMDAS acronym, as follows:

Hence the parenthesis takes precedence, thus:

(2.1)² + 5.2 - 7.2.

Then the power takes precedence, thus:

(2.1)² + 5.2 - 7.2 = 4.41 + 5.2 - 7.2

Addition and subtraction can be done in any order, hence:

4.41 + 5.2 - 7.2 = 2.41.

Then the multiplication is given as follows:

2.41 x 7.1 = 17.1.

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Answer:

O V=3(10XB)(12)

Step-by-step explanation:

Answer:

there would be 8 sides if there are 20 diagonals

Answer: x is -2 and y is 4 if needed (-2,4) is the origin form

Step-by-step explanation: first we take side walk one we subtract -3x on both sides then you get 3y=-3x+6 divide both by 3 you get y=-x+2 finally we can substitute. substitute y for x+6 you get x+6 = -x+2 do the inverse of -x on both sides you get 2x+6=2 do the inverse of 6 on both sides you get 2x=-4 divide 2 on both sides you get x=-2. substitute x of  y=-x+2 to y=-(-2)+2 mult  -1 x -2 is 2, 2+2 is four so y= 4 put that together x is -2 and y is 4

The price of a seven minute call direct to New York, in the evening, is given as follows:

$5.82.

The cost of the call is obtained considering the information given in the table, for which the proportions are applied.

We have a direct call, meaning that it is a person-to-person call, thus the flat rate is of $3.00 per minute.

Then the minute proportions, considering that the call happens in the evening, are given as follows:

A seven minute call is composed by six additional minutes after the first, hence the total cost is obtained as follows:

0.38 x 3 + 6 x 0.26 x 3 = $5.82.

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Answer:

6√2

Step-by-step explanation:

-√2×2×2 -√2×3×3×3 + 2√3×3

-2√2 - 3✓6 + 2×3

-2√2 - 3√2×2 +2 + 6

6√2

Answer:

[tex]y=x^2+2x-2[/tex]

Step-by-step explanation:

Vertex form is expressed as: [tex]y=a(x-h)^2+k[/tex], and is super useful when analyzing the vertex, which is given to be (h, k).

Standard form is expressed as: [tex]y=ax^2+bx+c[/tex], and is also useful in certain cases.

When converting standard to vertex we have to complete the square to rewrite the equation using a perfect square binomial, which is what really distinguishes the two. Now when we want to convert back into standard form, we simply need to get rid of this perfect square binomial, which we can do by expanding out the perfect square binomial into a trinomial.

So in other words, we want to multiply out the following: [tex](x+1)(x+1)[/tex], which becomes: [tex]x^2+2x+1[/tex] which you can solve by using polynomial multiplication, which is essentially just extending the logic of the distributive property. In general when given two polynomials to multiply, you look at one polynomial, and then multiply it by each term in the other polynomial, now repeat this for each term in the polynomial you were initially looking at. I'll provide a picture to better illustrate this. You can use FOIL if it helps you with multiplying binomials, but remembering how to generally use it, will help you when multiplying polynomials in general.

Now that we've multiplied out the expression, we can substitute it into the equation: [tex]y=x^2+2x+1-3[/tex], now just combine the constants: [tex]y=x^2+2x-2[/tex], and now you've converted it into standard form!

Step-by-step explanation:

D

Answer:

40 failed

Step-by-step explanation:

2/3 of 120 is 80, so you subtract the 80 who passed from the 120 total to get 40 students who failed

Answer:

Step-by-step explanation:

If [tex]\frac{2}{3}[/tex] passed the exam then:

[tex]\frac{3}{3} -\frac{2}{3} = \frac{1}{3}[/tex] failed the exam

now to find the number which failed we multiply:

[tex]\frac{1}{3} \cdot 120 = 40[/tex] and 40 is our answer

Answer:

8

Step-by-step explanation:

2/ 1/4 = 8

Answer: 8

Step-by-step explanation: 2 / 1/4 = 8

Answer:

The answer is A

Step-by-step explanation:

The shape is a rhombus when plotted on a quardanent plane. The shape is similar to a diamond.

11h+33

30p+15j

4p+8

i feel like im about to die, ur a lil scary

Answer:

-3,950

Step-by-step explanation:

First -5,000(1-0.21)

Then multiply -5,000 x 0.79 = -3,950

Answer:

-14

Explanation:

3 x -3 - 5 = -14

Answer:

-14, -5, 4, and 13

Step-by-step explanation:

For each x value, substitute it for x in the equation.

For the first one where x = -3,

y = 3(-3) - 5

y = -9 - 5

y = -14

So the first one is -14. The next x value is 0

y = 3(0) - 5

y = 0 - 5

y = -5

Second one is -5. The next x value is 3

y = 3(3) - 5

y = 9 - 5

y = 4

Third is 4. The next x value is 6

y = 3(6) - 5

y = 18 - 5

y = 13

So the last one is 13.