Jeff is baking a cake. The recipe says that he has to mix 32 grams of vanilla powder to the flour. Jeff knows that 1 cup of that particular vanilla powder has a mass of 128 grams. He added two over three of a cup of vanilla powder to the flour. Should Jeff add more vanilla powder to make the exact recipe, or did he go over and by what amount?

The function is increasing in:

                  x< -1

and it is decreasing in:

            x > -1

and nowhere constant.

Converting Sales Tax Rates and Sorting by Rate

Convert Fractions to Decimals:

Hamilton: 9/160 = 0.05625

Oakland: 5.75% = 5.75 / 100 = 0.0575

Green: 5 7/8% = 47/8 / 100 = 0.05859375

Campbell: 11/200 = 0.055

2. Sort Countries by Tax Rate:

1. Campbell: 0.055

2. Hamilton: 0.05625

3. Oakland: 0.0575

4. Green: 0.05859375

Therefore, the countries sorted from least to greatest tax rates are:

1. Campbell (0.055%)

2. Hamilton (0.05625%)

3. Oakland (0.0575%)

4. Green (0.05859375%)

200 +6m = 500-6m

add 6m to each side

200+12m = 500

subtract 200 from each side

12m = 300

divide both sides by 12

m = 300/12 = 25

 25 minutes

 check:

200+ 25*6 = 200 +150 = 350

500 - 25*6 = 500-150 = 350

The required answer of the given expression is 8/3.

Simplification generally means finding an answer for the complex calculation that may involve numbers on division, multiplication, square roots, cube roots, plus and minus.

The given expression is,

7/3 + 3(2/3 − 1/3)²

Solving the bracket,

= 7/3 + 3{(2− 1)/3}²

solving the fraction,

= 7/3 + 3(1/3)²

solving the square,

= 7/3 + 3(1/9)

= 7/3 + 1/3

adding them we get,

= 8/3

which is the required answer of the given expression.

Thus, the required answer of the given expression is 8/3.

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The change in the width of the beachfront from low to high tide is 102 feet, and the distance from the ocean to the homes at high tide is 248 feet.

a. To find the change in width from low to high tide, we multiply the rate of change (-17 feet/hour) by the time it takes for the ocean to move from low to high tide (6 hours).

So, -17 feet/hour * 6 hours = -102 feet. Therefore, the width of the beachfront decreases by 102 feet from low to high tide.

b. At high tide, the distance from the ocean to the homes is the sum of the original distance (350 feet) and the change in width during the tide change (-102 feet), resulting in 350 feet + (-102 feet) = 248 feet.

2.085 x 10^6 =

 move the decimal 6 places to the right: 2,085,000

Final answer:

A bisector cuts a line segment or angle into two equal parts, while a perpendicular bisector not only does that but also intersects the line segment at a right angle.

Explanation:

In mathematics, a bisector is a line segment or line that divides an angle or segment into two equal parts. It cuts the angle or segment into two congruent angles or segments. For example, if you have a line segment AB and its bisector is a line segment CD, then CD divides AB into two congruent segments AC and CB.

A perpendicular bisector is a type of bisector that not only divides a line segment into two equal parts, but it also intersects the line segment at a right angle (90 degrees). So, in addition to being equidistant from the two endpoints of the line segment, the perpendicular bisector is perpendicular to the line segment as well.

Answer:

#1)   4 1/5

#2)  7 1/2

#3)  8 4/5

#4)  18 1/2

#5)  10 1/2

Step-by-step explanation:

In order to convert to a mixed number, place the numbers to the right of the decimal over 10. Reduce the fraction.

I hope this helped!

Solution: The correct option is second option, i.e., [tex]y=(x+4)^2-1[/tex].

Explanation:

The standard form of the parabola along the y-axis with vertex (h,k) is [tex]y=a(x-h)^2+k[/tex].

Since the turning point is given as [tex](-4,-1)[/tex].

Put these values in the standard form of the parabola.

[tex]y=a(x+(-4))^2+(-1)[/tex]

[tex]y=a(x+4)^2-1[/tex]       .....(1)

The parabola passes through the points (-5,0), (-3,0) and (0,15). It means each point will satisfy the above condition.

Put x = 0 and y = 15 in the equation (1).

[tex]15=a(0+4)^2-1\\16=4^2a\\16=16a\\a=1[/tex]

Put a = 1 in equation (1).

[tex]y=1(x+4)^2-1[/tex]

Therefore, the The correct option is second option, i.e., [tex]y=(x+4)^2-1[/tex].

The number 0.912912 can be written in bar notation as 0.912, with a bar over 912 to indicate the repeating decimals. This method is commonly used in mathematics to represent repeating decimals.

To rewrite the number 0.912912 using bar notation, consider the part of the decimal that repeats. In this case, the repeating section is 912. Therefore, the number can be written as 0.912 where the 912 has a bar over it to represent the fact that it repeats. Bar notation is a way in mathematics to represent repeating decimals. The bar, or vinculum, shows which numbers repeat in the decimal. For this number, 0.912 with a bar over 912 is the way it would be written in bar notation.

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Final answer:

The sum of 60 and 84 expressed as a product of their Greatest Common Factor is 144. You determine this by first finding the GCF, which is 12, and then adding the other factors (5 and 7) together and multiplying by the GCF.

Explanation:

To find the sum of the numbers 60 and 84 as a product of their Greatest Common Factor (GCF), you first need to calculate the GCF of the two numbers. The GCF of 60 and 84 is 12. You can divide each number by 12 to find the other factors, which are 5 for 60 and 7 for 84. Therefore, the sum of the numbers can be expressed as the product of their GCF and the sum of these other factors:

60 + 84 = (12 × 5) + (12 × 7)

GCF × (sum of other factors) = 12 × (5 + 7)

Now you can add the other factors:

5 + 7 = 12

Then multiply by the GCF:

12 × 12 = 144

So, the sum of the numbers expressed as a product of their GCF is 144.

Answer: 58 %

Step-by-step explanation:

Let M represents the event of taking medicine, M' represents the event of not taking medicine and C represents the event of clearing skin,

Thus, according to the question,

n(M) = 55,

n(M') = 45,

n(M∩C) = 30,

n(M'∩C)= 22,

⇒ n(C) = n(M∩C) + n(M'∩C) = 30 + 22 = 52

Let S shows the total number of people,

⇒ n(S) = 100

Hence, the probability of cleared skin,

[tex]P(C)=\frac{n(C)}{n(S)}=\frac{52}{100}=0.52[/tex]

And, the probability of cleared skin of that people who took the medicines,

[tex]P(M\cap C)=\frac{n(M\cap C)}{n(S)}=\frac{30}{100}=0.3[/tex]

Thus, the probability that a patient chosen at random from this study took the medication, given that they reported clearer skin,

[tex]P(\frac{M}{C})=\frac{P(M\cap C)}{n(C)}=\frac{0.3}{0.52}=0.57692307692\approx 0.58 = 58\%[/tex]

Answer: 0.58

Step-by-step explanation:

Let A = Event that the patients received the acne medication.

B = Event that the patients did not receive the acne medication.

C = Patient reported  reported clearer skin.

Now,

[tex]P(A)=\dfrac{55}{100}=0.55\ \ ,P(B)=\dfrac{45}{100}=0.45[/tex]

[tex]P(C|A)=\dfrac{30}{55}\ \ , P(C|B)=\dfrac{22}{45}[/tex]

Using Bayes theorem, The probability that a patient chosen at random from this study took the medication, given that they reported clearer skin:

[tex]P(A|C)=\dfrac{P(A)\cdot P(C|A)}{P(A)\cdot P(C|A)+P(B)\cdot P(C|B)}\\\\=\dfrac{0.55\cdot\dfrac{30}{55}}{0.55\cdot\dfrac{30}{55}+0.45\cdot\dfrac{22}{45}}=0.576923076923\approx0.58[/tex]

Hence, the required probability : 0.58