Gavin bought two iPhone Chargers. His reward card at the store Staples saved him $4. He only had to pay $16. How much money did each iPhone Charger cost?

Answer:

2a:

[tex]a^6+\frac{64}{125} =(a^2)^3+(\sqrt[3]{\frac{64}{125} })^3[/tex]

Now, we can apply the sum of cubes formula that goes:

[tex]x^3+y^3=(x+y)(x^2-xy+y^2)[/tex]

Therefore,

[tex](a^2)^3+(\sqrt[3]{\frac{64}{125} })^3=(a^2+\frac{4}{5})(a^4-\frac{4a^2}{5}+(\frac{4}{5} )^2)[/tex]

[tex]=(a^2+\frac{4}{5})(a^4-\frac{4a^2}{5}+\frac{16}{25} )[/tex]

---------------------------------------------

2b:

[tex]16x^8-y^4=(4x^4)^2-(y^2)^2[/tex]

Now, we can apply the difference of two squares formula that goes:

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

Therefore,

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

You can apply the difference of two squares formula again:

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

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

Answer:

e

Step-by-step explanation:

chicken nuggets

A) 6/25

B) 13/15

C) 4/15

Explanation:

A) P(both will be alive) = (3/5)(2/5) = 6/25

B) P(at least one will be alive) = 1-P(both die) = 1-(2/5)(1/3) = 13/15

C) P(only the wife will be alive)=(2/5)(2/3) = 4/15

Answer:

x=7/10

Step-by-step explanation:

1/5=2/10

9/10-       =2/10

Substitute the blank with X

9/10-  X  =2/10

x=7/10

Answer:

7/10

Step-by-step explanation:

9/10 - _ = 1/5

Let's represent the unknown as x

Therefore,

9/10 - x = 1/5

9/10 - 1/5 = x

x = 9/10 - 1/5 = 7/10

Answer:

30 %

Step-by-step explanation:

Assumption: the increase is to be expressed as a percentage of 10.

We change from 10 to 13 so the increase is 3 We now need to change this into a percentage.

In fraction form we have increase Original value → 3 10 But we need to change this into the form some number 100 Let the unknown value be x giving: 3 10 ≡ some number 100 = x 100 To change the 10 from 3 10 into 100 we multiply by 10 Multiply by 1 and you do not change the value.

However, 1 comes in many forms.

3 10 × 1 = 3 10 × 10 10 = 30 100 This is the same as 30 × 1 100 but 1 100 is the same as %.

So 30 100 → 30 %

Variance is the exact average deviation of data values from the mean in squared units and the Standard deviation of data values from the mean in regular units.

Variance is a statistical measure of the dispersion of numbers in a data collection. Variance estimates how much more each number in the set deviates from the mean, and from each and every other number in the set.

The variance is a measure of the degree of variability. It is determined by averaging the squared deviations out of the mean.

The greater the spread of the data, the greater the variance in proportion to the mean.

The standard deviation is determined as the square root of variance by calculating the departure of each data point from the mean. The standard deviation represents the average level of variation in your dataset. It informs you how far each number deviates from the mean on average.

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Answer:

Step-by-step explanation:

Slope is change in y over the change in x

(r - 3) / (6 - 5) = -1

(r - 3) / (1) = -1

r - 3 = -1

r = 2

Answer:

1.NO  2. Yes

Step-by-step explanation:

Answer:

The first and second one is no

Step-by-step explanation:

(1/5) to the second power is 1/25 and adding 25/25 gets 26/25 which is not equal to 24/25

1 to the second power is still one and (1/4) to the second power is 1/16. 16/16 plus 1/16 is 17/16 which is not equal to 25/26

Answer:

M/140 = 50/60 or C

Step-by-step explanation:

Since the total is 200 it will be the denominator but we already have 60 gallons so we do 200-60=140

the ratio is 50 per 60

Answer:

Step-by-step explanation:

100% - 1.1% = 98.9% = 0.989

79000(0.989)¹ = 78,131

or

1.1% = 0.011

79000(0.011) = 869

79000 - 869 = 78,131

The area of the triangle is given by the product of 0.5 and the distances of the x and y intercepts from the origin.

Reasons:

The area of the triangle, A = 0.5·x·y

Where;

x and y are the values of the line at the intercepts

The equation of the line is; (y - 7) = m·(x - 8)

At the y-intercept, x = 0, therefore;

(y - 7) = m·(0 - 8) = -8·m

At the y-intercept, y = 7 - 8·m

At the x-intercept, y = 0, therefore;

(0 - 7) = m·(0 - 8) = -8·m

At the x-intercept, -7 = m·x - 8·m

8·m - 7 = m·x

[tex]\displaystyle x = \mathbf{8 - \frac{7}{m}}[/tex]

Therefore;

[tex]\displaystyle A = 0.5 \times \left(7 - 8 \cdot m\right) \times \left(8 - \frac{7}{m} \right) = \mathbf{\frac{-32 \cdot m^2 +56 \cdot m - 24.5}{m}}[/tex]

When the area is minimal, we have;

[tex]\displaystyle \frac{dA}{dm} =0 = \frac{d}{dm} \left(\frac{-32 \cdot m^2 +56 \cdot m - 24.5}{m}\right) = \mathbf{-\frac{32 \cdot m^2 - 24.5}{m^2}}[/tex]

m² × 0 = 24.5 - 32·m²

[tex]\displaystyle m^2 = \frac{24.5}{32} = \frac{49}{64}[/tex]

[tex]\displaystyle m = \sqrt{\frac{49}{64}} = \frac{7}{8}[/tex]

[tex]\displaystyle m = \pm \frac{7}{8}[/tex]

The equation of the line when [tex]\displaystyle m = + \frac{7}{8}[/tex] is therefore;

(y - 7) = m·(x - 8)

[tex]\displaystyle (y - 7) = \mathbf{\frac{7}{8} \cdot (x - 8)}[/tex]

[tex]\displaystyle (y - 7) = \frac{7}{8} \cdot (x - 8) = \frac{7}{8} \cdot x - \frac{7}{8} \times 8 = \frac{7}{8} \cdot x - 7[/tex]

[tex]\displaystyle y = \frac{7}{8} \cdot x - 7 + 7 = \frac{7}{8} \cdot x[/tex]

[tex]\displaystyle y = \mathbf{\frac{7}{8} \cdot x}[/tex]

The x and y intercept of the above line are 0

When [tex]\displaystyle m = - \frac{7}{8}[/tex], we have;

[tex]\displaystyle (y - 7) = -\frac{7}{8} \cdot (x - 8) = -\frac{7}{8} \cdot x + \frac{7}{8} \times 8 = -\frac{7}{8} \cdot x + 7[/tex]

Which gives;

[tex]\displaystyle y = \frac{7}{8} \cdot x + 7 + 7 = \frac{7}{8} \cdot x + 14[/tex]

[tex]\mathrm{The \ equation \ of \ the \ line \ is, }\displaystyle \ y = \mathbf{14 - \frac{7}{8} \cdot x}[/tex]

The equation of the line through P = (8, 7) such that the triangle bounded by the line and the axes in the first quadrant has minimal area is therefore;

[tex]\displaystyle \ \underline{ y = 14 - \frac{7}{8} \cdot x}[/tex]

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We need to find distance they travel as a function of time. This simply means that x is the function of time. The destination is 120 miles away, this is irrelevant for the question that is currently being asked. However, we know that they have already travelled 20 miles and are going 50 miles and hour. So lets plug in what we have.

50 is our rate of change, so we match that with the x.

20 is our constant, the distance already travelled.

This means our function is:

f(x) = 50x + 20

This means our answer is D) f(x) = 50x + 20

Lets also plug in 120 to solve how much further they need to travel before arriving.

120 is our f(x) as it is the final distance travelled.

120 = 50x + 20

120-20 = 50x

100 = 50x

100/50 = x

2 = x

This means that they need to travel 2 hours in addition to the 20 miles they have already gone.

I hope I've helped! :)

Answer:

x = 7

y = -5

Step-by-step explanation:

x + y = 2

x - y = 12

( x + y ) + ( x - y ) = 2 + 12

2x = 14

x = 7

7 + y = 2

y = -5

Check:

7 + -5 = 2

7 - (-5) = 12

Correct

-Chetan K

Answer:

Step-by-step explanation:

1 yd(36 in/yd)(2.54 cm/in) / (100cm/m) = 0.9144 m

(4(0.9144)) x (3(0.9144)) = 10.03352832 = 10.03 m²

Answer:

Step-by-step explanation:

-3 (xy+2y)+5y-x

-3xy-6y+5y-x

-3xy-y-x

The rate of growth will she need to achieve her goal is 2.8%

The formula for finding the compound amount is expressed as:

[tex]A =P(1+\frac{r}{n} )^{nt}[/tex]

P is the amount invested = $25000

t is the time in years = 25 years

A is the amount = $125000

r is the rate in %

Substitute the given parameters into the formula to have:

[tex]125000 =25000(1+r )^{25}\\5 =(1+r)^{25}\\log5=25log(1+r)\\log(1+r)=\frac{log5}{25} \\log(1+r)=0.02796\\1+r = e^{0.02795}\\1+r=1.0283\\r = 1.0283 -1\\r = 0.0283\\[/tex]

Hence the rate of growth will she need to achieve her goal is 2.8%

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Answer:

22 + 9 - S

Step-by-Step Explanation:

Amelia started with 22 seashells and found 9 more so you add that together then since she gave S amount of seashells away to her sister you minus it.

Answer: 924 / 6 = 154

Step-by-step explanation: Yes, you are correct 924 / 6 =154

Answer:

B= (-1,0,1)

Step-by-step explanation:

because -1 is not a whole number.

Answer:

B = {-1, 0, 1)

Step-by-step explanation:

The answer is B = {-1, 0, 1) because -1 is not a whole number.

Hope this helps :)

Answer:

7/50

Step-by-step explanation:

Here is an easy way of converting a decimal number to fraction.

Step 1:

Write it down as 0.14/1

Step 2:

Multiply bottom and top by 10 for every number after the decimal, since there is 2 numbers after the decimal you do 10*10 = 100

[tex]\frac{0.14(100)}{1(100)}[/tex] = 14/100

Step 3:

You can simplify 14/100 to 7/50 and thats why 7/50 is the answer

Answer:

[tex]\frac{14}{100}[/tex] or [tex]\frac{7}{50}[/tex]

Step-by-step explanation:

To find 0.14 we have to see what place it's in, since it was in the hundredths place, we put 14 over 100, which is 14/100.

To simplify this fraction we have to find the GCM (Greatest Common Factor), the GCM of 14 and 100 is 2. Then we divide both the bottom and the top by 2 (whatever you do to the bottom, you do to the top), which gives us 7/50.

To conclude, 0.14 as a fraction is 14/100 or 7/50.

Answer:

£0.00 probably is the answer

Answer:

7158

Step-by-step explanation:

Answer:

416

Step-by-step explanation:

Plug in the variables

8(7) + (5*2 * 6*6)

56 + (10 * 36)

56 + 360

416

Answer:

3/8 is the answer hope you do good

Answer:

the answer is [tex]\frac{3}{32} inch^{3}[/tex]

Step-by-step explanation:

hope this helps sorry if it's wrong have a great rest of your day :)❤

2 × 10 = 20

see Picture.

Answer:

27g of sucrose

Step-by-step explanation:

You would need 3g of sucrose per ever 100ml and you have 900ml therefore 27g

The constant of proportionality is usually used in stuff regarding to coordinates. It basically is that values increase or decrease proportionally to another value, such as on a graph, say you have a linear equation that gains 4 units up for every 3 units it moves to the right. Those two values are proportional because they'll continue to move at the same predictable rate. The image below is that line. It doesn't just apply to linear equations though, it can apply to other kinds, like exponential or absolute value equations.

Sorry if this wasn't super concise, as this is a really hard topic to explain just over text. However, if it did help a lot, please give me brainliest as I'm trying to rank up. Thanks!

Constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The  relationship between diameter of circle and radius of circle is d=2r

Relationship between Area of a circle vs. its diameter

Area of circle=π(d/2)²

The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship.

The values increase or decrease proportionally to another value, such as on a graph, say you have a linear equation that gains 4 units up for every 3 units it moves to the right.

The x and y values are proportional because they'll continue to move at the same rate.

Hence constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship.

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Answer:

B. P′ (−4, 0)

Step-by-step explanation:

You can look at the graph. The X-axis always goes first. SO -4 is first because it's on the x-axis. ANSWER= (-4, 0)

Answer:

Step-by-step explanation:

(180 - 127) / 2 = 26.5°

Compounded continuously model are evaluated using exponential functions

There are 8.177 bacteria left after 40 days

The given parameters are:

[tex]\mathbf{a = 10}[/tex] --- the initial number of bacteria

[tex]\mathbf{r = 0.502\%}[/tex] --- the decay rate

[tex]\mathbf{n = 40}[/tex] --- the number of days

The amount of bacteria left each day is calculated using:

[tex]\mathbf{T_n = a \times (1 - r)^n}[/tex]

So, we have:

[tex]\mathbf{T_{40} = 10 \times (1 - 0.502\%)^{40}}[/tex]

Express percentage as decimal

[tex]\mathbf{T_{40} = 10 \times (1 - 0.00502)^{40}}[/tex]

Simplify the expression in bracket

[tex]\mathbf{T_{40} = 10 \times 0.99498^{40}}[/tex]

Evaluate

[tex]\mathbf{T_{40} = 8.1766}[/tex]

Approximate

[tex]\mathbf{T_{40} = 8.177}[/tex]

Hence, there are 8.177 bacteria left after 40 days

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Answer:

3.34

Step-by-step explanation:

First step: 3x44=132, 132+15=147. Then use 147 as numerator and 44 as denominator.

Second step: Divide 147/44= 3.3409090909091, round and get 3.34.

Hope this helps.