A farmer sells apple cider in 2 quart bottles. How many bottles will he need to hold 70 gallons of cider

Step-by-step explanation:

Given

[tex]q + p = 2(q - p)[/tex]

as equation 1.

I used q-p as the difference as logically the woman will be older than her son.

Also given,

[tex]qp = 675[/tex]

as equation 2.

Using equation 2,

[tex]q = \frac{675}{p} [/tex]

substitute this equation into equation 1.

[tex] \frac{675}{p} + p = 2( \frac{675}{p} - p) \\ \frac{675}{p} + p = \frac{1350}{p} - 2p \\ \frac{675}{p} - \frac{1350}{p} = - 2p - p \\ - 3p = - \frac{675}{p} \\ - 3p \times p = - 675 \\ - 3 {p}^{2} = - 675 \\ {p}^{2} = - 675 \div - 3 \\ {p}^{2} = 225 \\ p = \sqrt{225} \\ = 15[/tex]

Substitute P into equation 2.

[tex]15q = 675 \\ q = 675 \div 15 \\ = 45[/tex]

Therefore the woman is 45 years old while her son is 15 years old.

Step-by-step explanation:

use the distance formula. calculate the distance between AB and then between CD showing AB = CD.

then use the distance formula on BC and AD, showing they are equal.

d=√((x_2-x_1)²+(y_2-y_1)²)

Answer:

Formula for percent change is C = {x_2 - x_1}/{x_1}  

C = relative change

x_1 = initial value

x_2 = final value

Step-by-step explanation:

Answer:

<_> daddy

Step-by-step explanation:

Answer:

(0.69, 0.91)

Step-by-step explanation:

Hope this helps!

The 99% confidence interval for p is (0.698, 0.902), which is closest to option (B) (0.70, 0.90).

A confidence interval is a range of values that are constrained by the statistic's mean and that are likely to include an unidentified population parameter. The proportion of likelihood, or certainty, that the confidence interval would include the real population parameter when a random sample is drawn several times is referred to as the confidence level.

To find the 99% confidence interval for the proportion of adults who shop online, we need to use the formula:

CI = p ± z√((p(1-p))/n)

where p is the sample proportion (72/90 = 0.8), n is the sample size (90), and z is the z-score corresponding to the 99% confidence level (from the z-table, this is 2.576).

Substituting the values, we get:

CI = 0.8 ± 2.576√((0.8(1-0.8))/90)

Simplifying, we get:

CI = 0.8 ± 0.102

Therefore, the 99% confidence interval for p is (0.698, 0.902).

To learn more about the confidence interval;

https://brainly.com/question/24131141

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Answer:

2

Step-by-step explanation:

So the common ratio is simply what a number can be multiplyied by. To find this, all we have to do is see how many times one number goes into the one after it.

So lets take the 20(2nd number), lets divide it by 10(1st number). What do we get when we divide the numbers? We get 2. since 10 goes into 20, 2 times.

Lets see if the common ratio 2 checks out for the other numbers. What is 80(4th number) divided by 40(3rd number)? Well again, thats 2. Since 40 goes into 80, 2 times.

So, we can conclude that the answer is 2.

Answer:

I think the common ratio is 20

Step-by-step explanation:

Each number is 20 times the previous number, so the Common Ratio would have to be 10

Answer:

[tex]1.2 \times 3.14[/tex]

Step-by-step explanation:

The ratio of a circumference to its diameter is equal to an irrational number, called pi, roughly equal to 3.14, denoted by symbol

[tex]\pi[/tex]

Therefore, knowing the diameter d, the circumference is equal to d*π

Answer:

When the line intercepts the x axis, this means that y will be 0.

therefore the 2 coordinates the line passes through are (2,-5) and (4,0)

given equation of line:

y=mx+b

where m = slope

b = y-intercept.

Let (2,-5) and (4,0) be (x1,y1) and (x2,y2) correspondingly.

slope of line = y1-y2 / x1 - x2

[tex] = \frac{ - 5 - 0}{2 - 4} \\ = \frac{ - 5}{ - 2} \\ = \frac{5}{2} [/tex]

Now substitute x = 4, y = 0 and m = 5/2 into equation of line to find b.

[tex]0 = ( \frac{5}{2} )(4) + b \\ 10 + b = 0 \\ b = 0 - 10 \\ = - 10[/tex]

therefore equation of line will be:

[tex]y = \frac{5}{2} x - 10[/tex]

Answer: 7/8 of a mile

Answer:

y = (x + 1)^2 + 2

Step-by-step explanation:

The graph is 2 units up and 1 unit to the left

a = 1 because from the vertex, it goes 1 up when left/right, then 4 up when left/right

Answer:

All the points in the scatter plot are written as (x, y)

Where x is the value in the horizontal axis (in this case the weight)

and y is the value in the vertical axis (in this case, the number of seeds)

We want to know the weight of 100 seeds.

We know that the number of seeds is represented in the vertical axis.

Then, first let's look at the vertical axis and find the value 100.

Now let's move horizontally the right until we meet the point.

Once we meet the point, let's move vertically to the horizontal axis, and see in which value we intersect the axis.

If we do that, we can see that we will intersect the x-axis at the value x = 5.

And this axis represents the weight in kg, then the weight of 100 seeds is 5kg.

Answer:

b

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

Answer:

Part A: 40 cubic feet. Part B: 20 cubic feet

Step-by-step explanation:

Part A: 5×4×2 = 40 feet3  

Part B: 5×4×1 = 20 feet3

Answer:

.78 cents

Step-by-step explanation:

To find the tax amount on any number, divide that number by 100 and then multiple it by the tax percentage.

In this case that would look like: $19.50/100 times 4 =.78

Answer:

try 28.4 inches to the 3rd power

Step-by-step explanation:

Answer:

27 and 50

Step-by-step explanation:

they are both greater than the original side length of 20

Answer:

3 units is the answer..

hope it helps

Answer:

X

Step-by-step explanation:

Mathematically, the tangent of an angle is the ratio of the opposite side to the adjacent side

So, for 20/22; 20

is the opposite while 22 is the adjacent

The opposite side simply refers to the side that faces the given angle

We have the opposite side here as facing the angle X and that makes X the correct answer

Step-by-step explanation:

Hi,

I agree with what you did. You could also add y on both sides and get 3x = y + 5 and then divided by three to get...

x = 5 + y /3

(the 5 and y are being divided by 3)

But that's just complicated, it works, but it's complicated. What you did is correct and what I gave you is the value of x, but I'm 100 percent sure yours is correct.

Hope this helps

Answer and Step-by-step explanation:

Yes (technically),  there is a different way to answer the equation 3x - y = 5. But, the first part of how you described it is a bit off.

Here is how you would explain it:

What you would do is Add y to both sides, then subtract 5 from both sides.

3x = y + 5

3x - 5 = y (aka y  = 3x - 5)

The other way to solve:

3x - y = 5

Subtract 3x from both sides.

-y = -3x + 5

Now divide both sides by -1.

-1(-y) = -1(-3x + 5)

y = 3x - 5

If you want to solve for x, you would:

Add y to both sides of the equation.

3x = 5 + y

Then divide each side by 3.

x = [tex]\frac{1}{3}y[/tex] + [tex]\frac{5}{3}[/tex]

#teamtrees #PAW (Plant And Water)

Answer:

I can't see the diagram could you attach it

Step-by-step explanation:

Answer:

i think its D

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

the angle is 37 degrees

Answer:

36.87°

Step-by-step explanation:

tan x= opposite/adjacen

x=tan ^-1(300/400)

x=36.86989765

Answer:

B. Slope-intercept form is y = mx + b. M is slope, so it would be the one right in front of x which is -3 :)

Answer:

h=4

Step-by-step explanation:

Subrtract 7, giving you 12.

Then divide by 3 to isolate h. Giving you 4.

Step-by-step explanation:

Total petrol consumption of the journey=

Total distance travelled ÷ Average petrol consumption

[tex] = 280 \div 35 \\ = 8 \: gallons[/tex]

Given 1 gallon = 4.5 litres,

[tex]8 \: gallons \: = 8 \times 4.5 \\ = 36 \: litres[/tex]

Total cost of petrol for this particular journey = Petrol consumed x cost of 1 litre of petrol

[tex] = 4.5 \times 49 \\ = 220.50 \: dollars[/tex]

Area of small rectange = 7 cm × 4 cm = 28 cm sq

Area of bigger rectangle = 4cm×10 cm = 40 cm sq

Area of traingle = 1/2 × 8*3 cm sq = 12 cm sq

total area of polygon = ( 28 + 40 + 12 ) cm sq

area of polygon = 80 cm sq