Answer:
C)
region C
Step-by-step explanation:
We have to use what is called the zero-interval test [test point] in order to figure out which portion of the graph these inequalities share:
![\displaystyle y ≤ -x + 2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%E2%89%A4%20-x%20%2B%202)
0 ≤ 2 ☑ [We shade the portion of the graph that CONTAIN THE ORIGIN, which is the bottom portion.]
![\displaystyle y ≥ 2x - 3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%E2%89%A5%202x%20-%203)
0 ≥ −3 ☑ [We shade the portion of the graph that CONTAINS THE ORIGIN, which is the left side.]
So, now that we got that all cleared up, we can tell that both graphs share a region where the ORIGIN IS VISIBLE. Therefore region C matches the above inequalities.
I am joyous to assist you anytime.
Answer:
2. 3.913 kg (3 dp)
3. light cream
4. 240 CoffeeStops
5. 7 CoffeeStops per square mile
6. 2,861 cups of coffee each day
Step-by-step explanation:
Given:
- Skim milk density at 20 °C = 1.033 kg/l
- Light cream density at 20 °C = 1.012 kg/l
- 1 liter = 0.264 gallons
<u>Question 2</u>
![\begin{aligned}\textsf{1 gallon} & = \sf \dfrac{1}{0.264}\:liters\\\\\implies \textsf{Mass (1 gallon of skim milk)} & = \sf Density \times Volume\\& = \sf 1.033\:kg/l \times \dfrac{1}{0.264}\:l\\& = \sf 3.913\:kg\:(3\:dp)\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Ctextsf%7B1%20gallon%7D%20%26%20%3D%20%5Csf%20%5Cdfrac%7B1%7D%7B0.264%7D%5C%3Aliters%5C%5C%5C%5C%5Cimplies%20%5Ctextsf%7BMass%20%281%20gallon%20of%20skim%20milk%29%7D%20%26%20%3D%20%5Csf%20Density%20%5Ctimes%20Volume%5C%5C%26%20%3D%20%5Csf%201.033%5C%3Akg%2Fl%20%5Ctimes%20%5Cdfrac%7B1%7D%7B0.264%7D%5C%3Al%5C%5C%26%20%3D%20%5Csf%203.913%5C%3Akg%5C%3A%283%5C%3Adp%29%5Cend%7Baligned%7D)
Therefore, the mass of 1 gallon of skim milk is 3.913 kg (3 dp)
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<u>Question 3</u>
Given:
- Volume of liquid = 9 liters
- Mass of liquid = 9.108 kg
![\begin{aligned}\implies \sf Density & = \sf \dfrac{Mass}{Volume}\\\\& = \sf \dfrac{9.108\:kg}{9\:l}\\\\& = \sf 1.012\:kg/l \end{alilgned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cimplies%20%5Csf%20Density%20%26%20%3D%20%5Csf%20%5Cdfrac%7BMass%7D%7BVolume%7D%5C%5C%5C%5C%26%20%3D%20%5Csf%20%5Cdfrac%7B9.108%5C%3Akg%7D%7B9%5C%3Al%7D%5C%5C%5C%5C%26%20%3D%20%5Csf%201.012%5C%3Akg%2Fl%20%5Cend%7Balilgned%7D)
Therefore, the container holds light cream.
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<u>Question 4</u>
Given:
- 15 CoffeeStops per 100,000 people
- Population of Manhattan ≈ 1,602,000 people
![\begin{aligned}\implies \textsf{Number of Coffeestops} & = \sf \dfrac{population}{density}\\\\& = \sf \dfrac{1,602,000}{100,000/15}\\\\& = \sf \dfrac{1,602,000}{100,000} \times 15\\\\& = \sf 240.3\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cimplies%20%5Ctextsf%7BNumber%20of%20Coffeestops%7D%20%26%20%3D%20%5Csf%20%5Cdfrac%7Bpopulation%7D%7Bdensity%7D%5C%5C%5C%5C%26%20%3D%20%5Csf%20%5Cdfrac%7B1%2C602%2C000%7D%7B100%2C000%2F15%7D%5C%5C%5C%5C%26%20%3D%20%5Csf%20%5Cdfrac%7B1%2C602%2C000%7D%7B100%2C000%7D%20%5Ctimes%2015%5C%5C%5C%5C%26%20%3D%20%5Csf%20240.3%5Cend%7Baligned%7D)
Therefore, there are 240 CoffeeStops.
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<u>Question 5</u>
Given
- Manhattan ≈ 34 square miles
![\begin{aligned}\implies \textsf{CoffeeStops density} & = \sf \dfrac{number\:of\:stores}{land\:area}\\\\& = \sf \dfrac{240}{34}\\\\& \approx \sf 7 \: \textsf{CoffeeStops per square mile}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cimplies%20%5Ctextsf%7BCoffeeStops%20density%7D%20%26%20%3D%20%5Csf%20%5Cdfrac%7Bnumber%5C%3Aof%5C%3Astores%7D%7Bland%5C%3Aarea%7D%5C%5C%5C%5C%26%20%3D%20%5Csf%20%5Cdfrac%7B240%7D%7B34%7D%5C%5C%5C%5C%26%20%5Capprox%20%5Csf%207%20%5C%3A%20%5Ctextsf%7BCoffeeStops%20per%20square%20mile%7D%5Cend%7Baligned%7D)
Therefore, the density of CoffeeStops is 7 per square mile.
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<u>Question 6</u>
Given:
- Each person buys 3 cups of coffee per week
![\begin{aligned}\implies \textsf{Cups served each week} & = \textsf{number of people} \times \textsf{number of cups per week}\\& = \sf 1,602,000 \times 3\\& = \sf 4,806,000\: \textsf{cups per week}\\\\\implies \textsf{Cups per day} & = \sf \dfrac{\textsf{cups per week}}{\textsf{days in a week}}\\\\& = \sf \dfrac{4,806,000}{7}\\\\& = \sf 686,571\:\textsf{(nearest whole number)}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cimplies%20%5Ctextsf%7BCups%20served%20each%20week%7D%20%26%20%3D%20%5Ctextsf%7Bnumber%20of%20people%7D%20%5Ctimes%20%5Ctextsf%7Bnumber%20of%20cups%20per%20week%7D%5C%5C%26%20%3D%20%5Csf%201%2C602%2C000%20%5Ctimes%203%5C%5C%26%20%3D%20%5Csf%204%2C806%2C000%5C%3A%20%5Ctextsf%7Bcups%20per%20week%7D%5C%5C%5C%5C%5Cimplies%20%5Ctextsf%7BCups%20per%20day%7D%20%26%20%3D%20%5Csf%20%5Cdfrac%7B%5Ctextsf%7Bcups%20per%20week%7D%7D%7B%5Ctextsf%7Bdays%20in%20a%20week%7D%7D%5C%5C%5C%5C%26%20%3D%20%5Csf%20%5Cdfrac%7B4%2C806%2C000%7D%7B7%7D%5C%5C%5C%5C%26%20%3D%20%5Csf%20686%2C571%5C%3A%5Ctextsf%7B%28nearest%20whole%20number%29%7D%5Cend%7Baligned%7D)
![\begin{aligned}\implies \textsf{Cups served per day per shop} & = \dfrac{\textsf{cups per day}}{\textsf{number of shops}}\\\\& = \sf \dfrac{686,571}{240}\\\\& = \sf 2,861\: \textsf{(nearest whole number)} \end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cimplies%20%5Ctextsf%7BCups%20served%20per%20day%20per%20shop%7D%20%26%20%3D%20%5Cdfrac%7B%5Ctextsf%7Bcups%20per%20day%7D%7D%7B%5Ctextsf%7Bnumber%20of%20shops%7D%7D%5C%5C%5C%5C%26%20%3D%20%5Csf%20%5Cdfrac%7B686%2C571%7D%7B240%7D%5C%5C%5C%5C%26%20%3D%20%5Csf%202%2C861%5C%3A%20%5Ctextsf%7B%28nearest%20whole%20number%29%7D%20%5Cend%7Baligned%7D)
Therefore, each Manhattan CoffeeStop serves approximately 2,861 cups of coffee each day.
First we need to know both the formula of A and B.
The formula of A is
C = 5 + 0.25p
with C representing total cost and p representing the amount of checks.
The formula of B is
C = 6 + 0.15p
with C representing total cost and p representing the amount of checks.
To find the point where A and B cost the same, we solve the following equation:
5 + 0.25p = 6 + 0.15p
Collecting terms gives us
-1 = -0.1p
Now we have to divide by -0.1 and we get.
10 = p
p = 10
So our answer: after 10 checks both accounts cost the same amount of money. Answer A.
Answer:
Option (D). G(x) = x³ - x
Step-by-step explanation:
Given function is the attachment,
G(x) = (x - 1.5)³ - (x - 1.5)
This function when translated by left by 1.5 units, rule for the translation is,
G(x) → G'(x + 1.5)
Therefore, translated function will be,
G'(x) = (x - 1.5 + 1.5)³ - (x - 1.5 + 1.5)
G'(x) = x³ - x
Therefore, Option (D) will be the answer.
Answer:
I don't know how to answer question 1, but the answer from question 2 is x=5
Step-by-step explanation:
The triangle shown is an isosceles triangle because it has two congruent sides. The base angles of isosceles triangles are congruent so ∠y=∠x. since the ∠x is 52 the ∠y is also 52. We subtract the measure of angles x and y in order to find the measure of the third angle. 180-(52+52) or 180-104 is 76. this means that 14x=6=76. All we have to do to get the answer now is solve. 76-6 is 70 and 70 divided by 14 is 5. x=5.