Answer:
5 hours and 15 bracelets
Step-by-step explanation:
Rachel makes 3 bracelets per hour so you can set that up as the equation y=3x. Oliver can make 2 bracelets per hour but already has 5 so the equation for that is y=2x+5. These equations form a system of equations because the values for x and y are the same in both equations. This is true because the goal is to find out when Rachel and Oliver swell the same amount of bracelets. In order to solve this, you must set both of the equations equal to each other, this can be done because both equations are equal to y. The equation you now have is 3x = 2x+5. This can be solved as you would solve any linear equation; by isolating the x value then dividing it. In this case, when you do this you subtract 2x from both sides then get x=5 there is not a number multiplied by x so dividing, in this case, is not necessary. Now plug the value of x back into one of the original equations, y=15 should be the answer. Now you know that after 5 hours both Rachel and Oliver will have made 15 bracelets.
Answer:
1/6
Step-by-step explanation:
An experimental probability is the number of times an event occurred when actually attempted.
So, if Jo does the experiment 60 times and receives 50 unpainted balls, then calculate how many painted balls she got:
60-50 = 10.
So, the probability of picking a painted ball = 10/60 = 1/6
Hope this helps
B) rolling a multiple of 3 and a multiple of 6
C) rolling an even number and an odd number
D) rolling a prime number and an even number
Answer: C) rolling an even number and an odd number
Step-by-step explanation:
For any event A and B , we say they are mutually exclusive if they are disjoint such that there have no elements in common.
Let's check all the options:
A) rolling a multiple of 2 and a multiple of 4
Multiple of 2 on dice = 2,4,6
Multiple of 4 on dice = 4
They are not disjoint since 4 is the common element.
B) rolling a multiple of 3 and a multiple of 6
Multiple of 3 on dice = 3,6
Multiple of 6 on dice = 6
They are not disjoint since 6 is the common element.
C) rolling an even number and an odd number
Even number on dice = 2,4,6
Odd number on dice = 1,3,5
∴ They are disjoint event as they have no common element.
D) rolling a prime number and an even number.
Prime number on dice = 2,3,5
They are not disjoint since 2 is the common element.
16y^2 – x^2
8x^2 – 40x + 25
64x^2 – 48x + 9
b. Express the temperature of the roast 30 minutes after being put in the oven in functional notation, and then calculate its value.
c. By how much did the temperature of the roast increase during the first 10 minutes of cooking?
d. By how much did the temperature of the roast increase from the first hour to 10 minutes after the first hour of cooking?
Answer:
Step-by-step explanation:
a. We are not given enough information to determine the temperature of the refrigerator.
b. We can express the temperature of the roast 30 minutes after being put in the oven as R(30). Its value depends on the specific function R(t) given in the problem.
c. To find the increase in temperature during the first 10 minutes of cooking, we need to find the difference between the temperature of the roast after 10 minutes and the temperature of the roast when it was put in the oven. This is given by:
R(10) - R(0)
d. To find the increase in temperature from the first hour to 10 minutes after the first hour of cooking, we need to find the difference between the temperature of the roast at 1 hour and 10 minutes and the temperature of the roast at 1 hour. This is given by:
R(70) - R(60)
The temperature of the refrigerator is the initial temperature of the roast. The temperature of the roast 30 minutes after being put in the oven can be expressed as R(30), but its value cannot be determined without a specific function. The temperature increase during specific time intervals can be calculated by finding the difference between the temperatures at the respective times.
a. To find the temperature of the refrigerator, we need to use the given information. Since the roast was in the refrigerator for several days before being placed in the oven, we can assume that the temperature of the refrigerator matches the temperature of the roast initially, which is denoted as R(0). Therefore, the temperature of the refrigerator is R(0).
b. Expressing the temperature of the roast 30 minutes after being put in the oven in functional notation is R(30). To calculate its value, we need the specific function or equation that relates the temperature to time. Without this information, we cannot determine the exact numerical value of R(30).
c. To determine the temperature increase during the first 10 minutes of cooking, we need the temperature difference between the initial temperature of the roast (R(0)) and the temperature after 10 minutes of cooking (R(10)). The increase is given by R(10) - R(0).
d. To find the temperature increase from the first hour to 10 minutes after the first hour of cooking, we need the temperature at the start of the first hour (R(60)) and the temperature at 10 minutes after the first hour (R(60 + 10)). The increase is given by R(60 + 10) - R(60).
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