To get a mixture that is 70% antifreeze, you would need 600 gallons of 80% antifreeze solution mixed with 100 gallons of 10% antifreeze solution.
Explanation:To solve this problem, we will use the six step method. Let's assign variables to our unknown quantities:
Let x be the number of gallons of 80% antifreeze solution.Now we can set up the equation using the information given:
0.8x + 0.1(100) = 0.7(100 + x)Simplifying the equation:
0.8x + 10 = 70 + 0.7x0.8x - 0.7x = 70 - 100.1x = 60x = 600Therefore, you would need 600 gallons of the 80% antifreeze solution to mix with 100 gallons of the 10% antifreeze solution to get a mixture that is 70% antifreeze.
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Solve (1-sin(x))(1+sin(x))
which expression has a value of 15 when p=12 18/p 3p. 18-p p+3
The required expression that has a value of 15 is given as P + 3.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Substitute the value of p in the expression,
= P + 3
= 12 + 3
= 15
When the value of p is put on another expression there output value is not 15.
Thus, the required expression that has a value of 15 is given as P + 3.
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Tony says that 4,400 is halfway between 4,000 and 5,000.is he correct?why or why not?
Tony is not correct. The midway point between 4,000 and 5,000 is found by calculating the average of the two numbers, which is 4,500. Therefore, the halfway point is 4,500, not 4,400.
Explanation:Tony states that 4,400 is halfway between 4,000 and 5,000. To determine if Tony is correct, we need to find the midpoint between the two numbers. The midpoint can be found by adding the two numbers together and dividing by 2:
(4,000 + 5,000) / 2 = 9,000 / 2 = 4,500.
Therefore, the exact halfway point between 4,000 and 5,000 is 4,500. This means that Tony's assertion that 4,400 is halfway between these two numbers is not correct; the correct halfway point is actually 4,500.
No, Tony is not correct. Halfway between 4,000 and 5,000 would be the average of the two numbers, which is 4,500.
Explanation:No, Tony is not correct. Halfway between 4,000 and 5,000 would be the average of the two numbers. To find the average, we add the two numbers together and divide by 2. In this case, the average of 4,000 and 5,000 would be (4,000 + 5,000) / 2 = 9,000 / 2 = 4,500. Therefore, 4,400 is not halfway between 4,000 and 5,000.
It takes 23 minutes for 6 people to paint 6 walls. How many minutes does it take 9 people to paint 9 walls?
Answer:
23
Step-by-step explanation:
Imagine that each person is assigned one wall, and all 6 people begin painting at the same time.
Since everyone will finish painting their assigned wall after 23 minutes, it takes one person 23 minutes to paint one wall.
If we have 9 people and 9 walls, we can again assign one wall to each person.
Everyone will take 23 minutes to paint their assigned wall.
In other words, it takes 23 minutes for 9 people to paint 9 walls.
Describe the pattern you see when you move from a lesser place-value position to the next greater place-value position.
The minimum sustained wind speed of a category 1 hurricane is 74 miles per hour. The maximum sustained wind speed is 95 miles per hour. Write an absolute value equation that represents the minimum and maximum speeds. Let V represent the wind speed.
The absolute value equation that represents the range of a category 1 hurricane's wind speed is |V - 84.5| ≤ 10.5. 84.5 is the average of the range and 10.5 is the difference from the range's center to the end.
Explanation:The absolute value equation that represents the minimum and maximum sustained wind speeds of a category 1 hurricane can be written as |V - 84.5| ≤ 10.5. Here, V stands for the wind speed. The middle value of 74 and 95 is 84.5 (the average of 74 and 95). And the distance from 84.5 to either end of the range (74 or 95) is 10.5. So, the range of speeds is represented by the absolute difference from the center of the range is less than or equal to 10.5.
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The answer and how to get it correctly on my own
Given CA=3x-4, AT=4x+1, and CT=32, find AT
How do you write 15 cubed in exponential notation
The Des Plaines River Bridge is 2.1 km long. Engineers are considering re-lighting the bridge with a pole placed every 100 feet of the bridge length starting from the south end. Each pole will support four light globes. How many globes will be required for the re-lighting project?
The s/n ration for a set of 50 measurements is 10. what number of measurements would make the s/n ratio 5
chase drew the number line below to show -4 + (-3). Is his model accurate? If not, tell what is wrong with his model.
Chase's model is only accurate if it shows starting at -4 on a number line and moving 3 units left to land at -7. Otherwise, the model requires correction to accurately portray the sum of -4 and -3.
The student's question relates to the operation of adding two negative numbers on a number line. When adding -4 and -3, you start at -4 on the number line and move 3 units to the left because you're adding another negative number. If Chase's model does not show starting at -4 and moving 3 units left to end at -7, then his model is inaccurate. To correct the model, ensure that the number line accurately reflects this movement and resulting position on the number line.
A school has two pathways through the math program. At this school,
two-sevenths of students follow the first path, and the rest take the second path. During one semester, 35% of the students who follow the first path pass the program, while 70% of the students who follow the second path pass it. Find the fraction of students who take the first path and pass.
A drinking glass has height of 4 inches in height,in a length of 2 inches and 2 inches in width,while a baking pan has a width of 4 inches lenght of 8 inches and a depth of 2 inches.if the baking pan is filled of water up to its half depth using the drinking glass,how many glasses of full water would be needed?
There are 2 glasses of full water would be needed to fill the baking pan.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A drinking glass has height of 4 inches ,in a length of 2 inches and 2 inches in width.
And, A baking pan has a width of 4 inches length of 8 inches and a depth of 2 inches.
Now,
The volume of drinking water = 4 x 2 x 2
= 16 inches³
And, The volume of baking pan = 4 x 8 x 2
= 64 inches³
So, Half depth of baking pan = 64 / 2
= 32 inches³
Here, The volume of drinking water = 16 inches³
Thus, Number of glass of full water would be needed to fill the baking pan = 32 / 16 = 2
Therefore, There are 2 glasses of full water would be needed to fill the baking pan.
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what is 5/6 divided by 1/12
One number exceeds another by 1 the sum of the numbers is 29 what are the numbers
Final answer:
To find the two numbers, we set up two equations, solve for one variable, and find the other. The numbers that satisfy the condition of one exceeding the other by 1 with their sum being 29 are 14 and 15.
Explanation:
The student's question involves finding two numbers where one number exceeds the other by 1 and their sum is 29. To solve this, let's set up a system of equations. We'll call the first number x and the second number y. Based on the question:
x = y + 1 (one number exceeds the other by 1)
x + y = 29 (the sum of the numbers is 29)
Substituting the first equation into the second gives us:
(y + 1) + y = 29
2y + 1 = 29
2y = 28
y = 14
Now that we have the value of y, we can find x:
x = y + 1
x = 14 + 1
x = 15
Therefore, the two numbers are 14 and 15.
Fifteen people volunteer for a park cleanup. The number of volunteers increases by 7 people each month for several months. After how many months will there be 50 volunteers
What is the equation of the circle shown in the graph
Answer: its the third option
find the value of x so that f( x ) = 7
The value for x so that f(x) = 7 is at x = -3.
Using the equation of slope-intercept form (y = mx + b), where m is the gradient and b is the constant, we can find the value of x at which f(x) is equal to 7 as follows:
By observation on the graph, when x = 1, y = 3 and when x = 2, y = 2.
3 = m + b...(1)
2 = 2m + b...(2)
we multiply equation (1) by 2 and subtract equation (2) from the result;
6 - 2 = 2m - 2m + 2b - b
4 = b
putting 4 for b in equation (1) gives;
m = -1
Thus we have the equation for f(x) as
f(x) = (-1)x + 4
For f(x) = 7;
-x + 4 = 7
x = 4 - 7
x = -3.
Therefore, for f(x) to be equal to 7, the value of x is equal to -3.
Write the number with the same value as 32 tens
Theo mom bought an 8 pack of juice boxes at the store for four dollars. Find the unit rate for the juice boxes
Every 3 days Seth goes to the grocery store. His best friend Brian goes every 5 days. On what day will they both go to the store on the same day???
A random sample of 50 units is drawn from a production process every half hour. the fraction of nonconforming product manufactured is 0.02. what is the probability that ????̂0.04 if the fraction nonconforming really is 0.02
The probability that p(hat) < 0.04 if the fraction nonconforming really is 0.02 can be calculated using the normal approximation to the binomial distribution.
Explanation:To find the probability that p(hat) < 0.04 if the fraction nonconforming really is 0.02, we can use the normal approximation to the binomial distribution.
1. Calculate the mean of the sampling distribution using the formula:
μ = np = 50 * 0.02 = 1
2. Calculate the standard deviation using the formula:
σ = sqrt(npq)
where q = 1 - p = 1 - 0.02 = 0.98
σ = sqrt(50 * 0.02 * 0.98) ≈ 0.99
3. Convert p(hat) to a z-score using the formula:
z = (p(hat) - μ) / σ
z = (0.04 - 1) / 0.99 ≈ -0.96
4. Look up the z-score in the standard normal distribution table to find the corresponding probability.
P(z < -0.96) ≈ 0.166
Therefore, the probability that p(hat) < 0.04 if the fraction nonconforming really is 0.02 is approximately 0.166.
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Complete question:
A random sample of 50 units is drawn from a production process every half hour. The fraction of non-conforming product manufactured is 0.02. What is the probability that p(hat) < 0.04 if the fraction nonconforming really is 0.02?
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The product of 6 and the sum of 5 and k
product means multiply, sum means add
so add 5+k = (5+k)
now multiply that by 6 to get
6(5+k)
what does a negative net worth indicate
Find three consecutive even integers such that the sum of the least integer and the middle integer is 30 more than the greatest integer
Let the first integer be represented by: 2k
the second integer by: 2(k+1)
and the third by: 2(k+2)
Then, 2k + 2(k+1) = 2(k+2) + 30
2k + 2k + 2 = 2k + 4 + 30
4k + 2 = 2k + 34
2k = 32
k = 16
first integer: 2k = 2(16) = 32
second integer: 2(k+1) = 2(16+1) = 2(17) = 34
third integer: 2(k+2) = 2(16+2) = 2(18) = 36
Answer: 32, 34, 36
solve the following problem correctly 6+6²÷(3+6) x 3
your local gas stations are having a price war during the past seven days they have lowered the price of regular gas by $0.2 each day define a variable then write and solve an equation to find the total change in gas price show your work
Let x denotes the number of days and y denotes the total change in gas price ( in dollars).
Given : During the past seven days the price of regular gas is decreased by $0.2 each day.
Rate of decrease =$0.2 per day
Then , Total change in gas price = Rate of decrease x Number of days
i.e.[tex]y= 0.2 \times x[/tex]
i.e. [tex]y=0.2x[/tex] (1)
To find the total change in gas price in 7 days , we put x= 7 in (1) , we get
[tex]y=0.2(7)=1.4[/tex]
Hence, the total change in gas price in 7 days = $1.4
Answer:
0.14
Step-by-step explanation:
Let t be the total reduction. Then ...
t = daily change * number of days
t = 7 * 0.02
t = $0.14!
meg knows that it takes 16 minutes for her to read 7/x of a chapter. How long will it take her to read the entire chapter?
Is this better? Its all.. There is no book to read it over so its confusing