Dustin has only nickels and quarters in his piggy bank. He has 49 coins total for a combined value of $8.85. How many of each does he have . SHow your work

Answers

Answer 1
Answer: x-\ nickels\ny-\ quarters\n\n0,05x+0,25y=8,85\nx+y=49\ \ \ \ x=49-y\n\n\0,05(49-y)+0,25y=8,85\n2,45-0,05y+0,25y=8,85\n0,2y+2,45=8,85\ \ \ | subtract\ 2,45\n0,2y=6,4\ \ \ | divide\ by\ 0,2\ny=32\n\nx=49-32=17\n\nHe\ had\ 17\ nickels\ and\ 32\ quarters.

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URGENT!!!!!!!!!!!!!!!!!! QUESTION BELOW

If f(x) is a continuous function defined for all real numbers, f(-2) = 10, f(-7) = -5, and f(x) = 0 for one and only one value of x, then which of the following could be that x value? a) -3 b) -8 c) 0 d) 2

Answers

Step-by-step explanation:

The given information tells us that f(x) is a continuous function, and it passes through the points (-2, 10) and (-7, -5). Additionally, it has exactly one value of x for which f(x) = 0. We need to find which of the given options (-3, -8, 0, 2) could be that x value.

Let's analyze each option:

a) -3: If f(-3) = 0, it's a possibility, but we need to check the others.

b) -8: If f(-8) = 0, it's a possibility, but we need to check the others.

c) 0: If f(0) = 0, it's a possibility, but we need to check the others.

d) 2: If f(2) = 0, it's a possibility, but we need to check the others.

Since we are told that there is only one value of x for which f(x) = 0, and there are multiple possibilities in this case (a, b, c, and d), the information provided does not allow us to determine a unique answer from the given options. Any of these values could be the x for which f(x) = 0, given that the function is continuous.

Final answer:

The question uses the concept of Intermediate Value Theorem in mathematics. The answer is option a) -3 as it falls between the range by the theorem, which states that for any continuous function within a certain range, the function must cross all values within that range.

Explanation:

This question is about the Intermediate Value Theorem, which states that if a function is continuous on a closed interval from a to b, and k is any number between f(a) and f(b), then there is at least one number c in the interval (a, b) such that f(c) = k.

Since the function is continuous for all real numbers and f(-2) = 10 and f(-7) = -5, the function must pass through 0 between -2 and -7 as it moves from 10 to -5. Therefore, the x value for which f(x) = 0 could be between -2 and -7. In the provided options, the only value falling within the interval (-2, -7) is -3.

So, based on the Intermediate Value Theorem, the answer is option a) -3.

Learn more about Intermediate Value Theorem here:

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Fg - 9h = 10j, for g

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fg-9h=10j\ \ \ \ |add\ 9h\ to\ both\ sides\n\nfg=10j+9h\ \ \ \ \ |divide\ both\ sides\ by\ f\n\n\boxed{g=(10j+9h)/(f)}

The histogram shows the duration, in minutes, of movies in theaters. What relationship between the median and mean is shown by the histogram?

The mean is less than the median.
The median is less than the mean.
The mean is equal to the median.
The median and mean cannot be compared from a histogram.

Answers

The correct answer is:

The median is less than the mean.

Explanation:

This histogram is skewed right; the data "peaks" further to the left than the center.

If a histogram is skewed right, the mean is greater than the median.

This is because skewed-right data have a few large values that increase the mean but do not affect where the exact middle of the data is.

Answer:

Option B) The median is less than the mean.

Step-by-step explanation:

We are given the following in the question:

A histogram showing the duration, in minutes, of movies in theaters.

  • If we observe the shape of the histogram, more values of the histogram lies on the right side, the tail of the distribution is longer on the right hand side than on the left hand side
  • Hence, the histogram is skewed right.
  • The histogram is not normal and shows skewness.
  • It is a right skewed histogram or positively skewed.
  • Now, for a positively skewed data the mean is greater than the median since more values lies on right side and have a greater value thus the mean increases.
  • \text{Mean} > \text{Median}
  • The relationship shown by the histogram between mean and median is that median is less than the mean

Simplify (3x-7)squared

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9x^2-42x+49... Sorry if I'm too late!

What is 1 1/5 times 2 1/4

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11 divided by 5 is 2.2 and you multiply that by 2 1/4 which is 2.25 in decimal form. The answer is 4.95
Turn 1 1/5 into an improper fracrion witch would be 6/5 and so the same for 2 1/4 witch would be 9/4 then you would multiply an d simplify to get 1 4/5

3 less the the opposite of the quotient of 10 and -5

Answers

The quotient of 10 and -5 is  10 /-5 =  -2.

Opposite of that, opposite of - 2 is -(-2) =  2.

3 less than 2  is 2 - 3 = -1.

So the answer is -1.