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Naily [24]
3 years ago
13

There is a jar containing 80 all of which are either quarters or die the total value of the coins is $13 how many of each coin a

re there in the jar make sure to write the Quetion social work
Mathematics
1 answer:
padilas [110]3 years ago
3 0

Answer:

There are 33 quarters and 47 dimes

Step-by-step explanation:

Let the number of quarters be q.

Let the number of dimes be d.

There are 80 coins in total. Therefore:

q + d = 80 ________(1)

The total value of coins is $13.

The value of a quarter is $0.25 and the value of a dime is $0.10. This means that:

0.25q + 0.10d = 13 _____(2)

We have a system of equations:

q + d = 80 ________(1)

0.25q + 0.10d = 13 ____(2)

From (1):

q = 80 - d

Put this in (2):

0.25(80 - d) + 0.10d = 13

20 - 0.25d + 0.10d = 13

Collecting like terms:

-0.15d = 13 - 20

-0.15d = -7

d = -7 / -0.15

d ≅ 47

Therefore:

q = 80 - 47 = 33

There are 33 quarters and 47 dimes.

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Samantha conjectures that for x < -1, it is true that x5 - 2 > x. Is her conjecture correct? Why or why not?
Ronch [10]

Answer:

  The conjecture cannot work for any negative numbers, It works for x > 1.3.

Step-by-step explanation:

An odd power preserves the sign. For |x| > 1, the power increases the magnitude. For x < 0, adding -2 only increases the magnitude more. A negative number of larger magnitude will not be "greater than" the reference. It will be "less than."

It only takes a counterexample to show the conjecture is incorrect.

  x^5 -2 ?? x

  (-2)^5 -2 ?? (-2)

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4 0
3 years ago
Which form of a quadratic function is easiest to use when finding the maximum or minimum value of the function?
alexandr402 [8]

Answer:

ax² + bx + c

Step-by-step explanation:

The form of a quadratic equation that is easy to use when finding the maximum or minimum value of the function is ax² + bx + c.

Suppose a quadratic function:

f(x) = 2x² - 8x + 9

Use ( -b/2a ,  f(-b/2a) ).

-b/2a

a = 2

b = -8

-(-8)/2(2)

8/4

= 2

f(2) = 2(2)² - 8(2) + 9

f(2) = 2(4) - 8(2) + 9

f(2) = 8 - 16 + 9

f(2) = 1

The minimum value of this quadratic function is (2, 1).

It represents a minimum value because a > 0.

4 0
3 years ago
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The side of a square is 2.5 cm . Find its perimeter and area
nika2105 [10]

Answer:

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Area: 2.5x4=10

Step-by-step explanation:

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3 years ago
A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 335335 babies were​ born
strojnjashka [21]

Answer:

The 99​% confidence interval estimate of the percentage of girls born is (74.37%, 85.63%).

Usually, 50% of the babies are girls. This confidence interval gives values considerably higher than that, so the method to increase the probability of conceiving a girl appears to be very effective.

Step-by-step explanation:

Confidence Interval for the proportion:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

n = 335, \pi = \frac{268}{335} = 0.8

99% confidence level

So \alpha = 0.01, z is the value of Z that has a pvalue of 1 - \frac{0.01}{2} = 0.995, so Z = 2.575.

The lower limit of this interval is:

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The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8 + 2.575\sqrt{\frac{0.8*0.2}{335}} = 0.8563

For the percentage:

Multiplying the proportions by 100.

The 99​% confidence interval estimate of the percentage of girls born is (74.37%, 85.63%).

Usually, 50% of the babies are girls. This confidence interval gives values considerably higher than that, so the method to increase the probability of conceiving a girl appears to be very effective.

7 0
3 years ago
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