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guajiro [1.7K]
3 years ago
10

There are 30 pieces of fruit in a bowl and 12 of them are oranges. What percentage of the pieces of fruit in the bowl are orange

s?
Mathematics
1 answer:
stira [4]3 years ago
4 0

Answer:

40% of the fruit in the bowl are oranges.

Step-by-step explanation:

12/30=0.4

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A new novel is selling for $21.95. If it is on sale at 20% off, find the amount of the discount and the sale price.
Finger [1]
21.95×.2=4.39
21.95-4.39=17.56

the discount is $4.39
and the total sale price is $17.56
7 0
4 years ago
Which statement describes the inverse of m(x) = x2 – 17x?
stealth61 [152]

Answer:

The correct option is;

The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}

Step-by-step explanation:

The given information is that m(x) = x² - 17·x

The above equation can be written in the form;

y = x² - 17·x

Therefore;

0 = x² - 17·x - y

From the general solution of a quadratic equation, 0 = a·x² + b·x + c we have;

x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}

By comparison to the equation,0 = x² - 17·x - y, we have;

a = 1, b = -17, and c = -y

Substituting the values of a, b and c into the formula for the general solution of a quadratic equation, we have;

x = \dfrac{-(-17)\pm \sqrt{(-17)^{2}-4\times (1) \times (-y)}}{2\times (1)} = \dfrac{17\pm \sqrt{289+4\cdot y}}{2}

Which can be simplified as follows;

x =  \dfrac{17\pm \sqrt{289+4\cdot y}}{2}= \dfrac{17}{2} \pm \dfrac{1}{2}  \times \sqrt{289+4\cdot y}} = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +\dfrac{4\cdot y}{4} }}

And further simplified as follows;

x = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +y }} = \dfrac{17}{2} \pm \sqrt{y + \dfrac{289}{4} }}

Interchanging x and y in the function of the inverse, m⁻¹(x), we have;

m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}

We note that the maximum or minimum point of the function, m(x) = x² - 17·x found by differentiating the function and equating the result to zero, gives;

m'(x) = 2·x - 17 = 0

x = 17/2

Similarly, the second derivative is taken to determine if the given point is a maximum or minimum point as follows;

m''(x) = 2 > 0, therefore, the point is a minimum point on the graph

Therefore, as x increases past the minimum point of 17/2, m⁻¹(x) increases to give;

The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }} to increase m⁻¹(x) above the minimum.

8 0
3 years ago
The quadratic 8x^2+12x-14 has two real roots. What is the sum of the squares of these roots? Express your answer as a common fra
leonid [27]

Answer:

23/4

Step-by-step explanation:

8 0
3 years ago
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Solve -3(-2x+20)=-8(x+12)+92 please?
sveta [45]
The answer is x=4 hope it helps
8 0
3 years ago
In the town of Maplewood a certain type of DVD player is sold at just two stores, 43% of the sales 13) are from store A and 57%
umka21 [38]

Answer:

Option A 0.312 is right

Step-by-step explanation:

Given that iN Maplewood a certain type of DVD player is sold at just two stores, 43% of the sales 13) are from store A and 57% of the sales are from store B. 2.4% of the DVD players sold at store A are defective while 4.0% of the DVD players sold at store B are defective.

Prob for any random item form store to be defective = Prob from A and defective +Prob from B and defective

=0.43(0.024)+0.57(0.04)\\=0.03312

Prob it came from A and defective = 0.0.43(0.024)=0.01032

If Kate receives one of these DVD players as a gift and finds that it is defective, what is the probability that it came from store A

=\frac{0.01032}{0.03312} \\=0.312

5 0
3 years ago
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