Finish the sequence of 10 numbers 100,90,80

Find the circumference of the given circle given a diameter of 40 cm.

andriy [413]

The circumference of the given circle would be 125.6 cm. This is due to finding the circumference is multiplying it’s diameter by PI (3.14) giving you the total circumference of the circle.

6 0

2 years ago

Read 2 more answers

A jeweler wants to make 14 grams of an alloy that is precisely 75% gold.. The jeweler has alloys that are 25% gold, 50% gold, &a

Goryan [66]

Given that the jeweler has alloys that are 25% gold, 50% gold, and 82% gold.

As he wants to make 14 grams of an alloy by adding two different alloys that is precisely 75% gold, so one alloy must have a percentage of gold more than 75%.

One alloy is 82% gold and, the second can be chosen between 25% gold, 50% gold, so there are two cases.

Case 1: 82% gold + 50% gold

Let x grams of 82% gold and y grams of 50% gold added to make x+y=14 grams of 75% gold, so

75% of 14 = 82% of x + 50% of y

$\Rightarrow 75/100 \times 14 = 82/100 \times x + 50/100 \times y \\\\$

$\Rightarrow 75/100 \times 14 = 82/100 \times x + 50/100 \times (14-x)$ [as x+y=14]

$\Rightarrow 75 \times 14 = 82 \times x + 50 \times (14-x) \\\\\Rightarrow 75 \times 14 = 82 \times x + 50 \times14-50\times x \\\\\Rightarrow 75 \times 14 = 32 \times x + 50 \times14 \\\\\Rightarrow 32 \times x =75 \times 14 - 50 \times14 \\\\$

$\Rightarrow x =(25 \times 14)/32=10.9375$ grams

and $y = 14-x= 14-10.9375=3.0625$ grams.

Hence, 10.9375 grams of 82% gold and 3.0625 grams of 50% gold added to make 14 grams of 75% gold.

Case 2: 82% gold + 25% gold

Let x grams of 82% gold and y grams of 25% gold added to make x+y=14 grams of 75% gold, so

75% of 14 = 82% of x + 25% of y

$\Rightarrow 75/100 \times 14 = 82/100 \times x + 25/100 \times y \\\\\Rightarrow 75/100 \times 14 = 82/100 \times x + 25/100 \times (14-x) \\\\ \Rightarrow 75 \times 14 = 82 \times x + 25 \times (14-x) \\\\\Rightarrow 75 \times 14 = 82 \times x + 25 \times14-25\times x \\\\\Rightarrow 75 \times 14 = 57 \times x + 25 \times14 \\\\\Rightarrow 57 \times x =75 \times 14 - 25 \times14 \\\\$

$\Rightarrow x =(50 \times 14)/57=12.28$ grams

and $y = 14-x= 14-12.28=1.72$ grams.

Hence, 12.28 grams of 82% gold and 1.72 grams of 50% gold added to make 14 grams of 75% gold.

3 0

2 years ago

The poplution of Las vegas, Nevada has been increasing at an annual rate of 7.0%. If the poplution of las vegas was 478,434 in t

bearhunter [10]

Where x is years after 1999, the population is predicted to be ...
p(x) = 478,434*1.07^x

For x=11, this is
p(11) = 478,434*1.07^11 ≈ 1,007,033

The relation predicts the Las Vegas population in 2010 to be 1,007,033.

5 0

3 years ago

43/645= I need the to show the work

Licemer1 [7]

I'm guessing you need 43/645 simplified:

First, we need to find the greatest common factor (GCF) of the numerator (43) and the denominator (645). To do so, we list all the factors of each number and find the common ones.

Factors of 43: 1, 43
Factors of 645: 1, 3, 5, 15, 43, 129, 215, 645

Out of the listed factors for each number, which numbers are common between the two? The common factors are 1 and 43. Since we are looking for the GREATEST common factor, which number out of 1 and 43 is the greatest? The GCF is 43.

Second, we can now divide the numerator (43) and the denominator (645) by the GCF we recently found which was 43.

$43 \div 43 = 1 \\ 645 \div 43 = 15$

Third, our new simplified fraction is 1/15. We collected our new numerator and denominator.

Answer in fraction form: $\fbox {1/15}$
Answer in decimal form: $\fbox {0.0667}$

4 0

2 years ago

Explain how the sign of a in the equation y=a(x-h)^2 + k tells you whether the parabola has a minimum or maximum value.

Svet_ta [14]

In short, for a vertical parabola, namely one whose independent variable is on the x-axis, usually is x², if the leading term coefficient is negative, the parabola opens downward, and its peak or vertex is at a maximum, check the picture below at the left-hand-side.

and when the leading term coefficient is positive, the parabola opens upwards, with a minimum, check the picture below at the right-hand-side.

8 0

3 years ago