The sum of the two numbers is 12, and their product is -28.

A particular shade of paint is made by mixing 5 parts red paint and 7 parts blue paint. To make this shade, Shannon mixed 12 qua

SSSSS [86.1K]

Answer:

No, Shannon didn’t mix the correct shade

Explanation:

Ratio required for the shade Red : Blue = 5 : 7

The ratio formed of Shannon must be equal to the above standard ratio

But Shannon’s ratio which was mixed for red and blue is

= Red : Blue

= 8 : 12

= 2 : 3, which is not equal to 5 : 7.

Therefore it is proved that Shannon mixing does not matches with the required mixing ratio which is 5:7.

6 0

3 years ago

7. The value of a computer has a decay factor of 0.85 per year. After 2 years, the computer is worth $1445. What was the origina

Readme [11.4K]

Answer:

$64222.22

Step-by-step explanation:

If we call the original value as x, we can write:

1445 = x * (0.15)² (Note: We write 1 - 0.85 = 0.15 and not 0.85 because 0.85 is the decay factor)

1445 = 0.0225x

x ≈ 64222.22

7 0

3 years ago

Read 2 more answers

A company surveyed adult Americans about their consumer debt. They reported that 48% of Millennials (those born between 1980 and

sergeinik [125]

Answer:

We reject H₀ at 95 % of CI the group of Gen Xers who do not pay their credit card each month, is greater than this proportion for Millennians

Step-by-step explanation:

Sample proportion 1: Born between 1980 and 1996

sample size n₁ = 450

p₁ = 0,48 p₁ = 48 %

x₁ = 0,48 * 450 x₁ = 216

Sample proportion 2: Born between 1965 and 1971

sample size n₂ = 300

p₂ = 0,60 p₂ = 60%

x₂ = 0,6* 300 x₂ = 180

Test Hypothesis:

Null Hypothesis H₀ p₂ = p₁

Alternative Hypothesis H p₂ > p₁

Samples both big enough to use the normal distribution as an approximation to the binomial distribution.

We assume CI = 95 % then significance level α = 5 % the alternative hypothesis tells us that we need to develop a one-tail test to the right.

z-score is z(c) for α = 0,05 from z-table z(c) = 1,64

To calculate z(s)

z(s) = ( p₂ - p₁ ) / √ p*q ( 1 /n₁ + 1 / n₂)

p₂ - p₁ = 0,60 - 0,48

p₂ - p₁ = 0,12

p = ( x₁ + x₂ ) / n₁ + n₂

p = ( 216 + 300) / 450 + 300

p = 516 / 750 p = 0,688 then q = 1 - p q = 0,312

z(s) = 0,12 / √ 0,688*0,312* ( 1/450) + 1/ 300)

z(s) = 0,12 / √ 0,2146* ( 0,0022 + 0,0033)

z(s) = 0,12 / √ 0,001192

z(s) = 0,12/ 0,03452

z(s) = 3,47

Comparing |z(c)| and |z(s)|

z(s) > z(c)

Then z(s) is in the rejection region. We reject H₀.

We can support the claim that the proportion of the group Gen Xers who do not pay their credit card is greater than Millennians

6 0

2 years ago

I can't figure this out

andriy [413]

Suppose that equation of parabola is
y =ax² + bx + c

Since parabola passes through the point (2,−15) then
−15 = 4a + 2b + c

Since parabola passes through the point (-5,-29), then
−29 = 25a − 5b + c

Since parabola passes through the point (−3,−5), then
−5 = 9a − 3b + c

Thus, we obtained following system:
4a + 2b + c = −15
25a − 5b + c = −29
9a − 3b + c = −5

Solving it we get that
a = −2, b = −4, c = 1

Thus, equation of parabola is
y = −2x²− 4x + 1

____________________

Rewriting in the form of
(x - h)² = 4p(y - k)

i) -2x² - 4x + 1 = y

ii) -3x² - 7x = y - 11
(-3x² and -7x are isolated)

iii) -3x² - 7x - 49/36 = y - 1 - 49/36
(Adding -49/36 to both sides to get perfect square on LHS)

iv) -3(x² + 7/3x + 49/36) = y - 3
(Taking out -3 common from LHS)

v) -3(x + 7/6)² = y - 445/36

vi) (x + 7/6)² = -⅓(y - 445/36)
(Shifting -⅓ to RHS)

vii) (x + 1)² = 4(-1/12)(y - 445/36)
(Rewriting in the form of 4(-1/12) ; This is 4p)

So, after rewriting the equation would be -

(x + 7/6)² = 4(-⅛)(y - 445/36)

__________________

I hope this is what you wanted.

Regards,
Divyanka♪
__________________

6 0

2 years ago

Read 2 more answers

Solve for the roots in simplest form by completing the square x^2-12x+20=0

Alex17521 [72]

Answer:

x = 10 or x = 2

Step-by-step explanation:

Solve for x:

x^2 - 12 x + 20 = 0

Hint: | Solve the quadratic equation by completing the square.

Subtract 20 from both sides:

x^2 - 12 x = -20

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 36 to both sides:

x^2 - 12 x + 36 = 16

Hint: | Factor the left hand side.

Write the left hand side as a square:

(x - 6)^2 = 16

Hint: | Eliminate the exponent on the left hand side.

Take the square root of both sides:

x - 6 = 4 or x - 6 = -4

Hint: | Look at the first equation: Solve for x.

Add 6 to both sides:

x = 10 or x - 6 = -4

Hint: | Look at the second equation: Solve for x.

Add 6 to both sides:

Answer: x = 10 or x = 2

5 0

3 years ago