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3 years ago

Drinks 1 pint of 2% 1 quart of 1 cup of 1 quart of

1 answer:

8 0

1 pint of 2% 1 quart of 1 cup of 1 quart of
milk orange juice chocolate milk lemonade
Price $1.34 $3.09 $0.99 $2.75

Budget of Mason $15.
2 gallons of orange juice: 1 gallon is equal to 4 quarts. 2 gallons * 4 quart/gallon = 8 quarts
1 quart of 2% milk: 1 quart is equal to 2 pints ; 1 quart * 2 pints / qt = 2 pints
1 quart of choco milk: 1 quart is equal to 4 cups; 1 quart * 4 cups/qt = 4 cups.

orange juice: 8 quarts * 3.09 = 24.72
2% milk: 2 pints * 1.34 = 2.68
choco milk: 4 cups * 0.99 = 3.96

24.72 + 2.68 + 3.96 = 31.36 total cost.

Mason did not have enough money. He needed an additional 16.36 to pay off his desired purchases.

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The 5th term in a geometric sequence is 160. The 7th term is 40. What are possible values of the 6th term of the sequence?

omeli [17]

Answer:

C. The 6th term is positive/negative 80

Step-by-step explanation:

Given

Geometric Progression

$T_5 = 160$

$T_7 = 40$

Required

$T_6$

To get the 6th term of the progression, first we need to solve for the first term and the common ratio of the progression;

To solve the common ratio;

Divide the 7th term by the 5th term; This gives

$\frac{T_7}{T_5} = \frac{40}{160}$

Divide the numerator and the denominator of the fraction by 40

$\frac{T_7}{T_5} = \frac{1}{4}$ ----- equation 1

Recall that the formula of a GP is

$T_n = a r^{n-1}$

Where n is the nth term

So,

$T_7 = a r^{6}$

$T_5 = a r^{4}$

Substitute the above expression in equation 1

$\frac{T_7}{T_5} = \frac{1}{4}$ becomes

$\frac{ar^6}{ar^4} = \frac{1}{4}$

$r^2 = \frac{1}{4}$

Square root both sides

$r = \sqrt{\frac{1}{4}}$

r = ± $\frac{1}{2}$

Next, is to solve for the first term;

Using $T_5 = a r^{4}$

By substituting 160 for T5 and ± $\frac{1}{2}$ for r;

We get

$160 = a \frac{1}{2}^{4}$

$160 = a \frac{1}{16}$

Multiply through by 16

$16 * 160 = a \frac{1}{16} * 16$

$16 * 160 = a$

$2560 = a$

Now, we can easily solve for the 6th term

Recall that the formula of a GP is

$T_n = a r^{n-1}$

Here, n = 6;

$T_6 = a r^{6-1}$

$T_6 = a r^5$

$T_6 = 2560 r^5$

r = ± $\frac{1}{2}$

So,

$T_6 = 2560( \frac{1}{2}^5)$ or $T_6 = 2560( \frac{-1}{2}^5)$

$T_6 = 2560( \frac{1}{32})$ or $T_6 = 2560( \frac{-1}{32})$

$T_6 = 80$ or $T_6 = -80$

$T_6 =$ ±80

Hence, the 6th term is positive/negative 80

8 0

2 years ago

To steam rice, Paul uses m cups of water for every p

GenaCL600 [577]

Answer:

$\frac{(p + 2)m}{p}$

Step-by-step explanation:

Given

m cups of water = p cups of rice

Required

Cups of water required for p + 2 cups of rice

The question shows a direct proportion between cups of rice and cups of water.

So, the first step is to get the proportionality constant (k)

This is calculated using the following expression;

$m = k * p$

Where k represents cups of water and p represents cups of rice

Make k the subject of formula

$k = \frac{m}{p}$

Let x represents cups of water when cups of rice becomes p + 2;

k becomes:

$k = \frac{x}{p + 2}$

Equate both expressions of k; to give

$\frac{m}{p} = \frac{x}{p + 2}$

Multiply both sides by p + 2

$(p + 2) * \frac{m}{p} =(p + 2) * \frac{x}{p + 2}$

$(p + 2) * \frac{m}{p} =x$

$x = (p + 2) * \frac{m}{p}$

$x = \frac{(p + 2)m}{p}$

Hence, the expression that represents the cups of water needed is $\frac{(p + 2)m}{p}$

4 0

3 years ago

Use the coordinates of the plotted points to complete the calculation below. Pay attention to negative signs.

MArishka [77]

Answer:

3
1
-3
1
-3

Step-by-step explanation:

The change in y is the difference in y-coordinates between the lower right point and the upper left point. Similarly, the change in x is the difference in the x-coordinates of those points.

$\text{Slope}=\dfrac{\text{change in y}}{\text{change in x}}=\dfrac{\boxed{3}-6}{2-\boxed{1}}\\\\=\dfrac{\boxed{-3}}{\boxed{1}}\\\\\\=\boxed{-3}$