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3 years ago

A girl weighs 5/8 as much as her brother does. If the girl weighs 110 lb, how much does her brother weigh?

Mathematics

2 answers:

mamaluj [8]3 years ago

5 0

176 is the brothers weight.

Gwar [14]3 years ago

3 0

Her brother weighs 68.75 pounds or 69 pounds if you round

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A type of bacteria has a very high exponential growth rate of 80% every hour. If there are 10 bacteria, determine how many will

Lana71 [14]

<h3>There are 189 bacteria in 5 hours</h3><h3>There are 13382588 bacteria in 1 day</h3><h3>There are $10(1.8)^{168}$ bacteria in 1 week</h3>

<em><u>Solution:</u></em>

Given that,

A type of bacteria has a very high exponential growth rate of 80% every hour

There are 10 bacteria

<em><u>The increasing function is given as:</u></em>

$y = a(1+r)^t$

Where,

y is future value

a is initial value

r is growth rate

t is time period

From given,

a = 10

$r = 80 \5 = \frac{80}{100} = 0.8$

<em><u>Determine how many will be in 5 hours</u></em>

Substitute t = 5

$y = 10(1 + 0.8)^5\\\\y = 10(1.8)^5\\\\y = 10 \times 18.89568\\\\y \approx 188.96$

y = 189

Thus, there are 189 bacteria in 5 hours

<em><u>Determine how many will be in 1 day ?</u></em>

1 day = 24 hours

Substitute t = 24

$y = 10(1 + 0.8)^{24}\\\\y = 10(1.8)^{24}\\\\y = 10 \times 1338258.84\\\\y = 13382588.45\\\\y \approx 13382588$

Thus, there are 13382588 bacteria in 1 day

<em><u>Determine how many will be in 1 week</u></em>

1 week = 168

Substitute t = 168

$y = 10(1 + 0.8)^{168}\\\\y = 10(1.8)^{168}$

Thus there are $10(1.8)^{168}$ bacteria in 1 week

6 0

3 years ago

Transforme em π rad :<br>a)30°<br>b)40°<br>c)45°<br>d) 50°

Roman55 [17]

Answers:

a) $\frac{1}{6} \pi rad$

b) $\frac{2}{9} \pi rad$

c) $\frac{1}{4} \pi rad$

d) $\frac{5}{18} \pi rad$

Step-by-step explanation:

In this case we are dealing with angles, which can be expressed in degrees ( $\°$ ) or radians ( $rad$ ).

Now, before making the conversions we have to know the equivalence between degrees and radians:

$180 \°=1 \pi rad$

Taking this information into account, let's begin with the answers:

a) $30\° \frac{1 \pi rad}{180 \°}=\frac{1}{6} \pi rad$

b) $40\° \frac{1 \pi rad}{180 \°}=\frac{2}{9} \pi rad$

c) $40\° \frac{1 \pi rad}{180 \°}=\frac{1}{4} \pi rad$

d) $50\° \frac{1 \pi rad}{180 \°}=\frac{5}{18} \pi rad$

3 0

4 years ago

What is the height of a rectangular prism that has a volume of 192 cubic feet and a base with an area of 48 square feet? Explain

Harman [31]

The formula for volume is length × width × height, so this is the same as area of cross section × height. So, if the base of the rectangular prism (the cross section) has an area of 48 square feet, then 48 × the height = 192 cubic feet. Working backwards, we can find out the height (h will stand for height):
48×h=192
h=192÷48
h=4
Therefore, the height of the rectangular prism is 4 feet

6 0

4 years ago

Part A. Find the domain and range

Rasek [7]

Answer:

d. {(-2, 5), (-1, 2), (0, 1), (1, 2), (2, 5)}; Domain: {-2, -1, 0, 1, 2}; Range: {1, 2, 5}

Step-by-step explanation:

Part A:

Domain = the set of all x-values plotted on the x-axis = {-2, -1, 0, 1, 2}

Range = the set of all possible y-values on the y-axis that corresponds with the x-values = {1, 2, 5}

Part B:

The set of coordinates that describes the function on the graph are:

When x = -2, y = 5 => (-2, 5)

When x = -1, y = 2 => (-1, 2)

When x = 0, y = 1 => (0, 1)

When x = 1, y = 2 => (1, 2)

When x = 2, y = 5 => (2, 5)

The set of coordinates is:

{(-2, 5), (-1, 2), (0, 1), (1, 2), (2, 5)}

8 0

3 years ago

Point-Slope form (5, 1); m = 1/3

Ludmilka [50]

$(\stackrel{x_1}{5}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{\cfrac{1}{3}}(x-\stackrel{x_1}{5})$

4 0

2 years ago

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