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3 years ago

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A biologist wants to know the width (w) of a river to properly set instruments for an experiment. From point A, the biologist wa

lks downstream 100 feet and sights to point C. From the sighting it is determined that 0=54°. How wide is the river?

1 answer:

nevsk [136]3 years ago

4 0

Answer:

w = 137.6 ft

Step-by-step explanation:

100 tan 54° = w/100 *100

Simplify w/100*100 = w

w = 100 tan 54°

w = 137.6 ft

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Every year, approximately 25,000,000 kg of hair is cut in the U.S. Each kg of hair contains about 0.0002 kg of zinc, and each kg

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Answer:

The annual haircut in the United States contains $ 20,000 from zinc

Step-by-step explanation:

1 kg of hair contains ___________________ 0.0002 kg of zinc

25,000,000 kg of hair _________________ X

$X=\frac{25,000,000 kg of hair X 0.0002 kg of zinc}{1 kg of hair}= 5,000 kg of zinc$

It means that 25,000,000 kg of hair contains 5000 kg of zinc.

Otherwise,

If 1 kg of zinc _____________ worths $4

5,000 kg of zinc___________ X

$X=\frac{5000 kg of zinc x 4$}{1kg of zinc}$

X= $20,000

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Which line most accurately represents the line of best fit for the scatter plot?

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Answer:

Hence two ordered pairs can be joined to best draw the line of best fit for this scatter plot are (0, 14) and (10, 1)

Option B is correct.

Step-by-step explanation:

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PLEASE HELP ME ON THESE PROBLEMS, ITS URGENT! (Help for any of these would be greatly appreciated!)

Anvisha [2.4K]

1.) We can solve the problem by developing a linear model.
Let x represent the quantity to be used of the grade of coffee that sells for $70 per pound, and y represent the quantity to be used of the grade of coffee that sells for $80 per pound, then
$\left\begin{array}{c}x+y=80 . . . (1)\\70x+80y=76(80) . . . (2)\end{array}\right \\ \\ \Rightarrow \left\begin{array}{c}80x+80y=6400 . . . (3)\\70x+80y=6080 . . . (4)\end{array}\right \\ \\ \Rightarrow10x=320 \\ \\ \Rightarrow x=32 \\ \\ \Rightarrow y=80-32=48$
Therefore, 32 pounds of the grade of coffee that sells for $70 per pound, and 48 pounds of the grade of coffee that sells for $80 per pound should be used.

2.) Volume of alcohol in the original mixture
$\frac{35}{100} \times 40=14$ quarts

Let x be the number of quarts of alcohol to be added, then
Volume of alcohol in the new mixture
$\frac{48}{100} \times (40+x)=14+x \\ \\ \Rightarrow19.2+0.48x=14+x \\ \\ \Rightarrow0.52x=5.2 \\ \\ \Rightarrow x=10$

Therefore, 10 quarts of pure alcohol should be added

3.) Original proportion of white paint in the mixture
$=\frac{5}{5+11}=\frac{5}{16}$

Let x be the number of gallons of white paint to be added, then
$\frac{5+x}{16+x}=\frac{2}{3} \\ \\ \Rightarrow3(5+x)=2(16+x) \\ \\ \Rightarrow15+3x=32+2x \\ \\ \Rightarrow x=32-15=17$
Therefore, 17 gallons of white paint should be added.

4a.) Let the three consecutive odd integers be x - 2, x and x + 2, then
$x - 2 + x + x + 2 = 25 \\ \\ \Rightarrow3x=25\Rightarrow x=8.33$
which is not an integer.
Hence, the sum of three consecutive odd integers cannot be 25.

4b.) Let the three consecutive odd integers be x - 2, x and x + 2, then
$x - 2 + x + x + 2 = 45 \\ \\ \Rightarrow3x=45\Rightarrow x=15$
Thus, the three consecutive odd intergers whose sum is 45 are 13, 15 and 17.

5.) If all pipes are open and the tank was initially empty, let t be the time it will take to fill the tank, then
$\frac{1}{t} = \frac{1}{9} + \frac{1}{12} - \frac{1}{15} = \frac{20+15-12}{180} = \frac{23}{180} \\ \\ \Rightarrow t= \frac{180}{23} =7.83$
Therefore, it will take 7.83 hours to get the tank filled up.

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3 years ago

Which correctly describes how the graph of the inequality 6y − 3x > 9 is shaded? -Above the solid line

baherus [9]

The statement which correctly describes the shaded region for the inequality is $\fbox{\begin\\\ Above the dashed line\\\end{minispace}}$

Further explanation:

In the question it is given that the inequality is $6y-3x>9$ .

The equation corresponding to the inequality $6y-3x>9$ is $6y-3x=9$ .

The equation $6y-3x=9$ represents a line and the inequality $6y-3x>9$ represents the region which lies either above or below the line $6y-3x=9$ .

Transform the equation $6y-3x=9$ in its slope intercept form as $y=mx+c$ , where $m$ represents the slope of the line and $c$ represents the $y$ -intercept.

$y$ -intercept is the point at which the line intersects the $y$ -axis.

In order to convert the equation $6y-3x=9$ in its slope intercept form add $3x$ to equation $6y-3x=9$ .

$6y-3x+3x=9+3x$

$6y=9+3x$

Now, divide the above equation by $6$ .

$\fbox{\begin\\\math{y=\dfrac{x}{2}+\dfrac{1}{2}}\\\end{minispace}}$

Compare the above final equation with the general form of the slope intercept form $\fbox{\begin\\\math{y=mx+c}\\\end{minispace}}$ .

It is observed that the value of $m$ is $\dfrac{1}{2}$ and the value of $c$ is $\dfrac{3}{2}$ .

This implies that the $y$ -intercept of the line is $\dfrac{3}{2}$ so, it can be said that the line passes through the point $\fbox{\begin\\\ \left(0,\dfrac{3}{2}\right)\\\end{minispace}}$ .

To draw a line we require at least two points through which the line passes so, in order to obtain the other point substitute $0$ for $y$ in $6y=9+3x$ .

$0=9+3x$

$3x=-9$

$\fbox{\begin\\\math{x=-3}\\\end{minispace}}$

This implies that the line passes through the point $\fbox{\begin\\\ (-3,0)\\\end{minispace}}$ .

Now plot the points $(-3,0)$ and $\left(0,\dfrac{3}{2}\right)$ in the Cartesian plane and join the points to obtain the graph of the line $6y-3x=9$ .

Figure $1$ shows the graph of the equation $6y-3x=9$ .

Now to obtain the region of the inequality $6y-3x>9$ consider any point which lies below the line $6y-3x=9$ .

Consider $(0,0)$ to check if it satisfies the inequality $6y-3x>9$ .

Substitute $x=0$ and $y=0$ in $6y-3x>9$ .

$(6\times0)-(3\times0)>9$

$0>9$

The above result obtain is not true as $0$ is not greater than $9$ so, the point $(0,0)$ does not satisfies the inequality $6y-3x>9$ .

Now consider $(-2,2)$ to check if it satisfies the inequality $6y-3x>9$ .

Substitute $x=-2$ and $y=2$ in the inequality $6y-3x>9$ .

$(6\times2)-(3\times(-2))>9$

$12+6>9$

$18>9$

The result obtain is true as $18$ is greater than $9$ so, the point $(-2,2)$ satisfies the inequality $6y-3x>9$ .

The point $(-2,2)$ lies above the line so, the region for the inequality $6y-3x>9$ is the region above the line $6y-3x=9$ .

The region the for the inequality $6y-3x>9$ does not include the points on the line $6y-3x=9$ because in the given inequality the inequality sign used is $>$ .

Figure $2$ shows the region for the inequality $\fbox{\begin\\\math{6y-3x>9}\\\end{minispace}}$ .

Therefore, the statement which correctly describes the shaded region for the inequality is $\fbox{\begin\\\ Above the dashed line\\\end{minispace}}$

Learn more:

A problem to determine the range of a function brainly.com/question/3852778
A problem to determine the vertex of a curve brainly.com/question/1286775
A problem to convert degree into radians brainly.com/question/3161884

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Linear inequality

Keywords: Linear, equality, inequality, linear inequality, region, shaded region, common region, above the dashed line, graph, graph of inequality, slope, intercepts, y-intercept, 6y-3x=9, 6y-3x>9, slope intercept form.

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