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Viefleur [7K]
2 years ago
11

Louden County Wildlife Conservancy counts butterflies each year. Data over the last three years regarding four types of butterfl

ies are shown below. What inference can be made about the butterflies in Louden County from the samples?
Mathematics
1 answer:
MrRa [10]2 years ago
5 0

Incomple question. However, here's the remaining part of the question:

14

2009

Meadow Fritillary= 5

Variegated Fritillary= 7

Zebra Swallowtail= 33

Eastern-Tailed Blue= 242

Louden County Butterfly Count

2010

Meadow Fritillary 34

Variegated Fritillary 95

Zebra Swallowtail 21

Eastern-Tailed Blue 168

2011

Meadow Fritillary

Variegated Fritillary

Zebra Swallowtail

Eastern-Tailed Blue

10

170

<u>Options</u>:

A) All butterfly populations are steadily decreasing.

B)All butterfly populations were larger than usual in 2010.

C)The Eastern-Tailed Blue butterfly is more common than the others.

D)The Meadow Fritillary is equally common as the Variegated Fritillary

Answer:

<u>C</u>

Step-by-step explanation:

Looking through the above count data by Louden County Wildlife Conservancy from 2009 to 2011 we notice the Eastern- Trailed Blue butterfly has a higher count, which implies that the Eastern-Tailed Blue butterfly is more common than the other butterflies.

Therefore, we could infer from the samples, that the Eastern-Tailed Blue butterfly is more common than others from the records of the past 3 three years.

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I tell you these facts about a mystery number, $c$: $\bullet$ $1.5 &lt; c &lt; 2$ $\bullet$ $c$ can be written as a fraction wit
makkiz [27]

Answer:

Possible answer: \displaystyle c = \frac{16}{10} = \frac{8}{5} = 1.6.

Step-by-step explanation:

Rewrite the bounds of c as fractions:

The simplest fraction for 1.5 is \displaystyle \frac{3}{2}. Write the upper bound 2 as a fraction with the same denominator:

\displaystyle 2 = 2 \times 1 = 2 \times \frac{2}{2} = \frac{4}{2}.

Hence the range for c would be:

\displaystyle \frac{3}{2} < c < \frac{4}{2}.

If the denominator of c is also 2, then the range for its numerator (call it p) would be 3 < p < 4. Apparently, no whole number could fit into this interval. The reason is that the interval is open, and the difference between the bounds is less than 2.

To solve this problem, consider scaling up the denominator. To make sure that the numerator of the bounds are still whole numbers, multiply both the numerator and the denominator by a whole number (for example, 2.)

\displaystyle \frac{3}{2} = \frac{2 \times 3}{2 \times 2} = \frac{6}{4}.

\displaystyle \frac{4}{2} = \frac{2\times 4}{2 \times 2} = \frac{8}{4}.

At this point, the difference between the numerators is now 2. That allows a number (7 in this case) to fit between the bounds. However, \displaystyle \frac{1}{c} = \frac{4}{7} can't be written as finite decimals.

Try multiplying the numerator and the denominator by a different number.

\displaystyle \frac{3}{2} = \frac{3 \times 3}{3 \times 2} = \frac{9}{6}.

\displaystyle \frac{4}{2} = \frac{3\times 4}{3 \times 2} = \frac{12}{6}.

\displaystyle \frac{3}{2} = \frac{4 \times 3}{4 \times 2} = \frac{12}{8}.

\displaystyle \frac{4}{2} = \frac{4\times 4}{4 \times 2} = \frac{16}{8}.

\displaystyle \frac{3}{2} = \frac{5 \times 3}{5 \times 2} = \frac{15}{10}.

\displaystyle \frac{4}{2} = \frac{5\times 4}{5 \times 2} = \frac{20}{10}.

It is important to note that some expressions for c can be simplified. For example, \displaystyle \frac{16}{10} = \frac{2 \times 8}{2 \times 5} = \frac{8}{5} because of the common factor 2.

Apparently \displaystyle c = \frac{16}{10} = \frac{8}{5} works. c = 1.6 while \displaystyle \frac{1}{c} = \frac{5}{8} = 0.625.

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2 years ago
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If a linear system has four equations and seven variables, then it must have infinitely many solutions. True or False
Savatey [412]

Answer:

The statement is False.

Step-by-step explanation:

Consider the provided information.

If a linear system has four equations and seven variables, then it must have infinitely many solutions.

We need to determine the above statement is true or false.

The above statement is false, it could be inconsistent, and therefore have no solutions,

For example:

x_1+x_2+x_3+x_4 +x_5+x_6+x_7=0\\x_1+x_2+x_3 =1\\x_4 +x_5 =1\\x_6+ x_7=1

Hence, there is no solution.

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2 years ago
Compare partial products and regrouping how the methods are alike and different
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Regrouping is just like the commutative or associative property of numbers.
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2 years ago
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Two boats leave port at noon. Boat 1 sails due east at 12 knots. Boat 2 sails due south at 8 knots. At 2 pm the wind diminishes
Ivan

Answer:

14.86 knots.

Step-by-step explanation:

<em>Given that:</em>

The boats leave the port at noon.

Speed of boat 1 = 12 knots due east

Speed of boat 2 = 8 knots due south

At 2 pm:

Distance traveled by boat 1 = 24 units due east

Distance traveled by boat 2 = 16 units due south

Now, speed of boat 1 changes to 9 knots:

At 3 pm:

Distance traveled by boat 1 = 24 + 9= 33 units due east

Distance traveled by boat 2 = 16+8 = 24 units due south

Now, speed of boat 1 changes to 8+7 = 15 knots

At 5 pm:

Distance traveled by boat 1 = 33 + 2\times 9= 51 units due east

Distance traveled by boat 2 = 24 + 2 \times 15 = 54 units due south

Now, the situation of distance traveled can be seen by the attached right angled \triangle AOB.

O is the port and A is the location of boat 1

B is the location of boat 2.

Using pythagorean theorem:

\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AB^{2} = OA^{2} + OB^{2}\\\Rightarrow AB^{2} = 51^{2} + 54^{2}\\\Rightarrow AB^{2} = 2601+ 2916 = 5517\\\Rightarrow AB = 74.28\ units

so, the total distance between the two boats is 74.28 units.

Change in distance per hour = \dfrac{Total\ distance}{Total\ time}

\Rightarrow \dfrac{74.28}{5} = 14.86\ knots

6 0
1 year ago
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