A 5 ft woman is standing next to a tree. her shadow is 10 ft long the trees casts a shadow that is 116 ft long. how tall is the tree? worksheet

The number 0.98 already has a zero in the thousandths place and no further digits; hence it remains as 0.980 when rounded to the nearest thousandth.

The given number, 0.98, when rounded to the nearest thousandth, does not change because it has a zero in the thousandths place. To round a number to the nearest thousandth, you look at the digit in the ten-thousandths place. If this digit is 5 or greater, you round up.

If it is less than 5, you keep the digit in the thousandths place as it is. Since 0.98 has a zero in the thousandths place already and there are no further digits, it remains as 0.980 when rounded to the nearest thousandth.

The perimeter of the polygon to the nearest tenth of a unit [tex]\boxed{13.6{\text{ units}}}[/tex]. Option (d) is correct.

Further explanation:

The distance between the two points can be calculated as follows,

[tex]\boxed{{\text{Distance}} = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} }[/tex]

Given:

The coordinates of the vertices of the polygon are [tex]\left( { -2, 7} \right),\left( {2, 5} \right),\left( {- 1, 5} \right)[/tex], and [tex]\left( { - 1, 3} \right).[/tex]

Explanation:

The coordinates of the vertices of the polygon are [tex]\left( { -2, 7} \right),\left( {2, 5} \right),\left( {- 1, 5} \right)[/tex], and [tex]\left( { - 1, 3} \right).[/tex]

The distance between points [tex]\left( { -2, 7} \right)[/tex] and [tex]\left( {2, 5} \right),[/tex] can be calculated as follows,

[tex]\begin{aligned}{\text{Distance}} &= \sqrt {{{\left( { - 2 - 2} \right)}^2} + {{\left( {5 - 7} \right)}^2}}\\&= \sqrt {16 + 4}\\&= \sqrt {20}\\&= 4.47\\\end{aligned}[/tex]

The distance between points [tex]\left( {2, 5} \right)[/tex] and [tex]\left( {- 1, 5} \right)[/tex] can be calculated as follows,

[tex]\begin{aligned}{\text{Distance}}&= \sqrt {{{\left( { - 1 - 2} \right)}^2} + {{\left( {5 - 5} \right)}^2}}\\&= \sqrt {9 + 0}\\&= \sqrt9\\&= 3\\\end{aligned}[/tex]

The distance between points [tex]\left( {- 1, 5} \right)[/tex], and [tex]\left( { - 1, 3} \right)[/tex] can be calculated as follows,

[tex]\begin{aligned}{\text{Distance}} &= \sqrt {{{\left( { - 1 + 1} \right)}^2} + {{\left( {3 - 5} \right)}^2}}\\&= \sqrt {0 + 4}\\&= \sqrt4\\&= 2\\\end{aligned}[/tex]

The distance between point [tex]\left( { -2, 7} \right)[/tex] and [tex]\left( { - 1, 3} \right)[/tex] can be calculated as follows,

[tex]\begin{aligned}{\text{Distance}} &= \sqrt {{{\left( { - 1 + 2} \right)}^2} + {{\left( {3 - 7} \right)}^2}} \\&= \sqrt {1 + 16} \\&= \sqrt {17} \\&= 4.13\\\end{aligned}[/tex]

The perimeter of the polygon can be calculated as follows,

[tex]\begin{aligned}{\text{Perimeter}} &= 4.47 + 3 + 2 + 4.13\\&= 13.6\\\end{aligned}[/tex]

Option (a) is not correct.

Option (b) is not correct.

Option (c) is not correct.

The perimeter of the polygon to the nearest tenth of a unit [tex]\boxed{13.6{\text{ units}}}.[/tex] Option (d) is correct.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Coordinate geometry

Keywords: perimeter, shape, perimeter of shape below, Coordinates, vertices, polygon, x-coordinate, y-coordinate, perimeter, circumference, nearest tenth unit, distance formula.

Answer: I just did the quiz in Plato the answer will be option A or (a-b) 2+b2/a2

Step-by-step explanation:

Answer:

9.61 and 10.24

Step-by-step explanation:

The data provided does not include specific information needed to calculate the empirical probability of a randomly selected single parent in the U.S. military being in the Army.

Unfortunately, the provided information does not give specific numbers for single parents actively serving in the different branches of the U.S. military, including the Army. Therefore, it is not possible to accurately calculate the empirical probability this question is asking for. However, if such data were available, you would calculate the empirical probability of a randomly selected single parent in the U.S. military being in the Army by dividing the number of single parents in the Army by the total number of single parents on active duty.

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The variances for the samples were calculated, and then the probability of each distinct variance value was found. The results were summarized in a table showing the probability distribution of the variances.

The variance of a sample is calculated using the formula:
s^2 = Σ ( xi - X_bar )^2 / (n - 1).
Where 'xi' represents each value in the sample, 'X_bar' is the mean of the sample and 'n' is the number of values in the sample. Let's calculate the variance for each of these samples:

Next, find the probability of each distinct variance value by counting the number of times it occurs and dividing by the total number of samples (9 in this case). The sampling distribution of the variances with probabilities looks something like this:

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Final answer:

After performing the multiplication 9/8*0.97, which equals 1.09125, we find that this number is closest to 1 as compared to the other options provided (0.5 and 2).

Explanation:

To determine which number 9/8x0.97 is closer to among the options 0.5, 1, and 2, we need to perform the multiplication. The fraction 9/8 can be converted to a decimal by dividing 9 by 8, which gives us 1.125. Next, we multiply 1.125 by 0.97 to find the result of the original expression.

Multiplying these two numbers gives us 1.125 x 0.97 = 1.09125. Comparing this result to the options provided, we can clearly see that 1.09125 is closest to 1.

Therefore, the answer to the question is (b) 1, since 1.09125 is very close to 1 and further away from 0.5 and 2.

To calculate the cost of 5 sweets when 6 sweets cost 24p, divide the total cost by the number of sweets to determine the cost of one sweet, then multiply by 5. The cost for 5 sweets is 20p.

To find out how much 5 sweets cost when 6 sweets cost 24p altogether, we first need to calculate the cost of one sweet. We divide the total cost by the number of sweets to get the cost per sweet. Here's how it's done:

Therefore, 5 sweets would cost 20p.