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1 day ago

Zoe draws ΔABC on the coordinate plane. What is the approximate perimeter of ΔABC

Mathematics

2 answers:

zzz [4K]1 day ago

6 0

Answer:

Correct answer is Option C.

Step-by-step explanation:

Provided: Triangle ABC plotted on the coordinate plane.

The coordinates given are A( 1, 1 ), B( 3, 5 ), and C( 5, 1 ).

We need to determine the approximate perimeter of the triangle.

We will utilize the distance formula for two points $(x_1,y_1)\:and\:(x_2,y_2)$

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Thus,

$AB=\sqrt{(3-1)^2+(5-1)^2}=\sqrt{(2)^2+(4)^2}=\sqrt{4+16}=\sqrt{20}=4.47\:(approx.)$

$CB=\sqrt{(5-3)^2+(1-5)^2}=\sqrt{(2)^2+(-4)^2}=\sqrt{4+16}=\sqrt{20}=4.47\:(approx.)$

$AC=\sqrt{(5-1)^2+(1-1)^2}=\sqrt{(4)^2+(0)^2}=\sqrt{16}=4$

Therefore, the Perimeter = AB + AC + CB = 4.47 + 4.47 + 4 = 12.94 units

Consequently, Option C is correct.

lawyer [4K]1 day ago

5 0

B. 12 units because the total length calculated together results in 12.

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A botanist found a correlation between the length of an aspen leaf and its surface area to be 0.94. Why does the correlation val

zzz [4022]

Answer:

A correlation coefficient of +1 or -1 reflects a perfect linear relationship, but a 0.94 indicates a strong positive correlation between the aspen leaf's length and surface area, though not guaranteeing linearity.

Step-by-step explanation:

The correlation coefficient (r) ranges between +1 and −1, where +1 means perfect positive correlation, −1 means perfect negative correlation, and 0 means no correlation.

The closer r is to ±1, the stronger the correlation. Generally, values between 0.7 and 1, or −0.7 and −1, indicate a significant correlation.

While 0.94 shows a strong direct association between the leaf's length and surface area, it does not definitively prove a linear relationship is the best fit.

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14 days ago

Emily invests $5,000 in an

lawyer [4008]

Answer:

50 years

Detailed breakdown:

Applying the simple interest formula:

PRT/100

Where P is the principal amount ($5000)

R represents the interest rate (4)

T signifies the time (x- unknown)

The total amount after time T is double the initial investment = 5000 * 2 = 10000

(5000 * 4 * x) / 100 = 10000

20000x / 100 = 10000

20000x = 100 * 10000

20000x = 1,000,000

x = 1,000,000 / 20,000

x = 50

It will require 50 years

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2 days ago

Read 2 more answers

A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standar

PIT_PIT [3919]

Answer:

The P-value ranges between 2.5% and 5% according to the t-table.

Step-by-step explanation:

A random sample of 16 students from a large university showed an average age of 25 years with a standard deviation of 2 years.

Let $\mu$ = true average age of all students at the university.

So, the Null Hypothesis, $H_0$ : $\mu \leq$ 24 years {indicating the average age is less than or equal to 24 years}

Alternate Hypothesis, $H_A$ : $\mu$ > 24 years {indicating the average age is significantly greater than 24 years}

Here we employ the One-sample t-test statistics as the population's standard deviation is unknown;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample average age = 25 years

s = sample standard deviation = 2 years

n = sample size = 16

This gives us the test statistics = $\frac{25-24}{\frac{2}{\sqrt{16} } }$ ~ $t_1_5$

= 2

The value of the t-test statistics is 2.

Moreover, the P-value of the test-statistics can be found as follows;

P-value = P( $t_1_5$ > 2) = 0.034 {as per the t-table}

Thus, the P-value lies between 2.5% and 5% based on the t-table.

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15 days ago

Mark and robyn used base-ten blocks to show that 200 is 100 times as much as 2. Whose model makes sense whose model is nonsense?

babunello [3635]

Answer:

Robyn's model is logical, while Mark's is illogical.

Step-by-step explanation:

This question doesn't require calculations. What we need to do is analyze each model logically.

Mark's

Mark's representation indicates 20 instead of 2, which signifies that 200 is ten times greater than 20, making it nonsensical.

Robyn's

Robyn's representation displays 2, suggesting that 200 is 100 times greater than 2, which is not only accurate but also reasonable since 100 * 2 equals 200.

4 0

1 day ago

Which are the roots of the quadratic function f(b) = b2 – 75? Select two options. b = 5 StartRoot 3 EndRoot b = Negative 5 Start

zzz [4022]

Answer:

b = 5√3

b = -5√3

Step-by-step explanation:

We have

$f(b)=b^{2}-75$