Which is a perfect square? 6 Superscript 1 6 squared 6 cubed 6 Superscript 5 Mark

Segment GI is congruent to Segment JL and Segment GH is congruent to Segment KL. I have to prove Segment HI is congruent to Segm

Zina [12379]

Solution:

Refer to the detailed explanation

Step-by-step process:

1 step: $\overline{GI}\cong \overline {JL}$ - provided

2 step: $\overline{GI}\cong \overline{GH}+\overline{HI}$ - Segments Addition Postulate

3 step: $\overline{GH}+\overline{HI}\cong \overline {JL}$ - Substitution Property

4 step: $\overline {JL}\cong \overline {JK}+\overline {KL}$ - Segments Addition Postulate

5 step: $\overline{GH}+\overline{HI}\cong \overline {JK}+\overline {KL}$ - Substitution Property

6 step: $\overline{GH}\cong \overline {KL}$ - provided

7 step: $\overline{GH}+\overline{HI}\cong \overline {JK}+\overline {GH}$ - Property of Substitution Equality

8 step: $\overline{HI}\cong \overline {JK}$ - Equality Subtraction Property

3 0

3 months ago

Exclude leap years from the following calculations. (a) Compute the probability that a randomly selected person does not have a

babunello [11817]

Answer:

a) There is a 99.73% chance that a randomly picked individual does not celebrate their birthday on March 14.

b) There is a 96.71% chance that a randomly picked individual does not celebrate their birthday on the 2nd day of any month.

c) There is a 98.08% chance that a randomly picked individual does not celebrate their birthday on the 31st day of a month.

d) There is a 92.33% chance that a randomly picked individual was not born in February.

Step-by-step explanation:

The probability is calculated as the number of successful outcomes divided by the total outcomes.

A standard year comprises 365 days.

(a) Calculating the probability that a randomly selected individual does not have a birthday on March 14:

Excluding March 14 yields 365-1 = 364 days. Thus,

364/365 = 0.9973

So, there is a 99.73% chance that a randomly selected person does not celebrate their birthday on March 14.

(b) Calculating the probability that a randomly selected person does not celebrate their birthday on the 2nd day of a month:

With 12 months, there are 12 occurrences of the 2nd day.

Thus,

(365-12)/365 = 0.9671

Hence, a 96.71% chance that someone does not have a birthday on the 2nd day of any month.

(c) Calculating the probability that a randomly chosen individual does not have a birthday on the 31st day of any month:

Months with 31 days include January, March, May, July, August, October, and December.

This totals 7 instances of the 31st day.

Thus,

(365-7)/365 = 0.9808

In conclusion, there's a 98.08% chance that a randomly selected person does not celebrate their birthday on the 31st day of any month.

(d) Calculating the probability that a randomly selected person was not born in February:

February has 28 days in a non-leap year. Thus,

(365-28)/365 = 0.9233

So, a 92.33% chance that a randomly picked individual was not born in February.

6 0

3 months ago

The population p of a small community on the outskirts of a city grows rapidly over a 20-year period: t05101520p1002004509502000

lawyer [12517]

Answer:

After five years beyond the initial 20-year stretch, the population of this small community will be 4268.

Step-by-step explanation:

t | 0 | 5 | 10 | 15 | 20

p | 100 | 200 | 450 | 950 | 2000

The representation of the exponential function is:

p = aeᵏᵗ

where a and k represent constants.

Taking the natural logarithm on both sides:

In p = In aeᵏᵗ

In p = In a + In eᵏᵗ

In p = In a + kt

In p = kt + In a.

We can apply linear regression to model the relationship between In p and t, thereby determining the values of k and In a.

t | 0 | 5 | 10 | 15 | 20

p | 100 | 200 | 450 | 950 | 2000

In p | 4.605 | 5.298 | 6.109 | 6.856 | 7.601

In p = kt + In a.

y = mx + b

Here m corresponds to k and b is In a

By conducting a linear regression on the transformed linear relationship among In p and t and creating a graph of the variables, we derive the regression equation:

y = 0.151x + 4.584

The first image illustrates the equations needed for estimating the parameters of linear regression.

The second image displays the regression calculations alongside the graph of In p versus t.

By comparing

y = 0.151x + 4.584

to

In p = kt + In a.

y = In p

k = 0.151

x = t

In a = 4.584

a = 97.905

Thus, the exponential relationship between p and t is formulated as:

p = 97.905 e⁰•¹⁵¹ᵗ

In order to forecast the population for 5 years ahead from the 20-year mark, we need to find p at t=25 years.

0.151 × 25 = 3.775

p(t=25) = 97.905 e³•⁷⁷⁵ = 4268.41, which rounds down to 4268.

Hope this assists!!!

7 0

3 months ago

−7x−50≤−1 AND−6x+70>−2

PIT_PIT [12445]

Answer:

$-7\geq x$ and $[-7,12)$ expressed in interval notation.

Step-by-step explanation:

A compound inequality $-7x-50\leq -1\text{ and }-6x+70>-2$ has been provided. Our task is to determine the solution for this inequality.

Initially, we will address each inequality independently, followed by merging the findings by combining the overlapping intervals.

$-7x-50\leq -1$

$-7x-50+50\leq -1+50$

$-7x\leq 49$

By dividing with a negative number, it is necessary to reverse the inequality sign:

$\frac{-7x}{-7}\geq \frac{49}{-7}$

$x\geq -7$

$-6x+70>-2$

$-6x+70-70>-2-70$

$-6x>-72$

Again, dividing by a negative requires flipping the inequality sign:

$\frac{-6x}{-6}$

$x$

In combining both intervals, we will arrive at:

$-7\geq x$

Thus, the solution for the inequality provided is $-7\geq x$ and $[-7,12)$ in interval notation.

7 0

3 months ago