Eric conducted an experiment in his science class and recorded the data below.



What is the constant of proportionality that relates the distance traveled, y, to the elapsed time in seconds, x, represented by this data?

The congruent segments, \( SC \cong HR \) and \( HR \cong AB\), according to the substitution property of equality, gives; \( SC \cong AB \)

The given parameters are;

Required;

To prove;

\( SC \cong AB\)

Solution;

From the given parameters, and the definition of congruency, we have;

According to the symmetric property of equality, we have;

SC = HR

Therefore;

According to the substitution property of equality, we have;

If a = b and a = c, therefore;

b = c

Which gives;

HR = SC

HR = AB

Therefore;

SC = AB

Which gives;

\( SC \cong AB \) (Inverse of the definition of congruency)

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Answer:

0.90x + 1.45y

Step-by-step explanation:

You put the vaiable with the price and add the 2 together to get the total.

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Answer:

It would cost 3.6 dollars to by 4 bags of trail mix and 4.35 dollors to by 3 packs of chip

Step-by-step explanation:

Let x = number of bags of trail mix

Let y = number of bags of chips

0.90x + 1.45y = the total amount

( plot the number in )
0.90(4) + 1.45(3) = the total amount

( now multiply 0.90 by 4 and 1.45 by 3 )

3.6 + 4.35

Therefore it would cost 3.6 dollars to by 4 bags of trail mix and 4.35 dollars to by 3 packs of chips

Hope it helps!

Answer:exp(1)

Step-by-step explanation:

E. Regression analysis is a statistical model.

Regression analysis is a statistical technique used to model the relationship between a dependent variable and one or more independent variables.

It aims to predict or explain the variation in the dependent variable based on the values of the independent variables.

Regression analysis considers the relationships and interactions between variables, and it provides insights into the statistical significance and magnitude of their effects.

Therefore, option E, which states that regression analysis is a statistical model, is the valid answer.

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Option B is correct, the inequality which represents the  length of segment AB is greater than  length of segment AD is 9x-16>1.5x+42

The given rectangle is ABCD.

The length of segment AB is 9x-16 units

The length of segment AD is 1.5x+42 units

We have to find the inequality which represents the  length of segment AB is greater than  length of segment AD

> is the symbol used to represent greater than

AB>AD

9x-16>1.5x+42

Hence, option B is correct, the inequality which represents the  length of segment AB is greater than  length of segment AD is 9x-16>1.5x+42

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Answer:

First shape: 366 in^2

Second shape: 376 in^2

Pretty sure these are correct, hope this helps!

1) The missing angles are;

z = 57°

v = 118°

w = 62°

2) The missing angles are;

b = f = g = 24°

a = e = 132°

c = d = 180° - 24°

h = i = 156°

G = 48°

1) Using concept of supplementary angles, we can say that;

z = 180 - 123

z = 57°

Similarly;

v = 180 - 62

v = 118°

Using the concept of alternate angles, we can say that;

w = 62°

We know that sum of angles in a straight line is 180°. Thus;

x = 180 - 57 - 62

x = 61°

2) Using the concept of isosceles triangles, we can say that;

b = f = g = 24°

Thus;

a = e = 180 - (24 + 24)

a = e = 132°

Also;

c = d = 180° - 24°

h = i = 156°

G = 180 - 132

G = 48°

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10=10=10 x,y ( 155/2 97/2

osea que x = 155/2 yY= 97/2

Answer:

11.1

Step-by-step explanation:

Using SOH CAH TOA (O=opposite, H=hypotenuse, A=adjacent). we can determine that to find x we need to use the cosine function.

Since cos=A/H, we can plug in the two numbers we have.

cos(42)=A/15  (Make sure your calculator is in degrees!!!)

Multiply 15 on both sides to isolate A and solve for cos(42) in your calculator.

15cos(42)=A,  or approximately 11.1

Answer:

answer is 0

Step-by-step explanation:

adding a negative is basically just subtracting

27-27 is 0

Answer:

6.4669322e+20

Step-by-step explanation:

Answer:

64 ounce container

ratio 3:13

Step-by-step explanation:

12 oz per can

water added is 4 1/3 cans=12x4 1/3=52 oz

52 (water)+12 (concentrate)=64 ounce container

Ratio=12:52

reduced

3:13

Answer:

3x + 15

Step-by-step explanation:

when distributing, multiply the number outside of the parentheses by the numbers inside the parentheses.

Hey there!

3(x + 5)

DISTRIBUTE 3 WITHIN the PARENTHESES

= 3(x) + 3(5)

= 3x + 15

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

6 and -6 because the positive 6 equals out the negative 6.

Answer:

\(924.96\ cm^3\)

Step-by-step explanation:

Given that,

The diameter of a hockey puck, d = 7.6 cm

Height, h = 3.4 cm

We need to find the volume of the volume of a cylindrical package containing six pucks.

Volume of 1 puck,

\(V=\pi r^2 h\\\\=3.14\times (3.8)^2\times 3.4\\\\=154.16\ cm^3\)

Volume of 6 pucks,

\(V=6\times 154.16\ cm^3\\\\=924.96\ cm^3\)

So, the volume of the 6 puck is \(924.96\ cm^3\).

Given the dimensions of a single hockey puck, we want to find the volume of a cylindrical package containing six pucks. We will see that the volume must be 925 cm^3

So the volume of a cylinder of diameter D and height H is:

V = 3.14*(D/2)^2*H

Here we have:

Then the volume of each single puck is:

V = 3.14*(7.6cm/2)^2*3.4cm = 154.16cm^3

Then the volume of a package that contains 6 of these must have at least 6 times that volume:

6*V = 6*154.16cm^2 = 924.96 cm^3

Rounding to the next cubic centimeter we get 925 cm^3

So the volume of the package must be 925 cm^3

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Answer:

4

Step-by-step explanation:

4-4 =0 so therefore the answer is 4

Answer:

I think it's 2 sorry if I am wrong but

Step-by-step explanation:

2 squared equals 4 and 4 minus 4 equals zero

Answer:

5%

Step-by-step explanation:

100 - 95 = 5

Answer:

2.996

Step-by-step explanation:

14.98 * 0.20 = 2.996

Hope this helps!

Answer:

\(69.8637\)

(4d.p)

Answer:

x = 80

Step-by-step explanation:

4x - 8 = 3x + 72

4x - 3x = 72 + 8

x = 80

To find the powers of a relation, we need to understand the composition of relations. The composition of two relations, denoted as \(R1*R2\), is defined as follows:

Given\(R\)= {(1, 1), (1, 2), (2, 3), (3, 1), (3, 4), (4, 2)}

\(R^2\) = {(1, 1), (1, 2), (1, 3), (2, 1), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3)}

Therefore,\(R^2\) = {(1, 1), (1, 2), (1, 3), (2, 1), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3)}

\(R^2*R\) = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 4), (3, 1), (3, 3), (4, 1), (4, 2), (4, 3)}

Therefore, \(R^3\)= {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 4), (3, 1), (3, 3), (4, 1), (4, 2), (4, 3)}

Hence, \(-R^2\) and\(R^3\)are:

\(-R^2\) = {(-1, -1), (-1, -2), (-1, -3), (-2, -1), (-3, -1), (-3, -2), (-4, -1), (-4, -2), (-4, -3)}

\(R^3\)= {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 4), (3, 1), (3, 3), (4, 1), (4, 2), (4, 3)}

The relation \(-R^2\) represents the negation of each element in the relation \(R^2\),assuming the set includes negative integers as well.

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r = {(1, 1), (1, 2), (2, 3), (3, 1), (3, 4), (4, 2)} on the set {1, 2, 3, 4}, the composition of r with itself, denoted as r^2, and the composition of r with itself three times, denoted as r^3, are calculated.

The composition of relations involves combining the ordered pairs from two relations based on a specific rule. In this case, we are considering the relation r = {(1, 1), (1, 2), (2, 3), (3, 1), (3, 4), (4, 2)} on the set {1, 2, 3, 4}.

To find r^2, we need to calculate the composition of r with itself. We multiply the ordered pairs from r in such a way that the second element of each pair matches the first element of another pair. Applying this rule, we have r^2 = {(1, 2), (2, 1), (2, 2), (3, 2), (3, 3), (4, 1)}.

To find r^3, we calculate the composition of r with itself three times. By applying the same rule as before, we have r^3 = {(1, 1), (1, 3), (2, 2), (2, 4), (3, 1), (3, 2), (3, 3), (4, 1), (4, 3)}.

Therefore, the compositions −r^2 and r^3 of the given relation r can be expressed as −r^2 = {(1, 3), (2, 1), (2, 3), (3, 1), (3, 3), (4, 1)} and r^3 = {(1, 1), (1, 3), (2, 2), (2, 4), (3, 1), (3, 2), (3, 3), (4, 1), (4, 3)}.

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The probability of selecting exactly 2 broken calculators out of 4 when randomly selecting 4 calculators from a box of 50 calculators is 0.255.

The probability formula allows us to determine the likelihood of an event by dividing the number of favorable outcomes by the total number of possible outcomes. The probability of an event occurring can range from 0 to 1, as the number of favorable outcomes can never be greater than the total number of outcomes.

Using this formula, we can calculate the probability of getting exactly 2 broken calculators:

P(X=2) = C(4,2) * (4/50)² * (46/50)²
where C(4,2) is the number of ways we can select 2 broken calculators from a total of 4 broken calculators, which is equal to 6.
Therefore, plugging in the values, we get:
P(X=2) = 6 * (4/50)² * (46/50)²

P(X=2) = 0.255
So the probability of selecting exactly 2 broken calculators out of 4 when randomly selecting 4 calculators from a box of 50 calculators is 0.255.

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the probability that a bulb lasts longer than the advertised figure of 4100 hours is approximately 0.8413 or 84.13%.

The probability that a bulb lasts longer than the advertised figure can be found using the normal distribution formula. In this case, we have a mean of 4400 hours and a standard deviation of 300 hours. The advertised lifetime is 4100 hours. We will calculate the z-score and then use the standard normal distribution table to find the probability. Here's the step-by-step explanation:
Calculate the z-score: The z-score is a measure of how many standard deviations away from the mean a data point is. To calculate the z-score for the advertised lifetime (4100 hours), use the formula:
z = (X - μ) / σ
where X is the advertised lifetime (4100 hours), μ is the mean (4400 hours), and σ is the standard deviation (300 hours).
z = (4100 - 4400) / 300
z = -300 / 300
z = -1
Use the standard normal distribution table: Now that we have the z-score (-1), we can use the standard normal distribution table to find the probability that a bulb lasts longer than the advertised figure. Look for the value corresponding to -1 in the table, which is 0.1587.
Calculate the probability: The value we found in the standard normal distribution table (0.1587) represents the probability that a bulb lasts less than the advertised figure (4100 hours). To find the probability that a bulb lasts longer, we need to subtract this value from 1:
Probability (bulb lasts longer than advertised figure) = 1 - 0.1587
Probability (bulb lasts longer than advertised figure) = 0.8413

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Answer:

I'm not for sure sorry but if u would look it up on here it night show u

The limit does not exist.

In order for such a limit to occur, the fraction \(\frac{x^{2} }{x^{2} +y^{2} }\) must be comparable to the same value \(L\), regardless of the way we take to get there \((0,0)\).

Try approaching \((0,0)\) along the x-axis.

This means setting \(y=0\) and finding the limit \(lim_{x-0} \frac{x^{2} }{x^{2} +y^{2} }\).

We obtain:

\(lim_{x-0,y=0}\frac{x^{2} }{x^{2} +y^{2} } =lim_{y=0}}\frac{x^{2} }{x^{2} +0 }\\=lim_{x-0}} \frac{x^{2} }{x^{2} } \\\\=lim_{x-0}}1\\=1\)

Now evaluate approaching \((0,0)\) along the y-axis.

This means setting \(x=0\) and finding the limit \(lim_{y-0} \frac{x^{2} }{x^{2} +y^{2} }\).

\(lim_{y-0,x-0} \frac{x^{2} }{x^{2} +y^{2} } =lim_{y-0} \frac{0}{0+y^{2} } \\=lim_{y-0} \frac{0}{y^{2} } \\=lim_{y-0} 0\\=0\)

Approaching the origin via these two methods results in distinct limits.

\(lim_{x-0,y-0} \frac{x^{2} }{x^{2} +y^{2} }\) ≠ \(lim_{y-0,x-0}\frac{x^{2} }{x^{2} +y^{2} }\)

Therefore the limit does not exist.

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The correct question is given below:

Find the limit, if it exists, or show that the limit does not exist.

\(lim_{(x,y) -(0,0)} \frac{x^{2} }{x^{2} +y^{2} }\)

Answer:

A. 200 minutes

Step-by-step explanation:

Answer:

d = 48

Step-by-step explanation:

Answer:

Step-by-step explanation:

X<= 2

Which is x is less than or equal to 2.

Answer:

\(n\leq 2\)

Step-by-step explanation:

Answer:

In statistics, the range is the spread of your data from the lowest to the highest value in the distribution.

Step-by-step explanation:

Answer:

The range of a set of data is the difference between the highest and lowest values in the set.