For a craft project, four students each chose three pieces of wire from a box. don’s wires measure 3 inches, 5 inches, and 12 inches. margo’s wires measure 6 inches, 8 inches, and 14 inches. sonji’s wires measure 12 inches, 8 inches, and 17 inches. liam’s wires measure 16 inches, 8 inches, and 27 inches. which student chose pieces that can be used to construct a triangle?

Answers

Answer 1

Only Sonji chose pieces that can be used to construct a proper triangle with given measurements.

To determine which student chose pieces that can be used to construct a triangle, we need to check whether the length of the longest wire is less than the sum of the other two wires. If this condition is true for any of the students, then they chose pieces that can be used to construct a triangle.

Let's start with Don. His longest wire is 12 inches. The sum of the other two wires is 3 + 5 = 8 inches, which is less than 12 inches. Therefore, Don's wires cannot be used to construct a triangle.

Moving on to Margo, her longest wire is 14 inches. The sum of the other two wires is 6 + 8 = 14 inches, which is equal to 14 inches. This means Margo's wires can form a degenerate triangle, which is essentially a straight line. So technically, Margo's wires can be used to construct a triangle, but not a proper one.

For Sonji, her longest wire is 17 inches. The sum of the other two wires is 12 + 8 = 20 inches, which is greater than 17 inches. This means that Sonji's wires can be used to construct a triangle.

Finally, for Liam, his longest wire is 27 inches. The sum of the other two wires is 16 + 8 = 24 inches, which is less than 27 inches. Therefore, Liam's wires cannot be used to construct a triangle.

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Related Questions

The probability of spinning a 4 on a spinner is 0.125.If you spun 150 times approximately how many times would the spinner land on 4?

Answers

Answer:

19

Step-by-step explanation:

To calculate this, all we need to do is 150 * 0.125 ≈ 18.75 which rounds to 19. We round to the nearest integer because you can't land on the 4 18.75 times.

Answer: 19

Step-by-step explanation:

.125 is equal to 1/8, so it will be roughly 1/8 of the 150 times so we can multiply

150(.125)=18.75, which rounded up, or normally becomes 19

Please help‼️ domain and range‼️

Please help domain and range

Answers

The domain and the range of the function are (-∝, ∝) and (0, ∝), respectively

Calculating the domain and range of the graph?

From the question, we have the following parameters that can be used in our computation:

The graph

The above graph is an exponential function

The rule of an function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (0, ∝)

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a race lasted 14.8 minutes. how many seconds did it take to complete this race

Answers

Answer:

888 seconds

Step-by-step explanation:

I hope this helps!

PLeaseee can i have brainlest i don't want to beg but i really want to level up

what is 120 euros to dollars?

Answers

The value of euros can be converted to dollars by simply multiplying euro by 1.06 so 120 euros be 127.89 dollars.

Unit conversion is the process of converting the dimension of a given quantum between colorful units, frequently by multiplicative conversion factors that alter the value of the measured volume without altering its goods.

The sanctioned currency of 20 of the EU's 27 member countries is the euro( symbol€; law EUR)( EU). By of 2023, this group of countries — officially known as the eurozone or euro area — will have around 344 million residers. One euro is equal to one hundred cents.

The United States bone ( symbol$; law USD; frequently shortened asUS$ orU.S. Bone to separate it from other bone - nominated currencies; also known as the bone ,U.S. bone , American bone , or informally buck) is the sanctioned coin of the United States and multitudinous other nations.

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In the standard (x,y) coordinate plane, a line intersects
the y-axis at (0,2) and contains the point (8,3). What is
the slope of the line?

Answers

Answer:

\(\sf Slope =\dfrac{1}{8}\)

Step-by-step explanation:

(0,2) ;  (8 ,3)

Slope:

\(\sf \boxed{Slope = \dfrac{y_2-y_1}{x_2-x_1}}\)

         \(\sf = \dfrac{3-2}{8-0}\\\\=\dfrac{1}{8}\)

A rectangular vegetable garden will have a width that is 3 feet less than the length, and an area of 54 square feet. If x represents the length, then the length can be found by solving the equation:x(x-3)=54 What is the length, x, of the garden? The length is blank feet.

Answers

Answer:

9

Step-by-step explanation:

What you do if first you draw your rectangle. You name length as x (as told in the question) and width as x-3 (since the width is 3 feet less). To obtain the area you have to do x × (x-3) because to find area you do length × width right.

So area is x(x-3) and it also tells you that area is 54 there

That's how you get x(x-3)=54

Now to solve it, you have to expand

x(x-3)=54

x²-3x-54 = 0 (you have to factorise this now)

(x+6) or (x-9) = 0

x = -6 or x = 9

As you can see you have two answers there. We have to eliminate the -6 because length can never be negative. The logic is simple, any length you take for example on a ruler (it has to be 0 or above) you can measure 1 feet, 2 feet, even 100 feet but you can't measure less than 0 right?

So the final answer is that x=9 and x represents the length

So length = 9

I NEED HELP PLZZ :((

5/2 ÷ 3/4
pls help me solve this

Answers

Answer:

3 1/3 Because When we divide two fractions, such as 5/2 ÷ 3/4, we flip the second fraction and then we simply multiply the numerators with each other and the denominator with each other.

Step-by-step explanation:

remember to simplify if ever possible!:D

soooo

in order to do this both fractions has to have the same denominator

so you find the CMD (common denominator)

which is 4

so you'd only change 5/2

5/2 * 2/2 to make it 10/4

now both fractions have the same denominator

you do keep change flip

you keep 10/4

change division to multiplication

and flip 3/4 TO 4/3

which would equal

10/4 * 4/3= 40/12

40/12

and you divide it with long division

you get 3 as ur quotient

divisor as 12

and remainder as 4

= 3 4/12

nd u simplify which u divide 4/12 by 4 and get 1/3

so the answer would be 3 1/3

and in order to check you can use an online fraction calculator

Ms. Lopez draws two cylinders on the whiteboard. The first cylinder has a diameter of 6 inches and a height of 14 inches.

Answers

If Ms. Lopez draws two cylinders on the whiteboard. The first cylinder has a diameter of 6 inches and a height of 14 inches. If the second cylinder has the same ratio of diameter to height,  its height is: 7 inches.

Height

Since the first cylinder has a diameter of 6 inches and a height of 14 inches the ratio for the first cylinder is 14 : 6

The ratio for the second cylinder is h : 3.

Where:

h= height

Hence

h/14 = 3/6

h= 14 × 3/6

h = 7 inches


Therefore If Ms. Lopez draws two cylinders on the whiteboard. The first cylinder has a diameter of 6 inches and a height of 14 inches. If the second cylinder has the same ratio of diameter to height,  its height is: 7 inches.

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The complete question is:

Ms. Lopez draws two cylinders on the whiteboard. The first cylinder has a diameter of 6 inches and a height of 14 inches. The second cylinder has a diameter of 3 inches.

If the second cylinder has the same ratio of diameter to height, what is its height?

True or false: The unit rate of 45km travelled in 30 minutes is 1.5 km per minute ?

Answers

Answer:

true

Step-by-step explanation:

30x1.5=45

Answer: True

Step-by-step explanation: If you divide 45km by 30 minutes, then you should get a unit rate of 1.5km per minute.

Will give u Brainly

Will give u Brainly

Answers

Answer:

Option B

Step-by-step explanation:

Set 1:

med: 76, Range: 50-65= 15IQR: 77-73= 4

find the median, range, and IQRfor each data set.

Set 2:

med: 60, Range: 68-55= 13,IQR: 63-59= 4

76- 60 =16

find the difference of the medians 16 is 4 times 4

so the difference of the medians is 4 times the IQR

----------------------------

hope it helps...

have a great day!!

A local ice cream shop wants to see if they should promote a new swizzleberry swirl or creamsicle flavored drink. In order to determine which one to promote, they took a sample of 80 patrons and asked them to choose which they preferred. The one that is significantly preferred over the other (at a .05 level of significance) will be promoted. It is expected that an equal number of patrons will choose each flavor. Based on the observed frequencies given below, what is the decision for this test

Answers

Heh I think it’s 2.65 Bc I haven’t done this for a while so let’s hope that’s right lol

during the school year, the 10 members of the chess club play a total of 900 games of chess during their practice matches. each member plays against every other member $n$ times. what is the value of $n$?

Answers

On solving the provided question, we can say that by permutation  900 games were actually played; N = 900/45 = 20

what is permutation?

The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order.

The number of matches would be if each player faced each other once.

\(^{10}C_2\) = 10! / 2! 8!

= 10 X 9 / 2 = 90/2

= 45

Given that 900 games were actually played,

N = 900/45 = 20

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What are the boundaries of the class 1.87-3.43? 3). A) 1.87-3.43 B) 1.82-3.48 C) 1.879-3.439 D) 1.865-3.435

Answers

The boundaries of the class 1.87-3.43 are D) 1.865-3.435. The lower boundary is 1.865 and the upper boundary is 3.435.

The boundaries of the class 1.87-3.43 can be determined by subtracting and adding half of the smallest possible unit of measurement to the given class limits. In this case, since the given class limits are 1.87 and 3.43, we need to find the boundaries by subtracting and adding half of the smallest possible unit of measurement.

Let's assume the smallest possible unit of measurement is 0.01.

To find the lower boundary:

Lower Boundary = Lower Limit - (0.01/2)

Lower Boundary = 1.87 - 0.005

Lower Boundary = 1.865

To find the upper boundary:

Upper Boundary = Upper Limit + (0.01/2)

Upper Boundary = 3.43 + 0.005

Upper Boundary = 3.435

Therefore, the boundaries of the class 1.87-3.43 are:

D) 1.865-3.435

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Which figure represents the image of trapezoid LMNP after a reflection across the x-axis? figure A figure B figure C figure D

Answers

Answer:

figure A

Step-by-step explanation:

it’s in the same cordinates but reflected across the x axis

figure A shows the reflect of trapezoid LMNP across the X-Axis.

Which figure represents the image of trapezoid LMNP after a reflection across the x-axis


What is trapezoid?

Trapezoid, it  is quadrilateral having only two sides are parallel to each other.

Since the question is incomplete there is no graph has been shown of the trapezoid.

So, the reflection of the trapezoid will same as the figure attached below in the image.

Thus the required reflection of the LMNP trapezoid is plotted in the image.

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Which figure represents the image of trapezoid LMNP after a reflection across the x-axis? figure A figure

A runner is 6/8 mile from the finish line. If she can travel 3/8 mile per minute, how long will it take her to finish the race? Answer in a complete sentence.

Answers

Answer:

it will take her 40 seconds to finish the race.

3/8 per minute, would make it 1/8 every 20 seconds. since she only has 2/8 of a mile left to go, 20 seconds +20 seconds = 40 seconds

(if you needed how long it takes her to run the whole race, it's 2 minutes 40 seconds, which would make her the fastest mile runner in the world)

Step-by-step explanation:

I hope this helps :)

A tailor cuts 234 yards from a roll of fabric to make one curtain. She has 1812 yards of fabric available to make curtains. Use the drop-down menus to answer each question.

Answers

The symbol that should be used is the division symbol. On the other hand, in the result the whole number represents the number of curtains, while the fraction represents a fraction of the next curtain.

Given :

The numerator: Number above.

The denominator: Number below.

A whole number: Optional element.

The number of curtains the tailor can make is equal to the total fabric divided by the fabric required for one curtain. Based on this, the symbol should be ÷.

= 18 1/2 ÷ 2 3/4

The whole number represents the number of curtains. The division of the total fabric and the total fabric required for one curtain will include a whole number and a fraction. In this situation, the whole number represents the number of curtains that can be made from the total fabric.

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The volume of a sample of gas is measured as 3266.1 cm
3
. Convert the volume to cubic meters.

Answers

The volume of the sample of gas is 0.0032661 cubic meters (m³).

How do you convert the volume of a gas from cubic centimeters to cubic meters?

To convert the volume from cubic centimeters (cm³) to cubic meters (m³), you need to understand the relationship between the two units. There are 1,000,000 cubic centimeters in one cubic meter.

So, to convert the given volume of 3266.1 cm³ to cubic meters, you divide it by the conversion factor:

3266.1 cm³ ÷ 1,000,000 = 0.0032661 m³

This means that the given sample of gas has a volume of approximately 0.0032661 cubic meters.

When converting between cubic centimeters and cubic meters, you are scaling the volume by a factor of 1,000,000.

Since a cubic meter is much larger than a cubic centimeter, dividing the volume by 1,000,000 results in a smaller value expressed in cubic meters.

Therefore, the volume of the sample of gas is approximately 0.0032661 cubic meters (m³).

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Find a point-slope form for the line with slope 1/5 and passing through the point (- 4. - 8).
The equation of the line in point-slope form is?
(Simplify your answer. Use integers or fractions for any numbers in the equation.)

Answers

Answer:

y+8 = 1/5(x+4)

Step-by-step explanation:

The point slope form of a line is

y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line

y- -8 = 1/5(x - -4)

y+8 = 1/5(x+4)

Does the equation y = √x-10 define y as a function of x?

Answers

y = √x-10

Since if we plug an input value x, we will obtain an output value y:

For example:

x =20

y = √20-10= √20

The answer is YES.

find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. vertical axis and passes through the point (5, 9)

Answers

The standard form of the equation of the parabola with a vertical axis, vertex at the origin, and passing through the point (5, 9) is y = 0.36x^2.

To find the equation of a parabola with these characteristics, we can use the standard form of a parabola with a vertical axis: y = ax^2, where a is a constant and the vertex is at the origin (0, 0). We need to find the value of a by using the given point (5, 9).

Step 1: Plug the coordinates of the point (5, 9) into the equation:
9 = a(5)^2

Step 2: Simplify the equation:
9 = 25a

Step 3: Solve for a:
a = 9/25
a = 0.36

Now that we have the value of a, we can write the equation of the parabola in standard form:
y = 0.36x^2

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Please, help with this question!

Please, help with this question!

Answers

Answer:

arc AM = 114°

Step-by-step explanation:

the measure of a tangent- chord angle is half the measure of its intercepted arc, that is

∠ MAC = \(\frac{1}{2}\) (AM )

57° = \(\frac{1}{2}\) AM ( multiply both sides by 2 to clear the fraction )

114° = AM

use the following information for question 2 - 6: tv advertising agencies face increasing challenges in reaching audience members because viewing tv programs via digital streaming is gaining in popularity. the harris poll reported on november 13, 2012, that 53% of 2343 american adults surveyed said they have watched digitally streamed tv programming on some type of device. question 2: what is the sample proportion?

Answers

The sample proportion is 0.530 and the z-critical value is 2.58 and the confidence interval at 99% is ( 0.503, 0.556 ).

Given that,

Because watching TV via digital streaming is becoming more and more common, tv advertising companies are having a harder time connecting with viewers. 53% of the 2343 American adults surveyed by the Harris Poll on November 13, 2012, claimed they had viewed digitally streamed television content on at least one device.

We have to find what is the sample proportion? firstly, the z-critical value is ? What is the confidence interval at 99%?

We know that,

n = 2343

Point estimate = sample proportion = \(\hat p\) = 0.530

1 - \(\hat p\) = 1 -0.530 = 0.470

At 99% confidence level

α = 1-0.99% =1-0.99 =0.01

α /2 =0.01/ 2= 0.005

Z(α /2) = Z0.005 = 2.576

Z (α/2) = 2.576 = 2.58

Margin of error = E = Z (α/2) × √((\(\hat p\) × (1 - \(\hat p\) )) / n)

=2.576 × (√(0.530×(0.470) /2343 )

= 0.027

A 99% confidence interval for population proportion p is ,

\(\hat p\)- E < p < \(\hat p\) + E

0.530 -0.027 < p < 0.530 +0.027

0.503 < p < 0.556

( 0.503, 0.556 )

Therefore, The sample proportion is 0.530 and the z-critical value is 2.58 and the confidence interval at 99% is ( 0.503, 0.556 ).

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The absolute value of a number is (sometimes, always, never) the opposite of the number.

Answers

Answer:

sometimes

Step-by-step explanation:

Pretend this symbol is the absolute value symbol because I don't have the actual one on my keyboard. ()

(-3) = 3

The answer above is opposite

(7) = 7

The answer above is the same

Conclusion: the opposite value of the number is sometimes the opposite of the number

Sometimes because it’s sometimes the opposite but sometimes the same value. |-7| is 7 (opposite) and |7| is 7 (same)

Pls help/ The y-intercept of f(x)=(1.6)x is ______________________ the y-intercept of the function in the graph:

Pls help/ The y-intercept of f(x)=(1.6)x is ______________________ the y-intercept of the function in

Answers

The y-intercept of f(x) = (1.6)x is (a) less than the y-intercept of the function in the graph

How to complete the blank?

The equation of the function is given as

f(x) = (1.6)x

To determine the y-intercept, we set x = 0

So, we have

f(0) = 1.6 * 0

Evaluate

f(0) = 0

For the graph, we have

When x = 0, the function has a value of 1

This means that

y-intercept is 1

0 is less than 1

Hence, the y-intercept of f(x) = (1.6)x is (a) less

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How many ways are there to roll eight distinct dice so that all six faces appear? (solve using inclusion-exclusion formula)

Answers

To solve this problem using the inclusion-exclusion principle, we need to consider the number of ways to roll eight distinct dice such that all six faces appear on at least one die.

Let's denote the six faces as F1, F2, F3, F4, F5, and F6.

First, we'll calculate the total number of ways to roll eight dice without any restrictions. Since each die has six possible outcomes, there are 6^8 total outcomes.

Next, we'll calculate the number of ways where at least one face is missing. Let's consider the number of ways where F1 is missing on at least one die. We can choose 7 dice out of 8 to be any face except F1. The remaining die can have any of the six faces. Therefore, the number of ways where F1 is missing on at least one die is (6^7) * 6.

Similarly, the number of ways where F2 is missing on at least one die is (6^7) * 6, and so on for F3, F4, F5, and F6.

However, if we simply add up these individual counts, we will be overcounting the cases where more than one face is missing. To correct for this, we need to subtract the counts for each pair of missing faces.

Let's consider the number of ways where F1 and F2 are both missing on at least one die. We can choose 6 dice out of 8 to have any face except F1 or F2. The remaining 2 dice can have any of the remaining four faces. Therefore, the number of ways where F1 and F2 are both missing on at least one die is (6^6) * (4^2).

Similarly, the number of ways for each pair of missing faces is (6^6) * (4^2), and there are 15 such pairs (6 choose 2).

However, we have subtracted these pairs twice, so we need to add them back once.

Continuing this process, we consider triplets of missing faces, subtract the counts, and then add back the counts for quadruplets, and so on.

Finally, we obtain the total number of ways to roll eight distinct dice with all six faces appearing using the inclusion-exclusion formula:

Total ways = 6^8 - 6 * (6^7) + 15 * (6^6) * (4^2) - 20 * (6^5) * (3^3) + 15 * (6^4) * (2^4) - 6 * (6^3) * (1^5) + (6^2) * (0^6)

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Exercise 3.4.3: Proving algebraic statements with direct proofs. Prove each of the following statements using a direct proof. (a) For any positive real numbers, x and y, x + y >= √xy.

Answers

The statement "For any positive real numbers x and y, x + y >= √xy" can be proven using a direct proof by squaring both sides of the inequality and manipulating the expressions to show their equivalence.

To prove the statement using a direct proof, we start by assuming that x and y are positive real numbers. Our goal is to show that x + y >= √xy.

First, we square both sides of the inequality:

(x + y)^2 >= (√xy)^2

Expanding the left side of the inequality:

x^2 + 2xy + y^2 >= xy

Next, we simplify the inequality by subtracting xy from both sides:

x^2 + xy + y^2 >= 0

This inequality holds true for any real numbers x and y because the sum of squares is always non-negative.

Since we assumed x and y to be positive real numbers, the inequality x^2 + xy + y^2 >= 0 is always true. Therefore, we have shown that x + y >= √xy using a direct proof.

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(02.01)
Solve −2(2x + 5) − 3 = −3(x − 1). (1 point)

16
−16
−10
−13

Answers

Answer:

-16

Step-by-step explanation:

can anyone help me with this, thank you.

can anyone help me with this, thank you.

Answers

Answer:

65

Step-by-step explanation:

i know its right :)

x =

y =

m ∠ H =

m ∠ G =

x = y = m H = m G =

Answers

Answer:

x=53

y=26

H=106

G=93

Step-by-step explanation:

By the inscribed quadrilateral conjecture:

\(2x+(x+21)=180\\(3y+9)+(4y-11)=180\\3x+21=180\\3x=159\\x=53\\7y-2=180\\7y=182\\y=26\\H=2(53)=106\\G=(4(26)-11)=104-11=93\)

Hope this helps!

A worker is getting a 4% raise. His current salary is $40,361. How much will his raise be?

Answers

We need to calculate the 4%

\(40361\cdot0.04=1614.44\)

The raise will be $1614.44

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