Perimeter or Area of the rectangle

The set of numbers {6, 8, 14} and the set {11, 14, 22} could represent the three sides of a triangle.

To determine whether a set of numbers could represent the sides of a triangle, we need to check if it satisfies the triangle inequality theorem. According to the theorem, the sum of any two sides of a triangle must be greater than the length of the third side.

Let's evaluate each set of numbers:

1. {6, 8, 14}

  The sum of the two smaller sides is 6 + 8 = 14, which is greater than the third side 14. Therefore, this set could represent the sides of a triangle.

2. {13, 20, 34}

  The sum of the two smaller sides is 13 + 20 = 33, which is less than the third side 34. Hence, this set cannot represent the sides of a triangle.

3. {11, 14, 22}

  The sum of the two smaller sides is 11 + 14 = 25, which is greater than the third side 22. Therefore, this set could represent the sides of a triangle.

4. {13, 20, 35}

  The sum of the two smaller sides is 13 + 20 = 33, which is less than the third side 35. Hence, this set cannot represent the sides of a triangle.

In summary, the sets {6, 8, 14} and {11, 14, 22} could represent the three sides of a triangle.

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Answer: $10 per boxed lunch

Step-by-step explanation: Take the total cost of the boxed lunches, $150, and divide it by the number of boxed lunches, 15, to get the answer, $10 per boxed lunch.

Step-by-step explanation:

the max. value is when the smaller set (A) is completely contained in the larger set (B).

then n(A n B) is n(A) = 50.

the set intersection between A and B cannot get bigger than that. or A gets bigger ...

after all, the intersection means it is a set of all elements that exist in BOTH sets.

but then there must be other elements besides A and B in the universal set too, because n(universal set) = 96, and n(A u B) would be only 60.

the min. value could be the empty set or 0. but because n(universal set) = 96, and n(A) + n(B) = 110 and larger than 96, it means that there have to be some shared elements. at least 110 - 96 = 14 elements.

in this case there cannot be other elements in the universal set than A and B. and n(universal set) = n(AuB) = 96.

Answer: 0.363636...

Step-by-step explanation:

100x = 36.363636...

-   x = 0.3636366...

99x = 36

x = 36/99

x = 4/11

Hope this helped!

Answer:

It's 12/5 . When u divide the BC by AB ie. tanC becomes 12/5 .......Try it hope it helps!

Answer:

see explanation

Step-by-step explanation:

tan C = \(\frac{opposite}{adjacent}\) = \(\frac{AB}{BC}\) = \(\frac{24}{10}\) = \(\frac{12}{5}\)

Answer:

t = -40

Step-by-step explanation:

the value of t is just the answer. Do not let the H confuse you.

210 - 250 = -40

t = -40

Answer:

x = 28

y = 83

Step-by-step explanation:

We can use ratios to solve

18           21

------  = -------

24            x

Using cross products

18x = 24*21

Divide each side by 18

x = 24*21/18

x =28

The angles must be equal

<M = <I

83 = y

Answer:

n=8

Step-by-step explanation:

\(13-\frac{3}{4} n=\frac{3}{4} n+1\\13=\frac{6}{4} n+1\\12=\frac{6}{4} n\\48=6n\\8=n\)

Answer:

-2.5-2.5 = -5

Answer:

2x^2+20x+100, 9x^2+24x+16, (1−2x)(−2x+1), (5x+4)(5x−4),  (7−3x)^2

The expressions that are perfect squares are:

2x² + 20x + 100

9x² + 24x + 16

(7 - 3x)²

To determine which expressions are perfect squares, we need to check if they can be written in the form of (a + b)², where a and b are real numbers.

Let's go through each expression:

2x² + 20x + 100:

This expression can be factored as (x + 10)², so it is a perfect square.

9x² + 24x + 16:

This expression can be factored as (3x + 4)², so it is a perfect square.

(7 - 3x)²:

This expression is already in the form (a - b)², so it is a perfect square.

(5x + 4)(5x - 4):

This is the difference of squares, not a perfect square itself.

(1 - 2x)(-2x + 1):

This is the difference of squares, not a perfect square itself.

4² + 6 + 9/4:

Simplifying, we get 16 + 6 + 9/4 = 22 + 9/4.

This expression is not a perfect square.

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The root of the graph of f(x) = \((x-5)^{3} + (x+2)^{2}\) touches the x axis at -2 and 5.

What is root of graph ?

A rooted graph is a graph in which one node is labeled in a special way so as to distinguish it from other nodes. The special node is called the root of the graph.

What is axis ?

An axis in mathematics is defined as a line that is used to make or mark measurements.

Have given ,  f(x) = \((x-5)^{3} + (x+2)^{2}\)

⇒ \((x-5)^{3} * (x+2)^{2}\)= 0.

But if ab = 0 ⇒ either a = 0 or b = 0 or both zero.

⇒ \((x-5)^{3}\)= 0 and \\((x+2)^{2}\) = 0

⇒ (x - 5) = 0 and x + 2 = 0

⇒ x = 5 and x = - 2.

The root of the graph of f(x) = \((x-5)^{3} + (x+2)^{2}\) touches the x axis at -2 and 5.

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Answer:

Below

Step-by-step explanation:

As I posted ....looks to be 147°

The process capability index for the process is 0.1754.

The first sided specification limit will be:

= (Upper specification limit - mean)/(3 × standard deviation)

= (23.1 - 22.9)/(3 × 0.19)

= 0.2/0.57

= 0.3508

The second sided specification limit will be:

= (22.9 - 22.8)/(3 × 0.19)

= 0.1/0.57

= 0.1754

The process capability index for the process is 0.1754 wine it's the lower value.

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The probability that a randomly chosen light bulb lasts more than 10,500 hours is 0.0668 (rounded to four decimal places).

The probability that a randomly chosen light bulb lasts more than 10,500 hours is 0.0668(rounded to four decimal places).Here's how to calculate it:Given data mean μ = 9,000 and standard deviation σ = 1,000.To calculate the probability that a random light bulb lasts more than 10,500 hours, convert the problem to a standard normal distribution.

z = (10,500 - μ)/σ = (10,500 - 9,000)/1000 = 1.50

Here's the standard normal distribution curve with the shaded area representing the probability required: Standard normal distribution curve with the shaded area

Now, the area under the curve to the right of z = 1.5 is the probability that a randomly chosen light bulb will last more than 10,500 hours.

Using the Z table, we can look up the value corresponding to a z-score of 1.5. The table gives us a value of 0.9332.Now, the area to the left of z = 1.5 is 1 - 0.9332 = 0.0668, which is the probability that a randomly chosen light bulb lasts more than 10,500 hours, rounded to four decimal places.

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Answer:

3 $10 coins and 5 $5 coins

Step-by-step explanation:

Answer:

When adding numbers to a number line you're going left when subtracting negative it's like adding a positive so you're going to the right

Answer:

3^2 = 9

8^2 = 64

10^2 = 100

The height of the cone is approximately 1.5 cm.

Both a cone and a cylinder have circular bottoms and are three-dimensional shapes. The lateral surfaces of the two shapes differ most noticeably from one another. A cone has a lateral surface that tapers from a point at the apex to a circular base, whereas a cylinder has a curved lateral surface that is parallel to its base. The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius of the base and h is the height, whereas the volume of a cone is calculated using V = (1/3)πr²h.

The volume of the cone is given as:

V = (1/3)πr²h

Rearranging the equation to isolate h we get:

3V = πr²h

h = (3V)/(πr²)

Now, for  volume

of 48 cm³ and a base with a radius of 4 cm we have:

h = (3(48))/(π(4)²)

h ≈ 1.5 cm

Hence, the height of the cone is approximately 1.5 cm.

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The following differential equations with a solution
y" + y = 0 corresponds to solution A: y = cos(2)

y" + y' + 28y = 0 corresponds to solution B: y = e^(-4x)

y" + 11y' + 28y = 0 corresponds to solution C: y = e^(7x)

2x^2y" + 3xy' = y corresponds to solution D: y = x^(1/2)

1. y" + y = 0:

This is a second-order homogeneous differential equation with constant coefficients. The characteristic equation is r^2 + 1 = 0, which has complex roots r = ±i. The general solution is therefore a linear combination of sine and cosine functions:

y = c1 cos(x) + c2 sin(x)

Using the initial condition y(0) = 1, we can solve for the constants to get:

y = cos(x)

2. y" + y' + 28y = 0:

This is a second-order homogeneous differential equation with constant coefficients. The characteristic equation is r^2 + r + 28 = 0, which has complex roots given by the quadratic formula:

r = (-1 ± sqrt(1 - 4*28)) / 2 = (-1 ± 7i) / 2

The general solution is therefore a linear combination of exponential and sine/cosine functions:

y = e^(-x/2) (c1 cos(7x/2) + c2 sin(7x/2))

Using the initial condition y(0) = 1, we can solve for the constants to get:

y = e^(-4x)

3. y" + 11y' + 28y = 0:

The characteristic equation is r^2 + 11r + 28 = 0, which can be factored as (r + 4)(r + 7) = 0. The roots are r = -4 and r = -7. Therefore, the general solution is a linear combination of exponential functions:

y = c1 e^(-4x) + c2 e^(-7x)

Using the initial condition y(0) = 1, we can solve for the constants to get:

y = e^(7x)

4. 2x^2y" + 3xy' = y:

Dividing both sides by x^2 and letting z = y/x^(1/2). Then, we get:

z' + (1/4x)z = 0

This is a first-order homogeneous differential equation with an integrating factor of e^(1/4 ln x) = x^(1/4). Multiplying both sides by the integrating factor, we get:

x^(1/4) z' + (1/4)x^(-3/4)z = 0

The left-hand side is the derivative of (x^(1/4) z), so we can integrate both sides to get:

x^(1/4) z = c1

Solving for z, we get:

z =c1/x^(1/4)

Substituting back for y, we get:

y = x^(1/2) z = c1 x^(1/4)

Using the initial condition y(1) = 1, we can solve for the constant to get:

y = x^(1/2)

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Answer:

75.9550

Step-by-step explanation:

Answer:

40% and yes she can afford the boots

Step-by-step explanation:

just multyply 60 by 40% and you'll get $24

Same for the second question $75*32%=24

Answer:

Remains on her gift card:

$3.07

Step-by-step explanation:

15 - ((2*2.65) + (2*1.79) + (1*3.05))

= 15 - (5.3 + 3.58 + 3.05)

= 15 - 11.93

= 3.07

Answer:

$3.07

Step-by-step explanation:

Ms. Gantt has a $15 gift card to Starbucks.

She buys 2 muffins for $2.65 each, = 2 × 2.65 = $5.3

2 hot chocolates for $1.79 each, = 2 × 1.79 = $3.58

and a juice for $3.05. = 1 × 3.05 = $3.05

Now,

$15 - $5.3 - $3.58 - $3.05 = $3.07

Thus, $3.07 remains on her gift card

Answer:

24

Step-by-step explanation:

hope this helps :D

Answer:

It is C

Step-by-step explanation:

Graph the inequality by finding the boundary line, then shading the appropriate area.

y > 3 5 x − 1.5

Answer:

7 pounds.

Step-by-step explanation:

3.60 for 3 pounds

1.20 per pound.

8.40/1.20 = 7 pounds

The integer $a$ consists of a sequence of 1985 eights in base 10 representation, while the integer $b$ consists of a sequence of 1985 fives. The sum of the digits of the base 10 representation of $9ab$ is 9925.

The integer $a$ consists of a sequence of 1985 eights in base 10 representation, while the integer $b$ consists of a sequence of 1985 fives. We need to find the sum of the digits of the base 10 representation of $9ab$.
To find the value of $9ab$, we first need to determine the value of $ab$. Since $a$ consists of 1985 eights and $b$ consists of 1985 fives, $ab$ will be a number with 3970 digits. Each digit in $ab$ will be either an eight or a five.
When we multiply $9$ by a digit $d$ that is either an eight or a five, the result will be a number that ends in a zero, except when $d$ is a five, in which case the result will end in a five.
Therefore, when we multiply $9$ by each digit in $ab$, we will obtain a number that ends in a zero for each eight and a number that ends in a five for each five. Since there are 1985 eights and 1985 fives in $ab$, the resulting number $9ab$ will have 3970 digits, all ending in either zero or five.
Now, let's find the sum of the digits in the base 10 representation of $9ab$. Since all the digits in $9ab$ end in either zero or five, the sum of the digits will depend on the number of zeros and fives.
In $ab$, there are 1985 zeros and 1985 fives. When we multiply these zeros and fives by 9, we obtain a number with 1985 zeros and 1985 fives as well.
Therefore, the sum of the digits in the base 10 representation of $9ab$ will be equal to $1985 \times 0 + 1985 \times 5$. Simplifying this expression, we have $0 + 9925 = 9925$.
Hence, the sum of the digits of the base 10 representation of $9ab$ is 9925.

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Answer:

c

Step-by-step explanation:

Answer:

C

1 or more includes from the 1st quartile to the rest of the graph, so it is 75%

Answer:

8<x<33/2

Step-by-step explanation:

A+B+C=180 ==> all three angles of a triangle=180 degrees

Let's say A=2x+1, B=3x-7. Solve for C:

2x+1 + 3x-7 + C=180

2x+3x+1-7+C=180 ==> join like terms

5x-6+C=180

5(8)-6+C=180  ==> substitute 8 for x

40-6+C=180  ==> simplify

34+C=180

34-34+C=180-34

C=146

5x+C=186

5x-5x+C=186-5x

C=186-5x

a+3x-7=180 ==> these two angles from a straight line (A is separate from a)

2x+1 + 3x-7 + C=180

a+3x-7=2x+1 + 3x-7 + C

a=2x+1 + C ==> subtract 3x-7 from both sides

a=2x+1 + 146  ==> substitute 146 for C

a=2x+147

a<180 ==> a can't be 180 degrees since a equals 180 minus an angle(C).

2x+147<180

2x+147-147<180-147

2x<33

2x/2<33/2

8<x<33/2

Answer:

3/10

Step-by-step explanation: