How many 2 1/3 m lengths of rope can be cut from a rope of length 21 m?​

Answer:

  b.  40

Step-by-step explanation:

You want the missing leg length in a right triangle with one side of length 9 and the hypotenuse of length 41.

The missing side of any triangle will be between the sum and difference of the other two side lengths.

  c-a < b < c+a

  32 < b < 50

In a right triangle, every side length is less than the length of the hypotenuse:

  b < c

  32 < b < 41

There is only one answer choice in this range: b = 40.

__

Additional comment

You can make use of your knowledge of Pythagorean triples. One of them is {9, 40, 41}, which tells you that b=40.

Or, you can use the Pythagorean theorem to compute b:

  a² +b² = c²

  9² +b² = 41²

  b² = 1681 -81 = 1600

  b = √1600 = 40

For any odd integer, there is a Pythagorean triple with sides 1 unit apart such that those longer side lengths are about half of the square of that odd integer:

  9² = 81 = 40+41

so {9, 40, 41} is a Pythagorean triple.

The simplest of these is ...

  3² = 9 = 4+5   ⇒   {3, 4, 5} is a Pythagorean triple.

From the given data, 6 employees are ill and 7 are not ill after ate in cafeteria. and 1 employee is ill and 25 are not ill after did not ate in cafeteria.

In the given question,

Results of the questionnaire were obtained for 39 of the 40 workers at the plant.

Six of the seven ill employees ate at the factory cafeteria on September 26 and 27.

7 of 32 non-stricken workers who ate at the factory cafeteria in both days.

We have to construct a 2x2 table using these data.

6 employees are ill and 7 are not ill after ate in cafeteria.

1 employee is ill and 25 are not ill after did not ate in cafeteria.

So the table should be

                                          ILL                    Not ILL                Total

Ate in Cafeteria                  6                          7                         13

Did not ate in cafeteria       1                          25                      26

TOTAL                                  7                         32                       39

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The right question is

Results of the questionnaire were obtained for 39 of the 40 workers at the plant. Six of the seven ill employees ate at the factory cafeteria on September 26 and 27, compared to 7 of 32 non-stricken workers who ate at the factory cafeteria in both days. You also learn that the factory cook died from respiratory complication 3 weeks after hospital admissions.

In the preliminary analysis of results that you will provide to the Health Commissioner, you set up a 2 x 2 table, relating exposure and disease. You calculate the attack rate, case-fatality rate, and the relative risk of getting botulism after eating at the factory cafeteria on September 26 and 27.

1) Construct a 2x2 table using these data.

                                          ILL                    Not ILL                Total

Ate in Cafeteria

Did not ate in cafeteria

TOTAL                                                                                         39

The required value of PE is given as 22. The correct option is (B).

The PE ratio can be calculated by taking the ratio of the price of stock to the earning of the company per share.

The given question can be solved as,

The earning per share is $1.80.

And, the closing price i s $40.

Thus, the PE ratio can be calculated as follows,

PE = 40/1.80

     = 22.2

Which is equivalent to 22, rounding to the nearest whole number.

Hence, the PE ratio is given as 22.

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Answer:

below!

Step-by-step explanation:

reasons for each of the statements.

1. this is given information so there is nothing to prove here.

2. this is also given information, nothing to prove here.

3. this is also given information, nothing to prove here.

4. This is just because they are both 2 parts of the big segment (not sure what exactly is the reason your question is looking for but it something along these lines should be in your dropdown menu).

5. same as 4

6. since QR is equal to TU you can substitute TU with QR. QT stays the same.

7. Since we can see based on 5 and 6 that they have the same values by the same equations.

8. SAA

9. CPCTC

Hope this was helpful! :)

We need to prove triangles are PQU and SRT are congruent and we can see they have two angles marked as congruent and the included sides partially marked as equal and include the common segment.

We'll first prove the sides RT and QU are congruent, then prove the triangles are congruent. It will then give us the corresponding sides' congruence.

Missing reasons:

The first 3 statements reflect the given fact.

The next 2 statements reflect segment addition postulate.

After substitution of equal segments we prove that partially overlapping sides are congruent. Then it gives us the missing bit to prove the congruence of triangles.

Corresponding Parts of Congruent Triangles are Congruent.

Answer:

y=2x-14

Step-by-step explanation:

Perpendicular lines have slopes that are opposite reciprocals:

Example: 4 and -1/4 are opposite reciprocals

y = -x/2+2  ==> slope for this equation is -1/2

Now take opposite reciprocal of -1/2

1/(-1/2) * (-1) =

1 * (-2/1) * (-1) =

1 * (-2) * (-1) =

1 * 2 = 2

y=mx+b  

-4 = 2(5) + b  ==> plug in y=-4, x=5, and m=2 from (5, -4) and a slope of 2

-4 = 10 + b  ==> solve for b

-4 - 10 = 10 - 10 + b  ==> subtract 10 on both sides to isolate b

b = -14

y=2x+(-14)  ==> plugin -14 for b in y=mx+b

y=2x-14

Answer:

c. h+j+k / 3

Step-by-step explanation:

The assertion that there exists a normal subgroup N of G such that N is of finite index in G and [N ⊂ H] is true and can be proved if "G" is a group and "H" is a subgroup of finite index.

Given,

The statement, "G" is a group and "H" is a subgroup of finite index.

We have to prove that there exists a normal subgroup N of G such that N is of finite index in G and [N ⊂ H].

Group: A group is a finite or infinite collection of elements and a binary operation (referred to as the group operation) in discrete mathematics that together meet the four essential qualities of closure, associativity, identity, and inverse.

Subgroup: If a subgroup "H" also satisfies the four essential criteria of closure, associativity, identity element, and inverse, it is a subset of a group, let's say "G" [denoted by (H ≤ G)].

Here,

By left multiplication, the group G affects the collection of left co-sets (G/H).

Hence it induces the permutation representation [ρ:G→Sₙ], where

[n = |G : H|].

(A permutation representation is a group homomorphism, it should be noted.)

Now, let (N = kerρ) be the kernel of the homomorphism (ρ). Then [N◃G].

The quotient group G/N is isomorphic to a subgroup of Sn according to the first isomorphism theorem.

In particular, G/N is a finite group, hence the index [G:N] is finite.

Finally, we show that [N ⊂ H].

For any (x ∈ N) = [ker (ρ)], we have [x(gH) = gH] for any [g ∈ G].

In particular we have (xH = H),

Hence (x ∈ H).

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Unit Fill Rate: The percentage of a customer's purchase that was shipped on time. This statistic calculates the quantity and time elapsed after the order was dispatched, rather than when the client made the purchase.

On-time delivery is a key performance indicator (KPI) used by ecommerce and other delivery organizations to evaluate their ability to complete a client purchase by the specified delivery date.

The metric used to quantify supply chain efficiency is on-time delivery, or OTD. This KPI indicates whether or not an organization is meeting its goals in terms of promised delivery times, and it is critical for measuring carrier performance as well as maintaining customer satisfaction.

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It is possible for the the two different non-isomorphic graphs can have same number of vertices and edges , and the two such graphs are drawn below .

Two graphs are said to be isomorphic if they contain same number of vertices connected in the same way.

So, Yes the two non-isomorphic graphs can have the same number of vertices and the same number of edges.

The two such graphs are drawn below

If the degrees of vertices in two graph are same then the graph will become isomorphic it will no longer be Non-Isomorphic.

Therefore, No two graphs that are non isomorphic can have same number of edges, vertices and degrees of vertices all at once.

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To prove that the triangles are congruent by ASA, the statement and reason could be used as part of the proof is option (A) ∠FGH ≅ ∠KGJ because vertical angles are congruent.

Here we have two triangle FHG and KJG,

The sides HF and the side JK are parallel

The length of the side of the HG and the length of the side JG are equal

HG ≅ JG

According to the ASA property of congruent, if the two angle and one side of the triangle are equal to the two angle and one side of the other triangle, then the both triangles are congruent

Here we have to prove that angle FHG and angle KJG are vertical angles

Here the vertical angles are congruent

Therefore, the statement that can be the part of proof is option (a) angle FGH ≅ angle KGJ because vertical angles are congruent.

I have solved the question in general, as the given question is incomplete

The complete question is:

Given: HF || JK; HG ≅ JG

Prove: FHG ≅ KJG

To prove that the triangles are congruent by ASA, which statement and reason could be used as part of the proof?

a) FGH ≅ KGJ because vertical angles are congruent.

b) JKG ≅ HFG because vertical angles are congruent.

c) FHG ≅ JKG because right angles are congruent.

d) HFG ≅ KJG because alternate interior angles are congruent.

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For given study the hours of sleep per night is independent of the age.

Also, estimate of the percentages of individuals

                           Hours of sleep

Age       <6      6-6.9       7-7.9         ≥8         Total

≤ 39       38        60           75            67          240

≥ 40       36        57           73            94          260

Total      74        117         148          161        500

%       14.8%   23.4%     29.6%      32.2%

Let the null hypothesis H0 : Hours of sleep per night is independent of age

alternate hypothesis Ha : Hours of sleep per night is not independent of age

Expected frequencies :

E1: ((38+60+75+67)*(38+36))/500 = 35.52

E2: ((38+60+75+67)*(60+57))/500 = 56.16

E3: ((38+60+75+67)*(77+75))/500 = 72.96

E4: ((38+60+75+67)*(65+92))/500 = 75.36

E5: ((36+57+73+94)*(38+36))/500 = 38.48

E6: ((36+57+73+94)*(60+57))/500 = 60.84

E7: ((36+57+73+94)*(77+75))/500 = 79.04

E8: ((36+57+73+94)*(65+92))/500 = 81.64

Then performing the Chi-square independence test X²

X² = Σ[(f1-e1)²/e1 + (f2-e2)²/e2... (fn - en)²/en]

F1 to f8 = 38,60,75,67,36,57,73,94

X² = ((38-49.92)^2)/35.52 + ((60-56.16)^2)/56.16 + ((77-72.96)^2)/72.96 + ((65-75.36)^2)/75.36 + ((36-38.48)^2)/38.48 + ((57-60.84)^2)/60.84 + ((75-79.04)^2)/79.04 + ((92-81.64)^2)/81.64

X² = 4.00

α = 0.05

Reject H0, if p < α

df = (row - 1)*( column - 1)

df = (2 - 1)*(4-1)

   = 3

To find the p value from the X² square score at α = 0.05 and 3 degree of freedom

p = 0.261

Since, p > α ( 0.261 > 0.05) ; The result is not significant at α = 0.05 ; Hence we fail to reject the H0 (null hypothesis).

Now we need to estimate of the percentages of individuals who sleep fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more per night.

                          Hours of sleep

Age       <6      6-6.9       7-7.9         ≥8         Total

≤ 39       38        60           75            67          240

≥ 40       36        57           73            94          260

Total      74        117         148          161        500

%       14.8%   23.4%     29.6%      32.2%

Therefore, we can conclude that the hours of sleep per night is independent of the age.

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The exponent in the term 5x⁶ is of the expression 6

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

Expression: 5x6+3yr-7yz2+2y/z

Rewrite the expression properly

So, we have the following representation

5x⁶ + 3yr - 7yz² + 2y/z

From the above expression, the spotlight is on the first term

i.e. 5x⁶

Considering an expression represented as axⁿ

Where x is a variable, the exponent is n

Using the above as a guide, we have the exponent of 5x⁶ to be 6

Hence, the exponent is 6

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Answer:

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

Total number of hours is w + l and it should be at least 17 hours, (equal to 17 or greater).

We can set inequality as:

The potential energy of an rock of 40 kg and at a height of 10m is 4000 kgm^2s^2

What is potential energy and its formula?

An object possesses potential energy as a result of its position in relation to other objects. Potential energy is so named because it has the ability to transform into other types of energy, such kinetic energy. the formula for potential energy is mgh where m is the mass, g is the acceleration due to gravity and h is the height of the object.

We are given a rock of mass 40 kg which is at a height of 10m

We substitute the values in the formula to find the potential energy of the rock

Potential energy = m*g*h

Potential energy = [tex]40*10*10[/tex]

Potential energy = 4000 kgm^2s^2

Hence the potential energy of the rock is 4000 kgm^2s^2

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From the given question, relation set - {(9, 1), (6,2), (3, 3), (6,4), (9,5)} does not represent the function.

In mathematics, a connection between one variable (the independent variable, x) and another variable is defined as an expression (the dependent variable, y).For example - f(x) = 4x + 6

The collection of ordered pairs from the question is presented.

It is evident that the relation set exists.

{(9, 1), (6,2), (3, 3), (6,4), (9,5)}

It not accurately depict the function since for x = 6, [y] has two potential values, none of which is possible.

so that's why relation set - {(9, 1), (6,2), (3, 3), (6,4), (9,5)} can not represent a function.

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Exponential smoothing of time collection records assigns exponentially lowering weights for latest to oldest observations.

In different words, the older the records, the much less priority (“weight”) the records is given; more moderns records is visible as extra applicable and is assigned extra weight. Smoothing parameters (smoothing constants),denoted through α,  decide the weights for observations.

The simple formulation is:

St = ayt-1 + (1 - a) S-1

Where:

α = the smoothing constant, a fee from zero to 1. When α is near zero, smoothing takes place extra slowly. Following this, the satisfactory fee for α is the only that outcomes withinside the smallest suggest squared error (MSE).and t = time period.

One of the blessings of Exponential smoothing is ,the forecast may be built the use of most effective 3 values.

Only 3 portions of records are required for exponential smoothing methods.

1. It  desires the forecast for the maximum latest time period.

2. It desires the real fee for that point period.

3. It desires the fee of the smoothing constant, a weighting thing that displays the load given to the maximum latest records values.

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The method for finding the instantaneous rate of change of the depth of the water; in feet per hour; at 6 AM is B. D' ( 6 ) = 0 .

Given :

The function D ( t ) = 10 + 4.9 cos ( pi/6 * t )

D is defined above models the depth, in feet, of the water t hours after 12 am. Which of he following shows the method for finding the instantaneous rate of change of the depth of the water, in feet per hour, at 6 am .

Differentiate :

D'( t )  = -4.9 sin ( πt / 6 ) ( π / 6 )

D'( 6 ) = -4.9 sin ( π ) ( π / 6 )

we know that

sin ( π ) = 0

so D'( 6 ) = 0

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In the given Fibonacci sequence , 8th number is 13 mad 11th number is 55 .

What is a Fibonacci Sequence?

The Fibonacci Sequence is the series of numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

The next number is found by adding up the two numbers before it:

In a Fibonacci sequence, the number is equal to the sum of the two preceding numbers.

so the seventh number is 3+5 = 8

8th number is 5+ 8 = 13

11th number is 21+34 = 55

now the sequence becomes 0,1,1,2,3,5,8,13,21,34,55

Hence , the 8th number is 13 mad 11th number is 55.

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If {v1, v2, v3} is an orthogonal basis for W, then multiplying v3 by a scalar c gives a new orthogonal basis {v1, v2, cv3 } is false statement.

Orthogonal basis:

Linear algebra, the orthogonal basis V of the inner product space is the basis of V whose vectors are mutually orthogonal.

When a vector of orthogonal basis is normalized, the resulting basis is an orthonormal basis.

let W be a vector space. The set S= {v₁,v₂,v₃} is an orthogonal basis for W.

The number of basis elements in W = 3 that is the dimensions of W is three.

If we multiply v₃ by c =0, then the set becomes

{v₁, v₂, cv₃} = {v₁, v₂,0}. The dimension of the set is 2, that is less than the dimension of W. If the scalar factor is 0, then it will not give a new orthogonal basis. Since in this case the number of basis elements will be reduced by 1 hence will change dimension of W.

Therefore, The statement is False.

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The confidence interval limits include 0, which suggests that the two population means might be equal. There does not appear to be a significant difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men.

The correct option is (a)

"Information available from the question:"

This is incomplete question:

Complete question is this:

A researcher was interested in comparing the amount of time spent watching television by women and by men. Independent simple random samples of 14 women and 17 men were selected, and each person was asked how many hours he or she had watched television during the previous week. The summary statistics are as follows.

Women             Men

x1 = 11.7hrs x2 = 14.2hrs

s1 = 3.9hrs s2 = 5.2hrs

n1 = 14         n2 = 17

The following 99% confidence interval was obtained for μ1 − μ2, the difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men:

-7.43hrs < μ1 − mμ2 < 2.43hrs

What does the confidence interval suggest about the population means?

a. The confidence interval limits include 0 which suggests that the two population means might be equal. There does not appear to be a significant difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men.

b. The confidence interval includes only negative values which suggest that the mean amount of time spent watching television for women is smaller than the mean amount of time spent watching television for men.

c. The confidence interval limits include 0 which suggests that the two population means are unlikely to be equal. There appears to be a significant difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men.

d. The confidence interval includes only positive values which suggest that the mean amount of time spent watching television for women is larger than the mean amount of time spent watching television for men.

Now, According to the question:

The given confidence interval is:

-7.43hrs < μ1 − mμ2 < 2.43hrs

The interval includes 0 and the populations sampled are small (< 30). Therefore, Option (a) is correct.

Hence, The confidence interval limits include 0, which suggests that the two population means might be equal. There does not appear to be a significant difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men.

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Answer:

9 pound

Step-by-step explanation:

We know

The new puppy's weight has increased by 32% since her last vet visit.

100% + 32% = 132%

First, we have to find 1%

12 divided by 132% = 0.09 pound

Then we take

0.09 times 100% = 9 pounds

So, the puppy weighs 9 pounds on her last visit.

If you can, please give me a Brainliest; thank you and have a good day!

Answer:

The answer to the problem is 9 pounds.

Step-by-step explanation:

100+32=132

12/132=.09

.09x100= 9

I know my explanation wasn't very detailed, but I know sometimes people learn by just seeing it instead of having a long drawn out explanation so I wanted to give you that option incase it works better for you.

The area of the triangle with the vertices (0, 5), (2, -2), and (5, 1) by using the calculus is  21 square unit.

We need to find the equation among all possible pairs and then integrate the equations from one co-ordinate to another co-ordinate

Equation of line passing through (0,5) and (2,-2) is

y-5 = [(-2-5)/(2-0)](x-0)

=>y-5 = (-7) /2x

=>y= (-7/2x)+5 -------(eq1)

Equation of line passing through (0,5) and (5,1) is

y-5 = [(1-5) / (5-0)](x-0)

=>y-5 = (-4/5)x

=>y = (-4/5)x+5-------(eq2)

Equation of line passing from (2,-2) and (5,1) is

y-(-2) = [[1 - (-2)] / (5-2)] / (x-2)

=>y+2=(3/3)(x-2)

=>y=x-4--------(eq3)

Now, we use definite integration to find the area between the different equation of line.

So, area enclosed between the equations is given by the

area =[tex]\int\limits^5_2[/tex][(-4/5)x+5 - (-7/2)x + 5)dx  + [tex]\int\limits^5_1[/tex][(-4/5)x+5 -(x-4)]dx

=>area=[tex]\int\limits^5_2[/tex](7/2-4/5)x dx + [tex]\int\limits^5_1[/tex]((-9/5)x+9)dx

Using properties of integration,[tex]\int\limits x\, dx=x^{2}/2[/tex]

=>area=[tex]\int\limits^5_2[/tex](27/10)x dx + [tex]\int\limits^5_1[/tex](-9/5)x+9)dx

=>area=([27/10)×[5² - 2²])/2 + [ (-9/5)×(5²-1²) ]/2 +9×(5-1)

=>area=(27/20)×(25-4) + (-9/5)×24+9×4

=>area = (27×21)/20 + (-216)/5+ 36

=>area=(567/20) - (216/5) + 36

=>area= [(567-261×4)+(36×20)]/20

=>area=[(567-864)+720]/20

=>area=423/20

=>area=21 square unit.

Hence, area of triangle is 21 square unit.

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The equation of the circle is [tex](x+3)^2 + (y-5)^2 = 5^2[/tex]

What does the equation for a circle look like in cartesian form?

Cartesian coordinate system with the origin indicated in red and a circle with a radius of two. A circle has the equation (x a)^2 + (y b)^2 = r^2, where a and b are the center's coordinates (a, b) and r is the radius.

The equation of a circle has the following conventional Cartesian form:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex] ---------- 1

where (h, k) is the circle's center, (x, y) is any point on the circle, and r is its radius

Substitute the center (-3,5) into equation [1]:

[tex](x+3)^2 + (y-5)^2 = r^2[/tex] --------------------- 2

Substitute the point (1,8) into equation [2] and solve for r:

[tex](1+3)^2 + (8-5)^2 = r^2\\(4)^2 + (3)^2 = r^2\\16 + 9 = r^2\\25 = r^2\\r = 5[/tex]

Substitute 5 for r into equation [2]

[tex](x+3)^2 + (y-5)^2 = 5^2[/tex]

Hence the equation of the circle is [tex](x+3)^2 + (y-5)^2 = 5^2[/tex]

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Distance that plane has flown is 2812.5 feet.

What do you mean by trignometry?

Trigonometry  “triangle” is a branch of mathematics that studies the relationship between the side lengths and angles of triangles.

Trigonometric ratios of triangles are also called trigonometric functions. Sine, cosine, and tangent are three important trigonometric functions, abbreviated sin, cos, and tan. Let's see how these ratios or functions are evaluated in the case of right triangles.

It is given that a plane rises from take-off and flies at an angle of 9° with the horizontal runway. It has gained 450 feet

Let the distance be x

According to the question:

sin 9 = 450/x

0.16 = 450/x

x = 450/0.16

x = 2812.5

Therefore, distance that plane has flown is 2812.5 feet.

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Answer:

20

Step-by-step explanation:

Since all sides are equal, it's an equilateral triangle.

Each medium interior angle of an equilateral triangle is 60.

So,

3x = 60

x = 60/3

x = 20

The distance from the point to the parametric line is given as follows:

5 units.

The first step is obtaining the vector from the line L(0, 5 + 3t, 2 + t) to the point P(5,5,2), as follows:

P - L = (5, -3t, -t).

The direction vector of the line is given as follows:

(0, 3, 1).

The dot product of the vector with the direction of the line is of zero, hence:

(5, -3t, -t)(0, 3, 1) = 0

-9t - t = 0

-10t = 0

t = 0.

Thus the point on the line which we will use to obtain the distance is of:

(0, 5 + 3(0), 2 + 0) = (0,5,2).

The the distance is obtained applying the formula for the distance between two points as follows:

Distance = square root [(5 - 0)² + (5 - 5)² + (2-2)²] = 5 units.

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Community colleges in the United States play an important role in higher education. In United States, everyone monitors they community colleges are primarily her two-year institutions of higher education that focus on teaching and learning and workforce preparation.

Community colleges are open access institutions that offer economically affordable entry into higher education. About half of first-time college-going students enroll in community colleges, which serve as her transition route to four-year colleges (Beach, 2011). However, despite the important role and primary focus of community colleges, students may view community college instruction as inferior and undesirable to her four-year college (Dougherty, Lahr, & Morest, 2017; Twombly, 2001; Twombly & Townsend, 2008). This general dissatisfied view of community college instruction has much to do with the historical legacy of community colleges, where most two-year schools are either officially called "junior colleges" or "junior colleges." is called Community colleges have reason to brag about progress. It tends to have a higher proportion of female and minority teachers compared to traditional her four-year colleges (Antonio, 2002; Marcotte, Bailey, Borkowski, & Kientz, 2005; Turner, 2001). While the high recruitment rate of minority teachers is laudable, most higher education institutions are still predominantly white and male dominated (with the exception of those serving minorities). Overall, despite the high proportion of women and minority teachers, empirical studies show that such teachers experience high levels of stress and frustration with the way students are treated in the classroom. (Allen et al., 2002; Pittman, 2010). For many teachers and teachers of color, the classroom environment serves as a reminder of the unfortunate social ills that plague our society (Harlow, 2003; Seo & Hinton, 2009).

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