9th Grade Geometry ​

Hence, the solution of this problem  is same side interior angles .

Congruent refers to objects that are the same size and shape. The concept of congruent can be utilized to figures, angles, and line segments. Any two line segments are deemed to be congruent if their lengths are the same. If the measure of two angles is the same, they are said to be congruent. The sides and angles of two shapes are said to be equal if they are congruent.

Here,

The alternate interior angles, alternate exterior angles, and equivalent angles are equal when a transversal cuts two parallel lines.

The same-side interior angle theorem states that when two parallel lines are intersected by a transversal, the same-side interior angles that are created are additional.

Thus, identical side internal angles are the answer to this difficulty.

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Answer:

  16 feet

Step-by-step explanation:

The geometry of the problem can be modeled by a right triangle. The Pythagorean theorem tells us the relationship between the various distances.

  EH² +HF² = EF²

  EH² + 12² = 20²

  EH² = 400 -144

  EH = √256 = 16

The hook is 16 feet below Edna.

Answer:

8 feet

Step-by-step explanation:

The relation given by the set of ordered pair that is a function is;

{(-2,5), (7, 5), (-4, 0), (3, 1), (0, -6)}

An ordered pair is defined as any pair of numbers for which order is important. Thus, the order of coordinates for a given point is very important for example (6, 3) and (3, 6) represent two very different points on a coordinate system.

here, we have,

For any of the ordered pair to be a function, there needs to be one unique value of y for every x.

Looking at the options, the only correct ordered pair that shows the law of an ordered pair being a function is Option A.

Hence, The relation given by the set of ordered pair that is a function is;

{(-2,5), (7, 5), (-4, 0), (3, 1), (0, -6)}

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complete question:

Which of the relations given by the following sets of ordered pairs is a function?

O {(-2,5), (7, 5), (-4, 0), (3, 1), (0, -6)}

O {(1, 3), (1, 1), (1, 1), (1, 3), (1,5)}

O {(1, 2), (2, 3), (3, 4), (2, 1), (1, 0)}

O

1

{(2,8), (6,4), ( – 3, 9), (2, 0), (-5,3)}

Answer:

m=1

c=7

I hope it will be useful.

Answer:

(2 + 6i)²

(2 + 6i)(2 + 6i)

2 + 12i + 12i -36

24i - 34

Answer:    0.185

Step-by-step explanation:

Divide 120.99 and 654:

120.99÷654=0.185

So the final answer is 0.185 units.

Step-by-step explanation:

∠4 = ∠1 & ∠2 = ∠3

360 - 2(98) = ∠2 + ∠3

∠3 = 164/2

∠3 = 82°

\(\huge\bold{Given :}\)

Angle 4 = 98°

\(\huge\bold{To\:find :}\)

The measure of angle 3.

\(\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}\)

\(\implies {\blue {\boxed {\boxed {\purple {\sf {∠\:3\:=\:82° }}}}}}\)

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

We know that,

\(\sf\pink{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}\)

➪ ∠ 3 + ∠ 4 = 180°

➪ ∠ 3 + 98° = 180°

➪ ∠ 3 = 180° - 98°

➪ ∠ 3 = 82°

Therefore, the measure of ∠ 3 is 82°.

\(\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}\)

∠ 3+ ∠ 4 = 180°

✒ 82° + 98° = 180°

✒ 180° = 180°

✒ L. H. S. = R. H. S.

\(\boxed{Hence\:verified.}\)

\(\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♨}}}}}\)

The numerical value "62" is a statistic because it is based on the sample of passengers aboard the Hindenburg airship.

In the given scenario, the numerical value is "62." We are told that there were 97 passengers aboard the Hindenburg airship and that 62 of them survived its explosion.

Since the numerical value is based on the sample (i.e., the passengers aboard the Hindenburg airship), it is a statistic. It describes the proportion of passengers who survived the explosion in the sample.

If we wanted to know the proportion of passengers who survived the explosion in the entire population (i.e., all passengers who have ever traveled on the Hindenburg airship), we would need to determine the parameter.

However, since we do not have data on the entire population, we cannot determine the parameter.

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The value of integral ∫ c ( x 2 y 2 z ) d s ∫c(x2 y2 z)ds is 156.864.

To evaluate the line integral ∫c(x^2 y^2 z)ds, we need to parameterise the curve C and then compute the integral along that curve.

The parameterization of C is given by → r ( t ) = ⟨ 2 cos ( 2 t ) , 2 sin ( 2 t ) , 5 t ⟩ r→(t)=〈2cos(2t),2sin(2t),5t〉 for 0 ≤ t ≤ 4 0≤t≤4.

To compute the line integral, we first need to get the unit tangent vector →T(t) of the curve C. The unit tangent vector is :

→T(t) = →r'(t)/|→r'(t)|

Taking the derivative of →r(t) gives:

→r'(t) = ⟨ -4 sin(2t), 4 cos(2t), 5 ⟩So, the magnitude of →r'(t) is:

|→r'(t)| = √( (-4 sin(2t))^2 + (4 cos(2t))^2 + 5^2 ) = √( 16 + 25 ) = √41

Therefore, the unit tangent vector is:

→T(t) = (1/√41) ⟨ -4 sin(2t), 4 cos(2t), 5 ⟩

Now, we can compute the line integral as follows:

∫c(x^2 y^2 z)ds = ∫0^4 (x^2 y^2 z) |→T(t)| dt

Substituting the parameterization and the unit tangent vector, we get:

∫c(x^2 y^2 z)ds = ∫0^4 (4 cos^2(2t) 4 sin^2(2t) 5t) (1/√41) dt

= (20/√41) ∫0^4 (16 cos^2(2t) sin^2(2t) t) dt

Using the identity sin(2θ) = 2sin(θ)cos(θ), we can simplify the integrand as follows:

16 cos^2(2t) sin^2(2t) = 4 sin^2(4t) = 2 (1 - cos(8t))

Substituting this back into the integral, we get:

∫c(x^2 y^2 z)ds = (20/√41) ∫0^4 [ 2 (1 - cos(8t)) t ] dt

Integrating by parts with u = t and dv = 1 - cos(8t), we get:

∫c(x^2 y^2 z)ds = (20/√41) [ t^2/2 - (1/8) sin(8t) ] |_0^4

= (20/√41) [ 8 - (1/8) sin(32) ]

≈ 156.864

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Answer:

y=-4/3

Step-by-step explanation:

Answer:

-4/3

Step-by-step explanation:

The length of segment RT for this problem is given as follows:

RT = 18.

Before obtaining the length of segment RT, we must obtain the value of x, applying the two secant segment theorem, which means that the following equation will hold true:

11(11 + x) = 9(9 + 13)

(we add the two parts), with the outer part being the multiplier.

Hence:

121 + 11x = 198

11x = 77

x = 7.

Then, applying the segment addition postulate, the length of segment RT is given as follows:

RT = x + 11

RT = 7 + 11

RT = 18.

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Answer:

B = (6, -6)

Step-by-step explanation:

(2+x)/2=4

2+x =2*4

x = 8 - 2

x = 6

(8+y)/2 = 1

8+y = 1*2

y = 2 - 8

y = - 6

We have a triangle with angles: 66 deg, 57 deg and (3x+21).

We have to solve for x.

We know that the sum of the interior angles of a triangles is 180 degrees.

Then, we can write and solve for x as:

The value of x is 12.

Answer: A) 12

Answer:

answers 0

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

-3+5=2

2-2=0

If 40% of a number is 120 and 55% of the same number is 165 then 15% of that number is 45.

According to the question,

We have the following information:

40% of a number = 120

55% of the same number = 165

Now, let's take the number to be x.

So, we have the following expression:

40x/100 = 120

Using the cross multiplication method:

40x = 120*100

x = 120*100/40

x = 300

Now, we will find 15% of 300 by following the given steps:

15*300/100

15*3

45

Hence, if 40% of a number is 120 and 55% of the same number is 165 then 15% of that number is 45.

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Answer:

Step-by-step explanation:

All we have to do here is to find the measure of the central angle; the measure of the central angle of a circle is the same measure as the arc it intercepts. Angle DQE in degrees = arc DE in degrees. Use the arc length formula to find the measure of the central angle:

\(AL=\frac{\theta}{360}*2 \pi r\) and filling in:

\(8.73=\frac{\theta}{360}*(2)(3.14)(10)\) which simplifies to

\(8.73=\frac{62.8\theta}{360}\) which simplifies a bit more to

\(\frac{360(8.73)}{62.8}=\theta\) so

\(\theta=50.04\) degrees. That means that arc DE also measures 50.04 degrees.

To determine the gross production of each industry to meet the market demand, we can set up a system of linear equations based on the given information and solve it using the Gauss-Jordan method.

Let's represent the gas production, oil production, and gasoline production as variables G, O, and A, respectively.

From the information provided, we can write the following equations:

1/5G + 2/5O + 1/5A = 100 (equation 1)

2/5G + 1/5O = 100 (equation 2)

1/5G + 1/5O = 100 (equation 3)

We can rearrange equation 2 to get G in terms of O: G = 250 - O/5. Then substitute this expression into equations 1 and 3. This will eliminate G, leaving only O and A in the equations.

After performing the necessary operations using the Gauss-Jordan method, we can find the values of O and A. The resulting values will represent the gross production of oil and gasoline, respectively, needed to meet the market demand.

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Answer:

6.7.

Step-by-step explanation:

sin 48 = 5/h

h * sin 48 = 5

h = 5 / sin 48

= 6.73

Answer:

Without the graphic, 5 1/8 would be 1 mark after the whole 5.

Step-by-step explanation:

There are 8 sections between 5 and 6. 5 1/8 is between those two numbers.

So a point would be about 12.5% of the way to 6.

There are 11 1/8 picec that equals 1 3/8

Answer:

The median is the middle number in the sequence

Step-by-step explanation:

a. The distribution of X is normal (X ~ N) as we assume workers' productivity follows a normal distribution.

b. The distribution of a is normal (a ~ N) as we assume the average number of computers per worker is normally distributed.

c. The distribution of Σa is normal (Σa ~ N) because the sum of normally distributed variables is also normally distributed.

d. The probability that a randomly selected worker puts together between 4.3 and 4.4 computers per hour can be calculated using the normal distribution.

e. The probability that the average number of computers per hour for the 49 workers is between 4.3 and 4.4 can be calculated using the distribution of sample means.

f. The probability that a 49-person shift puts together between 210.7 and 215.6 computers per hour can be calculated using the distribution of the sum of their productivity.

g. The assumption of a normal distribution is necessary for parts e) and f) due to the central limit theorem.

h. The least total number of computers produced by a group receiving a sticker can be found by calculating the cutoff value corresponding to the top 20% of productivity using z-scores and the normal distribution.

a. The distribution of X is normal (X ~ N) because we are assuming that the workers' productivity follows a normal distribution. This means that the number of computers each worker can put together per hour is normally distributed.

b. The distribution of a is also normal (a ~ N) because we are assuming that the workers' productivity, represented by variable 'a', follows a normal distribution. This is based on the assumption that the average number of computers each worker puts together per hour is normally distributed.

c. The distribution of Σa is also normal (Σa ~ N) because the sum of normally distributed variables is also normally distributed. In this case, Σa represents the total productivity of all 49 workers in a shift, and it follows a normal distribution.

d. To find the probability that a randomly selected worker will put together between 4.3 and 4.4 computers per hour, we can calculate the area under the normal distribution curve between those two values. This can be done using statistical software or standard normal distribution tables.

e. To find the probability that the average number of computers put together per hour for the 49 workers is between 4.3 and 4.4, we can calculate the area under the normal distribution curve for the distribution of sample means. The standard deviation of the sample means can be obtained by dividing the standard deviation of individual workers (0.8 computers) by the square root of the sample size (√49 = 7). We can then use this standard deviation and the sample mean to calculate the probability.

f. To find the probability that a 49-person shift will put together between 210.7 and 215.6 computers per hour, we need to consider the distribution of the sum of the 49 workers' productivity. The mean of the sum is the product of the average productivity per worker (4.4 computers) and the number of workers (49). The standard deviation of the sum can be obtained by multiplying the standard deviation of individual workers (0.8 computers) by the square root of the sample size (√49 = 7). We can then use this mean and standard deviation to calculate the probability.

g. The assumption of a normal distribution is necessary for both parts e) and f) because we are dealing with averages and sums of random variables. The central limit theorem states that the distribution of sample means and sums tends to be approximately normal, regardless of the shape of the population distribution, as long as the sample size is sufficiently large.

h. To determine the least total number of computers produced by a group that receives a sticker, we need to find the cutoff value corresponding to the top 20% of productivity. This can be done by finding the z-score associated with the 80th percentile of the normal distribution. We can then multiply this z-score by the standard deviation of individual workers (0.8 computers) and add it to the mean productivity per worker (4.4 computers) to obtain the least total number of computers required.

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The laplace transform of f(t) is \(F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}\) and it's values exists for \(s=w\pm\sqrt{3}wi\).

Given,

\(f(t)=sin^2(wt)\\\\\therefore sin^2x=\frac{1-cos2x}{2}\\\\f(t)=\frac{1-cos2wt}{2}\)

applying laplace transform on both sides,

\(L[f(t)]=L[\frac{1-cos2wt}{2}]\\\\F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}\)

The range for values of s for which F(s) exists is when F(s)≥0

\(\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)} \geq0\\\\\frac{1}{2s} \geq\frac{2w}{2(s^2+4w^2)}\\\\2(s^2+4w^2) \geq 2sw\\\\s^2-2sw+4w^2 \geq0\)

using formula to find roots,

\(s=\frac{-(-2w)\pm\sqrt{(-2w^2)-4(4w^2)}}{2}\\\\s=\frac{-(-2w)\pm\sqrt{(12w^2}}{2}\\\\s=w\pm\sqrt{3}wi\)

Thus,  the laplace transform of f(t) is \(F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}\) and it's values exists for \(s=w\pm\sqrt{3}wi\).

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- Events A, B, C, and D are exhaustive.
- Events A and B, B and D are not mutually exclusive.
- Events A and C, C and D, A and D are mutually exclusive.

To determine whether the events are exhaustive or mutually exclusive, we need to understand the definitions of these terms:
1. Exhaustive events: Events are considered exhaustive if the union of all the events covers the entire sample space S. In other words, there are no outcomes in the sample space that are not included in any of the events.
2. Mutually exclusive events: Events are considered mutually exclusive if they have no outcomes in common. In other words, the events cannot occur simultaneously.
Now let's analyze the given events:
A = {1, 2, 4}
B = {1, 2, 4, 5, 6}
C = {5, 6}
D = {2, 3, 6}
To determine if the events are exhaustive, we need to check if their union covers the entire sample space S.
The union of A, B, C, and D is {1, 2, 3, 4, 5, 6}, which covers the entire sample space S. Therefore, the events A, B, C, and D are exhaustive.

To determine if the events are mutually exclusive, we need to check if any outcomes are shared between the events.
The outcomes 1, 2, and 4 are shared between events A and B. Therefore, events A and B are not mutually exclusive.
The outcomes 2 and 6 are shared between events B and D. Therefore, events B and D are not mutually exclusive.
No outcomes are shared between events A and C, C and D, or A and D. Therefore, events A and C, C and D, and A and D are mutually exclusive.

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Answer:

\( \frac{5}{8} = \frac{22}{x - 6} \\ x≠6 \\ 5(x - 6) = 176 \\ 5x -30 = 176\)

The measure of the angles are: K, L, C, N, O G = -3/4, 65, 8 40.4, 89 and 44 respectively

To determine K

9x + 2 = 23 + 5x -1

9x -5x = -1 +2

4x = -3Making x the subject we have

x= -3/4

To find the value of L

Let angle L be x

x + 65 = 130

x=130-65

That is x = 65

To find the m<C

4x + 7 = 3x + 15

Collecting like terms

4x - 3x = 15-7

Making x the subject of the relation we have

x=8

To find the m<N

7x + 6x - 1 = 90

13x = 89

x=89/13

x= 6.9

Substitute x = 6.9 in 6x -1

6(6.9) -1

m<L = 40.4

To find the m<O

5x - 11 = 4x +9

5x-4x = 9 +11

x=20

By substitution in 4x +9 we have

4(20) +9

80+9

m<S = 89

To find the value of the angle G

6x - 4 = 5x +4

6x - 5x = 4+4

x = 8

Therefore the m<G is

5x +4

5(8) +4

40+4 = 44 digress

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Answer:

it is C

Step-by-step explanation:

Its c because i had the exact same problem

The formula to calculate the Mean Square for Treatments is given by; Mean Square for Treatments = Sum of Squares for Treatments / Degrees of Freedom associated with Sum of Squares for Treatments.

Step 1: Degrees of Freedom associated with Sum of Squares for TreatmentsDegree of freedom for Treatments = Number of Groups - 1Degree of freedom for Treatments = 3 - 1 = 2

Step 2: Mean Square for TreatmentsMean Square for Treatments = Sum of Squares for Treatments / Degrees of Freedom associated with Sum of Squares for TreatmentsGiven that;Sum of Squares for Treatments = 2.0060Degrees of Freedom associated with Sum of Squares for Treatments = 2Then the Mean Square for Treatments is calculated as;Mean Square for Treatments = 2.0060 / 2Mean Square for Treatments = 1.0030Therefore, Mean Square for Treatments is 1.0030.

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Answer:

8.33

Step-by-step explanation:

1hr=60 minutes

?hr = 500 minutes

To find how many hours, divide 500 by 60

500/60 = 8.33

500 minutes = 8.33 hours