A system of equations is shown on the graph below.
How many solutions does this system have?

This matches the placement of 10, 15, and 20 and hence the standard deviation will be the same in the two cases.

What is the standard deviation?

The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a wider range.

Standard deviation determines how far numbers deviate from the mean. The Standard deviation of the two sets will be the same if the numbers from the respective means are placed in the same order.

This is what 10, 15, and 20 will be on a number line

10_ _ _ _15 _ _ _ _20

(15 is the mean and 10 and 20 are 5 steps away from the mean)

i) Z - X = 10

This is what Z and X will be on the number line

X _ _ _ _ _ Z

ii) Z - Y = 5

This is what Z and Y will on the number line.

Y_ _ _ _ _ Z

Together, their relative placement on the number line:

X _ _ _ _ _  Y  _ _ _ _ _  Z

This matches the placement of 10, 15, and 20 and hence the standard deviation will be the same in the two cases.

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Answer:

There are 25 students in the class.

Step-by-step explanation:

Let x be the number of students in the class

12% failed and the number of students is 3

x*12% = 3

x*.12 = 3

Divide each side by .12

x * .12 /.12 = 3/.12

x =25

There are 25 students in the class

Answer:

25 students.

Step-by-step explanation:

12% is 3 students.

100% is the number of students in the class.

3 times 100 divided by 12 is 25.

So there are 25 students in the class.

Answer:

1.8.09

2.-6

Step-by-step explanation:

1. 11b=89

b=89/11

8.09

2. 13+k/3=11

k/3=11-13

k/3=-2

k=-2*3

=-6

Answer:

Number 2 is - 6

Step-by-step explanation:

2. 13 + k/3 = 11

We can start off my subtracting 13 in both sides.

-13 + 13 + k/3 = 11 - 13

k/3 = -2. now we have to multiply 3 in both sides

3 x k/3 = -2 x 3

k = -6

Hope this helps!!

Answer:

sorry po Hindi ko Alam ang answer

The value of -4(7/10) - 9(7/15) is -85 / 6.

A fraction represented with its quotient and remainder is a mixed fraction.

For example:

3 4/5 is a mixed fraction, where 3 is the quotient, and 4 is the remainder.

We have,

-4(7/10) - 9(7/15)

Convert each term into a proper fraction.

4 7/10 = (40+7) / 10 = 47 / 10

9 7/15 = (135 + 7) / 15 = 142 / 15

Now,

= -47 / 10 - 142 / 15

The LCM of 10 and 15 is 30

= [3 x (-47) - (2 x 142)] / 30

= (-141 - 284) / 30

= -425 / 30

We can divide by a common factor of 5

= - 85 / 6

Thus the value of -4(7/10) - 9(7/15) is -85 / 6.

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The complete question is

Evaluate -4(7/10) - 9(7/15)

Applying the midpoint formula, the coordinates of the midpoint of the line segment that has endpoints with coordinates (−8, −11) and (2, 5) is calculated as: M(-3, -3).

The formula that is used to find the coordinates of the midpoint of a line segment that has two endpoints is expressed as: M[(x2 + x1)/2, (y2 + y1)/2].

Given the following coordinates of the endpoints as (−8, −11) and (2, 5), let:

(−8, −11) = (x1, y1)

(2, 5) = (x2, y2)

Plug in the values into the midpoint formula, M[(x2 + x1)/2, (y2 + y1)/2]:

M[(2 + (-8))/2, (5 + (-11))/2]

M[(2 - 8))/2, (5 - 11)/2]

M[(-6))/2, (-6)/2]

M(-3, -3)

Thus, by applying the midpoint formula, M[(x2 + x1)/2, (y2 + y1)/2], the coordinates of the midpoint of the line segment that has endpoints with coordinates (−8, −11) and (2, 5) is calculated as: M(-3, -3).

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Answer:

5 feet each

Step-by-step explanation:

So we know that 4 pieces of rope out of 5 are equal. So, we simply subtract 10 from 30 for that 10-foot piece of rope, which leaves us with 20. Divide 20 by 4 (since there is 4 pieces of rope of equal value) and it leaves us with 5 feet.

Hope I helped! :)

Given that the product has a 0 in the thousands place, the value of k is C. 4.

The product is the result of multiplying two or more numbers together.

The product is the result of multiplication, which is one of the mathematical operators, including addition, subtraction, division, exponentiation, and modulus operations.

Product of 13,462 and 798k = 13,462 x 798 x k

= 10,742,676k

K = variable

If k = 1, the product of 10,742,676k = 10,742,676, the nearest thousand = 10,743,000

If k = 2, the product of 10,742,676k = 21,485,352, the nearest thousand = 21,485,000.

If k = 4, the product of 10,742,676k = 42,970,704, the nearest thousand = 42,970,000.

If k = 7, the product of 10,742,676k = 75,198,732, the nearest thousand = 75,199,000.

If k = 9, the product of 10,742,676k = 96,684,084, the nearest thousand = 96,684,000.

Thus, given that the product has a 0 in the thousands place, the value of k is C. 4.

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The statement 'If an integer is negative, its absolute value is also its additive inverse.' is True.

In this question, we have been given a statement 'If an integer is negative, its absolute value is also its additive inverse.'

We know that for any non zero real number 'm', the additive inverse is '-m'

as m + (-m) = 0

We know that the absolute value of any non-zero real number is always positive.

Consider a negative integer -p.

The absolute value of -p is |-p| = p

We can observe that -p + p = 0

-p + |-p| = 0

Therefore, the statement 'If an integer is negative, its absolute value is also its additive inverse.' is True.

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Answer:   LM = 57

==========================================================

Explanation:

A median of a triangle goes from a vertex to the midpoint of the opposite side. The three medians of this triangle are these segments:

The three medians intersect at the centroid point, which is point Q.

It turns out that the centroid cuts each median such that LQ is twice as long compared to QM. We can say

LQ = 2*QM

Applying the segment addition postulate and substitution, we then get,

LQ + QM = LM

2QM + QM = LM

3QM = LM

LM = 3QM

Now let's use LQ = 38 to find QM

LQ = 2*QM

38 = 2*QM

QM = 38/2

QM = 19

This then means,

LM = 3QM

LM = 3*19

LM = 57

Segment LM is 57 units long.

a) The center of G and determining the distinct conjugacy classes, we can calculate the class equation of the finite group G.

b) We have shown both implications: if a Sylow p-subgroup is normal, then it is unique, and if it is unique, then it is normal.

(a) Deriving the class equation of a finite group G involves partitioning the group into conjugacy classes. Conjugacy classes are sets of elements in the group that are related by conjugation, where two elements a and b are conjugate if there exists an element g in G such that b = gag^(-1).

To derive the class equation, we start by considering the group G and its conjugacy classes. Let [a] denote the conjugacy class containing the element a. The class equation is given by:

|G| = |Z(G)| + ∑ |[a]|

where |G| is the order of the group G, |Z(G)| is the order of the center of G (the set of elements that commute with all other elements in G), and the summation is taken over all distinct conjugacy classes [a].

The center of a group, Z(G), is the set of elements that commute with all other elements in G. It can be written as:

Z(G) = {z in G | gz = zg for all g in G}

The order of Z(G), denoted |Z(G)|, is the number of elements in the center of G.

The conjugacy classes [a] can be determined by finding representatives from each class. A representative of a conjugacy class is an element that cannot be written as a conjugate of any other element in the class. The number of distinct conjugacy classes is equal to the number of distinct representatives.

By finding the center of G and determining the distinct conjugacy classes, we can calculate the class equation of the finite group G.

(b) To prove that a Sylow p-subgroup of a finite group G is normal if and only if it is unique, we need to show two implications: if it is normal, then it is unique, and if it is unique, then it is normal.

If a Sylow p-subgroup is normal, then it is unique:

Assume that P is a normal Sylow p-subgroup of G. Let Q be another Sylow p-subgroup of G. Since P is normal, P is a subgroup of the normalizer of P in G, denoted N_G(P). Since Q is also a Sylow p-subgroup, Q is a subgroup of the normalizer of Q in G, denoted N_G(Q). Since the normalizer is a subgroup of G, we have P ⊆ N_G(P) ⊆ G and Q ⊆ N_G(Q) ⊆ G. Since P and Q are both Sylow p-subgroups, they have the same order, which implies |P| = |Q|. However, since P and Q are subgroups of G with the same order and P is normal, P = N_G(P) = Q. Hence, if a Sylow p-subgroup is normal, it is unique.

If a Sylow p-subgroup is unique, then it is normal:

Assume that P is a unique Sylow p-subgroup of G. Let Q be any Sylow p-subgroup of G. Since P is unique, P = Q. Therefore, P is equal to any Sylow p-subgroup of G, including Q. Hence, P is normal.

Therefore, we have shown both implications: if a Sylow p-subgroup is normal, then it is unique, and if it is unique, then it is normal.

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The value of TN for this problem is given as follows:

B. 30.

A chord of a circle is a straight line segment that connects two points on the circle, that is, it is a line segment whose endpoints are on the circumference of a circle.

When two chords intersect each other, then the products of the measures of the segments of the chords are equal.

Then the value of x is obtained as follows:

8(x + 20) = 12 x 20

x + 20 = 12 x 20/8

x + 20 = 30.

x = 10.

Then the length TN is given as follows:

TN = x + 20

TN = 10 + 20

TN = 30.

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Answer:

thank you so much!

Step-by-step explanation:

Answer:

20 units²

Step-by-step explanation:

I have included the answer as well as an explanation and formula above. Note that the formula is only for area of trapeziums/trapezoids

To complete each ordered pair using the function y = 200 tan(x) on the interval 0° ≤ x ≤ 141°, we need to substitute different values of x within that interval and calculate the corresponding values of y. Let's calculate the ordered pairs by rounding the answers to the nearest whole number:

1. For x = 0°:

  y = 200 tan(0°) = 0

  The ordered pair is (0, 0).

2. For x = 45°:

  y = 200 tan(45°) = 200

  The ordered pair is (45, 200).

3. For x = 90°:

  y = 200 tan (90°) = ∞ (undefined since the tangent of 90° is infinite)

  The ordered pair is (90, undefined).

4. For x = 135°:

  y = 200 tan (135°) = -200

  The ordered pair is (135, -200).

5. For x = 141°:

  y = 200 tan (141°) = -13

  The ordered pair is (141, -13).

So, the completed ordered pairs (rounded to the nearest whole number) are:

(0, 0), (45, 200), (90, undefined), (135, -200), (141, -13).

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The attachment shows different types of polygons that have 3 more sides then the other.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now depending on these we have following five possibilities:

Case 1: Triangle and hexagon

If first polygon is triangle with three angles, the second will have 6 angles and the second polygon will be hexagon.

Case 2: Quadrilateral and heptagon

If first polygon is quadrilateral with 4 angles, the second will have 4+3 =7 angles and the second polygon will be heptagon.

Case 3: Pentagon and Octagon

If first polygon is pentagon with 5 angles, the second will have 5+3=8 angles and the second polygon will be octagon.

Case 4: Hexagon and Nonagon

If first polygon is hexagon with 6 angles, the second will have 6+3=9 angles and the second polygon will be nonagon.

Case 5: Heptagon and Decagon

If first polygon is Heptagon with 7 angles, the second will have 7+3=10 angles and the second polygon will be decagon.

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Stress distribution can exist for a body in equilibrium if sigma x = - 2c1xy, sigma y = c2z2, sigma z = 0 tau xy = c1(c2 - y2) + c3xz, tau xz = -c3y, tau yz = 0.

Stress equilibrium specifies the pressure state of a body for a given external force field or body force distribution. The principle of stress equilibrium implies that the sum of the forces acting on the free body in equilibrium is zero, as well as the sum of the moments equal to zero.σx is the normal stress in the x direction that arises from the x-direction force acting on the plane. σy is the normal stress in the y direction that arises from the y-direction force acting on the plane.

σz is the normal stress in the z direction that arises from the z-direction force acting on the plane.τxy is the shear stress that arises from forces acting parallel to the xy plane. τxz is the shear stress that arises from forces acting parallel to the xz plane.τyz is the shear stress that arises from forces acting parallel to the yz plane.

Since there are no body forces acting on the object, it must be in equilibrium. The stress tensor is assumed to be symmetric, and the shear stresses must be equal. This is due to the plane orientation being perpendicular to the y-axis, which eliminates the need for a shear stress. As a result, we conclude that this stress distribution can exist for a body in equilibrium.

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Answer:

3 miles

Step-by-step explanation:

bc he ran .5 a mile in 10 minutes. an hour is sixty minutes, so 10x six. then you do .5 x six to get 3.

In terms of the philosophical debate between empiricism and rationalism, Gestaltists would likely fall more on the side of empiricism.

Gestalt psychology emphasizes the study of perception and the organization of sensory information, which is distinct from the traditional approaches of behaviorism and structuralism. Gestaltists believe that perception is more than the sum of its parts and that the mind constructs meaning through organizing sensory information into wholes or gestalts.

This is because they prioritize the role of sensory experience in shaping perception and understanding of the world. They argue that the mind is not a blank slate, but rather that it processes sensory information in a holistic manner to construct meaning.

However, it is important to note that Gestalt psychology is not necessarily tied to either the empiricist or rationalist tradition, as it has its own unique theoretical framework that emphasizes the importance of context, organization, and pattern recognition in perception and cognition.

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By using a right triangle as a model, we will see that height of the roof is 9.38 ft.

The slant height is equivalent to the hypotenuse of a right triangle, so we know the length of the base and the hypotenuse of a right triangle. The cathetus will be half of 18ft

We need to find the other cathetus, so we can use the Pythagorean theorem, if X is the other cathetus we will get:

X^2 + (9ft)^2 = (13 ft)^2

X = √( (13 ft)^2 - (9 ft)^2) = 9.38ft

So the height of the roof is 9.38 ft.

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Answer:

74 Degrees

Step-by-step explanation:

Mistakes were made when i said 37

Answer:

\(\Huge\boxed{74}\)

Step-by-step explanation:

Hello There!

First things first, we need to find the value of x

If you didn't know the measures of supplementary angles add up to equal 180 so we can use this equation to solve for x

180 = 2x + 3x - 5

step 1 combine like terms

2x + 3x = 5x

now we have

180 = 5x - 5 step 2 add 5 to each side

-5 + 5 cancels out

180 + 5 = 185

now we have 185 = 5x

step 3 divide each side by 5

5x/5=x

185/5=37

we're left with x = 37

Now we want to plug in 37 into x for angle A

angle a = 2(37)

2*37=74

so we can conclude that angle A = 74

The value of α = 6/√7 - that is the value of α that will make the solution to the initial value problem approaches zero as t → ∞.

From the question above, an initial value problem:y″ − y − 6y = 0y(0) = αy′(0) = 6

To find the value of α so that the solution to the initial value problem approaches zero as t → ∞

To obtain the solution, we assume that y = e^mt

Where y' = m e^mt and y" = m^2 e^mt

The equation becomes:

m^2 e^mt - e^mt - 6 e^mt = 0

e^mt (m^2 - 7) = 0

m = ±√7

We have two possible solutions:

y1 = e^√7 t, y2 = e^(-√7)t

Using the initial conditions:We have:y(0) = α = C1 + C2y'(0) = 6 = √7C1 - √7C2

Solving these equations simultaneously, we get:C1 = (α + 6/√7) / 2 and C2 = (α - 6/√7) / 2

Using the solutions above:y = C1 e^√7 t + C2 e^(-√7)t

Taking the limit as t approaches infinity:y = C1 e^√7 t → ∞ since √7 > 0

and C2 e^(-√7)t → 0 since e^(-√7)t → 0 as t → ∞

Hence, y → C1 e^√7 t → ∞

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If the histogram shows a bell-shaped curve and the normality test (if performed) supports the normality assumption, it appears safe to assume that the normality condition is satisfied for the wood pieces prepared for the lab session, considering them as an SRS of all similar pieces of Douglas fir.

To determine if the normality condition is satisfied, you can follow these steps:

1. Organize the data: Collect the measurements for the characteristics of the wood pieces in your sample (such as density, strength, etc.) and organize them in a list or a table.

2. Create a frequency distribution: Calculate the frequencies of the different measurements and arrange them in a frequency distribution table.

3. Plot a histogram: Using the frequency distribution, create a histogram to visually represent the data. The x-axis represents the measurements and the y-axis represents the frequency.

4. Evaluate the shape of the histogram: Examine the shape of the histogram to determine if it resembles a normal distribution. A normal distribution is characterized by a bell-shaped curve, which is symmetrical around the mean value.

5. Conduct a normality test (optional): If you want to statistically confirm the normality of the data, you can perform a normality test, such as the Shapiro-Wilk test or the Kolmogorov-Smirnov test.

For the wood pieces manufactured for the lab session, using them as an SRS of all comparable pieces of Douglas fir, it is acceptable to infer that the normality criterion is satisfied if the histogram displays a bell-shaped curve and the normality test (if performed) confirms the normality assumption.

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Answer:

27/28

Step-by-step explanation:

2/7 - x =5/4

-2/7      -2/7

    x=27/28

The function f(t) is piecewise continuous on the interval 0 ≤ t < ∞. The graph consists of a linear segment from 0 to 1, followed by a linear segment from 1 to 2, and then a constant value of 0 for t ≥ 2. The Laplace transform of f(t) can be computed by applying the Laplace transform to each segment separately.

To sketch the graph of f(t), we first observe that f(t) is defined differently for three intervals: 0 ≤ t < 1, 1 ≤ t < 2, and t ≥ 2. In the first interval, f(t) is a linear function of t, starting from 0 and increasing at a constant rate of 1. In the second interval, f(t) is also a linear function, but it starts from 2 and decreases at a constant rate of 1. Finally, for t ≥ 2, f(t) is a constant function with a value of 0. Therefore, the graph of f(t) will consist of a line segment from 0 to 1, followed by a line segment from 1 to 2, and then a horizontal line at 0 for t ≥ 2.

Regarding continuity, f(t) is continuous within each interval where it is defined. However, there is a jump discontinuity at t = 1 because the value of f(t) changes abruptly from 1 to 2. Therefore, f(t) is not continuous at t = 1. However, it is still piecewise continuous on the interval 0 ≤ t < ∞ because it consists of continuous segments and the discontinuity occurs at a single point.

To compute the Laplace transform of f(t), we apply the Laplace transform to each segment separately. For the first segment, 0 ≤ t < 1, the Laplace transform of t is 1/s^2. For the second segment, 1 ≤ t < 2, the Laplace transform of 2 - t is 2/s - 1/s^2. Finally, for t ≥ 2, the Laplace transform of the constant 0 is simply 0. Therefore, the Laplace transform of f(t) is 1/s^2 + (2/s - 1/s^2) + 0, which simplifies to (2 - 1/s)/s^2.

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Answer:

The 3rd one is correct.

Step-by-step explanation:

Answer:

3.2

Step-by-step explanation:

Answer:

The answer that best fits the graph is C

Hope this helps! Have a great day/night!

The probability that the product of the two top numbers is greater than their sum for eight-sided dice is 3/4.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a value between 0 and 1 and 1, wherein, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The formula for probability is;

Probability  =  Favourable outcome/ Total outcome

Now, according to the question;

Consequently, the sum is greater if at least a single of the integers is 1. Such possibilities are 15.

1×n = n < 1 +n

Now consider for 2

2×2 = 2 + 2

For n > 2,

where, 2×n = n + n > 2 + n.

For all 8×8 combinations,

15 + 1 = 16 is the case whose sum is greater than or equal to the product.

Thus, 8×8 = 64

64 -16 = 48 are the total cases for the sum which is smaller and satisfies the condition.

Thus, the probability is 48/ 64 = 3/4.

Therefore, the probability that the product of the two top numbers is greater than their sum is 3/4.

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