Which congruence theorem can be used to prove △BDA ≅ △DBC? Triangles B D A and D B C share side D B. Angles C B D and A D B are right angles. Sides C D and B A are congruent. HL SAS AAS SSS

If all the widgets from the three machines are mixed together, then the probability that a good widget will be drawn at random is 0.78 or 78%.

Probability is defined as how likely an event is to occur, or how likely it is that a proposition is true.

If machine 1 makes 3000/hour and 80% are good, then the chances of it being good is 80% also or, 2400 out of 3000.

80% of 3000 is 2400

If machine 2 makes 4000/hour and 90% are good, then the chances of it being good is 90% also or, 3600 out of 4000.

90% of 4000 is 3600

If machine 3 makes 3000/hour and 60% are good, then the chances of it being good is 60% also or, 1800 out of 3000.

60% of 3000 is 1800

Mixing together the widgets from the three machines, use the formula to calculate the probability of an event which is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Probability(good) = (2400 + 3600 + 1800)/(3000 + 4000 + 3000)

Probability(good) = 7800/10000

Probability(good) = 0.78 or 78%

Hence, the probability that a good widget drawn at random is 0.78 or 78%.

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Answer:

0.85

Step-by-step explanation:

The number of columns in the first matrix must equal the number of rows in the second matrix in order to multiply matrices with different dimensions.

    3. Determine the dot product of the corresponding row in matrix A          and the corresponding column in matrix B for each element in matrix C.

    4: The final response is matrix C, which is the union of the 2x3 matrix A and the 3x4 matrix B.

     Therefore, the result is a 2x4 matrix, which is produced by taking the dot product of the rows and columns of matrix A and matrix B.

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The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x. The cab charges $0.88 for a ride of 2 miles. And the cab charges $1.72 for a trip of 8 miles.

a. The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x

b. To find the number of miles for a cab ride that costs $0.88, we can set up the equation:

$0.88 = $0.60 + $0.14 * x

Subtracting $0.60 from both sides, we get:

$0.88 - $0.60 = $0.14 * x

$0.28 = $0.14 * x

Dividing both sides by $0.14, we find:

x = $0.28 / $0.14

x = 2 miles

Therefore, the cab charges $0.88 for a ride of 2 miles.

c. To calculate the cost of a trip of 8 miles, we can substitute x = 8 into the equation:

Cost = $0.60 + $0.14 * 8

Cost = $0.60 + $1.12

Cost = $1.72

Therefore, the cab charges $1.72 for a trip of 8 miles.

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A 20 year old has height below 3.7 feet and above 7.9 feet then 20 year old be considered abnormal.

The average height means that the given population determined by the interaction between the environment in which it lives and the resources it commands.

Abnormal means diffrent from what is normal or usual, in a way that worries you or that is unplesant.

We have given that average height is 5.8 feet.

And abnormal height a 20 year old must be 2.1 feet below average height or 2.1 feet above average height.

Therefore 5.8 - 2.1 = 3.7 feet

                 5.8 + 2.1 = 7.9 feet

Hence height below 3.7 feet abd above 7.9 feet is considered to be abnormal.

That means [-∞ , 3.7] and [7.9,∞] is considered to be abnormal height for 20 year old man.

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The table below shows the number of hits for 25 and 50 repetitions.

Answer and Step-by-step explanation: Expected Value or Mean of a probability distribution is calculated as:

E(X) = μ = ∑xP(X)

In a game for the 2012 baseball season, expected value is:

\(\mu=0(0.1670)+1(0.3320)+2(0.2864)+3(0.1499)+4(0.0381)+5(0.0266)\)

μ = 1.640

Standard Deviation (σ) of a probability distribution is:

\(\sigma=\sqrt{\Sigma (x-\mu)^{2}P(X)}\)

\(\sigma = \sqrt{(0-1.640)^{2}(0.1670)+...+(5-1.640)^{2}(0.0266)}\)

σ = 1.1883

The simulate experiment of 25 repetitions shows a table. With this table, it is possible to create a frequency table as follows:

x    |    f

0   |    4

1    |    7

2   |   11

3   |   2

4   |    1

With a frequency table, expected value is calculated as:

\(\mu=\frac{\Sigma (fx)}{\Sigma f}\)

\(\mu=\frac{0*4+1*7+2*11+3*2+4*1}{25}\)

μ = 1.56

Standard deviation, using a frequency table, is calculated as:

\(\sigma = \sqrt{\frac{n\Sigma (fx^{2})-(\Sigma fx)^{2}}{n(n-1)} }\)

\(\sigma=\sqrt{\frac{25(0*4^{2}+...+4*1^{2})-(0*4+...+4*1)^{2}}{25(24)} }\)

σ = 0.983

The same can be done for 50 repetitions.

The frequency table is

x      |      f

0     |      6

1      |     18

2     |     16

3     |     9

4     |     1

\(\mu=\frac{0*6+1*18+2*16+3*9+4*1}{50}\)

μ = 1.62

\(\sigma=\sqrt{\frac{50(0*6^{2}+...+4*1^{2})-(0*6+...4*1)^{2}}{50(49)} }\)

σ = 0.9775

Comparing expected values and standard deviations, observe that the bigger the repetition of the experiment, mean and standard deviation get closer to the theoretical statistical values. This is an example of the Law of Large Numbers, a theorem stating as the number of random, normally distributed values increase, their sample mean approaches the theoretical mean.

Size of x = 102°

In geometry, an angle is formed when two rays are joined at their endpoints. These rays are called the sides or arms of the angle.

Given,

In triangle ABC

Sum of interior angles is 180°

∠CAB + ∠ABC + ∠BCA = 180°

87° + ∠ABC + 36° = 180°

123° + ∠ABC = 180°

∠ABC = 180° - 123°

∠ABC = 57°

In triangle DBG

Exterior angle is equal to sum of two opposite interior angles.

DGF = GDB + DBG

DGF = GDB + ABC

DGF = 45° + 57°

DGF = 102°

DGF and EFC are alternate angles made by EF and DG on BC

∴ EFC = DGF

x = 102°

Hence, 102° is size of x.

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Answer:

yes

Step-by-step explanation:

every x value has at least one y value

Answer:  b.) 1 hour at 35 mph when the car spends 3 hours at 55mph

c.) The trip will take 3.64 hours which is about about  3 hours and 38 minutes if the car travels at 55mph the entire time.

(But it could take longer if the police stop the car to issue a ticket for going 55 mph in a 35mph zone!)

Step-by-step explanation:

b.) 55(3) + 35y = 200  Multiply 55(3) = 165

165 + 35y = 200.    Subtract 165 from both sides 200- 165 = 35

35y = 35 divide both sides by 35

y = 1, So the time traveling at 35mph is 1 hour

c.) 55x + 35y = 200

55x + 35(0) = 200  35×0 = 0

55x = 200 . Divide 200 miles by 55mph to find the time, x

200/55 = 3.63636 hours

To convert to minutes, multiply 60 × .63636 ≈ 38.18 minutes

Answer:

v=18

Step-by-step explanation:

26=8+v

Swap sides:

8+v=26

Subtract 8 from both sides:

8+v-8=26-8

Group like terms:

v+8-8=26-8

Simplify the arithmetic:

v=26-8

v=18

Answer:

D

Step-by-step explanation:

Answer:

I think I had a 6 streak going on but I blew it yesterday

Step-by-step explanation:

Answer:

My answer streak is 20. Sorry I’m new

To plot the direction field associated with the differential equation u^n + 192u = 0, we need to first rewrite the equation as: u' = -192u^(1-n) where u' denotes the derivative of u with respect to some independent variable, such as time. The direction field represents the slope of the solution curve u(x) at each point (x, u(x)) in the xy-plane. To find this slope, we evaluate the right-hand side of the equation at each point: dy/dx = -192y^(1-n)

We can then plot short line segments with this slope at each point in the plane. The resulting picture will show us how the solution curves behave over the entire domain of the equation.To plot the phase plot of the solution corresponding to the initial value problem (IVP), we need to find the specific solution that satisfies the given initial condition. In other words, we need to find u(x) such that u(0) = y0, where y0 is some given constant. The solution to this IVP is: u(x) = (y0^n) / ((y0^n - 192) * e^(192x)) To plot the phase plot, we need to graph this solution as a function of time (or whatever independent variable is relevant to the problem), with u(x) on the vertical axis and x on the horizontal axis. We can then mark the initial condition (0, y0) on this graph and sketch the solution curve that passes through this point.Overall, the direction field and phase plot provide us with a visual representation of how the solution to the differential equation behaves over time. By analyzing these plots, we can gain insight into the long-term behavior of the solution and make predictions about its future behavior.

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Answer:

Rectangle

Parallelogram

Step-by-step explanation:

The ratio 3:1:3:1 shows that lengths of opposite sides of the quadrilateral are equal.

So, the possible names for the quadrilateral are rectangle, parallelogram.

The parametric equation x = t^2, y = t + 4, -4 ≤ t ≤ 4 is open at right side.

Therefore the answer is Right.

A parametric equation is a set of equations that describes the position of a point in the xy-plane in terms of a third variable, usually called a parameter. In this case, the parametric equations x = t^2 and y = t + 4 describe the position of a point on the xy-plane in terms of the parameter t.

y = t + 4

So t = y - 4

x = t²

So x = (y - 4)²

This is of the form x = 1(y - 4)²

x = a(y – k)2 +h is the sidewise form of a parabola with vertex (h, k). So this parametric form represents a parabola with vertex (0, 4) open at right side.

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Answer:

x = 7/24  y = -1/18

Step-by-step explanation:

3y = -4x + 1

y = (-4/3)x + (1/3)

*plug into the other equation

12x - 9(-4/3x + 1/3) = 4

12x + 12x - 3 = 4

24x = 7

x = 7/24

*now plug into original equation

y = (-4/3)(7/24) + 1/3

y = -1/18

The actual weight is 0.0042 pounds lighter than the labeled weight.

The actual weight of the chocolates is 0.3798 pounds, while the label on the bag states it should weigh 0.384 pounds. To determine how much lighter the actual weight is, we can calculate the difference between the two weights.

Subtracting the actual weight from the labeled weight, we get:

0.384 pounds - 0.3798 pounds = 0.0042 pounds.

Therefore, the actual weight is 0.0042 pounds lighter than the labeled weight.

It's important to note that this difference may seem small, but it can be significant depending on the context. Accuracy in labeling is crucial for various reasons, such as complying with regulations, providing precise information to consumers, and ensuring fair trade practices. Even minor discrepancies can impact trust and customer satisfaction.

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Answer:

Step-by-step explanation:

5x-4+7x-8=180

12x-12=180

12x=192

x = 16

5(16)-4= 80-4= 76 degrees

7(16)-8= 112-8= 104 degrees

9y  +  5 = 104

9y = 99

y = 11

9(11) + 5 = 99 + 5 = 104

Answer:

Step-by-step explanation:

z³/xy²

Answer:

w

Step-by-step explanation:

The amount of water they need to bring depends on how long they will be hiking.

The discordance between the evolution of genes and culture relates to the concept of "mismatch" in the article, highlighting the misalignment between our genetics and the rapidly changing cultural environment.

The discordance between the evolution of genes and culture refers to the fact that human genes evolve slowly over long periods, while cultural changes occur rapidly. This raises the question of why our genes haven't caught up with the cultural changes happening around us. This concept of mismatch is explored in the article to highlight the misalignment between our genetic predispositions and the demands of the rapidly changing cultural environment.

The article likely delves into how this mismatch can lead to various challenges and conflicts, such as the prevalence of modern diseases or psychological conditions arising from the discrepancy between our evolutionary heritage and the cultural context we find ourselves in today. By examining this concept, the article aims to shed light on the potential consequences and implications of the evolutionary-cultural mismatch.

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The number of measurements, and the mode being the most frequently occurring value among the snowfall measurements.

The mean, median, and mode are all useful measures of central tendency when researching the amount of snowfall in Cleveland from December to February. The mean is calculated by adding up all of the snowfall measurements and dividing that by the number of measurements. For example, if there were 4 snowfall measurements of 10, 20, 30 and 40 inches, the mean would be 25 inches (10+20+30+40 / 4). The median is the middle value of the snowfall measurements when they are arranged from least to greatest. In this example, the median would be 25 inches as well. The mode is the most frequently occurring value among the snowfall measurements. In this example, the mode is also 25 inches.

The mean, median and mode are all useful measures of central tendency when researching the amount of snowfall in Cleveland from December to February, with the mean and median being calculated by adding up all of the snowfall measurements and dividing that by the number of measurements, and the mode being the most frequently occurring value among the snowfall measurements.

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Answer:

  \(a=-\frac{3}{5}\)

Step-by-step explanation:

\(15a-9=0\\\\15a=-9\\\\a=-\frac{9}{15} \\\\a=-\frac{3}{5}\)

Answer:

Step-by-step explanation:

Use distributive property

15a + 9 = 3*5*a + 3*3

           = 3 (5a + 3)

There is no line parallel to the line x + 2 · y + 8 = 0, as point (x, y) = (- 2, - 3) lies on the original line.

In this problem we need to determine the equation of line based on its slope relationship respect to another line and a given point. Two lines are parallel if and only if they have the same slope (m) and two distinct intercepts (b). First, transform the given equation of the line into slope-intercept form:

x + 2 · y + 8 = 0

2 · y = - x - 8

y = - (1 / 2) · x - 4

Then, the resulting line has a slope of - 1 / 2.

Second, determine the intercept of the resulting line:

y = m · x + b

b = y - m · x

b = - 3 - (- 1 / 2) · (- 2)

b = - 3 - 1

b = - 4

The intercept of the resulting line is - 4.

Third, transform the equation of the resulting line into standard form:

y = - (1 / 2) · x - 4

- 2 · y = x + 8

x + 2 · y + 8 = 0

There is no parallel line for the point (x, y) = (- 2, 3).

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Answer:

Exact form: -87/16

decimal from -5.4375

mixed number form -5 7/16

Step-by-step explanation:

I'ma god at math

The given field is F = − yi + xj. We are required to find the circulation and the flux of this field around and across the following curves.

A) \(The circle r(t) = (cost) i + (sint) j, 0 ≤ t ≤ 2πCirculation: For a vector field F = P i + Q j, the circulation of F around a simple closed curve C oriented counterclockwise is given by: circulation = ∮cF(r) · drHere, P = 0 and Q = x.∴ F(r) = P i + Q j = xj\)

\(The parameterization of the given curve is r(t) = (cost) i + (sint) j.\)

\(The differential element of the curve is given by:dr = dx i + dy j= -sin(t) i + cos(t) j\)

\(The circulation is given by:circulation = ∮cF(r) · dr= ∫₀²π F(r(t)) · dr/dt dt= ∫₀²π(xj)·(-sin(t)i+cos(t)j)·(-sin(t)i+cos(t)j)dt= ∫₀²πxdt= ∫₀²πcostdt= 0Flux:The flux of F across C is given by:flux = ∮cF(r) · n dsHere, P = 0 and Q = x.∴ F(r) = xj\)

\(The outward unit normal vector to the given curve is given by:n = sin(t) i − cos(t) j\)

\(The parameterization of the given curve is r(t) = (cost) i + (sint) j.\)

\(The differential element of the curve is given by:ds = |dr|=√((dx)²+(dy)²)=√(sin²t+cos²t)dt= dtThe flux is given by: flux = ∮cF(r) · n ds= ∫₀²π F(r(t)) · n(t) ds/dt dt= ∫₀²π(xj)·(sin(t)i-cos(t)j)·(1)dt= ∫₀²πxsin(t)dt= 0B)\)

\(The ellipse r(t) = (cost) i + (7sint) j, 0 ≤ t ≤ 2πCirculation: For a vector field F = P i + Q j, the circulation of F around a simple closed curve C oriented counterclockwise is given by: circulation = ∮cF(r) · drHere, P = 0 and Q = x.∴ F(r) = xj\)

\(The parameterization of the given curve is r(t) = (cost) i + (7sint) j.\)

\(The differential element of the curve is given by:dr = dx i + dy j= -7sin(t) i + 7cos(t) j\)

\(The circulation is given by:circulation = ∮cF(r) · dr= ∫₀²π F(r(t)) · dr/dt dt= ∫₀²π(xj)·(-7sin(t)i+7cos(t)j)·(-7cos(t)i-7sin(t)j)dt= ∫₀²π49xdt= 0Flux:The flux of F across C is given by:flux = ∮cF(r) · n dsHere, P = 0 and Q = x.∴ F(r) = xj\)

\(The outward unit normal vector to the given curve is given by:n = 7sin(t) i − cos(t) j\)

\(The parameterization of the given curve is r(t) = (cost) i + (7sint) j.\)

\(The differential element of the curve is given by:ds = |dr|=√((dx)²+(dy)²)=√(49sin²t+cos²t)dt=√(50cos²t-48)dt\)

\(The flux is given by: flux = ∮cF(r) · n ds= ∫₀²π F(r(t)) · n(t) ds/dt dt= ∫₀²π(xj)·(7sin(t)i-cos(t)j)·(7sin(t))√(50cos²t-48)dt= ∫₀²π7xsin(t)√(50cos²t-48)dt= 0\)

Hence, the circulation is zero and the flux is zero for both the given curves.

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Answer:

It is the distribution of the statistic if we were to draw all possible samples of a given size from the population and calculate the statistic for each sample.

Step-by-step explanation:

The sampling distribution of a statistic refers to the range of all possible sample values of the statistic that could be drawn from the parent population under the specified sampling plan.

In other words, it is the distribution of the statistic if we were to draw all possible samples of a given size from the population and calculate the statistic for each sample.

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If triangle JKL is rotated 180° clockwise, the location of J’ is: B. (6, 7).

Generally, there are different types of transformation and these include the following:

A rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

From the graph (see attachment), we have the following data:

In Geometry, rotating a point 180° about the origin in a clockwise or counterclockwise (anticlockwise) direction would produce a point that has the coordinates (-x, -y).

By applying a rotation of 180° clockwise to triangle JKL, the location of J’ is given by:

Points at J = (-6, -7)   →  Points at J' = (-(-6), -(-7))

Points at J = (-6, -7)   →  Points at J' = (6, 7).

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Complete Question:

If JKL is rotated 180° clockwise, which describes the location of J'?

A. (-7, 6)

B. (6, 7)

C. (7,-6)

D. (7,6)