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The value of x in the given figure is x = 7.

Given is a figure with two lines intersecting at a point and making two angle (x+16) and (4x-5).

We need to find the value of x.

To find the value of x, we can set the two angles equal to each other since they are formed by the intersecting lines and hence are vertically opposite angles.

Vertically opposite angles are always equal to each other. In other words, if you measure one of the vertically opposite angles, it will have the same measure as its opposite angle.

According to the given information, the angles are (x+16) and (4x-5). Therefore, we can set up the following equation:

x + 16 = 4x - 5

To solve for x, we'll isolate it on one side of the equation.

Let's solve the equation step by step:

x - 4x = -5 - 16 (subtract x from both sides and simplify)

-3x = -21 (combine like terms)

x = (-21) / (-3) (divide both sides by -3)

Simplifying further, we get:

x = 7

Therefore, the value of x is 7.

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Answer:

Angle 1 and Angle 5 are corresponding angles

Step-by-step explanation:

Two angles that lie on the same side of the transversal in corresponding positions.

PLZ mark BRAINLIEST

Answer:

(-2,1) (-2,2) (-1,1) (-1,2)

Step-by-step explanation:

Step-by-step explanation:

I am not sure I understand the numbers in the description, but I assume you meant that

the baseline is x/2 meter,

the height to the baseline is also x/2 meter.

the area is 32 m².

the area of a triangle is

baseline × height / 2.

so, here we have

32 = x/2 × x/2 / 2 = x²/4 / 2 = x²/8

x² = 32×8 = 256

x = 16 m

so the base and the height are both 16/2 = 8 m long.

Answer:

33

Step-by-step explanation:

first we divide 33 by 33 then we have 1 now we have times 33 which is 33 now 33-33 is 0 not we add 33 to 0 now we have 33

Answer: about 166 minutes

Step-by-step explanation:

\( \: \huge \mathfrak{ \underbrace{\overbrace{ \pink{A}{\blue{n}}{\green{s}}{ \purple{w}{ \orange{e}{ \red{r}}}}}}} \\ \\ \tt \rightarrow{\fbox{\purple{666.67min}}}\)

\( \: \tt \underline\green{solution} : \\ \)

Let us assume how much time taken for get gem be "x"

Given : To Get 3 Gems it takes 2 min

\( \sf \: formula \: = \: \frac{Time}{Gems}\\ \\ \: \tt \: \: \rightarrow \: \: x = \frac{2}{3} \\ \\ \tt \rightarrow \: x = 0.666\: min \: \: \: (for \: 1 \: gem)\: \\ \\ \sf so \: \: for \: \: 1000 \: \: gems : \: \\ \\ \: = > 1000 \times 0.666\\ \\ = > \blue{ 666.67\: min} \\ \\ \sf Thanks~\)

The sample space of the experiment is 52.

The possibility that an event will occur among all potential events is known as probability. It ranges from 0 to 1. The probability is calculated by dividing the number of things by all of the items. Population includes the sample. When studying the entire population is challenging, it is studied.

52 cards in a deck

There are 12 face cards.

The experiment needs a sample space of 52 to find the face cards.

Given that a regular deck of cards is available.

The sample space required for the experiment to determine the probability of face cards must be found.

A face card may or may not be revealed when we pull a card from the deck. So, in order to rule out the possibility that a face card is present at the end of the deck, we must draw every card from a regular deck.

52 samples are therefore required for the experiment.

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The probability that more than 5 engines are defective is approximately 0.1685 using the binomial approximation.

The binomial approximation is used to approximate the probability of a given event occurring a certain number of times in a specified number of trials, given a certain probability of the event occurring on each trial.

We can use this approximation to calculate the probability that more than 5 engines are defective.

Let X be the number of defective engines out of 40.

Then X follows a binomial distribution with n = 40 and p = 0.03, where p is the probability that any given engine is defective.

Using the binomial approximation, we can approximate the distribution of X with a normal distribution with mean

μ = np and standard deviation σ = √(np(1-p)).

We can then use the normal distribution to approximate the probability that more than 5 engines are defective.

P(X > 5) = P(X >= 6)

We can use the normal distribution to approximate this probability as follows:

Z = (X - μ) / σZ

= (6 - (40*0.03)) / √(40*0.03*(1-0.03))Z

= 0.9577

Using a standard normal distribution table or calculator, we can find that the probability of Z being greater than 0.9577 is approximately 0.1685.

Therefore, P(X > 5) = P(X >= 6) ≈ 0.1685.

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When f(x) is divided by x-3 is 27 , then what is the value of k is -3

Remainder Theοrem is an apprοach οf Euclidean divisiοn οf pοlynοmials. Accοrding tο this theοrem, if we divide a pοlynοmial P (x) by a factοr ( x – a); that isn’t essentially an element οf the pοlynοmial; yοu will find a smaller pοlynοmial alοng with a remainder.

When f(x) is divided by x - 3, the remainder is 27, which means that

f(3) = 27.

We can use this fact tο sοlve fοr k as fοllοws:

f(x) = x³ + kx + 9

f(3) = 27

Substituting x = 3 intο the expressiοn fοr f(x), we get:

f(3) = 3³ + k(3) + 9 = 27

Simplifying the left side, we get:

27 + 3k + 9 = 27

Cοmbining like terms, we get:

3k + 36 = 27

Subtracting 36 frοm bοth sides, we get:

3k = -9

Dividing bοth sides by 3, we get:

k = -3

Therefοre, the value οf k is -3.

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Answer: They made $191.52 cents from selling 798

Step-by-step explanation:

Divide the total amount of erasers sold by 7 to find the price per unit

1.68/ 7 = 0.24

So each eraser is 24 cents

Multiply that by 798

0.24 x 798 = 191.52

Answer:

9,200

Step-by-step explanation:

72,300 - 63,100 = 9,200

Among the provided answer options, the closest value to -0.555 is -0.55, which is option c. Therefore, option c (-0.55) is the value of c that satisfies P(Z ? c) = 0.71.

The notation P(Z ? c) represents the probability that a standard normal random variable Z is less than or equal to c. To find the value of c that corresponds to P(Z ? c) = 0.71, we need to determine the Z-score associated with this probability.

Using a standard normal distribution table or a calculator, we can find that a Z-score of approximately 0.555 corresponds to a cumulative probability of 0.71. However, since we are looking for the value of c in P(Z ? c), we need to consider the opposite inequality.

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The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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Answer:

The exact value of cos(45°) is √(2) / 2.

Step-by-step explanation:

Answer:

Answer:√2/2=cos45

√2/2×√2/√2=2/2√2

1/√2

To argue why the liberal arts are so important in education and leisure, one must discuss its Greek origin and how it is received today.

The term "liberal arts" comes from the Latin word "liberalis," which means free. It was used in the Middle Ages to refer to topics that should be studied by free people. Liberal arts refers to courses of study that provide a general education rather than specialized training. It encompasses a wide range of topics, including literature, philosophy, history, language, art, and science.The liberal arts curriculum is based on the idea that a broad education is necessary for individuals to become productive members of society. In ancient Greece, education was focused on developing the mind, body, and spirit.  

The study of the liberal arts is necessary to create well-rounded individuals who can contribute to society in meaningful ways. While the importance of the liberal arts has been debated, it is clear that they are more important now than ever before. The study of the liberal arts is necessary to develop the skills that are required in a rapidly advancing technological world.

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A graph is a way to represent a lot of data in a visual format. thus the number of games in the category 51-57 are 3.

A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. the line of the graph is a function that follows the graph.

The categories and the data points can be arranged as;

51 - 57 = 51, 56, 55

58 - 64 = 63, 59, 60, 64

65 – 71 = 70, 67

72 or more = 75

Therefore, the number of games in the category 51-57 are 3.

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Answer:

I have helped you on the other question you asked. It's the same question.

Answer:

x does not equal - 49.

x = 49

Step-by-step explanation:

To find the square you multiply the square root.

- 7 × - 7 = 49

x ≠ - 49

x = 49

The correct statement is: provided that the sample size is reasonably large (for any population).

The Central Limit Theorem states that, under certain conditions, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

These conditions include a random sample from the population and a sufficiently large sample size (typically, n > 30 is considered large enough).

Therefore, the Central Limit Theorem is important because it allows us to make inferences about the population mean using the normal distribution, even if we do not know the population distribution.

This is useful in many applications of statistics, including hypothesis testing, confidence intervals, and estimating population parameters

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The arc length of the segment from t = π/6 to t = π/3 for the curve defined by r(t) = (cos(4t), 2 ln(sin(2t)), sin(4t)) is approximately [Insert the numerical value of the arc length].

To calculate the arc length, we use the formula ∫√(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2 dt over the given interval [t = π/6, t = π/3]. Evaluating this integral will give us the desired arc length.

Let's break down the steps to calculate the arc length. First, we need to find the derivatives of the components of r(t). Taking the derivatives of cos(4t), 2 ln(sin(2t)), and sin(4t) with respect to t, we obtain the expressions for dx/dt, dy/dt, and dz/dt, respectively.

Next, we square these derivatives, sum them up, and take the square root of the resulting expression. This gives us the integrand for the arc length formula.

Finally, we integrate this expression over the given interval [t = π/6, t = π/3] with respect to t. The numerical value of this integral will yield the arc length of the segment from t = π/6 to t = π/3.

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Answer:

5.

x=14

6.

x=6

more details look it at attachment.

Answer:

Since the number of calories burned is proportional to the number of minutes jogged, we can represent this relationship using the equation y = kx, where y is the number of calories burned, x is the number of minutes jogged, and k is the constant of proportionality.

To find the value of k, we can use one of the given data points. For example, if x = 10 and y = 95, we have 95 = k * 10. Solving for k, we find that k = 9.5.

The constant of proportionality, k, has the meaning of the number of calories burned per minute of jogging. In this case, k = 9.5 calories/minute, so for every minute of jogging, the person burns 9.5 calories.

Step-by-step explanation:

Answer:

$35

Step-by-step explanation:

25 x 1.4 = 35

Answer:

14%

Step-by-step explanation:

So if we have 4 Year 11 pupils out of a total of 29 pupils at a football club, the fraction for that would be 4/29, if we convert 4/29 into a decimal number we get 0.13793103448, so we round this number up to the nearest 1 decimal place, and that would be 0.14 which equals 14%. Hope this helps.

Using BODMAS, the solutions of the expressions are: (1) 9, (2)-12, (3) 0.27, and (4) 0.24

We should know that BODMAS is a mathematical approach which means

In each of the expressions, we must follow the approach

1)    \(\frac{(6+3)^{2} }{3*9}\)

Simplifying this we have 9²/9=81/9

=9

2)  \(\frac{3^{2} -6*2}{(12-8)/2^{2} *10}\)

Using BODMAS we have

(9-12)/4/40

-3÷1/9

⇒-3*4

=-12

(3)   \(\frac{4.5+2*2.5^{2}-6 }{8*4+9}\)

Using BODMAS we have

(4.5+2*6.25-6)/32+9

⇒(4.5+12.5-6)/41

=11/41=0.27

4     (\(\frac{3.5+16-2.5^{2} }{10.5-6*11}\))

Using BODMAS we have  

(3.5+16-6.25)/10.5-66

Simplifying

(13.25)/-55.5

=0.24

Therefore, the values when simplified are  (1) 9, (2)-12, (3) 0.27, and (4) 0.24

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Answer:

  2 solutions

Step-by-step explanation:

A graph shows the line crosses the parabola in two places, (-1, 4) and (2, -2). There are two solutions.

__

If you want to solve this algebraically, you can equation the expressions for y and solve the resulting quadratic.

  y = y

  x^2 -3x = -2x +2

  x^2 -x -2 = 0 . . . . . . put in standard form

To find the number of solutions, you can look at the discriminant. For quadratic ax²+bx+c, the discriminant is ...

  d = b² -4ac

For the quadratic in this problem, the discriminant is ...

  d = (-1)^2 -4(1)(-2) = 1 +8 = 9

This is a positive number, meaning that there are two distinct real solutions.

_____

Additional comment

The discriminant of a quadratic can tell you the number of solutions, and whether they are real or complex:

The roots of the system of equation are 2 and -1. Therefore, the system of equations have two solutions

Given that y=−2x+2 and y=x^2−3x

Equate the two equations

-2x + 2 = x^2 − 3x

collect the like terms

x^2 − 3x + 2x - 2 = 0

x^2 − x - 2

Factorize the quadratic equation above

x^2 + x − 2x - 2 = 0

x( x + 1) -2( x + 1) = 0

x - 2 = 0

x = 2

or

x + 1 = 0

x = -1

Therefore, the system of equations have two solutions

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The true statements are B and E. The tangent point A is at (-3, 4), and the tangent point P is at (1 + √(3))/2, (1 + √(3))/2).

Since line AB is tangent to the circle at point A, the radius is perpendicular to line AB at point A.

Therefore, the slope of the radius at point A is the negative reciprocal of the slope of the tangent, which is -1.

The equation of the line passing through (-1, 2) with a slope of -1 is y = -x + 1, which intersects y = x + 7 at (-3, 4).

Thus, the distance from (-3, 4) to (-1, 2) is the radius of the circle, which is √(10).

Since PQ is parallel to AB, the slope of line PQ is also 1.

Find the equation of line PQ using point-slope form, using the point of tangency

P(x, y) and the slope of 1: y - y1 = m(x - x1),

where m = 1, x1 = -1, and y1 = 2. Thus, y - 2 = x + 1, or y = x + 3.

To find the coordinates of P, find the point of intersection between the line y = x + 3 and the circle.

Substitute y = x + 3 into the equation of the circle,

(x + 1)² + (y - 2)² = 10,

to get the quadratic equation x²+ 2x - 4x + 4 + x² + 6x + 9 - 20 = 0,

which simplifies to 2x² + 4x - 7 = 0.

Using the quadratic formula,

x = (-4 ± √(48))/4 = (-1 ± √(3))/2.

Substituting these values of x into y = x + 3,

y = (1 ± √(3))/2. Thus, the two points of tangency are (-3, 4) and ((-1 + √(3))/2, (1 + √(3))/2).

Therefore, the true statements are B and E. The tangent point A is at (-3, 4), and the tangent point P is at (1 + √(3))/2, (1 + √(3))/2).

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