indicate a good method for evaluating the integral ∫2−√27.

We know that the sum of all interior angles of a triangle is always \(180^\circ\). It is known as Angle Sum Property.

Here in triangle the angles are A, 90°, 30°.

So by Angle sum property in the given triangle,

\(m\angle A\) + 90° + 30° = 180°

\(m\angle A\) + 120° = 180°

\(m\angle A\) = 180° - 120° = 60°

So the value of \(m\angle A\) is 60°.

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Answer:

Step-by-step explanation:

The point that you will end up at is **(-0.5, -2)**.

To see this, we start at the origin, which is the point (0, 0). We then move 3.5 units right, which brings us to the point (3.5, 0). Finally, we move 2 units down, which brings us to the point (3.5, -2).

The other points are incorrect because they do not take into account the direction of the movement. For example, the point (-2, -0.5) is incorrect because we move 3.5 units **right**, not left. Similarly, the point (-2, 2) is incorrect because we move 2 units **down**, not up.

Therefore, the only point that you will end up at is (3.5, -2).

The probability mass function (PMF) for x is {0.0004, 0.0588, 0.3432, 0.941192}, and the cumulative mass function (CMF) for x is {0.0004, 0.0592, 0.4024, 1.0}.

The probability mass function (PMF) and cumulative mass function (CMF) for the random variable x, which denotes the number of parts correctly classified in an optical inspection system, can be determined.

Since the classifications of the parts are independent, we can use the binomial probability distribution to model this scenario. The PMF gives the probability of obtaining a specific value of x, and the CMF gives the probability of obtaining a value less than or equal to x.

The PMF of x is given by the binomial probability formula:

P(x) = (n C x) * p^x * (1 - p)^(n - x)

where n is the number of trials (number of parts inspected), x is the number of successes (number of parts correctly classified), and p is the probability of success (probability of correct classification of any part).

In this case, n = 3 (three parts inspected) and p = 0.98 (probability of correct classification).

Let's calculate the PMF for x:

P(x = 0) = (3 C 0) * (0.98^0) * (1 - 0.98)^(3 - 0) = 0.0004

P(x = 1) = (3 C 1) * (0.98^1) * (1 - 0.98)^(3 - 1) = 0.0588

P(x = 2) = (3 C 2) * (0.98^2) * (1 - 0.98)^(3 - 2) = 0.3432

P(x = 3) = (3 C 3) * (0.98^3) * (1 - 0.98)^(3 - 3) = 0.941192

The PMF for x is:

P(x = 0) = 0.0004

P(x = 1) = 0.0588

P(x = 2) = 0.3432

P(x = 3) = 0.941192

To calculate the CMF, we sum up the probabilities up to x:

F(x) = P(X ≤ x) = P(x = 0) + P(x = 1) + ... + P(x = x)

Using the calculated probabilities, the CMF for x is:

F(x = 0) = 0.0004

F(x = 1) = 0.0592

F(x = 2) = 0.4024

F(x = 3) = 1.0

Therefore, the probability mass function (PMF) for x is {0.0004, 0.0588, 0.3432, 0.941192}, and the cumulative mass function (CMF) for x is {0.0004, 0.0592, 0.4024, 1.0}.

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Answer:

151, 29, 151

Step-by-step explanation:

\(m\angle 2=29^{\circ}\) (vertical angles)

\(m\angle 1=m\angle 3=151^{\circ}\) (linear pair)

Answer:

\(m \angle 1= \boxed{151}\;^{\circ}\\\\m \angle 2= \boxed{29}\;^{\circ}\\\\m \angle 3= \boxed{151}\;^{\circ}\)

Step-by-step explanation:

Angles on a straight line sum to 180°.

⇒ m∠3 + m∠4 = 180°

⇒ m∠3 + 29° = 180°

⇒ m∠3 = 151°

Vertical Angle Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Applying the Vertical Angle Theorem:

Answer:

32, because when you are dividing by a fraction, you can multiply by the divident by reciprocal of the divisor.

Step-by-step explanation:

4 ÷ 1/8

4/1 ÷ 1/8

4/1 × 8/1

4 × 8

32

When you are dividing by a fraction, you can multiply by the divident by reciprocal of the divisor.

Answer:

32

Step-by-step explanation:

4

1

1

8

=(

4

1

)(

8

1

)

=

(4)(8)

(1)(1)

=32

Answer:

1: 5/2 = 2.5 eggs

2: 25 1/3 bags of gravel

Step-by-step explanation:

Domain of function w is (-∞, 0], the range of function w is (-∞, -4].

Given, F(x) = x^(1/2) is transformed into w(x) = -(3x)^(1/2) - 4We are supposed to find the domain and range of the function w. Domain of function w:Domain refers to the set of values that are allowed to be plugged into the function. Since the given function involves taking the square root of a value, the input value (x) must be non-negative. So, we can say that x ≥ 0.

Now, after the transformation, the expression (-3x)^(1/2) gives us a real number only if x ≤ 0. This is because -3x becomes a positive value only when x is negative. So, the domain of the function w is x ≤ 0, or (-∞, 0].Range of function w:Range refers to the set of output values that the function takes on. As per the transformation, we have w(x) = -(3x)^(1/2) - 4.Here, we can see that the square root of 3x will always be non-negative for all real values of x. So, the maximum value of -(3x)^(1/2) will be 0. Also, when x ≤ 0, the expression -(3x)^(1/2) is a negative value, and hence w(x) will always be less than -4. So, the range of the function w is (-∞, -4].Therefore, the domain of function w is (-∞, 0], the range of function w is (-∞, -4].

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Answer:

Step-by-step explanation:

a + b)^6 will have 7 terms so you want row 6 of the triangle 1 6 15 20 15 6 1

so (a + b)^6 = a^6 + 6a^(5)b + 15a^(4)b^2 + 20a^(3)b^3 + 15a^(2)b^4 + 6ab^5 + b^6

given a = d and b = -5y

∴ (d − 5y)^6 = d^6 + 6d^(5)(-5y) + 15d^(4)(-5y)^2 + 20d^(3)(-5y)^3 + 15d^(2)(-5y)^4 +

Answer:

The mean of the 10 sales amounts for store A is $40,000.

Step-by-step explanation:

Given;

yˆ= −3,000 + 1.2x ...................... (1)

Where;

x = sales amounts each day at store A or the mean of the 10 sales amounts for store A = ?

yˆ = sales amounts each day at store B or the mean of the 10 sales amounts for store B = $45,000

Substituting y = 45,000 into equation (1) and solve for x, we have:

45,000 = −3,000 + 1.2x

45,000 + 3,000 = 1.2x

48,000 = 1.2x

x = 48,000 / 1.2

x = 40,000

Therefore, the mean of the 10 sales amounts for store A is $40,000.

Answer:y=-6x+34

Step-by-step explanation: I hope this helps

Answer:

Sophia can drive 3672 miles using 18 galloons of gas.

Step-by-step explanation:

204 x 18 = 3672.

Calculate miles per gallon by dividing the miles she drove you the gallons used:

204/8 = 25.5 miles per gallon.

Now multiply miles per gallon by gallons:

25.5 x 18 = 459 miles

Answer: 459 miles

Answer: y= x^2/16-6x/16+41/16

Step-by-step explanation:

The equation of a parabola will be; y = x^2/16 - 6x/16 + 41/16

If a quadratic equation is written in the form

y=a(x-h)^2 + k

then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)

Otherwise, we had to use calculus to get critical points, then second derivative of functions to find the character of critical points as minima or maxima or saddle etc to get the location of vertex point.

This point (h,k) is called the vertex of the parabola that quadratic equation represents.

WE need to find the equation of a parabola that has a vertical axis, passes through the point (–1, 3), and has its vertex at (3, 2)

Thus, the equation of a parabola will be;

y = x^2/16 - 6x/16 + 41/16

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Answer:

40%

Step-by-step explanation:

10% of 40 is 4

4x4=16 meaning that 10% x 4 = 40%

Answer:

40%

Step-by-step explanation:

I dont know how to really explain it I just solved it using calculator

Given:

\(\cos \theta =\dfrac{3}{5}\)

\(\sin \theta <0\)

To find:

The quadrant of the terminal side of \(\theta\) and find the value of \(\sin\theta\).

Solution:

We know that,

In Quadrant I, all trigonometric ratios are positive.

In Quadrant II: Only sin and cosec are positive.

In Quadrant III: Only tan and cot are positive.

In Quadrant IV: Only cos and sec are positive.

It is given that,

\(\cos \theta =\dfrac{3}{5}\)

\(\sin \theta <0\)

Here cos is positive and sine is negative. So, \(\theta \) must be lies in Quadrant IV.

We know that,

\(\sin^2\theta +\cos^2\theta =1\)

\(\sin^2\theta=1-\cos^2\theta\)

\(\sin \theta=\pm \sqrt{1-\cos^2\theta}\)

It is only negative because \(\theta \) lies in Quadrant IV. So,

\(\sin \theta=-\sqrt{1-\cos^2\theta}\)

After substituting \(\cos \theta =\dfrac{3}{5}\), we get

\(\sin \theta=-\sqrt{1-(\dfrac{3}{5})^2}\)

\(\sin \theta=-\sqrt{1-\dfrac{9}{25}}\)

\(\sin \theta=-\sqrt{\dfrac{25-9}{25}}\)

\(\sin \theta=-\sqrt{\dfrac{16}{25}}\)

\(\sin \theta=-\dfrac{4}{5}\)

Therefore, the correct option is B.

    5 (4 + √3)/13 is the solution linear equation.

What is  linear equation?

An algebraic equation with simply a constant and a first- order( direct) element, similar as y = mx b, where m is the pitch and b is the y- intercept, is known as a linear equation.

                         The below is sometimes appertained to as a" direct equation of two variables," where y and x are the variables. Equations whose variables have a power of one are called direct equations. One illustration with only one variable is where layoff b = 0, where a and b are real values and x is the variable.

5/4 - √3

Multiply by 4 + √3 in nominator and dinominator .

\(\frac{5}{4 - \sqrt{3} } * \frac{4 + \sqrt{3} }{4 + \sqrt{3} }\)

=   5 (4 + √3)/(4)² - (√3)²

=  5 (4 + √3)/16 - 3

=   5 (4 + √3)/13

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As a result, the simplified formulation with a rationalized denominator is as follows:

= \(\frac{20 + 5\sqrt{3} }{`13} \\\)

deno

To rationalize the denominator, multiply both the numerator and the denominator by the denominator's conjugate, which is 4 + sqrt(3):

\(\frac{5}{(4-\sqrt{3} ) } * \frac{(4+\sqrt{3} )}{(4+\sqrt{3} )}\)

Using the distributive property to simplify the numerator and denominator, we get:

= \(\frac{5(4+\sqrt{3} )}{(4-\sqrt{3} )(4+\sqrt{3} ) } }\)

= \(\frac{20 + 5\sqrt{3} }{`16-3} \\\)

= \(\frac{20 + 5\sqrt{3} }{`13} \\\)

As a result, the simplified formulation with a rationalized denominator is as follows:

= \(\frac{20 + 5\sqrt{3} }{`13} \\\)

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Answer:

1a.) atlantic

1b.) california

2a.) Tennesee and north carolina

2b.) new mexico

3a.)  Add three and reflect accross the x axis

4.) texas (austin), quadrant 3

5.) alabama

6a.)  texas

6b.) quadrant 4

7.) penslyvannia

8.) reflect accross x and y axis (or rotate clockwise by 180 degrees) then go 8 right and up 3

9.) missouri

9b.) up 1 and right 3

10.) quadrant 3

bonus.) i colored it gray and it's in wisconsin

Step-by-step explanation:

1a.) to reflect over the y axis you keep the y axis but swap the x to a negative

1b.) to reflect over the x axis you keep the x value the same but y's sign is swapped

2a.) I've already explained how to reflect something over the x axis

2b.) I've already explained how to reflect something over the y axis

3a.) ohio lies around (5,3) and montana is around (-5,6)  so to get their just go up (or north?) three and reflect accross the y axis

4.) louisana is around (2,-3) and to rotate 90 degrees clockwise  would make the coordinates (-3, -2) which puts you around Texas

5.) new york's coordinates are around (8,5) to go left 4 and down three puts you at (4,2) to reflect it over the x axis gives you the coordinates (4,-2) which is in alabama

6a.) south dakota is around (-2,5) and to reflect it over the x axis gives you (-2,-5) which is texas

6b.) To reflect (-2,-5) over the y axis gives you (2,-5) which is gives you the fourth quadrant

7.) Kansas is around (-1,2) and to reflect over the y-axis gives you (1,2) and to go 6 right and 2 up gives you (7,4)

8.) new hampshiere is around (9, 6) and to get to texas which is around (-1,-3) so let's flip accross the x and y axis to get (-9,-6), then go 8 right and up 3

9.) idaho is around (-8,5) and to get 6 right gets you (-2,2) and to reflect over the y axis gives us (2,2) which is missouri and to get to ohio would require us to to get to (5,3) which would require us to go up 1 and right 3

10.) mississippi is around (3,-2) and to rotate 90 degrees clockwise puts us at (-2,-3) or (y,-x) which is quadrant 3

bonus.) north carolina is around (7,1), to reflect over the y axis puts us at (-7,1), to go up 5 and 4 right puts us at (-2,5) and to rotate 180 degrees clockwise gives us (2,-5)

Answer:

hope this helps you out good luck

Answer:

5x+3y-1475=0

Step-by-step explanation:

if this helps please mark brainliest <3

Answer:

Step-by-step explanation:

I'm going to take a leap here and say that the -41^2 should be a -41t^2 and that the expression should look like this:

\(-41t^2-13t+ 9\)

A term is a combination of variables and numbers separated by either a plus or a minus from another combination of variables and numbers. We have 3 terms: -41t^2 is one; -13t is another; 9 is the last. So this is a trinomial.

The degree of a polynomial is equal to the degree of the highest degree'd term. Since the leading term has a power of 2 and that's the highest degree of all the terms, this is a second degree polynomial, or a quadratic, to be more specific.

Answer: 12x^2 + 43x + 35 (if you go to k12)

Step-by-step explanation: took the quiz :) (also, sorry forgot to actually answer..)

After multiplication, we get \(12x^{2} +43x+35\)

We have to multiply,  

               \((3x+7)(4x+5)\)

Now multiplying both term,

                  \(=(3x+7)(4x+5)\\\\=12x^{2} +15x+28x+35\\\\=12x^{2} +43x+35\)

After multiplication, we get \(12x^{2} +43x+35\)

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Answer:

5 is the slope of the line

Answer:

slope = 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 5x + 4 ← is in slope- intercept form

with slope m = 5

The statement that knowing the value of x tells you nothing about the value of y can be explained by several scenarios. One possible scenario is when the values of x and y are not related in any way. In other words, there is no mathematical or logical connection between them.

Another scenario where knowing the value of x tells you nothing about the value of y is when there are multiple possible values of y for a given value of x. This occurs when the relationship between x and y is not one-to-one. For instance, if x represents a person's age and y represents their height, knowing someone's age does not determine their height since there are different heights for different ages.

Furthermore, it is possible that there is a relationship between x and y, but the value of y is affected by other factors besides x. For example, if x represents the amount of time a student spends studying and y represents their grade on a test, knowing the value of x does not completely predict the value of y because other factors like natural ability and test-taking skills may also play a role in determining the grade.

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In the context of analyzing the relationship between studying time and test grades, the domain of the scatterplot would be the number of minutes the students studied (option D).

The domain refers to the set of possible inputs or variables in a given context. In this case, the scatterplot is being created based on the relationship between the time students spent studying and their corresponding test grades. Therefore, the domain in this context would be the number of minutes the students studied (option D).

The domain represents the independent variable, which is the variable that is controlled or manipulated in the analysis. In this scenario, the math teacher wants to analyze the relationship between studying time and test grades, so the number of minutes studied would be the independent variable. The teacher surveys the students to collect data on the time spent studying, and this variable becomes the domain of the scatterplot.

The range, on the other hand, represents the dependent variable, which is the variable that is measured or observed as an outcome or response. In this case, the dependent variable would be the students' test grades. The scatterplot will show how the test grades correspond to the amount of time students studied.

To summarize, in the context of analyzing the relationship between studying time and test grades, the domain of the scatterplot would be the number of minutes the students studied (option D).

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Answer:

X = 12.645 round to 12.7

Step-by-step explanation:

∆LMN ~ ∆OPQ

so the coresponding side ratio are proportional

LM/OP = LN/OQ

LM/OP = LN/OQ49/OP = 31/8 ... the u solve x

X = 12.645 round to 12.7

The function g(t) is calculated to has one relative minimum and two absolute extrema over the domain [-1, 1].

To find the relative and absolute extrema of the function g(t) = \(e^{t}\) - t over the domain [-1, 1], we need to follow these steps:

Find the critical points of g(t) by setting its derivative equal to zero and solving for t.

Test the sign of the second derivative of g(t) at each critical point to determine whether it corresponds to a relative maximum, relative minimum, or an inflection point.

Evaluate g(t) at the endpoints of the domain [-1, 1] to check for absolute extrema.

Step 1: Find the critical points of g(t)

g'(t) = .\(e^{t}\) - 1

Setting g'(t) equal to zero, we get:

\(e^{t}\) - 1 = 0

\(e^{t}\) = 1

Taking the natural logarithm of both sides, we get:

t = ln(1) = 0

So, the only critical point of g(t) in the domain [-1, 1] is t = 0.

Step 2: Test the sign of the second derivative of g(t)

g''(t) = e^t

At t = 0, we have g''(0) = e⁰ = 1.

Since g''(0) is positive, the critical point t = 0 corresponds to a relative minimum.

Step 3: Evaluate g(t) at the endpoints of the domain [-1, 1]

g(-1) = e⁻¹ - (-1) = e⁻¹ + 1 ≈ 1.37

g(1) = e⁻¹ - 1 = e - 1 ≈ 1.72

Since g(t) is a continuous function over the closed interval [-1, 1], it must attain its absolute extrema at the endpoints of the interval. Therefore, the absolute minimum of g(t) over [-1, 1] occurs at t = -1, where g(-1) ≈ 1.37, and the absolute maximum occurs at t = 1, where g(1) ≈ 1.72.

To summarize:

Relative minimum: g(0) ≈ -1

Absolute minimum: g(-1) ≈ 1.37

Absolute maximum: g(1) ≈ 1.72

Therefore, the function g(t) has one relative minimum and two absolute extrema over the domain [-1, 1].

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Answer:

23.4units

Step-by-step explanation:

√(22)²+(8)²

√484+64

√548

23.4