The area of parallelogram is 36 square meters. If the height is 4 meters, what is the length of the base

The cosine of the angle θ in the circle s -12/13

From the question, we have the following parameters that can be used in our computation:

The unit circle

Where we have

(x, y) = (-12/13, -5/13)

In a unit circle, we have

(cos θ, sin θ) = (x, y)

Using the above as a guide, we have the following:

cos θ = -12/13

Hence, the cosine of the angle θ is -12/13

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so we have a point at -2-i or -2 - 1i, that means that both "x" and "y" are negative, the only occurs in the III Quadrant, so hmmm let's find the modulus and angle θ

[tex]\stackrel{a}{-2}\stackrel{b}{-1i}\hspace{5em} \begin{cases} r=\sqrt{(-2)^2 + (-1)^2}\\ \qquad \sqrt{5}\\ \theta =tan^{-1}\left( \frac{-1}{-2} \right)\\[1em] \qquad \approx 206.57^o \end{cases} \\\\\\ \stackrel{\textit{let's keep in mind that}}{\sqrt[3]{\sqrt{5}}\implies \left( 5^{\frac{1}{2}} \right)^{\frac{1}{3}}}\implies 5^{\frac{1}{6}}\implies \sqrt[6]{5} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\sqrt[n]{z}=\sqrt[n]{r}\left[ \cos\left( \cfrac{\theta+2\pi k}{n} \right) +i\sin\left( \cfrac{\theta+2\pi k}{n} \right)\right]\quad \begin{array}{llll} k\ roots\\ 0,1,2,3,... \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\boxed{k=0}\hspace{5em} \sqrt[ 3 ]{\sqrt{5}} \left[ \cos\left( \cfrac{ 206.57^o + 360^o( 0 )}{3} \right) +i \sin\left( \cfrac{ 206.57^o + 360^o( 0 )}{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 206.57^o }{3} \right) +i \sin\left( \cfrac{ 206.57^o }{3} \right)\right] \\\\\\ \sqrt[6]{5}\left[ \cos(68.86^o) +i \sin(68.86^o)\right] ~~ \approx ~~ 0.47~~ + ~~1.22i \\\\[-0.35em] ~\dotfill[/tex]

[tex]\boxed{k=1}\hspace{5em} \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 206.57^o + 360^o( 1 )}{3} \right) +i \sin\left( \cfrac{ 206.57^o + 360^o( 1 )}{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 566.57^o }{3} \right) +i \sin\left( \cfrac{ 566.57^o }{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos(188.86^o) +i \sin(188.86^o)\right] ~~ \approx ~~ -1.29~~ - ~~0.20i \\\\[-0.35em] ~\dotfill[/tex]

[tex]\boxed{k=2}\hspace{5em} \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 206.57^o + 360^o( 2 )}{3} \right) +i \sin\left( \cfrac{ 206.57^o + 360^o( 2 )}{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 926.57^o }{3} \right) +i \sin\left( \cfrac{ 926.57^o }{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos(308.86^o) +i \sin(308.86^o)\right] ~~ \approx ~~ 0.82~~ - ~~1.02i[/tex]

just a quick clarification, notice that if we get the inverse tangent of (-1 / -2) the angle we get will be in the range of ±π/2, that's because that is the range inverse tangent is restricted to, however, our terminal point on the complex plane is on the III Quadrant, not the 1st one, so we use the reference angle on the III Quadrant, and that is about 206.57°.

Step-by-step explanation:

To determine whether a triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let's denote the three sides of the given triangle as a = 23, b = 30, and c = 19. We can check if these side lengths satisfy the Pythagorean theorem as follows:

c^2 = a^2 + b^2

19^2 = 23^2 + 30^2

361 = 529 + 900

Since 361 is not equal to 529 + 900, we can see that the given triangle is not a right triangle.

Answer:

Step-by-step explanation:

The Axiom of Pairing in mathematics states that for any two sets, there exists a set that contains exactly those two sets as its only elements. In other words, given sets A and B, there exists a set {A, B} whose only elements are A and B.

For example, consider the sets A = {1, 2} and B = {3, 4}. According to the Axiom of Pairing, there exists a set that contains exactly these two sets as its only elements. We can form such a set as {A, B} = {{1, 2}, {3, 4}}, where A and B are the elements of the set. Thus, {A, B} is a set that satisfies the Axiom of Pairing.

The standard deviation is around 1.06, and there are on average 2 frogs having the feature.

Given that the trait is usually found in 1 out of every 8 frogs, the probability of a frog having the trait is p = 1/8. Therefore, the probability of a frog not having the trait is q = 1 - p = 7/8.

(a) To find the probability of not finding any frogs with the trait, we calculate the probability of a frog not having the trait and raise it to the power of the number of trials:

P(X = 0) = (7/8)¹⁶ ≈ 0.0747

(b) To find the probability of finding at least 1 frog with the trait, we subtract the probability of finding none from 1:

P(X ≥ 1) = 1 - P(X = 0) ≈ 1 - 0.0747 ≈ 0.9253

(c) The mean (μ) and standard deviation (σ) of the number of frogs with the trait can be calculated using the formulas:

μ = np

σ = √(npq)

For this case, n = 16, p = 1/8, and q = 7/8:

μ = 16 * (1/8) = 2

σ = √(16 * (1/8) * (7/8)) ≈ 1.06

Therefore, the mean number of frogs with the trait is 2, and the standard deviation is approximately 1.06.

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The acceleration of the runner is 0.2 m/s².

We can use the following equation to get the runner's acceleration:

Acceleration (a) = (Final Velocity - Initial Velocity) / Time

In this case, the initial velocity (u) is 0 m/s, the final velocity (v) can be calculated using the formula:

v = s / t

where t is the amount of time spent and s is the distance travelled.

The time taken (t) and the distance travelled (s) are both provided as 500 m.

Calculate the b (v):

v = 500 m / 50 s

v = 10 m/s

Plug into the formula for acceleration:

a = (10 m/s - 0 m/s) / 50 s

a = 10 m/s / 50 s

a = 0.2 m/s²

Therefore, the acceleration of the runner is 0.2 m/s².

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The proposition X^2 > 0 for every real number x is true.

We are given that;

The equation x^2 > 0

Now,

The square of any real number is always greater than or equal to zero.

An example of a mathematical proposition is “For all real numbers x, x + 1 = 2.” This is a proposition because it makes a claim about all real numbers x.

Therefore, by the given function X^2 > 0 the answer will be true.

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Answer:

The given function f(x) = alxl is not a valid absolute value function because the absolute value symbol is represented by two vertical bars (|) and not the letter "l". Additionally, the point (3,-4) cannot be on the graph of an absolute value function because the output of an absolute value function is always non-negative.

MARK AS BRAINLIEST!!!

Answer:

Step-by-step explanation:

You want to identify the graphs that go with each of these functions, along with a particular point on the curve.

The equations are written here in standard form, factored form, and vertex form. (The "factored form" is sometimes called "intercept form.") Each of these forms can be analyzed for characteristics relevant to identifying the corresponding graph.

In general, we can readily identify the opening direction, based on the sign of the leading coefficient. Depending on the form, we can also identify zeros, the vertex, and the y-intercept.

The line of symmetry (x-coordinate of the vertex) of the equation in the form ax² +bx +c is x = -b/(2a). That is, it will be left of the y-axis when the coefficients 'a' and 'b' have the same sign.

The graph of equation A will be graph 4, the only one with its vertex left of the y-axis. The y-intercept is the constant: point S = (0, 9).

Equation B has a positive leading coefficient, so opens upward. The zeros of the factors are -3 and +9, so identify the places where the graph crosses the x-axis. Graph 3 is the only one that opens upward and has x-intercepts. Point R is (9, 0).

The vertex form of a quadratic is ...

  y = a(x -h)² +k . . . . . . . vertex (h, k); leading coefficient 'a'

Equation C has its vertex at (h, k) = (3, 9) and opens upward (a>0). Graph 1 is the only one matching those characteristics. Point P is the vertex, so point P is (3, 9).

Equation D is the same as equation B, but with a negative leading coefficient. That is, it opens downward and crosses the x-axis in two places, at x = -3 and x = 9. Graph 2 is matches this description. The left zero is point Q, (-3, 0).

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The ordered pairs on the graph with the given equation will be of the form (x, 2).

Given a linear equation,

-4y = -8

We have to find the ordered pairs on the given graph.

Dividing both sides of the equation by -4,

y = 2

So for any point on the line, the y coordinate will be 2.

So any general point on the graph will be of the form, (x, 2).

Graph is a line parallel to the X axis.

Hence the orderd pairs are of the form (x, 2).

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The cardinal number for the given set. A {20, 22, 24, 26, 34} sees; The given set has a cardinal number of 5.

This is further explained below.

Generally, cardinal numbers are an extension of the natural numbers that are used to assess the cardinality of sets. Cardinals are often referred to by their shorter form, cardinals. A finite set has a cardinality that is equal to a natural number, which is the number of items that are included inside the set.

A set of counting numbers is called its cardinal number. There is speculation that they are cardinals as well. Cardinal numbers are whole, non-fractional numerals, beginning with 1 and continuing in numerical order. Cardinal numbers include 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20.

To conclude it, The provided set A equals {20, 22, 24, 26, 34}

The number of unique components that make up a set is referred to as the cardinal number.

The given set has a cardinal number of 5, which is denoted by the notation n(A).

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Answer: The cardinal number for the given set is 5

Step-by-step explanation:

The cardinal number for a set is the quantity, or how many numbers are in the set. Since Set A has these numbers {20, 22, 24, 26, 34}, you can easily indicate how many numbers are in there. The n(a) quantity in the set would be the number five.

Since there is five numbers in this set, therefore, the cardinal number for the given set would be simply 5.

Answer:

My friend you have to send a picture, we can't see through the screen

Answer:

I hope this helps.

Step-by-step explanation:

In an isosceles trapezoid, the two non-parallel sides (legs) are congruent, and the base angles opposite each other are also congruent. Let's denote the measures of the angles as follows:

Angle A: The top left angle.

Angle B: The top right angle.

Angle C: The bottom left angle.

Angle D: The bottom right angle.

In an isosceles trapezoid, angles A and B are congruent, and angles C and D are congruent. The sum of the interior angles of any quadrilateral is 360 degrees. Therefore, we can set up the following equation:

Angle A + Angle B + Angle C + Angle D = 360 degrees

Since angles A and B are congruent, and angles C and D are congruent, we can rewrite the equation as:

2(A) + 2(C) = 360 degrees

Simplifying further:

2A + 2C = 360 degrees

Dividing both sides of the equation by 2:

A + C = 180 degrees

In an isosceles trapezoid, the base angles (C and D) are supplementary angles, meaning they add up to 180 degrees. Therefore, the measure of each base angle (C and D) is 180 degrees divided by 2:

Each base angle (C and D) = 90 degrees.

Since the sum of the interior angles in a quadrilateral is 360 degrees, and angles C and D (the base angles) each have a measure of 90 degrees, the sum of angles A and B (the top angles) must be:

Angle A + Angle B = 360 degrees - (Angle C + Angle D)

Angle A + Angle B = 360 degrees - (90 degrees + 90 degrees)

Angle A + Angle B = 360 degrees - 180 degrees

Angle A + Angle B = 180 degrees

Therefore, in an isosceles trapezoid, each top angle (A and B) has a measure of 180 degrees divided by 2:

Each top angle (A and B) = 90 degrees.

To summarize:

Each top angle (Angle A and Angle B) measures 90 degrees.

Each base angle (Angle C and Angle D) measures 90 degrees.

Answer:

Shorter leg is 6

Step-by-step explanation:

In a 30°-60°-90° triangle, the hypotenuse is twice the length of the shorter leg. Therefore, if the hypotenuse is 12, then the shorter leg is 6.

Answer:

28.2 cm

Step-by-step explanation:

Circumference of circle = 2π r

Value of π = 3.14

Putting the required values,

Circumference = 2 × 3.14 × 4.5

= 6.28 × 4.5

= 28.2

Hence the circumference of the circle is 28.2 cm

The meaning of the number 30,500 is given as follows:

The maximum altitude of the airplane.

The coordinates of the vertex are (h,k), meaning that:

Considering a leading coefficient a, the quadratic function is given as follows:

y = a(x - h)² + k.

In which a is the leading coefficient.

The function for this problem is given as follows:

y = -16(t - 12)² + 30500.

The coordinates of the vertex are given as follows:

(12, 30500).

The leading coefficient is negative, hence the meaning of the vertex is given as follows:

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hello

the answer to the question is:

length A = 5 ft

length B = 4 ft

total volume = (8 × 3 × 2) + (4 × 5 × 2) = 88 ft³

There is no stationary point at x = 2. The nature of the curve at x = 2 cannot be determined since there is no stationary point.

To verify that the curve has a stationary point at x = 2, we need to find the derivative of the equation and set it equal to zero.

Given the equation:

y = 2x + 1/(x-1)²

Let's find the derivative dy/dx:

dy/dx = d/dx [2x + 1/(x-1)²]

To find the derivative, we can use the power rule and the chain rule. Let's differentiate each term separately:

For the first term, 2x, the derivative is 2.

For the second term, 1/(x-1)², we can rewrite it as (x-1)^(-2) to apply the power rule. The derivative is then:

d/dx [(x-1)^(-2)] = -2(x-1)^(-3) * d/dx (x-1)

Using the chain rule, d/dx (x-1) = 1, so the derivative becomes:

-2(x-1)^(-3) * 1 = -2/(x-1)^3

Now, let's set dy/dx equal to zero and solve for x:

-2/(x-1)^3 = 0

This equation is satisfied when the numerator is equal to zero:

-2 = 0

However, -2 is not equal to zero, which means there is no x value that makes dy/dx equal to zero.

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To find out what percentage 25 is of 500, you can use the following formula:

percentage = (part / whole) x 100

In this case, 25 is the part and 500 is the whole. So, we can substitute these values into the formula:

percentage = (25 / 500) x 100

Simplifying the equation:

percentage = 0.05 x 100

percentage = 5%

Therefore, 25 is 5% of 500.

I hope it helps!

Answer:

5 % of 500 is 25

Step-by-step explanation:

500 * x% = 25

Divide each side by 500

x% = 25/500

x% = .05

Change to percent

x = 5

5 % of 500 is 25

140

Step-by-step explanation:

Area of parallelogram=bxh

=14x10

=140

Answer:

140 square units

Step-by-step explanation:

The area of a parallelogram can be found by multiplying the length of its base by its height.

[tex]\boxed{\sf Area = base \times height}[/tex]

From inspection of the given parallelogram, its height is 10 units.

Since the lengths of opposite sides in a parallelogram are equal, the base of the given parallelogram is 14 units.

Therefore, the area of the parallelogram is:

[tex]\begin{aligned}\sf Area&=14 \times 10\\&=140\; \sf square\;units\end{aligned}[/tex]

A Normal distribution has skewness and kurtosis values close to zero.

There are several methods that can be used to assess whether a variable follows a normal distribution.

1. Histogram: Creating a histogram of the variable's data can provide a visual representation of its distribution. If the histogram displays a bell-shaped curve with a symmetric pattern, it suggests the variable may follow a normal distribution. However, this method is subjective and depends on the chosen bin width.

2. Normal probability plot: Also known as a Q-Q plot (quantile-quantile plot), this graphical tool compares the quantiles of the variable's data against the expected quantiles of a normal distribution. If the points on the plot roughly fall along a straight line, it suggests that the variable approximates a normal distribution.

3. Shapiro-Wilk test: The Shapiro-Wilk test is a statistical test that assesses the normality of a variable. It produces a test statistic and a p-value. If the p-value is greater than the chosen significance level (e.g., 0.05), it indicates that there is not enough evidence to reject the null hypothesis of normality.

4. Kolmogorov-Smirnov test: The Kolmogorov-Smirnov test compares the cumulative distribution function (CDF) of the variable's data with the expected CDF of a normal distribution. The test produces a test statistic and a p-value. Similarly, if the p-value is above the chosen significance level, it suggests the variable follows a normal distribution.

5. Skewness and kurtosis: Skewness measures the symmetry of a distribution, while kurtosis quantifies the shape of the distribution's tails. A normal distribution has skewness and kurtosis values close to zero. Assessing these measures can provide insights into the departure from normality.

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It will cost approximately $16 per person if 95 people rent the bus.

The price per person of renting a bus varies inversely with the number of people renting the bus. This means that as the number of people increases, the price per person decreases, and vice versa.

Given that it costs $20 per person when 76 people rent the bus, we can use this information to find the constant of variation (k) in the inverse variation equation. Let's denote the number of people as "n" and the cost per person as "c":

c = k/n

We can substitute the values into the equation to solve for k:

20 = k/76

Multiplying both sides by 76 gives:

k = 20 × 76 = 1520

Now, we can determine the cost per person when 95 people rent the bus by plugging the values into the equation:

c = 1520/95 ≈ 16.00

Therefore, it will cost approximately $16 per person if 95 people rent the bus.

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Answer:

  x = 1, 12

Step-by-step explanation:

You want the solutions to y = x² -13x +12 when y = 0, using the quadratic formula.

The quadratic formula gives the solutions to ...

  ax² +bx +c = 0

as ...

  [tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Your equation has a = 1, b = -13, c = 12, so the solutions are ...

  [tex]x = \dfrac{-(-13)\pm\sqrt{(-13)^2-4(1)(12)}}{2(1)}=\dfrac{13\pm\sqrt{169-48}}{2}\\\\\\x=\dfrac{13\pm11}{2}\\\\\boxed{x=\{12,1\}}[/tex]

This answer is correct because we used and evaluated the formula correctly. There are several ways to check the answer is correct.

A graph of the equation is attached. It shows the x-intercepts (zeros) to be x = 1 and x = 12.

When the equation is factored, it looks like ...

  y = (x -12)(x -1)

The zeros are the values of x that make the factors zero: 12 and 1.

The equation can be rewritten to simplify evaluating it:

  y = (x -13)x +12

For x = 1, y = (1 -13)(1) +12 = -12 +12 = 0.

For x = 12, y = (12 -13)(12) +12 = -12 +12 = 0.

The values x = 1 and x = 12 are zeros of the function.

<95141404393>

Answer:

36 hours

Step-by-step explanation:

1 person will be larger than 12 hours certainly

therefore 12*3 = 36

Answer:

36 hours

Step-by-step explanation:

P. : h

3. : 12

1. : ?

3÷1=3

12×3=36 times by 3 because if there are less people painting the room it's going to take more time

so it's takes 1 person 36 hours to paint the room

2x² - 6x = -7 equation has  imaginary solutions

To determine if an equation has imaginary solutions, we can examine the discriminant of the quadratic equation

x² + 3x - 5 = 0

a = 1, b = 3, c = -5

Discriminant = (3)² - 4(1)(-5) = 9 + 20 = 29

The equation has two real solutions

x⁴ - 5x ^ 2 + 3 = 0

This equation is a quartic equation, not a quadratic equation. Quartic equations can have both real and imaginary solutions

2x² - 6x = -7

2x^2 - 6x + 7 = 0

a = 2, b = -6, c = 7

Discriminant = (-6)²- 4(2)(7) = 36 - 56 = -20

Since the discriminant (-20) is negative, the equation has two complex (imaginary) solutions.

-3x² = -5

Dividing both sides by -3, we get:

x²= 5

a = 1, b = 0, c = -5

Discriminant = 0² - 4(1)(-5) = 20

The equation has two real solutions.

Hence, 2x² - 6x = -7 equation has imaginary solutions

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Hello !

2(5 - 2 * 3 - 4)​

= 2(5 - 6 - 4)

= 2 * (-5)

= -10

Answer:

average=9 hours

Step-by-step explanation:

10hours on Friday

12 hours on Saturday

300 mins to hours= 300÷60=5

5 hours on Sunday

average=10+12+5

average=27

average=27÷3

average=9 hours

Answer:

Step-by-step explanation:

sin 325=sin (360-35)=-sin 35=-t

cos 325=cos (360-35)=cos  35=√(1-sin²35)=√(1-t²)

tan 215=tan (180+35)=tan 35

[tex]=\frac{sin~35}{cos~35} \\=\frac{-t}{\sqrt{1-t^2} }[/tex]

Step-by-step explanation:

14 out of 20 were full in the experiment   14/20 = 7/10 chance that the next one will be full too.