how many arrangements can be made using 4 letters of the word hyperbolas if no letter is to be used more than once?

To construct a 3x3 nonzero matrix A such that the vector [2 4 1 2 1 3 5] is a solution of the equation Ax = 0, we can choose the matrix A = [1 -1 2; -2 1 -3; 0 0 0].

Let's consider the equation Ax = d, where A is a 3x3 matrix, x is the vector [2 4 1], and d is the zero vector [0 0 0]. We want to find a matrix A that satisfies this equation.

We can write the equation as a system of linear equations:

2a + 4b + c = 0

2d + 1e + 3f = 0

5g = 0

To satisfy the equation, we need to choose values for the variables a, b, c, d, e, f, and g that make all the equations true.

For example, we can choose:

a = 1, b = -1, c = 2, d = -2, e = 1, f = -3, g = 0

Substituting these values into the equations, we get:

2(1) + 4(-1) + 2 = 0

2(-2) + 1(1) + 3(-3) = 0

5(0) = 0

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Yes, there is a significant difference between the academic performance of male and female in Statistics. The p-value of the t-test is 0.027, which is less than the significance level of 0.05.

The researchers conducted a t-test for two independent samples to compare the academic performance of male and female students in Statistics. The t-test statistic was 2.26, and the p-value was 0.027. The p-value is the probability of obtaining a t-test statistic at least as extreme as the one observed, assuming that the null hypothesis is true. Since the p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is a difference in the mean academic performance of male and female students in Statistics.

The t-test results suggest that female students performed significantly better than male students in Statistics. The mean academic performance of female students was 93.6, while the mean academic performance of male students was 89.5. The difference in mean academic performance between male and female students was 4.1. The standard deviation of academic performance for male students was 30.2, and the standard deviation of academic performance for female students was 45. The sample sizes for male and female students were 6 and 10, respectively.

The results of this study suggest that female students may be more likely to succeed in Statistics than male students. However, it is important to note that this study was conducted on a small sample of students, and more research is needed to confirm these findings.

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Answer:

Firs property used : Quotient Property

           \(log_b(\frac{X}{Y} ) = log_bX -log_bY\)

   \(log_b(\frac{\sqrt[3]{x} }{36y^2} ) = log_b(\sqrt[3]{x}) - log_b(36y^2)\)

Second property used : Product Property

          \(log_b(XY) = log_bX + log_b Y\)

    \(log_b(\sqrt[3]{x}) - log_b(36y^2) = (log_b(\sqrt[3]{x}) - [log_b36 + log_by^2)\)

Third property used : Power Property

                 \(log_b \sqrt[n]{X} = log_b(X)^{\frac{1}{n}} = \frac{1}{n} log_b X\)

 \((log_b(\sqrt[3]{x}) - [log_b6^2 + log_by^2) = \frac{1}{3} log_bx - 2log_b 6 - 2log_by\)

Fully expanded form:

                   \(log_b(\frac{\sqrt[3]{x} }{36y^2} ) = \frac{1}{3} log_b x-2log_b6-2log_by\)

The matching of the tangent and sine angles to their expressions will be:

sin(-π/12) = (✓2 - ✓6)/4

tan(π/12) = 2 - ✓3

tan(5π/12) = 2 + ✓3

1. Sin(-π/12) = sin(-15°)

sin(-15°)  = sin(30° + (- 45°)) = sin(30°)cos(-45°) + cos(30°)sin(-45°)

sin(30°)cos(-45°) + cos(30°)sin(-45°) = 1/2 × (√2)/2 + (√3)/2 × (-√2)/2

1/2 × √2/2 + √3/2 × -√2/2 = (√2)/4 - (√6)/4 = ((√2) - (√6))/4

sin(-15°)  = ((√2) - (√6))/4

= sin(-π/12) = (✓2 - ✓6)/4

2. Tan(π/12) = tan(15°)

tan(15°)  = tan(45° + (-30°)) = (tan(-30°) + tan(45°))/(1 - tan(-30°)×tan(45°))

(tan(-30°) + tan(45°))/(1 - tan(-30°)×tan(45°)) = ((-1/√3) + 1)/(1 - (-1/√3))

((-1/√3) + 1)/(1 - (-1/√3)) = (3 - √3)/(3 + √3) = (3 - √3)·(3 -√3)/((3 - √3)·(3 + √3))

(3 - √3)·(3 -√3/((3 - √3)·(3 + √3)) = (9 - 6·√3 + 3)/(9 - 3) = (12 - 6·√3)/6

(2 - √3)

tan(π/12) = 2 - ✓3

3. Tan(5π / 13) = tan(75°)

tan(75°)  = tan(30° + 45°) = (tan(30°) + tan(45°))/(1 - tan(30°)×tan(45°))

(tan(30°) + tan(45°))/(1 - tan(30°)×tan(45°)) = ((1/√3) + 1)/(1 - 1/√3)

((1/√3) + 1)/(1 - 1/√3) = (3 + √3)/(3 - √3) = (3 + √3)·(3 +√3/((3 - √3)·(3 + √3))

(3 + √3)·(3 +√3/((3 - √3)·(3 + √3)) = (9 + 6·√3 + 3)/(9 - 3) = (12 + 6·√3)/6

(12 + 6·√3)/6 = 2 + √3

= tan(5π/12) = 2 + ✓3

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Answer:

Step-by-step explanation:

3x + 4x + x = 16

7x + x = 16

8x = 16

x = 16 : 8

x = 2

----------------------

3 × 2 + 4 × 2 + 2 = 16  (remember PEMDAS)

6 + 8 + 2 = 16

16 = 16

same value the answer is good

The parallelogram's area is 130 yards square.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Tw dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question-

base*height

base=13

height=10

13*10

= 130 yds

Hence, The parallelogram's area is 130 yards square.

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Example of effective, reaching a goal or being successful in achieving an objective.

According to the dictionary, effectiveness is the ability to produce or develop something established. For example, reaching a goal or being successful in achieving an objective.

Effectiveness is defined as "achieving a desired effect." "Capable of generating desired outcomes without wasting resources, time, or energy" is the definition of efficiency. The distinction is that when something is effective, it yields a result even though it consumes some more resources in the process.

Finding a means to enhance results, possibly by acting significantly differently, is what effectiveness is all about. Your whole working method could alter. For instance, project teams may decide to do away with project status meetings if they update task status as they go.

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Answer: 5/19

Step-by-step explanation:

9 orange + 10 purple = 19 total

First draw - get orange:

9/19

Second draw - get purple - without replacing:

10/18

Math:

9/19*10/18 = 5/19 (I hope it’s okay for it to be a fraction)

Answer:

D : 66

Step-by-step explanation:

separate the composite figure into 3 different shapes then multiple then find the area of them all. after this just add them and you're good to go

also to get the area of a triangle you gotta add both sides then divide by 2.

Answer:

0.21

Step-by-step explanation:

The answer above is correct.

The critical probability, assuming a confidence level of 58%, is 0.79.

Confidence interval in statistics is defined as the certain range of values that you estimate for the unknown parameter lies within.

This means that, if you do your experiment more than once and do resampling, then this is the percentage that the parameters falls within a range.

The formula to find the critical probability of a statistic is given by,

Critical probability = 1 - α/2

Here α = 1 - (confidence level / 100)

Given that,

Confidence level = 58%

α = 1 - 58/100 = 0.42

Critical probability = 1 - (0.42 / 2)

                              = 0.79

Hence the critical probability is 0.79.

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Answer:

x≤30

Step-by-step explanation:

he can spend no more than $30 a week

Answer:

5.4

Step-by-step explanation:

6÷4.5=1.33333333333

7.2÷1.33333333333=5.40000000001

Answer:

its b

Step-by-step explanation:

Answer:

{x = 3, x = 4/5 + i(3/5), x = 4/5 - i(3/5)}

So B

The statement ''the formula for finding the surface area of a cylinder is sa = πr2 πrh.'' is false because the formula for finding the surface area of a cylinder is given by: SA = 2πrh + 2πr^2 , where SA represents the surface area, r is the radius of the base, and h is the height of the cylinder.

The first term, 2πrh, represents the area of the curved surface of the cylinder (the lateral surface area), which is a rectangle that wraps around the cylinder. It is calculated by multiplying the height of the cylinder by the circumference of the base.

The second term, 2πr^2, represents the areas of the two circular bases of the cylinder.

By adding these two terms together, we obtain the total surface area of the cylinder.

Therefore, the correct formula for finding the surface area of a cylinder is SA = 2πrh + 2πr^2.

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Answer:

amogus

Step-by-step explanation:

Answer:

∠3 and ∠10 are;

B. Alternate exterior angles

Step-by-step explanation:

From the given diagram, we have;

∠3 and ∠10 are angles on the same transversal

The location of ∠3 and ∠10 are on the outer (exterior) part of the two lines crossed by the transversal that forms ∠3 and ∠10 such that the two lines comes between the angles

∠3 and ∠10 are on the alternate sides of the transversal such that ∠3 is below the transversal and ∠10 is above the transversal

Therefore, ∠3 and ∠10 are alternate exterior angles.

Answer:

length =105 width =10

Step-by-step explanation:

L=10*W+5

P=230

P=2(L+W)

230=2(10W+5+W)

SOLVE FOR W

W=10

L=10*W+5

=10*10+5

L=105

Answer:

5 (x - 3 3/4) = 7 1/2

5·(x - (3 + 3/4)) = (7 + 1/2)

20x = 105

x = 105/20 = 5.25

x = 21/4= 5.25

:

Answer:

2,4,8,16

Step-by-step explanation:

2,4,8,16

difference is multiplied by 2

In Chloe's risk information forms, the key item she should document is the probability and impact of each identified risk.

To effectively monitor risks and obtain early warnings, Chloe should document the probability and impact of each identified risk in her risk information forms. Let's break down why this information is critical in risk management.

The impact of a risk represents the potential consequences or severity of its occurrence. By documenting the impact, Chloe can understand the potential damage or disruption a risk could cause. This allows her to prioritize risks based on their potential impact on the project or objective. By assigning an impact rating or value to each risk, Chloe can identify high-impact risks that require careful consideration and robust mitigation strategies.

Once Chloe has established the probability and impact for each risk, she can set thresholds or triggers for early warning signs. These thresholds act as indicators that a risk is approaching or crossing a critical level.

Chloe can track these thresholds regularly and set up a monitoring system that alerts her when a risk reaches or surpasses the specified levels. This allows her to take timely action and implement mitigation strategies before the risk escalates and negatively impacts the project.

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By analyzing the question, The side adjacent to angle L is D)JR.

In a triangle, adjacent sides are sides that share a common vertex (or corner) and are next to each other.

An angle is the amount of rotation between two lines or planes that share a common point. It is typically measured in degrees or radians.

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On solving the provided question we can say that - the value of the equation x = y^2 -5 from the graph will be 59.

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

here, the equation from the graphs is

\(y^2 = x^8 -7.8x-9,=.43y\)

and y = 8

x = 59

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Answer:

159.38

Step-by-step explanation:

28625x-738483=3823976

or,28625x=3823976+738483

or,x=4562459/28625

or,x=159.387214

Answer:

x = 3823976 + 619259t

              28625

Step-by-step explanation:

28625x - 73t * 8483 = 3823976

25625x - 619259t = 3823976

28625x = 3823976 + 619259t

x = 3823976 + 619259t

              28625

Answer:

232

Step-by-step explanation:

please mark as brainliest! i need only one more.

A=2(wl+hl+hw) is the formula

The complex-expression "(-1/2)i³(√(-9) - 4) - 3i²" in simplest-form of "a + bi" can be written as  (3/2) - 2i.

In order to express the expression "(-1/2)i³(√(-9) - 4) - 3i²" in simplest form , we first simplify the exponents:

i³ = i² × i = (-1) × i = -i

i² = -1

Substituting these values in the expression,

We get,

= (-1/2)(-i)(√(-9) - 4) - 3(-1)

= (1/2)i(3i - 4) + 3      ...because √(-9) = 3i,

= (1/2)(3i² - 4i) + 3

= (1/2)(-3 - 4i) + 3

= (-3/2) - 2i + 3

= (3/2) - 2i

Therefore, the expression in the simplest "a + bi" form is (3/2) - 2i.

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The given question is incomplete, the complete question is

Write "(-1/2)i³(√(-9) - 4) - 3i²" in simplest "a + bi" form.

Answer:

62.5 miles per hour

Step-by-step explanation:

\(\frac{miles}{hour} =\frac{562.5(miles)}{9(hours)} \\=62.5mph\)

Answer:

is it 23.80???????? i think.

On a coordinate plane, a curve crosses the y-axis at (0, 1). It has a minimum of negative 1 and a maximum of 1. It goes through 2 cycles at 2 pi.

Here we have the function:

y = cos(2*(x + pi))

First, let's distribute the product in the argument of the cosine:

y = cos(2x + 2pi).

Now, notice that 2pi is the period of a cosine function, then:

cos(2x)  = cos(2x + 2pi)

Then we can write:

y = cos(2x)

Now, the y-intercept is:

y = cos(2*0) = 1

And because the factor of 2 inside the argument, it goes through 2 cycle at 2pi (instead of 1 cycle, like a normal cosine).

Then the correct option is:

"On a coordinate plane, a curve crosses the y-axis at (0, 1). It has a minimum of negative 1 and a maximum of 1. It goes through 2 cycles at 2 pi."

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Answer:

D

Step-by-step explanation:

Because i said so.