Two adjacent angles (two angles that share
a common side and vertex) form a straight
angle. One of the angles measures 140°.
What is the measure of the other angle?

The evaluated probability for chances of  randomly selecting an employee who will  have a starting salary of at least $31,000 is 11.51%. Here, we have to depend on the principles of standard normal distribution to find the percentage of probability,


Let us take  z-score for a starting salary of $31,000 as

z = (31000 - 25000) / 5000
= 1.2

Now after using a standard normal distribution table , the probability of a z-score of 1.2 or greater is approximately 0.1151
Converting it into percentage
0.1151 x 100
= 11.51%
The evaluated probability for chances of  randomly selecting an employee who will  have a starting salary of at least $31,000 is 11.51%.

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Answer:

15/12

Step-by-step explanation:

\(x = \frac{31}{12} - \frac{8}{6} = \frac{15}{12} \)

and it says don't reduce otherwise u could also say 5/4

Answer:

Hello,

Step-by-step explanation:

\(f(x)=\dfrac{4}{x} \\\\g(x)=\dfrac{4}{x} \\\\\\(gof)(x)=f(g(x))=f(\dfrac{4}{x} )=\dfrac{4}{\dfrac{4}{x} } =\dfrac{4*x}{4} =x\\\\\\(fog)(x)=g(f(x))=g(\dfrac{4}{x} )=\dfrac{4}{\dfrac{4}{x} } =\dfrac{4*x}{4} =x\\\)

Answer:

Step-by-step explanation:

25, i think

Answer: newtons

Step-by-step explanation:

Answer:

I believe it is Newtons :)

Step-by-step explanation:

Answer:

Area of the figure = 171 in²

Step-by-step explanation:

Composite figure given in the picture comprises of three figures, two right triangles and one rectangle.

Area of the composite figure = Area of two right triangles + Area of the rectangle at the center

Area of one right triangle = \(\frac{1}{2}(\text{Base})(\text{Height})\)

                                           = \(\frac{1}{2}(12)(9)\)

                                           = 54 in²

Area of the rectangle = Length × Width

                                    = 7 × 9

                                    = 63 in²

Area of the composite figure = 2(54) + 63

                                                  = 108 + 63

                                                  = 171 in²

Answer:

k

Step-by-step explanation:

To answer this question we will use the following trigonometric identity:

Solving the first equation for cosθ we get:

Solving the second equation for sinθ we get:

Substituting

in the trigonometric identity we get:

Simplifying the above result we get:

Finally, recall that:

Therefore:

Therefore x is on the interval:

Answer:

where x is on the interval

When the foundation of a 1-DOF (Degree of Freedom) mass-spring system with a natural frequency ωn causes displacement as a unit step function, the displacement response of the system can be obtained using the step response formula.

The displacement response of the system, denoted as y(t), can be expressed as:

y(t) = (1 - cos(ωn * t)) / ωn

where t represents time and ωn is the natural frequency of the system.

In this case, the unit step function causes an immediate change in the system's displacement. The displacement response gradually increases over time and approaches a steady-state value. The formula accounts for the dynamic behavior of the mass-spring system, taking into consideration the system's natural frequency.

By substituting the given natural frequency ωn into the step response formula, you can calculate the displacement response of the system at any given time t. This equation provides a mathematical representation of how the system responds to the unit step function applied to its foundation.

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The test statistic is at α = 0.10 we have sufficient evidence that means weight is given by μ = 132 lb.

What is p-value?

The p-value, used in null-hypothesis significance testing, represents the likelihood that the test findings will be at least as extreme as the result actually observed, presuming that the null hypothesis is true.

As given,

State the hypothesis,

Ha: μ = 132

Ha: μ ≠ 132 (two failed test)

Test satisfies:

As σ is unknown we will use t-test satisfies

t = (x - μ)/(s/√n)

Substitute values,

t = (137 - 132)/(14.2/√20)

t = 1.57

t satisfies is 1.57.

Critical values,

P(t < tc) = P(t < tc) = 0.05

using t table at df = 19

tc = ±1.729

So value is tc = (-1.729, 1.729)

P-value:

P(t > ItstatI) = p-value

P(t > I1.57I) = p-value

Using t-table

p-value = 0.1329

given

α = 0.10

So, p-value < α

Do not reject Null hypothesis.

Conclusion:

At α = 0.10 we have sufficient evidence that means weight is given by μ = 132 lb.

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Perceived lack of anonymity is the source of bias that is most relevant to the given situation.

The data collected in the study, which is Mood on a Happy/OK/Sad scale, is qualitative or categorical data.

This describes an observational study.

What is Statistics?

Statistics is a field of study that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of mathematical and statistical methods to extract meaningful insights from data and to draw conclusions or make decisions based on the findings.

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Answer:

2x+y>4 for all set of points which lies above the line 2x+y=4.

x+y<3 for all set of points which lies below the line x+y=3

solution is shaded part.

Step-by-step explanation:

Answer: Where is the figure??

Answer:

I think it this one but picture would help...

Angle DBC and angle BDA form a pair of vertical angles, not a pair of alternate interior angles, which are congruent.  

Using a graph, the points (-2.5, -5) and (0, -1.5) is attached below

1.

To find points on a graph, follow these steps:

Look at the axes of the graph: The horizontal axis is usually labeled as the x-axis, while the vertical axis is labeled as the y-axis. The x-axis represents the independent variable, while the y-axis represents the dependent variable.

2.

Locate the point on the graph: Look for the point you are interested in on the graph. The point is represented by an intersection of a horizontal and vertical line. The horizontal line represents the x-coordinate, and the vertical line represents the y-coordinate.

3.

Read the coordinates: Once you have located the point, read the values of the x-coordinate and y-coordinate at the intersection. The x-coordinate is the value on the x-axis where the vertical line intersects it, and the y-coordinate is the value on the y-axis where the horizontal line intersects it.

4.

Record the point: Write down the coordinates of the point as (x, y), where x is the x-coordinate and y is the y-coordinate.

To plot the points on the graph, we can use a graphing calculator to locate the points and then identify it.

Kindly find the attached graph below.

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An algebraic proof of the triangle inequality is ||u + v|| ≤ ||u|| + ||v||.

Let u and v be vectors in a vector space.

Using the properties of the inner product,

we have\(,|u + v|² = (u + v) · (u + v)= u · u + u · v + v · u + v · v= |u|² + 2u · v + |v|²\)

Now, take the square root of both sides of the above equation to get

|u + v| = sqrt(|u|² + 2u · v + |v|²) ≤ sqrt(|u|² + 2|u||v| + |v|²)= sqrt(|u|²) + sqrt(2|u||v|) + sqrt(|v|²) = |u| + |v|

Therefore, ||u + v|| ≤ ||u|| + ||v||. The equality holds if and only if u and v are linearly dependent.

Hence, the inequality is sometimes called the strict triangle inequality.

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The answer to the equation A=h(B+b) is 4

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation

From the given question

A=h(B+b);

when A=60, B=8, b=7

substituting the values into the equation

60= h(8+7)

60=h(15)

Expanding the bracket

60=15h

dividing both sides by 15

h=60/15

h=4

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The first step in hypothetical-deductive reasoning is to formulate a hypothesis. A hypothesis is an educated guess or prediction based on observations and previous knowledge. It is a statement that can be tested and possibly falsified through further observations and experiments. Once a hypothesis is formulated, the next step is to design an experiment or observation to test it. This involves identifying variables that can be manipulated or measured and determining the methods for manipulating or measuring them. After the experiment or observation is conducted, the data are analyzed and conclusions are drawn based on the results. The conclusions may confirm or reject the hypothesis, leading to further refinement of the hypothesis or the development of a new hypothesis.

The first step in hypothetical-deductive reasoning is the formulation of a hypothesis.

Hypothetical-deductive reasoning starts with the formulation of a hypothesis, which serves as a tentative explanation or prediction for a given phenomenon or problem. In this process, an individual or researcher uses their knowledge, observations, and previous information to generate a possible solution or explanation.

The formulation of a hypothesis involves considering the available evidence, conducting research, and analyzing the existing data. It requires critical thinking and creativity to develop a logical and testable statement that can be further investigated. The hypothesis should be specific, clear, and based on logical reasoning.

Once a hypothesis is formulated, it serves as a starting point for the deductive phase of reasoning. Deductive reasoning involves making specific predictions or deriving logical consequences based on the hypothesis. These predictions can then be tested through empirical research or experiments to evaluate the validity of the hypothesis and gather further evidence.

Overall, the first step in hypothetical-deductive reasoning is the formulation of a hypothesis, providing a framework for subsequent investigation and the generation of testable predictions.

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The 90% confidence interval for the population mean amount spent on lunch by college students is approximately $9.02 to $11.58.

To find the 90% confidence interval for the population mean amount spent on lunch by college students, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard deviation / square root of sample size)

In this case, the sample mean is $10.30, the standard deviation is $2.21, and the sample size is 10.

Step 1: Find the critical value for a 90% confidence level.
Since the sample size is small (n < 30), we need to use a t-distribution instead of a z-distribution. The degrees of freedom for a sample size of 10 is 10 - 1 = 9. By looking up the critical value in the t-distribution table with 9 degrees of freedom and a confidence level of 90%, we find the critical value to be approximately 1.833.

Step 2: Calculate the standard error.
The standard error is the standard deviation divided by the square root of the sample size.
Standard Error = $2.21 / √10 ≈ $0.699

Step 3: Calculate the margin of error.
The margin of error is the critical value multiplied by the standard error.
Margin of Error = 1.833 * $0.699 ≈ $1.28

Step 4: Calculate the confidence interval.
The confidence interval is the sample mean plus or minus the margin of error.
Confidence Interval = $10.30 ± $1.28

Putting it all together, the 90% confidence interval for the population mean amount spent on lunch by college students is approximately $9.02 to $11.58.

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Answer:

B

Step-by-step explanation:

Which word best describe reflection

A.Line of symmetry

B.Mirror-image

C.identical

D.All of the above

A rational expression is an algebraic expression that represents a ratio of two polynomials, where the denominator is not equal to zero.

To simplify the rational expression (\(x^2\) - 2x - 24) / (\(x^2\) + 7x + 12) * (\(x^2\) - 1) / (x - 6), we can follow these steps:

Step 1: Factorize the numerators and denominators.
The numerator (\(x^2\) - 2x - 24) can be factored as (x - 6)(x + 4), and the denominator (\(x^2\) + 7x + 12) can be factored as (x + 4)(x + 3).
The numerator (\(x^2\) - 1) can be factored as (x - 1)(x + 1), and the denominator (x - 6) cannot be factored any further.

Step 2: Cancel out any common factors between the numerators and denominators.
We can cancel out the (x - 6) and (x + 4) terms from both the numerator and the denominator.

Step 3: Simplify the expression.
After canceling out the common factors, we are left with the simplified expression:
(x + 4)(x - 1)(x + 1) / (x + 3)(x - 6)

Step 4: State any restrictions on the variable.
To find any restrictions on the variable, we need to look at the original expression. In this case, we have a denominator of (x - 6), so the variable x cannot be equal to 6.

Therefore, the simplified rational expression is:
(x + 4)(x - 1)(x + 1) / (x + 3)(x - 6), with a restriction on the variable x: x ≠ 6.

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Answer:

1x

Step-by-step explanation:

4x x 6x

It should be noted that z^4 will be -32 in rectangular form.

Based on the information, z = r(cos θ + i sin θ), and provided positive integer n, then it is implied that:

z^n = r^n (cos nθ + i sin nθ)

In this instance, we need to solve for z^4 in rectangular form when z = -2 - 2i. Firstly, we must calculate |z| and arg(z):

|z| = √((-2)^2 + (-2)^2) = 2√2

arg(z) = arctan(-2/-2) = π/4

Leveraging De Moivre's theorem, we can effectively deduce the value of z^4 as:

z^4 = (2√2)^4 (cos (4π/4) + i sin (4π/4))

= 32 (cos π + i sin π)

= -32

Concludedly, z^4  resolved in rectangular form is -32.

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Answer:

Period (B) = 180°

Step-by-step explanation:

Its a Cosine function.

The period it takes to do a complete cycle is 180°

Answer:

D. Hopelly its correct

Answer:

it's 6

Step-by-step explanation: Got it right on edg:D

Answer:

1. The hypothesis of the conditional statement  = If a polygon is a quadrilateral

2. The conclusion of the conditional statement = It is a square

3. The conditional statement is false

The counterexample is a rhombus is a quadrilateral, but it is not a square

4. The inverse of the conditional statement = If a polygon is not a quadrilateral, then it is not a square

5. The converse of the conditional statement is; If a polygon is a square, then it is a quadrilateral

6. The biconditional statement is; A polygon is a quadrilateral if and only if it is a square

Step-by-step explanation:

A conditional statement is of the following form;

                                 \({}\)                            In logical form

If M, then N                   \({}\)                         M → N

1) The hypothesis = M

2) The conclusion = N

3) A counterexample is a statement that is in line with the conditions of the statement but clearly does not lead to the conditions of the statement

4) The inverse of a conditional statement is; if not M then not N which is written mathematically as ~M → ~N

5) The converse of a conditional statement is; if N then N which is written mathematically as  N → M      

6) The biconditional statement is M if and only if N The inverse of a conditional statement is; if not M then not N which is written mathematically as M ↔ N

The solution to the given initial value problem is \(y(t) = 7t^2 + 7\). To solve the initial value problem, we first find the characteristic equation by substituting \(y = e^{(rt)\) into the given differential equation.

This gives us the equation \(r^2 - 7r = 0\). Factoring out r, we get r(r - 7) = 0. Thus, we have two possible values for r: r = 0 and r = 7.

For the case of r = 0, the corresponding solution is \(y_1(t) = c_1,\) where c_1 is a constant.

For the case of r = 7, the corresponding solution is \(y_2(t) = c_2e^{(7t)\), where c_2 is another constant.

To find the particular solution that satisfies the initial conditions, we substitute \(y = y_1(t) + y_2(t)\) into the initial conditions y(0) = 7 and y'(0) = 0. We obtain the following equations:

\(y_1(0) + y_2(0) = 7,\\y_1'(0) + y_2'(0) = 0.\)

Substituting the solutions for y_1(t) and y_2(t), we have:

\(c_1 + c_2 = 7,\\c_2 * 7 = 0.\)

From the second equation, we find \(c_2 = 0\). Substituting this value into the first equation, we get \(c_1 = 7.\)

Therefore, the particular solution satisfying the initial conditions is \(y(t) = 7t^2 + 7.\)

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Answer:

exponential

Step-by-step explanation:

put it on a graphing calculator and you'll see