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What are the midline, amplitude, period, and graph of the function f(x)=cos(x) ?

To perform a two-tailed hypothesis test with a sample size of 18 and a significance level of α = 0.10, the critical t-values are approximately ±2.110.

To find the critical values for a two-tailed hypothesis test with a sample size of 18 and a significance level of α = 0.10, you need to follow these steps:

1. Determine the degrees of freedom (df) for the t-distribution. In this case, df = n - 1 = 18 - 1 = 17.

2. Divide the significance level by 2 to account for the two tails. α/2 = 0.10/2 = 0.05.

3. Look up the critical t-value in the t-distribution table for a two-tailed test with a significance level of 0.05 and 17 degrees of freedom. The critical t-value is approximately ±2.110.

Therefore, the critical t-values for the two-tailed hypothesis test with a sample size of 18 and α = 0.10 are approximately ±2.110.

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Answer:

6(x+2)=66

6x+12=66 -12

6x= 54 :6

x=9

Step-by-step explanation:

prove me wrong

Explanation:

These two angles are a linear pair. They are supplementary (ie they add to 180) and they are adjacent. We know they are supplementary because line WXZ is a straight line. Put another way: point X is on line WZ.

-------

Side notes:

The correct statement is,

⇒ m ∠WXY + m ∠YXZ = 180°

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

To find the correct statement.

Now, We can find the correct statement as;

By definition of linear pair we get;

⇒ m ∠WXY + m ∠YXZ = 180°

Thus, The correct statement is,

⇒ m ∠WXY + m ∠YXZ = 180°

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The expression 6(5x8)+6(5-9)+87 is used by 6th graders as practice for order of operations. The answer to the expression is determined by following the order of operations, which involves evaluating parentheses, performing multiplication and division from left to right, and finally performing addition and subtraction from left to right.

To solve the expression 6(5x8)+6(5-9)+87, we need to follow the order of operations.

First, we evaluate the parentheses:

5x8 = 40

5-9 = -4

Next, we perform multiplication and division from left to right:

6(40) = 240

6(-4) = -24

Finally, we perform addition and subtraction from left to right:

240 + (-24) = 216

So, the answer to the expression is 216.

By practicing problems like these, 6th graders reinforce their understanding of the order of operations and learn how to correctly evaluate expressions involving multiple operations.

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The acceptance angle of a right-angle prism made from glass (n=1.5) is approximately 41.8 degrees. The acceptance angle of a corner reflector made from glass (n=1.5) is approximately 90 degrees.

(a) For a right-angle prism, the acceptance angle (2θ_out) is the angle at which the incident light ray inside the prism reaches the critical angle and undergoes total internal reflection. The critical angle can be determined using Snell's law, which states that sin(θ_c) = 1/n, where n is the refractive index of the medium (in this case, n=1.5 for glass). Solving for θ_c, we find θ_c = sin^(-1)(1/n). Since the incident angle inside the prism is equal to the critical angle, the acceptance angle is 2θ_c. Substituting n=1.5, we find 2θ_out ≈ 2 * sin^(-1)(1/1.5) ≈ 41.8 degrees.

(b) A corner reflector is formed by three mutually perpendicular plane mirrors, such as those in a prism. In a corner reflector made from glass (n=1.5), each mirror surface will have an acceptance angle equal to the critical angle. Using the same formula as in (a), we find θ_c = sin^(-1)(1/1.5). Since each mirror is perpendicular to the others, the total acceptance angle of the corner reflector is the sum of the acceptance angles of the individual mirrors, which results in 2θ_out ≈ 2 * sin^(-1)(1/1.5) ≈ 90 degrees.

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Explanation:

The angles SPT and TPU marked in red are congruent. They are congruent because of the similar arc markings.

Those angles add to the other angles to form a full 360 degree circle.

Let x be the measure of angle SPT and angle TPU.

86 + 154 + 60 + x + x = 360

300 + 2x = 360

2x = 360-300

2x = 60

x = 60/2

x = 30

Each red angle is 30 degrees.

Then,

angle SPQ = (angle SPT) + (angle TPU) + (angle UPQ)

angle SPQ = (30) + (30) + (86)

angle SPQ = 146 degrees

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Another approach:

Notice that angles QPR and RPS add to 154+60 = 214 degrees, which is the piece just next to angle SPQ. Subtract from 360 to get:

360 - 214 = 146 degrees

The equation of the parabola with the given vertex and focus is x^2 = 24y.

What is parabola?

A parabola is a U-shaped curve that is symmetric and can either open upward or downward. It is a conic section and is defined as the locus of points equidistant from a fixed point called the focus and a fixed line called the directrix

To find the equation of a parabola with the vertex at the origin (0, 0) and a focus at (-6, 0), we can use the standard form equation for a horizontally-oriented parabola:

(x - h)^2 = 4p(y - k)

where (h, k) represents the vertex coordinates, and p is the distance between the vertex and the focus.

In this case, the vertex is at (0, 0) and the focus is at (-6, 0). The distance between the vertex and focus is given by p = 6 (since the x-coordinate of the focus is 6 units away from the vertex).

Plugging these values into the standard form equation, we have:

(x - 0)^2 = 4(6)(y - 0)

Simplifying further, we get:

x^2 = 24y

Therefore, the equation of the parabola with the given vertex and focus is x^2 = 24y.

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Step-by-step explanation:

34666(8684x:#68095732)

Answer:

2x - 3 = 11

Step-by-step explanation:

"difference" means subtraction, so it is subtraction.

"twice a number" simply means 2x, since you do not know what the specified number is, it is x. and the 2 and just making it twice the number.

"Is 11" just means equals 11.

so, 2x - 3 = 11.

hope this helps!

The value of x in the triangle UVW is 45°.

A polygon which has three sides and three vertices is called as triangle.

The sum of all the angles of the triangle is 180°.

Given:

The measures of the angle of the triangle UVW are 24°, 30° and (3x - 9)°.

The sum of all the angles of the triangle is 180°.

24° + 30° + (3x - 9)° = 180°.

3x - 9 = 180 - 54

3x = 135

x = 45.

Therefore, the value of x is 45°.

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The Chi-square test is a statistical test used to determine if there is a significant difference between observed and expected frequencies in categorical data. In this example, the test is used to assess whether there is a significant difference in the mean breaking strengths of two types of cables.

The Chi-square test of significance is employed when dealing with categorical or nominal data. It compares the observed frequencies with the frequencies that would be expected if the variables were independent. In this case, the breaking strengths of the two cables are the variables of interest.

To perform the test, the first step is to define the null hypothesis (H0) and the alternative hypothesis (Ha). In this example, H0 assumes that there is no difference in the mean breaking strengths of the two cables, while Ha suggests that there is a difference.

Next, the test statistic, denoted by X2 (chi-square), is calculated using the formula X2 = Σ[(O - E)²/E], where O represents the observed frequencies and E represents the expected frequencies under the assumption of independence.

To determine the expected frequencies, we need to estimate the means and variances of the breaking strengths. Here, x = 1925 and sigma = 40 for the first cable, and x = 1905 and sigma = 30 for the second cable.

Once the test statistic is calculated, it is compared to a critical value from the Chi-square distribution with degrees of freedom equal to (r - 1)(c - 1), where r is the number of rows and c is the number of columns in the contingency table. The significance level of 0.01 determines the critical value.

If the calculated X2 value is greater than the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to indicate a difference in the mean breaking strengths of the two cables. Conversely, if the calculated X2 value is less than or equal to the critical value, we fail to reject the null hypothesis and conclude that there is no significant difference.

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Answer:

Hold on i have to work it out real quick

Step-by-step explanation:

Answer:

7 1/2 divided by 3/4 is 10

Step-by-step explanation:

10

Brainiest please and thank you

The points X(5,-3), Y(4,-1) and Z(6,-2) can be plotted as given below. From the obtained graph ∠XYZ is the obtuse angle.

The given coordinates are X(5,-3), Y(4,-1) and Z(6,-2).

We need to classify ∠XYZ whether it is right, acute, or obtuse.

A cartesian plane or coordinate plane can be defined as a plane formed by the intersection of two coordinate axes that are perpendicular to each other. The horizontal axis is called the x-axis and the vertical one is the y-axis. These axes intersect with each other at the origin whose location is given as (0, 0). Any point on the cartesian plane is represented in the form of (x, y). Here, x is the distance of the point from the y-axis and y is the distance from the x-axis.

Now, X(5,-3), Y(4,-1) and Z(6,-2) can be plotted as given below:

The given points X(5,-3), Y(4,-1) and Z(6,-2) have positive x-coordinate and negative y-coordinate.

In the cartesian plane, the fourth quadrant positive x-coordinate and negative y-coordinate.

So, all points X(5,-3), Y(4,-1) and Z(6,-2) lie in the fourth quadrant.

From the graph, we can see that the two lines make an obtuse angle, which is more than 180° and less than 360°.

From the obtained graph ∠XYZ is the obtuse angle.

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The amount of silk used in one minute by the factory was 126

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

A factory makes 3.5 silk flowers every second.

60 second = 1 minute

Amount of silk made in one minute = 3.5 silk flowers every second * 60 seconds = 210 silk flowers

Each flower uses 60.3 cm of silk.

Hence, for 210 silk flowers:

Amount of silk used = 210 silk flowers * 60 cm of silk = 12600 cm of silk

100 cm = 1 m

12600 cm =  12600 cm * 1 m per 100 cm = 126 m

The amount of silk used was 126

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Answer:

f(0)=1

Step-by-step explanation:

The question asks us to find f(0). We want to find what f(x), or y is, when x is equal to 0.

f(x)=3^x

Therefore, we can substitute 0 in for x.

f(0)=3^0

Evaluate the exponent, 3^0.

Any number raised to the power of zero is equal to 1.

f(0)=1

Answer:

1

Step-by-step explanation:

f(0) = 3^0

f(0) = 1

anything to the 0th power = 1

Answer:

3.15km²

Step-by-step explanation:

A = bh/2

Answer:

y=2.80x+1.60

y=3.20x+1.50

In order to express the confidence interval in the form p ± E, first we have to determine the midpoint of the interval, like this:

The value of the error, E, can be calculated by taking the difference between p and the end of the interval, like this:

Then, we can express 0.555 < p < 0.999 in p + E notation as 0.777 ± 0.222

The confidence interval can be written as 0.777 ± 0.222.

The confidence interval 0.555 < p < 0.999 can be expressed in the form of p ± E.

To find the margin of error (E), we can subtract the lower limit (0.555) from the upper limit (0.999) and divide it by 2:

E = (0.999 - 0.555) / 2

E = 0.222

Therefore, the confidence interval 0.555 < p < 0.999 can be expressed as:

p ± E

where p is the point estimate and E is the margin of error. In this case, the point estimate would be the midpoint of the interval, which is the average of the lower and upper limits:

p = (0.555 + 0.999) / 2

p = 0.777

Hence, the confidence interval can be written as 0.777 ± 0.222.

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Answer:

1.3455

Step-by-step explanation:

A 15% increase is a multiplication by 1.15

So a 15% and a 17% increase is a multiplication of 1.15*1.17 = 1.3455

Answer:

0.9545

Step-by-step explanation:

Let an integer be x.

If x is increased by 15%, then the value of the number would be

115/100x=1.15x

If 1.15x is decreased by 17%, then the value of the number would be:

(100-17)/100×1.15x

83/100×1.15x=0.9545x

We can see here that m∠MNQ = 100°.

Thus, by the Parallelogram Opposite Angles Theorem, ∠MNQ and ∠QLM are congruent.

A parallelogram is a type of quadrilateral, which is a four-sided polygon. It has two pairs of parallel sides, opposite sides are equal in length, and opposite angles are equal in measure.

A rectangle, rhombus and square are also parallelograms. A rectangle is a parallelogram with four right angles, a rhombus is a parallelogram with all sides congruent and a square is a special case of a rectangle with all sides congruent.

We can see here that according to the Parallelogram Opposite Angles Theorem, a quadrilateral is a parallelogram if both sets of opposite angle pairs are congruent.

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The opportunity cost is merely the expense of not making a decision.

As a result, if you chose Project P placed above a white Project Q, the opportunity cost for such a decision is 75,000 times the estimated NPV of Project Q.

The distinction between current value of money over time value of cash outflows over time is defined as net present value (NPV).

Some key features regarding the Net Present Value (NPV) are-

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Answer:

a.    \(T = 17s\)

b.    \(D = 72cm\)

Step-by-step explanation:

Given

Direct Variation

\(Distance(D)\ \alpha\ Time (T)\)

D = 264 cm when T = 11 s

Calculating (a)

First, the constant of variation (k) as to be calculated;

Since, there exist a direct proportion; then,

\(D\ \alpha\ T\)

\(D = kT\)

Make k the subject of formula

\(k = \frac{D}{T}\)

D = 264 cm when T = 11 s; So

\(k = \frac{264}{11}\)

\(k = 24\)

So: Solving for (a)

\(D = 408\)

Substitute 408 for D and 24 for k in \(D = kT\)

\(408 = 24 * T\)

Divide both sides by 24

\(\frac{408}{24} = T\)

\(T = \frac{408}{24}\)

\(T = 17s\)

Hence, time to move a distance of 408cm is 17s

Calculating (b)

\(T = 3\)

Substitute 3 for T and 24 for k in \(D = kT\)

\(D = 24 * 3\)

\(D = 72cm\)

Hence, distance covered in 3 seconds is 72cm

The range of the function g(x) = |x - 12| - 2 is {y | y > -2}, indicating that the function can take any value greater than -2.

To find the range of the function g(x) = |x - 12| - 2, we need to determine the set of all possible values that the function can take.

The absolute value function |x - 12| represents the distance between x and 12 on the number line. Since the absolute value always results in a non-negative value, the expression |x - 12| will always be greater than or equal to 0.

By subtracting 2 from |x - 12|, we shift the entire range downward by 2 units. This means that the minimum value of g(x) will be -2.

Therefore, the range of g(x) can be written as {y | y > -2}, which means that the function can take any value greater than -2. In other words, the range includes all real numbers greater than -2.

Visually, if we were to plot the graph of g(x), it would be a V-shaped graph with the vertex at (12, -2) and the arms extending upward infinitely. The function will never be less than -2 since we are subtracting 2 from the absolute value.

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Answer:

0.41 in.

Step-by-step explanation:

Given:

Frank has a sheet of paper of 1/624 inch thick

The sheet is folded in half, the total thickness is 1/312 inch

The sheet folded in half again and the total thickness is 1/156 inch

Required:  thickness of the sheet after folded 8 times=?

1st thickness= 1/624 inches

2nd thickness = 1/312 inch(after 1st fold)

3rd thickness=1/156 inch( after 2nd fold)

1/312 ÷ 1/624 = 2

1/156 ÷ 1/312 = 2

There is a common ratio 2 between each two fold

The thicknesses of the sheet after each fold formed a geometric series

Any term of the geometric series is \(a_{n}=a(r)^{n-1}\)

where,

a =first term

r = ratio between each two consecutive terms

n=position of the term

a = 1/312 because it is the thickness of the 1st fold

r = 2 , n = 8

\(a_{8}=\frac{1}{312}(2)^{8-1}=\frac{16}{39}\)=> 0.41 in

We can tell if a character is direct or Indirect  by the five methods which are action, reactions, physical description,  inner thoughts,  and speech.

The Characterization in literature is the process that the authors use to develop characters and create images of characters for audience.

There are two different approaches for characterization, which are Direct Characterization and Indirect Characterization.

The methods by which we can know that a character is Direct or Indirect are :

(i) Physical description - In this the character's physical appearance is described. For example, How the character dresses might reveal something about the character.

(ii) Action - Is the character a good person or a bad person can be told by his Action .

(iii) Inner thoughts - The inner thoughts of character reveals the personality .

(iv) Reactions - The Effect on other characters also reveals about the personality of character .

(v) Speech - What character says provides a great insight for the reader.

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