3x + 4y = 30
5x + 3 y = 17

Answer:

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

Use the formula:

where θ is the central angle in degrees, r is the radius

We have:

Substituting the given values, we get:

Therefore, the length of the arc is 14π cm.

The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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The writer's profit is $84.00. To calculate the writer's profit, you need to consider the premiums collected from selling the call options, the interest earned on those premiums, and the cost of buying the shares to complete the call contract.The premiums collected from selling the call options are:$0.91 x 100 = $91.00The interest earned on those premiums over 30 days at 5% is:($91.00 x 0.05 x 30) / 365 = $0.38The total amount of cash available to the writer at expiry is therefore:$91.00 + $0.38 = $91.38The cost of buying the shares to complete the call contract is:100 x $42 = $4,200.00Since the underlying asset is worth $39 at expiry, the writer can buy the necessary shares for:100 x $39 = $3,900.00The writer's profit is therefore:$91.38 - $3,900.00 = $84.00Since the writer made a profit, the answer is $84.00.

Hope I helped you...

The relationship is not a proportional relationship between S and w.

Saving, S, after w weeks, is represented by the equation

S = 50+45w

If y is proportional to x, then

y ∝ x

y =kx

where k is the constant of proportionality.

Here, no constant term and (0,0) satisfies this equation.

The given equation is

S = 50+45w

Here, we have a constant term.

For S=0 and w=0,

0=50+45×0

0=50

Which is not true as 0 ≠ 50.

Since there is a constant term 50 and the equation is not valid for (0,0), therefore, the given relationship is not a proportional relationship.

I hope this answer helps.

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The sets (0,1) and (1,∞) are homeomorphic.

In mathematics, two sets are considered homeomorphic if there exists a continuous and bijective function between them, with its inverse also being continuous. To prove that (0,1) and (1,∞) are homeomorphic, we can define the function f(x) = 1/x.

Firstly, let's show that f(x) is one-to-one (1-1). Suppose f(a) = f(b), where a and b are elements in (0,1). Then, 1/a = 1/b, implying a = b. Thus, f(x) is one-to-one.

Next, let's show that f(x) is onto. For any y > 1, there exists an x such that f(x) = 1/x = y. Therefore, f(x) is onto.

Now, to demonstrate that f(x) is continuous, consider an open interval (a,b) in (0,1). We need to show that the pre-image of this interval, f⁻¹((a,b)), is an open set in (1,∞). Since f(x) = 1/x is a continuous function, the pre-image of (a,b) will be an open set.

Lastly, f(x) is open. Let U be an open set in (0,1). We need to show that f(U) is open in (1,∞). Since f(x) = 1/x is a continuous function, the image of U under f(x) will also be an open set.

Therefore, the function f(x) = 1/x satisfies all the properties required for homeomorphism between (0,1) and (1,∞).So,the given sets are homeomorphic.

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Answer:

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

It is an isosceles triangle if two sides are same.

There are two possible triangles with given values.

If the 45° is between the two 8 cm sides, then as the isosceles triangle the other two angles have the measure:

So this is an acute triangle.

If the 45° angle is opposite to 8 cm side, then the other 8 cm side also has same opposite angle measure.

Then the third angle is:

It means it is a right triangle.

Answer:

Here you go!

Step-by-step explanation:

Answer:

If circles A and B are congruent, then AC, CD, DB, and BA are all congruent since they are all radii. We then have:

ACDB is a rhombus.

ADB is an equilateral triangle.

CD is perpendicular to AB.

CD bisects AB.

Probability that he will make the next free throw is 0.89% if larry bird made approximately 89% of all free throws during his nba career.

During nba career he made approximate 89% of all free throws.

To calculate the probability of the next 10 free throws given which will be

= No. of possible outcome / Total no. of outcome

= 89 / 100

= 0.89 %

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcome like how likely they are.

P(A) = (# of ways A can happen) / (Total number of outcomes)

which means that Probability that he will make the next free throw is 0.89 %

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No, the graph of a straight line need not always be a function.

The equation of a straight line is,

y = -mx + c

y = the y coordinate

x = the x coordinate

c = y-intercept of the line

m = slope of the line = tan(Ф)

Since the values of y are dependent on the values of x, the graph is a function. But for a line parallel to x-axis, the equation is,

y=a and x=0

That is, for any value of y, the value of x is 0

and for a line parallel to the y-axis, the equation is,

x=a and y=0

That is, for any value of x, the value of y is 0

The values of x and y don't depend on each other. Hence, the graphs of straight lines need not always be a function.

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Answer:

x=1 y=3

Step-by-step explanation:

Hello!

So, this says to use the substitution method. The substitution method is where you set one equation equal to one of the letters, and then put that whole equation in the other equation.

So->

3x-y=0

if we move the y to the other side we have:

3x=y

then we have our second equation:

2x+y=5

Now, we don't know what NUMBER y is yet, but we do know that it is equal to 3x. Thus, we can put it into the equation like this.

2x+(3x)=5

Then, we can add like terms and get:

5x=5

Dividing each term by five, we get

x=1

We could have also done this be solving for x in the equations and then substituting that in instead of y.

Now that we have x, we can easily put it into the equations and solve for y.

3x-y=0

3(1)-y=0

3=y

So now we know that x is equal to 1 and y is equal to 3.

Hyperkalemia is a medical condition that refers to an elevated level of potassium in the blood.

This condition can be caused by several factors, including kidney disease, certain medications, and hormone imbalances. Symptoms of hyperkalemia can range from mild to severe, depending on the level of potassium in the blood.

In a 60-year-old female diagnosed with hyperkalemia, the most likely symptom that would be observed is muscle weakness. This is because high levels of potassium can interfere with the normal functioning of muscles, leading to weakness, fatigue, and even paralysis in severe cases.

Other symptoms that may be observed in hyperkalemia include nausea, vomiting, irregular heartbeat, and numbness or tingling in the extremities. Treatment of hyperkalemia typically involves addressing the underlying cause of the condition, as well as managing symptoms through medication and lifestyle changes.

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Answer:

300

Step-by-step explanation:

I = interest earned

P = Principal

R = interest rate

T = Months

plug in all the numbers which would be...

45 = P x 0.03 x 5 *Note that 0.03 is 3% in decimal form

0.03 x 5 = 0.15

45 = P x 0.15

to make the P by itself you have to divide 0.15 to both sides

45/0.15 = 300

P = 300

Answer:

We know that x is the number of floor tickets they sell, and each one costs $15, then the amount of money they will get by those sells is x times $15, this is:

x*$15.

And y is the number of balcony tickets they sold, each one of these costs $12, then the total amount of money made in those tickets is:

y*$12.

Then the total amount of money that the band made is:

x*$15 + y*$12

And they want to make, at least, $3,000, then we will have the inequality:

x*$15 + y*$12 ≥ $3000

That can´t really be solved, because we have two variables and only one inequality, but this represents the given situation.

Answer:

Correct option: D

Step-by-step explanation:

First we need to find the rate of the series, and we can do that subtracting one term by the term before:

Second term minus first: 13/10 - 1/2 = 13/10 - 5/10 = 8/10 = 4/5

Third term minus second: 21/10 - 13/10 = 8/10 = 4/5

So the series increases by 4/5 for every term, and the first term is 1/2

We also need to find the number of terms of this series.

The last term is 93/10, so we have that:

1/2 + (4/5)*k = 93/10

(4/5)k = 88/10

k = 11

The index of the summatory should go from 0 to 11.

So the correct option is D

The length of y in the trapezium is 6 cm.

A trapezium is a quadrilateral. The area of the trapezium is 32.5 cm squared. Therefore, let's find the side y of the trapezium.

Hence,

area of a trapezium = 1 / 2 (a + b) h

where

Therefore,

a = 3 cm

b = y cm

h = 7 cm

area of a trapezium = 1 / 2 (3 + y)7

31.5 = 1 / 2 (3 + y)7

31.5 =  (3  / 2 + y  / 2)7

31.5 = 21 / 2 + 7y / 2

31.5 - 10.5  = 3.5y

21 = 3.5y

y = 21  /3.5

y = 6 cm

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Answer:

See below for answers and explanations (along with attached graph)

Step-by-step explanation:

It best helps to convert the equation into vertex form because it provides a lot of information about the characteristics of the parabola:

\(f(x)=2x^2-8x+4\\\\f(x)=2(x^2-4x+2)\\\\f(x)+2(2)=2(x^2-4x+2+2)\\\\f(x)+4=2(x^2-4x+4)\\\\f(x)+4=2(x-2)^2\\\\f(x)=2(x-2)^2-4\)

Now, recall that vertex form is \(y=a(x-h)^2+k\) where \((h,k)\) is the vertex, the axis of symmetry is the line \(x=h\), and \(a\) is the growth or shrink factor.

Vertex

This is pretty simple as you can just look at the equation, so \((h,k)\rightarrow(2,-4)\)

Axis of Symmetry

Again, also simple, so \(x=2\) would be the line.

X-intercepts

The beauty of having converted the equation to vertex form is that when we set \(f(x)=0\), we can easily find our x-intercepts with minimal work:

\(f(x)=2(x-2)^2-4\\\\0=2(x-2)^2-4\\\\4=2(x-2)^2\\\\2=(x-2)^2\\\\\pm\sqrt{2}=x-2\\\\x=2\pm\sqrt{2}\)

So, our x-intercepts are at the points \((2+\sqrt{2},0)\) and \((2-\sqrt{2},0)\).

Y-intercept

This is just a simple substitution of \(x=0\) and everything works out nicely:

\(f(x)=2(x-2)^2-4\\\\f(0)=2(0-2)^2-4\\\\f(0)=2(-2)^2-4\\\\f(0)=2(4)-4\\\\f(0)=8-4\\\\f(0)=4\)

So, our y-intercept would be at the point \((0,4)\).

Domain

If you try any real number for \(x\), there will always be a value for \(f(x)\), so the domain of the function is \((-\infty,\infty)\) in interval notation.

Range

Recall back to when we found our vertex of \((2,-4)\). Because the leading coefficient of the function is positive, our vertex is the minimum, which means \(f(x)\) cannot be lower than -4, but anything higher works, so our range is \([-4,\infty)\) in interval notation.

End Behavior

We can easily see that if we plug in a large value for \(x\), then \(f(x)\) will also be a large value, so our end behavior for the function is that as \(x\rightarrow\infty\), then \(f(x)\rightarrow \infty\). Another good indicator of this end behavior is the even leading degree of 2.

I hope these explanations helped! Please feel free to view the attached graph below to help give you a visual!

Answer:

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Since y_1(0) = 1, it satisfies the initial condition. However, y_2(0) = 0 does not satisfy the initial condition, as it should be y(0) = 1. Therefore, only y_1(t) is a solution of the initial value problem.

To verify that both y_1(t) = 1 - t and y_2(t) = -t^2/4 are solutions of the initial value problem, we first need to understand what the problem is. An initial value problem is a differential equation that includes an initial condition. In this case, we can assume that the initial condition is y(0) = 1.
Now, let's substitute both y_1(t) and y_2(t) into the differential equation and see if they satisfy the initial condition. The differential equation is not provided, but assuming it is y'(t) = -t/2, we have:
y_1'(t) = -1
y_2'(t) = -t/2
Substituting y_1(t) and y_2(t) into the differential equation gives:
y_1'(t) = -1

= -t/2 (when t = 2)
y_2'(t) = -t/2

= -t/2 (for all t)
Thus, both y_1(t) and y_2(t) satisfy the differential equation. Now, let's check if they satisfy the initial condition.
y_1(0) = 1 - 0

= 1
y_2(0) = -0^2/4

= 0
In conclusion, y_1(t) = 1 - t is the only solution that satisfies the differential equation and initial condition, while y_2(t) = -t^2/4 is not a solution since it does not satisfy the initial condition.

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By answering the presented question, we may conclude that the student parallel lines might subtract the known measure of that angle from 180 to determine the measure of 5.

In geometry, parallel lines are coplanar infinite lines that do not cross anywhere. Parallel planes are ones that never intersect in a given three-dimensional space. Parallel curves have a constant minimum distance between them and no points of touch or junction. In geometry, parallel lines are two lines that are in the same plane, equally spaced apart, and never overlap. It is possible to apply either horizontally or vertically. Parallel lines may be found in common items such as train tracks, notebook rows, and pedestrian crossings.

When a straight line meets two parallel lines, corresponding angles are generated. They are congruent (have the same measure) and are positioned in the same location at each junction.

The learner must seek for alternative angles that are congruent to 5 in order to obtain its measure. For example, if another angle in the diagram is vertical (opposite) to 5, it will have the same measurement as 5. If another angle in the diagram is supplemental (adds up to 180 degrees) to 5, the student might subtract the known measure of that angle from 180 to determine the measure of 5.

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Answer:14

Step-by-step explanation: so if you add 21 and 264 and 20 u would get 14 hehehehhehehe im da best your not :)

Mandy's actual direct labor rate per hour (AP), rounded to two decimal places, is approximately $42.00.

To find Mandy Company's actual direct labor rate per hour (AP), we need to use the given information and apply the formula for direct labor efficiency variance:

Direct Labor Efficiency Variance = (AQ - SQ) × AP

We are given the following information:

Standard direct labor hours allowed for units produced (SQ) = 3,800

Actual direct labor hours worked (AQ) = 3,650

Direct labor efficiency variance, favorable (F) = $6,300

We can rearrange the formula to solve for AP:

AP = Direct Labor Efficiency Variance / (AQ - SQ)

Substituting the values:

AP = $6,300 / (3,650 - 3,800)

AP = $6,300 / (-150)

AP ≈ -$42 per hour

However, a negative value of direct labor rate variance is called favorable direct labor rate variance, which is the result of the actual rate being less than the standard rate.

Therefore, Mandy's actual direct labor rate per hour (AP), rounded to two decimal places, is approximately $42.00.

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Complete question =

Mandy Company has the following information from last month:

Standard direct labor hours allowed for units produced (SQ) 3,800

Actual direct labor hours worked (AQ) 3,650

Direct labor efficiency variance, favorable (F) $ 6300

Total payroll $ 190530

What was Mandy's actual direct labor rate per hour (AP), rounded to two decimal places?

The value of v/2 +(3/4 +w) when v = 1 and w = 5/8 is 1 7/8

substitution of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables.

Since V = 1 and W = 5/8, by substituting 1 for V and 5/8 for w in the expression

v/2 +(3/4 +w) = 1/2+ ( 3/4 + 5/8)

= 1/2 + (6+5)/8

= 1/2 + 11/8

= (4+11)/8

= 15/8

= 1 7/8

Therefore the value of v/2 +(3/4 +w) when v is 1 , and w is 5/8 is 1 7/8

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Answer:

D, A, A, 130, 10

Step-by-step explanation:

99% sure these are correct pls mark brainliest

Answer:

I think the first is B and the second would be A

Step-by-step explanation:

.......

For a confidence level of 98% and a normally distributed variable with a known population standard deviation, the critical value can be determined using a z-score table or statistical software.

To find the critical value for a confidence level of 98% in a normally distributed variable with a known population standard deviation, we use the standard normal distribution (z-distribution).

Since the confidence level is 98%, we need to find the z-score that corresponds to an area of 0.98 in the tail of the distribution. In other words, we need to find the z-score such that the area to the right of it is 0.02.

Using a z-score table or a statistical software, we can determine that the z-score for an area of 0.02 in the upper tail is approximately 2.33. This means that 2.33 standard deviations above the mean will capture approximately 98% of the data.

Therefore, for a confidence level of 98%, the critical value for a normally distributed variable with a known population standard deviation is 2.33.

As for the effect of sample size on the size of a confidence interval, all else being equal, an increase in sample size will cause a decrease in the size of the confidence interval. This is because a larger sample size provides more information about the population, leading to a more precise estimate of the population parameter (e.g., mean or proportion). With more data points, the standard error of the estimate decreases, resulting in a narrower confidence interval. In other words, as the sample size increases, the margin of error decreases, leading to a smaller range of plausible values for the population parameter within the confidence interval.

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Tukey's procedure, also known as the Tukey-Kramer test, a statistical method used to compare multiple groups and identify significant differences in their means. Tukey's procedure is used to identify differences in the true average bond strengths among the five protocols in Example 10.3.

Tukey's procedure, also known as the Tukey-Kramer test, a statistical method used to compare multiple groups and identify significant differences in their means. In this case, we are applying Tukey's procedure to the data in Example 10.3, which consists of bond strengths measured under five different protocols.

To perform Tukey's procedure, we first calculate the mean bond strength for each protocol. Next, we compute the standard error of the mean for each protocol. Then, we calculate the Tukey's test statistic for pairwise comparisons between the protocols. The test statistic takes into account the means, standard errors, and sample sizes of the groups.

By comparing the Tukey's test statistic to the critical value from the studentized range distribution, we can determine if there are statistically significant differences in the true average bond strengths among the protocols. If the test statistic exceeds the critical value, it indicates that there is a significant difference between the means of the compared protocols.

Using Tukey's procedure on the data in Example 10.3 will allow us to identify which pairs of protocols have significantly different average bond strengths and provide insights into the relative performance of the protocols in terms of bond strength.

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Answer:

the answer is 27

Step-by-step explanation:

3x+9+90=180

3x+99=180

3x=180-99

x=81/3

x=27

Answer:

Step-by-step explanation:

3x + 9 + 90 = 180

3x + 99 = 180

3x = 81

x = 81/3

x = 27

3(27) + 9 = 81 + 9 = 90

The pH of the solution is approximately 3.04. This is calculated by taking the negative base-10 logarithm of the H_3O+ concentration.

To find the pH of a solution with a given H_3O^{+} concentration, we use the formula pH = -log10[H_3O^{+}]. In this case, the H_3O^{+} concentration is 9.17 × 10^{-4} moles/liter. To calculate the pH, follow these steps:

Calculation steps:
1. Write down the given H_3O^{+} concentration: 9.17 × 10^{-4} moles/liter
2. Plug the concentration into the pH formula: pH = -log10(9.17 × 10^{-4})
3. Calculate the base-10 logarithm of the concentration: log10(9.17 × 10^{-4}) ≈ -3.04
4. Multiply the result by -1: -(-3.04) = 3.04

The pH of the solution is approximately 3.04, which indicates that it is acidic, as a pH value below 7 represents an acidic solution.

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