The number line below is divided into 4 equal parts. Fill in the missing fractions and percentages.
Note that your fractions don't need to be in simplest form.

The measure of the central angle in degrees subtended by an arc of length 5 meter is 71.61 degrees

The radius of the circle = 4 meters

The circumference of the circle = 2πr

Where r is the radius of the circle

The value of π = 3.14

The circumference of the circle = 2π × 4

= 8π

The arc length = 5 meters

Consider the x as the central angle

The proportion of central angle and circumference will be

5/8π = x radiance / 2π

Cross multiply the terms

x × 8π = 5 × 2π

x = 10π / 8π

x = 5/4 radiance

Convert radiance to degrees

We know

1 radiance = 180/π degrees

5/4 radiance = 5/4 × 180/π degrees

= 71.61 degrees

Therefore, the central angle is 71.61 degrees

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Using the completing square method, the value of (C) x = ±√5 - 2.

A quadratic polynomial of the form ax2+bx+c can be transformed to the form in elementary algebra by using the "completing the square" method for certain values of h and k.

In other words, the quadratic expression is completed by inserting a perfect square trinomial.

So, we have:

x² + 4x = 1

The x-coefficient terms must be divided by two:

4/2 = 2

Square:
2² = 4

Add 4 on both sides as follows:

x² + 4x + 4 = 1 + 4

x² + 4x + 4 = 5

Transform into perfect squares:

(x + 2)² = 5

Both sides of the square root:

x + 2 = ±√5

x = ±√5 - 2

Therefore, using the completing the square method, the value of (C) x=±√5-2.

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Complete question:
Solve x2 + 4x = 1 for x by completing the square.

a. x = −3

b. x = −1

c. x equals plus or minus the square root of 5 minus 2

d. x equals plus or minus square root of 5 plus 2

Answer:

is c correct?

Step-by-step explanation:

Answer:

15[tex]\frac{17}{24}[/tex]

Step-by-step explanation:

5 [tex]\frac{7}{8}[/tex] + 9 [tex]\frac{5}{6}[/tex]  We can write the fractions as equivalent fractions with a common denominator of 24

[tex]\frac{7}{8}[/tex] x[tex]\frac{3}{3}[/tex] = [tex]\frac{21}{24}[/tex]

[tex]\frac{5}{6}[/tex] x [tex]\frac{4}{4}[/tex] = [tex]\frac{20}{24}[/tex]

5[tex]\frac{21}{24}[/tex] + 9[tex]\frac{20}{24}[/tex]

5 + 9 + [tex]\frac{21}{24}[/tex] + [tex]\frac{20}{24}[/tex]

14 + [tex]\frac{41}{24}[/tex]

14 + [tex]\frac{24}{24}[/tex] + [tex]\frac{17}{24}[/tex]   I broke up [tex]\frac{41}{24}[/tex] because [tex]\frac{24}{24}[/tex] is another name for 1

14+1 + [tex]\frac{17}{24}[/tex]

15[tex]\frac{17}{24}[/tex]

The characteristics of polynomial graphs' intercepts reveal the multiplicity's characteristics. The function is a potential representation of the graph; f(x) = x²·(x - a) (x - a) , ²·(x - b) (x - b),⁴·(x - c) (x - c).

The alternative provides a function that can represent a graph;

f(x) = x²·(x - a) (x - a)

²·(x - b) (x - b)

⁴·(x - c) (x - c)

Reason:

The graph's description is as follows:

Three points on the graph deviate from the x-axis.

Therefore;

The first equation is satisfied by the graph's even multiplicity at three places, such as x2, (x - a)2, and (x - b)4.

The graph once almost linearly crosses the x-axis.

Therefore;

The first equation's function contains a single zero or component, such as (x - c), so;

The function is a potential representation of the graph;

f(x) = x²·(x - a) (x - a)

²·(x - b) (x - b)

⁴·(x - c) (x - c).

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Answer: 13

Step-by-step explanation: To find f(2), you can put 2 into all of the x spots, thus making the equation 4(2)+5. From there you can do PEMDAS and multiply 4 and 2 to get 8, and then add 5 to get 13.

The order of calculate the confidence interval for the mean are as follows:

1. Select sample stat

2. select desired confidence

3. determine margin of error

4. specify upper and lower limits

Now, According to the question:

The order of calculate the confidence interval for the mean are as follows:

1. Select sample stat

2. select desired confidence

3. determine margin of error

4. specify upper and lower limits

Let's know:

What is Confidence Interval?

A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.

The common notation for the parameter in question is θ. Often, this parameter is the population mean μ , which is estimated through the sample mean bar x.

The level C of a confidence interval gives the probability that the interval produced by the method employed includes the true value of the parameter θ.

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Answer:

Step-by-step explanation:

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Therefore, the equation of the line with slope -4 and y-intercept 2 is y = (-4)x + 2.

Answer:

Hi!

The answer would be: 6 + 54t

I hope this helped you! :)

Step-by-step explanation:

Answer:

54t + 6

Step-by-step explanation:

Simplify the expression. Use the distributive property. The distributive property states that an expression which is given in form of a(b + c) can be solved into (ab) + (ac). Distribute and multiply 6 to all terms within the parenthesis. Then, simplify:

[tex]6(1 + 9t)\\\\=(6 * 1) + (6 * 9t)\\= (6) + (54t)\\ = 54t + 6[/tex]

54t + 6 is your answer.

~

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For the given diagram 1. d) all of them are correct, 2. d)none of them are correct and Total Revenue is 3. b. $90,125

1.

Marginal Revenue is

the change in Total Revenue/Change in units of output produced

In the given question the price of the output is fixed at $125.

Hence no matter what the quantity of output sold, every additional output produced will generate an additional revenue of $125.

hence option d) all of them are correct has to be chosen.

2.

Now we already know that if the price has been fixed at $125, the marginal revenue generated cannot be anything but $125.

Hence, option d) None of them are correct.

3.

Total Revenue = Price X Quantity

Here it is given that the Price is $175

Output is 515 units

Hence, the Total Revenue will be $(175  X  515)

= $90125

Hence, option b. $90125 is correct.

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Complete Question

(Image Attached)

The time management skill and amount of work done is an example of positive correlation.

Correlation or dependency pertains to any statistical link involving two random variables or bivariate data, whether causal or not. Although the term "correlation" can refer to any form of link, in statistics it is most usually used to refer to the degree to which two variables are statistically linearly associated.

The link between the heights of parents and their children, as seen in the enough that demand curve, and the correlation between the price of an item and the quantity of items that buyers are willing to acquire are examples of dependent phenomena.

The Pearson product-moment correlation coefficient (PPMCC), sometimes known as "Pearson's correlation coefficient," is the most commonly used measure of two-value dependency.

It is computed by dividing the covariance ratio of the two variables in our numerical dataset by the square root of their variances. The covariance of the two variables is simply divided by the product of their standard deviations in mathematics. The coefficient was calculated by Karl Pearson from Francis Galton's similar but slightly different idea.

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Option D is the correct answer, Universal Instantiation is The implicational rule of inference that permits us to derive a specific instance from a universal statement.

It is the process of deriving an individual statement from a general one by replacing the variable with a name or another referring expression called Instantiation.

Universal Instantiation is also called universal specification or universal elimination, it is a valid rule of inference from the truth about each member of a class of individuals to the truth about a particular individual of that class.

Example: "No humans can fly. John Doe is human. Therefore John Doe can not fly."

∀xA⇒A(x↔a}

for every formula A and every term a, where A(x↔a}  is the result of substituting a for each free occurrence of x in A. A(x↔a} is an instance of

∀xA.

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The given statement ,the analysis of total variability into between-treatments and within-treatments variability is the same for a repeated-measures ANOVA and an independent-measure ANOVA is true.

The first stage of the repeated-measures ANOVA is identical to the independent-measures analysis and splits the overall variability into two components: between-treatments and within-treatments

Measurements that are repeated ANOVA is the extension of the dependent t-test and is the equivalent of one-way ANOVA for related, rather than independent, groups.

A repeated measures ANOVA is often referred to as a within-subjects ANOVA or ANOVA for correlated samples. The term "responsibility" refers to the act of determining whether or not a person is responsible for his or her own actions.

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A. The top cycle in this case is a -> b -> c -> a.

B. The agenda that wins the candidate is:

First vote:

a vs b -> a wins

Second voice:

versus. c -> a wins

The agenda that Candidate B wins is:

First vote:

b vs c -> b wins

Second Voice:

b vs a -> b wins

The agenda that Candidate C wins is:

First vote:

c vs a -> c wins

Second Voice:

c vs b -> c wins

C. Using the Borda count system, the candidates' scores are as follows:

a:

18 points (6 points from voter 1, 4 points from voter 2, and 8 points from voter 3)

b:

18 points (4 points from voter 1, 6 points from voter 2, and 8 points from voter 3)

c:

18 points (6 points from voter 1, 8 points from voter 2, and 4 points from voter 3)

d:

12 points (8 points from voter 1, 4 points from voter 2, and 0 points from voter 3)

e:

12 points (4 points from voter 1, 8 points from voter 2, and 0 points from voter 3)

f:

12 points (8 points from voter 1, 0 points from voter 2, and 4 points from voter 3)

g:

6 points (4 points from voter 1, 0 points from voter 2, and 2 points from voter 3)

Therefore, candidates a, b, and c tie for first place with 18 points each.

D. No, the Borda count winner is not the Condorcet winner, because the Condorcet winner is the candidate who would win in a majority rule vote against every other candidate. In this case, candidate c is the Condorcet winner, because c beats a and b in majority rule votes.

E. The candidate with the worst score in the Borda count is  g of 6 points.

F. If a candidate fails, the original worst candidate may no longer be the worst. In this case, if candidate g fails, the remaining candidates will have the following results:

a:

15 points (Voters 1 to 5 points, Voters 2 to 4 points, Voters 3 to 6 points)

b:

15 points (Voters 1 to 4 points, Voters 2 to 5 points, Voters 3 to 6 points)

c:

15 points (Voters 1 to 5 points, Voters 2 to 6 points, Voters 3 to 4 points)

Day:

10 points (voters 1 to 6 points, voters 2 to 4 points, voters 3 to 0 points)

e:

10 points (voters 1 to 4 points, voters 2 to 6 points, voters 3 to 0 points)

f:

10 points (voters 1 to 6 points, voters 2 to 0 points, voters 3 to 4 points)

In this case, g's 6-point score is not included in the calculation, so candidate g is no longer last.

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Time is represented by the variable. Since a person's speed, which can take on nearly any value, determines how long it takes them to complete a mile, this variable is continuous.

If a quantitative variable is often obtained through measuring or counting, it can either be continuous or discrete. If a variable can take on any two particular real values and all other real values in between, it is said to be continuous over a range of real values.

First, when is a variable continuous and when is it discrete?

A variable is continuous if it can take any value (or at least a dense set of values) inside a certain interval as opposed to discrete if it can only take a few specific values on that interval.

For instance, the only possible values for the numbers one can roll on a dice are 1, 2, 3, 4, 5, and 6, to provide one example.

The variable in this instance now stands for time. Time is nearly always a continuous variable; in this instance, the time refers to the duration of a mile run. Therefore, that variable is capable of practically any value (depends on the speed of the person).

Therefore,

Time is represented by the variable. Since a person's speed, which can take on nearly any value, determines how long it takes them to complete a mile, this variable is continuous.

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The probability that 2 or fewer in the sample will favor the project is  4.368 × 10⁻⁶ and Also The data seem to indicate that the percent favoring the increase in fees is less than 70%

According to the question,

It is given that according to the student's government

The probability that number of students in favor of increment in fees : p = 0.70

The probability that number of students against the increment : q = 0.30

Sample Size : n = 12

Number of students follows Binomial distribution

(a) We have to find the probability that 2 or fewer in the sample will favor the project

P( x ≤ 2) = P(0) + P(1) + P(2)

As we know ,

P(x) = ⁿCₓpˣq⁽ⁿ⁻ˣ⁾

=> P( x ≤ 2) = ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹ + ¹²C₂p²q¹⁰

=>  P( x ≤ 2) = 1×(0.30)¹² + 12×(0.70)(0.30)¹¹  + 12×11/2 × (0.70)²(0.30)¹⁰

=> P( x ≤ 2) = (0.30)¹⁰ [ 0.09 + 0.21 + 0.48]

=>  P( x ≤ 2) = 5.9×10⁻⁶[0.78]

=>  P( x ≤ 2) = 4.368 × 10⁻⁶

Which is very close to zero

(b) The data doesn't support the student government claim.

The data seem to indicate that the percent favoring the increase in fees is less than 70%.

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According to the given questions the answer is for 3 hour $560, for 8 hour cost $685 and for 12 hour cost $785.

A crucial concept that time and labour have in common with some other mathematical topics is the concept of proportionality. Because efficiency grows inversely linked to the amount of time needed when the quantity of work is constant.

The fundamental equation for solving is 1/r+1/s=1/h. Let's choose Hrithik as our example. Let's assume that Hrithik completes 1/20 of something like the work in a day and Dhoni completes 1/30 of the work in a day. They will accomplish 1/20 + 1/30 = 5/60 = 1/12th of something like the work in a day if they collaborate.

Given that John paid $485 to build a deck.

And he will pay $25 per hour to his brother for building the deck.

one hour of work costs John $25 + $485 .

Total cost of building deck = $25 × h number of hours + $485

3 hour of work costs $25 × 3 = $75 + $485 = $560

8 hour of work costs = $25 × 8 = $200 + $485 = $685

12 hour of work costs = $25 × 12 = $300 + $485 = $785

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The complete question is-

John is having a new deck built. He paid $485 for the required materials, and he will pay his brother $25 an hour to build the deck. Which table shows the relationship between h, the number of hours John’s brother works, and c, the total cost of the project?

h c

0 485

3 510

8 535

12 560

h c

0 510

3 535

8 560

12 585

h c

0 485

3 560

8 685

12 785

h c

0 510

3 585

8 710

12 810

Answer:

y = - 0.4x -6

Step-by-step explanation:

The slope-intercept form of a line equation is

y = mx + b

where m is the slope and b the y-intercept where the line crosses the y axis.

From the figure it is clear that the line passes through (0, -6) and therefore the y-intercept is -6

To compute the slope, find another  convenient point on the line. Compute the ratio of change in y values(called rise) to the change in x values(called run). This will be the slope

We see that point (10, -10) has been identified on the graph.(Any of the 4 identified points will do, I just chose this)

So two points to consider are (0, -6) and (10, -10)

Change in y values = rise = -10 - (-6) = 1- + 6 = -4

Change in x values = run = 10 - 0 = 10

So slope m = -4/10 = -0.4

Equation of line is y = -0.4x -6

Answer:

[tex]27x^6y^6[/tex]

Step-by-step explanation:

The formatting of the question is a bit confusing, but if the expression is [tex](3x^2y^2)^3[/tex], use the power of a product exponent rule [tex](ab)^m=(a)^m(b)^m[/tex].  So,

[tex](3x^2y^2)^3=(3)^3(x^2)^3(y^2)^3[/tex].

Next, use the power of a power exponent rule [tex](a^m)^n=a^{m*n}[/tex].  So,

[tex](3)^3(x^2)^3(y^2)^3=27(x^{2*3})(y^{2*3})=27x^6y^6[/tex]

Answer: 15 - h - 3

Step-by-step explanation:

a. The probability that the second marble is red is 2/5, since there are 2 red marbles and a total of 5 marbles.

b. The probability that both marbles are the same color is 4/15, since there are two ways that this could happen (both red or both black) and there are 15 possible outcomes in total.

c. The probability that the second marble is black given the first marble is red is 3/4, because out of the 4 possible outcomes (RR, RB, BR, BB) the only way to get a black marble on the second draw is if it is BR.

d. The probability that the first marble is red given that the second marble is red is 2/3, because out of the 3 possible outcomes (RR, RB, BR) the only way to get a red marble on the first draw is if it is RR or RB.

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The value of z such that 7% of the area under the standard normal curve lies to the right of z is approximately -0.4

To find the value of z such that 7% of the area under the curve lies to the right of z, we need to find the value of z such that 43% of the area lies to the left of z.

This value of z is known as the 43rd percentile of the standard normal curve.

We can use a table of the standard normal distribution, also known as the z-table, to find the value of z corresponding to the 43rd percentile.

According to the z-table, the value of z corresponding to the 43rd percentile is approximately -0.4

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The value of BC = 25 using properties of triangle.

What are properties of triangle ?

Let us discuss here some of the properties of triangles.

1. A triangle has three sides and three angles.

2. The sum of the angles of a triangle is always 180 degrees.

3. The exterior angles of a triangle always add up to 360 degrees.

4. The sum of consecutive interior and exterior angle is supplementary.

Properties for isosceles:

Isosceles triangles are those triangles that have at least two sides of equal measure.

1. Two equal sides and two equal angles.

2. The two equal sides of an isosceles triangle are called the legs and the angle between them is called the vertex angle or apex angle.

3. The side opposite the vertex angle is called the base and base angles are equal.

Using 1st property,

in given triangle two angles are equal then opposite side will also be equal.

So, AB = AC

i.e. 4x+4 = 6x-14

4+14 = 6x-4x

18 = 2x

x = 9

Putting value of x in BC

BC = 2*9 +7

     = 18+7

     = 25.

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Answer:

x=5

Step-by-step explanation:

If p and q are parallel, then the two angles in question should be equal to one another.

So,

(3x+15)°=(8x-10)°

(3x+15)°+10°=(8x-10)°+10°

(3x+25)°=(8x)°

(3x+25)°-(3x)°=(8x)°-(3x)°

25°=5x°

5=x

So, the two angles should be (8(5)-10)° and (3(5)+15)°.  Both of these expressions equal 30°.  This makes sense, as the illustration shows that the two angles are acute.

The expression that could be used to determine the length of segment AB in the triangles given is: A. AB = AX * AC/AY.

When two triangles are stated to be similar to one another, it means both triangles have equal corresponding angles, but their corresponding sides have proportional lengths or have ratios that are equal.

This means similar triangles have the same shape but different sizes, since their corresponding side lengths have proportional length.

Given that triangle AXY is similar to triangle ABC, it means that:

m<A = m<A

m<X = m<B

m<Y = m<C

AX/AB = AY/AC = XY/BC

To find the length of AB, we could use the following expression derived from the ratios stated above:

AX/AB = AY/AC

Cross multiply:

(AB) * (AY) = (AX) * (AC)

Divide both sides by AY

(AB) * (AY) / AY = (AX) * (AC) / AY

AB = AX * AC/AY

The expression to use is: A. AB = AX * AC/AY

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The rate of change of the line that contains the two points (-1, -4) and (5, 4) is 4/3.

The rate of change for a line is the slope, the rise over run, or the change in over the change in.

The slope of line can be calculated using the formula, slope =(y2-y1)/(x2-x1).

The given coordinate points are (-1, -4) and (5, 4).

Now, slope = (4-(-4))/(5-(-1))

= (4+4)/(5+1)

= 8/6

= 4/3

Therefore, the slope of a line is 4/3.

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Answer: -433.15

Step-by-step explanation:

he's id debt and has to pay off the 433.15 later on.

Answer:

The McQuires' account is currently overdrawn by $483.15.

Step-by-step explanation:

If the McQuires' account balance was $750 on Friday and they wrote a check for $1,183.15 on Saturday, then the balance would be 750 - 1,183.15 = -$433.15 after the check cleared. Since the bank charges a $50 overdraft fee, the final balance in the McQuires' account would be -$433.15 - $50 = -$483.15. The McQuires' account is currently overdrawn by $483.15.

To solve this system of differential equations using the series method, we can assume that the solution can be expressed as a power series in both x and y:

[tex]u(x,y) = a0 + a1x + a2y + a3xy + a4x^2 + a5y^2 + ...[/tex]

Substituting this expression into each of the differential equations and collecting the coefficients of each term gives us the following system of equations:

a0 + 5a0 = 0

a1 + 5a2 = 0

a2 + 5a1 = 0

a4 + 5a4 = 0

a5 + 5*a5 = 0

Solving this system of equations gives us the following values for the coefficients:

a0 = 0

a1 = 0

a2 = 0

a3 = 0

a4 = 0

a5 = 0

Therefore, the power series expansion of the solution is:

u(x,y) = 0

This means that the only solution to the differential equations is the trivial solution u(x,y) = 0.

Note that this method of solving differential equations using power series is only applicable if the differential equations are linear and homogeneous, which means that the coefficients of the terms in the differential equations do not depend on x and y, and the right-hand sides of the equations are all equal to 0. If the differential equations are nonlinear or inhomogeneous, other methods may be required to find their solutions.

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a pair of congruent angles are:

3x+4 = (3×12) +4 = 40°

5x - 20 = (5×12) -20 = 40°

The sizes of congruent angles are same. Simply by looking at the specified angles' measurements, congruent angles may be discovered. However, it is not necessary for the terminals used to create these angles to be the same length and direction.

We have been given a different description for each angle.

Let, the number referred to be x

four more than three times a number: 3x + 4

twenty less than five times the number: 5x - 20

So, 5x - 20 =  3x + 4

or, 2x = 24

or, x = 12

The angles are:

3x+4 = (3×12) +4 = 40°

5x - 20 = (5×12) -20 = 40°

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The greatest common divisor is 12. The linear combination of 3984 and 588 is given by 12 = 61×588 - 9×3984.

The extended Euclidean algorithm is an algorithm to compute integers x and y such that: ax+by=gcd(a,b)The extended Euclidean algorithm can be viewed as the reciprocal of modular exponentiation.

By reversing the steps in the Euclidean algorithm, it is possible to find these integers x and y. The whole idea is to start with the GCD and recursively work our way backwards. This can be done by treating the numbers as variables until we end up with an expression that is a linear combination of our initial numbers.

First use Euclid's algorithm to find the GCD:

3984 = 588 ×6 + 456

588 = 456×1 +132

456= 132 ×3 + 60

132 =  60×2 +12

60 = 12×5+0

The last non-zero remainder is 12.

Thus, the greatest common divisor is 12.

Now we use the extended algorithm:

12 = 132 +(-2)×60

    = 132 + (-2)×(456 + (-3)×132))

    = (-2)×456 + 7×132

    = (-2)×456 + 7×(588 +(-1)×456))

   = 7×588 + (-9)×(3984 +(-6)×588))

   = 61×588 + (-9)×3984

Thus, a = -9 and b = 61.

Thus, the linear combination of 3984 and 588 is given by 12 = 61×588 - 9×3984.

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Answer:

add one black and one white marble

Step-by-step explanation:

you have to make bag b equivalent to a 2:3 ratio.

add 1 to 5 to make it divisible by 2

divide 6 by 2

=3

multiply 3 by 3 to get a 2:3 ratio

=9

subtract initial marbles

9-8=1