Identify the terminal point for a 45° angle in a unit circle.

Answer:

a) The first term of the progression is 4.5.

b) The common difference of the progression is 4.

c) The sum of the first 10 terms of the progression is 225.

Step-by-step explanation:

To solve this problem, you can use the formula for the sum of an arithmetic series. An arithmetic series is a sequence of numbers in which each term is obtained by adding a fixed number, called the common difference, to the preceding term.

The sum of an arithmetic series with n terms and a common difference d is given by:

Sum = n/2 * (2a + (n-1)d)

Where a is the first term of the series and d is the common difference.

In this problem, you are given that the sum of the 4th and 6th terms is 42 and the sum of the 3rd and 9th terms is 52. You can use these two equations to solve for a and d.

First, let's find the sum of the 4th and 6th terms:

Sum = 4/2 * (2a + 3d) = 42

This simplifies to:

2a + 3d = 21

Next, let's find the sum of the 3rd and 9th terms:

Sum = 6/2 * (2a + 5d) = 52

This simplifies to:

2a + 5d = 26

Now that we have two equations, we can solve for a and d by using substitution or elimination.

To use substitution, we can solve the second equation for d:

d = (26 - 2a)/5

Then, we can substitute this expression for d into the first equation:

2a + 3((26 - 2a)/5) = 21

This simplifies to:

2a + 3(26 - 2a)/5 = 21

Which simplifies to:

2a + 3(26)/5 - 3(2a)/5 = 21

This simplifies to:

2a + 3(26)/5 - 6a/5 = 21

This simplifies to:

-4a + 3(26)/5 = 21

This simplifies to:

-4a + 39 = 21

This simplifies to:

-4a = -18

This simplifies to:

a = 4.5

Now that we know the value of a, we can substitute it back into one of the original equations to find the value of d:

2(4.5) + 3d = 21

This simplifies to:

9 + 3d = 21

This simplifies to:

3d = 12

This simplifies to:

d = 4

Now that we have found the values of a and d, we can use the formula for the sum of an arithmetic series to find the sum of the first 10 terms of the progression:

Sum = 10/2 * (2(4.5) + (10-1)(4))

= 10/2 * (9 + 36)

= 10/2 * 45

= 225

Therefore, the sum of the first 10 terms of the progression is 225.

Answer:

Hence,

Common difference is

First term is

Sum of first 10 terms is 47

Step-by-step explanation:

a4 + a6 =42 eq1

a3 + a9 =52 eq

a1=?

d=?

S10=?

From eq 1,

a4 + a6=42

a1+3d + a1+5d =42

2a1 + 8d= 42 eq 3

From eq 2,

a3 + a9 =52

a1+2d + a1+8d = 52

2a1 + 10d = 52 eq 4

Subtract eq 3 from eq

2a1 + 10d =52

-2a1 -8d = -42

==============

2d = 10

d=5....

≈=======================

Putting value of d in eq

2a1 +10 d=52

2a1+ 50 =52

a1 =1

================

Now we find sum of first 10 terms,

S10 = 2a1 + 9d

S10 = 2+45

S10 = 47

===========

Answer: 4.8

Step-by-step explanation:

0.95 is Pearson correlation shows the greatest strength or consistency of relationship

Pearson correlation is a statistic measuring the linear interdependence between two variables or two sets of data.

The value of correlation coefficient must be between -1.00 and +1.00 that  measures the strength and direction of the relationship between two variables.

When one variable changes, the other variable changes in the same direction.

The closer to either indicates a stronger relationship or the greatest strength or the consistency of the relationship.

The strongest must be 0.95. It is a strong positive correlation.

The correct answer is = 0.95

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a)There is a 4% probability that all nine trials will last at least 225 days.

b)Approximately at least 163 days, 90% of the total of 9 of these trials will last.

Given, A typical criminal trial lasts 21 days on average, with a 7-day

standard variation. There are nine trials chosen at random.

Let's look at the mean, which is 21, and the standard deviation, which is 7, respectively. Sample size is 9 people.

Assume that X is the sum of the nine trails' days and X represents the total number of days.

It is understood that X may have any distribution if it is a random variable with an unknown or known distribution. If n is increased, the probability that the random variable X, which is made up of sums, has a normal distribution increases.

a)There is a 4% probability that all nine trials will last at least 225 days.

b)Approximately at least 163 days, 90% of the total of 9 of these trials will last.

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There is a 4% probability that all nine trials will last at least 225 days.

Approximately at least 163 days, 90% of the total of 9 of these trials will last.

Answer:

x = 3/5

Step-by-step explanation:

[tex]125x^{3} -27=0[/tex]

[tex]125x^{3} =27[/tex]

[tex]\sqrt[3]{125x^{3} } =\sqrt[3]{27}[/tex]

[tex]5x=3[/tex]

[tex]x=\frac{3}{5}[/tex]

Hope this helps

Answer:

55.5

Step-by-step explanation:

[tex]DE=\sqrt{(-9-9)^2+(8-5)^2}=\sqrt{333} \\ \\ DF=\sqrt{(-9-(-5))^2+(-9-8)^2}=\sqrt{305} \\ \\ EF=\sqrt{(-5-9)^2+(-9-5)^2}=\sqrt{392}[/tex]

The perimeter is thus [tex]\sqrt{333}+\sqrt{305}+\sqrt{392} \approx 55.5[/tex].

A statement which best describes one of these transformations is that: A. triangle 1 is rotated to result in triangle 2.

In Mathematics, there are four (4) main types of transformation and these include the following:

In Mathematics, a rotation simply refers to a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Since triangle 2 has identical (similar) side lengths and angle measures, but is rotated and triangles 1 and 4 are identical, we can logically deduce that triangle 1 underwent a rotation to produce triangle 2.

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Answer:

The price before tax at Barnes and Noble is $33, and the price before tax at Target is $33.25.

Step-by-step explanation:

Answer:

Step-by-step explanation: As we know the number of elements in set A are 7 and the formula to calculate the number of proper subsets is 2^n – 1

Therefore substituting the values in formula .  n is number of elements of set A. Here n=7

so 2^7-1= 128-1=127

Ans:127

Answer:

What's the question? Ill try to answer in comments

Step-by-step explanation:

If they purchased 7 bags of popcorn and 3 drinks, the price would be $44.25; p bags of popcorn and d beverages would cost 4.50p+4.25d.

What is a formula?

Equation is the name given to two or more expressions with the equal sign.

Due to that

$4.50 worth of popcorn

beverage for $4.25.

There are 3 drinks and 7 bags of popcorn.

So let's calculate the overall cost.

7(4.50)+3(4.25)

31.5+12.75

44.25

So if they purchased 7 bags of popcorn and 3 beverages, the price would be $44.25

The price for p bags of popcorn and d drinks must now be determined.

4.50p+4.25d

Therefore, the price would be $44.25 if they purchased 7 bags of popcorn and 3 drinks, and the cost would be 4.50p+4.25d for p bags of popcorn and d beverages.

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Answer:

The answer is that the third example illustrates the associative property for addition. The associative property states that the order in which numbers are added does not affect the result. In other words, (a + b) + c = a + (b + c) for all numbers a, b, and c.

The third example follows this pattern:

(3 + 7) + 8 = 3 + (7 + 8) = (3 + 8) + 7

The other examples do not follow this pattern, so they do not illustrate the associative property for addition.

Step-by-step explanation:

The third example illustrates the associative property for addition. The associative property states that the order in which numbers are added does not affect the result. In other words, (a + b) + c = a + (b + c) for all numbers a, b, and c.

The third example follows this pattern:

(3 + 7) + 8 = 3 + (7 + 8) = (3 + 8) + 7

The other examples do not follow this pattern, so they do not illustrate the associative property for addition.

The first example illustrates the associative property for multiplication, which states that the order in which numbers are multiplied does not affect the result. In other words, (a x b) x c = a x (b x c) for all numbers a, b, and c.

The second example is not a valid mathematical expression, as it attempts to add a number and a product.

Answer:

(3 + 7) + 8 = 3 + (7 + 8) = (3 + 8) + 7

Step-by-step explanation:

The equations for associative property for addition are:

(a + b) + c = a + (b + c)

So, (3 + 7) + 8 = 3 + (7 + 8) = (3 + 8) + 7 is the answer!

Answer:

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

Simplify considering that (n - 3) > (n - 5) and their difference is 2:

Answer:

The area is in contact with the ground if A box exerts 10,000 Pa of pressure on the ground. If the box weighs 1000 N is 10 m².

( which is D/10 m²).

Step-by-step explanation:

so what is pressure?

In the physical sciences, pressure is defined as the stress at a point within a confined fluid or the perpendicular force per unit area. A 42-pound box with a bottom area of 84 square inches will impose pressure on a surface equal to the force divided by the area it is applied to, or half a pound per square inch.

Answer: 10,000 pa

Step-by-step explanation:

Pressure = Force / Area

Force = 10,000

Area = 1 m^2

Pressure = 10,000 / 1

Pressure = 10,000 pa.

Answer:

2

Step-by-step explanation:

whose possible values are − 2 , 1 , 2 , 3 , and 6 .

Answer:

3/2

Step-by-step explanation:

9/6

(9:3)/(6:3) = 3/2

6/4

(6:2)/(4:2) = 3/2

3/2

Answer:

a₄ = 15

Step-by-step explanation:

using the recursive relation [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 3 and a₁ = 6 , then

a₂ = a₁ + 3 = 6 + 3 = 9

a₃ = a₂ + 13= 9 + 3 = 12

a₄ = a₃ + 3 = 12 + 3 = 15

Answer:

a. 750 pages

b. 45 pages

Step-by-step explanation:

If you're decreasing 45 of something each day from 750, it makes sense that the 'something' is pages; instead of decreasing, it's reading.

So

a. 750 pages

b. 45 pages

Weekly paycheck of Catherine is $573.5 and her annual income is $29,904.01.

Unit rate is defined as the number of one quantity needed for a single other quantity.

In other words, if we know the unit rate, we can calculate any amount of one quantity corresponding to any amount of the other quantity by multiplying the unit rate with the number of other quantity.

Here unit rate of Catherine's pay = $15.50 per hour

Given that Catherine works 37 hours per week.

Weekly paycheck of Catherine = unit rate × number of hours per week

                                                    = 15.50 × 37

                                                    = $573.5

Annual Income of Catherine = Unit rate × number of hours per year

There are 52.143 weeks in a year.

Catherine works 37 hours per week.

Number of hours Catherine working in an year = 52.143 × 37 = 1929.291

Annual Income of Catherine = 15.50 × 1929.291

                                               = $29,904.01

Hence, calculation of student is wrong since the weekly paycheck is $573.5 and her annual income is $29,904.01.

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Answer:

80 degrees

Step-by-step explanation:

π=180 degrees

4π/9 =

4*180/9 =   ==> substitute 180 for π

720/9 = ==> simplify

80 degrees

y = 1, and x = -1

if you need to show your work:

if you combine the two equations together (eliminating x), it goes like this

-3x - 4y = -1

3x - y = -4

-5y = -5

y = 1

this means:

-3x - 4 = -1

-3x = 3

x= -1

and

3x - 1 = -4

3x = -3

x = -1

The required weight of the two elephants together is 43369 pounds.

Addition  is an approach to consolidating things and considering them all together.Addition  in math is a course of consolidating at least two numbers. Addends are the numbers added, and the outcome or the last response we get after the interaction is known as the total.

We have,

One elephant weighs 23,453 pounds, and the other elephant weighs 19,916 pounds.

To find total weight of two elephant together,we have to add them.

23,453 pounds + 19,916 pounds

43369 pounds

Thus, required weight of two elephant is 43369 pounds.

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Answer:

Step-by-step explanation:

Given an ABCD inscribed quadrilateral, where the AB side is the diagonal of the circum-circle of the quadrilateral, we can calculate various properties by using basic trigonometry. Firstly, let us determine the length of BD. Since BCDZ = 120° and BC = 3cm ,we can use Sine rule to find out BD which will be equal to 4 cm. Secondly, we need to find AB and AD sides lengths as well as other angles in order for our calculations to be complete. To do this we will use Cosine rule since all three sides are known: BC=3cm; CD=5cm;BD=4 cm . This gives us a value for angle CBD which is approximately 39° and consequently angle BAD is also 39° since they add up together (BAD+CBD)to 180 degrees due their being opposite each other on a straight line..Finally ,using cosine again with these new values gives us both AB(6)and AD(2).

To summarise : Lengths -AB: 6 cm ; BD : 4 cm ;AD 2CM   Angles - BCDZ :120 ° ; CBD & BAD :39 °

In conclusion , given an ABCD inscribed quadrilateral whose one side was already identified as its circumference diameter it was possible through simple trigonometric equations such s Sines Rule or Cosines Rule determine its remaining lengths ans angles accurately .

Answer:

c = 50°

Step-by-step explanation:

Since Triangle QRP is an isosceles triangle, the base angles of the triangle are equal.

Angle RQP = 180 - 115

= 65° (sum of angles on straight line)

Angle RPQ = Angle RQP = 65°

c = 180 - 65 - 65

= 50° (sum of angles in a triangle)

Answer:

[tex]\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12} K & t\\\cline{1-2} \vphantom{\dfrac12} 1 & 0\\\vphantom{\dfrac12} 2 & 7.3\\\vphantom{\dfrac12} 3&11.6 \\\vphantom{\dfrac12} 4& 14.6\\\vphantom{\dfrac12} 6&18.9 \\\vphantom{\dfrac12} 8& 21.9\\\vphantom{\dfrac12} 10& 24.2\\\vphantom{\dfrac12} 12&26.2\\ \cline{1-2}\end{array}[/tex]

See attachment for the graph.

Step-by-step explanation:    

Given equation for t:

[tex]t=\dfrac{\ln (K)}{0.095}[/tex]

Substitute the given values of K into the equation for t and round the answers to one decimal place:

[tex]\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12} K & t\\\cline{1-2} \vphantom{\dfrac12} 1 & 0\\\vphantom{\dfrac12} 2 & 7.3\\\vphantom{\dfrac12} 3&11.6 \\\vphantom{\dfrac12} 4& 14.6\\\vphantom{\dfrac12} 6&18.9 \\\vphantom{\dfrac12} 8& 21.9\\\vphantom{\dfrac12} 10& 24.2\\\vphantom{\dfrac12} 12&26.2\\ \cline{1-2}\end{array}[/tex]

To sketch the graph of the given function (see attachment):

Answer:

The intensity of the light is inversely proportional to the square of the distance from the source of light. Therefore, in this situation, where one light source has an intensity ten times that of the​ other, the distance from the stronger light source would be 0.7m before the total illumination​ is the least.

Step-by-step explanation:

Answer:

F + S + T = 24 F= 1st number, S = 2nd, T = 3rd

Step-by-step explanation:

T = 2S - 11

9F = 7 + 2S

divide by 9

F + (7+2S)/9

substitute for F and T

(7+2S)/9 + S + 2S -11 = 24

7+2S + 9S + 18S - 99 = 216

29S = 216 + 99 - 7 = 308

S = 308/29 = the 2nd number

T = 2S -11 = 616/29 -11 = 616/29 - 319/29 = 297/29 = 3rd number

F = (7+2S)/9 = (7 +616/29)/9 = 819/261 = 1st number

the 3 numbers are 819/261, 308/29 and 297/29

they sum to 819/261 + 308/29 + 297/29 = about 3.14 + 10.62 +10.24 = 24

F =( 7+2(10.62))/9 = (7+ 21.24)/9 = 28.24/9 = 314

S = 308/29 = 10.62

T = 2S-11 = 2(10.62) - 11 = 21.24-11 = 10.24

although odds are the problem may have been mis-copied or has a slight typo, with more integer type solutions in the corrected version.  If the problem had an 8 instead of  9,  (8F = 7+ 2S)    then F=3.5, S=10.5, T = 10 as exact answers, not rounded off.    3.5+10.5+ 10 = 24

First number: [tex]\frac{167}{21}[/tex];

Second number: [tex]\frac{142}{21}[/tex];

Third number: [tex]\frac{130}{14}[/tex].

First number: "x";

Second number: "y";

Third number: "z".

Equation 1. "The sum of three numbers is 24", hence:

[tex](1)x+y+z=24[/tex]

Equation 2. "The third is 11 less than 3 times the second.", hence:

[tex](2)z=3y-11\\ \\(2)-3y+z=-11[/tex]

Equation 3. "8 times the first is 4 less than 10 times the second.", hence:

[tex](3)8x=10y-4\\\\(3)8x-10y=-4[/tex]

[tex](1)x+y+z=24\\\\(2)-3y+z=-11\\\\(3)8x-10y=-4[/tex]

As you may see, the 3 variables don't always appear on all 3 equations. Therefore, we'll have to introduce them even though they don't appear. For this, we write the variable with a coefficient of 0 next to it

[tex](1)x+y+z=24\\\\(2)0x-3y+z=-11\\\\(3)8x-10y+0z=-4[/tex]

Using the coefficient of each variable in each equation, rewrite the system of equation into a matrix like this:

[tex]\left[\begin{array}{cccc}1&1&1&24\\0&-3&1&-11\\8&-10&0&-4\end{array}\right][/tex]

Check the attached image to see the steps to making this convertion.

a) Getting the 1 on column 1.

Since there's already a 1 there, we skip this step.

b) Getting the 0 on column 1.

Since there's already a 0 there, we skip this step.

c) Getting the 0 on column 1.

Multiply row 1 values by "-8" and add them to row 3. The result of these operations should be:

[tex]\left[\begin{array}{cccc}1&1&1&24\\0&-3&1&-11\\0&-18&-8&-196\end{array}\right][/tex]

d) Getting the 1 on column 2.

Since we are working with column 2 and row 2, you may use the pivot value "-3" (the one that corresponds to the intersection of column 2 and row 2) and divide row 2 by itself to obtain a 1. Result is the following:

[tex]\left[\begin{array}{cccc}1&1&1&24\\0&1&-\frac{1}{3} &\frac{-11}{-3} \\0&-18&-8&-196\end{array}\right][/tex]

e) Getting the 0 on column 2.

Multiply row 2 by "18" and add it to row 3. Resulting table is:

[tex]\left[\begin{array}{cccc}1&1&1&24\\0&1&-\frac{1}{3} &\frac{-11}{-3} \\0&0&-14&-130\end{array}\right][/tex]

f) Getting the 1 on column 3.

We are working with column 3 and row 3, the intersection value is "-14" and we may use it as a pivot value. Hence, we may divide row 3 by "-14" in order to obtain the number 1 in column 3. Final table is:

[tex]\left[\begin{array}{cccc}1&1&1&24\\0&1&-\frac{1}{3} &\frac{-11}{-3} \\0&0&1&\frac{-130}{-14}\end{array}\right][/tex]

Starting from the bottom up, take the expression of the resulting matrix and calculate the values of each variable.

a) From row 3 we have:

[tex]0x+0y+z=\frac{-130}{-14} \\ \\z=\frac{130}{14}\\ \\[/tex]

b) From row 2 we have:

[tex]0x+y-\frac{1}{3} z=\frac{-11}{-3} \\ \\y-\frac{1}{3} z=\frac{11}{3}\\ \\y-\frac{1}{3} (\frac{130}{14} )=\frac{11}{3}\\ \\y-\frac{130}{42} =\frac{11}{3} \\ \\y=\frac{11}{3}+\frac{130}{42}\\\\y=\frac{11*14}{3*14}+\frac{130}{42}\\ \\y=\frac{154}{42}+\frac{130}{42}\\ \\y=\frac{284}{42} \\\\y=\frac{142}{21}[/tex]

c) From row 1 we have:

[tex]x+y+z=24\\ \\x+\frac{142}{21}+\frac{130}{14} =24\\ \\x=24-\frac{142}{21}-\frac{130}{14}\\ \\x=\frac{1008}{42} -\frac{284}{42} -\frac{390}{42} \\ \\x=\frac{167}{21}[/tex]

Equation 1: [tex]\frac{167}{21} +\frac{142}{21} +\frac{130}{14} =24[/tex] Correct.

Equation 2: [tex]-3(\frac{142}{21} )+\frac{130}{14} =-11[/tex] Correct.

Equation 3: [tex]8(\frac{167}{21} )-10(\frac{142}{21} )=-4[/tex] Correct.

First number: [tex]\frac{167}{21}[/tex];

Second number: [tex]\frac{142}{21}[/tex];

Third number: [tex]\frac{130}{14}[/tex].

Important: Check the attached Excel sheet to see the changes made in the matrix.

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The Total volume of sand in cubic inches needed for the playground when the height of the sand in each sandbox is 4.5 in is; 2700 in³

We are told that the height of the sand, in inches (in.), is proportional to

the volume of sand.

Let the volume be denoted as V

Let the height be denoted as h

Thus;

V ∝ h

Then to equate this, we will have a constant of proportionality;

V = kh

where k is constant of proportionality

When the height of the sand is 1.25 in., the volume of the sand is 280 in³ and this gives;

280 = 1.25k

k = 250/1.25

k = 200

Now, ware told that the height of sand in a box is now 4.5 inches and so;

V = 200 * 4.5

V = 900 in³

Since the playground has 3 of such boxes, then we can say that;

Total volume of sand on the playground = 900 * 3 = 2700 in³

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Answer:

p = 82°

Step-by-step explanation:

Since Triangle HIJ is an isosceles triangle, the base angles of the triangle are equal.

Angle IHJ = 180 - 131

= 49° (sum of angles on a straight line)

Angle IJH = Angle IHJ = 49°

p = 180 - 49 - 49

= 82° (sum of angles in a triangle)