3.14+24 is the sum rational or irrational?

The expected joint frequencies are

From the question, we have the following parameters that can be used in our computation:

The table of values

Also, we have

People = 160

This means that

Male and Drama = 12.5% * 160

Male and Drama = 20

Male and Comedy = 25% * 160

Male and Comedy = 40

Female and Drama = 46.9% * 160

Female and Drama = 75

Female and Comedy = 15.6% * 160

Female and Comedy = 25

In conclusion, we have

Because the expected and the joint frequencies are not the same, gender is not independent of movie type

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Being male and preferring Brand A are independent, as:

P(male|Brand A) = P(male).

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

From the table, we are already given the relative frequencies, hence we must simply identify the desired outcomes and the probability of being male is given as follows:

0.5 + 0.15 = 0.65.

The conditional probability of being male, given that the person prefers brand A, is given as follows:

P(male|Brand A) = P(male and Brand A)/P(Brand A) = 0.5/0.8 =  0.625.

As the probabilities are equal, the events are independent.

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Answer:

3x = 6y

Step-by-step explanation:

8 - 2y = 6y and 3x is by itself so it would be 3x is equal to 6y.

The rectangular piece of paper has a perimeter of 48.34 units.

The perimeter of a rectangle is given by the sum of the lengths of all its sides.

To find the perimeter of this rectangular sheet of paper, we need to add up the lengths of its four sides.

The length of the rectangle is 12 + 1 by 2 = 13.5 units, and its width is 10 + 2 by 3 = 11.67 units.

Therefore, the perimeter of the rectangle is:

P = 2(length + width)

P = 2(13.5 + 10.67)

P = 2(24.17)

P = 48.34 units

So the perimeter of the rectangular sheet of paper is 48.34 units.

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Step-by-step explanation:

a probability is always the ratio

"desired" cases / totally possible cases

the totally possible cases here are 100.

now, the question focuses on non-defective units.

how many out of the 100 are non-defective ?

well, 100 - 12 = 88 units.

so, the probability to select a non-defective (= working) unit is

88/100 = 22/25 = 0.88

in other words, as a mean and expected value, in 88 of 100 attempts, or in 22 of 25 attempts you will select a non-defective unit.

There are 100 DVRs in the inventory, and 12 of them are defective. Therefore, the number of non-defective DVRs is:

100 - 12 = 88

The probability of selecting a non-defective DVR can be found by dividing the number of non-defective DVRs by the total number of DVRs:

P(non-defective DVR) = number of non-defective DVRs / total number of DVRs

                     = 88 / 100

                     = 0.88

Therefore, the probability of randomly selecting a DVR that is not defective is 0.88, or 88%.

Answer:

Theoretical Probability

Step-by-step explanation:

Total number of possible outcomes

Answer: r=2sinθ.

Step-by-step explanation:To convert to polar coordinates, we use the relationships

xy=rcosθ=rsinθ.

Substituting these into the given equation, we find

x2+y2(rcosθ)2+(rsinθ)2r2cos2θ+r2sin2θ=2y=2(rsinθ)=2rsinθ

Factoring and applying the Pythagorean identity, we obtain

r2(cos2θ+sin2θ)r2(1)r2=2rsinθ=2rsinθ=2rsinθ

Dividing both sides by r yields

r2rr=2rsinθr=2sinθ

Thus, a polar equation representing the given function is r=2sinθ.

The value of k is given as follows:

k = 10.

The quadratic function in the context of this problem is defined as follows:

y = 3x² - 8x + 2k + 1.

The coefficients are given as follows:

a = 3, b = -8 and c = 2k + 1.

The product of the roots of  quadratic function is given as follows:

c/a.

For this problem, the product is of 7, hence the value of k is obtained as follows:

(2k + 1)/3 = 7

2k + 1 = 21

2k = 20

k = 10.

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The monthly payment required to made for the balance on credit card of $2400 with 13.5% of compound interest is given by $114.66.

Balance on credit card = $2,400

Rate of interest = 13.5%

Time period = 2 years

Let us consider monthly payment be 'M' required to pay off a balance 'B'.

Time period of time 'n' with monthly interest rate 'r' .

Use the formula of monthly compounding is ,

M = r ×  B / (1 - (1+r)⁻ⁿ )

Here, the balance is B = $2,400,

The interest rate is r = 0.135/12 = 0.01125 since the interest is compounded monthly.

And the period of time is n = 2 years ×  12 months/year

                                             = 24 months.

Plugging in these values, we get,

M = 0.01125 × $2,400 / (1 - (1+0.01125)⁻²⁴)

Simplifying this expression, we get,

⇒ m = 27 /(1 - (1.01125)⁻²⁴)

⇒ m = 27 / ( 1- 0.7645 )

⇒ m = $114.66

Therefore, the monthly payment required to pay off the $2,400 balance with compound interest in two years is $114.66.

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The measures of angles and classification for the triangles are:

(20). m∠A = 33, m∠B = 66, m∠C = 81. Acute triangle

(21) m∠R = 20, m∠S = 140, m∠T = 20. Isosceles triangle

(22). m∠W = 75, m∠Y = 15, m∠Z = 90. Right triangle.

The sum of the interior angles of a triangle is equal to 180°, thus;

(20). x + 2x + 2x + 15 = 180°

x = 165/5

x = 33°

m∠A = 33

m∠B = 2(33) = 66

m∠C = [2(33) + 15] = 81

This is an acute triangle, as all its angles are less than 90°.

(21). x + 7x + x = 180°

9x = 180

x = 20

m∠R = 20

m∠S = 7(20) = 140

m∠T = 20.

This is an Isosceles triangle, because it have two equal base angles.

(22). x - 15 + 2x - 165 + 90 = 180°

3x - 90 = 180°

x = 270/3

x = 90.

m∠W = (90 - 15) = 75

m∠Y = [2(90) - 165] = 15

m∠Z = 90.

This is a Right triangle because it as one of its angle equal to 90°.

Therefore, the measures of angles and classification for the triangles are:

(20). m∠A = 33, m∠B = 66, m∠C = 81. Acute triangle

(21) m∠R = 20, m∠S = 140, m∠T = 20. Isosceles triangle

(22). m∠W = 75, m∠Y = 15, m∠Z = 90. Right triangle.

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The Subtraction property of equality justifies the conclusion based on the given information.

The subtraction property of equality states that when the same number is subtracted from both sides of an equality, then the two sides of the equation still remain equal. In simple words, we can say that when a number is subtracted from one side of an equation, the same number must be subtracted from the other side of the equality.

if a = b

then;

a-c = b-c

We have:

If x + 5 = 15

By subtraction property of equality:

Subtract 5 from both sides we have;

x = 10

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Answer:

3

Step-by-step explanation:

The answer is three because u need to simply the fractions

[tex]7^n - 1[/tex] is divisible by 6 for every positive integer n.

To prove that [tex]7^n - 1[/tex] is divisible by 6 for every positive integer n, we will use mathematical induction.

First, we will check the base case, n = 1:

[tex]7^1 - 1 = 6[/tex], which is divisible by 6.

Now, we assume that [tex]7^k - 1[/tex]is divisible by 6 for some positive integer k. This means that there exists an integer m such that:

[tex]7^k - 1 = 6m[/tex]

Next, we need to show that this implies that 7^(k+1) - 1 is also divisible by 6. We can use the following algebraic manipulation:

[tex]7^{k+1} - 1 = 7*7^k - 1 = 6\\7^k + (7^k - 1)[/tex]

Since we know that [tex]7^k - 1[/tex] is divisible by 6 (by the induction hypothesis), we can substitute 6m for [tex]7^k - 1[/tex] in the above equation:

[tex]7^{k+1} - 1 = 67^k + (7^k - 1) = 67^k + 6m = 6(7^k + m)[/tex]

This shows that [tex]7^{k+1} - 1[/tex] is also divisible by 6, since it is a multiple of 6. Therefore, by mathematical induction, we can conclude that [tex]7^n - 1[/tex] is divisible by 6 for every positive integer n.

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Answer:

(5,5π/4)

(5,−3π/4)

(−5,π/4)

(−5,−7π/4)

Step-by-step explanation:The correct answer is:

r = 5 units (distance from the pole)

θ = 5π/4 radians (angle measured counterclockwise from the ray θ = 0)

Note: The polar coordinates for point A on the given graph are r = 5 and θ = 5π/4. The r-value represents the distance from the pole to the point, and the θ-value represents the angle measured counterclockwise from the reference ray θ = 0.

Sharon's employer deducts taxes from her salary to pay the federal government directly, which is a type of payroll tax. Nelson's company pays taxes based on a percentage of profits for the year, which is a type of corporate tax.

Priscilla pays more than the value listed on the price tag of a summer dress, which is a type of sales tax. Lincoln pays taxes directly to the government for the land he owns, which is a type of property tax.

Payroll taxes are levied on the earnings of employees and are used to fund social security, Medicare, and other federal and state programs. Corporate taxes are taxes on the profits earned by businesses.

Sales taxes are levied on the price of goods or services sold to consumers. Property taxes are levied on real estate owned by individuals or businesses based on the assessed value of the property.

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Answer:for the one in the middle, that one is 5.0, for the one in the top, that one is 7, and for the bottom one, that one is 50

Step-by-step explanation:

The value of angle k is 129⁰.

The value of angle b is 64.5⁰.

The value of angle b and angle k is calculated by applying the following principle of intersecting chord theorem.

k + 113 + 118 = 360 (sum of angles in a circle)

k + 231 = 360

k = 360 - 231

k = 129⁰

The value of angle b is calculated by applying the principle of intersecting chord theorem.

b = ¹/₂ arc k

b = ¹/₂ x 129

b = 64.5⁰

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Answer: A, D

Step-by-step explanation:

We have sinx cosx = -1/4. This means that either sinx = -1/2 and cosx = 1/2 or sinx = 1/2 and cosx = -1/2. In the first case, we get x = 7pi/6 + 2npi or x = 11pi/6 + 2npi. In the second case, we get x = 7pi/12 + 2npi or x = 17pi/12 + 2npi. Therefore, the solutions are x = 7pi/12 + npi and x = 11pi/12 + npi. So, options A and D are correct. Options B and C are not solutions to the given equation.

Answer:

The easiest method to remember when dividing fractions is Keep Change Flip (KCF)

Step-by-step explanation:

I wrote out some examples of KCF. Once you use KCF, you just multiply the fractions normally and then don't forget to write the improper fractions (ex: 12/7) as a mixed number (1 5/7)

If you have any questions about the steps just let me know. I hope this helps ^-^

We do not need both the Celsius and Fahrenheit formulas

From the question, we have the following parameters that can be used in our computation:

The temperature equations

The general rule is that we need any of the temperature units to find the other temperature unit

This in other words means that we do not need both temperature units to find any of these two temperature units

Hence the statement is false

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The total value of the annuity in 26 years is 179163.85 dollars.

Given that, Deandre deposits $97 each month in an annuity that pays 7.7 % interest, compounded quarterly.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].

Here, 26 years = 26×4

= 104

Now, A=97(1+7.5/100)¹⁰⁴

A=97(1+0.075)¹⁰⁴

A=97(1.075)¹⁰⁴

A=97×1847.05

A=$179163.85

Therefore, the total value of the annuity in 26 years is 179163.85 dollars.

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The value of x for the intersecting chords is derived to be 14 which makes option C correct.

The property of intersecting chords states that in a circle, if two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

x × 32 = 16 × 28

32x = 448

32x/32 = 144/32 {divide through by 32}

x = 14

Therefore, the value of x for the intersecting chords is derived to be 14

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After burning for x hours, the candle's length, y, is calculated using the formula: y = 9 - (1/2)x.

Let y represent the length of the candle that is still burning after burning for x hours.

Since the candle burns at a rate of 1/2 inch per hour, we can use the following equation to explain the connection between the candle's length and the number of hours burned:

y = 9 - (1/2)x

Here, 9 represents the original length of the candle, and (1/2)x represents the length of the candle burned after x hours.

By subtracting the length burned from the original length, we obtain the length remaining after x hours.

Therefore, the function that determines the length of the candle, y, after burning for x number of hours is:

y = 9 - (1/2)x

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Answer:

A= 7

B= 4

C= 10

D= 0

E= 13

answers in attachment below

Answer:

Given equations are,

5x+2y=−2        (1)

3x−5y=17.4      (2)

Multiply equation (1) by 5 and equation (2) by 2, we get,

5(5x+2y)=5×−2

∴25x+10y=−10          (3)

2(3x−5y)=2×17.4

∴6x−10y=34.8          (4)

Adding equations (3) and (4), we get,

31x=24.8

∴x=

31

24.8

​

Put this value in equation (1), we get,

5(

31

24.8

​

)+2y=−2

∴

31

124

​

+2y=−2

∴2y=−2−

31

124

​

∴2y=

31

−186

​

∴y=

31

−93

​

Step-by-step explanation:

The composition of functions is solved and gof ( -7 ) = 1,286

Given data ,

Let the first function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = 13 - 2x

Let the second function be represented as g ( x )

Now , the value of g ( x ) is

g ( x ) = 2x² - 6x - 10

Now , g o f ( x ) = 2 ( 13 - 2x )² - 6 ( 13 - 2x ) - 10

On simplifying , we get

g o f ( x ) = 2 ( 169 + 4x² - 52x ) - 78 + 12x - 10

g o f ( x ) = 250 + 8x² - 92x

Now , the composition of function is

g o f ( -7 ) = 8 ( -7 )² - 92 ( -7 ) + 250

g o f ( -7 ) = 392 + 894

g o f ( -7 ) = 1,286

Hence , the function is g o f ( -7 ) = 1,286

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The value of x in the intersecting secant and tangent lines is 40 degrees

From the question, we have the following parameters that can be used in our computation:

Intersecting secant and tangent lines

Using the theorem of intersecting secant and tangent lines, we have

x = 1/2 * difference of the arcs

Substitute the known values in the above equation, so, we have the following representation

x = 1/2 * (170 - 90)

Evaluate

x = 40 degrees

Hence, the value of x is 40

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The value of -5/6 ÷( -1/4) is 3 1/3

A fraction is a part of a whole. it consist of upper part( numerator) and lower part denominator.

In a simple fraction, both numerator and denominator are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Solving -5/6 ÷( -1/4)

-5/6 × -4/1

= 20/6

= 10/3

= 3 1/3

therefore the value of the expression is 3 1/3

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The volume of the file cabinet in this problem is given as follows:

V = 8 and 7/10 cu ft.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The dimensions for this problem are given as follows:

2.167 ft, 1.5 ft and 2.67 ft.

Hence the volume of the prism is given as follows:

V = 2.167 x 1.5 x 2.67

V = 8.7 ft³.

As a mixed number, the volume is given as follows:

V = 8 and 7/10 cu ft.

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The required rate of simple interest is 1.75%.

Here, we have,

(Principal + Interest) is a straightforward interest equation.

A = P(1 + rt)

Where: A is the sum of the accrued principal and interest.

Principal Amount is P.

I is the interest rate.

r is the annual percentage rate of interest, or R/100.

R is the annual percentage rate of interest; R = r * 100 t is the length of time involved in months or years.

Since I = Prt,

the initial formula A = P(1 + rt) evolved from A = P + I to A = P + Prt,

which may be represented as A = P(1 + rt).

Given: Principal is $1,300

Rate is 7% and the amount earned that is A-P is $159.25.

A = P(1 + rt)

Therefore substituting the values in the above mentioned equation, we get:

159.25= 1300(1+r×7)

On solving we get,

r= 1.75%

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complete question:

At the Blue Bank, Barry would earn $159.25 in simple interest in 7 years after depositing $1,300.

What rate of simple interest is offered at the

Blue Bank?