What is the probability that
both events will occur?
A coin and a die are tossed.
Event A: The coin lands on tails
Event B: The die is not a 6
P(A and B) = P(A) • P(B)
P(A and B) = [?]
Enter as a decimal rounded to the nearest hundredth.

The value of the trigonometric ratio indicated in the question for each are:

1) tan Z = 3/4, 2) sin C = 3/4, 3) tan Z = 20/21, 4) cos X = 3/5, 5) cos A = 5/13 and 6) tan Z = 3/4

Given are certain right angled triangles. We have to find the value of each of the trigonometric ratio indicated.

1) tan Z = opposite side / adjacent side

            = YX / YZ

            = 24/32 = 3/4

2) sin C = Opposite side / Hypotenuse

             = AB / AC

             = 24/40 = 3/5

3) tan Z = opposite side / adjacent side

             = YX / YZ

             = 20/21

4) cos X = adjacent side / Hypotenuse

              = XY / XZ

              = 15/25 = 3/5

5) cos A = adjacent side / Hypotenuse

              = AB / AC

              = 15/39 = 5/13

6) tan Z = opposite side / adjacent side

             = YX / YZ

             = 27/36 = 3/4

Hence the ratios are found.

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It is essential for a table to meet both criteria to represent a valid function.

Based on the given information, it appears that the table in question does not represent a function. This is because a function requires each element in the domain to be associated with exactly one element in the range (Statement B).

If any element in the domain has more than one corresponding element in the range, it violates the definition of a function.

Additionally, the table fails to show a function because each output does not have exactly one input (Statement D). In a true function, every output value should be associated with only one input value. If any output has multiple inputs, it indicates that the table is not a function.

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A specific X-value for the solution ,-4 is not equal to -3/2.

The x-value of the solution to the system of equations, we need to solve the given equation and the line represented by the data in the table. Let's begin by examining the first equation, 2x + 4y = 0.

We can rewrite this equation in terms of y:

4y = -2x

y = (-2/4)x

y = (-1/2)x

Now, let's use the data from the table to create a system of equations:

For the first data point (-1, 8):

y = (-1/2)x

8 = (-1/2)(-1)

8 = 1/2

Since 8 is not equal to 1/2, the first data point does not satisfy the equation.

For the second data point (3, -4):

y = (-1/2)x

-4 = (-1/2)(3)

-4 = -3/2

Again, -4 is not equal to -3/2, so the second data point does not satisfy the equation.

We can continue this process for the remaining data points, but from the information given, it seems that none of the data points satisfy the equation. Therefore, there is no solution to the system of equations.

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Answer:

To find the volume of the empty space in the box, we need to subtract the volume of the basketball from the volume of the box.

Volume of the basketball = (4/3) * π * r^3

= (4/3) * 3.14 * (4.75 in)^3

Volume of the box = side length^3

= (9.5 in)^3

Empty space volume = Volume of the box - Volume of the basketball

Empty space volume = (9.5 in)^3 - (4/3) * 3.14 * (4.75 in)^3

Calculating this equation will give us the volume of the empty space in cubic inches. Rounding the answer to the nearest cubic inch will provide the amount of packing foam needed to fill the empty space.

The area of the rectangle with a Length of 6 cm and a width of 3 cm is 18 cm².

The area of a rectangle, we use the formula:

Area = length × width

In this case, the length is given as 6 cm and the width is given as 3 cm. Substituting these values into the formula, we get:

Area = 6 cm × 3 cm

Multiplying these values together, we get:

Area = 18 cm²

Therefore, the area of the rectangle with a length of 6 cm and a width of 3 cm is 18 cm².

Looking at the answer choices, we see that (c) 18 cm² is the correct answer.  the area is expressed in square centimeters (cm²) because the lengths are in centimeters.

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A. The distributions of the periods is that using the five number summary is that

B. The box and whisker plot of the periods is attached

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

7th Period

66, 72, 77, 78, 78, 80, 82, 84, 84, 87, 88, 88, 89, 89, 90 92, 92, 93, 94, 94 96, 96

3rd Period

52, 60, 62, 64, 64, 65, 68, 71, 72, 74, 75, 76, 78, 79, 83, 84, 85, 88, 89, 93, 94, 97

The distributions of the periods will be compared using the five-number summaries

Using a graphing tool, the five-number summaries are:

7th Period

3rd Period

The box and whisker plot of the periods is added as an attachment

From the box and whisker plot attached, we can see the five-number summaries of the periods

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Answer:

C.

Step-by-step explanation:

I think the answer is C. or a point because a point is like a location in space and the question is asking which word means a location in space.

The value of b from the Equation 7b - 20 - 4b = -5 is 5.

An equation is a mathematical statement that states the equality between two expressions. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, etc.

We have the Equation:

7b - 20 - 4b = -5

Now, add 20 both side we get

7b - 20 - 4b + 20 = -5 + 20

7b  - 4b = 15

Now, combine like terms

3b = 15

Now, divide both side by 3 we get

3b/3 = 15/3

b= 5

Thus, the value of b is 5.

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Answer:

[tex]x[/tex] × 5 = 89

  ∴ [tex]x[/tex] = 89 ÷ 5

        = [tex]\frac{89}{5}[/tex] (improper fraction)

Answer:

Therefore, Marge's finance charge on the computer is $97.

Step-by-step explanation:

To calculate Marge's finance charge on the computer, we need to find the total amount she will pay for the computer through the installment plan and subtract the original purchase price.

Down payment = $100

Total amount paid for the computer = Down payment + Monthly payment * Number of months

Total amount paid = $100 + ($58 * 12)

Total amount paid = $100 + $696

Total amount paid = $796

Finance charge = Total amount paid - Purchase price

Finance charge = $796 - $699

Finance charge = $97

Therefore, Marge's finance charge on the computer is $97.

Answer: To determine when the delayed watch will meet the accurate watch again, we need to find the number of hours it takes for the delayed watch to catch up by 9 minutes.

Since the delayed watch falls behind by 9 minutes per hour, it will catch up by 9 minutes after every hour. Therefore, it will take 1 hour for the delayed watch to catch up by 9 minutes.

Hence, the delayed watch will meet the accurate watch again after 1 hour.

Submit the number: 1

Answer:

The selling price of the car is $152,220.

Step-by-step explanation:

To find the selling price of a car that is sold at a loss of 14% on the cost price, we can follow these steps:

Calculate the amount of the loss:

Loss = 14% of the cost price

Loss = 14/100 * $177,000

Subtract the loss from the cost price to find the selling price:

Selling Price = Cost Price - Loss

Selling Price = $177,000 - (14/100 * $177,000)

Simplify the expression:

Selling Price = $177,000 - ($24,780)

Selling Price = $152,220

Answer:

18 ft

Step-by-step explanation:

area = length × width

length = area/width

length = 18 ft² / 3 ft

length = 6 ft

perimeter = 2(length + width)

perimeter = 2(6 ft + 3 ft)

perimeter = 2(9 ft)

perimeter = 18 ft

Answer:

[tex]\mathrm{18ft.}[/tex]

Step-by-step explanation:

[tex]\mathrm{We\ have,}\\\mathrm{Width\ of\ rectangle(b)=3ft.}\\\mathrm{Area\ of\ rectangle(A)=18\ sq.\ ft}\\\mathrm{Let\ the\ length\ of\ the\ rectangle\ be\ 'l'\ and\ its\ perimeter\ be\ 'P'.}\\\mathrm{Now,}\\\mathrm{Area\ of\ rectangle=l\times b}\\\mathrm{or,\ 18=l\times 3}\\\mathrm{or,\ l=6ft.}\\\mathrm{So\ the\ length\ of\ rectangle\ is\ 6\ feet.}\\\mathrm{Finally,\ perimeter\ of\ rectangle\ is\ given\ by\ the\ formula:}\\\mathrm{P=2(l+b)=2(6+3)=2(9)=18ft.}\\[/tex]

[tex]\mathrm{\therefore Perimeter\ of\ rectangle\ is\ 18\ feet.}[/tex]

The area of the triangle FGH is equal to  13√10 unit²

Given that the vertices;

F(-5,-7), G(-2,-5), and H(-6,-2)

We have to find the area of the triangle as;

Area of triangle = 1/2bh²

Here,

Area of triangle FGH = 1/2 (GH) (FG)²

Now,

Length of FG =  √26

Length of GH =  √10

Then,

Area of triangle FGH = 1/2 (GH) (FG)²

Area of triangle = 1/2 × √10 × √26²

Area of triangle = 1/2 × √10 × 26

Area of triangle FGH = 13√10

Therefore,

The area of the triangle FGH = 13√10 unit²

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The volume of the larger cylinder is 201 cm³.

Given that,

Ratio of the heights of two cylinders = 1 : 3

We have to find the volume of the larger cylinder.

The formula to find the volume of a cylinder is,

Volume of cylinder = π r² h, where r is the radius and h is the height of the cylinder.

Let height of smaller cylinder = h

Height of larger cylinder = 3h

π r² (h) = 67

Volume of larger cylinder = π r² (3h)

                                          = 3 [π r² (h)]

                                          = 3 × 67

                                          = 201 cm³

Hence he volume is 201 cm³.

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Answer:

(12 × 3) × 8 = 12 × (3 × 8)

Step-by-step explanation:

The associative property of multiplication states that the way in which factors are grouped in a multiplication expression does not change the product. In other words, if we have three or more numbers to multiply, it doesn't matter which order we multiply them in.

Out of the given number sentences, the example of the associative property of multiplication is:

(12 × 3) × 8 = 12 × (3 × 8)

This is because we can group the factors in either of the two ways and get the same product.

Hope this helps!

The minimum amount that Mr. Khumalo can be charged for the cash deposit is R99.12.

To calculate the minimum amount charged for a cash deposit over the counter at Standard Bank, we'll use the given information.

The deposit charge includes an initial fee of R10.39, and an additional fee of K1.95 per R100 or part thereof, with a minimum charge of R16.00.

First, we calculate the additional fee based on the deposit amount:

Additional fee = (Deposit amount / 100) x K1.95

For Mr. Khumalo's deposit of R4,550.00:

Additional fee = (4,550.00 / 100) x 1.95

Additional fee = 88.725

Next, we compare the additional fee to the minimum charge of R16.00:

If the additional fee is less than the minimum charge, the minimum charge applies. Otherwise, the additional fee is charged.

Since the additional fee of R88.725 is greater than the minimum charge of R16.00, the additional fee will be charged.

Finally, we add the initial fee and the additional fee to get the total charge:

Total charge = Initial fee + Additional fee

Total charge = R10.39 + R88.725

Total charge = R99.115

Therefore, the minimum amount that Mr. Khumalo can be charged for the cash deposit is R99.12.

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Answer:

5 weeks

Step-by-step explanation:

the two linear equations are:

sibling (A)      and  sibling (B)

y = 10x + 25   and y = 5x + 50

where y = mx + c

and x represents the number of weeks

after how many weeks will their savings accounts have the same amount of money i.e. for which value of x will both equations have the same value

inserting the value of x in both equations:

for x = 2.5  A = 50 and B = 62.5

for x = 5     A = 75  and B = 75

for x = 15    A = 175 and B = 125

for x = 75   A = 775 and B = 425

thus, after 5 weeks both siblings A and B will have the same amount of money in their accounts

Total amount of money in the account will be $456.

Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest.

The formula for simple interest is: Simple Interest = Principal × Rate × Time

Principal (P) is $300

Rate (R) is 6.5%

Time (T) is 8 years.

Simple Interest = $300 × 0.065 × 8

Simple Interest = $156

Total Amount = Principal + Simple Interest

Total Amount = $300 + $156

Total Amount = $456.

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The  local minima at (-2, 0) and (-3, 0), and the local maxima at (1, 3) and (0, 3).

To determine the local minima and maxima of the polynomial function based on the given points:

Since the point (-2, 0) is on the graph, it represents a local minimum.

Since the point (1, 3) is on the graph, it represents a local maximum.

Since the point (-2, 0) is on the graph, it represents a local minimum.

Since the point (0, 3) is on the graph, it represents a local maximum.

Since the point (-3, 0) is on the graph, it represents a local minimum.

Since the point (1, 3) is on the graph, it represents a local maximum.

Since the point (-3, 0) is on the graph, it represents a local minimum.

Since the point (0, 3) is on the graph, it represents a local maximum.

Therefore, based on the given points, the local minima at (-2, 0) and (-3, 0), and the local maxima at (1, 3) and (0, 3).

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Answer:

5*9=45

9\45=5

5/45=9

Step-by-step explanation:

Answer:

20 lawyers

Step-by-step explanation:

48 ÷ 12 = 4

which means every year 4 lawyers are hired

5 × 4 = 20

so this means the law firm has hired 20 lawyers in the last 5 years

The cross-price elasticity of demand between good X and good Y will be 0.5. Thus, the correct option is A.

Given that5:

Old Quantity = 1,100

New Quantity = 900

The percentage change of good Y is calculated as,

P = ((900 - 1,100) / 1,100) * 100

P = (-200 / 1,100) * 100

P = -18.18%

Next, let's calculate the percentage change in the price of good X:

Old Price = GH¢6

New Price = GH¢4

The percentage change in the price of good X is calculated as,

P = ((4 - 6) / 6) * 100

P = (-2 / 6) * 100

P = -33.33%

The cross-price elasticity of demand is calculated as,

⇒ (-18.18% / -33.33%)

⇒ 0.546 or 0.5

Thus, the correct option is A.

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The correct statement for the transformation is,

⇒ Vertical translation 12 units up.

Since, A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

We have to given that;

After transformation the function is,

⇒ 7 √(x + 9) + 12

Let the parent function is,

⇒ y = √x

So, By given function we can see that,

12 is add to the function.

Hence, The correct statement for the transformation is,

⇒ Vertical translation 12 units up.

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i think option c must be the answer

The value of the underlined digit in the number 27,416,385.( 4 is the underlined number.) is the hundred thousandths place.

The symbols, from 0 to 9 can be described as a digit. For instance, the numbers 2 and 3 are used to represent the number 23.  however amount is represented by a number.

It should be noted that It may be expressed using one, two, three, or even more digits however only single symbol used to represent a number is a digit in the case above we can see that 4 is the hundred thousandths place.

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The monthly loan payment for a $60,000 loan with a $4,000 down payment, 13% interest rate, and a term of 60 months is approximately $1,289.49.

To calculate the monthly loan payment, we need to use the loan amount, down payment, interest rate, and term.

Loan amount: $60,000

Down payment: $4,000

Principal amount: Loan amount - Down payment = $60,000 - $4,000 = $56,000

Interest rate: 13% per annum (or 0.13 as a decimal)

Monthly interest rate: 13% / 12 = 0.0133 (approx.)

Term: 60 months (5 years)

Now, let's calculate the monthly loan payment using the formula for a fixed-rate loan:

Monthly payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

P = Principal amount

r = Monthly interest rate

n = Total number of payments

Substituting the values into the formula:

Monthly payment = $56,000 * (0.0133 * (1 + 0.0133)^60) / ((1 + 0.0133)^60 - 1)

Using a calculator, the approximate monthly loan payment comes out to be $1,289.49.

Therefore, the monthly loan payment for a $60,000 loan with a $4,000 down payment, 13% interest rate, and a term of 60 months is approximately $1,289.49.

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The triangle is solved using the Pythagoras theorem

Given data ,

Let's denote the age of the groom as G. According to the tradition in the Pythagorean Planet, the sum of the squares of the bride's age (33) and the groom's age (G) combined should be equal to the square of the bride's father's age (F).

The equation representing this condition is:

33² + G² = F²

We are given that at the time of the wedding, the bride's father was over 500 years old. Let's denote his age as F and rewrite the equation accordingly:

33² + G² = (500 + F)²

Hence , the equation is 33² + G² = (500 + F)²

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