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3 years ago

A rectangle is inside a circle with a 5cm radius.

Mathematics

1 answer:

Mumz [18]3 years ago

7 0

Answer:

The area of the shaded region is 30.5 cm^2.

Step-by-step explanation:

So, first you need to find the area of the circle and rectangle separately.

The diagram shows that the circle radius is 5 cm; use the formula pi*r^2 to solve for the area.

The area of this circle:

3.14*5^2

3.14*25

=78.5 cm

The area of this rectangle:

8 cm*6 cm = 48 cm

Now subtract the rectangle's area from the area of the circle.

78.5-48 = 30.5 cm

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Two cards are drawn with replacement, one after the other, and the outcomes recorded. What is the probability that at least one

babymother [125]

Answer:

The probability is 0.231

Step-by-step explanation:

In this question, we are tasked with calculating the probability that out of two cards drawn with replacement from a pack of cards , at least one of the two is a face card.

In a standard pack of cards, there are 52 cards.

Now let’s calculate the number of face cards we have.

There are 12 face cards in a pack of cards. There are 4 of each of Jack, Queen or King

The probability of drawing a face card is 12/52 = 3/13

Now, we want to calculate the probability of at least one of the cards drawn are face cards.

Mathematically, what we are needing to calculate is

Probability of drawing a single face card or probability of the two being a face card

Now let’s calculate.

The probability of the first card drawn being a face card is 3/13. The probability of the second card not being a face card will be 1-3/13 = 10/13

The joint probability under this first set of condition will be 3/13 * 10/13 = 30/169

Now, for the second condition, here we are considering that both cards drawn are face cards. What we have is 3/13 * 3/13 = 9/169

Now in probabilities, whenever we are having the statement or, we add the probabilities together

Thus, the probability here would be 30/169 + 9/169 = 39/169 = 3/13

In decimal this will be 0.231

8 0

3 years ago

Use the quadratic formula to findntge roots of the equation 2X2-28X+98=0

JulijaS [17]

The answer to that equation is {7,7}

3 0

3 years ago

Which of the following is the graph of y=sqr root -x-3

Elan Coil [88]

Answer:

The graph in the attached figure

see the explanation

Step-by-step explanation:

we have

$y=\sqrt{-x-3}$

we know that

The radicand must be greater than or equal to zero

$(-x-3)\geq 0$

solve for x

Adds 3 both sides

$-x\geq 0+3$

$-x\geq 3$

Multiply by -1 both sides

Remember that, when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

$x\leq -3$

The domain of the function is the interval (-∞,-3]

For x=-3 ---> the value of y=0

The range is the interval {0,∞)

therefore

The graph in the attached figure

3 0

3 years ago

Find the missing side. round to the nearest tenth.

horrorfan [7]

Answer:

24) x = 9.2

25) x = 30.8

Step-by-step explanation:

Given

See attachment for triangles

Solving (24)

To solve for x, we make use of cosine formula

i.e.

cos(40) = adjacent ÷ hypotenuse

So, we have:

cos(40) = x ÷ 12

Multiply both sides by 12

12 cos(40) = x

12 * 0.7660 = x

x = 9.2

Solving (25)

To solve for x, we make use of sine formula

i.e.

sin(25) = opposite ÷ hypotenuse

So, we have:

sin(25) = 13 ÷ x

Multiply both sides by

x sin(25) = 13

Divide by sin(25)

x = 13 ÷ sin(25)

Using a calculator

x = 30.8

5 0

2 years ago

Triangle ABC is congruent to triangle DFE. Find y.

kirza4 [7]

Angles D and A are equal (from the statement bc the name of triangle starts with A and D)

Now set an equation of the angles so
45 = 5y -10

Add 10 on both sides

55 = 5y
divide by 5

y = 11

6 0

3 years ago