A swim team consists of 4 boys and 5 girls. A relay team of 4
swimmers is chosen at random from the team members. What is the probability that 3
boys are selected for the relay team given that the first selection was a girl? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

The simplified expression in mathematical form is -45.36.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The expression given is -

(-15 + (-1.6 + 9.34) / 6) × (3² - 5.7)

Simplifying the terms inside the parentheses first, we get -

(-15 + 7.74 / 6) × (9 - 5.7)

Next, we simplify 7.74 / 6 by dividing the numerator by the denominator -

(-15 + 1.29) × (9 - 5.7)

We add -15 and 1.29 inside the first set of parentheses -

(-13.71) × (9 - 5.7)

We subtract 5.7 from 9 inside the second set of parentheses -

(-13.71) × 3.3

Multiplying these two terms, we get -

-45.363 ≈ -45.36

Therefore, the value is obtained as -45.36.

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Answer:

  x = 36

Step-by-step explanation:

Given a tangent segment of length 24, and a secant segment from the same point with an external length of 12 and a total length of (12+x), you want to find the value of x.

The product of lengths from the common point to the two intersections with the circle are the same for both segments. In the case of the tangent, the two intersections with the circle are the same point, so the square of the length is used.

  24² = 12(12 +x)

  2·24 = 12 +x . . . . . . . divide by 12

  36 = x . . . . . . . . . subtract 12

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Answer: 3/12  3 blues and 12 colors in total i dont know how to explain sorry

Answer:

Hills, mountains and rivers are example of ------------------ features

Answer: 8 to 7 and 15 to 8

Step-by-step explanation:

We can conclude that -

Given is that there are 7 roses in a vase of 15 flowers. The rest are daisies.

We have 7 roses in a vase of 15 flowers. The rest are daisies.

Therefore, we can conclude that -

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Answer:

The rate of decay is 12% or .12

Step-by-step explanation:

Answer:

a = 15

Step-by-step explanation:

1/3 (6a - 9) = 27

multiply through by 3

1/3 x 3(6a - 9) = 27 x 3

(6a - 9) = 81

Group like terms

6a = 81 + 9

6a = 90

Divide both side by 6

6a/6 = 90/6

a = 15

Answer:

A. x = 4.

Step-by-step explanation:

An extreme is the highest or lowest value of the function. In this case, the extreme of the parabola is the lowest point, or the vertex.

We can see that point is at about A. x = 4.

Hope this helps!

The balance in the account after 13 years is $8233.79.

From the question, we are to use the compound interest formula to compute the balance in the account

From the compound interest formula, we have that

A = P(1 + r/n)^nt

Where A is the amount

P is the principal

r is the interest rate

n is the number of times compounded per year

and t is the time.

From the given information,

P = $7000

r = 3.3%= 0.033

n = 1

t = 13

Putting the parameters into the formula

A = P(1 + r/n)^nt

A = 7000(1 + 0.033/1)^(1×5)

A = 7000(1 + 0.033)^5

A = $8233.79

Hence, the balance is $8233.79

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The value of the expression 4 1/5 ÷ 2 1/4 will be -28/15. Then the correct option is E.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The mixed fraction numbers are given below.

- 4 1/5 and 2 1/4

The mixed fraction number is converted into a fraction number.

-4 1/5 = -21/5

2 1/4 = 9/4

Then the division of the fraction numbers will be

⇒ -(21/5) ÷ (9/4)

⇒ -(21/5) · (4/9)

⇒ -28/15

Then the value of the expression 4 1/5 ÷ 2 1/4 will be -28/15.

Then the correct option is E.

The missing option will be negative 28 over 20.

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Answer:

he is incorrect.

no one can run for 5 miles everyday.

if so, my man atteo is a legend.

Answer:

the answer is 1.3x + 2 ≥ 20

Step-by-step explanation:

the tree is already 2ft which mean it would need to be added to the rate of growth, 1.3 by the amount of year to find out the height. The question is saying however that I can be at least 20ft. so no less than 20 which is why the greater or equal to sign is used (≥)

The distance between Ray-Ann and Steve, using the law of cosines, is given as follows:

11.5 feet.

The law of cosines states that we can find the length of the missing side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

The parameters of the equation are given as follows:

In the context of this problem, the values of these parameters are given as follows:

Hence the distance between Ray-Ann and Steve is obtained as follows:

c² = 6²+ 7² - 2 x 6 x 7 x cos(124)º

c² = 132

c = square root of 132

c = 11.5 feet.

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If there are already 3 fish in the aquarium. Then the number of fish in the aquarium should be less than 2.

Inequality is simply a type of equation that does not have an equal sign in it. Inequality is defined as a statement about the relative size as well as is used to compare two statements.

There must be fewer than 5 fish in the small aquarium. There are already 3 fish in the aquarium. Then the inequality equation will be

Let the number of fish in the aquarium be x. Then the inequality equation will be

x < 5

But there are already 3 fish in the aquarium, then we have

x - 3 < 2

Then the number of fish in the aquarium should be less than 2.

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a) For two distinct real roots: x > 0 or x > m

b) For two distinct real roots: x > 0 or x > 2m

c) For two distinct real roots: x > 0 or x > 4

This is based on the quadratic equation.

Only non-negative integer powers of x are present in the quadratic equation, making it a polynomial equation. In actuality, the Latin word quadratus, which means square, is the root of the term quadratic. The quadratic equation has the generic form ax² + bx + c = 0. where x is an unknowable variable and a, b, and c are mathematical coefficients.

a) Quadratic equation: x² - 4x + m = 0

The discriminant: Δ = b² - 4ac

Δ = (2x)² - 4.x.(m)

Δ = 4x² - 4mx

Δ = 4x (x - m)

For two distinct real roots: Δ > 0

4x (x - m) > 0

x > 0 or x > m

For two real roots: Δ ≥ 0

4x (x - m) ≥ 0

x ≥ 0 or x ≥ m

For a repeated root: Δ = 0

4x (x - m) = 0

x = 0 or x = m

(b) Quadratic equation: mx² + 3x + 2 = 0

The discriminant: Δ = b² - 4ac

Δ = (3x)² - 4.mx.(2)

Δ = 4x² - 8mx

Δ = 4x (x - 2m)

For two distinct real roots: Δ > 0

4x (x - 2m) > 0

x > 0 or x > 2m

For two real roots: Δ ≥ 0

4x (x - 2m) ≥ 0

x ≥ 0 or x ≥ 2m

For a repeated root: Δ = 0

4x (x - 2m) = 0

x = 0 or x = 2m

(c) Quadratic equation: x² - mx + 1 = 0

The discriminant: Δ = b² - 4ac

Δ = (x)² - 4.x.(1)

Δ = x² - 4x

Δ = x (x - 4)

For two distinct real roots: Δ > 0

x (x - 4) > 0

x > 0 or x > 4

For two real roots: Δ ≥ 0

x (x - 4) ≥ 0

x ≥ 0 or x ≥ 4

For a repeated root: Δ = 0

x (x - 4) = 0

x = 0 or x = 4

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The values in the boxes that correctly complete the division model and quotient are presented as follows;

\({}\)                 10                   2                4    

6        \({}\)      60                 16                  

            76  ÷ 6 = 12 R 4  

A division area model comprises of the number being divided, representing the area of a rectangle, and a factor or the divisor, being a side length of the rectangle.

The number 76 divided by 6 using the division model can be evaluated by setting the area of the rectangle as 76 and the length of side of the rectangle as 6, asw follows;

The division model

The model for the division of 76 ÷ 6 can be presented as follows;

        \({}\)        10                2                 4  

6    \({}\)            60              16

Therefore; 76 ÷ 6 = 10 + 2 = 12 Remainder 4

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Answer:

\(0.33\)

Step-by-step explanation:

There are 6 sides on dice, therefore the sample space would be 6 (the sample space is the denominator). We were asked to find the probability of getting a 1 or a 6. Since we were given 2 options 1 or 6, it therefore means that we are trying to find the probability of the dice rolling on 2 out of the 6 sides it has. Therefore the probability would be:

\( \frac{2}{6} \: or \: \frac{1}{3} \)

A third as a decimal is

\(0.33\)

Answer:

yes

Step-by-step explanation:

hope this helped

Answer:

The unit rate is $4 for 1 pound of rice.

Step-by-step explanation:

P.S Can I have brainliest?

Answer:

$4 per pound

Step-by-step explanation:

Unit rates are in terms of 1.

8/2 = 4

So $8 for 2 pounds is equivalent to $4 for 1 pound.

Answer: h=9 inches

Step-by-step explanation:

\(7.\\a.\\\displaystyle\\A=\frac{1}{2}bh \\\)

Multiply both parts of the equation by 2:

\(2A=bh\)

Divide both parts of the equation by b (b≠0):

\(\displaystyle\\\frac{2A}{b} =h\\\\Thus,\\\\ h=\frac{2A}{b}\)

\(\displaystyle\\b.\\\\A=54\ in.^2\ \ \ \ b=12\ in.\\\\h=\frac{2*54}{12} \\\\h=\frac{2*54}{2*6} \\\\h=\frac{54}{6} \\\\h=9 \ in.\)

Answer:

4 5/8

Step-by-step explanation:

Rewriting our equation with parts separated

=4+12+18

Solving the fraction parts

12+18=?

Find the LCD of 1/2 and 1/8 and rewrite to solve with the equivalent fractions.

LCD = 8

48+18=58

Combining the whole and fraction parts

4+58=458

Answer:

Not exactly sure what your asking but 11/3 as a mixed number is 3 2/3

Answer:

3 2/3 is the simplified version of 11/3

Step-by-step explanation:

Probability of an event A given B is;

Thus Probability of selecting a Junior student given it is a male is;

The probability of selecting a junior student given it is a male is 14%.

The complement of A ∪ B is the set of all elements not in A ∪ B.

If x is some element of A ∪ B, then x is either in A or B (or both).

So if x is some element of the complement of A ∪ B, that means x does not belong to A or B. In other words, x is not in A and x is not in B.

So (A ∪ B)' = A' ∩ B', where the ' symbol denotes set complement.

For example, if A = {1, 2, 3, 4} and B = {3, 4, 5, 6} are both subsets of U = {0, 1, 2, 3, 4, 5, 6, 7}, then

A ∪ B = {1, 2, 3, 4, 5, 6}

→   (A ∪ B)' = {0, 7}

Put another way,

A' = {0, 5, 6, 7}

B' = {0, 1, 2, 7}

→   A' ∩ B' = {0, 7}

and we see that both (A ∪ B)' and A' ∩ B' are the same set.

The skier's distance to the east of the center of the ski trail is

x = 1.25cosθ

The skier's distance to the north of the center of the ski trail is

y = 1.25sinθ

When radius 'r' and the angle θ are given, the coordinates (x,y) as shown

x = east direction

y = north direction

In this case we get,

x = r cosθ

y = r sinθ

Given r = 1.25 km

We get,

x = 1.25 cosθ in east direction

y = 1.25 sinθ in north direction

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Answer:

x=5/4, y=7/4

Step-by-step explanation:

This is a similar triangles problem.

The first triangle (the smaller one) has the lengths 5, 8 and 7.

The second triangle (the lager one) has the lengths 5+x, 10, and 7+y

Let's first solve for x

In any similar triangles problem, you can make two ratios (all the ratios of the sides are the same)

since we don't know the measures for x and y first, we can use the ratio of the parallel lines (the bases) as the first ratio (8/10)

For the second ratio, it's smaller/bigger, so it'll be 5/(x+5)

here's the proportion

5/(x+5)=8/10

But before we multiply, we can simplify 8/10 to 4/5

so

5/(x+5)=4/5

Cross multiply

25=4x+20

5=4x

5/4=x

For y, we can do a similar process

We can use 8/10 or 4/5 again

and the ratio of the sides for y will be 7/(y+7)

7/(y+7)=4/5

35=4y+28

7=4y

7/4=y

Hope this helps!

The solution set of this inequality is {x| x > -6.1}

Here we have the inequality:

2x + 8 > -4.2

To find the solution set, we need to isolate the variable x in one of the sides of the inequality. Doing that we will get:

2x + 8 > -4.2

2x > -4.2 - 8

2x > -12.2

x > -12.2/2

x > -6.1

So the set of all numbers larger than -6.1, this in number form is:

{x| x > -6.1}

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Using the fact that ∠A is congruent to ∠B and ∠C is a complement of ∠A, we determined that the measure of ∠B is 65° based on the given measure of ∠C as 25°.

If ∠A is congruent (≅) to ∠B and ∠C is a complement of ∠A, we can use the properties of complementary angles to find the measure of ∠B.

Given that m∠C = 25° and ∠C is a complement of ∠A, we know that ∠A + ∠C = 90°.

Since ∠A is congruent to ∠B, we can replace ∠A with ∠B in the equation:

∠B + ∠C = 90°.

Substituting the given value, we have:

∠B + 25° = 90°.

To isolate ∠B, we subtract 25° from both sides of the equation:

∠B = 90° - 25°.

Simplifying, we get:

∠B = 65°.

Therefore, the measure of ∠B is 65°.

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Answer:

K5.60.

Step-by-step explanation:

Answer:

2 real solutions

Step-by-step explanation:

a=-10, b=-4, c=2

(-4)^2-4x(-10)x2=96

Given:

Consider the three number are given by:

\(a=x^2-y^2\)

\(b=2xy\)

\(c=x^2+y^2\)

To find:

The three numbers are the Pythagorean triple generated by using 4 for x and 1 for y.

Solution:

We have,

\(a=x^2-y^2\)

\(b=2xy\)

\(c=x^2+y^2\)

Substituting 4 for x and 1 for y, we get

\(a=4^2-1^2\)

\(a=16-1\)

\(a=15\)

Similarly,

\(b=2(4)(1)\)

\(b=8\)

And,

\(c=4^2+1^2\)

\(c=16+1\)

\(c=17\)

The three three numbers are the Pythagorean triple are 8,15 and 17.

Therefore, the correct option is C.