of 30 students 1/3 play sports. of those who play sports 2/5 play soccer

The mass in scientific notation is \(5.45 * 10^3 kg\), this means that the mass of the African elephant is 5.45 multiplied by 1000,

To write the mass of the African elephant in scientific notation, we need to express it as a number between 1 and 10, multiplied by a power of 10. To do this, we can start by moving the decimal point in 5450 kg to the left until we have a number between 1 and 10. This gives us 5.45 kg.

Next, we need to determine the power of 10 that we multiplied by to get this number. To do this, we count the number of places we moved the decimal point, which is three places to the left. Therefore, the mass of the African elephant in scientific notation is:

\(5.45 * 10^3 kg\)

This means that the mass of the African elephant is 5.45 multiplied by 1000, which is the same as 5450 kg in standard notation. Writing the mass in scientific notation makes it easier to work with very large or small numbers, as it simplifies the representation of the number and makes it more manageable.

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Answer:

u = 5

Step-by-step explanation:

u/5 - 7 = - 6 -- add 7 to both sides.

u/5 = 1 -- clear the fraction by multiplying 5 to both sides.

u = 5

Answer:

Hello! I think the answer is D: $2.25. Please correct me if i'm wrong.

Step-by-step explanation:

Answer:

D: $2.25

Step-by-step explanation:

The missing reason is ∠ ABC ≅ ∠ DBE by vertically opposite angles postulate and Δ ABC ~ Δ  DBE by AA rule.

Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines. Vertically opposite angles are equal to each other. These are sometimes called vertical angles.

Given that, ∠ C ≅ ∠ E, and we need to find a reason to prove Δ ABC ~ Δ  DBE,

As we know that, to prove two triangles similar we can show two corresponding angles congruent in them, then they will be similar by AA rule,

Here, we already have, ∠ C ≅ ∠ E, we need one more,

If we see the figure, we get ∠ ABC and ∠ DBE are vertically opposite angles

We know that, Vertically opposite angles are equal to each other.

Therefore, ∠ ABC ≅ ∠ DBE

Hence, the missing reason is ∠ ABC ≅ ∠ DBE by vertically opposite angles postulate and Δ ABC ~ Δ  DBE by AA rule.

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In this question, we are asked to determine the truth-values of two statements involving sets A and B. For each statement, we need to determine if it is true or false. If it is false, we need to provide specific counterexamples by choosing appropriate sets A and B.

a. (A\B) ⊆ A

The statement (A\B) ⊆ A is true for any sets A and B. This is because the set difference (A\B) contains elements that are in A but not in B. Therefore, by definition, every element in (A\B) is also an element of A. There are no counterexamples to this statement.

b. A^c ⊆ (AUB)

The statement\(A^c\) ⊆ (AUB) is true for any sets A and B. This is because the complement of A, denoted as \(A^c\), contains all elements that are not in A.

On the other hand, the union of A and B, denoted as (AUB), contains all elements that are in A or in B or in both.

Since the complement of A contains all elements not in A, it includes all elements in B that are not in A as well.

Therefore, \(A^c\) ⊆ (AUB) holds true for any sets A and B. There are no counterexamples to this statement.

In conclusion, both statements are true for any sets A and B, and there are no counterexamples.

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Answer:

13

Step-by-step explanation:

Replace X with 2

Evaluate the function. g(x) = 3x^2 – 2x + 5 Find f(2)​

g(x) = 3(2)^2 – 2(2) + 5

Next conduct PEMDAS

Exponents are first so solve 2^2 which is 2 x 2 = 4

g(x) = 3(4) – 2(2) + 5

Next step is multiplication multiply 3 x 4 and 2x2

g(x) = 12 – 4 + 5

conduct adding and subtracting left from right

g(x) = 13

Answer:

1) -1

2) 3

3) 2

$10,000 is invested at annual compound interest. After 4 years, the investment has become $11,608.86. What annual rate of compound interest was used?

Answer: 3.8%

The annual rate of the compound interest is given as 3.8%.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Amount = principal[1 + r/n]ⁿᵃ

Principal = P rate= r Time =a  , n = compounding frequency

Here,
Amount = principal[1 + r/n]ⁿᵃ
11608.86 = 10000[1 + r/1]⁴
1.160886 = [1 + r]⁴
1 + r = 1.038
r = 1.038 - 1
r = 0.038
r% = 0.038 ×100%
r% = 3.8%

Thus, the annual rate of the compound interest is given as 3.8%.

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The equation for split times is 4x= 198.608  and the value of x is 49.652

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Let x be the split time

all 4 of the split times were the same.

4x= 198.608

=> x= 198.608/4 = 49.652

The equation for split times is 4x= 198.608  and the value of x is 49.652

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Step-by-step explanation:

=  6m* 4      - 7 *4

= 24 m - 28      

Answer:

x=142 degrees

Step-by-step explanation:

we know that a triangle adds up to 180 degrees, so we know 2 angles already which are 90 and 52 so we subtract them

180-90-52= 38

so 38 is the missing angle and we need to find the angle outside so we subtract 38 from 180

180-38= 142

so x=142

The square that you see at the bottom means 90 degrees

The outside angle (in this case "x") is equal to 90 + 52 which is 142 degrees

Answer:

x=19

Step-by-step explanation:

a

(9x-76)=5x and solve for algebric equation

Answer:

\(g=\frac{9}{2}, \\x=-6\)

Step-by-step explanation:

The perimeter of the rectangle is got increased by a factor of 2. The correct option is A.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In rectangle opposite sides are parallel and equal and each angle is 90 degrees. And its diagonals are also equal and intersect at mid-point.

Given

A rectangle has a width of 12.5 m and a length of 105 m.

We know the perimeter of the rectangle is given by

Perimeter = 2 (Lenght + Width)

Let x be the length and y be the width. Then

Perimeter = 2 (x + y)

If the dimensions are multiplied by 2. Then the effect on the perimeter will be

Perimeter = 2 (2x + 2y)

Perimeter = 2 [2 (x + y)]

The perimeter is increased by a factor of 2.

Thus, option A is correct.

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Using mathematical operators, the value of x in the equations are -1/3, (2.39 or 0.71) and no solution respectively.

To determine the value of x in the equations, we need to use mathematical functions or operators;

1. 8 + 9x(x + 4) = (3x - 2)(3x + 2)

Open the brackets

8 + 9x² + 36x = 9x² + 6x - 6x - 4

Collect like terms

8 + 9x² + 36x - 9x² + 4 = 0

8 + 4 + 36x = 0

12 + 36x = 0

36x = -12

x = -12/36

x = -1/3

2. 2x(2x - 2) - 17 = (5x + 2x)(2x - 5)

Open the brackets;

4x² - 4x - 17 = 10x² - 25x + 4x² - 10x

collect like terms

14x² - 35x - 4x² - 4x + 17 = 0

10x² - 31x + 17 = 0

solving the quadratic equation;

x = 2.39 or x = 0.71

3. (2x + 1)(4x² - 2x + 1) = 4x(2x² - 5)

Open brackets;

8x³ - 4x² + 2x + 4x² - 2x + 1 = 8x³ - 20x

collect like terms

8x³ + 1 - 8x³ + 20 = 0

21 = 0

The equation has no solution

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Answer:

A) -15, 5, 2

Step-by-step explanation:

Step-by-step explanation:

-4 -11 = ?

x X 3 = 15

4 x 2 x 3x = 48

Answer Choices:

B) 15, 4, 13

The experimental probability is \(3/10\)  that Clare won if Charlie's numbers were \(1\) and \(3\).

Some instances of probability in real life include: The forecast for the weather is based on probability. Several games that depend on chance or luck employ it. The optimal approach in sports is determined by the athletes using probability.

Probability is helpful in assessing the likelihood of an event in given circumstances. Probability has a lot of significance in daily life. whether analyzing political plans, determining blood kinds, playing video games, buying or selling insurance, shopping online, or playing games online.

Charlie picked two numbers between \(1\) and \(5\)

So the numbers should be \(2, 3\), and \(4\)

There is the number of favorable outcomes is \(3\)

To win the game, Clare must guess both his numbers in \(3\) tries

The experimental probability that Clare won if Charlie's numbers were \(1\)and \(3 = P(E)\)

There are \(10\) trials given

There are total number of possible outcomes is \(10\)

So the required experimental probability \(P(E) =\) favorable outcomes/total outcomes

\(= > P(E) = 3/10\)

Hence, the experimental probability is \(3/10\) that Clare won if Charlie's numbers were \(1\) and \(3\).

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Answer:

153.86

Step-by-step explanation:

circumference: 43.96

43.96/3.14= 14 = diameter

14/2= 7 = radius

Area= 3.14(7)^2

= 3.14(49)

= 153.86

Answer:

Step-by-step explanation:

(3zⁿ)³ = 27z¹⁸

3³z³ⁿ = 3³z¹⁸

z³ⁿ = z¹⁸

z³ⁿ = z¹⁸

n = 6

The probability that Bobby will require exactly 5 shots to knock down all three targets is p^3 * (1-p)^2.

1. Bobby must hit the first three targets in order to knock them down. The probability that he will hit the first three targets is p^3.

2. After hitting the first three targets, Bobby must miss the fourth shot in order to require 5 shots to accomplish the goal. The probability that he will miss the fourth shot is (1-p).

3. Bobby must hit the fifth shot in order to knock all three targets down. The probability that he will hit the fifth shot is p.

4. Therefore, the probability that Bobby will require exactly 5 shots to knock down all three targets is p^3 * (1-p)^2.

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Dividing the circumference of a pumpkin by its diameter gives a value approximately equal to pi (π)

When you divide the circumference of a pumpkin by its diameter, you get a value that is approximately equal to the mathematical constant pi (π), which is approximately 3.14159.

This is because pi represents the ratio of the circumference of a circle to its diameter, and a pumpkin is roughly spherical in shape. So, no matter how big or small the pumpkin is, if you measure its circumference and diameter and divide them, the result will be very close to pi.

Mathematically, this can be represented by the formula

pi ≈ circumference / diameter

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Answer:

x^87

Step-by-step explanation:

Multiplying x^22 and x^7 results in x^29.

Then we have:

(x^29)^3 = x^87

Recall that (a^b)^c = a^(bc) and that a^b*a^c = a^(b + c)

Answer:

x² + 27x + 180

Step-by-step explanation:

(12 + x)(15 +x) = 12*15 + 12x + 15x + x² = x² + 27x + 180

Answer:

G

E

F

H

Step-by-step explanation:

I don't know what the parent function is. you did not specify that.

I guess it is f(x) = x² ?

anyway, x² is the prime example of a parabola, which simply opens upward and has the vertex (its minimum) at 0, 0.

now, g(x) is first of all multiplying this by -1.

that turns the original curve upside-down.

therefore, g(x) opens downward, and it has a maximum.

because of the mentioned upside-down action, this is a reflection across the x-axis.

the multiplication by 1/4 actually decreases the functional values compared to the basic x² curve, so the curve is below the x² curve and that means it stretches the original curve.

Answer:

2.18 radians

Step-by-step explanation:

125/360=x/2π

2.18 radians

Answer:

The second one.

Step-by-step explanation:

For first function y = 2x the rate of change = 2.

Second function: rate of change = (12-6)/(3-1) = 6/2 = 3

Third: it's -0.2.

Fourth: it's  (2.5 -3)/ 1= -0.5.

Answer:

unlikely

Step-by-step explanation:

because the sooner is only spun once while the cube is only roles once as well.