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3 years ago

2.

Mathematics

1 answer:

viva [34]3 years ago

8 0

Please read "Step-by-step" if you're having trouble

Answer:

x²(1- $\frac{1}{4}$ $\pi$ )

Step-by-step explanation:

Each side of the cookie dough is x long, since there is no given number, the diameter of the plate is also x, its as long as the square is wide, making the radius 1/2x.

The area of the cookie dough is x², the area of the plate is 1/4 $\pi$ x².

You have the equation x²- $\frac{1}{4}$ $\pi$ x²the equation has a Greatest Common Factor of x² so your factored equation is x²(1- $\frac{1}{4}$ $\pi$ )

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Oliver has 3 times as many rocks in his collection as Katie. Then Oliver collected 75 more rocks and Katie collected 105 more ro

Evgesh-ka [11]

Answer:

The answer to your question is Katie had 15 rocks and Oliver 45 rocks.

Step-by-step explanation:

Conditions

Katie has x amount of rocks

Oliver has 3x amount of rocks

The final amount of rocks

Oliver = 3x + 75

Katie = x + 105

Now, they have the same amount of rocks, then we can equal both equations

3x + 75 = x + 105

Solve for x

3x - x = 105 - 75

2x = 30

x = 30/2

x = 15

Conclusions

At first Katie had 15 rocks and Oliver had 3(15) = 45 rocks

5 0

3 years ago

Read 2 more answers

Karl set out to Alaska on his truck.

tester [92]

Answer:

<u>The track consumes ≅ 61 liters of fuel every 100 kilometres</u>

Step-by-step explanation:

As we can see in the graph, the total distance that the truck can travel with 500 liters of fuel is ≅ 825 kilometres.

For answering the question properly, we use the Rule of Three Simple, this way:

Kilometres Liters of fuel

825 500

100 x

Solving for x, we have:

825 * x = 500 * 100

825x = 50,000

x = 50,000/825

x = 60.6 liters of fuel (61 rounding to the next whole)

x ≅ 61 liters of fuel

<u>The track consumes ≅ 61 liters of fuel every 100 kilometres</u>

6 0

3 years ago

Read 2 more answers

What is the solution set to the equation (3x−9)(5x−3)=0?

andreev551 [17]

This product could be zero if one or both of the parenthesis are zero.
3x-9=0; 3x=9; x= 3
5x-3=0; 5x=3; x=3/5

The solution is { 3/5, 3}

8 0

3 years ago

Read 2 more answers

Un padre cede al mayor de sus hijos la quinta parte de su capital, al segundo la cuarta parte del mismo y al tercero le da el re

spayn [35]

Answer:

El padre tenía un capital de 60,000 euros.

El hijo mayor recibe 12,000 euros.

El hijo segundo recibe 15,000 euros.

El hijo tercero recibe 33,000 euros.

Step-by-step explanation:

Sea $x$ el capital total del padre y $a,b,c$ son las asignaciones a los hijos mayor, segundo y tercero. A continuación, construimos las ecuaciones matemáticas a partir de lo descrito en el enunciado:

Hijo mayor

$a = \frac{1}{5}\cdot x$ (1)

Hijo segundo

$b = \frac{1}{4}\cdot x$ (2)

Hijo tercero

$c = \left(1-\frac{1}{5}-\frac{1}{4}\right)\cdot x = 33000$ (3)

De (3) tenemos que el capital del padre es:

$x = \frac{33000}{1-\frac{1}{5}-\frac{1}{4} }$

$x = 60000$

El padre tenía un capital de 60,000 euros.

Por (1) y (2) determinamos los capitales del hijo mayor y el hijo segundo:

$a = \frac{1}{5}\cdot x$

$x = 12000$

El hijo mayor recibe 12,000 euros.

$b = \frac{1}{4}\cdot x$

$b = 15000$

El hijo segundo recibe 15,000 euros.

4 0

3 years ago

The National Safety Council publishes information about automobile accidents in Accident Facts. According to that document, the

vladimir1956 [14]

Answer:

$P(X = x) = C_{8,x}.(0.4)^{x}.(0.6)^{8-x}$

In which x is the number of which we want to find the probability.

Step-by-step explanation:

For each traffic fatality, there are only two possible outcomes. EIther it involved an intoxicated or alcohol-impaired driver or nonoccupant, or it didn't. Traffic fatalities are independent of other traffic fatalities, which means that the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The probability is .40 that a traffic fatality involves an intoxication or alcohol-impaired driver or nonoccupant.

This means that $p = 0.4$

Eight traffic fatalities

This means that $n = 8$

Find the probability that the number which involve an intoxicated or alcohol-impaired driver or nonoccupant is

This is P(X = x), in which x is the number of which we want to find the probability. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = x) = C_{8,x}.(0.4)^{x}.(0.6)^{8-x}$

3 0

3 years ago