All categories

2 years ago

Find the distance between points K and H.

Mathematics

1 answer:

Usimov [2.4K]2 years ago

6 0

Answer:

Step-by-step explanation:

K is the midpoint between 60 and 80.

Distance between 60 and 80 is,

80 - 60 = 20

Distance between K and H is,

20 / 2 = 10

You might be interested in

Simplify. -5x^4(-3x^2+4x-2)

dybincka [34]

Simplification/ 15x^6-20x^5+10x^4

7 0

2 years ago

Helppppppppp

Anettt [7]

Answer:

The total number of U.S. high school students that played on a sports team that year can be estimated to be 7,950,000.

Step-by-step explanation:

From the random sample, we can expect that $\frac{250000}{500000}=\frac{1}{2}$ of all students played on a sports team that year. So in the bigger sample of 15900000 high school students, we can expect $15900000 \cdot \frac{1}{2} = 7950000$ students to have played on a sports team that year.

7 0

3 years ago

On a particular game show, there are 8 covered buckets and 2 of them contain a ball.

kobusy [5.1K]

Answer:

0.2143 = 21.43% probability that a contestant wins the game if he/she gets to select 4 of the buckets.

Step-by-step explanation:

The buckets are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

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

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

In this question:

8 covered buckets, so N = 8.

4 buckets are selected, so n = 4.

2 contain a ball, which means that k = 2.

Find the probability that a contestant wins the game if he/she gets to select 4 of the buckets.

This is P(X = 2). So

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 2) = h(2,8,4,2) = \frac{C_{2,2}*C_{6,2}}{C_{8,2}} = 0.2143$

0.2143 = 21.43% probability that a contestant wins the game if he/she gets to select 4 of the buckets.

7 0

2 years ago

You have saved $35.75. about how many tapes can you buy if each tape costs $8.47 tax included?

hammer [34]

you can buy about 4 tapes

Hope my answer helped

3 0

3 years ago

Use the discriminant to predict the nature of the solutions to the equation 4x-3x²=10. Then, solve the equation.

AleksandrR [38]

Answer:

Two imaginary solutions:

x₁= $\frac{2}{3} -\frac{1}{3} i\sqrt{26}$

x₂ = $\frac{2}{3} +\frac{1}{3} i\sqrt{26}$

Step-by-step explanation:

When we are given a quadratic equation of the form ax² +bx + c = 0, the discriminant is given by the formula b² - 4ac.

The discriminant gives us information on how the solutions of the equations will be.

If the discriminant is zero, the equation will have only one solution and it will be real
If the discriminant is greater than zero, then the equation will have two solutions and they both will be real.
If the discriminant is less than zero, then the equation will have two imaginary solutions (in the complex numbers)

So now we will work with the equation given: 4x - 3x² = 10

First we will order the terms to make it look like a quadratic equation ax²+bx + c = 0

So:

4x - 3x² = 10

-3x² + 4x - 10 = 0 will be our equation

with this information we have that a = -3 b = 4 c = -10

And we will find the discriminant: $b^{2} -4ac = 4^{2} -4(-3)(-10) = 16-120=-104$

Therefore our discriminant is less than zero and we know that our equation will have two solutions in the complex numbers.

To proceed to solve the equation we will use the general formula

x₁= (-b+√b²-4ac)/2a

so x₁ = $\frac{-4+\sqrt{-104} }{2(-3)} \\\frac{-4+\sqrt{-104} }{-6}\\\frac{-4+2\sqrt{-26} }{-6} \\\frac{-4+2i\sqrt{26} }{-6} \\\frac{2}{3} -\frac{1}{3} i\sqrt{26}$

The second solution x₂ = (-b-√b²-4ac)/2a

so x₂= $\frac{-4-\sqrt{-104} }{2(-3)} \\\frac{-4-\sqrt{-104} }{-6}\\\frac{-4-2\sqrt{-26} }{-6} \\\frac{-4-2i\sqrt{26} }{-6} \\\frac{2}{3} +\frac{1}{3} i\sqrt{26}$

These are our two solutions in the imaginary numbers.

7 0

2 years ago