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3 years ago

Need 78 pieces of wood 29 cm long. Boards are 6 m long. How many boards are needed?

1 answer:

5 0

I believe the answer is 4 because 6m/29= 20.6897 and so then you do 20.6897 x 3= 62.0691. So 3 is too small so do 20.6897x 4= <span>82.7588. 82 >78 so the answer is that you need 4 boards.
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What are the solutions to 3n-1>8 or 4n+3 < -1? *

hammer [34]

Answer:

3’d

Step-by-step explanation:

6 0

3 years ago

Please solve each of the following by factoring!

Oxana [17]

Answer:

see explanation

Step-by-step explanation:

(a)

x² - 36 = 0 ← is a difference of squares and factors as

(x - 6)(x + 6) = 0

equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

x - 6 = 0 ⇒ x = 6

(b)

x² - 5x + 4 = 0

consider the product of the factors of the constant term (+ 4) which sum to give the coefficient of the x- term (- 5)

the factors are - 1 and - 4 , since

- 1 × - 4 = + 4 and - 1 - 4 = - 5 , then

(x - 1)(x - 4) = 0 ← in factored form

equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 4 = 0 ⇒ x = 4

(c)

x² - 2x = 3 ( subtract 3 from both sides )

x² - 2x - 3 = 0 ← in standard form

consider the product of the factors of the constant term (- 3) which sum to give the coefficient of the x- term (- 2)

the factors are + 1 and - 3 , since

1 × - 3 = - 3 and 1 - 3 = - 2 , then

(x + 1)(x - 3) = 0 ← in factored form

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 3 = 0 ⇒ x = 3

(d)

6x² - 11x - 10 = 0

consider the product of the factors of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 6 × - 10 = - 60 and sum = - 11

the factors are + 4 and - 15

use these factors to split the x- term

6x² + 4x - 15x - 10 = 0 ( factor the first/second and third/fourth terms )

2x(3x + 2) - 5(3x + 2) = 0 ← factor out (3x + 2) from each term

(3x + 2)(2x - 5) = 0

equate each factor to zero and solve for x

3x + 2 = 0 ⇒ 3x = - 2 ⇒ x = - $\frac{2}{3}$

2x - 5 = 0 ⇒ 2x = 5 ⇒ x = $\frac{5}{2}$

6 0

2 years ago

Which of the following equations represents a linear function? Question 8 options: y =6x x3 – y = –2 y =4x−−√ 2x – 4y = 6

Alekssandra [29.7K]

Answer:

Following equations represents a linear function:

y = 6x

y = 4x - √2

x – 4y = 6

Step-by-step explanation:

We know that a linear function is of the form

$y = mx+b$

where m is the rate of change or slope and b is the y-intercept.

Please note that y = mx+b represents a straight line because the degree of a linear function is always 1.

Now, let us check whether the given functions represent the linear functions or not.

Checking y = 6x

y = 6x

comparing with the equation y = mx+b

slope = 6, and y-intercept b = 0

y = 6x is a straight line because the degree of the linear equation is always 1.

Checking x³- y = -2

x³- y = -2

As the power of x variable 3. So, its graph will no longer be a straight line,

Thus, it is not a linear function as a linear function can not have any exponent.

Hence, x³- y = -2 is not a linear function.

Checking y = 4x - √2

y = 4x - √2

comparing with the equation y = mx+b

slope = 4, and y-intercept b = -√2

Thus, y = 4x - √2 is a straight line because the degree of the linear equation is always 1. Thus, the graph of y = 4x - √2 is a straight line.

Checking x – 4y = 6

x – 4y = 6

writing the in the form y = mx+b

4y = x - 6

divide both sides by 4

4y/4 = x/4 - 6/4

y = x/4 - 3/2

comparing with the equation y = mx+b

slope = x/4, and y-intercept b = -3/2

Thus, x – 4y = 6 is a straight line because the degree of the linear equation is 1. Thus, the graph of x – 4y = 6 is a straight line.

SUMMARY:

Following equations represents a linear function:

y = 6x

y = 4x - √2

x – 4y = 6

4 0

3 years ago

Consider the probability that at least 88 out of 158 software users will not call technical support. Assume the probability that

Nookie1986 [14]

Answer:

$E(X) = 158*0.57 =90.06$

And the standard deviation for the random variable is given by:

$\sigma= \sqrt{158*0.57*(1-0.57)} = 6.223$

And the distribution for the approximation is given by:

$X \sim N (\mu = 90.06, \sigma = 6.223)$

We can use the z score formula given by:

$z = \frac{x -\mu}{\sigma}$

And using the complement rule we got:

$P(X \geq 88) = 1-P(X$

And using the standard normal table we got:

$P(X \geq 88) = 1-P(X$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Bin (n = 158, p =0.57)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

We want this probability:

$P(X\geq 88)$

Normal approximation

We need to check if we can use the normal approximation , the conditions are:

$np =158*0.57 = 90.06>10$

$n(1-p) = 158*(1-0.57) = 67.94>10$

Since we satisfy both conditions the normal approximation makes sense

The expected value is given by this formula:

$E(X) = 158*0.57 =90.06$

And the standard deviation for the random variable is given by:

$\sigma= \sqrt{158*0.57*(1-0.57)} = 6.223$

And the distribution for the approximation is given by:

$X \sim N (\mu = 90.06, \sigma = 6.223)$

We can use the z score formula given by:

$z = \frac{x -\mu}{\sigma}$

And using the complement rule we got:

$P(X \geq 88) = 1-P(X$

And using the standard normal table we got:

$P(X \geq 88) = 1-P(X$

4 0

3 years ago

What are the solutions of the quadratic equation (X+3)^2=49

Vesna [10]

Answer:

X = 4, x = -10

Step-by-step explanation:

Solve for x by finding a, b, and c.

5 0

3 years ago