Find three solutions of the equation.

If the value of a real number x satisfies -2x + 5= -1, then what is the value of 5x

Nitella [24]

-2x + 5 = -1

subtract 5 from both sides: -2x = -6

divide each side by -2: x = 3

plug in 3: 5(3)

multiply: 15

the value of 5x is 15.

8 0

3 years ago

Read 2 more answers

The ratio of the angles of a triangle is 8:6:4. find the measure of the angles

larisa86 [58]

If the ratio is 8:6:4, then the measure of the angles is 45, 60, and 70 degrees.

7 0

3 years ago

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Suppose a normal distribution has a mean of 38 and a standard deviation of

Sauron [17]

Answer:

77.4% probability that a data value is between 36 and 41

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 38, \sigma = 2$

What is the probability that a data value is between 36 and 41?

This is the pvalue of Z when X = 41 subtracted by the pvalue of Z when X = 36.

X = 41

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{41 - 38}{2}$

$Z = 1.5$

$Z = 1.5$ has a pvalue of 0.933

X = 36

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{36 - 38}{2}$

$Z = -1$

$Z = -1$ has a pvalue of 0.159

0.933 - 0.159 = 0.774

77.4% probability that a data value is between 36 and 41

3 0

3 years ago

X^5 + 243 divided by x+3

ch4aika [34]

-3   | 1   0   0   0   0   243 $\longleftarrow$ coefficients of the polynomial you're dividing
.     |                                   $\longleftarrow$ drop down the leading coefficient
- - - - - - - - - - - - - - - - - - -
.     | 1

On the left side of the frame, we write -3 because we're dividing by $x+3=x-(-3)$ . (The algorithm is followed for division of a polynomial by a factor of $x-c$ .) Since we're dividing a degree 5 polynomial by a degree 1 polynomial, we expect to get a degree 4 polynomial.

-3   | 1   0   0   0   0   243
.     |      -3                         $\longleftarrow$ multiply -3 by 1, write in next column, add to 0
- - - - - - - - - - - - - - - - - - -
.     | 1 -3

Repeat step for the remaining columns.

-3   | 1   0   0   0   0   243
.     |      -3   9
- - - - - - - - - - - - - - - - - - -
.     | 1 -3   9

-3   | 1   0   0      0   0   243
.     |      -3   9   -27
- - - - - - - - - - - - - - - - - - -
.     | 1 -3   9   -27

-3   | 1   0   0      0 0   243
.     |      -3   9   -27   81
- - - - - - - - - - - - - - - - - - - - -
.     | 1 -3   9   -27   81

-3   | 1   0   0      0 0 243
.     |      -3   9   -27   81 -243
- - - - - - - - - - - - - - - - - - - - -
.     | 1 -3   9   -27   81       0

which translates to

$\dfrac{x^5+243}{x+3}=x^4-3x^3+9x^2-27x+81$

So the bottom row of the frame gives the coefficients of each term in the quotient by descending order. Since the last coefficient is 0, this means the remainder upon division vanishes, i.e. $x^5+243$ is exactly divisible by $x+3$ .

- - -

Another way to get the same result is to use a well-known result: for $a+b\neq0$ ,

$a^5+b^5=(a+b)(a^4-a^3b+a^2b^2-ab^3+b^4)\implies\dfrac{a^5+b^5}{a+b}=a^4-a^3b+a^2b^2-ab^3+b^4$

and in this case $a=x$ and $b=3$

3 0

4 years ago

To make 3 glasses of orange squash you need 600 ml of water. How much water do you need to make: A or B?

Dimas [21]

For 5 you would need 1,000 ml of water and 7 you need 1,400 ml

5 0

2 years ago