Which statement is true? A. .8>.79 B. .4>.40 C. .76>1.2 D. .80>.9

The GCF of any two even numbers is always even. Determine whether the statement is true or false. If true, explain why. If false

choli [55]

True because the common factor to both numbers would be an even number.

4 0

3 years ago

Describe the rotation of J

Serga [27]

Answer:

The coordinates of J' when rotating by 90° counterclockwise will be: J'(3, 1)

The coordinates of J' when rotating by 90° clockwise will be: J'(-3, -1)

Step-by-step explanation:

Square JKLM with vertices

J(1, -3)

K(5, 0)

L(8, -4)

M(4, -7)

We have to determine the answer for the image J' of the point (1, -3) when we rotate the point by 90° counterclockwise, we need to switch x and y, make y negative.

In other words, the rule to rotate a point by 90° counterclockwise.

P(x, y) → P'(-y, x)

As we are given that J(1, -3), so the coordinates of J' will be:

J(1, -3) → J'(3, 1)

Therefore, the coordinates of J' when rotating by 90° counterclockwise will be: J'(3, 1).

When the point is rotated by 90° clockwise, we need to switch x and y, make x negative.

In other words, the rule to rotate a point by 90° clockwise.

P(x, y) → P'(y, -x)

As we are given that J(1, -3), so the coordinates of J' will be:

J(1, -3) → J'(-3, -1)

Therefore, the coordinates of J' when rotating by 90° clockwise will be: J'(-3, -1)

3 0

3 years ago

The power generated by an electrical circuit (in watts) as a function of its current c (in amperes) is modeled by: P(c) = -12c^2

Ksenya-84 [330]

Answer:

The maximum power generated by the circuit is 300 watts.

Step-by-step explanation:

A quadratic function is one that can be written as an equation of the form:

f (x) = ax² + bx + c

where a, b and c (called terms) are any real numbers and a is nonzero.

In this case, f(x) is P(c) [the power generated], x is the current c (in amperes), a = -12, b = 120 and c = 0.

The vertex is a point that is part of the parabola, which has the value as ordered minimum or maximum function. If the scalar a> 0, the parabola opens or faces up and the vertex is the minimum of the function. In contrast, if a <0, the parabola opens downward and the vertex is the maximum of the function.

The calculation of the vertex, which in this case will be the maximum of the function, is carried out as follows:

The value of x, in this case the value of current c in amperes, can be calculated with the formula $c=\frac{-b}{2*a}$ . In this case: $c=\frac{-120}{2*(-12)}$ So c= 5 amperes. The current is 5 amperes.
The value of y, in this case the value of the electric current in watts, is obtained by substituting the value of c previously obtained in the function. In this case: P(5)= -12*5²+120*5. So P(5)= 300 watts

The maximum power generated by the circuit is 300 watts.

7 0

3 years ago

Solve each equation for the specified variable dx + t =10 solve for x

Aleks [24]

Answer:

dx + t = 10

dx = 10 - t

x = (10 - t) / d

8 0

3 years ago

Read 2 more answers

The amount of coffee that a filling machine puts into an 8 dash ounce 8-ounce jar is normally distributed with a mean of 8.2 oun

Inessa [10]

Answer:

73.3% probability that the sampling error made in estimating the mean amount of coffee for all 8 dash ounce 8-ounce jars by the mean of a random sample of 100 jars, will be at most 0.02 ounce

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theore.

Normal probability distribution

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

$\mu = 8.2, \sigma = 0.18, n = 100, s = \frac{0.18}{\sqrt{100}} = 0.018$

What is the probability that the sampling error made in estimating the mean amount of coffee for all 8 dash ounce 8-ounce jars by the mean of a random sample of 100 jars, will be at most 0.02 ounce

That is, probability of the sample mean between 8.2-0.02 = 8.18 and 8.2 + 0.02 = 8.22, which is the pvalue of Z when X = 8.22 subtracted by the pvalue of Z when X = 8.18.

X = 8.22

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

By the Central Limit Theorem

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

$Z = \frac{8.22 - 8.2}{0.018}$

$Z = 1.11$

$Z = 1.11$ has a pvalue of 0.8665.

X = 8.18

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

$Z = \frac{8.18 - 8.2}{0.018}$

$Z = -1.11$

$Z = -1.11$ has a pvalue of 0.1335.

0.8665 - 0.1335 = 0.7330

73.3% probability that the sampling error made in estimating the mean amount of coffee for all 8 dash ounce 8-ounce jars by the mean of a random sample of 100 jars, will be at most 0.02 ounce

6 0

3 years ago