7. The ruler below has eleven marks and can be used to measure lengths

A direct variation function contains the points (–8, –6) and (12, 9). Which equation represents the function? y = –4/3x y = –3/4

Zina [9171]

Answer:

First, we must calculate the slope

m=Y2-Y1/X2-X1

= 9 - (-6) / 12 - (-8)

= 15/20

= 3/4

Therefore, the equation with the slope of 3/4 is Y=3/4x

8 0

25 days ago

A small-appliance manufacturer finds that the profit P (in dollars) generated by producing x microwave ovens per week is given b

PIT_PIT [9117]

Answer:

The amount of ovens that must be produced in a week to earn a $1610 profit is 70.

Step-by-step explanation:

Given:

A small-appliance manufacturer determines the profit P (in dollars) from producing x microwave ovens weekly by the formula:

$P=\frac{1}{10}x(300-x)$

with 0 ≤ x ≤ 200.

The target profit is $1610

So, set P = 1610, then solve for x:

$1610=\frac{1}{10}x(300-x)$

Multiply both sides by 10:

$1610\cdot \:10=\frac{1}{10}x\left(300-x\right)\cdot \:10$

$16100=x\left(300-x\right)$

$16100=300x-x^2$

$-x^2+300x-16100=0$

Next, factor the quadratic:

$(x-70)(x-230)=0$

Solving for x gives:

$x=70,x=230$

Since x=230 is outside the domain 0 ≤ x ≤ 200, we discard it.

Hence, the valid solution is x=70.

Therefore, to achieve a $1610 profit, the manufacturer must produce 70 ovens weekly.

7 0

1 month ago

In the xy-plane, point E has coordinates (4,5) and point O has coordinates (0,0). Which of the following is an equation of the l

lawyer [9240]

Answer:

D

Step-by-step explanation:

You should insert the provided x and y coordinates into the equations to determine which one satisfies both points.

D is valid for both:

5 = 5/4(4)

0 = 5/4(0)

6 0

1 month ago

If m abf=7b-24 and m Abe = 2b what is m EBF

Inessa [9000]

Since m∠abe = 2b, and angle abe consists of angles abf and ebf, we can write:
m∠abe = m∠abf + m∠ebf
To find m∠ebf, rearrange:
m∠ebf = m∠abe - m∠abf
Substitute the given expressions:
m∠ebf = 2b - (7b - 24)
Simplify:
m∠ebf = 2b - 7b + 24
m∠ebf = -5b + 24.

3 0

1 month ago

WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the

Inessa [9000]

Answer:

a) $P(X>20)=P(\frac{X-\mu}{\sigma}>\frac{20-\mu}{\sigma})=P(Z>\frac{20-15}{3.5})=P(z>1.43)$

The probability can be determined using the complement rule, with the standard normal distribution, an excel sheet, or a calculator.

$P(z>1.43)=1-P(z$

b) $P(X$

This probability can also be calculated using the normal standard distribution, an excel sheet, or a calculator.

$P(z$

c) $P($

For this one, the probability can likewise be derived from the standard normal distribution, excel, or a calculator, with specific adjustments:

$P(-1.43$

Step-by-step explanation:

Previous concepts

Normal distribution refers to a symmetric probability distribution centered around the mean, indicating that occurrences near the mean are more common than those far from it.

The Z-score is a statistic that represents a value's relationship to the average of a set of values, expressed in terms of how many standard deviations it is away from the mean.

Part a

Let X denote the random variable representing the lengths within a population, and for our case, the distribution for X is as follows:

$X \sim N(15,3.5)$

Where $\mu=15$ and $\sigma=3.5$

We seek the probability:

$P(X>20)$

The most effective way to solve this is by leveraging the normal distribution and the corresponding Z-score:

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

By applying this formula, we can find the probability:

$P(X>20)=P(\frac{X-\mu}{\sigma}>\frac{20-\mu}{\sigma})=P(Z>\frac{20-15}{3.5})=P(z>1.43)$

Again, this probability can be obtained either using the complement rule, the standard normal distribution, or a calculator.

$P(z>1.43)=1-P(z$

Part b

$P(X$

This probability can also be computed using either the normal standard distribution, an excel sheet, or a calculator.

$P(z$

Part c

$P($

In this case, the probability can similarly be acquired with the help of the standard normal distribution, an excel sheet, or a calculator, with particular adjustments:

$P(-1.43$

5 0

21 day ago