Given the equation of a line is5x - 4y = 24
What is the slope of the line?
What is the y-intercept?

Answers

Answer 1

Answer:

Answer:

the slope of the line is $(5)/(4)$ , and the y-intercept occurs at y = -6 (0, -6) on the plane

Step-by-step explanation:

In order to find the slope and y-intercept, we need to solve for y in the equation, and look at the coefficient accompanying the term in "x" (the slope), and at the pure numerical term (y-intercept):

$5\,x-4\,y= 24\n5\,x-24=4\,y\ny=(5)/(4) \,x-(24)/(4) \ny=(5)/(4) \,x-6$

Therefore the slope of the line is $(5)/(4)$ , and the y-intercept occurs at y = -6 (0, -6) on the plane

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A teacher is interested in performing a hypothesis test to compare the mean math score of the girls and the mean math score of the boys. She randomly selects 10 girls from the class and then randomly selects 10 boys. She arranges the girls' names alphabetically and uses this list to assign each girl a number between 1 and 10. She does the same thing for the boys. a. Paired t-test. Since there are 10 boys and 10 girls, we can link the two samples.b. Paired t-test. Since the boys and girls are in the same class, and are hence dependent samples, they are can be linked.c. 1-sample t-test. The teacher should compare the sample mean for the girls against the population mean for the boys.d. Two-sample t-test. There is no natural pairing between the two populations.

What is the domain of the function f (x) = StartFraction x + 1 Over x squared minus 6 x + 8 EndFraction?

Answers

Answer:

D Edg

Step-by-step explanation:

all real numbers except 2 and 4

Answer: (-∞, 2)∪(2, 3]∪(4, ∞)

Step-by-step explanation:

Domain is the allowed x values in the function. The numerator, x + 1 will be defined for all numbers. But that fraction wont be, the minute that fractions denominator is equal to zero, your entire function becomes undefined.

So lets figure out what number will make this undefined. Then we'll know the functions domain is everywhere but that x value.

Make x^2 - 6x + 8 = 0

What two numbers multiply to equal +8 but add to equal -6? Thats -4 and -2.

(x - 4)(x - 2) = 0 This means the function is undefined when x equals 4 and 2

(-∞, 2)∪(2, 3]∪(4, ∞)

A cereal comes in three different package sizes. 8 ounce box $12, 12 ounce box $16,16 ounce box $20 what is the ratio of the coast of an 8 ounce box to a 16 ounce box of cereal

Answers

The ratio between two numbers can be written in terms of fraction by writing the first number as numerator and the second number as denominator. The ratio of the given two boxes is 0.6.

What is the application ratio and proportion?

A ratio is the relation between two numbers a and b as a / b. A proportion is the equality of two ratios as a / b = c / d.

Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.

Given that,

The cost of 8 ounce box is $12,

The cost of 12 ounce box is $16,

And, the cost of 16 ounce box is $20.

The ratio of two numbers a and b is given as a : b = a / b.

Thus the ratio of the cost of an 8 ounce box to a 16 ounce box is given as,

12 : 20

= 12 / 20

= 0.6.

Hence, the ratio between the cost of the two boxes is 0.6.

To know more about ratio and proportion click on,

brainly.com/question/14279414

#SPJ2

Check and simplify ratios:

8 ounces to 12 dollars - 8:12
Simplified: 2:3

16 ounces to 20 dollars - 16:20
Simplified: 4:5

Percentages?

2 / 3 = 66.66%
4 / 5 = 80%

The 16 ounce box has a larger ratio than the 8 ounce box

In a manual on how to have a number one song, it is stated that a song must be no longer than 210 seconds. A simple random sample of 40 current hit songs results in a mean length of 241.4 sec. and a standard deviation of 57.59 sec. Use a 0.05 significance level and the accompanying minitab display to test the claim that the sample is from a population of songs with a mean great thatn 210 sec. What do these results suggest about the advice given in the manual.The mini tab displays the following:

One-sample T

Test of mu=210 vs.>210

N Mean St. Dev SE Mean 95% lower bound T p

40 241.40 57.59 9.11 226.06 3.45 0.001

A H0 u>210 sec. H1 u < 210sec

B H0 u=210 sec. H1 u < 210sec

C H0 u<210 sec. H1 u> 210sec

D H0 u=210 sec. H1 u> 210sec

Identify the test statistic:

T =

Identify the P-Value

P-value=

Stat the final conclusion that addresses the original claim. Choose from below:

A. Reject H0. There is insufficient evidence to support the claim that the sample is from a population of songs with a mean length greater than 210 sec.
B. Fail to reject H0. There is insufficient evidence to support the claim that the sample is from a population of songs with a mean length great thatn 210 sec.
C. Reject H0. There is sufficient evidence to spport the claim that the sample is from a population of songs with a mean length greater than 210 sec.
D. Fail to reject H0. There is sufficient evidence to support the claim tha tthe sample is from a population of songs with a mean lenght greater than 210 sec.

What do the results suggest about the advice given in the manual?

A. The results do not suggest that the advice of writing a song that must be no longer than 210 seconds is not sound advice.
B The results suggest that the advice of writing a song that must be no longer than 210 seconds is not sound advice
C. The results suggest that 241.4 seconds is the best song lenght.
D. The results are inconclusive because the average length of a hit song is constantly changing.

Answers

Answer:

D H0 u=210 sec. H1 u> 210sec

$t=(241.4-210)/((57.59)/(√(40)))=3.448$

$p_v =P(t_((39))>3.448)=0.000684$

C. Reject H0. There is sufficient evidence to spport the claim that the sample is from a population of songs with a mean length greater than 210 sec.

Step-by-step explanation:

Data given and notation

$\bar X=241.4$ represent the sample mean

$s=57.59$ represent the sample standard deviation for the sample

$n=40$ sample size

$\mu_o =210$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is greater than 210 seconds, the system of hypothesis would be:

Null hypothesis: $\mu \leq 210$

Alternative hypothesis: $\mu > 210$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=(\bar X-\mu_o)/((s)/(√(n)))$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=(241.4-210)/((57.59)/(√(40)))=3.448$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=40-1=39$

Since is a one side test the p value would be:

$p_v =P(t_((39))>3.448)=0.000684$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v<\alpha$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the mean is significantly higher than 210 seconds.

C. Reject H0. There is sufficient evidence to spport the claim that the sample is from a population of songs with a mean length greater than 210 sec.

Write the complex number 4(cos 60 + i sin 60) in standard form 10. Use DeMoivre's Theorem to find (2+3i)6

Answers

Answer:

a) The standard form of $z = 4\cdot (\cos 60^(\circ)+i\cdot \sin 60^(\circ))$ is $z = 2 + i\cdot 2√(3)$ , b) $z = (2+i\cdot 3)^(6) = 1219.585 + i \cdot 1829.381$ .

Step-by-step explanation:

a) The standard form of the complex number is $z = a + i\cdot b$ , $\forall \,a,b \in \mathbb{R}$ . If we get that $z = 4\cdot (\cos 60^(\circ)+i\cdot \sin 60^(\circ))$ , whose standard form is obtained by algebraic means: