MATHEMATICS COLLEGE

What is the image point of (4, 6) after the transformation
T 5,2 r y=-x?

Answers

Answer 1
Answer:

Answer:

(-1,-2)

Step-by-step explanation:

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What are the solutions to the equation 0=x squared- x-6
Will give brainliest
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Sand is poured onto a surface at 13 cm3/sec, forming a conical pile whose base diameter is always equal to its altitude. How fast is the altitude of the pile increasing when the pile is 1 cm high? Note that the volume of a cone is 13πr2h where r is the radius of the base and h is the height of the cone.

Please help 200*50/-9+564*-4= ? I

Answers

Answer:

-3367 1/9

Step-by-step explanation:

This is what calculators are for.

Perform the multiplication and division before the addition.

... = 10000/-9 -2256

... = -1111 1/9 -2256

... = -3367 1/9

_____

If you don't have a calculator, the Google and Bing search boxes can be relied upon to use the correct order of operations.

Suppose an airline policy states that all baggage must be box shaped with a sum of​ length, width, and height not exceeding 96 in. What are the dimensions and volume of a​ square-based box with the greatest volume under these​ conditions?

Answers

Answer:

Step-by-step explanation:

As the base is a square so the length is a, width is a and the height is h.

According to the question,

a + a + h = 96

h = 96 - 2a     .... (1)

Volume of the box, V = length x width x height

V = a x a x h

V = a² (96 - 2a)    from equation (1)

V = 96a² - 2a³

Differentiate both sides

(dV)/(da)=192 a -6a^(2)

Now put it equal to zero.

192 a - 6a² = 0

a = 32 in

h = 96 - 2 x 32

h = 32 in

Thus, the length and the width os teh base is 32 in and the height is 32 in.

Final answer:

A square-based box with the greatest volume under a restriction of the sum of length, width, and height not exceeding 96 inches must have each dimension equal to 32 inches. Therefore, its volume will be 32x32x32 = 32,768 cubic inches.

Explanation:

A square-based box with the greatest volume that can fit the airline's restrictions would have each side (length, width, height) be exactly one third of the total permitted sum, namely 32 inches each, because the volume of a square-based box (a cube in this specific case) is calculated by cubing the edge length. This is due to the nature of a cube, where all sides are equal.

So, the volume of the box would be 32in x 32in x 32in = 32,768 cubic inches. This is the maximum volume because the mathematical principle that for a given sum S of width, length & height, a cube always takes up the most volume.

Learn more about Optimization in Mathematics here:

brainly.com/question/32199704

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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.

4.1 Number Talk: DivisionFind each quotient mentally.

645 divided by 100

645 divided by 50

48.6 divided by 30

48.6 divided by x

Answers

Answer:

645/100 = 129/20 or 6.45

645/50 = 129/10 or 12.9

48.6/30 = 1.62

48 divided by x = 48.6/x

Step-by-step explanation:

645/100

Factor the number:

= 5*129/100

Factor the number:

= 5*129/5*20

Cancel the common factor:

= 129/20

645/50

Factor the number:

5*129/50

Factor the number:

5*129 / 5*10

Cancel the common factor:

= 129/10

48.6/30

Write the problem in long division format

Multiply the quotient digit (1) by the divisor (30)

Subtract 30 from 48

Add a decimal and bring down the next number

Divide 186 by 30 to get 6

Continue...A few steps later...

Subtract 60 from 60

Solution is 1.62

48.6/x

Re-write division as a fraction:

48.6/x

Points F (0,0), G (9,0), and H (9,12) are the vertices of a triangle.What is the distance from point F to point H?

A. 9
B. 12
C. 15
D. 21

Answers

The distance from point F to point H is 15 units. Option C is correct.

In order to get the distance from point F to point H, we will use the distance formula as shown:

D =√((x_2-x_1)^2+(y_2-y_1)^2)

Given the coordinate points F(0,0) and H(9, 12)

FH=√((12-0)^2+(9-0)^2)\nFH =√(12^2+9^2)\nFH=√(144+81)\nFH=√(225)\nFH = 15units

Hence the distance from point F to point H is 15 units. Option C is correct.

Learn more here: brainly.com/question/22624745

Answer:

15

Step-by-step explanation:

Because I said so

The number 3456 is divisible by wich single-digit number?

Answers

I'm assuming what you mean is what can you divide 3456 by to get a natural number.

First of all every number is divisible by 1.  

Every even number is divisible by 2, so since 3456 is an even number, it can be divided by 2.  That would equal 1728.

2456 can also be divided by 3, to get 1782.  

You can also divide it by 4, to get 865.

Divided by 6, it's 576.

Divided by 8, it's 432.

And lastly, 3456 divided by 9 is 384.

So, there isn't just one single-digit number you can divide 3456 by to get a natural number.  You can divide it by 1,2,3,4,6,8, and 9.

Hope that helps!
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