Please answer this correctly

Please Answer This Correctly

Answers

Answer 1

Answer:

13 students

Step-by-step explanation:

At least 30 and fewer than 67 makes it 30-66

So,

30-66 => 13 students

Answer 2

Answer:

16

Step-by-step explanation:

There are two columns in the diagram.

The column headed stem represents tens while the column headed leaf represents units. e.g. 2 3 = 23

So we just have to count how many of the numbers are less than 8 in the 6th Stem column and all the numbers below it, which are:

20, 23, 28, 31, 31, 34, 38, 40, 44, 50, 51, 53, 54, 65, 65, 66


Related Questions

An animal shelter has 5 times as many cats as it has dogs. There are 75cats at the shelter

Answers

Answer: 15 dogs

Step-by-step explanation:

75 / 5 = 15

Answer:

15 dogs

Step-by-step explanation:

Let the number of dogs be x

number of cats be y

5 times the number of cats = number of dogs

y = x*5

Since y = 75

75 = 5x

Bring 5 to the other side n divide

x= 75/5

= 15

EXREAMLY URGENT!! WILL FOREVER THANK YOU!!!! PLS JUST TAKE A LOOK!!!!!

17. Find the measure of DE

A) 14.5
B) 13.4
C) 12.3
D) 15.9

Answers

Answer:

C. 12.3

Step-by-step explanation:

We should use Law of Cosines: c² = a² + b² -2abcosC

If that is the case, then EF is a, DF is b, and ∠F is c. We then plug the known variables in:

c² = 12² + 13² - 2(12)(13)cos59°

Plug that into the calc and you should get 12.2313, rounded to 12.3 as your final answer!

Consider the function f(x) = 3x and the function g, which is shown below. G(x)=F(x)-2=3^x-2 How will the graph of g differ from the graph of f? A. The graph of g is the graph of f shifted 2 units up. B. The graph of g is the graph of f shifted 2 units to the right. C. The graph of g is the graph of f shifted 2 units down. D. The graph of g is the graph of f shifted 2 units to the left. Reset Next


H E L P

Answers

Answer:

  C.  The graph of g is the graph of f shifted 2 units down

Step-by-step explanation:

The transformation ...

  g(x) = f(x -h) +k

represents a translation h units right and k units up.

You have h=0 and k=-2, so the graph is shifted 0 units right and 2 units the opposite of up.

The graph of g is the graph of f shifted 2 units down.

Answer:

C

Step-by-step explanation:

I just took the test on edmentum

WORK OUT THE VALUE of 19+7⌹2-5

Answers

Answer:

17.5

Step-by-step explanation:

Remember PEMDAS

step 1 : divide 7 by 2

7 ÷ 2 = 3.5

step 2 : rewrite the equation

19 + 3.5 - 5

step 3  : add 19 + 3.5

19 + 3.5 = 22.5

step 4 : subtract 22.5 - 5

22.5 - 5 = 17.5

Assume A, B, P, and D are n times n matrices. Determine whether the following statements are true or false. Justify each answer.
A matrix A is diagonalizable if A has n eigenvectors.
The statement is false. A matrix is diagonalizable if and only if it has n -1 linearly independent eigenvectors.
The statement is true. A diagonalizable matrix must have more than one linearly independent eigenvector.
The statement is true. A diagonalizable matrix must have a minimum of n linearly independent eigenvectors.
The statement is false. A diagonalizable matrix must have n linearly independent eigenvectors.
If A is diagonalizable, then A has n distinct eigenvalues.
The statement is false. A diagonalizable matrix can have fewer than n eigenvalues and still have n linearly independent eigenvectors.
The statement is true. A diagonalizable matrix must have n distinct eigenvalues.
The statement is false. A diagonalizable matrix must have more than n eigenvalues.
The statement is true. A diagonalizable matrix must have exactly n eigenvalues.
If AP = PD, with D diagonal, then the nonzero columns of P must be eigenvectors of A.
The statement is true. AP = PD implies that the columns of the product PD are eigenvalues that correspond to the eigenvectors of A.
The statement is false. If P has a zero column, then it is not linearly independent and so A is not diagonalizable.
The statement is true. Let v be a nonzero column in P and let lambda be the corresponding diagonal element in D. Then AP = PD implies that Av = lambda v, which means that v is an eigenvector of A.
The statement is false. AP = PD cannot imply that A is diagonalizable, so the columns of P may not be eigenvectors of A.

Answers

Answer:

The correct answers are (1) Option d (2) option a (3) option a

Step-by-step explanation:

Solution

(1) Option (d) The statement is false. A diagonalizable matrix must have n linearly independent eigenvectors: what it implies is that a matrix is diagnostic if it has linearity independent vectors.

(2) Option (a) The statement is false. A diagonalizable matrix can have fewer than n eigenvalues and still have n linearly independent eigenvectors: what this implies is that a diagonalizable matrix  can have repeated eigenvalues.

(3) option (a) The statement is true. AP = PD implies that the columns of the product PD are eigenvalues that correspond to the eigenvectors of A : this implies that P is an invertible matrix whose column vectors are the linearity independent vectors of A.

Which is the better buy?. Store A $180 at 1/3 off Or Store B $110 at 10% off

Answers

Answer: Store B

Step-by-step explanation:

180 / 3 = 60. 180 - 60= $120. Store A cost is $120.

110 * 0.9 = $99. Store B's cost is $99.

Answer:

Store B

Step-by-step explanation:

Store A the price would be about $120.60

Store B price would be about $99

To find store a price, you first find the discount, so

0.33 x 180 = 59.40

Then subtract this from the original price to know the total after the discount

180-59.40=120.60

Do the same thing with the other Store

110 x 0.10 = 11

110-11=99

Which are the possible side lengths of a triangle?
O 3 cm, 5 cm, 9 cm
O 4 cm, 8 cm, 10 cm
O 6 cm, 9 cm, 17 cm
O 8 cm, 10 cm, 18 cm

Answers

Answer:

4 cm, 8 cm, 10 cm

Step-by-step explanation:

For a triangle to exist, two sides added up must be greater than the third side. The only quantities that satisfy this relationship is the second option.

A student said that the y-intercept of the function y = 3 · 4x is 4. What is their mistake? What is the actual y-intercept?

Answers

Answer:

The y intercept is 0

Step-by-step explanation:

the equation of a line is given as

[tex]y= mx+c[/tex]

where

m= is the slope

c= is the y intercept

their mistake is that they did not recall that if the "c" is not shown, it is assumed to be zero (0)

How many arrangements of the letters in the word olive can you make if each arrangement must use three letters

Answers

Answer:

60

Step-by-step explanation:

There are 5 letters that can be first.

There are 4 letters that can be second.

There are 3 letters that can be third.

The number of permutations is 5×4×3 = 60.

Find the vertex of the graphed function.
f(x) = |x-4| +3
AY
00
6
4
2
Y
4
The vertex is at

Answers

Answer:

The x-coordinate is the solution to x - 4 = 0, which is x = 4 and the y-coordinate is 3 so the answer is (4, 3).

You're pretty sure that your candidate for class president has about 6565​% of the votes in the entire school. But​ you're worried that only 100100 students will show up to vote. How often will the underdog​ (the one with 3535​% ​support) win? To find​ out, you

Answers

Answer:

You're pretty sure that your candidate for class president has about 55% of the votes in the entire school. but you're worried that only 100 students will show up to vote. how often will the underdog (the one with 45% support) win? to find out, you set up a simulation.

a. describe-how-you-will-simulate a component.

b. describe-how-you-will-simulate a trial.

c. describe-the-response-variable

Step-by-step explanation:

Part A:

A component is one voter's voting. An outcome is a vote in favor of our candidate.

Since there are 100 voters, we can stimulate the component by using two random digits from 00 - 99, where the digits 00 - 64 represents a vote for our candidate and the digits 65 - 99 represents a vote for the under dog.

Part B:

A trial is 100 votes. We can stimulate the trial by randomly picking 100 two-digits numbers from 00 - 99.

And counted how many people voted for each candidate.  Whoever gets the majority of the votes wins the trial.

Part C:

The response variable is whether the underdog  wins or not.

To calculate the experimental probability, divide the number of trials in which the simulated underdog wins by the total number of trials.

100 POINTS!!!!! PlZ help Find all possible values of the digits Y, E, A, R if YYYY - EEE + AA - R = 1234, and different letters represent different digits.

Answers

Answer:

Y = 1, E = -1, A= 1, R = -1

Step-by-step explanation:

YYYY - EEE + AA - R = 1234

First we would break down the digits in the whole numbers into their place value (thousands, hundreds, tens and units).

YYYY = 1000Y + 100Y +10Y + Y

EEE = 100E + 10E + E

-EEE = -100E - 10E - E

AA = 10A + A

R = R

-R = -R

1234 = 1000+200+30+4

Let's equate each place value for each of the numbers.

Thousands: 1000Y = 1000

Y = 1000/1000 = 1

Hundreds: 100Y - 100E = 200

100(1) - 100E = 200

-100E = 200-100

-100E= 100

E = -1

-EEE = -E(111)

Tens: 10Y - 10E + 10A = 30

10(1) - 10(-1) + 10A = 30

20+ 10A = 30

A = 10/10

A= 1

Units: Y - E + A - R = 4

1 - (-1) + 1 - R = 4

3-R = 4

R = 3-4 = -1

YYYY - EEE + AA - R = 1234

1111 - (-111) + 11 - (-1) = 1111+111+11+1 = 1234

All possible values of the digits Y, E, A, R are Y = 1, E = -1, A= 1, R = -1

Answer:

Y=2

E=9

A=1

R=0

Step-by-step explanation:

Let's check our work.

2,222 - 999 + 11 - 0

1,223 + 11 - 0

1,234 - 0

1,234

Also previous answerer how can digits be negative?

A consumer group surveyed 146 airplane travelers after a flight and found that 132 of them would fly that airline again. Find the standard error for the sample proportion of airline travelers who would fly on that airline again. Enter your answer as a decimal rounded to three decimal places.

Answers

Answer:

[tex]\hat p =\frac{X}{n}[/tex]

And replacing we got:

[tex]\hat p =\frac{132}{146}= 0.904[/tex]

And for this case the standard error assuming normality would be given by:

[tex] SE= \sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

And replacing we got:

[tex]SE= \sqrt{\frac{0.904*(1-0.904)}{146}}= 0.024[/tex]

Step-by-step explanation:

For this problem we know the following notation:

[tex] n= 146 [/tex] represent the sample size selected

[tex] X= 132[/tex] represent the number of airplane travelers who after a flight  would fly that airline again

The estimated proportion for this case would be:

[tex]\hat p =\frac{X}{n}[/tex]

And replacing we got:

[tex]\hat p =\frac{132}{146}= 0.904[/tex]

And for this case the standard error assuming normality would be given by:

[tex] SE= \sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

And replacing we got:

[tex]SE= \sqrt{\frac{0.904*(1-0.904)}{146}}= 0.024[/tex]

Please answer this correctly

Answers

Answer:

5/7

Step-by-step explanation:

There are 7 cards, all of which have an equal chance of being chosen.

And in this case, because there are 7 cards in total, they each have a 1/7 chance of being chosen. Because there are 5 cards greater than 4, you have a 5x1/7 chance =5/7 chance of choosing a number greater than 4.

P.S. If you need it as a percentage, then it is 71.428571%.

P.P.S. Remember if you like the answer then mark as brainliest thank you!

a personality test maybe given to assess what

Answers

Answer:

A personality test may be given to assess individual behavior patterns. A personality test may be given to assess individual behavior patterns. This answer has been confirmed as correct and helpful.

Step-by-step explanation:

hopes this helps

Answer:

Interests, values, skill set and basic personality

Step-by-step explanation:

Personality tests are mostly used as an assessment tool be HR managers and employers during the interview process. They can provide a potential employer with information about your interests, values, skill set and even basic personality, which can be very useful to help an employer make a decision about whether you are the best fit for a position.

I hope this helped. I am sorry if you get this wrong.

PLZZZZ HELPPP FOR BRAINLIEST! COMPARING EXPONENTIAL FUNCTIONS WHICH STATEMENT CORRECTLY COMPARES FUNCTIONS F AND G ​

Answers

Answer:

  B.  Left limits are the same; right limits are different.

Step-by-step explanation:

When we talk about "end behavior," we are generally concerned with the limiting behavior of the function for x-values of large magnitude. Decreasing exponential functions all have the same end behavior: they approach infinity on the left (for large negative values of x), and they approach a horizontal asymptote on the right (for large positive values of x).

If we are to write the end behavior in terms of specific limiting values, we would have to say that ...

  as x → -∞, f(x) → ∞

  as x → -∞, g(x) → ∞ . . . . . . the same end behavior as  f(x)

__

and ...

  as x → ∞, f(x) → -4

  as x → ∞, g(x) → (some constant between 0 and 5) . . . . . different from f(x)

__

So, in terms of these limiting values, the left-end behavior is the same; the right-end behavior is different for the two functions, matching choice B.

If three times a number, added to 2 is divided by the number plus 5, the result is eight thirds.

Answers

Answer:

Number = 34

Step-by-step explanation:

We are looking for our mystery "number". I will call this number N.

We can find out what our equation looks like based on what the question tells us.

"three times a number" is 3N

"added to 2" is + 2

Which so far is 3N + 2

"divided by the number plus 5" is ÷ [tex]{N+5}[/tex]

Combined with the first two parts to give us (3N + 2) ÷ (N + 5)

"the result is eight third" So the above equation is equal to 8/3

Combining all these comments together to get the following equation

(3N + 2) ÷ (N + 5) = 8/3

Rearrange by multiplying both sides of the = by (N+5)

3N + 2 ÷ (N + 5) × (N + 5) = 8/3 × (N + 5)

Simplify

3N + 2 = 8/3 × (N + 5)

3N + 2 = 8N/3 + 40/3

Bring the N numbers to one side and the non N numbers to the other side, by subtracting 2 from both sides of the =

3N + 2 - 2 = 8N/3 + 40/3 - 2

Simplify

3N = 8N/3 + 34/3

and then subtracting 8N/3 from both sides

3N - 8N/3 = 8N/3 - 8N/3 + 34/3

Simplify

1N/3 = 34/3

Simplify for our final answer by multiplying both sides of the = by 3

1N/3 x 3 = 34/3 x 3

N = 34

Many of these steps can be skipped when solving for yourself but I wanted to be thorough

A large school district notices that about 26% of its sophomore students fail Algebra I. An online education supplier suggests the district try its new technology software, which is designed to improve Algebra 1 skills and, thus, decrease the number of students who fail the course. The new technology software is quite expensive, so the company offers a free, one-year trial period to determine whether the Algebra 1 pass rate improves. If it works, the district will pay for continued use of the software. What would happen if the school district makes a Type I error

Answers

Answer:

In the case of a Type I error, the null hypothesis would be wrongly rejected and the school district will conclude that the new technology is effective when it is not.

They will start to pay for the software when in fact it does not improve Algebra 1 skills.

Step-by-step explanation:

A Type I error happens when a true null hypothesis is rejected.

The probability of a Type I error is equal to the significance level, as it is the probabilty of getting an sample result with low probability but only due to chance, as the null hypothesis is in fact true.

In this scenario, the null hypothesis would represent the claim that the new technology does not make significant improvement.

In the case of a Type I error, this null hypothesis would be wrongly rejected and the school district will conclude that the new technology is effective when it is not.

They will start to pay for the software when in fact it does not improve Algebra 1 skills.

I NEED HELP ASAP PLEASE!!! I REALLY NEED HELP!

Answers

Answer:

D.

Step-by-step explanation:

One slope is positive and one negative, so one line should go up and one down. B or D.

y = 1/2 x - 1 line goes up and y-int. = - 1.  Answer D.

y = - 1/2 x + 3 line goes up and y-int. = 3.  Answer D.

The number of bacteria in a refrigerated food product is given by N ( T ) = 22 T 2 − 123 T + 40 , 6 < T < 36 , where T is the temperature of the food. When the food is removed from the refrigerator, the temperature is given by T ( t ) = 8 t + 1.7 , where t is the time in hours. Find the composite function N ( T ( t ) ) : N ( T ( t ) ) = Find the time when the bacteria count reaches 8019. Time Needed = hours

Answers

Answer:

[tex]N(T(t)) = 1408t^2 - 385.6t - 105.52[/tex]

Time for bacteria count reaching 8019: t = 2.543 hours

Step-by-step explanation:

To find the composite function N(T(t)), we just need to use the value of T(t) for each T in the function N(T). So we have that:

[tex]N(T(t)) = 22 * (8t + 1.7)^2 - 123 * (8t + 1.7) + 40[/tex]

[tex]N(T(t)) = 22 * (64t^2 + 27.2t + 2.89) - 984t - 209.1 + 40[/tex]

[tex]N(T(t)) = 1408t^2 + 598.4t + 63.58 - 984t - 169.1[/tex]

[tex]N(T(t)) = 1408t^2 - 385.6t - 105.52[/tex]

Now, to find the time when the bacteria count reaches 8019, we just need to use N(T(t)) = 8019 and then find the value of t:

[tex]8019 = 1408t^2 - 385.6t - 105.52[/tex]

[tex]1408t^2 - 385.6t - 8124.52 = 0[/tex]

Solving this quadratic equation, we have that t = 2.543 hours, so that is the time needed to the bacteria count reaching 8019.

Pleasssseeee hheeelllppp

Answers

Answer:

No

Step-by-step explanation:

They are not congruent or similar because the figures themselves indicate no similar or congruent parts. Although they may seem congruent or similar, without telling us one thing, we cannot assume that they are similar or congruent.

The image of ABC after a reflection across EG is ABC which statement is true about point F ​

Answers

Answer: First option.

Step-by-step explanation:

As the triangle is reflected over the line EG, this means that the distance between each common point of the triangles and the line must be the same for both triangles.

This means that the distance between B and E, is the same distance as the distance between B' and E.

Now, as you know, the midpoint of a segment is a point such that the distance between that point and each endpoint is the same.

So, in the linea AA', the points A and A' are the endpoints, and because F lies in the line of reflection, the distance between A and F is the same distance than in between A' and F.

So F is the midpoint in  the line AA'

The correct option would be the first one, F is the midpoint of AA' because the line EG bisects AA', and F is colinear to E and G.

explain why the solution to the absolute value inequality |4x-9|>-12 is all real numbers

Answers

Answer:

Step-by-step explanation:

Hello,

by definition the absolute value is always positive

so |4x-9| >= 0

so the equation |4x-9| > -12 is always true

so all real numbers are solution of this equation

hope this helps

Find the exact value of each of the following under the given conditions.
a. cosine left parenthesis alpha plus beta right parenthesis        b. sine left parenthesis alpha plus beta right parenthesis        c. tangent left parenthesis alpha plus beta right parenthesis
tangent alpha equals one half
​, pi less than alpha less than StartFraction 3 pi Over 2 EndFraction
​, and cosine beta equals three fifths
​, StartFraction 3 pi Over 2 EndFraction less than beta less than 2 pi

Answers

Answer:

[tex](a)-\dfrac{11\sqrt{5}}{25} \\(b) -\dfrac{2\sqrt{5}}{25} \\(c)\dfrac{11}{2}[/tex]

Step-by-step explanation:

[tex]\tan \alpha =\dfrac12, \pi < \alpha< \dfrac{3 \pi}{2}[/tex]

Therefore:

[tex]\alpha$ is in Quadrant III[/tex]

Opposite = -1

Adjacent =-2

Using Pythagoras Theorem

[tex]Hypotenuse^2=Opposite^2+Adjacent^2\\=(-1)^2+(-2)^2=5\\Hypotenuse=\sqrt{5}[/tex]

Therefore:

[tex]\sin \alpha =-\dfrac{1}{\sqrt{5}}\\\cos \alpha =-\dfrac{2}{\sqrt{5}}[/tex]

Similarly

[tex]\cos \beta =\dfrac35, \dfrac{3 \pi}{2}<\beta<2\pi\\\beta $ is in Quadrant IV (x is negative, y is positive), therefore:\\Adjacent=$-3\\$Hypotenuse=5\\Opposite=4 (Using Pythagoras Theorem)[/tex]

[tex]\sin \beta =\dfrac{4}{5}\\\tan \beta =-\dfrac{4}{3}[/tex]

(a)

[tex]\cos(\alpha + \beta)=\cos\alpha\cos\beta-\sin \alpha\sin \beta\\[/tex]

[tex]=-\dfrac{2}{\sqrt{5}}\cdot \dfrac{3}{5}-(-\dfrac{1}{\sqrt{5}})(\dfrac{4}{5})\\=-\dfrac{2\sqrt{5}}{5}\cdot \dfrac{3}{5}+\dfrac{\sqrt{5}}{5}\cdot\dfrac{4}{5}\\=-\dfrac{2\sqrt{5}}{25}[/tex]

(b)

[tex]\sin(\alpha + \beta)=\sin\alpha\cos\beta+\cos \alpha\sin \beta[/tex]

[tex]\sin(\alpha + \beta)=\sin\alpha\cos\beta+\cos \alpha\sin \beta\\=-\dfrac{1}{\sqrt{5}}\cdot\dfrac35+(-\dfrac{2}{\sqrt{5}})(\dfrac{4}{5})\\=-\dfrac{\sqrt{5}}{5}\cdot\dfrac35-\dfrac{2\sqrt{5}}{5}\cdot\dfrac{4}{5}\\=-\dfrac{11\sqrt{5}}{25}[/tex]

(c)

[tex]\tan(\alpha + \beta)=\dfrac{\sin(\alpha + \beta)}{\sin(\alpha + \beta)}=-\dfrac{11\sqrt{5}}{25} \div -\dfrac{2\sqrt{5}}{25} =\dfrac{11}{2}[/tex]

PLEASEEEE HELLLPPPP COMPARING EXPONENTIAL FUNCTIONS ...an online retailer developed two exponential functions to model the weekly usage of two coupon codes where x os the number of weeks since the start of the year. ​

Answers

Answer:

  A.  The weekly usage of both coupons is decreasing and approaching a horizontal asymptote as x gets larger.

Step-by-step explanation:

You can see that f(x) is a decreasing exponential function because the base is 0.75, a value less than 1. The horizontal asymptote is 10, the constant added to the exponential term.

Obviously, g(x) is decreasing. If we assume it is an exponential function, we know there is a horizontal asymptote. (Every exponential function has a horizontal asymptote.)

__

If you use your graphing calculator's exponential regression function, you can find a good model for g(x) is ...

  g(x) = 950·0.7^x +12

That is, it is an exponential function that decays faster than f(x), but has a higher horizontal asymptote.

_____

Both functions are decreasing and approaching horizontal asymptotes.

The FDA regulates that fresh Albacore tuna fish that is consumed is allowed to contain 0.82 ppm of mercury or less. A laboratory is estimating the amount of mercury in tuna fish for a new company and needs to have a margin of error within 0.023 ppm of mercury with 97% confidence. Assume the population standard deviation is 0.143 ppm of mercury. What sample size is needed? Round up to the nearest integer, do not include any decimals. Answer:

Answers

Answer:

[tex]n=(\frac{2.17(0.143)}{0.023})^2 =182.03 \approx 183[/tex]

So the answer for this case would be n=183 rounded up to the nearest integer

Step-by-step explanation:

Information provided

[tex]\bar X[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

[tex]\sigma = 0.143[/tex] represent the population standard deviation

n represent the sample size  

[tex] ME = 0.023[/tex] the margin of error desired

Solution to the problem

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =0.023 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The confidence level is 97% or 0.97 and the significance would be [tex]\alpha=1-0.97=0.03[/tex] and [tex]\alpha/2 = 0.015[/tex] then the critical value would be: [tex]z_{\alpha/2}=2.17[/tex], replacing into formula (5) we got:

[tex]n=(\frac{2.17(0.143)}{0.023})^2 =182.03 \approx 183[/tex]

So the answer for this case would be n=183 rounded up to the nearest integer

You might need:

A circle is centered at J(3,3) and has a radius of 12.

Where does the point F(-6, -5) lie?

Choose 1 answer:

Answers

Answer:

Step-by-step explanation:

The equation of this circle is (x - 3)^2 + (y - 3)^2 = 12^2.

Let's substitute the coordinates of the given point and compare the results to the above equation:  do they produce a correct statement?

(-6 - 3)^2 + (-5 - 3)^2 = ?

9^2 + 8^2 = 145

Because r = 12, the above result would need to be 144, not 145, if the given point were actually on the circle.  We must conclude that (-6, -5) lies just outside the circle.

81 + 64 = 144  

justify each step x/3-7=11 x/3=18 x=6

Answers

This is the steps for equation solving for the value of x,

x/3-7 = 11

now 7 goes to the other side of equation by changing the sign from - to +,

x/3 = 11 + 7

x/3 = 18

now when we multiply both sides of equation with 3 or 3 goes to the other side of equation and multiply with 18 leaving x alone here for finding the value of x,

and we get, x = 54

at the end of equation we get x = 54, if the equation was in the form 3x - 7 = 11, then we will get x = 6

Suppose that the thickness of one typical page of a book printed by a certain publisher is a random variable with mean 0.1 mm and a standard deviation of 0.002 mm. A new book will be printed on 500 sheets of this paper. Approximate the probability that the

Answers

Answer:

The probability that the thicknesses at the entire book will be between 49.9 mm and 50.1 mm is 0.97.

Step-by-step explanation:

The complete question is:

Suppose that the thickness of one typical page of a book printed by a certain publisher is a random variable with mean 0.1 mm and a standard deviation of 0.002 mm Anew book will be printed on 500 sheets of this paper. Approximate the probability that the thicknesses at the entire book (excluding the cover pages) will be between 49.9 mm and 50.1 mm. Note: total thickness of the book is the sum of the individual thicknesses of the pages Do not round your numbers until rounding up to two. Round your final answer to the nearest hundredth, or two digits after decimal point.

Solution:

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e S, will be approximately normally distributed.  

Then, the mean of the distribution of the sum of values of X is given by,  

 [tex]\mu_{S}=n\mu[/tex]

And the standard deviation of the distribution of the sum of values of X is given by,  

[tex]\sigma_{S}=\sqrt{n}\sigma[/tex]

The information provided is:

[tex]n=500\\\mu=0.1\\\sigma=0.002[/tex]

As n = 500 > 30, the central limit theorem can be used to approximate the total thickness of the book.

So, the total thickness of the book (S) will follow N (50, 0.045²).

Compute the probability that the thicknesses at the entire book will be between 49.9 mm and 50.1 mm as follows:

[tex]P(49.9<S<50.1)=P(\frac{49.9-50}{0.045}<\frac{S-E(S)}{SD(S)}<\frac{50.1-50}{0.045})[/tex]

                               [tex]=P(-2.22<Z<2.22)\\\\=P (Z<2.22)-P(Z<-2.22)\\\\=0.98679-0.01321\\\\=0.97358\\\\\approx 0.97[/tex]

Thus, the probability that the thicknesses at the entire book will be between 49.9 mm and 50.1 mm is 0.97.

6 identical toys weigh 1.8kg how much would 4 weigh

Answers

Answer:

1.2kg

Step-by-step explanation:

6 identical toys weigh 1.8kg.

1 toy would weigh:

1.8/6 = 0.3

0.3 kg.

Multiply 0.3 with 4 to find how much 4 identical toys would weigh.

0.3 × 4 = 1.2

4 identical toys would weigh 1.2kg

Answer:

[tex]1.2kg[/tex]

Step-by-step explanation:

6 identical toys weigh = 1.8kg

Let's find the weight of 1 toy ,

[tex]1.8 \div 6 = 0.3[/tex]

Now, lets find the weigh of 6 toys,

[tex]0.3 \times 4 = 1.2kg[/tex]

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