prove that the square of an odd number is always 1 more than a multiple of 4

Answer:

probability[Number of 6 random sample do not have cavities] = 0.8

Step-by-step explanation

Given:

Number of student do not have cavities = 60%

Number of random sample = 9 children

Find:

Probability[Number of 6 random sample do not have cavities]

Computation:

n = 9

p = 60% = 0.6

P(At least 6)  

Probability[Number of 6 random sample do not have cavities] = 1 - P(Less than 6)  

Probability[Number of 6 random sample do not have cavities] = 1 - P(Less than or equal to 6)

Probability[Number of 6 random sample do not have cavities] = 0.8

Answer:

19 beers must be sampled.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

The population standard deviation for the temperature of beers found in Scooter's Tavern is 0.26 degrees.

This means that [tex]\sigma = 0.26[/tex]

If we want to be 90% confident that the sample mean beer temperature is within 0.1 degrees of the true mean temperature, how many beers must we sample?

This is n for which M = 0.1. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.1 = 1.645\frac{0.26}{\sqrt{n}}[/tex]

[tex]0.1\sqrt{n} = 1.645*0.26[/tex]

[tex]\sqrt{n} = \frac{1.645*0.26}{0.1}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.645*0.26}{0.1})^2[/tex]

[tex]n = 18.3[/tex]

Rounding up:

19 beers must be sampled.

Answer:

9. C

10. C

11. C

Step-by-step explanation:

9.

simply, [tex]\frac{4}{5} >\frac{2}{3}[/tex]

10.

the greatest divisor of 28 is 7, so:

28 + 7 = 35

11.

the greatest divisor of 15 is 5, so:

15 + 5 = 20

n = 20

the greatest divisor of 20 is 10, so:

20 + 10 = 30

Answer:

ಠ_ಠ

Step-by-step explanation:

Answer:

S = v1 t1 = 7 t1    traveling downstream

S = v2 t2 = 5 t2    traveling upstream

7 t1 = 5 t2

7 (6 - t2) = 5 t2     since t1 + t2 = 6

42 - 7 t2 = 5 t2

t2 = 42 / 12 = 3.5 hrs so t1 = 2.5 hrs

S = 7 t1 = 7 * 2.5 = 17.5 mi

Also, S = 5 t2 = 5 * 3.5 = 17.5 mi

Answer:

7 apples into 2 pieces and 4 apples into 4 pieces

Step-by-step explanation:

if you split 7 apples into 2 pieces each than you'l have 14 slices. You need 30 though which means you need 16 more. so you split 4 into 4 pieces. and the number of apples we used is 7 and 4 which make up 11. So this answer works

Answer:

68

Step-by-step explanation:

I did it on my test

The missing value in the table is 68. The correct answer would be option (B).

A linear relationship is a connection that takes the shape of a straight line on a graph between two distinct variables - x and y. When displaying a linear connection using an equation, the value of y is derived from the value of x, indicating their relationship.

The table shows the relationship between the number of faculty members and the number of students at a local school.

Faculty     Students

1                     17

2                   34

3                   51

4                    ?

The relationship between the number of faculty members and the number of students at the local school is that for every faculty member, there are 17 students.

Therefore, if there are 4 faculty members, we can find the number of students by multiplying 4 by 17, which gives us 68.

Thus, the missing value in the table is B. 68.

Learn about the linear relationship here :

https://brainly.com/question/11663530

#SPJ6

Answer:

Step-by-step explanation:

-2x +38 = 2(3 + 3x)

-2x + 38 = 2*3 + 2*3x

-2x + 38 = 6 + 6x

Add 2x to both sides

38 = 6 + 6x + 2x  

Combine like terms

38 = 6 + 8x

Subtract 8  from both sides

38 - 6 = 8x

8x = 32

Divide both sides by 8

x = 32/8

x = 4

Answer:

x = 4

Step-by-step explanation:

Use distributive property to multiply 2 by 3 and 3x

subtract 6x from both side

combine -2x and -6x to get -8x

subtract 38 from both side

subtract 38 from 6 to get -32

divide both side by -8

[tex] \small \sf \frac{-8x}{ -8} = \frac{-32}{-8} \\ \\ \small \sf x = \frac{- 32}{-8}[/tex]

divide -32 by -8 to get 4

Answer:

A F(x) it is the power function, make sure to take notes as well

9514 1404 393

Answer:

  2xy^2

Step-by-step explanation:

The terms are "like" so can be combined. It might be helpful to think of this as an application of the distributive property.

  -3xy^2 +5xy^2 = (-3 +5)xy^2 = 2xy^2

Step-by-step explanation:

Interest (I)=R9600

Rate(R)=16%

Time (T)=5years

Principal (P)=?

P=100×I÷R×T

P=100×R9600÷16×5

P=R960000÷80

P=R12, 000

Answer:

      The amount he took as loan = R12,000

Step-by-step explanation:

Simple Interest

Let loan amount be = P

R = 16%

T = 5years

I = 9600

Find P

  [tex]I = \frac{PRT}{100}\\\\9600 = \frac{P \times 16 \times 5}{100}\\\\P = \frac{9600 \times 100}{16 \times 5} = 12,000[/tex]

Answer:

e=12.5 or e=25/2

Step-by-step explanation:

Step 1: Distribute

-40a - 5 + 6 = 281

Step 2: Combine Like Terms

-40a + 1 = 281

Step 3: Move Variables and Constants to Different Sides

-40a = 280

Step 4: Divide

a = -7

Hope this helps!

a = -7

-5 ( 8a + 1 ) + 6 = 281

Step 1 :- Distribute -5 through parantheses.

Step 2 :- Combine like terms.

Step 3 :- Move constant to right-hand side and change their sign.

Step 4 :- Subtract the numbers.

Step 5 :- Divie both side by -40 .

Answer:

i think you need to attach a fine for us to do so?

Step-by-step explanation:

Answer:

I can't tell you without the problem

Answer:

251.33

Step-by-step explanation:

C=3.14(d)

C=3.14(80)

Answer:

[tex]P(\frac{A}{B'})[/tex]=0.111

Step-by-step explanation:

Given:

The probability of winning the first game is 10.1

The first game is won

The probability of winning the second game is 15

If the first is lost, the probability of winning the second game is 25

Solution:

[tex]P(B)=P(A)P(\frac{B}{A})+P(A')P(\frac{B}{A'})\\ =0.1(0.15)+(0.3)*0.25)\\P(B)=0.24 ------(1)\\P(\frac{A}{B})=\frac{P(\frac{B}{A})P(A) }{P(B)}\\ =\frac{0.15(0.1)}{0.24}\\ =0.0625 ------(2)\\P(B')=1-P(B)=0.76 ------(3)\\P(A)=P(B)P(\frac{A}{B})+P(B')P(\frac{A}{B'})\\0.1=0.24(0.0625)+0.76(p(\frac{A}{B'} ))\\P(\frac{A}{B'})=0.111[/tex]

Answer:

[tex]P(W_1/W_2')=0.1110[/tex]

Step-by-step explanation:

Probability of winning the first game be considering the given factors be, [tex]W_1=0.1[/tex]

Probability of winning the second game be considering the given factors be, [tex]W_2[/tex]= probability of winning the second game when the first game is won + probability of winning the second game when the first game is lost:

[tex]P(W_2)=P(W_1).P(W_2/W_1)+P(W_1').P(W_2/W_1')[/tex]

[tex]P(W_2)=0.1\times 0.15+0.9\times 0.25[/tex]

[tex]P(W_2)=0.24[/tex]

Hence the probability of losing the second game:

[tex]P(W_2')=1-P(W_2)[/tex]

[tex]P(W_2')=0.76[/tex]

Probability of winning the first game when the second game is won:

[tex]P(W_1/W_2)=\frac{P(W_2/W_1).P(W_1)}{P(W_2)}[/tex]

[tex]P(W_1/W_2)=\frac{0.15\times 0.1}{0.24}[/tex]

[tex]P(W_1/W_2)=0.0625[/tex]

Probability of winning the first game be considering the given factors, [tex]W_1[/tex]= probability of winning the first game when the second game is won + probability of winning the first game when the second game is lost:

[tex]P(W_1)=P(W_2).P(W_1/W_2)+P(W_2').P(W_1/W_2')[/tex]

[tex]0.1=0.24\times0.0625+0.76\times P(W_1/W_2')[/tex]

[tex]P(W_1/W_2')=0.1110[/tex]

Answer:

A. reflection.

Step-by-step explanation:

If you were to use the reflection rule, then your answer will be:

B' (Now D): (1 , 2)

A' (Now E): (4 , 2)

C' (Now F): (3 , 5)

In this case, the reflected triangle does not match the given points, therefore it cannot be reflection.

~

Answer:

Lf(x) = Lg(x) = Lh(x) =  1 - 2x

value of the functions and their derivative are the same at x = 0

Step-by-step explanation:

Given :

f(x) = (x − 1)^2,  

g(x) = e^−2x ,  

h(x) = 1 + ln(1 − 2x).

a) Determine Linearization of  f, g and h  at a = 0

L(x) = f (a) + f'(a) (x-a)  ( linearization of f at a )

for f(x) = (x − 1)^2  

f'(x ) = 2( x - 1 )

at x = 0

f' = -2  

hence the Linearization at a = 0

Lf (x) = f(0) + f'(0) ( x - 0 )

Lf (x) = 1 -2 ( x - 0 ) = 1 - 2x

For g(x) = e^−2x

g'(x) = -2e^-2x

at x = 0

g(0) = 1

g'(0) = -2e^0 = -2

hence linearization at a = 0

Lg(x) = g ( 0 ) + g' (0) (x - 0 )

Lg(x) = 1 - 2x

For h(x) = 1 + ln(1 − 2x).

h'(x) =  -2 / ( 1 - 2x )

at x = 0

h(0) = 1

h'(0) = -2

hence linearization at a = 0

Lh(x) = h(0) + h'(0) (x-0)

        = 1 - 2x

Observation and reason

The Linearization is the same in every function i.e. Lf(x) = Lg(x) = Lh(x) this is because the value of the functions and their derivative are the same at x = 0

Answer:

No.

Step-by-step explanation:

y/x has to be the same number no matter what except at point (0 0) which it must also include for it to be a direct variation.

*y=2x+3 is not a direct variation because you can not write it as y/x=k where k is some constant number. If we were y=2x, then yes since y/x=2.

*You could also take two points and see if they are proportional. That is, you can see if y2/x2 gives the same value as y1/x1 where (x1,y1) and (x2,y2) are points on the line y=2x+3. This must work for every pair of points on the linear relation except at x=0 (where you would or should have y=0 if it is directly proportional).

Let's try it out. If x=1, then y=2(1)+3=5.

5/1=5

If x=2, then y=2(2)+3=7

7/2=3.5

As you can see 5 doesn't equal 3.5.

*For it to be a direct variation, it also must contain the point (0,0) and be a diagonal line when graphed. It can also be written in form y=kx where k is a constant number. This fails two of the the things I mentioned. It doesn't contain point (0,0) because y=2(0)+3=3 not 0. It cannot be written in form y=kx because of the plus 3.

If it were y=2x, then the answer would be yes.

Answer:

[tex]\sigma = 1.8[/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} \ \\ P(x) & {0.2} & {0.1} & {0.1} & {0.2} & {0.2}& {0.2} \ \end{array}[/tex]

Required

The standard deviation

First, calculate the expected value E(x)

[tex]E(x) = \sum x * P(x)[/tex]

So, we have:

[tex]E(x) = 0 * 0.2 + 1 * 0.1 + 2 * 0.1 + 3 * 0.2 + 4 * 0.2 + 5 * 0.2[/tex]

[tex]E(x) = 2.7[/tex]

Next, calculate E(x^2)

[tex]E(x^2) = \sum x^2 * P(x)[/tex]

So, we have:

[tex]E(x^2) = 0^2 * 0.2 + 1^2 * 0.1 + 2^2 * 0.1 + 3^2 * 0.2 + 4^2 * 0.2 + 5^2 * 0.2[/tex]

[tex]E(x^2) = 10.5[/tex]

The standard deviation is:

[tex]\sigma = \sqrt{E(x^2) - (E(x))^2}[/tex]

[tex]\sigma = \sqrt{10.5 - 2.7^2}[/tex]

[tex]\sigma = \sqrt{10.5 - 7.29}[/tex]

[tex]\sigma = \sqrt{3.21}[/tex]

[tex]\sigma = 1.8[/tex] --- approximated

Answer:

The level of significance is the

b. maximum allowable probability of Type I error.

Step-by-step explanation:

The significance level provides the maximum probability of rejecting the null hypothesis when it is true.  It is the same as a type I error (also known as false-positive).  This error occurs when a researcher or investigator rejects a true null hypothesis that is supposed to be accepted.  It is the opposite of a type II error (false-negative), which occurs when the researcher fails to reject a false null hypothesis.

Answer:

4 places after the decimal.

the result is 0.0215

Step-by-step explanation:

I assume the expression is really

43 / (2⁴ × 5³)

this is the same as

(((((((43 / 2) / 2) / 2) / 2) / 5) / 5) / 5)

since the starting value is an odd number, the first division by 2 creates a first position after the decimal point, and it must be a 5, as the result is xx.5

the second division by 2 splits again the uneven end .5 in half, creating a second position after the decimal point again ending in 5, as the result is now xx.x5

the third division by 2 does the same thing with that last 5 and creates a third position after the decimal point ending again in 5, as the result is now xx.xx5

the fourth division by 2 does again the same thing, a fourth position after the decimal point is created ending in 5. now xx.xxx5

in essence, every division of the 0.5 part by 2 is the same as a multiplication by 0.5, which squares 0.5 leading to 0.5². the next division did the same thing leading to 0.5³.

and finally the fourth division to 0.5⁴.

0.5⁴ = (5/10)⁴ = 5⁴/10⁴

so, now we start to divide this result by 5. since the positions after the decimal point are divisible by 5 without remainder, as we have 5⁴ to work with.

every divisible by 5 takes one of these powers away.

so, we go from 5⁴/10⁴ to 5³/10⁴ to 5²/10⁴ to 5/10⁴.

all the time we maintain the 10⁴ in the denominator of the fraction. and that determines the positions after the decimal point.

so, after all the individual divisions we come to and end and are still limited to the 4 positions after the decimal point.

Answer:

1.92755 ,1.870320 i hope it will help you

Answer:

First bag's unit price=$1.92 per kg  Second bag's unit price=$1.87 per kg

Step-by-step explanation:

1.92 becomes 1.93

Answer:

The square root property should have been applied to both complete sides of the equation instead of to select

variables.

Answer:

26244π in³

Step-by-step explanation:

Applying,

Voluem of a sphere

V = 4/3(πr³).......... Equation 1

Where r = radius of the sphere, π = pie

From the diagram,

Given: r = 54/2  = 27 in

Substitute these value in equation 1

V = 4/3(27³)(π)

V = 26244π in³

Hence the volume of the figure expressed in terms of π is 26244π in³

Answer:

x = 69

Step-by-step explanation:

m<M = x

From the triangle we know that

m<M + m<MNQ + m<MQN = 180

From the parallel lines we know that

m<MNQ = m<UQN = x

x + x + 42 = 180

2x + 42 = 180

2x = 138

x = 69