You have 9kg of oats and cup scales that gears of 50g and 200g. How − in three weighings− can you measure 2kg of the oats?

Answer:

[tex]\huge\boxed{c = 14.9}[/tex]

Step-by-step explanation:

Using Cosine Rule

[tex]c^2 = a^2 + b^2 -2abCosC[/tex]

Where a = 11 , b = 7 and C = 110

[tex]c^2 = (11)^2+(7)^2-2(11)(7)Cos 110[/tex]

[tex]c^2 = 121+49-154 (-0.34)\\c^2 = 170+52.7\\c^2 = 222.7[/tex]

Taking sqrt on both sides

c = 14.9

Answer:

A

Step-by-step explanation:

f(x)→g(x)

(0, 0) → (3, -4)

Therefore it increases it x-axis from 0 to 3

And decreases in y-axis from 0 to -4

Answer:

20.8 hours

Step-by-step explanation:

Given that hours (h) varies inversely with age (a) then the equation relating them is

h = [tex]\frac{k}{a}[/tex] ← k is the constant of variation

To find k use the condition h = 52 when a = 20, thus

52 = [tex]\frac{k}{20}[/tex] ( multiply both sides by 20 )

1040 = k

h = [tex]\frac{1040}{a}[/tex] ← equation of variation

When a = 50, then

h = [tex]\frac{1040}{50}[/tex] = 20.8 hours

[tex]_nC_k=\dfrac{n!}{k!(n-k)!}\\\\\\_{34}C_{34}=\dfrac{34!}{34!0!}=1[/tex]

In general, [tex]_nC_n=1[/tex]

Answer:

a

  The point estimate of the population mean is  [tex]\= x = 56[/tex]

b

  The 80% confidence level is  [tex]50.57 < \mu < 61.43[/tex]

c

  There is  80% confidence that the true population mean lies within the confidence interval.

Step-by-step explanation:

From the question we are told that

   The  sample size is  n =  18

   The  standard deviation is  [tex]\sigma = 18 \ L[/tex]

   The  sample mean is  [tex]\= x = 56[/tex]

Generally the point estimate of the population mean is equivalent to the sample mean whose value is  [tex]\= x = 56[/tex]

Given that the confidence interval is 80% then the level of significance is mathematically represented as

      [tex]\alpha = 100 - 80[/tex]

      [tex]\alpha = 20 \%[/tex]

      [tex]\alpha = 0.20[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table

 The  value is   [tex]Z_{\frac{ \alpha }{2} } = 1.28[/tex]

 Generally the margin of error is mathematically evaluated as

          [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

=>       [tex]E = 1.28 * \frac{18 }{\sqrt{18} }[/tex]

=>       [tex]E = 5.43[/tex]

     Generally the 80% confidence interval is mathematically represented as

    [tex]\= x - E < \mu < \= x + E[/tex]

=>    [tex]56 - 5.43 < \mu < 56 + 5.43[/tex]

=>   [tex]50.57 < \mu < 61.43[/tex]

The  interpretation is that there is  80% confidence that the true population mean lies within the limit

Answer:

(-2, 2)

Step-by-step explanation:

Given:

Difference of coordinates:

The ratio of AB to AC is 2:1. So:

Then coordinates of point B should be 2/3 from the point A:

So point B has coordinates of (-2, 2)

Answer: x= -1, z=2, y= -4

Step-by-step explanation:

System of equations:

-5x - 4y - 3z= 15  +

-10x + 4y + 6z= 6

-15x         + 3z = 21  ------>  3 (-5x + z) = 7.3

-5x + z = 7

now,

-10x + 4y + 6z= 6

2(-5x + z) + 4y + 4z = 6

14 + 4y + 4z = 6

7 + 2y + 2z = 3

2y + 2z= -4

y+z=-2

Now we were using the equation: 20x + 4y + 4z = -28

20x + 4(y+z) = 20x -8= - 28

20 x = -20

x= -1

With this we can find y and z

X=-1

-5x + z = 7

z= 2

y+z=-2

y=-4

Finally we have: x= -1, z=2, y= -4

I hope this can help you.

Thank you

Answer:

x³ - 5x² - x + 5

Step-by-step explanation:

(x+1)(x-1)(x-5) = 0

fisrt step:

(x+1)(x-1) = x*x + x*-1 + 1*x + 1*-1 = x² - x + x - 1 = x² - 1

then:

(x+1)(x-1)(x-5) = (x²-1)(x-5)

(x²-1)(x-5) = x²*x + x²*-5 -1*x -1*-5 = x³ - 5x² - x + 5

Answer:

C. It is the product of the prime factors that are either unique to or shared by the polynomials.

Step-by-step explanation:

LCM of polynomials is:

=> Finding the factors of all the numbers and variable in the expression

=> Next, we multiply the unique numbers and the variable of the expression to find the LCM.

So, C is the correct answer.

The LCM of a set of polynomials  is the product of the prime factors that are either unique to or shared by the polynomials.  

To find the lowest common multiple (L.C.M.) of polynomials, we first find the factors of polynomials by the method of factorization and then adopt the same process of finding L.C.M.

Example : The L.C.M. of 4a2 - 25b2 and 6a2 + 15ab.

Factorizing 4a2 - 25b2 we get,

(2a)2 - (5b)2, by using the identity a2 - b2.

= (2a + 5b) (2a - 5b)

Also, factorizing 6a2 + 15ab by taking the common factor '3a', we get

= 3a(2a + 5b)

L.C.M.  is 3a(2a + 5b) (2a - 5b)

According to the question

The LCM of a set of polynomials is

 is the product of the prime factors that are either unique to or shared by the polynomials.  

(from above example we can see that )

Hence,  It is the product of the prime factors that are either unique to or shared by the polynomials.  

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Answer: Jake is 9 and his dad is 33.

Step-by-step explanation: 9x3=27+6=33 9+33=42

Answer:

Jake is 9 and Jake's dad is 33

Step-by-step explanation:

To solve this we need to create a equation where D is the age of Jake's dad and J is the age of Jake

J+D=42

3J+6=D

Solve by substitution

Answer:

3 inches

Step-by-step explanation:

The green bar reaches all the way to the 3 on the ruler, and each number represents an inch.

Answer:

A. The stepwise selection procedure uses Adjusted R-square as the "best" model criterion.

Step-by-step explanation:

Stepwise regression is a model which uses variables in step by step manner. The procedure involves removal or inclusion of independent variables one by one. It adds the most significant independent variable and removes the less significant independent variable. Usually stepwise selection uses R-square or Mallows Cp for picking the best fit.

Negative Integers are :

Answer: x=8/3 or x= 2.6666....

Step-by-step explanation:

[tex]2+3x-10=0[/tex]

[tex]2-10=-8[/tex]

[tex]3x-8=0[/tex]

add 8 on both sides

[tex]3x-8+8=0+8[/tex]

[tex]3x=8[/tex]

divide 3 on both sides

[tex]x=\frac{8}{3}[/tex]

Answer:

8/3

Step-by-step explanation:

2 +3x + 10 = 0

2-10 +3x = 0

-8 + 3x = 0

3x = 8

x = 8/3

Answer:

[tex] X^{\frac{8}{15}} [/tex]

Step-by-step explanation:

[tex] X^\frac{1}{3} \times X^\frac{1}{5} = [/tex]

To multiply two powers with the same base, write the base and add the exponents.

[tex] = X^{\frac{1}{3} + \frac{1}{5}} [/tex]

[tex] = X^{\frac{5}{15} + \frac{3}{15}} [/tex]

[tex] = X^{\frac{8}{15}} [/tex]

Answer:

Graph 1

Step-by-step explanation:

The only graph that could be possible would be graph 1.

As you can see the function x = 2t - 4 is linear, and the only graph that consists of a linear line would be the first graph.

Answer:

18km

Step-by-step explanation:

1cm:4.5km/4cm then get the answer as 18km

1 cm represents [tex]4.5[/tex] km. To find the actual distance between two towns that are 4 cm apart on the map, we can use the scale ratio.

Since 1 cm represents [tex]4.5[/tex] km, we can calculate the actual distance by multiplying the map distance with the scale ratio. Map distance: 4 cm Scale ratio: 1 cm represents [tex]4.5[/tex] km Actual distance = Map distance × Scale ratio Actual distance[tex]= 4 cm × 4.5[/tex] km/cm Actual distance[tex]= 18 km[/tex]

Therefore, the actual distance between the two towns is18 [tex]18[/tex] km. Using the given scale, 1 cm on the map corresponds to[tex]4.5[/tex]km in reality. As the towns are represented as 4 cm apart on the map, the actual distance between them is [tex]18[/tex]km.

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Answer: There is only 1 girl.

Step-by-step explanation:

As you can see the probability of choosing a girl is 4/11  out of the whole people which is 7 boys and 4 girls. And the same way the probability of choosing a boy  is 7/11 which is almost doubled the amount of girls. So to think about it, there will be more boys than girls if there is a random selection because the boys chances of getting picked is high.

Answer:

12/27

Step-by-step explanation:

Step 1

We find all the total number of possible outcomes of rolling two faces of a six-sided die are painted red, two are painted blue, and two are painted yellow.

Where

R = Red

B = Blue

Y = Yellow

RRR, BBB, YYY, RBY, RYB, YBR, YRB, BRY, BYR, BBY, BBR, YYB, RRY, RRB, BYB, BRB, YRY, YBY, RYR, RBR,YRR, BRR, RBB, RYY, BYY,YBB, YYR

We have 27 Total outcomes for this 6 faced die

Step 2

The event that exactly one of the colors that appears face up is red.

RBY, RYB, YBR, YRB, RBB, RYY, BBR,

BRB, BRY, YRY, BYR, YYR

Total number of Possible outcomes where EXACTLY one of the colours that appears face up is red = 12

The probability of the event that exactly one of the colors that appears face up is red = Number of possible outcomes/ Total number of outcomes

= 12/27

Answer:

NT = 14 units

Step-by-step explanation:

In this question we will apply the theorem of intersecting chords.

Two chords MY and TN are intersecting each other inside a circle at a point H.

Theorem states,

MH × HY = TH × HN

12(x) = 8(x + 2)

12x = 8x + 16

12x - 8x = 16

4x = 16

x = 4

Therefore, measure of chord NT = NH + HT

                                                       = 8 + (x + 2)

                                                       = x + 10

                                                       = 4 + 10

                                                       = 14 units

Answer:

solution below

Step-by-step explanation:

The question says 6 working mother's were selected so n = 6 not 0.6

We are expected to find

P(X = 0,1,2,3,4,4,6)

1. When x = 0

6C0*(0.34)⁰*(0.66)⁶

= 1 *1* 0.827

= 0.0827

2. When X = 1

6C1*(0.34)¹*(0.66)⁵

= 6 x 0.34 x 0.252

= 0.2555

3. When X = 2

6C2*(0.34)²*(0.66)⁴

= 15 x 0.1156 x 0.1897

= 0.3289

4. When x = 3

6C3*(0.34)³*(0.66)³

20 x 0.039304 x 0.2875

= 0.2599

5. When X = 4

6C4*(0.34)⁴*(0.66)²

= 15 x 0.01336 x 0.4356

= 0.8729

6. When x = 5

6C5*(0.34)⁵*(0.66)¹

= 6 x 0.0045 x 0.66

= 0.01782

7. When x = 6

6C6*(0.34)⁶*(0.66)⁰

1 x 0.0015 x 1

= 0.0015

Answer:

a. the probability that her pulse rate is less than 76 beats per minute is 0.5948

b. If 25 adult females are randomly​ selected,  the probability that they have pulse rates with a mean less than 76 beats per minute is 0.8849

c.   D. Since the original population has a normal​ distribution, the distribution of sample means is a normal distribution for any sample size.

Step-by-step explanation:

Given that:

Mean μ =73.0

Standard deviation σ =12.5

a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is less than 76 beats per minute.

Let X represent the random variable that is normally distributed with a mean of 73.0 beats per minute and a standard deviation of 12.5 beats per minute.

Then : X [tex]\sim[/tex] N ( μ = 73.0 , σ = 12.5)

The probability that her pulse rate is less than 76 beats per minute can be computed as:

[tex]P(X < 76) = P(\dfrac{X-\mu}{\sigma}< \dfrac{X-\mu}{\sigma})[/tex]

[tex]P(X < 76) = P(\dfrac{76-\mu}{\sigma}< \dfrac{76-73}{12.5})[/tex]

[tex]P(X < 76) = P(Z< \dfrac{3}{12.5})[/tex]

[tex]P(X < 76) = P(Z< 0.24)[/tex]

From the standard normal distribution tables,

[tex]P(X < 76) = 0.5948[/tex]

Therefore , the probability that her pulse rate is less than 76 beats per minute is 0.5948

b.  If 25 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 76 beats per minute.

now; we have a sample size n = 25

The probability can now be calculated as follows:

[tex]P(\overline X < 76) = P(\dfrac{\overline X-\mu}{\dfrac{\sigma}{\sqrt{n}}}< \dfrac{ \overline X-\mu}{\dfrac{\sigma}{\sqrt{n}}})[/tex]

[tex]P( \overline X < 76) = P(\dfrac{76-\mu}{\dfrac{\sigma}{\sqrt{n}}}< \dfrac{76-73}{\dfrac{12.5}{\sqrt{25}}})[/tex]

[tex]P( \overline X < 76) = P(Z< \dfrac{3}{\dfrac{12.5}{5}})[/tex]

[tex]P( \overline X < 76) = P(Z< 1.2)[/tex]

From the standard normal distribution tables,

[tex]P(\overline X < 76) = 0.8849[/tex]

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

In order to determine the probability in part (b);  the  normal distribution is perfect to be used here even when the sample size does not exceed 30.

Therefore option D is correct.

Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

heya friend

0.2

0.2**10/10

=2/10

in 2/10 2 and 10 are integers

and 10 is not zero

so it is sacrificed

hope this helps u

Answer:

0.2

0.2**10/10

=2/10

in 2/10 2 and 10 are integers

10 is not 0

Step-by-step explanation:

Answer:

math is really a difficult subject for me. sometimes i feel confident when i get my answers correct, but sometimes i feel bored when i dnt get my answer. Sometimes i feel anxious , sometimes i feel excited to solve the problems.

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Answer:

x = -2

Step-by-step explanation:

given f(x) = x² + 2x + 1

f(x+2) = (x+2)² + 2(x+2) + 1

= x² 4x+4+2x+4+1

= x² + 6x + 9

for f(x) = f(x+2), simply equate the two expressions and solve for x

f(x) = f(x+2)

x² + 2x + 1 = x² + 6x + 9      (x² terms cancel out)

2x + 1 = 6x + 9  (subtract 1 from both sides)

2x  = 6x + 9 - 1

2x  = 6x + 8  (subtract 6x from both sides)

2x - 6x = 8

-4x = 8 (divide both sides by -4)

x = 8 / (-4)

x = -2

Answer:

C. Infinitely many solutions

Step-by-step explanation:

First, simplify the second equation by dividing it by 2

2y = 6x + 2

y = 3x + 1

Now, we can see that both equations are the same, both y = 3x + 1.

Since they are the same line, this means that there are infinitely many solutions.

So, the correct answer is C.

Answer:

Standard deviation= 4.46

B) 4.89 is the nearest answer

Step-by-step explanation:

Standard deviation √variance

Variance= (summation (x-mean)²)/n

Mean= summation of numbers/total

Mean =( 12+13+ 7+5+15 18)/6

Mean= 70/6

Mean= 11.67

Variance=(( 12-11.67)²+(13-11.67)²+ (7-11.67)²+(5-11.67)²+(15-11.67)²+ (18-11.67)²)/6

Variance= (0.1089+1.7689+21.8089+44.4889+11.0889+40.0689)/6

Variance= 119.3334/6

Variance= 19.8889

Standard deviation= √variance

Standard deviation= √19.8889

Standard deviation= 4.46

Answer:

2x

Step-by-step explanation:

These are like terms so we can combine them

4x-2x

2x

Answer:

2x

Explanation:

Since both terms in this equation are common, we can simply subtract them.

4x - 2x = ?

4x - 2x = 2x

Therefore, the correct answer should be 2x.

The perimeter is 21.66

The figure is something like the one that is in the image below:

We want to find the total perimeter of the polygon ABECD

This will be:

AB + BE + EC + CD + DA

Remember that for a triangle rectangle of catheti A and B, the area is given by:

A*B/2

We know that the sides of the triangle rectangle are:

BE, EC, BC.

Because BE = EC, these can not be the hypotenuse of the triangle, then the catheti are BE and EC

Knowing that the area of the triangle rectangle is 8, we can write:

EC*BE/2 = 8

and EC = BE = x

x^2/2 = 8

x^2 = 8*2 = 16

x = √16 = 4

Then the two catheti of the triangle rectangle are 4 units long.

EC = 4

BE = 4

and we know that:

AB = BE = EC

then:

AB = 4

and because this is a rectangle, we also have:

DC = AB = 4

now we want to find the last side of the figure, AD,

Which we already know is equal to the hypotenuse of the triangle.

Remember the Pythagorean's theorem, which says that the sum of the squares of the catheti is equal to the square of the hypotenuse.

Both catethus are equal to 4, then we have:

H^2 = 4^2 + 4^2 = 32

H = √32 = 5.66

then:

DA = 5.66

Now we have:

AB = BE = EC = DC = 4

DA = 5.66

Then the perimeter is:

AB + BE + EC + CD + DA

4 +  4 + 4 + 4+ 5.66 = 21.66

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Answer:

Thus percentile lies between 53.3% and 55.6 %

Step-by-step explanation:

First we arrange the data in ascending order . Then find the number of the values corresponding to the given value. Then equate it with the number of observations and x and then multiply it to get the percentile. n= P/100 *N

where n is the ordinal rank of the given value

N is the number of values in ascending order.

The data in ascending order is

0.1 0.2 0.2 0.2 0.3 0.6 0.6 0.6 0.7 0.8 0.8 0.8 0.9 1.3

1.5 1.7 1.9 2.2 2.3 2.3 2.6 2.8 3.3 3.5 5.5 6.1 6.4 6.9 7.5 7.9 8.3 9.8 10.1 11.8 11.9 12.1 12.3 12.7 12.9 13.8 13.8 14.6 14.7 14.8 27.5

Number of observation = 45

4.9 lies between 3.3 and 5.5

x*n = 24 observation x*n = 25 observation

x*45= 24 x*45= 25

x= 0.533 x= 0.556

Thus percentile lies between 53.3% and 55.6 %