Part 3: Choose a proof method​

Answer:

14

Step-by-step explanation:

(segment piece) x (segment piece) =   (segment piece) x (segment piece)

12*x = 8 * (x+2)

Distribute

12x = 8x+16

Subtract 8x

12x-8x = 8x+16-8x

4x = 16

Divide by 4

4x/4 = 16/4

x = 4

We want NT

NT = 8+x+2

     = 10 +x

    = 10 +4

    = 14

                                                0        0

                                                      ,    

                                              ---------------

Answer:

-5

Step-by-step explanation:

For an expression to be undefined, the denominator must be equal to 0

Therefore, we must equate the denominator in the expression to 0

2v + 10 = 0

2v = 0 - 10

2v = -10

v = -10/2

v = -5

So in order for the expression to be undefined, v must be equal to -5

Answer:

[tex]\sqrt{85}[/tex].

Step-by-step explanation:

[tex]x[/tex]-coordinates:

[tex]y[/tex]-coordinates:

Refer to the diagram attached. Consider these two points as the two end points of the hypotenuse of a right triangle. The lengths of the two legs are equal to:

Apply Pythagorean Theorem to find the length of the hypotenuse (which is equal to the distance between the two points in question.)

[tex]\begin{aligned}\text{Hypotenuse} &= \sqrt{(\text{First Leg})^2 + (\text{Second Leg})^2} \\ &= \sqrt{7^2 + 6^2} \\ &= \sqrt{85}\end{aligned}[/tex].

Answer:

C

Step-by-step explanation:

it was all about equating some values

to bake the required number of cakes during the available 3-hour time period, 7 cooks are required.

Let's determine the number of cooks required to bake the required number of cakes during the available time.

We have the following information:

- Each cook can bake either 5 large cakes or 14 small cakes per hour.

- The kitchen is available for 3 hours.

- We need to bake 29 large cakes and 260 cakes in total.

First, let's calculate the number of large cakes that can be baked by one cook in 3 hours:

1 cook can bake 5 large cakes/hour × 3 hours = 15 large cakes.

Next, let's calculate the number of small cakes that can be baked by one cook in 3 hours:

1 cook can bake 14 small cakes/hour × 3 hours = 42 small cakes.

Now, let's calculate the number of large cakes that can be baked by all the cooks in 3 hours:

Total number of large cakes = Number of cooks × Large cakes per cook per 3 hours

We need to bake 29 large cakes, so:

29 = Number of cooks × 15

Number of cooks = 29 / 15 ≈ 1.93

Since we can't have a fraction of a cook, we need to round up to the nearest whole number. Therefore, we need at least 2 cooks to bake the required number of large cakes.

Similarly, let's calculate the number of small cakes that can be baked by all the cooks in 3 hours:

Total number of small cakes = Number of cooks × Small cakes per cook per 3 hours

We need to bake 260 small cakes, so:

260 = Number of cooks × 42

Number of cooks = 260 / 42 ≈ 6.19

Again, rounding up to the nearest whole number, we need at least 7 cooks to bake the required number of small cakes.

Since we need to satisfy both requirements for large and small cakes, we choose the larger number of cooks required, which is 7 cooks.

Therefore, to bake the required number of cakes during the available 3-hour time period, 7 cooks are required.

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Answer:

x^3 - x^2 + 11x - 1

-x^3 - 8x^2 + 5x + 7

Step-by-step explanation:

Find the sum

(x^3+5x^2+3x-7)+(8x-6x^2+6)

=x^3+5x^2+3x-7+8x-6x^+6

Collect like terms

=x^3 +5x^2-6x^2+3x+8x-7+6

Add the like terms

= x^3 - x^2 + 11x - 1

Find the difference (7x-3x^2+2)-(x^3+5x^2+2x-5)

(7x-3x^2+2)-(x^3+5x^2+2x-5)

= 7x-3x^2+2-x^3-5x^2-2x+5

Collect like terms

= -x^3-3x^2-5x^2+7x-2x+2+5

Add the like terms

= -x^3 - 8x^2 + 5x + 7

Answer:

The correct option is  A

Step-by-step explanation:

From the question we are told that

    The  population is  [tex]\mu = 6.6[/tex]

     The level of significance is [tex]\alpha = 5\% = 0.05[/tex]

      The sample data is  9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds

The Null hypothesis is [tex]H_o : \mu = 6.6[/tex]

 The Alternative hypothesis is  [tex]H_a : \mu > 6.6[/tex]

The critical value of the level of significance obtained from the normal distribution table is

                       [tex]Z_{\alpha } = Z_{0.05 } = 1.645[/tex]

Generally the sample mean is mathematically evaluated as

      [tex]\=x = \frac{\sum x_i }{n}[/tex]

substituting values

      [tex]\=x = \frac{9.0 + 7.3 + 6.0+ 8.8+ 6.8+ 8.4+6.6 }{7}[/tex]

      [tex]\=x = 7.5571[/tex]

The standard deviation is mathematically evaluated as

           [tex]\sigma = \sqrt{\frac{\sum [ x - \= x ]}{n} }[/tex]

substituting values

          [tex]\sigma = \sqrt{\frac{ [ 9.0-7.5571]^2 + [7.3 -7.5571]^2 + [6.0-7.5571]^2 + [8.8- 7.5571]^2 + [6.8- 7.5571]^2 + [8.4 - 7.5571]^2+ [6.6- 7.5571]^2 }{7} }[/tex][tex]\sigma = 1.1774[/tex]

Generally the test statistic is mathematically evaluated as

            [tex]t = \frac{\= x - \mu } { \frac{\sigma }{\sqrt{n} } }[/tex]

substituting values

           [tex]t = \frac{7.5571 - 6.6 } { \frac{1.1774 }{\sqrt{7} } }[/tex]

            [tex]t = 1.4274[/tex]

Looking at the value of  t and  [tex]Z_{\alpha }[/tex]   we see that [tex]t < Z_{\alpha }[/tex] hence we fail to reject the null hypothesis

  What this implies is that there is no sufficient evidence to state that the sample data show as significant increase in the average birth rate

The conclusion is that the mean is  [tex]\mu = 6.6 \ lb[/tex]

B(-6,9)is the answer

have a great dayyyy.

Answer:

Step-by-step explanation:

4r+3s=75 , r = 9

Since we know the value of r, we can substitute the value of r into the above equation to find s

That's

4( 9) + 3s = 75

36 + 3s = 75

Group like terms

3s = 75 - 36

3s = 39

Divide both sides by 3

That's

[tex] \frac{3s}{3} = \frac{39}{3} [/tex]

We have the final answer as

Hope this helps you

Answer:

f(x)=1/2x+2

Step-by-step explanation:

Using formula y=mx+b.

m is 0.5 or 1/2 as stated above

f(x)= 1/2x+b

If it were y=1/2x, it would intersect at 0,0 and we want 0,2

so b should be 2

therefore

Y=1/2x+2

or

f(x)=1/2x+2

Answer:

D

Step-by-step explanation:

Answer:

The probability is  [tex]P(X < 12) = 0.99286[/tex]

Step-by-step explanation:

From the question we are told that

        The population mean is [tex]\mu = 12 \ oz[/tex]

         The  standard deviation is  [tex]\sigma = 0.1 \ oz[/tex]

          The sample mean is  [tex]\= x = 12.1 \ oz[/tex]

          The sample size is  n = 6 packs

The standard error of the mean is mathematically represented as

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

substituting values

            [tex]\sigma_{\= x } = \frac{0.1}{\sqrt{6} }[/tex]

            [tex]\sigma_{\= x } = 0.0408[/tex]

Given that the can’s contents follow a Normal distribution then then  the probability that the mean contents of a six-pack are less than 12 oz is mathematically represented as

         [tex]P(X < 12) = P ( \frac{X - \mu }{ \sigma_{\= x }} < \frac{\= x - \mu }{ \sigma_{\= x }} )[/tex]

Generally  [tex]\frac{X - \mu }{ \sigma_{ \= x }} = Z (The \ standardized \ value \ of \ X )[/tex]

So

         [tex]P(X < 12) = P ( Z < \frac{\= x - \mu }{ \sigma_{\= x }} )[/tex]

substituting values

       [tex]P(X < 12) = P ( Z < \frac{12.2 -12 }{0.0408} )[/tex]

      [tex]P(X < 12) = P ( Z < 2.45 )[/tex]

From the normal distribution table the value of [tex]P ( Z < 2.45 )[/tex] is  

           [tex]P (Z < 2.45)0.99286[/tex]

=>   [tex]P(X < 12) = 0.99286[/tex]

Answer:

Variance is 256

Step-by-step explanation:

Variance:

[tex]var = \frac{ ({ \sum x})^{2} }{n} - {( \frac{ \sum x}{n} })^{2} [/tex]

x is the number or item in the data

n is the number of terms

[tex]{ \tt{ \sum x = (12 + 7 + 6 + 4 + 11)}} \\ { \tt{ \sum x = 40}}[/tex]

Therefore:

[tex]variance = \frac{ {40}^{2} }{5} - { (\frac{40}{5}) }^{2} \\ \\ = 320 - 64 \\ variance = 256[/tex]

===================================================

Work Shown:

a = first term = 3

d = common difference = 6

S(n) = sum of the first n terms of an arithmetic sequence

S(n) = (n/2)*(2a + d(n-1))

S(34) = (34/2)*(2*3 + 6(34-1))

S(34) = 3468

--------

Check:

3+9+15+21+27+33+39+45+51+57+63+69+75+81+87+93+99+105+111+117+123+129+135+141+147+153+159+165+171+177+183+189+195+201 = 3468

I used GeoGebra to generate the 34 terms shown above. You could do so by hand (start at 3; add 6 to each term to get the next one), but it's a tedious busywork type of problem in my opinion. It's best left to computer software.

Answer:

Music place has a better buy

Step-by-step explanation:

CD express

60 dollars / 4 cds = 15 dollars per cd

Music places

75 dollars / 6 cds = 12.50 per cd

Answer: At-least 89% of employees with commuting times between 54 minutes and 72 minutes .

Step-by-step explanation:

Given: Commuting times for employees of a local company have a mean of 63 minutes and a standard deviation of 3 minutes.

Now, 54 minutes = (63 - 9) minutes

= (63 -3(3)) minutes

= Mean - 3 standard deviation

72 minutes =  (63 + 9) minutes

=63 +3(3) minutes

= Mean + 3 standard deviation

According to Chebyshev's theorem, at least [tex]\dfrac{8}{9}[/tex] of the data lie within 3 standard deviations of the mean.

i.e. The percentage of employees with commuting times between 54 minutes and 72 minutes = [tex]\dfrac{8}{9}\times100\approx89\%[/tex]

Hence, at-least 89% of employees with commuting times between 54 minutes and 72 minutes .

Answer:

5/14

Step-by-step explanation:

1[tex]\frac{3}{4}[/tex] = 7/4

4[tex]\frac{9}{10}[/tex] = 49/10

[tex]\frac{7}{4}[/tex] / [tex]\frac{49}{10}[/tex]

[tex]\frac{7}{4}[/tex] x [tex]\frac{10}{49}[/tex] = [tex]\frac{70}{196}[/tex]

or

[tex]\frac{1}{2}[/tex] x [tex]\frac{5}{7}[/tex] = [tex]\frac{5}{14}[/tex]

Answer:

e

Step-by-step explanation:

e

First simplify the expression into polynomial form,

[tex](x-1)(x-3)(x+5)(x+7)=297[/tex]

[tex]x^4+8x^3-10x^2-104x+105=297[/tex]

[tex]x^4+8x^3-10x^2-104x-192=0[/tex]

Now factor into,

[tex](x-4)(x+8)(x^2+4x+6)=0[/tex]

Which means the solutions are,

[tex]x-4=0\implies\boxed{x_1=4}[/tex]

[tex]x+8=0\implies\boxed{x_2=-8}[/tex]

and then two complex solutions because determinant of the third factor [tex]D\lt0[/tex],

[tex]x^2+4x+6=0[/tex]

[tex]x^2+4x+4=-2[/tex]

[tex](x+2)^2=-2\implies\boxed{x_3=i\sqrt{2}-2},\boxed{x_4=-i\sqrt{2}-2}[/tex]

Hope this helps :)

Answer:

x=4

Step-by-step explanation:

(4-1)(4-3)(4+5)(4+7)=297

Answer: Check out the diagram below for the filled in boxes

14 goes in the first box (inside A, but outside B)

7 goes in the overlapping circle regions

5 goes in the third box (inside B, outside A)

3 goes in the box outside of the circles

==============================================================

Explanation:

[tex]n(A \cup B) = 26[/tex] means there are 26 items that are in A, B or both.

n(A) = 21 means there are 21 items in A

n(B) = 12 means there are 12 items in B

We don't know the value of [tex]n(A \cap B)[/tex] which is the number of items in both A and B at the same time. This is the intersecting or overlapping regions of the two circles. Let [tex]x = n(A \cap B)[/tex]

It turns out that adding n(A) to n(B), then subtracting off the stuff they have in common, leads to n(A u B) as shown below.

--------

[tex]n(A \cup B) = n(A) + n(B) - n(A \cap B)\\\\26 = 21+12 - x\\\\26 = 33 - x\\\\x+26 = 33\\\\x = 33-26\\\\x = 7\\\\n(A \cap B) = 7\\\\[/tex]

So there are 7 items in both regions.

This means there are [tex]n(A) - n(A \cap B) = 21 - 7 = 14[/tex] items that are in set A only. In other words, 14 items are in circle A, but not in circle B.

Notice how the values 14 and 7 add back up to 14+7 = 21, which represents everything in set A.

Similarly, there are [tex]n(B) - n(A \cap B) = 12 - 7 = 5[/tex] items that are in circle B, but not in circle A. The values 5 and 7 in circle B add to 5+7 = 12, matching with n(B) = 12.

The notation n(A') means the number of items that are not in set A. We're given n(A') = 8. We already know that 5 is outside circle A. So if 5+y = 8, then y = 3 must be the missing value for the box that is outside both circles.

Again the diagram is posted below with the filled in values.

A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.

The filled Venn diagram is given below.

A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.

We have,

n(A) = 21

This is the total of all the items included in Circle A.

n(B) = 12

This is the total of all the items included in Circle A.

n(A') = 8

The items that are not in circle A.

n(A U B ) = 26

The items that are in both circle A and circle B.

Now,

n (A U B) = n(A) + n(B) - n(A ∩ B)

26 = 21 + 12 - n(A ∩ B)

n(A ∩ B) = 33 - 26

n(A ∩ B) = 7

Thus,
The filled Venn diagram is given below.

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Given Equations

Let it has solution (x,y)

Add both

[tex]\\ \sf\longmapsto 5x+4x+3y+7y=8+34[/tex]

[tex]\\ \sf\longmapsto 9x+10y=42[/tex]

It will also have same solution (x,y)

The solution of the equations is (-2, 6) which satisfies the equation 9x + 10y = 42.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of linear equations is given below.

5x + 3y = 8               ...1

4x + 7y = 34            ...2

From equation 1, then we have

5x + 3y = 8

y = 8/3 - (5/3)x

Put in equation 2, then we have

4x + 7[8/3 - (5/3)x] = 34

12x + 56 - 35x = 102

-23x = 46

x = - 2

Then the value of y is calculated as,

y = 8/3 - (5/3)(-2)

y = 8/3 + 10/3

y = 18 / 3

y = 6

Let's check whether (-2, 6) satisfy the equation 9x + 10y = 42 or not. Then we have

9(-2) + 10(6) = 42

- 18 + 60 = 42

42 = 42

The solution of the equations is (-2, 6) which satisfies the equation 9x + 10y = 42.

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Answer:

9u^3 + 6u^2 - 7u + 6

Step-by-step explanation:

9514 1404 393

Answer:

  an infinite number

Step-by-step explanation:

Between any pair of numbers, there are ...

  an infinite number of rational numbers, and

  an infinite number of irrational numbers

Answer:

The  condition  are

           The  Null hypothesis is  [tex]H_o : \mu = 5[/tex]

           The  Alternative hypothesis is  [tex]H_a : \mu < 5[/tex]

The  check revealed that

             There is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons

Step-by-step explanation:

From the question we are told that

     The  population mean is  [tex]\mu = 5 \ year[/tex]

      The sample size is  n =  20

      The sample mean is  [tex]\= x = 4.6 \ years[/tex]

       The  standard deviation is [tex]\sigma = 2.2 \ years[/tex]

   The  Null hypothesis is  [tex]H_o : \mu = 5[/tex]

   The  Alternative hypothesis is  [tex]H_a : \mu < 5[/tex]

So i will be making use of  [tex]\alpha = 0.05[/tex] level of significance to test this claim

    The critical value of  [tex]\alpha[/tex] from the normal distribution table is  [tex]Z_\alpha = 1.645[/tex]

Generally the test statistics is mathematically evaluated as

                 [tex]t = \frac{\= x - \mu}{ \frac{\sigma }{\sqrt{n} } }[/tex]

substituting values

                 [tex]t = \frac{ 4.6 - 5}{ \frac{2.2}{\sqrt{20} } }[/tex]

                [tex]t = -0.8131[/tex]

Looking at the value of  t and [tex]Z_{\alpha }[/tex] we see that  [tex]t < Z_{\alpha }[/tex] so we fail to reject the null hypothesis  

  This implies that there is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons.

Answer:

The answer is [tex]1 \frac{4}{7}[/tex]

Step-by-step explanation:

First, you convert [tex]3 \frac{2}{3}[/tex] to an improper fraction. That is [tex]\frac{11}{3}[/tex]. Do the same for the other number.

Next, use KFC, or Keep, Flip, Change.

Keep the first number

Flip the second

Change the operation. Division becomes Multiplication. You should've gotten [tex]\frac{11}{3}[/tex]x[tex]\frac{3}{7}[/tex].

You can simplify now. You would've gotten 11 * [tex]\frac{1}{7}[/tex]. Multiply and you would get [tex]\frac{11}{7}[/tex]. Simplify into a mixed number. The answer is [tex]1 \frac{4}{7}[/tex].

Answer:

-2 is the y-intercept of this function.

Step-by-step explanation:

Answer:

The cost of 3 magnets is $1

The cost of 9 magnets is $3

The cost of 6 magnets is $2

Step-by-step explanation:

The cost of magnets is calculated using the equivalent ratio. If 3 magnets cost  $ then the multiple used for the calculations of more magnets is 3. The ratio for every magnet price is 1 : 3 which means every dollar will be equal to 3 magnets. The cost of 3 magnets is $1, the cost of 6 magnets is $2 and cost of 9 magnets is $3.

Answer:

y = z /n

Step-by-step explanation:

Answer:

y=z/n

Step-by-step explanation:

To isolate the y, divide both sides by n

The correct question is;

Calculate the derivative of the function. Then find the value of the derivative as specified:

f(x) = 5x + 9; f '(2)

A) f'(x) = 0; f'(2) = 0

B) f'(x) = 9; f '(2) = 9

C)f'(x) = 5; f'(2) = 5

D) f '(x) = 5x; f '(2) = 10

Answer:

Option C: f'(x) = 5 and f '(2) = 5

Step-by-step explanation:

We want to find the derivative of f(x) = 5x + 9.

Now, the derivative with respect to x will be;

f'(x) = 5

Now,we also want to find out f'(2)

This means we are to put 2 for x in the derivative function.

In the derivative function, we don't have x as we have just 5.

Thus,f'(2) = 5

Step-by-step explanation:

Suppose, John walks with a speed x

Then, John can jog at a speed 2x

[tex]total \: time \: = \frac{total \: distance}{average \: speed} [/tex]

TOTAL TIME

[tex]0.9 = \frac{5}{2x} + \frac{2}{x} [/tex]

Further solving :

x = 5 mph

Average jogging speed (2x) = 10 mph

Answer:

10mph

Step-by-step explanation:

We know that John's total trip is 0.9 hours, so let's try to figure out how much of that time is spent jogging, and how much of it is spent walking.

We can do that by naming the time he takes to jog a mile y.

An equation would be:

5y+2(2y)=0.9

5y+4y=0.9

y=0.1

It takes him 0.1 hours, or 6 minutes to jog a mile.

Since he jogged 5 miles, his jogging time is 0.5 hours, or 30 minutes.

Now,

Let's name the speed he jogs x (miles per hour)

This allows us to set up another equation.

Note that:

Speed=distance/time

His jogging speed is x.

x=5/0.5

x=10

His average jogging speed is 10 miles an hour.

Answer:

  (a) there are 10 sets of 3 friends, so in 21 games, at least one set must show 3 times

  (b) there are 20 sets of 3 friends, so  in 21 games, at least one set must show 2 times.

Step-by-step explanation:

(a) The number of combinations of 5 things taken 3 at a time is ...

  5C3 = 5!/(3!·2!) = 5·4/2 = 10

There can be 10 games in which the same 3 friends do not show up. There can be 10 more games such that the same 3 friends show up exactly twice. In the 21st game, some set of 3 friends must show up 3 times.

__

(b) The number of combinations of 6 things taken 3 at a time is ...

  6C3 = 6!/(3!·3!) = 6·5·4/(3·2) = 20

Hence, there can be 20 games in which the same 3 friends do not show up. In the 21st game, some set of 3 friends will show up a second time.