Irrational conjugate theorem

The average speed of John and Alice are determined first by dividing the total distance by the total time taken. The ratio of the average speeds is 25:45 or in simplified form, 5:9. Therefore, the correct answer to the question is (c) 5:9.

To find the ratio of the average speed of John to Alice, we first need to calculate their average speed individually. The average speed is obtained by dividing the total distance covered by the total time taken.

For John, his average speed would be 150km/6 hours = 25km/h. For Alice, her average speed would be 180km/4 hours = 45km/h.

So, the ratio of the average speed of John to Alice would be 25 : 45. In simplest form, this ratio becomes 5 : 9 (divided both numbers by 5).

Therefore, the answer is (c) 5:9.

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Answer:

Therefore the correct option is A. 7^11/4^11

[tex](\dfrac{7}{4})^{11}=\dfrac{7^{11}}{4^{11}}[/tex]

Step-by-step explanation:

Given:

[tex](\dfrac{7}{4})^{11}[/tex]

Solution:

We know the Identity For Law of Indices

[tex](\dfrac{x}{y})^{a}=\dfrac{x^{a}}{y^{a}}[/tex]

So here we have,

x = 7

y = 4

a = 11 , then

[tex](\dfrac{7}{4})^{11}=\dfrac{7^{11}}{4^{11}}[/tex]

Therefore the correct option is A. 7^11/4^11

[tex](\dfrac{7}{4})^{11}=\dfrac{7^{11}}{4^{11}}[/tex]

Answer:

(4, 6).

Step-by-step explanation:

7x – 5y = -2

y = 7x – 22  

-7x + y = -22   Adding this to equation 1:

-4y = -24

y = 6.

Plug this into the second equation:

6 = 7x - 22

7x = 28

x = 4.

Answer:

put a pic of the question

Step-by-step explanation:

plz

Answer:

Step-by-step explanation:

j + p = 178

j = p + 10

p + 10 + p = 178

2p + 10 = 178

2p = 178 - 10

2p = 168

p = 168/2

p = 84 <==== Phil's score

j = p + 10

j = 84 + 10

j = 94 <====Jerry's score

Final answer:

Jerry scored 94 and Phil scored 84.

Explanation:

To find Jerry and Phil's scores, we'll set up two equations based on the given information. Let's say Jerry's score is represented by 'J' and Phil's score is represented by 'P'. We know that Jerry scored 10 points higher than Phil, so J = P + 10. We also know that their scores combined equal 178, so J + P = 178. Now we can solve these two equations to find each student's score. Substituting the first equation into the second equation, we get (P + 10) + P = 178. Simplifying this equation gives us 2P + 10 = 178. Subtracting 10 from both sides gives us 2P = 168. Finally, dividing both sides by 2 gives us P = 84. So Phil's score is 84. Substituting this value back into the first equation, we get J = 84 + 10 which gives us J = 94. Therefore, Jerry's score is 94.

Answer:

the middle sequentially in a list of numbers (sorted from lowest to highest)

Step-by-step explanation:

for example, in the dataset 2, 4, 6, 8, 10, 6 would be the median because it is in the middle when sorted properly

Answer: The median is the middle value in the list of numbers

Step-by-step explanation:

For example: 5,3,7,10,22,12,15,100,98

The median is 22 because it is in the middle of all the number displayed

Answer:

p = (218-6)/4

Step-by-step explanation:

218-6 is in parenthesis because you want to remove the 6 people driving from the population you're dividing first, since they wont be on the buses. The divide that number by 4 to figure out how many people are on each bus. The answer to that is 53. There are 53 people on each bus.

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Answer:

the answer is 55

Step-by-step explanation:

Answer: [tex]5\frac{3}{10}[/tex]

We first write them as improper fraction.

[tex]1\frac{7}{10}=\frac{17}{10}[/tex]

[tex]3\frac{3}{5}=\frac{18}{5}[/tex]

Then we find the LCM of the denominators. That is 10.

Using LCD we find the sum:

[tex]1\frac{7}{10}+3\frac{3}{5}\\=\frac{17}{10}+\frac{18}{5}\\=\frac{17}{10}+\frac{36}{10}\\=\frac{53}{10}\\=5\frac{3}{10}[/tex]

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The sum of [tex]\( \frac{1}{7} \), \( \frac{10}{3} \), and \( \frac{3}{5} \) is \( \frac{428}{105} \).[/tex]

To find the sum of the fractions [tex]\( \frac{1}{7} \), \( \frac{10}{3} \), and \( \frac{3}{5} \)[/tex], let's first convert them to a common denominator.

The least common denominator for 7, 3, and 5 is 105 (since it's the smallest number divisible by all three denominators).

So, we need to express each fraction with a denominator of 105:

[tex]- \( \frac{1}{7} \) becomes \( \frac{15}{105} \) (multiplied by 15)[/tex]

[tex]- \( \frac{10}{3} \) becomes \( \frac{350}{105} \) (multiplied by 35)[/tex]

[tex]- \( \frac{3}{5} \) becomes \( \frac{63}{105} \) (multiplied by 21)[/tex]

Now, we add these fractions:

[tex]\( \frac{15}{105} + \frac{350}{105} + \frac{63}{105} = \frac{15 + 350 + 63}{105} = \frac{428}{105} \)[/tex]

So, the sum of [tex]\( \frac{1}{7} \), \( \frac{10}{3} \), and \( \frac{3}{5} \) is \( \frac{428}{105} \).[/tex]

Step-by-step explanation:

The exponent form of the given product is given by 8³

Exponent is a mathematical operation, written as an. Here the expression an involves two numbers, the base 'a and the exponent or power 'n'. Exponents are used to simplify algebraic expressions.

Given here: The product of 8×8×8

We know by the law of exponents that

a×a×a=a³

Thus 8×8×8=8³

Hence, The exponent form of the given product is given by 8³

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Answer:

No Solution.

Step-by-step explanation:

2x+3y=4

4x+6y=9

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

-2(2x+3y)=-2(4)

4x+6y=9

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

-4x-6y=-8

4x+6y=9

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

0=1

no solution

Answer:

No solution.

Step-by-step explanation:

2x + 3y = 4

4x + 6y = 9

Multiply both sides of the first equation by -2. Then write the second equation below it and add them.

       -4x - 6y = -8

+       4x + 6y = 9

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

           0 + 0 = 1

Since the statement 0 = 1 is false, there is no solution to this system of equation.

I'm going to assume that you want to know whether the coordinate satisfies the equation. Let's find out;

-3х - 6у = 17

-3(6) - 6(3) = 17

-18 - 18 = 17

-36 ≠ 17

The point (6, 3) does NOT satisfy the equation.

Best of Luck!

The length of flag is 760 feet and width of flag is 320 feet

Solution:

A seed company planted a floral mosaic of a national flag

Since, the flag is generally of shape rectangle, we can use the formula of rectangle

Let "a" be the length of rectangle

Let "b" be the width of rectangle

The length is 440 ft greater than the width

Length = 440 + width

a = 440 + b ----- eqn 1

The perimeter of the flag is 2,160 ft

The perimeter of rectangle is given as:

Perimeter = 2(length + width)

Substituting the given values, we get

2160 = 2(440 + b + b)

2160 = 880 + 4b

4b = 2160 - 880

4b = 1280

b = 320

Substitute b = 320 in eqn 1

a = 440 + 320

a = 760

Thus the length of flag is 760 feet and width of flag is 320 feet

Answer:

1

Step-by-step explanation:

Step-by-step explanation:

Given,

The area of the yard = 6,756 square yards and

The width of the yard (b) = 12 yards

To find, the length of the yard (l) = ?

We know that,

Area of the rectangle =  Length(l) × Breadth(b)

⇒ l × 12 = 6,756

⇒ l =[tex]\dfrac{6,756}{12}[/tex]

⇒ l = 563 yards

Thus, the length of the yard was 563 yards.

Answer:

Therefore the Length of the yard is 563 yards.

Step-by-step explanation:

Consider  the yard as a Rectangle

Area of the Yard = 6756 square yards

Width of the yard = W = 12 yards

To Find :

Length of the yard = L =?

Solution:

WE know that

[tex]\textrm{Area of Rectangle}=Length\times Width[/tex]

Substituting the values we get

[tex]\textrm{Area of Yard}=L\times W=L\times 12\\6756=L\times 12\\\\W=\dfrac{6756}{12}=563\ yard[/tex]

Therefore the Length of the yard is 563 yards.

Answer:

The base of the tree from a stake anchoring the wire is 18.67 feet far.

Step-by-step explanation:

Given:

the length of the wire  = 20 feet

Angle that the wire makes with the ground = 21 degrees

To Find:

The Distance from the base of the tree from the stake anchoring wire = ?

Solution:

We we construct a figure using the given data we end up with the right triangle as shown below

So now we can use the cosine ratio to find the distance from the base of the tree to the anchoring wire

Let d be the distance of  base of the tree from a stake anchoring the wire

[tex]Cos(angle) =\frac{\text{Adjacent side}}{Hypotenuse}[/tex]

On substituting the values we get

[tex]cos(21^{\circ}) =\frac{d}{20}[/tex]

[tex]d = cos(21^{\circ}) \times 20[/tex]

d = [tex]0.9335 \times 20[/tex]

d = 18.67 feet

Answer:

100 minutes

Step-by-step explanation:

25 x 10 = 250

10×10=100

Answer:

4 inches

Step-by-step explanation:

express the mixed fraction in improper form

3 1/4  = 13/4

4 3/4  = 19/4

hence total growth

=  3 1/4  +  4 3/4

=  13/4 + 19/4

= (13+19)/4

= 32/4

= 4 inches

Answer:

8 inches.

Step-by-step explanation:

3 1/4 + 4 3/4

= 3 + 4 + 1/4 + 3/4

= 7 + 4/4

= 7 + 1 = 8 inches.

there is no acute angle.......

Answer:

angle CPB is an acute angle cause it's measure is less than 90°

Answer:

0.0925 miles per second

Step-by-step explanation:

Answer:

16.9 seconds in 1 mile

Step-by-step explanation:

213miles => 3600s

1 mile => X

X=1*3600/213

X=16.9s

Answer:

Therefore the value of n is

[tex]n=-9[/tex]

Step-by-step explanation:

Given:

[tex]x^{12}y^{-13}x^{-5}y^{4}=x^{m}y^{n}[/tex]

To Find:

n = ?

Solution:

Using identity

[tex]1.\ x^{a}x^{b}=x^{a+b}[/tex]

[tex]2.\ x^{a}x^{-b}=x^{a-b}[/tex]

[tex]3.\ x^{-a}x^{b}=x^{-a+b}[/tex]

Therefore

[tex]x^{(12-5)}y^{(-13+4)}=x^{m}y^{n}[/tex]

[tex]x^{7}y^{-9}=x^{m}y^{n}[/tex]

Now on Comparing and Equality Property we get

[tex]m =7\\n=-9[/tex]

Therefore the value of n is

[tex]n=-9[/tex]

The final expression is  [tex]x^{7}[/tex] [tex]y^{-9}[/tex] , making n = -9.

The given expression is([tex]x^{12}[/tex])([tex]y^{-13}[/tex])([tex]x^{-5}[/tex])([tex]y^4[/tex]). We want to find the equivalent expression in the form [tex]x^{m}[/tex] [tex]y^n[/tex], where m and n are exponents that we need to determine.

Here's how to simplify it step by step:

[tex]x^{12}[/tex] * [tex]x^{-5}[/tex] = [tex]x^{12-5}[/tex] = [tex]x^{7}[/tex]

    2.  Combine the exponents of y:

[tex]y^{-13}[/tex] *[tex]y^{4}[/tex] = [tex]y^{-13+4}[/tex] = [tex]y^{-9}[/tex]

Therefore, the expression simplifies to [tex]x^{7}[/tex] [tex]y^{-9}[/tex]. This means that m = 7 and n = -9. Thus, the value of n is -9.

Question-The expression ([tex]x^{12}[/tex])([tex]y^{-13}[/tex])([tex]x^{-5}[/tex])([tex]y^4[/tex]) is equivalent to [tex]x^m y^n[/tex].

What is the value of n?

Answer:

2,325.58 Gallons

Step-by-step explanation:

20,000÷8.6=2,325.58

It snowed [tex]\frac{3}{10}[/tex] foot more yesterday than today

Solution:

Given that, At the Butler Ski Resort, it snowed 1/2 of a foot yesterday and 1/5 of a foot today

From given information,

[tex]\text{Snowed yesterday } = \frac{1}{2} \text{ foot }\\\\\text{Snowed today } = \frac{1}{5} \text{ foot }[/tex]

To find: how much more did it snow yesterday than today

So we have to find the difference between snowed yesterday and today

[tex]\text{Difference} = \text{Snowed yesterday } - \text{ snowed today }\\\\\text{Difference} = \frac{1}{2} - \frac{1}{5}\\\\\text{Difference} = \frac{1 \times 5}{2 \times 5}-\frac{1 \times 2}{5 \times 2}\\\\\text{Difference} = \frac{5}{10}-\frac{2}{10}\\\\\text{Difference} =\frac{3}{10}[/tex]

Hence it snowed [tex]\frac{3}{10}[/tex] foot more yesterday than today

They can not, there are only 2 sides and they probably flipped it different ways. They got 'lucky'.

Final answer:

Flipping a coin 100 times and getting 73 heads suggests a potential unbalanced coin. A chi-square statistical test is needed to determine if the deviation from the expected 50-50 ratio is significant. The large deviation in this scenario does suggest bias, but only a hypothesis test can confirm if the coin is unbalanced.

Explanation:

Intuitively, we might accept variations in coin flips as part of chance when the number of trials is small. However, as the number of trials increases, the expected 50-50 ratio of heads and tails should emerge. In the case where a person flipped a coin 100 times and obtained 73 heads, one could suspect an unbalanced coin, but to conclusively determine this, a statistical test, such as a chi-square, should be conducted to assess the significance of the deviation from the expected 50-50 ratio.

Flipping a coin 100 times should result in approximately 50 heads and 50 tails, according to the law of large numbers. A result of 73 heads is quite far from the expected outcome. The empirical observation suggests that there might be a bias towards heads, which indicates that the coin could be unbalanced.

To determine whether the coin is truly unbalanced or whether this was a fluke, one would perform a hypothesis test at a specified significance level to see if the observed results significantly differ from what is expected by random chance alone. If the results show a statistically significant difference, we could conclude that there is evidence to support the claim that the coin is unbalanced.

Step-by-step explanation:

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An equation is created to solve for the brother's age: b - 18 = 19. By adding 18 to both sides, we determine the brother is 37 years old.

To solve for the brother's age, you need to create an equation based on the information given. Since the sister is 19 years old, and the brother says his age minus eighteen is equal to the sister's age, the equation is: b - 18 = 19.

Now, solve for b (the brother's age) by adding 18 to both sides of the equation:

Therefore, the brother is 37 years old.

Answer:

The speed of the bus after it decreased by 55% is now 27 miles per hour.

Answer: The speed of the bus inside city limits is... 27 mph

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Answer:

Explanation:

The theoretical probability, P (A), of an event, A, is:

For 10 cranberry and 15 strawberry juices, the number of outcomes for two strawberry juices are:

[tex]C^{15}_{2}=\frac{15!}{(15-2)!(2!)}=\frac{15!}{13!2!}=\frac{15\times 14}{2}=105[/tex]

The total number of possible outcomes is:

[tex]C^{25}_{2}=\frac{25!}{(25-2)!(2!)}=\frac{25!}{23!2!}=\frac{25\times 24}{2}=300[/tex]

Thus, the probability of randomly picking two strawberry juices is:

Note that you can obtain it as the product of the probabilities that the first juice is a strawberry juice and the second juice is also strawberry juice:

[tex]15/25\times 14/24=(15\times 25)/(14\times 24)=210/600=7/20[/tex]

Sample 2 has least percent error

Step-by-step explanation:

We have to find the percent error in all samples to verify which sample had the least percent error

Percent error is given by:

[tex]Percent\ error = \frac{|actual\ amount-stated\ amount|}{Stated} * 100[/tex]

For sample 1:

Stated amount = 14 ounces

Actual amount = 13.7 ounces

[tex]Percent\ error = \frac{|13.7-14|}{14} * 100\\= \frac{|-0.3|}{14} * 100\\=\frac{0.3}{14} * 100\\= 0.021428*100\\=2.1428\%[/tex]

Sample 2:

Stated amount = 24 ounces

Actual amount = 24.4 ounces

[tex]Percent\ error = \frac{|24.4-24|}{24} * 100\\= \frac{|0.4|}{24} * 100\\=\frac{0.4}{24} * 100\\= 0.016666*100\\=1.666..\%[/tex]

Sample 3:

Stated amount = 25 ounces

Actual amount = 25.8 ounces

[tex]Percent\ error = \frac{|25.8-25|}{25} * 100\\= \frac{|0.8}{25} * 100\\=\frac{0.8}{25} * 100\\= 0.032*100\\=3.2\%[/tex]

Sample 4:

Stated amount = 39 ounces

Actual amount = 40.2 ounces

[tex]Percent\ error = \frac{|40.2-39|}{39} * 100\\= \frac{|-1.2|}{39} * 100\\=\frac{1.2}{39} * 100\\= 0.030769*100\\=3.0769\%[/tex]

Hence,

Sample 2 has least percent error

Keywords: Percent error, error

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Answer:

Mrs. McCarr buys 90 markers

Step-by-step explanation:

10 markers per package × 9 packages of markers = 90 markers in total

90 markers because 10 times 9 equals 90

Answer:

36

Step-by-step explanation:

10% of 360=10/100*360=1/10*360=360/10=36

Answer:

$36 or  $360

Step-by-step explanation: