Write a summary can Smartphones improve student lives? why or why not ( in your own words )

The smallest possible sum for this series is 20736 = 12^4.

Given:

A series of 288 consecutive odd integers has a non-zero sum that is a perfect fourth power.

S = a + (a+2) + (a+4) + ... + (a+2*287) = 288(a+(a+574))/2 = 288(a+287)

288 = 2^5 * 3^2

smallest value of (a+287) that will make S = 288(a+287) a perfect fourth power is:

a + 287 = 2^3 * 3^2 = 72

a = −215

Smallest sum = 288*72 = 20736 = 12^4

Smallest odd integer in series = −215

−215 + −213 + −211 + ... + −1 + 1 + 3 + ... + 213 + 215 + ... + 359

= 20736 = 12^4.

Therefore the smallest possible sum for this series is 20736 = 12^4.

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Answer:

1 11/64

Step-by-step explanation:

we will have to square root the numerator and the denominator that is 625/256 which will give us 25/16. No need to change it to mixed number then multiply 25/16 by 3/4, you can't divide through so you multiply and it will give you 75/64. Then change it to a mixed number, thats how we got 1 11/64.

Answer:

d. 0

Step-by-step explanation:

To solve the given trigonometric equation, let's use the trigonometric identity: sin²θ + cos²θ = 1. We can rewrite the equation provided as follows:

cos a + cos² B + cos² y = 3

Using the identity, we can rewrite it as:

1 - sin² a + 1 - sin² B + 1 - sin² y = 3

Simplifying further, we have:

3 - (sin² a + sin² B + sin² y) = 3

Rearranging the equation, we get:

sin² a + sin² B + sin² y = 3 - 3

sin² a + sin² B + sin² y = 0

Therefore, the value of sin² a + sin² B + sin² y is 0 (option d).

Answer:

144 km

Step-by-step explanation:

1 hour and a half hour = 90 minutes.

In 15 minutes a car travels 24 km

In 1 minute a car travels (24÷15) = 1.6 km

In 90 minutes a car travels (90×1.6)= 144 km

Ans.- 144 km

By using the Chinese Remainder Theorem separate the statement into two congruences we have x(p-1)(q−1)+1 (mod pq) for all x € Z.

Under the condition that the divisors are pairwise coprime (no two divisors share a common factor other than 1), the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then one can uniquely determine the remainder of the division of n by the product of these integers.

It suffices to show pq divides x(x(p-1)(q-1) - 1) for all x e Z. We consider three cases. Consider gcd (x, pq). It has 3 possibilities.

Case 1: If gcd(x, pq) 1. Then applying using Euler's Theorem we have

= x(pq) = 1 (mod pq)

= x(p-1)(−1) = 1 (mod pq)

= x(p-1)(q-1)+1 (mod pq)

and so the result holds if gcd(x, pq) = 1. EX

Case 2: If gcd(x, pq) p. This means x = 0 (mod p). In this case we have

= 0 = x (mod p).

Since gcd(x, pq) = p therefore qx and = 1 (mod q) by Fermat's Little Theorem. This gives us that x(p-1)(q-1)+1 so we have x9-1 x(p−1)(q−1) = 1 (mod q) = x(p-1)(q-1)+1 = x (mod q).

We have shown that x(p-1)(q-1)+1 = x (mod p) and x(p-1)(q-1)+1 = x (mod q). Using the Chinese Remainder Theorem we get x(p-1)(q−1)+1 = x (mod pq).

Case 3: If gcd(x, pq) = q. This case is same as Case 2, with p being replaced by q.

Thus we have extinguished all cases and we have shown x(p-1)(q−1)+1 (mod pq) for all x € Z.

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Complete question:

Let р and q be distinct primes. Show that for all x € Z, we have the congruence x(p-1)(9–1)+1 x (mod pq). (Hint: Use the Chinese Remainder Theorem/Sun Ze's Theorem to separate the statement into two congruences.)

Answer:

X= 5

Step-by-step explanation:

Answer:

let amount of games won and lost be x and y respectively

y+18=x

x+y=78

y+y+18=78

2y=78-18

2y=60

y=30

x=30+18

x=48

thus, games won is 48

Horatio has 6 trophies by equating the resultant linear equation in one variable.

Hence option b  is the correct option.

Patel has 19 trophies in total.

Its is said that Patel has five less than four times as many trophies as Horatio has.

Let the number of trophies Horatio has be x and that of Patel be y.

From the given relation of trophies of Patel and Horatio we get,

y = 4x - 5

This forms a linear equation.

We have y = 19.

Thus y = 4x - 5 can be written as,

19 = 4x - 5

Thus we have the equation in the form of a linear equation in one variable.

Simplifying the linear equation in one variable we get,

19 = 4x - 5

⇒ 19 + 5 = 4x

⇒ 24 = 4x

or, 4x = 24

⇒ x = 24/4

⇒ x = 6

Hence, Horatio has x = 6 trophies in total.

Hence option b is correct option.

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The following are the general steps to draw a hexagon inscribed in a circle:

First draw a circle with center A through B:

Then the intersection points will be vertex C and vertex D of the hexagon. Doing this for each vertex (from left to right) we will get the following:

Answer:

Step-by-step explanation:

According to angle bisector theorem we get the following ratio:

Substitute the lengths and solve for x:

Use angle bisector theorem

Answer:

Step-by-step explanation:

-2x + 5 = 3

-2x = -2

x = 1

Answer:

Option B = 108 cm

Step-by-step explanation:

Please refer the figure attached

As the given figure have four 90° angles,

AB = CH

BC = AH

So, AB = 30 cm , CH = 30 cm

BC = 15 cm, AH = 15 cm

Already given ED = FG = 5 cm, EF = 11 cm

Working note : As, AB = CH = 30 cm

CH = CD + 3cm + GH

30 = CD + 3cm + GH

CD + GH = 27 cm

Perimeter is the overall measure of the boundary of the given figure, ie

AB + BC + CD + DE + EF + FG + GH + AH

= 30 + 15 + CD + 5 + 11 + 5 + GH + 15

= CD + GH + 81

= 27 + 81

Perimeter = 108 cm

Answer:

Ans = (1.50 x 29 movies) + 16

Step-by-step explanation:

y represents total costs

x represents how many movie he rents

$1.50 is the rent of each movie

$16 is the fixed fee

thus

y = 1.50 x + 16

Ans = (1.50 x 29 movies) + 16

The number of total stories that the students will need to write to keep the same ratio of Blake's stories to real stories is J. 60.

To find the number of stories, we first need to find the proportion that Blake is to write currently to the total number of stories by the group. This can be found as :

= Blake's stories / Total number of stories

= 8 / ( 8 + 12 + 14 + 6 )

= 8 / 40

= 20 %

If Blake wants to increase the number of stories to 12 and the ratio needed to remain the same, the total number of short stories the students would write is:

= Blake target / Blake ratio

= 12 / 20 %

= 60 stories

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The 20th prize is $4400.

It is a sequence where the difference between each consecutive terms is the same.

Example:

2, 4, 6, 8 is an arithmetic sequence.

We have,

First prize = $12,000

Successive prize worth $400 less than the preceding prize.

Now,

We can make an arithmetic sequence.

12,000, 11,600, 11,200, ...

So,

a = 12,000

d = -400

The nth term of an arithmetic sequence.

= a + (n - 1)d

So,

The 20th prize.

= 12,000 + (20 -1)400

= 12,000 - 19 x 400

= 12,000 - 7600

= 4400

Thus,

20th prize = $4400

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Answer: looks at the picture

Step-by-step explanation: hope this help :)

Answer:

B. Right

C. Scalene

Step-by-step explanation:

The square shows that it's right angled

and the sides are different.

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

1. (4/9)^1/2

2. 4/9 + 2/9 = 6/9

3. simplify it gives you 2/3

Answer:

D. 2/3

Step-by-step explanation:

\((\frac{4}{9} )^{\frac{1}{2} } = \frac{\sqrt{4} }{\sqrt{9}} = \frac{2}{3}\)

When the book on baseball states that your favorite player gets on base 41% of the time he goes to bat, this percentage indicates the player's on-base percentage (OBP), a measure of how often a batter reaches base through hits, walks, or being hit by a pitch.

The on-base percentage is an important statistic in baseball as it helps to evaluate a player's offensive contribution to their team. A higher OBP means the player is more successful at getting on base, creating more scoring opportunities for their team. In this case, a 41% OBP for your favorite player signifies that they are quite proficient in reaching base.
To calculate the OBP, you can use the formula:
OBP = (Hits + Walks + Hit by Pitch) / (At Bats + Walks + Hit by Pitch + Sacrifice Flies)

Having a 41% OBP means that, on average, your favorite player reaches base 41 times out of 100 plate appearances. This is considered an above-average performance for a batter, as the league average OBP typically hovers around 32%. Your favorite player's OBP demonstrates that they are an effective offensive player, contributing to their team's success by getting on base more frequently than the average player.

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Answer:

The lengths of the diagonals are;

15.49 cm and 5.66 cm

Step-by-step explanation:

The given area of the parallelogram = 30 cm²

Also the length of 2 adjacent sides are 6 cm and 10 cm

Given that the formula for the area of a parallelogram = Base × Height, h where the base is either of the sides of the parallelogram we have;

When the base b = 10 m and the other side, a = 6 cm the diagonal, d is given by the relationship, d² = (a + √(b² - h²))² + h²

10 × h₁ = 30

h₁ = 30/10 = 3

d₁² = (b + √(a² - h₁²))² + h₁² = (10 + √(6² - 3²))² + 3² = 239.92 cm²

d₁ = √(239.92 cm²) = 15.49 cm

The other diagonal can be found from the following relationship;

d₂² = (b - √(a² - h₁²))² + h₁²

d₂² = (10 - √(6² - 3²))² + 3² = 32.08 cm²

d₂ = √(32.08 cm²) = 5.66 cm.

Al plantear un sistema de ecuaciones lineales, encontramos que el número de obreros que contrató el ingeniero civil fue 50.

Para encontrar el número de obreros que el ingeniero contrató debemos plantear un sistema de ecuaciones lineales de dos ecuaciones con dos incógnitas, tal como sigue:

\( M - 1400*x = -8000 \)   (1)

\( M - 1200*x = 2000 \)   (2)

En donde:

M: es la incógnita igual al monto de dinero del ingeniero

x: es la incógnita igual al número de obreros

De la ecuación (1) tenemos:

\( M = 1400*x - 8000 \)   (3)

Podemos encontrar el valor de x (número de obreros), introduciendo la ecuación (3) en la ec (2):

\( 1400*x - 8000 - 1200*x = 2000 \)

\( 200*x = 10000 \)

\( x = 50 \)

El monto de dinero inicial del ingeniero sería entonces (ec 3):

\( M = 1400*50 - 8000 = 62000 \)

Por lo tanto, el número de obreros que contrató el ingeniero es 50.

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Espero que te sea de utilidad!

Answer:

0.16 recurring

hope this helps!

Answer:

1\6

Step-by-step explanation:

\(\frac{-2}{3}+\frac{5}{6}=\frac{-4+5}{6}=\frac{1}{6}\)

Rounding 0.4571 to the nearest hundredth will be 0.46.

To round the nearest hundredth, look at the number that is three places to the right of the decimal point.  If the number is greater than or equal to 5, then round up.  If the number is less than 5, then round down.

0.4571

7 ≥ 5

Therefore, we round up.

0.4571 --> 0.46

Therefore, 0.4571 rounded to the nearest hundredth is 0.46.

For example, if the number is 123.456, the digit in the thousandths place is 6. Since 6 is greater than 5, 123.456 rounded to the nearest hundredth would be 123.46.

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Round 0.4571 to the nearest hundredth.

The stems are 0, 2, 3, 4, 5, 6, 8. Therefore option e, is the correct answer

Stem and leaf plot are used in statistics to organize data that are collected. Any number in a data is broken down into a stem and a leaf.

Stem displays data on the left while leaf displays data to the right

The data for the amounts of money (cents) in coins carried by 10 students in a statistics class: 50, 35, 0, 46, 86, 0, 5, 47, 23, 65 can be represented in the stem and leaf plot below:

2 I 3 ⇒ 2 on the stem and 3 on the leaf read as 23

3 I 5 ⇒ 3 on the stem and 5 on the leaf read as 35

4 I 6 ⇒ 4 on the stem and 6 on the leaf read as 46

4 I 7 ⇒ 4 on the stem and 7 on the leaf read as 47

5 I    ⇒ 5 on the stem as 5

5 I 0 ⇒ 5 on the stem and 0 on the leaf read as 50

6 I 5 ⇒ 6 on the stem and 5 on the leaf read as 65

8 I 6 ⇒ 8 on the stem and 6 on the leaf read as 86

Hence, stems are 0, 2, 3, 4, 5, 6, 8

Therefore, option e, is the correct answer

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Hi, I'm happy to help!

First off, we need to arrange an equation for what is being asked. 15 is 20% of her earnings and we don't know her total earnings.

15=20%×__

We can write this percentage as

15=0.2×__

We then change the equation to do the inverse operation, which is division, this makes it easier to solve.

15÷0.2=__

Now, we solve

15÷0.2=75

She earned $75

I hope this was helpful, keep learning! :D