1.A prime number is a number which has exactly two factors - 1 and itself. Suhani says, “The only even prime number is 2". Is she right?​

Step-by-step explanation:

A no

n + 7 = 16

n + 7 - 7 = 16 - 7

n = 9

that is not n = 15

B yes

(2/3)v = 8

3×(2/3)v = 3×8

2v = 24

2v/2 = 24/2

v = 12

C no

6z = 84

6z/6 = 84/6

z = 14

that is not z = 8

Step-by-step explanation:

a0 = 0 ft (starting on the ground)

a1 = a0 + 3 - 1 = a0 + 2

an = an-1 + 3 - 1 if an-1 +3 < 15

an = an-1 + 3 if an-1 + 3 >= 15

so, we need to find the n, so that

an = an-1 + 2 >= 12

but by looking at the structure, we see that every step just adds 2 ft to the total height.

an = a0 + 2n = 0 + 2n = 2n

2n >= 12

n >= 6

so, with day 6 the bug reaches 12 ft height. in day 7 it gets up to 15 ft and reached its goal.

it will take 7 days for the bug to reach the top and get the food.

Answer: because the mean is 48

Step-by-step explanation:

the average (mean) is 48 so therefore its reasonable that half scored under half scored higher

The cloud can ascend 9,616 metres in 17.5 minutes, based on the statement made.

Utilizing the measurement of air pressure, altitude may be calculated. The pressure decreases with increasing altitude. An instrument is referred to as a pressure analyzer or pneumatic altimeter when a barometer is given a nonlinear calibration to display altitude.

This may be calculated by dividing the cloud's speed (552 metres per minutes) by the distance it must travel (17.5 minutes). We now know the distance to be 9,616 meters.

The speed of said cloud and the length of time it is going are four pieces of information that must be known in order to determine the minimum distance the cloud might cover in 17.5 minutes. We must increase the cloud's stated speed of 552 meters a minute by the distance it is going across, which in itself is 17.5 minutes. As a result, we now have 9,616 meters overall.

Another way to see this is to picture the cloud beginning at place A (9,200 meters) or terminating at point B. (9,616 meters). The distance between points A and B will be covered in 17.5 minutes if the cloud is moving at a pace of 552 meters per minute.

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The equation to determine how many bags Trisha brought is: T = 180 - (4 + 6)

We know that the total number of clementines is 180, Sal brought 4 bags and Joe brought 6. To determine how many bags Trisha brought, we need to determine the total number of bags that Sal and Joe brought together. We can do this by combining the two numbers together (4 + 6). This will give us a total of 10 bags. To determine how many bags Trisha brought, we need to subtract the total number of bags that Sal and Joe brought (10) from the total number of clementines (180). This gives us an answer of 170. This means that Trisha brought 170 clementines, or 7 bags. Therefore, the equation to determine how many bags Trisha brought is: T = 180 - (4 + 6).

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The five vectors in span {v1,v2} are we first multiply each vector component (x, y, and z) of v1 and v2 by a constant and then add them together.

1. v3 = (3v1 + 2v2) = (18 8 −16)

2. v4 = (2v1 + 3v2) = (−12 6 0)

3. v5 = (4v1 + v2) = (0 6 −32)

4. v6 = (−2v1 + 5v2) = (36 10 0)

5. v7 = (−v1 + 4v2) = (−36 8 0)

To calculate the vectors, we first multiply each vector component (x, y, and z) of v1 and v2 by a constant and then add them together. For example, for v3 we multiplied v1 by 3 and v2 by 2 and then added the components together to get the vector (18 8 −16). We performed similar calculations for the other vectors.

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Using the trigonometric ratios the correct option is option a) 4.98.

We have a known hypotenuse, but an unknown opposite side. Use the sine ratio to tie the two together to be able to solve for x.

Trigonometric ratios are a set of ratios that relate the angles of a right triangle to the lengths of its sides. The most commonly used trigonometric ratios are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.

These ratios can be used to find missing side lengths or angle measures in a right triangle, and they have many applications in mathematics, physics, engineering, and other fields.

sin(angle) = opposite/hypotenuse

sin(50) = x/6.5

6.5*sin(50) = x

x = 6.5*sin(50)

x = 4.97928888027336, make sure your calculator is in degree mode

x = 4.98

Therefore, Using the trigonometric ratios the correct option is option a) 4.98.

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The first 4 terms and the 10th term of the sequences are listed below

From the question, we have the following parameters that can be used in our computation:

Calculate the first 4 terms and the 10th term.

A)n^2+6

Here, we have

First = 1^2 + 6 = 7

Second = 2^2 + 6 = 10

Third = 3^2 + 6 = 15

Fourth = 4^2 + 6 = 24

Tenth = 10^2 + 6 = 106

B)3n^2

Here, we have

First = 3 * 1^2 = 3

Second = 3 * 2^2 = 12

Third = 3 * 3^2 = 27

Fourth = 3 * 4^2 = 48

Tenth = 3 * 10^2 = 300

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[tex]\cfrac{22}{3}x=\cfrac{1.6}{~~ \frac{6 }{11 } ~~}\implies \cfrac{22x}{3}=\cfrac{\frac{16}{10}}{~~ \frac{6 }{11 } ~~}\implies \cfrac{22x}{3}=\cfrac{16}{10}\cdot \cfrac{11}{6}\implies \cfrac{22x}{3}=\cfrac{8}{5}\cdot \cfrac{11}{6}[/tex]

[tex]\cfrac{22x}{3}=\cfrac{8}{6}\cdot \cfrac{11}{5}\implies \cfrac{22x}{3}=\cfrac{4}{3}\cdot \cfrac{11}{5}\implies \cfrac{22x}{3}=\cfrac{44}{15} \\\\\\ \stackrel{\textit{multiplying boths sides by }\stackrel{LCD}{15}}{15\left( \cfrac{22x}{3} \right)=15\left( \cfrac{44}{15} \right)}\implies 110x=44\implies x=\cfrac{44}{110}\implies \boxed{x=\cfrac{2}{5}}[/tex]

Answer:

12

Step-by-step explanation:

Draw a horizontal line that splits the hexagon in half

x = 180 - measure of a angle in the pentagon - half of the angle in the hexagon

x = 180 - 540/5 - 1/2*(720/6)

x = 180 - 108 - 60 = 180 - 168 = 12

Hope this helps :)

Have a great day

Answer: The answer is 5x

Answer: x=1

Step-by-step explanation:

=3x-[tex]2x^{2}[/tex]-1+8x-3x+[tex]2x^{2}[/tex]-7

= -1+8x-7

= -8=-8x

X=1

Answer:

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Part A :

If a function is linear, then the function values have equal differences.

If a function is exponential, the function values have equal ratios.

For car 1 :

36450 / 40,500 = 9/10

32805 / 36450 = 9/10

Values of car have equal ratios.

This is exponential function.

For car 2 :

39000 - 42000 = -3000

36000 - 39000 = -3000

Values of car have equal differences

This is linear function.

Part B :

The initial value of car is 45,000.

For car 1 :

f(1) = 40,500, f(2) = 36,450, ............

For car 2 :

f(1) = 42,000, f(2) = 39,000, ..........

Part C :

For car 1 :

f(13) =   = 11438.396

For car 2 :

f(13) =  = 6000

There is a significant difference in the values of the car after 13 years. The value of the car 1 is greater.

Hence the value of the car 1 is described by an exponential function and that of car 2 by linear function. The value of car 1 is greater after 13 years.

Step-by-step explanation:

Answer:

6x^2y

Solution

6x2 y

Step-by-step explanation:

hopefully this helped.bye:)

The rate of change of the perimeter of the square is 11.2 cm/min when the side length is 6 cm.

Step 1: The area of a square is A = s2, where s is the side length.

Step 2: The rate of change of the area of the square is 28 cm2/min.

Step 3: The perimeter of the square is

P = 4s.

Step 4: Substitute s = 6 into the equation for P to get

P = 24 cm.

Step 5: Differentiate P with respect to time to get the rate of change of

the perimeter:

dP/dt = 4ds/dt.

Step 6: Substitute the rate of change of the area (dA/dt = 28 cm2/min) into the equation for dP/dt to get dP/dt = 4(28 cm2/min)/dt.

Step 7: Simplify the equation to get

dP/dt = 112 cm/min.

Conclusion: The rate of change of the perimeter of the square is 112 cm/min when the side length is 6 cm

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Answer:

x = 6

Step-by-step explanation:

5x+6=7x-6

-6           -6

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

5x = 7x - 12

-7x   -7x

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

-2x = -12

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

-2      -2

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

x = 6

Answer:

6

Step-by-step explanation:

first we combine like terms

6+6=7x-5x

then we simplify

12=2x

lastly we divide both sides by 2

2x ÷2=12÷2

an we simplify again

x=6

then the value of x is 6

check

5(6)+6=7(6)-6

30+6=42-6

36=36

Answer:

567 minutes each month.

Step-by-step explanation:

Let x be the number of minutes of talk time used each month.

The cost for talk time beyond 500 minutes is $0.08 * (x - 500)

The cost for email is $27.70 * 0.3 = $8.31

The total monthly cost is $27.70 + $0.08 * (x - 500) + $8.31 = $35.99

The total cost for 9 months is $35.99 * 9 = $323.91

So we can set up the equation:

$27.70 + $0.08 * (x - 500) + $8.31 * 9 = $367.29

Solving for x, we get:

x = 567

So the number of minutes of talk time used each month is 567 minutes.

The standard equation of hyperbola centered at the origin with the given values is  x^2 / 49  - y^2 / 100 = 1 .

What is Hyperbola ?

a plane curve generated by a factor so moving that the difference of the distances from two constant points is a consistent : a curve formed by way of the intersection of a double right circular cone with a plane that cuts each halves of the cone.

Given,

The standard equation of the hyperbola centered at the origin with given values a=7 and b=10 .

[(x2 / a2) – (y2 / b2)] = 1.

vertical axis with values a = 7 and b=10 .

[(x2 / a2) – (y2 / b2)] = 1.

(x^2 / 7*7)  -  ( y^2/ 10*10)  = 1

x^2 / 49  - y^2 / 100 = 1

Hence , the standard equation of hyperbola centered at the origin with the given values is x^2 / 49  - y^2 / 100 = 1 .

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The area of this hexagon is 374.4 in².

The area of the hexagon is calculated by applying the following formula.

total area of the regular hexagon = 6 x area of one face

Area of one face = ¹/₂bh

where;

Area of one face = ¹/₂ x ( 12 in ) x ( 10.4 in )

Area of one face = 62.4 in²

Total area of the hexagon = ( 6 ) x ( 62.4 in² ) = 374.4 in²

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Answer:

16x20

Step-by-step explanation:

I think, 200% likely means x2. Just an idea, try it if you'd like!

Answer:

Step-by-step explanation:

√2x + 5 = 5

       -5    - 5

√2x = 0

√2x^2=0^2

2x=0

2x/2 = 0/2

[tex]\huge\red{ANSWER}[/tex]

[tex]\sf \sqrt{2} x+5=5[/tex]

[tex]\sf \sqrt{2} x=5-5[/tex]

[tex]\sf \sqrt{2} x = 0[/tex]

[tex]\sf \frac{\sqrt{2} x }{2}=0[/tex]

[tex]\sf x=0[/tex]

________......

[tex]\pmb{ \orange{LearningLifeII}}[/tex]

The probability that the card is a face card (i.e., a jack, queen, or king) or a heart is 8/13

In the given question, suppose that you draw a card from a standard deck of cards.

We have to find the probability that the card is a face card (i.e., a jack, queen, or king) or a heart.

As we know that in a deck of cards have total 52 cards.

In which 26 cards are in heart shape.

Every different type of card have 3 face cards and have total four different type of cards. That means there are total 12 face cards.

In 26 cards of heart have total 6 face cards.

So, the probability that the card is a face card (i.e., a jack, queen, or king) or a heart

P = (Total face cards + total heart shape card - 6 face cards)/Total cards in a deck

P = (12 + 26 - 6)/52

P = (38 - 6)/52

P = 32/52

P = 8/13

Hence, the probability that the card is a face card (i.e., a jack, queen, or king) or a heart is 8/13.

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If the owner of a pet food store wants to mix birdseed that cost $1.25 per pound with sunflower seeds that cost $0.75 . The number of pounds of each type of sea he should use is: 25 pounds of $1.25 birdseed and 25 pounds of $.75 sunflower seed.

Let x represent the number of  pounds of $1.25 birdseed that is is used

1.25x+.75(50-x)=50×1

1.25x+37.5-.75x=50

Combine like terms

.50x=50-37.5

.50x=12.5

Divide both side by .50x

x=12.5/.5

x=25 pounds of $1.25 birdseed

So,

50-25=25 pounds of $.75 sunflower seed

Therefore the number of pounds is $1.25 birdseed and $.75 sunflower.

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The probability that he'll use both the bus and the train is 0.2222

What is probability and example?

Probability = the number of ways of achieving success. the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .

There are just two ways in which Justin use both the bus and the train on the same day:

1. He used bus in the morning and train in the evening

2. He used train in the morning and bus in the evening

Additionally, every day he has 9 possible ways to used the transportation, 3 in the morning multiply by 3 in the evening. This is:

       3         *         3           =  9

p= 0.222

So, the probability is calculate as a division between the possible ways in which he use both transportations and the total possible ways. This is:

p=0.222

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So, the teacher can give out the jerseys in 840 ways.

The teacher wants to divide the 12 students into 3 teams, each with at least one girl and one boy.

One possible way to count the number of ways to divide the students is to use the stars and bars method.

For the first team, we have 5 stars and 2 bars, so the number of ways to pick 6 students is:

(5+2)!/(5!2!) = 7

For the second team, we have 4 stars and 1 bar, so the number of ways to pick 6 students is:

(4+1)!/(4!1!) = 5

For the third team, we have 3 stars, so the number of ways to pick 6 students is:

(3+0)!/(3!0!) = 4

Then we can multiply the number of ways to pick students for each team together to find the total number of ways to divide the students:

7 * 5 * 4 = 140

Then, as the jerseys are indistinguishable, we just have to multiply the number of ways to divide the students by the number of ways to distribute jerseys:

140 * 3! = 840

Therefore, the teacher can give out the jerseys in 840 ways.

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The measure of ∠ ​ABC is 112°

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a shape with its angles.

Triangle BCD is an equilateral triangle. So all the angles are equal, that is 60° each.

∠ ​ADB = 64° (base angle of an isosceles triangle are equal)

∠ ​ABD = 180° - 64° - 64° (sum of angles in a triangle is 180°)

∠ ​ABD = 52°

∠ ​ABC = ∠ ​ABD + ∠ ​CBD

∠ ​ABC = 52° + 60°

∠ ​ABC = 112°

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The sum of numbers at B, C, D, E and F is 110.5

Since B, C, D, E, and F divide the segment AG into 6 equal pieces, each piece has a length of (59-13)/6 = 6.5.

Therefore, the numbers at B, C, D, E, and F are located at 13 + 6.5, 13 + 6.52, 13 + 6.53, 13 + 6.54, and 13 + 6.55 respectively.

The sum of the numbers at B, C, D, E and F is (13 + 6.5) + (13 + 6.52) + (13 + 6.53) + (13 + 6.54) + (13 + 6.55)

= 13 + 6.5*(1+2+3+4+5) = 13 + 6.5*15 = 13 + 97.5

= 110.5

In Maths, number lines are the horizontal straight lines in which the integers are placed in equal intervals. All the numbers in a sequence can be represented in a number line. This line extends indefinitely at both ends.

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El número natural 169 tiene como raíz cuadrada igual a 13.

Los números naturales comprenden a un conjunto discreto conformado por los números {1, 2, 3, 4, 5, ..., n, ...}, n ∈ N, donde N es el conjunto de los números naturales.

Los números naturales pueden ser números primos o números compuestos, los números compuestos pueden ser definidos como un producto de números primos. El número natural 169 es equivalente al siguiente producto de números primos:

169 = 13 × 13 = 13²

En consecuecia, la raíz cuadrada del número natural 169 es la siguiente: (nótese que la potencia al cuadrado es el opuesto a la raíz cuadrada)

x = √169

x = √(13²)

x = (13²)^(1 / 2)

x = 13

La raíz cuadrada del número natural 169 es igual a 13.

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The evaluation of the piecewise function gives:

when x = -3, f(x) = -4; when x = 2, f(x) = 0; and when x = 4, f(x) =  2.

when x = -3, w(x) = 2; when x = 2, f(x) = 5; and when x = 4, f(x) = 5

A piecewise function is a function that is defined by multiple sub-functions, each of which applies to a certain range of the input (or domain) values.

We want to evaluate the piecewise function when x = -3, x =2 and x = 4:

        { -4,   x < 2

f(x) = { x-2, -2 ≤ x≤ 4

         {0      x > 4

when x = -3:

f(x) = -4 because x < 2 (i.e. -3 < 2)

when x = 2:

f(x) = x-2

f(2) = 2-2 = 0

when x = 4:

f(x) = x-2

f(2) = 4-2 = 2

        { -x - 1,       x ≤ -3

w(x) = { 2x + 2,  -3 < x < 2

         {5,            x ≥ 2

when x = -3:

w(x) = -x - 1

w(-3) = -(-3) - 1 = 2

when x = 2:

f(x) = 5

when x = 4:

f(x) = 5

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Answer:

2a + 16

2(3) + 16

6 + 16 = 22

3b

3(-2) = -6

Step-by-step explanation:

Substitue the appropriate values into the expressions.