the length of a ruler is 170cm,if the ruler broke into four equal parts.what will be the sum of the length of three parts

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El número "Novecientos mil cuatrocientos ochenta y nueve" se representa como 900,489 en notación numérica.

Por otro lado, el número "cuarenta mil dos" se representa como 40,002.

Si estamos buscando determinar cuál de estos dos números es mayor, podemos comparar las cifras en cada posición.

Comenzando desde la izquierda, el primer dígito de 900,489 es 9, mientras que el primer dígito de 40,002 es 4.

Dado que 9 es mayor que 4, podemos concluir que 900,489 es mayor que 40,002.

En general, al comparar números, se debe observar cada posición en orden de mayor a menor importancia.

Esto significa que el primer dígito a la izquierda es el más significativo y tiene más peso en el valor total del número.

Si los dígitos en la posición más significativa son iguales, se debe pasar a la siguiente posición hasta que se encuentre una diferencia.

En este caso, dado que el primer dígito de 900,489 es mayor que el primer dígito de 40,002, no es necesario comparar los dígitos en posiciones posteriores.

Por lo tanto, podemos concluir que el número "Novecientos mil cuatrocientos ochenta y nueve" (900,489) es mayor que "cuarenta mil dos" (40,002).

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The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).

The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.

To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.

For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.

Therefore, the practical domain of the situation is x ≥ 0.

For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.

Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.

Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).

To summarize:

- The practical domain of the situation is x ≥ 0.

- The practical range of the situation is [140, ∞).

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Answer:111

Step-by-step explanation:

1111

Answer:

5

7

9

11

13

Step-by-step explanation:

u just have to plot the x values into the x variable if that makes sense

here is an exampla

A) The maximum of the periodic function is 1.

B) The minimum of the periodic function is - 3.

C) The equation of the midline of this periodic function is (1 - 3)/2 = - 1.

D) The amplitude of the periodic function is (1 + 3)/2 = 2.

E) the period of the periodic function is 2π/3.

F) We know frequency = 2π/period = 2π/2π/3 = 2π×(3/2π) = 3.

G) The amplitude of the periodic function is 2sin3((πx - π/6)) - 1.

A period is the amount of time between two waves, whereas a periodic function is one whose values recur at regular intervals or periods.

A function f will be periodic with period x, so if we have

f (a + x) = f (a), For every a > 0.

A) The periodic function's maximum value is 1.

B) The periodic function's minimum value is -3.

C) This periodic function's midline's equation is (1 - 3)/2 = - 1.

D) The periodic function's amplitude is (1 + 3)/2 = 2.

E) The periodic function's period is 2π/3.

F) We already know that frequency = 2π/period

= 2π/2π/3 = 2π×(3/2π) = 3.

G) The periodic function is  2sin3((πx - π/6)) - 1.

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Answer:

a) The probability distribution of X is given below:

Number of Major Storms (X) Probability (P(X))

0                                                  0.50

1                                                  0.30

2                                                  0.10

3                                                  0.08

4                                                  0.02

The sum of the probabilities is 0.50 + 0.30 + 0.10 + 0.08 + 0.02 = 1.00, which confirms that this is a valid probability distribution.

b) The expected number of major storms in a given year (E(X)) is calculated as the sum of all possible values of X multiplied by their respective probabilities:

E(X) = 0 * P(X=0) + 1 * P(X=1) + 2 * P(X=2) + 3 * P(X=3) + 4 * P(X=4)

= 0 * 0.50 + 1 * 0.30 + 2 * 0.10 + 3 * 0.08 + 4 * 0.02

= 0.30 + 0.20 + 0.20 + 0.24 + 0.08

= 1.02

The standard deviation of the number of storms in a given year (σ) is given by the square root of the variance (Var(X)), which is calculated as:

Var(X) = E((X - E(X))^2)

= E(X^2) - (E(X))^2

= (0^2 * P(X=0) + 1^2 * P(X=1) + 2^2 * P(X=2) + 3^2 * P(X=3) + 4^2 * P(X=4)) - (E(X))^2

= (0.50 + 0.30 + 0.10 + 0.08 + 0.02) - (1.02)^2

= 1.00 - 1.0404

= -0.0404

Since the variance cannot be negative, this suggests that the distribution is not well-defined and needs to be revised.

Step-by-step explanation:

Answer:

x is 5

Step-by-step explanation:

The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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Answer:

I and III

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

the perimeter (P) of a square is the sum of the 4 congruent sides.

the area of a square is calculated as

area = s² ( s is the length of a side )

here area is 36 , then

s² = 36 ( take square root of both sides )

s = \(\sqrt{36}\) = 6

then

P = 4s = 4 × 6 = 24 cm

When substituting y = 11 into the equation y = 1/2(x) - 25, we find that x = 72, confirming that (23.5, 11) is a valid point of intersection.

Given that x is 23.5, it is required to prove that it is an intersection point for the equation y = 1/2(x) - 25 when y is equal to 11.

The equation is given as y = 1/2(x) - 25

When y = 11, we can substitute the value of y in the equation to obtain 11 = 1/2(x) - 25

This can be simplified as 11 + 25 = 1/2(x)36 = 1/2(x)

On solving, x = 72Thus, when y is equal to 11 and x is equal to 72, the given point of intersection is valid.

Therefore, it can be concluded that x = 23.5 is a point of intersection for the equation y = 1/2(x) - 25 when y is equal to 11.

In summary, when given an equation with two variables, we can find the point of intersection by setting one of the variables to a given value and solving for the other variable. In this case, when y is equal to 11, we can solve for x and obtain the point of intersection as (72,11).

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Answer:

(a) Yes, E and F are independent events.

(b) P(E and F) = P(E)P(F) = (1/2)(1/2) = 1/4

(a) | BD | bisects | AC | (reason : Given)

(b) |AD| ≅ |CD| (reason: |BD| is the perpendicular bisector of segment AC).

(c) ∠ABD ≅ ∠CBD (reason: | BD |  bisects angle ABC)

(d) ∠A ≅ ∠ C (reason: complementary angles of a right triangle)

Congruent angles are the angles that have equal measure. So all the angles that have equal measure will be called congruent angles.

From the first statement, we will complete the flow chart as follows;

line BD bisects line AC (reason : Given)

line AD is congruent to line CD (reason: line BD is the perpendicular bisector of segment AC)

Angle ABD is congruent to angle CBD (reason: line BD bisects angle ABC)

Angle A is congruent to angle C (reason: angle ABD = angle CBD, and both triangles ABD and CBD are right triangles).

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Answer: \(x=4\)

Step-by-step explanation:

\(x+2=10-x\)

\(x+2-2=10-x-2\)

\(x=-x+8\)\(x+x=-x+8+x\)

\(2x=8\)

\(\frac{2x}{2}=\frac{8}{2}\)

\(x=4\)

Answer:

Step-by-step explanation:

30

hello

to compare or know the difference between rational numbers and integers

rational numbers are numbers in which are expressed as fractions of two integers eg a/b where b is a non zero number

integers are whole numbers in mathemathics without the expression in fraction or rather they're expressed in fractions but the denominator must be equal to 1

now when we want to compare and order integers, they're prefereably done using the number line system.

for an integer

while in rational numbers,

The key features of the given quadratic functions are listed below.

In Mathematics and Geometry, the graph of any quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0) i.e 3 > 0.

For the quadratic function y = 3x² - 5, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, -5).

Domain: [-∞, ∞]

Range: [-5, ∞]

For the quadratic function y = -2x² + 12x - 15, the key features are as follows;

Axis of symmetry: x = 3.

Vertex: (3, 3).

Domain: [-∞, ∞]

Range: [-∞, 3]

For the quadratic function y = -x² + 1, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, 1).

Domain: [-∞, ∞]

Range: [-∞, 1]

For the quadratic function y = 2x² - 16x + 30, the key features are as follows;

Axis of symmetry: x = 4.

Vertex: (4, -2).

Domain: [-∞, ∞]

Range: [-2, ∞]

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Using the exponent's rule we know that x = 5.

Exponentiation is a mathematical process that involves the base b and the exponent or power n.

It is represented as bn and is pronounced as "b to the n."

A number's exponent indicates how many times to multiply that particular number.

It appears as a little number above and to the right of the basic number.

For instance, 82 = 8 x 8 = 64.

(The exponent "2" instructs us to multiply by two and use the number eight.)

Another illustration is 53 = 5 * 5 * 5 = 125.

So, we have: 2ˣ = 32

We know that:

2 * 2 * 2 * 2 * 2 = 32

2 is multiplied 5 times which means:

2⁵ = 32

Hence, x = 5.

Therefore, using exponents we know that x = 5.

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Answer:

The second equation which is a(b+c) = ab + ac.

Step-by-step explanation:

Remember that when you think of the word distribute, you want to see a variable or a number behind the parentheses.  The fourth equation would not work despite there being distributive in which it will give you abc.  The second equation is a great example of what a distributive property problem may do.

The area is given exactly by the definite integral,

\(\displaystyle\int_{-3}^2(x^2+4)\,\mathrm dx=\left(\frac{x^3}3+5x\right)\bigg|_{-3}^2=\frac{95}3\approx31.67\)

We can write this as a Riemann sum, i.e. the infinite sum of rectangular areas:

• Split up the integration interval into n equally-spaced subintervals, each with length (2 - (-3))/n = 5/n - - this will be the width of each rectangle. The intervals would then be

[-3, -3 + 5/n], [-3 + 5/n, -3 + 10/n], …, [-3 + 5(n - 1)/n, 2]

• Over each subinterval, take the function value at some point x * to be the height.

Then the area is given by

\(\displaystyle\lim_{n\to\infty}\sum_{k=1}^nf(x^*)\Delta x_k=\lim_{n\to\infty}\sum_{k=1}^nf(x^*)\frac5n\)

Now, if we take x * to be the left endpoint of each subinterval, we have

x * = -3 + 5(k - 1)/n   →   f (x *) = (-3 + 5(k - 1)/n)² + 4

If we instead take x * to be the right endpoint, then

x * = -3 + 5k/n   →   f (x *) = (-3 + 5k/n)² + 4

So as a Riemann sum, the area is represented by

\(\displaystyle\lim_{n\to\infty}\sum_{k=1}^n\left(\left(-3+\frac{5k}n\right)^2+4\right)\frac5n\)

and if you expand the summand, this is the same as

\(\displaystyle\lim_{n\to\infty}\sum_{k=1}^n\left(13-\frac{30k}n+\frac{25k^2}{n^2}\right)\frac5n=\lim_{n\to\infty}\sum_{k=1}^n\left(\frac{65}n-\frac{150k}{n^2}+\frac{125k^2}{n^3}\right)\)

So from the given choices, the correct ones are

• row 1, column 1

• row 2, column 2

• row 4, column 2

Answer:

Step-by-step explanation:

Answer:

12000

Step-by-step explanation:

25/100 = 3000/total people surveyed

total people surveyed =  3000×100 / 25

                                     =   12000 people surveyed

Answer:

Parallelogram

Step-by-step explanation:

Opposite sides are parallel

Answer: use straightedge to draw a line segment from the new points

Step-by-step explanation:

The total number of coins that were in Kay's bank are 137 coins.

In order to determine the number of dimes and nickels, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:

Since she has 11 less dimes than nickels, an equation which models this situation is given by;

n = d + 11     ....equation 1.

Note: 1 nickel is equal to 0.05 dollar and 1 dime is equal to 0.1 dollar.

Additionally, the coins are worth 10 dollars;

0.1d + 0.05n = 10 ....equation 2.

By solving both equations simultaneously, we have:

0.1d + 0.05(d + 11) = 10

0.1d + 0.05d + 0.55 = 10

0.15d = 9.45

d = 63 dimes.

For nickels, we have:

n = d + 11

n = 63 + 11

n = 74

Now, we can determine the total number of coins;

Total number of coins = n + d

Total number of coins = 74 + 63

Total number of coins = 137 coins.

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y=3x - 5....(i)

6x+3y=15.....(ii)

Then,

Keeping value of y in (ii)equation;

or,6x+3(3x-5)=15

or,6x+9x-15=15

or,15x=15+15

or,x=30/15

:x=2

Now, Keeping value of x in (i) equation;

y= 3x-5

or, y= 3×2 - 5

or,y= 6-5

: y=1

Answer: 156.38 m

Step-by-step explanation:

Using the arc length formula, the answer is \(2\pi(8^2) \cdot \frac{140}{360} \approx 156.38\)

Answer with  explanation:

A x% confidence interval interprets that a person can be x% confident thatthe true mean lies in it.

Here, Credit card companies is using the collection agency to justify the cost of , the agency must collect an average of at least $200 per customer.

i.e. \(H_0:\mu \geq200,\ \ \ H_a:\mu<200\)

The 90% confidence interval on the mean collected amount was reported as ($190.25, $250.75) .

I recommend that we can be 90% sure that the true mean collected amount  lies in ($190.25, $250.75).

Also, $200 lies in it such that it is more far from $250.75 than $190.25, that means there are large chances of having an average is at least $200 per customer.

Answer:

Step-by-step explanation:

F=ma

28=7m

m=28/7=4

F=4a

when a=3 m/s²

F=4×3=12 N

Answer:

90

Step-by-step explanation:

Answer:

It seems like the chat transitioned to a different topic. However, based on the search results, it appears that the query was related to solving distance problems using linear equations. One common application of linear equations is in distance problems, where you can create and solve linear equations to find the distance between two points or the rate of travel. Here's an example problem:

Joe drove from city A to city B, which are 120 miles apart. He drove part of the distance at 60 miles per hour (mph) and the rest at 40 mph. If the entire trip took three hours, how many miles did he drive at each speed?

To solve this problem, you can use a system of two linear equations. Let x be the number of miles driven at 60 mph, and y be the number of miles driven at 40 mph. Then you have:

x + y = 120 (total distance is 120 miles) x/60 + y/40 = 3 (total time is 3 hours)

To solve for x and y, you can multiply the second equation by 120 to eliminate fractions and then use the first equation to solve for one of the variables. For example:

x/60 + 3y/120 = 3 x/60 + y/40 = 3 2x/120 + 3y/120 = 3 x/60 + y/40 = 3 x/60 = 3 - y/40 x = 180 - 3y/2 (from the first equation)

Substitute the expression for x into the second equation and solve for y:

x/60 + y/40 = 3 (180 - 3y/2)/60 + y/40 = 3 3 - 3y/160 + y/40 = 3 3 - 3y/160 = 2.75 -3y/160 = -0.25 y = 20

Substitute y = 20 into the expression for x to get:

x = 180 - 3y/2 x = 120

Therefore, Joe drove 120 - 20 = 100 miles at 60 mph and 20 miles at 40 mph.

Step-by-step explanation: