Please help me with this math problem by showing a step-by-step explanation. I will give 25 points :D

Without graphing, classify each system of equations as independent, dependent, or inconsistent. Solve independent systems by graphing. 3=4y+x & 4y=−x+3

The first term of the infinite geometric series is 625.Let's dive deeper into the explanation.

We are given that the sum of the infinite geometric series is \(\( \frac{15625}{24} \)\)and the common ratio is\(\( \frac{1}{25} \).\)The formula for the sum of an infinite geometric series is \(\( S = \frac{a}{1 - r} \)\), where \( a \) is the first term and \( r \) is the common ratio.
Substituting the given values into the formula, we have \(\( \frac{15625}{24} = \frac{a}{1 - \frac{1}{25}} \).\)To find the value of \( a \), we need to isolate it on one side of the equation.
To do this, we can simplify the denominator on the right-hand side.\(\( 1 - \frac{1}{25} = \frac{25}{25} - \frac{1}{25} = \frac{24}{25} \).\)
Now, we have \(\( \frac{15625}{24} = \frac{a}{\frac{24}{25}} \).\) To divide by a fraction, we multiply by its reciprocal. So, we can rewrite the equation as \( \frac{15625}{24} \times\(\frac{25}{24} = a \).\)
Simplifying the right-hand side of the equation, we get \(\( \frac{625}{1} = a \).\)Therefore, the first term of the infinite geometric series is 625.
In conclusion, the first term of the given infinite geometric series is 625, which corresponds to option (a).



learn more about geometric series here here

https://brainly.com/question/30264021



#SPJ11

Dan can paint approximately 8/9 of a wall using 1 can of paint.

We have,

To find out how many walls of this size Dan can paint using 1 can of paint, we need to determine the fraction of a wall that can be painted with 1 can of paint.

Since Dan painted 3/4 of a wall using 2/3 of a can of paint, we can set up a proportion:

(3/4) wall / (2/3) can = 1 wall / x cans

To solve for x (the number of cans needed for 1 wall), we can cross-multiply:

(3/4) wall  x (x cans) = (2/3) can x 1 wall

(3/4) x (x) = (2/3)

To isolate x, we can multiply both sides of the equation by the reciprocal of (3/4), which is (4/3):

x = (2/3) x (4/3)

x = 8/9

Therefore,

Dan can paint approximately 8/9 of a wall using 1 can of paint.

Learn more about fractions here:

https://brainly.com/question/24370499

#SPJ1

Answer: -3

Step-by-step explanation:

-3 - (-6) = 3

hope this helps

plz mark brainlesit

Answer:

a. 4r² b. 2r c. 6 cm

Step-by-step explanation:

The surface area A of the cube is A = 24r². We know that the surface area, A of a cube also equals A = 6L² where L is the length of its side.

Now, equating both expressions, 6L² = 24r²

dividing both sides by 6, we have

6L²/6 = 24r²/6

L² = 4r². Since the area of one face is L², the polynomial that determines the area of one face is A' = 4r².

b.  Since L² = 4r² the rea of one face of the cube, taking square roots of both sides, we have

√L² = √4r²

L = 2r

So, the polynomial that represents the length of an edge of the cube is L = 2r

c. The length of an edge of the cube is L = 2r. When r = 3 cm.

L = 2r = 2 × 3 cm = 6 cm

So, the length of an edge of the cube is 6 cm.

Answer:

Your Y-intercept is 4/3.

Step-by-step explanation:

The X intercept would be 0 and the Y intercept is 4/3, making the coordinate (0, 4/3).

Answer:

y > x+1 (D)

Step-by-step explanation:

this equation forms the same graph as shown in the question

The vertex point of the function f(x) = 3(x - 2)² + 1 is (2 , 1)

Any quadratic function represented graphically by a parabola

1. If the coefficient of x² is positive, then the parabola open upward

  and its vertex is a minimum point.

2. If the coefficient of x² is negative, then the parabola open

  downward and its vertex is a maximum point

3. The standard form of the quadratic function is: f(x) = ax² + bx + c

   where a, b , c are constants

4. The vertex form of the quadratic function is: f(x) = a(x - h)² + k,

  where h , k are the coordinates of its vertex point

∵ The function f(x) = 3(x - 2)² + 1

∵ The f(x) = a(x - h)² + k in the vertex form

∴ a = 3 , h = 2 , k = 1

∵ h , k are the coordinates of the vertex point

∴ The coordinates of the vertex point are (2 , 1)

The vertex point of the function f(x) = 3(x - 2)² + 1 is (2 , 1)

learn more about quadratic function at:

https://brainly.com/question/25841119

#SPJ1

If the coordinates of a point are (0, y), where x = 0 and y ≠ 0, the point is located on the y-axis. If the coordinates are (x, 0), where x ≠ 0 and y = 0, the point is located on the x-axis.

On a Cartesian coordinate system, the x-axis represents the horizontal axis, while the y-axis represents the vertical axis. If the x-coordinate of a point is 0 (x = 0) and the y-coordinate is any non-zero value (y ≠ 0), the point lies on the y-axis. This is because the point has no horizontal displacement (x = 0) but has a vertical position (y ≠ 0).

Conversely, if the y-coordinate of a point is 0 (y = 0) and the x-coordinate is any non-zero value (x ≠ 0), the point lies on the x-axis. In this case, the point has no vertical displacement (y = 0) but has a horizontal position (x ≠ 0).

Therefore, the location of a point on the x-axis or y-axis can be determined based on the values of its coordinates: (0, y) represents a point on the y-axis, and (x, 0) represents a point on the x-axis.

Learn more about coordinates here:

https://brainly.com/question/15300200

#SPJ11

Answer:

when there is 2 people that answered a question, it pops up a crown right beside a flag to report the question. just press the crown and it will give the person's answer brainiest

hope this helps

Confidence intervals are commonly used in statistics to estimate a population parameter based on a sample from that population. A confidence interval provides a range of values within which the true population parameter is expected to lie with a certain level of confidence. However, the width of the confidence interval can vary depending on several factors. In this answer, we will discuss how three different factors affect the width of a confidence interval: an increase in the level of confidence, an increase in the sample size, and an increase in the population standard deviation.

Firstly, let's consider an increase in the level of confidence. The level of confidence is the probability that the true population parameter lies within the confidence interval. The common levels of confidence are 90%, 95%, and 99%. An increase in the level of confidence means that we want to be more certain that the true population parameter lies within the interval. As a result, the width of the confidence interval will increase because we need to consider a larger range of values to capture the true population parameter with a higher probability. Therefore, the correct answer is that an increase in the level of confidence will widen the confidence interval.

Secondly, let's consider an increase in the sample size. Increasing the sample size means that we have more data to estimate the population parameter. As a result, the estimate of the population parameter will be more accurate, and the standard error of the estimate will decrease. A smaller standard error means that the range of values within which the true population parameter is expected to lie will be narrower. Therefore, the correct answer is that an increase in the sample size will narrow the confidence interval.

Finally, let's consider an increase in the population standard deviation. The population standard deviation measures the variability of the population data. An increase in the population standard deviation means that the data points are more spread out, and there is more uncertainty in the estimate of the population parameter. Therefore, a larger standard deviation will result in a wider range of values that the true population parameter could take. As a result, the correct answer is that an increase in the population standard deviation will widen the confidence interval.

Click the below link, to learn more about Interval depends :

https://brainly.com/question/8966024

#SPJ11

The probability that (x, y) falls inside a circle of radius r = 0 is 1/2, which is equivalent to saying that the probability that (x, y) is exactly equal to (0,0) is 1/2.

The joint distribution of x and y is given by:

f(x, y) = (1/(2π)) × exp (-(x²2 + y²2)/2)

To find the probability that (x,y) falls inside a circle of radius r, we need to integrate this joint distribution over the circle:

P(x²2 + y²2 <= r²2) = ∫∫[x²2 + y²2 <= r²2] f(x,y) dx dy

We can convert to polar coordinates, where x = r cos(θ) and y = r sin(θ):

P(x²+ y²2 <= r²2) = ∫(0 to 2π) ∫(0 to r) f(r cos(θ), r sin(θ)) r dr dθ

Simplifying the integrand and evaluating the integral, we get:

P(x²2 + y²2 <= r²2) = ∫(0 to 2π) (1/(2π)) ×exp(-r²2/2) r dθ ∫(0 to r) dr

= (1/2) × (1 - exp(-r²2/2))

Now we need to find the value of r for which this probability is 1/2:

(1/2) × (1 - exp(-r²2/2)) = 1/2

Simplifying, we get:

exp(-r²2/2) = 1

r²2 = 0

Since r is a non-negative quantity, the only possible value for r is 0.

To know more about probability here

https://brainly.com/question/32117953

#SPJ4

Answer: 9.2 years

Step-by-step explanation:

Given the following :

Mean(m) = 11.7 years

Standard deviation (s) = 1.2 years

Recall the z-score formula :

Z = (x - m) / s

We can find the z-score by locating the value of 2% in the negative z-table, then solve for x.

2% = 0.02

0.02 falls most closely to 0.02018whuch is under - 2.05.

Using the z-score value in the formula above :

-2.05 = (x - 11.7) / 1.2

Cross multiply

(-2.05 × 1.2) = x - 11.7

-2.46 = x - 11.7

x = - 2.46 + 11.7

x = 9.24 years

Answer:

it c

Step-by-step explanation:

it make scence

Answer:its b

Step-by-step explanation:

\(\boxed{\large{\bold{\blue{ANSWER~:) }}}}\)

see this attachment

Step-by-step explanation:

age of grandpa=72

age of grandson =16

Answer:

Linear - 4

Quadratic - 1

Quartic - 3

Quintic - 2

Step-by-step explanation:

Answer:

B.15/121

Step-by-step explanation:

total-11

In this investigation, the dependent variable is the number of fish in the stream and the independent variable is the amount of pollution.

Variables are symbols or names that are used to represent values in a mathematical or scientific investigation. They allow us to describe and analyze patterns and relationships in data.

There are two main types of variables:

1. Independent variables are variables that are manipulated or controlled in an experiment to determine their effect on the dependent variable. The independent variable is also referred to as the predictor variable or the explanatory variable.

2. Dependent variables are variables that are being measured in an experiment and are dependent on the independent variable. The dependent variable is also referred to as the response variable or the outcome variable. It is the variable that is being affected by the independent variable.

The dependent variable is dependent on the independent variable, as changes in the amount of pollution are expected to affect the number of fish in the stream. The goal of the investigation is to determine the relationship between the two variables and see how changes in the amount of pollution affect the number of fish in the stream.

Learn more about dependent and independent variables here: https://brainly.com/question/25223322

#SPJ4

Answer:

Step-by-step explanation:

68 = opp/7

opp= 7tan68

opp= 17•2cm

Answer:

Step-by-step explanation:

(5 + 4)/2 = 9/2

(1 - 4)/2= -3/2

The farmer will produce 700kg of rice this year, which is 30%(percentage) less

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

A farmer produces 1000kg of rice.

This year the production of rice decreased by 30%

30% of 1000 will be 1000*30/100 = 300

So total production this year will be 1000-300 = 700KG

Hence, the farmer will produce 700kg of rice this year.

Learn more about percentage, by the following link.

https://brainly.com/question/24304697

#SPJ1

The final value of the electric field at the point halfway between the 7C and 5C charges is approximately \(2.55 \times 10^{13} N/C.\)

We have,

To calculate the magnitude of the electric field at a point halfway between two point charges, we can use the formula:

\(E = k \times (|q1| / r1^2) + k \times (|q2| / r2^2)\)

Where:

E is the magnitude of the electric field

k is the electrostatic constant (k ≈ 8.99 x 10^9 N m^2/C^2)

|q1| and |q2| are the magnitudes of the charges

r1 and r2 are the distances from the charges to the point

In this case, we have two point charges: q1 = 7 C and q2 = 5 C, and they are 13 cm apart.

Since the point of interest is halfway between the charges, the distances r1 and r2 are both 6.5 cm (half of 13 cm).

Now we can substitute the values into the formula to calculate the electric field:

\(E = (8.99 \times 10^9 N m^2/C^2) \times [(7 C) / (0.065 m)^2 + (5 C) / (0.065 m)^2]\)

\((0.065 m)^2 = 0.004225 m^2\)

Then, we substitute the values and simplify the expression:

\(E = (8.99 x 10^9 N m^2/C^2) \times[(7 C) / 0.004225 m^2 + (5 C) / 0.004225 m^2]\)

\(= (8.99 x 10^9 N m^2/C^2) \times [1658.58 C/m^2 + 1183.09 C/m^2]\)

\(= (8.99 x 10^9 N m^2/C^2) \times 2841.67 C/m^2\)

\(=2.55 \times 10^{13} N/C\)

Therefore,

The final value of the electric field at the point halfway between the 7C and 5C charges is approximately \(2.55 \times 10^{13} N/C.\)

Learn more about the electric field here:

https://brainly.com/question/11482745

#SPJ12

The coordinates of triangle RST after it is translated four units right and three units up are (0, 5), (7, 8) and (0, -1)

From the figure, the coordinates of the triangle RST are:

R = (-4, 2)

S = (3, 5)

T = (-4, -4)

The rule of translation is given as:

This is represented as:

(x, y) = (x + 4, y + 3)

So, we have:

R' = (-4 + 4, 2 + 3) = (0, 5)

S' = (3 + 4, 5 + 3) = (7, 8)

T = (-4 + 4, -4 + 3) = (0, -1)

Hence, the coordinates of triangle RST after it is translated four units right and three units up are (0, 5), (7, 8) and (0, -1)

Read more about transformation at:

https://brainly.com/question/8797028

#SPJ1

Answer:

Alloys...................................

Answer:

Step-by-step explanation:

<DCE≅<BCA

BC≅CE

AC≅CD

BA≅DE

Answer:

Step-by-step explanation:

3x = f

2x = e

x is how many batches you want to make.

Area of each plot be 16 square units.

What do you mean by GCD?

The greatest common divisor (gcd) of two or more numbers is the greatest common divisor that divides them exactly. This is also known as the highest common factor (HCF).

If a and b are two numbers, the greatest common divisor of both numbers is given by gcd(a, b). To find the gcd of a number, we need to list all divisors of the number and find the greatest common divisor.

It is given that a farmer has a piece of land measuring 140 m by 936 m he divides it into square plots of equal size.

140 = 2 × 2 × 5 × 7

936 = 2 × 2 × 2 × 3 × 3 × 13

GCD = 2 × 2 = 4

Area = 4 × 4 = 16 square units.

Therefore, area of each plot be 16 square units.

To learn more about the GCD from the given link.

https://brainly.com/question/219464

#SPJ1