what is the value of n in the equation ? n = 0 n = 2 n = 4 n = 6; kate begins solving the equation 2/3(6x-3)=1/2(6x-4); what is the value of x in the equation ? 2 13; solve the equation. y + 3 = โy + 9 y = 1 y = 3 y = 6 y = 9; what value of x is in the solution set of 2x โ 3 > 11 โ 5x? โ3 0 2 4; what is the solution to the linear equation? + p = + p p = 1 p = 2 p = 8 p = 10; solve the equation. โ9x + 1 = โx + 17 x = โ8 x = โ2 x = 2 x = 8; which number line represents the solutions to โ2|x| = โ6?

Step 1: Isolate w^2:

     w^2 = 54

Step 2: Apply the sq. rt. property:

     w = ± sqrt(54)

Step 3: Simplify the sqrt:

     w = ± sqrt(9 · 6)

     w = ± sqrt(9) · sqrt(6)

     w = ± 3 sqrt(6)

Step 4: Approximate:

     w ≈ ± 7.3

Answer:

the slope is 1

Step-by-step explanation:

where: m is the slope and b is the y-intercept. Therefore, for the equation y=x+5 , the slope is 1 , and the y-intercept is 5

Answer:

3.35

Step-by-step explanation:

38.86=11.6x

x=3.35

Answer:

150-3x

Step-by-step explanation:

Use distrubitive property:

180-6x +3x-30

Factor:

150-3x

Answer:

-3x+150

Step-by-step explanation:

6(30-x)+3(x-10)

6(30)+6(-x)+3(x)+3(-10)

180-6x+3x-30

180-3x-30

-3x+150

hopes this helps please mark brainliest

The nth term of the given sequence is 8(3)ⁿ⁻¹. The given sequence is a geometric series and its common ratio is r = 3.

The nth term of a geometric series is calculated by the formula

tₙ = arⁿ⁻¹

Here a is the first term of the sequence and r is the common ratio of the sequence.

The common ratio is calculated by r = aⁿ⁺¹/aⁿ

The given sequence is 8, 24, 72, 216

Here, the first term in the given sequence is a = 8;

The ratios of the terms of the sequence are:

24/8 = 3

72/24 = 3

216/72 = 3

Since the ratios are the same, then the given sequence is geometric.

Thus, the common ratio is r = 3.

And the nth term of the given geometric sequence is

tₙ = arⁿ⁻¹ = (8)(3)ⁿ⁻¹

Therefore, the nth term of the given geometric sequence is 8(3)ⁿ⁻¹.

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2.5% of values will lie above 29.

What is normal distribution?

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

The 68-95-99.7 rule is an illustration of how those many percentage of values lie in between  mean +/- 1, 2, and 3 standard deviations respectively.

For values to lie above 29, their z value comes out to be

(29-19) / 5 = 10/5 = 2

(Note: z value means how many standard deviations above the mean)

Thus for a z value = 2 (which 29 is in this problem) the percentage of values that lie between mean +/- 2*(standard deviation) is 95 (as stated by the 68-95-99.7 rule).

Thus only 5% values wont lie between mean +/-2 standard deviations.

So 5% values wont lie between 29 (z value=2) and 9 (z value=-2).

Since normal curve is symmetric, half of the values of the 5% will lie above 29 and the rest half will lie below 9.

So 50% of 5 % which is 2.5% of values will lie above 29.

Hence, 2.5% of values will lie above 29.

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The floor area of a rhombus is equal to (1/2) × diag1 × diag2 is equal to 100 ft^2

diag1 = sqrt((10 ft)^2 + (10 ft)^2)

diag2 = sqrt((10 ft)^2 + (10 ft)^2)

Floor area = (1/2) × (sqrt((10 ft)^2 + (10 ft)^2)) × (sqrt((10 ft)^2 + (10 ft)^2))

= (1/2) × (14.14 ft) × (14.14 ft)

= 100 ft^2

1. Find the length of the diagonals of the rhombus.

diag1 = sqrt((10 ft)^2 + (10 ft)^2)

diag2 = sqrt((10 ft)^2 + (10 ft)^2)

2. Use the formula for the floor area of a rhombus.

Floor area = (1/2) × diag1 × diag2

3. Substitute the diagonals into the formula.

Floor area = (1/2) × (sqrt((10 ft)^2 + (10 ft)^2)) × (sqrt((10 ft)^2 + (10 ft)^2))

4. Simplify.

Floor area = (1/2) × (14.14 ft) × (14.14 ft)

= 100 ft^2

Find the length of the diagonals of the rhombus (sqrt((10 ft)^2 + (10 ft)^2)). Use the formula for the floor area of a rhombus (1/2 × diag1 × diag2). Substitute the diagonals into the formula and simplify to find the floor area (100 ft^2).

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1) The equation that solves for Katherine age, x is 5(x - 4) = 400.

2) Katherine is 84 years old.

3) Mabel is 80 years old.

An algebraic equation represents the mathematical form of two expressions that are related by an equal in between them.

From the given information, we can write,

Katherine's age is represented by 'x'

Mabel is 4 years younger than Katherine ie., x - 4

Five times Mabel's age is equal to 400 i.e., 5(x - 4) = 400

Thus, the equation that solves Katherine's age is 5(x - 4) = 400.

On simplifying the obtained equation, we get

5(x - 4) = 400

⇒ 5x - 20 = 400

⇒ 5x = 400 + 20

⇒ 5x = 420

∴ x = 420/5 = 84

Thus, the age of Katherine is 84 years.

Then, Mabel's age = x - 4 = 84 - 4 = 80 years.

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The value of x after simplification is 6/5.

What is an equation?

A mathematical equation is a formula that uses the equals sign to express the equality of two expressions. The meanings of the word equation as well as its cognates in those other languages can vary slightly. For instance, in French, an equation is defined as having one or even more variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign. Finding the values for the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables that the equation must be solved, and the unknown variable values that satisfy this same equality are known as the equation's solutions.

Main Body:

according to the given equation,

5x = 6

to solve it , divide by 5 on both sides,

5x *1/5  = 6*1/5

x = 6/5

Hence the value of x after simplification is 6/5.

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Answer:

Step-by-step explanation:

its all explained in picture

Internal validity refers to the accuracy of the evaluation in attributing the changes identified to the program and not to other factors, such as demographic differences between the participants and the control group.

To ensure internal validity, one must compare the participants and the control groups on demographic characteristics in order to show that the differences found in the evaluation are due to program differences and not to demographic differences. This is done by conducting a statistical comparison of the two groups and calculating the probability that any differences found between them are due to the program and not to some other factor. This is done by computing the probability that the two groups are the same, given the observed mean differences, and then evaluating the results to determine if the differences are statistically significant. For example, if the two groups have different means, the probability of them being the same is calculated, and if this probability is low, then the difference is likely to be due to the program and not to some other factor. This type of statistical analysis speaks to the internal validity of the evaluation.  

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The kinetic energy will be maximum if the potential energy is minimum.

Given that,

On the graph, an object's mechanical energy is represented by the horizontal red line, and its potential energy as a function of x is shown by the blue line beneath it. at what x value is:

Value of x at which

1) potential energy at the largest

2kinetic energy at the largest

3)The force on the object in the negative direction.

4)The force on the object the largest magnitude.

More above the x-axis, greater the value of potential energy. Therefore, the point at which potential energy is large at x = 4

Mechanical energy is sum of potential energy and kinetic energy

So, kinetic energy will be maximum if the potential energy is minimum.

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The area of the rectangle, in square meters, is 7.56 meters².

Rectangles are quadrilaterals having four equal vertices and parallel sides that are equal to one another.

Given;

a rectangle has a length of 42 centimeters,

and a width of 18 centimeters.

To find the area of the rectangle:

We multiply the length of the rectangle by the width of the rectangle.

Use formula,

The area of the rectangle = length x width

Substitute the value of length and width

The area of the rectangle = 42 x 18

The area of the rectangle = 756 cm².

To change centimeter to meter:

We have the rate of change,

1 centimeter = 0.01 meter

756 centimeters = 0.01 x 756 meters

756 centimeters = 7.56 meters

Therefore, the area of the rectangle = 7.56 meters².

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Option A) is correct

There is only one solution: x = 1. The solution x = 3 is an extraneous solution.  

Solution :

Given Equations:

[tex]\frac{1}{x} +\frac{1}{1-x} =\frac{x-2}{y-3}[/tex]

solving The given Equation have :

[tex]\frac{1}{x}+ \frac{1}{x-3} =\frac{x-2}{y-3}[/tex]

[tex]\frac{2x-3}{x(x-3)} =\frac{x-2}{y-3}[/tex]

[tex]2x-3=x^{2} -2x[/tex]

[tex]x^{2} -4x+3=0[/tex]

[tex]x^{2} -x-x3+3=0[/tex]

[tex]x(x-1)-3(x-3)=0\\x-3)(x-1)=0\\x=1,x=3[/tex]

Extraneous solutions:

Due to its exclusion from the original equation's domain, an auxiliary solution is not a root of the original equation.

We may get this conclusion, but we cannot accept it as a conclusion since it is insufficient.

However, x = 3 cannot be a solution to the preceding equation because it produces a denominator of zero when used in the provided equation.

As a result, the following equation's solution is x = 1, while its superfluous solution is x = 3.

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The formula for simple interest.

SI = P( x R x T) / 100

The outstanding balance of her loan after the first month is $608355

It is the interest calculated on the principal at a given rate for a time period.

The formula for simple interest.

SI = P( x R x T) / 100

We have,

The purchase price of the home = $210,000

The down payment.

= 30% of 210,000
= 3/10 x 210,000

= 3 x 21,000

= $63,000

Now,

The remaining amount.

= 210,000 - 63,000

= $147,000

Now,

Simple interest for 30 years.

= (147,000 x (21/2) x 30) / 100

= (147,000 x 21 x 30) / 200

= 1470 x 21 x 15

= $463,050

Thus,

The total amount to pay for 30 years.

= 147,000 + 463,050

= $610050

The monthly payment for 30 years.

= 610050 / (30 x 12)

= $1694.58

Now,

The outstanding balance of her loan after the first month.

= 610050 - 1694.58

= $608355

Thus,

The outstanding balance of her loan after the first month is $608355

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The value which is round off to the nearest thousand for 231469.335329 is 232000.

What is rounding off?

When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done. The important figures are preserved when numbers are rounded off.

The given value in the question is 231469.335329

The rules for rounding off says,

If the last digit of the given number is above 5 or equal to 5 then 1 is added to pre digit of last number and last digit is replaced by 0.

So, the given value,

231469.335329 the digit after the point is less than 5 so we eliminate the value without adding 1.

It becomes, 231469.00

In above value, if 231469 we add one to the before the last digit, it becomes 231470

As a next step, add the number in the 2 digit by adding 1 to before the 2nd digit, it becomes 231500.

Now Finally, the process of adding one to the 4 digit depends on the values of 3rd digit takes place and it becomes 232000.  

Hence, the number is 232000.

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The solution set of the quadratic inequality x² - 5 < 0 is - √5 < x < √5

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

The quadratic inequality is:

x^2-5<0

Express properly

x² - 5 < 0

Add 5 to both sides of the inequality

x² < 5

Take the square root of both sides

x < ±√5

Expand the inequality expression

- √5 < x < √5

Hence, the solution is - √5 < x < √5

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The statement is AB=CD,BC=AD due to definition of parallelogram. The statement is AC=AC due to Reflexive property of equality.

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. A quadrilateral with the opposing sides parallel is called a parallelogram. A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus.

Here,

1. Statement: AB=CD,BC=AD

Reason: By definition of parallelogram.

2. Statement: AC=AC

Reason: Reflexive property of equality.

The definition of a parallelogram causes the sentence to be AB=CD,BC=AD. Due to the reflexive feature of equality, the assertion is AC=AC.

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Acceleration resulting from gravity will be = (-9.8 ms sq.)

First of all we have to know more about gravity which means it is the force by which a planet or other body draws objects toward its center. The force of gravity keeps all of the planets in orbit around the sun.

When you throw a ball up in the air, its speed decreases, until it momentarily stops at the very top of the ball's motion. Its acceleration is

(−9.8 ms sq )

at the very top since the body is moving upward against the gravity. In other words, the acceleration due to gravity will be

g = 9.8 ms -sq

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The inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours landscaping, is  

w + l ≥ 17.

What is inequality?

In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.

Given:

Mackenzie is working two summer jobs, washing cars and landscaping. She must work at least 17 hours altogether between both jobs in a given week.

Total number of hours is w + l and it should be at least 17 hours, (equal to 17 or greater).

We can set inequality as:

w + l ≥ 17

Hence, the inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours landscaping, is  w + l ≥ 17.

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Answer:

48 reindeer

Step-by-step explanation:

the 5 part of the ratio relates to 60 moose , then

60 ÷ 5 = 12 ← value of 1 part of the ratio

then

4 × 12 = 48 ← number of reindeer

Answer: f

Step-by-step explanation:

The domain of a composite function f(g(x)) is the set of those inputs x in the domain of g for which g(x) is in the domain of .

Step-by-step explanation:

you marked the important pieces of information correctly.

a parallel line must have the same slope. otherwise it is tilted differently, and it is therefore not parallel.

the slope in a y = ... equation is always the factor of x.

in our case therefore 1/5.

so, the parallel line starts with

y = (1/5)x + b

and to get b we use the x and y coordinates of the given point :

3 = (1/5)×5 + b = 5/5 + b = 1 + b

b = 2

and our equation is

y = (1/5)x + 2

Answer:

To solve this system of equations, we need to find the values of x and y that make both equations true at the same time.

One way to solve this system is to use the substitution method. We can start by setting the two expressions for y equal to each other:

3x = -x + 4

Then we can solve for x by adding x to both sides and simplifying:

4x = 4

x = 1

Now that we know the value of x, we can substitute it back into either of the original equations to solve for y:

Y = 3x

Y = 3(1)

Y = 3

Therefore, the solution to the system of equations is (x, y) = (1, 3).

Standard Deviation is a measure of the spread of a data set. The smaller the standard deviation, the closer the values are to the mean.

In the box and whisker plots, the box represents the middle portion of the dataset (the middle 50%), the whiskers represent the outer 25% of the data, and the line inside the box is the median.In this case, the box and whisker plot with the smallest standard deviation is the plot on the right, which shows a box that is wider than the other plot but with less variation in the whiskers. This indicates that the values in the plot on the right are closer to the median than in the plot on the left, which suggests that the standard deviation of the plot on the right is smaller than the standard deviation of the plot on the left.

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The balance will be $34,677.45 in Jarad's account, at the end of 10 years.

The balance in the account is computed as illustrated follow as:

Future value = Present value (1 + r)n

Because the amount is compounded semi-annually, the interest rate is split by two and the number of time periods is multiplied by two.

So, the balance in the account is computed as follows:

= $10,000 x (1 + 0.10 / 2)10 x 2 + $5,000 x (1 + 0.10 / 2)5 x 2

= $26,532.97705 + $8,144.473134

= $34,677.45 Approximately

Thus, the balance will be $34,677.45 in Jarad's account, at the end of 10 years.

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Answer:

Below

Step-by-step explanation:

(x-10)^2 = 90     sqrt both sides

x-10  =  ± sqrt (90)

x  =   10 ± sqrt (90)

Using the regression model you predict the sales to be $ 250.38 on day 60.

A regression model is an equation used to ascertain the relationship between two variables.

Given that an electronics retailer used regression to find a simple model to predict sales growth in the first quarter of the new year (January through March). The model is good for 90 days, where x is the day.

The model can be written as follows:

ŷ = 103.38 + 2.45x

where ŷ is in thousands of dollars.

Since we require the sales gtowth after 0 days, substituting x = 60 into the equation for the regression model, we have that

ŷ = 103.38 + 2.45x

ŷ = 103.38 + 2.45(60)

ŷ = 103.38 + 2.45(60)

ŷ = 103.38 + 147

ŷ = 250.38

So, you predict the sales to be $ 250.38 on day 60.

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The answer choice which corrects justifies the step as described is; Choice B; addition property of equality.

It follows from the task content that the answer choice which corrects justifies the step as given is to be determined.

Since the starting step is;

2x + 3 = -5x - 1

By adding 5x to both sides of the equation;

2x + 5x + 3 = -5x - 1 + 5x

7x + 3 = -1

Recall that; the addition property of equality postulates that;

if x = y;

Then, x + a = y + a.

On this note, the property which justifies the step is; Choice B; Addition property of equality.

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Answer:

The answer is option (C). Four Rivers Bank

Explanation:

a). The total amount Jane will receive after 5 years after investing $40,000 in the Mystic Bank can be expressed as follows;

A = P (1 + r/n) (nt)

where;

A = the future value of the initial investment

P = initial investment amount/principal amount

r = the annual interest rate

n = the number of times that interest is compounded per unit t

t = the time the money is invested for

In our case;

P=$40,000

r=12/100=0.12

n=interest is compounded quarterly which is four times a year=4

t=5 years

Replacing values in the formula;

A=40,000(1+0.12/4)^(4×5)

A=40,000(1+0.03)^20

A=40,000×1.806

A=72,244.45

The total amount Jane will receive after 5 years if she chooses to invest with the Mystic Bank is $72,244.45

b). The total amount Jane will receive after 5 years after investing $40,000 in the Four Rivers Bank can be expressed as follows;

A = P (1 + r/n) (nt)

where;

P=$40,000

r=14/100=0.14

n=interest is compounded semiannually which is two times a year=2

t=5 years

Replacing values in the formula;

A=40,000(1+0.14/2)^(2×5)

A=40,000(1+0.07)^10

A=40,000×1.967

A=78,686.05

The total amount Jane will receive after 5 years if she chooses to invest with the Four Rivers Bank is $78,686.05

c). The best deal would be to invest with Four Rivers Bank for 5 years since the total amount Jane will receive after 5 years will be $78,686.05 which is greater than $72,244.45, which is the total amount she will receive if she chooses to invest with Mystic Bank