What is the value of f(2)? Use the graph.​

Answer:

If the sales 2 years ago were x, the sales last year were 1.12x and this year's sales were 1.12 * (1.12x). We can write 1.12 * (1.12x) = 81427 so that means x = $64913.

Answer: I'd say reflection

Answer:

It is a reflection

Step-by-step explanation:

In Geometry, a reflection is known as a flip. A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

The fraction of Jonas age represent the age of nick after 6 years is 7/10.

Given that, present age of nick is 8 years and Jonas age is 14 years.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

After 6 years

Nick's age =14 years and Joan's age =20 years

So, the fraction =14/20

= 7/10

Therefore, the fraction of Jonas age represent the age of nick after 6 years is 7/10.

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Answer:

1111/2500

Step-by-step explanation:

Answer:

$12

Step-by-step explanation:

10 apples = $1

10 dozen apples = 10 x 12 = $1 x 12 = $12

Answer:

$120

Step-by-step explanation

A dozen is 12 and 10 dozen would be 120 apples.

The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

Population: The containers of blueberries that are being sent to Stop and Shop.

Sample: The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

Therefore, the 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

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Answer: 1:4 x - 12 = 8. 4x−12=8. Add 12 to both sides. Add 12 to both sides.

2: 4x=8+12. 4x=8+12. Add 8 and 12 to get 20. Add 8 and 12 to get 20.

3: 4x=20. 4x=20. Divide both sides by 4. Divide both sides by 4.

4: x=\frac{20}{4} x=420​ Divide 20 by 4 to get 5. Divide 20 by 4 to get 5.

The closest probability is 0.1742.

To find the probability that fewer than 30% of the employees in the sample would respond that they spend more than 30 minutes commuting to work, we can use the binomial distribution.

Let's denote the probability of an employee responding that they spend more than 30 minutes commuting to work as p. In this case, p = 0.35.

We want to find the probability of having fewer than 30% of the employees respond in this way. So, we need to calculate the probability of having 0, 1, 2, ..., 23, 24, or 25 employees out of 80 respond in this way.

Using a binomial probability calculator or statistical software, we can sum up these individual probabilities to get the desired result. The closest answer provided is 0.1742.

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The length of OP is √(3) and the Pythagorean Theorem is used to find it.

A theorem is a statement that has been proven to be true based on rigorous mathematical reasoning and evidence. It is a fundamental concept in mathematics and plays a central role in building the structure of mathematical knowledge. Theorems are often used as a basis for further mathematical analysis and the development of new theories and applications.

The length of OP can be found using the Pythagorean Theorem.

By the Pythagorean Theorem, we know that:

MN² + NO² = MO²

Since angle MNP is congruent to angle ONP, we know that triangles MNP and ONP are similar. Therefore, we can set up a proportion:

MN/NP = ON/NP

Simplifying this proportion, we get:

MN = ON

Substituting this into the equation for MO², we get:

MN²  + NO²  = MO²

2(MN² ) = MO²

Since MP is given as 2, we can use the Pythagorean Theorem in triangle MOP to find OP:

MO² = MP² + OP²

2(MN²) = MP² + OP²

2(MN²) - MP² = OP²

2(2²) - 1² = OP²

3 = OP²

OP = √3

Therefore,

The length of OP is √(3) and the Pythagorean Theorem is used to find it.

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The angle pairs in this problem are classified as follows:

A linear pair is the angle formed with the intersection of two lines, hence angles 1 and 2 form a linear pair.

Alternate Interior angles are angles that are on the inner side of the two parallel lines but on opposite sides relative to the transversal, hence angles 6 and 12 are alternate interior angles.

Vertical angles are angles that are on the opposite by the same vertex, and this vertex is the intersection point of one of the parallel lines with the transversal, hence angles 10 and 16 are vertical angles.

Corresponding angles are angles that are on the same position relative to the transversal line, but on different parallel lines, hence angles 3 and 11 are corresponding angles.

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Answer:

We are given that:

- f(x) = x² - 2x - 4

- g(x) = x - 1We want to find fx for which f(x) = g(x) - 4, or in other words:

- f(x) = x - 1 - 4

- f(x) = x - 5

We can solve forTo find the value of x for which f(x) = g(x) - 4 (which is what I assume you meant by "f(x) = (x) = m - 4"), we can set up the following equation:

f(x) = g(x) - 4

Substituting the given expressions for f(x) and g(x), we get:

x² - 2x - 4 = x - 1 - 4

Simplifying, we have:

x² - 3x - 3 = 0

We can solve for x using the quadratic formula:

x = (-(-3) ± sqrt((-3)² - 4(1)(-3))) / (2(1))

x = (3 ± sqrt(21)) / 2

Therefore, the two values of x for which f(x) = g(x) - 4 are:

- x = (3 + sqrt(21)) / 2

- x = (3 - sqrt(21)) / 2

ANSWER:

9m is the answer

Answer:

log 7

Step-by-step explanation:

Using the rules of logarithms

log x + log y ⇔ log (xy )

log x - log y ⇔ log (\(\frac{x}{y}\) )

Given

log\(\frac{14}{3}\) + log\(\frac{11}{5}\) - log\(\frac{22}{15}\)

= log (\(\frac{14}{3}\) × \(\frac{11}{5}\) ) - log\(\frac{22}{15}\)

= log (\(\frac{154}{15}\) ) - log\(\frac{22}{15}\)

= log ( \(\frac{154}{15}\) ÷ \(\frac{22}{15}\) )

= log (\(\frac{154}{15}\) × \(\frac{15}{22}\) )

= log\(\frac{154}{22}\)

= log 7

a. Present value of $400 per year for 14 years at 14%: $2,702.83
b. Present value of $200 per year for 7 years at 7%: $1,155.54
c. Present value of $400 per year for 7 years at 0%: $2,800
d. Present value of $400 per year for 14 years at 14% (annuity due): $2,943.07
  Present value of $200 per year for 7 years at 7% (annuity due): $1,233.24
  Present value of $400 per year for 7 years at 0% (annuity due): $2,800

To find the present values of the ordinary annuities, we can use the formula for the present value of an annuity:

PV = PMT * [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present value
PMT = Payment per period
r = Interest rate per period
n = Number of periods

a. $400 per year for 14 years at 14%:
PV = $400 * [(1 - (1 + 0.14)^(-14)) / 0.14]

≈ $2,702.83

b. $200 per year for 7 years at 7%:
PV = $200 * [(1 - (1 + 0.07)^(-7)) / 0.07]

≈ $1,155.54

c. $400 per year for 7 years at 0%:
Since the interest rate is 0%, the present value is simply the total amount of payments over the 7 years:
PV = $400 * 7

= $2,800

d. Reworking previous parts assuming they are annuities due:
For annuities due, we need to adjust the formula by multiplying it by (1 + r):

a. Present value of $400 per year for 14 years at 14%:
PV = $400 * [(1 - (1 + 0.14)^(-14)) / 0.14] * (1 + 0.14)

≈ $2,943.07

b. Present value of $200 per year for 7 years at 7%:
PV = $200 * [(1 - (1 + 0.07)^(-7)) / 0.07] * (1 + 0.07)

≈ $1,233.24

c. Present value of $400 per year for 7 years at 0%:
Since the interest rate is 0%, the present value remains the same:
PV = $400 * 7

= $2,800

In conclusion:
a. Present value of $400 per year for 14 years at 14%: $2,702.83
b. Present value of $200 per year for 7 years at 7%: $1,155.54
c. Present value of $400 per year for 7 years at 0%: $2,800
d. Present value of $400 per year for 14 years at 14% (annuity due): $2,943.07
  Present value of $200 per year for 7 years at 7% (annuity due): $1,233.24
  Present value of $400 per year for 7 years at 0% (annuity due): $2,800

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Answer:

10

Step-by-step explanation:

The measure of an angle∠I  is 10 degrees between the 450 cm and 640 cm sides.

The Law of Cosines (also called the Cosine Rule) is defined as it relates all three sides of a triangle with an angle of a triangle.

c² = a² + b² − 2ab cos(C)

The cosine rule, also known as the law of cosines, relates all 3 sides of a triangle with an angle of a triangle. it relates the lengths of the sides of a triangle to the cosine of one of its angles.

In the given triangle ΔHIJ,

Sides:

h = 450 m

i = 210 m

j = 640 m

The angle of ∠I  is 10 degrees between the 450 cm and 640 cm sides.

According to the cosine rule,

j² = h² + i² − 2ab cos(I)

Substitute the values in the Cosine Rule,

450² = 210² + 640² - 2(210)(640)cos(I)

After solving we get the value of  angle ∠I :

∠I = 9.56038°

Rounded to the nearest degree.

∠I = 10°

Thus, the measure of an angle∠I  is 10 degrees.

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The four pairs of coordinates for the locus of points that are both 10 units from the origin and 8 units from the x-axis are (6, 8), (-6, 8), (6, -8), and (-6, -8).

To find the locus of points that are both 10 units from the origin and 8 units from the x-axis, we can use a combination of the distance formula and the Pythagorean theorem. Let's denote the coordinates of a point on the locus as (x, y).

From the distance formula, the distance between the origin (0, 0) and (x, y) is given by \(\sqrt(x^2 + y^2)\). So, for a point to be 10 units from the origin, we have the equation \(\sqrt(x^2 + y^2) = 10.\)

Similarly, the distance between (x, y) and any point on the x-axis is simply the y-coordinate, |y|. Since we want the point to be 8 units from the x-axis, we have |y| = 8.

Now we can solve these two equations simultaneously to find the coordinates. There are four pairs of coordinates that satisfy these conditions: (6, 8), (-6, 8), (6, -8), and (-6, -8).

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Answer:

true

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

EDGE2021

The value should be used for n, the number of periods over which the loan is repaid in 60 periods.

The value of the monthly payment is given by;

P = PV × i / 1-(1+i)⁻ⁿ

Where,

PV is the present value or the amount of the loan.

i is the interest rate per period and is calculated by dividing the yearly percent rate by 100 and by the number of periods in a year.

n is the total number of periods and is calculated as the product of the number of periods in a year times the number of years.

Therefore,

The value should be used for n, the number of periods over which the loan is repaid;

n = 6 years × 12 months/year = 60 months = 60 periods.

Hence, The value should be used for n, the number of periods over which the loan is repaid in 60 periods.

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Answer:

Addition Property of Equality.

Step-by-step explanation:

The Addition property of equality states that: "If two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal" (http://content.nroc.org).

For example:

x = x is the same as x + 1 = x + 1

the one is the added same value "to both sides of the equation".

Solving in extremely detailed steps:
(you only take one step normally, from 5x-2=0 to 5x=2, but because we are explaining the concept of the property, we will use lots detailed of steps)

5x - 2 = 0

5x - 2 + 2 = 0 + 2

5x + 0 = 2

5x = 2

Answer:

The percentage increase is by 1.75

Step-by-step explanation:

78,200 x 1.75 = 136,850

The given system with two coupled subsystems has an undamped natural frequency of 6.714 rad/s and a damping ratio of 0.3001.

The given system consists of two coupled subsystems: a rotational system and a field-controlled motor system. The rotational system is described by the equation of motion 30 dtdt​ + 10w = T(t), where T(t) is the torque applied by an electric motor. The motor system is modeled by the equation 0.001 dtdi​ + 5i = v(t), where i is the field current in amperes and v(t) is the voltage applied to the motor.

The damping ratio of the combined system can be determined by dividing the sum of the two time constants by the undamped natural frequency, i.e. ζ = (τ1 + τ2)ωn​. Given the time constants of the rotational and motor systems as 3 seconds and 0.001 seconds respectively, and the undamped natural frequency as ωn​ = 10 rad/s, we can calculate the damping ratio as ζ = (3 + 0.001) x 10 / 10 = 0.3001.

The combined system's undamped natural frequency is determined by solving the characteristic equation of the system, which is given by (30I + 10ωs)(0.001s + 5) = 0, where I is the identity matrix. This yields the roots s = -0.1667 ± 6.714i. The undamped natural frequency is therefore ωn​ = 6.714 rad/s.

In summary, the given system with two coupled subsystems has an undamped natural frequency of 6.714 rad/s and a damping ratio of 0.3001.

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The probability that the balls are both white be 1/7.

Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.

Number of black balls = 4

Number of white balls = 3

Total number of balls = 7

Number of ways of picking up a white ball out of 7 balls, P(W) = 3/7

Number of ways of picking up a second white ball ,P(W) = 2/6

Therefore, the probability of picking up 2 white balls

P(WW) = 3/7 \(*\) 2/6 = 1/7

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LCL and UCL values of both scenarios are (158.61,161.39),(69.65,70.35) respectively.

To calculate the lower confidence limit (LCL) and upper confidence limit (UCL) for each given scenario, you'll need to use the following formula:

LCL = X - (z * (sigma / √n))
UCL = X+ (z * (sigma / √n))

where X is the sample mean, n is the sample size, sigma is the population standard deviation, and z is the z-score corresponding to the desired confidence level (1 - alpha).

First Scenario:
X = 160, n = 436, sigma = 30, alpha = 0.01

1. Find the z-score for the given alpha (0.01).
For a two-tailed test, look up the z-score for 1 - (alpha / 2) = 1 - 0.005 = 0.995.
The corresponding z-score is 2.576.

2. Calculate LCL and UCL.
LCL = 160 - (2.576 * (30 / √436)) ≈ 158.61
UCL = 160 + (2.576 * (30 / √436)) ≈ 161.39

First Scenario Result:
LCL = 158.61
UCL = 161.39

Second Scenario:
X= 70, n = 323, sigma = 4, alpha = 0.05

1. Find the z-score for the given alpha (0.05).
For a two-tailed test, look up the z-score for 1 - (alpha / 2) = 1 - 0.025 = 0.975.
The corresponding z-score is 1.96.

2. Calculate LCL and UCL.
LCL = 70 - (1.96 * (4 / √323)) ≈ 69.65
UCL = 70 + (1.96 * (4 / √323)) ≈ 70.35

Second Scenario Result:
LCL = 69.65
UCL = 70.35

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Answer:

63mi/h = 0.0175 mi/sec , hope this helps you

In ANOVA, if the observed F equals or exceeds the critical F, the experimental outcome is considered statistically significant.

Analysis of Variance (ANOVA) is a statistical method used to compare the means of two or more groups. The F-statistic is the test statistic used in ANOVA. When conducting an ANOVA test, we compare the observed F-value to the critical F-value to determine the significance of the results.

Step 1: Calculate the observed F-value using the given data.

Step 2: Determine the critical F-value using the F-distribution table, taking into account the degrees of freedom and the desired significance level (usually set at 0.05).

Step 3: Compare the observed F-value to the critical F-value.

If the observed F-value equals or exceeds the critical F-value, it indicates that there is a statistically significant difference between the group means, and we reject the null hypothesis. In other words, the experimental outcome suggests that at least one of the group means is significantly different from the others.

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Answer:

There should be 5 lines of symmetry.

Step-by-step explanation:

Carla's draw only one line of symmetry but in a regular pentagon there should be 5 line of symmetry.

Here,

Carla was asked to draw all the lines of symmetry for a regular pentagon.

She drew the picture as shown.

We have to find Carla's mistake.

What is Regular Pentagon?

A regular pentagon is a pentagon that has 5 equal sides and 5 equal angles.

Now,

As shown in figure,

Carla's draw only one line of symmetry.

But in a regular pentagon there should be 5 line of symmetry.

Hence, There should be 5 line of symmetry.

Option 4 is true.

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Answer:

27, correct me if im wrong

Step-by-step explanation:

Answer:

35/7 = 5

5*5 = 25

25+2 = 27

Step-by-step explanation:

C) f is decreasing for x<0 because f′(x)<0 for x<0. , we can conclude that the function f is decreasing for x<0 because f′(x)<0 for x<0.

The derivative of f is f′(x)=x2−a2=(x−a)(x+a).

This implies that f′(x)<0 when x<−a or x>a. From the derivative, we can deduce that f is decreasing for x<0 because f′(x)<0 for x<0.

The derivative of the function f is f′(x)=x2−a2=(x−a)(x+a), where a is a positive constant. This means that the derivative is negative when x<−a or x>a. We can use this information to determine the behavior of the function. Since the derivative is negative when x is less than zero, we can conclude that the function f is decreasing for x<0 because f′(x)<0 for x<0.

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