Please help!! :)
In the figure, GH = HI = IJ. Find each length.

The limit of f(x), which must exist at x = 1 and be equal to k, is required for f(x) to be continuous at x = 1. (1).

The limit of f(x), which must exist at x = 1 and be equal to k, is required for f(x) to be continuous at x = 1. (1).

While the limit of f(x) is 1 - (1)2 = 0 as x approaches 1 from the left, it is 1+1 = 2 as x approaches 1 from the right. The limit of f(x) as x approaches 1 therefore does not exist because the one-sided limits are not the same.

As a result, at x = 1, f(x) is not continuous.

The function has a gap at x = 1, which can be seen if you graph it. Gaps and holes don't exist in continuous function graphs.

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The laptop worth after five halves years will be $1,543. Then the correct option is E.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

You purchase a new laptop today. The value of that laptop depreciates based on the function is given below.

f(x) = 4,300(0.83)ˣ.

Where 'x' is the number of years.

The laptop worth after five halves years will be given as,

[tex]\rm f(x) = \$4,300 \times (0.83)^{5.5}[/tex]

f(x) = $4,300 × 0.35886

f(x) = $1,543

The laptop worth after five halves years will be $1,543. Then the correct option is E.

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The missing options are given below.

$2,105

$1,601

$2,699

$3,215

$1,543

The worth of the laptop after 2.5 years is $2,699.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(t) = 4,300 [tex](0.83)^t[/tex]

Now,

For t = 5/2,

t = 2.5

f(5) = 4300 x [tex]0.83^{2.5}[/tex]

f(5) = 2699

Thus,

The laptop is worth $2,699 after 2.5 years.

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Answer:

6n+2

Step-by-step explanation:

Answer: 1.68

Step-by-step explanation: Okay, to find this we need to use this formula:

Amount = Part percent * whole number / 100

So, now let's plug in the numbers:

Amount = 14 * 12 / 100

= 168/100

= 1.68

Therefore the amount of gold in the rock is 1.68 oz out of the 12 ounces.

I hope this helped!

Answer: 1.68

Step-by-step explanation: So, if we want to find how much gold is in the rock, it's a good idea to set up a proportion. So, it would be like this:

[tex]\frac{14}{100} = \frac{?}{12}[/tex]

Now, we would cross-multiply the 12 and the 14, which is 168, and then divide it by 100. That can be found by moving the decimal 2 places left of 168.00. So, that would be 1.68. Therefore, there are 1.68 ounces of gold in the rock. I hope this helped!

The mean is calculated by taking the sum of all the values and then dividing by the total number of occurrences.

This is known as the arithmetic mean. The mode is the most frequently occurring value, and the weighted mean takes into account the frequency of each value when calculating the mean by multiplying each value by its frequency and then dividing by the total number of occurrences.

The mean is calculated by taking the sum of all the values and dividing by the total number of occurrences, which is known as the arithmetic mean. The mode is the most frequently occurring value, and the weighted mean takes into account the frequency of each value when calculating the mean by multiplying each value by its frequency and then dividing by the total number of occurrences.

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Answer:

x < 5

Step-by-step explanation:

4x-2 < - 22

=4x < -22 + 2

=4x < -20

=4x/4 < -20/4

x < 5.

The plot of both lines is given below.

y = 2r-5,

r + y = -8.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

The system of equations,

y = 2r-5,

r + y = -8.

And the intersection point is the solution of the equation.

The plot of the lines is given in the attached image.

Therefore, plots are given in the attached image.

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525 millimeters of compound A are needed.

What is a mixture?

Combining two or more substances and identifying a property of the ingredients or the resulting combination is the focus of mixture problems. For instance, we could need to figure out how much water to add to a saline solution to make it more diluted, or we might need to know how much of an orange juice bottle is concentrated.

Here, we have

Given: A certain drug is made from only two ingredients: compound A and compound B. There are 7 millimeters of compound A used for every 5 millimeters of compound B. If a chemist wants to make 900 millimeters of the drug.

Given the following ratio

A : B = 7 : 5

Mixture = 900 millimeters

To calculate the amount of compound A needed, we make use of the following formula:

A = A/(A+B)×mixture

A = 7/(7+5)×900

A = 525 millimeters.

Hence, 525 millimeters of compound A are needed.

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Jai paddles 8 miles each day for 4 days, a total of 8*4 = 32 miles.

What is an example of a unitary method?

A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.

We know that in 5 days he paddles 40 miles in total.

So on the fifth day he paddles 40-32 = 8 miles.

Therefore, Jai paddles 8 miles on the kayak on the fifth day.

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So if you own 10,000 shares of the company, you would receive $4,500 in dividends.

A dividend is a portion of a company's profits and retained earnings that it distributes to its shareholders and owners. When a company makes a profit and accumulates retained earnings, those earnings can be reinvested in the company or distributed to shareholders as a dividend.

The amount of dividends you will receive if you own 10,000 shares can be calculated as follows:

Dividend per share = Share price * dividend yield

Dividend per share = $18 * 0.025

Dividend per share = $0.45

Total dividends received = number of shares * dividend per share

Total dividends received = 10,000 * $0.45

Total dividends received = $4,500

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5.62% percentage of his adjusted gross income is he paying in property tax.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

Jimmy paid $8,200 in property taxes.

His adjusted gross income is $146,000.

The percentage of his adjusted gross income is he paying in property tax is, (8200/146000)*100%

 =5.62%

Hence, 5.62% percentage of his adjusted gross income is he paying in property tax.

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option D 3,125!/(3,125-10)! is the correct expression, because it represents the number of ways to choose 10 people from a group of 3,125 people (without regard to order) and accounts for the fact that each person can win only once.

A. (3,125-10)!/3,125! is not the correct expression, because this would represent the number of ways that 10 people can be chosen from a group of 3,115 people (without regard to order) and doesn't account for the fact that each person can win only once.

B. (3,125-10)! 10!/3,125! is also not the correct expression, because this is the number of ways to choose 10 people out of 3,115 and then arrange them in a specific order of 10 gift cards, and this doesn't account that each person can win only once.

C. (3,125)!/(3,125-10)!10! is also not the correct expression, because this represents the number of ways to arrange 3,125 people, regardless of the fact that only 10 can win, and this doesn't account for the fact that each person can win only once.

Therefore, the correct expression is D. 3,125!/(3,125-10)!

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The 34% would be considered a statistic.

A statistic is a numerical measurement of a characteristic of a population.

It is calculated by taking the number of individuals in the sample with a certain characteristic, such as preferring charcoal to gas grills, and dividing it by the total number of individuals in the sample.

For example, in the survey of 1000 adults, if 340 of them prefer charcoal to gas grills, then the statistic would be calculated as 340/1000 = 0.34 = 34%. This statistic can then be used to make inferences about the entire population. In this case, it can be inferred that 34% of the population prefers charcoal grills to gas grills.

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Answer:

x =1,69 or x= -0,44

Answer:

a) 12

b) 56

Step-by-step explanation:

In this problem we are asked to plug the given a and b values into the expressions [tex]3b \div (2a - 1) + b[/tex] and [tex]9b+a^4\div8[/tex] then evaluate them.

[tex]a = 2[/tex], [tex]b=6[/tex]

a) [tex]3b \div (2a - 1) + b[/tex]

↓ plug in the given [tex]a[/tex] and [tex]b[/tex] values

[tex]3(6) \div (2(2) - 1) + 6[/tex]

↓ simplify value inside parentheses

[tex]3(6) \div 3 + 6[/tex]

↓ execute multiplication

[tex]18 \div 3 + 6[/tex]

↓ execute division

[tex]6 + 6[/tex]

↓ execute addition

[tex]12[/tex]

b) [tex]9b+a^4\div8[/tex]

↓ plug in the given [tex]a[/tex] and [tex]b[/tex] values

[tex]9(6)+2^4\div8[/tex]

↓ simplify exponent

[tex]9(6)+16\div8[/tex]

↓ execute multiplication

[tex]54+16\div8[/tex]

↓ execute division

[tex]54+2[/tex]

↓ execute addition

[tex]56[/tex]

Answer:

1.2 grams (or) 1200 mg per day

Step-by-step explanation:

The amount needed for 1 hour,

→ 200 mg ÷ 4 hour

→ 200 ÷ 4

→ 50 mg

Patient will receive in one day is,

→ 1 day = 24 hours

→ 50mg × 1 day

→ 50 × 24

→ 1200 mg

Converting mg into grams,

→ 1 g = 1000 mg

→ 1200 mg

→ 1200 ÷ 1000

→ 1.2 grams

Hence, the answer is 1.2 grams.

Answer:

1.2 grams

Step-by-step explanation:

There are 24 hours in one day.

Therefore, if the medication is to be taken every 4 hours, the patient receives:

Given that the doctor prescribes 200 mg of medication every 4 hours, the amount in milligrams that the patient will receive in one day is:

There are 1000 milligrams in one gram.

Therefore, to convert milligrams to grams, divide by 1000:

Therefore, the patient should receive 1.2 grams of medication in one day.

Answer: False.

Step-by-step explanation:

       We will compute the different expressions to see if the equations are true.

16 + 1 = 17

17 = 17 ✓

(16 + 1) -1 = 17 - 2

(17) -1 = 15

16 ≠ 15 ✗

       The second equation is incorrect. We can tell right away because 2 is being subtracted from 2, but nothing is being taken away from the 16 (1 - 1 = 0).

The probability of randomly selecting a can that is not of grape is:

P =  0.67

We know that on the ice chest there are:

For a total of 6 + 9 + 8 + 4 = 27

The probability of selecting a can that is not of grape juice is equal to the quotient between the numbers of cans that are not of grape, and the total number of cans.

There are 27 cans in total and 18 of these aren't of grape, then the probability is:

P = 18/27 = 0.67

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As a result, when a park's size is 3/5 square miles and its length is 7/8 miles, the park's width is equal to 24/35.

A quadrilateral having four right angles, or rectangle, in Euclidean plane geometry. A quadrilateral that is equiangular, or one in which all of the angles are equal, is another way to describe it. Also possible is a straight angle in the parallelogram. With four sides that are of the same size, a square is a rectangle. Four 90-degree vertices and equal parallel sides make up a quadrilateral with a rectangle-like shape. Its equirectangular rectangle moniker derives from this. The term "parallelogram" also refers to a rectangle, which has equal and parallel opposite sides.

given

Area of a park with a rectangular shape is equal to 3/5 of a mile squared.

A rectangular park is 7/8 of a mile long.

3/5 = 7/8 * Park's rectangular width

As a result, when a park's size is 3/5 square miles and its length is 7/8 miles, the park's width is equal to 24/35.

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The population will reach 100,000 in 2047 and the population will reach 200,000 in 2082.

Total population of the city = 50,000

Growth annual rate = 2%

Using the formula of compound growth -

A = P ( 1 +r)^t

Substituting the values -

P=50,000, r =2% = 0.02 and A=100,000

Thus,

1,00,000 = 50,000 ( 1 + 0.02)^t

= 1.02^t = 1,00,000/50,000

= 1.02^t = 2

Taking ln both sides, thus -

= In( 1.02^t) = In (2)

t = In( 1.02^t)/ In (2)

t = 35

The population will reach 100,000 in the year -

= 2012+35

= 2047

Similarly,

P=50,000, r =2% = 0.02 and A=2,00,000

Thus,

2,00,000 = 50,000 ( 1 + 0.02)^t

= 1.02^t = 2,00,000/50,000

= 1.02^t = 4

Taking ln both sides, thus -

= In( 1.02^t) = In (4)

t = In( 1.02^t)/ In (4)

t = 70

The population will reach 100,000 in the year -

= 2012 + 70

= 2082

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The best estimate for the solution to a system of linear equations can be found by using the Substitution Method.

To solve for the solution, the equations must be written in the form y = mx + b. The slope, m, and the y-intercept, b, of each equation can then be calculated. The x-coordinate of the solution can be found by setting the two equations equal to each other to create an equation in one variable. This equation can then be solved for x. The y-coordinate of the solution can be found by substituting the x-coordinate into one of the original two equations. The ordered pair that is the estimated solution can then be formed.

For example, consider the system of equations y = 3x + 2 and y = -x + 5. The slope of the first equation is m1 = 3, and the y-intercept is b1 = 2. The slope of the second equation is m2 = -1, and the y-intercept is b2 = 5. Setting the two equations equal to each other yields 3x + 2 = -x + 5. Solving for x gives x = 3. Substituting this x-coordinate into either of the original equations yields y = 3(3) + 2 = 11. The ordered pair that is the estimated solution to the system is (3, 11).

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A) 20 ft B) 80 ft C) 40 ft D) 24 ft. The equation y=-1/640 x2 + 1/4 x + 20 can be used to calculate the height, distance, maximum height, and horizontal distance of the stunt motorcyclist's jump.

A) The motorcycle's height when it lands on the ramp is 20 feet. This can be calculated by plugging 0 in for x in the equation y=-1/640 x2 + 1/4 x + 20. When you plug in 0 for x, you get y=-1/640 (0)2 + 1/4 (0) + 20, which simplifies to y=20. This means that when the motorcycle lands on the ramp, it is 20 feet off the ground.

B) The distance between the ramps is 80 feet. This can be calculated by finding the value of x when y=20. Solve the equation y=-1/640 x2 + 1/4 x + 20 for x when y=20. When you solve this equation, you get x=80. This means that the distance between the ramps is 80 feet.

C) The horizontal distance the motorcycle has traveled when it reaches its maximum height is 40 feet. This can be calculated by finding the value of x when y=24. Solve the equation y=-1/640 x2 + 1/4 x + 20 for x when y=24. When you solve this equation, you get x=40. This means  that the horizontal distance the motorcycle has traveled when it reaches its maximum height is 40 feet.

D) The motorcycle's maximum height above the ground is 24 feet. This can be calculated by finding the maximum value of y in the equation y=-1/640 x2 + 1/4 x + 20. When you calculate the maximum value of y, you get y=24. This means that the motorcycle's maximum height above the ground is 24 feet.

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The image point of.tge given pair of coordinates; (12, -12) after a dilation by a scale factor of 1/3 centered at the origin is; (4, -4).

It follows from transformations that; when a point (x, y) is dilated by a scale factor of 1 / 3 centered at the origin, the resulting image point is; ( kx , ky ).

On this note, since the transformation in discuss is such that; the scale factor is 1/3 centered at the origin; the resulting image point is;

( 1/3 • 12 , 1/3 • -12 )

= ( 4, -4 ).

Ultimately, the image point which results from the dilation is; ( 4, -4 ).

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On solving the provided question, we can say that from the graphs the equation we have [tex]f(x) = y^2 + 5y -9[/tex]  => f(1/3) = -29/9

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

here,

from the graphs the equation we have

[tex]f(x) = y^2 + 5y -9\\f(1/3) = 1/9 + 5/3 - 9\\f(1/3) = 1 + 15 - 45 / 9\\f(1/3) = -29/9[/tex]

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The function that best represented by this graph is f(x) = −x² + 1.

The correct option is C.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

A graph of a function is given in the image.

The parent function of the graph is g(x) = x².

And the graph is negative of the parent function.

And shifted upwards to 1 point.

That means, the function is f(x) = −x² + 1.

Therefore, the function is f(x) = −x² + 1.

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In the case where v1 and v2 are two vectors in the vector space V and v1 is a scalar multiple of v2, let's say v1 = k * v2, where k is a scalar, we can write:

v1 = k * v2

Linearly dependent vectors are a set of vectors that can be expressed as a linear combination of the other vectors in the set. In other words, one vector in the set can be written as a scalar multiple of the other vectors in the set.

As a result, v1 can be expressed as the linear combination of v2 and k, where k is a scalar. Thus, v1 and v2 are linearly dependent on one another.

In contrast, if variables v1 and v2 are linearly dependent, v1 can be expressed as a linear combination of variables v2, and vice versa. That is, scalars k1 and k2 can exist such that:

v2 = k2 * v1 and v1 = k1 * v2.

This suggests that v1 = k1 + k2 + v1. We can divide both sides by v1 because it is not a zero vector, and the result is:

1 = k1*k2

Therefore, let's argue that v1 is a scalar multiple of v2, the other vector.

In conclusion, if and only if one of the vectors is a scalar multiple of the other, v1 and v2 are linearly dependent.

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E(Y|X) is the conditional expectation of Y given X. We can use the law of iterated expectations to show that E(u) = 0.

This law states that E(E(X|Y)) = E(X). Therefore, E(u) = E(Y - E(Y|X)) = E(Y) - E(E(Y|X)) = E(Y) - E(Y) = 0.

b. We can use the law of iterated expectations again to show that E(uX) = 0. This law states that E(E(XY|Z)) = E(X)E(Y|Z). Therefore, E(uX) = E(YX - E(YX|X)) = E(YX) - E(E(YX|X)) = E(YX) - E(Y)E(X) = 0.

c. Let Ỹ = g(x) denote a different prediction of Y using X and let v = Y - Ỹ denote its error. We can use the equation h(X) = g(x) - E(Y|X), so that v = [Y - E(Y|X)] - h(X). Using this equation, we can derive E(v2) = E[(Y - E(Y|X))2] - 2E[(Y - E(Y|X))h(X)] + E[h(X)2]. Since E(Y - E(Y|X)) = 0, this reduces to E(v2) = E[h(X)2] < E[(Y - Ỹ)2], which shows that E[(Y - Ỹ)?] > E[(Y - Ỹ)2].

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(B) LC > LB > LA is the correct statement for satellites

The magnitudes of the angular momenta of the satellites as measured about the planet are LA, LB, and LC.

The angular momentum of each satellite is conserved independently so we can compare the orbits at any location. Looking at the common point between orbit A and B shows that satellite A is moving faster at that point than satellite B, showing LA > LB. A similar analysis at the common point between B and C shows LB > L A because three equal mass satellites are in coplanar orbits around a planet

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Answer:

Rate=6

Step-by-step explanation:

First multiply the interest by 100

50.40×100=5040

then multiply the investment by the number of years

210×4=840

then divide the two answers together

5040÷840=6

Product of (a - b)(a - b) is never a perfect square trinomial, the product of (x + 5)² is x² + 10x + 25.

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

The algebraic expression (a + b) (a b) should be multiplied.

(a + b) = a² - ab + ba - b² (a + b)

(a + b) = a² - b² (a b) [ - ab + ba = 0 ]

Since there are only 2 terms in the final formula, a² - b² is a binomial.

As a result, the result of (a + b) (a b) is not a trinomial with a perfect square.

product of (x + 5)²

⇒ (x+5)(x+5)

⇒ x² + 5x + 5x + 25

⇒ x² + 10x + 25

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