The function g(x) is shown on the graph.

The graph shows an upward opening parabola with a vertex at negative 3 comma negative 2, a point at negative 5 comma 2, and a point at negative 1 comma 2.

What is the equation of g(x) in vertex form?

g(x) = (x − 3)2 − 2
g(x) = (x − 3)2 + 2
g(x) = (x + 3)2 − 2
g(x) = (x + 3)2 + 2

Answer:

Step-by-step explanation:

From Point 1 to Point 2 on the trail, the bike rider is traveling uphill, which means that the change in kinetic energy is negative because the rider is slowing down due to the work required to move against gravity. The rider is losing kinetic energy and converting it into potential energy.

On the other hand, the change in potential energy from Point 1 to Point 2 is positive because the rider is gaining height and storing potential energy due to the work done against gravity. As the rider climbs uphill, the potential energy of the rider-bike system increases.

So, to summarize:

Change in kinetic energy from Point 1 to Point 2: Negative

Change in potential energy from Point 1 to Point 2: Positive

Answer:0.6

Step-by-step explanation: 4 divided by 5 = 0.6

please make me brainalist and keep smiling dude I hope you will be satisfied with my answer is updated

Answer: 3/5 as a decimal is 0.6

Answer: 3/5 as a decimal is 0.6Let us see how to convert 3/5 to a decimal using two methods.

Answer: 3/5 as a decimal is 0.6Let us see how to convert 3/5 to a decimal using two methods.Explanation

Step 1: To convert any fraction to decimal form, we just need to divide its numerator by denominator.

Step 2: Here, the fraction is 3/5 which means we need to perform 3 ÷ 5

Step 3: This gives the answer as 0.6. So, 3/5 as a decimal is 0.6

Step 1: Find a number that we can multiply by the denominator of the fraction to make it 10 or 100 or 1000 and so on. In this case, if we multiply the denominator by 2 it becomes 10. Therefore, we will multiply both the numerator and the denominator by 2 which will make it 3/5 = (3 × 2) / (5 × 2) = 6/10

Step 2: After multiplying both numerator and denominator by that number, we have converted it into its equivalent fraction.

Step 3: Then, we write down just the numerator by putting the decimal point in the correct place, that is, one space to the left starting from the right-hand side for every zero in the denominator. This means 6/10 = 0.6

Step 3: Then, we write down just the numerator by putting the decimal point in the correct place, that is, one space to the left starting from the right-hand side for every zero in the denominator. This means 6/10 = 0.6Irrespective of the methods used, the answer to 3/5 as a decimal number will always remain the same. Therefore, now we know what is 3/5 in decimal form.

Step 3: Then, we write down just the numerator by putting the decimal point in the correct place, that is, one space to the left starting from the right-hand side for every zero in the denominator. This means 6/10 = 0.6Irrespective of the methods used, the answer to 3/5 as a decimal number will always remain the same. Therefore, now we know what is 3/5 in decimal form.Thus, 3/5 as a decimal is 0.6

Except than x = 1, all real numbers fall within the function's domain.

Since there are no limitations on what we can substitute for x, the domain of a function, f(x), is all real numbers because any real numbers would make f(x) a defined function. As a result, when this is not the case, the domain of a function, f(x), is not all real numbers.

The rational function r(x) = 2x/(x-1) is defined as follows.

So, we set the denominator to zero and solve for x in order to determine the domain of r(x):

x - 1 = 0

x = 1

Hence, x = 1 is the only value of x that causes the denominator to equal 0. R(x) therefore has a domain of all real numbers other than x = 1.

We can express the domain as follows in interval notation:

(-∞, 1) U (1, ∞)

Except than x = 1, all real numbers fall within the function's domain.

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Question:

Which of the following correctly describes the domain of the function shown below?

r(x) = 2x x-1

A. {x:x0}

B. {x: x = 1}

c. x all .real .numbers}

D. xx1}

The mass of dog having weight as 19 kg has its mass in grams as 1.9 x 10⁴ grams, option C.

In physics, mass is a quantitative measurement of inertia, a basic characteristic of all matter. It essentially refers to a body of matter's resistance to changing its speed or location in response to the application of a force. The change caused by an applied force is smaller the more mass a body has.

Measuring units to determine the size, weight, or quantity of any object. Seven fundamental measurement units are utilized in daily life and across the globe.

A dog has a mass of 19 kg

The mass of the dog in grams is:

1 kilogram = 1000 grams

19.5 kg × (10³ g/1 kg) = 1.95 × 10⁴ g.

Thus, the mass of the dog in grams is 1.95 × 10⁴ g.

1000 grammes make to 1 kilogram (kg) (g).

1 kg = 1000 g

The mass m in kilogram (kg) multiplied by 1000 gives the mass m in grams (g)

m(g) = m(kg) × 1000.

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Answer:

Step-by-step explanation:

You want to know the dimensions of a cuboid cereal box with volume 975 cm³ that is 3 times as wide as deep, and 2 cm shorter than wide.

Let x represent the depth of the box. Then the width is 3 times that, or 3x. The length is 2 cm less than the width, so is (3x -2). The volume is the product of these dimensions.

  V = DWL

  975 = x(3x)(3x -2)

We like to graph an equation like this in the form ...

  f(x) = 0

so the solution is the x-intercept of the graph of f(x). Subtracting 975 puts the equation in that form:

  x(3x)(3x -2) -975 = 0

The attachment shows the graph of x(3x)(3x -2), and that it has its only real solution at x=5. This means the dimensions are ...

__

Alternate solution

Sometimes finding the solution to a cubic isn't easy. As a starting point, we can recognize that 3x-2 is about the same as 3x, so the value of x will be approximately the solution to ...

  975 = x(3x)(3x) = 9x³

  x = ∛(975/9) ≈ 4.8

The nearest integer to this value is x=5, so that can be a good value to check: 5(3·5)(3·5 -2) = 5·15·13 =975. (x = 5 works!)

Iterated solution

We can rewrite the equation as ...

  975 = 3x²(3x -2)

  325 = x²(3x -2)

  325/(3x -2) = x²

  x = √(325/(3x -2))

A value of x will be a solution to this equation if it makes the right side equal to the left side. This equation works as an "iterator," meaning we can use a value of x on the right side, and the value of that function will give a value of x on the left that is closer to the solution. The table in the second attachment shows this convergence to x=5.

It isn't always easy to find a suitable iteration function for a cubic or higher degree polynomial equation. The usual tools are Descartes' Rule of Signs, and the Rational Root Theorem. The best iteration functions are found using calculus.

Here option A is correct: "The change in expected height for every one additional centimeter of femur length."

What is a centimetre?

A centimetre is a metric unit of length equal to one-hundredth of a meter. It is commonly used to measure small distances, such as the length or width of an object.

What is meant by femur length?

Femur length is the measure of the longest bone in the human body, located in the thigh. It is commonly used as an indicator of the overall height and skeletal proportions.

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The correct option is A) 3; 4; no money. Ned should eat 3 pounds of oranges and 4 pounds of starfruit, as this combination maximizes his total utility and fully utilizes his $26 budget, resulting in a total utility of 280.

He should eat 3 oranges and 4 pounds of star fruits and he will have no money left over

Because by comsuming this combination it will maximize Calvin's total utility and his money will be distributed correctly according to the utility maximization

Like if he consume 8 orange and 2 pound of star fruit in option(B)

8 units of orange consumption is not given but we'll assume it will give total utility of 84

And 2 pound of star fruit will give 130

130 + 84 = 214

Opt (c) = only 5 star fruit no orange

= 5 Star fruit = 250 total utility

Opt (D) = is not possible because

4 orange will take $2 each = 4×2 = $8

And 5 pounds of star fruit takes $5 each = $5×5 = $25

$25 +$8 = $33 but he have only $26 so option (d) cant be considered

Opt (a)

3 orange = 60

And 4 pounds of star fruit = 220

220 + 60 = 280 total utility so this option gave us maximum total utility and the $26 is Fully utilized

3×$2 = $6

4 × $5  = $20

$6 + $20 = $26

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Complete question is in the image attahed below

The distance D between points A and B is approximately 8.25 units.

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using the given points, we have:

a = (2, -3)

b = (4, 5)

We have:

D = √( ( 4 - 2 )² + ( 5 - (-3) )² )

D = √( ( 2 )² + ( 5 + 3 )² )

D = √( 2² + 8² )

D = √( 4 + 64 )

D = √68

D = 8.25

Therefore, the distance is 8.25 units.

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Number of measurements that must be made so that the diameter can be estimated with an uncertainty of only 0.5 mm is 16

To estimate the diameter with an uncertainty of 0.5 mm, we need to reduce the uncertainty to that level. Let's call the number of measurements we need to make "N". We can use the formula for the standard deviation of the mean

σ_mean = σ / sqrt(N)

where σ is the standard deviation of the individual measurements. In this case, the uncertainty of each measurement is given as 1.4 mm, which we can assume is the standard deviation.

To reduce the uncertainty to 0.5 mm, we need

0.5 = 1.4 / sqrt(N)

Solving for N, we get

N = (1.4 / 0.5)^2 = 15.68

≈ 16

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Answer:

(9x10^4)+(7x10) = 90,000 + 70 = 90,070

Answer:

Let x = the cost of a movieLet y = the cost of a gameUsing these variables,

we can set up equations.3x + 5y = 42 eq19x + 7y = 72 eq2

We have here a system of equations, where we have two or more equations with two or more different variables.

We use the elimination method to solve for the variables.

Multiply eq1 by 3. Keep eq2.

9x + 15y = 126 eq1

9x + 7y = 72 eq2

Subtract eq2 from eq1 to eliminate the x terms.

8y = 54y  

= 6.75

This rental cost of one video game is $6.75

Substitute the value of y into eq1 to solve for x.

This will give you the rental cost of one movie.

Step-by-step explanation:

The experimental probability of drawing the cards, 2, 3, or 4, from the deck of 52 cards, with the frequency obtained from 200 draws is about 15.5%

An experimental probability is the probability of a specified event taking place, based on repeated trials or sampling.

The number of draws Rayna drew from the standard deck of cards = 200 draws

The frequency of the cards drawn, obtained from the frequency table are;

Frequency of 2 = 8

Frequency of 3 = 12

Frequency of 4 = 11

The experimental probability of drawing a card that has a value of 2 or a card that has a value of 3 or a card that has a value of 4 is therefore;

P(2, 3, 4) = (Frequency of 2 + Frequency of 3 + Frequency of 4)/The total number of draws Rayna drew

P(2, 3, 4) = (8 + 12 + 11)/200 = 0.155 = 15.5%

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Answer:

To find the simple interest on a principal of $600 at a rate of 2% for a time period of 2 years, we can use the formula:

Simple Interest = (Principal * Rate * Time)

where Rate is the annual interest rate as a decimal, and Time is the time period in years.

In this case, we have:

Principal = $600

Rate = 0.02 (2% expressed as a decimal)

Time = 2 years

So, the formula becomes:

Simple Interest = ($600 * 0.02 * 2)

= $24

Therefore, the simple interest on a principal of $600 at a rate of 2% for 2 years is $24.

There are 1960 different ways to distribute 8 identical pieces of candy to the five children, where the twins get an equal amount of candy.

First, distribute the candy to the twins.

Split the 8 pieces of candy into two equal parts for the twins using combinations:

C(8, 4)

This means selecting 4 pieces of candy from the 8 identical pieces for one twin, and the remaining 4 pieces will automatically go to the other twin.

C(8, 4) is calculated as:

[tex]^8C_4 = \dfrac{8!}{4!(8-4)!}[/tex]

     = 8! / (4! * 4!)

     = (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1)

     = 70

Now, you have distributed 4 pieces of candy to each of the twins. Y

In this case, you have 6 pieces of candy to distribute among 3 children, and you can use two dividers (bars) to separate the candy for each child.

This can be represented as:

OO|OO|OO

The two bars split the 6 pieces of candy into three sections for the three children.

So, you have C(6 + 2, 2) ways to distribute the remaining candy:

[tex]^{6+2}C_2 = \dfrac{8!}{2!(8-2)!}[/tex]

         = 8! / (2!(8 - 2)!)

         = 8! / (2! * 6!)

         = (8 * 7) / (2 * 1)

         = 28

Now, the total number of ways to distribute the candy

Total ways = C(8, 4) * C(8, 2) = 70 * 28 = 1960

So, there are 1960 different ways to distribute.

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A Home Equity Conversion Mortgage (HECM) is a type of mortgage specifically designed for homeowners over the age of 62. It allows the homeowner to access their home’s equity without having to sell it. The HECM loan is secured by the equity in the home and is repaid when the homeowner passes away or sells the home. This type of mortgage is popular with the elderly due to the lack of monthly payments and the flexibility to use the loan proceeds in any way they want. The funds can be used for medical expenses, home repairs, travel, or to supplement retirement income. A HECM is a great way for an elderly homeowner to access the equity in their home without having to make a large upfront payment or sell the home.

A Home Equity Conversion Mortgage (HECM) is a type of mortgage specifically designed for homeowners over the age of 62. It allows the homeowner to access their home’s equity without having to sell it. The HECM loan is secured by the equity in the home and is repaid when the homeowner passes away or sells the home. This type of mortgage is popular with the elderly due to the lack of monthly payments and the flexibility to use the loan proceeds in any way they want. The funds can be used for medical expenses, home repairs, travel, or to supplement retirement income. A HECM is a great way for an elderly homeowner to access the equity in their home without having to make a large upfront payment or sell the home.

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Simplifying the expression resulted to x° = x

The expression x° = ½ • (30 + 2x – 30) can be simplified as follows:

The term 30 - 30 simplifies to 0, so we can remove it from the expression:

x° = ½ • (30 + 2x - 30)

x° = ½ • (2x)

We can simplify the fraction ½ by dividing the numerator by the denominator:

x° = x

Therefore, the solution to the equation x° = ½ • (30 + 2x – 30) is x = x°. In other words, any value of x is equal to its corresponding value in degrees.

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Therefore, the expression that would give the total number of elements in the array list is n*m.

The Student question is given below :Assume that Item is some class available to the code below and that n and m are two integer variables correctly initialized. Consider the following array declaration and initialization.

[tex]Item[][] list= new Item[n][m];[/tex]

What expression would give the total number of elements in the array list?

The expression that would give the total number of elements in the array list is n*m. The given array declaration and initialization is Item[][] list= new Item[n][m]; This declaration and initialization signify that the array list is a 2D array with n rows and m columns. The total number of elements in this array can be determined by computing the product of the total number of rows (n) and the total number of columns (m).

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Let p be the probability of an adult over 50 wearing glasses for driving. Since we don't know the value of p, we can't use the binomial distribution directly. However, we can use the normal approximation to the binomial distribution since n is large (assuming n * p >= 10 and n * (1-p) >= 10).

Let X be the number of adults over 50 wearing glasses for driving in a random sample of n adults. Then X ~ Binomial(n, p) can be approximated by a normal distribution with mean µ = n * p and standard deviation σ = sqrt(n * p * (1-p)).

We want to find the probability that at least six adults over 50 in a random sample of n wear glasses for driving. This is equivalent to finding P(X >= 6) = 1 - P(X < 6) using the normal approximation.

To apply the normal approximation, we need to standardize the random variable X:

Z = (X - µ) / σ

Using continuity correction:

P(X >= 6) = P(X > 5.5)

Z = (5.5 - n * p) / sqrt(n * p * (1-p))

We can use the standard normal distribution table or calculator to find the probability:

P(Z >= (5.5 - n * p) / sqrt(n * p * (1-p)))

Since we don't know the value of p, we can use a conservative estimate of p = 0.5 (assuming 50% of adults over 50 wear glasses for driving). Then:

P(Z >= (5.5 - n * 0.5) / sqrt(n * 0.5 * (1-0.5)))

For example, if we sample n = 100 adults over 50, the probability of at least six wearing glasses is:

P(Z >= (5.5 - 100 * 0.5) / sqrt(100 * 0.5 * (1-0.5)))

= P(Z >= 0.5)

Using a standard normal distribution table or calculator, P(Z >= 0.5) = 0.3085.

Therefore, the probability of at least six adults over 50 wearing glasses for driving in a random sample of 100 is approximately 0.3085 or 30.85%.

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The percent change in size from 983 to 2,349 square feet was 138.8%.

The average American home swelled from 983 square feet in 1950 to 2,349 square feet in 2004, representing a change of 1366 square feet. This change can be expressed as a percent change by dividing the change (1366 square feet) by the starting value (983 square feet). The resulting percent change is 138.8%.

To calculate the percent change, we can use the following equation:
Percent Change = (Ending Value - Starting Value) / Starting Value x 100
Using this equation, the percent change in the size of the average American home is calculated as follows:
Percent Change = (2349 - 983) / 983 x 100 = 138.8%

This means that the average American home increased by 138.8% in size between 1950 and 2004. This is an impressive rate of growth and may be attributed to a number of factors. In 1950, the United States was in the midst of a period of rapid economic growth, and this may have allowed people to buy larger homes and upgrade to more luxurious accommodations. In addition, advances in technology and manufacturing may have made larger homes more affordable for more people.

Whatever the cause of the growth in home size, it is clear that the average American home saw a substantial increase in size between 1950 and 2004. The percent change in size from 983 to 2,349 square feet was 138.8%.

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The algebraic expression to represent the cost of buying r records and c CDs is given as, Cost = 3r + 1.5c

The music store is selling the records for a price of $3.00 and the CDs for $1.50 each. Let us say someone buys r number of record and c number of CDs.

So, the final algebraic expression that we will get from the above mentioned information is Cost = 3r + 1.5c.

Here, 3r represents the cost of buying "r" number of records at $3.00 each, and 1.5c represents the cost of buying "c" number of  CDs at $1.50 each. By adding these two costs together, we can find the total cost of buying r number of records and c number of CDs.

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In total, there are 126 cans in the showcase.

We will use the method for the sum of an arithmetic sequence to solve this problem. The formulation is:

S = (n/2)(a + l)

Wherein S is the sum of the sequence, n is the range of terms, a is the first term, and l is the last term.

In this example, the primary time period is 20, and the closing term is 4. The common difference among the terms is -2, given that we are subtracting 2 cans from each row. we will discover the number of terms using the formulation:

l = a + (n-1)d

Wherein d is the common distinction. solving for n, we get:

n = (l - a)/d + 1

n = (4 - 20)/(-2) + 1

n = 9

Now we can plug within the values for a, l, and n into the system for the sum:

S = (n/2)(a + l)

S = (9/2)(20 + 4)

S = 126

Thus, there are 126 cans in the display in total.

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The pediatrician writes an order for robinul injection 35 mcg iv now. The nurse will administer 0.035 ml of Robinul injection for 35 mcg of medication.

The question is about calculating the number of milliliters a nurse should administer for a 35 mcg Robinul injection. Let's first understand the meaning of Robinul.Robinul is a medication used to treat excess sweating or salivation in the human body. It reduces the secretion of fluids by blocking the chemicals that stimulate their production. It is available in the form of tablets, injection, or solution.

The nurse is instructed to administer 35 mcg of Robinul injection now.Let's calculate the number of milliliters of Robinul injection to be administered by the nurse.

Now, 1 ml = 1000 mcg35 mcg = (35/1000) ml= 0.035 ml (rounded to the nearest hundredth).

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Answer:

23 but not

Step-by-step explanation:

The exponential function that shows the relationship between the city's population y and the number of years t since the start of the study is [tex]y = 390000 * (1.073)^t[/tex]

Population tends to change with time. It might increase or decrease. Let y be the city's population after t years since the start of the study, and let [tex]Po[/tex] be the initial population at the start of the study. We can use the formula for exponential growth to represent the relationship between y and t:

Final population = Initial population x (growth rate)^years

[tex]y = Po*(1+0.073)^t[/tex]

[tex]y = Po* (1.073)^{(t)[/tex]

Substituting the values in the above equation we get the following equation:

[tex]y = 390,000*(1.073)^t[/tex]

The above function when represented in exponential form will be equal to [tex]y=390,000*(e)^{(0.073t)[/tex]

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Refer to complete question below:

At the beginning of a population study, a city had 390,000 people. Each year since, the population has grown by 7.3% . Let t be the number of years since start of the study. Let y be the city's population. Write an exponential function showing the relationship between y and t .

If each basket contains the same number of eggs and there are at least 4 eggs in each basket, Jenny put 3 red eggs in each of 6 baskets, and 4 orange eggs in each of 6 baskets.

Let's call the number of eggs in each basket "x." We know that Jenny placed a total of 18 red eggs, so the number of baskets with red eggs can be represented as 18/x. Similarly, the number of baskets with orange eggs can be represented as 24/x.

Since we know that each basket contains at least 4 eggs, we can set up the inequality 4 ≤ x.

Now we can use this information to set up an equation:

18/x + 24/x = total number of baskets

Simplifying this equation, we get:

42/x = total number of baskets

But we also know that the total number of baskets is an integer (you can't have a fraction of a basket), so x must be a factor of 42.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. But we also know that each basket must contain at least 4 eggs, so we can eliminate 1, 2, and 3 as possible values of x.

Therefore, the possible values of x are 6, 7, 14, 21, and 42. But we also know that there are 18 red eggs and 24 orange eggs, so x must be a factor of both 18 and 24.

The common factors of 18 and 24 are 1, 2, 3, and 6. Therefore, the only possible value of x is 6.

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Complete question is:

Jenny places a total of 18 red Easter eggs in several green baskets and a total of 24 orange Easter eggs in some blue baskets. Each basket contains the same number of eggs and there are at least 4 eggs in each basket. How many eggs did Jenny put in each basket?

Answer:

39°

Step-by-step explanation:

angles are alternate exterior angles making them congruent

for example:

The volume of Laura's gold ring is 21.6 cubic centimeters.

To find the volume of the gold ring, we need to determine the volume of water that is displaced when the ring is dropped into the glass.

The initial volume of water in the glass can be calculated as the product of the base area and the height of the water:

V1 = base area x height of water = 7 cm x 4.5 cm x 8.8 cm = 277.2 cm³

When the gold ring is dropped into the glass, it displaces some of the water, causing the water level to rise. The new volume of water in the glass can be calculated using the same formula, but with the new height of the water:

V2 = base area x height of water with ring = 7 cm x 4.5 cm x 9.2 cm = 298.8 cm³

The volume of the gold ring can be calculated by subtracting the initial volume of water (before the ring was added) from the new volume of water (after the ring was added):

Volume of gold ring = V2 - V1 = 298.8 cm³ - 277.2 cm³ = 21.6 cm³

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Th given question is incomplete, the complete question is:

Laura wants to know the volume of her gold ring in cubic centimeters. She gets a rectangular glass with a base 7 cm by 4.5 cm and fills the glass 8.8 cm high with water. Laura drops her gold ring in the glass and measures the new height of the water to be 9.2 cm. What is the volume of Laura'5 ring in cubic centimeters? cm? 8.8 cm 9.2 cm 4.5 cm 4.5 cm 7cm 7 cm

Answer:

THE OTHER GUY IS WRONG  the answer is 3.6cm

Step-by-step explanation:

I had this question on khan

The matrix that shows the prices in U.S. dollars is:

[1.81  6.32  0.56 0.36]

Here we have a simple row matrix which can be written as:

[80  280  25  16]

You can see this as a row vector or something like that, notice that if we multiply this by an scalar, we just need to multiply each element by an scalar.

Now, we know that:

1 dollar = 44.32 Nu

then:

1 Nu = (1/44.32) dollars.

So to get the matrix in dollars, just multiply each number by (1/44.32), then we will get:

(1/44.32)*[80  280  25  16] = [80/44.32  280/44.32  25/44.32  16/44.32]

= [1.81  6.32  0.56 0.36]

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"The speed of a randomly selected car on a highway" and "the percent change in the price of a share of IBM stock in a month" are examples of continuous random variables. Options A and C are the correct answers.

Continuous random variables are those that can take on any value within a given range, as opposed to discrete random variables, which can only take on certain values.The speed of a randomly selected car on a highway and the percent change in the price of a share of IBM stock in a month are examples of continuous random variables.

These variables have a range of values and can take on any value within that range.The number of claims on a medical insurance policy on a given year, the number of customers that enter a particular store on a randomly selected day, and the time that elapses between two customer service calls are examples of discrete random variables. These variables can only take on certain values, such as whole numbers or specific times.

Thus option A and option C are the correct answers.

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The length of the rectangle is 19 cm.

The formula for the area of a rectangle,

Area = Length x Width

Given that the area is 336 cm squared.

So, we can set up an equation,

⇒ 336 = (w + 5)w

where w represents the width of the rectangle.

Expanding this equation,

⇒ 336 = w² + 5w

Moving all terms to one side:

⇒ w² + 5w - 336 = 0

This is a quadratic equation that we can solve using the quadratic formula,

⇒ w = (-5 ± √(5² - 4(1)(-336))) / (2(1))

⇒ w = (-5 ± 23) / 2

We'll take the positive value,

⇒ w = 14

So, the width of the rectangle is 14 cm.

We also know that the length is 5 cm more than the width,

Therefore,

⇒ l = w + 5

⇒ l = 14 + 5

⇒ l = 19

Therefore, the length of the rectangle is 19 cm.

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