Which values are solutions to StartFraction k minus 3 Over 4 EndFraction >–2? Select two options.

Answer:

$11.74

Step-by-step explanation:

195.60/100 X 6 = 11.736

monetary unit so round to 2dp

11.74

Answer:

1,216 dollars

Step-by-step explanation:

Do 32 x 38 = 1,216

Answer:

Rs 12,500

Step-by-step explanation:

the price before VAT = 100/10 × Rs 5000 =

Rs 50,000

the price before discount = 50,000 / 80%

= 50,000/0.8 = 62,500

so the discount amount = 62,500-50,000

= Rs 12,500

since the population standard deviations (σ1 and σ2) are not provided, we cannot calculate the exact test statistic Z.

To test the null hypothesis H0: (μ1 - μ2) = 0 versus the alternative hypothesis Ha: (μ1 - μ2) ≠ 0, we can use a two-sample z-test. The test statistic is calculated as:

Z = (x bar1 - x bar2) / sqrt((σ1^2 / n1) + (σ2^2 / n2))

Where:
X bar1 and x bar2 are the sample means of the two groups,
σ1 and σ2 are the population standard deviations of the two groups,
n1 and n2 are the sample sizes of the two groups.

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Distance can be defined as the amount of ground covered (traveled) by a physical object over a specific period of time and speed, regardless of its direction, starting point or ending point.

Mathematically, the distance (traveled) by a physical object can be calculated by using this formula:

Distance = speed × time

Making time the subject of formula, we have:

Time = distance/speed

Next, we would calculate the amount of time it will take for the two couriers to meet:

t = d/(Vm + Vn)

t = 8/(1 + 3)

t = 8/4

Time, t = 2 hours.

For the meeting time, we have:

Meeting time = 8:00 AM + 2 hours

Meeting time = 10:00 AM.

For the distance from M, we have:

Distance = 1 × 4

Distance = 4 km.

For the distance from N, we have:

Distance = 3 × 4

Distance = 12 km.

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Complete Question:

Two couriers leave two cities M and N(N is west of M) distant from each other 8kms and both go east. The one from M leaves at 6:00am and goes 1k/h and the one from N leaves at 8:00am and walks 3k/h. At what time did they meet and at what distance from M and N?

Answer:

rational

Step-by-step explanation:

213 +33=246

A quick way to check this is to see if 246 is a perfect square. If it is, then it is a rational number. If it's not a perfect square then it's an irrational number. We already know if 246 is a perfect square so we also can see that √246 is an irrational number.

246 is a rational number because it can be expressed as the quotient of two integers: 246 ÷ 1.

\(\huge\boxed{Hello~there!}\)

First, let's add 213 and 33:

\(\bf{213+33\)

Add:

\(\bf{246\)

Now, is 246 rational or irrational?

Tip:

Irrational numbers have an infinite number of digits after their decimal point.

Example: 3.333333333... is an irrational number, because the 3's go on for ever.

Now, is 246 rational or irrational?

It doesn't have an infinite number of digits after its decimal point.

Thus, it's rational.

Hope it helps! Enjoy your day!

Feel free to ask if you have any doubts.

~Just a determined teenager

\(\bf{erutaNtneliS\)

The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

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Answer:

Approximately 0.131 mol of aluminum hydroxide can be formed from 48 grams of sodium hydroxide.

Step-by-step explanation:

To find the number of moles of aluminum hydroxide that can be formed from 48 grams of sodium hydroxide, we can use the formula:

Number of moles = Mass / Molecular Weight

Where:

Moles = number of moles

Mass = 48 grams

Molecular Weight = 234.43 grams per mole

Plugging in these values, we get:

Number of Moles = (48 grams) / (234.43 grams per mole) = 0.131 mol

Answer:

To answer this question, we need to know the balanced chemical equation for the reaction between aluminum and sodium hydroxide. According to the web search results, the reaction is as follows:

2Al (s) + 2NaOH (aq) + 6H₂O (l) → 2Na[Al(OH)₄] (aq) + 3H₂ (g)

From this equation, we can see that two moles of aluminum react with two moles of sodium hydroxide to produce two moles of sodium aluminate and three moles of hydrogen gas. Therefore, the mole ratio between sodium hydroxide and sodium aluminate is 1:1.

To find out how many moles of sodium hydroxide are in 48 grams, we need to use the molar mass of sodium hydroxide, which is 40 g/mol. Using the formula:

moles = mass / molar mass

We get:

moles of NaOH = 48 g / 40 g/mol

moles of NaOH = 1.2 mol

Since the mole ratio between sodium hydroxide and sodium aluminate is 1:1, we can conclude that the same amount of moles of sodium aluminate can be formed from 48 grams of sodium hydroxide, which is 1.2 moles.

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Answer:This is an exponential growth problem.  If the population doubles periodically, it follows a law like this:

P(t) = P(0)ekt

where P(0) is the initial population at time t=0, and k is a constant with units of years-1.

To find k, let t=0.  Then P(t) = P(0) = initial population = 5000.

Since the population doubles every 12 years, we can write

P(t+12) = 2P(t)

P(0)ek(t+12) = 2[P(0)ekt]

Simplifying,

e12k = 2

k = ln(2) / 12 = 0.0577623 years-1

Finally,

P(t) = 5000e0.0577623t, t in years

Then at t=48 years from now,

P(48) = 5000e(0.0577623 * 48) = 80,000

Step-by-step explanation:

Answer:

x < 3 and x > -1

Step-by-step explanation:

Step 1: Subtract 2 from both sides.

Step 2: Solve absolute value.

Condition 1:

Condition 2:

Therefore, the answer is x < 3 and x > -1.

According to the division property of equality, if both sides of an equation are divided by a common real integer that is not zero, the quotients remain equal.

Commutative property, associative property, distributive property, and identity property are the four number properties. Only the algebraic operations addition, subtraction, multiplication, and division are linked with number characteristics.

The four key terminology used in the division process are dividend, divisor, quotient and remainder. Dividend Divisor = Quotient + Remainder is the formula for dividing two numbers.

Commutative property, associative property, distributive property, and identity property are the four number properties. Only the algebraic operations addition, subtraction, multiplication, and division are linked with number characteristics.

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Answer:

1,2,3,5,8,13,.......

Step-by-step explanation:

We can have a sequence that adds the previous two terms to get the next term

1,2,3,5,8,13,.......

This is neither geometric nor arithmetic

Answer:

$ 20833.33

Step-by-step explanation:

A = P (1+r/100)^t

Here, A = 25000, r = 3.6% per annum = 0.3% per month, t = 5 years = 60 months, P = ?

So,

25000 = P[1+(0.3)/(100)]^60

Or, 25000 = P (1.003)^60= 1.962P = 1.2 P (approx)

Or, P = (25000)/(1.2) = 20833.33

To prove that in any group, an element and its inverse have the same order, we need to show that if we have an element `a` in a group and `n` is the order of `a`, then the order of `a`'s inverse, denoted as `a⁻¹`, is also `n`.

Let's assume that `a` has order `n`. This means that the smallest positive integer `n` such that `aⁿ = e` (the identity element) is `n`. We want to show that the order of `a⁻¹` is also `n`.

First, let's consider the order of `a⁻¹`. By definition, the order of `a⁻¹` is the smallest positive integer `m` such that `(a⁻¹)ᵐ = e`.

Now, we can use the fact that `aⁿ = e` to rewrite `a⁻¹` raised to the power of `n`:

(a⁻¹)ᵐ = ((aⁿ)⁻¹)ᵐ = (e⁻¹)ᵐ = eᵐ = e.

This shows that `(a⁻¹)ᵐ = e`, which implies that the order of `a⁻¹` is at most `m`.

To prove that the order of `a⁻¹` is exactly `n`, we need to show that `m` cannot be smaller than `n`.

Suppose, for contradiction, that `m < n`. Then we have:

(aⁿ)⁻¹ = (aⁿ)⁻¹ᵐ = aⁿᵐ = e.

This would imply that `aⁿ` has an inverse and `(aⁿ)⁻¹` has order `m`, which contradicts the definition of `n` as the smallest positive integer satisfying `aⁿ = e`.

Therefore, we conclude that the order of `a⁻¹` cannot be smaller than `n`. Since we have shown that it is at most `m` and not smaller than `n`, it follows that the order of `a⁻¹` is exactly `n`.

Hence, in any group, an element and its inverse have the same order.

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Answer:

-n-10

Step-by-step explanation:

(n-8)-(2n+2)

n-8-(2n+2)

n-8-2n-2

-n-8-2

-n-10

Step-by-step explanation:

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Answer: x=12

Step-by-step explanation:

1/3 x -4

1/3x=4               <---- First add 4 to each side of the equation (moves the "-4")

1/3x(3)=4(3)     <---- Muliply each side by "3" to get rid of the fraction

x=12

The value of K is 2.

Let's denote the scale factor as K. The surface area of a solid after dilation is directly proportional to the square of the scale factor.

We are given that the initial surface area of the solid is 50 units^2, and after dilation, the surface area becomes 200 units^2.

Using the formula for the surface area, we have:

Initial surface area * (scale factor)^2 = Final surface area

50 * K^2 = 200

Dividing both sides of the equation by 50:

K^2 = 200/50

K^2 = 4

Taking the square root of both sides:

K = √4

K = 2

Therefore, the value of K is 2.

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The probability that no more than one adult out of the 18 attendees visited the doctor despite not being sick can be calculated using the binomial distribution.

Given that 13.2% of adults visit the doctor even when not sick, we can consider this as the probability of success (p) in a binomial experiment. The probability of failure (q) would then be 1 - p.

To find the probability, we need to calculate the cumulative probability of 0 or 1 success out of 18 trials using the binomial distribution formula. The probability that no adults visited the doctor despite not being sick is given by P(X = 0), and the probability of only one adult visiting the doctor is P(X = 1). The final probability can be obtained by summing these two probabilities.

Using the binomial distribution formula and substituting the values, we get:

P(X ≤ 1) = P(X = 0) + P(X = 1) = C(18, 0) * (0.132)^0 * (1 - 0.132)^(18-0) + C(18, 1) * (0.132)^1 * (1 - 0.132)^(18-1)

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The area of the floor in the scale drawing will be equal to 150 in².

An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass the surface of a compact figure. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.

As per the given information in the question,

Length of the classroom, l = 30 feet and,

The width of the classroom, w = 20 feet.

As per the scale drawing, the length of the classroom, l' = 15 feet

Let the scale width, w' = x feet

As we can see that the original length is twice the scale drawing.

Then, the original width also is twice the scale drawing.

So, w' = 20/2 = 10 feet.

Now, the area of the floor in the scale drawing will be,

A = wl

A = (15)(10)

A = 150 in².  

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Answer:

a) 5 is the answer

The difference between the volumes of the solids is given as follows:

A. 72π.

The volume of a sphere of radius r is given by the equation presented as follows:

V = 4πr³/3.

The radius is of 6 inches, hence the volume is given as follows:

V = 4π x 6³/3

V = 288π cubic inches.

The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

Both the radius and the height are of 6 inches, hence the volume is given as follows:

V = π x 6³

V = 216π cubic inches.

Then the difference of the volumes is given as follows:

π(288 - 216) = 72π.

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Answer:

A ::repeat

Step-by-step explanation:

A function is a relation in which the members of the domain (x-values) DO NOT repeat. So, for every x-value there is only one y-value that corresponds to it. y-values can be repeated.

A common everyday counting unit that is used to mean 12 of an object is a Dozen

Dozen is derived from the Old French word "douzaine" which means twelve each. In most situations, a dozen is used to refer to a group of twelve items. The term dozen is also used in informal situations to refer to a very large number of objects. For example, one might say "I have dozens of friends!" to mean that they have a lot of friends.

Dozen is a useful term when counting items. It allows for large numbers to be easily broken down into manageable groups. For example, if you have 120 pencils, you could easily count them by saying that you have 10 dozen pencils. It can also be useful when talking about fractions. For example, instead of saying "one and a half of an item," one could say "one and a half dozen of an item."

Dozen is a common everyday counting unit that is used to mean 12 of an object. It is a useful term when counting items and when talking about fractions, and can be used in both formal and informal settings.

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Answer:

a) (2,9); b) no points of intersection

Step-by-step explanation:

a)

Set the two equations equal to each other

7x - 5 = -2x + 13

Rearrange collecting like terms and solve

9x = 18

x = 2

Sub in x = 2 into either of the equations and it should yield the same result

Eq.1 y = 7(2) - 5 = 9

Eq.2 y = -2(2) + 13 = 9

Therefore the point of intersection is (2,9)

The graph confirms this result (see graph 1 with red and blue lines)

b)

As the gradients are the same, we can tell straight away that the two lines should be parallel and never intersect, but we'll try to solve it algebraically using the same method as in part a.

3x - 1 = 3x + 2

When rearranging, the x's cancel out which can be seen when subtracting 3x from both sides

-1 = 2

This equation is clearly incorrect. This means that there are no values of x at which the two equations are equal. Graphically, this means that the two lines are parallel and there are no points of intersection (see graph 2 with purple and green lines)

The correct answer is (d) The price must be replaced with a relative price, and the marginal values must be replaced with the corresponding Marginal Rates of Substitution.

When the value of a public good cannot be expressed in monetary terms, the Samuelson condition still holds, but some modifications are required. In this case, the per-unit price (p) used in the Samuelson condition needs to be replaced with a relative price, which represents the trade-off between the public good and other goods or services. Additionally, the marginal values (MV) of the public good need to be replaced with the Marginal Rates of Substitution (MRS), which measure the rate at which one person is willing to substitute the public good for another good.

Therefore, to determine the efficient level of the public good, the modified Samuelson condition uses a relative price and the corresponding Marginal Rates of Substitution.

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Answer:  The answer that I got was J.

a) the function that models the level M of morphine (in mg) in the blood t hours after one dose is M = \(3 * (0.69)^t\)

b) 0.50 mg of morphine remains in the blood after 5 hours.

c) it will take approximately 14.67 hours for the amount of morphine left to drop to 0.1 mg.

(a) To construct a function that models the level M of morphine (in mg) in the blood t hours after one dose, we can use the formula for exponential decay:

M = \(initial amount * (1 - decay rate)^t\)

Given that the patient is initially given 3 mg of morphine and 31% (0.31) of any morphine is washed out every hour, we can write the function as:

M = \(3 * (1 - 0.31)^t\)

Simplifying further, we have:

M = \(3 * (0.69)^t\)

Therefore, the function that models the level M of morphine (in mg) in the blood t hours after one dose is M = \(3 * (0.69)^t\)

(b) To find out how much morphine remains in the blood after 5 hours, we can substitute t = 5 into the function and calculate the value of M:

M = 3 * (0.69)⁵

M ≈ 3 * 0.1681

M ≈ 0.5043

So, approximately 0.50 mg of morphine remains in the blood after 5 hours.

(c) To estimate how long it will take for the amount of morphine left to drop to 0.1 mg, we need to find the value of t when M = 0.1 in the function:

0.1 = \(3 * (0.69)^t\)

Dividing both sides by 3:

0.0333 ≈ \((0.69)^t\)

Taking the logarithm of both sides:

log(0.0333) ≈ \(log[(0.69)^t]\)

Using the logarithm properties, we can bring down the exponent:

log(0.0333) ≈ t * log(0.69)

Now, we can solve for t by dividing both sides by log(0.69):

t ≈ log(0.0333) / log(0.69)

Calculating this expression:

t ≈ -2.3859 / -0.1625

t ≈ 14.67

So, it will take approximately 14.67 hours for the amount of morphine left to drop to 0.1 mg.

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The inverse of the statement is "If a number does not have exactly two distinct factors, then the number is not prime." Thus Option 2 is the answer.

   When a conditional statement is reversed, the hypothesis and conclusion are both negated. The hypothesis in the original statement is "a number with exactly two distinct factors," while the conclusion is "is prime."

  To make the inverse, we negate both sections. "A number does not have exactly two distinct factors" is the antonym of "A number that has exactly two distinct factors." "Is not prime" is the opposite of "is prime."

    As a result, the inverse statement is "If a number does not have exactly two distinct factors, then the number is not prime."

     It's crucial to remember that a statement's inverse could or might not be accurate. In this instance, the inverse is true since the definition of a prime number is incompatible with the fact that a number has more than two components if it has more than exactly two different factors.

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Answer:

-2,-9

Step-by-step explanation:

im not 100 perent sure ifthis is right or not

Answer:(-2,-9)

Step-by-step explanation: