How to estimate 6x219​

Answer:  False

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Explanation:

To see if the x value is a solution or not, we plug it into the equation given

2x+7 = 30 .... original equation

2*3 + 7 = 30 .... replace every x with 3, since we claim that x = 3

6 + 7 = 30 .... multiply 2 and 3 to get 6

13 = 30 ...... add 6 and 7 to get 13

We get two different numbers on either side, so the last equation is not true. We get a contradiction or false statement. So the original equation is false when x = 3. Therefore, x = 3 is not the solution.

That's why the overall claim is false.

Answer:

16^15

Step-by-step explanation:

16 is 2^4

So 2^60 = (2^4)^x power

2^60=2^4x

exponents of same bases are equal

60=4x

15=x

remember, (2^4) is still 16

lets convert it back to 16

2^60=16^x

and we know x is 15

2^60 = 16^15

Answer:

Step-by-step explanation:

The slopes of both those lines are the same so there is no solution. Use slope triangles to find out the slope. They are both 1/4.

A. No solution

y = 1/4x+5

x - 4y = 4

You can simplify the second equation into y = 1/4x - 1

Since these equations both have the same slope, they are parallel. When two lines are parallel, they have no solutions.

Answer:

2 x 2 x 2 x 2 x 3.

Step-by-step explanation:

The number 48 expressed as a product of its prime factors is 2 x 2 x 2 x 2 x 3.

Answer:

2 x 2 x 2 x 2 x 3.

Step-by-step explanation:

^^^

If there are 2. 2 pounds in 1 kilogram then there are 1.91 kilograms in 4.21 pounds.

We need to find how  many kilograms are there in 4. 21 pounds if there are 2. 2 pounds in 1 kilogram. This can be calculated by using unitary method.

There are 2. 2 pounds in 1 kilogram,

We need to find the kilograms are there in 4. 21 pounds

If there are 2. 2 pounds in 1 kilogram,

Then, 1 pound is 1/2.2 kilogram

1 pound = 0.4545

4.21 pound is (1/2.2) 4.21 kilogram

4.21 pound is 1.91 kilogram.

Therefore,  if there are 2. 2 pounds in 1 kilogram then there are 1.91 kilograms in 4.21 pounds.

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Answer:

2 and 6

Step-by-step explanation:

2 and 6 is the correct option

↝ Quadratic Function has the domain of all real numbers. (Even not given the specific domain.)

↝ The equation \(y=-3(x-5)+8\) is a parabola with (5,8) as a vertex. We call the equation \(y=a(x-h)^2+k\) as vertex equation.

The domain of -3(x-5)+8 is all set of real numbers.

↝ Interval Notation ↝

Since the domain of the equation is set of all real numbers.

Therefore, the domain is x ∈ R or (-∞,∞) or -∞<x<∞

There of them work. Recall that the domain of quadratic function is all set of real numbers.

a.

5 minutes

b.

30 litres per minute

Answer:

From the box plot we get:

Answer:

the other person is correct!

Step-by-step explanation:

Show them some love <3!

Answer:

C.  (x + 4)(x − 3)

Step-by-step explanation:

A quadratic expression in complete factored form can be written as the product of two linear factors, where each factor is in the form of (ax + b). The expression (x + 4)(x - 3) is in this form and can be expanded to the quadratic expression x^2 + x - 12.

Option A is a sum of two linear expressions, but it is not factored. Option B is a product of two linear expressions, but it can be simplified to the quadratic expression 3x^2 - 3x. Option D is a product of two linear expressions, but it can be simplified to the quadratic expression 2x^2 + 10x + 12.

Answer:

exterior angle = 36°

Step-by-step explanation:

In any polygon

exterior angle + interior angle = 180°

let x be the exterior angle then interior angle is 4x , then

x + 4x = 180

5x = 180 ( divide both sides by 5 )

x = 36

thus exterior angle = 36°

The first problem is asking for the number of combinations which is 20, while the second problem is asking for the number of permutations which is 336.

In the first problem, the homeowners' association needs to form a committee of 3 people from a board of 6 supervisors. Here, the order in which the committee members are selected does not matter, and only the combination of individuals is important. Therefore, the problem is asking for the number of combinations, and the formula to calculate it is nCr = n! / (r!(n-r)!), where n is the total number of items (6 supervisors) and r is the number of items to be selected (3 committee members). Thus, the answer to the first problem is the number of combinations: 6C3 = 6! / (3!(6-3)!) = 6! / (3!3!) = (6x5x4) / (3x2x1) = 20.

In the second problem, the director needs to cast the male roles of Romeo, Mercutio, and Benvolio from a pool of 8 actors. Here, the order in which the actors are selected matters, as each actor will be assigned to a specific role. Therefore, the problem is asking for the number of permutations, and the formula to calculate it is nPr = n! / (n-r)!, where n is the total number of items (8 actors) and r is the number of items to be selected (3 roles). Thus, the answer to the second problem is the number of permutations: 8P3 = 8! / (8-3)! = 8! / 5! = (8x7x6) / (3x2x1) = 336.

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Thus, working together, Marie and Gloria would take 56/15 hours, or approximately 3.73 hours, to paint the living room.

Let's analyze the situation using the terms "work rate" and "combined work rate" to determine how long it would take Marie and Gloria to paint the living room together.

Marie's work rate is 1/7, as she can complete the job in 7 hours.

Gloria's work rate is 1/8, as she can finish the task in 8 hours. To find their combined work rate, we simply add their individual work rates: (1/7) + (1/8).

To add these fractions, we need a common denominator, which in this case is 56.

So, we can rewrite the fractions as (8/56) + (7/56). Adding them together, we get a combined work rate of 15/56.

Now that we have their combined work rate, we can find out how long it would take them to complete the job together. To do this, we need to find the reciprocal of their combined work rate, which is 56/15.

Therefore, working together, Marie and Gloria would take 56/15 hours, or approximately 3.73 hours, to paint the living room.

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The formula to calculate the volume of the brick is given to be:

We have the following dimensions, converted to meters, as follows:

Therefore, the volume is:

Opportunity cost of producing 70 more bagels:

On Day 2, Raj produces 70 more bagels than on Day 1. That means, he produces 140 - 70 = 70 bagels on Day 1. Now, to produce 70 more bagels on Day 2, he has to reduce the production of doughnuts as doughnuts and bagels both need the same amount of flour for production. On Day 1, Raj produces 600 doughnuts, and on Day 2, he produces 500 doughnuts. Therefore, opportunity cost of producing 70 more bagels is the quantity of doughnuts sacrificed for producing 70 more bagels.

= Quantity of Doughnuts on Day 1 - Quantity of Doughnuts on Day 2

= 600 - 500

= 100

Opportunity cost of producing 70 more bagels is 100. Opportunity cost of producing 50 more croissants:

On Day 3, Raj makes 50 more croissants than on Day 2. On Day 2, he makes 50 croissants, and on Day 3, he makes 100 croissants. Therefore, opportunity cost of producing 50 more croissants is the quantity of bagels sacrificed for producing 50 more croissants. As bagels and croissants require the same oven, reducing the production of bagels will enable Raj to produce more croissants. On Day 2, Raj produces 140 bagels, and on Day 3, he produces 70 bagels. Hence, he has to reduce the production of bagels by 140 - 70 = 70 to produce 50 more croissants.

Opportunity cost of producing 50 more croissants

= Quantity of Bagels on Day 2 - Quantity of Bagels on Day 3

= 140 - 70= 70

Therefore, opportunity cost of producing 50 more croissants is 70.

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Answer:

1. 100 doughnuts

2. 70 bagels

guy on top said a whole lot of nothing ngl

Step-by-step explanation:

F

1) For variables like these, we most often use the mean that will compute all data points (in this case, the number of jobs a person had throughout his life ) for a central tendency measure.

2) Examining the options, then we can state that the answer is: F

and that is the answer.

Answer:

In principle, there is no direct relationship between the area and the perimeter of a rectangle, but both are calculated taking into account the measure of its base and its height.

Thus, the perimeter is equal to the sum of the length of the base and the height of the rectangle, and this result multiplied by 2.

In turn, the area of the rectangle is equal to the multiplication of its base by its height.

So, for example, if the base of the rectangle measured 10 cm and the height measured 5 cm, the perimeter would be equal to 30 cm (10 x 2 + 5 x 2) and the area would be equal to 50 cm2 (10 x 5).

Step-by-step explanation:

To answer the questions, you must fill out the table.

a=65+48=113

b=157-65=92

c=92+33=125

d=48+33=81

e=157+81=238 or 113+92=238

5. To find the probability of picking a customer that is lactose intolerant, you need to find the total number of lactose intolerant people out of all the people.

81/238 or 34%

6. To find the probability of randomly picking a customer over 30 years old, you find the total number of people over 30 years old out of all the people.

125/238 or 52.5%

7. This problem specifically asks for people that are not lactose intolerant.

Under 30 years old: 65/157 or 41%

Over 30 years old: 92/157 or 59%

Based on these statistics, is it obvious that it is more likely for a customer to me over 30.

The probability that a randomly chosen student did not get an A in Psychology is 0.83., the probability that a randomly chosen student got an A in Statistics or Psychology or both is 0.3175.

Part 1:

Let's calculate the probability that a randomly chosen student got an A in statistics or psychology or both.

We can use the principle of inclusion-exclusion to find this probability. The formula is:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Given:

Number of students enrolled in both Statistics I and Psychology I (A ∩ B) = 31

Number of students who got an A in Statistics I (A) = 90

Number of students who got an A in Psychology I (B) = 68

Using these values, we can calculate the probability:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

         = 90/400 + 68/400 - 31/400

         = 0.225 + 0.17 - 0.0775

         = 0.3175

So, the probability that a randomly chosen student got an A in Statistics or Psychology or both is 0.3175.

Part 2:

To find the probability that a randomly chosen student did not get an A in Psychology, we need to subtract the probability of getting an A in Psychology from 1.

P(not A) = 1 - P(A)

Given:

Number of students who got an A in Psychology I (A) = 68

Using this value, we can calculate the probability:

P(not A) = 1 - P(A)

        = 1 - 68/400

        = 1 - 0.17

        = 0.83

So, the probability that a randomly chosen student did not get an A in Psychology is 0.83.

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Answer:

\(\displaystyle E(x)=\frac{26}{3}\)

Step-by-step explanation:

\(\displaystyle E(x)=\int^b_axf(x)dx\\\\E(x)=\int^3_1x^2dx\\\\E(x)=\frac{x^3}{3}\biggr|^3_1\\\\E(x)=\frac{3^3}{3}-\frac{1^3}{3}\\\\E(x)=\frac{27}{3}-\frac{1}{3}\\\\E(x)=\frac{26}{3}\)

The mean of the sampling distribution of means will be equal to the mean of the population from which the samples were drawn when the sampling distribution is unbiased.

The unbiased sampling distribution of means is one in which the sample means are drawn such that their average equals the population mean. Therefore, an unbiased sample should be representative of the population mean.The sampling distribution is a statistical term that refers to the probability distribution of a given random sample of size n that is taken from the population's larger dataset.

The distribution of the statistics collected from different samples is known as the sampling distribution. The mean of the sampling distribution is equal to the population mean. Sampling distribution provides insight into the sample data's variation, which can be used to make population inferences.

The mean of the sampling distribution of means is also known as the expected value of the sampling distribution. It is the mean of the population, which is equal to the mean of the sampling distribution of means. If the sample means are unbiased, the mean of the sampling distribution of means equals the population mean. The central limit theorem states that, as the sample size increases, the sampling distribution of means approaches a normal distribution with a mean equal to the population mean.

The mean of the sampling distribution is a critical statistic in inferential statistics because it aids in determining the statistical significance of the sample. If the sample mean is significantly different from the population mean, the results of the test can be used to reject or accept the null hypothesis.

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Answer:

480

Step-by-step explanation:

If you take length times width times height so it'll be 8 times 10 = 80 times 6 =480

As x approaches 0, (5x⁴+8x²)/(3x⁴-16x²) is -1/2.

What is L'Hopital's rule?

L'Hopital's rule which states that if the limit of a function f(x)/g(x) as x approaches a is of the form 0/0 or ∞/∞, then the limit is equal to the limit of the derivative of f(x) divided by the derivative of g(x) as x approaches a.

Here given expression is (5x⁴+8x²)/(3x⁴-16x²)

Here we want to find limit of the function (5x⁴+8x²)/(3x⁴-16x²) as x approaches 0.

Applying L'Hopital's rule,

(20x³+16x)/(12x³-32x)

Now, as x approaches 0, we can evaluate the limit by plugging in x=0 in the above expression. However, plugging in x=0 results in a denominator of 0, which is undefined. This suggests that we should simplify the expression further.

We can factor out x from the numerator and denominator to get:

(5x²+8)/(3x²-16)

Now, plugging in x=0 gives us:

(5(0)²+8)/(3(0)²-16) = 8/-16 = -1/2

So, as x approaches 0, (5x⁴+8x²)/(3x⁴-16x²) approaches -1/2.

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Hence, in response to the provided question, we can say that As a result,  function the discus takes approximately 0.03125 seconds to strike the ground.

Mathematicians research numbers and their variants, equation and related structures, objects and their locations, and prospective locations for these things. The term "module" is used to describe the connection that exists in between set of inputs, each of which has a corresponding output. A function is an input-output connection in which each inputs results in something like a single, distinct return. A domain, codomain, or scope is assigned to each function. Functions are usually denoted by the letter f. (x). An x is used for entry. On capabilities, one-to-one capabilities, multiple prowess, in capabilities, and on capabilities are the four major types of accessible functions.

The supplied function for discus height is as follows:

\(h(t) = -16t^2 + 38t + 5\\h(0) = -16(0)^2 + 38(0) + 5 = 5\)

As a result, the discus's starting height is 5 feet.

\(-16t^2 + 38t + 5 = 0\\\)

To find t, we can apply the quadratic formula:

t = (-b \sqrt(b2 - 4ac)) (2a)

where a=-16, b=38, and c=5.

\(t = (-38 + \sqrt(38^2 - 4(-16)(5))) / (2(-16))\\t = (-38 + \sqrt(1524)) / (-32) (-32)\\t = (-38 + 39) / (-32) (-32)\\\)

As a result, \(t = (-38 + 39) / (32) or t = (-38 - 39) / (32) (-32)\)

t = 1/32 or t = 77/32

As the negative value doesn't make sense in this situation, we chose the positive value:

t = 1/32

As a result, the discus takes approximately 0.03125 seconds to strike the ground.

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Answer:

I getting the probability of the adult female that will rent the action movies in DVDs in by dividing the possible probability outcome which is 10% of all adults by the total number of possible outcome. So all of the population of the female is 51% and the ones who rent is only 10%. the probability is 19%

The solution is, 0.20 is the probability that the person rents action-movie DVDs, given that the person is female.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

given that,

Data:

A: the adult is a male, P(A) = 0.49

B: the adult rent action-movie DVDs

C: the adult is a female,  P(C) = 1 - P(A) = 1 - 0.49 = 0.51  

24% of the adults are male and rent action-movie DVDs, then P(A ∩ B) = 0.24

10% of the adults are female and rent action-movie DVDs, then P(C ∩ B) = 0.10

The conditional probability of B (the adult rents action-movie DVDs) given C (the adult is female) is computed as follows:

P(B|C) = P(C ∩ B)/P(C)

          = 0.1/0.51

          = 0.2

Hence, The solution is, 0.20 is the probability that the person rents action-movie DVDs, given that the person is female.

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To find the equation of the line that comes closest to passing through the given points, we need to find the coefficients c0 and c1 that minimize the sum of squared errors between the actual y-values and the predicted y-values on the line.

Let's denote the actual y-values as y1, y2, and y3, and the corresponding x-values as x1=0, x2=1, and x3=2. The predicted y-values on the line are given by:

y_pred = c0 + c1*x

The sum of squared errors is then:

SSE = (y1 - y_pred(0))^2 + (y2 - y_pred(1))^2 + (y3 - y_pred(2))^2

Substituting the values of the given points and simplifying, we get:

SSE = (1 - c0)^2 + (c1 - 2)^2 + (4 - 2c1 - c0)^2

To minimize SSE, we need to find the values of c0 and c1 that satisfy the first-order conditions:

d(SSE)/dc0 = -2(1 - c0) - 2(4 - 2c1 - c0) = 4c0 - 8c1 + 6 = 0

d(SSE)/dc1 = -2(c1 - 2) + 2(4 - 2c1 - c0)(-2) = 16c0 - 24c1 + 20 = 0

Solving these equations simultaneously, we get:

c0 = 1.6

c1 = 0.8

So the equation of the least squares line is:

y = 1.6 + 0.8x

Therefore, the answer is y = 1.6 + 0.8x.

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