All of the following are rational except _____. - 3.14159... 0

1/2 of 32 is equal to 16.

Answer:

16

Step-by-step explanation:

Step 1:

0.5 × 32

Answer:

16

Hope This Helps :)

Answer:

80

Step-by-step explanation:

Use Bidmas. First do the brackets, then indecies, then multiplication

\( 5(1+3)^2 \)

\( 5(4)^2 \)

\( 5(16) \)

\( 80 \)

Answer:

805

Given:

x=4

Step-by-step explanation:

f(x) = 3x + 13(17x-7)

f(x) = 3 × 4 + 13(17 × 4 - 7)

f(x) = 12 + 13(68 - 7)

f(x) = 12 + 13 × 68 - 13 × 7

f(x) = 12 + 884 - 91

f(x) = 12 + 793

f(x) = 805

hope you understood❤❤

Answer:

M is the independent variable and t is the dependent variable

Step-by-step explanation:

She can change the number of mushrooms and it will effect how many tarts she can make.

Answer:

C

Step-by-step explanation:

hi <3

no, that wouldn't be correct.

angles on a straight line sum to 180 degrees so you have to do 180 - 90 (the right angle) to get your answer of 90 degrees

hope this helps :)

Answer:

  a) 45/4

  b) 3

  c) 12

  d) 24

  e) no; rate of change varies

Step-by-step explanation:

The average rate of change on interval [a, b] is given by ...

  m = (f(b) -f(a))/(b -a)

The function values are read from the table.

__

a) m = (f(4) -f(0))/(4 -0) = (48 -3)/(4 -0) = 45/4

b) m = (f(1) -f(0))/(1 -0) = (6 -3)/(1 -0) = 3

c) m = (f(3) -f(2))/(3 -2) = (24 -12)/(3 -2) = 12

d) m = (f(4) -f(3))/(4 -3) = (48 -24)/(4 -3) = 24

e) Not a linear function. The rate of change is not constant.

The ratio of the given expression is equal to 1:16.

Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion.

We apply the concepts of ratio and proportion every day, for example, while dealing with money in business or when preparing any meal, etc. Sometimes, pupils struggle to understand the relationship between ratio and proportion.

We have x=1 and y=2, and we have to find the ratio of x4:y4,

x=1 and y=2 (given)

\(x^4:y^4=(1)^4:(2)^4\\\\x^4:y^4=1:16=1/16\)

the ratio of the given expression is equal to 1:16.

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The statement that best describes the Central Limit Theorem is (a) The distribution of means of random samples pulled from a population will be normally distributed if the sample size is large enough.

The Central Limit Theorem (CLT) states that if repeated random samples is taken from a population with a finite mean and standard deviation, then the distribution of the sample means will approach a normal distribution, even if the original population is not normally distributed.

The larger the sample size, the more closely the sample means will approximate a normal distribution.

which means that, for example, if we take multiple samples of size 100 from a population and calculate the average of each sample, the distribution of those sample means will be approximately normally distributed, regardless of the original shape of the population.

The given question is incomplete , the complete question is

Which best describes what the Central Limit Theorem states ?

(a) The distribution of means of random samples pulled from a population will be normally distributed if the sample size is large enough.

(b) All distributions have the same mean.

(c) The distribution of standard deviations of random samples pulled from a population will be normally distributed if the sample size is large enough.

(d) All distributions are close enough to normally distributed to use the normal distribution as a approximation.

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Answer:

Whats the question?

Step-by-step explanation:

Here, I made a graph through MS Paint.

Answer:

volume = l×b×h

5/4 ×4/3 × 3/5 = 1 cubic centimeter

Volume = length x width x height

5/4 x 4/3 = 20/12

20/12 x 3/5 = 60/60 = 1

Volume = 1 cm^3

Answer:

Step-by-step explanation:

Use slope formula and compare with the actual slope m = -2:

Answer:

x=3 this is my answer. ......

The two figures are said to be congruent if you can change one into the other through a series of translations, rotations, and/or reflections.

In the given question we have to explain, a congruence transformation is translating.

A figure moved in a congruence transformation keeps its original size, shape, angles, and side lengths. The figures are precisely the same as one another, although they could have been rotated, shifted, or reflected from the original image, or pre-image.

The three sorts of transformations that are congruence transformations are thus reflection, rotation, and translation.

The two figures are said to be congruent if you can change one into the other through a series of translations, rotations, and/or reflections.

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The value of k will be equal to 3.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The given expression will be solved as follows:-

3 log 3x- log 9x⁴ + log x = log( 3x)³ -log9x⁴ + logx

                                        = log( 27x³) - log(9x⁴) + logx

                                        = log\(\dfrac{27x^3}{9x^4}\) + logx

                                        = log \(\dfrac{3}{x}\) + logx

                                        = log\(\dfrac{3}{x}\times x\)

                                        = log3

Therefore the value of k will be equal to 3.

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Answer:

1/125

Step-by-step explanation:

Answer:

150 minutes

Step-by-step explanation:

30 × 5 = 150 minutes

Method of sampling applies to populations that are divided into natural subsets and allocates the appropriate proportion of samples to each subset: Stratified sampling. The correct answer is D.

Stratified sampling is a technique used in research where a population is divided into natural subsets or strata based on specific characteristics or attributes. Each stratum is then proportionally represented in the sample to ensure accurate representation of the overall population.

This method helps to improve the accuracy and precision of the results obtained, as it takes into consideration the variability within the different subgroups of the population. In contrast, continuous process sampling, systematic sampling, and cluster sampling are other types of sampling methods that do not specifically allocate proportional samples to each subset in a divided population. The correct answer is D.

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Complete question:

Which method of sampling applies to populations that are divided into natural subsets and allocates the appropriate proportion of samples to each subset?

a. Continuous process sampling

b. Systematic sampling

c. Cluster sampling

d. Stratified sampling

Answer:

D

Step-by-step explanation:

every other answer makes no sense because it's either adding or subtracting normally therefore it has to be D that uses proportion

The limit exists and converges at \(e^{6}\)

Given: We need to find if an converges or not and if converges then find the limit of \(a_n\)

\(a_{n}\) = \(( 1 + \frac{6}{n} )^{n}\)  

Taking log on both sides we get,

  ln(\(a_{n}\))  = ln[\(( 1 + \frac{6}{n} )^{n}\)]    

= n.ln[ \(( 1 + \frac{6}{n} )\) ]    

= \(\frac{ln[ 1 + \frac{6}{n} ]} {(\frac{1}{n})}\)

  ln(\(a_{n}\))  = \(\frac{ln[ 1 + \frac{6}{n} ]} {(\frac{1}{n})}\)

now applying limit on both sides, as  \({n \to \infty}\),

\(\lim_{n \to \infty}\) ln(\(a_{n}\)) = \(\lim_{n \to \infty} \frac{ln[ 1 + \frac{6}{n} ]} {(\frac{1}{n})}\)

The limit is the form of 0 / 0 , so we can apply L'Hôpital's rule.

By L'Hôpital's rule, we get,

\(\lim_{n \to \infty}\)ln(\(a_{n}\)) = \(\lim_{n \to \infty} \frac{\frac{1}{1 + \frac{6}{n} } * \frac{-6}{n^{2} } }{\frac{-1}{n^{2} } }\)

    =  \(\lim_{n \to \infty} \frac{6}{1 + \frac{6}{n} }\)

Now removing the limit from RHS we get,

\(\lim_{n \to \infty}\) ln(\(a_{n}\))  = \(\frac{6}{1 + 0}\) = 6

Therefore as \({n \to \infty}\), ln(\(a_{n}\)) \(\to\) 6

So, as \({n \to \infty}\) , \(e^{ln(a_n )}\) \(\to\) \(e^{6}\)

Therefore, as \({n \to \infty}\), \(a_{n}\) \(\to\) \(e^{6}\)

Hence, the limit exists and \(a_n\) converges at \(e^{6}\)

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Disclaimer: The question is incomplete. The complete question is written below,

Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)

\(a_{n}\) = \(( 1 + \frac{6}{n} )^{n}\)  

The minute hand passes through an angle of 7π/30 Radians between 9:05 A.M. and 9:47 A.M.

The radian angle measure through which the minute hand passes between 9:05 A.M. and 9:47 A.M.

The minute hand completes one full revolution (360 degrees or 2π radians) every 60 minutes. Therefore, in one minute, it covers an angle of 2π/60 = π/30 radians.

Step 1: Determine the number of minutes from 9:05 A.M. to 9:47 A.M.

47 minutes - 5 minutes = 42 minutes.

Step 2: Calculate the angle covered in radians:

Angle in radians = (π/30) * (number of minutes)

Angle in radians = (π/30) * 42

Angle in radians = (7π/30).

Therefore, the minute hand passes through an angle of 7π/30 radians between 9:05 A.M. and 9:47 A.M.

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The probability that at most 1 Democrat was chosen given that at most 1 of the committee members is a Republican is 0.13095.

The probability that at most 1 Democrat was chosen given that at most 1 of the committee members is a Republican can be found by using the formula for conditional probability, which is P(A|B) = P(A∩B)/P(B). In this case, A is the event that at most 1 Democrat was chosen and B is the event that at most 1 Republican was chosen.

First, we need to find P(A∩B), which is the probability that both events occur. This can be found by calculating the number of ways to choose at most 1 Democrat and at most 1 Republican, divided by the total number of ways to choose 5 people from 18.

The number of ways to choose at most 1 Democrat is 8C0 + 8C1 = 1 + 8 = 9. The number of ways to choose at most 1 Republican is 10C0 + 10C1 = 1 + 10 = 11. The total number of ways to choose 5 people from 18 is 18C5 = 8568.

Therefore, P(A∩B) = (9*11)/8568 = 99/8568.

Next, we need to find P(B), which is the probability that at most 1 Republican was chosen. This can be found by calculating the number of ways to choose at most 1 Republican and 4 or 5 Democrats, divided by the total number of ways to choose 5 people from 18.

The number of ways to choose at most 1 Republican and 4 or 5 Democrats is (10C0*8C5) + (10C1*8C4) = (1*56) + (10*70) = 56 + 700 = 756.

Therefore, P(B) = 756/8568.

Finally, we can use the formula for conditional probability to find P(A|B) = P(A∩B)/P(B) = (99/8568)/(756/8568) = 99/756 = 0.13095.

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Answer: The first and the fourth option

Step-by-step explanation:

   Every input of a function can have only one output.

   Option one is a function.

   See the attached image as to why option two is not a function.

   Option three has two outputs for the input value of "20" meaning it is not a function.

   Option four is a function.

Answer:

y = 4x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 4 , then

y = 4x + c ← is the partial equation

to find c substitute (- 1, 1 ) into the partial equation

1 = - 4 + c ⇒ c = 1 + 4 = 5

y = 4x + 5 ← equation of line

The equivalent equation solved for y is y = a/πx. Half the length of the smaller diameter of the ellipse is 2.12 units, and the ellipse has dimensions of 6 units by 2.12 units. (Option 3)

To solve for y, we start with the equation for the area of an ellipse:

a = πxy

Dividing both sides by πx, we get:

a/πx = y

Therefore, the equivalent equation solved for y is y = a/πx. This equation gives us the value of y, which is half the length of the smaller diameter of the ellipse, in terms of the area of the ellipse and half the length of the larger diameter.

For example, if the area of an ellipse is 20 square units and half the length of the larger diameter is 6 units, we can use the equation y = a/πx to find the value of y:

y = 20/π(6) = 1.06 units

Therefore, half the length of the smaller diameter of the ellipse is 2.12 units, and the ellipse has dimensions of 6 units by 2.12 units.

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Complete Question:

The area, a, of an ellipse can be determined using the formula a = πxy, where x and y are half the lengths of the largest and smallest diameters of the ellipse. which is an equivalent equation solved for y?

The work done lifting the bucket and rope is 1465.1 J.

Work done is defined as involving both forces applied to the body and displacement of the body.

Consider a frictionless horizontal floor and a block. This block is acted upon by a constant force F. The action of this force is to move the body d distance in a straight line in the force's direction.

The weight of the water = density × volume

Weight of the water,

\(1000kg/m^3*100cm^3\\=0.1 kg.\)

weight of the bucket  = 5 kg

weight of the rope=2×10-2x=20-2x.

\(leakage=\frac{0.1}{10}*x\)

Total weight= 5 + 20 - 2x - 0.01x   = 25-2.01x

Force=wg

force=9.8(25-2.01x)

Finally; the amount of work spent in lifting the bucket, rope, and water is calculated as follows: the work done is

\(W=\int_0^{10}(25-2.01x)9.8dx\\\\W=9.8[25x-2.01x^2/2]_0^{10}\\\\W=9.8[25*10-2.01*50]\\\\W=1465.1 J.\)

The complete question is-

A 5 kg bucket is lifted from the ground into the air by pulling in 10 meters of rope with a linear density of 2 kg/m at a constant speed. The bucket starts with 100 cm^3 of water and leaks at a constant rate. It finishes draining just as it reaches the 10-meter mark. How much work was spent lifting the bucket, rope, and water?

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Answer:

-2x - 3

Step-by-step explanation:

f(x) = -1/2(x + 3)  is the same as  y = -1/2(x + 3)

change all y terms to x terms and all x terms to y terms

So  change  y = -1/2(x + 3) to x = -1/2(y + 3)

Now use the new equation and slove for y

x = -1/2(y + 3)

-2x = -2· -1/2 (y + 3)

-2x = y + 3

-2x - 3 = y

Rewrite your answer y = -2x - 3

Write the equation in the  inverse