a survey of 50 people were taken 30 like chocolate 20 like vanilla 10 like both how mnay like choclate

The identities among the given statements are:

tan x = sin x / cos x

sin x / tan x = cos x

We have,

Let's analyze each of the given statements to determine whether they are identities:

tan x = sin x / cos x:

This is an identity.

It is known as the fundamental identity of trigonometry, as it holds true for all values of x (except when cos x is equal to 0).

tan x cos x = sin x:

This is not an identity.

It is a specific equation that may be true for certain values of x, but it does not hold true for all values of x.

cos x = tan x sin x:

This is not an identity.

Similar to the previous statement, it is a specific equation that may be true for certain values of x, but it does not hold true for all values of x.

sin x / tan x = cos x:

This is an identity.

It can be derived from the fundamental identity by dividing both sides by cos x, resulting in sin x / cos x = cos x / cos x, which simplifies to sin x / tan x = cos x.

Thus,

The identities among the given statements are:

tan x = sin x / cos x

sin x / tan x = cos x

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The coefficient of variation for the given dataset with a mean of 36 and a variance of 16 is 11.1%, indicating a relatively low level of variability compared to the mean. Thus, the correct option is : 11.1%.

The coefficient of variation is a statistical measure that represents the relative variability of a dataset compared to its mean. It is calculated by dividing the standard deviation of the data by the mean and expressing it as a percentage.

In this case, we are given that the mean of the data is 36 and the variance is 16. To find the standard deviation, we take the square root of the variance, which gives us √16 = 4.

Next, we calculate the coefficient of variation by dividing the standard deviation (4) by the mean (36) and multiplying by 100 to express it as a percentage. Thus, (4 / 36) * 100 = 11.1%.

The coefficient of variation of 11.1% indicates that the dataset has relatively low variability compared to its mean. It suggests that the values in the dataset are relatively close to the mean, with a small amount of dispersion or spread.

Thus, the correct answer is : 11.1%.

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Time taken by Adam to complete his seventh lap of the circular track as per given data is equal to 1minute 28seconds.

As given in the question,

Time taken by Adam to complete hi first lap of circular track = 1 min 58 sec

First term t₁ = 1 minute 58seconds

Time taken by each successive lap is 5seconds less then the previous lap

Common difference 'd' = -5seconds

let time taken to complete the seventh lap be t₇

t₇ = t₁ + ( 7 - 1 ) d

⇒ t₇ = 1 minute 58 seconds + ( 6 ) (- 5seconds)

       =  1 minute 58 seconds - 30seconds

      = 1 minute 28 seconds

Therefore, the time taken by Adam to complete his seventh lap is equal to

1 minute 28 seconds.

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Answer:

180-46=134

so if u do the math u get

X=134

The value of 80 as fraction is 80/1.

To make 80 as a fraction, we need to place it over a denominator. The denominator can be any number as long as it is not equal to zero.

To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor (GCF), which is 10 in this case.

Therefore, the fraction 80 can be written as 80/1 or simplified as 8/1. This means that 80 is equivalent to 8 wholes or 8 times the unit.

In summary, 80 as a fraction is 80/1 or 8/1 when simplified.

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Given: The dimension as shown in the image

To determine: The name of the shape and the surface area

Solution

The name of the shape is a square-based pyramid

The area of a square-based pyramid can be calculated using the formula below

Substitute the given dimension into the formula

Hence, the name of the shape is a square-based pyramid and the surface area is 980in²

A ratio which would not be involved in the altitude or leg rule include the following: AB/AD = AD/AC.

By using the altitude theorem or leg rule, the ratio of the side lengths of this triangle can be calculated as follows;

Based on the similar triangles ABC and CDB, the ratio of the hypotenuse to adjacent side is given by this mathematical expression:

AB/CB = CB/DB (Hypotenuse/Adjacent side).

Based on the similar triangles ABC and ACD, the ratio of the hypotenuse to opposite side is given by this mathematical expression:

AB/AC = AC/AD (Hypotenuse/Opposite side)

Based on the similar triangles BCD and ACD, the ratio of the adjacent side to opposite side is given by this mathematical expression:

BD/CD = CD/AD

Therefore, AB/AD = AD/AC is not a correct ratio.

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Answer:

DG/EG = EG/GF

Step-by-step explanation:

Answer: No

Step-by-step explanation:

Hi there,

No, that is not a right triangle. A triangle with those side lengths would create an isosceles triangle with the angles 69.6 degrees, 69.6 degrees, and 40.7. Because there is no 90 degree angle, it is not a right triangle.

I hope this helps.

Answer:

(5, 4)

Step-by-step explanation:

Use the formula at the top of the page:

(x, y)⇒(y, -x)

So, in this case, x = -4 and y = 5.

Use the formula, and you get:

(-4, 5)⇒(5, 4) ------ A negative number with a minus in front of it becomes a positive number.

Answer: She will sell the entire pie for $7.5.

Step-by-step explanation:

Given: Number of slices in each  pumpkin pie = 6

Selling price for each slice = $1.25

Now , Selling price for 6 slices = 6 x (Selling price for each slice)

= 6 x $1.25

= $ 7.5

i.e. Selling price for entire pie = $ 7.5

Hence, She will sell the entire pie for $7.5.

Step-by-step explanation:

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): (28/5,0)

y-intercept(s): (0,4)

Therefore, The Coordinates of the THIRD VERTEX is:  ( 5, -3 )

        Calculate the midpoint of the given vertices:

        MidPoint = ( -5 + 5/2,  3 + 3/2 )

        MidPoint = ( 0, 3 )

        Distance = √( -5 -5 )^2 + ( 3 - 3 )^2

        Distance = √( -10 )^2  +  (0)^2

        Distance = √100

        Distance =  10

        Side Length =  10/√3

        Side Length = 10/1.7

        Side Length = 5.88

        Height = √3/2  *  Side Length

        Height  = 1.7/2  *  5.88

        Height  =  5

Since the origin lies inside the triangle, The Third Vertex will have a Positive  X-Coordinate and a Negative Y-Coordinate.

       ( x, y )

        x  =  -5 + x/2

        y   =  3 + y/2

       x  =  5

       y  = -3

        Hence, The Coordinate  of the Third Vertex is:  ( 5, -3 )

I hope this helps!

Answer:

Step-by-step explanation:

There is a missing operator in the second equation.

If the equation is 4x - 8y = 4, then the system is dependent. The second equation is a non-zero multiple of the first.

We are 95% confident that the true proportion of healthy students who could correctly identify a Skittles flavor blindly lies within the interval (0.4282, 0.5848).

To find the confidence interval, we can use the formula:

CI = p ± zsqrt(p(1-p)/n)

Where:

CI: Confidence Interval

p: Proportion of students who correctly identified the flavor (sample proportion)

z: Z-score corresponding to the desired confidence level (95% confidence level corresponds to z=1.96)

n: Sample size

Plugging in the values we have:

p = 78/154 = 0.5065

z = 1.96

n = 154

CI = 0.5065 ± 1.96sqrt(0.5065(1-0.5065)/154)

CI = 0.5065 ± 0.0783

CI = (0.4282, 0.5848)

Therefore, we are 95% confident that the true proportion of healthy students who could correctly identify a Skittles flavor blindly lies within the interval (0.4282, 0.5848).

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To solve the differential equation:

y(3xy' + 3)dx + (3x^2y + 3y')dy = 0

We can see that this is not in the form of a separable differential equation, so we need to use an integrating factor. To do this, we first find the coefficients of y and y':

M(x,y) = 3xy' + 3

N(x,y) = 3x^2y + 3y'

Then, we calculate the partial derivative of N with respect to x:

∂N/∂x = 6xy

Now, we can find an integrating factor by dividing both sides by M:

(y' + 1/y)dx + (3x/y)dy = 0

Multiplying both sides by the integrating factor u(x):

u(x)(y' + 1/y)dx + u(x)(3x/y)dy = 0

where u(x) = e^(int 3x/y dx)

Integrating w.r.t. x to find the exponential factor:

ln|u(x)| = ∫ 3x/y dx

=> ln|u(x)| = 3ln|x| + C1

=> u(x) = e^(3ln|x|+C1)

=> u(x) = e^(ln|x^3|+C1)

=> u(x) = K|x^3|

where K = e^C1

Multiplying both sides by the integrating factor:

Kx^3(y' + 1/y)dx + K3x^4dy/y = 0

d/dx(Kx^3y) = 0

Integrating both sides w.r.t. x:

Kx^3y = C2

where C2 is the constant of integration.

Therefore, the solution to the differential equation is:

Kx^3y = C2

where K and C2 are constants.

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The correct answer is c. 4 and 31.

In a multiple regression model, the numerator degrees of freedom is equal to the number of independent variables, and the denominator degrees of freedom is equal to the number of observations minus the number of independent variables minus 1. In this case, there are 4 independent variables and 36 observations, so the numerator degrees of freedom are 4 and the denominator degrees of freedom are 36 - 4 - 1 = 31. Here is a more detailed explanation of how to calculate the numerator and denominator degrees of freedom for a multiple regression model: The numerator degrees of freedom is equal to the number of independent variables. The denominator degrees of freedom is equal to the number of observations minus the number of independent variables minus 1. In this case, there are 4 independent variables and 36 observations, so the numerator degrees of freedom are 4 and the denominator degrees of freedom are 36 - 4 - 1 = 31.

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Using the Poisson distribution, the probability of an earthquake in the 0.8-0.9 magnitude range sometime in the next 30 years is

1 - 1.9287 x 10⁻²².

It is given that mean recurrence of an earthquake is the 8.0-9.0 magnitude is approximately 1500 years.

We have to find the probability of an earthquake in this magnitude range sometime in the next 30 years.

Since, an occurrence of an earthquake is a rare event, we can use Poisson distribution here.

Poisson distribution gives the probability of occurrence of any event in a given time interval.

Let the average number of event per year in 30 years of period is λ.

\(\lambda = \frac{1500}{30}\)

λ = 50

Let, the occurrence of an earthquake is a random variable x.

Then the probability that at least an earthquake occur in next 30 years is calculated as:

P(x ≥ 1) = 1 - P(x<1)

P(x ≥ 1) = 1- P(x=0)   -----(1)

PDF of Poisson distribution with parameter λ is given as:

\(P(X = x) = \dfrac{e^{-\lambda}{\lambda}^x}{x!}\)

So, in this case

\(P(x=0)= \dfrac{e^{-50}{(50)}^0}{0!}\)

\(P(x=0)= \dfrac{1.9287 \times 10^{-22}}{1}\)

\(P(x=0)={1.9287 \times 10^{-22}\)

Substitute this value in equation (1)

P(x ≥ 1) = 1 - 1.9287 x 10⁻²²

Hence, the probability of an earthquake in next 30 years is

1 - 1.9287 x 10⁻²².

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The pages that are filled with stamps ​are 252

From the question, we have the following parameters that can be used in our computation:

Stamps = 900

Empty = 72%

Using the above as a guide, we have the following:

Filled = (1 - Empty) * Stamps

So, we have

Filled = (1 - 72%) * 900

Evaluate

Filled = 252

Hence, 252 are filled

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Answer:

5

Step-by-step explanation:

Take the number of 6th graders and multiply by the percent that have red hair

100 * 5%

100 * .05

5

Answer:

on edg its 5!

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

6x+5=3x+14

3x+5=14

3x=9

x=3

Answer:

x = 3

Step-by-step explanation:

"Solve" means find out what number we need to fill in for x in order for this to be a true math sentence.

Start with the given equation.

6x + 5 = 3x + 14

Subtract 3x from both sides (the equal sign is the middle)

3x + 5 = 14

Subtract 5 from both sides

3x = 9

Divide both sides by 3.

x = 3

You can check it by putting 3 in place of x, you get a true statement:

6(3) + 5 = 3(3) + 14

18 + 5 = 9 + 14

23 = 23

It works! The solution is x = 3

well, let's keep in mind that a meter has 100 centimeters, thus 1.3 meters will be 1.3 * 100 cm, namely 130 cm.

\(\begin{array}{ccll} cm&year\\ \cline{1-2} 2 & 1\\ 130& x \end{array} \implies \cfrac{2}{130}~~=~~\cfrac{1}{x}\implies \cfrac{1}{65}=\cfrac{1}{x}\implies x=65\)

Answer:

z=-3

Step-by-step explanation:

1:open the brackets.

2:take 21 to the other side to be subtracted by 42

3:you get a -z but you can take it to the other side to get a +z but -21 divide to get the answer

42=-7(z-3)

-7(z-3)=42

-7z+21=42

-7z=42-21

-7z=21

therefore,

z=21\-7

that is, -21\7=-3

Answer: Hi love, Your answer is B

Step-by-step explanation:

Answer:

the answer is B

Step-by-step explanation:

Answer:

The answer is 28

Step-by-step explanation:

Since the total measurements of triangle corners are equal to 180

Then

\(2x + 3x - 10 + 50 = 180 \\ 5x - 40 = 180 \\ 5x = 140 \\ x = 28\)

The probability of at most 8 of the students being full-time is approximately 0.988, or 98.8%.

To answer this question, we can use the binomial distribution function in R. The formula for the binomial distribution is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where:
- P(X=k) is the probability of getting exactly k successes
- n is the total number of trials
- p is the probability of success in each trial
- (n choose k) is the number of ways to choose k items from a set of n items

(a) To find the probability that exactly 6 of the students will be full-time, we can use the following command in R:

dbinom(6, 10, 0.6)

This will give us the probability of getting exactly 6 full-time students out of a random sample of 10 students, assuming that the probability of a student being full-time is 0.6 (since there are 30 full-time students out of a total of 50 students).

The output of this command is:

[1] 0.2508227

So the probability of exactly 6 of the students being full-time is approximately 0.251, or 25.1%.

(b) To find the probability that at most 8 of the students will be full-time, we can use the following command in R:

pbinom(8, 10, 0.6)

This will give us the probability of getting 8 or fewer full-time students out of a random sample of 10 students.

The output of this command is:

[1] 0.9884969

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Answer:

not factorable

Step-by-step explanation

Answer:

UwU

Step-by-step explanation:

are know men sorry:c

The piece of wood is as long as 48 nails. It is the quotient of the length of wood by the length of nail. In calculation, they should have the same unit length, that is inch.

One foot is equal to 12 inches.

Mathematically, it is expressed as

1 ft = 12 in

A piece of wood is 12 feet long. The nail has the length of 3 inches. Find the number of the nails so it equals the length of the piece of wood!

The length of piece of wood in inches would be

12 feet = 12 × 12 inches

12 feet = 144 inches

The number of nails needed so that the length would be as long as a piece of wood is

= length of wood / length of nail

= 144 inches / 3 inches

= 48 nails

Hence, a piece of wood is equal to 48 nails.

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Answer:

i^3 = -i

Step-by-step explanation:

i^3

Rewriting as

i^2 *i

We know that i^2 = -1

-1 *i

-i