A sinusoidal function of the form y = a sin(x - c) + d is
changed by increasing d by 2. The new graph will have
moved:
A.2 units left
B.2 units up
C.expanded vertically by a factor of 2
D.2 units down

By using the formula for mean and variance, it can be calculated that

Mean of X = 25

Variance of X = 51.67

What is mean and variance?

Suppose there is a data set. Mean gives the average of the values of the data set

Variance is the square of the sum of deviation from mean.

Let x be the total; of the numbers on the two card

Possible values of X= 15, 20, 25, 30, 35

P(X = 15) = [tex]\frac{2}{12}[/tex]

P(X = 20) = [tex]\frac{2}{12}[/tex]

P(X = 25) = [tex]\frac{4}{12}[/tex]

P(X= 30) = [tex]\frac{2}{12}[/tex]

P(X = 35) = [tex]\frac{2}{12}[/tex]

Mean of X =

[tex]15 \times \frac{2}{12} + 20 \times \frac{2}{12} +25 \times \frac{4}{12} + 30 \times \frac{2}{12} + 35 \times \frac{2}{12}\\\\\frac{300}{12}\\\\25[/tex]

Variance of X =

= [tex](225 \times \frac{2}{12} + 400 \times \frac{2}{12}+625 \times \frac{4}{12}+900 \times \frac{2}{12}+1225 \times \frac{2}{12}) - (25)^2\\\\\frac{8000}{12} - 625}\\\\666.67 - 625\\\\51.67[/tex]

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Complete Question

In a box are four cards numbered 5, 10, 15, 20. two cards are taken out at random without replacement, and X is the total; of the numbers on the two card. Find the mean and variance of X .

The correct option b. 0.004629 for  the probability of observing a 1 three times in a row.

Probability of an event = (Number of favorable events) /   (total number of event).

P(B) = (Event B) / (total number of event).

The number of times the dice are rolled has no bearing on the outcome of the roll.

The likelihood of receiving 1 is 1/6.

The likelihood of obtaining 1 three times in a row is equal to the likelihood of getting 1 the first time, the second time, and the third time.

Receiving 1 three times in succession has a probability;

= 1/6 x 1/6 x 1/6

= 1/216.

As a result, there is a 0.463% chance that you'll get 1 three times in a row.

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The table which shows probability distribution is ,

X    P(X)

0    0.25

1      0.05

2     0.7

What is probability distribution?

   In mathematics, a probability distribution is a function that expresses the likelihood of many possible values for a variable. Utilizing graphs or probability tables, probability distributions are frequently represented. For a specific data generation process, a probability distribution shows the anticipated results of potential values. According to the mean, standard deviation, skewness, and kurtosis, probability distributions can take many different forms and exhibit a variety of properties.

A= Older eaglet survive

B = Younger eaglet survive

Given the older eaglet has 50% of survival ,

P(A) = 50% = 50/100 = 0.5

Now the older eaglet survive , the younger eaglet have only 10% of survival chance,

=> P(B/A)=10% = 10/100 = 0.1

Here P(B/A) = P(B∩A)/P(A)

=> 0.1 = P(B∩A) ×0.5

=> P(B∩A) = 0.05.

Both eaglet survives is P(B∩A) = 0.05. -------> 1

Now if the older eaglet does not have survive , the younger eaglet has 30% of survival chance,

=>P(B/A') = 30% = 0.3

Here P(B/A') = P(B∩A')/P(A')

Here P(A') = 1-P(A) = 1-0.50 = 0.50.

=> P(B∩A') = P(B/A')*P(A')

=> P(B∩A') = 0.3*05

=> P(B∩A') = 0.15

Now P(B) = P(B∩A)+P(B∩A')

=> P(B) = 0.05+0.15

=> P(B) = 0.20

P(only one eaglet survive) = P(A)+P(B)

=> 0.5+0.2 = 0.7 .-------> 2

Let x be the number of eaglet that survive,

Here x takes value of 0,1,2.

P(both eaglet survive ) = 0.05 ( from equation 1)=P(X=2)

P(only one eaglet survive) = 0.7 (from equation 2) =P(x=1)

As we know x takes only 3 values and we want to find probability distribution of x,

=> P(X=0) = 1-P(X=1)-P(x=2)

=> P(X=0) = 1-0.7-0.05

=> P(X=0) = 0.25 .

Therefore the table which shows probability distribution ,

X    P(X)

0    0.25

1      0.05

2     0.7

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Answer:

a. parameter

Step-by-step explanation:

A parameter is any descriptive measure of a population characteristic.

Answer:

Step-by-step explanation:

None of these ordered pairs work. Each is false for at least one of the 2 equations.

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

(1, 0) is false for equation 1.

y > -3x + 3

0 > -3(1) + 3

0 > -3 + 3

0 > 0 (FALSE)

(-1, 1) is false for equation 1.

y > -3x + 3

1 > -3(-1) + 3

1 > 3 + 3

1 > 6 (FALSE)

(2, 2) is false for equation 2.

y > 2x - 2

2 > 2(2) - 2

2 > 4 - 2

2 > 2 (FALSE)

And (0, 3) is false for equation 1.

y > -3x + 3

3 > -3(0) + 3

3 > 3 (FALSE)

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Question:

Which ordered pair makes both inequalities true? y > –3x + 3 y > 2x – 2 (1,0) (–1,1) (2,2) (0,3)

The p-value for this hypothesis test for a proportion p is 0.039.

What is a random sample?

In statistics, a simple random sample is a subset of individuals chosen from a larger set in which a subset of individuals is chosen randomly, all with the same probability. It is a process of selecting a sample in a random way.

For the null hypothesis,

H0 : p = 0.63

For the alternative hypothesis,

Ha : p < 0.63

This is a left-tailed test

Considering the population proportion, probability of success, p = 0.63

q = probability of failure = 1 - p

q = 1 - 0.63 = 0.37

Considering the sample,

Sample proportion, P = x/n

Where,

x = number of success = 478

n = number of samples = 800

P = 478/800 = 0.6

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.6 - 0.63)/√(0.63 × 0.37)/800 = - 1.76

From the normal distribution table, the area below the test z score in the left tail is 0.039

Thus,

p = 0.039

Hence, the p-value for this hypothesis test for a proportion p is 0.039.

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Yes, the given curves are orthogonal.

In mathematics, an orthogonal trajectory is a curve, which intersects any curve of a given pencil of (planar) curves orthogonally.

Given equation is,

x²+y²=ax

Differentiating,

2x+2yy'=a

y' = (a-2x)/2y = m1

Again,

x²+y²=by

Differentiating,

2x+2yy'=by'

y' = -2x/(2y-b) = m2

For both curves are orthogonal, we have

m1*m2 = -1

(a-2x)/2y*-2x/(2y-b)  = -1

-2ax+4x² = -4y²+2yb

4(x²+y²) = 2ax+2yb

Since, ax = (x²+y²)

by = (x²+y²)

Then,

4(x²+y²) = 2(x²+y²) +2(x²+y²)

4(x²+y²) = 4(x²+y²)      (true)

Hence, the above response is appropriate.

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The height of the tree to the nearest centimeter is 613 centimeters

A proportion can be described as an equation having two ratios set equal to each other.

It is also seen as the mathematical comparison of two elements, numbers of ratios.

From the information given, we have that;

If 57 centimeters = 161 centimeters

Then 217 centimeters = x

cross multiply

x = 161(217)/57

multiply the values

x = 34, 937/57

x = 613 centimeters

Hence, the value is 613 centimeters

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Answer:

A

Step-by-step explanation:

the equation of a circle in standard form is

(x - h )² + (y - k )² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (- 3, 6 ) and r = 2 , then

(x - (- 3) )² + (y - 6)² = 2² , that is

(x + 3)² + (y - 6)² = 4

If the is lets say 5 years old, in 2 years, she will be 5 + 2 = 7 years old, and in 10 years 5 + 10 = 15 years old

so age in the future is the present age + how many years from now she will be

in this example the present age is 5 years old , if you replace that 5 with an x, the age in 10 years will be x + 10

Answer:

The answer is b

Step-by-step explanation:

The equation of a line perpendicular to p(t) = 3t + 4 and passing through the point (3, 1) is: P(t) = -1/3 + 1

Given:

p(t) = 3t + 4

point (3,1)

To find this out, we must use the slope perpendicular to 3

perpendicular slopes are the slope's reciprocal's negative, which in this case it is -1/3

to find the line with the points (3,1), we simply use the equation y = -1/3x + b and then plug them in

1 = -1/3(3) + b

1 = -1 + b

b = 2

the y intercept is 2 and so we can write the equation like this:

P(t) = -1/3t + 2

Hence we get the required equation of a line.

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The probability that, with random samples of seven measurements the sample mean for species a and b by at least 1 unit is 0.9999

1) Using by the central limiting theorem:

We know the formula for the z-score for the normal distribution is given by:

z = (x - μ) /( ρ√n)  

Follows normal distribution with mean 0 and the variance of 1.

Where

x is the  sample mean,

μ is the  population mean,

ρ denotes population standard deviation

n = sample size

The required probability is

P(z < 0.5/[0.4/√ 10])

= P(z < 3.95)

P = 0.9999

Therefore the probability that, with random samples of seven measurements the sample mean for species a and b by at least 1 unit is 0.9999 .

Normal distributions are crucial to statistics because they are commonly used in the natural and social sciences to describe real-valued random variables with uncertain distributions. They are important in part because of the central limit theorem.

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The way fuel consumption of a car change as its speed increases represents a relationship that is curved with higher at extremes when scatter plot is constructed. It shows fuel efficiency is high at moderate speeds.

What is scatter plot?

A scatter plot is a type of mathematical diagram using Cartesian coordinates to demonstrate values for typically two variables for a set of data.

Main body:

In the given case, the scatter plot shows a relationship between the speeds of a car and fuel consumption.

The curved relationship which is high on extreme and low in the middle. As the car speed increases from 10km/h to 60 km/h, the fuel consumption decreases. As the car speed increases from 60km/h to 150khm/h, the fuel consumption increases. Hence, the fuel consumption is lowest at 60km/h and its generally low for moderate speeds – 40 km/hr to 100 km/h. It can be deduced that fuel efficiency (which pertains to how well a vehicle uses fuel) is high for moderate speeds.

Hence, at moderate speeds best performance is achieved.

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A polynomial is a function with two or more terms that have positive integer exponents. The terms can be constants and/or have variables. They are separated by either addition or subtraction signs.

fundamental coefficients are the numbers written in front of the variable with the maximum important exponent. just like ordinary coefficients, they may be fine, terrible, real, or imaginary further to whole numbers, fractions, or decimals. for instance, inside the equation [tex]-7x^4[/tex] +[tex]2x^(3-11)[/tex], the very satisfactory exponent is four.

The degree of the polynomial is the best strength of the variable that takes location in the polynomial. the number one time period is the time period containing the very high-quality energy of the variable: the term with the very wonderful degree.

In a polynomial, the principal term is the term with the very first-rate electricity of x. for instance, the principal term of 7+x−3x² is −3x². the principal coefficient of a polynomial is the coefficient of the primary term. within the above instance, the primary coefficient is −3.

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The highest temperature can be increased by any amount without changing the median.

Here, we are given the following data set-

94, 93, 98, 101, 98, 96, and 93

To find the median of the given numbers, we first need to arrange the numbers in an ascending or descending order. Let us arrange them in an ascending order as follows-

93, 93, 94, 96, 98, 98, 101

Now, the median of the middlemost value of a data set.

Here, we have 7 values, thus, the middlemost value will be given by the 4th term in the series.

As we can see from above, the fourth value is 96. Hence, 96 is the median of the data set.

Now, as we can see the highest temperature value is 101. We can increase it by any amount and it will still be the last term in the series, and the median will remain the same middle value, that is, 96.

Thus, the highest temperature can be increased by any amount without changing the median.

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The expected value of this game is $20.The typical net gain or loss that we would anticipate from playing a game of chance several times is known as the anticipated value.

Simply multiply each value of the discrete random variable by the probability associated with that value to obtain the expected value, E(X), or mean. E (X) = = x P (x) is the formula that is given.

The typical net gain or loss that we would anticipate from playing a game of chance several times is known as the anticipated value. By dividing the value of each outcome by the likelihood that it will occur, we can calculate the expected value. Then, we total up all the results.

The formula is given as E ( X ) = μ = ∑ x P ( x ) .

                                                         = $5 * $4

                                                          = $20.    

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The ordered pair (4, 0) makes both inequalities true.

What is inequality equation?

The mathematical expressions in which both sides are not equal are called inequalities.

Main body:

In inequality, unlike in equations, we compare two values.

The equal to sign in between is replaced by less than, greater than or not equal to sign.

It is given that

y < 3x -1 …. (1)

y > -x + 4 …. (2)

Let us take the point (4, 0)

In inequality (1)

y < 3x-1

0 < 3 (4) - 1

0 < 12 - 1

0 < 11 which is true

In inequality (2)

y ≥ - x + 4

0 ≥ -4 + 4

0 ≥ 0 …. Which is true

Therefore, the ordered pair (4, 0) makes both inequalities true.

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The probability of all 3 selected were rated excellent is 1/114 and the probability of one from each category was selected, is 7/114.

In the given question,

In a certain department, 5 employees received excellent ratings, 14 received good ratings, and 1 received a marginal rating.

So total number of employees = 5+14+1 = 20

If 3 employees in this department are randomly selected to complete a form for an internal study of the firm, then we have to find the probability that the following occurs.

The following occurs given below:

(a) We have to find the probability of all 3 selected were rated excellent.

5 employees who got excellent rating. So the selection of 3 employees from 5 employees who got excellent rating is:

selection of 3 employees from 5 employees = [tex]^5C_{3}[/tex]

Using, [tex]^nC_{r}=\frac{n!}{r!(n-r)!}[/tex]

selection of 3 employees from 5 employees = [tex]\frac{5!}{3!(5-3)!}[/tex]

selection of 3 employees from 5 employees = [tex]\frac{5!}{3!2!}[/tex]

selection of 3 employees from 5 employees = [tex]\frac{5\times4\times3!}{3!\times2\times1}[/tex]

selection of 3 employees from 5 employees = 5×2

selection of 3 employees from 5 employees = 10

Selection of 3 employees from 20 employees= [tex]^{20}C_{3}[/tex] = 1140

Probability of 3 employees who got excellent rating

P(E) = 10/1140

P(E) = 1/114

(b) We have to find the probability of one from each category was selected.

One candidate selected from excellent category = [tex]^5C_{1}[/tex] = 5

One candidate selected from marginal category = [tex]^1C_{1}[/tex] = 1

One candidate selected from good category = [tex]^{14}C_{1}[/tex] = 14

Selection of 3 employees from 20 employees= [tex]^{20}C_{3}[/tex] = 1140

The probabilty of one from each category = (5*1*14)/1140

The probabilty of one from each category = 70/1140

The probabilty of one from each category = 7/117

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If the mean of a statistic's sample distribution perfectly matches the actual value of the parameter being evaluated, the statistic is said to be unbiased. The population proportion p is best estimated objectively using the sample proportion (p hat) from an SRS.

If the expected value of an estimate for a given parameter is the same as the parameter's true value, the estimator is said to be impartial. To put it another way, an estimator is impartial if it generates parameter estimates that are generally accurate.

The mean of a sample taken from a population is calculated to produce a point estimate of the population mean. The mean is calculated by dividing the total sample values by the total number of values.

Hence we get the required answer.

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The minimum height is 6ft and length is 12 ft.

Let  [tex]l[/tex] be side of square base and h be the height.

we know  [tex]l^{2}[/tex] × h  = 864

We have minimize

[tex]l^{2}[/tex] + 4 × [tex]lh[/tex]

=  [tex]l^{2}[/tex] + 4 × 864/l

diffrentitate and equate to 0

2[tex]l[/tex] - 4 × 964/ [tex]l^{2}[/tex]  = 0

[tex]l[/tex] = [tex]\sqrt[3]{2 * 864}[/tex] = 12

so h = 6

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Answer:

a function is like f(X)=2x+6 where X can be anything , you just substitute in the number u have been given

Step-by-step explanation:

other examples could include

f(X)=X+1

or they can start with

g(X)=3x+7

h(X)=4-3x

and there are inverse functions witch can be found be rearranging the function

example if substituteing a function

if

f(X)= 2x+1

f(3)=2(3)+1

f(3)=6+1=7

Hope this helps

Answer:

A triangle in which each angle is less than 90 degrees is called an acute angled triangle.

Step-by-step explanation:

Applying the given exponential function  y = 7.1(1.03)ˣ, the amount produced in 2006 was approximately 7.8 billion pounds and the estimated amount in 2014 will be approximately 9.8 billion pounds

An exponential function is a function of form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

In the function given;

y = 7.1(1.03)ˣ

a) What is the estimated number in 2006

The value of x in 2006 is

x = 3

Plug the values into the formula above;

y = 7.1(1.03)³

y = 7.76 ≅ 7.8 billion pounds

b)

The cheese produced in 2014

The value of x in 2014 = 11

Plug in the value

y = 7.1(1.03)¹¹

y = 9.83 ≅ 9.8 billion pounds

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The required value of g would be 7.

The slope of a line is defined as the gradient of the line.

We have been given that a line that includes the points (0, – 3) and (g, 3) has a gradient of 6/ 7.

The gradient of line = (3 - (-3))/(g - 0)

⇒ 6/7 = (3 + 3)/g

⇒ 6/7 = 6/g

Apply the cross-multiplication operation,

⇒ 6g = 42

⇒ g = 42/6

Apply the division operation,

⇒ g = 7

Therefore, the required value of g would be 7.

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Answer:

an obtuse angle are angles that are greater than 90 degrees

Step-by-step explanation:

an obtuse angle are angles that are greater than 90 degrees

Applying the distance formula, the length of the bike path as shown in the coordinate plane is approximately 28 feet.

To find the distance between two points that are on a coordinate plane, the formula used is the distance formula which is given as:

d = [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex].

Point G on the coordinate plane is at (20, 20), while point E is at (0, 0):

Therefore:

E (0, 0) = [tex](x_1, y_1)[/tex]

G (20, 20) = [tex](x_2, y_2)[/tex]

Plug in the values into the distance formula:

EG = √[(20 − 0)² + (20 − 0)²]

EG √[(20)² + (20)²]

EG = √(400 + 400)

EG = √800

EG ≈ 28 feet

The length of the bike path would be approximately 28 feet.

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Answer:

[tex]\sqrt{178}[/tex] or 13.3 rounded to the nearest tenth

Step-by-step explanation: