a) use the appropriate formula to find the value of the annuity.
b) Find the interest. Periodic Deposit: $3000 every three months Rate: 6.25% at the end of compounded quarterly
Time :4 years a. The value of the annuity is $.

The probability that Alex takes out three red apples is 1/30.

The probability that Alex takes out one green apple and two red apples is 1/10.

The probability that Alex takes out three red apples = (number of red apples / total number of apples) x (number of red apples - 1 / total number of apples - 1) x (number of red apples - 2 / total number of apples - 2)

4/10 x 3/9 x 2 /8 = 1 / 30

The probability that Alex takes out one green apple and two red apples = (number of green apples / total number of apples) x (number of red apples / total number of apples - 1) x (number of red apples - 1 / total number of apples - 2)

6/10 x 4/9 x 3/8 = 1 / 10

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Answer: B

Step-by-step explanation:

1. multiply (-3x+1) by -2 to get -6x+2 -> -6x+2<8

2. then subtract 2 from both sides, -6x+2 -2 < 8 -2 -> -6x<6

3. divide both sides by -6, when dividing an inequality, the inequality symbol switches so you'd have x > -1

so the answer would be B

1. The population does not need to be normally distributed for the sampling distribution of x bar to be approximately normally distributed because the Central Limit Theorem states that regardless of the shape of the underlying population, the sampling distribution of ¯x becomes approximately normal as the sample size, n, increases. Therefore, the correct option is A.

2. The sampling distribution of ¯x is normal or approximately normal with μx = 68 and σx = 0.464. Therefore, the correct option is A.

1. The answer to 'does the population need to be normally distributed for the sampling distribution of x bar to be approximately normally distributed?' is no  because the Central Limit Theorem states that regardless of the shape of the underlying population, the sampling distribution of ¯x becomes approximately normal as the sample size, n, increases. In this case, the sample size is 41, which is large enough for the Central Limit Theorem to apply.

2. The sampling distribution of ¯x is normal or approximately normal with μx = 68 and σx = 0.464. The standard error (SE) of the sampling distribution of the sample mean is σ/√n. Here, the mean of the population is 68 and the standard deviation is 3.

The formula for the sampling distribution of the mean can be used to find the standard error. SE= σ/√n = 3/√41 = 0.464. The sampling distribution of ¯x is normally distributed, and since the sample size is 41, the sample mean can be considered approximately normally distributed.

Thus, the sample mean follows the normal distribution with μ = 68 and σx = 0.464. Therefore, the answer is: The sampling distribution of ¯x is normal or approximately normal with μx = 68 and σx = 0.464.

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A valid conclusion is one that naturally follows from informed, formulated hypotheses, prudent experimental design, and accurate data analysis.

If an argument is invalid, then it must have at least one false premise. If an argument has a conclusion that is certainly false, then the argument must be invalid. If the premises and conclusion are all false, the argument must be invalid.

A biased sample occurs when the group selected for a statistical study or survey is not random and doesn't properly represent the larger population. This is a result of sampling bias which occurs when the sample of the population is not representative of the population at large.

If an overestimate or underestimate does happen, the mean of the difference is called a “bias.” In more mathematical terms, an estimator is unbiased if: That's just saying if the estimator (i.e. the sample mean) equals the parameter (i.e. the population mean), then it's an unbiased estimator.

Cohort studies are an appropriate study design when: (1) there is good evidence to suggest an association between an exposure and an outcome (perhaps through prior cross-sectional studies); (2) the interval between exposure and development of the outcome is relatively short to minimize loss to follow-up; and (3) the outcome is not too rare (so that the size of the cohort is reasonable).

Hence,

No actual study was done, only observation.

From the above explanation, we can say that

The conclusion drawn from the study is not valid because the sample is Biased.In this instance, an inappropriate study was conducted

Answer:

0.25 pages per minute

Step-by-step explanation:

4 pages per 16 mins.

4/16 = 0.25

0.25 pages per minute

its a word equation, hopefully this helped!

Answer: c=-5

Step-by-step explanation: first you have to rearrange terms

6=1-c

6=-c+1

second you have subtract 1 on both sides

6=-c+1

6-1= -c+1-1

third and final you have to Simplify

5=-c

c=-5

1. twice: This higher-order function takes a function f as input and returns a new function that applies f twice.
  λf.λx.f (f x) 2. inc_n: This higher-order function takes an integer n and a function g as inputs and returns a new function that increments the input by n before applying g.
  λn.λg.λx.g (x + n)

To write lambda calculus expressions for the higher-order functions "twice" and "inc_n", we can use the following notation:
- The lambda abstraction symbol is represented as "\x", where "x" is the variable being abstracted.
- Function application is denoted by writing the function first, followed by its argument in parentheses.
Lambda calculus expression for "twice":
The "twice" function takes another function f as input and returns a new function that applies f twice to its argument. Here's how we can define it in lambda calculus:
(\f. \x. f (f x))
In this expression, "\f" is the lambda abstraction that binds the variable "f" as a parameter, and "\x" binds the variable "x" as a second parameter. The body of the function is "f (f x)", which applies the function "f" twice to the argument "x".
Lambda calculus expression for "inc_n":
The "inc_n" function takes a number n as input and returns a new function that increments its argument by n. Here's how we can define it in lambda calculus:
(\n. \x. x + n)
In this expression, "\n" is the lambda abstraction that binds the variable "n" as a parameter, and "\x" binds the variable "x" as a second parameter. The body of the function is "x + n", which adds "n" to the argument "x" to produce the final result.
Remember that lambda calculus expressions use the λ symbol to denote a function and its input variables, followed by the function's body.

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Part A: 23

Part B: 13

Part C: Median for the males

Mean for the females

Part D: The day the movie premiered

Process to arrive at the above answers

The likely missing part of the question; The Box Plots are to compare The Number of Males and The Number of Females attending the latest superhero movie every day in a given month

The known parameters

The 5 number summary in a are;

\(\begin{array}{lcc}\mathbf{Summary}&\mathbf{Males}&\mathbf{Females}\\\\Minimum &0&0\\First \ Quartile, \ Q_1&2&5\\Second \ Quartile, \ median, Q_2&20&7\\Third \ Quartile, Q_3&25&10\\Maximum &50&18\\Outlier&&46\end{array}\)

Part A: The Inter Quartile Range, IQR = Q₃ - Q₁

For the males, we have, IQR = 25 - 2 = 23

Part B: The difference between the median values for the males and females is given as follows;

Difference between median = Q₂ Males - Q₂ Females

∴ Difference between median = 20 - 7 = 13

The difference between the median values for the males and females = 13

Part C:

The distribution of the data for the males is skewed left, with almost all the data in the first half

The better measure of center for the skewed data is the median, given

that three quarter of the data have values that are less than half of the

range of values in the data set, and that the median is close to the third

quartile, the mean will be located further towards the minimum value of

the data than the median

The distribution of the data for the females consists of the interquartile

range located approximately in the middle between the max and the min

values with the median being close to the first quartile, therefore, the

mean will be a better measure of center as it will be located further from

the first quartile and closer midway in the IQR

Part D;

The possible reason for the outlier in the data set may be due to the first day the latest super hero movie is premiered

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Answer:

C

Step-by-step explanation:

the bottom 2 angles are congruent or they have the same measure, and you can find the interior angles because they are linear pairs with the exterior angle.

so you do 180-108 to get 72, and if you multiply that by 2, you find the measure of the sum of the 2 bottom angles. Becuase the sum of the angles of a triangle is 180 degrees, you can subtract that sum (144) and you can get 36 degrees

Answer:

36

Step-by-step explanation:

the whole triangle should equal 180

so 108+36=144 and 180-144=36

Answer:

The competitor will run 48,225.81 copies.

Step-by-step explanation:

Brand x copier run 59,800 copies between services

Brand X copiers run 24% longer between service calls than its competitor.

Let x = copies run by the competitor between services

Number of copies the competitor will run is

24% of x + x = 59,800

0.24x + x = 59,800

1.24x = 59,800

x= 59,800 / 1.24

x = 48,225.81

Therefore, the competitor will run 48,225.81 copies.

In the right triangle , the value οf x is 51.7°.

The functiοns οf an angle in a triangle are knοwn as trigοnοmetric functiοns, cοmmοnly referred tο as circular functiοns. In οther wοrds, these trig functiοns prοvide the relatiοnship between a triangle's angles and sides. There are five fundamental trigοnοmetric functiοns: sine, cοsine, tangent, cοtangent, secant, and cοsecant.

Here in the given right angle PQ=3.1 , PR=5 .

Nοw using trigοnοmetric functiοn,

=> cos(P) = \(\frac{adjacent}{hypotenuse}\)

=> cos (x) = \(\frac{PQ}{PR}\)

=> cos (x) = \(\frac{3.1}{5}\)

=> x = \(cos^{-1}\frac{3.1}{5}\)

=> x = 51.7°.

Hence the value of x is 51.7°.

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Answer:

3/2

Step-by-step explanation:

Answer:

\(\large\boxed{\tt x = 2}\)

Step-by-step explanation:

\(\textsf{We are asked to solve for x in the given equation.}\)

\(\textsf{We should know that x is cubed, meaning that it's multiplied by itself 3 times.}\)

\(\textsf{We should isolate x on the left side of the equation, then find x by cubic rooting}\)

\(\textsf{both sides of the equation.}\)

\(\large\underline{\textsf{How is this possible?}}\)

\(\textsf{To isolate variables, we use Properties of Equality to prove that expressions}\)

\(\textsf{are still equal once a constant has changed both sides of the equation. A Cubic}\)

\(\textsf{Root is exactly like a square root, but it's square rooting the term twice instead}\)

\(\textsf{of once.}\)

\(\large\underline{\textsf{For our problem;}}\)

\(\textsf{We should use the Subtraction Property of Equality to isolate x, then cubic root}\)

\(\textsf{both sides of the equation.}\)

\(\large\underline{\textsf{Solving;}}\)

\(\textsf{Subtract 1 from both sides of the equation keeping in mind the Subtraction}\)

\(\textsf{Property of Equality;}/tex]

\(\tt \not{1} - \not{1} - x^{3} = 9 - 1\)

\(\tt - x^{3} = 8\)

\(\textsf{Because x}^{3} \ \textsf{is negative, we should exponentiate both sides of the equation by}\)

\(\textsf{the reciprocal of 3, which is} \ \tt \frac{1}{3} .\)

\(\tt (- x^{3})^{\frac{1}{3}} = 8^{\frac{1}{3}}\)

\(\underline{\textsf{Evaluate;}}\)

\(\tt (- x^{3})^{\frac{1}{3}} \rightarrow -x^{3 \times \frac{1}{3} } \rightarrow \boxed{\tt -x}\)

\(\textsf{*Note;}\)

\(\boxed{\tt A^{\frac{1}{C}} = \sqrt[\tt C]{\tt A}}\)

\(\tt 8^{\frac{1}{3}} \rightarrow \sqrt[3]{8} \rightarrow 2^{1} \rightarrow \boxed{\tt 2}\)

\(\underline{\textsf{We should have;}}\)

\(\tt -x=2\)

\(\textsf{Use the Division Property of Equality to divide each side of the equation by -1;}\)

\(\large\boxed{\tt x = 2}\)

Ignatius of Loyola, the Spanish priest and theologian who founded the Society of Jesus (Jesuits) in the 16th century, focused on several key issues during the period of the Counter-Reformation.

These issues can be broadly categorized into spiritual, educational, and institutional reforms.

Spiritual Reforms: Ignatius emphasized the importance of personal piety and spiritual discipline. He promoted the practice of spiritual exercises, including meditation, prayer, and self-examination, to cultivate a deep and intimate relationship with God. Ignatius encouraged individuals to reflect on their sins and seek forgiveness through confession and penance.

Educational Reforms: Ignatius recognized the power of education in shaping individuals and society. He established schools and universities to provide a comprehensive education that combined intellectual rigor with spiritual formation. The Jesuits placed great emphasis on academic excellence, encouraging critical thinking, the pursuit of knowledge, and the integration of faith and reason.

Pastoral Reforms: Ignatius focused on improving the quality of pastoral care and religious instruction. He trained his followers to be skilled preachers and spiritual directors, equipping them to guide and support individuals in their spiritual journey. Ignatius also emphasized the importance of catechesis, ensuring that people received proper religious education and understood the teachings of the Catholic Church.

Missionary Work: Ignatius and the Jesuits had a strong missionary zeal. They undertook extensive missionary endeavors, particularly in newly discovered territories during the Age of Exploration. They sought to bring Christianity to non-Christian lands and convert indigenous populations to Catholicism. The Jesuits established missions, schools, and hospitals in various parts of the world, playing a significant role in spreading Catholicism.

Overall, Ignatius of Loyola's reforms aimed to strengthen and revitalize the Catholic Church in response to the challenges posed by the Protestant Reformation. His focus on personal spirituality, education, pastoral care, and missionary work contributed to the renewal and expansion of the Catholic Church during the Counter-Reformation.

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Answer:

Step-by-step explanation:

Answer:

5%

Step-by-step explanation:

he earned 50 so his investment grew from 1000 to 1050

now simply calculate the percentage change

(1050-1000)/1000 *100

=5%

Answer:

yes it she is

Step-by-step explanation:

Answer:

The argument of the logarithmic function should be greater than zero.

Thus, for y = log(-x + 3) - 1 to be real-valued, we need:

-x + 3 > 0

or

x < 3

So, the domain of the function is all real numbers less than 3.

To find the range, let's consider the behavior of the logarithmic function.

As x approaches 3 from the left, the argument of the logarithm approaches zero from the negative side, which means the logarithm approaches negative infinity.

As x approaches negative infinity, the argument of the logarithm becomes very large and negative, which means the logarithm approaches negative infinity.

Therefore, the range of the function y = log(-x + 3) - 1 is all real numbers.

Step-by-step explanation:

Answer: P

Step-by-step explanation:

Answer:

Function B > Function A > Function C

Step-by-step explanation:

For function A,

From the given table,

Two points are (3, 3) and (5, 7).

Rate of change of the function between these points = \(\frac{y_2-y_1}{x_2-x_1}\)

                                                                                         = \(\frac{7-3}{5-3}\)

                                                                                         = 2

For function B,

Rate of change = \(\frac{\triangle y}{\triangle x}\)

Here, Δy = y-intercept = 3

And Δx = x-intercept = -5

Therefore, rate of change = \(\frac{3}{-5}\)

                                            = -0.6

For function C,

Equation of the line → y = 3x + 1

By comparing this equation with slope-intercept form of the equation,

y = mx + b

Slope of the line = m = 3

Rate of change = 3

Now we can write the rate of changes of each function from least to greatest.

-0.6 > 2 > 3

Function B > Function A > Function C

Answer:

see below

Step-by-step explanation:

From the graph the slope is -1 and the y-intercept is 9. Therefore we can use slope-intercept form (y = mx + b) which will be y = -x + 9.

Answer:

x=17

Step-by-step explanation:

ok

The third choice is the correct.

If a quadrilateral is a parallelogram then opposite sides are parallel.

Answer:

y = x - 10, y = x, y = x + 1, y = x - 37,654,356, which are just a few examples

Step-by-step explanation:

There are infinite solutions to this, but one of them is y = x - 10. Just change the y-intercept in this equation, then you can see that the lines never touch, and are parallel, which is what we want.

Answer:

Divide your interest rate by the number of payments you'll make in the year (interest rates are expressed annually). ...

Multiply it by the balance of your loan, which for the first payment, will be your whole principal amount.

Step-by-step explanation:

Divide your interest rate by the number of payments you'll make in the year (interest rates are expressed annually). ...

Multiply it by the balance of your loan, which for the first payment, will be your whole principal amount.Divide your interest rate by the number of payments you'll make in the year (interest rates are expressed annually). ...

Multiply it by the balance of your loan, which for the first payment, will be your whole principal amount.Divide your interest rate by the number of payments you'll make in the year (interest rates are expressed annually). ...

Multiply it by the balance of your loan, which for the first payment, will be your whole principal amount.Divide your interest rate by the number of payments you'll make in the year (interest rates are expressed annually). ...

Multiply it by the balance of your loan, which for the first payment, will be your whole principal amount.Divide your interest rate by the number of payments you'll make in the year (interest rates are expressed annually). ...

Multiply it by the balance of your loan, which for the first payment, will be your whole principal amount.

Answer:

y=720

Step-by-step explanation:

Multiply both sides of the equation by −15.

−675+1y=45

Add 675 to both sides.

1y=45+675

1y=720

--   -----

1      1

y=720

Answer:

point-slope form, standard form, and slope-intercept form

Step-by-step explanation:

The three main types of linear functions are: point-slope form, standard form, and slope-intercept form.

Here is an image with each form

Answer:

\(x + 2 = - 3x\)

\( - 4x = 2\)

\(x = - \frac{1}{2} \)

\( - 3( - \frac{1}{2} ) = \frac{3}{2} = 1 \frac{1}{2} \)

So the lines intersect at (-1/2, 1 1/2), or

(-.5, 1.5).

Answer:

\(y = 2x^2 + 1\)

Step-by-step explanation:

The graph you see there is called a parabola. The general equation for the graph is as below

\(y = a*x^2 + b\)

To find the equation we need to find the constants a and b. The constant b is just how much we're lifting the parabola by. Notice it's lifted by 1 on the y axis.

To find a it's a little more tricky. Let's use the graph to find a value for a by plugging in values we know. We know that b is 1 from the previous step, and we know that when x=1, y=3. Let's use that!

\(3 = a * (1)^2 + 1\\2 = a\)

Awesome, we've found both values. And we can write the result.

\(y = 2x^2 + 1\)

I'll include a plotted graph with our equation just so you can verify it is indeed the same.