For the sample size and confidence interval, which of the following Excel functions will find the value of Student's t ? n= 16 and 92% confidence. =t inv .2t(0.08,16) =t.inv.2t(0.08,15) =t.inv.2t(0.04,15) =t inv .2t(0.04,16) θ

based on the principle of mathematical induction, we conclude that \(2^{n}\) > \(n^{2}\) for all n greater than 4.

By using mathematical induction, we can prove that \(2^{n}\) > \(n^{2}\) for all n greater than 4.

Base case (n = 5):

When n = 5, we have \(2^{5}\) = 32 and \(5^{2}\) = 25. Since 32 is indeed greater than 25, the inequality holds for n = 5.

Inductive step:

Assuming the inequality holds for some positive integer k: \(2^{k}\) > \(k^{2}\), we need to show that it also holds for k + 1: \(2^{(k+1) }\) > \((k+1)^{2}\)

Starting with the left-hand side:

\(2^{(k+1) }\) = 2 × \(2^{k}\)

Using the inductive assumption, we can rewrite it as:

\(2^{(k+1) }\) > 2 ×\(k^{2}\)

Now let's consider the right-hand side:

\((k+1)^{2}\) = \(k^{2}\) + 2k + 1

We want to show that 2 × \(k^{2}\) > \(k^{2}\) + 2k + 1.

Simplifying the inequality, we have:

\(k^{2}\) - 2k - 1 > 0

By analyzing the quadratic function f(k) = \(k^{2}\) - 2k - 1, we find that it is positive for all k greater than 4.

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Answer:

C.  \(f(x)=(x+1)^2-4\)

Step-by-step explanation:

A. the graph is a straight line with slope 1.  It goes up/down infinitely far so the range is all real numbers.  Not A!

B. The graph is a straight line with slope -4, so, like the function in A, the range is all real numbers.  Not B!

D. The graph is an absolute value function  y = |x|, reflected over the x-axis, shifted right 3 units, then shifted down 4 units.  So the graph starts witha "vee" shape opening up, becomes a vee opening down, then ultimately gets shifted down 4 units.  The range is all real numbers less than or equal to -4.

See the attached graphs.  image2 is the function in answer choice D.

Answer:

True

Step-by-step explanation:

When displaying any sort of data, it is important to make the table or chart as easy to understand and read as possible without compromising the data. In this case, it is simpler to understand the pie chart if we use as few slices as possible that still makes sense for displaying the data set.

Alex has $15.78 and Rick has $12.15 money.

According to the question,

We have the following information:

Alex had $3.63 more than Rick. Together they had $27.93.

Let's take the money Rick has to be $x.

Now, we have the following expression for the money Alex has:

3.63+x

Now, we have:

x+3.63+x = 27.93

2x+3.63 = 27.93

Subtracting 3.63 from both the sides:

2x = 27.93-3.63

2x = 24.3

Dividing by 2 on both the sides:

x = 24.3/2

x = $12.15

So, Rick has $12.15.

Now, the money Alex has:

3.63+12.15

$15.78

Hence, Alex has $15.78 and Rick has $12.15 money.

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Refer to the attachment for figure:

The height of the rectangle = 11 inches

What is rectangle?

A rectangle is a type of quadrilateral with parallel sides equal to each other and four equal 90-degree vertices. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

Let x= height

Width becomes x+49

Diagonal BD=61 inches

By pythagoras theorem,

BD²=BC²+CD²

61²= (x+49)²+x²

3721=x²+98x+2401+x²

On simplification,

x²+49x-660=0

Find the factors

(x+60)(x-11)=0

x=-60, x=11

Consider positive value for height

height = 11 inches

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Using technology, the correlation coefficient is 0.997

We should know that correlation coefficient is a statistical model which is used to determine or measure the relationship between two variables.

The table is

                            x               y              x²            y²             xy

                          8              22             64          484            176

                         12              23            144          529            276

                         18             26             324         676           468

                         24             30            567         900         720

                          30           32              900        1024         960

                        32              33              1024     1089         1056

                         35             35             1225       1225         1225

                          37             36            1369        1369         1332

                          40             38           1600         1444         1520

    Total          236           275          7226         8740        7733

\(r= \frac{nExy)-(Ex)(Ey)}{\sqrt{[n(EX^{2}][nEy^{2}(Ey)^{2} } }\)

applying the figures from the table we have

r=\(\frac{9*7733-(236)(275)}{\sqrt{[9*7226-55696][9*8740-75625]} }\)

Simplifying the expression we have

r=\(\frac{4697}{\sqrt{28340830} }\)

r=0.88

r=0.9 approximately

Therefore the correct answer is 0.997 which is the correlation coefficient.

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Answer:

The values of a,b and c are 1, -3 and -2 respectively.

Step-by-step explanation:

The general form of quadratic equation is given by :

\(ax^2+bx+c=0\) .....(1)

Here, a,b and c are constants

The given equation is :

\(x^2-3x-2=0\)

We can also write the above equation as :

\(x^2+(-3x)+(-2)=0\) ....(2)

If we compare equation (1) and (2), we get :

a = 1

b = -3 and

c = -2

So, the values of a,b and c are 1, -3 and -2 respectively.

Answer:

i think its option B

Step-by-step explanation:

i dont know if its right or not sorry but hope this helps :)

Contour maps are a way to depict functions with a two-dimensional input and a one-dimensional output. By creating a topographical map of the graph of function z = f(x, y), the contour map is displayed below:

Given, \(f(x, y)=x^{3} -y\)

Now for several level curves, we take \(f(x, y) = constant =c\)

So we have, \(x^{3}-y =c\)

Now, varying the value of c we get the several level curves,

By taking the values of c as \(0, \pm0.5, \pm1, \pm2\) etc.

Now sketching for c = 0,

We have \(x^{3}-y=0 \ or\ y=x^{2}\)

Checking for Points :

Repeating the similar process for \(c=\pm 0.5, \pm1, \pm2\) etc.

We get the following contours.

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Answer:

48 flowers

Step-by-step explanation:

Since, the ratio of tulips to daisies are the same.

Hence, if we have x number of daisies, then the number of tulips will also be x.

Therefore, with number of tulips being 21 and equal ratio of daisies will also mean that Anna has 21 daisies .

The total number of flowers will be :

Number of tulips + Number of daisies

21 + 21 = 42 flowers

Divide the principal by the time, interest rate, and time period to calculate simple interest.Annual interest rate is 0.02.

Divide the principal by the time, interest rate, and time period to calculate simple interest.The equation is expressed as "Simple Interest = Principal x Interest Rate x Time."It is easiest to calculate interest using this equation.

I, or the interest earned or charged on a loan, can be calculated using the straightforward interest formula.

I = Prt, where P is the principal, r is the yearly interest rate stated in decimal form, and t is the loan term expressed in years, gives the amount of interest.

It is necessary to transform the rate r from percentage to decimal form.

Then, 2,000 = 1,000 * r * 10 ;

Finally, r = 2 ÷ 10 = 20 ÷ 100 = 0.02

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By the vertex form of the parabola, the equation of the parabola shown in the diagram is equal to the quadratic equation y - 1 = (2/3) · (x - 3)².

Parabolae are represented mathematically by second order polynomials, which can be described either in standard form or in vertex form. In accordance to the picture, we have a parabola with a vertical axis of symmetry. The formula in vertex form is described by this expression:

y - k = C · (x - h)²

Where:

Please notice that vertices represent the absolute extreme of the parabola. We can determine the equation by knowing the vertex and another point. Let be (h, k) = (3, 1) and (x, y) = (0, 7), then we find that the vertex constant is:

7 - 1 = C · (0 - 3)²

6 = 9 · C

C = 2/3

By the vertex form of the parabola, the equation of the parabola shown in the diagram is equal to the quadratic equation y - 1 = (2/3) · (x - 3)².

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The fraction of coefficient factor out is 3/8.

What is Fraction?
A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals. The numerator and denominator of positive common fractions are natural numbers.

The given expression is , 3/8d+3/4

From this, we have to eliminate the fraction for that we have to make common denominators like that,3/8 d + (3 * 2) / (4 * 2)=> 3/8 d + 6/8

Next, take out the common value i.e, 3/8=> 3/8 ( d + 2)

Therefore, the coefficient factor out is 3/8.

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The percent decrease for the given numbers is 25%.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

Given that,

The number is decreasing from 40 to 30.

The difference is 40 - 30 = 10.

The percent decrease can be found by multiplying the ratio of the difference to the initial value by 100 as follows,

Percent decrease = 10/40 × 100

                              = 25%

Hence, the percent decrease from 40 to 30 is 25%.

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The correct answer is up until now, you have gained 18,963,816 coins.

Initially, you were gaining 5 coins per minute. After 4 hours, the rate increased by 1 coin per minute, so you were gaining 6 coins per minute.

To calculate the number of coins gained, we need to convert the given time of 52674 hours to minutes. There are 60 minutes in an hour, so:

52674 hours * 60 minutes/hour = 3,160,440 minutes

Now we can calculate the number of coins gained:

For the first 4 hours:

4 hours * 60 minutes/hour * 5 coins/minute = 1,200 coins

For the remaining time:

(3,160,440 minutes - 4 hours * 60 minutes/hour) * 6 coins/minute = 18,962,616 coins

Adding the coins gained during the initial 4 hours to the coins gained during the remaining time:

1,200 coins + 18,962,616 coins = 18,963,816 coins

Therefore, up until now, you have gained 18,963,816 coins.

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The Answer:the answer is D

Step-by-step explanation:

The solutions in radical form is

This is of the form

(3 ± √7)²

Then we have to write this in two cases such that

Case 1: (3 + √7)²

Case 2: (3 - √7)²

Solve the first case

(3 + √7)²

(3 + √7)(3 + √7)

= 3² + 2(3)(√7) + (√7)² =

9 + 6√7 + 7

= 16 + 6√7

Next we have to solve for case 2

(3 - √7)²

(3 - √7)(3 - √7)

= 3² - 2(3)(√7) + (√7)²

= 9 - 6√7 + 7

= 16 - 6√7

The values and solutions would be:

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\( \qquad \qquad \huge \underline{\boxed{ \sf {Answer}}}\)

Let's solve ~

The given equations are :

\( \qquad \dashrightarrow \bf \: 3x + 4y = 36 \sf \: \: \: \: \: \: \: \: \: \: (1)\)

and

\( \qquad \dashrightarrow \sf \:y = - \frac{1}{2} x + 8\)

[ multiply each sides by 2 ]

\( \qquad \dashrightarrow \sf \: 2y = - x + 16\)

\( \qquad \dashrightarrow \sf \:x + 2y = 16\)

[ multiply both sides by 2 ]

\( \qquad \dashrightarrow \bf \: 2x + 4y = 32 \: \: \: \: \: \: \: \: \: \: \: \sf(2)\)

Now, subtract equation (2) from (1)

\( \qquad \dashrightarrow \sf \: 3x + 4y - (2x + 4y) = 36 - 32\)

\( \qquad \dashrightarrow \sf \: 3x + \cancel{4y }- 2x - \cancel{4y }= 4\)

\( \qquad \dashrightarrow \bf \: x = 4\)

Now, as we got the value of x, let's solve for y :

\( \qquad \dashrightarrow \sf \: y = - \dfrac{1}{2} x+ 8\)

\( \qquad \dashrightarrow \sf \: y = -\dfrac{1}{2} (4)+8\)

\( \qquad \dashrightarrow \sf \: y = - 2 + 8\)

\( \qquad \dashrightarrow \bf \: y = 6\)

Polynomials are algebraic expressions consisting of terms that include real numbers, variables, and positive integer exponents. Each term in a polynomial has a variable raised to a non-negative integer power, and the coefficient of each term is a real number. Polynomials are classified by the degree of their highest power. If two or more terms in a polynomial have the same variable raised to the same power, they can be combined into a single term.

1. -x² + x - x² + 1

Combine like terms: -x² + x - x² + 1 = -2x² + x + 1

This polynomial has degree 2 because the highest power of the variable is 2.

2. x² + x + 2x³ - x

Rearrange terms: 2x³ + x² + x - x = 2x³ + x²

This polynomial has degree 3 because the highest power of the variable is 3.

3. 4x + x + x - 2

Combine like terms: 4x + x + x - 2 = 6x - 2

This polynomial has degree 1 because the highest power of the variable is 1.

4. 3x² + 4 - 3x² - 1

Combine like terms: 3x² - 3x² + 4 - 1 = 3

This polynomial has degree 0 because there is no variable term.

Therefore, the four given polynomials have degrees 2, 3, 1, and 0, respectively.

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By using recursion, the function can keep track of the number of sit-ups for each day, allowing Fatoumata to easily determine the number of sit-ups she needs to do on any given day.

To represent Fatoumata's daily exercise routine using recursion, we can define a recursive function that calculates the number of sit-ups she will do on a given day. Let's call this function "sit-ups".

The base case of the recursive function is when the day is equal to 1. In this case, the function should return the initial number of sit-ups, which is 5. For the recursive case, the function should return the sum of the sit-ups on the previous day plus 3. This can be represented as:
sit-ups (day) = sit-ups (day - 1) + 3
To summarize:
- Base case: sit-ups (1) = 5
- Recursive case: sit-ups(day) = sit-ups (day - 1) + 3
Therefore, the recursive function to represent Fatoumata's daily exercise routine is:
def sit-ups(day):
   if day == 1:
       return 5
   else:
       return sit-ups (day - 1) + 3
The recursive function "sit-ups" represents Fatoumata's daily exercise routine of doing sit-ups. It calculates the number of sit-ups she will do on a given day based on the number of sit-ups she did on the previous day. In the base case, which is when the day is equal to 1, the function returns the initial number of sit-ups, which is 5.

This is the starting point for Fatoumata's routine. In the recursive case, the function calculates the number of sit-ups on the current day by adding 3 to the number of sit-ups on the previous day. This means that each day after the first day, Fatoumata will do 3 more sit-ups than the day before. By using recursion, the function can keep track of the number of sit-ups for each day, allowing Fatoumata to easily determine the number of sit-ups she needs to do on any given day.

The recursive function "sitUps" accurately represents Fatoumata's daily exercise routine of doing sit-ups. By using this function, Fatoumata can easily determine the number of sit-ups she needs to do on any day, starting from 5 sit-ups on the first day and increasing by 3 sit-ups each subsequent day.

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Step-by-step explanation:

999.99 × x% = 299.99

999.99÷100 × x = 299.99

9.9999 × x = 299.99

9.9999x = 299.99

D.B.S by 9.9999 to make x the subject

9.9999x÷9.9999 = 299.99÷9.9999

x=29.999299993

To the nearest tenth of a percent, x=30

Therefore, x = 30%

The equation for the line in point-(1, 1) is y = -0.5x + 0.5.

Given that the slope of the line below is -0.5. We are to enter the equation for the line in point-(1, 1).The equation for the slope-intercept form of the line is y = mx + c where m is the slope and c is the y-intercept.

Now, the slope of the line is given as -0.5.Therefore, the equation for the slope-intercept form of the line is y = -0.5x + c. Now we need to find the value of c for the equation of the line.

To find the value of c, substitute the values of x and y in the equation of the slope-intercept form of the line.

Given that the point is (-1,1), x=-1 and y=1y = -0.5x + c⇒ 1 = (-0.5) (-1) + c⇒ 1 = 0.5 + c⇒ c = 1 - 0.5⇒ c = 0.5

Therefore, the equation for the line in point-(1, 1) is y = -0.5x + 0.5.The slope of a line refers to how steep the line is and is used to describe its direction. Slope is defined as the vertical change between two points divided by the horizontal change between them.A positive slope moves up and to the right, while a negative slope moves down and to the right. If a line has a slope of zero, it is said to be a horizontal line.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept, or the point at which the line crosses the y-axis. To find the equation of a line with a given slope and a point, we can use the point-slope form of a linear equation.

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\( \qquad \qquad\huge \color{blue}{ \boxed{{ \colorbox{black}{ \underline{ \: \: \: \: \: \: \: \: ANSWER\: \: \: \: \: \: \: \: }}}}} \)

the polynomial 2a +3b -2 is also called a TRINOMIAL

What is TRINOMIAL?

ln elementary algebra,a trinomial is a polynomial consisting of three terms or monomials.

68 = Diane's score x 4

Equation

68= 4d

___________________

Can you see the updates?

_________________

Diane's score

4d= 68

d= 17

Answer:

Twenty Seven (27) cubic yards

Answer:

volume =27 cubic yards

Step-by-step explanation:

Volume = Base Area x Height

Volume= 3·3·3

Volume= 27

Answer: After 5 bags of mulch, the cost for both companies will be the same.

Step-by-step explanation:

The cost for Company can be represented by the equation: y= 10m+100

The cost for Company B can be represented by the equation: y= 30m

To find the amount of mulch, their cost needs to be the same, I will solve for m

10m+100=30m

-10m 10m

100=20m

Divide both side by 20

100/20=20m/20

5=m or m=5

So after 5 bags of mulch, the total cost for both companies is the same.

Answer:

No,

Step-by-step explanation:

X^-2 is equal to 1/X^2. so any number or letter to negative power, is the same as 1 divided by that number or letter to the positive power..(power remains with denominator

Answer: 83r^2 - 59 + 60

Step-by-step explanation:

R^2 - 59R - 82r^2 + 60

= 83r^2 - 59 + 60

Answer:

3 is first

4 is second

1 is third

2 is fourth

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

it helps keep the insulation in so their feet get cold