Scores on a statistics final in a large class were normally distributed with a mean of 79 and a standard deviation of 12. Use the TI-84 PLUS calculator to answer the following. Round the answers to at least two decimals. (a) Find the 36th percentile of the scores. (b) Find the 70th percentile of the scores. (c) The instructor wants to give an A to the students whose scores were in the top 12% of the class. What is the minimum score needed to get an A

Answers

Answer 1

Answer:

a) The 36th percentile of the scores is of 74.68.

b) The 70th percentile of scores is 85.3.

c) The minimum score needed to get an A is 93.1.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 79 and a standard deviation of 12.

This means that [tex]\mu = 79, \sigma = 12[/tex]

(a) Find the 36th percentile of the scores.

This is X when Z has a pvalue of 0.36. So X when Z = -0.36.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.36 = \frac{X - 79}{12}[/tex]

[tex]X - 79 = -0.36*12[/tex]

[tex]X = 74.68[/tex]

The 36th percentile of the scores is of 74.68.

(b) Find the 70th percentile of the scores.

This is X when Z has a pvalue of 0.7, so X when Z = 0.525.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.525 = \frac{X - 79}{12}[/tex]

[tex]X - 79 = 0.525*12[/tex]

[tex]X = 85.3[/tex]

The 70th percentile of scores is 85.3.

(c) The instructor wants to give an A to the students whose scores were in the top 12% of the class. What is the minimum score needed to get an A?

The 100 - 12 = 88th percentile, which is X when Z has a pvalue of 0.88, so X when Z = 1.175.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.175 = \frac{X - 79}{12}[/tex]

[tex]X - 79 = 1.175*12[/tex]

[tex]X = 93.1[/tex]

The minimum score needed to get an A is 93.1.


Related Questions

The following expressions (-9a3b2 + 13ab5) and (-10ab5 + 12a3b2) represents the length and width of the pizza box respectfully. Find the perimeter of the pizza box. Express the perimeter of the pizza box in the order of descending exponents of a. Please use the palette below to input your answer.

Answers

The perimeter of the box has been obtained as 6a^3b^2 + 6ab^5.

What is the perimeter of the box?

We know that a box has the shape of a rectangle thus we would have to apply the formula for the area of a rectangle in this case and we would have;

P = 2(l + b)

P = perimeter

l =length

b = breadth

Then we have;

2[(-9a^3b^2 + 13ab^5) + (-10ab^5 + 12a^3b^2)]

Collect the like terms

2[(-9a^3b^2) + 12a^3b^2 + 13ab^5 +(-10ab^5)]

2[3a^3b^2 + 3 ab^5]

6a^3b^2 + 6ab^5

In  order of descending exponents of a, the perimeter is 6a^3b^2 + 6ab^5.

Learn more about perimeter:https://brainly.com/question/6465134

#SPJ1

Caroline baked cookies from a recipe that called for 3/4 cups of sugar she planned to triple the recipe how much sugar did she need?

Answers

The amount of sugar needed for the recipe to be tripled is 9 / 4 cups.

How to find the amount of sugar needed?

Caroline baked cookies from a recipe that called for 3/4 cups of sugar. she planned to triple the recipe. Therefore, the amount of sugar she needs is calculated as follows:

1 recipe = 3 / 4 cups of sugar

She wants to triple the recipe.

Hence,

1 recipe = 3 / 4 cups of sugar

3 recipe = ?

cross multiply

amount of sugar needed = 3 / 4 × 3

amount of sugar needed = 9 / 4

amount of sugar needed = 9 / 4 cups of sugars

learn more on cups here: https://brainly.com/question/7421436

#SPJ1

Student grades on a chemistry exam were: 77, 78, 75, 81, 89, 53; 79, 82, 84; 91 a. Select the stem-and-leaf plot of the data. Stem Leaf 5 3 6 7 5 7 8 9
8 1 2 4 9 9 1 Stem Leaf 50 53 60 70 75 77 78 79 80 81 82 84 89 90 91 Stem Leaf 5 53 6
7 77 78 75 79 8 81 89 82 84 9 91 Stem Leaf 5 3 6 7 7859 8 1924 9 1

Answers

The correct stem-and-leaf plot for the data is:

i. Stem: 5,6,7,8,9 Leaf: 3, , 5 7 8 9, 1 2 4 9, 1

This plot shows the distribution of the data values, with the stems representing the tens place and the leaves representing the ones place. For example, the value 53 is represented by the stem 5 and the leaf 3, and the value 82 is represented by the stem 8 and the leaf 2.

The other three stem-and-leaf plots are incorrect because they do not accurately represent the distribution of the data.

A stem-and-leaf plot is a graphical representation of data that shows the distribution of values. The stems represent the tens place and the leaves represent the ones place. It is useful for identifying patterns and trends in the data.

Read more about stem-and-leaf plots here:

https://brainly.com/question/8649311

#SPJ4

let days-on-the-market be the dependent variable and price be the independent variable. b-1. determine the regression equation

Answers

To determine the regression equation, we need to fit a line to the data that best describes the relationship between the dependent variable and the independent variable. The equation of the line is typically expressed in the form:

y = a + bx

where y is the dependent variable, x is the independent variable, a is the y-intercept (the point at which the line crosses the y-axis), and b is the slope of the line (the rate of change of y with respect to x).

If we determine that a = 10 and b = 0.5, the regression equation would be:

Days-on-the-market = 10 + 0.5 * price

This equation describes the relationship between the dependent variable (days-on-the-market) and the independent variable (price). It tells us that for every unit increase in price, the number of days on the market is expected to increase by 0.5.

Learn more Regression equation here:

https://brainly.com/question/26843436

#SPJ4

Which of the following are factor pairs for 54?select all that apply.

Answers

Answer:

The Pair Factors of 54 are (1, 54), (2, 27), (3, 18), and (6, 9) and its Prime Factors are 1, 2, 3, 6, 9, 18, 27, 54.

Step-by-step explanation:

hope this helped:)

brainliest for the brains........................

The Pair Factors of 54 are (1, 54), (2, 27), (3, 18), and (6, 9) and its Prime Factors are 1, 2, 3, 6, 9, 18, 27, 54.

Here, we have,

The factors of 54 are the numbers, that can divide 54 completely or evenly. When a pair of factors are multiplied together to produce the 54, then they are said to be pair factors. The factors divide the number completely. Hence, these factors cannot be a fraction.

Factors of 54: 1,2,3,6,9,18,27 and 54

Factor pairs of the number 54 are the whole numbers which are not a fraction or decimal number.

To find the factors of a number, 54, we will use the factorization method.

To find factors of 54, we have to divide 54 by all natural numbers from 1 to 54.

54 ÷ 1 = 54

54 ÷ 2 = 27

54 ÷ 3 = 18

54 ÷ 6 = 9

To learn more on division click:

brainly.com/question/21416852

#SPJ6

II. Given that cos A = 0.42 and sin B = 0.73, evaluate
i. sin (A – B)
ii. cos (A – B)
iii. tan (A + B)

Answers

The trigonometric identities values are;

i. sin (A – B) = -0.15

ii. cos (A – B) = 0.5368

iii. tan (A + B) = -3.536

How to solve trigonometric Identity?

We are given;

cos A = 0.42

sin B = 0.73

Since cos A = 0.42 , then sin A = 0.58

Since sin B = 0.73, then cos B = 0.27

i) sin (A – B)

By trigonometric identities, we know that;

sin (A – B) = sinA cos B - cosA sinB

Thus;

sin (A – B) = (0.58 * 0.27) - (0.42 * 0.73)

sin (A – B) = -0.15

ii)  cos (A – B)

By trigonometric identities, we know that;

cos (A – B) = cosA cosB + sinA sinB

cos (A – B) = (0.42 * 0.27) + (0.58 * 0.73)

cos (A – B) = 0.5368

iii) tan (A + B)

By trigonometric identities, we know that;
(tan A + tan B)/(1 - tanAtanB)

tan A = sinA/cosA = 0.58/0.42 = 1.389

tan B = sinB/cosB = 0.73/0.58 = 1.259

Thus;

tan (A + B) = (1.389 + 1.259)/(1 - (1.389 * 1.259))

tan (A + B) = -3.536

Read more about Trigonometric identity at; https://brainly.com/question/7331447

#SPJ1

Mr. Muehlenweg S class used 1 3/4 cups baking soda for an experiment. If his students performed the experiment 6 1/2 times, how much baking soda did they use?

Answers

Mr. Muehlenweg S class used 1 3/4 cups baking soda for an experiment. If his students performed the experiment 6 1/2 times, he used 19/4 baking soda.

Define subtraction.

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference.

Given,

Mr. Muehlenweg S class used 1 3/4 cups baking soda for an experiment.

Converting mixed fraction to improper function

1 3/4 = 7/4

If his students performed the experiment 6 1/2 times,

Converting mixed fraction to improper function

6 1/2 = 13/2

Subtracting,

7/4 - 13/2

7/4 - 26/4

19/4

Mr. Muehlenweg S class used 1 3/4 cups baking soda for an experiment. If his students performed the experiment 6 1/2 times, he used 19/4 baking soda.

To learn more about subtraction, visit:

https://brainly.com/question/28734654

#SPJ1

Leia is setting up 417 toy cars. Each car needs 3 batteries to drive.
How many batteries does Leia need for her cars?

Answers

Answer:

Leia needs 3 * 417 = <<3*417=1251>>1251 batteries for her cars.

Step-by-step explanation:

To find out how many batteries Leia needs for her cars, we need to multiply the number of toy cars by the number of batteries needed for each car. Since each car needs 3 batteries and Leia has 417 toy cars, the total number of batteries she needs is 3 * 417 = 1251.

In order to add
3/4 and 7/10
you need to find equivalent fractions that have the same denominators. What is a common denominator?

Answers

Thus ,after adding  3/4 and 7/10  we get 29/20 where 20 is common denominator

Describe the common denominator.

The smallest common multiple among the denominators of a group of fractions is known as the lowest common denominator (least common denominator) in mathematics. Fraction comparison, addition, and subtraction are made easier.

Here,

In order to add 3/4 and 7/10

we have to find LCM of 4 and 10

which comes out to be = 20

Thus,

addding =>  15+`14 /20

=>29/20

Thus ,after adding  3/4 and 7/10  we get 29/20 where 20 is common denominator

To know more about  common denominator , visit

https://brainly.com/question/28843174

#SPJ1

segments in circles maze

Answers

Answer:

  x = 6

Step-by-step explanation:

You want to know the value of x given a tangent to a circle from an external point has length x, while a secant from that point has length x-2 to the first intersection with the circle, and an additional 5 to the second intersection.

Secant/Tangent relation

The product of the segments of the secant to the two points of intersection with the circle is equal to the square of the tangent segment.

  (x -2)(x -2 +5) = (x)² . . . . . use given values

  x² +x -6 = x² . . . . . . simplify

  x -6 = 0 . . . . . . subtract x²

  x = 6 . . . . . . add 6

__

Additional comment

There are rules for two secants, for a tangent and secant (as here), and for two chords internal to the circle. These can be easier to remember if you generalize them to a single rule: the product of the distance from the common point to the first circle intersection and the distance to the second circle intersection is the same for each segment.

For a tangent, the two circle intersections are the same point, hence the distance is squared. For chords, the two circle intersections are at the ends of the chords, and the common point is where the chords cross.

If a train is accelerating at 30m/s after it takes off from the train station and travels for 60 seconds, what was its final velocity?

Answers

The final velocity of the train is 30m/s.

What is acceleration?

The rate at which an object's velocity with respect to time changes is referred to as acceleration. When an object's velocity changes, it is said to have or be accelerating.

The rate of change in velocity over time is another name for acceleration. The magnitude of an acceleration vector indicates how much the velocity will change, while the vector's direction indicates how the velocity will change—whether the speed is rising or falling, the vector's direction is changing, or some combination of the three.

Given, initial velocity = 0 m/s (as the train starts from rest)

          time = 60 seconds

Acceleration = v - u / t = 30 - 0/ 60 =0.5 m/s square

We know,

v = u + at

v = 0 + (0.5 x 60)v = 30 m/s

To learn more about velocity visit the link given below

brainly.com/question/18084516

#SPJ1

If x + 3y^(1/3) = y what is dy/dx at the point (2,8)

Answers

The dy/dx at point (2,8) is 4/3

How to find dy/dx at a point?

From the information illustrated, x + 3y^(1/3) = y and point (2,8)

Find the derivative of this equation with respect to x and solve for dy/dx:

x + 3y^(1/3) = y

1 + [3 × 1/3 × y^(-2/3)]dy/dx = dy/dx

1 + [y^(-2/3)]dy/dx = dy/dx

dy/dx -  [y^(-2/3)]dy/dx = 1

dy/dx [1-  y^(-2/3)] = 1

dy/dx = 1/ [1 - y^(-2/3)]

At point (2,8), x = 2 and y = 8.

Substitute into dy/dx:

dy/dx = 1/ [1 - y^(-2/3)]

dy/dx = 1/ [1 - 8^(-2/3)]

dy/dx  = 1/ [1 - 1/4)]

dy/dx = 4/3

Learn more about dy/dx at a point on:

https://brainly.com/question/2948458

#SPJ1

5 - 2x^2+y^3 =-x^3 -3y then find (dy)/(dx) at the point (3,-2)

Answers

The value of the differentiation dy / dx will be 13 / 5.

What is calculus?

Calculus, also known as infinitesimal calculus or "the calculus of infinitesimals," is the mathematical study of continuous change, similar to how geometry studies shape and algebra studies generalizations of arithmetic operations.

Given that the expression is 5 - 2x²+y³ =-x³ -3y. The coordinate is (3,-2).

The value of dy / dx is calculated as,

5 - 2x²+y³ =-x³ -3y.

Differentiate the above equation with respect to x,

5 - 2x²+y³ =-x³ -3y

-4x + 3y² dy /dx = 3x² -3dy / dx

-4x - 3x² = (-3y² -3)dy/dx

dy /dx = [-4x - 3x²] / [ (-3y² -3) ]

Substitute the value of x and y in the above equation,

dy /dx = [-4x - 3x²] / [ (-3y² -3) ]

dy /dx = [-4 x 3- 3(3)²] / [ (-3(-2)² -3) ]

dy / dx = [ -12 - 27 ] / [ -15]

dy /dx = -39 /- 15 = 13 / 5

To know more about calculus follow

https://brainly.com/question/11623637

#SPJ1

Find the value of x.

Answers

Answer:

x=142

Step-by-step explanation:

47+95=x

x=142

the two angles equal x

NO LINKS!!
Find a logarithmic equation that relates y and x. (Round any numeric values to 3 decimal places.)

ln(y)=

x y
1 1.250
2 1.051
3 0.950
4 0.884
5 0.836
6 0.799

Answers

Answer:

[tex]\ln (y) = -0.250 \ln (x)+0.223[/tex]

Step-by-step explanation:

Given table:

[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12}x & y\\\cline{1-2} \vphantom{\dfrac12} 1 & 1.250\\\cline{1-2} \vphantom{\dfrac12} 2 & 1.051\\\cline{1-2} \vphantom{\dfrac12} 3& 0.950\\\cline{1-2} \vphantom{\dfrac12} 4& 0.884\\\cline{1-2} \vphantom{\dfrac12} 5& 0.836\\\cline{1-2} \vphantom{\dfrac12} 6& 0.799\\\cline{1-2} \end{array}[/tex]

To convert  y = axⁿ  to linear form, take natural logs of both sides and rearrange:

[tex]\begin{aligned}y=ax^n \implies \ln y &= \ln ax^n\\\implies \ln y &= \ln a + \ln x^n\\\implies \ln y &= \ln a + n \ln x\\\implies \ln y &=n \ln x+ \ln a\end{aligned}[/tex]

This is in the straight-line form y = mx + c.

Substitute the first values of x and y from the table into the natural log formula and solve for ln(a):

[tex]\implies \ln 1.250= n \ln 1+\ln a[/tex]

[tex]\implies \ln 1.250= n (0)+\ln a[/tex]

[tex]\implies \ln a = \ln 1.250[/tex]

[tex]\implies \ln a = 0.223\; \sf (3 \; d.p.)[/tex]

Substitute the found value of ln(a) and the last values of x and y from the table into the  natural log formula and solve for n:

[tex]\implies \ln 0.799= n \ln 6+\ln 1.250[/tex]

[tex]\implies n \ln 6=\ln 0.799-\ln 1.250[/tex]

[tex]\implies n =\dfrac{\ln 0.799-\ln 1.250}{\ln 6}[/tex]

[tex]\implies n =-0.250\;\sf (3 \; d.p.)[/tex]

Substitute the found values of n and ln(a) into the formula to create an equation for ln(y):

[tex]\boxed{\ln (y) = -0.250 \ln (x)+0.223}[/tex]

Carla divided 28 bracelets equally among 4 friends. Then, she gave Megan 3 more bracelets. Which equation shows how many bracelets, b, Megan has now?

Answers

The required number of bracelets that in the given question are 10.

What is equation?

In math, the meaning of a  equation is a numerical explanation that shows that two numerical articulations are equivalent. For example, 3x + 5 = 14 is a condition, where 3x + 5 and 14 are two articulations isolated by an 'equivalent' sign.

According to question:

Carla divided 28 bracelets equally among 4 friends.

Number of bracelets each friends has = 28/4 = 7 bracelets

Then Carla gave 3 more bracelets to Magan.

So, Total bracelets Magan has = 7 + 3 = 10 bracelets

To know more about equation visit:

brainly.com/question/21511618

#SPJ1

Which of these expressions is equivalent to log(16 • 14)?
CA. 16 log (14)
OB. log(16)+ log(14)
C. log(16) log(14)
D. log(16)-log(14)

Answers

The equivalent expression of log(16 × 14) is log 16 + log 14.

How to find equivalent expression?

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Equivalent expressions are expressions that have similar value or worth but do not look the same.

Therefore, the equivalent expression of log(16 × 14) can be found as follows:

using logarithm law,

The log of a product is the sum of the logs.

logₐ xy = logₐ x + logₐ y

Therefore,

log(16 × 14) = log 16 + log 14

learn more on equivalent expression here: https://brainly.com/question/28170201

#SPJ1

Hello, this is a Pythagorean math problem. Help pls.

Answers

The triangles 1, 2, 4, 7 and 8 are right triangles by Pythagorean relationship.

How to determine if a triangle is a right triangle

Triangles are closed figures formed by three line segments, a right triangle is a triangle with one right angle. Right triangles have a long side known as hypotenuse (r) and two shorter sides known as legs (x, y), whose Pythagorean relationship is shown below:

r = √(x² + y²)

Now we proceed to check whether each triangle is a right triangle or not:

Case 1:

D = √(8² + 6²)

D = 10 (YES)

Case 2:

D = √(5² + 12²)

D = 13 (YES)

Case 3:

D = √(12² + 9²)

D = 15 (NO)

Case 4:

D = √(8² + 15²)

D = 17 (YES)

Case 5:

D = √(4² + 9²)

D ≈ 9.849 (NO)

Case 6:

D = √(14² + 5²)

D ≈ 14.866 (NO)

Case 7:

D = √(20² + 15²)

D = 25 (YES)

Case 8:

D = √(24² + 10²)

D = 26 (YES)

To learn more on Pythagorean relationship: https://brainly.com/question/14930619

#SPJ1

All changes Given: A(0,6), B(6,6), C(6,0), D(0,0); ZDAB, LABC, ZBCD, LCDA are right angles. Prove: ABCD is a square.

Answers

Since ABCD has four equal angles and four equal sides, then it is a square.

How to find the distance between two coordinates?

The formula for the distance between two coordinates (x₁, y₁) and (x₂, y₂) is;  Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

We are given the coordinates;

A(0, 6)

B(6, 6)

C(6, 0)

D(0, 0)

Thus;

AB = √[(6 - 0)² + (6 - 6)²]

AB = 6

BC = √[(6 - 6)² + (0 - 6)²]

BC = 6

CD = √[(0 - 0)² + (0 - 6)²]

CD = 6

AD = √[(0 - 0)² + (0 - 6)²]

AD = 6

Thus, we conclude that all the sides are equal and it is a square.

Read more about distance between two coordinates at; https://brainly.com/question/7243416

#SPJ1

2. JOY leather, a manufacturer of leather Products, makes three types of belts A, B and C which are processed on three machines M1, M2 and M3. Belt A requires 2 hours on machine (M1) and 3 hours on machine (M2) and 2 hours on machine (M3). Belt B requires 3 hours on machine (M1), 2 hours on machine (M2) and 2 hour on machine (M3) and Belt C requires 5 hours on machine (M2) and 4 hours on machine (M3). There are 8 hours of time per day available on machine M1, 10 hours of time per day available on machine M2 and 15 hours of time per day available on machine M3. The profit gained from belt A is birr 3.00 per unit, from Belt B is birr 5.00 per unit, from belt C is birr 4.00 per unit. What should be the daily production of each type of belt so that the profit is maximum?
a) Formulate the problem as LPM
b) Solve the LPM using simplex algorithm.
c) Interpret the shadow prices

Answers

The shadow price of a constraint, the change in the objective function value for a unit change in (RHS) value of the constraint, with all other variables held constant.

What are constraints?

A constraint is a condition of an optimization problem that should be satisfied the condition.

We can formulate this problem as a linear programming model (LPM):

Suppose X1 be the number of belt A produced per day, X2 be the number of belt B produced per day and X3 be the number of belt C produced per day

The objective function is to maximize the profit;

3X1 + 5X2 + 4X3.

The constraints are as :

The time spent on machine M1 must be less than or equal to 8 hours per day so we get;

2X1 + 3X2 <= 8

The time spent on machine M2 must be less than or equal to 10 hours per day so we get;

3X1 + 2X2 + 5X3 <= 10

The time spent on machine M3 must be less than or equal to 15 hours per day so we get

2X1 + 2X2 + 4X3 <= 15

Thus number of belts produced must be positive:

X1, X2, X3 >= 0

To solve this LPM using the simplex algorithm,

Also the objective function is to minimize the cost, and all constraints are in the form of "less than or equal to" a certain value.

The pivot row is the row that corresponds to the smallest positive ratio between (RHS) value and the corresponding pivot column element the constraint 2X1 + 3X2 ≤ 8.

Now Interpret the shadow prices.

The shadow price of a constraint is the change in the objective function value for a unit change in (RHS) value of the constraint, with all other variables held constant.

Here the value of the constraints in the LPM and how they contribute to the optimal solution.

Learn more about constraints;

brainly.com/question/14438192

#SPJ1

A function is shown: f(x)= 2/3x+3
What is the value of f(18)?

Answers

Answer:

15

Step-by-step explanation:

When you see something like f (18), this means 18 needs to be plugged in for x

let's plug in 18

f (18) = [tex]\frac{2}{3} (18) + 3[/tex]

Let's solve

(18 × 2) ÷ 3 = 12

12 + 3 = 15

f (18) = 15

The value is of f(18) is 15.

NO LINKS!!!
Assume that the following statement, S_k, is true:
A factor of (2^(2k-1) + 3^(2k-1)))is 5.
Show that for each integer k ≥ 1, if S_k is true, then S_(k+1) is true.
2^2(k + 1) - 1)) + 3^2(k + 1) - 1)) = 2^(2k + ____) - 1)) + 3^2k + ___) - 1))
= 2^(2k - 1) * 2^(___) + 3^(2k - 1) * 3^(___)
= ______ * 2^(2k-1) + ______ * 3^(2k-1)
= (2^(2k-1) + 3^(2k-1)) + (2^(2k-1) + 3^(2k-1)) + (2^(2k-1) + (3^(2k-1) + ______*3^(2k-1)

Hence, S_k+1 is true or false, which completes the inductive step and the proof by the mathematical induction.

Answers

It is assumed the statement is true for [tex]S_k[/tex]:

A factor of [tex]2^{2k-1}+3^{2k-1}[/tex] is 5.

Show that [tex]S_{k+1}[/tex] is also divisible by 5:

[tex]2^{2(k+1)-1}+3^{2(k+1)-1}=[/tex][tex]2^{2k+2-1}+3^{2k+2-1}=[/tex][tex]2^{(2k-1)+2}+3^{(2k-1)+2}=[/tex][tex]2^{2k-1}*2^2+3^{2k-1}*3^2=[/tex][tex]4*2^{2k-1}+9*3^{2k-1}=[/tex][tex]4*2^{2k-1}+4*3^{2k-1}+5*3^{2k-1}=[/tex][tex]4(2^{2k-1}+3^{2k-1})+5*3^{2k-1}[/tex]

The first part is divisible by 5 as we assumed in the beginning and the second part has a factor of 5 so the sum is divisible by 5.

Hence it makes [tex]S_{k+1}[/tex] true, so the proof is complete.

10.​ The study of the relationships among thermal energy, heat, and work is called dynamics.

True or false

Answers

Answer:

False.

Step-by-step explanation:

False. The study of the relationships among thermal energy, heat, and work is called thermodynamics, not dynamics. Dynamics is a branch of mechanics that deals with the motion of objects and the forces that cause that motion. Thermodynamics, on the other hand, is the study of the relationships between heat, work, and other forms of energy, and how these relationships can be used to understand the behavior of systems. It is a branch of physics that is concerned with the study of heat and its effects on matter.

Write an expression for the height, h, of a cylinder with a volume of 547 cubic inches
in terms of its radius, r.

Answers

The expression for the height (h) in terms of radius r is h = 547/(∏r²).

What is a cylinder?

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.

Given that the volume of the cylinder is 547 cubic inches.

The volume of a cylinder is V = ∏r²h

Where r is the radius of the cylinder.

h is the height of the cylinder.

Putting V = 547, r = r and h = h in V = ∏r²h

547 = ∏r²h

∏r²h = 547

Divide both sides by ∏r²:

h = 547/∏r².

To learn more about expression, click on below link:

https://brainly.com/question/25311881

#SPJ1

Point A is located at (5, 6). Find the coordinates of the image A' after the
point is reflected across the x-axis.
(5,-6)
(-5,6)
(-5, -6)
(5,6)

Answers

Answer:

Step-by-step explanation:

Point A = (5, 6)  is reflected across the x axis which is y =0.

When the point is reflected across the x axis, the x coordinate

remains positive, but the y coordinate becomes negative.

The 6 becomes negative (-6).

So the coordinates of A' are (5, -6) which is the first answer.

At a meeting for math enthusiasts, two entrance fees are charged. Anyone who knows the code word “algemath” only pays 2 euros. Those who are unlucky and do not know the code word pay three euros more. You know that 7338 people were present and that the cashier received 17487 euros. How many people knew the password?

Answers

Number of People who knows the Code are 6401

What is Linear Equation in Two Variable?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

Let, Number of People who kows the Code be x

Number of Peoplee who do not know the Code be y

According to the Question:

x + y = 7338 ----------(i)

2x + 5y = 17487 ----------(ii)

Multiplying Equation (i) by 2

2x + 2y = 14676 ---------(iii)

Substracting Equation (iii) from Equation (ii)

3y = 2811

y = 937

This means x = 6401

To learn more baout Linear Equation in Two ariables from the given link

https://brainly.com/question/24085666

#SPJ1

A concession stand sells hot dogs for $2 and cheeseburgers for $3. One day, 486 items were sold and the owners earned $1218.
How many hot dogs and cheeseburgers were sold?

Answers

The Total Number of Hot Dogs sold were 240 and Cheese Burgers sold were 246

What is Linear Equation in Two Variables?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

Let, Number of Hot Dogs Sold = x

Number of Cheese Burgers Sold = y

According to the Question:

x + y = 486 ----------(i)

2x + 3y = 1218 ----------(ii)

Multiplying Equation (i) by 2

2x + 2y = 972 ----------(iii)

Substracting Equation (iii) from Equation (ii)

y = 246

x = 240

To learn more about Linear Equation in Two Variables from the given link'

https://brainly.com/question/24085666

#SPJ1

Select all the expressions that are equivalent to 8-12-(6+4).
(Select all that apply.)
8-(6+4)-12
(6+4)-8-12
8-12-6-4
8-6-12+4

Answers

Answer:

8-(6+4)-12

8-12-6-4

Step-by-step explanation:

8-(6+4)-12 and 8-12-6-4 are equivalent expressions because they both compute to -6. This is because in both expressions, the 6+4 is calculated first, yielding 10. Then, the 8 is subtracted from 10, yielding -2. Finally, the 12 is subtracted from -2, yielding -6.

6+4)-8-12 is not an equivalent expression because it does not compute to -6. In this expression, the 6+4 is calculated first, yielding 10. Then, the 8 is subtracted from 10, yielding 2. Finally, the 12 is subtracted from 2, yielding -10.

8-6-12+4 is not an equivalent expression because it does not compute to -6. In this expression, the 8 is subtracted from 6, yielding -2. Then, the 12 is subtracted from -2, yielding -14. Finally, 4 is added to -14, yielding -10.

please help me i will give brainliest thank you so much

Answers

The answer is 10 hours!

The problem can be made into the equation 8X + 50 = 130, with X being the hours worked. This can be solved like this:
8X + 50 = 130
8X = 80
X = 10

Hope this helps!

An object has a mass of 10.0 g and a volume of 50.0 mL. What is the density of that object?

5 ml/g
0.2 g/mL
500 g/mL​

Answers

Answer:

0.2 g/mL

Step-by-step explanation:

The calculation for density is density=mass/volume.
With a mass of 10g and a volume of 50mL, you divide them to get 0.2

Other Questions
The main limiting factor for the plants and animals that live in the deciduous biome is ________________. Question 7 options: tornadoes cold temperatures in winter high temperatures poor soil Solve for x and round to the nearest tenth why do oxygen gas and hydrogen gas have different properties? Help me please... help The immediate future of "je mange" is:O A. je ne mange pas.O B. Je manger allerO C. je vais mangeO D. je vais manger.Question 2What does "d'abord" mean?O A nextOB. first of allO C. to meD. after what of the following uses heat from deep inside the earth that generates steam to make electricity what is 3 13/20 as a decimal One marble is picked at random and NOT replaced from a box that has 3 red marbles, 4 green marbles 2 blue marbles and one yellow marble. Find the probability of selecting a red and a red marble. Evelyn is going to invest $3,500 and leave it in an account for 16 years. Assuming the interest is compounded quarterly, what interest rate, to the nearest tenth of a percent, would be required in order for Evelyn to end up with $6,200? Shelley had 53 until she spent 1 quarter. How much money does Shelley have now? WILL GIVE BRIANELIST!!!!!!!!!!!!!!! IT IS WORTH 80 PONITSWrite a three- to five-paragraph summary of what you believe the poem is about. Remember that the summary should include the three images you have identifiedThe owl is the poem by Edward Thomas1878-1917 Which of the following is not an example of a strategy you should use to help your comprehension of the text?a.skip confusing sections onlyc.rereadb.graphic organizersd.visualization Find the domain and range of y = 8x + 7.5.plz help Can someone Help me plz which lens have plus power The Great Gatsby Chapter 2Which answer choice is not located in the Valley of Ashes?A)George's shopB) The eyes of Dr. T.J. EckleburgC) Nick's rented homeD)A section of the railroad Tommy took one of his friends out to dinner. The dinner cost $100 and he paid 3% sales tax. If Tommy left an 18% tip on the $100, how much in total did he pay? What conclusions can you make about kinetic energy and temperature? 2. Triangle ABC is similar to triangle PQR. Which statement is not always true?1) ZA-ZP 2) ZR-ZC 3) 2B-ZR 4) 2C-ZR Which word means "to move out of?'A. regressB. progressC. egress