a sample of size 115 will be drawn from a population with mean 48 and standard deviation 12 . use the ti-83 plus/ti-84 plus calculator. (b) find the 25th percentile of x . round the answer to at least two decimal places. the 25th percentile is

Answers

Answer 1

Using the ti-83 plus/ti-84 plus calculator, the 25th percentile of x is equal to 47.25 with a mean of 48 and a standard deviation of 12, respectively.

what is mean ?

A dataset's mean is calculated by dividing the sum of all values by the total number of values. The term "average" is frequently used to describe it because it is the most widely used central tendency metric.

calculation

a) µ =     48    

σ =     12    

n=    115    

X =    45    

Z =(X - µ )/(σ/√n)  =     (45-48)/(12/√115)=    -2.68

P(X<45) = P(Z<-2.68) =         0.0037

b) µ =     48.00    

σ =     12.00    

n=    115.00    

P(X ≤ x) =    0.2500    

z value at  0.25=    -0.674        (excel formula =NORMSINV(0.25))

z=(x-µ)/(σ/√n)        

X=z * σ/√n +µ= -0.674*12/√115+48=        47.25

Using the ti-83 plus/ti-84 plus calculator, the 25th percentile of x is equal to 47.25 with a mean of 48 and a standard deviation of 12, respectively.

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Related Questions

Neha drives a car that gets 25 miles per gallon when she is driving in the city and 40 miles per
gallon when she is driving on the highway. Her car's fuel tank will hold 15 gallons of gas. What
equation can we write to represent all the combinations of city miles and highway miles she can
drive on one tank of gas?
1. Record an equation that is a prediction.

Answers

Answer:

C/25 + H/40 = 15

Step-by-step explanation:

Let's call C the number of city miles, and H the number of highway miles.

The total gas used is therefore:

C/25 + H/40

The fuel tank holds 15 gallons, so:

C/25 + H/40 = 15

If [tex]$4^x = 3$[/tex], what is [tex]$4^{2x-2}?$[/tex]

Answers

[tex]4^x=3 \\\\[-0.35em] ~\dotfill\\\\ 4^{2x-2}\implies 4^{2x}\cdot 4^{-2}\implies (4^x)^2\cdot \cfrac{1}{4^2}\implies \cfrac{(4^x)^2}{16}\implies \cfrac{(3)^2}{16}\implies \cfrac{9}{16}[/tex]

The diameter of a circle is 6 cm. Find its area to the nearest whole number.

Answers

Answer:

28.26

Step-by-step explanation:

A=3.14r^2

A=3.14(3)^2

A=3.14(9)

A=28.26

Answer: 28 cm

Step-by-step explanation: Area=π·r² and diameter =2r

So if we need to  find what our radius is. As shown by d=2r our radius is 1/2 our diameter. If our diameter is 6cm our radius is 3cm.

Now plug 3cm into A= 2πr²⇒ A= 2(3.14)(3²) = 28.26

Now round to the nearest whole number ⇒ 28.

Caroline is planting flowers in her garden. She plants her first 7 flowers in 4 minutes. After 12 minutes, she has planted 21 different flowers. If caroline keeps planting flowers at this rate, how long will it take her to plant all 70 flowers that she has?.

Answers

It will take 40 minutes for her to plant all 70 flowers that she has. By using proportions, we can find this value.

How to calculate a word problem using proportions?

To calculate a word problem using proportions is as follows:

Consider the details of the word problem in proportions as

a : b = c : d

Here, a: b is the ratio of an event, and c : d is the ratio of another event.

Then, to find the value of c we need to reframe the above proportion into

c = ad/b

This is also said to be a cross formula in terms of word problems.

Calculation:

It is given that, Caroline is planting flowers in her garden.

She plants her first 7 flowers in 4 minutes.

After 12 minutes, she planted 21 different flowers.

Then, she takes x minutes for planting 70 flowers.

(Since the rate of planting is the same)

So, we can write

70 : 21 = x : 12

⇒ x = (70× 12)/21 = 40 minutes

Therefore, Caroline takes 40 minutes for planting all 70 flowers.

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how many ways are there to list the letters of the word mathematics so that no two consecutive letters are the same?

Answers

There are 22 different ways to organize the word mathematics because no two consecutive letters are the same.

Explain the term combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the ordering of the selection is irrelevant. You can choose the components of combos in any order.

Total number of ways to organize the word "mathematics".

The same letter does not appear twice.

The following word has the letters 2M, 2A, 2T, H, E, I, C, and S.

We will first organize H,E,I,C,S in five different ways;

−H−E−I−C−S−

No, we could arrange 2M, 2T, and 2A as we have 6 gaps;

= 6!/(2!.2!.2!)

So there are a total of;

= 5 x 6!/(2!.2!.2!)

= 22.5

= 22 ways

Thus, there are 22 different ways to organize the word mathematics because no two consecutive letters are the same.

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The diameter of a circle is 12 ft. Find its area to the nearest whole number.

Answers

Answer:

77.04

Step-by-step explanation:

A=3.14r^2

a=3.14(6)^2

A=3.14(36)

A=77.04

Answer: 113 ft^2

Step-by-step explanation:

Jermaine plays classical guitar at a local restaurant in the evenings. If jermaine plays 23 songs per evening, how many songs does he play in 73 evenings?.

Answers

Answer:

1679 songs

Step-by-step explanation:

         23

       x73

----------------------------

            69

    +   1610

-------------------------------

         1679

Order these numbers from least to greatest.

1.4 comma space 1.04 comma space 16 over 10 comma space 1 1 half

Answers

Answer:

1.04, 1.4, 1.5 (one and a half), 10, 16

Answer:

1.04, 1.4, 1.5, 1.6

Step-by-step explanation:

1 1 half = 1.5

16 over 10 = 1.6

hope this helps!

If x=6 what is 4x
??????????????

Answers

Answer:

24

Step-by-step explanation:

6*4=24

6 times 4 is 24 …………

write an equation of the line that passes through (7,10) and is perpendicular to the line y=-1/5x-9

Answers

An equation of the line that passes through (7,10) and is perpendicular to the given line is y=5x-25.

Given that, the line that passes through (7,10) and is perpendicular to the line y=-1/5x-9.

What is slope of a line?

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

Here, slope of a line y=-1/5x-9 is m=-1/5.

The slope of a line perpendicular to given line is m1=-1/m2

So, slope =5

Substitute m=5 and (x, y)=(7, 10) in y=mx+c, we get

10=5(7)+c

⇒c=-25

Substitute m=5 and c=-25 in y=mx+c, we get

y=5x-25

Hence, an equation of the line that passes through (7,10) and is perpendicular to the given line is y=5x-25.

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Janet made 7 1/3 pounds of trail mix. If she puts 1 5/6 pounds into each bag, how many
bags can Janet fill?

Answers

Janet can fill 3 bags, while still having some trail mix left over. The decimal for what she can fill is 3.989 so if your teacher wants you to round then 4.

what goes in the missing box

Answers

Answer:

10

Step-by-step explanation:

in the first one, 6 16 8, (6×8)/3=16

in the third one, 9 21 7, (9×7)/3=21

using the same comcept, 5 ? 6, (5×6)/3=10

so, ?=10

42 out of the 84 teachers in a school staff meeting were first-year teachers. What percentage of the teachers in the meeting were first-year teachers? Write your answer using a percent sign (%).

Answers

50%
84-42= 42
There for half where first year teachers

Find the equation of the line that passes through (4,4) and is parallel to y = 3 x + 4.

Answers

The line's equation that is parallel to the given line is=  3x - 8

What is Equation?

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, etc.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.

According to our question-

The line's equation in the form of the slope intercept is,

y = mx + c

m is the line's slope, and c is its y-intercept.

line equation provided that,

Therefore, the line's slope is

Finding the equation of the line that crosses (4,4) and runs parallel to the provided lines is necessary.

Because all parallel lines have the same slope.

Equation for the necessary line is,

Replace point (4,4) in the line above.

In order for the line equation to become,

3x - 8

Hence, The line's equation that is parallel to the given line is=  3x - 8

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Find the x- and y-intercepts of the graph of -3x + y = 6. State each answer as an
integer or an improper fraction in simplest form.

Answers

Answer:

X-intercept : (-2,0)

Y-intercept : (0,6)

Answer:y-intercept (0,6),x-intercept (-2,0)

Step-by-step explanation:

To find the y-intercept set x=0

-3(0)+y=6

y=6

y-intercept (0,6)

To find the X-intercept set y=0

-3x+0=6

-3x=6

x=-2

x-intercept (-2,0)

At the beginning of an experiment, a scientist has 176 grams of radioactive goo. After 135 minutes, her sample has decayed to 11 grams. What is the half-life of the goo in minutes? Find a formula for G ( t ) , the amount of goo remaining at time t . G ( t ) = How many grams of goo will remain after 32 minutes?

Answers

Answer:

The amount of goo remaining after 32 minutes is approximately 54.7 grams.

Step-by-step explanation:

The half-life of a substance is the amount of time it takes for half of the substance to decay. To find the half-life of the goo in the experiment, we need to solve the equation G ( t ) = G ( 0 ) / 2 for t , where G ( 0 ) is the initial amount of goo and G ( t ) is the amount of goo remaining after time t .In this case, G ( 0 ) = 176 grams and G ( 135 minutes ) = 11 grams, so we can write the equation as follows:11 grams = 176 grams / 2Solving for t , we get:t = 135 minutes * ( 1 / 2 ) = 67.5 minutesThis is the half-life of the goo in the experiment.To find the amount of goo remaining after time t , we can use the equation G ( t ) = G ( 0 ) * ( 1 / 2 ) ^ ( t / t1/2 ) , where G ( 0 ) is the initial amount of goo, t is the time at which we want to find the amount of goo remaining, and t1/2 is the half-life of the goo.In this case, G ( 0 ) = 176 grams, t = 32 minutes, and t1/2 = 67.5 minutes, so we can plug these values into the equation to find the amount of goo remaining after 32 minutes:G ( 32 minutes ) = 176 grams * ( 1 / 2 ) ^ ( 32 minutes / 67.5 minutes )This equation tells us that the amount of goo remaining after 32 minutes is approximately 54.7 grams.

O
Nolan is going to a carnival that has games and rides. Each game costs $2.50 and
each ride costs $3.50. Nolan spent $52.50 altogether on 17 games and rides. Write a
system of equations that could be used to determine the number of games Nolan
played and the number of rides Nolan went on. Define the variables that you use to
write the system.

Answers

Answer: g + r = 17

2.5g + 3.5r = 52.5

Step-by-step explanation: Let g be the number of games Nolan played and r be the number of rides Nolan went on. We can write the following system of equations to represent the problem:

g + r = 17

2.5g + 3.5r = 52.5

We can solve this system of equations using elimination, substitution, or graphing.

What is the solution of the equation?:
-2(3x+1)-2x=-4(2x)-4

Answers

it doesn't have solution

16 miles out of 40 miles

Answers

The 16 miles out of 40 miles. Then the percentage will be 40%.

What is the percentage?

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The 16 miles out of 40 miles. Then the percentage is calculated as,

P = (16 / 40) x 100

P = 0.40 x 100

P = 40%

The 16 miles out of 40 miles. Then the percentage will be 40%.

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The missing part of the question is given below.

Determine the percentage.

A drawer contains one pair of brown socks and one pair of white socks. The table shows the possible outcomes, or sample space, for choosing a sock, replacing it, and then choosing another sock.

Answers

Given that the drawer includes one pair of brown socks and one pair of white socks, the likelihood of selecting one sock, replacing it, and then selecting another sock is 1/16.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here,

n(s)=4

n(e)=1

Probability of choosing a sock, replacing it, and then choosing another sock,

=1/4*1/4

=1/16

Probability of choosing a sock, replacing it, and then choosing another sock will be 1/16 as the drawer contains one pair of brown socks and one pair of white socks.

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Find the equation of the​ line, in​ lope-intercept form, containing the point ( 5,2. 2) and (9,2. 6)

Answers

The equation of the​ line, in​ slope-intercept form, containing the point ( 5,2. 2) and (9,2. 6) is  y=0.025x+2.375 where 0.025 is the value of slope and 2.375 is the y-intercept.

What is an example of a slope intercept form?

Take into account the slope-intercept form of the equation y = 6 x + 9 y=6x+9. The x and y intercepts are known. When x = 0, the y-intercept also happens, and when y equals 0, the x-intercept also happens. By setting the value of y to 0, we may find the x-intercept.

What is the slope and y-intercept?

The values of the slope and y-intercept reveal details of the relationship between the two variables, x and y. The slope shows how quickly y changes for every unit change in x. When the x-value is 0, the y-intercept shows the y-value.

To calculate the equation of line containing points (5,2.5) and (9,2.6) we will use the formula y=mx+b

Here, m = (y2-y1)/(x2-x1)

So, m = (2.6-2.5)/(9-5)

m= 1/40

m=0.025

Now finding b by using formula y=mx+b using x= 5 and y= 2.5

2.5=(0.025)(5)+b

2.5=(0.125)+b

b=2.375

so equation of line is y=0.025x+2.375 in slope-intercept form.

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Show your work, (I am stuck on this because I’m not smart lol)

Answers

Answer:

She needs to get at least 96 on the 4th test to earn an average of at least 90 in the class.

Step-by-step explanation:

(97+78+89+?) divided by 4 at\geq 90

It is divided by 4 because it is the average of 4 test scores.

To Solve: (97+78+89+?) divided by 4 at\geq 90

Multiply by 4 on both sides 97+78+89+? at\geq 360

Isolate variable: ? at\geq 96

Determine if the two triangles are necessarily congruent. If so, fill in a flowchart proof to prove that they are.

Help please

Answers

The given statements are:

angle A = angle O   (note the single tickmarks)side AC = side OM  (these sides share a similar tickmark)angle C = angle M  (note the double tickmarks)

We can then use the ASA congruence theorem to prove the triangles are congruent, aka they are mirror copies of one another.

Each "A" refers to facts (1) and (3) shown above. Fact (2) is the "S" of ASA.

ASA = angle side angle

please help meeeee!!

Answers

Answer:

f(2) = 9

Step-by-step explanation:

to evaluate f(2) substitute x = 2 into f(x) , that is

f(2) = 4(2) + 1 = 8 + 1 = 9

Pls answer it quickly

Answers

The two-column method can be used to prove that the triangles ΔACD and ΔBCD are congruent is presented as follows;

Statements [tex]{}[/tex]                                         Reasons

1. AC ≅ BC   [tex]{}[/tex]                                        1 Given

2 D is the midpoint of AB [tex]{}[/tex]                  2 Given

3. CD ≅ CD [tex]{}[/tex]                                         3 Reflexive property → CD = CD

4 ∠ACD ≅ ∠BCD [tex]{}[/tex]                               4 Median line of an isosceles triangle bisects the vertex angle

5 ΔACD ≅ ΔBCD  [tex]{}[/tex]                              5. SAS congruency postulate

What is the two-column method used to prove statements in geometry?

The two-column method consists of two columns, including a statement column and a reasons column, in which each statement made is provided with an accompanying reason.

The reasons in the prove for the congruency of the triangles, ΔACD and ΔBCD are as follows;

Reflexive property

The reflexive property of equality indicates that the value of a number or measure is equal to itself, therefore, the length of the segment CD is the same as the length of the segment CD.

Median of an isosceles triangle

In an isosceles triangle, two sides are congruent. The median segment drawn from the altitude of an isosceles triangle forms two congruent segment at the base, such that the two triangles formed by the median line are congruent, by Side-Side-Side, SSS congruency postulate, therefore, the angles formed at the vertex of the triangle by the median segment are also congruent

SAS congruency postulate

The Side-Angle-Side congruency postulate states that two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.

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One angle measures 27°, and another angle measures (8d − 9)°. If the angles are complementary, what is the value of d?

d = 72
d = 21
d = 3
d = 9

Answers

Answer:

d = 9°

Step-by-step explanation:

When the sum of two angles is equal to 90 degrees, they are called complementary angles.

soln

27° + (8d – 9)° = 90°

27° + 8d – 9° = 90°

27°–9° + 8d = 90°

18° + 8d = 90°

8d = 90° – 18°

8d = 72°

divide both sides by (8)

d = 9°

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Kona work at a bakery. She baked 3308 muffin. She diplayed the muffin on tray that each hold 12 muffin. How many tray did Kona ue to diplay the muffin?

Answers

Using mathematical operations, we know that Kona needs a 276 trays to display all her 3308 muffins.

What are mathematical operations?

The process of calculating a value using operands and a math operator is known as a mathematical "operation."

The provided operands or integers must follow certain established rules that are associated with the math operator's symbol.

Addition, subtraction, multiplication, division, and modular forms are the five fundamental operations in mathematics.

So, a tray will be needed to display all the cakes:

The total number of muffins is 3308.

Each tray can have 12 muffins.

The total trays needed are:

3308/12

275.66

Rounding off: 276

Therefore, using mathematical operations, we know that Kona needs a 276 tray to display all her 3308 muffins.

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if 14 meter of ribbion cost 19$ how much will 21 meters cost

Answers

Answer: 21 meters cost $28.5

Step-by-step explanation:

divide 19 by 14 and multiply by 21

21 meters cost $28.5

What is an equation of the line that passes through the point (5, -8) and is
perpendicular to the line 5x - 4y = 16?

Answers

The equation of the line which is perpendicular to 5x - 4y = 16 is  [tex]y = -\frac{4}{5}x -4[/tex].

What is Coordinate Geometry?

The study of geometry using coordinate points is known as coordinate geometry (also known as analytical geometry). Finding the distance between two points, breaking lines into m:n segments, locating a line's midpoint, computing a triangle's area in the Cartesian plane, and other operations are all feasible using coordinate geometry.

Not all crossing lines are parallel ones. If the intersecting lines satisfy the following conditions, they are said to be perpendicular lines. Following are the two primary characteristics of perpendicular lines:

The intersection of perpendicular lines is always at a right angle.Two lines will always be parallel to one another if they are perpendicular to the same line.

Let's say that lines AB and CD are parallel to one another. Line AB has a slope of m1, whereas line CD has a slope of m2.

If and only if the product of the slopes of the two lines equals negative of unity, two lines are perpendicular to one another.

As a result, the following is the formula for the perpendicular's slope:

m1.m2 = -1

The equation of the line be "y = mx + c".

Equation of the line Perpendicular to the line is 5x - 4y = 16

Therefore,  4y = 5x - 16

⇒ [tex]y = \frac{5}{4}x -4[/tex]

Slope of the line Perpendicular to the required line is [tex]\frac{5}{4}[/tex].

Slope of the required ine be m .

Therefore, m * [tex]\frac{5}{4} = -1[/tex]

⇒ [tex]m = -\frac{4}{5}[/tex].

Equation of the line is ,

[tex]y = -\frac{4}{5}x + c[/tex]

The line passes through (5,-8)

Therefore,

[tex]-8 = \frac{-4}{5}*5 + c[/tex]

⇒ c = -4

The equation of the line is [tex]y = -\frac{4}{5}x -4[/tex].

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when finding 6.1 divided by 0.1 how is the decimal point moved?

Answers

well, let's just divide them anyway and check it out.

hmmm 6.1 ÷ 0.1, well, when dividing decimals, we can first check the decimals on each hmmm 6.1 has one decimal and 0.1 has one decimal, so for the one decimal on 6.1 0.1 gets one "0" and for each decimal on 0.1, 6.1 gets  one "0".

That means we can change the values with no dots to say 610 and 10, so we end up with a division of 610 ÷ 10 = 61.  We can write that as 61.0 hmmm woopsie, the dot moved to the right by one slot.

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