Find the average value of f(x) = x^3 on [-1,2]. Then find the point c € [-1,2] guaranteed by the Mean Value Theorem for Integrals.

Scoring in the 60th percentile on her math exam means that the student performed better than 60% of other test takers.

Percentile is a measure that indicates the percentage of data points that are below a particular value in a given dataset. In this case, the student's score is in the 60th percentile, which means she scored better than 60% of the other test takers.

Imagine arranging all the scores of the test takers in ascending order. The 60th percentile represents the score that is greater than 60% of the scores below it and less than 40% of the scores above it. It is a way of understanding how a particular score compares to the rest of the scores in the group.

However, it also means that 40% of the test takers scored higher than her.  If the student scored in the 60th percentile, it indicates that she performed relatively well compared to the majority of the test takers.

Percentiles provide a useful way to interpret individual scores in relation to the entire distribution of scores in a dataset.

To know more about percentile, refer here:

https://brainly.com/question/32266700#

#SPJ11

Answer: i think 23x

Step-by-step explanation: i might be incorrect

Answer:

23x + 250

Step-by-step explanation:

x representing the amount of jerseys and 250 representing the one time fee and the y intercept

Best way to solve this is by using

\( \sqrt{s(s - a)(s - b)(s - c)} \)

\(where \: s = \frac{a + b + c}{2} \)

s=(12+8+17)/2

=18.5

using the formulae

area =43.5

\(2 \sec^2 x = 3- \tan x \\\\\implies 2(1 +\tan^2 x) = 3- \tan x \\\\\implies 2 + 2 \tan^2 x +\tan x -3 =0\\\\\implies 2 \tan^2 x + \tan x -1 =0\\\\\implies 2u^2 + u -1 =0~~~ ;[\text{set} \tan x = u]\\\\\implies u = \dfrac{-1\pm \sqrt{1-4\cdot 2 \cdot (-1)}}{2(2)}\\\\\implies u =\dfrac{-1 \pm\sqrt{9}}{4}\\\\\implies u = \dfrac{-1 \pm 3}{4}\\\\\implies u = \dfrac{2}{4}=\dfrac 12~~ \text{or} ~~u =\dfrac{-4}{4} =-1\\\\\)

\(\implies \tan x = \dfrac 12 ~~ \text{or} ~~ \tan x =-1~~~ ;[\text{Substitute back u =tan x}]\\\\\text{Now,}~ \\\\\tan x = -1,\\\\\implies x = n\pi - \dfrac{\pi}4\\\\\\\text{For interval,}~ [0,2\pi) \\\\x = \dfrac{3\pi}4, \dfrac{7\pi}4\\\\\text{In degrees,}~ x = 135^{\circ}, x =315^{\circ}\\\\\tan x = \dfrac 12\\\\\implies x = n\pi + \tan^{-1} \left(\dfrac 12 \right)\\\\\text{For interval} ~[0,2\pi),\\\\\)

\(x=\tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\text{in degrees,} ~~x=\tan^{-1} \left(\dfrac 12 \right), \left[180^{\circ} +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\\\\text{Combine all solutions:}\\\\x=\dfrac{3\pi}4, \dfrac{7\pi}4, \tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\\)

\(\text{In degrees,}~ x = 135^{\circ},~315^{\circ},~\tan^{-1} \left(\dfrac 12 \right), \left[180^{\circ} +\tan^{-1} \left( \dfrac 12 \right)\right]\)

Answer:

Step-by-step explanation:

Comment

There is only 1 number under probability that is greater than or equal to 5. That number is 15

There are 4 possible answers. Only 1 is successful.

Answer: P(y≥5) = 1/4 or 0.25

The situation in which it is safe to employ t-procedures is described by option (c) where both samples are approximately normal.

option (c) is identified as the situation where it is safe to use t-procedures.

t-procedures are appropriate when certain assumptions are met, including the assumption of normality of the population or sample distributions. Option (c) states that both samples are approximately normal, which fulfills this requirement. This means that the data in both samples have a symmetric bell-shaped distribution, allowing t-procedures to be used for hypothesis testing or confidence interval estimation.

Options (a), (b), and (d) describe scenarios where either one or both samples are moderately skewed or contain outliers, which violates the assumption of normality. Skewness and outliers can impact the validity of t-procedures, making them less reliable. Therefore, these options do not fulfill the requirement for safely employing t-procedures.

Option (e) states that it is safe to use t-procedures in more than one of the situations above. However, based on the analysis provided, only option (c) meets the criteria of having both samples approximately normal, making it the only situation where t-procedures can be safely employed.

Learn more about assumption of normality here:

https://brainly.com/question/30932454

#SPJ11

Answer:

The length of FG is 2.

Step-by-step explanation: B and F are the same point, just reflected, so BC=FG.

Answer:

\(b^6\)

Step-by-step explanation:

a^4+-4 * b^2+4

a^0*b^6

Answer:

\(f(x)=-(x+8)(x-2)\)

Step-by-step explanation:

Start by factoring out a -1...

\(f(x)=-(x^2+6x-16)\)

Now, we have to find two integers that multiply to get -16 and have a sum of 6:

(-2)*8=-16

-2+8=8-2=6

Using this, we can split 6x into -2x and 8x...

\(f(x)=-(x^2-2x+8x+16)\)

Factor  the first and second half separately...

\(f(x)=-[(x^2-2x)+(8x-16)]\\f(x)=-[x(x-2)+8(x-2)]\\\)

Since both x and 8 are being multiplied by x-2, we can combine them to get...

\(f(x)=-(x+8)(x-2)\)

Answer:

31.4 in.

Step-by-step explanation:

10 ÷ 5 = 2

2 × 3.14 × 5

31.4

Tossing two coins in a  sample space has four possible outcomes. (T,H,) (T,T), (H,H), (H,T).

All possible outcomes form the sampling space of a randomized experiment. A subset of the sample space are events associated with randomized experiments.

Given that, Ava tossed the coin her twice. T represents a coin that lands heads up, H represents a coin that lands heads up.

If the first coin is tails, the second coin is either tails or heads. So you have two options. (T,H) (T,T) (T,T)

If the first coin is heads, the second coin is either heads or tails. So you have two options. (H,H) (H,T) (H,T)

Tossing two coins in a pattern room has four possible outcomes.

(T,H,) (T,T), (H,H), (H,T)

To learn more about sample space, visit:

https://brainly.com/question/10188362

#SPJ4

Answer:

17 nickels

Step-by-step explanation:

To be able to find the answer, you can say that the sum of the value of each coin multiply for its quantity is equal to 10.08, which you can express as follows:

quarters= 0.25

dimes= 0.10

nickels= 0.05

pennies= 0.01

(0.25*19)+(0.10*39)+(0.05*x)+(0.01*58)=10.08, where

x= the quantity of nickels

Now, you can solve for x:

4.75+3.9+0.05x+0.58=10.08

0.05x=10.08-4.75-3.9-0.58

0.05x=0.85

x=0.85/0.05

x=17

According to this, the answer is that there are 17 nickels in the cup holder.

An equation is formed of two equal expressions. The missing pieces of the solution of the quadratic equation are 50, 3, and -8.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

To fill the missing piece of the solution of the quadratic equation, you need to balance each of the equations. Therefore, the solution to the problem can be written as,

\(-32 = 2(x^2 + 10x)\\\\-32 + 50 = 2(x^2 + 10x + 25)\\\\18 = 2(x + 5)^2\\\\9 = (x + 5)2\\\\\pm 3= x + 5\\\\x = -2\ \ {\rm or}\ \ x = -8\)

Thus, the solution of the quadratic equation is -2 or -8.

Hence, the missing pieces of the solution of the quadratic equation are 50, 3, and -8.

Learn more about Equation:

https://brainly.com/question/2263981

Answer:

Percentile = 90

Therefore, the test score 12 is at the 90th percentile.

Step-by-step explanation:

Percentile = (Number of scores less than or equal to score) / (Total number of scores) * 100

Percentile = (9) / (10) * 100

Answer:

Percentile = 90Therefore, the test score 12 is at the 90th percentile

Percentile = (Number of scores less than or equal to score) / (Total number of scores) * 100Percentile = (9) / (10) * 100Step-by-step explanation:

In given triangle ABC the length if BC is 7.1 .

What is trigonometric functions?

A subfield of mathematics called trigonometry is concerned with the study of triangles. It is frequently referred to as "trig" casually. In trigonometry, mathematicians look at how triangles' sides and angles relate to one another.

Here in given triangle contains 90°, So it is right triangle.

Now using tangent function then

=> tan B = \(\frac{opposite}{adjacent}\) then

=> tan 38° = \(\frac{AC}{BC}\)

=> BC = tan 38° × AC

=> BC = tan 38° × 9.1

=> BC = 7.1

Hence the length of the side BC is 7.1.

To learn more about trigonometric function refer the below link

https://brainly.com/question/30174294

#SPJ1

The length of BC in the triangle ABC is 7.109.

Trigonometry is a branch of mathematics concerned with the study of triangles. It is commonly referred to as "trig" in a casual manner. Trigonometry examines how the sides and angles of triangles relate to one another.

Because the given triangle contains 90°, it is a right triangle.

Now, using the tangent function,

The tangent function is one of trigonometry's six primary functions.

Tan A = Opposite Side/Adjacent Side is the Tangent Formula. In terms of sine and cosine, tangent may be represented as: Tan A = Sin

then,

= tan B = opposite side / adjacent side

= tan 38° = AC/BC

= BC = 38° tan x AC

= BC = tan 38° × 9.1

= BC = 7.109

As a result, the length of the side BC is 7.109.

To learn more trigonometry refer to :

https://brainly.com/question/24349828

#SPJ1

Answer:

B is correct answer mark as brainliest answer

Answer:

  (x, y) = (-1, 5)

Step-by-step explanation:

You want to solve this system of equations by substitution.

The idea of substitution means we want to replace an expression in one equation for an equivalent expression based on the other equation.

Here, the second equation gives an expression equivalent to "y", so we can use that expression in place of y in the first equation:

  5x +2(-2x +3) = 5 . . . . . . . . (-2x+3) substitutes for y

  x +6 = 5 . . . . . . . . . . simplify

  x = -1 . . . . . . . . . subtract 6

  y = -2(-1) +3 = 5 . . . . . use the second equation to find y

The solution is (x, y) = (-1, 5).

__

Additional comment

Choosing substitution as the solution method often works well if one of the equations gives an expression for one of the variables, or if it can be solved easily for one of the variables. The "y=" equation is a good candidate for providing an expression that can be substituted for y.

Any equation that has one of the variables with a coefficient of +1 or -1 is also a good candidate for providing a substitution expression.

  4x -y = 3   ⇒   y = 4x -3 . . . . . for example

The attached graph confirms the solution above.

To find the total number of balloons used, we need to add the quantities of white, yellow, blue, and red balloons together.

Let's break down the given information:
- The number of white balloons used is 1243.
- There are 7559 more yellow balloons than white balloons.
- The number of blue balloons is 1138 more than the number of white balloons.
- The number of red balloons is equal to the combined quantity of yellow and blue balloons.

First, let's determine the number of yellow balloons. Since there are 7559 more yellow balloons than white balloons, we add 7559 to the quantity of white balloons:
1243 + 7559 = 8802 yellow balloons.

Next, let's determine the number of blue balloons. As there are 1138 more blue balloons than white balloons, we add 1138 to the quantity of white balloons:
1243 + 1138 = 2381 blue balloons.

Now, let's calculate the number of red balloons. The number of red balloons is equal to the sum of yellow and blue balloons:
8802 + 2381 = 11183 red balloons.

Finally, to find the total number of balloons used, we add the quantities of white, yellow, blue, and red balloons:
1243 + 8802 + 2381 + 11183 = 23609 balloons in total.

In total, 23609 balloons were used for the party. For the party, a total of 23609 balloons were used. The breakdown of balloon colors is as follows: 1243 white balloons, 8802 yellow balloons, 2381 blue balloons, and 11183 red balloons. To arrive at these numbers, we followed the given information step by step. First, we determined the quantity of yellow balloons by adding 7559 (the number of yellow balloons that exceeded the white balloons) to the initial quantity of white balloons (1243). This gave us a total of 8802 yellow balloons. Then, we calculated the quantity of blue balloons by adding 1138 (the number of blue balloons that exceeded the white balloons) to the initial quantity of white balloons (1243). This resulted in 2381 blue balloons. Finally, we found the quantity of red balloons by adding the number of yellow balloons (8802) and the number of blue balloons (2381), resulting in 11183 red balloons. Adding up the quantities of white, yellow, blue, and red balloons, we obtained a total of 23609 balloons for the party.

In conclusion, the total number of balloons used for the party was 23609, consisting of 1243 white balloons, 8802 yellow balloons, 2381 blue balloons, and 11183 red balloons.

To learn more about initial quantity visit:

brainly.com/question/1578659

#SPJ11

Answer:

9 people

Step-by-step explanation:

We can use a ratio to solve

3 lbs          x lbs

----------    = ----------

7 people     21 people

Using cross products

3 *21 = 7x

63 = 7x

Divide by 7

63/7 = 7x/7

9 =x

Answer:

9 pounds of fruits serve 21 people

Step-by-step explanation:

3 pounds = 7 people

x pounds = 21 people

Using cross multiplication method

3 × 7 = 7 × x

multiply

63 = 7 x.

Divide each side by 7

63 / 7 = 7 x / 7

9 = x

The velocity (v) at the tip of the minute hand of a 2 cm long clock is (2π/15) cm per minute.

To find the velocity of the tip of the minute hand of a clock, we need to calculate the linear velocity in centimeters per minute assuming the length of the hand is 2 cm.

The hour hand of the clock completes one rotation in 60 minutes. This corresponds to 360 degrees. You can calculate the linear velocity of the tip of the minute hand by considering the distance traveled in one minute.

The distance covered by one rotation of the tip of the minute hand corresponds to a circle with a radius of 2 cm. So \(2\pi (2) = 4\pi\) cm. Since the minute hand makes one revolution in 60 minutes, the linear velocity can be calculated as 4π cm divided by 60 minutes, which simplifies to \((2\pi /15)\)cm per minute. 

Learn more about velocity here:

https://brainly.com/question/30559316

#SPJ11

Answer:

you would get 33.6 lbs of bananas

Step-by-step explanation:

420 ÷ 252 = 1.6 repeating

21 lb * 1.6 = 33.6

Answer:

Step-by-step explanation:

if 21 lbs of bananas cost 252 dollars

1 lb costs 252/21=12 dollars/pound

420/21=35

with 420 dollars you can buy 35 lbs

The roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x=-7 and x=1.

Any equation in algebra that can be written in the standard form where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation.

In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.

So, the roots of 0 = 2x² + 12x-14 are:

2x² + 12x-14  = 0

2x² + 14x - 2x -14

2x(x + 7) - 2(x + 7)

(2x - 2) (x + 7)

Now, use the zero product property as follows:

2x - 2 = 0

2x = 2

x = 2/2

x = 1

And

x + 7 = 0

x = -7

Therefore, the roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x = -7 and x = 1.

Know more about a quadratic equation here:

https://brainly.com/question/1214333

#SPJ1

Correct question:

What are the roots of the quadratic equation 0 = 2x² + 12x-14?

a. 1,6, -7

b. 2,12,-14

c. -7,1

d. -1,7

Answer:

800 cm

Step-by-step explanation:

x = height of lamp post

set up a proportion:

90/160 = 450/x

cross-multiply:

90x = 72000

x = 800

Answer:

Since you did not want the answer the things you need to solve this question are below.

Step-by-step explanation:

In order to solve this, you will need to read about the scale factor. Here is a picture telling about it briefly.

The graph indicates that any value of p to the right of the open circle (greater than 27) satisfies the inequality 3 < p/9.

To solve the inequality 3 < p/9, we can start by multiplying both sides of the inequality by 9 to eliminate the fraction:

3 * 9 < p

27 < p

So the solution to the inequality is p > 27.

Now, let's graph the solution on a number line. Since the inequality is p > 27, we will represent it with an open circle at 27 and an arrow pointing to the right to indicate that the values of p are greater than 27. Here's how the graph would look:

markdown

Copy code

----------------------> (number line)

      o

     27

The graph indicates that any value of p to the right of the open circle (greater than 27) satisfies the inequality 3 < p/9.

For such more questions on Inequality Solution

https://brainly.com/question/30604125

#SPJ8

The more appropriate measure of center is mean.

The more appropriate measure of spread is standard deviation.

Mean is a measure of central tendency that determines the average of a set of numbers. Standard deviation is used to determine the spread of a dataset. It does this by determining the square root of the average of the squared differences of the numbers from the mean of the data set.

To learn more about standard deviation, please check: https://brainly.com/question/16555520

#SPJ1

Answer:

the answer is number 1 make my answer brainlist answer

Part (a)

This is the empty set

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

Explanation:

It doesn't matter what set A is composed of. Intersecting any set with the empty set Ø will always result in the empty set.

This is because we're asking the question: "What does some set A and the empty set have in common?". The answer of course being "nothing" because there's nothing in Ø. Not even the value zero is in this set.

We can write Ø as { } which is a set of curly braces with nothing inside it.

=========================================================

Part (b)

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

Explanation:

When you union the universal set with any other set, you'll get the universal set.

The rule is \(A \cup B = B\) where I've made B the universal set to avoid confusion of the letter U and the union symbol \(\cup\) which looks nearly identical.

Why does this rule work? Well if an item is in set \(\overline{A}\), then it's automatically in set U (everything is in set U; it's the universe). So we're not adding anything to the universe when applying a union involving this largest set.

It's like saying

we can see that \(\overline{A} \cup U\) will basically form the set of every item, aka the universal set.

Answer:

63 sandwiches

Step-by-step explanation:

Pete and his friend Danny volunteered to bring sandwiches for lunch at a homeless shelter

They brought 7 loaves of bread

Each loaves have 18 slices

They used 2 slices each to make the sandwich

The first step is to calculate the total number of slices

Sinces 7 loaves of bread are used and each of them contain 18 slices then, the total number of slices can be calculated as follows

= 7 ×18

= 126 slices

Therefore since 2 slices of bread is used to make one sandwich then, the number of sandwiches that was made can be calculated as follows

= 126/2

= 63

Hence 63 sandwiches were made for the shelter

Answer:

37500

Step-by-step explanation:

40%=$15,000

100%=?

100%×$15,000/40%

$1,500,000/40

=37500